Moessbauer Characterization of Magnetite/Polyaniline Magnetic Nanocomposite

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rodriguez, Anselmo F. R.; Faria, Fernando S. E. D. V.; Lopez, Jorge L.

2010-12-02

Aniline surface coated Fe{sub 3}O{sub 4} nanoparticles have been successfully synthesized by UV irradiation varying the time and the acid media (HCl, HNO{sub 3}, or H{sub 2}SO{sub 4}). The synthesized material represents a promising platform for application in nerve regeneration. XRD patterns are consistent with the crystalline structure of magnetite. Nevertheless, for UV irradiation times longer than 2 h, extra XRD lines reveal the presence of goethite. The mean crystallite size of uncoated particles is estimated to be 25.4 nm, meanwhile that size is reduced to 19.9 nm for the UV irradiated sample in HCl medium for 4 h. Moessbauermore » spectra of uncoated nanoparticles reveal the occurrence of thermal relaxation at room temperature, while the 77 K-Moessbauer spectrum suggests the occurrence of electron localization effects similar to that expected in bulk magnetite. The Mossbauer spectra of UV irradiated sample in HCl medium during 4 h, confirms the presence of the goethite phase. For this sample, the thermal relaxation is more evident, since the room temperature spectrum shows larger spectral area for the nonmagnetic component due to the smaller crystallite size. Meanwhile, the 77 K-Moessbauer spectrum suggests the absence of the electron localization effect above 77 K.« less

Hematite at Meridiani Planum and Gusev Crater as identified by the Moessbauer Spectrometer MIMOS II

NASA Technical Reports Server (NTRS)

Klingelhoefer, G.; Morris, R. V.; Rodionov, D.; Schroeder, C.; de Souza, P. A.; Yen, A.; Renz, F.; Wdowiak, T.

2006-01-01

The Moessbauer (MB) spectrometers on the MER rovers Opportunity and Spirit, which landed on Mars in January 2004, have identified the iron-containing mineral hematite (a-Fe2O3) at both landing sites. On Earth, hematite can occur either by itself or with other iron oxides as massive deposits, in veins , and as particles dispersed through a silicate or other matrix material. Hematite particle size can range from nanophase (superparamagnetic) to multidomain and particle shape ranges from equant to acicular to platy. Fine-grained hematite is red in color and is a pigmenting agent. Coarse-grained hematite can be spectrally neutral (gray) at visible wavelengths. Substitutional impurities, particularly Al, are common in hematite. Chemically pure, coarse-grained, and well-crystalline hematite has a magnetic transition (the Morin transition) at 260 K. Moessbauer spectra, recorded as a function of temperature, provide a way to characterize Martian hematite with respect to some of the physical and chemical characteristics. At Meridiani Planum besides the iron-sulfate mineral jarosite also the Fe-oxide hematite has been identified by the Moessbauer spectrometer, mainly in three distinct types of reservoir: - outcrop matrix material dominated by the mineral jarosite in the MB spectrum, certain basaltic soils, and mm-sized spherules dubbed blueberries. Moessbauer spectra of each reservoir yield a distinct set of hyperfine parameters for hematite, suggesting different degrees of crystallinity and particle size. The hematite found by MB instrument MIMOS II in the outcrop material shows the Morin transition at relatively high temperatures (ca. 250 K) which is an indication of pure and well-crystallized hematite. The source of the hematite in the Blueberries as identified by Moessbauer spectroscopy, and also by MiniTES, is not known. These spherules, covering nearly the whole landing site area (Eagle crater, plains, Endurance crater), may be concretions formed in the outcrop

Nuclear resonance scattering of synchrotron radiation as a unique electronic, structural and thermodynamic probe

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alp, E. Ercan; Sturhahn, Wolfgang; Toellner, Thomas S.

2012-05-09

Discovery of Moessbauer effect in a nuclear transition was a remarkable development. It revealed how long-lived nuclear states with relatively low energies in the kiloelectron volt (keV) region can be excited without recoil. This new effect had a unique feature involving a coupling between nuclear physics and solid-state physics, both in terms of physics and sociology. Physics coupling originates from the fact that recoilless emission and absorption or resonance is only possible if the requirement that nuclei have to be bound in a lattice with quantized vibrational states is fulfilled, and that the finite electron density on the nucleus couplesmore » to nuclear degrees of freedom leading to hyperfine interactions. thus, Moessbauer spectroscopy allows peering into solid-state effects using unique nuclear transitions. Sociological aspects of this coupling had been equally startling and fruitful. The interaction between diverse scientific communities, who learned to use Moessbauer spectroscopy proved to be very valuable. For example, biologists, geologists, chemists, physics, materials scientists, and archeologists, all sharing a common spectroscopic technique, also learned to appreciate the beauty and intricacies of each other's fields. As a laboratory-based technique, Moessbauer spectroscopy matured by the end of the 1970s. Further exciting developments took place when accelerator-based techniques were employed, like synchrotron radiation or 'in-beam'Moessbauer experiments with implanted radioactive ions. More recently, two Moessbauer spectrometers on the surface of the Mars kept the technique vibrant and viable up until present time. In this chapter, the authors look into some of the unique aspects of nuclear resonance excited with synchrotron radiation as a probe of condensed matter, including magnetism, valence, vibrations, and lattice dynamics, and review the development of nuclear resonance inelastic x-ray scattering (NRIXS) and synchrotron Moessbauer

SEM, optical, and Moessbauer studies of submicrometer chromite in Allende

NASA Technical Reports Server (NTRS)

Housley, R. M.

1982-01-01

New scanning electron and optical microscope results are presented showing that sub-micrometer chromite is abundant along healed cracks and grain boundaries in Allende chondrule olivine. Some wider healed cracks also contain pentlandite and euhedral Ni3Fe grains. Also reported are Moessbauer measurements on Allende HF-HCl residues confirming a high Fe(+++)/Fe(++) ratio.

Moessbauer spectra of olivine-rich achondrites - Evidence for preterrestrial redox reactions

NASA Technical Reports Server (NTRS)

Burns, R. G.; Martinez, S. L.

1991-01-01

Moessbauer spectral measurements at 4.2 K were made on several ureilites and the two shergottites found in Antarctica, as well as two ureilite falls, three SNC meteorite falls, and two finds in order to distinguish products of preterrestrial redox reactions from phases formed during oxidative weathering on the earth. The spectra indicated that several ureilites contain major proportions of metallic iron, much of which resulted from preterrestrial carbon-induced reduction of ferrous iron in the outermost 10-100 microns of olivine grains in contact with carbonaceous material in the ureilites. The cryptocrystalline nature of these Fe inclusions in olivine renders the metal extremely vulnerable to aerial oxidation, even in ureilites collected as falls. It is inferred that the nanophase ferric oxides or oxyhydroxides identified in Brachina and Lafayette were produced by terrestrial weather of olivines before the meteorites were found. The absence of goethite in two olivine-bearing Antarctic shergottites suggests that the 2 percent ferric iron determined in their Moessbauer spectra also originated from oxidation on Mars.

Moessbauer study in thin films of FeSi2 and FeSe systems

NASA Technical Reports Server (NTRS)

Escue, W. J.; Aggarwal, K.; Mendiratta, R. G.

1978-01-01

Thin films of FeSi2 and FeSe were studied using Moessbauer spectroscopy information regarding dangling bond configuration and nature of crystal structure in thin films was derived. A significant influence of crystalline aluminum substrate on film structure was observed.

Hematite at Meridiani Planum and Gusev Crater as identified by the Moessbauer Spectrometer MIMOS II

NASA Astrophysics Data System (ADS)

Klingelhoefer, G.; Morris, R. V.; Rodionov, D.; Schroeder, C.; de Souza, P. A.; Yen, A.; Renz, F.; Wdowiak, T.

2004-12-01

The Moessbauer (MB) spectrometers on the MER rovers Opportunity and Spirit, which landed on Mars in January 2004, have identified the iron-containing mineral hematite (a-Fe2O3) at both landing sites. On Earth, hematite can occur either by itself or with other iron oxides as massive deposits, in veins , and as particles dispersed through a silicate or other matrix material. Hematite particle size can range from nanophase (superparamagnetic) to multidomain and particle shape ranges from equant to acicular to platy. Fine-grained hematite is red in color and is a pigmenting agent. Coarse-grained hematite can be spectrally neutral (gray) at visible wavelengths. Substitutional impurities, particularly Al, are common in hematite. Chemically pure, coarse-grained, and well-crystalline hematite has a magnetic transition (the Morin transition) at ~260 K. Moessbauer spectra, recorded as a function of temperature, provide a way to characterize Martian hematite with respect to some of the physical and chemical characteristics. At Meridiani Planum besides the iron-sulfate mineral jarosite also the Fe-oxide hematite has been identified by the Moessbauer spectrometer, mainly in three distinct types of reservoir: - outcrop matrix material dominated by the mineral jarosite in the MB spectrum, certain basaltic soils, and mm-sized spherules dubbed blueberries. Moessbauer spectra of each reservoir yield a distinct set of hyperfine parameters for hematite, suggesting different degrees of crystallinity and particle size. The hematite found by MB instrument MIMOS II in the outcrop material shows the Morin transition at relatively high temperatures (ca. 250 K) which is an indication of pure and well-crystallized hematite. The source of the hematite in the `Blueberries' as identified by Moessbauer spectroscopy, and also by MiniTES, is not known. These spherules, covering nearly the whole landing site area (Eagle crater, plains, Endurance crater), may be concretions formed in the outcrop

Iron-oxide Aerogel and Xerogel Catalyst Formulations: Characterization by 57Fe Mössbauer and XAFS Spectroscopies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huggins, F.; Bali, S; Huffman, G

2010-01-01

Iron in various iron-oxide aerogel and xerogel catalyst formulations ({ge}85% Fe{sub 2}O{sub 3}; {le}10% K, Co, Cu, or Pd) developed for possible use in Fischer-Tropsch synthesis (FTS) or the water-gas-shift (WGS) reaction has been examined by {sup 57}Fe Moessbauer spectroscopy. The seventeen samples consisted of both as-prepared and calcined aerogels and xerogels and their products after use as catalysts for FTS or the WGS reaction. Complementary XAFS spectra were obtained on the occurrence of the secondary elements in some of the same materials. A broad, slightly asymmetric, two-peak Moessbauer spectrum was obtained from the different as-prepared and calcined catalyst formulationsmore » in the majority of cases. Such spectra could only be satisfactorily fit with three quadrupole doublet components, but no systematic trends in the isomer shift and quadrupole splitting parameters and area ratios of the individual components could be discerned that reflected variations in the composition or preparation of the aerogel or xerogel materials. However, significant reductions were noted in the Moessbauer effective thickness (recoilless absorption effect per unit mass of iron) parameter, {chi}{sub eff}/g, determined at room temperature, for aerogels and xerogels compared to bulk iron oxides, reflecting the openness and lack of rigidity of the aerogel and xerogel structures. Moessbauer measurements for two aerogels over the range from 15 to 292 K confirmed the greatly diminished nature of this parameter at room temperature. Major increases in the effective thickness parameter were observed when the open structure of the aerogel or xerogel collapsed during calcination resulting in the formation of iron oxides (hematite, spinel ferrite). Similar structural changes were indicated by increases in this parameter after use of iron-oxide aerogels as catalysts for FTS or the WGS reaction, during which the iron-oxide aerogel was converted to a mixture of nonstoichiometric

Mechanism of groundwater arsenic removal by goethite-coated mineral sand

NASA Astrophysics Data System (ADS)

Cashion, J. D.; Khan, S. A.; Patti, A. F.; Adeloju, S.; Gates, W. P.

2017-11-01

Skye sand (Vic, Australia) has been considered for arsenic removal from groundwater. Analysis showed that the silica sand is coated with poorly crystalline goethite, hematite and clay minerals. Mössbauer spectra taken following arsenic adsorption revealed changes in the recoilless fraction and relaxation behaviour of the goethite compared to the original state, showing that the goethite is the main active species.

Reflectivity (visible and near IR), Moessbauer, static magnetic, and X ray diffraction properties of aluminum-substituted hematites

NASA Technical Reports Server (NTRS)

Morris, Richard V.; Schulze, Darrell G.; Lauer, Howard V., Jr.; Agresti, David G.; Shelfer, Tad D.

1992-01-01

The effect of substituting iron by aluminum in polymorphs of Fe2O3 and FeOOH on their reflectivity characteristics was investigated by comparing data on visible and NIR reflectivities and on static magnetic, XRD, and Moessbauer properties for a family of aluminum-substituted hematites alpha-(Fe,Al)2O3, with compositions where the values of the Al/(Al+Fe) ratio were up to 0.61. Samples were prepared by oxidation of magnetite, dehydroxylation of goethite, and direct precipitation. The analytical methods used for obtaining diffuse reflectivity spectra (350-2200 nm), Moessbauer spectra, and static magnetic data are those described by Morris et al. (1989).

Mutual solubility of scandium oxide-hematite magnetic nanocomposites: Mössbauer spectroscopy investigation

NASA Astrophysics Data System (ADS)

Allwes, Mark; Mekaoui, Mehdi; Sorescu, Monica

2017-08-01

xSc2O3-(1-x)α-Fe2O3 (x = 0.1, 0.3 and 0.5) nanocomposite systems were successfully synthesized by mechanochemical activation of Sc2O3 and α-Fe2O3 mixtures for 0-12 h of ball milling time. Mössbauer investigations were performed to study the structural and magnetic properties of xSc2O3-(1-x)α-Fe2O3 nanoparticle systems during the mechanochemical activation treatment. The Mössbauer studies showed that the spectrum of the mechanochemically activated composites evolved from a sextet for hematite to sextets and a doublet upon duration of the milling process with scandium oxide. Mutual solubility was achieved at the nanoscopic level only. A comprehensive Mössbauer study was performed by recording the recoilless fraction f as function of the ball milling time using our dual absorber method. The results obtained indicate that prolonged ball milling times favor formation of the Fe:Sc2O3 non-magnetic phase and decrease of the grain sizes for both magnetic and non-magnetic components, leading to a maximum in the recoilless fraction followed by its decay.

Use of Moessbauer spectroscopy to study reaction products of polyphenols and iron compounds

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gust, J.; Suwalski, J.

1994-05-01

Moessbauer spectroscopy was used to study parameters of the reaction products of iron compounds (Fe[sup III]) and polyphenols with hydroxyl (OH) groups in ortho positions. Polyphenols used in the reaction were catechol, pyrogallol, gallic acid, and oak tannin. The Fe-containing compounds were hydrated ferric sulfate (Fe[sub 2][SO[sub 4

The Miniaturized Moessbauer Spectrometers MIMOS II on MER: Four Years of Operation - A Summary

NASA Technical Reports Server (NTRS)

Fleischer, I.; Klingelhoefer, G.; Morris, R. V.; Rodionov, D.; Blumers, M.; Bernhardt, B.; Schroeder, C.; Ming, D. W.; Yen, A. S.; Cohen, B. A.;

Moessbauer spectroscopy analysis of {sup 57}Fe-doped YBaCo{sub 4}O{sub 7+{delta}}: Effects of oxygen intercalation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsipis, E.V.; Department of Ceramics and Glass Engineering, CICECO, University of Aveiro, 3810-193 Aveiro; Waerenborgh, J.C.

2009-03-15

Moessbauer spectroscopy of layered YBaCo{sub 3.96}Fe{sub 0.04}O{sub 7+{delta}} ({delta}=0.02 and 0.80), where 1% cobalt is substituted with {sup 57}Fe isotope, revealed no evidence of charge ordering at 4-293 K. The predominant state of iron cations was found trivalent, irrespective of their coordination and oxygen stoichiometry variations determined by thermogravimetric analysis. The extremely slow kinetics of isothermal oxidation at 598 K in air, and the changes of Fe{sup 3+} fractions in the alternating triangular and Kagome layers in oxidized YBaCo{sub 3.96}Fe{sub 0.04}O{sub 7.80}, may suggest that oxygen intercalation is accompanied with a substantial structural reconstruction stagnated due to sluggish cation diffusion.more » Decreasing temperature below 75-80 K leads to gradual freezing of the iron magnetic moments in inverse correlation with the content of extra oxygen. The formation of metal-oxygen octahedra and resultant structural distortions extend the temperature range where the paramagnetic and frozen states co-exist, down to 45-50 K. - Graphical abstract: Moessbauer spectroscopy of layered YBaCo{sub 3.96}Fe{sub 0.04}O{sub 7+{delta}} ({delta}=0.02 and 0.80), with 1% {sup 57}Fe isotope substituted for cobalt, revealed no evidence of charge ordering at 4-293 K. The predominant state of iron cations was found trivalent, irrespective of their coordination and oxygen stoichiometry variations determined by thermogravimetric analysis. Decreasing temperature below 75-80 K leads to gradual freezing of the iron magnetic moments in inverse correlation with the content of extra oxygen extending the temperature range where the paramagnetic and frozen states co-exist down to 45-50 K.« less

Copper(II) cyanido-bridged bimetallic nitroprusside-based complexes: Syntheses, X-ray structures, magnetic properties, {sup 57}Fe Moessbauer spectroscopy and thermal studies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Travnicek, Zdenek, E-mail: zdenek.travnicek@upol.c; Herchel, Radovan; Mikulik, Jiri

2010-05-15

Three heterobimetallic cyanido-bridged copper(II) nitroprusside-based complexes of the compositions [Cu(tet)Fe(CN){sub 5}NO].H{sub 2}O (1), where tet=N,N'-bis(3-aminopropyl)ethylenediamine, [Cu(hto)Fe(CN){sub 5}NO].2H{sub 2}O (2), where hto=1,3,6,9,11,14-hexaazatricyclo[12.2.1.1{sup 6,9}]octadecane and [Cu(nme){sub 2}Fe(CN){sub 5}NO].H{sub 2}O (3), where nme=N-methylethylenediamine, were synthesized and characterized by elemental analyses, {sup 57}Fe Moessbauer and FTIR spectroscopies, thermal analysis, magnetic measurements and single-crystal X-ray analysis. The products of thermal degradation processes of 2 and 3 were studied by XRD, {sup 57}Fe Moessbauer spectroscopy, SEM and EDS, and they were identified as mixtures of CuFe{sub 2}O{sub 4} and CuO. - Three heterobimetallic cyano-bridged copper(II) nitroprusside-based complexes of the general compositions of [Cu(L)Fe(CN){sub 5}NO].xH{sub 2}O, wheremore » L=N,N'-bis(3-aminopropyl)ethylenediamine (complex 1), 1,3,6,9,11,14-hexaazatricyclo[12.2.1.1{sup 6,9}]-octadecane (complex 2) and N-methylethylenediamine (complex 3), were synthesized, and fully structurally and magnetically characterized. SEM, EDS, XRD and {sup 57}Fe Moessbauer experiments were used for characterization of thermal decomposition products of complexes 2 and 3.« less

An East to West Mineralogical Trend in Mars Exploration Rover Spirit Moessbauer Spectra of Home Plate

NASA Technical Reports Server (NTRS)

Schroder, C.; Di, K.; Morris, R. V.; Klingelhofer, G.; Li, R.

2008-01-01

Home Plate is a light-toned plateau approx.90 m in diameter within the Inner Basin of the Columbia Hills in Gusev crater on Mars. It is the most extensive exposure of layered bedrock encountered by Spirit to date, and it is composed of clastic rocks of moderately altered alkali basalt composition, enriched in some highly volatile elements. Textural observations suggest an explosive origin and geochemical observations favor volcanism, probably a hydrovolcanic explosion [1]. Since it first arrived at Home Plate on sol 744, Spirit has circumnavigated the plateau (Fig. 1) and is now, since sol 1410, resting at its Winter Haven 3 location at the north end of Home Plate. Results: The MER Moessbauer spectrometers determine Fe oxidation states, identify Fe-bearing mineral phases and quantify the distribution of Fe among oxidation states and mineral phases [2]. Moessbauer spectra of Home Plate bedrock were obtained in five different locations from nine different targets (Fig. 1): Barnhill Ace, Posey Manager, and James Cool Papa Bell Stars at the northwest side of Home Plate; Pesapallo, June Emerson, and Elizabeth Emery on the east side; Texas Chili on the south side; Pecan Pie on the west side; and Chanute on the north side.

Mineralogical diversity (spectral reflectance and Moessbauer data) in compositionally similar impact melt rocks from Manicouagan Crater, Canada

NASA Technical Reports Server (NTRS)

Morris, R. V.; Bell, J. F., III; Golden, D. C.; Lauer, H. V., Jr.

1993-01-01

Meteoritic impacts under oxidizing surface conditions occur on both earth and Mars. Oxidative alteration of impact melt sheets is reported at several terrestrial impact structures including Manicouagan, West Clearwater Lake, and the Ries Basin. A number of studies have advocated that a significant fraction of Martian soil may consist of erosional products of oxidatively altered impact melt sheets. If so, the signature of the Fe-bearing mineralogies formed by the process may be present in visible and near infrared reflectivity data for the Martian surface. Of concern is what mineral assemblages form in impact melt sheets produced under oxidizing conditions and what their spectral signatures are. Spectral and Moessbauer data for 19 powder samples of impact melt rock from Manicouagan Crater are reported. Results show for naturally occurring materials that composite hematite-pyroxene bands have minima in the 910-nm region. Thus many of the anomalous Phobos-2 spectra, characterized by a shallow band minimum in the near-IR whose position varies between approximately 850 and 1000 nm, can be explained by assemblages whose endmembers (hematite and pyroxene) are accepted to be present on Mars. Furthermore, results show that a mineralogically diverse suite of rocks can be generated at essentially constant composition, which implies that variations in Martian surface mineralogy do not necessarily imply variations in chemical composition.

Moessbauer spectroscopy and scanning electron microscopy of the Murchison meteorite

NASA Technical Reports Server (NTRS)

Brown, Christopher L.; Oliver, Frederick W.; Hammond, Ernest C., Jr.

1989-01-01

Meteorites provide a wealth of information about the solar system's formation, since they have similar building blocks as the Earth's crust but have been virtually unaltered since their formation. Some stony meteorites contain minerals and silicate inclusions, called chondrules, in the matrix. Utilizing Moessbauer spectroscopy, we identified minerals in the Murchison meteorite, a carbonaceous chondritic meteorite, by the gamma ray resonance lines observed. Absorption patterns of the spectra were found due to the minerals olivine and phyllosilicate. We used a scanning electron microscope to describe the structure of the chondrules in the Murchison meteorite. The chondrules were found to be deformed due to weathering of the meteorite. Diameters varied in size from 0.2 to 0.5 mm. Further enhancement of the microscopic imagery using a digital image processor was used to describe the physical characteristics of the inclusions.

YPdSn and YPd{sub 2}Sn: Structure, {sup 89}Y solid state NMR and {sup 119}Sn Moessbauer spectroscopy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hoeting, Christoph; Eckert, Hellmut; Langer, Thorsten

2012-06-15

The stannides YPdSn and YPd{sub 2}Sn were synthesized by high-frequency melting of the elements in sealed tantalum tubes. Both structures were refined on the basis of single crystal X-ray diffractometer data: TiNiSi type, Pnma, a=715.4(1), b=458.8(1), c=789.1(1) pm, wR2=0.0461, 510 F{sup 2} values, 20 variables for YPdSn and MnCu{sub 2}Al type, Fm3 Macron m, a=671.44(8), wR2=0.0740, 55 F{sup 2} values, 5 parameters for YPd{sub 2}Sn. The yttrium atoms in the new stannide YPdSn are coordinated by two tilted Pd{sub 3}Sn{sub 3} hexagons (ordered AlB{sub 2} superstructure). In the Heusler phase YPd{sub 2}Sn each yttrium atom has octahedral tin coordination andmore » additionally eight palladium neighbors. The cubic site symmetry of yttrium is reflected in the {sup 119}Sn Moessbauer spectrum which shows no quadrupole splitting. In contrast, YPdSn shows a single signal at {delta}=1.82(1) mm/s subjected to quadrupole splitting of {Delta}E{sub Q}=0.93(1) mm/s. Both compounds have been characterized by high-resolution {sup 89}Y solid state NMR spectroscopy, which indicates the presence of strong Knight shifts. The spectrum of YPd{sub 2}Sn is characterized by an unusually large linewidth, suggesting the presence of a Knight shift distribution reflecting local disordering effects. The range of {sup 89}Y Knight shifts of several binary and ternary intermetallic yttrium compounds is briefly discussed. - Graphical abstract: YPdSn and YPd{sub 2}Sn: Structure, {sup 89}Y solid state NMR and {sup 119}Sn Moessbauer spectroscopy. Highlights: Black-Right-Pointing-Pointer Synthesis and structure of ternary stannides YPdSn and YPd{sub 2}Sn. Black-Right-Pointing-Pointer {sup 119}Sn Moessbauer spectroscopic investigation of YPdSn and YPd{sub 2}Sn. Black-Right-Pointing-Pointer {sup 89}Y solid state NMR of intermetallics.« less

Mineralogy at Gusev Crater and Meridiani Planum from the Moessbauer Spectrometers on the Mars Exploration Rovers

NASA Technical Reports Server (NTRS)

Morris, Richard V.; Klingelhoefer, Goestar

2006-01-01

The Moessbauer spectrometers on the twin MER rovers Spirit and Opportunity have provided significant new information on the distribution of iron among its oxidation states, the identification of the mineralogical composition of iron-bearing phases, and the distribution of iron among those phases for rock and soil at Gusev Crater and Meridiani Planum. The plains of Gusev Crater are dominated by olivine-bearing basalt (approximately Fo(60)) and Fe(3+)/Fe(total)=0.1 - 0.5. The oxide mineral generally present is magnetite. In contrast, initial results for the Columbia Hills are consistent with the presence of hematite and a ferrous iron phase, possibly pyroxene. Gusev spectra also have a ferric doublet (not jarosite) that is tentatively associated with nano-phase ferric oxide. A wider diversity of material is present at Meridiani Planum. Significantly, jarosite-bearing outcrop is present throughout the region, with good exposures in impact craters such as Eagle and Endurance (Fe(3+)/Fe (total) approx. 0.9). The Moessbauer identification of jarosite (a hydroxyl-bearing sulfate mineral) is evidence for aqueous, acid-sulfate processes on Mars. Hematite is observed within the outcrop matrix and in the spheroidal particles (Blueberries) found within the outcrop and as a surface lag. An isolated rock (Bounce Rock) was the only sample at either landing site whose iron-bearing phase was dominated by pyroxene. The basaltic sand in the central portion of Eagle crater, in the intercrater plains, and between slabs of outcrop at both Eagle and Endurance craters is olivine-bearing basalt. The widespread occurrence of olivine-bearing basalt at both MER landing sites implies that physical, rather than chemical, weathering processes dominate at the surface of contemporary Mars.

Decomposition of Potassium Ferrate(VI)(K{sub 2}FeO{sub 4}) and Potassium Ferrate(III)(KFeO{sub 2}): In-situ Moessbauer Spectroscopy Approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Machala, Libor; Zboril, Radek; Sharma, Virender K.

2008-10-28

Moessbauer spectroscopy was shown to be very useful technique studying the mechanism of thermal decomposition or aging processes of the most known ferrate(VI), K{sub 2}FeO{sub 4}. In-situ Moessbauer spectroscopy approach was used to monitor the phase composition during the studied processes. The experimental set-up was designed to perform in-situ measurements at high temperatures and at different air humid conditions at room temperature. The potassium ferrate(III), KFeO{sub 2} was demonstrated to be the primary product of thermal decomposition of K{sub 2}FeO{sub 4}. The KFeO{sub 2} was unstable in a humid air at room temperature and reacted with components of air, H{submore » 2}O and CO{sub 2} to give Fe{sub 2}O{sub 3} nanoparticles and KHCO{sub 3}. The aging kinetics of K{sub 2}FeO{sub 4} and KFeO{sub 2} under humid air were significantly dependent on the relative air humidity.« less

Synchrotron-radiation based perturbed angular correlations from 119Sn

NASA Astrophysics Data System (ADS)

Strohm, C.; Sergueev, I.; van Bürck, U.

2008-03-01

We report the observation of γ-γ-correlations from 119Sn using nuclear resonant scattering of synchrotron radiation, extending nuclear resonant spectroscopy with 119Sn to vanishing recoilless fractions and new applications. The 23.87 keV M1 (+E2) Ig:1/2→Ie:3/2 Mössbauer transition was excited from the ground state, and the time differential correlations between the incident and the scattered photons were recorded for different angles in the plane perpendicular to the incident beam. The experiments were performed on samples of tributyltin-fluoride, which has a very low Lamb-Mössbauer factor at ambient temperature. In the time spectra we observed quantum beats from the static perturbation through electric quadrupole interaction.

Moessbauer spectrometer based on UNO-4096-90 accumulator and Elektronika D3-28 microcomputer for simultaneous recording of four spectra

DOE Office of Scientific and Technical Information (OSTI.GOV)

Romanov, E.S.; Ivoilov, N.G.

A buffer memory unit and an interface for the UNO-4096-90 accumulator with an Elektronika D3-28 microcomputer are described that allow simultaneous recording of four Moessbauer spectra with zero dead time. For complete elimination of dead time, the pulses from each detector are fed to two buffer counters units, which operate alternately in the write and interrogate modes. This organization of the buffer memory also completely eliminates the effect of the sensors on one another. The use of these circuits does not require any modifications of the computer or accumulator.

Chemostratigraphy and Fe Mineralogy of the Victoria Crater Duck Bay Section: Opportunity APXS and Moessbauer Results

NASA Technical Reports Server (NTRS)

Mittlefehldt, D. W.; Schroeder, C.; Gellert, R.; Klingelhoefer, G.; Jolliff, B. L.; Morris, R. V.

2008-01-01

Meridiani Planum is a vast plain of approximately horizontally bedded sedimentary rocks composed of mixed and reworked basaltic and evaporitic sands containing secondary, diagenetic minerals [e.g., 1-5]. Because bedding planes are subparallel to topography, investigation of contiguous stratigraphy requires examining exposures in impact craters. Early in the mission (sols 130-317), Opportunity was commanded to do detailed study of exposed outcrops in Endurance crater, including the contiguous Karatepe section at the point of ingress. Just over 1000 sols later and roughly 7 km to the south, the rover is being commanded to do a similar study of the Duck Bay section of Victoria crater. Here we report on the preliminary results from the Alpha Particle X-ray Spectrometer (APXS) and Moessbauer instruments.

Moessbauer Spectroscopy of Martian and Sverrefjell Carbonates

NASA Technical Reports Server (NTRS)

Agresti, David G.; Morris, Richard V.

2011-01-01

Mars, in its putative "warmer, wetter: early history, could have had a CO2 atmosphere much denser than its current value of <10 mbar. The question of where all this early CO2 has gone has long been debated. Now, several instruments on Mars Exploration Rover (MER) Spirit, including its Moessbauer spectrometer MIMOS II, have identified Mg-Fe carbonate in rock outcrops at Comanche Spur in the Columbia Hills of Gusev Crater. With this finding, carbonate cements in volcanic breccia collected on Sverrefjell Volcano on Spitzbergen Island in the Svalbard Archipelago (Norway) during the AMASE project are mineralogical and possible process analogues of the newly discovered martian carbonate. We report further analyses of Mossbauer spectra from Comanche Spur and discuss their relationship to Mossbauer data acquired on Sverrefjell carbonates. The spectra were velocity calibrated with MERView and fit using MERFit. Instead of the "average temperature" Comanche spectrum (data from all temperature windows summed), we refit the Comanche data for QS within each temperature window, modeling as doublets for Fe2+(carbonate), Fe2+(olivine), and Fe3+(npOx). The temperature dependences of QS for the Comanche carbonate and for a low-Ca carbonate from Chocolate Pots in Yellowstone National Park (YNP) are shown; they are the same within error. For Comanche carbonate summed over 210-270 K, (CS, QS) = (1.23, 1.95) mm/s. The value of QS for Sverrefjell carbonate at 295 K, (CS, QS) = (1.25, 1.87) mm/s, is also plotted, and the plot shows that the QS for the Sverrefjell carbonate agrees within error with the Comanche data extrapolated to 295 K. This agreement is additional evidence that the Sverrefjell carbonates are Mossbauer analogues for the Comanche carbonates, and that both carbonates might have precipitated from solutions that became carbonate rich by passing through buried carbonate deposits.

Fe-Bearing Phases Identified by the Moessbauer Spectrometers on the Mars Exploration Rovers: An Overview

NASA Technical Reports Server (NTRS)

Morris, R. V.; Klingelhoefer, G.; Rodionov, D.; Yen, A.; Gellert, R.

2006-01-01

The twin Mars Exploration Rovers Spirit and Opportunity have explored the martian surface at Gusev Crater (GC) and Meridiani Planum (MP), respectively, for about two Earth years. The Moessbauer (MB) spectrometers on both rovers have analyzed an aggregate of 200 surface targets and have returned to Earth information on the oxidation state of iron, the mineralogical composition of Febearing phases, and the distribution of Fe among oxidation states and phases at the two landing sites [1-7]. To date, 15 component subspectra (10 doublets and 5 sextets) have been identified and most have been assigned to mineralogical compositions. Two subspectra are assigned to phases (jarosite and goethite) that are marker minerals for aqueous processes because they contain hydroxide anion in their structures. In this paper, we give an overview of the Febearing phases identified and their distributions at Gusev crater and Meridiani Planum.

Fe-Bearing Phases Indentified by the Moessbauer Spectrometers on the Mars Exploration Rovers: An Overview

NASA Technical Reports Server (NTRS)

Morris, R. V.; Klingelhoefer, G.; Ming, D. W.; Schroeder, C.; Rodionov, D.; Yen, A.; Gellert, R.

2006-01-01

The twin Mars Exploration Rovers Spirit and Opportunity have explored the martian surface at Gusev Crater (GC) and Meridiani Planum (MP), respectively, for about two Earth years. The Moessbauer (MB) spectrometers on both rovers have analyzed an aggregate of approx.200 surface targets and have returned to Earth information on the oxidation state of iron, the mineralogical composition of Fe-bearing phases, and the distribution of Fe among oxidation states and phases at the two landing sites [1-7]. To date, 15 component subspectra (10 doublets and 5 sextets) have been identified and most have been assigned to mineralogical compositions. Two subspectra are assigned to phases (jarosite and goethite) that are marker minerals for aqueous processes because they contain hydroxide anion in their structures. In this paper, we give an overview of the Febearing phases identified and their distributions at Gusev crater and Meridiani Planum.

Development of the Fast Scintillation Detector with Programmable High Voltage Adjustment Suitable for Moessbauer Spectroscopy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Prochazka, R.; Frydrych, J.; Pechousek, J.

2010-07-13

This work is focused on a development of a compact fast scintillation detector suitable for Moessbauer spectroscopy (low energy X-ray/{gamma}-ray detection) where high counting rates are inevitable. Optimization of this part was necessary for a reliable function, better time resolution and to avoid a detector pulses pile-up effect. The pile-up effect decreases the measurement performance, significantly depends on the source activity and also on the pulse duration. Our new detection unit includes a fast scintillation crystal YAP:Ce, an R6095 photomultiplier tube, a high voltage power supply socket C9028-01 assembly, an AD5252 digital potentiometer with an I2C interface and an AD8000more » ultra fast operation preamplifier. The main advantages of this solution lie in a short pulse duration (less than 200 ns), stable operation for high activities, programmable gain of the high voltage supply and compact design in the aluminum housing.« less

Pressure effect on Fe3+/FeT in silicate melts and applications to magma redox, particularly in magma oceans

NASA Astrophysics Data System (ADS)

Zhang, H.; Hirschmann, M. M.

2014-12-01

The proportions of Fe3+ and Fe2+ in magmas reflect the redox conditions of their origin and influence the chemical and physical properties of natural silicate liquids, but the relationship between Fe3+/FeT and oxygen fugacity depends on pressure owing to different molar volumes and compressibilities of Fe3+ and Fe2+ in silicates. An important case where the effect of pressure effect may be important is in magma oceans, where well mixed (and therefore potentially uniform Fe3+/FeT) experiencses a wide range of pressures, and therefore can impart different ƒO2 at different depths, influencing magma ocean degassing and early atmospheres, as well as chemical gradients within magma oceans. To investigate the effect of pressure on magmatic Fe3+/FeT we conducted high pressure expeirments on ƒO2-buffered andestic liquids. Quenched glasses were analyzed by Mössbauer spectroscopy. To verify the accuracy of Mössbauer determinations of Fe3+/FeT in glasses, we also conducted low temperature Mössbauer studies to determine differences in the recoilless fraction (ƒ) of Fe2+ and Fe3. These indicate that room temperature Mössbauer determinations of on Fe3+/FeT glasses are systematically high by 4% compared to recoilless-fraction corrected ratios. Up to 7 GPa, pressure decreases Fe3+/FeT, at fixed ƒO2 relative to metal-oxide buffers, meaning that an isochemical magma will become more reduced with decreasing pressure. Consequently, for small planetary bodies such as the Moon or Mercury, atmospheres overlying their MO will be highly reducing, consisting chiefly of H2 and CO. The same may also be true for Mars. The trend may reverse at higher pressure, as is the case for solid peridotite, and so for Earth, Venus, and possibly Mars, more oxidized atmospheres above MO are possible. Diamond anvil experiments are underway to examine this hypothesis.

Blast Effects of Recoilless Guns

DTIC Science & Technology

1947-02-01

severely in a number of places. 10 18 r— • ~ ’ ’ 18 1 9 None. j Crack in atar - board side of fuselaged deepened aral...NnrnO mo. bxsaa tto. fSame) OA1l> DOC OASS. Feb 󈧳 I Secret COUNTST Gr. Brit. English 24 nuBTCAnow Photos, tables, diagr ^ X0T ABSTRACT

Moessbauer and Electron Microprobe Studies of Density Separates of Martian Nakhlite Mil03346: Implications for Interpretation of Moessbauer Spectra Acquired by the Mars Exploration Rovers

NASA Technical Reports Server (NTRS)

Morris, R. V.; McKay, G. A.; Agresti, D. G.; Li, Loan

2008-01-01

Martian meteorite MIL03346 is described as an augite-rich cumulate rock with approx.80%, approx.3%, and approx.21% modal phase proportions of augite (CPX), olivine and glassy mesostasis, respectively, and is classified as a nakhlite [1]. The Mossbauer spectrum for whole rock (WR) MIL 03346 is unusual for Martian meteorites in that it has a distinct magnetite subspectrum (7% subspectral area) [2]. The meteorite also has products of pre-terrestrial aqueous alteration ("iddingsite") that is associated primarily with the basaltic glass and olivine. The Mossbauer spectrometers on the Mars Exploration Rovers have measured the Fe oxidation state and the Fe mineralogical composition of rocks and soils on the planet s surface since their landing in Gusev Crater and Meridiani Planum in January, 2004 [3,4]. The MIL 03346 meteorite provides an opportunity to "ground truth" or refine Fe phase identifications. This is particularly the case for the so-called "nanophase ferric oxide" (npOx) component. NpOx is a generic name for a ferric rich product of oxidative alteration. On Earth, where we can take samples apart and study individual phases, examples of npOx include ferrihydrite, schwertmannite, akagaaneite, and superparamagnetic (small particle) goethite and hematite. It is also possible for ferric iron to be associated to some unknown extent with igneous phases like pyroxene. We report here an electron microprobe (EMPA) and Moessbauer (MB) study of density separates of MIL 03346. The same separates were used for isotopic studies by [5]. Experimental techniques are described by [6,7].

Innovative instrumentation for mineralogical and elemental analyses of solid extraterrestrial surfaces: The Backscatter Moessbauer Spectrometer/X Ray Fluorescence analyzer (BaMS/XRF)

NASA Technical Reports Server (NTRS)

Shelfer, T. D.; Morris, Richard V.; Nguyen, T.; Agresti, D. G.; Wills, E. L.

1994-01-01

We have developed a four-detector research-grade backscatter Moessbauer spectrometer (BaMS) instrument with low resolution x-ray fluorescence analysis (XRF) capability. A flight-qualified instrument based on this design would be suitable for use on missions to the surfaces of solid solar-system objects (Moon, Mars, asteroids, etc.). Target specifications for the flight instrument are as follows: mass less than 500 g; volumes less than 300 cu cm; and power less than 2 W. The BaMS/XRF instrument would provide data on the oxidation state of iron and its distribution among iron-bearing mineralogies and elemental composition information. This data is a primary concern for the characterization of extraterrestrial surface materials.

Fractional vector calculus for fractional advection dispersion

NASA Astrophysics Data System (ADS)

Meerschaert, Mark M.; Mortensen, Jeff; Wheatcraft, Stephen W.

2006-07-01

We develop the basic tools of fractional vector calculus including a fractional derivative version of the gradient, divergence, and curl, and a fractional divergence theorem and Stokes theorem. These basic tools are then applied to provide a physical explanation for the fractional advection-dispersion equation for flow in heterogeneous porous media.

Fractional Number Operator and Associated Fractional Diffusion Equations

NASA Astrophysics Data System (ADS)

Rguigui, Hafedh

2018-03-01

In this paper, we study the fractional number operator as an analog of the finite-dimensional fractional Laplacian. An important relation with the Ornstein-Uhlenbeck process is given. Using a semigroup approach, the solution of the Cauchy problem associated to the fractional number operator is presented. By means of the Mittag-Leffler function and the Laplace transform, we give the solution of the Caputo time fractional diffusion equation and Riemann-Liouville time fractional diffusion equation in infinite dimensions associated to the fractional number operator.

Coordination of Fe, Ga and Ge in high pressure glasses by Moessbauer, Raman and X-ray absorption spectroscopy, and geological implications

NASA Technical Reports Server (NTRS)

Fleet, M. E.; Henderson, G. S.; Herzberg, C. T.; Crozier, E. D.; Osborne, M. D.; Scarfe, C. M.

1984-01-01

For some time, it has been recognized that the structure of silicate liquids has a great bearing on such magma properties as viscosity, diffusivity, and thermal expansion and on the extrapolation of thermodynamic quantities outside of the experimentally measurable range. In this connection it is vital to know if pressure imposes changes in melt structure similar to the pressure-induced reconstructive transformations in crystals. In the present study on 1 bar and high pressure glasses, an investigation is conducted regarding the coordination of Fe(3+) in Fe silicate glasses by Moessbauer spectroscopy. Raman spectroscopy is employed to explore the coordinations of Ge(4+) in GeO2 glasses and of Ga(3+) in NaGa silicate glasses, while the coordination of Ga(3+) in NaGaSiO4 glasses is studied with the aid of methods of X-ray absorption spectroscopy.

Coordination of Fe, Ga and Ge in high pressure glasses by Moessbauer, Raman and X-ray absorption spectroscopy, and geological implications

NASA Astrophysics Data System (ADS)

Fleet, M. E.; Herzberg, C. T.; Henderson, G. S.; Crozier, E. D.; Osborne, M. D.; Scarfe, C. M.

1984-07-01

For some time, it has been recognized that the structure of silicate liquids has a great bearing on such magma properties as viscosity, diffusivity, and thermal expansion and on the extrapolation of thermodynamic quantities outside of the experimentally measurable range. In this connection it is vital to know if pressure imposes changes in melt structure similar to the pressure-induced reconstructive transformations in crystals. In the present study on 1 bar and high pressure glasses, an investigation is conducted regarding the coordination of Fe(3+) in Fe silicate glasses by Moessbauer spectroscopy. Raman spectroscopy is employed to explore the coordinations of Ge(4+) in GeO2 glasses and of Ga(3+) in NaGa silicate glasses, while the coordination of Ga(3+) in NaGaSiO4 glasses is studied with the aid of methods of X-ray absorption spectroscopy.

Fractionally charged skyrmions in fractional quantum Hall effect

DOE PAGES

Balram, Ajit C.; Wurstbauer, U.; Wójs, A.; ...

2015-11-26

The fractional quantum Hall effect has inspired searches for exotic emergent topological particles, such as fractionally charged excitations, composite fermions, abelian and nonabelian anyons and Majorana fermions. Fractionally charged skyrmions, which support both topological charge and topological vortex-like spin structure, have also been predicted to occur in the vicinity of 1/3 filling of the lowest Landau level. The fractional skyrmions, however, are anticipated to be exceedingly fragile, suppressed by very small Zeeman energies. Here we show that, slightly away from 1/3 filling, the smallest manifestations of the fractional skyrmion exist in the excitation spectrum for a broad range of Zeemanmore » energies, and appear in resonant inelastic light scattering experiments as well-defined resonances slightly below the long wavelength spin wave mode. The spectroscopy of these exotic bound states serves as a sensitive tool for investigating the residual interaction between composite fermions, responsible for delicate new fractional quantum Hall states in this filling factor region.« less

Fractionally charged skyrmions in fractional quantum Hall effect

PubMed Central

Balram, Ajit C.; Wurstbauer, U.; Wójs, A.; Pinczuk, A.; Jain, J. K.

2015-01-01

The fractional quantum Hall effect has inspired searches for exotic emergent topological particles, such as fractionally charged excitations, composite fermions, abelian and nonabelian anyons and Majorana fermions. Fractionally charged skyrmions, which support both topological charge and topological vortex-like spin structure, have also been predicted to occur in the vicinity of 1/3 filling of the lowest Landau level. The fractional skyrmions, however, are anticipated to be exceedingly fragile, suppressed by very small Zeeman energies. Here we show that, slightly away from 1/3 filling, the smallest manifestations of the fractional skyrmion exist in the excitation spectrum for a broad range of Zeeman energies, and appear in resonant inelastic light scattering experiments as well-defined resonances slightly below the long wavelength spin wave mode. The spectroscopy of these exotic bound states serves as a sensitive tool for investigating the residual interaction between composite fermions, responsible for delicate new fractional quantum Hall states in this filling factor region. PMID:26608906

Iron Mineralogy and Aqueous Alteration on Mars from the MER Moessbauer Spectrometers. Chapter 15

NASA Technical Reports Server (NTRS)

Morris, Richard V.; Klingelhoefer, Goestar

2007-01-01

The twin Mars Exploration Rovers Spirit (Gusev crater) and Opportunity (Meridiani Planum) used MIMOS II Moessbauer spectrometers to analyze martian surface materials in the first application of extraterrestrial Moessbauer spectroscopy. The instruments acquired spectra that identified the speciation of Fe according to oxidation state, coordination state, and mineralogical composition and provided quantitative information about the distribution of Fe among oxidation states, coordination states, and Fe-bearing phases. A total of 12 unique Fe-bearing phases were identified: Fe(2+) in olivine, pyroxene, and ilmenite; Fe(2+) and Fe(3+) in magnetite and chromite; Fe(3+) in nanophase ferric oxide (npOx), hematite, goethite, jarosite, an unassigned Fe3+ sulfate, and an unassigned Fe(3+) phase associated with jarosite; and Fe(0) in kamacite. Weakly altered basalts at Gusev crater (SO3 = 2.5 +/- 1.4 wt.% and Fe(3+)/Fe(sub T) = 0.24 +/- 0.11) are widespread on the Gusev plains and occur in less abundance on West Spur and Husband Hill in the Columbia Hills. Altered low-S rocks (SO3 = 5.2 +/- 2.0 wt.% and Fe(3+)/Fe(sub T) = 0.63 +/- 0.18) are the most common type of rock in the Columbia Hills. Ilm-bearing, weakly altered basalts were detected only in the Columbia Hills, as was the only occurrence of chromite in an altered low-S rock named Assemblee. Altered high-S rocks (SO3 > 14.2 wt.% and Fe(3+)/Fe(sub T) = 0.83 +/- 0.05) are the outcrop rocks of the ubiquitous Burns formation at Meridiani Planum. Two Fe(0)-bearing rocks at Meridiani Planum (Barberton and Heat Shield Rock) are meteorites. Laguna Class soil is weakly altered (SO3 = 6 +/- 2 wt.% and Fe(3+)/Fe(sub T) = 0.29 +/- 0.08) and widely distributed at both Gusev crater and Meridiani Planum, implying efficient global mixing processes or a global distribution of precursor rocks with comparable Fe mineralogical compositions. Paso Robles Class soil is heavily altered (SO3 approx. 31 wt.% and Fe(3+)/Fe(sub T) = 0.83 +/- 0

Tempered fractional calculus

NASA Astrophysics Data System (ADS)

Sabzikar, Farzad; Meerschaert, Mark M.; Chen, Jinghua

2015-07-01

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.

Tempered fractional calculus

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sabzikar, Farzad, E-mail: sabzika2@stt.msu.edu; Meerschaert, Mark M., E-mail: mcubed@stt.msu.edu; Chen, Jinghua, E-mail: cjhdzdz@163.com

2015-07-15

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a temperedmore » fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.« less

Moessbauer Spectroscopy for Lunar Resource Assessment: Measurement of Mineralogy and Soil Maturity

NASA Technical Reports Server (NTRS)

Morris, R. V.; Agresti, D. G.; Shelfer, T. D.; Pimperl, M. M.; Shen, M.-H.; Gibson, M. A.; Wills, E. L.

1992-01-01

First-order assessment of lunar soil as a resource includes measurement of its mineralogy and maturity. Soils in which the mineral ilmenite is present in high concentrations are desirable feedstock for the production of oxygen at a lunar base. The maturity of lunar soils is a measure of their relative residence time in the upper 1 mm of the lunar surface. Increasing maturity implies increasing load of solar wind species (e.g., N, H, and He-3), decreasing mean grain size, and increasing glass content. All these physicochemical properties that vary in a regular way with maturity are important parameters for assessing lunar soil as a resource. For example, He-3 can be extracted and potentially used for nuclear fusion. A commonly used index for lunar soil maturity is I(sub s)/FeO, which is the concentration of fine-grained metal determined by ferromagnetic resonance (I(sub s)) normalized to the total iron content (as FeO). I(sub s)/FeO has been measured for virtually every soil returned by the Apollo and Luna missions to the Moon. Because the technique is sensitive to both oxidation state and mineralogy, iron Moessbauer spectroscopy (FeMS) is a viable technique for in situ lunar resource assessment. Its utility for mineralogy is apparent from examination of published FeMS data for lunar samples. From the data published, it can be inferred that FeMS data can also be used to determine soil maturity. The use of FeMS to determine mineralogy and maturity and progress on development of a FeMS instrument for lunar surface use are discussed.

Fractional Hopfield Neural Networks: Fractional Dynamic Associative Recurrent Neural Networks.

PubMed

Pu, Yi-Fei; Yi, Zhang; Zhou, Ji-Liu

2017-10-01

This paper mainly discusses a novel conceptual framework: fractional Hopfield neural networks (FHNN). As is commonly known, fractional calculus has been incorporated into artificial neural networks, mainly because of its long-term memory and nonlocality. Some researchers have made interesting attempts at fractional neural networks and gained competitive advantages over integer-order neural networks. Therefore, it is naturally makes one ponder how to generalize the first-order Hopfield neural networks to the fractional-order ones, and how to implement FHNN by means of fractional calculus. We propose to introduce a novel mathematical method: fractional calculus to implement FHNN. First, we implement fractor in the form of an analog circuit. Second, we implement FHNN by utilizing fractor and the fractional steepest descent approach, construct its Lyapunov function, and further analyze its attractors. Third, we perform experiments to analyze the stability and convergence of FHNN, and further discuss its applications to the defense against chip cloning attacks for anticounterfeiting. The main contribution of our work is to propose FHNN in the form of an analog circuit by utilizing a fractor and the fractional steepest descent approach, construct its Lyapunov function, prove its Lyapunov stability, analyze its attractors, and apply FHNN to the defense against chip cloning attacks for anticounterfeiting. A significant advantage of FHNN is that its attractors essentially relate to the neuron's fractional order. FHNN possesses the fractional-order-stability and fractional-order-sensitivity characteristics.

The Codevelopment of Children's Fraction Arithmetic Skill and Fraction Magnitude Understanding

ERIC Educational Resources Information Center

Bailey, Drew H.; Hansen, Nicole; Jordan, Nancy C.

2017-01-01

The importance of fraction knowledge to later mathematics achievement, along with U.S. students' poor knowledge of fraction concepts and procedures, has prompted research on the development of fraction learning. In the present study, participants' (N = 536) development of fraction magnitude understanding and fraction arithmetic skills was assessed…

TEMPERED FRACTIONAL CALCULUS.

PubMed

Meerschaert, Mark M; Sabzikar, Farzad; Chen, Jinghua

2015-07-15

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.

TEMPERED FRACTIONAL CALCULUS

PubMed Central

MEERSCHAERT, MARK M.; SABZIKAR, FARZAD; CHEN, JINGHUA

2014-01-01

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series. PMID:26085690

Pitch Fractionation.

DTIC Science & Technology

1981-12-15

The solvent fractions were obtained by sequential Soxhlet extraction with solvents such as hexane, cyclohexane, toluene, and pyridine. The most severe...Continued) *.AISYRACT (Continued) fraction increased, the pyrolysis yield and bloating increased, and the msicrostructure of the coke became finer...28 8. Coking Yield and Bloating Behavior of Fractionation Sequence AG 162-4

The Incredible Diversity of Fe-bearing Phases at Gusev Crater, Mars, According to the Mars Exploration Rover Moessbauer Spectrometer

NASA Technical Reports Server (NTRS)

Morris, R. V.; Klingelhoefer, G.; Schroeder, C.; Rodionov, D. S.; Ming, D. W.; Yen, A.

2006-01-01

The Mars Exploration Rover (MER) Spirit landed on the plains of Gusev Crater on 4 January 2004. One primary scientific objective for the mission is to characterize the mineralogical and elemental composition of surface materials, searching for evidence of water and clues for assessing past and current climates and their suitability for life [1]. The role of the Moessbauer (MB) spectrometer on Spirit is to provide quantitative information about the distribution of Fe among its oxidation and coordination states, identification of Fe-bearing phases, and relative distribution of Fe among those phases. The speciation and distribution of Fe in Martian rock and soil constrains the primary rock types, redox conditions under which primary minerals crystallized, the extent of alteration and weathering, the type of alteration and weathering products, and the processes and environmental conditions for alteration and weathering. In this abstract, we discuss the incredible diversity of Fe-bearing phases detected by Spirit s MB instrument during its first 540 sols of exploration at Gusev crater [2,3].

Meaning of Fractions

NASA Astrophysics Data System (ADS)

Dewi, D. A. K.; Suryadi, D.; Suratno, T.; Mulyana, E.; Kurniawan, H.

2017-02-01

Introducing fractions is identical to divide an object. Suppose we divide the apple into two parts. One divided into two parts, the question arises whether one part can be called a half or not. Based on this activity, how can students give meaning to fractions. This study aims at designing a different fractions lesson by applying Didactical Design Research. In doing so, we undertook several research phases: 1) thinking what is fractions and why students should learn this concept; 2) designing didactical situation based on identified learning obstacles; and 3) reflecting retrospectively on the lesson design and its implementation as to redesign the fractions lesson. Our analysis revealed that most students held epistemological obstacles in giving meaning of fractions because they only know fractions as numbers that have numerator and denominator. By positioning ourselves as students, we discuss the ideal design to help students in constructing the meaning of fractions.

Characterization of Coconut Oil Fractions Obtained from Solvent Fractionation Using Acetone.

PubMed

Sonwai, Sopark; Rungprasertphol, Poonyawee; Nantipipat, Nantinee; Tungvongcharoan, Satinee; Laiyangkoon, Nantikan

2017-09-01

This work was aimed to study the solvent fraction of coconut oil (CNO). The fatty acid and triacylglycerol compositions, solid fat content (SFC) and the crystallization properties of CNO and its solid and liquid fractions obtained from fractionation at different conditions were investigated using various techniques. CNO was dissolved in acetone (1:1 w/v) and left to crystallize isothermally at 10°C for 0.5, 1 and 2 h and at 12°C for 2, 3 and 6 h. The solid fractions contained significantly lower contents of saturated fatty acids of ≤ 10 carbon atoms but considerably higher contents of saturated fatty acids with > 12 carbon atoms with respect to those of CNO and the liquid fractions. They also contained higher contents of high-melting triacylglycerol species with carbon number ≥ 38. Because of this, the DSC crystallization onset temperatures and the crystallization peak temperatures of the solid fractions were higher than CNO and the liquid fractions. The SFC values of the solid fractions were significantly higher than CNO at all measuring temperatures before reaching 0% just below the body temperature with the fraction obtained at 12°C for 2 h exhibiting the highest SFC. On the contrary, the SFC values of the liquid fractions were lower than CNO. The crystallization duration exhibited strong influence on the solid fractions. There was no effect on the crystal polymorphic structure possibly because CNO has β'-2 as a stable polymorph. The enhanced SFC of the solid fractions would allow them to find use in food applications where a specific melting temperature is desired such as sophisticated confectionery fats, and the decreased SFC of the liquid fractions would provide them with a higher cold stability which would be useful during extended storage time.

What Is a Fraction? Developing Fraction Understanding in Prospective Elementary Teachers

ERIC Educational Resources Information Center

Reeder, Stacy; Utley, Juliana

2017-01-01

Classroom teachers need a well-developed deep understanding of fractions and pedagogic practices so they can provide meaningful experiences for students to explore and construct ideas about fractions. This study sought to examine prospective elementary teachers' understandings of fraction by focusing specifically on their use of fractions meanings…

Initialized Fractional Calculus

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.; Hartley, Tom T.

2000-01-01

This paper demonstrates the need for a nonconstant initialization for the fractional calculus and establishes a basic definition set for the initialized fractional differintegral. This definition set allows the formalization of an initialized fractional calculus. Two basis calculi are considered; the Riemann-Liouville and the Grunwald fractional calculi. Two forms of initialization, terminal and side are developed.

Fractional corresponding operator in quantum mechanics and applications: A uniform fractional Schrödinger equation in form and fractional quantization methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Xiao; Science and Technology on Electronic Information Control Laboratory, 610036, Chengdu, Sichuan; Wei, Chaozhen

2014-11-15

In this paper we use Dirac function to construct a fractional operator called fractional corresponding operator, which is the general form of momentum corresponding operator. Then we give a judging theorem for this operator and with this judging theorem we prove that R–L, G–L, Caputo, Riesz fractional derivative operator and fractional derivative operator based on generalized functions, which are the most popular ones, coincide with the fractional corresponding operator. As a typical application, we use the fractional corresponding operator to construct a new fractional quantization scheme and then derive a uniform fractional Schrödinger equation in form. Additionally, we find thatmore » the five forms of fractional Schrödinger equation belong to the particular cases. As another main result of this paper, we use fractional corresponding operator to generalize fractional quantization scheme by using Lévy path integral and use it to derive the corresponding general form of fractional Schrödinger equation, which consequently proves that these two quantization schemes are equivalent. Meanwhile, relations between the theory in fractional quantum mechanics and that in classic quantum mechanics are also discussed. As a physical example, we consider a particle in an infinite potential well. We give its wave functions and energy spectrums in two ways and find that both results are the same.« less

Engineering Design Handbook: Recoilless Rifle Weapon Systems.

DTIC Science & Technology

1976-01-15

rifles also creates danger of physiological damage also exists. psychological factors which may be signifi- The extent and nature of the damage caused...the intensity of the bla&st, its disruption often cause psychological effects impulse, the position of the subject with of extreme lethargy and...General. 6. AD 3S 1 905, Capt. L. R. Creelman , A 2. David E. Walters and Edith F. Reilly, Parameiric Study of the Probability of Hit Hitting

The Fractions SNARC Revisited: Processing Fractions on a Consistent Mental Number Line.

PubMed

Toomarian, Elizabeth Y; Hubbard, Edward M

2017-07-12

The ability to understand fractions is key to establishing a solid foundation in mathematics, yet children and adults struggle to comprehend them. Previous studies have suggested that these struggles emerge because people fail to process fraction magnitude holistically on the mental number line (MNL), focusing instead on fraction components (Bonato et al. 2007). Subsequent studies have produced evidence for default holistic processing (Meert et al., 2009; 2010), but examined only magnitude processing, not spatial representations. We explored the spatial representations of fractions on the MNL in a series of three experiments: Experiment 1 replicated Bonato et al. (2007); 30 naïve undergraduates compared unit fractions (1/1-1/9) to 1/5, resulting in a reverse SNARC effect. Experiment 2 countered potential strategic biases induced by the limited set of fractions used by Bonato et al. by expanding the stimulus set to include all irreducible, single-digit proper fractions, and asked participants to compare them against 1/2. We observed a classic SNARC effect, completely reversing the pattern from Experiment 1. Together, Experiments 1 and 2 demonstrate that stimulus properties dramatically impact spatial representations of fractions. In Experiment 3, we demonstrated within-subjects reliability of the SNARC effect across both a fractions and whole number comparison task. Our results suggest that adults can indeed process fraction magnitudes holistically, and that their spatial representations occur on a consistent MNL for both whole numbers and fractions.

Reply to "Comment on 'Fractional quantum mechanics' and 'Fractional Schrödinger equation' ".

PubMed

Laskin, Nick

2016-06-01

The fractional uncertainty relation is a mathematical formulation of Heisenberg's uncertainty principle in the framework of fractional quantum mechanics. Two mistaken statements presented in the Comment have been revealed. The origin of each mistaken statement has been clarified and corrected statements have been made. A map between standard quantum mechanics and fractional quantum mechanics has been presented to emphasize the features of fractional quantum mechanics and to avoid misinterpretations of the fractional uncertainty relation. It has been shown that the fractional probability current equation is correct in the area of its applicability. Further studies have to be done to find meaningful quantum physics problems with involvement of the fractional probability current density vector and the extra term emerging in the framework of fractional quantum mechanics.

Fractionation of Organosolv Lignin Using Acetone:Water and Properties of the Obtained Fractions

DOE PAGES

Sadeghifar, Hasan; Wells, Tyrone; Le, Rosemary Khuu; ...

2016-11-07

In this study, lignin fractions with different molecular weight were prepared using a simple and almost green method from switchgrass and pine organosolv lignin. Different proportions of acetone in water, ranging from 30 to 60%, were used for lignin fractionation. A higher concentration of acetone dissolved higher molecular weight fractions of the lignin. Fractionated organosolv lignin showed different molecular weight and functional groups. Higher molecular weight fractions exhibited more aliphatic and less phenolic OH than lower molecular weight fractions. Lower molecular weight fractions lead to more homogeneous structure compared to samples with a higher molecular weight. In conclusion, all fractionsmore » showed strong antioxidant activity.« less

DIY Fraction Pack.

ERIC Educational Resources Information Center

Graham, Alan; Graham, Louise

2003-01-01

Describes a very successful attempt to teach fractions to year 5 pupils based on pupils making their own fraction pack. Children decided for themselves how to make the fractional slices used in the activity using colored cardboard sheets and templates of a paper circle consisting of 24 equal slices. (Author/NB)

Controllability of fractional higher order stochastic integrodifferential systems with fractional Brownian motion.

PubMed

Sathiyaraj, T; Balasubramaniam, P

2017-11-30

This paper presents a new set of sufficient conditions for controllability of fractional higher order stochastic integrodifferential systems with fractional Brownian motion (fBm) in finite dimensional space using fractional calculus, fixed point technique and stochastic analysis approach. In particular, we discuss the complete controllability for nonlinear fractional stochastic integrodifferential systems under the proved result of the corresponding linear fractional system is controllable. Finally, an example is presented to illustrate the efficiency of the obtained theoretical results. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Dividing Fractions: A Pedagogical Technique

ERIC Educational Resources Information Center

Lewis, Robert

2016-01-01

When dividing one fraction by a second fraction, invert, that is, flip the second fraction, then multiply it by the first fraction. To multiply fractions, simply multiply across the denominators, and multiply across the numerators to get the resultant fraction. So by inverting the division of fractions it is turned into an easy multiplication of…

Arbitrage with fractional Gaussian processes

NASA Astrophysics Data System (ADS)

Zhang, Xili; Xiao, Weilin

2017-04-01

While the arbitrage opportunity in the Black-Scholes model driven by fractional Brownian motion has a long history, the arbitrage strategy in the Black-Scholes model driven by general fractional Gaussian processes is in its infancy. The development of stochastic calculus with respect to fractional Gaussian processes allowed us to study such models. In this paper, following the idea of Shiryaev (1998), an arbitrage strategy is constructed for the Black-Scholes model driven by fractional Gaussian processes, when the stochastic integral is interpreted in the Riemann-Stieltjes sense. Arbitrage opportunities in some fractional Gaussian processes, including fractional Brownian motion, sub-fractional Brownian motion, bi-fractional Brownian motion, weighted-fractional Brownian motion and tempered fractional Brownian motion, are also investigated.

Exact solutions to the time-fractional differential equations via local fractional derivatives

NASA Astrophysics Data System (ADS)

Guner, Ozkan; Bekir, Ahmet

2018-01-01

This article utilizes the local fractional derivative and the exp-function method to construct the exact solutions of nonlinear time-fractional differential equations (FDEs). For illustrating the validity of the method, it is applied to the time-fractional Camassa-Holm equation and the time-fractional-generalized fifth-order KdV equation. Moreover, the exact solutions are obtained for the equations which are formed by different parameter values related to the time-fractional-generalized fifth-order KdV equation. This method is an reliable and efficient mathematical tool for solving FDEs and it can be applied to other non-linear FDEs.

Fractional bosonic strings

NASA Astrophysics Data System (ADS)

Diaz, Victor Alfonzo; Giusti, Andrea

2018-03-01

The aim of this paper is to present a simple generalization of bosonic string theory in the framework of the theory of fractional variational problems. Specifically, we present a fractional extension of the Polyakov action, for which we compute the general form of the equations of motion and discuss the connection between the new fractional action and a generalization the Nambu-Goto action. Consequently, we analyze the symmetries of the modified Polyakov action and try to fix the gauge, following the classical procedures. Then we solve the equations of motion in a simplified setting. Finally, we present a Hamiltonian description of the classical fractional bosonic string and introduce the fractional light-cone gauge. It is important to remark that, throughout the whole paper, we thoroughly discuss how to recover the known results as an "integer" limit of the presented model.

FRACTIONAL PEARSON DIFFUSIONS.

PubMed

Leonenko, Nikolai N; Meerschaert, Mark M; Sikorskii, Alla

2013-07-15

Pearson diffusions are governed by diffusion equations with polynomial coefficients. Fractional Pearson diffusions are governed by the corresponding time-fractional diffusion equation. They are useful for modeling sub-diffusive phenomena, caused by particle sticking and trapping. This paper provides explicit strong solutions for fractional Pearson diffusions, using spectral methods. It also presents stochastic solutions, using a non-Markovian inverse stable time change.

Well-conditioned fractional collocation methods using fractional Birkhoff interpolation basis

NASA Astrophysics Data System (ADS)

Jiao, Yujian; Wang, Li-Lian; Huang, Can

2016-01-01

The purpose of this paper is twofold. Firstly, we provide explicit and compact formulas for computing both Caputo and (modified) Riemann-Liouville (RL) fractional pseudospectral differentiation matrices (F-PSDMs) of any order at general Jacobi-Gauss-Lobatto (JGL) points. We show that in the Caputo case, it suffices to compute F-PSDM of order μ ∈ (0 , 1) to compute that of any order k + μ with integer k ≥ 0, while in the modified RL case, it is only necessary to evaluate a fractional integral matrix of order μ ∈ (0 , 1). Secondly, we introduce suitable fractional JGL Birkhoff interpolation problems leading to new interpolation polynomial basis functions with remarkable properties: (i) the matrix generated from the new basis yields the exact inverse of F-PSDM at "interior" JGL points; (ii) the matrix of the highest fractional derivative in a collocation scheme under the new basis is diagonal; and (iii) the resulted linear system is well-conditioned in the Caputo case, while in the modified RL case, the eigenvalues of the coefficient matrix are highly concentrated. In both cases, the linear systems of the collocation schemes using the new basis can be solved by an iterative solver within a few iterations. Notably, the inverse can be computed in a very stable manner, so this offers optimal preconditioners for usual fractional collocation methods for fractional differential equations (FDEs). It is also noteworthy that the choice of certain special JGL points with parameters related to the order of the equations can ease the implementation. We highlight that the use of the Bateman's fractional integral formulas and fast transforms between Jacobi polynomials with different parameters, is essential for our algorithm development.

Fractional Poisson Fields and Martingales

NASA Astrophysics Data System (ADS)

Aletti, Giacomo; Leonenko, Nikolai; Merzbach, Ely

2018-02-01

We present new properties for the Fractional Poisson process (FPP) and the Fractional Poisson field on the plane. A martingale characterization for FPPs is given. We extend this result to Fractional Poisson fields, obtaining some other characterizations. The fractional differential equations are studied. We consider a more general Mixed-Fractional Poisson process and show that this process is the stochastic solution of a system of fractional differential-difference equations. Finally, we give some simulations of the Fractional Poisson field on the plane.

A study of fractional Schrödinger equation composed of Jumarie fractional derivative

NASA Astrophysics Data System (ADS)

Banerjee, Joydip; Ghosh, Uttam; Sarkar, Susmita; Das, Shantanu

2017-04-01

In this paper we have derived the fractional-order Schrödinger equation composed of Jumarie fractional derivative. The solution of this fractional-order Schrödinger equation is obtained in terms of Mittag-Leffler function with complex arguments, and fractional trigonometric functions. A few important properties of the fractional Schrödinger equation are then described for the case of particles in one-dimensional infinite potential well. One of the motivations for using fractional calculus in physical systems is that the space and time variables, which we often deal with, exhibit coarse-grained phenomena. This means infinitesimal quantities cannot be arbitrarily taken to zero - rather they are non-zero with a minimum spread. This type of non-zero spread arises in the microscopic to mesoscopic levels of system dynamics, which means that, if we denote x as the point in space and t as the point in time, then limit of the differentials d x (and d t) cannot be taken as zero. To take the concept of coarse graining into account, use the infinitesimal quantities as (Δ x) α (and (Δ t) α ) with 0 < α < 1; called as `fractional differentials'. For arbitrarily small Δ x and Δ t (tending towards zero), these `fractional' differentials are greater than Δ x (and Δ t), i.e. (Δ x) α > Δ x and (Δ t) α > Δ t. This way of defining the fractional differentials helps us to use fractional derivatives in the study of dynamic systems.

Sensitivity of jet substructure to jet-induced medium response

NASA Astrophysics Data System (ADS)

Milhano, Guilherme; Wiedemann, Urs Achim; Zapp, Korinna Christine

2018-04-01

Jet quenching in heavy ion collisions is expected to be accompanied by recoil effects, but unambiguous signals for the induced medium response have been difficult to identify so far. Here, we argue that modern jet substructure measurements can improve this situation qualitatively since they are sensitive to the momentum distribution inside the jet. We show that the groomed subjet shared momentum fraction zg, and the girth of leading and subleading subjets signal recoil effects with dependencies that are absent in a recoilless baseline. We find that recoil effects can explain most of the medium modifications to the zg distribution observed in data. Furthermore, for jets passing the Soft Drop Condition, recoil effects induce in the differential distribution of subjet separation ΔR12 a characteristic increase with ΔR12, and they introduce a characteristic enhancement of the girth of the subleading subjet with decreasing zg. We explain why these qualitatively novel features, that we establish in JEWEL+PYTHIA simulations, reflect generic physical properties of recoil effects that should therefore be searched for as telltale signatures of jet-induced medium response.

The Effects of the "Fraction Ruler" Manipulative for Teaching Computation of Fractions

ERIC Educational Resources Information Center

Schiller, Diane Profita

1977-01-01

Explores the hypothesis that students in the fourth, fifth and sixth grade who were exposed to the "fraction ruler" as a manipulative for exploring basic fraction operations would perform more successfully in addition, subtraction and multiplication problems than students taught fraction operations by the traditional method. (Author/RK)

A fractional model with parallel fractional Maxwell elements for amorphous thermoplastics

NASA Astrophysics Data System (ADS)

Lei, Dong; Liang, Yingjie; Xiao, Rui

2018-01-01

We develop a fractional model to describe the thermomechanical behavior of amorphous thermoplastics. The fractional model is composed of two parallel fractional Maxwell elements. The first fractional Maxwell model is used to describe the glass transition, while the second component is aimed at describing the viscous flow. We further derive the analytical solutions for the stress relaxation modulus and complex modulus through Laplace transform. We then demonstrate the model is able to describe the master curves of the stress relaxation modulus, storage modulus and loss modulus, which all show two distinct transition regions. The obtained parameters show that the modulus of the two fractional Maxwell elements differs in 2-3 orders of magnitude, while the relaxation time differs in 7-9 orders of magnitude. Finally, we apply the model to describe the stress response of constant strain rate tests. The model, together with the parameters obtained from fitting the master curve of stress relaxation modulus, can accurately predict the temperature and strain rate dependent stress response.

Permutation entropy of fractional Brownian motion and fractional Gaussian noise

NASA Astrophysics Data System (ADS)

Zunino, L.; Pérez, D. G.; Martín, M. T.; Garavaglia, M.; Plastino, A.; Rosso, O. A.

2008-06-01

We have worked out theoretical curves for the permutation entropy of the fractional Brownian motion and fractional Gaussian noise by using the Bandt and Shiha [C. Bandt, F. Shiha, J. Time Ser. Anal. 28 (2007) 646] theoretical predictions for their corresponding relative frequencies. Comparisons with numerical simulations show an excellent agreement. Furthermore, the entropy-gap in the transition between these processes, observed previously via numerical results, has been here theoretically validated. Also, we have analyzed the behaviour of the permutation entropy of the fractional Gaussian noise for different time delays.

Weighted fractional permutation entropy and fractional sample entropy for nonlinear Potts financial dynamics

NASA Astrophysics Data System (ADS)

Xu, Kaixuan; Wang, Jun

2017-02-01

In this paper, recently introduced permutation entropy and sample entropy are further developed to the fractional cases, weighted fractional permutation entropy (WFPE) and fractional sample entropy (FSE). The fractional order generalization of information entropy is utilized in the above two complexity approaches, to detect the statistical characteristics of fractional order information in complex systems. The effectiveness analysis of proposed methods on the synthetic data and the real-world data reveals that tuning the fractional order allows a high sensitivity and more accurate characterization to the signal evolution, which is useful in describing the dynamics of complex systems. Moreover, the numerical research on nonlinear complexity behaviors is compared between the returns series of Potts financial model and the actual stock markets. And the empirical results confirm the feasibility of the proposed model.

Tactical Symbology Catalog

DTIC Science & Technology

1983-05-01

FM 7.8.1 COMMUJICATIOIV FM 21-30 Te lephone/ Q ( 54 164 CATEGORY/CONCEPT/ SYMBOL SOURCE AMFV W 7.8.2 COMMUN4ICATION/ FM 21-30 Telephone/ center - not...I.7. Z LL ?. .F ’l 21-30B, YCC Ji. 7.3 FmPv ’n2-3, TO recoilless, heavq 11.8.1 * " TOS iuncifferentiated I Mr~ CATEGORYCOrNCEPT/ SYMIDOL SOLIRCE AMFV

The Military Technology of the Polish People’s Army, 30 Years of Development,

DTIC Science & Technology

1983-12-20

armed with light self - propelled cannon mounted on tracked vehicles (adapted also to transport aircraft) as well as recoilless guns with...with radar-computers, mounted on self propelled tracked vehicles . The modernization of artillery has led to the expansion of technical-repair...light tracked vehicles and on self propelled areal vehicles . 4 . , A very important factor influencing the improvement of the effectiveness of artillery

Gauge invariant fractional electromagnetic fields

NASA Astrophysics Data System (ADS)

Lazo, Matheus Jatkoske

2011-09-01

Fractional derivatives and integrations of non-integers orders was introduced more than three centuries ago but only recently gained more attention due to its application on nonlocal phenomenas. In this context, several formulations of fractional electromagnetic fields was proposed, but all these theories suffer from the absence of an effective fractional vector calculus, and in general are non-causal or spatially asymmetric. In order to deal with these difficulties, we propose a spatially symmetric and causal gauge invariant fractional electromagnetic field from a Lagrangian formulation. From our fractional Maxwell's fields arose a definition for the fractional gradient, divergent and curl operators.

Creating, Naming, and Justifying Fractions

ERIC Educational Resources Information Center

Siebert, Daniel; Gaskin, Nicole

2006-01-01

For students to develop meaningful conceptions of fractions and fraction operations, they need to think of fractions in terms other than as just whole-number combinations. In this article, we suggest two powerful images for thinking about fractions that move beyond whole-number reasoning. (Contains 5 figures.)

Fractionation of Poly(butyl methacrylate) by Molecular Topology Using Multidetector Thermal Field-Flow Fractionation.

PubMed

Greyling, Guilaume; Pasch, Harald

2015-12-01

Thermal field-flow fractionation (ThFFF) is an interesting alternative to column-based fractionation being able to address different molecular parameters including size and composition. Until today it has not been shown to be able to fractionate polymers of similar molar masses and chemical compositions by molecular topology. The present study demonstrates that poly(butyl methacrylates) with identical molar masses can be fractionated by ThFFF according to the topology of the butyl group. The influence of the solvent polarity on the thermal diffusion behavior of these polymers is presented and it is shown to have a significant influence on the fractionation of poly(n-butyl methacrylate) and poly(t-butyl methacrylate). Fractionation improves with increasing solvent polarity and solvent polarity may have a greater influence on fractionation than solvent viscosity. It is found that the thermal diffusion coefficient, D(T), as well as the hydrodynamic diameter, D(h), exhibit increasing trends with increasing solvent polarity. The solvent quality has a significant influence on the fractionation. It is found that cyclohexane, being a theta solvent for poly(t-butyl methacrylate) but not for poly(n-butyl methacrylate), significantly improves the fractionation of the samples by decreasing the diffusion rate of the former but not the latter. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Fractions--Concepts before Symbols.

ERIC Educational Resources Information Center

Bennett, Albert B., Jr.

The learning difficulties that students experience with fractions begin immediately when they are shown fraction symbols with one numeral written above the other and told that the "top number" is called the numerator and the "bottom number" is called the denominator. This introduction to fractions will usually include a few visual diagrams to help…

Fraction Reduction through Continued Fractions

ERIC Educational Resources Information Center

Carley, Holly

2011-01-01

This article presents a method of reducing fractions without factoring. The ideas presented may be useful as a project for motivated students in an undergraduate number theory course. The discussion is related to the Euclidean Algorithm and its variations may lead to projects or early examples involving efficiency of an algorithm.

Fractional quiver W-algebras

NASA Astrophysics Data System (ADS)

Kimura, Taro; Pestun, Vasily

2018-04-01

We introduce quiver gauge theory associated with the non-simply laced type fractional quiver and define fractional quiver W-algebras by using construction of Kimura and Pestun (Lett Math Phys, 2018. https://doi.org/10.1007/s11005-018-1072-1; Lett Math Phys, 2018. https://doi.org/10.1007/s11005-018-1073-0) with representation of fractional quivers.

soil organic matter fractionation

NASA Astrophysics Data System (ADS)

Osat, Maryam; Heidari, Ahmad

2010-05-01

Carbon is essential for plant growth, due to its effects on other soil properties like aggregation. Knowledge of dynamics of organic matter in different locations in the soil matrix can provide valuable information which affects carbon sequestration and soil the other soil properties. Extraction of soil organic matter (SOM) fractions has been a long standing approach to elucidating the roles of soil organic matter in soil processes. Several kind fractionation methods are used and all provide information on soil organic matter function. Physical fractionation capture the effects on SOM dynamics of the spatial arrangement of primary and secondary organomineral particles in soil while chemical fractionation can not consider the spatial arrangement but their organic fractions are suitable for advanced chemical characterization. Three method of physical separation of soil have been used, sieving, sedimentation and densitometry. The distribution of organic matter within physical fractions of the soil can be assessed by sieving. Sieving separates soil particles based strictly on size. The study area is located on north central Iran, between 35° 41'- 36° 01' N and 50° 42'- 51° 14' E. Mean annual precipitation about 243.8 mm and mean annual air temperature is about 14.95 °C. The soil moisture and temperature regime vary between aridic-thermic in lower altitudes to xeric-mesic in upper altitudes. More than 36 surface soil samples (0-20 cm) were collected according to land-use map units. After preliminary analyzing of samples 10 samples were selected for further analyses in five size fractions and three different time intervals in September, January and April 2008. Fractionation carried out by dry sieving in five classes, 1-2 mm, 0.5-1 mm, 270 μm-0.5mm, 53-270 μm and <53 μm. Organic matter and C/N ratio were determined for all fractions at different time intervals. Chemical fractionation of organic matter also carried out according to Tan (2003), also Mineralogical

Coefficient of restitution in fractional viscoelastic compliant impacts using fractional Chebyshev collocation

NASA Astrophysics Data System (ADS)

Dabiri, Arman; Butcher, Eric A.; Nazari, Morad

2017-02-01

Compliant impacts can be modeled using linear viscoelastic constitutive models. While such impact models for realistic viscoelastic materials using integer order derivatives of force and displacement usually require a large number of parameters, compliant impact models obtained using fractional calculus, however, can be advantageous since such models use fewer parameters and successfully capture the hereditary property. In this paper, we introduce the fractional Chebyshev collocation (FCC) method as an approximation tool for numerical simulation of several linear fractional viscoelastic compliant impact models in which the overall coefficient of restitution for the impact is studied as a function of the fractional model parameters for the first time. Other relevant impact characteristics such as hysteresis curves, impact force gradient, penetration and separation depths are also studied.

One Adaptive Synchronization Approach for Fractional-Order Chaotic System with Fractional-Order 1 < q < 2

PubMed Central

Zhou, Ping; Bai, Rongji

2014-01-01

Based on a new stability result of equilibrium point in nonlinear fractional-order systems for fractional-order lying in 1 < q < 2, one adaptive synchronization approach is established. The adaptive synchronization for the fractional-order Lorenz chaotic system with fractional-order 1 < q < 2 is considered. Numerical simulations show the validity and feasibility of the proposed scheme. PMID:25247207

Toward lattice fractional vector calculus

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2014-09-01

An analog of fractional vector calculus for physical lattice models is suggested. We use an approach based on the models of three-dimensional lattices with long-range inter-particle interactions. The lattice analogs of fractional partial derivatives are represented by kernels of lattice long-range interactions, where the Fourier series transformations of these kernels have a power-law form with respect to wave vector components. In the continuum limit, these lattice partial derivatives give derivatives of non-integer order with respect to coordinates. In the three-dimensional description of the non-local continuum, the fractional differential operators have the form of fractional partial derivatives of the Riesz type. As examples of the applications of the suggested lattice fractional vector calculus, we give lattice models with long-range interactions for the fractional Maxwell equations of non-local continuous media and for the fractional generalization of the Mindlin and Aifantis continuum models of gradient elasticity.

Some Properties of the Fractional Equation of Continuity and the Fractional Diffusion Equation

NASA Astrophysics Data System (ADS)

Fukunaga, Masataka

2006-05-01

The fractional equation of continuity (FEC) and the fractional diffusion equation (FDE) show peculiar behaviors that are in the opposite sense to those expected from the equation of continuity and the diffusion equation, respectively. The behaviors are interpreted in terms of the memory effect of the fractional time derivatives included in the equations. Some examples are given by solutions of the FDE.

Heavy-tailed fractional Pearson diffusions.

PubMed

Leonenko, N N; Papić, I; Sikorskii, A; Šuvak, N

2017-11-01

We define heavy-tailed fractional reciprocal gamma and Fisher-Snedecor diffusions by a non-Markovian time change in the corresponding Pearson diffusions. Pearson diffusions are governed by the backward Kolmogorov equations with space-varying polynomial coefficients and are widely used in applications. The corresponding fractional reciprocal gamma and Fisher-Snedecor diffusions are governed by the fractional backward Kolmogorov equations and have heavy-tailed marginal distributions in the steady state. We derive the explicit expressions for the transition densities of the fractional reciprocal gamma and Fisher-Snedecor diffusions and strong solutions of the associated Cauchy problems for the fractional backward Kolmogorov equation.

Intracellular Cadmium Isotope Fractionation

NASA Astrophysics Data System (ADS)

Horner, T. J.; Lee, R. B.; Henderson, G. M.; Rickaby, R. E.

2011-12-01

Recent stable isotope studies into the biological utilization of transition metals (e.g. Cu, Fe, Zn, Cd) suggest several stepwise cellular processes can fractionate isotopes in both culture and nature. However, the determination of fractionation factors is often unsatisfactory, as significant variability can exist - even between different organisms with the same cellular functions. Thus, it has not been possible to adequately understand the source and mechanisms of metal isotopic fractionation. In order to address this problem, we investigated the biological fractionation of Cd isotopes within genetically-modified bacteria (E. coli). There is currently only one known biological use or requirement of Cd, a Cd/Zn carbonic anhydrase (CdCA, from the marine diatom T. weissfloggii), which we introduce into the E. coli genome. We have also developed a cleaning procedure that allows for the treating of bacteria so as to study the isotopic composition of different cellular components. We find that whole cells always exhibit a preference for uptake of the lighter isotopes of Cd. Notably, whole cells appear to have a similar Cd isotopic composition regardless of the expression of CdCA within the E. coli. However, isotopic fractionation can occur within the genetically modified E. coli during Cd use, such that Cd bound in CdCA can display a distinct isotopic composition compared to the cell as a whole. Thus, the externally observed fractionation is independent of the internal uses of Cd, with the largest Cd isotope fractionation occurring during cross-membrane transport. A general implication of these experiments is that trace metal isotopic fractionation most likely reflects metal transport into biological cells (either actively or passively), rather than relating to expression of specific physiological function and genetic expression of different metalloenzymes.

Fractional diffusion: recovering the distributed fractional derivative from overposed data

NASA Astrophysics Data System (ADS)

Rundell, W.; Zhang, Z.

2017-03-01

There has been considerable recent study in ‘subdiffusion’ models that replace the standard parabolic equation model by a one with a fractional derivative in the time variable. There are many ways to look at this newer approach and one such is to realize that the order of the fractional derivative is related to the time scales of the underlying diffusion process. This raises the question of what order α of derivative should be taken and if a single value actually suffices. This has led to models that combine a finite number of these derivatives each with a different fractional exponent {αk} and different weighting value c k to better model a greater possible range of time scales. Ultimately, one wants to look at a situation that combines derivatives in a continuous way—the so-called distributional model with parameter μ ≤ft(α \\right) . However all of this begs the question of how one determines this ‘order’ of differentiation. Recovering a single fractional value has been an active part of the process from the beginning of fractional diffusion modeling and if this is the only unknown then the markers left by the fractional order derivative are relatively straightforward to determine. In the case of a finite combination of derivatives this becomes much more complex due to the more limited analytic tools available for such equations, but recent progress in this direction has been made, (Li et al 2015 Appl. Math. Comput. 257 381-97, Li and Yamamoto 2015 Appl. Anal. 94 570-9). This paper considers the full distributional model where the order is viewed as a function μ ≤ft(α \\right) on the interval (0, 1]. We show existence, uniqueness and regularity for an initial-boundary value problem including an important representation theorem in the case of a single spatial variable. This is then used in the inverse problem of recovering the distributional coefficient μ ≤ft(α \\right) from a time trace of the solution and a uniqueness result is proven.

Fraction magnitude understanding and its unique role in predicting general mathematics achievement at two early stages of fraction instruction.

PubMed

Liu, Yingyi

2017-09-08

Prior studies on fraction magnitude understanding focused mainly on students with relatively sufficient formal instruction on fractions whose fraction magnitude understanding is relatively mature. This study fills a research gap by investigating fraction magnitude understanding in the early stages of fraction instruction. It extends previous findings to children with limited and primary formal fraction instruction. Thirty-five fourth graders with limited fraction instruction and forty fourth graders with primary fraction instruction were recruited from a Chinese primary school. Children's fraction magnitude understanding was assessed with a fraction number line estimation task. Approximate number system (ANS) acuity was assessed with a dot discrimination task. Whole number knowledge was assessed with a whole number line estimation task. General reading and mathematics achievements were collected concurrently and 1 year later. In children with limited fraction instruction, fraction representation was linear and fraction magnitude understanding was concurrently related to both ANS and whole number knowledge. In children with primary fraction instruction, fraction magnitude understanding appeared to (marginally) significantly predict general mathematics achievement 1 year later. Fraction magnitude understanding emerged early during formal instruction of fractions. ANS and whole number knowledge were related to fraction magnitude understanding when children first began to learn about fractions in school. The predictive value of fraction magnitude understanding is likely constrained by its sophistication level. © 2017 The British Psychological Society.

Fractional laser skin resurfacing.

PubMed

Alexiades-Armenakas, Macrene R; Dover, Jeffrey S; Arndt, Kenneth A

2012-11-01

Laser skin resurfacing (LSR) has evolved over the past 2 decades from traditional ablative to fractional nonablative and fractional ablative resurfacing. Traditional ablative LSR was highly effective in reducing rhytides, photoaging, and acne scarring but was associated with significant side effects and complications. In contrast, nonablative LSR was very safe but failed to deliver consistent clinical improvement. Fractional LSR has achieved the middle ground; it combined the efficacy of traditional LSR with the safety of nonablative modalities. The first fractional laser was a nonablative erbium-doped yttrium aluminum garnet (Er:YAG) laser that produced microscopic columns of thermal injury in the epidermis and upper dermis. Heralding an entirely new concept of laser energy delivery, it delivered the laser beam in microarrays. It resulted in microscopic columns of treated tissue and intervening areas of untreated skin, which yielded rapid reepithelialization. Fractional delivery was quickly applied to ablative wavelengths such as carbon dioxide, Er:YAG, and yttrium scandium gallium garnet (2,790 nm), providing more significant clinical outcomes. Adjustable laser parameters, including power, pitch, dwell time, and spot density, allowed for precise determination of percent surface area, affected penetration depth, and clinical recovery time and efficacy. Fractional LSR has been a significant advance to the laser field, striking the balance between safety and efficacy.

Paper Folding Fractions

ERIC Educational Resources Information Center

Pagni, David

2007-01-01

In this article, the author presents a paper folding activity that can be used for teaching fractions. This activity can be used to describe areas of folded polygons in terms of a standard unit of measure. A paper folding fractions worksheet and its corresponding solutions are also presented in this article. (Contains 2 figures.)

Fractional dynamics pharmacokinetics–pharmacodynamic models

PubMed Central

2010-01-01

While an increasing number of fractional order integrals and differential equations applications have been reported in the physics, signal processing, engineering and bioengineering literatures, little attention has been paid to this class of models in the pharmacokinetics–pharmacodynamic (PKPD) literature. One of the reasons is computational: while the analytical solution of fractional differential equations is available in special cases, it this turns out that even the simplest PKPD models that can be constructed using fractional calculus do not allow an analytical solution. In this paper, we first introduce new families of PKPD models incorporating fractional order integrals and differential equations, and, second, exemplify and investigate their qualitative behavior. The families represent extensions of frequently used PK link and PD direct and indirect action models, using the tools of fractional calculus. In addition the PD models can be a function of a variable, the active drug, which can smoothly transition from concentration to exposure, to hyper-exposure, according to a fractional integral transformation. To investigate the behavior of the models we propose, we implement numerical algorithms for fractional integration and for the numerical solution of a system of fractional differential equations. For simplicity, in our investigation we concentrate on the pharmacodynamic side of the models, assuming standard (integer order) pharmacokinetics. PMID:20455076

Fractional vector calculus and fluid mechanics

NASA Astrophysics Data System (ADS)

Lazopoulos, Konstantinos A.; Lazopoulos, Anastasios K.

2017-04-01

Basic fluid mechanics equations are studied and revised under the prism of fractional continuum mechanics (FCM), a very promising research field that satisfies both experimental and theoretical demands. The geometry of the fractional differential has been clarified corrected and the geometry of the fractional tangent spaces of a manifold has been studied in Lazopoulos and Lazopoulos (Lazopoulos KA, Lazopoulos AK. Progr. Fract. Differ. Appl. 2016, 2, 85-104), providing the bases of the missing fractional differential geometry. Therefore, a lot can be contributed to fractional hydrodynamics: the basic fractional fluid equations (Navier Stokes, Euler and Bernoulli) are derived and fractional Darcy's flow in porous media is studied.

Control of Initialized Fractional-Order Systems

NASA Technical Reports Server (NTRS)

Hartly, Tom T.; Lorenzo, Carl F.

2002-01-01

Due to the importance of historical effects in fractional-order systems, this paper presents a general fractional-order control theory that includes the time-varying initialization response. Previous studies have not properly accounted for these historical effects. The initialization response, along with the forced response, for fractional-order systems is determined. Stability properties of fractional-order systems are presented in the complex Airplane, which is a transformation of the s-plane. Time responses are discussed with respect to pole positions in the complex Airplane and frequency response behavior is included. A fractional-order vector space representation, which is a generalization of the state space concept, is presented including the initialization response. Control methods for vector representations of initialized fractional-order systems are shown. Nyquist, root-locus, and other input-output control methods are adapted to the control of fractional-order systems. Finally, the fractional-order differintegral is generalized to continuous order-distributions that have the possibility of including a continuum of fractional orders in a system element.

Exact solutions of fractional mBBM equation and coupled system of fractional Boussinesq-Burgers

NASA Astrophysics Data System (ADS)

Javeed, Shumaila; Saif, Summaya; Waheed, Asif; Baleanu, Dumitru

2018-06-01

The new exact solutions of nonlinear fractional partial differential equations (FPDEs) are established by adopting first integral method (FIM). The Riemann-Liouville (R-L) derivative and the local conformable derivative definitions are used to deal with the fractional order derivatives. The proposed method is applied to get exact solutions for space-time fractional modified Benjamin-Bona-Mahony (mBBM) equation and coupled time-fractional Boussinesq-Burgers equation. The suggested technique is easily applicable and effectual which can be implemented successfully to obtain the solutions for different types of nonlinear FPDEs.

How Weird Are Weird Fractions?

ERIC Educational Resources Information Center

Stuffelbeam, Ryan

2013-01-01

A positive rational is a weird fraction if its value is unchanged by an illegitimate, digit-based reduction. In this article, we prove that each weird fraction is uniquely weird and initiate a discussion of the prevalence of weird fractions.

Fractional Diffusion Equations and Anomalous Diffusion

NASA Astrophysics Data System (ADS)

Evangelista, Luiz Roberto; Kaminski Lenzi, Ervin

2018-01-01

Preface; 1. Mathematical preliminaries; 2. A survey of the fractional calculus; 3. From normal to anomalous diffusion; 4. Fractional diffusion equations: elementary applications; 5. Fractional diffusion equations: surface effects; 6. Fractional nonlinear diffusion equation; 7. Anomalous diffusion: anisotropic case; 8. Fractional Schrödinger equations; 9. Anomalous diffusion and impedance spectroscopy; 10. The Poisson–Nernst–Planck anomalous (PNPA) models; References; Index.

On the ψ-Hilfer fractional derivative

NASA Astrophysics Data System (ADS)

Vanterler da C. Sousa, J.; Capelas de Oliveira, E.

2018-07-01

In this paper we introduce a new fractional derivative with respect to another function the so-called ψ-Hilfer fractional derivative. We discuss some properties and important results of the fractional calculus. In this sense, we present some results involving uniformly convergent sequence of function, uniformly continuous function and examples including the Mittag-Leffler function with one parameter. Finally, we present a wide class of integrals and fractional derivatives, by means of the fractional integral with respect to another function and the ψ-Hilfer fractional derivative.

(N+1)-dimensional fractional reduced differential transform method for fractional order partial differential equations

NASA Astrophysics Data System (ADS)

Arshad, Muhammad; Lu, Dianchen; Wang, Jun

2017-07-01

In this paper, we pursue the general form of the fractional reduced differential transform method (DTM) to (N+1)-dimensional case, so that fractional order partial differential equations (PDEs) can be resolved effectively. The most distinct aspect of this method is that no prescribed assumptions are required, and the huge computational exertion is reduced and round-off errors are also evaded. We utilize the proposed scheme on some initial value problems and approximate numerical solutions of linear and nonlinear time fractional PDEs are obtained, which shows that the method is highly accurate and simple to apply. The proposed technique is thus an influential technique for solving the fractional PDEs and fractional order problems occurring in the field of engineering, physics etc. Numerical results are obtained for verification and demonstration purpose by using Mathematica software.

Shot-noise evidence of fractional quasiparticle creation in a local fractional quantum Hall state.

PubMed

Hashisaka, Masayuki; Ota, Tomoaki; Muraki, Koji; Fujisawa, Toshimasa

2015-02-06

We experimentally identify fractional quasiparticle creation in a tunneling process through a local fractional quantum Hall (FQH) state. The local FQH state is prepared in a low-density region near a quantum point contact in an integer quantum Hall (IQH) system. Shot-noise measurements reveal a clear transition from elementary-charge tunneling at low bias to fractional-charge tunneling at high bias. The fractional shot noise is proportional to T(1)(1-T(1)) over a wide range of T(1), where T(1) is the transmission probability of the IQH edge channel. This binomial distribution indicates that fractional quasiparticles emerge from the IQH state to be transmitted through the local FQH state. The study of this tunneling process enables us to elucidate the dynamics of Laughlin quasiparticles in FQH systems.

Fractional Stochastic Field Theory

NASA Astrophysics Data System (ADS)

Honkonen, Juha

2018-02-01

Models describing evolution of physical, chemical, biological, social and financial processes are often formulated as differential equations with the understanding that they are large-scale equations for averages of quantities describing intrinsically random processes. Explicit account of randomness may lead to significant changes in the asymptotic behaviour (anomalous scaling) in such models especially in low spatial dimensions, which in many cases may be captured with the use of the renormalization group. Anomalous scaling and memory effects may also be introduced with the use of fractional derivatives and fractional noise. Construction of renormalized stochastic field theory with fractional derivatives and fractional noise in the underlying stochastic differential equations and master equations and the interplay between fluctuation-induced and built-in anomalous scaling behaviour is reviewed and discussed.

Accessible solitons of fractional dimension

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhong, Wei-Ping, E-mail: zhongwp6@126.com; Texas A&M University at Qatar, P.O. Box 23874, Doha; Belić, Milivoj

We demonstrate that accessible solitons described by an extended Schrödinger equation with the Laplacian of fractional dimension can exist in strongly nonlocal nonlinear media. The soliton solutions of the model are constructed by two special functions, the associated Legendre polynomials and the Laguerre polynomials in the fraction-dimensional space. Our results show that these fractional accessible solitons form a soliton family which includes crescent solitons, and asymmetric single-layer and multi-layer necklace solitons. -- Highlights: •Analytic solutions of a fractional Schrödinger equation are obtained. •The solutions are produced by means of self-similar method applied to the fractional Schrödinger equation with parabolic potential.more » •The fractional accessible solitons form crescent, asymmetric single-layer and multilayer necklace profiles. •The model applies to the propagation of optical pulses in strongly nonlocal nonlinear media.« less

Control of Initialized Fractional-Order Systems

NASA Technical Reports Server (NTRS)

Hartley, Tom T.; Lorenzo, Carl F.

2004-01-01

Fractional-Order systems, or systems containing fractional derivatives and integrals, have been studied by many in the engineering area. Additionally, very readable discussions, devoted specifically to the subject, are presented by Oldham and Spanier, Miller and Ross, and Pudlubny (1999a). It should be noted that there are a growing number of physical systems whose behavior can be compactly described using fractional system theory. Of specific interest to electrical engineers are long lines, electrochemical processes, dielectric polarization, colored noise, viscoelastic materials, and chaos. With the growing number of applications, it is important to establish a theory of control for these fractional-order systems, and for the potential use of fractional-order systems as feedback compensators. This topic is addressed in this paper. The first section discusses the control of fractional-order systems using a vector space representation, where initialization is included in the discussion. It should be noted that Bagley and Calico and Padovan and Sawicki both present a fractional state-space representation, which do not include the important historic effects. Incorporation of these effects based on the initialized fractional calculus is presented . The control methods presented in this paper are based on the initialized fractional order system theory. The second section presents an input-output approach. Some of the problems encountered in these sections are: a) the need to introduce a new complex plane to study the dynamics of fractional-order systems, b) the need to properly define the Laplace transform of the fractional derivative, and c) the proper inclusion of the initialization response in the system and control formulation. Following this, the next section generalizes the proportional-plus-integral-control (PI-control) and PID-control (PI-plus- derivative) concepts using fractional integrals. This is then further generalized using general fractional- order

Learning to Use Fractions: Examining Middle School Students Emerging Fraction Literacy

ERIC Educational Resources Information Center

Johanning, Debra I.

2008-01-01

This article describes one prevalent practice that a group of 6th- and 7th-grade students engaged in when they used fractions in the context of area and perimeter, decimal operations, similarity, and ratios and proportions. The study's results revealed that students did not simply take the concepts and skills learned in formal fractions units and…

PREFACE: Fractional Differentiation and its Applications (FDA08) Fractional Differentiation and its Applications (FDA08)

NASA Astrophysics Data System (ADS)

Baleanu, Dumitru; Tenreiro Machado, J. A.

2009-10-01

The international workshop, Fractional Differentiation and its Applications (FDA08), held at Cankaya University, Ankara, Turkey on 5-7 November 2008, was the third in an ongoing series of conferences dedicated to exploring applications of fractional calculus in science, engineering, economics and finance. Fractional calculus, which deals with derivatives and integrals of any order, is now recognized as playing an important role in modeling multi-scale problems that span a wide range of time or length scales. Fractional calculus provides a natural link to the intermediate-order dynamics that often reflects the complexity of micro- and nanostructures through fractional-order differential equations. Unlike the more established techniques of mathematical physics, the methods of fractional differentiation are still under development; while it is true that the ideas of fractional calculus are as old as the classical integer-order differential operators, modern work is proceeding by both expanding the capabilities of this mathematical tool and by widening its range of applications. Hence, the interested reader will find papers here that focus on the underlying mathematics of fractional calculus, that extend fractional-order operators into new domains, and that apply well established methods to experimental and theoretical problems. The organizing committee invited presentations from experts representing the international community of scholars in fractional calculus and welcomed contributions from the growing number of researchers who are applying fractional differentiation to complex technical problems. The selection of papers in this topical issue of Physica Scripta reflects the success of the FDA08 workshop, with the emergence of a variety of novel areas of application. With these ideas in mind, the guest editors would like to honor the many distinguished scientists that have promoted the development of fractional calculus and, in particular, Professor George M

Do Children Understand Fraction Addition?

ERIC Educational Resources Information Center

Braithwaite, David W.; Tian, Jing; Siegler, Robert S.

2017-01-01

Many children fail to master fraction arithmetic even after years of instruction. A recent theory of fraction arithmetic (Braithwaite, Pyke, & Siegler, in press) hypothesized that this poor learning of fraction arithmetic procedures reflects poor conceptual understanding of them. To test this hypothesis, we performed three experiments…

The random continued fraction transformation

NASA Astrophysics Data System (ADS)

Kalle, Charlene; Kempton, Tom; Verbitskiy, Evgeny

2017-03-01

We introduce a random dynamical system related to continued fraction expansions. It uses random combinations of the Gauss map and the Rényi (or backwards) continued fraction map. We explore the continued fraction expansions that this system produces, as well as the dynamical properties of the system.

Using Steffe's Advanced Fraction Schemes

ERIC Educational Resources Information Center

McCloskey, Andrea V.; Norton, Anderson H.

2009-01-01

Recognizing schemes, which are different from strategies, can help teachers understand their students' thinking about fractions. Using Steffe's advanced fraction schemes, the authors describe a progression of development that upper elementary and middle school students might follow in understanding fractions. Each scheme can be viewed as a…

Fractional diffusion on bounded domains

DOE PAGES

Defterli, Ozlem; D'Elia, Marta; Du, Qiang; ...

2015-03-13

We found that the mathematically correct specification of a fractional differential equation on a bounded domain requires specification of appropriate boundary conditions, or their fractional analogue. In this paper we discuss the application of nonlocal diffusion theory to specify well-posed fractional diffusion equations on bounded domains.

Extension of many-body theory and approximate density functionals to fractional charges and fractional spins.

PubMed

Yang, Weitao; Mori-Sánchez, Paula; Cohen, Aron J

2013-09-14

The exact conditions for density functionals and density matrix functionals in terms of fractional charges and fractional spins are known, and their violation in commonly used functionals has been shown to be the root of many major failures in practical applications. However, approximate functionals are designed for physical systems with integer charges and spins, not in terms of the fractional variables. Here we develop a general framework for extending approximate density functionals and many-electron theory to fractional-charge and fractional-spin systems. Our development allows for the fractional extension of any approximate theory that is a functional of G(0), the one-electron Green's function of the non-interacting reference system. The extension to fractional charge and fractional spin systems is based on the ensemble average of the basic variable, G(0). We demonstrate the fractional extension for the following theories: (1) any explicit functional of the one-electron density, such as the local density approximation and generalized gradient approximations; (2) any explicit functional of the one-electron density matrix of the non-interacting reference system, such as the exact exchange functional (or Hartree-Fock theory) and hybrid functionals; (3) many-body perturbation theory; and (4) random-phase approximations. A general rule for such an extension has also been derived through scaling the orbitals and should be useful for functionals where the link to the Green's function is not obvious. The development thus enables the examination of approximate theories against known exact conditions on the fractional variables and the analysis of their failures in chemical and physical applications in terms of violations of exact conditions of the energy functionals. The present work should facilitate the calculation of chemical potentials and fundamental bandgaps with approximate functionals and many-electron theories through the energy derivatives with respect to the

16 CFR 500.17 - Fractions.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 16 Commercial Practices 1 2010-01-01 2010-01-01 false Fractions. 500.17 Section 500.17 Commercial... LABELING ACT § 500.17 Fractions. (a) SI metric declarations of net quantity of contents of any consumer commodity may contain only decimal fractions. Other declarations of net quantity of contents may contain...

The fractional dynamics of quantum systems

NASA Astrophysics Data System (ADS)

Lu, Longzhao; Yu, Xiangyang

2018-05-01

The fractional dynamic process of a quantum system is a novel and complicated problem. The establishment of a fractional dynamic model is a significant attempt that is expected to reveal the mechanism of fractional quantum system. In this paper, a generalized time fractional Schrödinger equation is proposed. To study the fractional dynamics of quantum systems, we take the two-level system as an example and derive the time fractional equations of motion. The basic properties of the system are investigated by solving this set of equations in the absence of light field analytically. Then, when the system is subject to the light field, the equations are solved numerically. It shows that the two-level system described by the time fractional Schrödinger equation we proposed is a confirmable system.

Theory of Random Copolymer Fractionation in Columns

NASA Astrophysics Data System (ADS)

Enders, Sabine

Random copolymers show polydispersity both with respect to molecular weight and with respect to chemical composition, where the physical and chemical properties depend on both polydispersities. For special applications, the two-dimensional distribution function must adjusted to the application purpose. The adjustment can be achieved by polymer fractionation. From the thermodynamic point of view, the distribution function can be adjusted by the successive establishment of liquid-liquid equilibria (LLE) for suitable solutions of the polymer to be fractionated. The fractionation column is divided into theoretical stages. Assuming an LLE on each theoretical stage, the polymer fractionation can be modeled using phase equilibrium thermodynamics. As examples, simulations of stepwise fractionation in one direction, cross-fractionation in two directions, and two different column fractionations (Baker-Williams fractionation and continuous polymer fractionation) have been investigated. The simulation delivers the distribution according the molecular weight and chemical composition in every obtained fraction, depending on the operative properties, and is able to optimize the fractionation effectively.

Fractional Ornstein-Uhlenbeck noise

NASA Astrophysics Data System (ADS)

Fa, Kwok Sau

2018-06-01

Fractional Ornstein-Uhlenbeck noise is considered and investigated. The fractional Ornstein-Uhlenbeck noise may be linked with a supercapacitor driven by the white noise, and its correlation function for the stationary state shows monotonic and oscillatory decays. In the case of the oscillatory behavior the correlation function presents behaviors similar to those of the harmonic noise (harmonic oscillator driven by the white noise). For application, the Langevin equation with the harmonic potential driven by the fractional Ornstein-Uhlenbeck noise is considered; the first two moments and mean energy are investigated.

Fractional finite Fourier transform.

PubMed

Khare, Kedar; George, Nicholas

2004-07-01

We show that a fractional version of the finite Fourier transform may be defined by using prolate spheroidal wave functions of order zero. The transform is linear and additive in its index and asymptotically goes over to Namias's definition of the fractional Fourier transform. As a special case of this definition, it is shown that the finite Fourier transform may be inverted by using information over a finite range of frequencies in Fourier space, the inversion being sensitive to noise. Numerical illustrations for both forward (fractional) and inverse finite transforms are provided.

Using Number Sense to Compare Fractions

ERIC Educational Resources Information Center

Bray, Wendy S.; Abreu-Sanchez, Laura

2010-01-01

One mathematical focus for third graders is to develop deep understanding of fractions and fraction equivalence, including comparing fractions through use of models and reasoning strategies. Before reading further, consider how you might solve the following problem: Which fraction is greater, 14/24 or 17/36? The initial impulse of many adults is…

12 CFR 5.67 - Fractional shares.

Code of Federal Regulations, 2010 CFR

2010-01-01

... fair price upon the fraction not being issued through its sale, or the purchase of the additional fraction required for a full share, if there is an established and active market in the national bank's stock; (c) Remit the cash equivalent of the fraction not being issued to those to whom fractional shares...

Time-fractional Cahn-Allen and time-fractional Klein-Gordon equations: Lie symmetry analysis, explicit solutions and convergence analysis

NASA Astrophysics Data System (ADS)

Inc, Mustafa; Yusuf, Abdullahi; Isa Aliyu, Aliyu; Baleanu, Dumitru

2018-03-01

This research analyzes the symmetry analysis, explicit solutions and convergence analysis to the time fractional Cahn-Allen (CA) and time-fractional Klein-Gordon (KG) equations with Riemann-Liouville (RL) derivative. The time fractional CA and time fractional KG are reduced to respective nonlinear ordinary differential equation of fractional order. We solve the reduced fractional ODEs using an explicit power series method. The convergence analysis for the obtained explicit solutions are investigated. Some figures for the obtained explicit solutions are also presented.

Correlation Structure of Fractional Pearson Diffusions.

PubMed

Leonenko, Nikolai N; Meerschaert, Mark M; Sikorskii, Alla

2013-09-01

The stochastic solution to a diffusion equations with polynomial coefficients is called a Pearson diffusion. If the first time derivative is replaced by a Caputo fractional derivative of order less than one, the stochastic solution is called a fractional Pearson diffusion. This paper develops an explicit formula for the covariance function of a fractional Pearson diffusion in steady state, in terms of Mittag-Leffler functions. That formula shows that fractional Pearson diffusions are long range dependent, with a correlation that falls off like a power law, whose exponent equals the order of the fractional derivative.

Pathways to fraction learning: Numerical abilities mediate the relation between early cognitive competencies and later fraction knowledge.

PubMed

Ye, Ai; Resnick, Ilyse; Hansen, Nicole; Rodrigues, Jessica; Rinne, Luke; Jordan, Nancy C

2016-12-01

The current study investigated the mediating role of number-related skills in the developmental relationship between early cognitive competencies and later fraction knowledge using structural equation modeling. Fifth-grade numerical skills (i.e., whole number line estimation, non-symbolic proportional reasoning, multiplication, and long division skills) mapped onto two distinct factors: magnitude reasoning and calculation. Controlling for participants' (N=536) demographic characteristics, these two factors fully mediated relationships between third-grade general cognitive competencies (attentive behavior, verbal and nonverbal intellectual abilities, and working memory) and sixth-grade fraction knowledge (concepts and procedures combined). However, specific developmental pathways differed by type of fraction knowledge. Magnitude reasoning ability fully mediated paths from all four cognitive competencies to knowledge of fraction concepts, whereas calculation ability fully mediated paths from attentive behavior and verbal ability to knowledge of fraction procedures (all with medium to large effect sizes). These findings suggest that there are partly overlapping, yet distinct, developmental pathways from cognitive competencies to general fraction knowledge, fraction concepts, and fraction procedures. Copyright © 2016 Elsevier Inc. All rights reserved.

Fractional Volterra hierarchy

NASA Astrophysics Data System (ADS)

Liu, Si-Qi; Zhang, Youjin; Zhou, Chunhui

2018-02-01

The generating function of cubic Hodge integrals satisfying the local Calabi-Yau condition is conjectured to be a tau function of a new integrable system which can be regarded as a fractional generalization of the Volterra lattice hierarchy, so we name it the fractional Volterra hierarchy. In this paper, we give the definition of this integrable hierarchy in terms of Lax pair and Hamiltonian formalisms, construct its tau functions, and present its multi-soliton solutions.

REFractions: The Representing Equivalent Fractions Game

ERIC Educational Resources Information Center

Tucker, Stephen I.

2014-01-01

Stephen Tucker presents a fractions game that addresses a range of fraction concepts including equivalence and computation. The REFractions game also improves students' fluency with representing, comparing and adding fractions.

Phenolic compounds containing/neutral fractions extract and products derived therefrom from fractionated fast-pyrolysis oils

DOEpatents

Chum, H.L.; Black, S.K.; Diebold, J.P.; Kreibich, R.E.

1993-06-29

A process is described for preparing phenol-formaldehyde novolak resins and molding compositions in which portions of the phenol normally contained in said resins are replaced by a phenol/neutral fractions extract obtained from fractionating fast-pyrolysis oils. The fractionation consists of a neutralization stage which can be carried out with aqueous solutions of bases or appropriate bases in the dry state, followed by solvent extraction with an organic solvent having at least a moderate solubility parameter and good hydrogen bonding capacity. Phenolic compounds-containing/neutral fractions extracts obtained by fractionating fast-pyrolysis oils from a lignocellulosic material, is such that the oil is initially in the pH range of 2-4, being neutralized with an aqueous bicarbonate base, and extracted into a solvent having a solubility parameter of approximately 8.4-9.11 [cal/cm[sup 3

A new fractional wavelet transform

NASA Astrophysics Data System (ADS)

Dai, Hongzhe; Zheng, Zhibao; Wang, Wei

2017-03-01

The fractional Fourier transform (FRFT) is a potent tool to analyze the time-varying signal. However, it fails in locating the fractional Fourier domain (FRFD)-frequency contents which is required in some applications. A novel fractional wavelet transform (FRWT) is proposed to solve this problem. It displays the time and FRFD-frequency information jointly in the time-FRFD-frequency plane. The definition, basic properties, inverse transform and reproducing kernel of the proposed FRWT are considered. It has been shown that an FRWT with proper order corresponds to the classical wavelet transform (WT). The multiresolution analysis (MRA) associated with the developed FRWT, together with the construction of the orthogonal fractional wavelets are also presented. Three applications are discussed: the analysis of signal with time-varying frequency content, the FRFD spectrum estimation of signals that involving noise, and the construction of fractional Harr wavelet. Simulations verify the validity of the proposed FRWT.

Proceedings of the International Symposium on Shock Tubes and Waves (13th), Niagara Falls, July 6-9, 1981.

DTIC Science & Technology

1981-07-01

266 The Blast-Noise Environment of Recoilless Rifles. AD-POOO 267 Shock-Excited hission Spectrum of Tungsten Oxide . AD-POO0 268 Rotational...Absorption Measurements of Atom Concentrations in Reacting Gas Mixtures. 9. Measurements of 0 Atoms in Oxidation of H2 and D2. AD-POOO 283 Direct Measurements...PuIverized Lignite in a Single-Pulse Shock-Tube. AD-POOO 306 Short Residence-Time Pyrolysis and Oxidative Pyrolysis of Bituminous Coals. AD-POOO 307 Shock

U. S. Naval Forces, Vietnam Monthly Historical Supplement for November 1967

DTIC Science & Technology

1968-03-23

Institute USA Special Warfare School (Attn: USN/MC Liaison Off.), Ft. Bragg, N. C. USMC Kap., U. S. krmy Infantry School, Ft. Banning, Ga . DIA...miles southeast of Can Tho, are attacked by heavy Viet Cong recoillesa-rifle, automatic-weapons and smll-arms fire. PBR 28 is hit by a recoilless...operations. On the 13th the WPB assigned to area IG, ap- proxloately 15 miles southeast of Danang, provided a blocking pa- trol for Operation BADGER

Discrete fractional solutions of a Legendre equation

NASA Astrophysics Data System (ADS)

Yılmazer, Resat

2018-01-01

One of the most popular research interests of science and engineering is the fractional calculus theory in recent times. Discrete fractional calculus has also an important position in fractional calculus. In this work, we acquire new discrete fractional solutions of the homogeneous and non homogeneous Legendre differential equation by using discrete fractional nabla operator.

Can Kindergartners Do Fractions?

ERIC Educational Resources Information Center

Cwikla, Julie

2014-01-01

Mathematics professor Julie Cwikla decided that she needed to investigate young children's understandings and see what precurricular partitioning notions young minds bring to the fraction table. Cwikla realized that only a handful of studies have examined how preschool-age and early elementary school-age students solve fraction problems (Empson…

Improving Children’s Knowledge of Fraction Magnitudes

PubMed Central

Fazio, Lisa K.; Kennedy, Casey A.; Siegler, Robert S.

2016-01-01

We examined whether playing a computerized fraction game, based on the integrated theory of numerical development and on the Common Core State Standards’ suggestions for teaching fractions, would improve children’s fraction magnitude understanding. Fourth and fifth-graders were given brief instruction about unit fractions and played Catch the Monster with Fractions, a game in which they estimated fraction locations on a number line and received feedback on the accuracy of their estimates. The intervention lasted less than 15 minutes. In our initial study, children showed large gains from pretest to posttest in their fraction number line estimates, magnitude comparisons, and recall accuracy. In a more rigorous second study, the experimental group showed similarly large improvements, whereas a control group showed no improvement from practicing fraction number line estimates without feedback. The results provide evidence for the effectiveness of interventions emphasizing fraction magnitudes and indicate how psychological theories and research can be used to evaluate specific recommendations of the Common Core State Standards. PMID:27768756

Fractionating power and outlet stream polydispersity in asymmetrical flow field-flow fractionation. Part I: isocratic operation.

PubMed

Williams, P Stephen

2016-05-01

Asymmetrical flow field-flow fractionation (As-FlFFF) has become the most commonly used of the field-flow fractionation techniques. However, because of the interdependence of the channel flow and the cross flow through the accumulation wall, it is the most difficult of the techniques to optimize, particularly for programmed cross flow operation. For the analysis of polydisperse samples, the optimization should ideally be guided by the predicted fractionating power. Many experimentalists, however, neglect fractionating power and rely on light scattering detection simply to confirm apparent selectivity across the breadth of the eluted peak. The size information returned by the light scattering software is assumed to dispense with any reliance on theory to predict retention, and any departure of theoretical predictions from experimental observations is therefore considered of no importance. Separation depends on efficiency as well as selectivity, however, and efficiency can be a strong function of retention. The fractionation of a polydisperse sample by field-flow fractionation never provides a perfectly separated series of monodisperse fractions at the channel outlet. The outlet stream has some residual polydispersity, and it will be shown in this manuscript that the residual polydispersity is inversely related to the fractionating power. Due to the strong dependence of light scattering intensity and its angular distribution on the size of the scattering species, the outlet polydispersity must be minimized if reliable size data are to be obtained from the light scattering detector signal. It is shown that light scattering detection should be used with careful control of fractionating power to obtain optimized analysis of polydisperse samples. Part I is concerned with isocratic operation of As-FlFFF, and part II with programmed operation.

LYSOSOMAL FRACTIONS FROM TRANSITIONAL EPITHELIUM

PubMed Central

Kanczak, Norbert M.; Krall, Joseph I.; Hayes, E. Russell; Elliott, Willard B.

1965-01-01

Histochemical data suggested that the so called lipoid granules of transitional epithelium in some species are equivalent to lysosomes. Scrapings of bovine and canine transitional epithelium were subjected to differential centrifugation to confirm this identification biochemically. Fractions of rat liver, the classic source of lysosomes, were also prepared by the same methods to compare with the fractions obtained from urinary epithelium. In contrast to rat liver, uroepithelial fractions with a high relative specific activity for hydrolases were sedimented before the heavy mitochondria. Microscopically, these fractions contained the highest proportion of lipoid granules. The size and sedimentation characteristics of lysosomes from transitional epithelium more closely resembled those of lysosomes derived from rat kidney than those isolated from liver. PMID:14326111

Fractions Learning in Children With Mathematics Difficulties.

PubMed

Tian, Jing; Siegler, Robert S

Learning fractions is difficult for children in general and especially difficult for children with mathematics difficulties (MD). Recent research on developmental and individual differences in fraction knowledge of children with MD and typically achieving (TA) children has demonstrated that U.S. children with MD start middle school behind their TA peers in fraction understanding and fall further behind during middle school. In contrast, Chinese children, who like the MD children in the United States score in the bottom one third of the distribution in their country, possess reasonably good fraction understanding. We interpret these findings within the framework of the integrated theory of numerical development. By emphasizing the importance of fraction magnitude knowledge for numerical understanding in general, the theory proved useful for understanding differences in fraction knowledge between MD and TA children and for understanding how knowledge can be improved. Several interventions demonstrated the possibility of improving fraction magnitude knowledge and producing benefits that generalize to fraction arithmetic learning among children with MD. The reasonably good fraction understanding of Chinese children with MD and several successful interventions with U.S. students provide hope for the improvement of fraction knowledge among American children with MD.

An Appetite for Fractions

ERIC Educational Resources Information Center

Wilkerson, Trena L.; Bryan, Tommy; Curry, Jane

2012-01-01

This article describes how using candy bars as models gives sixth-grade students a taste for learning to represent fractions whose denominators are factors of twelve. Using paper models of the candy bars, students explored and compared fractions. They noticed fewer different representations for one-third than for one-half. The authors conclude…

Fractional Bateman—Feshbach Tikochinsky Oscillator

NASA Astrophysics Data System (ADS)

Dumitru, Baleanu; Jihad, H. Asad; Ivo, Petras

2014-02-01

In the last few years the numerical methods for solving the fractional differential equations started to be applied intensively to real world phenomena. Having these things in mind in this manuscript we focus on the fractional Lagrangian and Hamiltonian of the complex Bateman—Feshbach Tikochinsky oscillator. The numerical analysis of the corresponding fractional Euler-Lagrange equations is given within the Grünwald—Letnikov approach, which is power series expansion of the generating function.

The Future of Fractions

ERIC Educational Resources Information Center

Usiskin, Zalman P.

2007-01-01

In the 1970s, the movement to the metric system (which has still not completely occurred in the United States) and the advent of hand-held calculators led some to speculate that decimal representation of numbers would render fractions obsolete. This provocative proposition stimulated Zalman Usiskin to write "The Future of Fractions" in 1979. He…

Fraction Sense: Foundational Understandings

ERIC Educational Resources Information Center

Fennell, Francis; Karp, Karen

2017-01-01

The intent of this commentary is to identify elements of fraction sense and note how the research studies provided in this special issue, in related but somewhat different ways, validate the importance of such understandings. Proficiency with fractions serves as a prerequisite for student success in higher level mathematics, as well as serving as…

Control of Initialized Fractional-Order Systems. Revised

NASA Technical Reports Server (NTRS)

Hartley, Tom T.; Lorenzo, Carl F.

2002-01-01

Due to the importance of historical effects in fractional-order systems, this paper presents a general fractional-order control theory that includes the time-varying initialization response. Previous studies have not properly accounted for these historical effects. The initialization response, along with the forced response, for fractional-order systems is determined. Stability properties of fractional-order systems are presented in the complex w-plane, which is a transformation of the s-plane. Time responses are discussed with respect to pole positions in the complex w-plane and frequency response behavior is included. A fractional-order vector space representation, which is a generalization of the state space concept, is presented including the initialization response. Control methods for vector representations of initialized fractional-order systems are shown. Nyquist, root-locus, and other input-output control methods are adapted to the control of fractional-order systems. Finally, the fractional-order differintegral is generalized to continuous order-distributions that have the possibility of including a continuum of fractional orders in a system element.

Developmental Foundations of Children's Fraction Magnitude Knowledge.

PubMed

Mou, Yi; Li, Yaoran; Hoard, Mary K; Nugent, Lara D; Chu, Felicia W; Rouder, Jeffrey N; Geary, David C

2016-01-01

The conceptual insight that fractions represent magnitudes is a critical yet daunting step in children's mathematical development, and the knowledge of fraction magnitudes influences children's later mathematics learning including algebra. In this study, longitudinal data were analyzed to identify the mathematical knowledge and domain-general competencies that predicted 8 th and 9 th graders' (n=122) knowledge of fraction magnitudes and its cross-grade gains. Performance on the fraction magnitude measures predicted 9 th grade algebra achievement. Understanding and fluently identifying the numerator-denominator relation in 7 th grade emerged as the key predictor of later fraction magnitudes knowledge in both 8 th and 9 th grades. Competence at using fraction procedures, knowledge of whole number magnitudes, and the central executive contributed to 9 th but not 8 th graders' fraction magnitude knowledge, and knowledge of whole number magnitude contributed to cross-grade gains. The key results suggest fluent processing of numerator-denominator relations presages students' understanding of fractions as magnitudes and that the integration of whole number and fraction magnitudes occurs gradually.

Momentum fractionation on superstrata

DOE PAGES

Bena, Iosif; Martinec, Emil; Turton, David; ...

2016-05-11

Superstrata are bound states in string theory that carry D1, D5, and momentum charges, and whose supergravity descriptions are parameterized by arbitrary functions of (at least) two variables. In the D1-D5 CFT, typical three-charge states reside in highdegree twisted sectors, and their momentum charge is carried by modes that individually have fractional momentum. Understanding this momentum fractionation holographically is crucial for understanding typical black-hole microstates in this system. We use solution-generating techniques to add momentum to a multi-wound supertube and thereby construct the first examples of asymptotically-flat superstrata. The resulting supergravity solutions are horizonless and smooth up to well-understood orbifoldmore » singularities. Upon taking the AdS3 decoupling limit, our solutions are dual to CFT states with momentum fractionation. We give a precise proposal for these dual CFT states. Lastly, our construction establishes the very nontrivial fact that large classes of CFT states with momentum fractionation can be realized in the bulk as smooth horizonless supergravity solutions.« less

Comment on "Fractional quantum mechanics" and "Fractional Schrödinger equation"

NASA Astrophysics Data System (ADS)

Wei, Yuchuan

2016-06-01

In this Comment we point out some shortcomings in two papers [N. Laskin, Phys. Rev. E 62, 3135 (2000), 10.1103/PhysRevE.62.3135; N. Laskin, Phys. Rev. E 66, 056108 (2002), 10.1103/PhysRevE.66.056108]. We prove that the fractional uncertainty relation does not hold generally. The probability continuity equation in fractional quantum mechanics has a missing source term, which leads to particle teleportation, i.e., a particle can teleport from a place to another. Since the relativistic kinetic energy can be viewed as an approximate realization of the fractional kinetic energy, the particle teleportation should be an observable relativistic effect in quantum mechanics. With the help of this concept, superconductivity could be viewed as the teleportation of electrons from one side of a superconductor to another and superfluidity could be viewed as the teleportation of helium atoms from one end of a capillary tube to the other. We also point out how to teleport a particle to an arbitrary destination.

Comment on "Fractional quantum mechanics" and "Fractional Schrödinger equation".

PubMed

Wei, Yuchuan

2016-06-01

In this Comment we point out some shortcomings in two papers [N. Laskin, Phys. Rev. E 62, 3135 (2000)10.1103/PhysRevE.62.3135; N. Laskin, Phys. Rev. E 66, 056108 (2002)10.1103/PhysRevE.66.056108]. We prove that the fractional uncertainty relation does not hold generally. The probability continuity equation in fractional quantum mechanics has a missing source term, which leads to particle teleportation, i.e., a particle can teleport from a place to another. Since the relativistic kinetic energy can be viewed as an approximate realization of the fractional kinetic energy, the particle teleportation should be an observable relativistic effect in quantum mechanics. With the help of this concept, superconductivity could be viewed as the teleportation of electrons from one side of a superconductor to another and superfluidity could be viewed as the teleportation of helium atoms from one end of a capillary tube to the other. We also point out how to teleport a particle to an arbitrary destination.

Limited Intervention at Sub Concept of Fractions in the Object Conversion into Fractions

ERIC Educational Resources Information Center

Kurniawan, Henry; Nusantara, Toto; Subanji; Susiswo; Setiawan, Iwan; Sutawidjaja, Akbar; As'ari, Abdur Rahman; Muksar, Makbul

2016-01-01

This research is an exploratory study with a qualitative approach, which is based on interviews with a task-based the purpose of this study is to describe the understanding of elementary school students in interpreting sub concept fractions in changing of the object is given to fractions with limit intervention. While intervention on problems…

Teaching Fractions. Educational Practices Series-22

ERIC Educational Resources Information Center

Fazio, Lisa; Siegler, Robert

2011-01-01

Students around the world have difficulties in learning about fractions. In many countries, the average student never gains a conceptual knowledge of fractions. This research guide provides suggestions for teachers and administrators looking to improve fraction instruction in their classrooms or schools. The recommendations are based on a…

36 CFR 254.34 - Mineral survey fractions.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 36 Parks, Forests, and Public Property 2 2010-07-01 2010-07-01 false Mineral survey fractions. 254... LANDOWNERSHIP ADJUSTMENTS Conveyance of Small Tracts § 254.34 Mineral survey fractions. (a) Mineral survey... survey fractions under this subpart: (1) The mineral survey fractions are interspersed among and are more...

36 CFR 254.34 - Mineral survey fractions.

Code of Federal Regulations, 2012 CFR

2012-07-01

... 36 Parks, Forests, and Public Property 2 2012-07-01 2012-07-01 false Mineral survey fractions. 254... LANDOWNERSHIP ADJUSTMENTS Conveyance of Small Tracts § 254.34 Mineral survey fractions. (a) Mineral survey... survey fractions under this subpart: (1) The mineral survey fractions are interspersed among and are more...

36 CFR 254.34 - Mineral survey fractions.

Code of Federal Regulations, 2014 CFR

2014-07-01

... 36 Parks, Forests, and Public Property 2 2014-07-01 2014-07-01 false Mineral survey fractions. 254... LANDOWNERSHIP ADJUSTMENTS Conveyance of Small Tracts § 254.34 Mineral survey fractions. (a) Mineral survey... survey fractions under this subpart: (1) The mineral survey fractions are interspersed among and are more...

36 CFR 254.34 - Mineral survey fractions.

Code of Federal Regulations, 2011 CFR

2011-07-01

... 36 Parks, Forests, and Public Property 2 2011-07-01 2011-07-01 false Mineral survey fractions. 254... LANDOWNERSHIP ADJUSTMENTS Conveyance of Small Tracts § 254.34 Mineral survey fractions. (a) Mineral survey... survey fractions under this subpart: (1) The mineral survey fractions are interspersed among and are more...

Analytical method for dissolved-organic carbon fractionation

USGS Publications Warehouse

Leenheer, Jerry A.; Huffman, Edward W. D.

1979-01-01

A standard procedure for analytical-scale dissolved organic carbon fractionation is presented, whereby dissolved organic carbon in water is first fractionated by a nonionic macroreticular resin into acid, base, and neutral hydrophobic organic solute fractions, and next fractionated by ion-exchange resins into acid, base, and neutral hydrophilic solute fractions. The hydrophobic solutes are defined as those sorbed on a nonionic, acrylic-ester macroreticular resin and are differentiated into acid, base, and nautral fractions by sorption/desorption controlled by pH adjustment. The hydrophilic bases are next sorbed on strong-acid ion-exchange resin, followed by sorption of hydrophilic acids on a strong-base ion-exchange resin. Hydrophilic neutrals are not sorbed and remain dissolved in the deionized water at the end of the fractionation procedure. The complete fractionation can be performed on a 200-milliliter filtered water sample, whose dissolved organic carbon content is 5-25 mg/L and whose specific conductance is less than 2,000 μmhos/cm at 25°C. The applications of dissolved organic carbon fractionation analysis range from field studies of changes of organic solute composition with synthetic fossil fuel production, to fundamental studies of the nature of sorption processes.

Identifying Fractions on a Number Line

ERIC Educational Resources Information Center

Wong, Monica

2013-01-01

Fractions are generally introduced to students using the part--whole model. Yet the number line is another important representation which can be used to build fraction concepts (Australian Curriculum Assessment and Reporting Authority [ACARA], 2012). Number lines are recognised as key in students' number development not only of fractions, but…

Fractionation of Pb and Cu in the fine fraction (<10 mm) of waste excavated from a municipal landfill.

PubMed

Kaczala, Fabio; Orupõld, Kaja; Augustsson, Anna; Burlakovs, Juris; Hogland, Marika; Bhatnagar, Amit; Hogland, William

2017-11-01

The fractionation of metals in the fine fraction (<10 mm) of excavated waste from an Estonian landfill was carried out to evaluate the metal (Pb and Cu) contents and their potential towards not only mobility but also possibilities of recovery/extraction. The fractionation followed the BCR (Community Bureau of Reference) sequential extraction, and the exchangeable (F1), reducible (F2), oxidizable (F3) and residual fractions were determined. The results showed that Pb was highly associated with the reducible (F2) and oxidizable (F3) fractions, suggesting the potential mobility of this metal mainly when in contact with oxygen, despite the low association with the exchangeable fraction (F1). Cu has also shown the potential for mobility when in contact with oxygen, since high associations with the oxidizable fraction (F3) were observed. On the other hand, the mobility of metals in excavated waste can be seen as beneficial considering the circular economy and recovery of such valuables back into the economy. To conclude, not only the total concentration of metals but also a better understanding of fractionation and in which form metals are bound is very important to bring information on how to manage the fine fraction from excavated waste both in terms of environmental impacts and also recovery of such valuables in the economy.

STOCHASTIC INTEGRATION FOR TEMPERED FRACTIONAL BROWNIAN MOTION.

PubMed

Meerschaert, Mark M; Sabzikar, Farzad

2014-07-01

Tempered fractional Brownian motion is obtained when the power law kernel in the moving average representation of a fractional Brownian motion is multiplied by an exponential tempering factor. This paper develops the theory of stochastic integrals for tempered fractional Brownian motion. Along the way, we develop some basic results on tempered fractional calculus.

Symmetry classification of time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Naeem, I.; Khan, M. D.

2017-01-01

In this article, a new approach is proposed to construct the symmetry groups for a class of fractional differential equations which are expressed in the modified Riemann-Liouville fractional derivative. We perform a complete group classification of a nonlinear fractional diffusion equation which arises in fractals, acoustics, control theory, signal processing and many other applications. Introducing the suitable transformations, the fractional derivatives are converted to integer order derivatives and in consequence the nonlinear fractional diffusion equation transforms to a partial differential equation (PDE). Then the Lie symmetries are computed for resulting PDE and using inverse transformations, we derive the symmetries for fractional diffusion equation. All cases are discussed in detail and results for symmetry properties are compared for different values of α. This study provides a new way of computing symmetries for a class of fractional differential equations.

Fractional charge revealed in computer simulations of resonant tunneling in the fractional quantum Hall regime.

PubMed

Tsiper, E V

2006-08-18

The concept of fractional charge is central to the theory of the fractional quantum Hall effect. Here I use exact diagonalization as well as configuration space renormalization to study finite clusters which are large enough to contain two independent edges. I analyze the conditions of resonant tunneling between the two edges. The "computer experiment" reveals a periodic sequence of resonant tunneling events consistent with the experimentally observed fractional quantization of electric charge in units of e/3 and e/5.

Fractional Brownian motion and motion governed by the fractional Langevin equation in confined geometries.

PubMed

Jeon, Jae-Hyung; Metzler, Ralf

2010-02-01

Motivated by subdiffusive motion of biomolecules observed in living cells, we study the stochastic properties of a non-Brownian particle whose motion is governed by either fractional Brownian motion or the fractional Langevin equation and restricted to a finite domain. We investigate by analytic calculations and simulations how time-averaged observables (e.g., the time-averaged mean-squared displacement and displacement correlation) are affected by spatial confinement and dimensionality. In particular, we study the degree of weak ergodicity breaking and scatter between different single trajectories for this confined motion in the subdiffusive domain. The general trend is that deviations from ergodicity are decreased with decreasing size of the movement volume and with increasing dimensionality. We define the displacement correlation function and find that this quantity shows distinct features for fractional Brownian motion, fractional Langevin equation, and continuous time subdiffusion, such that it appears an efficient measure to distinguish these different processes based on single-particle trajectory data.

Locating Fractions on a Number Line

ERIC Educational Resources Information Center

Wong, Monica

2013-01-01

Understanding fractions remains problematic for many students. The use of the number line aids in this understanding, but requires students to recognise that a fraction represents the distance from zero to a dot or arrow marked on a number line which is a linear scale. This article continues the discussion from "Identifying Fractions on a…

Fostering Remainder Understanding in Fraction Division

ERIC Educational Resources Information Center

Zembat, Ismail O.

2017-01-01

Most students can follow this simple procedure for division of fractions: "Ours is not to reason why, just invert and multiply." But how many really understand what division of fractions means--especially fraction division with respect to the meaning of the remainder. The purpose of this article is to provide an instructional method as a…

Bio-oil fractionation and condensation

DOEpatents

Brown, Robert C; Jones, Samuel T; Pollard, Anthony

2013-07-02

A method of fractionating bio-oil vapors which involves providing bio-oil vapors comprising bio-oil constituents is described. The bio-oil vapors are cooled in a first stage which comprises a condenser having passages for the bio-oil separated by a heat conducting wall from passages for a coolant. The coolant in the condenser of the first stage is maintained at a substantially constant temperature, set at a temperature in the range of 75 to 100.degree. C., to condense a first liquid fraction of liquefied bio-oil constituents in the condenser of the first stage. The first liquid fraction of liquified bio-oil constituents from the condenser in the first stage is collected. Also described are steps for subsequently recovering further liquid fractions of liquefied bio-oil constituents. Particular compositions of bio-oil condensation products are also described.

Making Sense of Instruction on Fractions when a Student Lacks Necessary Fractional Schemes: The Case of Tim

ERIC Educational Resources Information Center

Olive, John; Vomvoridi, Eugenia

2006-01-01

This paper critically examines the discrepancies among the pre-requisite fractional concepts assumed by a curricular unit on operations with fractions, the teacher's assumptions about those concepts and a particular student's understanding of fractions. The paper focuses on the case of one student (Tim) in the teacher's 6th grade class who was…

Fractional calculus in bioengineering, part 3.

PubMed

Magin, Richard L

2004-01-01

Fractional calculus (integral and differential operations of noninteger order) is not often used to model biological systems. Although the basic mathematical ideas were developed long ago by the mathematicians Leibniz (1695), Liouville (1834), Riemann (1892), and others and brought to the attention of the engineering world by Oliver Heaviside in the 1890s, it was not until 1974 that the first book on the topic was published by Oldham and Spanier. Recent monographs and symposia proceedings have highlighted the application of fractional calculus in physics, continuum mechanics, signal processing, and electromagnetics, but with few examples of applications in bioengineering. This is surprising because the methods of fractional calculus, when defined as a Laplace or Fourier convolution product, are suitable for solving many problems in biomedical research. For example, early studies by Cole (1933) and Hodgkin (1946) of the electrical properties of nerve cell membranes and the propagation of electrical signals are well characterized by differential equations of fractional order. The solution involves a generalization of the exponential function to the Mittag-Leffler function, which provides a better fit to the observed cell membrane data. A parallel application of fractional derivatives to viscoelastic materials establishes, in a natural way, hereditary integrals and the power law (Nutting/Scott Blair) stress-strain relationship for modeling biomaterials. In this review, I will introduce the idea of fractional operations by following the original approach of Heaviside, demonstrate the basic operations of fractional calculus on well-behaved functions (step, ramp, pulse, sinusoid) of engineering interest, and give specific examples from electrochemistry, physics, bioengineering, and biophysics. The fractional derivative accurately describes natural phenomena that occur in such common engineering problems as heat transfer, electrode/electrolyte behavior, and sub

Generalized Fractional Derivative Anisotropic Viscoelastic Characterization.

PubMed

Hilton, Harry H

2012-01-18

Isotropic linear and nonlinear fractional derivative constitutive relations are formulated and examined in terms of many parameter generalized Kelvin models and are analytically extended to cover general anisotropic homogeneous or non-homogeneous as well as functionally graded viscoelastic material behavior. Equivalent integral constitutive relations, which are computationally more powerful, are derived from fractional differential ones and the associated anisotropic temperature-moisture-degree-of-cure shift functions and reduced times are established. Approximate Fourier transform inversions for fractional derivative relations are formulated and their accuracy is evaluated. The efficacy of integer and fractional derivative constitutive relations is compared and the preferential use of either characterization in analyzing isotropic and anisotropic real materials must be examined on a case-by-case basis. Approximate protocols for curve fitting analytical fractional derivative results to experimental data are formulated and evaluated.

Derivative with two fractional orders: A new avenue of investigation toward revolution in fractional calculus

NASA Astrophysics Data System (ADS)

Atangana, Abdon

2016-10-01

In order to describe more complex problems using the concept of fractional derivatives, we introduce in this paper the concept of fractional derivatives with orders. The new definitions are based upon the concept of power law together with the generalized Mittag-Leffler function. The first order is included in the power law function and the second one is in the generalized Mittag-Leffler function. Each order therefore plays an important role while modeling, for instance, problems with two layers with different properties. This is the case, for instance, in thermal science for a reaction diffusion within a media with two different layers with different properties. Another case is that of groundwater flowing within an aquifer where geological formation is formed with two layers with different properties. The paper presents new fractional operators that will open new doors for research and investigations in modeling real world problems. Some useful properties of the new operators are presented, in particular their relationship with existing integral transforms, namely the Laplace, Sumudu, Mellin and Fourier transforms. The numerical approximation of the new fractional operators are presented. We apply the new fractional operators on the model of groundwater plume with degradation and limited sorption and solve the new model numerically with some numerical simulations. The numerical simulation leaves no doubt in believing that the new fractional operators are powerfull mathematical tools able to portray complexes real world problems.

Measuring local volume fraction, long-wavelength correlations, and fractionation in a phase-separating polydisperse fluid

DOE Office of Scientific and Technical Information (OSTI.GOV)

Williamson, J. J., E-mail: johnjosephwilliamson@gmail.com; Evans, R. M. L.

We dynamically simulate fractionation (partitioning of particle species) during spinodal gas-liquid separation of a size-polydisperse colloid, using polydispersity up to ∼40% and a skewed parent size distribution. We introduce a novel coarse-grained Voronoi method to minimise size bias in measuring local volume fraction, along with a variety of spatial correlation functions which detect fractionation without requiring a clear distinction between the phases. These can be applied whether or not a system is phase separated, to determine structural correlations in particle size, and generalise easily to other kinds of polydispersity (charge, shape, etc.). We measure fractionation in both mean size andmore » polydispersity between the phases, its direction differing between model interaction potentials which are identical in the monodisperse case. These qualitative features are predicted by a perturbative theory requiring only a monodisperse reference as input. The results show that intricate fractionation takes place almost from the start of phase separation, so can play a role even in nonequilibrium arrested states. The methods for characterisation of inhomogeneous polydisperse systems could in principle be applied to experiment as well as modelling.« less

Pre-K-8 Prospective Teachers' Understanding of Fractions: An Extension of Fractions Schemes and Operations Research

ERIC Educational Resources Information Center

Lovin, LouAnn H.; Stevens, Alexis L.; Siegfried, John; Wilkins, Jesse L. M.; Norton, Anderson

2018-01-01

In an effort to expand our knowledge base pertaining to pre-K-8 prospective teachers' understanding of fractions, the present study was designed to extend the work on fractions schemes and operations to this population. One purpose of our study was to validate the fractions schemes and operations hierarchy with the pre-K-8 prospective teacher…

Small (13)C/(12)C fractionation contrasts with large enantiomer fractionation in aerobic biodegradation of phenoxy acids.

PubMed

Qiu, Shiran; Gözdereliler, Erkin; Weyrauch, Philip; Lopez, Eva C Magana; Kohler, Hans-Peter E; Sørensen, Sebastian R; Meckenstock, Rainer U; Elsner, Martin

2014-05-20

Phenoxy acid herbicides are important groundwater contaminants. Stable isotope analysis and enantiomer analysis are well-recognized approaches for assessing in situ biodegradation in the field. In an aerobic degradation survey with six phenoxyacetic acid and three phenoxypropionic acid-degrading bacteria we measured (a) enantiomer-specific carbon isotope fractionation of MCPP ((R,S)-2-(4-chloro-2-methylphenoxy)-propionic acid), DCPP ((R,S)-2-(2,4-dichlorophenoxy)-propionic acid), and 4-CPP ((R,S)-2-(4-chlorophenoxy)-propionic acid); (b) compound-specific isotope fractionation of MCPA (4-chloro-2-methylphenoxyacetic acid) and 2,4-D (2,4-dichlorophenoxyacetic acid); and (c) enantiomer fractionation of MCPP, DCPP, and 4-CPP. Insignificant or very slight (ε = -1.3‰ to -2.0‰) carbon isotope fractionation was observed. Equally small values in an RdpA enzyme assay (εea = -1.0 ± 0.1‰) and even smaller fractionation in whole cell experiments of the host organism Sphingobium herbicidovorans MH (εwc = -0.3 ± 0.1‰) suggest that (i) enzyme-associated isotope effects were already small, yet (ii) further masked by active transport through the cell membrane. In contrast, enantiomer fractionation in MCPP, DCPP, and 4-CPP was pronounced, with enantioselectivities (ES) of -0.65 to -0.98 with Sphingomonas sp. PM2, -0.63 to -0.89 with Sphingobium herbicidovorans MH, and 0.74 to 0.97 with Delftia acidovorans MC1. To detect aerobic biodegradation of phenoxypropionic acids in the field, enantiomer fractionation seems, therefore, a stronger indicator than carbon isotope fractionation.

Rational Exponentials and Continued Fractions

ERIC Educational Resources Information Center

Denny, J. K.

2012-01-01

Using continued fraction expansions, we can approximate constants, such as pi and e, using an appropriate integer n raised to the power x[superscript 1/x], x a suitable rational. We review continued fractions and give an algorithm for producing these approximations.

Bio-oil fractionation and condensation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brown, Robert C.; Jones, Samuel T.; Pollard, Anthony

The present invention relates to a method of fractionating bio-oil vapors which involves providing bio-oil vapors comprising bio-oil constituents. The bio-oil vapors are cooled in a first stage which comprises a condenser having passages for the bio-oil separated by a heat conducting wall from passages for a coolant. The coolant in the condenser of the first stage is maintained at a substantially constant temperature, set at a temperature in the range of 75 to 100.degree. C., to condense a first liquid fraction of liquefied bio-oil constituents in the condenser of the first stage. The first liquid fraction of liquified bio-oilmore » constituents from the condenser in the first stage is collected. Also disclosed are steps for subsequently recovering further liquid fractions of liquefied bio-oil constituents. Particular compositions of bio-oil condensation products are also described.« less

Fractional, biodegradable and spectral characteristics of extracted and fractionated sludge extracellular polymeric substances.

PubMed

Wei, Liang-Liang; Wang, Kun; Zhao, Qing-Liang; Jiang, Jun-Qiu; Kong, Xiang-Juan; Lee, Duu-Jong

2012-09-15

Correlation between fractional, biodegradable and spectral characteristics of sludge extracellular polymeric substances (EPS) by different protocols has not been well established. This work extracted sludge EPS using alkaline extractants (NH₄OH and formaldehyde + NaOH) and physical protocols (ultrasonication, heating at 80 °C or cation exchange resin (CER)) and then fractionated the extracts using XAD-8/XAD-4 resins. The alkaline extractants yielded more sludge EPS than the physical protocols. However, the physical protocols extracted principally the hydrophilic components which were readily biodegradable by microorganisms. The alkaline extractants dissolved additional humic-like substances from sludge solids which were refractory in nature. Different extraction protocols preferably extracted EPS with distinct fractional, biodegradable and spectral characteristics which could be applied in specific usages. Copyright © 2012 Elsevier Ltd. All rights reserved.

Water dynamics in different biochar fractions.

PubMed

Conte, Pellegrino; Nestle, Nikolaus

2015-09-01

Biochar is a carbonaceous porous material deliberately applied to soil to improve its fertility. The mechanisms through which biochar acts on fertility are still poorly understood. The effect of biochar texture size on water dynamics was investigated here in order to provide information to address future research on nutrient mobility towards plant roots as biochar is applied as soil amendment. A poplar biochar has been stainless steel fractionated in three different textured fractions (1.0-2.0 mm, 0.3-1.0 mm and <0.3 mm, respectively). Water-saturated fractions were analyzed by fast field cycling (FFC) NMR relaxometry. Results proved that 3D exchange between bound and bulk water predominantly occurred in the coarsest fraction. However, as porosity decreased, water motion was mainly associated to a restricted 2D diffusion among the surface-site pores and the bulk-site ones. The X-ray μ-CT imaging analyses on the dry fractions revealed the lowest surface/volume ratio for the coarsest fraction, thereby corroborating the 3D water exchange mechanism hypothesized by FFC NMR relaxometry. However, multi-micrometer porosity was evidenced in all the samples. The latter finding suggested that the 3D exchange mechanism cannot even be neglected in the finest fraction as previously excluded only on the basis of NMR relaxometry results. X-ray μ-CT imaging showed heterogeneous distribution of inorganic materials inside all the fractions. The mineral components may contribute to the water relaxation mechanisms by FFC NMR relaxometry. Further studies are needed to understand the role of the inorganic particles on water dynamics. Copyright © 2015 John Wiley & Sons, Ltd.

Generalized continued fractions and ergodic theory

NASA Astrophysics Data System (ADS)

Pustyl'nikov, L. D.

2003-02-01

In this paper a new theory of generalized continued fractions is constructed and applied to numbers, multidimensional vectors belonging to a real space, and infinite-dimensional vectors with integral coordinates. The theory is based on a concept generalizing the procedure for constructing the classical continued fractions and substantially using ergodic theory. One of the versions of the theory is related to differential equations. In the finite-dimensional case the constructions thus introduced are used to solve problems posed by Weyl in analysis and number theory concerning estimates of trigonometric sums and of the remainder in the distribution law for the fractional parts of the values of a polynomial, and also the problem of characterizing algebraic and transcendental numbers with the use of generalized continued fractions. Infinite-dimensional generalized continued fractions are applied to estimate sums of Legendre symbols and to obtain new results in the classical problem of the distribution of quadratic residues and non-residues modulo a prime. In the course of constructing these continued fractions, an investigation is carried out of the ergodic properties of a class of infinite-dimensional dynamical systems which are also of independent interest.

Generalized hydrodynamic correlations and fractional memory functions

NASA Astrophysics Data System (ADS)

Rodríguez, Rosalio F.; Fujioka, Jorge

2015-12-01

A fractional generalized hydrodynamic (GH) model of the longitudinal velocity fluctuations correlation, and its associated memory function, for a complex fluid is analyzed. The adiabatic elimination of fast variables introduces memory effects in the transport equations, and the dynamic of the fluctuations is described by a generalized Langevin equation with long-range noise correlations. These features motivate the introduction of Caputo time fractional derivatives and allows us to calculate analytic expressions for the fractional longitudinal velocity correlation function and its associated memory function. Our analysis eliminates a spurious constant term in the non-fractional memory function found in the non-fractional description. It also produces a significantly slower power-law decay of the memory function in the GH regime that reduces to the well-known exponential decay in the non-fractional Navier-Stokes limit.

Unwrapping Students' Ideas about Fractions

ERIC Educational Resources Information Center

Lewis, Rebecca M.; Gibbons, Lynsey K.; Kazemi, Elham; Lind, Teresa

2015-01-01

Supporting students to develop an understanding of the meaning of fractions is an important goal of elementary school mathematics. This involves developing partitioning strategies, creating representations, naming fractional quantities, and using symbolic notation. This article describes how teachers can use a formative assessment problem to…

Fractional Klein-Gordon equation composed of Jumarie fractional derivative and its interpretation by a smoothness parameter

NASA Astrophysics Data System (ADS)

Ghosh, Uttam; Banerjee, Joydip; Sarkar, Susmita; Das, Shantanu

2018-06-01

Klein-Gordon equation is one of the basic steps towards relativistic quantum mechanics. In this paper, we have formulated fractional Klein-Gordon equation via Jumarie fractional derivative and found two types of solutions. Zero-mass solution satisfies photon criteria and non-zero mass satisfies general theory of relativity. Further, we have developed rest mass condition which leads us to the concept of hidden wave. Classical Klein-Gordon equation fails to explain a chargeless system as well as a single-particle system. Using the fractional Klein-Gordon equation, we can overcome the problem. The fractional Klein-Gordon equation also leads to the smoothness parameter which is the measurement of the bumpiness of space. Here, by using this smoothness parameter, we have defined and interpreted the various cases.

Approximate Solution of Time-Fractional Advection-Dispersion Equation via Fractional Variational Iteration Method

PubMed Central

İbiş, Birol

2014-01-01

This paper aims to obtain the approximate solution of time-fractional advection-dispersion equation (FADE) involving Jumarie's modification of Riemann-Liouville derivative by the fractional variational iteration method (FVIM). FVIM provides an analytical approximate solution in the form of a convergent series. Some examples are given and the results indicate that the FVIM is of high accuracy, more efficient, and more convenient for solving time FADEs. PMID:24578662

Studies on proinsulin and proglucagon biosynthesis and conversion at the subcellular level: I. Fractionation procedure and characterization of the subcellular fractions

PubMed Central

Noe, BD; Baste, CA; Bauer, GE

1977-01-01

Anglerfish islets were homogenized in 0.25 M sucrose and separated into seven separate subcellular fractions by differential and discontinuous density gradient centrifugation. The objective was to isolate microsomes and secretory granules in a highly purified state. The fractions were characterized by electron microscopy and chemical analyses. Each fraction was assayed for its content of protein, RNA, DNA, immunoreactive insulin (IRI), and immunoreactive glucagon (IRG). Ultrastructural examination showed that two of the seven subcellular fractions contain primarily mitochondria, and that two others consist almost exclusively of secretory granules. A fifth fraction contains rough and smooth microsomal vesicles. The remaining two fractions are the cell supernate and the nuclei and cell debris. The content of DNA and RNA in all fractions is consistent with the observed ultrastructure. More than 82 percent of the total cellular IRI and 89(percent) of the total cellular IRG are found in the fractions of secretory granules. The combined fractions of secretory granules and microsomes consistently yield >93 percent of the total IRG. These results indicate that the fractionation procedure employed yields fractions of microsomes and secretory granules that contain nearly all the immunoassayable insulin and glucagons found in whole islet tissue. These fractions are thus considered suitable for study of proinsulin and proglucagon biosynthesis and their metabolic conversion at the subcellular level. PMID:328517

A review and evaluation of numerical tools for fractional calculus and fractional order controls

NASA Astrophysics Data System (ADS)

Li, Zhuo; Liu, Lu; Dehghan, Sina; Chen, YangQuan; Xue, Dingyü

2017-06-01

In recent years, as fractional calculus becomes more and more broadly used in research across different academic disciplines, there are increasing demands for the numerical tools for the computation of fractional integration/differentiation, and the simulation of fractional order systems. Time to time, being asked about which tool is suitable for a specific application, the authors decide to carry out this survey to present recapitulative information of the available tools in the literature, in hope of benefiting researchers with different academic backgrounds. With this motivation, the present article collects the scattered tools into a dashboard view, briefly introduces their usage and algorithms, evaluates the accuracy, compares the performance, and provides informative comments for selection.

Understanding Magnitudes to Understand Fractions

ERIC Educational Resources Information Center

Gabriel, Florence

2016-01-01

Fractions are known to be difficult to learn and difficult to teach, yet they are vital for students to have access to further mathematical concepts. This article uses evidence to support teachers employing teaching methods that focus on the conceptual understanding of the magnitude of fractions.

Lattices for fractional Chern insulators

NASA Astrophysics Data System (ADS)

Repellin, Cécile; Regnault, Nicolas

2018-04-01

Individual electrons are elementary particles, but in some solid-state systems, electrons can act collectively as though they had a fraction of an electron's charge. This emergent behavior is spectacularly observed in two-dimensional (2D) electron gases as the fractional quantum Hall (FQH) effect in the form of a fractional quantized transverse (or Hall) conductivity and in shot-noise experiments. These experiments require low temperatures and very large magnetic fields in order to create strong electron interactions. This latter condition now appears not to be as essential as originally thought. On page 62 of this issue, Spanton et al. (1) report on an experimental platform based on bilayer graphene that forms a moiré pattern with an encapsulating hexagonal boron nitride layer. They observed incompressible phases with a fractional filling of the band structure with a nonzero Chern number (it has quantized properties robust to local perturbations, or topologically invariant). Some of which have no analog in traditional FQH systems (see the figure).

Mass fractionation processes of transition metal isotopes

NASA Astrophysics Data System (ADS)

Zhu, X. K.; Guo, Y.; Williams, R. J. P.; O'Nions, R. K.; Matthews, A.; Belshaw, N. S.; Canters, G. W.; de Waal, E. C.; Weser, U.; Burgess, B. K.; Salvato, B.

2002-06-01

Recent advances in mass spectrometry make it possible to utilise isotope variations of transition metals to address some important issues in solar system and biological sciences. Realisation of the potential offered by these new isotope systems however requires an adequate understanding of the factors controlling their isotope fractionation. Here we show the results of a broadly based study on copper and iron isotope fractionation during various inorganic and biological processes. These results demonstrate that: (1) naturally occurring inorganic processes can fractionate Fe isotope to a detectable level even at temperature ˜1000°C, which challenges the previous view that Fe isotope variations in natural system are unique biosignatures; (2) multiple-step equilibrium processes at low temperatures may cause large mass fractionation of transition metal isotopes even when the fractionation per single step is small; (3) oxidation-reduction is an importation controlling factor of isotope fractionation of transition metal elements with multiple valences, which opens a wide range of applications of these new isotope systems, ranging from metal-silicate fractionation in the solar system to uptake pathways of these elements in biological systems; (4) organisms incorporate lighter isotopes of transition metals preferentially, and transition metal isotope fractionation occurs stepwise along their pathways within biological systems during their uptake.

A chaotic secure communication scheme using fractional chaotic systems based on an extended fractional Kalman filter

NASA Astrophysics Data System (ADS)

Kiani-B, Arman; Fallahi, Kia; Pariz, Naser; Leung, Henry

2009-03-01

In recent years chaotic secure communication and chaos synchronization have received ever increasing attention. In this paper, for the first time, a fractional chaotic communication method using an extended fractional Kalman filter is presented. The chaotic synchronization is implemented by the EFKF design in the presence of channel additive noise and processing noise. Encoding chaotic communication achieves a satisfactory, typical secure communication scheme. In the proposed system, security is enhanced based on spreading the signal in frequency and encrypting it in time domain. In this paper, the main advantages of using fractional order systems, increasing nonlinearity and spreading the power spectrum are highlighted. To illustrate the effectiveness of the proposed scheme, a numerical example based on the fractional Lorenz dynamical system is presented and the results are compared to the integer Lorenz system.

Developmental Foundations of Children’s Fraction Magnitude Knowledge

PubMed Central

Mou, Yi; Li, Yaoran; Hoard, Mary K.; Nugent, Lara D.; Chu, Felicia W.; Rouder, Jeffrey N.; Geary, David C.

2016-01-01

The conceptual insight that fractions represent magnitudes is a critical yet daunting step in children’s mathematical development, and the knowledge of fraction magnitudes influences children’s later mathematics learning including algebra. In this study, longitudinal data were analyzed to identify the mathematical knowledge and domain-general competencies that predicted 8th and 9th graders’ (n=122) knowledge of fraction magnitudes and its cross-grade gains. Performance on the fraction magnitude measures predicted 9th grade algebra achievement. Understanding and fluently identifying the numerator-denominator relation in 7th grade emerged as the key predictor of later fraction magnitudes knowledge in both 8th and 9th grades. Competence at using fraction procedures, knowledge of whole number magnitudes, and the central executive contributed to 9th but not 8th graders’ fraction magnitude knowledge, and knowledge of whole number magnitude contributed to cross-grade gains. The key results suggest fluent processing of numerator-denominator relations presages students’ understanding of fractions as magnitudes and that the integration of whole number and fraction magnitudes occurs gradually. PMID:27773965

Representing Numbers as Continued Fractions and an N-Spire. tns Document to Do Some Basic Continued Fraction Arithmetic

ERIC Educational Resources Information Center

Leinbach, L. Carl

2015-01-01

This paper illustrates a TI N-Spire .tns file created by the author for generating continued fraction representations of real numbers and doing arithmetic with them. The continued fraction representation provides an alternative to the decimal representation. The .tns file can be used as tool for studying continued fractions and their properties as…

[Plasma fractionation in the world: current status].

PubMed

Burnouf, T

2007-05-01

From 22 to 25 million liters of plasma are fractionated yearly in about 70 fractionation plants, either private or government-owned, mainly located in industrialized countries, and with a capacity ranging from 50000 to three million liters. In an increasingly global environment, the plasma industry has recently gone through a major consolidation phase that has seen mergers and acquisitions, and has led to the closure of a number of small plants in Europe. Currently, some fifteen countries are involved into contract plasma fractionation programs to ensure a supply of plasma-derived medicinal products. The majority of the plasma for fractionation is obtained by automated plasmapheresis, the remaining (recovered plasma) being prepared from whole blood as a by-product of red cell production. Plasma for fractionation should be produced, and controlled following well established procedures to meet the strict quality requirements set by regulatory authorities and fractionators. The plasma fractionation technology still relies heavily on the cold ethanol fractionation process, but has been improved by the introduction of modern chromatographic purification methods, and efficient viral inactivation and removal treatments, ensuring quality and safety to a large portfolio of fractionated plasma products. The safety of these products with regards to the risk of transmission of variant Creutzfeldt-Jakob disease seems to be provided, based on current scientific data, by extensive removal of the infectious agent during certain fractionation steps. The leading plasma product is now the intravenous immunoglobulin G, which has replaced factor VIII and albumin in this role. The supply of plasma products (most specifically coagulation products and immunoglobulin) at an affordable price and in sufficient quantity remains an issue; the problem is particularly acute in developing countries, as the switch to recombinant factor VIII in rich countries has not solved the supply issue and has

Fractional calculus in hydrologic modeling: A numerical perspective

PubMed Central

Benson, David A.; Meerschaert, Mark M.; Revielle, Jordan

2013-01-01

Fractional derivatives can be viewed either as handy extensions of classical calculus or, more deeply, as mathematical operators defined by natural phenomena. This follows the view that the diffusion equation is defined as the governing equation of a Brownian motion. In this paper, we emphasize that fractional derivatives come from the governing equations of stable Lévy motion, and that fractional integration is the corresponding inverse operator. Fractional integration, and its multi-dimensional extensions derived in this way, are intimately tied to fractional Brownian (and Lévy) motions and noises. By following these general principles, we discuss the Eulerian and Lagrangian numerical solutions to fractional partial differential equations, and Eulerian methods for stochastic integrals. These numerical approximations illuminate the essential nature of the fractional calculus. PMID:23524449

Sampling Martian Soil

NASA Technical Reports Server (NTRS)

2004-01-01

Scientists were using the Moessbauer spectrometer on NASA's Mars Exploration Rover Spirit when something unexpected happened. The instrument's contact ring had been placed onto the ground as a reference point for placement of another instrument, the alpha particle X-ray spectrometer, for analyzing the soil. After Spirit removed the Moessbauer from the target, the rover's microscopic imager revealed a gap in the imprint left behind in the soil. The gap, about a centimeter wide (less than half an inch), is visible on the left side of this mosaic of images. Scientists concluded that a small chunk of soil probably adhered to the contact ring on the front surface of the Moessbauer. Before anyone saw that soil may have adhered to the Moessbauer, that instrument was placed to analyze martian dust collected by a magnet on the rover. The team plans to take images to see if any soil is still attached to the Moessbauer. Spirit took these images on the rover's 240th martian day, or sol (Sept. 4, 2004).

Continued fractions with limit periodic coefficients

NASA Astrophysics Data System (ADS)

Buslaev, V. I.

2018-02-01

The boundary properties of functions represented by limit periodic continued fractions of a fairly general form are investigated. Such functions are shown to have no single-valued meromorphic extension to any neighbourhood of any non-isolated boundary point of the set of convergence of the continued fraction. The boundary of the set of meromorphy has the property of symmetry in an external field determined by the parameters of the continued fraction. Bibliography: 26 titles.

On the Conformable Fractional Quantum Mechanics

NASA Astrophysics Data System (ADS)

Mozaffari, F. S.; Hassanabadi, H.; Sobhani, H.; Chung, W. S.

2018-05-01

In this paper, a conformable fractional quantum mechanic has been introduced using three postulates. Then in such a formalism, Schr¨odinger equation, probability density, probability flux and continuity equation have been derived. As an application of considered formalism, a fractional-radial harmonic oscillator has been considered. After obtaining its wave function and energy spectrum, effects of the conformable fractional parameter on some quantities have been investigated and plotted for different excited states.

Few Fractional Order Derivatives and Their Computations

ERIC Educational Resources Information Center

Bhatta, D. D.

2007-01-01

This work presents an introductory development of fractional order derivatives and their computations. Historical development of fractional calculus is discussed. This paper presents how to obtain computational results of fractional order derivatives for some elementary functions. Computational results are illustrated in tabular and graphical…

Early Predictors of Middle School Fraction Knowledge

ERIC Educational Resources Information Center

Bailey, Drew H.; Siegler, Robert S.; Geary, David C.

2014-01-01

Recent findings that earlier fraction knowledge predicts later mathematics achievement raise the question of what predicts later fraction knowledge. Analyses of longitudinal data indicated that whole number magnitude knowledge in first grade predicted knowledge of fraction magnitudes in middle school, controlling for whole number arithmetic…

Improving Children's Knowledge of Fraction Magnitudes

ERIC Educational Resources Information Center

Fazio, Lisa K.; Kennedy, Casey A.; Siegler, Robert S.

2016-01-01

We examined whether playing a computerized fraction game, based on the integrated theory of numerical development and on the Common Core State Standards' suggestions for teaching fractions, would improve children's fraction magnitude understanding. Fourth and fifth-graders were given brief instruction about unit fractions and played "Catch…

Chromium isotope fractionation in ferruginous sediments

NASA Astrophysics Data System (ADS)

Bauer, Kohen W.; Gueguen, Bleuenn; Cole, Devon B.; Francois, Roger; Kallmeyer, Jens; Planavsky, Noah; Crowe, Sean A.

2018-02-01

Ferrous Fe is a potent reductant of Cr(VI), and while a number of laboratory studies have characterized Cr isotope fractionation associated with Cr(VI) reduction by ferrous iron, the expression of this fractionation in real-world ferrous Fe-rich environments remains unconstrained. Here we determine the isotope fractionation associated with Cr(VI) reduction in modern ferrous Fe-rich sediments obtained from the previously well studied Lake Matano, Indonesia. Whole core incubations demonstrate that reduction of Cr(VI) within ferruginous sediments provides a sink for Cr(VI) leading to Cr(VI) concentration gradients and diffusive Cr(VI) fluxes across the sediment water interface. As reduction proceeded, Cr(VI) remaining in the overlying lake water became progressively enriched in the heavy isotope (53Cr), increasing δ53Cr by 2.0 ± 0.1‰ at the end of the incubation. Rayleigh distillation modelling of the evolution of Cr isotope ratios and Cr(VI) concentrations in the overlying water yields an effective isotope fractionation of εeff = 1.1 ± 0.2‰ (53Cr/52Cr), whereas more detailed diagenetic modelling implies an intrinsic isotope fractionation of εint = 1.80 ± 0.04‰. Parallel slurry experiments performed using anoxic ferruginous sediment yield an intrinsic isotope fractionation of εint = 2.2 ± 0.1‰. These modelled isotope fractionations are corroborated by direct measurement of the δ53Cr composition on the upper 0.5 cm of Lake Matano sediment, revealing an isotopic offset from the lake water of Δ53Cr = 0.21-1.81‰. The data and models reveal that effective isotope fractionations depend on the depth at which Cr(VI) reduction takes place below the sediment water interface-the deeper the oxic non-reactive zone, the smaller the effective fractionation relative to the intrinsic fractionation. Based on the geochemistry of the sediment we suggest the electron donors responsible for reduction are a combination of dissolved Fe(II) and 0.5 M HCl extractable (solid

Fractions, Number Lines, Third Graders

ERIC Educational Resources Information Center

Cramer, Kathleen; Ahrendt, Sue; Monson, Debra; Wyberg, Terry; Colum, Karen

2017-01-01

The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) outlines ambitious goals for fraction learning, starting in third grade, that include the use of the number line model. Understanding and constructing fractions on a number line are particularly complex tasks. The current work of the authors centers on ways to successfully…

21 CFR 862.1630 - Protein (fractionation) test system.

Code of Federal Regulations, 2010 CFR

2010-04-01

... 21 Food and Drugs 8 2010-04-01 2010-04-01 false Protein (fractionation) test system. 862.1630... Systems § 862.1630 Protein (fractionation) test system. (a) Identification. A protein (fractionation) test system is a device intended to measure protein fractions in blood, urine, cerebrospinal fluid, and other...

The fractional Fourier transform and applications

NASA Technical Reports Server (NTRS)

Bailey, David H.; Swarztrauber, Paul N.

1991-01-01

This paper describes the 'fractional Fourier transform', which admits computation by an algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the discrete Fourier transform (DFT) is based on integral roots of unity e exp -2(pi)i/n, the fractional Fourier transform is based on fractional roots of unity e exp -2(pi)i(alpha), where alpha is arbitrary. The fractional Fourier transform and the corresponding fast algorithm are useful for such applications as computing DFTs of sequences with prime lengths, computing DFTs of sparse sequences, analyzing sequences with noninteger periodicities, performing high-resolution trigonometric interpolation, detecting lines in noisy images, and detecting signals with linearly drifting frequencies. In many cases, the resulting algorithms are faster by arbitrarily large factors than conventional techniques.

Couple of the Variational Iteration Method and Fractional-Order Legendre Functions Method for Fractional Differential Equations

PubMed Central

Song, Junqiang; Leng, Hongze; Lu, Fengshun

2014-01-01

We present a new numerical method to get the approximate solutions of fractional differential equations. A new operational matrix of integration for fractional-order Legendre functions (FLFs) is first derived. Then a modified variational iteration formula which can avoid “noise terms” is constructed. Finally a numerical method based on variational iteration method (VIM) and FLFs is developed for fractional differential equations (FDEs). Block-pulse functions (BPFs) are used to calculate the FLFs coefficient matrices of the nonlinear terms. Five examples are discussed to demonstrate the validity and applicability of the technique. PMID:24511303

Stability Analysis of Distributed Order Fractional Chen System

PubMed Central

Aminikhah, H.; Refahi Sheikhani, A.; Rezazadeh, H.

2013-01-01

We first investigate sufficient and necessary conditions of stability of nonlinear distributed order fractional system and then we generalize the integer-order Chen system into the distributed order fractional domain. Based on the asymptotic stability theory of nonlinear distributed order fractional systems, the stability of distributed order fractional Chen system is discussed. In addition, we have found that chaos exists in the double fractional order Chen system. Numerical solutions are used to verify the analytical results. PMID:24489508

Devices, systems, and methods for microscale isoelectric fractionation

DOEpatents

Sommer, Gregory J.; Hatch, Anson V.; Wang, Ying-Chih; Singh, Anup K.

2016-08-09

Embodiments of the present invention provide devices, systems, and methods for microscale isoelectric fractionation. Analytes in a sample may be isolated according to their isoelectric point within a fractionation microchannel. A microfluidic device according to an embodiment of the invention includes a substrate at least partially defining a fractionation microchannel. The fractionation microchannel has at least one cross-sectional dimension equal to or less than 1 mm. A plurality of membranes of different pHs are disposed in the microchannel. Analytes having an isoelectric point between the pH of the membranes may be collected in a region of the fractionation channel between the first and second membranes through isoelectric fractionation.

Devices, systems, and methods for microscale isoelectric fractionation

DOEpatents

Sommer, Gregory J; Hatch, Anson V; Wang, Ying-Chih; Singh, Anup K

2015-04-14

Embodiments of the present invention provide devices, systems, and methods for microscale isoelectric fractionation. Analytes in a sample may be isolated according to their isoelectric point within a fractionation microchannel. A microfluidic device according to an embodiment of the invention includes a substrate at least partially defining a fractionation microchannel. The fractionation microchannel has at least one cross-sectional dimension equal to or less than 1 mm. A plurality of membranes of different pHs are disposed in the microchannel. Analytes having an isoelectric point between the pH of the membranes may be collected in a region of the fractionation channel between the first and second membranes through isoelectric fractionation.

Optimization in fractional aircraft ownership

NASA Astrophysics Data System (ADS)

Septiani, R. D.; Pasaribu, H. M.; Soewono, E.; Fayalita, R. A.

2012-05-01

Fractional Aircraft Ownership is a new concept in flight ownership management system where each individual or corporation may own a fraction of an aircraft. In this system, the owners have privilege to schedule their flight according to their needs. Fractional management companies (FMC) manages all aspects of aircraft operations, including utilization of FMC's aircraft in combination of outsourced aircrafts. This gives the owners the right to enjoy the benefits of private aviations. However, FMC may have complicated business requirements that neither commercial airlines nor charter airlines faces. Here, optimization models are constructed to minimize the number of aircrafts in order to maximize the profit and to minimize the daily operating cost. In this paper, three kinds of demand scenarios are made to represent different flight operations from different types of fractional owners. The problems are formulated as an optimization of profit and a daily operational cost to find the optimum flight assignments satisfying the weekly and daily demand respectively from the owners. Numerical results are obtained by Genetic Algorithm method.

Table-sized matrix model in fractional learning

NASA Astrophysics Data System (ADS)

Soebagyo, J.; Wahyudin; Mulyaning, E. C.

2018-05-01

This article provides an explanation of the fractional learning model i.e. a Table-Sized Matrix model in which fractional representation and its operations are symbolized by the matrix. The Table-Sized Matrix are employed to develop problem solving capabilities as well as the area model. The Table-Sized Matrix model referred to in this article is used to develop an understanding of the fractional concept to elementary school students which can then be generalized into procedural fluency (algorithm) in solving the fractional problem and its operation.

Long-Term Dynamics of Autonomous Fractional Differential Equations

NASA Astrophysics Data System (ADS)

Liu, Tao; Xu, Wei; Xu, Yong; Han, Qun

This paper aims to investigate long-term dynamic behaviors of autonomous fractional differential equations with effective numerical method. The long-term dynamic behaviors predict where systems are heading after long-term evolution. We make some modification and transplant cell mapping methods to autonomous fractional differential equations. The mapping time duration of cell mapping is enlarged to deal with the long memory effect. Three illustrative examples, i.e. fractional Lotka-Volterra equation, fractional van der Pol oscillator and fractional Duffing equation, are studied with our revised generalized cell mapping method. We obtain long-term dynamics, such as attractors, basins of attraction, and saddles. Compared with some existing stability and numerical results, the validity of our method is verified. Furthermore, we find that the fractional order has its effect on the long-term dynamics of autonomous fractional differential equations.

Dividing Fractions and Problem Solving

ERIC Educational Resources Information Center

Cramer, Kathleen; Monson, Debra; Whitney, Stephanie; Leavitt, Seth; Wyberg, Terry

2010-01-01

Fraction division is generally introduced in sixth or seventh grade with this rule: "Invert and multiply." The authors examined current commercial curricula and found that few textbooks use context as a way to build meaning for the division of fractions. When context is used, the connection between the invert-and-multiply rule and the context is…

Measuring Fraction Comparison Strategies with Eye-Tracking

ERIC Educational Resources Information Center

Obersteiner, Andreas; Tumpek, Christine

2016-01-01

Research suggests that people use a variety of strategies for comparing the numerical values of two fractions. They use holistic strategies that rely on the fraction magnitudes, componential strategies that rely on the fraction numerators or denominators, or a combination of both. We investigated how mathematically skilled adults adapt their…

7 CFR 718.5 - Rule of fractions.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 7 2010-01-01 2010-01-01 false Rule of fractions. 718.5 Section 718.5 Agriculture Regulations of the Department of Agriculture (Continued) FARM SERVICE AGENCY, DEPARTMENT OF AGRICULTURE FARM... General Provisions § 718.5 Rule of fractions. (a) Fractions shall be rounded after completion of the...

Preparing for Algebra by Building Fraction Sense

ERIC Educational Resources Information Center

Rodrigues, Jessica; Dyson, Nancy I.; Hansen, Nicole; Jordan, Nancy C.

2016-01-01

Fractions are troublesome for many children, especially students with learning difficulties and disabilities in mathematics. To address this serious educational concern, this article recommends the use of number lines to build fraction sense. Math activities that center on the number line build fraction concepts as early as third grade. A number…

Size fractionation of waste-to-energy boiler ash enables separation of a coarse fraction with low dioxin concentrations.

PubMed

Weidemann, E; Allegrini, E; Fruergaard Astrup, T; Hulgaard, T; Riber, C; Jansson, S

2016-03-01

Polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDD/F) formed in modern Waste-to-Energy plants are primarily found in the generated ashes and air pollution control residues, which are usually disposed of as hazardous waste. The objective of this study was to explore the occurrence of PCDD/F in different grain size fractions in the boiler ash, i.e. ash originating from the convection pass of the boiler. If a correlation between particle size and dioxin concentrations could be found, size fractionation of the ashes could reduce the total amount of hazardous waste. Boiler ash samples from ten sections of a boiler's convective part were collected over three sampling days, sieved into three different size fractions - <0.09 mm, 0.09-0.355 mm, and >0.355 mm - and analysed for PCDD/F. The coarse fraction (>0.355 mm) in the first sections of the horizontal convection pass appeared to be of low toxicity with respect to dioxin content. While the total mass of the coarse fraction in this boiler was relatively small, sieving could reduce the amount of ash containing toxic PCDD/F by around 0.5 kg per tonne input waste or around 15% of the collected boiler ash from the convection pass. The mid-size fraction in this study covered a wide size range (0.09-0.355 mm) and possibly a low toxicity fraction could be identified by splitting this fraction into more narrow size ranges. The ashes exhibited uniform PCDD/F homologue patterns which suggests a stable and continuous generation of PCDD/F. Copyright © 2016 Elsevier Ltd. All rights reserved.

GOLGI FRACTIONS PREPARED FROM RAT LIVER HOMOGENATES

PubMed Central

Ehrenreich, J. H.; Bergeron, J. J. M.; Siekevitz, P.; Palade, G. E.

1973-01-01

In devising a new procedure for the isolation of Golgi fractions from rat liver homogenates, we have taken advantage of the overloading with very low density lipoprotein (VLDL) particles that occurs in the Golgi elements of hepatocytes ∼90 min after ethanol is administered (0.6 g/100 g body weight) by stomach tube to the animals. The VLDLs act as morphological markers as well as density modifiers of these elements. The starting preparation is a total microsomal fraction prepared from liver homogenized (1:5) in 0.25 M sucrose. This fraction is resuspended in 1.15 M sucrose and loaded at the bottom of a discontinuous sucrose density gradient. Centrifugation at ∼13 x 106 g·min yields by flotation three Golgi fractions of density >1.041 and <1.173. The light and intermediate fractions consist essentially of VLDL-loaded Golgi vacuoles and cisternae. Nearly empty, often collapsed, Golgi cisternae are the main component of the heavy fraction. A procedure which subjects the Golgi fractions to hypotonic shock and shearing in a French press at pH 8.5 allows the extraction of the content of the Golgi elements and the subsequent isolation of their membranes by differential centrifugation. PMID:4356571

An Alternative Starting Point for Fraction Instruction

ERIC Educational Resources Information Center

Cortina, José Luis; Višnovská, Jana; Zúñiga, Claudia

2015-01-01

We analyze the results of a study conducted for the purpose of assessing the viability of an alternative starting point for teaching fractions. The alternative is based on Freudenthal's insights about fraction as comparison. It involves portraying the entities that unit fractions quantify as always being apart from the reference unit, instead of…

Fractionation of Java Citronella Oil and Citronellal Purification by Batch Vacuum Fractional Distillation

NASA Astrophysics Data System (ADS)

Eden, W. T.; Alighiri, D.; Cahyono, E.; Supardi, K. I.; Wijayati, N.

2018-04-01

The aim of this work was to assess the performance of a vacuum fractionating column for the fractionation of Java Citronella Oil (Cymbopogon winterianus) and citronellal purification during batch mode operation at vacuum -76 cmHg and reflux ratios 5:1. Based on GC-MS analysis of Java Citronella Oil is known that citronellal, citronellol, and geraniol has yielded 21,59%; 7,43%; and 34,27%, respectively. Fractional distillation under reduced pressure and continued redistilled are needed to isolate the component of Java Citronella Oil. Redistilled can improve the purity, then distillate collected while the temperature changed. In the first distillate yielded citronellal with a purity of 75.67%. The first distillate obtained residue rhodinol product will then be carried back to separation into citronellol and geraniol. The purity of citronellol reached 80,65% purity, whereas geraniol reached 76.63% purity. Citronellal Purification resulting citronellal to 95.10% purity and p-menthane-3,8-diol reached 75.95% purity.

Ejection Fraction: What Does It Measure?

MedlinePlus

... does the term "ejection fraction" mean? What does it measure? Answers from Rekha Mankad, M.D. Ejection fraction ... percentage of blood leaving your heart each time it contracts. During each heartbeat pumping cycle, the heart ...

Lucky Fractions: Where Bad Arithmetic Gives Correct Results

ERIC Educational Resources Information Center

Osler, Thomas J.

2007-01-01

The fraction 16 over 64 has a well known, interesting property. If one incorrectly cancels the sixes, a correct answer of 1 over 4 is obtained. This is an example of a lucky fraction. In this article, the author presents several examples of lucky fractions and proves two interesting properties of these fractions. This article provides students the…

Adsorption characterizations of fulvic acid fractions onto kaolinite.

PubMed

Li, Aimin; Xu, Minjuan; Li, Wenhui; Wang, Xuejun; Dai, Jingyu

2008-01-01

Fulvic acids extracted from a typical rice-production region near Taihu Lake of China were fractionated into three fractions including F4.8, F7.0 and F11.0 (eluted by pH 4.8 buffer, pH 7.0 buffer and pH 11.0 buffer, respectively). Sorption of fulvic acid (FA) fractions onto kaolinite was studied by batch adsorption experiments, and characterizations of kaolinite before and after adsorption were investigated using scanning electron microscopy (SEM). Adsorption isotherms of kaolinite for three FA fractions fit well with the Langmuir adsorption model. The adsorption density of the three fractions was positively correlated with the ratio of the amount of the alkyl carbon to that of carboxyl and carbonyl carbon in FA fractions and followed an order of F11.0 > F7.0 > F4.8. Hydrophobic interaction was one of the control mechanisms for the sorption of FA fraction onto kaolinite. SEM images confirmed that compared to blank kaolinite samples, kaolinite samples coated by a FA fraction displayed an opener and more dispersed conformation resulting from the disruption of the floc structure in complex. Dispersion of kaolinite after adsorption was due to the repulsion between negatively charged FA-coated particles, which is closely related to the amount of FA fractions absorbed on kaolinite.

To the problem about the origin of lunar maria and continents (Moessbauer investigations)

NASA Technical Reports Server (NTRS)

Malysheva, T. V.

1977-01-01

A comparative study of Mossbauer spectra of regolith returned by the Luna 16 and Luna 20 spacecraft is presented. The Mossbauer spectra of the mare regolith differs significantly for all fractions from the spectra for the same fractions of continental regolith. The total quantity of iron is 1.85 times greater in the mare regolith. There is 2.4 times less olivine in the mare region than in the continental region. The pyroxene component of the mare regolith is less homogeneous in composition (contains more augite and glass) and is present in larger quantities. Ilmenite was found only in the mare regolith. In the continental region, the predominant titanium-containing phase is ulvospinel. The mare regolith contains more metallic iron, which is more finely dispersed and contains less nickel. Troilite is found in the maria region. Based on these differences, it is concluded that the formation of continental rocks occurred at an earlier stage of crystallization from the melt and at higher temperatures and higher partial pressures of oxygen. The mare basalts crystallized from a more reduced magma, apparently in a later process.

Probing Schrodinger equation with a continued fraction potential

NASA Astrophysics Data System (ADS)

Ahmed, Nasr; Alamri, Sultan Z.; Rassem, M.

2018-06-01

We suggest a new perturbed form of the quantum potential and investigate the possible solutions of Schrodinger equation. The new form can be written as a finite or infinite continued fraction. a comparison has been given between the continued fractional potential and the non-perturbed potential. We suggest the validity of this continued fractional quantum form in some quantum systems. As the order of the continued fraction increases the difference between the perturbed and the ordinary potentials decreases. The physically acceptable solutions critically depend on the values of the continued fraction coefficients αi .

Phenolic compounds containing/neutral fractions extract and products derived therefrom from fractionated fast-pyrolysis oils

DOEpatents

Chum, Helena L.; Black, Stuart K.; Diebold, James P.; Kreibich, Roland E.

1993-01-01

A process for preparing phenol-formaldehyde novolak resins and molding compositions in which portions of the phenol normally contained in said resins are replaced by a phenol/neutral fractions extract obtained from fractionating fast-pyrolysis oils. The fractionation consists of a neutralization stage which can be carried out with aqueous solutions of bases or appropriate bases in the dry state, followed by solvent extraction with an organic solvent having at least a moderate solubility parameter and good hydrogen bonding capacity. Phenolic compounds-containing/neutral fractions extracts obtained by fractionating fast-pyrolysis oils from a lignocellulosic material, is such that the oil is initially in the pH range of 2-4, being neutralized with an aqueous bicarbonate base, and extracted into a solvent having a solubility parameter of approximately 8.4-9.11 [cal/cm.sup.3 ].sup.1/2 with polar components in the 1.8-3.0 range and hydrogen bonding components in the 2-4.8 range and the recovery of the product extract from the solvent with no further purification being needed for use in adhesives and molding compounds. The product extract is characterized as being a mixture of very different compounds having a wide variety of chemical functionalities, including phenolic, carbonyl, aldehyde, methoxyl, vinyl and hydroxyl. The use of the product extract on phenol-formaldehyde thermosetting resins is shown to have advantages over the conventional phenol-formaldehyde resins.

Levi-Civita cylinders with fractional angular deficit

NASA Astrophysics Data System (ADS)

Krisch, J. P.; Glass, E. N.

2011-05-01

The angular deficit factor in the Levi-Civita vacuum metric has been parametrized using a Riemann-Liouville fractional integral. This introduces a new parameter into the general relativistic cylinder description, the fractional index α. When the fractional index is continued into the negative α region, new behavior is found in the Gott-Hiscock cylinder and in an Israel shell.

19 CFR 159.3 - Rounding of fractions.

Code of Federal Regulations, 2010 CFR

2010-04-01

... 19 Customs Duties 2 2010-04-01 2010-04-01 false Rounding of fractions. 159.3 Section 159.3 Customs... (CONTINUED) LIQUIDATION OF DUTIES General Provisions § 159.3 Rounding of fractions. (a) Value. In the... cents or more, the lower fractions shall be dropped, and if it is necessary to take up as whole dollars...

Maximizing Tumor Immunity With Fractionated Radiation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schaue, Doerthe, E-mail: dschaue@mednet.ucla.edu; Ratikan, Josephine A.; Iwamoto, Keisuke S.

Purpose: Technologic advances have led to increased clinical use of higher-sized fractions of radiation dose and higher total doses. How these modify the pathways involved in tumor cell death, normal tissue response, and signaling to the immune system has been inadequately explored. Here we ask how radiation dose and fraction size affect antitumor immunity, the suppression thereof, and how this might relate to tumor control. Methods and Materials: Mice bearing B16-OVA murine melanoma were treated with up to 15 Gy radiation given in various-size fractions, and tumor growth followed. The tumor-specific immune response in the spleen was assessed by interferon-{gamma}more » enzyme-linked immunospot (ELISPOT) assay with ovalbumin (OVA) as the surrogate tumor antigen and the contribution of regulatory T cells (Tregs) determined by the proportion of CD4{sup +}CD25{sup hi}Foxp3{sup +} T cells. Results: After single doses, tumor control increased with the size of radiation dose, as did the number of tumor-reactive T cells. This was offset at the highest dose by an increase in Treg representation. Fractionated treatment with medium-size radiation doses of 7.5 Gy/fraction gave the best tumor control and tumor immunity while maintaining low Treg numbers. Conclusions: Radiation can be an immune adjuvant, but the response varies with the size of dose per fraction. The ultimate challenge is to optimally integrate cancer immunotherapy into radiation therapy.« less

Intra-fraction motion of larynx radiotherapy

NASA Astrophysics Data System (ADS)

Durmus, Ismail Faruk; Tas, Bora

2018-02-01

In early stage laryngeal radiotherapy, movement is an important factor. Thyroid cartilage can move from swallowing, breathing, sound and reflexes. The effects of this motion on the target volume (PTV) during treatment were examined. In our study, the target volume movement during the treatment for this purpose was examined. Thus, setup margins are re-evaluated and patient-based PTV margins are determined. Intrafraction CBCT was scanned in 246 fractions for 14 patients. During the treatment, the amount of deviation which could be lateral, vertical and longitudinal axis was determined. ≤ ± 0.1cm deviation; 237 fractions in the lateral direction, 202 fractions in the longitudinal direction, 185 fractions in the vertical direction. The maximum deviation values were found in the longitudinal direction. Intrafraction guide in laryngeal radiotherapy; we are sure of the correctness of the treatment, the target volume is to adjust the margin and dose more precisely, we control the maximum deviation of the target volume for each fraction. Although the image quality of intrafraction-CBCT scans was lower than the image quality of planning CT, they showed sufficient contrast for this work.

Current Status of Fractional Laser Resurfacing.

PubMed

Carniol, Paul J; Hamilton, Mark M; Carniol, Eric T

2015-01-01

Fractional lasers were first developed based on observations of lasers designed for hair transplantation. In 2007, ablative fractional laser resurfacing was introduced. The fractionation allowed deeper tissue penetration, leading to greater tissue contraction, collagen production and tissue remodeling. Since then, fractional erbium:YAG resurfacing lasers have also been introduced. These lasers have yielded excellent results in treating photoaging, acne scarring, and dyschromia. With the adjustment of microspot density, pulse duration, number of passes, and fluence, the surgeon can adjust the treatment effects. These lasers have allowed surgeons to treat patients with higher Fitzpatrick skin types (types IV to VI) and greater individualize treatments to various facial subunits. Immunohistochemical analysis has demonstrated remodeling effects of the tissues for several months, producing longer lasting results. Adjuvant treatments are also under investigation, including concomitant face-lift, product deposition, and platelet-rich plasma. Finally, there is a short recovery time from treatment with these lasers, allowing patients to resume regular activities more quickly. Although there is a relatively high safety profile for ablative fractionated lasers, surgeons should be aware of the limitations of specific treatments and the associated risks and complications.

The mental representations of fractions: adults' same–different judgments

PubMed Central

Gabriel, Florence; Szucs, Denes; Content, Alain

2013-01-01

Two experiments examined whether the processing of the magnitude of fractions is global or componential. Previously, some authors concluded that adults process the numerators and denominators of fractions separately and do not access the global magnitude of fractions. Conversely, others reported evidence suggesting that the global magnitude of fractions is accessed. We hypothesized that in a fraction matching task, participants automatically extract the magnitude of the components but that the activation of the global magnitude of the whole fraction is only optional or strategic. Participants carried out same/different judgment tasks. Two different tasks were used: a physical matching task and a numerical matching task. Pairs of fractions were presented either simultaneously or sequentially. Results showed that participants only accessed the representation of the global magnitude of fractions in the numerical matching task. The mode of stimulus presentation did not affect the processing of fractions. The present study allows a deeper understanding of the conditions in which the magnitude of fractions is mentally represented by using matching tasks and two different modes of presentation. PMID:23847562

Thermomechanical Fractional Model of TEMHD Rotational Flow

PubMed Central

Hamza, F.; Abd El-Latief, A.; Khatan, W.

2017-01-01

In this work, the fractional mathematical model of an unsteady rotational flow of Xanthan gum (XG) between two cylinders in the presence of a transverse magnetic field has been studied. This model consists of two fractional parameters α and β representing thermomechanical effects. The Laplace transform is used to obtain the numerical solutions. The fractional parameter influence has been discussed graphically for the functions field distribution (temperature, velocity, stress and electric current distributions). The relationship between the rotation of both cylinders and the fractional parameters has been discussed on the functions field distribution for small and large values of time. PMID:28045941

Effects of Sterilization on the Physico-Chemical Properties of Natural Sediments From the Oak Ridge Reservation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bank, T.L.; Kukkadapu, R.K.; Madden, A.S.

2009-04-29

Batch U(VI) sorption/reduction experiments were completed on sterilized and non-sterilized sediment samples to elucidate biological and geochemical reduction mechanisms. Results from X-ray absorption near-edge structure (XANES) spectroscopy revealed that {gamma}-sterilized sediments were actually better sorbents of U(VI), despite the absence of any measurable biological activity. These results indicate that {gamma}-irradiation induced significant physico-chemical changes in the sediment which is contrary to numerous other studies identifying {gamma}-sterilization as an effective and minimally invasive technique. To identify the extent and method of alteration of the soil as a result of {gamma}-sterilization, untreated soil samples, physically separated size fractions, and chemically extracted fractionsmore » of the soil were analyzed pre- and post-sterilization. The effects of sterilization on mineralogy, pH, natural organic matter (NOM), cation exchange capacity (CEC), and iron oxidation state were determined. Results indicated that major mineralogy of the clay and whole sediment samples was unchanged. Sediment pH decreased only slightly with {gamma}-irradiation; however, irradiation produced a significant decrease in CEC of the untreated sediments and affected both the organic and inorganic fractions. Moessbauer spectra of non-sterile and {gamma}-sterilized sediments measured more reduced iron present in {gamma}-sterilized sediments compared to non-sterile samples. Our results suggest that sterilization by {gamma}-irradiation induced iron reduction that may have increased the sorption and/or reduction of U(VI) onto these sediments. However, Moessbauer and batch sorption data are somewhat contradictory, the former indicates that the iron oxide or iron hydroxide minerals are more significantly reduced while the later indicates that reduced clay minerals account for greater sorption of U(VI).« less

Effects of gamma-sterilization on the physicochemical properties of natural sediments

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bank, Tracy L; Madden, Andrew; Baldwin, Mark E

2008-06-01

Batch U(VI) sorption/reduction experiments were completed on sterilized and non-sterilized sediment samples to elucidate biological and geochemical reduction mechanisms. Results from X-ray absorption near-edge structure (XANES) spectroscopy revealed that {gamma}-sterilized sediments were actually better sorbents of U(VI), despite the absence of any measurable biological activity. These results indicate that {gamma}-irradiation induced significant physico-chemical changes in the sediment which is contrary to numerous other studies identifying {gamma}-sterilization as an effective and minimally invasive technique. To identify the extent and method of alteration of the soil as a result of {gamma}-sterilization, untreated soil samples, physically separated size fractions, and chemically extracted fractionsmore » of the soil were analyzed pre- and post-sterilization. The effects of sterilization on mineralogy, pH, natural organic matter (NOM), cation exchange capacity (CEC), and iron oxidation state were determined. Results indicated that major mineralogy of the clay and whole sediment samples was unchanged. Sediment pH decreased only slightly with {gamma}-irradiation; however, irradiation produced a significant decrease in CEC of the untreated sediments and affected both the organic and inorganic fractions. Moessbauer spectra of non-sterile and {gamma}-sterilized sediments measured more reduced iron present in {gamma}-sterilized sediments compared to non-sterile samples. Our results suggest that sterilization by {gamma}-irradiation induced iron reduction that may have increased the sorption and/or reduction of U(VI) onto these sediments. However, Moessbauer and batch sorption data are somewhat contradictory, the former indicates that the iron oxide or iron hydroxide minerals are more significantly reduced while the later indicates that reduced clay minerals account for greater sorption of U(VI).« less

Mystery Fractions

ERIC Educational Resources Information Center

Bhattacharyya, Sonalee; Namakshi, Nama; Zunker, Christina; Warshauer, Hiroko K.; Warshauer, Max

2016-01-01

Making math more engaging for students is a challenge that every teacher faces on a daily basis. These authors write that they are constantly searching for rich problem-solving tasks that cover the necessary content, develop critical-thinking skills, and engage student interest. The Mystery Fraction activity provided here focuses on a key number…

Solution of a modified fractional diffusion equation

NASA Astrophysics Data System (ADS)

Langlands, T. A. M.

2006-07-01

Recently, a modified fractional diffusion equation has been proposed [I. Sokolov, J. Klafter, From diffusion to anomalous diffusion: a century after Einstein's brownian motion, Chaos 15 (2005) 026103; A.V. Chechkin, R. Gorenflo, I.M. Sokolov, V.Yu. Gonchar, Distributed order time fractional diffusion equation, Frac. Calc. Appl. Anal. 6 (3) (2003) 259279; I.M. Sokolov, A.V. Checkin, J. Klafter, Distributed-order fractional kinetics, Acta. Phys. Pol. B 35 (2004) 1323.] for describing processes that become less anomalous as time progresses by the inclusion of a second fractional time derivative acting on the diffusion term. In this letter we give the solution of the modified equation on an infinite domain. In contrast to the solution of the traditional fractional diffusion equation, the solution of the modified equation requires an infinite series of Fox functions instead of a single Fox function.

Fractional order uncertainty estimator based hierarchical sliding mode design for a class of fractional order non-holonomic chained system.

PubMed

Deepika; Kaur, Sandeep; Narayan, Shiv

2018-06-01

This paper proposes a novel fractional order sliding mode control approach to address the issues of stabilization as well as tracking of an N-dimensional extended chained form of fractional order non-holonomic system. Firstly, the hierarchical fractional order terminal sliding manifolds are selected to procure the desired objectives in finite time. Then, a sliding mode control law is formulated which provides robustness against various system uncertainties or external disturbances. In addition, a novel fractional order uncertainty estimator is deduced mathematically to estimate and mitigate the effects of uncertainties, which also excludes the requirement of their upper bounds. Due to the omission of discontinuous control action, the proposed algorithm ensures a chatter-free control input. Moreover, the finite time stability of the closed loop system has been proved analytically through well known Mittag-Leffler and Fractional Lyapunov theorems. Finally, the proposed methodology is validated with MATLAB simulations on two examples including an application of fractional order non-holonomic wheeled mobile robot and its performances are also compared with the existing control approach. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Mediants Make (Number) Sense of Fraction Foibles

ERIC Educational Resources Information Center

McDowell, Eric L.

2016-01-01

By the time they reach middle school, all students have been taught to add fractions. However, not all have "learned" to add fractions. The common mistake in adding fractions is to report that a/b + c/d is equal to (a + c)/(b + d). It is certainly necessary to correct this mistake when a student makes it. However, this occasion also…

The macromolecular properties of blood-group-specific glycoproteins. Characterization of a series of fractions obtained by solvent fractionation

PubMed Central

Creeth, J. Michael; Bhaskar, K. Ramakrishnan; Donald, Alastair S. R.; Morgan, Walter T. J.

1974-01-01

1. The glycoprotein components of a human ovarian-cyst fluid were isolated by a solvent [95% (w/w) phenol]-extraction procedure; the phenol-insoluble water-soluble glycoprotein was further fractionated by (NH4)2SO4 and by ethanol to yield eight fractions. 2. The fractions were analysed in terms of amino acids, fucose, galactose, N-acetylglucosamine, N-acetylgalactosamine and sialic acid. Variations occurred, particularly in the proportion of peptide; these were partly correlated with varying extent of serological activity. 3. The fractions were characterized physicochemically in terms of buoyant density and degree of spreading in a density gradient, sedimentation velocity and molecular weight; their partial specific volumes and specific refraction increments were also determined. 4. The fractions showed wide variations in their sedimentation-velocity and density-gradient patterns, and gave evidence of pauci-dispersity in density. The fraction regarded as the most typical blood-group-specific glycoprotein sedimented as a single rapidly spreading peak and was of high molecular weight. 5. Significant correlations were observed between the physical properties of the glycoprotein fractions and the amount of their peptide component. The buoyant densities and sedimentation coefficients varied in a manner that suggested the existence of two families of glycoproteins. 6. It is suggested that variability in the extent of glycosylation, or in the degree of cross-linking, might account for the two families of glycoproteins, and that the extent of cross-linkage might also be a factor determining the solubility of these glycoproteins in hot saturated (NH4)2SO4. ImagesFig. 1.PLATE 1 PMID:4219280

Application of the principal fractional meta-trigonometric functions for the solution of linear commensurate-order time-invariant fractional differential equations.

PubMed

Lorenzo, C F; Hartley, T T; Malti, R

2013-05-13

A new and simplified method for the solution of linear constant coefficient fractional differential equations of any commensurate order is presented. The solutions are based on the R-function and on specialized Laplace transform pairs derived from the principal fractional meta-trigonometric functions. The new method simplifies the solution of such fractional differential equations and presents the solutions in the form of real functions as opposed to fractional complex exponential functions, and thus is directly applicable to real-world physics.

Fractional populations in sex-linked inheritance

NASA Astrophysics Data System (ADS)

Pyo Lee, Seung; Chung, Myung-Hoon; Koo Kim, Chul; Nahm, Kyun

2001-03-01

We study the fractional populations in chromosome inherited diseases. The governing equations for the fractional populations are found and solved in the presence of mutation and selection. The physical fixed points obtained are used to discuss the cases of color blindness and hemophilia.

THEORETICAL AND EXPERIMENTAL ASPECTS OF ISOTOPIC FRACTIONATION.

USGS Publications Warehouse

O'Neil, James R.

1986-01-01

Essential to the interpretation of natural variations of light stable isotope ratios is knowledge of the magnitude and temperature dependence of isotopic fractionation factors between the common minerals and fluids. These fractionation factors are obtained in three ways: (1) Semi-empirical calculations using spectroscopic data and the methods of statistical mechanics. (2) Laboratory calibration studies. (3) Measurements of natural samples whose formation conditions are well-known or highly constrained. In this chapter methods (1) and (2) are evaluated and a review is given of the present state of knowledge of the theory of isotopic fractionation and the fraction that influence the isotopic properties of minerals.

Fast deuterium fractionation in magnetized and turbulent filaments

NASA Astrophysics Data System (ADS)

Körtgen, B.; Bovino, S.; Schleicher, D. R. G.; Stutz, A.; Banerjee, R.; Giannetti, A.; Leurini, S.

2018-04-01

Deuterium fractionation is considered as an important process to infer the chemical ages of prestellar cores in filaments. We present here the first magneto-hydrodynamical simulations including a chemical network to study deuterium fractionation in magnetized and turbulent filaments, with a line-mass of Mlin = 42 M⊙ pc-1 within a radius of R = 0.1 pc, and their substructures. The filaments typically show widespread deuterium fractionation with average values ≳ 0.01. For individual cores of similar age, we observe the deuteration fraction to increase with time, but also to be independent of their average properties such as density, virial or mass-to-magnetic flux ratio. We further find a correlation of the deuteration fraction with core mass, average H2 density and virial parameter only at late evolutionary stages of the filament and attribute this to the lifetime of the individual cores. Specifically, chemically old cores reveal higher deuteration fractions. Within the radial profiles of selected cores, we notice differences in the structure of the deuteration fraction or surface density, which we can attribute to their different turbulent properties. High deuteration fractions of the order 0.01 - 0.1 may be reached within approximately 200 kyrs, corresponding to two free-fall times, as defined for cylindrical systems, of the filaments.

Fast deuterium fractionation in magnetized and turbulent filaments

NASA Astrophysics Data System (ADS)

Körtgen, B.; Bovino, S.; Schleicher, D. R. G.; Stutz, A.; Banerjee, R.; Giannetti, A.; Leurini, S.

2018-07-01

Deuterium fractionation is considered as an important process to infer the chemical ages of prestellar cores in filaments. We present here the first magnetohydrodynamical simulations including a chemical network to study deuterium fractionation in magnetized and turbulent filaments, with a line-mass of Mlin = 42 M⊙ pc-1 within a radius of R= 0.1 pc, and their sub-structures. The filaments typically show widespread deuterium fractionation with average values ≳0.01. For individual cores of similar age, we observe the deuteration fraction to increase with time, but also to be independent of their average properties such as density, virial, or mass-to-magnetic flux ratio. We further find a correlation of the deuteration fraction with core mass, average H2 density, and virial parameter only at late evolutionary stages of the filament and attribute this to the lifetime of the individual cores. Specifically, chemically old cores reveal higher deuteration fractions. Within the radial profiles of selected cores, we notice differences in the structure of the deuteration fraction or surface density, which we can attribute to their different turbulent properties. High deuteration fractions of the order of 0.01-0.1 may be reached within approximately 200 kyr, corresponding to two free-fall times, as defined for cylindrical systems, of the filaments.

Competence with Fractions Predicts Gains in Mathematics Achievement

PubMed Central

Bailey, Drew H.; Hoard, Mary K.; Nugent, Lara; Geary, David C.

2012-01-01

Competence with fractions predicts later mathematics achievement, but the co-developmental pattern between fractions knowledge and mathematics achievement is not well understood. We assessed this co-development through examination of the cross-lagged relation between a measure of conceptual knowledge of fractions and mathematics achievement in sixth and seventh grade (n = 212). The cross-lagged effects indicated that performance on the sixth grade fractions concepts measure predicted one year gains in mathematics achievement (β = .14, p<.01), controlling for the central executive component of working memory and intelligence, but sixth grade mathematics achievement did not predict gains on the fractions concepts measure (β = .03, p>.50). In a follow-up assessment, we demonstrated that measures of fluency with computational fractions significantly predicted seventh grade mathematics achievement above and beyond the influence of fluency in computational whole number arithmetic, performance on number fluency and number line tasks, and central executive span and intelligence. Results provide empirical support for the hypothesis that competence with fractions underlies, in part, subsequent gains in mathematics achievement. PMID:22832199

Competence with fractions predicts gains in mathematics achievement.

PubMed

Bailey, Drew H; Hoard, Mary K; Nugent, Lara; Geary, David C

2012-11-01

Competence with fractions predicts later mathematics achievement, but the codevelopmental pattern between fractions knowledge and mathematics achievement is not well understood. We assessed this codevelopment through examination of the cross-lagged relation between a measure of conceptual knowledge of fractions and mathematics achievement in sixth and seventh grades (N=212). The cross-lagged effects indicated that performance on the sixth grade fractions concepts measure predicted 1-year gains in mathematics achievement (ß=.14, p<.01), controlling for the central executive component of working memory and intelligence, but sixth grade mathematics achievement did not predict gains on the fractions concepts measure (ß=.03, p>.50). In a follow-up assessment, we demonstrated that measures of fluency with computational fractions significantly predicted seventh grade mathematics achievement above and beyond the influence of fluency in computational whole number arithmetic, performance on number fluency and number line tasks, central executive span, and intelligence. Results provide empirical support for the hypothesis that competence with fractions underlies, in part, subsequent gains in mathematics achievement. Copyright © 2012 Elsevier Inc. All rights reserved.

Unpacking Referent Units in Fraction Operations

ERIC Educational Resources Information Center

Philipp, Randolph A.; Hawthorne, Casey

2015-01-01

Although fraction operations are procedurally straightforward, they are complex, because they require learners to conceptualize different units and view quantities in multiple ways. Prospective secondary school teachers sometimes provide an algebraic explanation for inverting and multiplying when dividing fractions. That authors of this article…

The aluminosilicate fraction of North Pacific manganese nodules

USGS Publications Warehouse

Bischoff, J.L.; Piper, D.Z.; Leong, K.

1981-01-01

Nine nodules collected from throughout the deep North Pacific were analyzed for their mineralogy and major-element composition before and after leaching with Chester-Hughes solution. Data indicate that the mineral phillipsite accounts for the major part (> 75%) of the aluminosilicate fraction of all nodules. It is suggested that formation of phillipsite takes place on growing nodule surfaces coupled with the oxidation of absorbed manganous ion. All the nodules could be described as ternary mixtures of amorphous iron fraction (Fe-Ti-P), manganese oxide fraction (Mn-Mg Cu-Ni), and phillipsite fraction (Al-Si-K-Na), these fractions accounting for 96% of the variability of the chemical composition. ?? 1981.

Thermal Dose Fractionation Affects Tumor Physiologic Response

PubMed Central

Thrall, Donald E; Maccarini, Paolo; Stauffer, Paul; MacFall, James; Hauck, Marlene; Snyder, Stacey; Case, Beth; Linder, Keith; Lan, Lan; McCall, Linda; Dewhirst, Mark W.

2013-01-01

Purpose It is unknown whether a thermal dose should be administered using a few large fractions with higher temperatures or a larger number of fractions with lower temperatures. To evaluate this, we assessed the effect of administering the same total thermal dose, approximately 30 CEM43T90, in 1 versus 3–4 fractions per week, over 5 weeks. Materials and Methods Canine sarcomas were randomized to receive one of the hyperthermia fractionation schemes along with fractionated radiotherapy. Tumor response was based on changes in tumor volume, oxygenation, water diffusion quantified using MRI, and a panel of histologic and immunohistochemical endpoints. Results There was a greater reduction in tumor volume and water diffusion at the end of therapy In tumors receiving 1 hyperthermia fraction per week. There was a weak but significant association between improved tumor oxygenation 24 hours after the first hyperthermia treatment and extent of volume reduction at the end of therapy. Finally, the direction of change of HIF 1α and CA IX immunoreactivity after the first hyperthermia fraction was similar and there was an inverse relationship between temperature and the direction of change of CA IX. There were no significant changes in interstitial fluid pressure, VEGF, wVf, apoptosis or necrosis as a function of treatment group or temperature. Conclusions We did not identify an advantage to a 3–4/week hyperthermia prescription and response data pointed to a 1/week prescription being superior. PMID:22804741

Spatiotemporal Fractionation Schemes for Irradiating Large Cerebral Arteriovenous Malformations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Unkelbach, Jan, E-mail: junkelbach@mgh.harvard.edu; Bussière, Marc R.; Chapman, Paul H.

2016-07-01

Purpose: To optimally exploit fractionation effects in the context of radiosurgery treatments of large cerebral arteriovenous malformations (AVMs). In current practice, fractionated treatments divide the dose evenly into several fractions, which generally leads to low obliteration rates. In this work, we investigate the potential benefit of delivering distinct dose distributions in different fractions. Methods and Materials: Five patients with large cerebral AVMs were reviewed and replanned for intensity modulated arc therapy delivered with conventional photon beams. Treatment plans allowing for different dose distributions in all fractions were obtained by performing treatment plan optimization based on the cumulative biologically effective dosemore » delivered at the end of treatment. Results: We show that distinct treatment plans can be designed for different fractions, such that high single-fraction doses are delivered to complementary parts of the AVM. All plans create a similar dose bath in the surrounding normal brain and thereby exploit the fractionation effect. This partial hypofractionation in the AVM along with fractionation in normal brain achieves a net improvement of the therapeutic ratio. We show that a biological dose reduction of approximately 10% in the healthy brain can be achieved compared with reference treatment schedules that deliver the same dose distribution in all fractions. Conclusions: Boosting complementary parts of the target volume in different fractions may provide a therapeutic advantage in fractionated radiosurgery treatments of large cerebral AVMs. The strategy allows for a mean dose reduction in normal brain that may be valuable for a patient population with an otherwise normal life expectancy.« less

Some theorems and properties of multi-dimensional fractional Laplace transforms

NASA Astrophysics Data System (ADS)

Ahmood, Wasan Ajeel; Kiliçman, Adem

2016-06-01

The aim of this work is to study theorems and properties for the one-dimensional fractional Laplace transform, generalize some properties for the one-dimensional fractional Lapalce transform to be valid for the multi-dimensional fractional Lapalce transform and is to give the definition of the multi-dimensional fractional Lapalce transform. This study includes: dedicate the one-dimensional fractional Laplace transform for functions of only one independent variable with some of important theorems and properties and develop of some properties for the one-dimensional fractional Laplace transform to multi-dimensional fractional Laplace transform. Also, we obtain a fractional Laplace inversion theorem after a short survey on fractional analysis based on the modified Riemann-Liouville derivative.

Fractional domain varying-order differential denoising method

NASA Astrophysics Data System (ADS)

Zhang, Yan-Shan; Zhang, Feng; Li, Bing-Zhao; Tao, Ran

2014-10-01

Removal of noise is an important step in the image restoration process, and it remains a challenging problem in image processing. Denoising is a process used to remove the noise from the corrupted image, while retaining the edges and other detailed features as much as possible. Recently, denoising in the fractional domain is a hot research topic. The fractional-order anisotropic diffusion method can bring a less blocky effect and preserve edges in image denoising, a method that has received much interest in the literature. Based on this method, we propose a new method for image denoising, in which fractional-varying-order differential, rather than constant-order differential, is used. The theoretical analysis and experimental results show that compared with the state-of-the-art fractional-order anisotropic diffusion method, the proposed fractional-varying-order differential denoising model can preserve structure and texture well, while quickly removing noise, and yields good visual effects and better peak signal-to-noise ratio.

Fractionating power and outlet stream polydispersity in asymmetrical flow field-flow fractionation. Part II: programmed operation.

PubMed

Williams, P Stephen

2017-01-01

Asymmetrical flow field-flow fractionation (As-FlFFF) is a widely used technique for analyzing polydisperse nanoparticle and macromolecular samples. The programmed decay of cross flow rate is often employed. The interdependence of the cross flow rate through the membrane and the fluid flow along the channel length complicates the prediction of elution time and fractionating power. The theory for their calculation is presented. It is also confirmed for examples of exponential decay of cross flow rate with constant channel outlet flow rate that the residual sample polydispersity at the channel outlet is quite well approximated by the reciprocal of four times the fractionating power. Residual polydispersity is of importance when online MALS or DLS detection are used to extract quantitative information on particle size or molecular weight. The theory presented here provides a firm basis for the optimization of programmed flow conditions in As-FlFFF. Graphical abstract Channel outlet polydispersity remains significant following fractionation by As-FlFFF under conditions of programmed decay of cross flow rate.

Role of Representation in Prospective Teachers' Fractions Schemes

ERIC Educational Resources Information Center

Boyce, Steven; Moss, Diana

2017-01-01

This research report explores relationships between fractions' task representations (discrete, rectangular, or circular) and elementary prospective teachers' (PTs) fractions conceptions. Studies show PTs' conceptions of fractions are centered on a part-whole understanding, which may be problematic when teaching children about improper fractions.…

The Whole Story: Understanding Fraction Computation

ERIC Educational Resources Information Center

Dixon, Juli K.; Tobias, Jennifer M.

2013-01-01

What does it look like to "understand" operations with fractions? The Common Core State Standards for Mathematics (CCSSM) uses the term "understand" when describing expectations for students' knowledge related to each of the fraction operations within grades 4 through 6 (CCSSI 2010). Furthermore, CCSSM elaborates that…

Fractionation of Mastic Gum in Relation to Antimicrobial Activity.

PubMed

Sharif Sharifi, Mohammad; Hazell, Stuart Loyd

2009-04-01

Mastic gum is a viscous light-green liquid obtained from the bark of Pistacia lentiscus var. chia. which belongs to the Anacardiaceae family. The gum has been fractionated to investigate the antimicrobial activity of the whole gum and its fractions against various strains of Helicobacter pylori. The polymeric gum fraction was separated from the essential oil and the resin (trunk exudates without essential oil) to assess and compare the anti-H. pylori activity of the polymer fraction against lower molecular weight fractions, the gum itself and masticated gum. The polymer fraction was also oxidized and assessed for antimicrobial activity.

Unpacking the Division Interpretation of a Fraction

ERIC Educational Resources Information Center

Poon, Rebecca C.; Lewis, Priscilla Eide

2015-01-01

One of the challenges in learning fractions is understanding how and why a fraction can have multiple interpretations. As presented in one textbook, a fraction is "a symbol, such as 2/3, 5/1, or 8/5, used to name a part of a whole, a part of a set, a location on a number line, or a division of whole numbers" (Charles et al. 2012, p.…

Equilibrium stable-isotope fractionation of thallium and mercury

NASA Astrophysics Data System (ADS)

Schauble, E. A.

2005-12-01

In this study first-principles quantum mechanical and empirical force-field models are used to estimate equilibrium mass-dependent isotopic fractionations among a variety of thallium and mercury compounds. High-precision MC-ICP-MS measurements have recently uncovered evidence of stable isotope fractionation for many elements, including 2-4‰ variability in the isotopic compositions of thallium[1] (atomic no. 81) and mercury[2] (atomic no. 80). The observed thallium- and mercury-isotope fractionations are remarkable, given that the magnitude of isotopic fractionation typically decreases as atomic number increases[3]. Stable isotope measurements could improve our understanding of geochemical and biogeochemical cycling of both elements, but little is known about the mechanisms driving these fractionations. A better understanding of the chemical processes controlling stable isotope compositions could help maximize the utility of these new geochemical tracers. Standard equilibrium stable isotope fractionation theory holds that the energy driving fractionation comes from isotopic effects on vibrational frequencies, which have generally not been measured. In the present study both quantum-mechanical and empirical force fields are used to estimate unknown frequencies. Results suggest that thallium and mercury fractionations of ≥ 0.5‰ are likely during the relevant redox reactions Tl+ ↔ Tl3+ and HgO ↔ Hg2+. Methyl-mercury and mercury-halide compounds like CH3HgCl will have ~ 1‰ higher 202Hg/198Hg than atomic vapor at room temperature. Fractionations between coexisting Hg2+ species appear to be much smaller, however. 205Tl/203Tl in Tl(H2O)_63+ is predicted to be ~0.5‰ higher than in coexisting Tl+-bearing substances. This result is in qualitative agreement with data from ferromanganese crusts [1], suggesting that Tl3+ in manganese-oxides will have higher 205Tl/203Tl than aqueous Tl+. Equilibrium fractionations for both elements are much smaller than the observed

Fermentation and dry fractionation increase bioactivity of cloudberry (Rubus chamaemorus).

PubMed

Puupponen-Pimiä, Riitta; Nohynek, Liisa; Juvonen, Riikka; Kössö, Tuija; Truchado, Pilar; Westerlund-Wikström, Benita; Leppänen, Tiina; Moilanen, Eeva; Oksman-Caldentey, Kirsi-Marja

2016-04-15

Phenolic composition and bioactivity of cloudberry was modified by bioprocessing, and highly bioactive fractions were produced by dry fractionation of the press cake. During fermentation polymeric ellagitannins were partly degraded into ellagic acid derivatives. Phenolic compounds were differentially distributed in seed coarse and fine fractions after dry fractionation process. Tannins concentrated in fine fraction, and flavonol derivatives were mainly found in coarse fraction. Ellagic acid derivatives were equally distributed between the dry fractions. Fermentation and dry fractionation increased statistically significantly anti-adhesion and anti-inflammatory activity of cloudberry. The seed fine fraction showed significant inhibition of P fimbria-mediated haemagglutination assay of uropathogenic Escherichia coli. The seed coarse fraction significantly reduced NO and IL-6 production and iNOS expression in activated macrophages. Fermentation did not affect antimicrobial activity, but slight increase in activity was detected in dry fractions. The results indicate the potential of cloudberry in pharma or health food applications. Copyright © 2015 Elsevier Ltd. All rights reserved.

Generalized Functions for the Fractional Calculus

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.; Hartley, Tom T.

1999-01-01

Previous papers have used two important functions for the solution of fractional order differential equations, the Mittag-Leffler functionE(sub q)[at(exp q)](1903a, 1903b, 1905), and the F-function F(sub q)[a,t] of Hartley & Lorenzo (1998). These functions provided direct solution and important understanding for the fundamental linear fractional order differential equation and for the related initial value problem (Hartley and Lorenzo, 1999). This paper examines related functions and their Laplace transforms. Presented for consideration are two generalized functions, the R-function and the G-function, useful in analysis and as a basis for computation in the fractional calculus. The R-function is unique in that it contains all of the derivatives and integrals of the F-function. The R-function also returns itself on qth order differ-integration. An example application of the R-function is provided. A further generalization of the R-function, called the G-function brings in the effects of repeated and partially repeated fractional poles.

Tunneling time in space fractional quantum mechanics

NASA Astrophysics Data System (ADS)

Hasan, Mohammad; Mandal, Bhabani Prasad

2018-02-01

We calculate the time taken by a wave packet to travel through a classically forbidden region of space in space fractional quantum mechanics. We obtain the close form expression of tunneling time from a rectangular barrier by stationary phase method. We show that tunneling time depends upon the width b of the barrier for b → ∞ and therefore Hartman effect doesn't exist in space fractional quantum mechanics. Interestingly we found that the tunneling time monotonically reduces with increasing b. The tunneling time is smaller in space fractional quantum mechanics as compared to the case of standard quantum mechanics. We recover the Hartman effect of standard quantum mechanics as a special case of space fractional quantum mechanics.

Making Sense of Fractions and Percentages

ERIC Educational Resources Information Center

Whitin, David J.; Whitin, Phyllis

2012-01-01

Because fractions and percentages can be difficult for children to grasp, connecting them whenever possible is beneficial. Linking them can foster representational fluency as children simultaneously see the part-whole relationship expressed numerically (as a fraction and as a percentage) and visually (as a pie chart). NCTM advocates these…

Mathematical Knowledge for Teaching Fraction Multiplication

ERIC Educational Resources Information Center

Izsak, Andrew

2008-01-01

The present study contrasts mathematical knowledge that two sixth-grade teachers apparently used when teaching fraction multiplication with the Connected Mathematics Project materials. The analysis concentrated on those tasks from the materials that use drawings to represent fractions as length or area quantities. Examining the two teachers'…

Octree Bin-to-Bin Fractional-NTC Collisions

DTIC Science & Technology

2015-09-17

Briefing Charts 3. DATES COVERED (From - To) 24 August 2015 – 17 September 2015 4. TITLE AND SUBTITLE Octree bin-to-bin fractional -NTC collisions...Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std. 239.18 OCTREE BIN-TO-BIN FRACTIONAL -NTC COLLISIONS Robert Martin ERC INC., SPACECRAFT PROPULSION...AFTC/PA clearance No. TBD ROBERT MARTIN (AFRL/RQRS) DISTRIBUTION A: APPROVED FOR PUBLIC RELEASE 1 / 15 OUTLINE 1 BACKGROUND 2 FRACTIONAL COLLISIONS 3 BIN

Assessing Students' Understanding of Fraction Multiplication

ERIC Educational Resources Information Center

Rumsey, Chepina; Guarino, Jody; Beltramini, Jennie; Cole, Shelbi; Farmer, Alicia; Gray, Kristin; Saxby, Morgan

2016-01-01

In this article the authors describe a project during which they unpacked fraction standards, created rigorous tasks and lesson plans, and developed formative and summative assessments to analyze students' thinking about fraction multiplication. The purpose of this article is to (1) illustrate a process that can be replicated by educators…

Fractions: A New Slant on Slope

ERIC Educational Resources Information Center

Cheng, Ivan

2010-01-01

An understanding of fractions is foundational to proportional reasoning and algebra. For example, a direct-variation relationship may include a constant of proportionality that is rational, and linear equations may have solutions that are fractions. Beyond that, a grasp of the concept of proportionality and of rational numbers is necessary for…

Developmental and Individual Differences in Understanding of Fractions

PubMed Central

Siegler, Robert S.; Pyke, Aryn A.

2014-01-01

We examined developmental and individual differences in 6th and 8th graders’ fraction arithmetic and overall mathematics achievement and related them to differences in understanding of fraction magnitudes, whole number division, executive functioning, and metacognitive judgments within a cross sectional design. Results indicated that the difference between low achieving and higher achieving children’s fraction arithmetic knowledge, already substantial in 6th grade, was much greater in 8th grade. The fraction arithmetic knowledge of low achieving children was similar in the two grades, whereas higher achieving children showed much greater knowledge in 8th than 6th grade, despite both groups having been in the same classrooms, using the same textbooks, and having the same teachers and classmates. Individual differences in both fraction arithmetic and mathematics achievement test scores were predicted by differences in fraction magnitude knowledge and whole number division, even after the contributions of reading achievement and executive functioning were statistically controlled. Instructional implications of the findings are discussed. PMID:23244401

Extraction, fractionation and re-fractionation of Artemisia nilagirica for anticancer activity and HPLC-ESI-QTOF-MS/MS determination.

PubMed

Sahu, Neha; Meena, Sanjeev; Shukla, Vijaya; Chaturvedi, Priyank; Kumar, Brijesh; Datta, Dipak; Arya, K R

2018-03-01

Medicinal plants used in traditional medicines are affordable, easily accessible, safer, less toxic and considered as a rich or efficient source of bioactive molecules for modern therapeutics. Artemisia nilagirica (AR) has a long history of use in Indian traditional medicine to combat a wide variety of diseases including cancer. Considering the vast potential of traditional healing plants to deliver safer, less toxic and efficient chemotherapeutics, we have examined anticancer activity of ethanolic extract, bioactive fractions and sub-fractions of AR against different human cancer cell lines along with their phytochemical analysis to understand the insights of novel anticancer activities for further preclinical studies. Fresh plant material of AR was procured from the wild, dried and ground. The grinded materials was extracted in ethanol (AR-01) and fractionated into butanol (AR-02), ethyl acetate (AR-03), hexane (AR-04) and water (AR-05). The cytotoxicity was evaluated against three different human cancer cell lines, i.e. colon (DLD-1), lung (A-549), and breast (MCF-7) using Sulforhodamine B (SRB) assay along with non-cancerous VERO cells as control and doxorubicin (DOX) as positive control. As we observed strong cytotoxicity of AR-03 and AR-04 fractions against tested cells and marked cytotoxic effects particularly in colon cancer cell lines, we further re-fractionated, AR-03 into (AR-03A, AR-03B, AR-03C, AR-03D, AR-03E) and AR-04 into (AR-04A, AR-04B, AR-04C) sub-fractions by column chromatography and investigated against the same panel of cell lines in addition to one more colon cancer cell line (HT-29). Phytochemical analysis was performed through HPLC-ESI-QTOF-MS/MS fragmentation. Ethyl acetate (AR-03) and hexane (AR-04) fractions were found to be the most cytotoxic against all the tested cell lines. Further, AR-03E and AR-04A sub-fractions were found more specific cytotoxic selectively against DLD-1 cancer cell lines at 100µg/ml concentration. HPLC

Fraction Flags: Learning from Children to Help Children Learn.

ERIC Educational Resources Information Center

Kieren, Tom; And Others

1996-01-01

Describes "fraction flags", an activity through which fraction concepts can be explored. The activity was invented by 2 12-year-old students and this article is presented with emphasis on the students' viewpoint. It begins with an overview of the fractions unit and presents vignettes of students exploring the fraction flags. (AIM)

7 CFR 1405.2 - Basic rule of fractions.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 10 2010-01-01 2010-01-01 false Basic rule of fractions. 1405.2 Section 1405.2 Agriculture Regulations of the Department of Agriculture (Continued) COMMODITY CREDIT CORPORATION, DEPARTMENT... rule of fractions. Fractions shall be rounded in accordance with the provisions of 7 CFR part 718. ...

Students' Conceptions of Models of Fractions and Equivalence

ERIC Educational Resources Information Center

Jigyel, Karma; Afamasaga-Fuata'i, Karoline

2007-01-01

A solid understanding of equivalent fractions is considered a steppingstone towards a better understanding of operations with fractions. In this article, 55 rural Australian students' conceptions of equivalent fractions are presented. Data collected included students' responses to a short written test and follow-up interviews with three students…

Prospective Elementary Teachers' Development of Fraction Number Sense

ERIC Educational Resources Information Center

Utley, Juliana; Reeder, Stacy

2012-01-01

Can prospective elementary teachers "unlearn" harmful algorithms used with fractions as they are invited to develop fraction number sense? This study examined the development of prospective elementary teachers' fraction number sense during an intermediate (grades 5-8) mathematics methods course. During this course, participants' were involved in a…

Development of fraction comparison strategies: A latent transition analysis.

PubMed

Rinne, Luke F; Ye, Ai; Jordan, Nancy C

2017-04-01

The present study investigated the development of fraction comparison strategies through a longitudinal analysis of children's responses to a fraction comparison task in 4th through 6th grades (N = 394). Participants were asked to choose the larger value for 24 fraction pairs blocked by fraction type. Latent class analysis of performance over item blocks showed that most children initially exhibited a "whole number bias," indicating that larger numbers in numerators and denominators produce larger fraction values. However, some children instead chose fractions with smaller numerators and denominators, demonstrating a partial understanding that smaller numbers can yield larger fractions. Latent transition analysis showed that most children eventually adopted normative comparison strategies. Children who exhibited a partial understanding by choosing fractions with smaller numbers were more likely to adopt normative comparison strategies earlier than those with larger number biases. Controlling for general math achievement and other cognitive abilities, whole number line estimation accuracy predicted the probability of transitioning to normative comparison strategies. Exploratory factor analyses showed that over time, children appeared to increasingly represent fractions as discrete magnitudes when simpler strategies were unavailable. These results support the integrated theory of numerical development, which posits that an understanding of numbers as magnitudes unifies the process of learning whole numbers and fractions. The findings contrast with conceptual change theories, which propose that children must move from a view of numbers as counting units to a new view that accommodates fractions to overcome whole number bias. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Early Predictors of Middle School Fraction Knowledge

PubMed Central

Bailey, Drew H.; Siegler, Robert S.; Geary, David C.

2014-01-01

Recent findings that earlier fraction knowledge predicts later mathematics achievement raise the question of what predicts later fraction knowledge. Analyses of longitudinal data indicated that whole number magnitude knowledge in first grade predicted knowledge of fraction magnitudes in middle school, controlling for whole number arithmetic proficiency, domain general cognitive abilities, parental income and education, race, and gender. Similarly, knowledge of whole number arithmetic in first grade predicted knowledge of fraction arithmetic in middle school, controlling for whole number magnitude knowledge in first grade and the other control variables. In contrast, neither type of early whole number knowledge uniquely predicted middle school reading achievement. We discuss the implications of these findings for theories of numerical development and for improving mathematics learning. PMID:24576209

On the origins of generalized fractional calculus

NASA Astrophysics Data System (ADS)

Kiryakova, Virginia

2015-11-01

In Fractional Calculus (FC), as in the (classical) Calculus, the notions of derivatives and integrals (of first, second, etc. or arbitrary, incl. non-integer order) are basic and co-related. One of the most frequent approach in FC is to define first the Riemann-Liouville (R-L) integral of fractional order, and then by means of suitable integer-order differentiation operation applied over it (or under its sign) a fractional derivative is defined - in the R-L sense (or in Caputo sense). The first mentioned (R-L type) is closer to the theoretical studies in analysis, but has some shortages - from the point of view of interpretation of the initial conditions for Cauchy problems for fractional differential equations (stated also by means of fractional order derivatives/ integrals), and also for the analysts' confusion that such a derivative of a constant is not zero in general. The Caputo (C-) derivative, arising first in geophysical studies, helps to overcome these problems and to describe models of applied problems with physically consistent initial conditions. The operators of the Generalized Fractional Calculus - GFC (integrals and derivatives) are based on commuting m-tuple (m = 1, 2, 3, …) compositions of operators of the classical FC with power weights (the so-called Erdélyi-Kober operators), but represented in compact and explicit form by means of integral, integro-differential (R-L type) or differential-integral (C-type) operators, where the kernels are special functions of most general hypergeometric kind. The foundations of this theory are given in Kiryakova 18. In this survey we present the genesis of the definitions of the GFC - the generalized fractional integrals and derivatives (of fractional multi-order) of R-L type and Caputo type, analyze their properties and applications. Their special cases are all the known operators of classical FC, their generalizations introduced by other authors, the hyper-Bessel differential operators of higher integer

Three-dimensional fractional-spin gravity

NASA Astrophysics Data System (ADS)

Boulanger, Nicolas; Sundell, Per; Valenzuela, Mauricio

2014-02-01

Using Wigner-deformed Heisenberg oscillators, we construct 3D Chern-Simons models consisting of fractional-spin fields coupled to higher-spin gravity and internal nonabelian gauge fields. The gauge algebras consist of Lorentz-tensorial Blencowe-Vasiliev higher-spin algebras and compact internal algebras intertwined by infinite-dimensional generators in lowest-weight representations of the Lorentz algebra with fractional spin. In integer or half-integer non-unitary cases, there exist truncations to gl(ℓ , ℓ ± 1) or gl(ℓ|ℓ ± 1) models. In all non-unitary cases, the internal gauge fields can be set to zero. At the semi-classical level, the fractional-spin fields are either Grassmann even or odd. The action requires the enveloping-algebra representation of the deformed oscillators, while their Fock-space representation suffices on-shell. The project was funded in part by F.R.S.-FNRS " Ulysse" Incentive Grant for Mobility in Scientific Research.

Measuring memory with the order of fractional derivative

NASA Astrophysics Data System (ADS)

Du, Maolin; Wang, Zaihua; Hu, Haiyan

2013-12-01

Fractional derivative has a history as long as that of classical calculus, but it is much less popular than it should be. What is the physical meaning of fractional derivative? This is still an open problem. In modeling various memory phenomena, we observe that a memory process usually consists of two stages. One is short with permanent retention, and the other is governed by a simple model of fractional derivative. With the numerical least square method, we show that the fractional model perfectly fits the test data of memory phenomena in different disciplines, not only in mechanics, but also in biology and psychology. Based on this model, we find that a physical meaning of the fractional order is an index of memory.

A Computational Model of Fraction Arithmetic

ERIC Educational Resources Information Center

Braithwaite, David W.; Pyke, Aryn A.; Siegler, Robert S.

2017-01-01

Many children fail to master fraction arithmetic even after years of instruction, a failure that hinders their learning of more advanced mathematics as well as their occupational success. To test hypotheses about why children have so many difficulties in this area, we created a computational model of fraction arithmetic learning and presented it…

In Search of the Prototypical Fraction

ERIC Educational Resources Information Center

Wright, Vince

2013-01-01

Vince Wright makes a convincing argument for presenting children with a different "prototype" of a fraction to the typical one-half. Consider how the prototype that Wright mentions may be applied to a variety of fraction concepts. We are sure that you will never look at a doughnut in quite the same way.

Analysis of Drude model using fractional derivatives without singular kernels

NASA Astrophysics Data System (ADS)

Jiménez, Leonardo Martínez; García, J. Juan Rosales; Contreras, Abraham Ortega; Baleanu, Dumitru

2017-11-01

We report study exploring the fractional Drude model in the time domain, using fractional derivatives without singular kernels, Caputo-Fabrizio (CF), and fractional derivatives with a stretched Mittag-Leffler function. It is shown that the velocity and current density of electrons moving through a metal depend on both the time and the fractional order 0 < γ ≤ 1. Due to non-singular fractional kernels, it is possible to consider complete memory effects in the model, which appear neither in the ordinary model, nor in the fractional Drude model with Caputo fractional derivative. A comparison is also made between these two representations of the fractional derivatives, resulting a considered difference when γ < 0.8.

Development of Fraction Comparison Strategies: A Latent Transition Analysis

ERIC Educational Resources Information Center

Rinne, Luke F.; Ye, Ai; Jordan, Nancy C.

2017-01-01

The present study investigated the development of fraction comparison strategies through a longitudinal analysis of children's responses to a fraction comparison task in 4th through 6th grades (N = 394). Participants were asked to choose the larger value for 24 fraction pairs blocked by fraction type. Latent class analysis of performance over item…

Developing Children's Understanding of Fractions: An Intervention Study

ERIC Educational Resources Information Center

Gabriel, Florence; Coche, Frederic; Szucs, Denes; Carette, Vincent; Rey, Bernard; Content, Alain

2012-01-01

Fractions constitute a stumbling block in mathematics education. To improve children's understanding of fractions, we designed an intervention based on learning-by-doing activities, which focused on the representation of the magnitude of fractions. Participants were 292 Grade 4 and 5 children. Half of the classes received experimental instruction,…

Foam Fractionation of Lycopene: An Undergraduate Chemistry Experiment

ERIC Educational Resources Information Center

Wang, Yan; Zhang, Mingjie; Hu, Yongliang

2010-01-01

A novel experiment for the extraction of lycopene from tomato paste by foam fractionation is described. Foam fractionation is a process for separating and concentrating chemicals by utilizing differences in their surface activities. Extraction of lycopene by foam fractionation is a new method that has not been previously reported in the…

A Comparison of Textbooks' Presentation of Fractions

ERIC Educational Resources Information Center

Cady, Jo A.; Hodges, Thomas E.; Collins, R. Lee

2015-01-01

In the United States, fractions are an important part of the middle school curriculum, yet many middle school students struggle with fraction concepts. Teachers also have difficulty with the conceptual understanding needed to teach fractions and rely on textbooks when making instructional decisions. This reliance on textbooks, the idea that…

Isotopic fractionation of tritium in biological systems.

PubMed

Le Goff, Pierre; Fromm, Michel; Vichot, Laurent; Badot, Pierre-Marie; Guétat, Philippe

2014-04-01

Isotopic fractionation of tritium is a highly relevant issue in radiation protection and requires certain radioecological considerations. Sound evaluation of this factor is indeed necessary to determine whether environmental compartments are enriched/depleted in tritium or if tritium is, on the contrary, isotopically well-distributed in a given system. The ubiquity of tritium and the standard analytical methods used to assay it may induce biases in both the measurement and the signification that is accorded to the so-called fractionation: based on an exhaustive review of the literature, we show how, sometimes large deviations may appear. It is shown that when comparing the non-exchangeable fraction of organically bound tritium (neOBT) to another fraction of tritium (e.g. tritiated water) the preparation of samples and the measurement of neOBT reported frequently led to underestimation of the ratio of tritium to hydrogen (T/H) in the non-exchangeable compartment by a factor of 5% to 50%. In the present study, corrections are proposed for most of the biological matrices studied so far. Nevertheless, the values of isotopic fractionation reported in the literature remain difficult to compare with each other, especially since the physical quantities and units often vary between authors. Some improvements are proposed to better define what should encompass the concepts of exchangeable and non-exchangeable fractions. Copyright © 2014 Elsevier Ltd. All rights reserved.

Paper Plate Fractions: The Counting Connection

ERIC Educational Resources Information Center

McCoy, Ann; Barnett, Joann; Stine, Tammy

2016-01-01

Without a doubt, fractions prove to be a stumbling block for many children. Researchers have suggested a variety of explanations for why this is the case. The introduction of symbolization and operations before the development of conceptual understanding of fractions, a lack of understanding of the role of the numerator and denominator, and an…

5 CFR 551.521 - Fractional hours of work.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 5 Administrative Personnel 1 2010-01-01 2010-01-01 false Fractional hours of work. 551.521 Section... ADMINISTRATION UNDER THE FAIR LABOR STANDARDS ACT Overtime Pay Provisions Fractional Hours of Work § 551.521 Fractional hours of work. (a) An employee shall be compensated for every minute of regular overtime work. (b...

5 CFR 551.521 - Fractional hours of work.

Code of Federal Regulations, 2011 CFR

2011-01-01

... 5 Administrative Personnel 1 2011-01-01 2011-01-01 false Fractional hours of work. 551.521 Section... ADMINISTRATION UNDER THE FAIR LABOR STANDARDS ACT Overtime Pay Provisions Fractional Hours of Work § 551.521 Fractional hours of work. (a) An employee shall be compensated for every minute of regular overtime work. (b...

38 CFR 3.112 - Fractions of one cent.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 38 Pensions, Bonuses, and Veterans' Relief 1 2010-07-01 2010-07-01 false Fractions of one cent. 3... Pension, Compensation, and Dependency and Indemnity Compensation Administrative § 3.112 Fractions of one cent. In all cases where the amount to be paid under any award involves a fraction of a cent, the...

Posing Problems to Understand Children's Learning of Fractions

ERIC Educational Resources Information Center

Cheng, Lu Pien

2013-01-01

In this study, ways in which problem posing activities aid our understanding of children's learning of addition of unlike fractions and product of proper fractions was examined. In particular, how a simple problem posing activity helps teachers take a second, deeper look at children's understanding of fraction concepts will be discussed. The…

21 CFR 640.90 - Plasma Protein Fraction (Human).

Code of Federal Regulations, 2010 CFR

2010-04-01

... 21 Food and Drugs 7 2010-04-01 2010-04-01 false Plasma Protein Fraction (Human). 640.90 Section...) BIOLOGICS ADDITIONAL STANDARDS FOR HUMAN BLOOD AND BLOOD PRODUCTS Plasma Protein Fraction (Human) § 640.90 Plasma Protein Fraction (Human). (a) Proper name and definition. The proper name of the product shall be...

21 CFR 640.90 - Plasma Protein Fraction (Human).

Code of Federal Regulations, 2012 CFR

2012-04-01

... 21 Food and Drugs 7 2012-04-01 2012-04-01 false Plasma Protein Fraction (Human). 640.90 Section...) BIOLOGICS ADDITIONAL STANDARDS FOR HUMAN BLOOD AND BLOOD PRODUCTS Plasma Protein Fraction (Human) § 640.90 Plasma Protein Fraction (Human). (a) Proper name and definition. The proper name of the product shall be...

21 CFR 640.90 - Plasma Protein Fraction (Human).

Code of Federal Regulations, 2011 CFR

2011-04-01

... 21 Food and Drugs 7 2011-04-01 2010-04-01 true Plasma Protein Fraction (Human). 640.90 Section 640...) BIOLOGICS ADDITIONAL STANDARDS FOR HUMAN BLOOD AND BLOOD PRODUCTS Plasma Protein Fraction (Human) § 640.90 Plasma Protein Fraction (Human). (a) Proper name and definition. The proper name of the product shall be...

21 CFR 640.90 - Plasma Protein Fraction (Human).

Code of Federal Regulations, 2013 CFR

2013-04-01

... 21 Food and Drugs 7 2013-04-01 2013-04-01 false Plasma Protein Fraction (Human). 640.90 Section...) BIOLOGICS ADDITIONAL STANDARDS FOR HUMAN BLOOD AND BLOOD PRODUCTS Plasma Protein Fraction (Human) § 640.90 Plasma Protein Fraction (Human). (a) Proper name and definition. The proper name of the product shall be...

21 CFR 640.90 - Plasma Protein Fraction (Human).

Code of Federal Regulations, 2014 CFR

2014-04-01

... 21 Food and Drugs 7 2014-04-01 2014-04-01 false Plasma Protein Fraction (Human). 640.90 Section...) BIOLOGICS ADDITIONAL STANDARDS FOR HUMAN BLOOD AND BLOOD PRODUCTS Plasma Protein Fraction (Human) § 640.90 Plasma Protein Fraction (Human). (a) Proper name and definition. The proper name of the product shall be...

The True Ultracool Binary Fraction Using Spectral Binaries

NASA Astrophysics Data System (ADS)

Bardalez Gagliuffi, Daniella; Burgasser, Adam J.; Schmidt, Sarah J.; Gagné, Jonathan; Faherty, Jacqueline K.; Cruz, Kelle; Gelino, Chris

2018-01-01

Brown dwarfs bridge the gap between stars and giant planets. While the essential mechanisms governing their formation are not well constrained, binary statistics are a direct outcome of the formation process, and thus provide a means to test formation theories. Observational constraints on the brown dwarf binary fraction place it at 10 ‑ 20%, dominated by imaging studies (85% of systems) with the most common separation at 4 AU. This coincides with the resolution limit of state-of-the-art imaging techniques, suggesting that the binary fraction is underestimated. We have developed a separation-independent method to identify and characterize tightly-separated (< 5 AU) binary systems of brown dwarfs as spectral binaries by identifying traces of methane in the spectra of late-M and early-L dwarfs. Imaging follow-up of 17 spectral binaries yielded 3 (18%) resolved systems, corroborating the observed binary fraction, but 5 (29%) known binaries were missed, reinforcing the hypothesis that the short-separation systems are undercounted. In order to find the true binary fraction of brown dwarfs, we have compiled a volume-limited, spectroscopic sample of M7-L5 dwarfs and searched for T dwarf companions. In the 25 pc volume, 4 candidates were found, three of which are already confirmed, leading to a spectral binary fraction of 0.95 ± 0.50%, albeit for a specific combination of spectral types. To extract the true binary fraction and determine the biases of the spectral binary method, we have produced a binary population simulation based on different assumptions of the mass function, age distribution, evolutionary models and mass ratio distribution. Applying the correction fraction resulting from this method to the observed spectral binary fraction yields a true binary fraction of 27 ± 4%, which is roughly within 1σ of the binary fraction obtained from high resolution imaging studies, radial velocity and astrometric monitoring. This method can be extended to identify giant

Fractional Progress Toward Understanding the Fractional Diffusion Limit: The Electromagnetic Response of Spatially Correlated Geomaterials

NASA Astrophysics Data System (ADS)

Weiss, C. J.; Beskardes, G. D.; Everett, M. E.

2016-12-01

In this presentation we review the observational evidence for anomalous electromagnetic diffusion in near-surface geophysical exploration and how such evidence is consistent with a detailed, spatially-correlated geologic medium. To date, the inference of multi-scale geologic correlation is drawn from two independent methods of data analysis. The first of which is analogous to seismic move-out, where the arrival time of an electromagnetic pulse is plotted as a function of transmitter/receiver separation. The "anomalous" diffusion is evident by the fractional-order power law behavior of these arrival times, with an exponent value between unity (pure diffusion) and 2 (lossless wave propagation). The second line of evidence comes from spectral analysis of small-scale fluctuations in electromagnetic profile data which cannot be explained in terms of instrument, user or random error. Rather, the power-law behavior of the spectral content of these signals (i.e., power versus wavenumber) and their increments reveals them to lie in a class of signals with correlations over multiple length scales, a class of signals known formally as fractional Brownian motion. Numerical results over simulated geology with correlated electrical texture - representative of, for example, fractures, sedimentary bedding or metamorphic lineation - are consistent with the (albeit limited, but growing) observational data, suggesting a possible mechanism and modeling approach for a more realistic geology. Furthermore, we show how similar simulated results can arise from a modeling approach where geologic texture is economically captured by a modified diffusion equation containing exotic, but manageable, fractional derivatives. These derivatives arise physically from the generalized convolutional form for the electromagnetic constitutive laws and thus have merit beyond mere mathematical convenience. In short, we are zeroing in on the anomalous, fractional diffusion limit from two converging

Isotope Fractionation in the Interstellar Medium

NASA Technical Reports Server (NTRS)

Charnley, Steven

2011-01-01

Anomalously fractionated isotopic material is found in many primitive Solar System objects, such as meteorites and comets. It is thought, in some cases, to trace interstellar matter that was incorporated into the Solar Nebula without undergoing significant processing. We will present the results of models of the nitrogen, oxygen, and carbon fractionation chemistry in dense molecular clouds, particularly in cores where substantial freeze-out of molecules on to dust has occurred. The range of fractionation ratios expected in different interstellar molecules will be discussed and compared to the ratios measured in molecular clouds, comets and meteoritic material. These models make several predictions that can be tested in the near future by molecular line observations, particularly with ALMA.

Sampling Martian Soil (3-D)

NASA Technical Reports Server (NTRS)

2004-01-01

[figure removed for brevity, see original site] [figure removed for brevity, see original site] Figure 1Figure 2

Scientists were using the Moessbauer spectrometer on NASA's Mars Exploration Rover Spirit when something unexpected happened. The instrument's contact ring had been placed onto the ground as a reference point for placement of another instrument, the alpha particle X-ray spectrometer, for analyzing the soil. After Spirit removed the Moessbauer from the target, the rover's microscopic imager revealed a gap in the imprint left behind in the soil. The gap, about a centimeter wide (less than half an inch), is visible on the left side of this stereo view. Scientists concluded that a small chunk of soil probably adhered to the contact ring on the front surface of the Moessbauer. Before anyone saw that soil may have adhered to the Moessbauer, that instrument was placed to analyze martian dust collected by a magnet on the rover. The team plans to take images to see if any soil is still attached to the Moessbauer. Spirit took these images on the rover's 240th martian day, or sol (Sept. 4, 2004).

Figure 1 is the left-eye view of a stereo pair and Figure 2 is the right-eye view of a stereo pair.

Estimation's Role in Calculations with Fractions

ERIC Educational Resources Information Center

Johanning, Debra I.

2011-01-01

Estimation is more than a skill or an isolated topic. It is a thinking tool that needs to be emphasized during instruction so that students will learn to develop algorithmic procedures and meaning for fraction operations. For students to realize when fractions should be added, subtracted, multiplied, or divided, they need to develop a sense of…

Exp-function method for solving fractional partial differential equations.

PubMed

Zheng, Bin

2013-01-01

We extend the Exp-function method to fractional partial differential equations in the sense of modified Riemann-Liouville derivative based on nonlinear fractional complex transformation. For illustrating the validity of this method, we apply it to the space-time fractional Fokas equation and the nonlinear fractional Sharma-Tasso-Olver (STO) equation. As a result, some new exact solutions for them are successfully established.

Binary Star Fractions from the LAMOST DR4

NASA Astrophysics Data System (ADS)

Tian, Zhi-Jia; Liu, Xiao-Wei; Yuan, Hai-Bo; Chen, Bing-Qiu; Xiang, Mao-Sheng; Huang, Yang; Wang, Chun; Zhang, Hua-Wei; Guo, Jin-Cheng; Ren, Juan-Juan; Huo, Zhi-Ying; Yang, Yong; Zhang, Meng; Bi, Shao-Lan; Yang, Wu-Ming; Liu, Kang; Zhang, Xian-Fei; Li, Tan-Da; Wu, Ya-Qian; Zhang, Jing-Hua

2018-05-01

Stellar systems composed of single, double, triple or higher-order systems are rightfully regarded as the fundamental building blocks of the Milky Way. Binary stars play an important role in formation and evolution of the Galaxy. Through comparing the radial velocity variations from multi-epoch observations, we analyze the binary fraction of dwarf stars observed with LAMOST. Effects of different model assumptions, such as orbital period distributions on the estimate of binary fractions, are investigated. The results based on log-normal distribution of orbital periods reproduce the previous complete analyses better than the power-law distribution. We find that the binary fraction increases with T eff and decreases with [Fe/H]. We first investigate the relation between α-elements and binary fraction in such a large sample as provided by LAMOST. The old stars with high [α/Fe] dominate with a higher binary fraction than young stars with low [α/Fe]. At the same mass, earlier forming stars possess a higher binary fraction than newly forming ones, which may be related with evolution of the Galaxy.

A componential view of children's difficulties in learning fractions.

PubMed

Gabriel, Florence; Coché, Frédéric; Szucs, Dénes; Carette, Vincent; Rey, Bernard; Content, Alain

2013-01-01

Fractions are well known to be difficult to learn. Various hypotheses have been proposed in order to explain those difficulties: fractions can denote different concepts; their understanding requires a conceptual reorganization with regard to natural numbers; and using fractions involves the articulation of conceptual knowledge with complex manipulation of procedures. In order to encompass the major aspects of knowledge about fractions, we propose to distinguish between conceptual and procedural knowledge. We designed a test aimed at assessing the main components of fraction knowledge. The test was carried out by fourth-, fifth- and sixth-graders from the French Community of Belgium. The results showed large differences between categories. Pupils seemed to master the part-whole concept, whereas numbers and operations posed problems. Moreover, pupils seemed to apply procedures they do not fully understand. Our results offer further directions to explain why fractions are amongst the most difficult mathematical topics in primary education. This study offers a number of recommendations on how to teach fractions.

A componential view of children's difficulties in learning fractions

PubMed Central

Gabriel, Florence; Coché, Frédéric; Szucs, Dénes; Carette, Vincent; Rey, Bernard; Content, Alain

2013-01-01

Fractions are well known to be difficult to learn. Various hypotheses have been proposed in order to explain those difficulties: fractions can denote different concepts; their understanding requires a conceptual reorganization with regard to natural numbers; and using fractions involves the articulation of conceptual knowledge with complex manipulation of procedures. In order to encompass the major aspects of knowledge about fractions, we propose to distinguish between conceptual and procedural knowledge. We designed a test aimed at assessing the main components of fraction knowledge. The test was carried out by fourth-, fifth- and sixth-graders from the French Community of Belgium. The results showed large differences between categories. Pupils seemed to master the part-whole concept, whereas numbers and operations posed problems. Moreover, pupils seemed to apply procedures they do not fully understand. Our results offer further directions to explain why fractions are amongst the most difficult mathematical topics in primary education. This study offers a number of recommendations on how to teach fractions. PMID:24133471

Fractional-order difference equations for physical lattices and some applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru

2015-10-15

Fractional-order operators for physical lattice models based on the Grünwald-Letnikov fractional differences are suggested. We use an approach based on the models of lattices with long-range particle interactions. The fractional-order operators of differentiation and integration on physical lattices are represented by kernels of lattice long-range interactions. In continuum limit, these discrete operators of non-integer orders give the fractional-order derivatives and integrals with respect to coordinates of the Grünwald-Letnikov types. As examples of the fractional-order difference equations for physical lattices, we give difference analogs of the fractional nonlocal Navier-Stokes equations and the fractional nonlocal Maxwell equations for lattices with long-range interactions.more » Continuum limits of these fractional-order difference equations are also suggested.« less

Heterogeneous fractionation profiles of meta-analytic coactivation networks.

PubMed

Laird, Angela R; Riedel, Michael C; Okoe, Mershack; Jianu, Radu; Ray, Kimberly L; Eickhoff, Simon B; Smith, Stephen M; Fox, Peter T; Sutherland, Matthew T

2017-04-01

Computational cognitive neuroimaging approaches can be leveraged to characterize the hierarchical organization of distributed, functionally specialized networks in the human brain. To this end, we performed large-scale mining across the BrainMap database of coordinate-based activation locations from over 10,000 task-based experiments. Meta-analytic coactivation networks were identified by jointly applying independent component analysis (ICA) and meta-analytic connectivity modeling (MACM) across a wide range of model orders (i.e., d=20-300). We then iteratively computed pairwise correlation coefficients for consecutive model orders to compare spatial network topologies, ultimately yielding fractionation profiles delineating how "parent" functional brain systems decompose into constituent "child" sub-networks. Fractionation profiles differed dramatically across canonical networks: some exhibited complex and extensive fractionation into a large number of sub-networks across the full range of model orders, whereas others exhibited little to no decomposition as model order increased. Hierarchical clustering was applied to evaluate this heterogeneity, yielding three distinct groups of network fractionation profiles: high, moderate, and low fractionation. BrainMap-based functional decoding of resultant coactivation networks revealed a multi-domain association regardless of fractionation complexity. Rather than emphasize a cognitive-motor-perceptual gradient, these outcomes suggest the importance of inter-lobar connectivity in functional brain organization. We conclude that high fractionation networks are complex and comprised of many constituent sub-networks reflecting long-range, inter-lobar connectivity, particularly in fronto-parietal regions. In contrast, low fractionation networks may reflect persistent and stable networks that are more internally coherent and exhibit reduced inter-lobar communication. Copyright © 2017 Elsevier Inc. All rights reserved.

Heterogeneous fractionation profiles of meta-analytic coactivation networks

PubMed Central

Laird, Angela R.; Riedel, Michael C.; Okoe, Mershack; Jianu, Radu; Ray, Kimberly L.; Eickhoff, Simon B.; Smith, Stephen M.; Fox, Peter T.; Sutherland, Matthew T.

2017-01-01

Computational cognitive neuroimaging approaches can be leveraged to characterize the hierarchical organization of distributed, functionally specialized networks in the human brain. To this end, we performed large-scale mining across the BrainMap database of coordinate-based activation locations from over 10,000 task-based experiments. Meta-analytic coactivation networks were identified by jointly applying independent component analysis (ICA) and meta-analytic connectivity modeling (MACM) across a wide range of model orders (i.e., d = 20 to 300). We then iteratively computed pairwise correlation coefficients for consecutive model orders to compare spatial network topologies, ultimately yielding fractionation profiles delineating how “parent” functional brain systems decompose into constituent “child” sub-networks. Fractionation profiles differed dramatically across canonical networks: some exhibited complex and extensive fractionation into a large number of sub-networks across the full range of model orders, whereas others exhibited little to no decomposition as model order increased. Hierarchical clustering was applied to evaluate this heterogeneity, yielding three distinct groups of network fractionation profiles: high, moderate, and low fractionation. BrainMap-based functional decoding of resultant coactivation networks revealed a multi-domain association regardless of fractionation complexity. Rather than emphasize a cognitive-motor-perceptual gradient, these outcomes suggest the importance of inter-lobar connectivity in functional brain organization. We conclude that high fractionation networks are complex and comprised of many constituent sub-networks reflecting long-range, inter-lobar connectivity, particularly in fronto-parietal regions. In contrast, low fractionation networks may reflect persistent and stable networks that are more internally coherent and exhibit reduced inter-lobar communication. PMID:28222386

Numerical analysis for the fractional diffusion and fractional Buckmaster equation by the two-step Laplace Adam-Bashforth method

NASA Astrophysics Data System (ADS)

Jain, Sonal

2018-01-01

In this paper, we aim to use the alternative numerical scheme given by Gnitchogna and Atangana for solving partial differential equations with integer and non-integer differential operators. We applied this method to fractional diffusion model and fractional Buckmaster models with non-local fading memory. The method yields a powerful numerical algorithm for fractional order derivative to implement. Also we present in detail the stability analysis of the numerical method for solving the diffusion equation. This proof shows that this method is very stable and also converges very quickly to exact solution and finally some numerical simulation is presented.

On the singular perturbations for fractional differential equation.

PubMed

Atangana, Abdon

2014-01-01

The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.

Applications and Implications of Fractional Dynamics for Dielectric Relaxation

NASA Astrophysics Data System (ADS)

Hilfer, R.

This article summarizes briefly the presentation given by the author at the NATO Advanced Research Workshop on "Broadband Dielectric Spectroscopy and its Advanced Technological Applications", held in Perpignan, France, in September 2011. The purpose of the invited presentation at the workshop was to review and summarize the basic theory of fractional dynamics (Hilfer, Phys Rev E 48:2466, 1993; Hilfer and Anton, Phys Rev E Rapid Commun 51:R848, 1995; Hilfer, Fractals 3(1):211, 1995; Hilfer, Chaos Solitons Fractals 5:1475, 1995; Hilfer, Fractals 3:549, 1995; Hilfer, Physica A 221:89, 1995; Hilfer, On fractional diffusion and its relation with continuous time random walks. In: Pekalski et al. (eds) Anomalous diffusion: from basis to applications. Springer, Berlin, p 77, 1999; Hilfer, Fractional evolution equations and irreversibility. In: Helbing et al. (eds) Traffic and granular flow'99. Springer, Berlin, p 215, 2000; Hilfer, Fractional time evolution. In: Hilfer (ed) Applications of fractional calculus in physics. World Scientific, Singapore, p 87, 2000; Hilfer, Remarks on fractional time. In: Castell and Ischebeck (eds) Time, quantum and information. Springer, Berlin, p 235, 2003; Hilfer, Physica A 329:35, 2003; Hilfer, Threefold introduction to fractional derivatives. In: Klages et al. (eds) Anomalous transport: foundations and applications. Wiley-VCH, Weinheim, pp 17-74, 2008; Hilfer, Foundations of fractional dynamics: a short account. In: Klafter et al. (eds) Fractional dynamics: recent advances. World Scientific, Singapore, p 207, 2011) and demonstrate its relevance and application to broadband dielectric spectroscopy (Hilfer, J Phys Condens Matter 14:2297, 2002; Hilfer, Chem Phys 284:399, 2002; Hilfer, Fractals 11:251, 2003; Hilfer et al., Fractional Calc Appl Anal 12:299, 2009). It was argued, that broadband dielectric spectroscopy might be useful to test effective field theories based on fractional dynamics.

Identification of a Phosphodiesterase-Inhibiting Fraction from Roasted Coffee (Coffea arabica) through Activity-Guided Fractionation.

PubMed

Röhrig, Teresa; Liesenfeld, David; Richling, Elke

2017-05-17

Recent reports that coffee can significantly inhibit cAMP phosphodiesterases (PDEs) in vitro, as well as in vivo, have described another beneficial effect of coffee consumption. However, the PDE-inhibiting substances remain mostly unknown. We chose activity-guided fractionation and an in vitro test system to identify the coffee components that are responsible for PDE inhibition. This approach indicated that a fraction of melanoidins reveals strong PDE-inhibiting potential (IC 50 = 130 ± 42 μg/mL). These melanoidins were characterized as water-soluble, low-molecular weight melanoidins (<3 kDa) with a nitrogen content of 4.2% and a carbohydrate content lower than those of other melanoidins. Fractions containing known PDE inhibitors such as chlorogenic acids, alkylpyrazines, or trigonelline as well as N-caffeoyl-tryptophan and N-p-coumaroyl-tryptophan did not exert PDE-inhibiting activity. We also observed that the known PDE inhibitor caffeine does not contribute to the PDE-inhibiting effects of coffee.

Emerging Indications for Fractionated Gamma Knife Radiosurgery.

PubMed

McTyre, Emory; Helis, Corbin A; Farris, Michael; Wilkins, Lisa; Sloan, Darrell; Hinson, William H; Bourland, J Daniel; Dezarn, William A; Munley, Michael T; Watabe, Kounosuke; Xing, Fei; Laxton, Adrian W; Tatter, Stephen B; Chan, Michael D

2017-02-01

Gamma Knife radiosurgery (GKRS) allows for the treatment of intracranial tumors with a high degree of dose conformality and precision. There are, however, certain situations wherein the dose conformality of GKRS is desired, but single session treatment is contraindicated. In these situations, a traditional pin-based GKRS head frame cannot be used, as it precludes fractionated treatment. To report our experience in treating patients with fractionated GKRS using a relocatable, noninvasive immobilization system. Patients were considered candidates for fractionated GKRS if they had one or more of the following indications: a benign tumor >10 cc in volume or abutting the optic pathway, a vestibular schwannoma with the intent of hearing preservation, or a tumor previously irradiated with single fraction GKRS. The immobilization device used for all patients was the Extend system (Leksell Gamma Knife Perfexion, Elekta, Kungstensgatan, Stockholm). We identified 34 patients treated with fractionated GKRS between August 2013 and February 2015. There were a total of 37 tumors treated including 15 meningiomas, 11 pituitary adenomas, 6 brain metastases, 4 vestibular schwannomas, and 1 hemangioma. At last follow-up, all 21 patients treated for perioptic tumors had stable or improved vision and all 4 patients treated for vestibular schwannoma maintained serviceable hearing. No severe adverse events were reported. Fractionated GKRS was well-tolerated in the treatment of large meningiomas, perioptic tumors, vestibular schwannomas with intent of hearing preservation, and in reirradiation of previously treated tumors.

Emerging Indications for Fractionated Gamma Knife Radiosurgery

PubMed Central

McTyre, Emory; Helis, Corbin A.; Farris, Michael; Wilkins, Lisa; Sloan, Darrell; Hinson, William H.; Bourland, J. Daniel; Dezarn, William. A.; Munley, Michael T.; Watabe, Kounosuke; Xing, Fei; Laxton, Adrian W.; Tatter, Stephen B.; Chan, Michael D.

2016-01-01

BACKGROUND Gamma Knife radiosurgery (GKRS) allows for the treatment of intracranial tumors with a high degree of dose conformality and precision. There are, however, certain situations wherein the dose conformality of GKRS is desired, but single session treatment is contraindicated. In these situations, a traditional pin-based GKRS head frame cannot be used, as it precludes fractionated treatment. OBJECTIVE To report our experience in treating patients with fractionated GKRS using a relocatable, noninvasive immobilization system. METHODS Patients were considered candidates for fractionated GKRS if they had one or more of the following indications: a benign tumor >10 cc in volume or abutting the optic pathway, a vestibular schwannoma with the intent of hearing preservation, or a tumor previously irradiated with single fraction GKRS. The immobilization device used for all patients was the Extend system (Leksell Gamma Knife Perfexion, Elekta, Kungstensgatan, Stockholm). RESULTS We identified 34 patients treated with fractionated GKRS between August 2013 and February 2015. There were a total of 37 tumors treated including 15 meningiomas, 11 pituitary adenomas, 6 brain metastases, 4 vestibular schwannomas, and 1 hemangioma. At last follow-up, all 21 patients treated for perioptic tumors had stable or improved vision and all 4 patients treated for vestibular schwannoma maintained serviceable hearing. No severe adverse events were reported. CONCLUSION Fractionated GKRS was well-tolerated in the treatment of large meningiomas, perioptic tumors, vestibular schwannomas with intent of hearing preservation, and in reirradiation of previously treated tumors. PMID:28536486

Fractional Relativistic Yamaleev Oscillator Model and Its Dynamical Behaviors

NASA Astrophysics Data System (ADS)

Luo, Shao-Kai; He, Jin-Man; Xu, Yan-Li; Zhang, Xiao-Tian

2016-07-01

In the paper we construct a new kind of fractional dynamical model, i.e. the fractional relativistic Yamaleev oscillator model, and explore its dynamical behaviors. We will find that the fractional relativistic Yamaleev oscillator model possesses Lie algebraic structure and satisfies generalized Poisson conservation law. We will also give the Poisson conserved quantities of the model. Further, the relation between conserved quantities and integral invariants of the model is studied and it is proved that, by using the Poisson conserved quantities, we can construct integral invariants of the model. Finally, the stability of the manifold of equilibrium states of the fractional relativistic Yamaleev oscillator model is studied. The paper provides a general method, i.e. fractional generalized Hamiltonian method, for constructing a family of fractional dynamical models of an actual dynamical system.

Characterization of pea (Pisum sativum) seed protein fractions.

PubMed

Rubio, Luis A; Pérez, Alicia; Ruiz, Raquel; Guzmán, M Ángeles; Aranda-Olmedo, Isabel; Clemente, Alfonso

2014-01-30

Legume seed proteins have to be chemically characterized in order to properly link their nutritional effects with their chemical structure. Vicilin and albumin fractions devoid of cross-contamination, as assessed by mass peptide fingerprinting analysis, were obtained from defatted pea (Pisum sativum cv. Bilbo) meal. The extracted protein fractions contained 56.7-67.7 g non-starch polysaccharides kg⁻¹. The vicilin fraction was higher than legumins in arginine, isoleucine, leucine, phenylalanine and lysine. The most abundant amino acids in the albumin fraction were aspartic acid, glutamic acid, lysine and arginine, and the amounts of methionine were more than double than those in legumins and vicilins. The pea albumin fraction showed a clear enrichment of protease inhibitory activity when compared with the seed meal. In vitro digestibility values for pea proteins were 0.63 ±  0.04, 0.88 ±  0.04 and 0.41 ±  0.23 for legumins, vicilins and albumins respectively. Vicilin and albumin fractions devoid of cross-contamination with other proteins were obtained from pea seed meal. The vicilin fraction also contained low amounts of soluble non-starch polysaccharides and was enriched in isoleucine, leucine, phenylalanine and lysine. In vitro digestibility values for pea proteins were similar or even numerically higher than those for control proteins. © 2013 Society of Chemical Industry.

Sources of Group and Individual Differences in Emerging Fraction Skills

PubMed Central

Hecht, Steven A.; Vagi, Kevin J.

2010-01-01

Results from a two year longitudinal study of 181 children from fourth through fifth grade are reported. Levels of growth in children’s computation, word problem, and estimation skills using common fractions were predicted by working memory, attentive classroom behavior, conceptual knowledge about fractions, and simple arithmetic fluency. Comparisons of 55 participants identified as having mathematical difficulties to those without mathematical difficulties revealed that group differences in emerging fraction skills were consistently mediated by attentive classroom behavior and conceptual knowledge about fractions. Neither working memory nor arithmetic fluency mediated group differences in growth in fraction skills. It was also found that the development of basic fraction skills and conceptual knowledge are bidirectional in that conceptual knowledge exerted strong influences on all three types of basic fraction skills, and basic fraction skills exerted a more modest influence on subsequent conceptual knowledge. Results are discussed with reference to how the identification of potentially malleable student characteristics that contribute to the difficulties that some students have with fractions informs interventions and also will contribute to a future theoretical account concerning how domain general and domain specific factors influence the development of basic fraction skills. PMID:21170171

Ablative Fractional 10 600 nm Carbon Dioxide Laser Versus Non-ablative Fractional 1540 nm Erbium-Glass Laser in Egyptian Post-acne Scar patients.

PubMed

Elsaie, Mohamed L; Ibrahim, Shady M; Saudi, Wael

2018-01-01

Introduction: Non-ablative fractional erbium-doped glass 1540 nm and fractional ablative 10600 nm carbon dioxide lasers are regarded as effective modalities for treating acne atrophic scars. In this study, we aimed to compare the effectiveness of fractional CO 2 laser and fractional nonablative 1540 nm erbium doped glass laser in treating post acne atrophic scars in Egyptian patients. Methods: Fifty-eight patients complaining of moderate and severe acne atrophic scars were randomly divided into 2 groups of 29 patients each. Both groups were subjected to 4 treatment sessions with 3 weeks interval and were followed up for 3 months. In group A, enrolled patient sreceived C2 laser, while in group B, patients were treated with 1540 nm erbium glass fractional laser. Results: Clinical assessment revealed that the mean grades of progress and improvement were higher with fractional 10600 nm CO2 laser but with non-significant difference between both treatments ( P = 0.1). The overall patients' satisfaction with both lasers were not significantly different ( P = 0.44). Conclusion: Both fractional ablative CO2 and fractional non-ablative erbium glass lasers are good modalities for treating acne scars with a high efficacy and safety profile and good patient satisfaction. The fractional ablative laser showed higher efficacy while non-ablative laser offered less pain and shorter downtime.

From Students' Problem-Solving Strategies to Connections in Fractions

ERIC Educational Resources Information Center

Flores, Alfinio; Klein, Erika

2005-01-01

Strategies that children used to solve a fraction problem are presented, and an insight into how students think about divisions and fractions is described. Teachers can use these strategies to help students establish connections related to fractions.

High-order fractional partial differential equation transform for molecular surface construction.

PubMed

Hu, Langhua; Chen, Duan; Wei, Guo-Wei

2013-01-01

Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily high-order fractional partial differential equations (PDEs) to describe fractional hyperdiffusions. The fractional PDEs are constructed via fractional variational principle. A fast fractional Fourier transform (FFFT) is proposed to numerically integrate the high-order fractional PDEs so as to avoid stringent stability constraints in solving high-order evolution PDEs. The proposed high-order fractional PDEs are applied to the surface generation of proteins. We first validate the proposed method with a variety of test examples in two and three-dimensional settings. The impact of high-order fractional derivatives to surface analysis is examined. We also construct fractional PDE transform based on arbitrarily high-order fractional PDEs. We demonstrate that the use of arbitrarily high-order derivatives gives rise to time-frequency localization, the control of the spectral distribution, and the regulation of the spatial resolution in the fractional PDE transform. Consequently, the fractional PDE transform enables the mode decomposition of images, signals, and surfaces. The effect of the propagation time on the quality of resulting molecular surfaces is also studied. Computational efficiency of the present surface generation method is compared with the MSMS approach in Cartesian representation. We further validate the present method by examining some benchmark indicators of macromolecular surfaces, i.e., surface area, surface enclosed volume, surface electrostatic potential and solvation free energy. Extensive numerical experiments and comparison with an established surface model

High-order fractional partial differential equation transform for molecular surface construction

PubMed Central

Hu, Langhua; Chen, Duan; Wei, Guo-Wei

2013-01-01

Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily high-order fractional partial differential equations (PDEs) to describe fractional hyperdiffusions. The fractional PDEs are constructed via fractional variational principle. A fast fractional Fourier transform (FFFT) is proposed to numerically integrate the high-order fractional PDEs so as to avoid stringent stability constraints in solving high-order evolution PDEs. The proposed high-order fractional PDEs are applied to the surface generation of proteins. We first validate the proposed method with a variety of test examples in two and three-dimensional settings. The impact of high-order fractional derivatives to surface analysis is examined. We also construct fractional PDE transform based on arbitrarily high-order fractional PDEs. We demonstrate that the use of arbitrarily high-order derivatives gives rise to time-frequency localization, the control of the spectral distribution, and the regulation of the spatial resolution in the fractional PDE transform. Consequently, the fractional PDE transform enables the mode decomposition of images, signals, and surfaces. The effect of the propagation time on the quality of resulting molecular surfaces is also studied. Computational efficiency of the present surface generation method is compared with the MSMS approach in Cartesian representation. We further validate the present method by examining some benchmark indicators of macromolecular surfaces, i.e., surface area, surface enclosed volume, surface electrostatic potential and solvation free energy. Extensive numerical experiments and comparison with an established surface model

Fractionated laser skin resurfacing treatment complications: a review.

PubMed

Metelitsa, Andrei I; Alster, Tina S

2010-03-01

Fractional photothermolysis represents a new modality of laser skin resurfacing that was developed to provide a successful clinical response while minimizing postoperative recovery and limiting treatment complications. To review all of the reported complications that develop as a result of fractional ablative and nonablative laser skin resurfacing. A literature review was based on a MEDLINE search (1998-2009) for English-language articles related to laser treatment complications and fractional skin resurfacing. Articles presenting the highest level of evidence and the most recent reports were preferentially selected. Complications with fractional laser skin resurfacing represent a full spectrum of severity and can be longlasting. In general, a greater likelihood of developing post-treatment complications is seen in sensitive cutaneous areas and in patients with intrinsically darker skin phototypes or predisposing medical risk factors. Although the overall rate of complications associated with fractional laser skin resurfacing is much lower than with traditional ablative techniques, recent reports suggest that serious complications can develop. An appreciation of all of the complications associated with fractional laser skin resurfacing is important, especially given that many of them can be potentially prevented. The authors have indicated no significant interest with commercial supporters.

Serum protein fractionation using supported molecular matrix electrophoresis.

PubMed

Dong, Weijie; Matsuno, Yu-ki; Kameyama, Akihiko

2013-08-01

Supported molecular matrix electrophoresis (SMME), in which a hydrophilic polymer such as PVA serves as a support within a porous PVDF membrane, was recently developed. This method is similar to cellulose acetate membrane electrophoresis but differs in the compatibility to glycan analysis of the separated bands. In this report, we describe the first instance of the application of SMME to human serum fractionation, and demonstrate the differences with serum fractionation by cellulose acetate membrane electrophoresis. The SMME membrane exhibited almost no EOF during electrophoresis, unlike the cellulose acetate membrane, but afforded comparative results for serum fractionation. The visualization of each fraction was achieved by conventional staining with dye such as Direct Blue-71, and objective quantification was obtained by densitometry after inducing membrane transparency with 1-nonene. Immunostaining was also achieved. Moreover, mass spectrometric analysis of both N-linked and O-linked glycans from the separated bands was demonstrated. Serum fractionation and glycan profiling of each fraction using SMME will enable novel insights into the relationships between various glycosylation profiles and disease states. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Eye movements reflect and shape strategies in fraction comparison.

PubMed

Ischebeck, Anja; Weilharter, Marina; Körner, Christof

2016-01-01

The comparison of fractions is a difficult task that can often be facilitated by separately comparing components (numerators and denominators) of the fractions--that is, by applying so-called component-based strategies. The usefulness of such strategies depends on the type of fraction pair to be compared. We investigated the temporal organization and the flexibility of strategy deployment in fraction comparison by evaluating sequences of eye movements in 20 young adults. We found that component-based strategies could account for the response times and the overall number of fixations observed for the different fraction pairs. The analysis of eye movement sequences showed that the initial eye movements in a trial were characterized by stereotypical scanning patterns indicative of an exploratory phase that served to establish the kind of fraction pair presented. Eye movements that followed this phase adapted to the particular type of fraction pair and indicated the deployment of specific comparison strategies. These results demonstrate that participants employ eye movements systematically to support strategy use in fraction comparison. Participants showed a remarkable flexibility to adapt to the most efficient strategy on a trial-by-trial basis. Our results confirm the value of eye movement measurements in the exploration of strategic adaptation in complex tasks.

Variability estimation of urban wastewater biodegradable fractions by respirometry.

PubMed

Lagarde, Fabienne; Tusseau-Vuillemin, Marie-Hélène; Lessard, Paul; Héduit, Alain; Dutrop, François; Mouchel, Jean-Marie

2005-11-01

This paper presents a methodology for assessing the variability of biodegradable chemical oxygen demand (COD) fractions in urban wastewaters. Thirteen raw wastewater samples from combined and separate sewers feeding the same plant were characterised, and two optimisation procedures were applied in order to evaluate the variability in biodegradable fractions and related kinetic parameters. Through an overall optimisation on all the samples, a unique kinetic parameter set was obtained with a three-substrate model including an adsorption stage. This method required powerful numerical treatment, but improved the identifiability problem compared to the usual sample-to-sample optimisation. The results showed that the fractionation of samples collected in the combined sewer was much more variable (standard deviation of 70% of the mean values) than the fractionation of the separate sewer samples, and the slowly biodegradable COD fraction was the most significant fraction (45% of the total COD on average). Because these samples were collected under various rain conditions, the standard deviations obtained here on the combined sewer biodegradable fractions could be used as a first estimation of the variability of this type of sewer system.

On the Singular Perturbations for Fractional Differential Equation

PubMed Central

Atangana, Abdon

2014-01-01

The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method. PMID:24683357

Cod Fractions In Mechanical-Biological Wastewater Treatment Plant

NASA Astrophysics Data System (ADS)

Płuciennik-Koropczuk, Ewelina; Jakubaszek, Anita; Myszograj, Sylwia; Uszakiewicz, Sylwia

2017-03-01

The paper presents results of studies concerning the designation of COD fraction in the raw, mechanically treated and biologically treated wastewater. The test object was a wastewater treatment plant with the output of over 20,000 PE. The results were compared with data received in the ASM models. During investigation following fractions of COD were determined: dissolved non-biodegradable SI, dissolved easily biodegradable SS, in organic suspension slowly degradable XS and in organic suspension non-biodegradable XI. Methodology for determining the COD fraction was based on the guidelines ATV-A 131. The real percentage of each fraction in total COD in raw wastewater are different from data received in ASM models.

Fractional CO2 Laser Resurfacing Complications

PubMed Central

Ramsdell, William M.

2012-01-01

Fractionated CO2 laser technology has allowed physicians to resurface patients with a lower rate of complications than nonfractionated ablative laser treatment. Unfortunately, adverse effects can still occur even with the best technology and physician care. Complication prevention, detection, and treatment are an important part of a physician's ability to provide the best result when treating a patient with fractionated CO2 resurfacing. PMID:23904822

Circulating gamma-glutamyltransferase fractions in cirrhosis.

PubMed

Elawdi, Hassan A; Franzini, Maria; Paolicchi, Aldo; Emdin, Michele; Fornaciari, Irene; Fierabracci, Vanna; De Simone, Paolo; Carrai, Paola; Filipponi, Franco

2014-08-01

Four gamma-gultamyltransferases (GGT) fractions (b-, m-, s-, and f-GGT) have been identified in human plasma and their concentrations and ratios vary in different pathological conditions. To assess the behaviour of fractional GGT in cirrhotic patients evaluated for liver transplantation. This was a single-centre, cross-sectional study; GGT fractions were determined by gel-filtration chromatography. 264 cirrhotic patients (215 males; median age 54.5 years) were included and compared against a group of 200 healthy individuals (100 males; median age 41.5). Median (25th-75th percentile) total and fractional GGT were higher in cirrhotics, with s-GGT showing the greatest increase [36.6 U/L (21.0-81.4) vs. 5.6 U/L (3.2-10.2), P<0.0001], while the median b-GGT/s-GGT ratio was lower in cirrhotics than in healthy controls [0.06 (0.04-0.10)] vs. 0.28 (0.20-0.40), P<0.0001]. The ratio showed higher diagnostic accuracy (ROC-AUC, 95% CI: 0.951, 0.927-0.969) then either s-GGT (0.924, 0.897-0.947; P<0.05) or total GGT (0.900, 0.869-0.925; P<0.001). The diagnostic accuracy of the ratio was maintained (0.940, 0.907-0.963) in cirrhotic patients (n=113) with total GGT values within the reference range. The s-GGT fraction consisted of two components, with one (s2-GGT) showing a significant positive correlation with serum aspartate aminotransferases, alanine aminotransferase, lactate dehydrogenases (LDH), alkaline phosphatases and bilirubin, and negative with albumin. The b-GGT fraction showed a positive correlation with albumin, fibrinogen, and platelet counts, and negative with international normalized ratio, bilirubin and LDH. The ratio performs as a sensitive biomarker of the liver parenchymal rearrangement, irrespective of aetiology of cirrhosis and presence of hepatocellular carcinoma, even in patients with total GGT values within the reference range. © 2014 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

Fractionation and mobility of thallium in areas impacted by mining-metallurgical activities: Identification of a water-soluble Tl(I) fraction.

PubMed

Cruz-Hernández, Yusniel; Ruiz-García, Mismel; Villalobos, Mario; Romero, Francisco Martin; Meza-Figueroa, Diana; Garrido, Fernando; Hernández-Alvarez, Elizabeth; Pi-Puig, Teresa

2018-06-01

Mining and metallurgy generate residues that may contain thallium (Tl), a highly toxic metal, for which it is currently not feasible to determine its geochemical speciation through X-ray absorption spectroscopy due to a combination of very low contents and the interference of accompanying high arsenic contents. Therefore, fractionation studies in residues and soils are required to analyze the mobility and bioavailability of this metal, which in turn provide information to infer its speciation. For this purpose, in this work a modification of the BCR procedure was applied to residues and contaminated soils from three mining zones of Mexico and two mining zones of Spain, spanning samples with acidic to alkaline pH values. The Tl extraction procedure consisted of the following fractions: (1) water-extractable, (2) easily exchangeable and associated to carbonates, associated to (3) poorly-crystalline and (4) crystalline Fe and Mn oxyhydroxides, and (5) associated to organic matter and sulfides; and finally a residual fraction as associated to refractory primary and other secondary minerals. The extracted contents were analyzed by Inductively-Coupled Plasma with Mass Spectrometry. Surprisingly, water-soluble, in Tl(I) oxidation state, was detected in most areas, regardless of the pH, a fact that has not been reported before in these environments, and alerts to potential health risks not previously identified. Most of the samples from a metallurgy area showed high levels of Tl in non-residual fractions and a strong correlation was obtained between extracted Mn and Tl in the third fraction, suggesting its association to poorly crystalline manganese oxides. In the majority of samples from purely mining environments, most of the Tl was found in the residual fraction, most probably bound to alumino-silicate minerals. The remaining Tl fractions were extracted mainly associated to the reducible mineral fractions, and in one case also in the oxidizable fraction (presumably

Carbon and hydrogen isotope fractionation by moderately thermophilic methanogens

NASA Astrophysics Data System (ADS)

Valentine, David L.; Chidthaisong, Amnat; Rice, Andrew; Reeburgh, William S.; Tyler, Stanley C.

2004-04-01

A series of laboratory studies were conducted to increase understanding of stable carbon (13C/12C) and hydrogen (D/H) isotope fractionation arising from methanogenesis by moderately thermophilic acetate- and hydrogen-consuming methanogens. Studies of the aceticlastic reaction were conducted with two closely related strains of Methanosaeta thermophila. Results demonstrate a carbon isotope fractionation of only 7‰ (α = 1.007) between the methyl position of acetate and the resulting methane. Methane formed by this process is enriched in 13C when compared with other natural sources of methane; the magnitude of this isotope effect raises the possibility that methane produced at elevated temperature by the aceticlastic reaction could be mistaken for thermogenic methane based on carbon isotopic content. Studies of H2/CO2 methanogenesis were conducted with Methanothermobacter marburgensis. The fractionation of carbon isotopes between CO2 and CH4 was found to range from 22 to 58‰ (1.023 ≤ α ≤ 1.064). Greater fractionation was associated with low levels of molecular hydrogen and steady-state metabolism. The fractionation of hydrogen isotopes between source H2O and CH4 was found to range from 127 to 275‰ (1.16 ≤ α ≤ 1.43). Fractionation was dependent on growth phase with greater fractionation associated with later growth stages. The maximum observed fractionation factor was 1.43, independent of the δD-H2 supplied to the culture. Fractionation was positively correlated with temperature and/or metabolic rate. Results demonstrate significant variability in both hydrogen and carbon isotope fractionation during methanogenesis from H2/CO2. The relatively small fractionation associated with deuterium during H2/CO2 methanogenesis provides an explanation for the relatively enriched deuterium content of biogenic natural gas originating from a variety of thermal environments. Results from these experiments are used to develop a hypothesis that differential

Effect of Drying on Heavy Metal Fraction Distribution in Rice Paddy Soil

PubMed Central

Qi, Yanbing; Huang, Biao; Darilek, Jeremy Landon

2014-01-01

An understanding of how redox conditions affect soil heavy metal fractions in rice paddies is important due to its implications for heavy metal mobility and plant uptake. Rice paddy soil samples routinely undergo oxidation prior to heavy metal analysis. Fraction distribution of Cu, Pb, Ni, and Cd from paddy soil with a wide pH range was investigated. Samples were both dried according to standard protocols and also preserved under anaerobic conditions through the sampling and analysis process and heavy metals were then sequentially extracted for the exchangeable and carbonate bound fraction (acid soluble fraction), iron and manganese oxide bound fraction (reducible fraction), organic bound fraction (oxidizable fraction), and residual fraction. Fractions were affected by redox conditions across all pH ranges. Drying decreased reducible fraction of all heavy metals. Curesidual fraction, Pboxidizable fraction, Cdresidual fraction, and Niresidual fraction increased by 25%, 33%, 35%, and >60%, respectively. Pbresidual fraction, Niacid soluble fraction, and Cdoxidizable fraction decreased 33%, 25%, and 15%, respectively. Drying paddy soil prior to heavy metal analysis overestimated Pb and underestimated Cu, Ni, and Cd. In future studies, samples should be stored after injecting N2 gas to maintain the redox potential of soil prior to heavy metal analysis, and investigate the correlation between heavy metal fraction distribution under field conditions and air-dried samples. PMID:24823670

Content knowledge of prospective elementary school teacher for fractional concepts

NASA Astrophysics Data System (ADS)

Pattimukay, N.; Juniati, D.; Budiarto, M. T.

2018-03-01

The aim of this study was to describe the content knowledge especially the concept of fraction of prospective elementary school teacher. The purpose of this study is to describe the content knowledge, especially the concept of fraction of prospective elementary school teacher. The subject of the study was one of prospective elementary school teacher of Pattimura University. This research is qualitative research. Data were collected through the provision of tests to explore the knowledge content of primary school teacher candidates about fractional concepts. Then continued with qualitative data analysis. The results of this study are as follows: that the prospective primary school teacher defines fractions as part of the whole if an object is divided into equal parts, so that the part that has been divided is part of the whole. Furthermore, the prospective elementary school teacher understood the fractions as division shown in two ways, namely the prospective elementary school teacher understood the fraction as a division operation, the primary school teacher candidate interpreted the fraction as a division when an object is divided be part of the same. Meanwhile, the fraction as a ratio is interpreted as the relationship between a pair of numbers. Then, the denominations are interpreted as a ratio between the numerator and the denominator of the same value. The prospective elementary school teacher also understands fractions of value when simplifying fractions. Primary school teacher candidates understand the concept of fractional operations.

Fraction-variant beam orientation optimization for non-coplanar IMRT

NASA Astrophysics Data System (ADS)

O'Connor, Daniel; Yu, Victoria; Nguyen, Dan; Ruan, Dan; Sheng, Ke

2018-02-01

Conventional beam orientation optimization (BOO) algorithms for IMRT assume that the same set of beam angles is used for all treatment fractions. In this paper we present a BOO formulation based on group sparsity that simultaneously optimizes non-coplanar beam angles for all fractions, yielding a fraction-variant (FV) treatment plan. Beam angles are selected by solving a multi-fraction fluence map optimization problem involving 500-700 candidate beams per fraction, with an additional group sparsity term that encourages most candidate beams to be inactive. The optimization problem is solved using the fast iterative shrinkage-thresholding algorithm. Our FV BOO algorithm is used to create five-fraction treatment plans for digital phantom, prostate, and lung cases as well as a 30-fraction plan for a head and neck case. A homogeneous PTV dose coverage is maintained in all fractions. The treatment plans are compared with fraction-invariant plans that use a fixed set of beam angles for all fractions. The FV plans reduced OAR mean dose and D 2 values on average by 3.3% and 3.8% of the prescription dose, respectively. Notably, mean OAR dose was reduced by 14.3% of prescription dose (rectum), 11.6% (penile bulb), 10.7% (seminal vesicle), 5.5% (right femur), 3.5% (bladder), 4.0% (normal left lung), 15.5% (cochleas), and 5.2% (chiasm). D 2 was reduced by 14.9% of prescription dose (right femur), 8.2% (penile bulb), 12.7% (proximal bronchus), 4.1% (normal left lung), 15.2% (cochleas), 10.1% (orbits), 9.1% (chiasm), 8.7% (brainstem), and 7.1% (parotids). Meanwhile, PTV homogeneity defined as D 95/D 5 improved from .92 to .95 (digital phantom), from .95 to .98 (prostate case), and from .94 to .97 (lung case), and remained constant for the head and neck case. Moreover, the FV plans are dosimetrically similar to conventional plans that use twice as many beams per fraction. Thus, FV BOO offers the potential to reduce delivery time for non-coplanar IMRT.

Implementation of quantum and classical discrete fractional Fourier transforms.

PubMed

Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N; Szameit, Alexander

2016-03-23

Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools.

Implementation of quantum and classical discrete fractional Fourier transforms

PubMed Central

Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N.; Szameit, Alexander

2016-01-01

Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools. PMID:27006089

Numerical simulation for solution of space-time fractional telegraphs equations with local fractional derivatives via HAFSTM

NASA Astrophysics Data System (ADS)

Pandey, Rishi Kumar; Mishra, Hradyesh Kumar

2017-11-01

In this paper, the semi-analytic numerical technique for the solution of time-space fractional telegraph equation is applied. This numerical technique is based on coupling of the homotopy analysis method and sumudu transform. It shows the clear advantage with mess methods like finite difference method and also with polynomial methods similar to perturbation and Adomian decomposition methods. It is easily transform the complex fractional order derivatives in simple time domain and interpret the results in same meaning.

A remark on fractional differential equation involving I-function

NASA Astrophysics Data System (ADS)

Mishra, Jyoti

2018-02-01

The present paper deals with the solution of the fractional differential equation using the Laplace transform operator and its corresponding properties in the fractional calculus; we derive an exact solution of a complex fractional differential equation involving a special function known as I-function. The analysis of the some fractional integral with two parameters is presented using the suggested Theorem 1. In addition, some very useful corollaries are established and their proofs presented in detail. Some obtained exact solutions are depicted to see the effect of each fractional order. Owing to the wider applicability of the I-function, we can conclude that, the obtained results in our work generalize numerous well-known results obtained by specializing the parameters.

Fractional-dimensional Child-Langmuir law for a rough cathode

NASA Astrophysics Data System (ADS)

Zubair, M.; Ang, L. K.

2016-07-01

This work presents a self-consistent model of space charge limited current transport in a gap combined of free-space and fractional-dimensional space (Fα), where α is the fractional dimension in the range 0 < α ≤ 1. In this approach, a closed-form fractional-dimensional generalization of Child-Langmuir (CL) law is derived in classical regime which is then used to model the effect of cathode surface roughness in a vacuum diode by replacing the rough cathode with a smooth cathode placed in a layer of effective fractional-dimensional space. Smooth transition of CL law from the fractional-dimensional to integer-dimensional space is also demonstrated. The model has been validated by comparing results with an experiment.

The 2010 ILSO-ISRU Field Test at Mauna Kea, Hawaii: Results from the Miniaturised Mossbauer Spectrometers Mimos II and Mimos IIA

NASA Technical Reports Server (NTRS)

Klingelhoefer, G.; Morris, R. V.; Blumers, M.; Bernhardt, B.; Graff, T.

2011-01-01

For the advanced Moessbauer instrument MIMOS IIA, the new detector technologies and electronic components increase sensitivity and performance significantly. In combination with the high energy resolution of the SDD it is possible to perform X-ray fluorescence analysis simultaneously to Moessbauer spectroscopy. In addition to the Fe-mineralogy, information on the sample's elemental composition will be gathered. The ISRU 2010 field campaign demonstrated that in-situ Moessbauer spectroscopy is an effective tool for both science and feedstock exploration and process monitoring. Engineering tests showed that a compact nickel metal hydride battery provided sufficient power for over 12 hr of continuous operation for the MIMOS instruments.

Optimal Campaign Strategies in Fractional-Order Smoking Dynamics

NASA Astrophysics Data System (ADS)

Zeb, Anwar; Zaman, Gul; Jung, Il Hyo; Khan, Madad

2014-06-01

This paper deals with the optimal control problem in the giving up smoking model of fractional order. For the eradication of smoking in a community, we introduce three control variables in the form of education campaign, anti-smoking gum, and anti-nicotive drugs/medicine in the proposed fractional order model. We discuss the necessary conditions for the optimality of a general fractional optimal control problem whose fractional derivative is described in the Caputo sense. In order to do this, we minimize the number of potential and occasional smokers and maximize the number of ex-smokers. We use Pontryagin's maximum principle to characterize the optimal levels of the three controls. The resulting optimality system is solved numerically by MATLAB.

The efficacy and safety of combined microneedle fractional radiofrequency and sublative fractional radiofrequency for acne scars in Asian skin.

PubMed

Park, Jae Yang; Lee, Eo Gin; Yoon, Moon Soo; Lee, Hee Jung

2016-06-01

Microneedle fractional radiofrequency has been reported to be effective for improving wrinkles, enlarged pores and various scars. Sublative fractional radiofrequency has been shown to induce both fractional ablation of epidermis and upper dermal remodelling, which had rejuvenation effects in photoaged skin. Both modalities may have the potential synergy to improve acne scars. To evaluate the efficacy and safety of combined microneedle and sublative fractional radiofrequency for acne scars in Asian skin. Twenty subjects comprised 11 males and 9 females (mean age 23.65 ± 2.94, skin phototype III-IV) with moderate to severe acne scars. The subjects received three consecutive combined microneedle and sublative fractional radiofrequency at 4-week intervals over 12 weeks. Both blinded dermatologists and subjects assessed the clinical improvement based on the standardized photography and questionnaires, respectively. The quartile grading scale was utilized and defined as follows: grade 1, 0-25% improvement; grade 2, 26-50% improvement; grade 3, 51-75% improvement and grade 4, 76-100% improvement. All 20 subjects were assessed to have grade 2 or more clinical improvement by physicians; four (20%) had grade 4, 10 (50%) had grade 3, and six (30%) had grade 2 improvement. The subjects' grading also showed a good concordance as indicated by Kappa index of 0.695. The mean duration of post-therapy crusting was 5.2 days and post-therapy erythema lasted 2.5 days. Combined microneedle and sublative fractional radiofrequency can have a positive therapeutic effect with no serious complications and may provide a new therapeutic approach on acne scars in Asians. © 2015 Wiley Periodicals, Inc.

36 CFR 254.34 - Mineral survey fractions.

Code of Federal Regulations, 2013 CFR

2013-07-01

... 36 Parks, Forests, and Public Property 2 2013-07-01 2013-07-01 false Mineral survey fractions. 254... LANDOWNERSHIP ADJUSTMENTS Conveyance of Small Tracts § 254.34 Mineral survey fractions. (a) Mineral survey...) Forest Service officials shall consider the following criteria in determining whether to convey mineral...

Fractional-order in a macroeconomic dynamic model

NASA Astrophysics Data System (ADS)

David, S. A.; Quintino, D. D.; Soliani, J.

2013-10-01

In this paper, we applied the Riemann-Liouville approach in order to realize the numerical simulations to a set of equations that represent a fractional-order macroeconomic dynamic model. It is a generalization of a dynamic model recently reported in the literature. The aforementioned equations have been simulated for several cases involving integer and non-integer order analysis, with some different values to fractional order. The time histories and the phase diagrams have been plotted to visualize the effect of fractional order approach. The new contribution of this work arises from the fact that the macroeconomic dynamic model proposed here involves the public sector deficit equation, which renders the model more realistic and complete when compared with the ones encountered in the literature. The results reveal that the fractional-order macroeconomic model can exhibit a real reasonable behavior to macroeconomics systems and might offer greater insights towards the understanding of these complex dynamic systems.

Ablative fractional laser treatment for hypertrophic scars: comparison between Er:YAG and CO2 fractional lasers.

PubMed

Choi, Jae Eun; Oh, Ga Na; Kim, Jong Yeob; Seo, Soo Hong; Ahn, Hyo Hyun; Kye, Young Chul

2014-08-01

Nonablative fractional photothermolysis has been reported to show early promise in the treatment of hypertrophic scars, but there are few reports on ablative fractional photothermolysis for the treatment of hypertrophic scars. To evaluate and compare the efficacy and safety of Er:YAG fractional laser (EYFL) and CO2 fractional laser (CO2FL) for treatment of hypertrophic scars. Thirteen patients with hypertrophic scars were treated with 2,940 nm EYFL, and ten were treated with 10,600 nm CO2FL. An independent physician evaluator assessed the treatment outcomes using Vancouver scar scale (VSS) and 5-point grading scale (grade 0, no improvement; grade 1, 1-25%; grade 2, 26-50%; grade 3, 51-75%; grade 4, 76-100% improvement). Patients are queried about their subjective satisfaction with the treatment outcomes. After the final treatment, average percentage changes of VSS were 28.2% for EYFL and 49.8% for CO2FL. Improvement was evident in terms of pliability, while insignificant in terms of vascularity and pigmentation. Based on physician's global assessment, mean grade of 1.8 for EYFL and 2.7 for CO2FL was achieved. Patient's subjective satisfaction scores paralleled the physician's objective evaluation. CO2FL is a potentially effective and safe modality for the treatment of hypertrophic scars, particularly in terms of pliability.

Teaching Prospective Teachers about Fractions: Historical and Pedagogical Perspectives

ERIC Educational Resources Information Center

Park, Jungeun; Gucler, Beste; McCrory, Raven

2013-01-01

Research shows that students, and sometimes teachers, have trouble with fractions, especially conceiving of fractions as numbers that extend the whole number system. This paper explores how fractions are addressed in undergraduate mathematics courses for prospective elementary teachers (PSTs). In particular, we explore how, and whether, the…

Evaluating fractionated space systems - Status

NASA Astrophysics Data System (ADS)

Cornford, S.; Jenkins, S.; Wall, S.; Cole, B.; Bairstow, B.; Rouquette, N.; Dubos, G.; Ryan, T.; Zarifian, P.; Boutwell, J.

DARPA has funded a number of teams to further refine its Fractionated Spacecraft vision. Several teams, including this team led by JPL, have been tasked to develop a tool for the evaluation of the Business case for a fractionated system architecture. This evaluation is to understand under what conditions and constraints the fractionated architecture make more sense (in a cost/benefit sense) than the traditional monolithic paradigm. Our approach to this evaluation is to generate and evaluate a variety of trade space options. These options include various sets of stimuli, various degrees of fractionation and various subsystem element properties. The stimuli include many not normally modeled such as technology obsolescence, funding profile changes and changes in mission objectives during the mission itself. The degrees of fractionation enable various traditional subsystem elements to be distributed across different free flyers which then act in concert as needed. This will enable key technologies to be updated as need dictates and availability allows. We have described our approach in a previous IEEE Aerospace conference paper but will briefly summarize here. Our approach to generate the Business Case evaluation is to explicitly model both the implementation and operation phases for the life cycle of a fractionated constellation. A variety of models are integrated into the Phoenix ModelCenter framework and are used to generate various intermediate data which is aggregated into the Present Strategic Value (PSV). The PSV is essentially the value (including the value of the embedded real options) minus the cost. These PSVs are calculated for a variety of configurations and scenarios including variations of various stimuli or uncertainties (e.g. supply chain delays, launch vehicle failures and orbital debris events). There are various decision options (e.g. delay, accelerate, cancel) which can now be exercised for each stimulus. We can compute the PSV for the various comb

Equilibrium lithium isotope fractionation in Li-rich minerals

NASA Astrophysics Data System (ADS)

Liu, S.; Li, Y.; Liu, J.

2017-12-01

Lithium is the lightest alkali metal, and only exhibits +1 valence state in minerals. It is widely distributed on the Earth, and usually substitutes for Mg in silicate minerals. Li has two stable isotopes, 6Li and 7Li, with the relative abundances of 7.52% and 92.48%, respectively. The large mass difference between 6Li and 7Li could induce significant isotope fractionation in minerals. Li isotopes can provide an important geochemical tracer for mantle processes. However, the fractionation factors for Li in most minerals remain poorly known, which makes the geochemical implications of Li isotope fractionations in minerals difficult to assess. Here, we try to use the vibrational frequencies obtained by the first-principles methods based on density-functional theory to calculate the Li isotope fractionation parameters for amblygonite (LiAlPO4F), bikitaite (LiSi2AlO7H2), eucryptite (LiAlSiO4), lithiophilite (LiMnPO4), lithiophosphate (Li3PO4), montebrasite (LiAlPO5H), and spodumene (LiAlSi2O6) in the temperature range of 0-1200 ºC. For forsterite (Mg2SiO4) and diopside (CaMgSi2O6) in which Li takes the place of Mg, the equilibrium Li isotope fractionation between them also be studied. Our preliminary calculations show that the coordination number of Li seems to play an important role in controlling Li isotope fractionation in these minerals, and concentration of Li in forsterite and diopside seems to have great effects on Li isotope fractionation factors of them.

Fractional labelmaps for computing accurate dose volume histograms

NASA Astrophysics Data System (ADS)

Sunderland, Kyle; Pinter, Csaba; Lasso, Andras; Fichtinger, Gabor

2017-03-01

PURPOSE: In radiation therapy treatment planning systems, structures are represented as parallel 2D contours. For treatment planning algorithms, structures must be converted into labelmap (i.e. 3D image denoting structure inside/outside) representations. This is often done by triangulated a surface from contours, which is converted into a binary labelmap. This surface to binary labelmap conversion can cause large errors in small structures. Binary labelmaps are often represented using one byte per voxel, meaning a large amount of memory is unused. Our goal is to develop a fractional labelmap representation containing non-binary values, allowing more information to be stored in the same amount of memory. METHODS: We implemented an algorithm in 3D Slicer, which converts surfaces to fractional labelmaps by creating 216 binary labelmaps, changing the labelmap origin on each iteration. The binary labelmap values are summed to create the fractional labelmap. In addition, an algorithm is implemented in the SlicerRT toolkit that calculates dose volume histograms (DVH) using fractional labelmaps. RESULTS: We found that with manually segmented RANDO head and neck structures, fractional labelmaps represented structure volume up to 19.07% (average 6.81%) more accurately than binary labelmaps, while occupying the same amount of memory. When compared to baseline DVH from treatment planning software, DVH from fractional labelmaps had agreement acceptance percent (1% ΔD, 1% ΔV) up to 57.46% higher (average 4.33%) than DVH from binary labelmaps. CONCLUSION: Fractional labelmaps promise to be an effective method for structure representation, allowing considerably more information to be stored in the same amount of memory.

Evaluation and Validation of the Messinger Freezing Fraction

NASA Technical Reports Server (NTRS)

Anderson, David N.; Tsao, Jen-Ching

2005-01-01

One of the most important non-dimensional parameters used in ice-accretion modeling and scaling studies is the freezing fraction defined by the heat-balance analysis of Messinger. For fifty years this parameter has been used to indicate how rapidly freezing takes place when super-cooled water strikes a solid body. The value ranges from 0 (no freezing) to 1 (water freezes immediately on impact), and the magnitude has been shown to play a major role in determining the physical appearance of the accreted ice. Because of its importance to ice shape, this parameter and the physics underlying the expressions used to calculate it have been questioned from time to time. Until now, there has been no strong evidence either validating or casting doubt on the current expressions. This paper presents experimental measurements of the leading-edge thickness of a number of ice shapes for a variety of test conditions with nominal freezing fractions from 0.3 to 1.0. From these thickness measurements, experimental freezing fractions were calculated and compared with values found from the Messinger analysis as applied by Ruff. Within the experimental uncertainty of measuring the leading-edge thickness, agreement of the experimental and analytical freezing fraction was very good. It is also shown that values of analytical freezing fraction were entirely consistent with observed ice shapes at and near rime conditions: At an analytical freezing fraction of unity, experimental ice shapes displayed the classic rime shape, while for conditions producing analytical freezing fractions slightly lower than unity, glaze features started to appear.

Fractional ablative laser skin resurfacing: a review.

PubMed

Tajirian, Ani L; Tarijian, Ani L; Goldberg, David J

2011-12-01

Ablative laser technology has been in use for many years now. The large side effect profile however has limited its use. Fractional ablative technology is a newer development which combines a lesser side effect profile along with similar efficacy. In this paper we review fractional ablative laser skin resurfacing.

Void Fraction Instrument operation and maintenance manual

DOE Office of Scientific and Technical Information (OSTI.GOV)

Borgonovi, G.; Stokes, T.I.; Pearce, K.L.

This Operations and Maintenance Manual (O&MM) addresses riser installation, equipment and personnel hazards, operating instructions, calibration, maintenance, removal, and other pertinent information necessary to safely operate and store the Void Fraction Instrument. Final decontamination and decommissioning of the Void Fraction Instrument are not covered in this document.

Phosphorus content in three physical fractions of typical Chernozem

NASA Astrophysics Data System (ADS)

Kotelnikova, Anna; Egorova, Zoya; Sushkov, Nikolai; Matveeva, Natalia; Fastovets, Ilya; Rogova, Olga; Volkov, Dmitriy

2017-04-01

The widespread use of fertilizers makes it necessary to study not only the content but also the forms of occurrence of nutrients in soil, as well as the phase in which nutrients are transferred. These characteristics determine the availability of chemical elements for plants, but remain insufficiently studied. In this work we attempted to gain insight into the distribution of organo-mineral fractions in agriculturally used Chernozem from Voronezh (Russia) and the distribution of phosphorus - one of the most important nutrient elements - in this type of soil. We compared the distributions of phosphorus in physical fractions of the soil in 3 experimental groups: the control group (without fertilizers), the group fertilized with 1 dose of NPK, and the group fertilized with 2 doses of NPK. The soil was sampled during the period of treatment with fertilizers and during the period of aftereffect (4 years after the last application of fertilizers). In order to analyze organo-mineral fractions, we used size-density fractionation to separate the soil samples into three physical fractions: clay-associated fraction with particle size < 1μm (CF), light fraction with particle density < 2.0 g cm-3 (LF), and residual fraction > 2.0 g cm-3 (RF). Total phosphorus content (TPC) in the fractions was determined with Agilent 5100 ICP-AES spectrometer. To compare groups, simultaneous confidence intervals were computed from pooled variance estimators in ANOVA, and Fisher's LSD test was used. We showed that during the period of treatment with fertilizers LF increased proportionally to the dose of fertilizers, and a simultaneous reduction in RF was observed. During the period of aftereffect, the content of these fractions tended to the control value. The increase of LF may indicate increasing availability of nutrients, since this fraction is likely to participate in biological cycles. The analysis of TPC in fractions suggested that during the period of treatment with fertilizers most of

An enriched finite element method to fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Luan, Shengzhi; Lian, Yanping; Ying, Yuping; Tang, Shaoqiang; Wagner, Gregory J.; Liu, Wing Kam

2017-08-01

In this paper, an enriched finite element method with fractional basis [ 1,x^{α }] for spatial fractional partial differential equations is proposed to obtain more stable and accurate numerical solutions. For pure fractional diffusion equation without advection, the enriched Galerkin finite element method formulation is demonstrated to simulate the exact solution successfully without any numerical oscillation, which is advantageous compared to the traditional Galerkin finite element method with integer basis [ 1,x] . For fractional advection-diffusion equation, the oscillatory behavior becomes complex due to the introduction of the advection term which can be characterized by a fractional element Peclet number. For the purpose of addressing the more complex numerical oscillation, an enriched Petrov-Galerkin finite element method is developed by using a dimensionless fractional stabilization parameter, which is formulated through a minimization of the residual of the nodal solution. The effectiveness and accuracy of the enriched finite element method are demonstrated by a series of numerical examples of fractional diffusion equation and fractional advection-diffusion equation, including both one-dimensional and two-dimensional, steady-state and time-dependent cases.

Perfluorinated surfactants (PFSs) in size-fractionated street dust in Tokyo.

PubMed

Murakami, Michio; Takada, Hideshige

2008-11-01

We investigated perfluorinated surfactants (PFSs) in size-fractionated street dust to identify their occurrence, contributions from traffic, and potential routes of entry into waters. Street dust was collected from residential areas and heavily trafficked areas in Tokyo and sorted into fine (<63 microm) and coarse fractions (63-2000 microm). Five PFS species were analyzed by liquid chromatography-tandem mass spectrometry: perfluorooctanesulfonate (PFOS), perfluorooctanoate (PFOA), perfluorononanoate (PFNA), perfluorodecanoate (PFDA), and perfluoroundecanoate (PFUA). In fine fractions, PFS contents were significantly higher in heavily trafficked street dust than in residential street dust, but in coarse fractions, no significant differences were observed. Additionally, in heavily trafficked areas, PFS contents were significantly higher in fine fractions than in coarse fractions, but in residential areas, no significant differences were observed. PFS compositions differed between size fractions, not locations, indicating differences in sources between size fractions. Fine particles from traffic contributed to PFSs in street dust. Street dust possibly acts as the origin of PFSs in street runoff and eventually enters waters. This is the first report of PFSs in street dust.

A Tutorial Review on Fractal Spacetime and Fractional Calculus

NASA Astrophysics Data System (ADS)

He, Ji-Huan

2014-11-01

This tutorial review of fractal-Cantorian spacetime and fractional calculus begins with Leibniz's notation for derivative without limits which can be generalized to discontinuous media like fractal derivative and q-derivative of quantum calculus. Fractal spacetime is used to elucidate some basic properties of fractal which is the foundation of fractional calculus, and El Naschie's mass-energy equation for the dark energy. The variational iteration method is used to introduce the definition of fractional derivatives. Fractal derivative is explained geometrically and q-derivative is motivated by quantum mechanics. Some effective analytical approaches to fractional differential equations, e.g., the variational iteration method, the homotopy perturbation method, the exp-function method, the fractional complex transform, and Yang-Laplace transform, are outlined and the main solution processes are given.

Quasiparticle Tunneling in the Fractional Quantum Hall effect at filling fraction ν=5/2

NASA Astrophysics Data System (ADS)

Radu, Iuliana P.

2009-03-01

In a two-dimensional electron gas (2DEG), in the fractional quantum Hall regime, the quasiparticles are predicted to have fractional charge and statistics, as well as modified Coulomb interactions. The state at filling fraction ν=5/2 is predicted by some theories to have non-abelian statistics, a property that might be exploited for topological quantum computing. However, alternative models with abelian properties have been proposed as well. Weak quasiparticle tunneling between counter-propagating edges is one of the methods that can be used to learn about the properties of the state and potentially distinguish between models describing it. We employ an electrostatically defined quantum point contact (QPC) fabricated on a high mobility GaAs/AlGaAs 2DEG to create a constriction where quasiparticles can tunnel between counter-propagating edges. We study the temperature and dc bias dependence of the tunneling conductance, while preserving the same filling fraction in the constriction and the bulk of the sample. The data show scaling of the bias-dependent tunneling over a range of temperatures, in agreement with the theory of weak quasiparticle tunneling, and we extract values for the effective charge and interaction parameter of the quasiparticles. The ranges of values obtained are consistent with those predicted by certain models describing the 5/2 state, indicating as more probable a non-abelian state. This work was done in collaboration with J. B. Miller, C. M. Marcus, M. A. Kastner, L. N. Pfeiffer and K. W. West. This work was supported in part by the Army Research Office (W911NF-05-1-0062), the Nanoscale Science and Engineering Center program of NSF (PHY-0117795), NSF (DMR-0701386), the Center for Materials Science and Engineering program of NSF (DMR-0213282) at MIT, the Microsoft Corporation Project Q, and the Center for Nanoscale Systems at Harvard University.

Measurement of prominent eta-decay branching fractions.

PubMed

Lopez, A; Mehrabyan, S; Mendez, H; Ramirez, J; Ge, J Y; Miller, D H; Sanghi, B; Shipsey, I P J; Xin, B; Adams, G S; Anderson, M; Cummings, J P; Danko, I; Hu, D; Moziak, B; Napolitano, J; He, Q; Insler, J; Muramatsu, H; Park, C S; Thorndike, E H; Yang, F; Artuso, M; Blusk, S; Khalil, S; Li, J; Menaa, N; Mountain, R; Nisar, S; Randrianarivony, K; Sia, R; Skwarnicki, T; Stone, S; Wang, J C; Bonvicini, G; Cinabro, D; Dubrovin, M; Lincoln, A; Asner, D M; Edwards, K W; Naik, P; Briere, R A; Ferguson, T; Tatishvili, G; Vogel, H; Watkins, M E; Rosner, J L; Adam, N E; Alexander, J P; Cassel, D G; Duboscq, J E; Ehrlich, R; Fields, L; Galik, R S; Gibbons, L; Gray, R; Gray, S W; Hartill, D L; Heltsley, B K; Hertz, D; Jones, C D; Kandaswamy, J; Kreinick, D L; Kuznetsov, V E; Mahlke-Krüger, H; Mohapatra, D; Onyisi, P U E; Patterson, J R; Peterson, D; Riley, D; Ryd, A; Sadoff, A J; Shi, X; Stroiney, S; Sun, W M; Wilksen, T; Athar, S B; Patel, R; Yelton, J; Rubin, P; Eisenstein, B I; Karliner, I; Lowrey, N; Selen, M; White, E J; Wiss, J; Mitchell, R E; Shepherd, M R; Besson, D; Pedlar, T K; Cronin-Hennessy, D; Gao, K Y; Hietala, J; Kubota, Y; Klein, T; Lang, B W; Poling, R; Scott, A W; Zweber, P; Dobbs, S; Metreveli, Z; Seth, K K; Tomaradze, A; Ernst, J; Ecklund, K M; Severini, H; Love, W; Savinov, V

2007-09-21

The decay psi(2S) --> etaJ/psi is used to measure, for the first time, all prominent eta-meson branching fractions with the same experiment in the same dataset, thereby providing a consistent treatment of systematics across branching fractions. We present results for eta decays to gamma gamma, pi(+)pi(-)pi(0), 3pi(0), pi(+)pi(-)gamma and e(+)e(-)gamma, accounting for 99.9% of all eta decays. The precision of several of the branching fractions and their ratios is improved. Two channels, pi(+)pi(-)gamma and e(+)e(-)gamma, show results that differ at the level of three standard deviations from those previously determined.

Measurement of Prominent η-Decay Branching Fractions

NASA Astrophysics Data System (ADS)

Lopez, A.; Mehrabyan, S.; Mendez, H.; Ramirez, J.; Ge, J. Y.; Miller, D. H.; Sanghi, B.; Shipsey, I. P. J.; Xin, B.; Adams, G. S.; Anderson, M.; Cummings, J. P.; Danko, I.; Hu, D.; Moziak, B.; Napolitano, J.; He, Q.; Insler, J.; Muramatsu, H.; Park, C. S.; Thorndike, E. H.; Yang, F.; Artuso, M.; Blusk, S.; Khalil, S.; Li, J.; Menaa, N.; Mountain, R.; Nisar, S.; Randrianarivony, K.; Sia, R.; Skwarnicki, T.; Stone, S.; Wang, J. C.; Bonvicini, G.; Cinabro, D.; Dubrovin, M.; Lincoln, A.; Asner, D. M.; Edwards, K. W.; Naik, P.; Briere, R. A.; Ferguson, T.; Tatishvili, G.; Vogel, H.; Watkins, M. E.; Rosner, J. L.; Adam, N. E.; Alexander, J. P.; Cassel, D. G.; Duboscq, J. E.; Ehrlich, R.; Fields, L.; Galik, R. S.; Gibbons, L.; Gray, R.; Gray, S. W.; Hartill, D. L.; Heltsley, B. K.; Hertz, D.; Jones, C. D.; Kandaswamy, J.; Kreinick, D. L.; Kuznetsov, V. E.; Mahlke-Krüger, H.; Mohapatra, D.; Onyisi, P. U. E.; Patterson, J. R.; Peterson, D.; Riley, D.; Ryd, A.; Sadoff, A. J.; Shi, X.; Stroiney, S.; Sun, W. M.; Wilksen, T.; Athar, S. B.; Patel, R.; Yelton, J.; Rubin, P.; Eisenstein, B. I.; Karliner, I.; Lowrey, N.; Selen, M.; White, E. J.; Wiss, J.; Mitchell, R. E.; Shepherd, M. R.; Besson, D.; Pedlar, T. K.; Cronin-Hennessy, D.; Gao, K. Y.; Hietala, J.; Kubota, Y.; Klein, T.; Lang, B. W.; Poling, R.; Scott, A. W.; Zweber, P.; Dobbs, S.; Metreveli, Z.; Seth, K. K.; Tomaradze, A.; Ernst, J.; Ecklund, K. M.; Severini, H.; Love, W.; Savinov, V.

2007-09-01

The decay ψ(2S)→ηJ/ψ is used to measure, for the first time, all prominent η-meson branching fractions with the same experiment in the same dataset, thereby providing a consistent treatment of systematics across branching fractions. We present results for η decays to γγ, π+π-π0, 3π0, π+π-γ and e+e-γ, accounting for 99.9% of all η decays. The precision of several of the branching fractions and their ratios is improved. Two channels, π+π-γ and e+e-γ, show results that differ at the level of three standard deviations from those previously determined.

A Procedure to Construct Exact Solutions of Nonlinear Fractional Differential Equations

PubMed Central

Güner, Özkan; Cevikel, Adem C.

2014-01-01

We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions. PMID:24737972

A procedure to construct exact solutions of nonlinear fractional differential equations.

PubMed

Güner, Özkan; Cevikel, Adem C

2014-01-01

We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions.

Spiking and bursting patterns of fractional-order Izhikevich model

NASA Astrophysics Data System (ADS)

Teka, Wondimu W.; Upadhyay, Ranjit Kumar; Mondal, Argha

2018-03-01

Bursting and spiking oscillations play major roles in processing and transmitting information in the brain through cortical neurons that respond differently to the same signal. These oscillations display complex dynamics that might be produced by using neuronal models and varying many model parameters. Recent studies have shown that models with fractional order can produce several types of history-dependent neuronal activities without the adjustment of several parameters. We studied the fractional-order Izhikevich model and analyzed different kinds of oscillations that emerge from the fractional dynamics. The model produces a wide range of neuronal spike responses, including regular spiking, fast spiking, intrinsic bursting, mixed mode oscillations, regular bursting and chattering, by adjusting only the fractional order. Both the active and silent phase of the burst increase when the fractional-order model further deviates from the classical model. For smaller fractional order, the model produces memory dependent spiking activity after the pulse signal turned off. This special spiking activity and other properties of the fractional-order model are caused by the memory trace that emerges from the fractional-order dynamics and integrates all the past activities of the neuron. On the network level, the response of the neuronal network shifts from random to scale-free spiking. Our results suggest that the complex dynamics of spiking and bursting can be the result of the long-term dependence and interaction of intracellular and extracellular ionic currents.

Communication: a density functional with accurate fractional-charge and fractional-spin behaviour for s-electrons.

PubMed

Johnson, Erin R; Contreras-García, Julia

2011-08-28

We develop a new density-functional approach combining physical insight from chemical structure with treatment of multi-reference character by real-space modeling of the exchange-correlation hole. We are able to recover, for the first time, correct fractional-charge and fractional-spin behaviour for atoms of groups 1 and 2. Based on Becke's non-dynamical correlation functional [A. D. Becke, J. Chem. Phys. 119, 2972 (2003)] and explicitly accounting for core-valence separation and pairing effects, this method is able to accurately describe dissociation and strong correlation in s-shell many-electron systems. © 2011 American Institute of Physics

Using Technology Effectively to Teach about Fractions

ERIC Educational Resources Information Center

Hensberry, Karina K. R.; Moore, Emily B.; Perkins, Katherine

2015-01-01

In this article, the authors describe classroom use of technology that successfully engaged fourth grade students (typically aged 9-10) in the United States in learning about fractions. The activities involved the use of an interactive simulation designed to support student learning of fractions, and whole-class discussion where students were…

Fractions Learning in Children with Mathematics Difficulties

ERIC Educational Resources Information Center

Tian, Jing; Siegler, Robert S.

2017-01-01

Learning fractions is difficult for children in general and especially difficult for children with mathematics difficulties (MD). Recent research on developmental and individual differences in fraction knowledge of children with MD and typically achieving (TA) children has demonstrated that U.S. children with MD start middle school behind their TA…

Fractions Learning in Children with Mathematics Difficulties

ERIC Educational Resources Information Center

Tian, Jing; Siegler, Robert S.

2016-01-01

Learning of fractions is difficult for children in general and especially difficult for children with mathematics difficulties (MD). Recent research on developmental and individual differences in fraction knowledge of MD and typically achieving (TA) children has demonstrated that U.S. children with MD start middle school behind TA peers in…

Understanding Division of Fractions: An Alternative View

ERIC Educational Resources Information Center

Fredua-Kwarteng, E.; Ahia, Francis

2006-01-01

The purpose of this paper is to offer three alternatives to patterns or visualization used to justify division of fraction "algorithm" invert and multiply". The three main approaches are historical, similar denominators and algebraic, that teachers could use to justify the standard algorithm of division of fraction. The historical approach uses…

Microbial Enzyme Activity and Carbon Cycling in Grassland Soil Fractions

NASA Astrophysics Data System (ADS)

Allison, S. D.; Jastrow, J. D.

2004-12-01

Extracellular enzymes are necessary to degrade complex organic compounds present in soils. Using physical fractionation procedures, we tested whether old soil carbon is spatially isolated from degradative enzymes across a prairie restoration chronosequence in Illinois, USA. We found that carbon-degrading enzymes were abundant in all soil fractions, including macroaggregates, microaggregates, and the clay fraction, which contains carbon with a mean residence time of ~200 years. The activities of two cellulose-degrading enzymes and a chitin-degrading enzyme were 2-10 times greater in organic matter fractions than in bulk soil, consistent with the rapid turnover of these fractions. Polyphenol oxidase activity was 3 times greater in the clay fraction than in the bulk soil, despite very slow carbon turnover in this fraction. Changes in enzyme activity across the restoration chronosequence were small once adjusted for increases in soil carbon concentration, although polyphenol oxidase activity per unit carbon declined by 50% in native prairie versus cultivated soil. These results are consistent with a `two-pool' model of enzyme and carbon turnover in grassland soils. In light organic matter fractions, enzyme production and carbon turnover both occur rapidly. However, in mineral-dominated fractions, both enzymes and their carbon substrates are immobilized on mineral surfaces, leading to slow turnover. Soil carbon accumulation in the clay fraction and across the prairie restoration chronosequence probably reflects increasing physical isolation of enzymes and substrates on the molecular scale, rather than the micron to millimeter scale.

Air pollution and heart failure: Relationship with the ejection fraction

PubMed Central

Dominguez-Rodriguez, Alberto; Abreu-Afonso, Javier; Rodríguez, Sergio; Juarez-Prera, Ruben A; Arroyo-Ucar, Eduardo; Gonzalez, Yenny; Abreu-Gonzalez, Pedro; Avanzas, Pablo

2013-01-01

AIM: To study whether the concentrations of particulate matter in ambient air are associated with hospital admission due to heart failure in patients with heart failure with preserved ejection fraction and reduced ejection fraction. METHODS: We studied 353 consecutive patients admitted into a tertiary care hospital with a diagnosis of heart failure. Patients with ejection fraction of ≥ 45% were classified as having heart failure with preserved ejection fraction and those with an ejection fraction of < 45% were classified as having heart failure with reduced ejection fraction. We determined the average concentrations of different sizes of particulate matter (< 10, < 2.5, and < 1 μm) and the concentrations of gaseous pollutants (carbon monoxide, sulphur dioxide, nitrogen dioxide and ozone) from 1 d up to 7 d prior to admission. RESULTS: The heart failure with preserved ejection fraction population was exposed to higher nitrogen dioxide concentrations compared to the heart failure with reduced ejection fraction population (12.95 ± 8.22 μg/m3 vs 4.50 ± 2.34 μg/m3, P < 0.0001). Multivariate analysis showed that nitrogen dioxide was a significant predictor of heart failure with preserved ejection fraction (odds ratio ranging from (1.403, 95%CI: 1.003-2.007, P = 0.04) to (1.669, 95%CI: 1.043-2.671, P = 0.03). CONCLUSION: This study demonstrates that short-term nitrogen dioxide exposure is independently associated with admission in the heart failure with preserved ejection fraction population. PMID:23538391

Doubly labeled water method: in vivo oxygen and hydrogen isotope fractionation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schoeller, D.A.; Leitch, C.A.; Brown, C.

The accuracy and precision of the doubly labeled water method for measuring energy expenditure are influenced by isotope fractionation during evaporative water loss and CO/sub 2/ excretion. To characterize in vivo isotope fractionation, we collected and isotopically analyzed physiological fluids and gases. Breath and transcutaneous water vapor were isotopically fractionated. The degree of fractionation indicated that the former was fractionated under equilibrium control at 37/sup 0/C, and the latter was kinetically fractionated. Sweat and urine were unfractionated. By use of isotopic balance models, the fraction of water lost via fractionating routes was estimated from the isotopic abundances of body water,more » local drinking water, and dietary solids. Fractionated water loss averaged 23% (SD = 10%) of water turnover, which agreed with our previous estimates based on metabolic rate, but there was a systematic difference between the results based on O/sub 2/ and hydrogen. Corrections for isotopic fractionation of water lost in breath and (nonsweat) transcutaneous loss should be made when using labeled water to measure water turnover or CO/sub 2/ production.« less

[Polycyclic aromatic hydrocarbons and soluble organic fraction in fine particles from solid fraction of biodiesel exhaust fumes].

PubMed

Szewczyńska, Małgorzata; Pośniak, Małgorzata

2012-01-01

This paper presents the results of investigations into the distribution of fine particles in the biodiesel exhaust fumes (bio-DEP), as well as into the content of polycyclic aromatic hydrocarbons (PAHs) and soluble organic fraction (SOF) in the study fractions. Samples of biodiesel B20 and B40 exhaust combustion fumes were generated at the model station composed of a diesel engine from Diesel TDI 2007 Volkswagen. Sioutas personal cascade impactor (SPCI) with Teflon filters and low-pressure impactor ELIPI (Dekati Low Pressure Impactor) were used for sampling diesel exhaust fine particles. The analysis of PAHs adsorbed on particulate fractions was performed by high performance liquid chromatography with fluorescence detection (HPLC/FL). For the determination of dry residue soluble organic fraction of biodiesel exhaust particles the gravimetric method was used. The combustion exhaust fumes of 100% ON contained mainly naphthalene, acenaphthalene, fluorene, phenanthrene, fluoranthene, pyrene, benzo(a)anthracene and chrysene, whilst the exhaust of B40-single PAHs of 4 and 5 rings, such as chrysene, benzo(k)fluoranthene, dibenzo (ah)anthracene and benzo(ghi)perylene. The total content of PAHs in diesel exhaust particles averaged 910 ng/m3 for 100% ON and 340 ng/m3 for B40. The concentrations of benzo(a)antarcene were at the levels of 310 ng/m3 (100% ON) and 90 ng/m3 (B40). The investigations indicated that a fraction < 025 microm represents the main component of diesel exhaust particles, regardless of the used fuel. Bioester B 100 commonly added to diesel fuel (ON) causes a reduction of the total particulates emission and thus reduces the amount of toxic substances adsorbed on their surface.

Power-law spatial dispersion from fractional Liouville equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tarasov, Vasily E.

2013-10-15

A microscopic model in the framework of fractional kinetics to describe spatial dispersion of power-law type is suggested. The Liouville equation with the Caputo fractional derivatives is used to obtain the power-law dependence of the absolute permittivity on the wave vector. The fractional differential equations for electrostatic potential in the media with power-law spatial dispersion are derived. The particular solutions of these equations for the electric potential of point charge in this media are considered.

Fractional excretion of sodium

MedlinePlus

FE sodium; FENa ... a lab. There, they are examined for salt (sodium) and creatinine levels. Creatinine is a chemical waste ... Chernecky CC, Berger BJ. Excretion fraction of filtered sodium-blood and urine. In: Chernecky CC, Berger BJ, ...

Variable Order and Distributed Order Fractional Operators

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.; Hartley, Tom T.

2002-01-01

Many physical processes appear to exhibit fractional order behavior that may vary with time or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. This paper develops the concept of variable and distributed order fractional operators. Definitions based on the Riemann-Liouville definitions are introduced and behavior of the operators is studied. Several time domain definitions that assign different arguments to the order q in the Riemann-Liouville definition are introduced. For each of these definitions various characteristics are determined. These include: time invariance of the operator, operator initialization, physical realization, linearity, operational transforms. and memory characteristics of the defining kernels. A measure (m2) for memory retentiveness of the order history is introduced. A generalized linear argument for the order q allows the concept of "tailored" variable order fractional operators whose a, memory may be chosen for a particular application. Memory retentiveness (m2) and order dynamic behavior are investigated and applications are shown. The concept of distributed order operators where the order of the time based operator depends on an additional independent (spatial) variable is also forwarded. Several definitions and their Laplace transforms are developed, analysis methods with these operators are demonstrated, and examples shown. Finally operators of multivariable and distributed order are defined in their various applications are outlined.

Minimizing metastatic risk in radiotherapy fractionation schedules

NASA Astrophysics Data System (ADS)

Badri, Hamidreza; Ramakrishnan, Jagdish; Leder, Kevin

2015-11-01

Metastasis is the process by which cells from a primary tumor disperse and form new tumors at distant anatomical locations. The treatment and prevention of metastatic cancer remains an extremely challenging problem. This work introduces a novel biologically motivated objective function to the radiation optimization community that takes into account metastatic risk instead of the status of the primary tumor. In this work, we consider the problem of developing fractionated irradiation schedules that minimize production of metastatic cancer cells while keeping normal tissue damage below an acceptable level. A dynamic programming framework is utilized to determine the optimal fractionation scheme. We evaluated our approach on a breast cancer case using the heart and the lung as organs-at-risk (OAR). For small tumor α /β values, hypo-fractionated schedules were optimal, which is consistent with standard models. However, for relatively larger α /β values, we found the type of schedule depended on various parameters such as the time when metastatic risk was evaluated, the α /β values of the OARs, and the normal tissue sparing factors. Interestingly, in contrast to standard models, hypo-fractionated and semi-hypo-fractionated schedules (large initial doses with doses tapering off with time) were suggested even with large tumor α/β values. Numerical results indicate the potential for significant reduction in metastatic risk.

Ultrasound speckle reduction based on fractional order differentiation.

PubMed

Shao, Dangguo; Zhou, Ting; Liu, Fan; Yi, Sanli; Xiang, Yan; Ma, Lei; Xiong, Xin; He, Jianfeng

2017-07-01

Ultrasound images show a granular pattern of noise known as speckle that diminishes their quality and results in difficulties in diagnosis. To preserve edges and features, this paper proposes a fractional differentiation-based image operator to reduce speckle in ultrasound. An image de-noising model based on fractional partial differential equations with balance relation between k (gradient modulus threshold that controls the conduction) and v (the order of fractional differentiation) was constructed by the effective combination of fractional calculus theory and a partial differential equation, and the numerical algorithm of it was achieved using a fractional differential mask operator. The proposed algorithm has better speckle reduction and structure preservation than the three existing methods [P-M model, the speckle reducing anisotropic diffusion (SRAD) technique, and the detail preserving anisotropic diffusion (DPAD) technique]. And it is significantly faster than bilateral filtering (BF) in producing virtually the same experimental results. Ultrasound phantom testing and in vivo imaging show that the proposed method can improve the quality of an ultrasound image in terms of tissue SNR, CNR, and FOM values.

Colloquium: Fractional calculus view of complexity: A tutorial

NASA Astrophysics Data System (ADS)

West, Bruce J.

2014-10-01

The fractional calculus has been part of the mathematics and science literature for 310 years. However, it is only in the past decade or so that it has drawn the attention of mainstream science as a way to describe the dynamics of complex phenomena with long-term memory, spatial heterogeneity, along with nonstationary and nonergodic statistics. The most recent application encompasses complex networks, which require new ways of thinking about the world. Part of the new cognition is provided by the fractional calculus description of temporal and topological complexity. Consequently, this Colloquium is not so much a tutorial on the mathematics of the fractional calculus as it is an exploration of how complex phenomena in the physical, social, and life sciences that have eluded traditional mathematical modeling become less mysterious when certain historical assumptions such as differentiability are discarded and the ordinary calculus is replaced with the fractional calculus. Exemplars considered include the fractional differential equations describing the dynamics of viscoelastic materials, turbulence, foraging, and phase transitions in complex social networks.

Eye movements reflect and shape strategies in fraction comparison

PubMed Central

Ischebeck, Anja; Weilharter, Marina; Körner, Christof

2016-01-01

The comparison of fractions is a difficult task that can often be facilitated by separately comparing components (numerators and denominators) of the fractions—that is, by applying so-called component-based strategies. The usefulness of such strategies depends on the type of fraction pair to be compared. We investigated the temporal organization and the flexibility of strategy deployment in fraction comparison by evaluating sequences of eye movements in 20 young adults. We found that component-based strategies could account for the response times and the overall number of fixations observed for the different fraction pairs. The analysis of eye movement sequences showed that the initial eye movements in a trial were characterized by stereotypical scanning patterns indicative of an exploratory phase that served to establish the kind of fraction pair presented. Eye movements that followed this phase adapted to the particular type of fraction pair and indicated the deployment of specific comparison strategies. These results demonstrate that participants employ eye movements systematically to support strategy use in fraction comparison. Participants showed a remarkable flexibility to adapt to the most efficient strategy on a trial-by-trial basis. Our results confirm the value of eye movement measurements in the exploration of strategic adaptation in complex tasks. PMID:26039819

Iteration: Unit Fraction Knowledge and the French Fry Tasks

ERIC Educational Resources Information Center

Tzur, Ron; Hunt, Jessica

2015-01-01

Often, students who solve fraction tasks respond in ways that indicate inadequate conceptual grounding of unit fractions. Many elementary school curricula use folding, partitioning, shading, and naming parts of various wholes to develop children's understanding of unit and then nonunit fractions (e.g., coloring three of four parts of a pizza and…

Analytical study of fractional equations describing anomalous diffusion of energetic particles

NASA Astrophysics Data System (ADS)

Tawfik, A. M.; Fichtner, H.; Schlickeiser, R.; Elhanbaly, A.

2017-06-01

To present the main influence of anomalous diffusion on the energetic particle propagation, the fractional derivative model of transport is developed by deriving the fractional modified Telegraph and Rayleigh equations. Analytical solutions of the fractional modified Telegraph and the fractional Rayleigh equations, which are defined in terms of Caputo fractional derivatives, are obtained by using the Laplace transform and the Mittag-Leffler function method. The solutions of these fractional equations are given in terms of special functions like Fox’s H, Mittag-Leffler, Hermite and Hyper-geometric functions. The predicted travelling pulse solutions are discussed in each case for different values of fractional order.

Bifurcation and chaos of a new discrete fractional-order logistic map

NASA Astrophysics Data System (ADS)

Ji, YuanDong; Lai, Li; Zhong, SuChuan; Zhang, Lu

2018-04-01

The fractional-order discrete maps with chaotic behaviors based on the theory of ;fractional difference; are proposed in recent years. In this paper, instead of using fractional difference, a new fractionalized logistic map is proposed based on the numerical algorithm of fractional differentiation definition. The bifurcation diagrams of this map with various differential orders are given by numerical simulation. The simulation results show that the fractional-order logistic map derived in this manner holds rich dynamical behaviors because of its memory effect. In addition, new types of behaviors of bifurcation and chaos are found, which are different from those of the integer-order and the previous fractional-order logistic maps.

Mathematical Analogs and the Teaching of Fractions.

ERIC Educational Resources Information Center

Charles, Kathy; Nason, Rod; Cooper, Tom

The literature has noted that some mathematical analogs are more effective than others for the teaching of fractions. This study aimed to evaluate the efficacy of seven mathematical analogs commonly used in the teaching of the partitive quotient fraction construct. A sample of twelve purposively selected Year Three children were presented with…

Methane-producing bacteria - Natural fractionations of the stable carbon isotopes

NASA Technical Reports Server (NTRS)

Games, L. M.; Hayes, J. M.; Gunsalus, R. P.

1978-01-01

Procedures for determining the C-13/C-12 fractionation factors for methane-producing bacteria are described, and the fractionation factors (CO2/CH4) for the reduction of CO2 to CH4 by pure cultures are 1.045 for Methanosarcina barkeri at 40 C, 1.061 for Methanobacterium strain M.o.H. at 40 C, and 1.025 for Methanobacterium thermoautotrophicum at 65 C. The data are consistent with the field determinations if fractionation by acetate dissimilation approximates fractionations observed in natural environments. In other words, the acetic acid used by acetate dissimilating bacteria, if they play an important role in natural methane production, must have an intramolecular isotopic fractionation (CO2H/CH3) approximating the observed CO2/CH4 fractionation.

Multiswitching combination synchronisation of non-identical fractional-order chaotic systems

NASA Astrophysics Data System (ADS)

Bhat, Muzaffar Ahmad; Khan, Ayub

2018-06-01

In this paper, multiswitching combination synchronisation (MSCS) scheme has been investigated in a class of three non-identical fractional-order chaotic systems. The fractional-order Lorenz and Chen systems are taken as the drive systems. The combination of multidrive systems is then synchronised with the fractional-order Lü chaotic system. In MSCS, the state variables of the two drive systems synchronise with different state variables of the response system, simultaneously. Based on the stability of fractional-order chaotic systems, the MSCS of three fractional-order non-identical systems has been investigated. For the synchronisation of three non-identical fractional-order chaotic systems, suitable controllers have been designed. Theoretical analysis and numerical results are presented to demonstrate the validity and feasibility of the applied method.

R-Function Relationships for Application in the Fractional Calculus

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.; Hartley, Tom T.

2000-01-01

The F-function, and its generalization the R-function, are of fundamental importance in the fractional calculus. It has been shown that the solution of the fundamental linear fractional differential equation may be expressed in terms of these functions. These functions serve as generalizations of the exponential function in the solution of fractional differential equations. Because of this central role in the fractional calculus, this paper explores various intrarelationships of the R-function, which will be useful in further analysis. Relationships of the R-function to the common exponential function, e(t), and its fractional derivatives are shown. From the relationships developed, some important approximations are observed. Further, the inverse relationships of the exponential function, el, in terms of the R-function are developed. Also, some approximations for the R-function are developed.

R-function relationships for application in the fractional calculus.

PubMed

Lorenzo, Carl F; Hartley, Tom T

2008-01-01

The F-function, and its generalization the R-function, are of fundamental importance in the fractional calculus. It has been shown that the solution of the fundamental linear fractional differential equation may be expressed in terms of these functions. These functions serve as generalizations of the exponential function in the solution of fractional differential equations. Because of this central role in the fractional calculus, this paper explores various intrarelationships of the R-function, which will be useful in further analysis. Relationships of the R-function to the common exponential function, et, and its fractional derivatives are shown. From the relationships developed, some important approximations are observed. Further, the inverse relationships of the exponential function, et, in terms of the R-function are developed. Also, some approximations for the R-function are developed.

Quenching oscillating behaviors in fractional coupled Stuart-Landau oscillators

NASA Astrophysics Data System (ADS)

Sun, Zhongkui; Xiao, Rui; Yang, Xiaoli; Xu, Wei

2018-03-01

Oscillation quenching has been widely studied during the past several decades in fields ranging from natural sciences to engineering, but investigations have so far been restricted to oscillators with an integer-order derivative. Here, we report the first study of amplitude death (AD) in fractional coupled Stuart-Landau oscillators with partial and/or complete conjugate couplings to explore oscillation quenching patterns and dynamics. It has been found that the fractional-order derivative impacts the AD state crucially. The area of the AD state increases along with the decrease of the fractional-order derivative. Furthermore, by introducing and adjusting a limiting feedback factor in coupling links, the AD state can be well tamed in fractional coupled oscillators. Hence, it provides one an effective approach to analyze and control the oscillating behaviors in fractional coupled oscillators.

Study of the AC machines winding having fractional q

NASA Astrophysics Data System (ADS)

Bespalov, V. Y.; Sidorov, A. O.

2018-02-01

The winding schemes with a fractional numbers of slots per pole and phase q have been known and used for a long time. However, in the literature on the low-noise machines design there are not recommended to use. Nevertheless, fractional q windings have been realized in many applications of special AC electrical machines, allowing to improve their performance, including vibroacoustic one. This paper deals with harmonic analysis of windings having integer and fractional q in permanent magnet synchronous motors, a comparison of their characteristics is performed, frequencies of subharmonics are revealed. Optimal winding pitch design is found giving reduce the amplitudes of subharmonics. Distribution factors for subharmonics, fractional and high-order harmonics are calculated, results analysis is represented, allowing for giving recommendations how to calculate distribution factors for different harmonics when q is fractional.

Fractional-dimensional Child-Langmuir law for a rough cathode

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zubair, M., E-mail: muhammad-zubair@sutd.edu.sg; Ang, L. K., E-mail: ricky-ang@sutd.edu.sg

This work presents a self-consistent model of space charge limited current transport in a gap combined of free-space and fractional-dimensional space (F{sup α}), where α is the fractional dimension in the range 0 < α ≤ 1. In this approach, a closed-form fractional-dimensional generalization of Child-Langmuir (CL) law is derived in classical regime which is then used to model the effect of cathode surface roughness in a vacuum diode by replacing the rough cathode with a smooth cathode placed in a layer of effective fractional-dimensional space. Smooth transition of CL law from the fractional-dimensional to integer-dimensional space is also demonstrated. The model has beenmore » validated by comparing results with an experiment.« less

Analysis of fractionation in corn-to-ethanol plants

NASA Astrophysics Data System (ADS)

Nelson, Camille

As the dry grind ethanol industry has grown, the research and technology surrounding ethanol production and co-product value has increased. Including use of back-end oil extraction and front-end fractionation. Front-end fractionation is pre-fermentation separation of the corn kernel into 3 fractions: endosperm, bran, and germ. The endosperm fraction enters the existing ethanol plant, and a high protein DDGS product remains after fermentation. High value oil is extracted out of the germ fraction. This leaves corn germ meal and bran as co-products from the other two streams. These 3 co-products have a very different composition than traditional corn DDGS. Installing this technology allows ethanol plants to increase profitability by tapping into more diverse markets, and ultimately could allow for an increase in profitability. An ethanol plant model was developed to evaluate both back-end oil extraction and front-end fractionation technology and predict the change in co-products based on technology installed. The model runs in Microsoft Excel and requires inputs of whole corn composition (proximate analysis), amino acid content, and weight to predict the co-product quantity and quality. User inputs include saccharification and fermentation efficiencies, plant capacity, and plant process specifications including front-end fractionation and backend oil extraction, if applicable. This model provides plants a way to assess and monitor variability in co-product composition due to the variation in whole corn composition. Additionally the co-products predicted in this model are entered into the US Pork Center of Excellence, National Swine Nutrition Guide feed formulation software. This allows the plant user and animal nutritionists to evaluate the value of new co-products in existing animal diets.

The Vertical Linear Fractional Initialization Problem

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.; Hartley, Tom T.

1999-01-01

This paper presents a solution to the initialization problem for a system of linear fractional-order differential equations. The scalar problem is considered first, and solutions are obtained both generally and for a specific initialization. Next the vector fractional order differential equation is considered. In this case, the solution is obtained in the form of matrix F-functions. Some control implications of the vector case are discussed. The suggested method of problem solution is shown via an example.

Laser Resurfacing: Full Field and Fractional.

PubMed

Pozner, Jason N; DiBernardo, Barry E

2016-07-01

Laser resurfacing is a very popular procedure worldwide. Full field and fractional lasers are used in many aesthetic practices. There have been significant advances in laser resurfacing in the past few years, which make patient treatments more efficacious and with less downtime. Erbium and carbon dioxide and ablative, nonablative, and hybrid fractional lasers are all extremely effective and popular tools that have a place in plastic surgery and dermatology offices. Copyright © 2016 Elsevier Inc. All rights reserved.

Multidimensional fractional Schrödinger equation

NASA Astrophysics Data System (ADS)

Rodrigues, M. M.; Vieira, N.

2012-11-01

This work is intended to investigate the multi-dimensional space-time fractional Schrödinger equation of the form (CDt0+αu)(t,x) = iħ/2m(C∇βu)(t,x), with ħ the Planck's constant divided by 2π, m is the mass and u(t,x) is a wave function of the particle. Here (CDt0+α,C∇β are operators of the Caputo fractional derivatives, where α ∈]0,1] and β ∈]1,2]. The wave function is obtained using Laplace and Fourier transforms methods and a symbolic operational form of solutions in terms of the Mittag-Leffler functions is exhibited. It is presented an expression for the wave function and for the quantum mechanical probability density. Using Banach fixed point theorem, the existence and uniqueness of solutions is studied for this kind of fractional differential equations.

Chemical and nutritional characteristics of high-fibre rye milling fractions.

PubMed

Kołodziejczyk, Piotr; Makowska, Agnieszka; Pospieszna, Barbara; Michniewicz, Jan; Paschke, Hanna

2018-01-01

Many studies have demonstrated the potential health benefits of consuming more high-fibre cereal-based food products. Therefore, there is a need to discover new ways to improve the overall nutritional balance of refined cereal products and focus on increasing their dietary fibre content, at the expense of readily digestible carbohydrates. Lab-scale milling and sieving of whole rye grain was used to obtain two fractions rich in dietary fibre. The fractions were analysed and compared, in terms of microstructure, chemical com- position and nutritional quality. The two fractions significantly obtained differed in their particle size and contents of minerals, available saccharides, and nutritional fractions of starch and dietary fibre and its major components. The total dietary fibre concentrations in the coarse and fine fractions were 50.0 and 36.0 g/100 g, respectively, i.e. three and 2.2 times higher than that of wholegrain rye flour. Both fractions also differed in their relative proportions of major fibre components. In the fine fraction, the levels of soluble fibre, as well as soluble arabinoxylans and fructans, were significantly higher than those in the coarse fraction. It was shown that the application of a simple dry-fractionation method to wholemeal rye flour allows the preparation of two rye products which can serve as concentrated sources of dietary fibre low in available saccharides.

Early Fractions Learning of 3rd Grade Students in SD Laboratorium Unesa

ERIC Educational Resources Information Center

Sari, Elisabet Ayunika Permata; Juniati, Dwi; Patahudin, Sitti Maesuri

2012-01-01

Fractions varied meanings is one of the causes of difficulties in learning fractions. These students should be given greater opportunities to explore the meaning of fractions before they learn the relationship between fractions and operations on fractions. Although students shading an area represents a fraction, it does not mean they really…

C and N Content in Density Fractions of Whole Soil and Soil Size Fraction Under Cacao Agroforestry Systems and Natural Forest in Bahia, Brazil

NASA Astrophysics Data System (ADS)

Rita, Joice Cleide O.; Gama-Rodrigues, Emanuela Forestieri; Gama-Rodrigues, Antonio Carlos; Polidoro, Jose Carlos; Machado, Regina Cele R.; Baligar, Virupax C.

2011-07-01

Agroforestry systems (AFSs) have an important role in capturing above and below ground soil carbon and play a dominant role in mitigation of atmospheric CO2. Attempts has been made here to identify soil organic matter fractions in the cacao-AFSs that have different susceptibility to microbial decomposition and further represent the basis of understanding soil C dynamics. The objective of this study was to characterize the organic matter density fractions and soil size fractions in soils of two types of cacao agroforestry systems and to compare with an adjacent natural forest in Bahia, Brazil. The land-use systems studied were: (1) a 30-year-old stand of natural forest with cacao (cacao cabruca), (2) a 30-year-old stand of cacao with Erythrina glauca as shade trees (cacao + erythrina), and (3) an adjacent natural forest without cacao. Soil samples were collected from 0-10 cm depth layer in reddish-yellow Oxisols. Soil samples was separated by wet sieving into five fraction-size classes (>2000 μm, 1000-2000 μm, 250-1000 μm, 53-250 μm, and <53 μm). C and N accumulated in to the light (free- and intra-aggregate density fractions) and heavy fractions of whole soil and soil size fraction were determined. Soil size fraction obtained in cacao AFS soils consisted mainly (65 %) of mega-aggregates (>2000 μm) mixed with macroaggregates (32-34%), and microaggregates (1-1.3%). Soil organic carbon (SOC) and total N content increased with increasing soil size fraction in all land-use systems. Organic C-to-total N ratio was higher in the macroaggregate than in the microaggregate. In general, in natural forest and cacao cabruca the contribution of C and N in the light and heavy fractions was similar. However, in cacao + erythrina the heavy fraction was the most common and contributed 67% of C and 63% of N. Finding of this study shows that the majority of C and N in all three systems studied are found in macroaggregates, particularly in the 250-1000 μm size aggregate class

C and N content in density fractions of whole soil and soil size fraction under cacao agroforestry systems and natural forest in Bahia, Brazil.

PubMed

Rita, Joice Cleide O; Gama-Rodrigues, Emanuela Forestieri; Gama-Rodrigues, Antonio Carlos; Polidoro, Jose Carlos; Machado, Regina Cele R; Baligar, Virupax C

2011-07-01

Agroforestry systems (AFSs) have an important role in capturing above and below ground soil carbon and play a dominant role in mitigation of atmospheric CO(2). Attempts has been made here to identify soil organic matter fractions in the cacao-AFSs that have different susceptibility to microbial decomposition and further represent the basis of understanding soil C dynamics. The objective of this study was to characterize the organic matter density fractions and soil size fractions in soils of two types of cacao agroforestry systems and to compare with an adjacent natural forest in Bahia, Brazil. The land-use systems studied were: (1) a 30-year-old stand of natural forest with cacao (cacao cabruca), (2) a 30-year-old stand of cacao with Erythrina glauca as shade trees (cacao + erythrina), and (3) an adjacent natural forest without cacao. Soil samples were collected from 0-10 cm depth layer in reddish-yellow Oxisols. Soil samples was separated by wet sieving into five fraction-size classes (>2000 μm, 1000-2000 μm, 250-1000 μm, 53-250 μm, and <53 μm). C and N accumulated in to the light (free- and intra-aggregate density fractions) and heavy fractions of whole soil and soil size fraction were determined. Soil size fraction obtained in cacao AFS soils consisted mainly (65 %) of mega-aggregates (>2000 μm) mixed with macroaggregates (32-34%), and microaggregates (1-1.3%). Soil organic carbon (SOC) and total N content increased with increasing soil size fraction in all land-use systems. Organic C-to-total N ratio was higher in the macroaggregate than in the microaggregate. In general, in natural forest and cacao cabruca the contribution of C and N in the light and heavy fractions was similar. However, in cacao + erythrina the heavy fraction was the most common and contributed 67% of C and 63% of N. Finding of this study shows that the majority of C and N in all three systems studied are found in macroaggregates, particularly in the 250-1000 μm size

Lord Brouncker's Forgotten Sequence of Continued Fractions for Pi

ERIC Educational Resources Information Center

Osler, Thomas J.

2010-01-01

"Lord Brouncker's continued fraction for pi" is a well-known result. In this article, we show that Brouncker found not only this one continued fraction, but an entire infinite sequence of related continued fractions for pi. These were recorded in the "Arithmetica Infinitorum" by John Wallis, but appear to have been ignored and forgotten by modern…

Bertrand's theorem and virial theorem in fractional classical mechanics

NASA Astrophysics Data System (ADS)

Yu, Rui-Yan; Wang, Towe

2017-09-01

Fractional classical mechanics is the classical counterpart of fractional quantum mechanics. The central force problem in this theory is investigated. Bertrand's theorem is generalized, and virial theorem is revisited, both in three spatial dimensions. In order to produce stable, closed, non-circular orbits, the inverse-square law and the Hooke's law should be modified in fractional classical mechanics.

In vitro antimicrobial activity of ethanolic fractions of Cryptolepis sanguinolenta

PubMed Central

2012-01-01

Background Following claims that some plants have antimicrobial activities against infectious microbes, the in vitro antimicrobial activities of different solvent fractions of ethanolic extract of Cryptolepis sanguinolenta were evaluated against eight standard bacteria and clinical isolates. Methods The solvent partitioning protocol involving ethanol, petroleum ether, chloroform, ethyl acetate and water, was used to extract various fractions of dried pulverized Cryptolepis sanguinolenta roots. Qualitative phyto-constituents screening was performed on the ethanol extract, chloroform fraction and the water fraction. The Kirby Bauer disk diffusion method was employed to ascertain the antibiogram of the test organisms while the agar diffusion method was used to investigate the antimicrobial properties of the crude plant extracts. The microplate dilution method aided in finding the MICs while the MBCs were obtained by the method of Nester and friends. The SPSS 16.0 version was used to analyze the percentages of inhibitions and bactericidal activities. Results The phytochemical screening revealed the presence of alkaloids, reducing sugars, polyuronides, anthocyanosides and triterpenes. The ethanol extract inhibited 5 out of 8 (62.5%) of the standard organisms and 6 out of 8 (75%) clinical isolates. The petroleum ether fraction inhibited 4 out of 8 (50%) of the standard microbes and 1 out of 8 (12.5%) clinical isolates. It was also observed that the chloroform fraction inhibited the growth of all the organisms (100%). Average inhibition zones of 14.0 ± 1.0 mm to 24.67 ± 0.58 mm was seen in the ethyl acetate fraction which halted the growth of 3 (37.5%) of the standard organisms. Inhibition of 7 (87.5%) of standard strains and 6 (75%) of clinical isolates were observed in the water fraction. The chloroform fraction exhibited bactericidal activity against all the test organisms while the remaining fractions showed varying degrees of bacteriostatic activity

Characteristic of student’s false concessive failure on fractions concept

NASA Astrophysics Data System (ADS)

Kurniawan, H.; Sutawidjaja, A.; As’ari, A. R.; Muksar, M.

2018-03-01

False concessive failure of students is students construction failure in achieving goals, where the process is false, the results obtained is true. This failure occurs because the schemes are not connected to each other, so it cannot form a new scheme. This research is a qualitative research that aim to describe the characteristics of students' false concessive failure on fractional concepts. This fractional concept is a fraction of the same part of the whole. To be able to solve the concept of this fraction, students must possess the concept of partition, the concept of addition and the concept of multiplication of the fraction.

A partially coupled, fraction-by-fraction modelling approach to the subsurface migration of gasoline spills

NASA Astrophysics Data System (ADS)

Fagerlund, F.; Niemi, A.

2007-01-01

The subsurface spreading behaviour of gasoline, as well as several other common soil- and groundwater pollutants (e.g. diesel, creosote), is complicated by the fact that it is a mixture of hundreds of different constituents, behaving differently with respect to e.g. dissolution, volatilisation, adsorption and biodegradation. Especially for scenarios where the non-aqueous phase liquid (NAPL) phase is highly mobile, such as for sudden spills in connection with accidents, it is necessary to simultaneously analyse the migration of the NAPL and its individual components in order to assess risks and environmental impacts. Although a few fully coupled, multi-phase, multi-constituent models exist, such models are highly complex and may be time consuming to use. A new, somewhat simplified methodology for modelling the subsurface migration of gasoline while taking its multi-constituent nature into account is therefore introduced here. Constituents with similar properties are grouped together into eight fractions. The migration of each fraction in the aqueous and gaseous phases as well as adsorption is modelled separately using a single-constituent multi-phase flow model, while the movement of the free-phase gasoline is essentially the same for all fractions. The modelling is done stepwise to allow updating of the free-phase gasoline composition at certain time intervals. The output is the concentration of the eight different fractions in the aqueous, gaseous, free gasoline and solid phases with time. The approach is evaluated by comparing it to a fully coupled multi-phase, multi-constituent numerical simulator in the modelling of a typical accident-type spill scenario, based on a tanker accident in northern Sweden. Here the PCFF method produces results similar to those of the more sophisticated, fully coupled model. The benefit of the method is that it is easy to use and can be applied to any single-constituent multi-phase numerical simulator, which in turn may have

On some new properties of fractional derivatives with Mittag-Leffler kernel

NASA Astrophysics Data System (ADS)

Baleanu, Dumitru; Fernandez, Arran

2018-06-01

We establish a new formula for the fractional derivative with Mittag-Leffler kernel, in the form of a series of Riemann-Liouville fractional integrals, which brings out more clearly the non-locality of fractional derivatives and is easier to handle for certain computational purposes. We also prove existence and uniqueness results for certain families of linear and nonlinear fractional ODEs defined using this fractional derivative. We consider the possibility of a semigroup property for these derivatives, and establish extensions of the product rule and chain rule, with an application to fractional mechanics.

Procedural and Conceptual Knowledge: Adults Reviewing Fractions

ERIC Educational Resources Information Center

Baker, William J.; Czarnocha, Bronislaw; Dias, Olen; Doyle, Kathleen; Kennis, James R.

2012-01-01

In the United States a majority of the students who enroll in community colleges require a review of secondary math before they are eligible for college level mathematics. In the pre-algebra course, that has a high drop-out rate, the most difficult topic for students is fractions. In order to better understand the fraction concept, Kieren…

Generalized modeling of the fractional-order memcapacitor and its character analysis

NASA Astrophysics Data System (ADS)

Guo, Zhang; Si, Gangquan; Diao, Lijie; Jia, Lixin; Zhang, Yanbin

2018-06-01

Memcapacitor is a new type of memory device generalized from the memristor. This paper proposes a generalized fractional-order memcapacitor model by introducing the fractional calculus into the model. The generalized formulas are studied and the two fractional-order parameter α, β are introduced where α mostly affects the fractional calculus value of charge q within the generalized Ohm's law and β generalizes the state equation which simulates the physical mechanism of a memcapacitor into the fractional sense. This model will be reduced to the conventional memcapacitor as α = 1 , β = 0 and to the conventional memristor as α = 0 , β = 1 . Then the numerical analysis of the fractional-order memcapacitor is studied. And the characteristics and output behaviors of the fractional-order memcapacitor applied with sinusoidal charge are derived. The analysis results have shown that there are four basic v - q and v - i curve patterns when the fractional order α, β respectively equal to 0 or 1, moreover all v - q and v - i curves of the other fractional-order models are transition curves between the four basic patterns.

Silica fractionation and reactivity in soils

NASA Astrophysics Data System (ADS)

Unzué Belmonte, Dácil; Barão, Lúcia; Vandevenne, Floor; Schoelynck, Jonas; Struyf, Eric; Meire, Patrick

2014-05-01

The Si cycle is a globally important biogeochemical cycle, with strong connections to other biogeochemical cycles, including C. Silica is taken up by plants to form protective structures called phytoliths, which become a part of the soil and contribute strongly to soil Si cycling upon litter burial. Different silica fractions are found in soils, with phytoliths among the most easily soluble, especially compared to silicate minerals. A whole set of secondary non-biogenic fractions exist, that also have a high reactivity (adsorbed Si, reactive secondary minerals…). A good characterization of the different fractions of reactive silica is crucial to move forward knowledge on ecosystem Si cycling, which has been recognized in the last decade as crucial for terrestrial Si fluxes. A new method to analyze the different fractions of silica in soils has been described by Koning et al. (2002) and adapted by our research team (Barão et al. 2013). Using a continuous extraction of Si and aluminum in 0.5M NaOH, biogenic and non-biogenic reactive fractions are separated based on their Si/Al ratios and their reactivity in NaOH. Applying this new method I will investigate three emerging ideas on how humans can affect directly terrestrial Si fluxes. -Land use. I expect strong silica fractionation and reactivity differences in different land uses. These effects due to agricultural and forestry management have already been shown earlier in temperate soils (Vandevenne et al. 2012). Now we will test this hypothesis in recently deforested soils, in the south of Brazil. 'Pristine' forest, managed forest and tobacco field soils (with and without rotation crops) will be studied. This research belongs to an interdisciplinary project on soils and global change. -Fire. According to the IPCC report, extreme events such as fires (number and intensity) would increase due to climate change. We analyzed litter from spruce forest, beech forest and peat soils at two burning levels, after 350°C and

Common magnitude representation of fractions and decimals is task dependent.

PubMed

Zhang, Li; Fang, Qiaochu; Gabriel, Florence C; Szűcs, Denes

2016-01-01

Although several studies have compared the representation of fractions and decimals, no study has investigated whether fractions and decimals, as two types of rational numbers, share a common representation of magnitude. The current study aimed to answer the question of whether fractions and decimals share a common representation of magnitude and whether the answer is influenced by task paradigms. We included two different number pairs, which were presented sequentially: fraction-decimal mixed pairs and decimal-fraction mixed pairs in all four experiments. Results showed that when the mixed pairs were very close numerically with the distance 0.1 or 0.3, there was a significant distance effect in the comparison task but not in the matching task. However, when the mixed pairs were further apart numerically with the distance 0.3 or 1.3, the distance effect appeared in the matching task regardless of the specific stimuli. We conclude that magnitudes of fractions and decimals can be represented in a common manner, but how they are represented is dependent on the given task. Fractions and decimals could be translated into a common representation of magnitude in the numerical comparison task. In the numerical matching task, fractions and decimals also shared a common representation. However, both of them were represented coarsely, leading to a weak distance effect. Specifically, fractions and decimals produced a significant distance effect only when the numerical distance was larger.

Wastewater characterisation by combining size fractionation, chemical composition and biodegradability.

PubMed

Ravndal, Kristin T; Opsahl, Eystein; Bagi, Andrea; Kommedal, Roald

2017-12-18

The potential for resource recovery from wastewater can be evaluated based on a detailed characterisation of wastewater. In this paper, results from fractionation and characterisation of two distinct wastewaters are reported. Using tangential flow filtration, the wastewater was fractionated into 10 size fractions ranging from 1 kDa to 1 mm, wherein the chemical composition and biodegradability were determined. Carbohydrates were dominant in particulate size fractions larger than 100 μm, indicating a potential of cellulose recovery from these fractions. While the particulate size fractions between 0.65 and 100 μm show a potential as a source for biofuel production due to an abundance of saturated C16 and C18 lipids. Both wastewaters were dominated by particulate (>0.65 μm), and oligo- and monomeric (<1 kDa) COD. Polymeric (1-1000 kDa) and colloidal (1000 kDa-0.65 μm) fractions had a low COD content, expected due to degradation in the sewer system upstream of the wastewater treatment plant. Biodegradation rates of particulate fractions increase with decreasing size. However, this was not seen in polymeric fractions where degradation rate was governed by chemical composition. Analytical validation of molecular weight and particle size distribution showed below filter cut-off retention of particles and polymers close to nominal cut-off, shifting the actual size distribution. Copyright © 2017. Published by Elsevier Ltd.

THE SERUM PROTEIN FRACTIONS IN THYMOQUINONE TREATED RATS.

PubMed

A, Güllü; S, Dede

2016-01-01

TQ has been used as treatment and preventive agent for many diseases over the years. The goal of this study was to investigate the effects of TQ supplement on fractions of serum proteins. Fourteen male Wistar-Albino rats (200-250 g weight) were used as material for two groups; (control (C) and thymoquinone (TQ) respectively. Each group contained seven rats. The control group had only corn oil, while the TQ group was dissolved in corn oil. 30 mg/kg/day were given by oral gavage for four weeks. The serum protein fractions were identified using cellulose acetate technique. The total protein level and albumin, α-1, α-2 fractions and A/G ratio have showed no difference between groups (p>0.05). β-globulin fractions of TQ group were higher than control's (p<0.05). In addition, it was observed that the γ-globulin levels of TQ group were lower than that of the control group's (p<0.05). From the results, it was observed that the changes of these fractions may have originated from elevation or decline synthesis, or activities of containing proteins.

THE SERUM PROTEIN FRACTIONS IN THYMOQUINONE TREATED RATS

PubMed Central

A, Güllü; S, Dede

2016-01-01

Background: TQ has been used as treatment and preventive agent for many diseases over the years. The goal of this study was to investigate the effects of TQ supplement on fractions of serum proteins. Materials and methods: Fourteen male Wistar-Albino rats (200-250 g weight) were used as material for two groups; (control (C) and thymoquinone (TQ) respectively. Each group contained seven rats. The control group had only corn oil, while the TQ group was dissolved in corn oil. 30 mg/kg/day were given by oral gavage for four weeks. The serum protein fractions were identified using cellulose acetate technique. Results: The total protein level and albumin, α-1, α-2 fractions and A/G ratio have showed no difference between groups (p>0.05). β-globulin fractions of TQ group were higher than control’s (p<0.05). In addition, it was observed that the γ-globulin levels of TQ group were lower than that of the control group’s (p<0.05). Conclusion: From the results, it was observed that the changes of these fractions may have originated from elevation or decline synthesis, or activities of containing proteins. PMID:28480357

Efficacy of fractional lasers in treating alopecia: a literature review.

PubMed

Perper, Marina; Aldahan, Adam S; Fayne, Rachel A; Emerson, Christopher P; Nouri, Keyvan

2017-11-01

Hair loss stemming from different types of alopecia, such as androgenic alopecia and alopecia areata, negatively affects over half the population and, in many circumstances, causes serious psychosocial distress. Current treatment options for alopecia, such as minoxidil, anthralin, and intralesional corticosteroids, vary efficacy and side effect profiles. It is known that low-level laser/light therapies (LLLT), or photobiomodulations, such as the US FDA-cleared HairMax Lasercomb®, He-Ne laser, and excimer laser, are relatively affordable, user-friendly, safe, and effective forms of treatment for hair loss. While less is known about the effectiveness of fractional lasers for combating hair loss, research suggests that by creating microscopic thermal injury zones, fractional lasers may cause an increase in hair growth from a wound healing process, making them potential therapeutic options for alopecia. A literature review was performed to evaluate the effectiveness of fractional lasers on hair regrowth. The specific fractional laser therapies include the 1550-nm nonablative fractional erbium-glass laser, the ablative fractional 2940-nm erbium:YAG laser, and the ablative fractional CO 2 fractional laser. Additional randomized controlled trials are necessary to further evaluate the effectiveness of the lasers, as well as to establish appropriate parameters and treatment intervals.

A study on rheological characteristics of roller milled fenugreek fractions.

PubMed

Sakhare, Suresh D; Inamdar, Aashitosh A; Prabhasankar, P

2016-01-01

Fenugreek seeds were fractionated by roller milling to get various fractions. The roller milled fractions and whole fenugreek flour (WFF) were evaluated for the flow behavior and time-dependent flow properties using a rotational viscometer at the temperatures of 10-60 (0)C. The samples subjected to a programmed shear rate increase linearly from 0 to 300 s(-1) in 3 min and successive decrease linearly shear rate from 300 s(-1) to 0 in 3 min. The roller milled fractions and WFF paste exhibited non-Newtonian pseudoplastic behavior. Difference in hysteresis loop area was observed among the roller milled fractions and WFF, being more noticeable at lower temperatures. Power law and Casson models were used to predict flow properties of samples. The power law model described well the flow behavior of the roller milled fractions and WFF at temperatures tested. Except flour (FL) fraction, consistency coefficient, m, increased with the temperature both in the forward and backward measurements. The roller milled fractions and WFF exhibited rheopectic behavior that increased viscosity with increasing the shear speed and the temperature. For all the sample tested, initial shear stress increased with increase in shear rate and temperature.

Randomized clinical trial of postoperative strontium-90 radiation therapy for pterygia: treatment using 30 Gy/3 fractions vs. 40 Gy/4 fractions.

PubMed

Nakamatsu, Kiyoshi; Nishimura, Yasumasa; Kanamori, Shuichi; Koike, Ryuta; Tachibana, Izumi; Nishikawa, Tatsuyuki; Shibata, Toru

2011-07-01

Postoperative adjuvant treatment with strontium-90 radiation therapy (RT) is a proven technique for reducing the recurrence of pterygium. This randomized trial was conducted to evaluate whether a total dose of 40 Gy provides a better local control rate than a total dose of 30 Gy for surgically resected pterygia. A single institutional randomized trial was conducted. Between 1999 and 2003, 74 pterygia in 71 patients were randomly allocated to 30 Gy/3 fractions/15 days (arm A) or to 40 Gy/4 fractions/22 days (arm B). Only primary pterygia for which RT could be started within 3 days of surgical resection were included. Postoperative RT was given by a strontium-90 eye applicator, and a dose of 10 Gy per fraction was delivered in weekly fractions (day 1, 8, 15, 22). Of the 74 pterygia treated, 73 in 70 patients were analyzed. Of the 73 pterygia, 41 were allocated to arm A, and the remaining 32 to arm B. The 2-year local control rates for arm A and arm B were 85% and 75%, respectively, without significant difference. No serious acute and late complications were noted in either arm. Our new standard fractionation for postoperative RT for pterygia is 30 Gy/3 fractions.

Fractional lattice charge transport

NASA Astrophysics Data System (ADS)

Flach, Sergej; Khomeriki, Ramaz

2017-01-01

We consider the dynamics of noninteracting quantum particles on a square lattice in the presence of a magnetic flux α and a dc electric field E oriented along the lattice diagonal. In general, the adiabatic dynamics will be characterized by Bloch oscillations in the electrical field direction and dispersive ballistic transport in the perpendicular direction. For rational values of α and a corresponding discrete set of values of E(α) vanishing gaps in the spectrum induce a fractionalization of the charge in the perpendicular direction - while left movers are still performing dispersive ballistic transport, the complementary fraction of right movers is propagating in a dispersionless relativistic manner in the opposite direction. Generalizations and the possible probing of the effect with atomic Bose-Einstein condensates and photonic networks are discussed. Zak phase of respective band associated with gap closing regime has been computed and it is found converging to π/2 value.

Fractional condensation of pyrolysis vapors produced from Nordic feedstocks in cyclone pyrolysis

DOE PAGES

Johansson, Ann-Christine; Lisa, Kristiina; Sandström, Linda; ...

2016-12-06

Pyrolysis oil is a complex mixture of different chemical compounds with a wide range of molecular weights and boiling points. Due to its complexity, an efficient fractionation of the oil may be a more promising approach of producing liquid fuels and chemicals than treating the whole oil. In this work a sampling system based on fractional condensation was attached to a cyclone pyrolysis pilot plant to enable separation of the produced pyrolysis vapors into five oil fractions. The sampling system was composed of cyclonic condensers and coalescing filters arranged in series. Our objective was to characterize the oil fractions producedmore » from three different Nordic feedstocks and suggest possible applications. The oil fractions were thoroughly characterized using several analytical techniques including water content; elemental composition; heating value, and chemical compound group analysis using solvent fractionation, quantitative 13C NMR and 1H NMR and GC x GC - TOFMS. The results show that the oil fractions significantly differ from each other both in chemical and physical properties. The first fractions and the fraction composed of aerosols were highly viscous and contained larger energy-rich compounds of mainly lignin-derived material. The middle fraction contained medium-size compounds with relatively high concentration of water, sugars, alcohols, hydrocarbonyls and acids and finally the last fraction contained smaller molecules such as water, aldehydes, ketones and acids. But, the properties of the respective fractions seem independent on the studied feedstock types, i.e. the respective fractions produced from different feedstock are rather similar. Furthermore, this promotes the possibility to vary the feedstock depending on availability while retaining the oil properties. Possible applications of the five fractions vary from oil for combustion and extraction of the pyrolytic lignin in the early fractions to extraction of sugars from the early and middle

Fractional condensation of pyrolysis vapors produced from Nordic feedstocks in cyclone pyrolysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Johansson, Ann-Christine; Lisa, Kristiina; Sandström, Linda

Pyrolysis oil is a complex mixture of different chemical compounds with a wide range of molecular weights and boiling points. Due to its complexity, an efficient fractionation of the oil may be a more promising approach of producing liquid fuels and chemicals than treating the whole oil. In this work a sampling system based on fractional condensation was attached to a cyclone pyrolysis pilot plant to enable separation of the produced pyrolysis vapors into five oil fractions. The sampling system was composed of cyclonic condensers and coalescing filters arranged in series. Our objective was to characterize the oil fractions producedmore » from three different Nordic feedstocks and suggest possible applications. The oil fractions were thoroughly characterized using several analytical techniques including water content; elemental composition; heating value, and chemical compound group analysis using solvent fractionation, quantitative 13C NMR and 1H NMR and GC x GC - TOFMS. The results show that the oil fractions significantly differ from each other both in chemical and physical properties. The first fractions and the fraction composed of aerosols were highly viscous and contained larger energy-rich compounds of mainly lignin-derived material. The middle fraction contained medium-size compounds with relatively high concentration of water, sugars, alcohols, hydrocarbonyls and acids and finally the last fraction contained smaller molecules such as water, aldehydes, ketones and acids. But, the properties of the respective fractions seem independent on the studied feedstock types, i.e. the respective fractions produced from different feedstock are rather similar. Furthermore, this promotes the possibility to vary the feedstock depending on availability while retaining the oil properties. Possible applications of the five fractions vary from oil for combustion and extraction of the pyrolytic lignin in the early fractions to extraction of sugars from the early and middle

Soil tension mediates isotope fractionation during soil water evaporation

NASA Astrophysics Data System (ADS)

Gaj, Marcel; McDonnell, Jeffrey

2017-04-01

Isotope tracing of the water cycle is increasing in its use and usefulness. Many new studies are extracting soil waters and relating these to streamflow, groundwater recharge and plant transpiration. Nevertheless, unlike isotope fractionation factors from open water bodies, soil water fractionation factors are poorly understood and until now, only empirically derived. In contrast to open water evaporation where temperature, humidity and vapor pressure gradient define fractionation (as codified in the well-known Craig and Gordon model), soil water evaporation includes additionally, fractionation by matrix effects. There is yet no physical explanation of kinetic and equilibrium fraction from soil water within the soil profile. Here we present a simple laboratory experiment with four admixtures of soil grain size (from sand to silt to clay). Oven-dried samples were spiked with water of known isotopic composition at different soil water contents. Soils were then stored in sealed bags and the headspace filled with dry air and allowed to equilibrate for 24hours. Isotopic analysis of the headspace vapor was done with a Los Gatos Inc. water vapor isotope analyzer. Soil water potential of subsamples were measured with a water potential meter. We show for the first time that soil tension controls isotope fractionation in the resident soil water. Below a Pf 3.5 the δ-values of 18O and 2H of the headspace vapor is more positive and increases with increasing soil water potential. Surprisingly, we find that the relationship between soil tension and equilibrium fractionation is independent of soil type. However, δ-values of each soil type plot along a distinct evaporation line. These results indicate that equilibrium fractionation is affected by soil tension in addition to temperature. Therefore, at high soil water tension (under dry conditions) equilibrium fractionation is not consistent with current empirical formulations that ignore these effects. These findings may have

Trigonometric Integrals via Partial Fractions

ERIC Educational Resources Information Center

Chen, H.; Fulford, M.

2005-01-01

Parametric differentiation is used to derive the partial fractions decompositions of certain rational functions. Those decompositions enable us to integrate some new combinations of trigonometric functions.

Transient aging in fractional Brownian and Langevin-equation motion.

PubMed

Kursawe, Jochen; Schulz, Johannes; Metzler, Ralf

2013-12-01

Stochastic processes driven by stationary fractional Gaussian noise, that is, fractional Brownian motion and fractional Langevin-equation motion, are usually considered to be ergodic in the sense that, after an algebraic relaxation, time and ensemble averages of physical observables coincide. Recently it was demonstrated that fractional Brownian motion and fractional Langevin-equation motion under external confinement are transiently nonergodic-time and ensemble averages behave differently-from the moment when the particle starts to sense the confinement. Here we show that these processes also exhibit transient aging, that is, physical observables such as the time-averaged mean-squared displacement depend on the time lag between the initiation of the system at time t=0 and the start of the measurement at the aging time t(a). In particular, it turns out that for fractional Langevin-equation motion the aging dependence on t(a) is different between the cases of free and confined motion. We obtain explicit analytical expressions for the aged moments of the particle position as well as the time-averaged mean-squared displacement and present a numerical analysis of this transient aging phenomenon.

Application of fractional derivative with exponential law to bi-fractional-order wave equation with frictional memory kernel

NASA Astrophysics Data System (ADS)

Cuahutenango-Barro, B.; Taneco-Hernández, M. A.; Gómez-Aguilar, J. F.

2017-12-01

Analytical solutions of the wave equation with bi-fractional-order and frictional memory kernel of Mittag-Leffler type are obtained via Caputo-Fabrizio fractional derivative in the Liouville-Caputo sense. Through the method of separation of variables and Laplace transform method we derive closed-form solutions and establish fundamental solutions. Special cases with homogeneous Dirichlet boundary conditions and nonhomogeneous initial conditions, as well as for the external force are considered. Numerical simulations of the special solutions were done and novel behaviors are obtained.

Intitialization, Conceptualization, and Application in the Generalized Fractional Calculus

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.; Hartley, Tom T.

1998-01-01

This paper provides a formalized basis for initialization in the fractional calculus. The intent is to make the fractional calculus readily accessible to engineering and the sciences. A modified set of definitions for the fractional calculus is provided which formally include the effects of initialization. Conceptualizations of fractional derivatives and integrals are shown. Physical examples of the basic elements from electronics are presented along with examples from dynamics, material science, viscoelasticity, filtering, instrumentation, and electrochemistry to indicate the broad application of the theory and to demonstrate the use of the mathematics. The fundamental criteria for a generalized calculus established by Ross (1974) are shown to hold for the generalized fractional calculus under appropriate conditions. A new generalized form for the Laplace transform of the generalized differintegral is derived. The concept of a variable structure (order) differintegral is presented along with initial efforts toward meaningful definitions.

Initialization, conceptualization, and application in the generalized (fractional) calculus.

PubMed

Lorenzo, Carl F; Hartley, Tom T

2007-01-01

This paper provides a formalized basis for initialization in the fractional calculus. The intent is to make the fractional calculus readily accessible to engineering and the sciences. A modified set of definitions for the fractional calculus is provided which formally include the effects of initialization. Conceptualizations of fractional derivatives and integrals are shown. Physical examples of the basic elements from electronics are presented along with examples from dynamics, material science, viscoelasticity, filtering, instrumentation, and electrochemistry to indicate the broad application of the theory and to demonstrate the use of the mathematics. The fundamental criteria for a generalized calculus established by Ross (1974) are shown to hold for the generalized fractional calculus under appropriate conditions. A new generalized form for the Laplace transform of the generalized differintegral is derived. The concept of a variable structure (order) differintegral is presented along with initial efforts toward meaningful definitions.

Composition of the water-soluble fraction of different cheeses.

PubMed

Taborda, Gonzalo; Molina, Elena; Martínez-Castro, Isabel; Ramos, Mercedes; Amigo, Lourdes

2003-01-01

Volatile and nonvolatile compounds present in the water-soluble fraction (WSF) and water-soluble fraction with molecular weight lower than 1000 Da (WSF < 1000 Da) of six Spanish cheeses, Cabrales, Idiazábal, Mahón, Manchego, Roncal, and a goat's milk cheese, were analyzed. Different nitrogen fractions (determined by Kjeldahl method), caseins (by capillary electrophoresis), peptides and amino acids (by HPLC), and volatile components (by dynamic headspace coupled to GC-MS) as well as mineral content in the cheese fractions were analyzed and compared. The different nitrogen and volatile compounds identified in the WSF were characteristic of each cheese variety. Cabrales cheese displayed the highest content of free amino acids and the highest quantity and variety of volatile compounds. The WSF < 1000 Da fraction was less representative, especially for volatile compounds, as some of the components were lost in the ultrafiltration. Alcohols were better recovered than ketones and esters.

Enhanced thermoelectric response in the fractional quantum Hall effect

NASA Astrophysics Data System (ADS)

Roura-Bas, Pablo; Arrachea, Liliana; Fradkin, Eduardo

2018-02-01

We study the linear thermoelectric response of a quantum dot embedded in a constriction of a quantum Hall bar with fractional filling factors ν =1 /m within Laughlin series. We calculate the figure of merit Z T for the maximum efficiency at a fixed temperature difference. We find a significant enhancement of this quantity in the fractional filling in relation to the integer-filling case, which is a direct consequence of the fractionalization of the electron in the fractional quantum Hall state. We present simple theoretical expressions for the Onsager coefficients at low temperatures, which explicitly show that Z T and the Seebeck coefficient increase with m .

Detection of fractional solitons in quantum spin Hall systems

NASA Astrophysics Data System (ADS)

Fleckenstein, C.; Traverso Ziani, N.; Trauzettel, B.

2018-03-01

We propose two experimental setups that allow for the implementation and the detection of fractional solitons of the Goldstone-Wilczek type. The first setup is based on two magnetic barriers at the edge of a quantum spin Hall system for generating the fractional soliton. If then a quantum point contact is created with the other edge, the linear conductance shows evidence of the fractional soliton. The second setup consists of a single magnetic barrier covering both edges and implementing a long quantum point contact. In this case, the fractional soliton can unambiguously be detected as a dip in the conductance without the need to control the magnetization of the barrier.

Estimating dead-space fraction for secondary analyses of ARDS clinical trials

PubMed Central

Beitler, Jeremy R.; Thompson, B. Taylor; Matthay, Michael A.; Talmor, Daniel; Liu, Kathleen D.; Zhuo, Hanjing; Hayden, Douglas; Spragg, Roger G.; Malhotra, Atul

2015-01-01

Objective Pulmonary dead-space fraction is one of few lung-specific independent predictors of mortality from acute respiratory distress syndrome (ARDS). However, it is not measured routinely in clinical trials and thus altogether ignored in secondary analyses that shape future research directions and clinical practice. This study sought to validate an estimate of dead-space fraction for use in secondary analyses of clinical trials. Design Analysis of patient-level data pooled from ARDS clinical trials. Four approaches to estimate dead-space fraction were evaluated: three required estimating metabolic rate; one estimated dead-space fraction directly. Setting U.S. academic teaching hospitals. Patients Data from 210 patients across three clinical trials were used to compare performance of estimating equations with measured dead-space fraction. A second cohort of 3,135 patients from six clinical trials without measured dead-space fraction was used to confirm whether estimates independently predicted mortality. Interventions None. Measurements and Main Results Dead-space fraction estimated using the unadjusted Harris-Benedict equation for energy expenditure was unbiased (mean ± SD Harris-Benedict 0.59 ± 0.13; measured 0.60 ± 0.12). This estimate predicted measured dead-space fraction to within ± 0.10 in 70% of patients and ± 0.20 in 95% of patients. Measured dead-space fraction independently predicted mortality (OR 1.36 per 0.05 increase in dead-space fraction, 95% CI 1.10–1.68; p < .01). The Harris-Benedict estimate closely approximated this association with mortality in the same cohort (OR 1.55, 95% CI 1.21–1.98; p < .01) and remained independently predictive of death in the larger ARDSNet cohort. Other estimates predicted measured dead-space fraction or its association with mortality less well. Conclusions Dead-space fraction should be measured in future ARDS clinical trials to facilitate incorporation into secondary analyses. For analyses where dead

Comparison of different fractionation schedules toward a single fraction in high-dose-rate brachytherapy as monotherapy for low-risk prostate cancer using 3-dimensional radiobiological models.

PubMed

Mavroidis, Panayiotis; Milickovic, Natasa; Cruz, Wilbert F; Tselis, Nikolaos; Karabis, Andreas; Stathakis, Sotirios; Papanikolaou, Nikos; Zamboglou, Nikolaos; Baltas, Dimos

2014-01-01

The aim of the present study was the investigation of different fractionation schemes to estimate their clinical impact. For this purpose, widely applied radiobiological models and dosimetric measures were used to associate their results with clinical findings. The dose distributions of 12 clinical high-dose-rate brachytherapy implants for prostate were evaluated in relation to different fractionation schemes. The fractionation schemes compared were: (1) 1 fraction of 20 Gy; (2) 2 fractions of 14 Gy; (3) 3 fractions of 11 Gy; and (4) 4 fractions of 9.5 Gy. The clinical effectiveness of the different fractionation schemes was estimated through the complication-free tumor control probability (P+), the biologically effective uniform dose, and the generalized equivalent uniform dose index. For the different fractionation schemes, the tumor control probabilities were 98.5% in 1×20 Gy, 98.6% in 2×14 Gy, 97.5% in 3×11 Gy, and 97.8% in 4×9.5 Gy. The corresponding P+ values were 88.8% in 1×20 Gy, 83.9% in 2×14 Gy, 86.0% in 3×11 Gy, and 82.3% in 4×9.5 Gy. With use of the fractionation scheme 4×9.5 Gy as reference, the isoeffective schemes regarding tumor control for 1, 2, and 3 fractions were 1×19.68 Gy, 2×13.75 Gy, and 3×11.05 Gy. The optimum fractionation schemes for 1, 2, 3, and 4 fractions were 1×19.16 Gy with a P+ of 91.8%, 2×13.2 Gy with a P+ of 89.6%, 3×10.6 Gy with a P+ of 88.4%, and 4×9.02 Gy with a P+ of 86.9%. Among the fractionation schemes 1×20 Gy, 2×14 Gy, 3×11 Gy, and 4×9.5 Gy, the first scheme was more effective in terms of P+. After performance of a radiobiological optimization, it was shown that a single fraction of 19.2 to 19.7 Gy (average 19.5 Gy) should produce at least the same benefit as that given by the 4×9.5 Gy scheme, and it should reduce the expected total complication probability by approximately 40% to 55%. Copyright © 2014 Elsevier Inc. All rights reserved.

Comparison of Different Fractionation Schedules Toward a Single Fraction in High-Dose-Rate Brachytherapy as Monotherapy for Low-Risk Prostate Cancer Using 3-Dimensional Radiobiological Models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mavroidis, Panayiotis, E-mail: mavroidis@uthscsa.edu; Department of Medical Radiation Physics, Karolinska Institutet and Stockholm University, Stockholm; Milickovic, Natasa

2014-01-01

Purpose: The aim of the present study was the investigation of different fractionation schemes to estimate their clinical impact. For this purpose, widely applied radiobiological models and dosimetric measures were used to associate their results with clinical findings. Methods and Materials: The dose distributions of 12 clinical high-dose-rate brachytherapy implants for prostate were evaluated in relation to different fractionation schemes. The fractionation schemes compared were: (1) 1 fraction of 20 Gy; (2) 2 fractions of 14 Gy; (3) 3 fractions of 11 Gy; and (4) 4 fractions of 9.5 Gy. The clinical effectiveness of the different fractionation schemes was estimatedmore » through the complication-free tumor control probability (P{sub +}), the biologically effective uniform dose, and the generalized equivalent uniform dose index. Results: For the different fractionation schemes, the tumor control probabilities were 98.5% in 1 × 20 Gy, 98.6% in 2 × 14 Gy, 97.5% in 3 × 11 Gy, and 97.8% in 4 × 9.5 Gy. The corresponding P{sub +} values were 88.8% in 1 × 20 Gy, 83.9% in 2 × 14 Gy, 86.0% in 3 × 11 Gy, and 82.3% in 4 × 9.5 Gy. With use of the fractionation scheme 4 × 9.5 Gy as reference, the isoeffective schemes regarding tumor control for 1, 2, and 3 fractions were 1 × 19.68 Gy, 2 × 13.75 Gy, and 3 × 11.05 Gy. The optimum fractionation schemes for 1, 2, 3, and 4 fractions were 1 × 19.16 Gy with a P{sub +} of 91.8%, 2 × 13.2 Gy with a P{sub +} of 89.6%, 3 × 10.6 Gy with a P{sub +} of 88.4%, and 4 × 9.02 Gy with a P{sub +} of 86.9%. Conclusions: Among the fractionation schemes 1 × 20 Gy, 2 × 14 Gy, 3 × 11 Gy, and 4 × 9.5 Gy, the first scheme was more effective in terms of P{sub +}. After performance of a radiobiological optimization, it was shown that a single fraction of 19.2 to 19.7 Gy (average 19.5 Gy) should produce at least the same benefit as that given by the 4 × 9.5 Gy scheme, and it should reduce the expected total complication probability by

Intra-fraction motion of the prostate is a random walk

NASA Astrophysics Data System (ADS)

Ballhausen, H.; Li, M.; Hegemann, N.-S.; Ganswindt, U.; Belka, C.

2015-01-01

A random walk model for intra-fraction motion has been proposed, where at each step the prostate moves a small amount from its current position in a random direction. Online tracking data from perineal ultrasound is used to validate or reject this model against alternatives. Intra-fraction motion of a prostate was recorded by 4D ultrasound (Elekta Clarity system) during 84 fractions of external beam radiotherapy of six patients. In total, the center of the prostate was tracked for 8 h in intervals of 4 s. Maximum likelihood model parameters were fitted to the data. The null hypothesis of a random walk was tested with the Dickey-Fuller test. The null hypothesis of stationarity was tested by the Kwiatkowski-Phillips-Schmidt-Shin test. The increase of variance in prostate position over time and the variability in motility between fractions were analyzed. Intra-fraction motion of the prostate was best described as a stochastic process with an auto-correlation coefficient of ρ = 0.92  ±  0.13. The random walk hypothesis (ρ = 1) could not be rejected (p = 0.27). The static noise hypothesis (ρ = 0) was rejected (p < 0.001). The Dickey-Fuller test rejected the null hypothesis ρ = 1 in 25% to 32% of cases. On average, the Kwiatkowski-Phillips-Schmidt-Shin test rejected the null hypothesis ρ = 0 with a probability of 93% to 96%. The variance in prostate position increased linearly over time (r2 = 0.9  ±  0.1). Variance kept increasing and did not settle at a maximum as would be expected from a stationary process. There was substantial variability in motility between fractions and patients with maximum aberrations from isocenter ranging from 0.5 mm to over 10 mm in one patient alone. In conclusion, evidence strongly suggests that intra-fraction motion of the prostate is a random walk and neither static (like inter-fraction setup errors) nor stationary (like a cyclic motion such as breathing, for example). The prostate tends to drift away from the

Fractional Parts. Elementary Module for Use in a Mathematics Laboratory Setting.

ERIC Educational Resources Information Center

Charbonneau, Manon P.

This module, concerned with fractional parts, contains 15 activity sheets, 12 of these involve students in making fractional parts and discovering the relationships of less than, equal to, and greater than, between different fractional parts. The last three sheets are for extending and enriching experiences with fractional parts. Teaching…

A comparison of soil organic matter physical fractionation methods

NASA Astrophysics Data System (ADS)

Duddigan, Sarah; Alexander, Paul; Shaw, Liz; Collins, Chris

2017-04-01

Selecting a suitable physical fractionation to investigate soil organic matter dynamics from the plethora that are available is a difficult task. An initial investigation of four different physical fractionation methods was conducted (i) Six et al. (2002); (ii) Zimmermann et al. (2007); (iii) Sohi et al. (2001); and (iv) Plaza et al. (2013). Soils used for this were from a long-term organic matter field plot study where a sandy loam soil was subjected to the following treatments: Peat (Pt), Horse Manure (H), Garden Compost (GCf), Garden Compost at half rate (GCh), and a bare plot control (BP). Although each of these methods involved the isolation of unique fractions, in the interest of comparison, each fraction was categorised as either being (i) physically protected (i.e. in aggregates); (ii) chemically protected (such as in organo-mineral complexes); or (iii) unprotected by either of these mechanisms (so-called 'free' organic matter). Regardless of the fractionation method used, a large amount of the variation in total C contents of the different treated soils is accounted for by the differences in unprotected particulate organic matter. When comparing the methods to one another there were no consistent differences in carbon content in the physically protected, chemically protected, or unprotected fractions as operationally defined across all the five organic matter treatments. Therefore fractionation method selection, for this research, was primarily driven by the practicalities of conducting each method in the lab. All of the methods tested had their limitations, for use in this research. This is not a criticism of the methods themselves but largely a result of the lack of suitability for these particular samples. For example, samples that contain a lot of gravel can lead to problems for methods that use size distribution for fractionation. Problems can also be encountered when free particulate organic matter contributes a large proportion of the sample

Immunogenic Activity of a Ribosomal Fraction Obtained from Mycobacterium tuberculosis

PubMed Central

Youmans, Anne S.; Youmans, Guy P.

1965-01-01

Youmans, Anne S. (Northwestern University Medical School, Chicago, Ill.), and Guy P. Youmans. Immunogenic activity of a ribosomal fraction obtained from Mycobacterium tuberculosis. J. Bacteriol. 89:1291–1298. 1965.—The highly immunogenic particulate fraction obtained from mechanically ruptured cells of the H37Ra strain of Mycobacterium tuberculosis was suspended and centrifuged at 20,360 × g. The supernatant liquid from this centrifugation was centrifuged at 56,550 × g to remove the larger particles, and the supernatant liquid from this was centrifuged at 144,000 × g to obtain a ribosomal fraction. The sediments from the first two centrifugations were highly immunogenic, but the ribosomal fraction showed only slight capacity to immunize mice. However, when the ribosomal fraction was mixed with Freund's incomplete adjuvant, the immunogenic activity was equivalent to the particulate fraction from which it was prepared. To test the hypothesis that some membranous substance in the particulate fraction was acting as an adjuvant for the smaller particles in the ribosomal fraction, portions of the particulate fraction were treated separately with each of the membrane-disrupting agents, sodium deoxycholate, sodium lauryl sulfate, and 1 m sodium chloride. The treated materials were then centrifuged at 144,000 × g, and the sediments were tested for immunogenicity both with and without the addition of Freund's incomplete adjuvant. Without the adjuvant, the immunizing activities were very weak or absent; with the adjuvant, they were equivalent to that of the particulate fraction from which they were prepared. Other factors which have been found to damage or destroy membranes, such as freezing and thawing, and heat, also significantly decreased the immunogenic activity of the particulate fraction unless it was incorporated into Freund's incomplete adjuvant. The larger particles which sedimented at 56,550 × g were also treated with sodium lauryl sulfate and sodium

Chemical and isotopic fractionations by evaporation and their cosmochemical implications

NASA Astrophysics Data System (ADS)

Ozawa, Kazuhito; Nagahara, Hiroko

2001-07-01

A kinetic model for evaporation of a multi-component condensed phase with a fixed rate constant of the reaction is developed. A binary system with two isotopes for one of the components undergoing simple thermal histories (e.g., isothermal heating) is investigated in order to evaluate the extent of isotopic and chemical fractionations during evaporation. Diffusion in the condensed phase and the effect of back reaction from ambient gas are taken into consideration. Chemical and isotopic fractionation factors and the Péclet number for evaporation are the three main parameters that control the fractionation. Dust enrichment factor (η), the ratio of the initial dust quantity to that required for attainment of gas-dust equilibrium, is critical when back reactions become significant. Dust does not reach equilibrium with gas at η < 1. Notable chemical and isotopic fractionations usually take place under these conditions. There are two circumstances in which isotopic fractionation of a very volatile element does not accompany chemical fractionation during isothermal heating. One is free evaporation when diffusion in the condensed phase is very slow (η = 0), and the other is evaporation in the presence of ambient gas (η > 0). In the former case, a quasi-steady state in the diffusion boundary layer is maintained for isotopic fractionation but not for chemical fractionation. In the latter case, the back reaction brings the strong isotopic fractionation generated in the earlier stage of evaporation back to a negligibly small value in the later stage before complete evaporation. The model results are applied to cosmochemical fractionation of volatile elements during evaporation from a condensed phase that can be regarded as a binary solution phase. The wide range of potassium depletion without isotopic fractionation in various types of chondrules (Alexander et al., 2000) is explained by instantaneous heating followed by cooling in a closed system with various degrees of

Electrochemically controlled iron isotope fractionation

NASA Astrophysics Data System (ADS)

Black, Jay R.; Young, Edward D.; Kavner, Abby

2010-02-01

Variations in the stable isotope abundances of transition metals have been observed in the geologic record and trying to understand and reconstruct the physical/environmental conditions that produced these signatures is an area of active research. It is clear that changes in oxidation state lead to large fractionations of the stable isotopes of many transition metals such as iron, suggesting that transition metal stable isotope signatures could be used as a paleo-redox proxy. However, the factors contributing to these observed stable isotope variations are poorly understood. Here we investigate how the kinetics of iron redox electrochemistry generates isotope fractionation. Through a combination of electrodeposition experiments and modeling of electrochemical processes including mass-transport, we show that electron transfer reactions are the cause of a large isotope separation, while mass transport-limited supply of reactant to the electrode attenuates the observed isotopic fractionation. Furthermore, the stable isotope composition of electroplated transition metals can be tuned in the laboratory by controlling parameters such as solution chemistry, reaction overpotential, and solution convection. These methods are potentially useful for generating isotopically-marked metal surfaces for tracking and forensic purposes. In addition, our studies will help interpret stable isotope data in terms of identifying underlying electron transfer processes in laboratory and natural samples.

Efficacy and safety of fractional CO2 laser versus fractional Er:YAG laser in the treatment of facial skin wrinkles.

PubMed

Robati, Reza M; Asadi, Elmira

2017-02-01

Ablative fractional lasers were introduced for treating facial rhytides. Few studies have compared fractional CO 2 and Er:YAG lasers on cutaneous photodamages by a split trial. The aim of the present study was to compare these modalities in a randomized controlled double-blind split-face design with multiple sessions and larger sample size compared to previous studies done before. Forty patients with facial wrinkles were enrolled. Patients were randomly assigned to receive three monthly treatments on each side of the face, one with a fractional CO 2 and one with a fractional Er:YAG laser. The evaluations included investigating clinical outcome determined by two independent dermatologists not enrolled in the treatment along with measuring skin biomechanical property of cheeks using a sensitive biometrologic device with the assessment of cutaneous resonance running time (CRRT). Moreover, possible side effects and patients' satisfaction have been recorded at baseline, 1 month after each treatment, and 3 months after the last treatment session. Clinical assessment showed both modalities significantly reduce facial wrinkles (p value < 0.05), with no appreciable difference between two lasers. Mean CRRT values also decreased significantly after the laser treatment compared to the baseline in both laser groups. There was no serious long-standing adverse effect after both laser treatments, but the discomfort was more pronounced by the participants after CO 2 laser treatment. According to the present study, both fractional CO 2 and fractional Er:YAG lasers show considerable clinical improvement of facial skin wrinkles with no serious adverse effects, but post-treatment discomfort seems to be lower with Er:YAG laser.

Modeling electron fractionalization with unconventional Fock spaces.

PubMed

Cobanera, Emilio

2017-08-02

It is shown that certain fractionally-charged quasiparticles can be modeled on D-dimensional lattices in terms of unconventional yet simple Fock algebras of creation and annihilation operators. These unconventional Fock algebras are derived from the usual fermionic algebra by taking roots (the square root, cubic root, etc) of the usual fermionic creation and annihilation operators. If the fermions carry non-Abelian charges, then this approach fractionalizes the Abelian charges only. In particular, the mth-root of a spinful fermion carries charge e/m and spin 1/2. Just like taking a root of a complex number, taking a root of a fermion yields a mildly non-unique result. As a consequence, there are several possible choices of quantum exchange statistics for fermion-root quasiparticles. These choices are tied to the dimensionality [Formula: see text] of the lattice by basic physical considerations. One particular family of fermion-root quasiparticles is directly connected to the parafermion zero-energy modes expected to emerge in certain mesoscopic devices involving fractional quantum Hall states. Hence, as an application of potential mesoscopic interest, I investigate numerically the hybridization of Majorana and parafermion zero-energy edge modes caused by fractionalizing but charge-conserving tunneling.

Inter-fraction variations in respiratory motion models

NASA Astrophysics Data System (ADS)

McClelland, J. R.; Hughes, S.; Modat, M.; Qureshi, A.; Ahmad, S.; Landau, D. B.; Ourselin, S.; Hawkes, D. J.

2011-01-01

Respiratory motion can vary dramatically between the planning stage and the different fractions of radiotherapy treatment. Motion predictions used when constructing the radiotherapy plan may be unsuitable for later fractions of treatment. This paper presents a methodology for constructing patient-specific respiratory motion models and uses these models to evaluate and analyse the inter-fraction variations in the respiratory motion. The internal respiratory motion is determined from the deformable registration of Cine CT data and related to a respiratory surrogate signal derived from 3D skin surface data. Three different models for relating the internal motion to the surrogate signal have been investigated in this work. Data were acquired from six lung cancer patients. Two full datasets were acquired for each patient, one before the course of radiotherapy treatment and one at the end (approximately 6 weeks later). Separate models were built for each dataset. All models could accurately predict the respiratory motion in the same dataset, but had large errors when predicting the motion in the other dataset. Analysis of the inter-fraction variations revealed that most variations were spatially varying base-line shifts, but changes to the anatomy and the motion trajectories were also observed.

Representations of Fractions: Evidence for Accessing the Whole Magnitude in Adults

ERIC Educational Resources Information Center

Sprute, Lisa; Temple, Elise

2011-01-01

Proficiency with fractions serves as a foundation for later mathematics and is critical for learning algebra, which plays a role in college success and lifetime earnings. Yet children often struggle to learn fractions. Educators have argued that a conceptual understanding of fractions involves learning that a fraction represents a magnitude…

Improvement of dry fractionation ethanol fermentation by partial germ supplementation

USDA-ARS?s Scientific Manuscript database

Ethanol fermentation of dry fractionated grits (corn endosperm pieces) containing different levels of germ was studied using the dry grind process. Partial removal of germ fraction allows for marketing the germ fraction and potentially more efficient fermentation. Grits obtained from a dry milling p...

Anti-inflammatory activity of bioaccessible fraction from Eryngium foetidum leaves.

PubMed

Dawilai, Suwitcha; Muangnoi, Chawanphat; Praengamthanachoti, Phawachaya; Tuntipopipat, Siriporn

2013-01-01

Eryngium foetidum (EF) has long been used as a medicinal plant and culinary spice in tropical regions. Phytochemicals in its leaves have been proposed to be responsible for the anti-inflammatory and antioxidant activities. The present study used in vitro digestion coupled with Caco-2 cells to assess such activities. Caco-2 cells were incubated with aqueous fraction from simulated digestion (bioaccessible fraction) of EF leaves with/without bile extract prior to stimulation with interleukin-1 beta (IL-1β). Monocyte chemoattractant protein-1 (MCP-1) and IL-8 in culture media and the intracellular reactive oxygen species (ROS) were measured. Approximately 24% β-carotene and 35% lutein of leaves were present in the aqueous fraction. The transfer of caffeic and chlorogenic acids to the aqueous fraction was 76%-81%, while that of kaempferol was 48%. Prior incubation of Caco-2 cells with the bioaccessible fraction suppressed IL-1β activated IL-8 and MCP-1 by 33%, but the fraction lacking mixed micelles decreased IL-8 and MCP-1 levels only by 11%. The pretreatment of Caco-2 cells with the bioaccessible fraction of EF reduced ROS by 34%; the fraction lacking mixed micelles decreased ROS by 28%. These data suggest that bioactive compounds partitioning in mixed micelles play a significant role to suppress the proinflammatory insult but with a modest antioxidant effect.

Anti-Inflammatory Activity of Bioaccessible Fraction from Eryngium foetidum Leaves

PubMed Central

Dawilai, Suwitcha; Muangnoi, Chawanphat; Praengamthanachoti, Phawachaya; Tuntipopipat, Siriporn

2013-01-01

Eryngium foetidum (EF) has long been used as a medicinal plant and culinary spice in tropical regions. Phytochemicals in its leaves have been proposed to be responsible for the anti-inflammatory and antioxidant activities. The present study used in vitro digestion coupled with Caco-2 cells to assess such activities. Caco-2 cells were incubated with aqueous fraction from simulated digestion (bioaccessible fraction) of EF leaves with/without bile extract prior to stimulation with interleukin-1 beta (IL-1β). Monocyte chemoattractant protein-1 (MCP-1) and IL-8 in culture media and the intracellular reactive oxygen species (ROS) were measured. Approximately 24% β-carotene and 35% lutein of leaves were present in the aqueous fraction. The transfer of caffeic and chlorogenic acids to the aqueous fraction was 76%–81%, while that of kaempferol was 48%. Prior incubation of Caco-2 cells with the bioaccessible fraction suppressed IL-1β activated IL-8 and MCP-1 by 33%, but the fraction lacking mixed micelles decreased IL-8 and MCP-1 levels only by 11%. The pretreatment of Caco-2 cells with the bioaccessible fraction of EF reduced ROS by 34%; the fraction lacking mixed micelles decreased ROS by 28%. These data suggest that bioactive compounds partitioning in mixed micelles play a significant role to suppress the proinflammatory insult but with a modest antioxidant effect. PMID:24151629

Stabilization of Bio-Oil Fractions for Insertion into Petroleum Refineries

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brown, Robert C.; Smith, Ryan; Wright, Mark

This project is part of a collaboration effort between Iowa State University (ISU), University of Oklahoma (OK) and Pacific Northwest National Laboratory (PNNL). The purpose of this project is to stabilize bio-oil fractions and improve their suitability for insertion into petroleum refineries. Bio-oil from fast pyrolysis of biomass is a complex mixture of unstable organic compounds. These organic compounds react under standard room conditions resulting in increases in bio-oil viscosity and water content – both detrimental for bio-oil storage and transportation. This study employed fractionation and upgrading systems to improve the stability of bio-oil. The fractionation system consists of amore » series of condensers, and electrostatic precipitators designed to separate bio-oil into five fractions: soluble carbohydrates (SF1&2), clean phenolic oligomers (CPO) and middle fraction (SF3&4), light oxygenates (SF5). A two-stage upgrading process was designed to process bio-oil stage fractions into stable products that can be inserted into a refinery. In the upgrading system, heavy and middle bio-oil fractions were upgraded into stable oil via cracking and subsequent hydrodeoxygenation. The light oxygenate fraction was steam reformed to provide a portion of requisite hydrogen for hydroprocessing. Hydrotreating and hydrocracking employed hydrogen from natural gas, fuel gas and light oxygenates reforming. The finished products from this study consist of gasoline- and diesel-blend stock fuels.« less

Electrophoretic fractional elution apparatus employing a rotational seal fraction collector

NASA Technical Reports Server (NTRS)

Bier, M. (Inventor)

1977-01-01

Electrophoretic fractional elution apparatus which has a column with a rotating seal joint is described. A thin jet of eluting buffer is directed across the lumen of the electrophoretic column in a direction perpendicular to that of electrophoretic migration. Either the content of the column is rotated with respect to the stationary jet, or the jet is rotated with respect to the column. The system may employ electrophoresis either in free solution or in packed columns.

Antioxidant Activity of Coconut (Cocos nucifera L.) Protein Fractions.

PubMed

Li, Yan; Zheng, Yajun; Zhang, Yufeng; Xu, Jianguo; Gao, Gang

2018-03-20

Coconut cake is an abundant and good potential edible protein source. However, until now it has not been extensively used in the food industry. To promote its usage, the characterization, nutrition value and antioxidant activity of coconut cake protein fractions (albumin, globulin, prolamine, glutelin-1 and glutelin-2) were studied. Results revealed that all the albumin, globulin, glutelin-1 and glutelin-2 fractions showed a high nutrition value. The prolamine, glutelin-1 and glutelin-2 all exhibited good radical scavenging activity and reducing power, and the globulin and prolamine showed high ion chelating ability (89.14-80.38%). Moreover, all the fractions except glutelin-2 could effectively protect DNA against oxidative damage. Several peptides containing five to eight amino acids with antioxidant activity were also identified by LC-MS/MS from the globulin and glutelin-2 fractions. The results demonstrated that the coconut cake protein fractions have potential usages in functional foods.

Single-Fraction Versus 5-Fraction Radiation Therapy for Metastatic Epidural Spinal Cord Compression in Patients With Limited Survival Prognoses: Results of a Matched-Pair Analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rades, Dirk, E-mail: Rades.Dirk@gmx.net; Huttenlocher, Stefan; Šegedin, Barbara

Purpose: This study compared single-fraction to multi-fraction short-course radiation therapy (RT) for symptomatic metastatic epidural spinal cord compression (MESCC) in patients with limited survival prognosis. Methods and Materials: A total of 121 patients who received 8 Gy × 1 fraction were matched (1:1) to 121 patients treated with 4 Gy × 5 fractions for 10 factors including age, sex, performance status, primary tumor type, number of involved vertebrae, other bone metastases, visceral metastases, interval between tumor diagnosis and MESCC, pre-RT ambulatory status, and time developing motor deficits prior to RT. Endpoints included in-field repeated RT (reRT) for MESCC, overall survival (OS), and impact of RT onmore » motor function. Univariate analyses were performed with the Kaplan-Meier method and log-rank test for in-field reRT for MESCC and OS and with the ordered-logit model for effect of RT on motor function. Results: Doses of 8 Gy × 1 fraction and 4 Gy × 5 fractions were not significantly different with respect to the need for in-field reRT for MESCC (P=.11) at 6 months (18% vs 9%, respectively) and 12 months (30% vs 22%, respectively). The RT regimen also had no significant impact on OS (P=.65) and post-RT motor function (P=.21). OS rates at 6 and 12 months were 24% and 9%, respectively, after 8 Gy × 1 fraction versus 25% and 13%, respectively, after 4 Gy × 5 fractions. Improvement of motor function was observed in 17% of patients after 8 Gy × 1 fraction and 23% after 4 Gy × 5 fractions, respectively. Conclusions: There were no significant differences with respect to need for in-field reRT for MESCC, OS, and motor function by dose fractionation regimen. Thus, 8 Gy × 1 fraction may be a reasonable option for patients with survival prognosis of a few months.« less

Attitude Estimation in Fractionated Spacecraft Cluster Systems

NASA Technical Reports Server (NTRS)

Hadaegh, Fred Y.; Blackmore, James C.

2011-01-01

An attitude estimation was examined in fractioned free-flying spacecraft. Instead of a single, monolithic spacecraft, a fractionated free-flying spacecraft uses multiple spacecraft modules. These modules are connected only through wireless communication links and, potentially, wireless power links. The key advantage of this concept is the ability to respond to uncertainty. For example, if a single spacecraft module in the cluster fails, a new one can be launched at a lower cost and risk than would be incurred with onorbit servicing or replacement of the monolithic spacecraft. In order to create such a system, however, it is essential to know what the navigation capabilities of the fractionated system are as a function of the capabilities of the individual modules, and to have an algorithm that can perform estimation of the attitudes and relative positions of the modules with fractionated sensing capabilities. Looking specifically at fractionated attitude estimation with startrackers and optical relative attitude sensors, a set of mathematical tools has been developed that specify the set of sensors necessary to ensure that the attitude of the entire cluster ( cluster attitude ) can be observed. Also developed was a navigation filter that can estimate the cluster attitude if these conditions are satisfied. Each module in the cluster may have either a startracker, a relative attitude sensor, or both. An extended Kalman filter can be used to estimate the attitude of all modules. A range of estimation performances can be achieved depending on the sensors used and the topology of the sensing network.

Molybdenum isotope fractionation during adsorption to organic matter

USGS Publications Warehouse

King, Elizabeth K.; Perakis, Steven; Pett-Ridge, Julie C.

2018-01-01

Organic matter is of emerging interest as a control on molybdenum (Mo) biogeochemistry, and information on isotope fractionation during adsorption to organic matter can improve interpretations of Mo isotope variations in natural settings. Molybdenum isotope fractionation was investigated during adsorption onto insolubilized humic acid (IHA), a surrogate for organic matter, as a function of time (2–170 h) and pH (2–7). For the time series experiment performed at pH 4.2, the average Mo isotope fractionation between the solution and the IHA (Δ98Mosolution-IHA) was 1.39‰ (± 0.16‰, 2σ, based on 98Mo/95Mo relative to the NIST 3134 standard) at steady state. For the pH series experiment, Mo adsorption decreased as pH increased from 2.0 to 6.9, and the Δ98Mosolution-IHA increased from 0.82‰ to 1.79‰. We also evaluated natural Mo isotope patterns in precipitation, foliage, organic horizon, surface mineral soil, and bedrock from 12 forested sites in the Oregon Coast Range. The average Mo isotope offset observed between precipitation and organic (O) horizon soil was 2.1‰, with light Mo isotopes adsorbing preferentially to organic matter. Fractionation during adsorption to organic matter is similar in magnitude and direction to prior observations of Mo fractionation during adsorption to Fe- and Mn- (oxyhydr)oxides. Our finding that organic matter influences Mo isotope composition has important implications for the role of organic matter as a driver of trace metal retention and isotopic fractionation.

Lyman-Werner escape fractions from the first galaxies

NASA Astrophysics Data System (ADS)

Schauer, Anna T. P.; Agarwal, Bhaskar; Glover, Simon C. O.; Klessen, Ralf S.; Latif, Muhammad A.; Mas-Ribas, Lluís; Rydberg, Claes-Erik; Whalen, Daniel J.; Zackrisson, Erik

2017-05-01

Direct collapse black holes forming in pristine, atomically cooling haloes at z ≈ 10-20 may act as the seeds of supermassive black holes (BHs) at high redshifts. In order to create a massive BH seed, the host halo needs to be prevented from forming stars. H2 therefore needs to be irradiated by a large flux of Lyman-Werner (LW) UV photons in order to suppress H2 cooling. A key uncertainty in this scenario is the escape fraction of LW radiation from first galaxies, which is the dominant source of UV photons at this epoch. To better constrain this escape fraction, we have performed radiation-hydrodynamical simulations of the growth of H II regions and their associated photodissociation regions in the first galaxies using the zeus-mp code. We find that the LW escape fraction crucially depends on the propagation of the ionization front (I-front). For an R-type I-front overrunning the halo, the LW escape fraction is always larger than 95 per cent. If the halo recombines later from the outside-in, due to a softened and weakened spectrum, the LW escape fraction in the rest frame of the halo (the near-field) drops to zero. A detailed and careful analysis is required to analyse slowly moving, D-type I-fronts, where the escape fraction depends on the microphysics and can be as small as 3 per cent in the near-field and 61 per cent in the far-field or as large as 100 per cent in both the near-field and the far-field.

Antimicrobial activity of Carpolobia lutea extracts and fractions.

PubMed

Nwidu, Lucky L; Nwafor, Paul A; Vilegas, Wagner

2012-01-01

Carpolobia lutea (G. Don) (Polygalaceae) is a tropical medicinal plant putative in traditional medicines against gonorrhea, gingivitis, infertility, antiulcer and malaria. The present study evaluated the antimicrobial, antifungal and antihelicobacter effects of extracts C. lutea leaf, stem and root. The extracts were examined using the disc-diffusion and Microplates of 96 wells containing Muller-Hinton methods against some bacterial strains: Eschericia coli (ATCC 25922), E. coli (ATCC10418), Pseudomonas aeruginosa (ATCC 27853), Staphylococcus aureus (ATCC 25923), Staphyllococus aureus (ATCC 6571), Enterococcus faecalis (ATCC 29212) and Bacillus subtilis (NCTC 8853) and four clinical isolates: one fungi (Candida albican) and three bacteria (Salmonella, Sheigella and staphylococcus aureus). The Gram-positive bacteria: Staphylococcus aureus (ATCC 25923), Enterococcus faecalis (ATCC 29212), Bacillus subtilis (ATCC 19659) and the Gram-negative bacteria: Escherichia coli (ATCC 25922), Pseudomonas aeruginosa (ATCC 27853), Cândida albicans (ATCC 18804) and Helicobacter pylori (ATCC 43504). Some of these extracts were found to be active against some tested strains but activity against H. pylori was >1000mg/ml and good fungistatic activity against C. albican. The MIC against C. albican is in the order n-HF > CHF > ETF= EAF.The order of potency of fraction was the ethanol root > n-HF leaf > ethanol fraction stem > chloroform fraction leaf = ethyl acetate fraction leaf. Polyphenols were demonstrated in ethanol fraction, ethyl acetate fraction, crude ethyl acetate extract and ethanol extract, respectively. These polyphenols isolated may partly explain and support the use of C. lutea for the treatment of infectious diseases in traditional Ibibio medicine of Nigeria.

Molybdenum isotope fractionation during adsorption to organic matter

NASA Astrophysics Data System (ADS)

King, E. K.; Perakis, S. S.; Pett-Ridge, J. C.

2018-02-01

Organic matter is of emerging interest as a control on molybdenum (Mo) biogeochemistry, and information on isotope fractionation during adsorption to organic matter can improve interpretations of Mo isotope variations in natural settings. Molybdenum isotope fractionation was investigated during adsorption onto insolubilized humic acid (IHA), a surrogate for organic matter, as a function of time (2-170 h) and pH (2-7). For the time series experiment performed at pH 4.2, the average Mo isotope fractionation between the solution and the IHA (Δ98Mosolution-IHA) was 1.39‰ (±0.16‰, 2σ, based on 98Mo/95Mo relative to the NIST 3134 standard) at steady state. For the pH series experiment, Mo adsorption decreased as pH increased from 2.0 to 6.9, and the Δ98Mosolution-IHA increased from 0.82‰ to 1.79‰. We also evaluated natural Mo isotope patterns in precipitation, foliage, organic horizon, surface mineral soil, and bedrock from 12 forested sites in the Oregon Coast Range. The average Mo isotope offset observed between precipitation and organic (O) horizon soil was 2.1‰, with light Mo isotopes adsorbing preferentially to organic matter. Fractionation during adsorption to organic matter is similar in magnitude and direction to prior observations of Mo fractionation during adsorption to Fe- and Mn- (oxyhydr)oxides. Our finding that organic matter influences Mo isotope composition has important implications for the role of organic matter as a driver of trace metal retention and isotopic fractionation.

Observation of fractional Chern insulators in a van der Waals heterostructure

NASA Astrophysics Data System (ADS)

Spanton, Eric M.; Zibrov, Alexander A.; Zhou, Haoxin; Taniguchi, Takashi; Watanabe, Kenji; Zaletel, Michael P.; Young, Andrea F.

2018-04-01

Topologically ordered phases are characterized by long-range quantum entanglement and fractional statistics rather than by symmetry breaking. First observed in a fractionally filled continuum Landau level, topological order has since been proposed to arise more generally at fractional fillings of topologically nontrivial Chern bands. Here we report the observation of gapped states at fractional fillings of Harper-Hofstadter bands arising from the interplay of a magnetic field and a superlattice potential in a bilayer graphene–hexagonal boron nitride heterostructure. We observed phases at fractional filling of bands with Chern indices C=‑1, ±2, and ±3. Some of these phases, in C=‑1 and C=2 bands, are characterized by fractional Hall conductance—that is, they are known as fractional Chern insulators and constitute an example of topological order beyond Landau levels.

Rational-number comparison across notation: Fractions, decimals, and whole numbers.

PubMed

Hurst, Michelle; Cordes, Sara

2016-02-01

Although fractions, decimals, and whole numbers can be used to represent the same rational-number values, it is unclear whether adults conceive of these rational-number magnitudes as lying along the same ordered mental continuum. In the current study, we investigated whether adults' processing of rational-number magnitudes in fraction, decimal, and whole-number notation show systematic ratio-dependent responding characteristic of an integrated mental continuum. Both reaction time (RT) and eye-tracking data from a number-magnitude comparison task revealed ratio-dependent performance when adults compared the relative magnitudes of rational numbers, both within the same notation (e.g., fractions vs. fractions) and across different notations (e.g., fractions vs. decimals), pointing to an integrated mental continuum for rational numbers across notation types. In addition, eye-tracking analyses provided evidence of an implicit whole-number bias when we compared values in fraction notation, and individual differences in this whole-number bias were related to the individual's performance on a fraction arithmetic task. Implications of our results for both cognitive development research and math education are discussed. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

Periodicity and positivity of a class of fractional differential equations.

PubMed

Ibrahim, Rabha W; Ahmad, M Z; Mohammed, M Jasim

2016-01-01

Fractional differential equations have been discussed in this study. We utilize the Riemann-Liouville fractional calculus to implement it within the generalization of the well known class of differential equations. The Rayleigh differential equation has been generalized of fractional second order. The existence of periodic and positive outcome is established in a new method. The solution is described in a fractional periodic Sobolev space. Positivity of outcomes is considered under certain requirements. We develop and extend some recent works. An example is constructed.

Characterization of taste-active fractions in red wine combining HPLC fractionation, sensory analysis and ultra performance liquid chromatography coupled with mass spectrometry detection.

PubMed

Sáenz-Navajas, María-Pilar; Ferreira, Vicente; Dizy, Marta; Fernández-Zurbano, Purificación

2010-07-19

Five Tempranillo wines exhibiting marked differences in taste and/or astringency were selected for the study. In each wine the non-volatile extract was obtained by freeze-drying and further liquid extraction in order to eliminate remaining volatile compounds. This extract was fractionated by semipreparative C18-reverse phase-high performance liquid chromatography (C18-RP-HPLC) into nine fractions which were freeze-dried, reconstituted with water and sensory assessed for taste attributes and astringency by a specifically trained sensory panel. Results have shown that wine bitterness and astringency cannot be easily related to the bitter and astringent character of the HPLC fractions, what can be due to the existence of perceptual and physicochemical interactions. While the bitter character of the bitterest fractions may be attributed to some flavonols (myricetin, quercetin and their glycosides) the development of a sensitive UPLC-MS method to quantify astringent compounds present in wines has made it possible to demonstrate that proanthocyanidins monomers, dimers, trimers and tetramers, both galloylated or non-galloylated are not relevant compounds for the perceived astringency of the fractions, while cis-aconitic acid, and secondarily vainillic, and syringic acids and ethyl syringate, are the most important molecules driving astringency in two of the fractions (F5 and F6). The identity of the chemicals responsible for the astringency of the third fraction could be assigned to some proanthocyanidins (higher than the tetramer) capable to precipitate with ovalbumin. 2010 Elsevier B.V. All rights reserved.

Nootropic Effects of Filipendula Vulgaris Moench Water Extract Fractions.

PubMed

Shilova, I V; Suslov, N I; Amelchenko, V P

2015-07-01

Nootropic activity of water extract fractions from aerial parts of Filipendula vulgaris Moench was demonstrated on the models of hermetic volume hypoxia, conditioned passive avoidance response, open field test, and forced swimming with a load. The fractions stimulated hypoxic resistance, normalized orientation and exploratory behavior, improved conditioned response reproduction during testing after hypoxic injury, and increased exercise tolerance. Fractionation of the extract led to dissociation of the effect components, which suggests that individual constituents have specific characteristics. Ethylacetate fraction exhibited most pronounced nootropic activity and was superior to plant extract by some characteristics. The detected effects seemed to be caused by modulation of the hippocampus activity the under the effects of phenol and triterpene compounds.

Nonlinear acoustic wave equations with fractional loss operators.

PubMed

Prieur, Fabrice; Holm, Sverre

2011-09-01

Fractional derivatives are well suited to describe wave propagation in complex media. When introduced in classical wave equations, they allow a modeling of attenuation and dispersion that better describes sound propagation in biological tissues. Traditional constitutive equations from solid mechanics and heat conduction are modified using fractional derivatives. They are used to derive a nonlinear wave equation which describes attenuation and dispersion laws that match observations. This wave equation is a generalization of the Westervelt equation, and also leads to a fractional version of the Khokhlov-Zabolotskaya-Kuznetsov and Burgers' equations. © 2011 Acoustical Society of America