Some Extensions of Discrete Fixed Point Theorems and Their Applications to the Game Theory
NASA Astrophysics Data System (ADS)
Kawasaki, Hidefumi
2009-09-01
As is well-known in the game theory, fixed point theorems are useful to show the existence of Nash equilibrium. Since they are mathematical tools in continuous variables, it is expected that discrete fixed point theorems also useful to guarantee the existence of pure-strategy Nash equilibrium. In this talk, we review three types of discrete fixed point theorems, give some extensions, and apply them to non-cooperative games.
A fixed point theorem for certain operator valued maps
NASA Technical Reports Server (NTRS)
Brown, D. R.; Omalley, M. J.
1978-01-01
In this paper, we develop a family of Neuberger-like results to find points z epsilon H satisfying L(z)z = z and P(z) = z. This family includes Neuberger's theorem and has the additional property that most of the sequences q sub n converge to idempotent elements of B sub 1(H).
Partial Rectangular Metric Spaces and Fixed Point Theorems
2014-01-01
The purpose of this paper is to introduce the concept of partial rectangular metric spaces as a generalization of rectangular metric and partial metric spaces. Some properties of partial rectangular metric spaces and some fixed point results for quasitype contraction in partial rectangular metric spaces are proved. Some examples are given to illustrate the observed results. PMID:24672366
Common Coupled Fixed Point Theorems for Two Hybrid Pairs of Mappings under φ-ψ Contraction
Handa, Amrish
2014-01-01
We introduce the concept of (EA) property and occasional w-compatibility for hybrid pair F : X × X → 2X and f : X → X. We also introduce common (EA) property for two hybrid pairs F, G : X → 2X and f, g : X → X. We establish some common coupled fixed point theorems for two hybrid pairs of mappings under φ-ψ contraction on noncomplete metric spaces. An example is also given to validate our results. We improve, extend and generalize several known results. The results of this paper generalize the common fixed point theorems for hybrid pairs of mappings and essentially contain fixed point theorems for hybrid pair of mappings. PMID:27340688
Searching for fixed point combinators by using automated theorem proving: A preliminary report
Wos, L.; McCune, W.
1988-09-01
In this report, we establish that the use of an automated theorem- proving program to study deep questions from mathematics and logic is indeed an excellent move. Among such problems, we focus mainly on that concerning the construction of fixed point combinators---a problem considered by logicians to be significant and difficult to solve, and often computationally intensive and arduous. To be a fixed point combinator, THETA must satisfy the equation THETAx = x(THETAx) for all combinators x. The specific questions on which we focus most heavily ask, for each chosen set of combinators, whether a fixed point combinator can be constructed from the members of that set. For answering questions of this type, we present a new, sound, and efficient method, called the kernel method, which can be applied quite easily by hand and very easily by an automated theorem-proving program. For the application of the kernel method by a theorem-proving program, we illustrate the vital role that is played by both paramodulation and demodulation---two of the powerful features frequently offered by an automated theorem-proving program for treating equality as if it is ''understood.'' We also state a conjecture that, if proved, establishes the completeness of the kernel method. From what we can ascertain, this method---which relies on the introduced concepts of kernel and superkernel---offers the first systematic approach for searching for fixed point combinators. We successfully apply the new kernel method to various sets of combinators and, for the set consisting of the combinators B and W, construct an infinite set of fixed point combinators such that no two of the combinators are equal even in the presence of extensionality---a law that asserts that two combinators are equal if they behave the same. 18 refs.
2014-01-01
We introduce an iterative process for finding an element of a common fixed point of a finite family of Bregman weak relatively nonexpansive mappings. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators. PMID:24757423
Fixed points for weakly inward mappings in Banach spaces
NASA Astrophysics Data System (ADS)
Xu, Shaoyuan; Jia, Baoguo; Li, Guo-Zhen
2006-07-01
S. Hu and Y. Sun [S. Hu, Y. Sun, Fixed point index for weakly inward mappings, J. Math. Anal. Appl. 172 (1993) 266-273] defined the fixed point index for weakly inward mappings, investigated its properties and studied the fixed points for such mappings. In this paper, following S. Hu and Y. Sun, we continue to investigate boundary conditions, under which the fixed point index for the completely continuous and weakly inward mapping, denoted by i(A,[Omega],P), is equal to 1 or 0. Correspondingly, we can obtain some new fixed point theorems of the completely continuous and weakly inward mappings and existence theorems of solutions for the equations Ax=[mu]x, which extend many famous theorems such as Leray-Schauder's theorem, Rothe's two theorems, Krasnoselskii's theorem, Altman's theorem, Petryshyn's theorem, etc., to the case of weakly inward mappings. In addition, our conclusions and methods are different from the ones in many recent works.
Characterizations of fixed points of quantum operations
Li Yuan
2011-05-15
Let {phi}{sub A} be a general quantum operation. An operator B is said to be a fixed point of {phi}{sub A}, if {phi}{sub A}(B)=B. In this note, we shall show conditions under which B, a fixed point {phi}{sub A}, implies that B is compatible with the operation element of {phi}{sub A}. In particular, we offer an extension of the generalized Lueders theorem.
Using Technology to Unify Geometric Theorems about the Power of a Point
ERIC Educational Resources Information Center
Contreras, Jose N.
2011-01-01
In this article, I describe a classroom investigation in which a group of prospective secondary mathematics teachers discovered theorems related to the power of a point using "The Geometer's Sketchpad" (GSP). The power of a point is defines as follows: Let "P" be a fixed point coplanar with a circle. If line "PA" is a secant line that intersects…
NASA Astrophysics Data System (ADS)
Edler, F.; Ederer, P.
2014-07-01
The paper describes the construction and investigation of multiple fixed-point cells usable for the calibration of thermocouples at temperatures above 1100 C. These fixed-point cells made of pure graphite are characterized by a simple construction as well as by a flexible application. The cylindrical basic mount is equipped with a central hole for the insertion of a thermocouple, and with eight drill holes containing exchangeable cartridges which surround the central bore axially symmetrically. The cartridges are filled with different metal-carbon (Me-C) eutectics: cobalt-carbon (Co-C), nickel-carbon (Ni-C), palladium-carbon (Pd-C), and rhodium-carbon (Rh-C). The melting temperatures of the different Me-C eutectics of the cartridges were compared to the melting temperatures of commonly used Me-C eutectic fixed-point cells of the Physikalisch-Technische Bundesanstalt by using a Pt/Pd thermocouple (Co-C, Ni-C) and Type B thermocouples (Pd-C, Rh-C). The uncertainties () of the emfs measured at the inflection points of the melting curves are in the order of a few V which correspond to temperature equivalents between 0.3 K and 0.6 K. Furthermore, the difference between the melting temperatures of the Co-C and Ni-C cartridges was found to be 4.2 K by using simultaneously two sets of four cartridges filled with the two materials and placed alternately in the eight outer holes of one basic mount.
Contractive multifunctions, fixed point inclusions and iterated multifunction systems
NASA Astrophysics Data System (ADS)
Kunze, H. E.; La Torre, D.; Vrscay, E. R.
2007-06-01
We study the properties of multifunction operators that are contractive in the Covitz-Nadler sense. In this situation, such operators T possess fixed points satisfying the relation x[set membership, variant]Tx. We introduce an iterative method involving projections that guarantees convergence from any starting point x0[set membership, variant]X to a point x[set membership, variant]XT, the set of all fixed points of a multifunction operator T. We also prove a continuity result for fixed point sets XT as well as a "generalized collage theorem" for contractive multifunctions. These results can then be used to solve inverse problems involving contractive multifunctions. Two applications of contractive multifunctions are introduced: (i) integral inclusions and (ii) iterated multifunction systems.
Anderson Acceleration for Fixed-Point Iterations
Walker, Homer F.
2015-08-31
The purpose of this grant was to support research on acceleration methods for fixed-point iterations, with applications to computational frameworks and simulation problems that are of interest to DOE.
NASA Astrophysics Data System (ADS)
Young, Frederic; Siegel, Edward
Cook-Levin theorem theorem algorithmic computational-complexity(C-C) algorithmic-equivalence reducibility/completeness equivalence to renormalization-(semi)-group phase-transitions critical-phenomena statistical-physics universality-classes fixed-points, is exploited via Siegel FUZZYICS =CATEGORYICS = ANALOGYICS =PRAGMATYICS/CATEGORY-SEMANTICS ONTOLOGY COGNITION ANALYTICS-Aristotle ``square-of-opposition'' tabular list-format truth-table matrix analytics predicts and implements ''noise''-induced phase-transitions (NITs) to accelerate versus to decelerate Harel [Algorithmics (1987)]-Sipser[Intro.Thy. Computation(`97)] algorithmic C-C: ''NIT-picking''(!!!), to optimize optimization-problems optimally(OOPO). Versus iso-''noise'' power-spectrum quantitative-only amplitude/magnitude-only variation stochastic-resonance, ''NIT-picking'' is ''noise'' power-spectrum QUALitative-type variation via quantitative critical-exponents variation. Computer-''science''/SEANCE algorithmic C-C models: Turing-machine, finite-state-models, finite-automata,..., discrete-maths graph-theory equivalence to physics Feynman-diagrams are identified as early-days once-workable valid but limiting IMPEDING CRUTCHES(!!!), ONLY IMPEDE latter-days new-insights!!!
ASIC For Complex Fixed-Point Arithmetic
NASA Technical Reports Server (NTRS)
Petilli, Stephen G.; Grimm, Michael J.; Olson, Erlend M.
1995-01-01
Application-specific integrated circuit (ASIC) performs 24-bit, fixed-point arithmetic operations on arrays of complex-valued input data. High-performance, wide-band arithmetic logic unit (ALU) designed for use in computing fast Fourier transforms (FFTs) and for performing ditigal filtering functions. Other applications include general computations involved in analysis of spectra and digital signal processing.
Precise Point Positioning with Partial Ambiguity Fixing.
Li, Pan; Zhang, Xiaohong
2015-01-01
Reliable and rapid ambiguity resolution (AR) is the key to fast precise point positioning (PPP). We propose a modified partial ambiguity resolution (PAR) method, in which an elevation and standard deviation criterion are first used to remove the low-precision ambiguity estimates for AR. Subsequently the success rate and ratio-test are simultaneously used in an iterative process to increase the possibility of finding a subset of decorrelated ambiguities which can be fixed with high confidence. One can apply the proposed PAR method to try to achieve an ambiguity-fixed solution when full ambiguity resolution (FAR) fails. We validate this method using data from 450 stations during DOY 021 to 027, 2012. Results demonstrate the proposed PAR method can significantly shorten the time to first fix (TTFF) and increase the fixing rate. Compared with FAR, the average TTFF for PAR is reduced by 14.9% for static PPP and 15.1% for kinematic PPP. Besides, using the PAR method, the average fixing rate can be increased from 83.5% to 98.2% for static PPP, from 80.1% to 95.2% for kinematic PPP respectively. Kinematic PPP accuracy with PAR can also be significantly improved, compared to that with FAR, due to a higher fixing rate. PMID:26067196
Precise Point Positioning with Partial Ambiguity Fixing
Li, Pan; Zhang, Xiaohong
2015-01-01
Reliable and rapid ambiguity resolution (AR) is the key to fast precise point positioning (PPP). We propose a modified partial ambiguity resolution (PAR) method, in which an elevation and standard deviation criterion are first used to remove the low-precision ambiguity estimates for AR. Subsequently the success rate and ratio-test are simultaneously used in an iterative process to increase the possibility of finding a subset of decorrelated ambiguities which can be fixed with high confidence. One can apply the proposed PAR method to try to achieve an ambiguity-fixed solution when full ambiguity resolution (FAR) fails. We validate this method using data from 450 stations during DOY 021 to 027, 2012. Results demonstrate the proposed PAR method can significantly shorten the time to first fix (TTFF) and increase the fixing rate. Compared with FAR, the average TTFF for PAR is reduced by 14.9% for static PPP and 15.1% for kinematic PPP. Besides, using the PAR method, the average fixing rate can be increased from 83.5% to 98.2% for static PPP, from 80.1% to 95.2% for kinematic PPP respectively. Kinematic PPP accuracy with PAR can also be significantly improved, compared to that with FAR, due to a higher fixing rate. PMID:26067196
Existence and data dependence of fixed points for multivalued operators on gauge spaces
NASA Astrophysics Data System (ADS)
Espínola, Rafael; Petrusel, Adrian
2005-09-01
The purpose of this note is to present some fixed point and data dependence theorems in complete gauge spaces and in hyperconvex metric spaces for the so-called Meir-Keeler multivalued operators and admissible multivalued a[alpha]-contractions. Our results extend and generalize several theorems of Espínola and Kirk [R. Espínola, W.A. Kirk, Set-valued contractions and fixed points, Nonlinear Anal. 54 (2003) 485-494] and Rus, Petrusel, and Sîntamarian [I.A. Rus, A. Petrusel, A. Sîntamarian, Data dependence of the fixed point set of some multivalued weakly Picard operators, Nonlinear Anal. 52 (2003) 1947-1959].
NASA Astrophysics Data System (ADS)
Liu, Xuan-Zuo; Tian, Dong-Ping; Chong, Bo
2016-06-01
Liu et al. [Phys. Rev. Lett. 90(17), 170404 (2003)] proved that the characters of transition probabilities in the adiabatic limit should be entirely determined by the topology of energy levels and the stability of fixed points in the classical Hamiltonian system, according to the adiabatic theorem. In the special case of nonlinear Landau-Zener model, we simplify their results to be that the properties of transition probabilities in the adiabatic limit should just be determined by the attributes of fixed points. It is because the topology of energy levels is governed by the behavior and symmetries of fixed points, and intuitively this fact is represented as a correspondence between energy levels and evolution curves of the fixed points which can be quantitatively described as the same complexity numbers.
Secure Computation with Fixed-Point Numbers
NASA Astrophysics Data System (ADS)
Catrina, Octavian; Saxena, Amitabh
Secure computation is a promising approach to business problems in which several parties want to run a joint application and cannot reveal their inputs. Secure computation preserves the privacy of input data using cryptographic protocols, allowing the parties to obtain the benefits of data sharing and at the same time avoid the associated risks. These business applications need protocols that support all the primitive data types and allow secure protocol composition and efficient application development. Secure computation with rational numbers has been a challenging problem. We present in this paper a family of protocols for multiparty computation with rational numbers using fixed-point representation. This approach offers more efficient solutions for secure computation than other usual representations.
Floating-to-Fixed-Point Conversion for Digital Signal Processors
NASA Astrophysics Data System (ADS)
Menard, Daniel; Chillet, Daniel; Sentieys, Olivier
2006-12-01
Digital signal processing applications are specified with floating-point data types but they are usually implemented in embedded systems with fixed-point arithmetic to minimise cost and power consumption. Thus, methodologies which establish automatically the fixed-point specification are required to reduce the application time-to-market. In this paper, a new methodology for the floating-to-fixed point conversion is proposed for software implementations. The aim of our approach is to determine the fixed-point specification which minimises the code execution time for a given accuracy constraint. Compared to previous methodologies, our approach takes into account the DSP architecture to optimise the fixed-point formats and the floating-to-fixed-point conversion process is coupled with the code generation process. The fixed-point data types and the position of the scaling operations are optimised to reduce the code execution time. To evaluate the fixed-point computation accuracy, an analytical approach is used to reduce the optimisation time compared to the existing methods based on simulation. The methodology stages are described and several experiment results are presented to underline the efficiency of this approach.
A new compact fixed-point blackbody furnace
Hiraka, K.; Oikawa, H.; Shimizu, T.; Kadoya, S.; Kobayashi, T.; Yamada, Y.; Ishii, J.
2013-09-11
More and more NMIs are realizing their primary scale themselves with fixed-point blackbodies as their reference standard. However, commercially available fixed-point blackbody furnaces of sufficient quality are not always easy to obtain. CHINO Corp. and NMIJ, AIST jointly developed a new compact fixed-point blackbody furnace. The new furnace has such features as 1) improved temperature uniformity when compared to previous products, enabling better plateau quality, 2) adoption of the hybrid fixed-point cell structure with internal insulation to improve robustness and thereby to extend lifetime, 3) easily ejectable and replaceable heater unit and fixed-point cell design, leading to reduced maintenance cost, 4) interchangeability among multiple fixed points from In to Cu points. The replaceable cell feature facilitates long term maintenance of the scale through management of a group of fixed-point cells of the same type. The compact furnace is easily transportable and therefore can also function as a traveling standard for disseminating the radiation temperature scale, and for maintaining the scale at the secondary level and industrial calibration laboratories. It is expected that the furnace will play a key role of the traveling standard in the anticipated APMP supplementary comparison of the radiation thermometry scale.
47 CFR 101.137 - Interconnection of private operational fixed point-to-point microwave stations.
Code of Federal Regulations, 2014 CFR
2014-10-01
... point-to-point microwave stations. 101.137 Section 101.137 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Technical Standards § 101.137 Interconnection of private operational fixed point-to-point microwave stations....
47 CFR 101.137 - Interconnection of private operational fixed point-to-point microwave stations.
Code of Federal Regulations, 2013 CFR
2013-10-01
... point-to-point microwave stations. 101.137 Section 101.137 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Technical Standards § 101.137 Interconnection of private operational fixed point-to-point microwave stations....
47 CFR 101.137 - Interconnection of private operational fixed point-to-point microwave stations.
Code of Federal Regulations, 2012 CFR
2012-10-01
... point-to-point microwave stations. 101.137 Section 101.137 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Technical Standards § 101.137 Interconnection of private operational fixed point-to-point microwave stations....
47 CFR 101.137 - Interconnection of private operational fixed point-to-point microwave stations.
Code of Federal Regulations, 2010 CFR
2010-10-01
... point-to-point microwave stations. 101.137 Section 101.137 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Technical Standards § 101.137 Interconnection of private operational fixed point-to-point microwave stations....
47 CFR 101.137 - Interconnection of private operational fixed point-to-point microwave stations.
Code of Federal Regulations, 2011 CFR
2011-10-01
... point-to-point microwave stations. 101.137 Section 101.137 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Technical Standards § 101.137 Interconnection of private operational fixed point-to-point microwave stations....
Stray thermal influences in zinc fixed-point cells
Rudtsch, S.; Aulich, A.; Monte, C.
2013-09-11
The influence of thermal effects is a major uncertainty contribution to the calibration of Standard Platinum Resistance Thermometers (SPRTs) in fixed-point cells. Axial heat losses strongly depend on the fixed-point temperature, constructional details of cells and SPRTs and the resulting heat transfer between cell, thermometer, furnace and environment. At the zinc point contributions by heat conduction and thermal radiation must be considered. Although the measurement of temperature gradients in the re-entrant well of a fixed-point cell provides very important information about the influence of axial heat losses, further investigations are required for a reliable estimate of the resulting uncertainty contribution. It is shown that specific modifications of a zinc fixed-point cell, following generally accepted principles, may result in systematic deviations of the measured fixed-point temperatures larger than typically stated in the uncertainty budget of National Metrology Institutes (NMIs). The underlying heat transport processes are investigated and the consequences for the construction of zinc cells are discussed.
Taylor's Theorem and Derivative Tests for Extrema and Inflection Points
ERIC Educational Resources Information Center
Gordon, Sheldon P.
2005-01-01
The standard derivative tests for extrema and inflection points from Calculus I can be revisited subsequently from the perspective of Taylor polynomial approximations to provide additional insights into those tests, as well as to extend them to additional criteria. (Contains 3 figures.)
Design and DSP Implementation of Fixed-Point Systems
NASA Astrophysics Data System (ADS)
Coors, Martin; Keding, Holger; Lüthje, Olaf; Meyr, Heinrich
2002-12-01
This article is an introduction to the FRIDGE design environment which supports the design and DSP implementation of fixed-point digital signal processing systems. We present the tool-supported transformation of signal processing algorithms coded in floating-point ANSI C to a fixed-point representation in SystemC. We introduce the novel approach to control and data flow analysis, which is necessary for the transformation. The design environment enables fast bit-true simulation by mapping the fixed-point algorithm to integral data types of the host machine. A speedup by a factor of 20 to 400 can be achieved compared to C++-library-based bit-true simulation. FRIDGE also provides a direct link to DSP implementation by processor specific C code generation and advanced code optimization.
Border collisions inside the stability domain of a fixed point
NASA Astrophysics Data System (ADS)
Avrutin, Viktor; Zhusubaliyev, Zhanybai T.; Mosekilde, Erik
2016-05-01
Recent studies on a power electronic DC/AC converter (inverter) have demonstrated that such systems may undergo a transition from regular dynamics (associated with a globally attracting fixed point of a suitable stroboscopic map) to chaos through an irregular sequence of border-collision events. Chaotic dynamics of an inverter is not suitable for practical purposes. However, the parameter domain in which the stroboscopic map has a globally attracting fixed point has generally been considered to be uniform and suitable for practical use. In the present paper we show that this domain actually has a complicated interior structure formed by boundaries defined by persistence border collisions. We describe a simple approach that is based on symbolic dynamics and makes it possible to detect such boundaries numerically. Using this approach we describe several regions in the parameter space leading to qualitatively different output signals of the inverter although all associated with globally attracting fixed points of the corresponding stroboscopic map.
Fixed point structure of the Abelian Higgs model
NASA Astrophysics Data System (ADS)
Fejős, G.; Hatsuda, T.
2016-06-01
The order of the superconducting phase transition is analyzed via the functional renormalization group approach. For the first time, we derive fully analytic expressions for the β functions of the charge and the self-coupling in the Abelian Higgs model with one complex scalar field in d =3 dimensions that support the existence of two charged fixed points: an infrared (IR) stable fixed point describing a second-order phase transition and a tricritical fixed point controlling the region of the parameter space that is attracted by the former one. It is found that the region separating first- and second-order transitions can be uniquely characterized by the Ginzburg-Landau parameter κ , and the system undergoes a second-order transition only if κ >κc≈0.62 /√{2 }.
Fixed-Rate Compressed Floating-Point Arrays.
Lindstrom, Peter
2014-12-01
Current compression schemes for floating-point data commonly take fixed-precision values and compress them to a variable-length bit stream, complicating memory management and random access. We present a fixed-rate, near-lossless compression scheme that maps small blocks of 4(d) values in d dimensions to a fixed, user-specified number of bits per block, thereby allowing read and write random access to compressed floating-point data at block granularity. Our approach is inspired by fixed-rate texture compression methods widely adopted in graphics hardware, but has been tailored to the high dynamic range and precision demands of scientific applications. Our compressor is based on a new, lifted, orthogonal block transform and embedded coding, allowing each per-block bit stream to be truncated at any point if desired, thus facilitating bit rate selection using a single compression scheme. To avoid compression or decompression upon every data access, we employ a software write-back cache of uncompressed blocks. Our compressor has been designed with computational simplicity and speed in mind to allow for the possibility of a hardware implementation, and uses only a small number of fixed-point arithmetic operations per compressed value. We demonstrate the viability and benefits of lossy compression in several applications, including visualization, quantitative data analysis, and numerical simulation. PMID:26356981
Measurement of thermodynamic temperature of high temperature fixed points
Gavrilov, V. R.; Khlevnoy, B. B.; Otryaskin, D. A.; Grigorieva, I. A.; Samoylov, M. L.; Sapritsky, V. I.
2013-09-11
The paper is devoted to VNIIOFI's measurements of thermodynamic temperature of the high temperature fixed points Co-C, Pt-C and Re-C within the scope of the international project coordinated by the Consultative Committee for Thermometry working group 5 'Radiation Thermometry'. The melting temperatures of the fixed points were measured by a radiance mode radiation thermometer calibrated against a filter radiometer with known irradiance spectral responsivity via a high temperature black body. This paper describes the facility used for the measurements, the results and estimated uncertainties.
Fixed Point Problems for Linear Transformations on Pythagorean Triples
ERIC Educational Resources Information Center
Zhan, M.-Q.; Tong, J.-C.; Braza, P.
2006-01-01
In this article, an attempt is made to find all linear transformations that map a standard Pythagorean triple (a Pythagorean triple [x y z][superscript T] with y being even) into a standard Pythagorean triple, which have [3 4 5][superscript T] as their fixed point. All such transformations form a monoid S* under matrix product. It is found that S*…
A fixed-point framework for launch vehicle ascent guidance
NASA Astrophysics Data System (ADS)
Zhang, Lijun
Recent interests in responsive launch have highlighted the need for rapid and fully automated ascent guidance planning and guidance parameter generation for launch vehicles. This dissertation aims at developing methodology and algorithms for on-demand generation of optimal launch vehicle ascent trajectories from lift-off to achieving targeting conditions outside the atmosphere. The entire ascent trajectory from lift-off to final target point is divided into two parts: atmospheric ascent portion and vacuum ascent portion. The two portions are integrated via a fixed-point iteration based on the continuity condition at the switch point between atmospheric ascent portion and vacuum ascent portion. The previous research works on closed-loop endo-atmospheric ascent guidance shows that the classical finite difference method is well suited for fast solution of the constrained optimal three-dimensional ascent problem. The exploitation of certain unique features in the integration procedure between the atmospheric portion and vacuum portion and the finite difference method, allows us to cast the atmospheric ascent problem into a nested fixed-point iteration problem. Therefore a novel Fixed-Point Iteration algorithm is presented for solving the endo-atmospheric ascent guidance problem. Several approaches are also provided for facilitating the convergence of the fixed-point iteration. The exo-atmospheric ascent portion allows an optimal coast in between the two vacuum powered stages. The optimal coast enables more efficient usage of the propellant. The Analytical Multiple-Shooting algorithm is developed to find the optimal trajectory for this portion. A generic launch vehicle model is adopted in the numerical simulation. A series of open-loop and closed-loop simulations are performed. The results verify the effectiveness, robustness and reliability of the Fixed-Point Iteration (FPI) algorithm and Analytical Multiple-Shooting (AMS) algorithm developed in this research. In
Komnik, A; Saleur, H
2011-09-01
We verify the validity of the Cohen-Gallavotti fluctuation theorem for the strongly correlated problem of charge transfer through an impurity in a chiral Luttinger liquid, which is realizable experimentally as a quantum point contact in a fractional quantum Hall edge state device. This is accomplished via the development of an analytical method to calculate the full counting statistics of the problem in all the parameter regimes involving the temperature, the Hall voltage, and the gate voltage. PMID:21981487
Fixed-rate compressed floating-point arrays
Energy Science and Technology Software Center (ESTSC)
2014-03-30
ZFP is a library for lossy compression of single- and double-precision floating-point data. One of the unique features of ZFP is its support for fixed-rate compression, which enables random read and write access at the granularity of small blocks of values. Using a C++ interface, this allows declaring compressed arrays (1D, 2D, and 3D arrays are supported) that through operator overloading can be treated just like conventional, uncompressed arrays, but which allow the user tomore » specify the exact number of bits to allocate to the array. ZFP also has variable-rate fixed-precision and fixed-accuracy modes, which allow the user to specify a tolerance on the relative or absolute error.« less
Gravity Duals of Lifshitz-Like Fixed Points
Kachru, Shamit; Liu, Xiao; Mulligan, Michael; /Stanford U., Phys. Dept. /SLAC
2008-11-05
We find candidate macroscopic gravity duals for scale-invariant but non-Lorentz invariant fixed points, which do not have particle number as a conserved quantity. We compute two-point correlation functions which exhibit novel behavior relative to their AdS counterparts, and find holographic renormalization group flows to conformal field theories. Our theories are characterized by a dynamical critical exponent z, which governs the anisotropy between spatial and temporal scaling t {yields} {lambda}{sup z}t, x {yields} {lambda}x; we focus on the case with z = 2. Such theories describe multicritical points in certain magnetic materials and liquid crystals, and have been shown to arise at quantum critical points in toy models of the cuprate superconductors. This work can be considered a small step towards making useful dual descriptions of such critical points.
Fixed points, stable manifolds, weather regimes, and their predictability
Deremble, Bruno; D'Andrea, Fabio; Ghil, Michael
2009-10-27
In a simple, one-layer atmospheric model, we study the links between low-frequency variability and the model’s fixed points in phase space. The model dynamics is characterized by the coexistence of multiple ''weather regimes.'' To investigate the transitions from one regime to another, we focus on the identification of stable manifolds associated with fixed points. We show that these manifolds act as separatrices between regimes. We track each manifold by making use of two local predictability measures arising from the meteorological applications of nonlinear dynamics, namely, ''bred vectors'' and singular vectors. These results are then verified in the framework of ensemblemore » forecasts issued from clouds (ensembles) of initial states. The divergence of the trajectories allows us to establish the connections between zones of low predictability, the geometry of the stable manifolds, and transitions between regimes.« less
Fixed points, stable manifolds, weather regimes, and their predictability
Deremble, Bruno; D'Andrea, Fabio; Ghil, Michael
2009-10-27
In a simple, one-layer atmospheric model, we study the links between low-frequency variability and the model’s fixed points in phase space. The model dynamics is characterized by the coexistence of multiple ''weather regimes.'' To investigate the transitions from one regime to another, we focus on the identification of stable manifolds associated with fixed points. We show that these manifolds act as separatrices between regimes. We track each manifold by making use of two local predictability measures arising from the meteorological applications of nonlinear dynamics, namely, ''bred vectors'' and singular vectors. These results are then verified in the framework of ensemble forecasts issued from clouds (ensembles) of initial states. The divergence of the trajectories allows us to establish the connections between zones of low predictability, the geometry of the stable manifolds, and transitions between regimes.
The computational core and fixed point organization in Boolean networks
NASA Astrophysics Data System (ADS)
Correale, L.; Leone, M.; Pagnani, A.; Weigt, M.; Zecchina, R.
2006-03-01
In this paper, we analyse large random Boolean networks in terms of a constraint satisfaction problem. We first develop an algorithmic scheme which allows us to prune simple logical cascades and underdetermined variables, returning thereby the computational core of the network. Second, we apply the cavity method to analyse the number and organization of fixed points. We find in particular a phase transition between an easy and a complex regulatory phase, the latter being characterized by the existence of an exponential number of macroscopically separated fixed point clusters. The different techniques developed are reinterpreted as algorithms for the analysis of single Boolean networks, and they are applied in the analysis of and in silico experiments on the gene regulatory networks of baker's yeast (Saccharomyces cerevisiae) and the segment-polarity genes of the fruitfly Drosophila melanogaster.
Fixed point structure of quenched, planar quantum electrodynamics
Love, S.T.
1986-07-01
Gauge theories exhibiting a hierarchy of fermion mass scales may contain a pseudo-Nambu-Boldstone boson of spontaneously broken scale invariance. The relation between scale and chiral symmetry breaking is studied analytically in quenched, planar quantum electrodynamics in four dimensions. The model possesses a novel nonperturbative ultraviolet fixed point governing its strong coupling phase which requires the mixing of four fermion operators. 12 refs.
On the transient fluctuation dissipation theorem after a quench at a critical point
NASA Astrophysics Data System (ADS)
Theurkauff, Isaac; Caussarieu, Aude; Petrosyan, Artyom; Ciliberto, Sergio
2015-08-01
The Modified Fluctuation Dissipation Theorem (MFDT) proposed by G. Verley et al. (EPL, 93 (2011) 10002) for non-equilibrium transient states is experimentally studied. We apply MFDT to the transient relaxation dynamics of the director of a liquid crystal after a quench close to the critical point of the Fréedericksz Transition (FrTr), which has several properties of a second-order phase transition driven by an electric field. Although the standard Fluctuation Dissipation Theorem (FDT) is not satisfied, because the system is strongly out of equilibrium, the MFDT is perfectly verified during the transient in a system which is only partially described by a Landau-Ginzburg (LG) equation, to which our observations are compared. The results can be useful in the study of material aging.
Finiteness of fixed equilibrium configurations of point vortices in the plane with a background flow
NASA Astrophysics Data System (ADS)
Cheung, Pak-Leong; Ng, Tuen Wai
2014-10-01
For a dynamic system consisting of n point vortices in an ideal plane fluid with a steady, incompressible and irrotational background flow, a more physically significant definition of a fixed equilibrium configuration is suggested. Under this new definition, if the complex polynomial w that determines the aforesaid background flow is non-constant, we have found an attainable generic upper bound \\frac{(m+n-1)!}{(m-1)!\\,n_1!\\cdots n_{i_0}!} for the number of fixed equilibrium configurations. Here, m = deg w, i0 is the number of species, and each ni is the number of vortices in a species. We transform the rational function system arising from fixed equilibria into a polynomial system, whose form is good enough to apply the BKK theory (named after Bernshtein (1975 Funct. Anal. Appl. 9 183-5), Khovanskii (1978 Funct. Anal. Appl. 12 38-46) and Kushnirenko (1976 Funct. Anal. Appl. 10 233-5)) to show the finiteness of its number of solutions. Having this finiteness, the required bound follows from Bézout's theorem or the BKK root count by Li and Wang (1996 Math. Comput. 65 1477-84).
Fluctuation theorem for a double quantum dot coupled to a point-contact electrometer
Golubev, D.; Utsumi, Y.; Marthaler, M.; Schön, G.
2013-12-04
Motivated by recent experiments on the real-time single-electron counting through a semiconductor GaAs double quantum dot (DQD) by a nearby quantum point contact (QPC), we develop the full-counting statistics of coupled DQD and QPC system. By utilizing the time-scale separation between the dynamics of DQD and QPC, we derive the modified master equation with tunneling rates depending on the counting fields, which fulfill the detailed fluctuation theorem. Furthermore, we derive universal relations between the non-linear corrections to the current and noise, which can be verified in experiments.
Fate of CPN-1 fixed points with q monopoles.
Block, Matthew S; Melko, Roger G; Kaul, Ribhu K
2013-09-27
We present an extensive quantum Monte Carlo study of the Néel to valence-bond solid (VBS) phase transition on rectangular- and honeycomb-lattice SU(N) antiferromagnets in sign-problem-free models. We find that in contrast to the honeycomb lattice and previously studied square-lattice systems, on the rectangular lattice for small N, a first-order Néel-VBS transition is realized. On increasing N≥4, we observe that the transition becomes continuous and with the same universal exponents as found on the honeycomb and square lattices (studied here for N=5, 7, 10), providing strong support for a deconfined quantum critical point. Combining our new results with previous numerical and analytical studies, we present a general phase diagram of the stability of CPN-1 fixed points with q monopoles. PMID:24116811
Accuracy and Efficiency in Fixed-Point Neural ODE Solvers.
Hopkins, Michael; Furber, Steve
2015-10-01
Simulation of neural behavior on digital architectures often requires the solution of ordinary differential equations (ODEs) at each step of the simulation. For some neural models, this is a significant computational burden, so efficiency is important. Accuracy is also relevant because solutions can be sensitive to model parameterization and time step. These issues are emphasized on fixed-point processors like the ARM unit used in the SpiNNaker architecture. Using the Izhikevich neural model as an example, we explore some solution methods, showing how specific techniques can be used to find balanced solutions. We have investigated a number of important and related issues, such as introducing explicit solver reduction (ESR) for merging an explicit ODE solver and autonomous ODE into one algebraic formula, with benefits for both accuracy and speed; a simple, efficient mechanism for cancelling the cumulative lag in state variables caused by threshold crossing between time steps; an exact result for the membrane potential of the Izhikevich model with the other state variable held fixed. Parametric variations of the Izhikevich neuron show both similarities and differences in terms of algorithms and arithmetic types that perform well, making an overall best solution challenging to identify, but we show that particular cases can be improved significantly using the techniques described. Using a 1 ms simulation time step and 32-bit fixed-point arithmetic to promote real-time performance, one of the second-order Runge-Kutta methods looks to be the best compromise; Midpoint for speed or Trapezoid for accuracy. SpiNNaker offers an unusual combination of low energy use and real-time performance, so some compromises on accuracy might be expected. However, with a careful choice of approach, results comparable to those of general-purpose systems should be possible in many realistic cases. PMID:26313605
Epidemiological study of fixed drug eruption in Pointe-Noire.
Ognongo-Ibiaho, A N; Atanda, H L
2012-11-01
A prospective study was conducted over a 27 month period in order to determine the epidemiological profile of fixed drug eruption (FDE) observed during a dermatological consultation at Pointe-Noire. During the study period 54 out of 9,070 persons consulting (0.6%) suffered from clinically diagnosed FDE. The variables studied were: age, sex, medicine and point of sale. The average age of onset was 30 years. The frequency of onset was higher in males (38 patients) than in females (16 patients). The incriminated medicines were: the sulfamides (48 patients) including Cotrimoxazole (45 patients ) and Sulfadoxine and Pyremethamine (3 patients) Coartem(®) + Doliprane(®) (1 patient), Chloramphenicol(®) (1 patient), Amidol(®) (1 patient), Duocotexin(®) + Paracetamol(®) (1 patient), Surquina(®) (1 patient), Amodiaquine(®) (1 patient). The point of sale was illicit (peddlers, markets) for 44 patients; for 10 patients it was a lawful outlet (pharmacies). This study shows that cotrimoxazole bought at illicit points of sale is the main etiology of FDE in the department, confirming that these medicines are counterfeit. The involvement of dermatologists in the fight against the illicit sale of medicines should be made a priority. PMID:23210952
A Fixed-Point Iteration Method with Quadratic Convergence
Walker, Kevin P.; Sham, Sam
2012-01-01
The fixed-point iteration algorithm is turned into a quadratically convergent scheme for a system of nonlinear equations. Most of the usual methods for obtaining the roots of a system of nonlinear equations rely on expanding the equation system about the roots in a Taylor series, and neglecting the higher order terms. Rearrangement of the resulting truncated system then results in the usual Newton-Raphson and Halley type approximations. In this paper the introduction of unit root functions avoids the direct expansion of the nonlinear system about the root, and relies, instead, on approximations which enable the unit root functions to considerably widen the radius of convergence of the iteration method. Methods for obtaining higher order rates of convergence and larger radii of convergence are discussed.
Fixed Point Transformations Based Iterative Control of a Polymerization Reaction
NASA Astrophysics Data System (ADS)
Tar, József K.; Rudas, Imre J.
As a paradigm of strongly coupled non-linear multi-variable dynamic systems the mathematical model of the free-radical polymerization of methyl-metachrylate with azobis (isobutyro-nitrile) as an initiator and toluene as a solvent taking place in a jacketed Continuous Stirred Tank Reactor (CSTR) is considered. In the adaptive control of this system only a single input variable is used as the control signal (the process input, i.e. dimensionless volumetric flow rate of the initiator), and a single output variable is observed (the process output, i.e. the number-average molecular weight of the polymer). Simulation examples illustrate that on the basis of a very rough and primitive model consisting of two scalar variables various fixed-point transformations based convergent iterations result in a novel, sophisticated adaptive control.
Fixed-point error analysis of Winograd Fourier transform algorithms
NASA Technical Reports Server (NTRS)
Patterson, R. W.; Mcclellan, J. H.
1978-01-01
The quantization error introduced by the Winograd Fourier transform algorithm (WFTA) when implemented in fixed-point arithmetic is studied and compared with that of the fast Fourier transform (FFT). The effect of ordering the computational modules and the relative contributions of data quantization error and coefficient quantization error are determined. In addition, the quantization error introduced by the Good-Winograd (GW) algorithm, which uses Good's prime-factor decomposition for the discrete Fourier transform (DFT) together with Winograd's short length DFT algorithms, is studied. Error introduced by the WFTA is, in all cases, worse than that of the FFT. In general, the WFTA requires one or two more bits for data representation to give an error similar to that of the FFT. Error introduced by the GW algorithm is approximately the same as that of the FFT.
Fixed-Point Optimization of Atoms and Density in DFT.
Marks, L D
2013-06-11
I describe an algorithm for simultaneous fixed-point optimization (mixing) of the density and atomic positions in Density Functional Theory calculations which is approximately twice as fast as conventional methods, is robust, and requires minimal to no user intervention or input. The underlying numerical algorithm differs from ones previously proposed in a number of aspects and is an autoadaptive hybrid of standard Broyden methods. To understand how the algorithm works in terms of the underlying quantum mechanics, the concept of algorithmic greed for different Broyden methods is introduced, leading to the conclusion that if a linear model holds that the first Broyden method is optimal, the second if a linear model is a poor approximation. How this relates to the algorithm is discussed in terms of electronic phase transitions during a self-consistent run which results in discontinuous changes in the Jacobian. This leads to the need for a nongreedy algorithm when the charge density crosses phase boundaries, as well as a greedy algorithm within a given phase. An ansatz for selecting the algorithm structure is introduced based upon requiring the extrapolated component of the curvature condition to have projected positive eigenvalues. The general convergence of the fixed-point methods is briefly discussed in terms of the dielectric response and elastic waves using known results for quasi-Newton methods. The analysis indicates that both should show sublinear dependence with system size, depending more upon the number of different chemical environments than upon the number of atoms, consistent with the performance of the algorithm and prior literature. This is followed by details of algorithm ranging from preconditioning to trust region control. A number of results are shown, finishing up with a discussion of some of the many open questions. PMID:26583869
Consistent Perturbative Fixed Point Calculations in QCD and Supersymmetric QCD
NASA Astrophysics Data System (ADS)
Ryttov, Thomas A.
2016-08-01
We suggest how to consistently calculate the anomalous dimension γ* of the ψ ¯ ψ operator in finite order perturbation theory at an infrared fixed point for asymptotically free theories. If the n +1 loop beta function and n loop anomalous dimension are known, then γ* can be calculated exactly and fully scheme independently in a Banks-Zaks expansion through O (Δfn) , where Δf=N¯ f-Nf , Nf is the number of flavors, and N¯f is the number of flavors above which asymptotic freedom is lost. For a supersymmetric theory, the calculation preserves supersymmetry order by order in Δf. We then compute γ* through O (Δf2) for supersymmetric QCD in the dimensional reduction scheme and find that it matches the exact known result. We find that γ* is astonishingly well described in perturbation theory already at the few loops level throughout the entire conformal window. We finally compute γ* through O (Δf3) for QCD and a variety of other nonsupersymmetric fermionic gauge theories. Small values of γ* are observed for a large range of flavors.
Consistent Perturbative Fixed Point Calculations in QCD and Supersymmetric QCD.
Ryttov, Thomas A
2016-08-12
We suggest how to consistently calculate the anomalous dimension γ_{*} of the ψ[over ¯]ψ operator in finite order perturbation theory at an infrared fixed point for asymptotically free theories. If the n+1 loop beta function and n loop anomalous dimension are known, then γ_{*} can be calculated exactly and fully scheme independently in a Banks-Zaks expansion through O(Δ_{f}^{n}), where Δ_{f}=N[over ¯]_{f}-N_{f}, N_{f} is the number of flavors, and N[over ¯]_{f} is the number of flavors above which asymptotic freedom is lost. For a supersymmetric theory, the calculation preserves supersymmetry order by order in Δ_{f}. We then compute γ_{*} through O(Δ_{f}^{2}) for supersymmetric QCD in the dimensional reduction scheme and find that it matches the exact known result. We find that γ_{*} is astonishingly well described in perturbation theory already at the few loops level throughout the entire conformal window. We finally compute γ_{*} through O(Δ_{f}^{3}) for QCD and a variety of other nonsupersymmetric fermionic gauge theories. Small values of γ_{*} are observed for a large range of flavors. PMID:27563948
NASA Astrophysics Data System (ADS)
Heikkila, S.
2007-08-01
In this paper we apply generalized iteration methods to prove comparison results which show how fixed points of a multifunction can be bounded by least and greatest fixed points of single-valued functions. As an application we prove existence and comparison results for fixed points of multifunctions. These results are applied to normal-form games, by proving existence and comparison results for pure and mixed Nash equilibria and their utilities.
Composition analysis of large samples with PGNAA using a fixed point iteration
NASA Astrophysics Data System (ADS)
Akkurt, Hatice
2002-09-01
The composition problem in large sample prompt gamma neutron activation analysis (PGNAA) is a nonlinear inverse problem. The basic form of the nonlinear inverse composition problem is presented. This problem is then formulated in a general way, as a fixed point problem, without addressing any specific application or sample type or linearization approach. This approach of formulating the problem as a fixed point problem suggested a natural fixed point iteration. The algorithm of the fixed point iteration solves the nonlinear composition problem using a combination of measured and computed data. The effectiveness of the fixed point iteration for composition analysis is demonstrated using purely numerical experiments. These numerical experiments showed that the fixed point iteration can be successfully applied to find the bulk composition of large samples, with excellent agreement between the estimated and true composition of the samples, in a few iterations, independent of the initial guess. In order to test the fixed point iteration using real experimental data, a series of large sample PGNAA measurements were performed at ANL-W. These experiments are described and the measured spectra for the samples are presented. Then, the fixed point iteration is applied for these real experiments to find the composition of the samples. In all of the cases, except borated polyethylene, the composition of the large samples are found in a few iterations with errors less than +/-1.3%. The effectiveness of the fixed point iteration is thus demonstrated with many proof-of-principle measurements. While testing the fixed point iteration algorithm, published values of the source spectrum and relative detector efficiencies are used. The sensitivity of the fixed point iteration to source spectrum is investigated and it is shown that the estimated composition results are not very sensitive to the change in the source spectrum. The reason behind the slow convergence for the borated
Triple point of e-deuterium as an accurate thermometric fixed point
Pavese, F.; McConville, G.T.
1986-01-01
The triple point of deuterium (18.7/sup 0/K) is the only possibility for excluding vapor pressure measurements in the definition of a temperature scale based on fixed points between 13.81 and 24.562/sup 0/K. This paper reports an investigation made at the Istituto di Metrologia and Mound Laboratory, using extremely pure deuterium directly sealed at the production plant into small metal cells. The large contamination by HD of commercially available gas, that cannot be accounted and corrected for due to its increase in handling, was found to be very stable with time after sealing in IMGC cells. HD contamination can be limited to less than 100 ppM in Monsanto cells, both with n-D/sub 2/ and e-D/sub 2/, when filled directly from the thermal diffusion column and sealed at the factory. e-D/sub 2/ requires a special deuterated catalyst. The triple point temperature of e-D/sub 2/ has been determined to be: T(NPL-IPTS-68) = 18.7011 +- 0.002/sup 0/K. 20 refs., 3 figs., 2 tabs.
Area law for fixed points of rapidly mixing dissipative quantum systems
Brandão, Fernando G. S. L.; Cubitt, Toby S.; Lucia, Angelo; Michalakis, Spyridon; Perez-Garcia, David
2015-10-15
We prove an area law with a logarithmic correction for the mutual information for fixed points of local dissipative quantum system satisfying a rapid mixing condition, under either of the following assumptions: the fixed point is pure or the system is frustration free.
A 64-bit orthorectification algorithm using fixed-point arithmetic
NASA Astrophysics Data System (ADS)
French, Joseph C.; Balster, Eric J.; Turri, William F.
2013-10-01
As the cost of imaging systems have decreased, the quality and size has increased. This dynamic has made the practicality of many aerial imaging applications achievable such as cost line monitoring and vegetation indexing. Orthorectification is required for many of these applications; however, it is also expensive, computationally. The computational cost is due to oating point operations and divisions inherent in the orthorecti cation process. Two novel algorithm modi cations are proposed which signi cantly reduce the computational cost. The rst modi cation uses xed-point arithmetic in place of the oating point operations. The second replaces the division with a multiplication of the inverse. The result in an increase of 2x of the throughput while remaining within 15% of a pixel size in position.
NASA Astrophysics Data System (ADS)
Dittmore, Andrew; Trail, Collin; Olsen, Thomas; Wiener, Richard J.
2003-11-01
We have previously demonstrated the experimental control of chaos in a Modified Taylor-Couette system with hourglass geometry( Richard J. Wiener et al), Phys. Rev. Lett. 83, 2340 (1999).. Identifying fixed points susceptible to algorithms for the control of chaos is key. We seek to learn about this process in the accessible numerical model of the damped, driven pendulum. Following Baker(Gregory L. Baker, Am. J. Phys. 63), 832 (1995)., we seek points susceptible to the OGY(E. Ott, C. Grebogi, and J. A. Yorke, Phys. Rev. Lett. 64), 1196 (1990). algorithm. We automate the search for fixed points that are candidates for control. We present comparisons of the space of candidate fixed points with the bifurcation diagrams and Poincare sections of the system. We demonstrate control at fixed points which do not appear on the attractor. We also show that the control algorithm may be employed to shift the system between non-communicating branches of the attractor.
Fixed point sensitivity analysis of interacting structured populations.
Barabás, György; Meszéna, Géza; Ostling, Annette
2014-03-01
Sensitivity analysis of structured populations is a useful tool in population ecology. Historically, methodological development of sensitivity analysis has focused on the sensitivity of eigenvalues in linear matrix models, and on single populations. More recently there have been extensions to the sensitivity of nonlinear models, and to communities of interacting populations. Here we derive a fully general mathematical expression for the sensitivity of equilibrium abundances in communities of interacting structured populations. Our method yields the response of an arbitrary function of the stage class abundances to perturbations of any model parameters. As a demonstration, we apply this sensitivity analysis to a two-species model of ontogenetic niche shift where each species has two stage classes, juveniles and adults. In the context of this model, we demonstrate that our theory is quite robust to violating two of its technical assumptions: the assumption that the community is at a point equilibrium and the assumption of infinitesimally small parameter perturbations. Our results on the sensitivity of a community are also interpreted in a niche theoretical context: we determine how the niche of a structured population is composed of the niches of the individual states, and how the sensitivity of the community depends on niche segregation. PMID:24368160
Analysis of fixed point FFT for Fourier domain optical coherence tomography systems.
Ali, Murtaza; Parlapalli, Renuka; Magee, David P; Dasgupta, Udayan
2009-01-01
Optical coherence tomography (OCT) is a new imaging modality gaining popularity in the medical community. Its application includes ophthalmology, gastroenterology, dermatology etc. As the use of OCT increases, the need for portable, low power devices also increases. Digital signal processors (DSP) are well suited to meet the signal processing requirements of such a system. These processors usually operate on fixed precision. This paper analyzes the issues that a system implementer faces implementing signal processing algorithms on fixed point processor. Specifically, we show the effect of different fixed point precisions in the implementation of FFT on the sensitivity of Fourier domain OCT systems. PMID:19965018
Extending the Nonlinear-Beam-Dynamics Concept of 1D Fixed Points to 2D Fixed Lines.
Franchetti, G; Schmidt, F
2015-06-12
The origin of nonlinear dynamics traces back to the study of the dynamics of planets with the seminal work of Poincaré at the end of the nineteenth century: Les Méthodes Nouvelles de la Mécanique Céleste, Vols. 1-3 (Gauthier Villars, Paris, 1899). In his work he introduced a methodology fruitful for investigating the dynamical properties of complex systems, which led to the so-called "Poincaré surface of section," which allows one to capture the global dynamical properties of a system, characterized by fixed points and separatrices with respect to regular and chaotic motion. For two-dimensional phase space (one degree of freedom) this approach has been extremely useful and applied to particle accelerators for controlling their beam dynamics as of the second half of the twentieth century. We describe here an extension of the concept of 1D fixed points to fixed lines in two dimensions. These structures become the fundamental entities for characterizing the nonlinear motion in the four-dimensional phase space (two degrees of freedom). PMID:26196806
Extending the Nonlinear-Beam-Dynamics Concept of 1D Fixed Points to 2D Fixed Lines
NASA Astrophysics Data System (ADS)
Franchetti, G.; Schmidt, F.
2015-06-01
The origin of nonlinear dynamics traces back to the study of the dynamics of planets with the seminal work of Poincaré at the end of the nineteenth century: Les Méthodes Nouvelles de la Mécanique Céleste, Vols. 1-3 (Gauthier Villars, Paris, 1899). In his work he introduced a methodology fruitful for investigating the dynamical properties of complex systems, which led to the so-called "Poincaré surface of section," which allows one to capture the global dynamical properties of a system, characterized by fixed points and separatrices with respect to regular and chaotic motion. For two-dimensional phase space (one degree of freedom) this approach has been extremely useful and applied to particle accelerators for controlling their beam dynamics as of the second half of the twentieth century. We describe here an extension of the concept of 1D fixed points to fixed lines in two dimensions. These structures become the fundamental entities for characterizing the nonlinear motion in the four-dimensional phase space (two degrees of freedom).
NASA Astrophysics Data System (ADS)
Viesca, R. C.
2014-12-01
A fault's transition from slow creep to the propagation of an earthquake-generating dynamic rupture is thought to start as a quasi-static slip instability. Here we examine how such an instability develops on a sliding interface whose strength is governed by a slip rate- and state-dependent friction, where the state variable evolves according to the aging law. We find that the development occurs as the attraction of a dynamical system to a fixed point. The fixed points are such that the state of slip and the rate at which velocity diverges (and its spatial distribution) are known. The fixed points are independent of the manner of external forcing and the values of slip rate and state before the onset of instability. For a fault under uniform normal stress and frictional properties, the sole parameter that determines the fixed point (to within a translational invariance) is the ratio of the frictional parameters, a/b (where, for steady-state rate weakening, 0fixed points are asymptotically stable; however, stability is lost for a/b above that value. Increasing a/b above this critical value leads to a series of Hopf bifurcations. This cascade of bifurcations signals a quasi-periodic route to chaos, implying the existence of a second, larger, critical value of a/b (corresponding to the value at which the third Hopf bifurcation occurs), above which the slip instability may develop in a chaotic fashion. The fixed-point solutions, as well as the critical thresholds concerning their stability, depend on the configuration of slip (e.g., in/anti-plane or mixed-mode slip) and the elastic environment in which the interface is embedded (e.g., a slip surface between elastic half-spaces or one lying below and parallel to a free surface); solving for a fixed point reduces to the solution of an equivalent problem of an equilibrium slip-weakening fracture; and fixed-point stability is determined by linear stability analysis. Solutions of
Infrared fixed point in SU(2) gauge theory with adjoint fermions
DeGrand, Thomas; Shamir, Yigal; Svetitsky, Benjamin
2011-04-01
We apply Schroedinger-functional techniques to the SU(2) lattice gauge theory with N{sub f}=2 flavors of fermions in the adjoint representation. Our use of hypercubic smearing enables us to work at stronger couplings than did previous studies, before encountering a critical point and a bulk phase boundary. Measurement of the running coupling constant gives evidence of an infrared fixed point g{sub *} where 1/g{sub *}{sup 2}=0.20(4)(3). At the fixed point, we find a mass anomalous dimension {gamma}{sub m}(g{sub *})=0.31(6).
Dark energy as a fixed point of the Einstein Yang-Mills Higgs equations
NASA Astrophysics Data System (ADS)
Rinaldi, Massimiliano
2015-10-01
We study the Einstein Yang-Mills Higgs equations in the SO(3) representation on a isotropic and homogeneous flat Universe, in the presence of radiation and matter fluids. We map the equations of motion into an autonomous dynamical system of first-order differential equations and we find the equilibrium points. We show that there is only one stable fixed point that corresponds to an accelerated expanding Universe in the future. In the past, instead, there is an unstable fixed point that implies a stiff-matter domination. In between, we find three other unstable fixed points, corresponding, in chronological order, to radiation domination, to matter domination, and, finally, to a transition from decelerated expansion to accelerated expansion. We solve the system numerically and we confirm that there are smooth trajectories that correctly describe the evolution of the Universe, from a remote past dominated by radiation to a remote future dominated by dark energy, passing through a matter-dominated phase.
Listak, J.M.; Goodman, G.V.R.; Jankowski, R.A.
1999-07-01
Respirable dust studies were conducted at several underground coal mining operations to evaluate and compare the dust measurements of fixed-point machine-mounted samples on a continuous miner and personal samples of the remote miner operator. Fixed-point sampling was conducted at the right rear corner of the continuous miner which corresponded to the traditional location of the operator's cab. Although it has been documented that higher concentrations of dust are present at the machine-mounted position, this work sought to determine whether a relationship exists between the concentrations at the fixed-point position and the dust levels experienced at the remote operator position and whether this relationship could be applied on an industry-wide basis. To achieve this objective, gravimetric samplers were used to collect respirable dust data on continuous miner sections. These samplers were placed at a fixed position at the cab location of the continuous mining machine and on or near the remote miner operator during the 1 shift/day sampling periods. Dust sampling took place at mines with a variety of geographic locations and in-mine conditions. The dust concentration data collected at each site and for each sampling period were reduced to ratios of fixed-point to operator concentration. The ratios were calculated to determine similarities, differences, and/or variability at the two positions. The data show that dust concentrations at the remote operator position were always lower than dust concentrations measured at the fixed-point continuous miner location. However, the ratios of fixed-point to remote operator dust levels showed little consistency from shift to shift or from operation to operation. The fact that these ratios are so variable may introduce some uncertainty into attempting to correlate dust exposures of the remote operator to dust levels measured on the continuous mining machine.
Entanglement storage by classical fixed points in the two-axis countertwisting model
NASA Astrophysics Data System (ADS)
Kajtoch, Dariusz; Pawłowski, Krzysztof; Witkowska, Emilia
2016-02-01
We analyze a scheme for storage of entanglement quantified by the quantum Fisher information in the two-axis countertwisting model. A characteristic feature of the two-axis countertwisting Hamiltonian is the existence of the four stable center and two unstable saddle fixed points in the mean-field phase portrait. The entangled state is generated dynamically from an initial spin-coherent state located around an unstable saddle fixed point. At an optimal moment of time the state is shifted to a position around the stable center fixed points by a single rotation, where its dynamics and properties are approximately frozen. We also discuss evolution with noise. In some cases the effect of noise turns out to be relatively weak, which is explained by parity conservation.
Discovering and quantifying nontrivial fixed points in multi-field models
NASA Astrophysics Data System (ADS)
Eichhorn, A.; Helfer, T.; Mesterházy, D.; Scherer, M. M.
2016-02-01
We use the functional renormalization group and the ɛ -expansion concertedly to explore multicritical universality classes for coupled bigoplus _i O(N_i) vector-field models in three Euclidean dimensions. Exploiting the complementary strengths of these two methods we show how to make progress in theories with large numbers of interactions, and a large number of possible symmetry-breaking patterns. For the three- and four-field models we find a new fixed point that arises from the mutual interaction between different field sectors, and we establish the absence of infrared-stable fixed-point solutions for the regime of small N_i. Moreover, we explore these systems as toy models for theories that are both asymptotically safe and infrared complete. In particular, we show that these models exhibit complete renormalization group trajectories that begin and end at nontrivial fixed points.
Normal form solutions of dynamical systems in the basin of attraction of their fixed points
NASA Astrophysics Data System (ADS)
Bountis, Tassos; Tsarouhas, George; Herman, Russell
1998-10-01
The normal form theory of Poincaré, Siegel and Arnol'd is applied to an analytically solvable Lotka-Volterra system in the plane, and a periodically forced, dissipative Duffing's equation with chaotic orbits in its 3-dimensional phase space. For the planar model, we determine exactly how the convergence region of normal forms about a nodal fixed point is limited by the presence of singularities of the solutions in the complex t-plane. Despite such limitations, however, we show, in the case of a periodically driven system, that normal forms can be used to obtain useful estimates of the basin of attraction of a stable fixed point of the Poincaré map, whose ``boundary'' is formed by the intersecting invariant manifolds of a second hyperbolic fixed point nearby.
Entanglement entropy at infinite-randomness fixed points in higher dimensions.
Lin, Yu-Cheng; Iglói, Ferenc; Rieger, Heiko
2007-10-01
The entanglement entropy of the two-dimensional random transverse Ising model is studied with a numerical implementation of the strong-disorder renormalization group. The asymptotic behavior of the entropy per surface area diverges at, and only at, the quantum phase transition that is governed by an infinite-randomness fixed point. Here we identify a double-logarithmic multiplicative correction to the area law for the entanglement entropy. This contrasts with the pure area law valid at the infinite-randomness fixed point in the diluted transverse Ising model in higher dimensions. PMID:17930713
Parallel fixed point implementation of a radial basis function network in an FPGA.
de Souza, Alisson C D; Fernandes, Marcelo A C
2014-01-01
This paper proposes a parallel fixed point radial basis function (RBF) artificial neural network (ANN), implemented in a field programmable gate array (FPGA) trained online with a least mean square (LMS) algorithm. The processing time and occupied area were analyzed for various fixed point formats. The problems of precision of the ANN response for nonlinear classification using the XOR gate and interpolation using the sine function were also analyzed in a hardware implementation. The entire project was developed using the System Generator platform (Xilinx), with a Virtex-6 xc6vcx240t-1ff1156 as the target FPGA. PMID:25268918
Parallel Fixed Point Implementation of a Radial Basis Function Network in an FPGA
de Souza, Alisson C. D.; Fernandes, Marcelo A. C.
2014-01-01
This paper proposes a parallel fixed point radial basis function (RBF) artificial neural network (ANN), implemented in a field programmable gate array (FPGA) trained online with a least mean square (LMS) algorithm. The processing time and occupied area were analyzed for various fixed point formats. The problems of precision of the ANN response for nonlinear classification using the XOR gate and interpolation using the sine function were also analyzed in a hardware implementation. The entire project was developed using the System Generator platform (Xilinx), with a Virtex-6 xc6vcx240t-1ff1156 as the target FPGA. PMID:25268918
Chiral symmetry breaking in three-dimensional quantum electrodynamics as fixed point annihilation
NASA Astrophysics Data System (ADS)
Herbut, Igor F.
2016-07-01
Spontaneous chiral symmetry breaking in three-dimensional (d =3 ) quantum electrodynamics is understood as annihilation of an infrared-stable fixed point that describes the large-N conformal phase by another unstable fixed point at a critical number of fermions N =Nc. We discuss the root of universality of Nc in this picture, together with some features of the phase boundary in the (d ,N ) plane. In particular, it is shown that as d →4 , Nc→0 with a constant slope, our best estimate of which suggests that Nc=2.89 in d =3 .
NASA Astrophysics Data System (ADS)
Katzav, Eytan
2013-04-01
In this paper, a mode of using the Dynamic Renormalization Group (DRG) method is suggested in order to cope with inconsistent results obtained when applying it to a continuous family of one-dimensional nonlocal models. The key observation is that the correct fixed-point dynamical system has to be identified during the analysis in order to account for all the relevant terms that are generated under renormalization. This is well established for static problems, however poorly implemented in dynamical ones. An application of this approach to a nonlocal extension of the Kardar-Parisi-Zhang equation resolves certain problems in one-dimension. Namely, obviously problematic predictions are eliminated and the existing exact analytic results are recovered.
Fixed-point distributions of short-range Ising spin glasses on hierarchical lattices
NASA Astrophysics Data System (ADS)
Almeida, Sebastião T. O.; Nobre, Fernando D.
2015-03-01
Fixed-point distributions for the couplings of Ising spin glasses with nearest-neighbor interactions on hierarchical lattices are investigated numerically. Hierarchical lattices within the Migdal-Kadanoff family with fractal dimensions in the range 2.58 ≤D ≤7 , as well as a lattice of the Wheatstone-Bridge family with fractal dimension D ≈3.58 are considered. Three initial distributions for the couplings are analyzed, namely, the Gaussian, bimodal, and uniform ones. In all cases, after a few iterations of the renormalization-group procedure, the associated probability distributions approached universal fixed shapes. For hierarchical lattices of the Migdal-Kadanoff family, the fixed-point distributions were well fitted either by stretched exponentials, or by q -Gaussian distributions; both fittings recover the expected Gaussian limit as D →∞ . In the case of the Wheatstone-Bridge lattice, the best fit was found by means of a stretched-exponential distribution.
Combined GPS/GLONASS Precise Point Positioning with Fixed GPS Ambiguities
Pan, Lin; Cai, Changsheng; Santerre, Rock; Zhu, Jianjun
2014-01-01
Precise point positioning (PPP) technology is mostly implemented with an ambiguity-float solution. Its performance may be further improved by performing ambiguity-fixed resolution. Currently, the PPP integer ambiguity resolutions (IARs) are mainly based on GPS-only measurements. The integration of GPS and GLONASS can speed up the convergence and increase the accuracy of float ambiguity estimates, which contributes to enhancing the success rate and reliability of fixing ambiguities. This paper presents an approach of combined GPS/GLONASS PPP with fixed GPS ambiguities (GGPPP-FGA) in which GPS ambiguities are fixed into integers, while all GLONASS ambiguities are kept as float values. An improved minimum constellation method (MCM) is proposed to enhance the efficiency of GPS ambiguity fixing. Datasets from 20 globally distributed stations on two consecutive days are employed to investigate the performance of the GGPPP-FGA, including the positioning accuracy, convergence time and the time to first fix (TTFF). All datasets are processed for a time span of three hours in three scenarios, i.e., the GPS ambiguity-float solution, the GPS ambiguity-fixed resolution and the GGPPP-FGA resolution. The results indicate that the performance of the GPS ambiguity-fixed resolutions is significantly better than that of the GPS ambiguity-float solutions. In addition, the GGPPP-FGA improves the positioning accuracy by 38%, 25% and 44% and reduces the convergence time by 36%, 36% and 29% in the east, north and up coordinate components over the GPS-only ambiguity-fixed resolutions, respectively. Moreover, the TTFF is reduced by 27% after adding GLONASS observations. Wilcoxon rank sum tests and chi-square two-sample tests are made to examine the significance of the improvement on the positioning accuracy, convergence time and TTFF. PMID:25237901
Fixed-point arithmetic for mobile devices: a fingerprinting verification case study
NASA Astrophysics Data System (ADS)
Moon, Yiu S.; Luk, Franklin T.; Ho, Ho C.; Tang, T. Y.; Chan, Kit C.; Leung, C. W.
2002-12-01
Mobile devices use embedded processors with low computing capabilities to reduce power consumption. Since floating-point arithmetic units are power hungry, computationally intensive jobs must be accomplished with either digital signal processors or hardware co-processors. In this paper, we propose to perform fixed-point arithmetic on an integer hardware unit. We illustrate the advantages of our approach by implementing fingerprint verification on mobile devices.
Long-Term Stability of WC-C Peritectic Fixed Point
NASA Astrophysics Data System (ADS)
Khlevnoy, B. B.; Grigoryeva, I. A.
2015-03-01
The tungsten carbide-carbon peritectic (WC-C) melting transition is an attractive high-temperature fixed point with a temperature of . Earlier investigations showed high repeatability, small melting range, low sensitivity to impurities, and robustness of WC-C that makes it a prospective candidate for the highest fixed point of the temperature scale. This paper presents further study of the fixed point, namely the investigation of the long-term stability of the WC-C melting temperature. For this purpose, a new WC-C cell of the blackbody type was built using tungsten powder of 99.999 % purity. The stability of the cell was investigated during the cell aging for 50 h at the cell working temperature that tooks 140 melting/freezing cycles. The method of investigation was based on the comparison of the WC-C tested cell with a reference Re-C fixed-point cell that reduces an influence of the probable instability of a radiation thermometer. It was shown that after the aging period, the deviation of the WC-C cell melting temperature was with an uncertainty of.
Fixed point analysis of a scalar theory with an external field
Bonanno, A.; Zappala, D.
1997-09-01
A momentum dependent projection of the Wegner-Hougton equation is derived for a scalar theory coupled to an external field. This formalism is useful to discuss the phase diagram of the theory. In particular we study some properties of the Gaussian fixed point. {copyright} {ital 1997} {ital The American Physical Society}
Code of Federal Regulations, 2010 CFR
2010-10-01
... 47 Telecommunication 5 2010-10-01 2010-10-01 false Operation of internal transmitter control... Transmitter Control Internal Transmitter Control Systems § 90.473 Operation of internal transmitter control systems through licensed fixed control points. An internal transmitter control system may be...
NASA Astrophysics Data System (ADS)
Bojkovski, J.; Veliki, T.; Zvizdić, D.; Drnovšek, J.
2011-08-01
The objective of project EURAMET 1127 (Bilateral comparison of triple point of mercury and melting point of gallium) in the field of thermometry is to compare realization of a triple point of mercury (-38.8344 °C) and melting point of gallium (29.7646 °C) between the Slovenian national laboratory MIRS/UL-FE/LMK and the Croatian national laboratory HMI/FSB-LPM using a long-stem 25 Ω standard platinum resistance thermometer (SPRT). MIRS/UL/FE-LMK participated in a number of intercomparisons on the level of EURAMET. On the other hand, the HMI/LPM-FSB laboratory recently acquired new fixed-point cells which had to be evaluated in the process of intercomparisons. A quartz-sheathed SPRT has been selected and calibrated at HMI/LPM-FSB at the triple point of mercury, the melting point of gallium, and the water triple point. A second set of measurements was made at MIRS/UL/FE-LMK. After its return, the SPRT was again recalibrated at HMI/LPM-FSB. In the comparison, the W value of the SPRT has been used. Results of the bilateral intercomparison confirmed that the new gallium cell of the HMI/LPM-FSB has a value that is within uncertainty limits of both laboratories that participated in the exercise, while the mercury cell experienced problems. After further research, a small leakage in the mercury fixed-point cell has been found.
NASA Astrophysics Data System (ADS)
Pearce, Jonathan V.; Gisby, John A.; Steur, Peter P. M.
2016-08-01
A knowledge of the effect of impurities at the level of parts per million on the freezing temperature of very pure metals is essential for realisation of ITS-90 fixed points. New information has become available for use with the thermodynamic modelling software MTDATA, permitting calculation of liquidus slopes, in the low concentration limit, of a wider range of binary alloy systems than was previously possible. In total, calculated values for 536 binary systems are given. In addition, new experimental determinations of phase diagrams, in the low impurity concentration limit, have recently appeared. All available data have been combined to provide a comprehensive set of liquidus slopes for impurities in ITS-90 metal fixed points. In total, liquidus slopes for 838 systems are tabulated for the fixed points Hg, Ga, In, Sn, Zn, Al, Ag, Au, and Cu. It is shown that the value of the liquidus slope as a function of impurity element atomic number can be approximated using a simple formula, and good qualitative agreement with the existing data is observed for the fixed points Al, Ag, Au and Cu, but curiously the formula is not applicable to the fixed points Hg, Ga, In, Sn, and Zn. Some discussion is made concerning the influence of oxygen on the liquidus slopes, and some calculations using MTDATA are discussed. The BIPM’s consultative committee for thermometry has long recognised that the sum of individual estimates method is the ideal approach for assessing uncertainties due to impurities, but the community has been largely powerless to use the model due to lack of data. Here, not only is data provided, but a simple model is given to enable known thermophysical data to be used directly to estimate impurity effects for a large fraction of the ITS-90 fixed points.
Device-independent test of causal order and relations to fixed-points
NASA Astrophysics Data System (ADS)
Baumeler, Ämin; Wolf, Stefan
2016-03-01
Bell non-local correlations cannot be naturally explained in a fixed causal structure. This serves as a motivation for considering models where no global assumption is made beyond logical consistency. The assumption of a fixed causal order between a set of parties, together with free randomness, implies device-independent inequalities—just as the assumption of locality does. It is known that local validity of quantum theory is consistent with violating such inequalities. Moreover, for three parties or more, even the (stronger) assumption of local classical probability theory plus logical consistency allows for violating causal inequalities. Here, we show that a classical environment (with which the parties interact), possibly containing loops, is logically consistent if and only if whatever the involved parties do, there is exactly one fixed-point, the latter being representable as a mixture of deterministic fixed-points. We further show that the non-causal view allows for a model of computation strictly more powerful than computation in a world of fixed causal orders.
A Fixed-Point Phase Lock Loop in a Software Defined Radio
NASA Astrophysics Data System (ADS)
Johannes, Michael T.
2002-09-01
A software defined radio is a much more flexible platform than traditional, hardware implemented radios, By implementing radio functions in software, and putting those functions on a Field Programmable Gate Array (FPGA) chip, users will have the ability to download mission specific radio capabilities. This thesis examines a fundamental piece of the receiver, the Phase-Lock Loop (PLL), simulates a software PLL, and investigates the effects of fixed-point versus floating point mathematics required for an FPGA based PLL. With a fixed-point PLL simulator, figures of merit such as lock-time, lock range, and pull-in range are determined% for typical signal-to-noise ratio (SNR) levels.
NASA Astrophysics Data System (ADS)
Canet, Léonie; Delamotte, Bertrand; Wschebor, Nicolás
2016-06-01
We investigate the regime of fully developed homogeneous and isotropic turbulence of the Navier-Stokes (NS) equation in the presence of a stochastic forcing, using the nonperturbative (functional) renormalization group (NPRG). Within a simple approximation based on symmetries, we obtain the fixed-point solution of the NPRG flow equations that corresponds to fully developed turbulence both in d =2 and 3 dimensions. Deviations to the dimensional scalings (Kolmogorov in d =3 or Kraichnan-Batchelor in d =2 ) are found for the two-point functions. To further analyze these deviations, we derive exact flow equations in the large wave-number limit, and show that the fixed point does not entail the usual scale invariance, thereby identifying the mechanism for the emergence of intermittency within the NPRG framework. The purpose of this work is to provide a detailed basis for NPRG studies of NS turbulence; the determination of the ensuing intermittency exponents is left for future work.
On Harnack's theorem and extensions
NASA Astrophysics Data System (ADS)
Costa, Antonio F.; Parlier, Hugo
Harnack's theorem states that the fixed points of an orientation reversing involution of a compact orientable surface of genus g are a set of k disjoint simple closed geodesic where 0≤ k≤ g+1 . The first goal of this article is to give a purely geometric, complete and self-contained proof of this fact. In the case where the fixed curves of the involution do not separate the surface, we prove an extension of this theorem, by exhibiting the existence of auxiliary invariant curves with interesting properties. Although this type of extension is well known (see, for instance, Comment. Math. Helv. 57(4): 603-626 (1982) and Transl. Math. Monogr., vol. 225, Amer. Math. Soc., Providence, RI, 2004), our method also extends the theorem in the case where the surface has boundary. As a byproduct, we obtain a geometric method on how to obtain these auxiliary curves. As a consequence of these constructions, we obtain results concerning presentations of Non-Euclidean crystallographic groups and a new proof of a result on the set of points corresponding to real algebraic curves in the compactification of the Moduli space of complex curves of genus g , overline{M_{g}} . More concretely, we establish that given two real curves there is a path in overline{M_{g}} which passes through at most two singular curves, a result of M. Seppaelae (Ann. Sci. Ecole Norm. Sup. (4), 24(5), 519-544 (1991)).
NASA Astrophysics Data System (ADS)
Machin, G.; Teixeira, R.; Lu, X.; Lowe, D.
2015-03-01
There is an on-going requirement to perform scale comparisons above the silver point with reduced uncertainties. Previous comparisons have been performed with high stability lamps or radiation thermometers, neither of which were able to achieve the required uncertainty. Ideally a set of driftless unknown temperature fixed points would be used to compare scales, but up to now such artifacts did not exist. This study develops blind high-temperature comparison artifacts based on doped versions of the high-temperature fixed point (HTFP) Ni-C (nominal temperature ). At INMETRO three HTFP blackbodies were constructed, one of pure Ni-C and two doped with different levels of Cu. To ascertain the effect of doping on the transition temperature, the cells were compared to the reference pure Ni-C cell. The doped cells were then transported to NPL and their temperatures measured. NPL was not informed of the INMETRO result ensuring that the measurements remained blind. The cells were then returned to INMETRO and re-measured to establish their stability. The temperatures measured at INMETRO and NPL were then compared and showed very good equivalence of the scale at the fixed-point temperatures. The results of the comparison of the NPL and INMETRO temperature scale, at nominally , are reported, along with evidence of the stability of the artifacts determined from repeat measurements. These promising results indicate that it may be possible to make HTFPs with altered temperatures which are stable enough to serve as comparison artifacts.
Tympanic thermometer performance validation by use of a body-temperature fixed point blackbody
NASA Astrophysics Data System (ADS)
Machin, Graham; Simpson, Robert
2003-04-01
The use of infrared tympanic thermometers within the medical community (and more generically in the public domain) has recently grown rapidly, displacing more traditional forms of thermometry such as mercury-in-glass. Besides the obvious health concerns over mercury the increase in the use of tympanic thermometers is related to a number of factors such as their speed and relatively non-invasive method of operation. The calibration and testing of such devices is covered by a number of international standards (ASTM1, prEN2, JIS3) which specify the design of calibration blackbodies. However these calibration sources are impractical for day-to-day in-situ validation purposes. In addition several studies (e.g. Modell et al4, Craig et al5) have thrown doubt on the accuracy of tympanic thermometers in clinical use. With this in mind the NPL is developing a practical, portable and robust primary reference fixed point source for tympanic thermometer validation. The aim of this simple device is to give the clinician a rapid way of validating the performance of their tympanic thermometer, enabling the detection of mal-functioning thermometers and giving confidence in the measurement to the clinician (and patient!) at point of use. The reference fixed point operates at a temperature of 36.3 °C (97.3 °F) with a repeatability of approximately +/- 20 mK. The fixed-point design has taken into consideration the optical characteristics of tympanic thermometers enabling wide-angled field of view devices to be successfully tested. The overall uncertainty of the device is estimated to be is less than 0.1°C. The paper gives a description of the fixed point, its design and construction as well as the results to date of validation tests.
Convergence theorems for generalized nonexpansive multivalued mappings in hyperbolic spaces.
Kim, Jong Kyu; Pathak, Ramesh Prasad; Dashputre, Samir; Diwan, Shailesh Dhar; Gupta, Rajlaxmi
2016-01-01
In this paper, we establish the existence of a fixed point for generalized nonexpansive multivalued mappings in hyperbolic spaces and we prove some [Formula: see text]-convergence and strong convergence theorems for the iterative scheme proposed by Chang et al. (Appl Math Comp 249:535-540, 2014) to approximate a fixed point for generalized nonexpansive multivalued mapping under suitable conditions. Our results are the extension and improvements of the recent well-known results announced in the current literature. PMID:27386356
Infrared fixed point of the top Yukawa coupling in split supersymmetry
Huitu, Katri; Laamanen, Jari; Roy, Probir; Roy, Sourov
2005-09-01
The severe constraints imposed on the parameter space of the minimal split supersymmetry model by the infrared fixed point solution of the top Yukawa coupling Y{sub t} are studied in detail in terms of the value of the top-quark mass measured at the Tevatron together with the lower bound on the lightest Higgs mass established by LEP. The dependence of the Higgsino mass parameter {mu}, the gaugino coupling strengths g-tilde{sub u,d}, g-tilde{sub u,d}{sup '} and of the Higgs quartic self-coupling {lambda} on the value of Y{sub t} in the vicinity of the Landau pole is discussed. A few interesting features emerge, though the model is found to be disfavored within the infrared fixed point scenario because of the need to have several unnatural cancellations at work on account of the requirement of a low upper bound on tan{beta}.
The fixed point formulation for large sample PGNAA—Part 1: theory
NASA Astrophysics Data System (ADS)
Holloway, J. P.; Akkurt, H.
2004-04-01
The determination of large sample composition via prompt gamma measurements is examined as a non-linear inverse problem. We show that this non-linear problem can be formulated as a fixed point problem that always has a physically meaningful solution, even in the presence of significant contributions to photopeak area from gammas emitted by the surroundings. The formulation involves only ratios of measured photopeak areas, and, separately, ratios of modeled photopeak areas. It therefore does not require the absolute comparison of measured or modeled quantities. The proof of the existence of meaningful solutions relies on very simple and natural hypotheses of positivity and continuity. The natural fixed point iteration is examined, and certain physical limits where its global convergence can be guaranteed are examined. Several computational examples are presented.
The fixed point formulation for large sample PGNAA—Part 2: experimental demonstration
NASA Astrophysics Data System (ADS)
Akkurt, H.; Holloway, J. P.; Smith, L. E.
2004-04-01
We present composition estimation results using fixed point iteration compared to the true composition of sample for prompt gamma measurements. The analysis showed that the fixed point iteration algorithm converges very rapidly to true composition of the sample independent of the initial guess when there is no significant background contribution. Even in the presence of significant background contribution, the true composition of the sample was estimated with high precision but with slower convergence. Although approximate data for neutron source spectrum and relative efficiency of the detector was used for analysis, the results showed that the method is not very sensitive to the details of the model since it is based on ratios. Despite the approximate data used for computations, the composition estimation results are in excellent agreement with chemical analysis.
The virial theorem for the polarizable continuum model
Cammi, R.
2014-02-28
The electronic virial theorem is extended to molecular systems within the framework of the Polarizable Continuum Model (PCM) to describe solvation effects. The theorem is given in the form of a relation involving the components of the energy (kinetic and potential) of a molecular solute and its electrostatic properties (potential and field) at the boundary of the cavity in the continuum medium. The virial theorem is also derived in the presence of the Pauli repulsion component of the solute-solvent interaction. Furthermore, it is shown that these forms of the PCM virial theorem may be related to the virial theorem of more simple systems as a molecule in the presence of fixed point charges, and as an atom in a spherical box with confining potential.
The virial theorem for the Polarizable Continuum Model.
Cammi, R
2014-02-28
The electronic virial theorem is extended to molecular systems within the framework of the Polarizable Continuum Model (PCM) to describe solvation effects. The theorem is given in the form of a relation involving the components of the energy (kinetic and potential) of a molecular solute and its electrostatic properties (potential and field) at the boundary of the cavity in the continuum medium. The virial theorem is also derived in the presence of the Pauli repulsion component of the solute-solvent interaction. Furthermore, it is shown that these forms of the PCM virial theorem may be related to the virial theorem of more simple systems as a molecule in the presence of fixed point charges, and as an atom in a spherical box with confining potential. PMID:24588153
New Experimental Technique for the Study of Phase Transition Evolution in Fixed-Point Cells
NASA Astrophysics Data System (ADS)
Nemeth, T.; Nemeth, S.; Turzo-Andras, E.
2015-08-01
A new advanced technique was developed at the Hungarian Metrological Institute (MKEH), devoted to optimizing the realization of the International Temperature Scale ITS-90. The work was performed within the framework of the European project "Novel techniques for traceable temperature dissemination." The paper is devoted to describing this new measurement technique and its setup. The time evolution of the solid fraction and melt fraction along the phase transformation has been followed, using a technique based on the difference of the electrical conductivity between the solid and liquid phases of the metal. The measurement technique provides electrical signals, which are suitable for improving the quality of the freezing plateaus realized in the case of different fixed-point realizations, covering the temperature range from to . The ideal section of the freezing plateau can be maintained by ensuring a continuous flow of mass and energy of the fixed-point substance in the axial direction. The intervention is achieved by modifying the temperatures of the different zones of the furnace controller with more degrees, with the aid of developed intervening devices. Recent developments permit the selection of the ideal section of a freezing plateau and, what is more, the increase of this plateau section to practically unlimited for all metal fixed points.
A new constrained fixed-point algorithm for ordering independent components
NASA Astrophysics Data System (ADS)
Zhang, Hongjuan; Guo, Chonghui; Shi, Zhenwei; Feng, Enmin
2008-10-01
Independent component analysis (ICA) aims to recover a set of unknown mutually independent components (ICs) from their observed mixtures without knowledge of the mixing coefficients. In the classical ICA model there exists ICs' indeterminacy on permutation and dilation. Constrained ICA is one of methods for solving this problem through introducing constraints into the classical ICA model. In this paper we first present a new constrained ICA model which composed of three parts: a maximum likelihood criterion as an objective function, statistical measures as inequality constraints and the normalization of demixing matrix as equality constraints. Next, we incorporate the new fixed-point (newFP) algorithm into this constrained ICA model to construct a new constrained fixed-point algorithm. Computation simulations on synthesized signals and speech signals demonstrate that this combination both can eliminate ICs' indeterminacy to a certain extent, and can provide better performance. Moreover, comparison results with the existing algorithm verify the efficiency of our new algorithm furthermore, and show that it is more simple to implement than the existing algorithm due to its advantage of not using the learning rate. Finally, this new algorithm is also applied for the real-world fetal ECG data, experiment results further indicate the efficiency of the new constrained fixed-point algorithm.
Fixed points of the SRG evolution and the on-shell limit of the nuclear force
NASA Astrophysics Data System (ADS)
Arriola, E. Ruiz; Szpigel, S.; Timóteo, V. S.
2016-08-01
We study the infrared limit of the similarity renormalization group (SRG) using a simple toy model for the nuclear force aiming to investigate the fixed points of the SRG evolution with both the Wilson and the Wegner generators. We show how a fully diagonal interaction at the similarity cutoff λ → 0 may be obtained from the eigenvalues of the Hamiltonian and quantify the diagonalness by means of operator norms. While the fixed points for both generators are equivalent when no bound-states are allowed by the interaction, the differences arising from the presence of the Deuteron bound-state can be disentangled very clearly by analyzing the evolved interactions in the infrared limit λ → 0 on a finite momentum grid. Another issue we investigate is the location on the diagonal of the Hamiltonian in momentum-space where the SRG evolution places the Deuteron bound-state eigenvalue once it reaches the fixed point. This finite momentum grid setup provides an alternative derivation of the celebrated trace identities, as a by product. The different effects due to either the Wilson or the Wegner generators on the binding energies of A = 2 , 3 , 4 systems are investigated and related to the occurrence of a Tjon-line which emerges as the minimum of an avoided crossing between Eα = 4Et - 3Ed and Eα = 2Et. All infrared features of the flow equations are illustrated using the toy model for the two-nucleon S-waves.
Study on the Impurity Effect in the Realization of Silver Fixed Point
NASA Astrophysics Data System (ADS)
Tsai, S. F.
2016-03-01
The application of a thermal analysis model to estimate the temperature depression from the ideal fixed-point temperature is important, especially when the chemical analysis of the sample in a cell is insufficient or the cell might have been contaminated during fabrication. This study extends previous work, on thermal analysis with the tin point, to an investigation of the impurity dependence of the silver-point temperature. Close agreement was found between the temperature depression (-0.36 mK) inferred from the thermal analysis of the measured fixed-point plateau and the temperature depression (-0.32 mK) inferred using the sum of individual estimates (SIE) method with an impurity analysis based on glow discharge mass spectrometry. Additionally, the results of the thermal analysis manifest no significant dependence on the rate of solidification, and the scatter of observed gradients was within 0.36 mK among five plateaux with different temperature settings of the furnace. Although the results support the application of both the SIE method and thermal analysis for the silver point, further experiments with cell-to-cell comparisons linked to thermal analysis, a study of the thermometer-furnace systematic effects, the oxygen effect, and the locus of the freezing plateau should be investigated to reach a firm conclusion.
Berges, Jürgen; Rothkopf, Alexander; Schmidt, Jonas
2008-07-25
Strongly correlated systems far from equilibrium can exhibit scaling solutions with a dynamically generated weak coupling. We show this by investigating isolated systems described by relativistic quantum field theories for initial conditions leading to nonequilibrium instabilities, such as parametric resonance or spinodal decomposition. The nonthermal fixed points prevent fast thermalization if classical-statistical fluctuations dominate over quantum fluctuations. We comment on the possible significance of these results for the heating of the early Universe after inflation and the question of fast thermalization in heavy-ion collision experiments. PMID:18764319
Infinite-randomness fixed points for chains of non-Abelian quasiparticles.
Bonesteel, N E; Yang, Kun
2007-10-01
One-dimensional chains of non-Abelian quasiparticles described by SU(2)k Chern-Simons-Witten theory can enter random singlet phases analogous to that of a random chain of ordinary spin-1/2 particles (corresponding to k-->infinity). For k=2 this phase provides a random singlet description of the infinite-randomness fixed point of the critical transverse field Ising model. The entanglement entropy of a region of size L in these phases scales as S(L) approximately lnd/3 log(2)L for large L, where d is the quantum dimension of the particles. PMID:17930652
Infinite randomness fixed point of the superconductor-metal quantum phase transition.
Del Maestro, Adrian; Rosenow, Bernd; Müller, Markus; Sachdev, Subir
2008-07-18
We examine the influence of quenched disorder on the superconductor-metal transition, as described by a theory of overdamped Cooper pairs which repel each other. The self-consistent pairing eigenmodes of a quasi-one-dimensional wire are determined numerically. Our results support the recent proposal by Hoyos et al. [Phys. Rev. Lett. 99, 230601 (2007)10.1103/PhysRevLett.99.230601] that the transition is characterized by the same strong-disorder fixed point describing the onset of ferromagnetism in the random quantum Ising chain in a transverse field. PMID:18764263
Unitarity violation at the Wilson-Fisher fixed point in 4 -ɛ dimensions
NASA Astrophysics Data System (ADS)
Hogervorst, Matthijs; Rychkov, Slava; van Rees, Balt C.
2016-06-01
We consider the continuation of free and interacting scalar field theory to noninteger spacetime dimension d . We find that the correlation functions in these theories are necessarily incompatible with unitarity (or with reflection positivity in Euclidean signature). In particular, the theories contain negative-norm states unless d is a positive integer. These negative-norm states can be obtained via the operator product expansion from simple positive-norm operators, and are therefore an integral part of the theory. At the Wilson-Fisher fixed point the nonunitarity leads to the existence of complex anomalous dimensions. We demonstrate that they appear already at leading order in the epsilon expansion.
Infinite Randomness Fixed Point of the Superconductor-Metal Quantum Phase Transition
NASA Astrophysics Data System (ADS)
Del Maestro, Adrian; Rosenow, Bernd; Müller, Markus; Sachdev, Subir
2008-07-01
We examine the influence of quenched disorder on the superconductor-metal transition, as described by a theory of overdamped Cooper pairs which repel each other. The self-consistent pairing eigenmodes of a quasi-one-dimensional wire are determined numerically. Our results support the recent proposal by Hoyos et al. [Phys. Rev. Lett. 99, 230601 (2007)PRLTAO0031-900710.1103/PhysRevLett.99.230601] that the transition is characterized by the same strong-disorder fixed point describing the onset of ferromagnetism in the random quantum Ising chain in a transverse field.
Uncertainty due to non-linearity in radiation thermometers calibrated by multiple fixed points
Yamaguchi, Y.; Yamada, Y.
2013-09-11
A new method to estimate the uncertainty due to non-linearity is described on the n= 3 scheme basis. The expression of uncertainty is mathematically derived applying the random walk method. The expression is simple and requires only the temperatures of the fixed points and a relative uncertainty value for each flux-doubling derived from the non-linearity measurement. We also present an example of the method, in which the uncertainty of temperature measurement by a radiation thermometer is calculated on the basis of non-linearity measurement.
Isotopic effects in the neon fixed point: uncertainty of the calibration data correction
NASA Astrophysics Data System (ADS)
Steur, Peter P. M.; Pavese, Franco; Fellmuth, Bernd; Hermier, Yves; Hill, Kenneth D.; Seog Kim, Jin; Lipinski, Leszek; Nagao, Keisuke; Nakano, Tohru; Peruzzi, Andrea; Sparasci, Fernando; Szmyrka-Grzebyk, Anna; Tamura, Osamu; Tew, Weston L.; Valkiers, Staf; van Geel, Jan
2015-02-01
The neon triple point is one of the defining fixed points of the International Temperature Scale of 1990 (ITS-90). Although recognizing that natural neon is a mixture of isotopes, the ITS-90 definition only states that the neon should be of ‘natural isotopic composition’, without any further requirements. A preliminary study in 2005 indicated that most of the observed variability in the realized neon triple point temperatures within a range of about 0.5 mK can be attributed to the variability in isotopic composition among different samples of ‘natural’ neon. Based on the results of an International Project (EUROMET Project No. 770), the Consultative Committee for Thermometry decided to improve the realization of the neon fixed point by assigning the ITS-90 temperature value 24.5561 K to neon with the isotopic composition recommended by IUPAC, accompanied by a quadratic equation to take the deviations from the reference composition into account. In this paper, the uncertainties of the equation are discussed and an uncertainty budget is presented. The resulting standard uncertainty due to the isotopic effect (k = 1) after correction of the calibration data is reduced to (4 to 40) μK when using neon of ‘natural’ isotopic composition or to 30 μK when using 20Ne. For comparison, an uncertainty component of 0.15 mK should be included in the uncertainty budget for the neon triple point if the isotopic composition is unknown, i.e. whenever the correction cannot be applied.
NASA Astrophysics Data System (ADS)
Andres, Jan; Górniewicz, Lech
The existence of essential fixed points is proved for compact self-maps of arbitrary absolute neighborhood retracts, provided the generalized Lefschetz number is nontrivial and the topological dimension of a fixed point set is equal to zero. Furthermore, continuous self-maps of some special compact absolute neighborhood retracts, whose Lefschetz number is nontrivial, are shown to possess pseudo-essential fixed points even without the zero dimensionality assumption. Both results are applied to the existence of essential and pseudo-essential multivalued fractals. An illustrative example of this application is supplied.
Development of a new radiometer for the thermodynamic measurement of high temperature fixed points
NASA Astrophysics Data System (ADS)
Dury, M. R.; Goodman, T. M.; Lowe, D. H.; Machin, G.; Woolliams, E. R.
2013-09-01
The National Physical Laboratory (NPL) has developed a new radiometer to measure the thermodynamic melting point temperatures of high temperature fixed points with ultra-low uncertainties. In comparison with the NPL's Absolute Radiation Thermometer (ART), the "THermodynamic Optical Radiometer" (THOR) is more portable and compact, with a much lower size-of-source effect and improved performance in other parameters such as temperature sensitivity. It has been designed for calibration as a whole instrument via the radiance method, removing the need to calibrate the individual subcomponents, as required by ART, and thereby reducing uncertainties. In addition, the calibration approach has been improved through a new integrating sphere that has been designed to have greater uniformity.
Non-thermal fixed points and solitons in a one-dimensional Bose gas
NASA Astrophysics Data System (ADS)
Schmidt, Maximilian; Erne, Sebastian; Nowak, Boris; Sexty, Dénes; Gasenzer, Thomas
2012-07-01
Single-particle momentum spectra for a dynamically evolving one-dimensional Bose gas are analysed in the semi-classical wave limit. Representing one of the simplest correlation functions, these provide information on a possible universal scaling behaviour. Motivated by the previously discovered connection between (quasi-) topological field configurations, strong wave turbulence and non-thermal fixed points of quantum field dynamics, soliton formation is studied with respect to the appearance of transient power-law spectra. A random-soliton model is developed for describing the spectra analytically, and the analogies and differences between the emerging power laws and those found in a field theory approach to strong wave turbulence are discussed. The results open a new perspective on solitary wave dynamics from the point of view of critical phenomena far from thermal equilibrium and the possibility of studying this dynamics by experiment without the need for detecting solitons in situ.
Development of a new radiometer for the thermodynamic measurement of high temperature fixed points
Dury, M. R.; Goodman, T. M.; Lowe, D. H.; Machin, G.; Woolliams, E. R.
2013-09-11
The National Physical Laboratory (NPL) has developed a new radiometer to measure the thermodynamic melting point temperatures of high temperature fixed points with ultra-low uncertainties. In comparison with the NPL's Absolute Radiation Thermometer (ART), the 'THermodynamic Optical Radiometer' (THOR) is more portable and compact, with a much lower size-of-source effect and improved performance in other parameters such as temperature sensitivity. It has been designed for calibration as a whole instrument via the radiance method, removing the need to calibrate the individual subcomponents, as required by ART, and thereby reducing uncertainties. In addition, the calibration approach has been improved through a new integrating sphere that has been designed to have greater uniformity.
Influence of Impurities and Filling Protocol on the Aluminum Fixed Point
NASA Astrophysics Data System (ADS)
Renaot, E.; Valin, M. H.; Elgourdou, M.
2008-06-01
To improve the uncertainty of the aluminum fixed point, a study was launched by LNE-INM/CNAM in the framework of the EUROMET Project 732 “Toward more accurate temperature fixed points” (Coordinating laboratory: LNE-INM/CNAM, 17 partner countries). A new open cell was filled with aluminum of 99.99995% purity. A French laboratory carried out elemental analysis of the sample using glow discharge-mass spectrometry (GD-MS). The values of the equilibrium distribution coefficient k and of the derivative {δ T_{{l}}/δ ci_{{l}}} of the temperature of the liquidus line with respect to the concentration of impurity i will be obtained through collaboration with a French physical and chemical laboratory. In the past, some aluminum cells were opened after several melts and freezes. The aluminum ingot was sticking to the graphite crucible, indicating that physicochemical reactions had likely occurred between Al and C. To avoid this reaction, an effort was made to draw benefit from the Al2O3 film that appears immediately on the surface of the aluminum ingot when it is exposed to oxygen. The open aluminum cell was tested in different furnaces and with different thermal insulator arrangements inside the fixed-point assembly. The observed drifts of the plateaux were always larger than the expected values. The cell was opened to inspect the aluminum ingot. The ingot was extracted easily, since no sticking to the crucible had occurred. The aluminum showed a very bright surface, but the presence of many “craters” throughout the thickness of the ingot was surprising. In some cases, the thermometer well was even apparent.
Stability of cobalt-carbon high temperature fixed points doped with iron and platinum
NASA Astrophysics Data System (ADS)
Kňazovická, L.; Lowe, D.; Machin, G.; Davies, H.; Rani, A.
2015-04-01
High temperature fixed points (HTFPs) are stable and repeatable and make comparison of temperature scales possible at a level of uncertainty not previously possible. However, they potentially lack objectivity if the fixed-point temperature is known. Five HTFPs were constructed, one pure Co-C, two Co-C doped with Fe and two Co-C doped with Pt of differing concentrations. The candidate dopants were identified through thermochemical modelling as likely to give maximum temperature shift with minimum increase in melting range. The temperature differences of the doped systems from the pure system were determined and it was found that the addition of Fe depressed the melting temperature and the addition of Pt elevated the melting temperature, qualitatively in line with the thermochemical modelling. The higher concentration doped HTFPs were then aged for approximately 100 h with continuous melting-freezing cycles and the difference to the undoped Co-C HTFP remeasured. These differences were found to agree with those of the unaged results within the measurement uncertainties, confirming artefact stability. It is clear that the doping of HTFPs is a powerful way of constructing stable and reliable high temperature scale comparison artefacts of unknown temperature.
Minato, K; Tang, Y N; Bennett, G W; Brill, A
1987-01-01
Attenuation correction for single-photon emission computed tomography (SPECT) usually assumes a uniform attenuation distribution within the body surface contour. Previous methods to estimate this contour have used thresholding of a reconstructed section image. This method is often very sensitive to the selection of a threshold value, especially for nonuniform activity distributions within the body. We have proposed the "fixed-point Hachimura-Kuwahara filter" to extract contour primitives from SPECT images. The Hachimura-Kuwahara filter, which preserves edges but smoothes nonedge regions, is applied repeatedly to identify the invariant set-the fixed-point image-which is unchanged by this nonlinear, two-dimensional filtering operation. This image usually becomes a piecewise constant array. In order to detect the contour, the tracing algorithm based on the minimum distance connection criterion is applied to the extracted contour primitives. This procedure does not require choice of a threshold value in determining the contour. SPECT data from a water-filled elliptical phantom containing three sources was obtained and scattered projections were reconstructed. The automatic edge detection procedure was applied to the scattered window reconstruction, resulting in a reasonable outline of the phantom. PMID:18230438
NASA Astrophysics Data System (ADS)
Goldberg, Daniel N.; Krishna Narayanan, Sri Hari; Hascoet, Laurent; Utke, Jean
2016-05-01
We apply an optimized method to the adjoint generation of a time-evolving land ice model through algorithmic differentiation (AD). The optimization involves a special treatment of the fixed-point iteration required to solve the nonlinear stress balance, which differs from a straightforward application of AD software, and leads to smaller memory requirements and in some cases shorter computation times of the adjoint. The optimization is done via implementation of the algorithm of Christianson (1994) for reverse accumulation of fixed-point problems, with the AD tool OpenAD. For test problems, the optimized adjoint is shown to have far lower memory requirements, potentially enabling larger problem sizes on memory-limited machines. In the case of the land ice model, implementation of the algorithm allows further optimization by having the adjoint model solve a sequence of linear systems with identical (as opposed to varying) matrices, greatly improving performance. The methods introduced here will be of value to other efforts applying AD tools to ice models, particularly ones which solve a hybrid shallow ice/shallow shelf approximation to the Stokes equations.
Optimization of the thermogauge furnace for realizing high temperature fixed points
Wang, T.; Dong, W.; Liu, F.
2013-09-11
The thermogauge furnace was commonly used in many NMIs as a blackbody source for calibration of the radiation thermometer. It can also be used for realizing the high temperature fixed point(HTFP). According to our experience, when realizing HTFP we need the furnace provide relative good temperature uniformity to avoid the possible damage to the HTFP. To improve temperature uniformity in the furnace, the furnace tube was machined near the tube ends with a help of a simulation analysis by 'ansys workbench'. Temperature distributions before and after optimization were measured and compared at 1300 °C, 1700°C, 2500 °C, which roughly correspond to Co-C(1324 °C), Pt-C(1738 °C) and Re-C(2474 °C), respectively. The results clearly indicate that through machining the tube the temperature uniformity of the Thermogage furnace can be remarkably improved. A Pt-C high temperature fixed point was realized in the modified Thermogauge furnace subsequently, the plateaus were compared with what obtained using old heater, and the results were presented in this paper.
Use of Eutectic Fixed Points to Characterize a Spectrometer for Earth Observations
NASA Astrophysics Data System (ADS)
Salim, Saber G. R.; Fox, Nigel P.; Woolliams, Emma R.; Winkler, Rainer; Pegrum, Heather M.; Sun, Tong; Grattan, Ken T. V.
2007-12-01
A small palm-sized, reference spectrometer, mounted on a remote-controlled model helicopter is being developed and tested by the National Physical Laboratory (NPL) in conjunction with City University, London. The developed system will be used as a key element for field vicarious calibration of optical earth observation systems in the visible-near infrared (VNIR) region. The spectrometer is hand held, low weight, and uses a photodiode array. It has good stray light rejection and wide spectral coverage, allowing simultaneous measurements from 400 to 900 nm. The spectrometer is traceable to NPL’s primary standard cryogenic radiometer via a high-temperature metal-carbon eutectic fixed-point blackbody. Once the fixed-point temperature has been determined (using filter radiometry), the eutectic provides a high emissivity and high stability source of known spectral radiance over the emitted spectral range. All wavelength channels of the spectrometer can be calibrated simultaneously using the eutectic transition without the need for additional instrumentation. The spectrometer itself has been characterized for stray light performance and wavelength accuracy. Its long-term and transportation stability has been proven in an experiment that determined the “World’s Bluest Sky”—a process that involved 56 flights, covering 100,000 km in 72 days. This vicarious calibration methodology using a eutectic standard is presented alongside the preliminary results of an evaluation study of the spectrometer characteristics.
Stability of a cubic fixed point in three dimensions: Critical exponents for generic N
NASA Astrophysics Data System (ADS)
Varnashev, K. B.
2000-06-01
The detailed analysis of the global structure of the renormalization-group (RG) flow diagram for a model with isotropic and cubic interactions is carried out in the framework of the massive field theory directly in three dimensions (3D) within an assumption of isotropic exchange. Perturbative expansions for RG functions are calculated for arbitrary N up to four-loop order and resummed by means of the generalized Padé-Borel-Leroy technique. Coordinates and stability matrix eigenvalues for the cubic fixed point are found under the optimal value of the transformation parameter. Critical dimensionality of the model is proved to be equal to Nc=2.89+/-0.02 that agrees well with the estimate obtained on the basis of the five-loop ɛ expansion [H. Kleinert and V. Schulte-Frohlinde, Phys. Lett. B 342, 284 (1995)] resummed by the above method. As a consequence, the cubic fixed point should be stable in 3D for N>=3, and the critical exponents controlling phase transitions in three-dimensional magnets should belong to the cubic universality class. The critical behavior of the random Ising model being the nontrivial particular case of the cubic model when N=0 is also investigated. For all physical quantities of interest the most accurate numerical estimates with their error bounds are obtained. The results achieved in the work are discussed along with the predictions given by other theoretical approaches and experimental data.
Woolliams, E R; Anhalt, K; Ballico, M; Bloembergen, P; Bourson, F; Briaudeau, S; Campos, J; Cox, M G; del Campo, D; Dong, W; Dury, M R; Gavrilov, V; Grigoryeva, I; Hernanz, M L; Jahan, F; Khlevnoy, B; Khromchenko, V; Lowe, D H; Lu, X; Machin, G; Mantilla, J M; Martin, M J; McEvoy, H C; Rougié, B; Sadli, M; Salim, S G R; Sasajima, N; Taubert, D R; Todd, A D W; Van den Bossche, R; van der Ham, E; Wang, T; Whittam, A; Wilthan, B; Woods, D J; Woodward, J T; Yamada, Y; Yamaguchi, Y; Yoon, H W; Yuan, Z
2016-03-28
The thermodynamic temperature of the point of inflection of the melting transition of Re-C, Pt-C and Co-C eutectics has been determined to be 2747.84 ± 0.35 K, 2011.43 ± 0.18 K and 1597.39 ± 0.13 K, respectively, and the thermodynamic temperature of the freezing transition of Cu has been determined to be 1357.80 ± 0.08 K, where the ± symbol represents 95% coverage. These results are the best consensus estimates obtained from measurements made using various spectroradiometric primary thermometry techniques by nine different national metrology institutes. The good agreement between the institutes suggests that spectroradiometric thermometry techniques are sufficiently mature (at least in those institutes) to allow the direct realization of thermodynamic temperature above 1234 K (rather than the use of a temperature scale) and that metal-carbon eutectics can be used as high-temperature fixed points for thermodynamic temperature dissemination. The results directly support the developing mise en pratique for the definition of the kelvin to include direct measurement of thermodynamic temperature. PMID:26903099
ERIC Educational Resources Information Center
Benyi, Arpad; Casu, Ioan
2009-01-01
Pompeiu's theorem states that if ABC is an "equilateral" triangle and M a point in its plane, then MA, MB, and MC form a new triangle. In this article, we have a new look at this theorem in the realm of arbitrary triangles. We discover what we call Pompeiu's Area Formula, a neat equality relating areas of triangles determined by the points A, B,…
NASA Astrophysics Data System (ADS)
Lampitt, Richard; Cristini, Luisa
2014-05-01
The Fixed point Open Ocean Observatory network (FixO3) seeks to integrate the 23 European open ocean fixed point observatories and to improve access to these key installations for the broader community. These will provide multidisciplinary observations in all parts of the oceans from the air-sea interface to the deep seafloor. Coordinated by the National Oceanography Centre, UK, FixO3 builds on the significant advances achieved through the previous Europe-funded FP7 programmes EuroSITES, ESONET and CARBOOCEAN. Started in September 2013 with a budget of 7 Million Euros over 4 years the project has 29 partners drawn from academia, research institutions and SME's. In addition 12 international experts from a wide range of disciplines comprise an Advisory Board. On behalf of the FixO3 Consortium, we present the programme that will be achieved through the activities of 12 Work Packages: 1. Coordination activities to integrate and harmonise the current procedures and processes. Strong links will be fostered with the wider community across academia, industry, policy and the general public through outreach, knowledge exchange and training. 2. Support actions to offer a) free access to observatory infrastructures to those who do not have such access, and b) free and open data services and products. 3. Joint research activities to innovate and enhance the current capability for multidisciplinary in situ ocean observation. Support actions include Transnational Access (TNA) to FixO3 infrastructure, meaning that European organizations can apply to free-of-charge access to the observatories for research and testing in two international calls during the project lifetime. The first call for TNA opens in summer 2014. More information can be found on FixO3 website (www.fixo3.eu/). Open ocean observation is currently a high priority for European marine and maritime activities. FixO3 will provide important data on environmental products and services to address the Marine Strategy
NASA Astrophysics Data System (ADS)
Lampitt, Richard; Cristini, Luisa; Alexiou, Sofia
2015-04-01
The Fixed point Open Ocean Observatory network (FixO3, http://www.fixo3.eu/ ) integrates 23 European open ocean fixed point observatories and improves access to these infrastructures for the broader community. These provide multidisciplinary observations in all parts of the oceans from the air-sea interface to the deep seafloor. Started in September 2013 with a budget of 7 Million Euros over 4 years, the project has 29 partners drawn from academia, research institutions and SME's coordinated by the National Oceanography Centre, UK. Here we present the programme's achievements in the 18 months and the activities of the 12 Work Packages which have the objectives to: • integrate and harmonise the current procedures and processes • offer free access to observatory infrastructures to those who do not have such access, and free and open data services and products • innovate and enhance the current capability for multidisciplinary in situ ocean observation Open ocean observation is a high priority for European marine and maritime activities. FixO3 provides important data and services to address the Marine Strategy Framework Directive and in support of the European Integrated Maritime Policy. FixO3 provides a strong integrated framework of open ocean facilities in the Atlantic from the Arctic to the Antarctic and throughout the Mediterranean, enabling an integrated, regional and multidisciplinary approach to understand natural and anthropogenic change in the ocean.
New Filling Technique and Performance Evaluations of the Cr3C2-C Peritectic Fixed Point
NASA Astrophysics Data System (ADS)
Sasajima, N.; Lowe, D.; Bai, C.; Yamada, Y.; Ara, C.
2011-12-01
The Cr3C2-C peritectic fixed point was investigated to test its capability to serve as a practical high-temperature fixed point. An improved filling technique where C/C sheet works as a wick and graphite paper as a hopper was applied successfully, and the long-term stability of the peritectic cell was evaluated by means of radiation thermometry. The repeatability of the melting point in one day was 7 mK with a melting range of approximately 100 mK. The cell was aged for 7 days, and the evaluated 56 melting temperatures during this period all fall within 90 mK, with a standard deviation of 19 mK. X-ray transmission photos showed that the ingot was filled uniformly in the crucible. After the evaluation of long-term stability, no clear degradation of the ingot shape and no leakage of molten metal were observed. From these results, it can be concluded that the Cr3C2-C peritectic cell has good stability and robustness, and the new filling technique was established. The impurity effect on the Cr3C2-C peritectic cell was also investigated by adding tungsten powder to another cell as the impurity component. After the observation of melting and freezing plateaux, the cell was cut in half to analyze the microstructure by means of electron probe microanalysis (EPMA) and laser ablation inductively coupled plasma mass spectrometer (LA-ICP-MS). The high concentration of impurity was observed in the area of the chromium-rich domain (eutectic mixture of Cr7C3 and Cr3C2), which suggests that impurities were rejected from the Cr3C2 peritectic phase during the peritectic freezing and were accumulated in the Cr7C3-Cr3C2 eutectic phase. This explains why the impurity effect is more severe for the Cr7C3-Cr3C2 eutectic point than for the Cr3C2-C peritectic point.
Fixed points and stability in the two-network frustrated Kuramoto model
NASA Astrophysics Data System (ADS)
Kalloniatis, Alexander C.; Zuparic, Mathew L.
2016-04-01
We examine a modification of the Kuramoto model for phase oscillators coupled on a network. Here, two populations of oscillators are considered, each with different network topologies, internal and cross-network couplings and frequencies. Additionally, frustration parameters for the interactions of the cross-network phases are introduced. This may be regarded as a model of competing populations: internal to any one network phase synchronisation is a target state, while externally one or both populations seek to frequency synchronise to a phase in relation to the competitor. We conduct fixed point analyses for two regimes: one, where internal phase synchronisation occurs for each population with the potential for instability in the phase of one population in relation to the other; the second where one part of a population remains fixed in phase in relation to the other population, but where instability may occur within the first population leading to 'fragmentation'. We compare analytic results to numerical solutions for the system at various critical thresholds.
Development and investigation of WC-C fixed-point cells
NASA Astrophysics Data System (ADS)
Khlevnoy, B. B.; Grigoryeva, I. A.; Otryaskin, D. A.
2012-04-01
Three cells of the WC-C peritectic fixed point with a temperature of about 3021 K were built and investigated. Two different sources of tungsten with nominal purities of 5N and 3N were used, and two different filling techniques were applied. There was no difference in plateau shapes between the cells. The 3N purity cell showed a small difference (0.22 K) in the melting temperature from the 5N cell, which indicates significant purification of initially contaminated tungsten. The typical melting range and repeatability of the observed peritectic melting plateaux were 100 mK and 15 mK, respectively. The melting point was stable and reproducible within 25 mK per two weeks. T90 temperature of the WC-C melting point was found to be (2747.6 ± 1.1) °C (k = 2). The observed freezing plateaux were flat and repeatable within 50 mK and 15 mK, respectively. The WC1-x-WC eutectic transition showed a melting temperature about 29 K lower than the peritectic one with a repeatability of about 0.2 K. The problem of deep supercooling is discussed and a method for its solution is shown and tested.
Matrix triangularization by fixed-point redundant CORDIC with constant scale factor
NASA Astrophysics Data System (ADS)
Lee, Jeong-A.; Lang, Tomas
1990-11-01
We develop a redundani CORDIC scheme where the scale factor is forced to be constant while computing angles for 2 x 1 plane rotations. Based on the scheme we present a fixed-point implementation of matrix triangularization by Luk''s parallel algorithm with the following additional features: (1) the final scaling operation is done by shifting (2) the number of iterations in CORDIC rotation unit is reduced by about 25 by expressing the direction of the rotation in radix-2 and radix-4 and (3) the conventional number representation of rotated output is obtained on-thefly not from a carry-propagate adder. The number of hardware modules and the speed are evaluated and compared with the previous CORDIC schemes.
Density equalized map projections: a method for analysing clustering around a fixed point.
Schulman, J; Selvin, S; Merrill, D W
1988-04-01
Cases plotted on a geopolitical map entail difficulties in interpretation and analysis because of variable population density in the study area. Density equalized map projections (DEMPs) eliminate the distribution of the resident population as an interfering influence by transforming map area to be proportional to population. This paper discusses a transformation algorithm, its properties, and develops statistical methods to detect clustering of cases around a fixed point for data plotted on DEMPs. We suggest two numeric methods where exact solutions are too complicated or do not exist. Finally, we illustrate these methods using data from Denver and Jefferson counties in Colorado to investigate whether lung cancer and leukaemia incidence patterns are associated with plutonium exposure from the Rocky Flats plant site. PMID:3368676
Point and Fixed Plot Sampling Inventory Estimates at the Savannah River Site, South Carolina.
Parresol, Bernard, R.
2004-02-01
This report provides calculation of systematic point sampling volume estimates for trees greater than or equal to 5 inches diameter breast height (dbh) and fixed radius plot volume estimates for trees < 5 inches dbh at the Savannah River Site (SRS), Aiken County, South Carolina. The inventory of 622 plots was started in March 1999 and completed in January 2002 (Figure 1). Estimates are given in cubic foot volume. The analyses are presented in a series of Tables and Figures. In addition, a preliminary analysis of fuel levels on the SRS is given, based on depth measurements of the duff and litter layers on the 622 inventory plots plus line transect samples of down coarse woody material. Potential standing live fuels are also included. The fuels analyses are presented in a series of tables.
NASA Astrophysics Data System (ADS)
Bhole, Gaurav; Anjusha, V. S.; Mahesh, T. S.
2016-04-01
A robust control over quantum dynamics is of paramount importance for quantum technologies. Many of the existing control techniques are based on smooth Hamiltonian modulations involving repeated calculations of basic unitaries resulting in time complexities scaling rapidly with the length of the control sequence. Here we show that bang-bang controls need one-time calculation of basic unitaries and hence scale much more efficiently. By employing a global optimization routine such as the genetic algorithm, it is possible to synthesize not only highly intricate unitaries, but also certain nonunitary operations. We demonstrate the unitary control through the implementation of the optimal fixed-point quantum search algorithm in a three-qubit nuclear magnetic resonance (NMR) system. Moreover, by combining the bang-bang pulses with the crusher gradients, we also demonstrate nonunitary transformations of thermal equilibrium states into effective pure states in three- as well as five-qubit NMR systems.
Progress report for the CCT-WG5 high temperature fixed point research plan
Machin, G.; Woolliams, E. R.; Anhalt, K.; Bloembergen, P.; Sadli, M.; Yamada, Y.
2013-09-11
An overview of the progress in High Temperature Fixed Point (HTFP) research conducted under the auspices of the CCT-WG5 research plan is reported. In brief highlights are: Provisional long term stability of HTFPs has been demonstrated. Optimum construction methods for HTFPs have been established and high quality HTFPs of Co-C, Pt-C and Re-C have been constructed for thermodynamic temperature assignment. The major sources of uncertainty in the assignment of thermodynamic temperature have been identified and quantified. The status of absolute radiometric temperature measurement has been quantified through the circulation of a set of HTFPs. The measurement campaign to assign low uncertainty thermodynamic temperatures to a selected set of HTFPs will begin in mid-2012. It is envisaged that this will be complete by 2015 leading to HTFPs becoming routine reference standards for radiometry and high temperature metrology.
NASA Astrophysics Data System (ADS)
Hoyos Velasco, Fredy Edimer; García, Nicolás Toro; Garcés Gómez, Yeison Alberto
In this paper, the output voltage of a buck power converter is controlled by means of a quasi-sliding scheme. The Fixed Point Inducting Control (FPIC) technique is used for the control design, based on the Zero Average Dynamics (ZAD) strategy, including load estimation by means of the Least Mean Squares (LMS) method. The control scheme is tested in a Rapid Control Prototyping (RCP) system based on Digital Signal Processing (DSP) for dSPACE platform. The closed loop system shows adequate performance. The experimental and simulation results match. The main contribution of this paper is to introduce the load estimator by means of LMS, to make ZAD and FPIC control feasible in load variation conditions. In addition, comparison results for controlled buck converter with SMC, PID and ZAD-FPIC control techniques are shown.
Infra-red fixed point structure characterising SUSY SU(5) symmetry breaking
NASA Astrophysics Data System (ADS)
Allanach, B. C.; Amelino-Camelia, G.; Philipsen, O.
1997-02-01
We analyze the one-loop renormalisation group equations for the parameters of the Higgs potential of a supersymmetric SU(5) model with first step of symmetry breaking involving an adjoint Higgs. In particular, we investigate the running of the parameters that decide the first step of symmetry breaking in an attempt to establish which symmetry-breaking scenarios would be most likely if the model is the effective low-energy description of some more fundamental theory. An infra-red fixed point is identified analytically. We show that it is located at the boundary between the region of Higgs parameter space corresponding to unbroken SU(5) and the region corresponding to the breaking of SU(5) to the Standard Model, and we elaborate on its implications. We also observe that certain forms of the Higgs potential discussed at tree level in the literature are not renormalisation group invariant.
Bratu's problem: A novel approach using fixed-point iterations and Green's functions
NASA Astrophysics Data System (ADS)
Kafri, H. Q.; Khuri, S. A.
2016-01-01
In this article, the one-dimensional non-linear Bratu's boundary value problem is solved via a novel approach that combines Green's function and fixed point iterative schemes, such as Picard's and Krasnoselskii-Mann's. The convergence of the introduced iterative algorithm is proved using the contraction principle. The method is supported by considering a number of numerical examples that correspond to different cases of eigenvalues. The procedure underlying the strategy reduces calculations and provides highly accurate results in comparison with the exact solution and/or numerical solutions provided in the literature. The current method overcomes the difficulty of treating the problem for eigenvalues near and at the critical value, such as λ = 3 and λ = 3.51, and handles them reliably and very efficiently.
NASA Technical Reports Server (NTRS)
Shimada, Seiichi; Bock, Yehuda
1992-01-01
Results are presented from temporally dense measurements of crustal deformation associated with the convergence of the Eurasian (EUR), Pacific, North American, and Philippine Sea (PHS) plates, carried out in April 1988 by a 10-station GPS fixed-point network established in central Japan. Using regional orbit relaxation methods, the analysis of the first 17-month data revealed significant horizontal deformation across the Suruga trough. Namely, it was found that a site in the northern tip of PHS plate moved nearly westward with a velocity of 28 +/-5 mm per year, and a site at the southeastern tip of EUR plate moved south-southwestward with a velocity of 18 +/-5 mm per year. A significant vertical uplift with a velocity of 20 mm/yr was detected at a site inland of the Tokai district located in the Akaishi uplift zone and at a site on the Hatsushima Island in Sagami Bay.
On the fixed points of monotonic operators in the critical case
NASA Astrophysics Data System (ADS)
Engibaryan, N. B.
2006-10-01
We consider the problem of constructing positive fixed points x of monotonic operators \\varphi acting on a cone K in a Banach space E. We assume that \\Vert\\varphi x\\Vert\\le\\Vert x\\Vert+\\gamma, \\gamma>0, for all x\\in K. In the case when \\varphi has a so-called non-trivial dissipation functional we construct a solution in an extension of E, which is a Banach space or a Fréchet space. We consider examples in which we prove the solubility of a conservative integral equation on the half-line with a sum-difference kernel, and of a non-linear integral equation of Urysohn type in the critical case.
Infrared cameras are potential traceable "fixed points" for future thermometry studies.
Yap Kannan, R; Keresztes, K; Hussain, S; Coats, T J; Bown, M J
2015-01-01
The National physical laboratory (NPL) requires "fixed points" whose temperatures have been established by the International Temperature Scale of 1990 (ITS 90) be used for device calibration. In practice, "near" blackbody radiators together with the standard platinum resistance thermometer is accepted as a standard. The aim of this study was to report the correlation and limits of agreement (LOA) of the thermal infrared camera and non-contact infrared temporal thermometer against each other and the "near" blackbody radiator. Temperature readings from an infrared thermography camera (FLIR T650sc) and a non-contact infrared temporal thermometer (Hubdic FS-700) were compared to a near blackbody (Hyperion R blackbody model 982) at 0.5 °C increments between 20-40 °C. At each increment, blackbody cavity temperature was confirmed with the platinum resistance thermometer. Measurements were taken initially with the thermal infrared camera followed by the infrared thermometer, with each device mounted in turn on a stand at a fixed distance of 20 cm and 5 cm from the blackbody aperture, respectively. The platinum thermometer under-estimated the blackbody temperature by 0.015 °C (95% LOA: -0.08 °C to 0.05 °C), in contrast to the thermal infrared camera and infrared thermometer which over-estimated the blackbody temperature by 0.16 °C (95% LOA: 0.03 °C to 0.28 °C) and 0.75 °C (95% LOA: -0.30 °C to 1.79 °C), respectively. Infrared thermometer over-estimates thermal infrared camera measurements by 0.6 °C (95% LOA: -0.46 °C to 1.65 °C). In conclusion, the thermal infrared camera is a potential temperature reference "fixed point" that could substitute mercury thermometers. However, further repeatability and reproducibility studies will be required with different models of thermal infrared cameras. PMID:26468981
Assessment of tungsten/rhenium thermocouples with metal-carbon eutectic fixed points up to 1500°C
Gotoh, M.
2013-09-11
Four Type A thermocouples and two Type C thermocouples were calibrated at the Au fixed point and Co-C and Pd-C eutectic fixed points. The thermocouples were exposed to 1330 °C for a total of 100 hours. The maximum drift due to the exposure was found to be 4.8 °C. The fixed-point calibration EMF of these thermocouples deviated by less than 0.86% from the temperature specified by the standards ASTM E230-2003 for Type C and GOSTR 8.585-2001 for Type A. The length of one of Type A thermocouples A52 is longer than the others by 150mm. Making use of this provision it was possible to place annealed part of A52 to the temperature gradient part of calibration arrangement every time. Therefore observed aging effect was as low as 0.5 °C compared to the other thermocouples.
NASA Astrophysics Data System (ADS)
Wang, T.; Lowe, D.; Machin, G.
2009-02-01
National Institute of Metrology (NIM) (China) and National Physical Laboratory (NPL) (UK) have collaborated to construct metal-carbon eutectic alloy fixed points at NPL. A modified NPL Thermogauge furnace was vertically used to construct fixed points of Pd-C, Pt-C, Ru-C, and Ir-C. Breakage of Pd-C and Ru-C cells was traced to changes in furnace temperature gradients resulting from changing from horizontal to vertical operation. Subsequently, it was found that positioning the cell being filled so that the metal melting always starts from the top and freezing from the bottom to solve this problem. The constructed Pt-C cell was then compared to a Pt-C fixed point previously constructed by NIM. The results indicate that the two cells made independently agreed to be better than 40 mK.
Hao, X.; Yuan, Z.; Wang, J.; Lu, X.
2013-09-11
In this paper, we describe an InGaAs detector based radiation thermometer (IRT) and new design of fixed-point blackbodies, including Sn, Zn, Al and Cu, for the establishment of a temperature scale from 200 °C to 1085 °C at the National Institute of Metrology of China. The construction and calibration of the IRT with the four fixed-point blackbodies are described. Characteristics of the IRT, such as the size-of-source effect, the amplifier performance and its stability are determined. The design of the four fixed-points, with 10 mm diameter of aperture and 0.9999 emissivity, is described. The uncertainty of the scale realization is elaborated.
NASA Astrophysics Data System (ADS)
Hao, X.; Yuan, Z.; Wang, J.; Lu, X.
2013-09-01
In this paper, we describe an InGaAs detector based radiation thermometer (IRT) and new design of fixed-point blackbodies, including Sn, Zn, Al and Cu, for the establishment of a temperature scale from 200 °C to 1085 °C at the National Institute of Metrology of China. The construction and calibration of the IRT with the four fixed-point blackbodies are described. Characteristics of the IRT, such as the size-of-source effect, the amplifier performance and its stability are determined. The design of the four fixed-points, with 10 mm diameter of aperture and 0.9999 emissivity, is described. The uncertainty of the scale realization is elaborated.
NASA Astrophysics Data System (ADS)
Piñeiro Orioli, Asier; Boguslavski, Kirill; Berges, Jürgen
2015-07-01
We investigate universal behavior of isolated many-body systems far from equilibrium, which is relevant for a wide range of applications from ultracold quantum gases to high-energy particle physics. The universality is based on the existence of nonthermal fixed points, which represent nonequilibrium attractor solutions with self-similar scaling behavior. The corresponding dynamic universality classes turn out to be remarkably large, encompassing both relativistic as well as nonrelativistic quantum and classical systems. For the examples of nonrelativistic (Gross-Pitaevskii) and relativistic scalar field theory with quartic self-interactions, we demonstrate that infrared scaling exponents as well as scaling functions agree. We perform two independent nonperturbative calculations, first by using classical-statistical lattice simulation techniques and second by applying a vertex-resummed kinetic theory. The latter extends kinetic descriptions to the nonperturbative regime of overoccupied modes. Our results open new perspectives to learn from experiments with cold atoms aspects about the dynamics during the early stages of our universe.
NASA Astrophysics Data System (ADS)
Mishra, Puneet; Singla, Sunil Kumar
2013-01-01
In the modern world of automation, biological signals, especially Electroencephalogram (EEG) and Electrocardiogram (ECG), are gaining wide attention as a source of biometric information. Earlier studies have shown that EEG and ECG show versatility with individuals and every individual has distinct EEG and ECG spectrum. EEG (which can be recorded from the scalp due to the effect of millions of neurons) may contain noise signals such as eye blink, eye movement, muscular movement, line noise, etc. Similarly, ECG may contain artifact like line noise, tremor artifacts, baseline wandering, etc. These noise signals are required to be separated from the EEG and ECG signals to obtain the accurate results. This paper proposes a technique for the removal of eye blink artifact from EEG and ECG signal using fixed point or FastICA algorithm of Independent Component Analysis (ICA). For validation, FastICA algorithm has been applied to synthetic signal prepared by adding random noise to the Electrocardiogram (ECG) signal. FastICA algorithm separates the signal into two independent components, i.e. ECG pure and artifact signal. Similarly, the same algorithm has been applied to remove the artifacts (Electrooculogram or eye blink) from the EEG signal.
Realization of the WC-C peritectic fixed point at NIM and NMIJ
Wang, T.; Bai, C.; Yuan, Z.; Dong, W.; Lu, X.; Sasajima, N.; Yamada, Y.; Ara, C.
2013-09-11
Three WC-C peritectic fixed point cells, constructed from different sources of tungsten with different nominal purities, were measured at NIM and NMIJ. The three cells were constructed at NMIJ by NIM and NMIJ staffs, and T{sub 90} values of the three cells were measured at NMIJ during the period 31 Aug. to 25 Dec. 2009. Thereafter, the three cells were then transported to NIM, and T{sub 90} values of these cells were measured from 7 Dec. 2011 to 9 Jan. 2012. The results showed that T{sub 90} values of the three cells measured at the two institutes agreed within 0.4 °C with the combined scale comparison uncertainty of 1.7 °C (k= 2). The main component of the uncertainty is not the uncertainty due to impurities of the cells but the scale uncertainty and the stability of the measurement system. From these results it can be concluded that the WC-C cell is stable enough to provide new means of international high-temperature scale comparison above 3000 K.
NASA Astrophysics Data System (ADS)
Yokoyama, Yoshiaki; Kim, Minseok; Arai, Hiroyuki
At present, when using space-time processing techniques with multiple antennas for mobile radio communication, real-time weight adaptation is necessary. Due to the progress of integrated circuit technology, dedicated processor implementation with ASIC or FPGA can be employed to implement various wireless applications. This paper presents a resource and performance evaluation of the QRD-RLS systolic array processor based on fixed-point CORDIC algorithm with FPGA. In this paper, to save hardware resources, we propose the shared architecture of a complex CORDIC processor. The required precision of internal calculation, the circuit area for the number of antenna elements and wordlength, and the processing speed will be evaluated. The resource estimation provides a possible processor configuration with a current FPGA on the market. Computer simulations assuming a fading channel will show a fast convergence property with a finite number of training symbols. The proposed architecture has also been implemented and its operation was verified by beamforming evaluation through a radio propagation experiment.
Chiampi, M.; Repetto, M.; Chiarabaglio, D.
1995-11-01
The hysteresis phenomenon can significantly affect the behavior of magnetic cores in electrical machines and devices. This paper presents a finite element solution of periodic steady state magnetic field problems in soft materials with scalar hysteresis. The Jiles-Atherton model is employed for the generation of symmetric B-H loops and it is coupled with the Fixed Point Technique for handling magnetic nonlinearities. The proposed procedure is applied to a hysteretic model problem whose analytical solution is available. The results show that the Fixed Point Technique can efficiently deal with non-single valued material characteristics under periodic operating conditions.
NASA Astrophysics Data System (ADS)
Castro, P.; Machin, G.; Bloembergen, P.; Lowe, D.; Whittam, A.
2014-07-01
This study forms part of the European Metrology Research Programme project implementing the New Kelvin to assign thermodynamic temperatures to a selected set of high-temperature fixed points (HTFPs), Cu, Co-C, Pt-C, and Re-C. A realistic thermal model of these HTFPs, developed in finite volume software ANSYS FLUENT, was constructed to quantify the uncertainty associated with the temperature drop across the back wall of the cell. In addition, the widely applied software package, STEEP3 was used to investigate the influence of cell emissivity. The temperature drop, , relates to the temperature difference due to the net loss of heat from the aperture of the cavity between the back wall of the cavity, viewed by the thermometer, defining the radiance temperature, and the solid-liquid interface of the alloy, defining the transition temperature of the HTFP. The actual value of can be used either as a correction (with associated uncertainty) to thermodynamic temperature evaluations of HTFPs, or as an uncertainty contribution to the overall estimated uncertainty. In addition, the effect of a range of furnace temperature profiles on the temperature drop was calculated and found to be negligible for Cu, Co-C, and Pt-C and small only for Re-C. The effective isothermal emissivity is calculated over the wavelength range from 450 nm to 850 nm for different assumed values of surface emissivity. Even when furnace temperature profiles are taken into account, the estimated emissivities change only slightly from the effective isothermal emissivity of the bare cell. These emissivity calculations are used to estimate the uncertainty in the temperature assignment due to the uncertainty in the emissivity of the blackbody.
NASA Technical Reports Server (NTRS)
Alefeld, Goetz; Koshelev, Misha; Mayer, Guenter
1997-01-01
At first glance. it may seem that reconstructing the past is, in general, easier than predicting the future, because the past has already occurred and it has already left its traces, while the future is still yet to come, and so no traces of the future are available. However, in many real life situations, including problems from geophysics and celestial mechanics, reconstructing the past is much more computationally difficult than predicting the future. In this paper, we give an explanation of this difficulty. This explanation is given both on a formal level (as a theorem) and on the informal level (as a more intuitive explanation).
Noether's second theorem and Ward identities for gauge symmetries
NASA Astrophysics Data System (ADS)
Avery, Steven G.; Schwab, Burkhard U. W.
2016-02-01
Recently, a number of new Ward identities for large gauge transformations and large diffeomorphisms have been discovered. Some of the identities are reinterpretations of previously known statements, while some appear to be genuinely new. We use Noether's second theorem with the path integral as a powerful way of generating these kinds of Ward identities. We reintroduce Noether's second theorem and discuss how to work with the physical remnant of gauge symmetry in gauge fixed systems. We illustrate our mechanism in Maxwell theory, Yang-Mills theory, p-form field theory, and Einstein-Hilbert gravity. We comment on multiple connections between Noether's second theorem and known results in the recent literature. Our approach suggests a novel point of view with important physical consequences.
Formalin Fixed Paraffin Embedded Tissue as a Starting Point for PrPSc Detection by ELISA
Technology Transfer Automated Retrieval System (TEKTRAN)
Introduction: Formalin fixed paraffin embedded tissue are regularly employed in TSE diagnosis by IHC, the standard by which all other diagnostic protocols are currently judged. While IHC affords advantages over diagnostic approaches that typically utilize fresh or frozen tissue, such as Western blot...
The Knaster-Kuratowski-Mazurkiewicz theorem and abstract convexities
NASA Astrophysics Data System (ADS)
Cain, George L., Jr.; González, Luis
2008-02-01
The Knaster-Kuratowski-Mazurkiewicz covering theorem (KKM), is the basic ingredient in the proofs of many so-called "intersection" theorems and related fixed point theorems (including the famous Brouwer fixed point theorem). The KKM theorem was extended from Rn to Hausdorff linear spaces by Ky Fan. There has subsequently been a plethora of attempts at extending the KKM type results to arbitrary topological spaces. Virtually all these involve the introduction of some sort of abstract convexity structure for a topological space, among others we could mention H-spaces and G-spaces. We have introduced a new abstract convexity structure that generalizes the concept of a metric space with a convex structure, introduced by E. Michael in [E. Michael, Convex structures and continuous selections, Canad. J. MathE 11 (1959) 556-575] and called a topological space endowed with this structure an M-space. In an article by Shie Park and Hoonjoo Kim [S. Park, H. Kim, Coincidence theorems for admissible multifunctions on generalized convex spaces, J. Math. Anal. Appl. 197 (1996) 173-187], the concepts of G-spaces and metric spaces with Michael's convex structure, were mentioned together but no kind of relationship was shown. In this article, we prove that G-spaces and M-spaces are close related. We also introduce here the concept of an L-space, which is inspired in the MC-spaces of J.V. Llinares [J.V. Llinares, Unified treatment of the problem of existence of maximal elements in binary relations: A characterization, J. Math. Econom. 29 (1998) 285-302], and establish relationships between the convexities of these spaces with the spaces previously mentioned.
Competition Between Transients in the Rate of Approach to a Fixed Point*
Day, Judy; Rubin, Jonathan E.; Chow, Carson C.
2009-01-01
The goal of this paper is to provide and apply tools for analyzing a specific aspect of transient dynamics not covered by previous theory. The question we address is whether one component of a perturbed solution to a system of differential equations can overtake the corresponding component of a reference solution as both converge to a stable node at the origin, given that the perturbed solution was initially farther away and that both solutions are nonnegative for all time. We call this phenomenon tolerance, for its relation to a biological effect. We show using geometric arguments that tolerance will exist in generic linear systems with a complete set of eigenvectors and in excitable nonlinear systems. We also define a notion of inhibition that may constrain the regions in phase space where the possibility of tolerance arises in general systems. However, these general existence theorems do not not yield an assessment of tolerance for specific initial conditions. To address that issue, we develop some analytical tools for determining if particular perturbed and reference solution initial conditions will exhibit tolerance. PMID:20011076
The EuroSITES network: Integrating and enhancing fixed-point open ocean observatories around Europe
NASA Astrophysics Data System (ADS)
Lampitt, Richard S.; Larkin, Kate E.; EuroSITES Consortium
2010-05-01
EuroSITES is a 3 year (2008-2011) EU collaborative project (3.5MEuro) with the objective to integrate and enhance the nine existing open ocean fixed point observatories around Europe (www.eurosites.info). These observatories are primarily composed of full depth moorings and make multidisciplinary in situ observations within the water column as the European contribution to the global array OceanSITES (www.oceansites.org). In the first 18 months, all 9 observatories have been active and integration has been significant through the maintenance and enhancement of observatory hardware. Highlights include the enhancement of observatories with sensors to measure O2, pCO2, chlorophyll, and nitrate in near real-time from the upper 1000 m. In addition, some seafloor missions are also actively supported. These include seafloor platforms currently deployed in the Mediterranean, one for tsunami detection and one to monitor fluid flow related to seismic activity and slope stability. Upcoming seafloor science missions in 2010 include monitoring benthic biological communities and associated biogeochemistry as indicators of climate change in both the Northeast Atlantic and Mediterranean. EuroSITES also promotes the development of innovative sensors and samplers in order to progress capability to measure climate-relevant properties of the ocean. These include further developing current technologies for autonomous long-term monitoring of oxygen consumption in the mesopelagic, pH and mesozooplankton abundance. Many of these science missions are directly related to complementary activities in other European projects such as EPOCA, HYPOX and ESONET. In 2010 a direct collaboration including in situ field work will take place between ESONET and EuroSITES. The demonstration mission MODOO (funded by ESONET) will be implemented in 2010 at the EuroSITES PAP observatory. Field work will include deployment of a seafloor lander system with various sensors which will send data to shore in real
Two-stage fixed-bed gasifier with selectable middle gas off-take point
Strickland, Larry D.; Bissett, Larry A.
1992-01-01
A two-stage fixed bed coal gasifier wherein an annular region is in registry with a gasification zone underlying a devolatilization zone for extracting a side stream of high temperature substantially tar-free gas from the gasifier. A vertically displaceable skirt means is positioned within the gasifier to define the lower portion of the annular region so that vertical displacement of the skirt means positions the inlet into the annular region in a selected location within or in close proximity to the gasification zone for providing a positive control over the composition of the side stream gas.
Two-stage fixed-bed gasifier with selectable middle gas off-take point
Strickland, L.D.; Bissett, L.A.
1991-12-31
A two-stage fixed bed coal gasifier wherein an annular region is in registry with a gasification zone underlying a devolatilization zone for extracting a side stream of high temperature substantially tar-free gas from the gasifier. A vertically displaceable skirt means is positioned within the gasifier to define the lower portion of the annular region so that vertical displacement of the skirt means positions the inlet into the annular region in a selected location within or in close proximity to the gasification zone for providing a positive control over the composition of the side stream gas.
Antila, Hanne S; Salonen, Emppu
2015-04-15
The Thole induced point dipole model is combined with three different point charge fitting methods, Merz-Kollman (MK), charges from electrostatic potentials using a grid (CHELPG), and restrained electrostatic potential (RESP), and two multipole algorithms, distributed multipole analysis (DMA) and Gaussian multipole model (GMM), which can be used to describe the electrostatic potential (ESP) around molecules in molecular mechanics force fields. This is done to study how the different methods perform when intramolecular polarizability contributions are self-consistently removed from the fitting done in the force field parametrization. It is demonstrated that the polarizable versions of the partial charge models provide a good compromise between accuracy and computational efficiency in describing the ESP of small organic molecules undergoing conformational changes. For the point charge models, the inclusion of polarizability reduced the the average root mean square error of ESP over the test set by 4-10%. PMID:25753482
Kainz, K; Prah, D; Ahunbay, E; Li, X
2014-06-01
Purpose: A novel modulated arc therapy technique, mARC, enables superposition of step-and-shoot IMRT segments upon a subset of the optimization points (OPs) of a continuous-arc delivery. We compare two approaches to mARC planning: one with the number of OPs fixed throughout optimization, and another where the planning system determines the number of OPs in the final plan, subject to an upper limit defined at the outset. Methods: Fixed-OP mARC planning was performed for representative cases using Panther v. 5.01 (Prowess, Inc.), while variable-OP mARC planning used Monaco v. 5.00 (Elekta, Inc.). All Monaco planning used an upper limit of 91 OPs; those OPs with minimal MU were removed during optimization. Plans were delivered, and delivery times recorded, on a Siemens Artiste accelerator using a flat 6MV beam with 300 MU/min rate. Dose distributions measured using ArcCheck (Sun Nuclear Corporation, Inc.) were compared with the plan calculation; the two were deemed consistent if they agreed to within 3.5% in absolute dose and 3.5 mm in distance-to-agreement among > 95% of the diodes within the direct beam. Results: Example cases included a prostate and a head-and-neck planned with a single arc and fraction doses of 1.8 and 2.0 Gy, respectively. Aside from slightly more uniform target dose for the variable-OP plans, the DVHs for the two techniques were similar. For the fixed-OP technique, the number of OPs was 38 and 39, and the delivery time was 228 and 259 seconds, respectively, for the prostate and head-and-neck cases. For the final variable-OP plans, there were 91 and 85 OPs, and the delivery time was 296 and 440 seconds, correspondingly longer than for fixed-OP. Conclusion: For mARC, both the fixed-OP and variable-OP approaches produced comparable-quality plans whose delivery was successfully verified. To keep delivery time per fraction short, a fixed-OP planning approach is preferred.
Typical Orbits of Quadratic Polynomials with a Neutral Fixed Point: Brjuno Type
NASA Astrophysics Data System (ADS)
Cheraghi, Davoud
2013-09-01
We describe the topological behavior of typical orbits of complex quadratic polynomials {P_{α}(z) = e^{2 π α {i}} z + z2}, with α of high return type. Here we prove that for such Brjuno values of α the closure of the critical orbit, which is the measure theoretic attractor of the map, has zero area. Then we show that the limit set of the orbit of a typical point in the Julia set of P α is equal to the closure of the critical orbit. Our method is based on the near parabolic renormalization of Inou-Shishikura, and a uniform optimal estimate on the derivative of the Fatou coordinate that we prove here.
Construction of Home-Made Tin Fixed-Point Cell at TUBITAK UME
NASA Astrophysics Data System (ADS)
Kalemci, M.; Arifovic, N.; Bağçe, A.; Aytekin, S. O.; Ince, A. T.
2015-08-01
TUBITAK UME Temperature Laboratory initiated a new study which focuses on the construction of a tin freezing-point cell as a primary temperature standard. The design is an open-cell type similar to the National Institute of Standards and Technology design. With this aim, a brand new vacuum and filling line employing an oil diffusion pump and two cold traps (liquid nitrogen and dry ice) was set-up. The graphite parts (crucible, thermometer well, etc.) have been baked at high temperature under vacuum. Each cell was filled with approximately 1 kg of high-purity tin (99.9999 %) in a three-zone furnace. Then several melting and freezing curves were obtained to assess the quality of the home-made cell, and also the new cell was compared with the existing reference cell of the laboratory. The results obtained are very close to the reference cell of UME, indicating that the method used for fabrication was promising and satisfactory and also seems to meet the requirements to have a primary level temperature standard.
Bring the Pythagorean Theorem "Full Circle"
ERIC Educational Resources Information Center
Benson, Christine C.; Malm, Cheryl G.
2011-01-01
Middle school mathematics generally explores applications of the Pythagorean theorem and lays the foundation for working with linear equations. The Grade 8 Curriculum Focal Points recommend that students "apply the Pythagorean theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and…
A Phase-Field Solidification Model of Almost Pure ITS-90 Fixed Points
NASA Astrophysics Data System (ADS)
Large, M. J.; Pearce, J. V.
2014-07-01
A two-dimensional axisymmetric phase-field model of thermo-solutal solidification in freezing-point cells used for calibrating standard platinum resistance thermometers for realization and dissemination of the International Temperature Scale of 1990 is presented. The cell is essentially a graphite crucible containing an ingot of very pure metal (of order 99.9999 %). A graphite tube is inserted along the axis of the ingot to enable immersion of the thermometer in the metal. In this study, the metal is tin (freezing temperature of ). During the freezing of these cells, a steady, reproducible temperature is realized, with a defined temperature that can be used to calibrate thermometers with uncertainties mK. The model is applied to understand the effect of experimental parameters, such as initiation technique and furnace homogeneity, on the measured freezing curve. Results show that freezing curves whose behavior is consistent with the Scheil theory of solidification can be obtained with a specific furnace temperature profile, and provided that the freeze is of a long duration, the results are consistent with previous one-dimensional models and experiments. Morphological instability is observed with the inner interface initiation technique, causing the interface to adopt a cellular structure. This elevates the measured temperature, in accordance with the Gibbs-Thomson effect. In addition, the influence of initiation techniques on the solidification behavior is examined. The model indicates that an initially smooth inner mantle can `de-wet' from the thermometer well-forming agglomerated solid droplets, following recalescence, under certain conditions. This manifests as a measured temperature depression due to the Gibbs-Thomson effect, with a magnitude of to in simulations. The temperature rises to that of the stable outer mantle as freezing progresses and the droplets re-melt. It is demonstrated that the effect occurs below a critical mantle thickness. A physical
NASA Astrophysics Data System (ADS)
Todd, A. D. W.; Woods, D. J.
2013-02-01
This paper outlines measurements made at the National Research Council Canada (NRC) of the thermodynamic melting temperatures of Co-C, Pt-C and Re-C fixed points that have been part of the high-temperature fixed-point research plan of Working Group 5 of the Consultative Committee for Thermometry (CCT-WG5) to assign melting temperatures to those fixed points. This document will outline the equipment used, describe the scheme used to calibrate a pyrometer with traceability to a cryogenic electrical substitution radiometer, and detail the method of measuring the fixed points. It will then report the uncertainties in the measurements and the results. A brief description of the improvements that we plan to implement to the scheme to reduce the uncertainties for future measurements will be given. The thermodynamic temperatures determined for the three fixed points are: 1597.776 K with an expanded uncertainty of 0.36 K, 2011.390 K with an expanded uncertainty of 0.55 K, and 2748.056 K with an expanded uncertainty of 0.95 K, for the Co-C, Pt-C and Re-C fixed points, respectively (all expanded uncertainties assume a 95% confidence interval and a Gaussian distribution).
NASA Astrophysics Data System (ADS)
Kafri, H. Q.; Khuri, S. A.; Sayfy, A.
2016-03-01
In this paper, a novel approach is introduced for the solution of the non-linear Troesch's boundary value problem. The underlying strategy is based on Green's functions and fixed-point iterations, including Picard's and Krasnoselskii-Mann's schemes. The resulting numerical solutions are compared with both the analytical solutions and numerical solutions that exist in the literature. Convergence of the iterative schemes is proved via manipulation of the contraction principle. It is observed that the method handles the boundary layer very efficiently, reduces lengthy calculations, provides rapid convergence, and yields accurate results particularly for large eigenvalues. Indeed, to our knowledge, this is the first time that this problem is solved successfully for very large eigenvalues, actually the rate of convergence increases as the magnitude of the eigenvalues increases.
Selbig, William R.; Bannerman, Roger T.
2011-01-01
The U.S Geological Survey, in cooperation with the Wisconsin Department of Natural Resources (WDNR) and in collaboration with the Root River Municipal Stormwater Permit Group monitored eight urban source areas representing six types of source areas in or near Madison, Wis. in an effort to improve characterization of particle-size distributions in urban stormwater by use of fixed-point sample collection methods. The types of source areas were parking lot, feeder street, collector street, arterial street, rooftop, and mixed use. This information can then be used by environmental managers and engineers when selecting the most appropriate control devices for the removal of solids from urban stormwater. Mixed-use and parking-lot study areas had the lowest median particle sizes (42 and 54 (u or mu)m, respectively), followed by the collector street study area (70 (u or mu)m). Both arterial street and institutional roof study areas had similar median particle sizes of approximately 95 (u or mu)m. Finally, the feeder street study area showed the largest median particle size of nearly 200 (u or mu)m. Median particle sizes measured as part of this study were somewhat comparable to those reported in previous studies from similar source areas. The majority of particle mass in four out of six source areas was silt and clay particles that are less than 32 (u or mu)m in size. Distributions of particles ranging from 500 (u or mu)m were highly variable both within and between source areas. Results of this study suggest substantial variability in data can inhibit the development of a single particle-size distribution that is representative of stormwater runoff generated from a single source area or land use. Continued development of improved sample collection methods, such as the depth-integrated sample arm, may reduce variability in particle-size distributions by mitigating the effect of sediment bias inherent with a fixed-point sampler.
Fogle, W.E.; Hornung, E.W.; Mayberry, M.C.; Phillips, N.E.
1981-08-01
Comparison of a powdered CMN thermometer with an NBS fixed point device demonstrates an internal inconsistency in the T/sub c/'s assigned to the fixed point device. T/sub c/'s between 100 and 200 mK are in excellent agreement with a temperature scale interpolated between He vapor pressure temperatures and nuclear orientation temperatures, but there is a discrepancy of 8% at the 15 mK point. Evidence for different susceptibility-temperature relations for superficially similar CMN thermometers is also presented.
A Note on Laplace's Expansion Theorem
ERIC Educational Resources Information Center
Janji, Milan
2005-01-01
A short proof of Laplace's expansion theorem is given. The proof is elementary and can be presented at any level of undergraduate studies where determinants are taught. It is derived directly from the definition so that the theorem may be used as a starting point for further investigation of determinants.
NASA Astrophysics Data System (ADS)
Weiss, John
1991-11-01
Previously, we have found a factorization of the (1+1)-dimensional Toda lattice by the periodic fixed points of its Bäcklund transformations. The Toda flow is realized by two commuting, one-dimensional Hamiltonian flows. By a result of Konopelchenko, the Laplace-Darboux transformation is a Bäcklund transformation for the (2+1)-dimensional Boiti-Leon-Pempinelli (BLP) equation. A periodic fixed point of the Laplace transformation is an invariant manifold of the BLP flow. This manifold is determined by solutions of the (1+1)-dimensional Toda lattice equations. From these results we find that the 2+1 BLP flow is factored by three commuting, one-dimensional Hamiltonian flows that are the periodic fixed points of its Bäcklund transformations.
Geometric optics and the "hairy ball theorem"
NASA Astrophysics Data System (ADS)
Bormashenko, Edward; Kazachkov, Alexander
Applications of the hairy ball theorem to the geometrical optics are discussed. When the ideal mirror, topologically equivalent to a sphere, is illuminated at every point, the "hairy ball theorem" prescribes the existence of at least one point at which the incident light will be normally reflected. For the more general case of the surface, topologically equivalent to a sphere, which is both reflecting and refracting the "hairy ball theorem" predicts the existence of at least one point, at which the incident light will be normally reflected and also normally refracted.
NASA Astrophysics Data System (ADS)
Siegel, J.; Siegel, Edward Carl-Ludwig
2011-03-01
Cook-Levin computational-"complexity"(C-C) algorithmic-equivalence reduction-theorem reducibility equivalence to renormalization-(semi)-group phase-transitions critical-phenomena statistical-physics universality-classes fixed-points, is exploited with Gauss modular/clock-arithmetic/model congruences = signal X noise PRODUCT reinterpretation. Siegel-Baez FUZZYICS=CATEGORYICS(SON of ``TRIZ''): Category-Semantics(C-S) tabular list-format truth-table matrix analytics predicts and implements "noise"-induced phase-transitions (NITs) to accelerate versus to decelerate Harel [Algorithmics(1987)]-Sipser[Intro. Theory Computation(1997) algorithmic C-C: "NIT-picking" to optimize optimization-problems optimally(OOPO). Versus iso-"noise" power-spectrum quantitative-only amplitude/magnitude-only variation stochastic-resonance, this "NIT-picking" is "noise" power-spectrum QUALitative-type variation via quantitative critical-exponents variation. Computer-"science" algorithmic C-C models: Turing-machine, finite-state-models/automata, are identified as early-days once-workable but NOW ONLY LIMITING CRUTCHES IMPEDING latter-days new-insights!!!
Hahl, Sayuri K.; Kremling, Andreas
2016-01-01
In the mathematical modeling of biochemical reactions, a convenient standard approach is to use ordinary differential equations (ODEs) that follow the law of mass action. However, this deterministic ansatz is based on simplifications; in particular, it neglects noise, which is inherent to biological processes. In contrast, the stochasticity of reactions is captured in detail by the discrete chemical master equation (CME). Therefore, the CME is frequently applied to mesoscopic systems, where copy numbers of involved components are small and random fluctuations are thus significant. Here, we compare those two common modeling approaches, aiming at identifying parallels and discrepancies between deterministic variables and possible stochastic counterparts like the mean or modes of the state space probability distribution. To that end, a mathematically flexible reaction scheme of autoregulatory gene expression is translated into the corresponding ODE and CME formulations. We show that in the thermodynamic limit, deterministic stable fixed points usually correspond well to the modes in the stationary probability distribution. However, this connection might be disrupted in small systems. The discrepancies are characterized and systematically traced back to the magnitude of the stoichiometric coefficients and to the presence of nonlinear reactions. These factors are found to synergistically promote large and highly asymmetric fluctuations. As a consequence, bistable but unimodal, and monostable but bimodal systems can emerge. This clearly challenges the role of ODE modeling in the description of cellular signaling and regulation, where some of the involved components usually occur in low copy numbers. Nevertheless, systems whose bimodality originates from deterministic bistability are found to sustain a more robust separation of the two states compared to bimodal, but monostable systems. In regulatory circuits that require precise coordination, ODE modeling is thus still
ERIC Educational Resources Information Center
Bellver-Cebreros, Consuelo; Rodriguez-Danta, Marcelo
2009-01-01
An apparently unnoticed analogy between the torque-free motion of a rotating rigid body about a fixed point and the propagation of light in anisotropic media is stated. First, a new plane construction for visualizing this torque-free motion is proposed. This method uses an intrinsic representation alternative to angular momentum and independent of…
La, Moonwoo; Park, Sang Min; Kim, Dong Sung
2015-01-01
In this study, a multiple sample dispenser for precisely metered fixed volumes was successfully designed, fabricated, and fully characterized on a plastic centrifugal lab-on-a-disk (LOD) for parallel biochemical single-end-point assays. The dispenser, namely, a centrifugal multiplexing fixed-volume dispenser (C-MUFID) was designed with microfluidic structures based on the theoretical modeling about a centrifugal circumferential filling flow. The designed LODs were fabricated with a polystyrene substrate through micromachining and they were thermally bonded with a flat substrate. Furthermore, six parallel metering and dispensing assays were conducted at the same fixed-volume (1.27 μl) with a relative variation of ±0.02 μl. Moreover, the samples were metered and dispensed at different sub-volumes. To visualize the metering and dispensing performances, the C-MUFID was integrated with a serpentine micromixer during parallel centrifugal mixing tests. Parallel biochemical single-end-point assays were successfully conducted on the developed LOD using a standard serum with albumin, glucose, and total protein reagents. The developed LOD could be widely applied to various biochemical single-end-point assays which require different volume ratios of the sample and reagent by controlling the design of the C-MUFID. The proposed LOD is feasible for point-of-care diagnostics because of its mass-producible structures, reliable metering/dispensing performance, and parallel biochemical single-end-point assays, which can identify numerous biochemical. PMID:25610516
Mixing rates and limit theorems for random intermittent maps
NASA Astrophysics Data System (ADS)
Bahsoun, Wael; Bose, Christopher
2016-04-01
We study random transformations built from intermittent maps on the unit interval that share a common neutral fixed point. We focus mainly on random selections of Pomeu-Manneville-type maps {{T}α} using the full parameter range 0<α <∞ , in general. We derive a number of results around a common theme that illustrates in detail how the constituent map that is fastest mixing (i.e. smallest α) combined with details of the randomizing process, determines the asymptotic properties of the random transformation. Our key result (theorem 1.1) establishes sharp estimates on the position of return time intervals for the quenched dynamics. The main applications of this estimate are to limit laws (in particular, CLT and stable laws, depending on the parameters chosen in the range 0<α <1 ) for the associated skew product; these are detailed in theorem 3.2. Since our estimates in theorem 1.1 also hold for 1≤slant α <∞ we study a second class of random transformations derived from piecewise affine Gaspard-Wang maps, prove existence of an infinite (σ-finite) invariant measure and study the corresponding correlation asymptotics. To the best of our knowledge, this latter kind of result is completely new in the setting of random transformations.
NASA Astrophysics Data System (ADS)
Hong, Shihuang
2007-09-01
In this paper, we present sufficient conditions for the existence of at least three positive solutions of three-point boundary value problems for p-Laplacian dynamic equations on a time scale. To show our main results, we apply a new fixed point theorem due to Avery and Peterson [Three positive fixed points of nonlinear operators on ordered Banach spaces, Comput. Math. Appl. 42 (2001) 313-322].
A variational proof of Thomson's theorem
NASA Astrophysics Data System (ADS)
Fiolhais, Miguel C. N.; Essén, Hanno; Gouveia, Tomé M.
2016-08-01
Thomson's theorem of electrostatics, which states the electric charge on a set of conductors distributes itself on the conductor surfaces to minimize the electrostatic energy, is reviewed in this letter. The proof of Thomson's theorem, based on a variational principle, is derived for a set of normal charged conductors, with and without the presence of external electric fields produced by fixed charge distributions. In this novel approach, the variations are performed on both the charge densities and electric potentials, by means of a local Lagrange multiplier associated with Poisson's equation, constraining the two variables.
ERIC Educational Resources Information Center
Parameswaran, Revathy
2009-01-01
This paper reports on an experiment studying twelfth grade students' understanding of Rolle's Theorem. In particular, we study the influence of different concept images that students employ when solving reasoning tasks related to Rolle's Theorem. We argue that students' "container schema" and "motion schema" allow for rich concept images.…
The Interaction Equivalency Theorem
ERIC Educational Resources Information Center
Miyazoe, Terumi; Anderson, Terry
2010-01-01
This paper examines the key issues regarding The Interaction Equivalency Theorem posited by Anderson (2003a), which consists of the three interaction elements found in formal education courses among teacher, student, and content. It first examines the core concepts of the theorem and argues that two theses of different dimensions can be…
ERIC Educational Resources Information Center
Smith, Michael D.
2016-01-01
The Parity Theorem states that any permutation can be written as a product of transpositions, but no permutation can be written as a product of both an even number and an odd number of transpositions. Most proofs of the Parity Theorem take several pages of mathematical formalism to complete. This article presents an alternative but equivalent…
NASA Astrophysics Data System (ADS)
Grigor'ev, K. G.; Zapletina, E. V.; Zapletin, M. P.
1992-06-01
The paper presents an analysis and results of a numerical solution, based on the maximum principle, of three types of problems concerning the optimal launching of a space vehicle with a high-thrust rocket engine from the lunar surface to a fixed point on the circular orbit of a lunar artificial satellite. Attention is given to the problems of the fastest possible launching time, launching with minimal mass expenditure, and minimal trade-off functional (a compromise between expenditures for launch time and mass). The shooting method is used to obtain exact numerical solutions for the appropriate maximum principle boundary problems.
NASA Astrophysics Data System (ADS)
Chagas, E. A.; Furuya, K.
2008-08-01
In the present work we analyze the quantum phase transition (QPT) in the N-atom Jaynes-Cummings model (NJCM) with an additional symmetry breaking interaction term in the Hamiltonian. We show that depending on the type of symmetry breaking term added the transition order can change or not and also the fixed point associated to the classical analogue of the Hamiltonian can bifurcate or not. We present two examples of symmetry broken Hamiltonians and discuss based on them, the interconnection between the transition order, appearance of bifurcation and the behavior of the entanglement.
NASA Astrophysics Data System (ADS)
Lowe, Dave; Kodwani, Darsh
2015-11-01
Re-calibration of a thermocouple after it has been installed in a process is often not practical. In situ monitoring of performance is desirable and can be done with built-in reference standards based on melting or freezing phase transitions. Binary alloys with a monotectic reaction frequently have two invariant melt/freeze phase transitions taking place in the same material over a range of compositions. This makes them potentially well suited to be in situ temperature calibration artifacts, enabling correction for thermocouple drift without the need to disturb the thermocouple. A zinc-bismuth fixed-point cell was constructed and has been shown to be stable with two well-defined melting plateaus at nominally 255°C and 415°C. Two miniature fixed-point cells (each designed to be permanently installed with a thermocouple) based on zinc-bismuth and aluminum-indium alloys were made. Measurements have shown that the phase transitions can be identified despite the small quantity of metals used and that the alloys were sufficiently stable to have the potential to provide improved long-term confidence in process control and monitoring.
On Viviani's Theorem and Its Extensions
ERIC Educational Resources Information Center
Abboud, Elias
2010-01-01
Viviani's theorem states that the sum of distances from any point inside an equilateral triangle to its sides is constant. Here, in an extension of this result, we show, using linear programming, that any convex polygon can be divided into parallel line segments on which the sum of the distances to the sides of the polygon is constant. Let us say…
An Elementary Proof of Pick's Theorem.
ERIC Educational Resources Information Center
Pullman, Howard W.
1979-01-01
Pick's Theorem, a statement of the relationship between the area of a polygonal region on a lattice and its interior and boundary lattice points, is familiar to those whose students have participated in activities and discovery lessons using the geoboard. The proof presented, although rather long, is well within the grasp of the average geometry…
NASA Astrophysics Data System (ADS)
Pérez-Espigares, Carlos; Redig, Frank; Giardinà, Cristian
2015-08-01
For non-equilibrium systems of interacting particles and for interacting diffusions in d-dimensions, a novel fluctuation relation is derived. The theorem establishes a quantitative relation between the probabilities of observing two current values in different spatial directions. The result is a consequence of spatial symmetries of the microscopic dynamics, generalizing in this way the Gallavotti-Cohen fluctuation theorem related to the time-reversal symmetry. This new perspective opens up the possibility of direct experimental measurements of fluctuation relations of vectorial observables.
Soft theorems from effective field theory
NASA Astrophysics Data System (ADS)
Larkoski, Andrew J.; Neill, Duff; Stewart, Iain W.
2015-06-01
The singular limits of massless gauge theory amplitudes are described by an effective theory, called soft-collinear effective theory (SCET), which has been applied most successfully to make all-orders predictions for observables in collider physics and weak decays. At tree-level, the emission of a soft gauge boson at subleading order in its energy is given by the Low-Burnett-Kroll theorem, with the angular momentum operator acting on a lower-point amplitude. For well separated particles at tree-level, we prove the Low-Burnett-Kroll theorem using matrix elements of subleading SCET Lagrangian and operator insertions which are individually gauge invariant. These contributions are uniquely determined by gauge invariance and the reparametrization invariance (RPI) symmetry of SCET. RPI in SCET is connected to the infinite-dimensional asymptotic symmetries of the S-matrix. The Low-Burnett-Kroll theorem is generically spoiled by on-shell corrections, including collinear loops and collinear emissions. We demonstrate this explicitly both at tree-level and at one-loop. The effective theory correctly describes these configurations, and we generalize the Low-Burnett-Kroll theorem into a new one-loop subleading soft theorem for amplitudes. Our analysis is presented in a manner that illustrates the wider utility of using effective theory techniques to understand the perturbative S-matrix.
Virial Theorem and Scale Transformations.
ERIC Educational Resources Information Center
Kleban, Peter
1979-01-01
Discussed is the virial theorem, which is useful in classical, quantum, and statistical mechanics. Two types of derivations of this theorem are presented and the relationship between the two is explored. (BT)
''CPT Theorem'' for Accelerators
Vladimir Shiltsev
2004-08-05
In this paper we attempt to reveal common features in evolution of various colliders' luminosity over commissioning periods. A simplified formula, ''CPT theorem'' or CP = T, is proposed which relates the time needed for commissioning T, the ''complexity'' of the machine C and performance increase goal P.
ERIC Educational Resources Information Center
Musto, Garrod
2010-01-01
Within his classroom, the author is often confronted by students who fail to see, or accept, the relevance of mathematics both to their lives and the world around them. One topic which is regularly perceived as being disconnected from people's daily lives is that of circle theorems, especially among less motivated students. In this article, the…
A Schwinger disentangling theorem
Cross, Daniel J.; Gilmore, Robert
2010-10-15
Baker-Campbell-Hausdorff formulas are exceedingly useful for disentangling operators so that they may be more easily evaluated on particular states. We present such a disentangling theorem for general bilinear and linear combinations of multiple boson creation and annihilation operators. This work generalizes a classical result of Schwinger.
Weinberg, Steven
2008-09-15
It is shown that the generating function for tree graphs in the ''in-in'' formalism may be calculated by solving the classical equations of motion subject to certain constraints. This theorem is illustrated by application to the evolution of a single inflaton field in a Robertson-Walker background.
An Epistemological Criticism to the Bell-Kochen-Specker Theorem
NASA Astrophysics Data System (ADS)
Garola, Claudio
2009-03-01
The Bell-Kochen-Specker theorem is criticized from an epistemological point of view, showing that its proofs rest on an implicit epistemological assumption which does not fit in with the operational and antimetaphysical attitude of orthodox quantum mechanics.
Cooperation Among Theorem Provers
NASA Technical Reports Server (NTRS)
Waldinger, Richard J.
1998-01-01
This is a final report, which supports NASA's PECSEE (Persistent Cognizant Software Engineering Environment) effort and complements the Kestrel Institute project "Inference System Integration via Logic Morphism". The ultimate purpose of the project is to develop a superior logical inference mechanism by combining the diverse abilities of multiple cooperating theorem provers. In many years of research, a number of powerful theorem-proving systems have arisen with differing capabilities and strengths. Resolution theorem provers (such as Kestrel's KITP or SRI's, SNARK) deal with first-order logic with equality but not the principle of mathematical induction. The Boyer-Moore theorem prover excels at proof by induction but cannot deal with full first-order logic. Both are highly automated but cannot accept user guidance easily. The PVS system (from SRI) in only automatic within decidable theories, but it has well-designed interactive capabilities: furthermore, it includes higher-order logic, not just first-order logic. The NuPRL system from Cornell University and the STeP system from Stanford University have facilities for constructive logic and temporal logic, respectively - both are interactive. It is often suggested - for example, in the anonymous "QED Manifesto"-that we should pool the resources of all these theorem provers into a single system, so that the strengths of one can compensate for the weaknesses of others, and so that effort will not be duplicated. However, there is no straightforward way of doing this, because each system relies on its own language and logic for its success. Thus. SNARK uses ordinary first-order logic with equality, PVS uses higher-order logic. and NuPRL uses constructive logic. The purpose of this project, and the companion project at Kestrel, has been to use the category-theoretic notion of logic morphism to combine systems with different logics and languages. Kestrel's SPECWARE system has been the vehicle for the implementation.
ERIC Educational Resources Information Center
Russell, Alan R.
2004-01-01
Pick's theorem can be used in various ways just like a lemon. This theorem generally finds its way in the syllabus approximately at the middle school level and in fact at times students have even calculated the area of a state considering its outline with the help of the above theorem.
ERIC Educational Resources Information Center
Abramovitz, Buma; Berezina, Miryam; Berman, Abraham; Shvartsman, Ludmila
2009-01-01
In this article we describe the process of studying the assumptions and the conclusion of a theorem. We tried to provide the students with exercises and problems where we discuss the following questions: What are the assumptions of a theorem and what are the conclusions? What is the geometrical meaning of a theorem? What happens when one or more…
Han, Houzeng; Xu, Tianhe; Wang, Jian
2016-01-01
Precise Point Positioning (PPP) makes use of the undifferenced pseudorange and carrier phase measurements with ionospheric-free (IF) combinations to achieve centimeter-level positioning accuracy. Conventionally, the IF ambiguities are estimated as float values. To improve the PPP positioning accuracy and shorten the convergence time, the integer phase clock model with between-satellites single-difference (BSSD) operation is used to recover the integer property. However, the continuity and availability of stand-alone PPP is largely restricted by the observation environment. The positioning performance will be significantly degraded when GPS operates under challenging environments, if less than five satellites are present. A commonly used approach is integrating a low cost inertial sensor to improve the positioning performance and robustness. In this study, a tightly coupled (TC) algorithm is implemented by integrating PPP with inertial navigation system (INS) using an Extended Kalman filter (EKF). The navigation states, inertial sensor errors and GPS error states are estimated together. The troposphere constrained approach, which utilizes external tropospheric delay as virtual observation, is applied to further improve the ambiguity-fixed height positioning accuracy, and an improved adaptive filtering strategy is implemented to improve the covariance modelling considering the realistic noise effect. A field vehicular test with a geodetic GPS receiver and a low cost inertial sensor was conducted to validate the improvement on positioning performance with the proposed approach. The results show that the positioning accuracy has been improved with inertial aiding. Centimeter-level positioning accuracy is achievable during the test, and the PPP/INS TC integration achieves a fast re-convergence after signal outages. For troposphere constrained solutions, a significant improvement for the height component has been obtained. The overall positioning accuracies of the height
Han, Houzeng; Xu, Tianhe; Wang, Jian
2016-01-01
Precise Point Positioning (PPP) makes use of the undifferenced pseudorange and carrier phase measurements with ionospheric-free (IF) combinations to achieve centimeter-level positioning accuracy. Conventionally, the IF ambiguities are estimated as float values. To improve the PPP positioning accuracy and shorten the convergence time, the integer phase clock model with between-satellites single-difference (BSSD) operation is used to recover the integer property. However, the continuity and availability of stand-alone PPP is largely restricted by the observation environment. The positioning performance will be significantly degraded when GPS operates under challenging environments, if less than five satellites are present. A commonly used approach is integrating a low cost inertial sensor to improve the positioning performance and robustness. In this study, a tightly coupled (TC) algorithm is implemented by integrating PPP with inertial navigation system (INS) using an Extended Kalman filter (EKF). The navigation states, inertial sensor errors and GPS error states are estimated together. The troposphere constrained approach, which utilizes external tropospheric delay as virtual observation, is applied to further improve the ambiguity-fixed height positioning accuracy, and an improved adaptive filtering strategy is implemented to improve the covariance modelling considering the realistic noise effect. A field vehicular test with a geodetic GPS receiver and a low cost inertial sensor was conducted to validate the improvement on positioning performance with the proposed approach. The results show that the positioning accuracy has been improved with inertial aiding. Centimeter-level positioning accuracy is achievable during the test, and the PPP/INS TC integration achieves a fast re-convergence after signal outages. For troposphere constrained solutions, a significant improvement for the height component has been obtained. The overall positioning accuracies of the height
A generalized antenna theorem for broadband pulses
NASA Astrophysics Data System (ADS)
Johnson, Michael A.
1989-03-01
Using a very general argument, one can place an upper limit on the fluence that can be delivered to a distant point by passing a pulse with finite energy through an aperture of finite area. Based on a time-dependent form of Huygen's principle, shown is the maximum possible fluence produced by an arbitrary scalar field passing through an aperture to an observation point is about equal to the fluence produced by a nearly monochromatic pulse of the same energy. This fictitious pulse uniformly illuminates the aperture and converges to a geometric focal spot at the observation point. The frequency of the monochromatic wave is made equal to the aperture-averaged root-mean-square frequency of the actual diffracting field. Thus, a pulse with arbitrary time dependence satisfies an antenna theorem very similar to the more well-known version of the theorem satisfied by monochromatic waves.
NASA Astrophysics Data System (ADS)
Greaves, Hilary; Thomas, Teruji
2014-02-01
We provide a careful development and rigorous proof of the CPT theorem within the framework of mainstream (Lagrangian) quantum field theory. This is in contrast to the usual rigorous proofs in purely axiomatic frameworks, and non-rigorous proof-sketches in the mainstream approach. We construct the CPT transformation for a general field directly, without appealing to the enumerative classification of representations, and in a manner that is clearly related to the requirements of our proof. Our approach applies equally in Minkowski spacetimes of any dimension at least three, and is in principle neutral between classical and quantum field theories: the quantum CPT theorem has a natural classical analogue. The key mathematical tool is that of complexification; this tool is central to the existing axiomatic proofs, but plays no overt role in the usual mainstream approaches to CPT.
THE PARKER MAGNETOSTATIC THEOREM
Low, B. C.
2010-08-01
We demonstrate the Parker Magnetostatic Theorem in terms of a small neighborhood in solution space containing continuous force-free magnetic fields in small deviations from the uniform field. These fields are embedded in a perfectly conducting fluid bounded by a pair of rigid plates where each field is anchored, taking the plates perpendicular to the uniform field. Those force-free fields obtainable from the uniform field by continuous magnetic footpoint displacements at the plates have field topologies that are shown to be a restricted subset of the field topologies similarly created without imposing the force-free equilibrium condition. The theorem then follows from the deduction that a continuous nonequilibrium field with a topology not in that subset must find a force-free state containing tangential discontinuities.
NASA Astrophysics Data System (ADS)
Pearce, J. V.; Elliott, C. J.; Lowe, D. H.; Failleau, G.; Deuzé, T.; Bourson, F.; Sadli, M.; Machin, G.
2014-04-01
A series of high-temperature fixed points (HTFPs) Pt-C (1738 , and Ru-C (1953 ) have been constructed at the National Physical Laboratory (NPL) and the Laboratoire National de métrologie et d'Essais and Conservatoire national des arts et métiers (LNE-Cnam). These are required for the calibration of high-temperature thermocouples in the framework of work package 6 of the European Metrology Research Programme IND01 project "HiTeMS." The goal of this work package is to establish a European capability that can determine low-uncertainty reference functions of non-standard high-temperature thermocouples. For reference functions to be widely applicable, measurements must be performed by more than one institute and preferably by more than one method. Due to the high price of the ingot materials, miniature HTFP cells are used. NPL and LNE-Cnam constructed their HTFP cells with different designs; these are described here, together with the performance of the cells using both radiation thermometry and thermocouples. The melting temperature of the Ru-C cells (for thermocouple calibrations) was determined using radiation thermometry at both NPL and LNE-Cnam, and the two results are compared. The suitability of the cells for calibration of W-Re and Rh-Ir thermocouples is evaluated, and some results are presented. Some discussion is given regarding the materials challenges when calibrating Rh-Ir thermocouples up to 2000 C.
NASA Astrophysics Data System (ADS)
Kawaguchi, Y.; Inoue, J.; Nishino, S.
2015-12-01
A fixed-point observation using the R/V Mirai was conducted in the ice-free northern Chukchi Sea of the Arctic Ocean during September of 2013. During the program the authors performed repeated microstructure measurements to reveal the temporal evolution of the surface mixed layer and mixing processes in the upper water column. The shelf region was initially characterized by a distinct two-layer system comprising a warmer/ fresher top layer and a colder/saltier bottom layer. During the two-week observation period, the top-layer water showed two types of mixing processes: near-surface turbulence due to strong wind forcing and subsurface mixing due to internal gravity waves. In the first week, when the top layer was stratified with fresh sea ice meltwater, turbulent energy related to internal waves propagated through the subsurface stratification, resulting in a mechanical overturning near the pycnocline, followed by enhanced mixing there. In the second week, gale winds directly stirred up the upper water and then established a deeper homogenous layer. The combination of internal wave mixing and wind-driven turbulence may contribute to releasing the oceanic heat into the atmosphere, consequently promoting the preconditioning of surface water freezing.
NASA Astrophysics Data System (ADS)
Sarbicki, Gniewomir; Chruściński, Dariusz; Mozrzymas, Marek
2016-07-01
We analyse linear maps of operator algebras {{ B }}H({ H }) mapping the set of rank-k projectors onto the set of rank-l projectors surjectively. A complete characterisation of such maps for prime n={dim} { H } is provided. A particular case corresponding to k=l=1 is well known as Wigner’s theorem. Hence our result may be considered as a generalisation of this celebrated Wigner’s result.
The Steep Nekhoroshev's Theorem
NASA Astrophysics Data System (ADS)
Guzzo, M.; Chierchia, L.; Benettin, G.
2016-03-01
Revising Nekhoroshev's geometry of resonances, we provide a fully constructive and quantitative proof of Nekhoroshev's theorem for steep Hamiltonian systems proving, in particular, that the exponential stability exponent can be taken to be {1/(2nα_1\\cdotsα_{n-2}}) ({α_i}'s being Nekhoroshev's steepness indices and {n ≥ 3} the number of degrees of freedom). On the base of a heuristic argument, we conjecture that the new stability exponent is optimal.
Special ergodic theorems and dynamical large deviations
NASA Astrophysics Data System (ADS)
Kleptsyn, Victor; Ryzhov, Dmitry; Minkov, Stanislav
2012-11-01
Let f : M → M be a self-map of a compact Riemannian manifold M, admitting a global SRB measure μ. For a continuous test function \\varphi\\colon M\\to R and a constant α > 0, consider the set Kφ,α of the initial points for which the Birkhoff time averages of the function φ differ from its μ-space average by at least α. As the measure μ is a global SRB one, the set Kφ,α should have zero Lebesgue measure. The special ergodic theorem, whenever it holds, claims that, moreover, this set has a Hausdorff dimension less than the dimension of M. We prove that for Lipschitz maps, the special ergodic theorem follows from the dynamical large deviations principle. We also define and prove analogous result for flows. Applying the theorems of Young and of Araújo and Pacifico, we conclude that the special ergodic theorem holds for transitive hyperbolic attractors of C2-diffeomorphisms, as well as for some other known classes of maps (including the one of partially hyperbolic non-uniformly expanding maps) and flows.
Nagai, Satoshi; Hida, Kohsuke; Urushizaki, Shingo; Onitsuka, Goh; Yasuike, Motoshige; Nakamura, Yoji; Fujiwara, Atushi; Tajimi, Seisuke; Kimoto, Katsunori; Kobayashi, Takanori; Gojobori, Takashi; Ototake, Mitsuru
2016-02-01
In this study, we investigated the influence of diurnal sampling bias on the community structure of plankton by comparing the biodiversity among seawater samples (n=9) obtained every 3h for 24h by using massively parallel sequencing (MPS)-based plankton monitoring at a fixed point conducted at Himedo seaport in Yatsushiro Sea, Japan. The number of raw operational taxonomy units (OTUs) and OTUs after re-sampling was 507-658 (558 ± 104, mean ± standard deviation) and 448-544 (467 ± 81), respectively, indicating high plankton biodiversity at the sampling location. The relative abundance of the top 20 OTUs in the samples from Himedo seaport was 48.8-67.7% (58.0 ± 5.8%), and the highest-ranked OTU was Pseudo-nitzschia species (Bacillariophyta) with a relative abundance of 17.3-39.2%, followed by Oithona sp. 1 and Oithona sp. 2 (Arthropoda). During seawater sampling, the semidiurnal tidal current having an amplitude of 0.3ms(-1) was dominant, and the westward residual current driven by the northeasterly wind was continuously observed during the 24-h monitoring. Therefore, the relative abundance of plankton species apparently fluctuated among the samples, but no significant difference was noted according to G-test (p>0.05). Significant differences were observed between the samples obtained from a different locality (Kusuura in Yatsushiro Sea) and at different dates, suggesting that the influence of diurnal sampling bias on plankton diversity, determined using the MPS-based survey, was not significant and acceptable. PMID:26475937
Recurrence theorems: A unified account
Wallace, David
2015-02-15
I discuss classical and quantum recurrence theorems in a unified manner, treating both as generalisations of the fact that a system with a finite state space only has so many places to go. Along the way, I prove versions of the recurrence theorem applicable to dynamics on linear and metric spaces and make some comments about applications of the classical recurrence theorem in the foundations of statistical mechanics.
A theorem in relativistic electronics
NASA Astrophysics Data System (ADS)
Yongjian, Yu
1990-04-01
This paper presents a theorem that connects the dispersion relation of the Electron Cyclotron Maser' and the oscillation equation of the Gyromonotron. This theorem gives us a simple way of obtaining the osscillating characteristics of the Gyromonotron provided that dispersion relation of the ECRM is given. Though the theorem is proved only with the case of ECRM and Gyromonotron, it holds for other kinds of Electron Masers, FEL4etc. and corresponding osscillators.
Applications of square-related theorems
NASA Astrophysics Data System (ADS)
Srinivasan, V. K.
2014-04-01
The square centre of a given square is the point of intersection of its two diagonals. When two squares of different side lengths share the same square centre, there are in general four diagonals that go through the same square centre. The Two Squares Theorem developed in this paper summarizes some nice theoretical conclusions that can be obtained when two squares of different side lengths share the same square centre. These results provide the theoretical basis for two of the constructions given in the book of H.S. Hall and F.H. Stevens , 'A Shorter School Geometry, Part 1, Metric Edition'. In page 134 of this book, the authors present, in exercise 4, a practical construction which leads to a verification of the Pythagorean theorem. Subsequently in Theorems 29 and 30, the authors present the standard proofs of the Pythagorean theorem and its converse. In page 140, the authors present, in exercise 15, what amounts to a geometric construction, whose verification involves a simple algebraic identity. Both the constructions are of great importance and can be replicated by using the standard equipment provided in a 'geometry toolbox' carried by students in high schools. The author hopes that the results proved in this paper, in conjunction with the two constructions from the above-mentioned book, would provide high school students an appreciation of the celebrated theorem of Pythagoras. The diagrams that accompany this document are based on the free software GeoGebra. The author formally acknowledges his indebtedness to the creators of this free software at the end of this document.
A Middle School Extension of Pick's Theorem to Areas of Nonsimple Closed Polygonal Regions.
ERIC Educational Resources Information Center
Boykin, Wilfred E.
1995-01-01
Presents an extension of Pick's theorem for simple closed polygonal regions to unions of simple closed polygonal regions. Students are guided to discover Pick's theorem from sets of data including numbers of boundary points and numbers of interior points. (Author/MKR)
Geometry of the Adiabatic Theorem
ERIC Educational Resources Information Center
Lobo, Augusto Cesar; Ribeiro, Rafael Antunes; Ribeiro, Clyffe de Assis; Dieguez, Pedro Ruas
2012-01-01
We present a simple and pedagogical derivation of the quantum adiabatic theorem for two-level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov, among others. We have chosen to use only the minimum geometric structure needed for the understanding of the adiabatic theorem for this case.…
Roo: A parallel theorem prover
Lusk, E.L.; McCune, W.W.; Slaney, J.K.
1991-11-01
We describe a parallel theorem prover based on the Argonne theorem-proving system OTTER. The parallel system, called Roo, runs on shared-memory multiprocessors such as the Sequent Symmetry. We explain the parallel algorithm used and give performance results that demonstrate near-linear speedups on large problems.
A Decomposition Theorem for Finite Automata.
ERIC Educational Resources Information Center
Santa Coloma, Teresa L.; Tucci, Ralph P.
1990-01-01
Described is automata theory which is a branch of theoretical computer science. A decomposition theorem is presented that is easier than the Krohn-Rhodes theorem. Included are the definitions, the theorem, and a proof. (KR)
Correlation dimension Wonderland theorems
NASA Astrophysics Data System (ADS)
Carvalho, Silas L.; de Oliveira, César R.
2016-06-01
Existence of generic sets of self-adjoint operators, related to correlation dimensions of spectral measures, is investigated in separable Hilbert spaces. Typical results say that, given an orthonormal basis, the set of operators whose corresponding spectral measures are both 0-lower and 1-upper correlation dimensional is generic. The proofs rely on details of the relations among Fourier transform of spectral measures and Hausdorff and packing measures on the real line. Then such results are naturally combined with the Wonderland theorem. Applications are to classes of discrete one-dimensional Schrödinger operators and general (bounded) self-adjoint operators as well. Physical consequences include a proof of exotic dynamical behavior of singular continuous spectrum in some settings.
Extension of the Blasius force theorem to subsonic speeds
NASA Astrophysics Data System (ADS)
Barsony-Nagy, A.
1985-11-01
The theorem considered by Blasius (1910) represents a well-known method for calculating the force on a body situated in an incompressible, inviscid two-dimensional flow. The efficiency of the Blasius theorem is due to its quality of expressing the forces with the aid of contour integrals of analytic functions of complex variables. The present note has the objective to deduce an analog of Blasius theorem for the aerodynamic forces in subsonic flow. It is assumed that an approximate velocity potential of the subsonic flow has been calculated by using the Imai-Lamla method. It is pointed out that this method is a variant specially suited for the two-dimensionally flows of the Janzen-Rayleigh expansion method. The derived formula expresses the aerodynamic forces with the aid of contour integrals of analytic complex functions. It can be regarded as the Blasius theorem with first-order compressibility correction for the subsonic speed regime.
On the generalized virial theorem for systems with variable mass
NASA Astrophysics Data System (ADS)
Ganghoffer, Jean-François; Rahouadj, Rachid
2016-03-01
We presently extend the virial theorem for both discrete and continuous systems of material points with variable mass, relying on developments presented in Ganghoffer (Int J Solids Struct 47:1209-1220, 2010). The developed framework is applicable to describe physical systems at very different scales, from the evolution of a population of biological cells accounting for growth to mass ejection phenomena occurring within a collection of gravitating objects at the very large astrophysical scales. As a starting basis, the field equations in continuum mechanics are written to account for a mass source and a mass flux, leading to a formulation of the virial theorem accounting for non-constant mass within the considered system. The scalar and tensorial forms of the virial theorem are then written successively in both Lagrangian and Eulerian formats, incorporating the mass flux. As an illustration, the averaged stress tensor in accreting gravitating solid bodies is evaluated based on the generalized virial theorem.
Formulation of Liouville's theorem for grand ensemble molecular simulations
NASA Astrophysics Data System (ADS)
Delle Site, Luigi
2016-02-01
Liouville's theorem in a grand ensemble, that is for situations where a system is in equilibrium with a reservoir of energy and particles, is a subject that, to our knowledge, has not been explicitly treated in literature related to molecular simulation. Instead, Liouville's theorem, a central concept for the correct employment of molecular simulation techniques, is implicitly considered only within the framework of systems where the total number of particles is fixed. However, the pressing demand of applied science in treating open systems leads to the question of the existence and possible exact formulation of Liouville's theorem when the number of particles changes during the dynamical evolution of the system. The intention of this paper is to stimulate a debate about this crucial issue for molecular simulation.
A Theorem and its Application to Finite Tampers
DOE R&D Accomplishments Database
Feynman, R. P.
1946-08-15
A theorem is derived which is useful in the analysis of neutron problems in which all neutrons have the same velocity. It is applied to determine extrapolated end-points, the asymptotic amplitude from a point source, and the neutron density at the surface of a medium. Formulas fro the effect of finite tampers are derived by its aid, and their accuracy discussed.
Hohenberg-Kohn theorems in electrostatic and uniform magnetostatic fields
Pan, Xiao-Yin; Sahni, Viraht
2015-11-07
The Hohenberg-Kohn (HK) theorems of bijectivity between the external scalar potential and the gauge invariant nondegenerate ground state density, and the consequent Euler variational principle for the density, are proved for arbitrary electrostatic field and the constraint of fixed electron number. The HK theorems are generalized for spinless electrons to the added presence of an external uniform magnetostatic field by introducing the new constraint of fixed canonical orbital angular momentum. Thereby, a bijective relationship between the external scalar and vector potentials, and the gauge invariant nondegenerate ground state density and physical current density, is proved. A corresponding Euler variational principle in terms of these densities is also developed. These theorems are further generalized to electrons with spin by imposing the added constraint of fixed canonical orbital and spin angular momenta. The proofs differ from the original HK proof and explicitly account for the many-to-one relationship between the potentials and the nondegenerate ground state wave function. A Percus-Levy-Lieb constrained-search proof expanding the domain of validity to N-representable functions, and to degenerate states, again for fixed electron number and angular momentum, is also provided.
Subsubleading soft theorems of gravitons and dilatons in the bosonic string
NASA Astrophysics Data System (ADS)
Di Vecchia, Paolo; Marotta, Raffaele; Mojaza, Matin
2016-06-01
Starting from the amplitude with an arbitrary number of massless closed states of the bosonic string, we compute the soft limit when one of the states becomes soft to subsubleading order in the soft momentum expansion, and we show that when the soft state is a graviton or a dilaton, the full string amplitude can be expressed as a soft theorem through subsubleading order. It turns out that there are string corrections to the field theoretical limit in the case of a soft graviton, while for a soft dilaton the string corrections vanish. We then show that the new soft theorems, including the string corrections, can be simply obtained from the exchange diagrams where the soft state is attached to the other external states through the three-point string vertex of three massless states. In the soft-limit, the propagator of the exchanged state is divergent, and at tree-level these are the only divergent contributions to the full amplitude. However, they do not form a gauge invariant subset and must be supplemented with extra non-singular terms. The requirement of gauge invariance then fixes the complete amplitude through subsubleading order in the soft expansion, reproducing exactly what one gets from the explicit calculation in string theory. From this it is seen that the string corrections at subsubleading order arise as a consequence of the three-point amplitude having string corrections in the bosonic string. When specialized to a soft dilaton, it remarkably turns out that the string corrections vanish and that the non-singular piece of the subsubleading term of the dilaton soft theorem is the generator of space-time special conformal transformation.
NASA Astrophysics Data System (ADS)
Guney, Veli Ugur
In this work we look for novel classes of Bell's inequalities and methods to produce them. We also find their quantum violations including, if possible, the maximum one. The Jordan bases method that we explain in Chapter 2 is about using a pair of certain type of orthonormal bases whose spans are subspaces related to measurement outcomes of incompatible quantities on the same physical system. Jordan vectors are the briefest way of expressing the relative orientation of any two subspaces. This feature helps us to reduce the dimensionality of the parameter space on which we do searches for optimization. The work is published in [24]. In Chapter 3, we attempt to find a connection between group theory and Bell's theorem. We devise a way of generating terms of a Bell's inequality that are related to elements of an algebraic group. The same group generates both the terms of the Bell's inequality and the observables that are used to calculate the quantum value of the Bell expression. Our results are published in [25][26]. In brief, Bell's theorem is the main tool of a research program that was started by Einstein, Podolsky, Rosen [19] and Bohr [8] in the early days of quantum mechanics in their discussions about the core nature of physical systems. These debates were about a novel type of physical states called superposition states, which are introduced by quantum mechanics and manifested in the apparent inevitable randomness in measurement outcomes of identically prepared systems. Bell's huge contribution was to find a means of quantifying the problem and hence of opening the way to experimental verification by rephrasing the questions as limits on certain combinations of correlations between measurement results of spatially separate systems [7]. Thanks to Bell, the fundamental questions related to the nature of quantum mechanical systems became quantifiable [6]. According to Bell's theorem, some correlations between quantum entangled systems that involve incompatible
Extension of Euler's theorem to n-dimensional spaces
NASA Technical Reports Server (NTRS)
Bar-Itzhack, Itzhack Y.
1989-01-01
Euler's theorem states that any sequence of finite rotations of a rigid body can be described as a single rotation of the body about a fixed axis in three-dimensional Euclidean space. The usual statement of the theorem in the literature cannot be extended to Euclidean spaces of other dimensions. Equivalent formulations of the theorem are given and proved in a way which does not limit them to the three-dimensional Euclidean space. Thus, the equivalent theorems hold in other dimensions. The proof of one formulation presents an algorithm which shows how to compute an angular-difference matrix that represents a single rotation which is equivalent to the sequence of rotations that have generated the final n-D orientation. This algorithm results also in a constant angular velocity which, when applied to the initial orientation, eventually yields the final orientation regardless of what angular velocity generated the latter. The extension of the theorem is demonstrated in a four-dimensional numerical example.
Extension to Eulers's theorem to n-dimensional spaces
NASA Technical Reports Server (NTRS)
Bar-Itzhack, Itzhack Y.
1989-01-01
Euler's theorem states that any sequence of finite rotations of a rigid body can be described as a single rotation of the body about a fixed axis in three-dimensional Euclidean space. The usual statement of the theorem in the literature cannot be extended to Euclidean spaces of other dimensions. Equivalent formulations of the theorem are given in this paper and proven in a way which does not limit them to the three-dimensional Euclidean space. Thus, the equivalent theorems hold in other dimensions. The proof of one formulation presents an algorithm which shows how to compute an angular-difference matrix that represents a single rotation which is equivalent to the sequence of rotations that have generated the final n-D orientation. This algorithm results also in a constant angular-velocity which, when applied to the initial orientation, yields eventually the final orientation regardless of what angular velocity generated the latter. Finally, the extension of the theorem is demonstrated in a four-dimensional numerical example.
Nonrenormalization Theorems without Supersymmetry.
Cheung, Clifford; Shen, Chia-Hsien
2015-08-14
We derive a new class of one-loop nonrenormalization theorems that strongly constrain the running of higher dimension operators in a general four-dimensional quantum field theory. Our logic follows from unitarity: cuts of one-loop amplitudes are products of tree amplitudes, so if the latter vanish then so too will the associated divergences. Finiteness is then ensured by simple selection rules that zero out tree amplitudes for certain helicity configurations. For each operator we define holomorphic and antiholomorphic weights, (w,w[over ¯])=(n-h,n+h), where n and h are the number and sum over helicities of the particles created by that operator. We argue that an operator O_{i} can only be renormalized by an operator O_{j} if w_{i}≥w_{j} and w[over ¯]_{i}≥w[over ¯]_{j}, absent nonholomorphic Yukawa couplings. These results explain and generalize the surprising cancellations discovered in the renormalization of dimension six operators in the standard model. Since our claims rely on unitarity and helicity rather than an explicit symmetry, they apply quite generally. PMID:26317712
Kharitonov's theorem: Generalizations and algorithms
NASA Technical Reports Server (NTRS)
Rublein, George
1989-01-01
In 1978, the Russian mathematician V. Kharitonov published a remarkably simple necessary and sufficient condition in order that a rectangular parallelpiped of polynomials be a stable set. Here, stable is taken to mean that the polynomials have no roots in the closed right-half of the complex plane. The possibility of generalizing this result was studied by numerous authors. A set, Q, of polynomials is given and a necessary and sufficient condition that the set be stable is sought. Perhaps the most general result is due to Barmish who takes for Q a polytope and proceeds to construct a complicated nonlinear function, H, of the points in Q. With the notion of stability which was adopted, Barmish asks that the boundary of the closed right-half plane be swept, that the set G is considered = to (j(omega)(bar) - infinity is less than omega is less than infinity) and for each j(omega)(sigma)G, require H(delta) is greater than 0. Barmish's scheme has the merit that it describes a true generalization of Kharitonov's theorem. On the other hand, even when Q is a polyhedron, the definition of H requires that one do an optimization over the entire set of vertices, and then a subsequent optimization over an auxiliary parameter. In the present work, only the case where Q is a polyhedron is considered and the standard definition of stability described, is used. There are straightforward generalizations of the method to the case of discrete stability or to cases where certain root positions are deemed desirable. The cases where Q is non-polyhedral are less certain as candidates for the method. Essentially, a method of geometric programming was applied to the problem of finding maximum and minimum angular displacements of points in the Nyquist locus (Q(j x omega)(bar) - infinity is less than omega is less than infinity). There is an obvious connection with the boundary sweeping requirement of Barmish.
Noether’s theorem for dissipative quantum dynamical semi-groups
Gough, John E.; Ratiu, Tudor S.; Smolyanov, Oleg G.
2015-02-15
Noether’s theorem on constants of the motion of dynamical systems has recently been extended to classical dissipative systems (Markovian semi-groups) by Baez and Fong [J. Math. Phys. 54, 013301 (2013)]. We show how to extend these results to the fully quantum setting of quantum Markov dynamics. For finite-dimensional Hilbert spaces, we construct a mapping from observables to completely positive maps that leads to the natural analogue of their criterion of commutativity with the infinitesimal generator of the Markov dynamics. Using standard results on the relaxation of states to equilibrium under quantum dynamical semi-groups, we are able to characterise the constants of the motion under quantum Markov evolutions in the infinite-dimensional setting under the usual assumption of existence of a stationary strictly positive density matrix. In particular, the Noether constants are identified with the fixed point of the Heisenberg picture semi-group.
Local virial and tensor theorems.
Cohen, Leon
2011-11-17
We show that for any wave function and potential the local virial theorem can always be satisfied 2K(r) = r·ΔV by choosing a particular expression for the local kinetic energy. In addition, we show that for each choice of local kinetic energy there are an infinite number of quasi-probability distributions which will generate the same expression. We also consider the local tensor virial theorem. PMID:21863837
Generalized acceleration theorem for spatiotemporal Bloch waves
Arlinghaus, Stephan; Holthaus, Martin
2011-08-01
A representation is put forward for wave functions of quantum particles in periodic lattice potentials subjected to homogeneous time-periodic forcing, based on an expansion with respect to Bloch-like states which embody both the spatial and the temporal periodicity. It is shown that there exists a generalization of Bloch's famous acceleration theorem which grows out of this representation and captures the effect of a weak probe force applied in addition to a strong dressing force. Taken together, these elements point at a ''dressing and probing'' strategy for coherent wave-packet manipulation, which could be implemented in present experiments with optical lattices.
Penrose's singularity theorem in a Finsler spacetime
NASA Astrophysics Data System (ADS)
Babak Aazami, Amir; Javaloyes, Miguel Angel
2016-01-01
We translate Penrose's singularity theorem to a Finsler spacetime. To that end, causal concepts in Lorentzian geometry are extended, including definitions and properties of focal points and trapped surfaces, with careful attention paid to the differences that arise in the Finslerian setting. This activity is supported by the programme 'Young leaders in research' 18942/JLI/13 by Fundación Séneca, Regional Agency for Science and Technology from the Region of Murcia, and by the World Premier International Research Center Initiative (WPI), MEXT, Japan.
An evaluation based theorem prover
Degano, P.; Sirovich, F.
1985-01-01
A noninductive method for mechanical theorem proving is presented, which deals with a recursive class of theorems involving iterative functions and predicates. The method is based on the symbolic evaluation of the formula to be proved and requires no inductive step. Induction is avoided since a metatheorem is proved which establishes the conditions on the evaluation of any formula which are sufficient to assure that the formula actually holds. The proof of a supposed theorem consists in evaluating the formula and checking the conditions. The method applies to assertions that involve element-by-element checking of typed homogeneous sequences which are hierarchically constructed out of the primitive type consisting of the truth values. The sequences can be computed by means of iterative and ''accumulator'' functions. The paper includes the definition of a simple typed iterative language in which both predicates and functions are expressed. The language precisely defines the scope of the proof method. The method proves a wide variety of theorems about iterative functions on sequences, including that which states that REVERSE is its own inverse, and that it can be inversely distributed on APPEND, that FLATTEN can be distributed on APPEND and that each element of any sequence is a MEMBER of the sequence itself. Although the method is not complete, it does provide the basis for an extremely efficient tool to be used in a complete mechanical theorem prover.
Nambu-Goldstone theorem and spin-statistics theorem
NASA Astrophysics Data System (ADS)
Fujikawa, Kazuo
2016-05-01
On December 19-21 in 2001, we organized a yearly workshop at Yukawa Institute for Theoretical Physics in Kyoto on the subject of “Fundamental Problems in Field Theory and their Implications”. Prof. Yoichiro Nambu attended this workshop and explained a necessary modification of the Nambu-Goldstone theorem when applied to non-relativistic systems. At the same workshop, I talked on a path integral formulation of the spin-statistics theorem. The present essay is on this memorable workshop, where I really enjoyed the discussions with Nambu, together with a short comment on the color freedom of quarks.
New double soft emission theorems
NASA Astrophysics Data System (ADS)
Cachazo, Freddy; He, Song; Yuan, Ellis Ye
2015-09-01
We study the behavior of the tree-level S-matrix of a variety of theories as two particles become soft. By analogy with the recently found subleading soft theorems for gravitons and gluons, we explore subleading terms in double soft emissions. We first consider double soft scalar emissions and find subleading terms that are controlled by the angular momentum operator acting on hard particles. The order of the subleading theorems depends on the presence or not of color structures. Next we obtain a compact formula for the leading term in a double soft photon emission. The theories studied are a special Galileon, Dirac-Born-Infeld, Einstein-Maxwell-Scalar, nonlinear sigma model and Yang-Mills-Scalar. We use the recently found Cachazo-He-Yuan representation of these theories in order to give a simple proof of the leading order part of all these theorems.
Khinchin Theorem and Anomalous Diffusion
NASA Astrophysics Data System (ADS)
Lapas, Luciano C.; Morgado, Rafael; Vainstein, Mendeli H.; Rubí, J. Miguel; Oliveira, Fernando A.
2008-12-01
A recent Letter [M. H. Lee, Phys. Rev. Lett. 98, 190601 (2007)PRLTAO0031-900710.1103/PhysRevLett.98.190601] has called attention to the fact that irreversibility is a broader concept than ergodicity, and that therefore the Khinchin theorem [A. I. Khinchin, Mathematical Foundations of Statistical Mechanics (Dover, New York, 1949)] may fail in some systems. In this Letter we show that for all ranges of normal and anomalous diffusion described by a generalized Langevin equation the Khinchin theorem holds.
Generalized Bezout's Theorem and its applications in coding theory
NASA Technical Reports Server (NTRS)
Berg, Gene A.; Feng, Gui-Liang; Rao, T. R. N.
1996-01-01
This paper presents a generalized Bezout theorem which can be used to determine a tighter lower bound of the number of distinct points of intersection of two or more curves for a large class of plane curves. A new approach to determine a lower bound on the minimum distance (and also the generalized Hamming weights) for algebraic-geometric codes defined from a class of plane curves is introduced, based on the generalized Bezout theorem. Examples of more efficient linear codes are constructed using the generalized Bezout theorem and the new approach. For d = 4, the linear codes constructed by the new construction are better than or equal to the known linear codes. For d greater than 5, these new codes are better than the known codes. The Klein code over GF(2(sup 3)) is also constructed.
Angle Defect and Descartes' Theorem
ERIC Educational Resources Information Center
Scott, Paul
2006-01-01
Rene Descartes lived from 1596 to 1650. His contributions to geometry are still remembered today in the terminology "Descartes' plane". This paper discusses a simple theorem of Descartes, which enables students to easily determine the number of vertices of almost every polyhedron. (Contains 1 table and 2 figures.)
Generalized Pump-restriction Theorem
Sinitsyn, Nikolai A; Chernyak, Vladimir Y
2008-01-01
We formulate conditions under which periodic modulations of parameters on a finite graph with stochastic transitions among its nodes do not lead to overall pump currents through any given link. Our theorem unifies previously known results with the new ones and provides a universal approach to explore futher restrictions on stochastic pump effect in non-adiabatically driven systems with detailed balance.
Expanding the Interaction Equivalency Theorem
ERIC Educational Resources Information Center
Rodriguez, Brenda Cecilia Padilla; Armellini, Alejandro
2015-01-01
Although interaction is recognised as a key element for learning, its incorporation in online courses can be challenging. The interaction equivalency theorem provides guidelines: Meaningful learning can be supported as long as one of three types of interactions (learner-content, learner-teacher and learner-learner) is present at a high level. This…
Discovering the Inscribed Angle Theorem
ERIC Educational Resources Information Center
Roscoe, Matt B.
2012-01-01
Learning to play tennis is difficult. It takes practice, but it also helps to have a coach--someone who gives tips and pointers but allows the freedom to play the game on one's own. Learning to act like a mathematician is a similar process. Students report that the process of proving the inscribed angle theorem is challenging and, at times,…
Illustrating the Central Limit Theorem
ERIC Educational Resources Information Center
Corcoran, Mimi
2016-01-01
Statistics is enjoying some well-deserved limelight across mathematics curricula of late. Some statistical concepts, however, are not especially intuitive, and students struggle to comprehend and apply them. As an AP Statistics teacher, the author appreciates the central limit theorem as a foundational concept that plays a crucial role in…
Equivalence theorem and infrared divergences
Torma, T.
1996-08-01
We look at the equivalence theorem as a statement about the absence of polynomial infrared divergences when {ital m}{sub {ital W}}{r_arrow}0. We prove their absence in a truncated toy model and conjecture that, if they exist at all, they are due to couplings between light particles. {copyright} {ital 1996 The American Physical Society.}
NASA Astrophysics Data System (ADS)
Lavin, Alicia; Cano, Daniel; González-Pola, Cesar; Tel, Elena; Rodriguez, Carmen; Ruiz, Manuel; Somavilla, Raquel
2015-04-01
, but Dissolved Oxygen sensor is also problematic. Periods of realistic smooth variations present strong offset that is corrected based on the Winkler analysis of water samples. The incorporation of these observatories on larger scale research programs, as done in 2003 in the framework of the VACLAN and COVACLAN projects, is important in order to provide them with a larger spatial dimension and maximize its utility for process-oriented studies. In 2003, the Santander section was extended 90 miles offshore in the framework of a large-scale hydrographic and circulation monitoring program. Partnerships in a large EU project as FixO3 has provided tools for coordination, homogenization and data validation as well as improve the use of chemical-biological data.
Investigating the Fundamental Theorem of Calculus
ERIC Educational Resources Information Center
Johnson, Heather L.
2010-01-01
The fundamental theorem of calculus, in its simplified complexity, connects differential and integral calculus. The power of the theorem comes not merely from recognizing it as a mathematical fact but from using it as a systematic tool. As a high school calculus teacher, the author developed and taught lessons on this fundamental theorem that were…
A Fundamental Theorem on Particle Acceleration
Xie, Ming
2003-05-01
A fundamental theorem on particle acceleration is derived from the reciprocity principle of electromagnetism and a rigorous proof of the theorem is presented. The theorem establishes a relation between acceleration and radiation, which is particularly useful for insightful understanding of and practical calculation about the first order acceleration in which energy gain of the accelerated particle is linearly proportional to the accelerating field.
Pythagorean Theorem Proofs: Connecting Interactive Websites
ERIC Educational Resources Information Center
Lin, Cheng-Yao
2007-01-01
There are over 400 proofs of the Pythagorean Theorem. Some are visual proofs, others are algebraic. This paper features several proofs of the Pythagorean Theorem in different cultures--Greek, Chinese, Hindu and American. Several interactive websites are introduced to explore ways to prove this beautiful theorem. (Contains 8 figures.)
Generalizations of Ptolemy and Brahmagupta Theorems
ERIC Educational Resources Information Center
Ayoub, Ayoub B.
2007-01-01
The Greek astronomer Ptolemy of Alexandria (second century) and the Indian mathematician Brahmagupta (sixth century) each have a significant theorem named after them. Both theorems have to do with cyclic quadrilaterals. Ptolemy's theorem states that: In a cyclic quadrilateral, the product of the diagonals is equal to the sum of the products of two…
Lin, C.; Kalyuzhnyi, Y.V. |; Stell, G.
1998-04-01
A multidensity integral-equation theory for polymerization into freely jointed hard-sphere homonuclear chain fluids proposed earlier [J. Chem. Phys. {bold 106}, 1940 (1997)] is extended to the case of multicomponent heteronuclear chain polymerization. The theory is based on the analytical solution of the polymer Percus{endash}Yevick (PPY) approximation for the totally flexible sticky two-point (S2P) model of associating fluids. The model consists of an n-component mixture of hard spheres of different sizes with species 2,{hor_ellipsis},n{minus}1 bearing two sticky sites A and B, randomly distributed on its surface, and species 1 and n with only one B and A site per particle, respectively. Due to some specific restrictions imposed on the possibility of forming bonds between particles of various species, the present version of the S2P model represents an associating fluid that is able to polymerize into a mixture of heteronuclear chain macromolecules. The structural properties of such a model are studied in the complete-association limit and compared with computer-simulation results for homonuclear hard-sphere chain mixtures, symmetrical diblock copolymers, alternating copolymers, and homonuclear hard-sphere chains in a hard-sphere solvent. Some results for the case of partial association are also presented. The PPY theory represents a quantitatively successful theory for the mixtures of short homonuclear chains and the short copolymer systems studied here. We also expect that the theory will prove to be of the same order of accuracy in investigating the case of partial association. {copyright} {ital 1998 American Institute of Physics.}
Navier Stokes Theorem in Hydrology
NASA Astrophysics Data System (ADS)
Narayanan, M.
2005-12-01
In a paper presented at the 2004 AGU International Conference, the author outlined and stressed the importance of studying and teaching certain important mathematical techniques while developing a course in Hydrology and Fluid Mechanics. The Navier-Stokes equations are the foundation of fluid mechanics, and Stokes' theorem is used in nearly every branch of mechanics as well as electromagnetics. Stokes' Theorem also plays a vital role in many secondary theorems such as those pertaining to vorticity and circulation. Mathematically expressed, Stokes' theorem can be expressed by considering a surface S having a bounding curve C. Here, V is any sufficiently smooth vector field defined on the surface and its bounding curve C. In an article entitled "Corrections to Fluid Dynamics" R. F. Streater, (Open Systems and Information Dynamics, 10, 3-30, 2003.) proposes a kinetic model of a fluid in which five macroscopic fields, the mass, energy, and three components of momentum, are conserved. The dynamics is constructed using the methods of statistical dynamics, and results in a non-linear discrete-time Markov chain for random fields on a lattice. In the continuum limit he obtains a non-linear coupled parabolic system of field equations, showing a correction to the Navier-Stokes equations. In 2001, David Hoff published an article in Journees Equations aux derivees partielles. (Art. No. 7, 9 p.). His paper is entitled : Dynamics of Singularity Surfaces for Compressible Navier-Stokes Flows in Two Space Dimensions. In his paper, David Hoff proves the global existence of solutions of the Navier-Stokes equations of compressible, barotropic flow in two space dimensions with piecewise smooth initial data. These solutions remain piecewise smooth for all time, retaining simple jump discontinuities in the density and in the divergence of the velocity across a smooth curve, which is convected with the flow. The strengths of these discontinuities are shown to decay exponentially in time
Recursion relations from soft theorems
NASA Astrophysics Data System (ADS)
Luo, Hui; Wen, Congkao
2016-03-01
We establish a set of new on-shell recursion relations for amplitudes satisfying soft theorems. The recursion relations can apply to those amplitudes whose additional physical inputs from soft theorems are enough to overcome the bad large- z behaviour. This work is a generalization of the recursion relations recently obtained by Cheung et al. for amplitudes in scalar effective field theories with enhanced vanishing soft behaviours, which can be regarded as a special case of those with non-vanishing soft limits. We apply the recursion relations to tree-level amplitudes in various theories, including amplitudes in the Akulov-Volkov theory and amplitudes containing dilatons of spontaneously-broken conformal symmetry.
A generalization of Bernoulli's theorem
Schaer, C. )
1993-05-15
The conservation of potential vorticity Q can be expressed as [partial derivative]([rho]Q)/[partial derivative]t + [del] [center dot] J = 0, where J denotes the total flux of potential vorticity. It is shown that J is related under statistically steady conditions to the Bernoulli function B by J = [del] [theta] [times] [del] B, where [theta] is the potential temperature. This relation is valid even in the nonhydrostatic limit and in the presence of arbitrary nonconservative forces (such as internal friction) and heating rates. In essence, it can be interpreted as a generalization of Bernoulli's theorem to the frictional and diabatic regime. The classical Bernoulli theorem-valid for inviscid adiabatic and steady flows-states that the intersections of surfaces at constant potential temperature and constant Bernoulli function yield streamlines. In the presence of frictional and diabatic effects, these intersections yield the flux lines along which potential vorticity is transported. 18 refs., 2 figs.
A Randomized Central Limit Theorem
NASA Astrophysics Data System (ADS)
Eliazar, Iddo; Klafter, Joseph
2010-05-01
The Central Limit Theorem (CLT), one of the most elemental pillars of Probability Theory and Statistical Physics, asserts that: the universal probability law of large aggregates of independent and identically distributed random summands with zero mean and finite variance, scaled by the square root of the aggregate-size (√{n}), is Gaussian. The scaling scheme of the CLT is deterministic and uniform - scaling all aggregate-summands by the common and deterministic factor √{n}. This Letter considers scaling schemes which are stochastic and non-uniform, and presents a "Randomized Central Limit Theorem" (RCLT): we establish a class of random scaling schemes which yields universal probability laws of large aggregates of independent and identically distributed random summands. The RCLT universal probability laws, in turn, are the one-sided and the symmetric Lévy laws.
Aging Wiener-Khinchin Theorem.
Leibovich, N; Barkai, E
2015-08-21
The Wiener-Khinchin theorem shows how the power spectrum of a stationary random signal I(t) is related to its correlation function ⟨I(t)I(t+τ)⟩. We consider nonstationary processes with the widely observed aging correlation function ⟨I(t)I(t+τ)⟩∼t(γ)ϕ(EA)(τ/t) and relate it to the sample spectrum. We formulate two aging Wiener-Khinchin theorems relating the power spectrum to the time- and ensemble-averaged correlation functions, discussing briefly the advantages of each. When the scaling function ϕ(EA)(x) exhibits a nonanalytical behavior in the vicinity of its small argument we obtain the aging 1/f-type of spectrum. We demonstrate our results with three examples: blinking quantum dots, single-file diffusion, and Brownian motion in a logarithmic potential, showing that our approach is valid for a wide range of physical mechanisms. PMID:26340172
Extended Ehrenfest theorem with radiative corrections
NASA Astrophysics Data System (ADS)
de la Peña, L.; Cetto, A. M.; Valdés-Hernández, A.
2015-10-01
A set of basic evolution equations for the mean values of dynamical variables is obtained from the Fokker-Planck equation applied to the general problem of a particle subject to a random force. The specific case of stochastic electrodynamics is then considered, in which the random force is due to the zero-point radiation field. Elsewhere it has been shown that when this system reaches a state of energy balance, it becomes controlled by an equation identical to Schrödinger’s, if the radiationless approximation is made. The Fokker-Planck equation was shown to lead to the Ehrenfest theorem under such an approximation. Here we show that when the radiative terms are not neglected, an extended form of the Ehrenfest equation is obtained, from which follow, among others, the correct formulas for the atomic lifetimes and the (nonrelativistic) Lamb shift.