Extract of the Chinese herbal formula Huo Luo Xiao Ling Dan inhibited adjuvant arthritis in rats
Zhang, Rui-Xin; Fan, Arthur Yin; Zhou, An-Nan; Moudgil, Kamal D.; Ma, Zhong-Ze; Lee, David Yue-Wei; Fong, Harry HS; Berman, Brian M.; Lao, Lixing
2010-01-01
Ethnopharmacological relevance The herbal formula Huo Luo Xiao Ling Dan (HLXL) and its modifications have been used in traditional Chinese medicine for about one hundred years to alleviate pain and inflammation. Aim To investigate the effects of HLXL on complete Freund’s adjuvant (CFA)-induced multiple-joint arthritis in rats. Materials and Methods Male Lewis rats, 190–210g, were immunized subcutaneously at the base of the tail with 200 µl of heat-killed M. tuberculosis in mineral oil (5 mg/ml). HLXL (2.30g/kg and 4.60g/kg) or vehicle control (n=8 per group) was administered orally (i.g.) once a day between days 16–25 post-CFA injection. The rats were observed for signs of arthritis with arthritic changes (erythema, edema, induration) being scored on a scale of 0 to 4 of increasing severity using a standard scoring system. The maximum arthritis score per rat was 16. A plethysmometer was used to measure edema volume in each paw. Adverse effects of HLXL were monitored by closely observing the animals for unusual behavioral changes. Levels of tumor necrosis factor alpha (TNF-α) and interleukin 1 beta (IL-1β) in local tissue were measured by enzyme-linked immunosorbent assay on day 25 post-CFA. Results HLXL significantly decreased arthritis scores between days 23–25 in the 2.30g/kg group and 21–25 in the 4.60g/kg group (p<0.05). It reduced paw edema on days 22 and 24 in the 2.30g/kg group and on days 20, 22 and 24 in the 4.60g/kg group compared to control (p<0.05). Local tissue TNF-α and IL-1β levels on day 25 post-CFA injection were significantly (p<0.05) lower in rats treated with HLXL than in control rats. No observable adverse effects were found. Conclusion The data suggest that HLXL produces significant anti-arthritic effects that may be mediated by suppressing pro-inflammatory cytokines, and it appears to be safe. PMID:19100323
Yang, Ying-Hua; Rajaiah, Rajesh; Lee, David Y.-W; Ma, Zhongze; Yu, Hua; Fong, Harry H. S.; Lao, Lixing; Berman, Brian M.; Moudgil, Kamal D.
2011-01-01
Rheumatoid arthritis (RA) is one of the major autoimmune diseases of global prevalence. The use of the anti-inflammatory drugs for the treatment of RA is associated with severe adverse reactions and toxicity. This limitation has necessitated the search for novel therapeutic products. We report here a traditional Chinese medicine-based herbal formula, Huo luo xiao ling dan (HLXL), which has potent antiarthritic activity as validated in the rat adjuvant-induced arthritis (AA) model. HLXL (2.3 g/Kg) was fed to Lewis (RT.11) rats daily by gavage beginning at the onset of arthritis and then continued through the observation period. HLXL inhibited the severity of ongoing AA. This suppression of arthritis was associated with significant alterations in the T cell proliferative and cytokine responses as well as the antibody response against the disease-related antigen, mycobacterial heat-shock protein 65 (Bhsp65). There was a reduction in the level of the proinflammatory cytokines IL-17 and IL-1β but enhancement of the anti-inflammatory cytokine IL-10 level. In addition, there was inhibition of both the anti-Bhsp65 antibody response and the serum level of nitric oxide. Thus, HLXL is a promising CAM modality for further testing in RA patients. PMID:20981317
Han, Xiang-Dong; Zhou, Zhi-Wei; Yang, Wei; Ye, Hang-Cheng; Xu, Ying-Zi; Huang, Yun-Feng; Zhang, Tong; Zhou, Shu-Feng
2015-01-01
Ischemic heart disease (IHD) is the leading cause of death worldwide and remains a major life-threatening factor in humans. Apoptosis has been implicated in the pathogenesis of IHD. The Chinese herbal formula Huo Luo Xiao Ling Dan (HLXLD), one of the commonly used Chinese herbal formulas, consists of Salviae miltiorrhizae, Angelica sinensis, Gummi olibanum, and Commiphora myrrha, with a wide spectrum of pharmacological activity. However, the mechanism of action and molecular targets of HLXLD in the treatment of IHD are unclear. This study aimed to computationally predict the molecular interactions between the major active components of HLXLD and key regulators of apoptosis and then examine the effect of HLXLD on coronary artery ligation-induced acute myocardial ischemia in rats. The molecular interactions between the major active components of HLXLD, including ferulic acid, ligustilide, succinic acid, vanillic acid, tanshinone IIA, tanshinone IIB, danshensu, salvianolic acid A, salvianolic acid C, protocatechuic aldehyde, and β-boswellic acid and human protein molecules including B cell lymphoma-extra large (Bcl-xl), B cell lymphoma 2 antagonist/killer 1 (Bak1), B cell lymphoma 2 (Bcl-2), procaspase 3, and caspase 9 with regard to hydrogen bond formation, charge interaction, and π-π stacking using Discovery Studio® program 3.1. The 12 HLXLD components were predicted by ADMET (absorption, distribution, metabolism, excretion and toxicity) Predictor to have favorable pharmacokinetic and low hepatotoxicity profiles. The acute myocardial ischemia was established by surgical ligation of the left anterior descending coronary artery. The rats were divided into a sham operative group, a model group, a positive control group treated with 0.2 mg/kg isosorbide mononitrate, and groups treated with 2.7, 5.4, or 10.8 g/kg HLXLD. The results showed that administration of HLXLD increased mean arterial pressure, left ventricular systolic pressure, heart rate, and maximal rate of
Wang, Fenrong; Wu, Yun; Ai, Yu; Bian, Qiaoxia; Ma, Wen; Lee, David Y-W; Dai, Ronghua
2016-03-01
Huo Luo Xiao Ling Dan (HLXLD), a Chinese herbal formula, is used in folk medicine for the treatment of arthritis and other chronic inflammatory diseases. However, the in vivo integrated metabolism of its multiple components remains unknown. In this paper, an ultra-performance liquid chromatography coupled with quadrupole time-of-flight tandem mass spectrometry (UPLC-Q-TOF-MS) method was developed for detection and identification of HLXLD metabolites in rat urine at high and normal clinical dosages. The prototype constituents and their metabolites in urine were analyzed. The mass measurements were accurate within 8 ppm, and subsequent fragment ions offered higher quality structural information for interpretation of the fragmentation pathways of various compounds. A total of 85 compounds were detected in high dosages urine samples by a highly sensitive extracted ion chromatograms method, including 31 parent compounds and 54 metabolites. Our results indicated that phase 2 reactions (e.g. glucuronidation, glutathionidation and sulfation) were the main metabolic pathways of lactones, alkaloids and flavones, while phase I reactions (e.g. hydrogenation and hydroxylation) were the major metabolic reaction for coumarins, paeoniflorin and iridoids. This investigation provided important structural information on the metabolism of HLXLD and provided scientific evidence to obtain a more comprehensive metabolic profile. PMID:26174205
Ma, Wen; Wang, Weihui; Peng, Yan; Bian, Qiaoxia; Wang, Nannan; Lee, David Y-W; Dai, Ronghua
2016-06-01
A fast, sensitive, and reliable ultra-high performance liquid chromatography with tandem mass spectrometry method has been developed and validated for the simultaneous quantitation and pharmacokinetic study of five phthalides (senkyunolide A, ligustilide, butylidenephthalide, 3-butylphthalide, and levistilide A) in rat plasma after oral administration of Huo Luo Xiao Ling Dan (HLXLD) or Angelica sinensis--Ligusticum chuanxiong herb pair (DG-CX) between normal and arthritis rats. After extraction from blood, the analytes and internal standard were subjected to ultra-high performance liquid chromatography with a Shim-pack XR-ODS column (75 × 3.0 mm(2) , 2.2 μm particles) and mobile phase was composed of methanol and water (containing 0.05% formic acid) under gradient elution conditions, with an electrospray ionization source in the positive ionization and multiple reaction monitoring mode. The lower limits of quantification were 0.192-0.800 ng/mL for all the analytes. Satisfactory linearity, precision, accuracy, mean extraction recovery, and acceptable matrix effect have been achieved. The validated method was successfully applied to a comparative pharmacokinetic study of five bioactive components in rat plasma after oral administration of HLXLD or DG-CX alone, respectively, between normal and arthritic rats. The results showed that there were unlike characters of pharmacokinetics among different groups. PMID:27062714
NASA Technical Reports Server (NTRS)
2002-01-01
[figure removed for brevity, see original site] (Released 12 July 2002) This image shows another example of an ancient channel in the Arabia Terra region of Mars. As with other channels observed on Mars, the geomorphology of Huo Hsing Vallis is suggestive of, and assumed to have been carved by, running water, although the fluid that flowed through these channels cannot be proven to have been water. This channel cuts through several layers of rocks. These rock layers may be sedimentary, composed of particles of other rocks that have been cemented together somehow, or they may be igneous layers, formed by the repeated eruption of lava (or some combination of sedimentary and igneous layers). The distinctive appearance of this terrain has led to its being described as 'etched'. Because the channel cuts through these rocks, the layered rocks must be older than the channel (see previous discussion of superposition). At the lower left side of the image, several intersecting ridges can be seen. These ridges may be inverted topography, or they may be exposed dikes, which form by linear intrusions of lava into rock underground; dikes are exposed by erosion of the overlying rock. The most recent activity in the region appears to be the formation of mega-ripples in the channel. Wind moving particles of rock forms these ripples perpendicular to the wind direction.
NASA Technical Reports Server (NTRS)
2002-01-01
(Released 5 June 2002) The Science A portion of an ancient channel called the Huo Hsing Vallis seen in the center of this image. As with all channel forms on Mars, it was carved by some moving fluid but that fluid can not automatically be assumed to be water. Lava and even wind can sculpt channel forms that mimic those of flowing water. In this case, the presence of pronounced oxbow bends in the channel favors the conclusion that water was the fluid. It is interesting that the ripple-like ridges on the channel floor mimic current ripples found in many streams on Earth. But the fluid responsible for their formation likely is the wind. Similar ripples occur in many places on Mars that have no relationship to channels. Surrounding the channel is an intensely eroded landscape known as etched terrain. The many layers that were deposited in the past are now being eroded away by the wind. In the process, unusual polygonal ridges are being exposed, the most prominent of which appear just north of the oxbow bends. The mechanism by with they form is poorly understood. It is possible that they began as polygonal troughs similar in form and origin as those that form in permafrost regions on Earth like the Canadian Arctic. If the troughs were subsequently filled in by sediment that solidified into a more resistant deposit than the surrounding material, later erosion would leave behind ridges in place of the former troughs. Known as inverted topography, there are examples of this type of landform in other etched terrains on Mars. The Story For thousands of years, many cultures the world over have studied the planets, first by observing their motions in the night sky, later through telescopes, and today through up-close observation enabled by spacecraft. Many places on Mars are given names that honor the long history of contributions by all peoples to Mars exploration. Huo Hsing, the Chinese word for the planet Mars, is the namesake of the ancient channel shown above. As with all
Chwuech Manimba: Indigenous Creative Education among Women of the Luo Community of Western Kenya
ERIC Educational Resources Information Center
Wadende, Pamela Akinyi
2011-01-01
The aim of this dissertation is to present the procedure and proceedings of an instructional research into the teaching and learning among Luo women of Western Kenya. The purposes of the research are threefold. First, it seeks to document a system of indigenous adult education that has proved sustainable among Luo women from generation to…
... it okay to feed my baby formula? Breast milk is the best source of nutrition for your ... will probably recommend a formula made from cow's milk. Some formulas are iron-fortified. This means they ...
Assessment of effect of Zhu-tan Tong-luo decoction on CYP450 isoforms activity of rats
Jin, Yongxi; Shao, Lingjiu; Li, Gaowen; Shao, Mengmeng; Zhi, Yinghao; Zhu, Wenzong
2015-01-01
In order to investigate the effects of Zhu-tan Tong-luo decoction on the metabolic capacity of cytochrome P450 (CYP) enzymes, a cocktail method was employed to evaluate the activities of CYP2B6, CYP2C19, CYP1A2, CYP3A4, CYP2C9, CYP2D6. The rats were randomly divided into acute Zhu-Tan Tong-Luo decoction group (Low, High), chronic Zhu-Tan Tong-Luo decoction group (Low, High) and control group. The acute group rats were given 0.6, 1.2 g/kg (Low, High) Zhu-tan Tong-luo decoction by intragastric administration for 1 day, and the chronic group for 14 days. Six probe drugs bupropion, omeprazole, phenacetin, testosterone, tolbutamide, and metroprolol were given to rats through intragastric administration, and the plasma concentrations were determined by UPLC-MS/MS. There statistical pharmacokinetics differences for omeprazole, phenacetin, testosterone, tolbutamide, and metroprolol in rats were observed by comparing acute Zhu-tan Tong-luo decoction group with control group; and statistical pharmacokinetics differences for bupropion, omeprazole, phenacetin, testosterone, tolbutamide, and metroprolol were observed by comparing chronic Zhu-Tan Tong-Luo decoction group with control group. After intragastric administration of Zhu-Tan Tong-Luo decoction may slightly induce the activities of CYP2B6, CYP2C19, CYP1A2, CYP3A4, CYP2C9, CYP2D6 of rats. Induction of drug metabolizing enzyme by Zhu-Tan Tong-Luo decoction would reduce the efficacy of other drug. Additional, there no statistical difference for biochemical results after 1 or 14 intragastric administration of Zhu-Tan Tong-Luo decoction. PMID:26629097
Lu, Ming-Xin
2012-11-01
ZHU Gong's Huo ren shu (A Book for Saving Life) is a famous work in the history of research on Treatise on Cold Damage Diseases. It has great influence on the study of cold pathogenic disease, especially that of the Song dynasty. Many authors reedited or annotated this book to inherit and developed the idea of the Huo ren shu. Thus, a lot of new books, including annotations, revisions, citations, or discussions, appeared. WANG Su's Zeng shi nan yang huo ren shu (Amplified Annotated Huorenshu), for example, is one of them. Those compiled as rhymes or knacks include XU Shu-wei's Shang han bai zheng ge (The Rhymes of Hundred Kinds of Cold Damage Disease), LI Zhi-xian's Huo ren shu kuo (Introduction to Huorenshu), QIAN Wen-li's Shang han bai wen ge (Hundred Questions on Cold Damage Disease), YANG Shi-ying's Shang han lei shu huo ren zong kuo (A General Introduction to Huorenshu, a Classified Book of Cold Damage Disease), and TANG Yin-cai's Shang han jie huo lun (Essay to Answering Suspicions on Cold Damage Disease). Those cited or inherited the book include LI Cheng's Shang han yao zhi (Gist of Cold Damage Disease), GUO Yong's Shang han bu wang lun (Supplements to Cold Damage Disease), SUN Zhi-ning's Shang han jian yao shi shuo (Ten Simple Discourses on Cold Damage Disease), and CHEN Zi-ming's Guan jian da quan liang fang (A Complete Effective Formulary with my Own Opinions). Those differentiating the essentials of the Huorenshu including CHENG Jiong's Huo ren shu bian (Differentiation for Huorenshu), and LU Zu-chang's Ni jin huo ren can tong yu yi (An Elaboration on Huorenshu to be Presented). All the above books indicate the impact of the Huorenshu, and show its influence on later ages as well. PMID:23363846
ERIC Educational Resources Information Center
Gardner, John C.
1974-01-01
Presents the mathematical formula devised by George O. Weber on budgeting for physical plants of colleges and universities. Uses four functions of administration, maintenance (operational), housekeeping/custodial, and grounds as a base. (Author/MLF)
Chen, Yan; Li, Jinlong; Li, Qiang; Wang, Tengteng; Xing, Lianping; Xu, Hao; Wang, Yongjun; Shi, Qi; Zhou, Quan; Liang, Qianqian
2016-01-01
To investigate whether Du-Huo-Ji-Sheng-Tang (DHJST) attenuate inflammation of RA related to lymphatic drainage function in vivo, we treated eight 3-month-old TNF-Tg mice with DHJST (12 g/kg) or the same volume of physiological saline once every day for 12 weeks, and 3-month-old WT littermates were used as negative control. After twelve weeks, we performed NIR-ICG imaging and found that DHJST increased the ICG clearance at the footpad and the pulse of efferent lymphatic vessel between popliteal lymph node and footpad. Histology staining at ankle joints showed that DHJST decreases synovial inflammation, bone erosion, cartilage erosion, and TRAP+ osteoclast area in TNF-Tg mice. Immunohistochemical staining by using anti-Lyve-1 and anti-podoplanin antibody showed that DHJST stimulated lymphangiogenesis in ankle joints of TNF-Tg mice. And zebrafish study suggested that DHJST promoted the formation of lymphatic thoracic duct. In conclusion, DHJST inhibits inflammation severity and promotes lymphangiogenesis and lymphatic drainage function of TNF-Tg mice. PMID:27239212
ERIC Educational Resources Information Center
Bosch, William; Sizzo, Jennifer; Curtis, Anita; Klein, Shannon; Micale, Cheryl; Lin, E-Sin
1997-01-01
Describes an activity presented in sports fishing magazines on developing a formula that predicts the weight in pounds of a game fish given its length in inches by using a TI-83 graphing calculator. Highlights the importance of using real-life problems and mathematical explorations. (ASK)
Subchronic 90-day oral (Gavage) toxicity study of a Luo Han Guo mogroside extract in dogs.
Qin, X; Xiaojian, S; Ronggan, L; Yuxian, W; Zhunian, T; Shouji, G; Heimbach, J
2006-12-01
A combined 28-day and 90-day oral (Gavage) study was conducted in male and female dogs to investigate the safety of PureLo, a non-caloric sweetener derived from the Chinese fruit Luo Han Guo, which achieves its sweetness from the presence of triterpene glycosides known as mogrosides. Three dogs of each sex were administered 10 mL/kg bw/day of either an aqueous solution providing 3000 mg/kg bw/day of PureLo or distilled water for either 28 days or 90 days. Measurements included clinical observations, body weight, food consumption, hematology, blood chemistry, urinalysis, gross necropsy, organ weight, and histopathology. There were no significant adverse effects on any of these measures. Based on the lack of toxicological effects in the study, the NOAEL for PureLo is 3000 mg/kg bw/day when administered to dogs by Gavage for 90 consecutive days. PMID:17011100
Operator splitting and adaptive mesh refinement for the Luo-Rudy I model
NASA Astrophysics Data System (ADS)
Trangenstein, John A.; Kim, Chisup
2004-05-01
We apply second-order operator splitting to the Luo-Rudy I model for electrical wave propagation in the heart. The purpose of the operator splitting is to separate the nonlinear but local reaction computations from the linear but globally coupled diffusion computations. This approach allows us to use local nonlinear iterations for the stiff nonlinear reactions and to solve global linear systems for the implicit treatment of diffusion. For computational efficiency, we use dynamically adaptive mesh refinement (AMR), involving hierarchies of unions of grid patches on distinct levels of refinement. The linear system for the discretization of the diffusion on the composite AMR grid is formulated via standard conforming finite elements on unions grid patches within a level of refinement and aligned mortar elements along interfaces between levels of refinement. The linear systems are solved iteratively by preconditioned conjugate gradients. Our preconditioner uses multiplicative domain decomposition between levels of refinement; the smoother involves algebraic additive domain decomposition between patches within a level of refinement, and Gauss-Seidel iteration within grid patches. Numerical results are presented in 1D and 2D, including spiral waves.
Topical treatment with Tong-Luo-San-Jie Gel alleviates bone cancer pain in rats
Wang, Juyong; Zhang, Ruixin; Dong, Changsheng; Jiao, Liying; Xu, Ling; Liu, Jiyong; Wang, Zhengtao; Ying, Qi Liang Mao; Fong, Harry; Lao, Lixing
2012-01-01
Ethnopharmacological relevance The herbal analgesic gel Tong-Luo-San-Jie (TLSJ) and its modifications are used in traditional Chinese medicine to manage cancer pain. However, its mechanisms are still unknown. Aim of the study To investigate the effects and mechanisms of TLSJ gel on bone cancer pain in a rat model. Materials and Methods A bone cancer pain rat model was established by inoculating Walker 256 rat carcinoma cells directly into the right tibial medullary cavity of Sprague-Dawley rats (150–170 g); Phosphate buffered saline (PBS) tibial inoculation was used as control. Cancer-bearing rats were treated twice a day with external TLSJ gel (0.5 g/cm2/day) or inert gel control for 21 days (n=10/group). Behavioral tests such as mechanical threshold and paw withdrawal latency (PWL) were carried out. Osteoclastic activities were determined and carboxyterminal pyridinoline cross-linked type I collagen telopeptides (ICTP) and bone-specific alkaline phosphatase (BAP) concentrations were detected with ELISA after treatment. Adverse effects were monitored, and biochemical and histological tests were performed in naïve rats treated with local TLSJ gel for six weeks. Results TLSJ treatment significantly restored bone cancer-induced decrease of PWL and mechanical threshold compared to inert gel. It also decreased the level of blood serum ICTP and BAP and inhibited osteoclast activities. No adverse effects or abnormal biochemical and histological changes were detected after TLSJ treatment. Conclusion The present study shows that TLSJ significantly inhibits bone cancer-induced thermal and mechanical sensitization. It suggests that the gel may be useful in managing cancer pain and that it may act by inhibiting osteoclastic activity. PMID:22960543
Yu, Yanyan; Tong, Qing; Ren, Ying; Jin, Zhe
2013-01-01
The purpose of this study was to explore the positive effects of Bu Shen Huo Xue Decoction (BSHXF) on assisted reproduction. The study aimed to evaluate whether BSHXD could improve endometrial morphology and increase the expression of LIF in a gonadotrophin-releasing hormone agonists (GnRHa) long protocol-induced rat model during metestrus, diestrus, proestrus, and oestrus. The BSHXD group presented significantly increased endometrium thickness and decreased MVD compared with the GnRHa long protocol group. In addition, the expression of LIF was significantly higher in the BSHXD group. There were no significant differences between the control group and the BSHXD group in terms of MVD and LIF expression. These results suggested that BSHXD can improve the endometrium development, reduce the abnormal angiogenesis, and increase the expression of receptivity markers in a GnRHa long protocol-induced rat model during the oestrous cycle, which might result in an endometrial environment better suited for female reproduction. PMID:23710223
NASA Astrophysics Data System (ADS)
Kanakov, O. I.; Osipov, G. V.; Chan, C.-K.; Kurths, J.
2007-03-01
We study collective phenomena in nonhomogeneous cardiac cell culture models, including one- and two-dimensional lattices of oscillatory cells and mixtures of oscillatory and excitable cells. Individual cell dynamics is described by a modified Luo-Rudy model with depolarizing current. We focus on the transition from incoherent behavior to global synchronization via cluster synchronization regimes as coupling strength is increased. These regimes are characterized qualitatively by space-time plots and quantitatively by profiles of local frequencies and distributions of cluster sizes in dependence upon coupling strength. We describe spatio-temporal patterns arising during this transition, including pacemakers, spiral waves, and complicated irregular activity.
... meet all their nutritional needs. Infant formulas include powders, concentrated liquids, and ready-to-use forms. ... it. Reflux formulas are pre-thickened with rice starch. They are usually needed only for infants with ...
Breastfeeding vs. Formula Feeding
... breastfeed your baby or bottle feed using infant formula . Health experts agree that breastfeeding is the healthiest ... is hungry. You do not need to make formula before feeding, worry about clean water, or carry ...
... 6 months of life, infants need only breast milk or formula to meet all their nutritional needs. ... 12 months old who are not drinking breast milk . While there are some differences, infant formulas sold ...
NASA Astrophysics Data System (ADS)
Chen, Weiwei; Huang, Hao; Chen, Rong; Feng, Shangyuan; Yu, Yun; Lin, Duo; Lin, Jia
2014-11-01
This study aimed to assess, through surface-enhanced Raman scattering (SERS) spectroscopy, the incorporation of calcium hydroxyapatite (CHA ~960 cm-1) and other biochemical substances in the repair of complete radial fractures in rabbits treated with or without Huo-Xue-Hua-Yu decoction (HXHYD) therapy. A total of 18 rabbits with complete radial fractures were randomly divided into two groups; one group was treated with HXHYD therapy and the other without therapy acted as a control. The animals were sacrificed at 15, 30 and 45 d after surgery. Specimens were routinely prepared for SERS measurement and high quality SERS spectra from a mixture of bone tissues and silver nanoparticles were obtained. The mineral-to-matrix ratios from the control and treated groups were calculated. Results showed that both deposition content of CHA measured by SERS spectroscopy and the mineral-to-matrix ratio in the treated group were always greater than those of the control group during the experiment, demonstrating that HXHYD therapy is effective in improving fracture healing and that SERS spectroscopy might be a novel tool to assess fracture healing.
NASA Astrophysics Data System (ADS)
Chen, Weiwei; Lin, Jia; Chen, Rong; Feng, Shangyuan; Yu, Yun; Lin, Duo; Huang, Meizhen; Shi, Hong; Huang, Hao
2015-04-01
We have evaluated the capabilities of surface-enhanced Raman scattering (SERS) technology for analyzing two Huo-Xue-Hua-Yu decoctions (HXHYDs) prepared according to different prescriptions. The aim of this study was to evaluate the relevance of SERS technology applied to decoction of traditional Chinese medicines (TCM). HXHYD I was prepared according to the original prescription; the same preparation method was used for the HXHYD II, except for the crudeweight ratio described in the original prescription. There was no Raman signal in conventional Raman spectra of HXHYDs. Silver nanoparticles were directly mixed with HXHYDs to enhance the Raman scattering of biochemical constituents, and high quality SERS spectra were obtained. Significant differences in SERS spectra between HXHYD I and II can be observed, which showed special changes in the percentage of biochemical constituents in different decoctions. Principal components analysis (PCA) combined with linear discriminant analysis (LDA) were employed to generate diagnostic algorithms for classification of SERS spectra of two HXHYDs, and showed that a diagnostic accuracy of 100% can be achieved. This work demonstrated that the SERS technique has potential for spectral characteristic detection for decoction of TCM with high sensitivity, and that this technique, combined with PCA-LDA, can be used for quality control of the extracted decoction of TCM and production management of Chinese herbal preparations.
ERIC Educational Resources Information Center
Zhao, Bo; Bradbury, Katharine
2009-01-01
This paper designs a new equalization-aid formula based on fiscal gaps of local communities. When states are in transition to a new local aid formula, the issue of whether and how to hold existing aid harmless poses a challenge. The authors show that some previous studies and the formulas derived from them give differential weights to existing and…
ERIC Educational Resources Information Center
Steen, Ralph W.; And Others
Explained and illustrated is the formula funding system used for colleges and universities in Texas. This system is considerably more complicated than the formulas used in other states. Data for institutions in the state system for fiscal 1978 are presented; actual appropriations are used rather than requests, and formula-produced amounts are…
NASA Technical Reports Server (NTRS)
Miller, Roy G
1927-01-01
The ultimate test of a load factor formula is experience. The chief advantages of a semi rational formula over arbitrary factors are that it fairs in between points of experience and it differentiates according to variables within a type. Structural failure of an airplane apparently safe according to the formula would call for a specific change in the formula. The best class of airplanes with which to check a load factor formula seems to be those which have experienced structural failure. Table I comprises a list of the airplanes which have experienced failure in flight traceable to the wing structure. The load factor by formula is observed to be greater than the designed strength in each case, without a single exception. Table II comprises the load factor by formula with the designed strength of a number of well-known service types. The formula indicates that by far the majority of these have ample structural strength. One case considered here in deriving a suitable formula is that of a heavy load carrier of large size and practically no reserve power.
ERIC Educational Resources Information Center
Bogdany, Melvin
This manual is designed to help baking students learn to use formulas in the preparation of baking products. Tested and proven formulas are, for the most part, standard ones with only slight modifications. The recipes are taken mainly from bakery product manufacturers and are presented in quantities suitable for school-shop use. Each recipe…
Zou, Da-Wei; Gao, Yan-Bin; Zhu, Zhi-Yao; Zhou, Hui; Zhang, Tao-Jing; Li, Bu-Man; Wang, Jin-Yang; Li, Min-Zhou; Ma, Ming-Fei; Zhang, Na
2013-01-01
Diabetic peripheral neuropathy (DPN) is a common microvascular complication of diabetes associated with high disability rate and low quality of life. Tang-Luo-Ning (TLN) is an effective traditional Chinese medicine for the treatment of DPN. To illustrate the underlying neural protection mechanisms of TLN, the effect of TLN on electrophysiology and sciatic nerve morphology was investigated in a model of streptozotocin-induced DPN, as well as the underlying mechanism. Sciatic motor nerve conduction velocity and digital sensory nerve conduction velocity were reduced in DPN and were significantly improved by TLN or α-lipoic acid at 10 and 20 weeks after streptozotocin injection. It was demonstrated that TLN intervention for 20 weeks significantly alleviated pathological injury as well as increased the phosphorylation of ErbB2, Erk, Bad (Ser112), and the mRNA expression of neuregulin 1 (Nrg1), GRB2-associated binding protein 1 (Gab1), and mammalian target of rapamycin (Mtor) in injured sciatic nerve. These novel therapeutic properties of TLN to promote Schwann cell survival may offer a promising alternative medicine for the patients to delay the progression of DPN. The underlying mechanism may be that TLN exerts neural protection effect after sciatic nerve injury through Nrg1/ErbB2→Erk/Bad Schwann cell survival signaling pathway. PMID:24288572
Breastfeeding vs. Formula Feeding
... Story" 5 Things to Know About Zika & Pregnancy Breastfeeding vs. Formula Feeding KidsHealth > For Parents > Breastfeeding vs. ... for you and your baby. continue All About Breastfeeding Nursing can be a wonderful experience for both ...
Readability Formulas: Pluses and Minuses.
ERIC Educational Resources Information Center
Rygiel, Mary Ann
1982-01-01
Examines readability formulas and examples of their misuse. Analyzes an essay by George Orwell which was given a grade 10 readability level by one formula and discusses characteristics of Orwell's style that refute the accuracy of formula rating. (HTH)
The Mystical "Quadratic Formula."
ERIC Educational Resources Information Center
March, Robert H.
1993-01-01
Uses projectile motion to explain the two roots found when using the quadratic formula. An example is provided for finding the time of flight for a projectile which has a negative root implying a negative time of flight. This negative time of flight also has a useful physical meaning. (MVL)
The Formula Essay Reconsidered
ERIC Educational Resources Information Center
Haluska, Jan
2012-01-01
Bruce Pirie offers the following criticism about formula essays: "What does a five-paragraph essay teach about writing? It teaches that there are rules, and that those rules take the shape of a preordained form, like a cookie-cutter, into which we can pour ideas and expect them to come out well shaped." He goes on to discredit such essays as being…
Research Timeline: Formulaic language
ERIC Educational Resources Information Center
Wray, Alison
2013-01-01
Creating a timeline for formulaic language is far from simple, because several partially independent lines of research have contributed to the emerging picture. Each exhibits cycles of innovation and consolidation over time: domains take a leading role in developing new knowledge and then fall back, while another area comes to the fore. Thus, some…
Introducing Chemical Formulae and Equations.
ERIC Educational Resources Information Center
Dawson, Chris; Rowell, Jack
1979-01-01
Discusses when the writing of chemical formula and equations can be introduced in the school science curriculum. Also presents ways in which formulae and equations learning can be aided and some examples for balancing and interpreting equations. (HM)
Budget Formulas and Model Building.
ERIC Educational Resources Information Center
Cope, Robert G.
Selected budget formulas currently in use for university operations are described as a background for examining a budgetary model that would provide for the integration of separate formulas. Data on the formulas were collected from states with system-wide coordinating boards that are responsible for budgetary reviews. The most common formula…
Positive quadrature formulas III
NASA Astrophysics Data System (ADS)
Peherstorfer, Franz
2008-12-01
First we discuss briefly our former characterization theorem for positive interpolation quadrature formulas (abbreviated qf), provide an equivalent characterization in terms of Jacobi matrices, and give links and applications to other qf, in particular to Gauss-Kronrod quadratures and recent rediscoveries. Then for any polynomial t_n which generates a positive qf, a weight function (depending on n ) is given with respect to which t_n is orthogonal to mathbb{P}_{n-1} . With the help of this result an asymptotic representation of the quadrature weights is derived. In general the asymptotic behaviour is different from that of the Gaussian weights. Only under additional conditions do the quadrature weights satisfy the so-called circle law. Corresponding results are obtained for positive qf of Radau and Lobatto type.
Quadrature formulas for Fourier coefficients
NASA Astrophysics Data System (ADS)
Bojanov, Borislav; Petrova, Guergana
2009-09-01
We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node formula for the Fourier-Tchebycheff coefficients given by Micchelli and Sharma and construct new Gaussian formulas for the Fourier coefficients of a function, based on the values of the function and its derivatives.
On generalized averaged Gaussian formulas
NASA Astrophysics Data System (ADS)
Spalevic, Miodrag M.
2007-09-01
We present a simple numerical method for constructing the optimal (generalized) averaged Gaussian quadrature formulas which are the optimal stratified extensions of Gauss quadrature formulas. These extensions exist in many cases in which real positive Kronrod formulas do not exist. For the Jacobi weight functions w(x)equiv w^{(alpha,beta)}(x)D(1-x)^alpha(1+x)^beta ( alpha,beta>-1 ) we give a necessary and sufficient condition on the parameters alpha and beta such that the optimal averaged Gaussian quadrature formulas are internal.
A note on generalized averaged Gaussian formulas
NASA Astrophysics Data System (ADS)
Spalevic, Miodrag
2007-11-01
We have recently proposed a very simple numerical method for constructing the averaged Gaussian quadrature formulas. These formulas exist in many more cases than the real positive Gauss?Kronrod formulas. In this note we try to answer whether the averaged Gaussian formulas are an adequate alternative to the corresponding Gauss?Kronrod quadrature formulas, to estimate the remainder term of a Gaussian rule.
A Salary Formula for Principals
ERIC Educational Resources Information Center
Gilbert, Michael B.
1975-01-01
When each administrative salary contract is negotiated individually, inequities creep in, many administrators feel. This article suggests a formula for determining principals' salaries based on education and experience, days of work, and responsibilities. (Editor)
Formulas for Image Factor Scores
ERIC Educational Resources Information Center
Hakstian, A. Ralph
1973-01-01
Formulas are presented in this paper for computing scores associated with factors of G, the image covariance matrix, under three conditions. The subject of the paper is restricted to "pure" image analysis. (Author/NE)
ERIC Educational Resources Information Center
Evans, Peter O.
1983-01-01
Presents the formula for writing poetry as containing three elements: the content of the poet's mind; the poetic medium--language; and the creative spark that fuses experience and language, or content and medium, into poetry. (MM)
Summation formulae on trigonometric functions
NASA Astrophysics Data System (ADS)
Wang, Xin; Zheng, De-Yin
2007-11-01
Trigonometric sums over the angles equally distributed on the upper half plane are investigated systematically. Their generating functions and explicit formulae are established through the combination of the formal power series method and partial fraction decompositions.
Heron's Remarkable Triangle Area Formula.
ERIC Educational Resources Information Center
Oliver, Bernard M.
1993-01-01
Presents Heron's original geometric proof to his formula to calculate the area of a triangle. Attempts to improve on this proof by supplying a chain of reasoning that leads quickly from premises to the conclusion. (MDH)
An energy loss straggling formula
NASA Astrophysics Data System (ADS)
Novković, D.; Subotić, K.; Milošević, Z.; Manić, S.; Stojanović, M.
1994-12-01
The analytical formulae for straggling widths were obtained solving Symon's equations for the second and third order central moments of the straggling distributions in non-relativistic approximation, enabling prediction of peak widths and asymmetry parameters of charged particle energy loss distributions for thick targets. The respective calculations based on these formulae were found to be in good agreement with experimental values for particle energy losses of light ions up to 70% of the nominal projectile energy value.
Infant Formula - Buying, Preparing, Storing, and Feeding
... page: //medlineplus.gov/ency/patientinstructions/000806.htm Infant Formula – Buying, Preparing, Storing, and Feeding To use the ... using infant formula . Buying, Preparing, and Storing Infant Formula The following tips can help you buy, prepare, ...
Zhang, Lin; Wu, Yiling; Jia, Zhenhua; Zhang, Yun; Shen, Hu Ying; Li Wang, Xing
2008-01-01
Background Tong-Xin-Luo (TXL) – a mixture of herbal extracts, has been used in Chinese medicine with established therapeutic efficacy in patients with coronary artery disease. Methods We investigated the protective role of TXL extracts on endothelial cells injured by a known risk factor – palmitic acid (PA), which is elevated in metabolic syndrome and associated with cardiovascular complications. Human aortic endothelial cells (HAECs) were preconditioned with TXL extracts before exposed to PA for 24 hours. Results We found that PA (0.5 mM) exposure induced 73% apoptosis in endothelial cells. However, when HAECs were preconditioned with ethanol extracted TXL (100 μg/ml), PA induced only 7% of the endothelial cells into apoptosis. Using antibody-based protein microarray, we found that TXL attenuated PA-induced activation of p38-MAPK stress pathway. To investigate the mechanisms involved in TXL's protective effects, we found that TXL reduced PA-induced intracellular oxidative stress. Through AMPK pathway, TXL restored the intracellular antioxidant system, which was depressed by the PA treatment, with an increased expression of thioredoxin and a decreased expression of the thioredoxin interacting protein. Conclusion In summary, our study demonstrates that TXL protects endothelial cells from PA-induced injury. This protection is likely mediated by boosting intracellular antioxidant capacity through AMPK pathway, which may account for the therapeutic efficacy in TXL-mediated cardiovascular protection. PMID:18625049
24 CFR 92.50 - Formula allocation.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 24 Housing and Urban Development 1 2011-04-01 2011-04-01 false Formula allocation. 92.50 Section 92.50 Housing and Urban Development Office of the Secretary, Department of Housing and Urban Development HOME INVESTMENT PARTNERSHIPS PROGRAM Allocation Formula § 92.50 Formula allocation. (a) Jurisdictions eligible for a formula allocation. HUD...
Readability Formulas--Fact or Fiction.
ERIC Educational Resources Information Center
Olson, Arthur V.
Four readability formulas were analyzed to determine the reading grade equivalence of instructional materials at the middle grades and above: the Dale-Chall formula, the Gunning-Fog Index, the Flesch Reading Ease Formula, and the McLaughlin SMOG Grading. In addition, Spache and Wheeler/Smith formulas were analyzed for evaluating primary grade…
27 CFR 17.121 - Product formulas.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Product formulas. 17.121... PRODUCTS Formulas and Samples § 17.121 Product formulas. (a) General. Except as provided in §§ 17.132 and 17.182, manufacturers shall file quantitative formulas for all preparations for which they intend...
27 CFR 25.57 - Formula information.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula information. 25.57... OF THE TREASURY LIQUORS BEER Miscellaneous Provisions Formulas § 25.57 Formula information. (a) Ingredient information. (1) For each formula you must list each separate ingredient and the specific...
CHY formula and MHV amplitudes
NASA Astrophysics Data System (ADS)
Du, Yi-Jian; Teng, Fei; Wu, Yong-Shi
2016-05-01
In this paper, we study the relation between the Cachazo-He-Yuan (CHY) formula and the maximal-helicity-violating (MHV) amplitudes of Yang-Mills and gravity in four dimensions. We prove that only one special rational solution of the scattering equations found by Weinzierl supports the MHV amplitudes. Namely, localized at this solution, the integrated CHY formula produces the Parke-Taylor formula for MHV Yang-Mills amplitudes as well as the Hodges formula for MHV gravitational amplitudes, with an arbitrary number of external gluons/gravitons. This is achieved by developing techniques, in a manifestly Möbius covariant formalism, to explicitly compute relevant reduced Pfaffians/determinants. We observe and prove two interesting properties (or identities), which facilitate the computations. We also check that all the other ( n - 3)! - 1 solutions to the scattering equations do not support the MHV amplitudes, and prove analytically that this is indeed true for the other special rational solution proposed by Weinzierl, that actually supports the anti-MHV amplitudes. Our results reveal a mysterious feature of the CHY formalism that in Yang-Mills and gravity theory, solutions of scattering equations, involving only external momenta, somehow know about the configuration of external polarizations of the scattering amplitudes.
Stature estimation formulae for Nigerians.
Didia, Blessing C; Nduka, Ethelbert C; Adele, Okechukwu
2009-01-01
In stature estimation, long limbs and the stature formula of Trotter and Gleser easily come to mind. In the recent past, a lot of workers have established formulae specific to their populations using whole length of limbs, fragmented bones, circumference of long bones, and even length of the vertebrae. We have in this work used tibia length, height of subjects, and the regression models to establish formulae specific to Nigerians. We measured height and tibia length of 200 (96 male and 104 female) adult Nigerians. The tibia length was measured from upper limit of the medial condoyle to the tip of medial malleolus using a measuring tape calibrated in meters while the height of individuals were also measured using meter scales. All measurements were made by one person, to avoid interobserver error, and repeatedly until a constant value is obtained. We obtained general formulae for males and females which compares favorably with that of Duyar and Pelin, and can be relied upon. PMID:19018931
Developing the Vertex Formula Meaningfully
ERIC Educational Resources Information Center
Nebesniak, Amy L.; Burgoa, A. Aaron
2015-01-01
As teachers working with students in entry-level algebra classes, authors Amy Nebesniak and A. Aaron Burgoa realized that their instruction was a major factor in how their students viewed mathematics. They often presented students with abstract formulas that seemed to appear out of thin air. One instance occurred while they were teaching students…
Financial Formulas for Library Networks.
ERIC Educational Resources Information Center
Hayes, Phoebe F.
Formulas for the fiscal support of library networks are discussed against the perspective of present patterns of library funding. Provisions for financing current cooperative library programs are illustrative of the problems which might be encountered in networks. Several proposals for network development have been concerned with and provide some…
Formulas for determining rotational constants
NASA Astrophysics Data System (ADS)
Guelachvili, G.
This document is part of Subvolume B `Linear Triatomic Molecules', Part 9, of Volume 20 `Molecular Constants mostly from Infrared Spectroscopy' of Landolt-Börnstein Group II `Molecules and Radicals'. Part of the introduction, it states formulas for determining rotational constants, band center, band origin, and quadrupole coupling. Specific comments relate to BHO (HBO) and COS (OCS).
Blackhole formula and example relativity
NASA Astrophysics Data System (ADS)
Shin, Philip
Black hole formula 1) Second dimension (x,y) f(x)=y Energy E=m*c2 2) Third dimension (x,y,z) really x=y=z Black hole formula Root(c2)=c=Root(E/m) As mass go the velocity of light, mass become black hole so there are energy as multiply by mass. Example relativity When E=m*c2 1) Root(c2)=c=Root(E/m) 2) 3*c*Root(c2)=3*c*Root(E/m)=3*c2 From 1) to 2) as an example, As velocity is faster, mass increased. It means when velocity is increased, sec(time) is slower, and m(distance) is increased. The number is good to study physics.
Trace formula for broken symmetry
Creagh, S.C.
1996-05-01
We derive a trace formula for systems that exhibit an approximate continuous symmetry. It interpolates between the sum over continuous families of periodic orbits that holds in the case of exact continuous symmetry, and the discrete sum over isolated orbits that holds when the symmetry is completely broken. It is based on a simple perturbation expansion of the classical dynamics, centered around the case of exact symmetry, and gives an approximation to the usual Gutzwiller formula when the perturbation is large. We illustrate the computation with some 2-dimensional examples: the deformation of the circular billiard into an ellipse, and anisotropic and anharmonic perturbations of a harmonic oscillator. Copyright {copyright} 1996 Academic Press, Inc.
Discretization formulas for unstructured grids
NASA Technical Reports Server (NTRS)
Baumeister, Kenneth J.
1988-01-01
The Galerkin weighted residual technique using linear triangular weight functions is employed to develop finite difference formula in cartesian coordinates for the Laplacian operator, first derivative operators and the function for unstructured triangular grids. The weighted residual coefficients associated with the weak formulation of the Laplacian operator are shown to agree with the Taylor series approach on a global average. In addition, a simple algorithm is presented to determine the Voronoi (finite difference) area of an unstructured grid.
Hydrolyzed Formula for Every Infant?
Fleischer, David M; Venter, Carina; Vandenplas, Yvan
2016-01-01
Presently, hydrolyzed formulas (HF) are used primarily in infants that cannot be exclusively breastfed, those with cow's milk allergy and for primary prevention of allergic disease, but HFs are increasingly being used worldwide, begging the question if they may be recommended as the optimal choice for all standard-risk, full-term, non-exclusively breastfed infants. Data regarding the nutritional adequacy of modern-day HFs are scarce and lack long-term data suggesting that growth in infants fed HF versus an intact protein formula (IPF) is different. While human breast milk is the optimal source of nutrition for multiple reasons, a 2006 systematic review determined there were no comparable long-term studies regarding prolonged use of HFs versus breastfeeding. Meta-analyses of formula consumption and risk of atopic dermatitis (AD) have found that infants fed partially HF compared to IPF had a lower risk of AD, but there are significant limitations to these studies, making conclusions about the general use of HFs problematic. Costs should be considered in decision-making regarding the choice of the formula, but global comparison of this is difficult given large cost differences in different countries. Despite the issues raised here, the desire to provide concrete recommendations of widespread HF use needs to be balanced carefully in order not to overstate claims of benefit. Long-term studies are needed to investigate the feasibility of HF as a routine feeding option for healthy, standard-risk infants. Because of the paucity of data, routine use of HF as an equivalent option to breastfeeding or IPF cannot be supported at present based on available scientific evidence. PMID:27336594
Composition formulas of binary eutectics
NASA Astrophysics Data System (ADS)
Ma, Y. P.; Dong, D. D.; Dong, C.; Luo, L. J.; Wang, Q.; Qiang, J. B.; Wang, Y. M.
2015-12-01
The present paper addresses the long-standing composition puzzle of eutectic points by introducing a new structural tool for the description of short-range-order structural unit, the cluster-plus-glue-atom model. In this model, any structure is dissociated into a 1st-neighbor cluster and a few glue atoms between the clusters, expressed by a cluster formula [cluster]gluex. This model is applied here to establish the structural model for eutectic liquids, assuming that a eutectic liquid consist of two subunits issued from the relevant eutectic phases, each being expressed by the cluster formula for ideal metallic glasses, i.e., [cluster](glue atom)1 or 3. A structural unit is then composed of two clusters from the relevant eutectic phases plus 2, 4, or 6 glue atoms. Such a dual cluster formulism is well validated in all boron-containing (except those located by the extreme phase diagram ends) and in some commonly-encountered binary eutectics, within accuracies below 1 at.%. The dual cluster formulas vary extensively and are rarely identical even for eutectics of close compositions. They are generally formed with two distinctly different cluster types, with special cluster matching rules such as cuboctahedron plus capped trigonal prism and rhombidodecahedron plus octahedral antiprism.
Composition formulas of binary eutectics.
Ma, Y P; Dong, D D; Dong, C; Luo, L J; Wang, Q; Qiang, J B; Wang, Y M
2015-01-01
The present paper addresses the long-standing composition puzzle of eutectic points by introducing a new structural tool for the description of short-range-order structural unit, the cluster-plus-glue-atom model. In this model, any structure is dissociated into a 1(st)-neighbor cluster and a few glue atoms between the clusters, expressed by a cluster formula [cluster]gluex. This model is applied here to establish the structural model for eutectic liquids, assuming that a eutectic liquid consist of two subunits issued from the relevant eutectic phases, each being expressed by the cluster formula for ideal metallic glasses, i.e., [cluster](glue atom)(1 or 3). A structural unit is then composed of two clusters from the relevant eutectic phases plus 2, 4, or 6 glue atoms. Such a dual cluster formulism is well validated in all boron-containing (except those located by the extreme phase diagram ends) and in some commonly-encountered binary eutectics, within accuracies below 1 at.%. The dual cluster formulas vary extensively and are rarely identical even for eutectics of close compositions. They are generally formed with two distinctly different cluster types, with special cluster matching rules such as cuboctahedron plus capped trigonal prism and rhombidodecahedron plus octahedral antiprism. PMID:26658618
Composition formulas of binary eutectics
Ma, Y. P.; Dong, D. D.; Dong, C.; Luo, L. J.; Wang, Q.; Qiang, J. B.; Wang, Y. M.
2015-01-01
The present paper addresses the long-standing composition puzzle of eutectic points by introducing a new structural tool for the description of short-range-order structural unit, the cluster-plus-glue-atom model. In this model, any structure is dissociated into a 1st-neighbor cluster and a few glue atoms between the clusters, expressed by a cluster formula [cluster]gluex. This model is applied here to establish the structural model for eutectic liquids, assuming that a eutectic liquid consist of two subunits issued from the relevant eutectic phases, each being expressed by the cluster formula for ideal metallic glasses, i.e., [cluster](glue atom)1 or 3. A structural unit is then composed of two clusters from the relevant eutectic phases plus 2, 4, or 6 glue atoms. Such a dual cluster formulism is well validated in all boron-containing (except those located by the extreme phase diagram ends) and in some commonly-encountered binary eutectics, within accuracies below 1 at.%. The dual cluster formulas vary extensively and are rarely identical even for eutectics of close compositions. They are generally formed with two distinctly different cluster types, with special cluster matching rules such as cuboctahedron plus capped trigonal prism and rhombidodecahedron plus octahedral antiprism. PMID:26658618
Simple and Clear Proofs of Stirling's Formula
ERIC Educational Resources Information Center
Niizeki, Shozo; Araki, Makoto
2010-01-01
The purpose of our article is to show two simpler and clearer methods of proving Stirling's formula than the traditional and conventional ones. The distinction of our method is to use the simple trapezoidal formula.
NASA Astrophysics Data System (ADS)
He, Z.; Bao, M.; Zhao, Y. M.; Arima, A.
2014-11-01
In this paper we improve an empirical mass formula constructed by Jänecke and collaborators. This formula is enlightened by the Garvey-Kelson mass relations. The new version of the Jänecke formula reproduces 2275 atomic masses with neutron number N ≥10 and proton number Z ≥6 , at an average accuracy of 128 keV, by employing 576 parameters. The predictive power of our formula is exemplified by comparison with predicted results of other mass models.
24 CFR 92.50 - Formula allocation.
Code of Federal Regulations, 2014 CFR
2014-04-01
... 24 Housing and Urban Development 1 2014-04-01 2014-04-01 false Formula allocation. 92.50 Section 92.50 Housing and Urban Development Office of the Secretary, Department of Housing and Urban Development HOME INVESTMENT PARTNERSHIPS PROGRAM Allocation Formula § 92.50 Formula allocation....
24 CFR 92.50 - Formula allocation.
Code of Federal Regulations, 2013 CFR
2013-04-01
... 24 Housing and Urban Development 1 2013-04-01 2013-04-01 false Formula allocation. 92.50 Section 92.50 Housing and Urban Development Office of the Secretary, Department of Housing and Urban Development HOME INVESTMENT PARTNERSHIPS PROGRAM Allocation Formula § 92.50 Formula allocation....
24 CFR 92.50 - Formula allocation.
Code of Federal Regulations, 2012 CFR
2012-04-01
... 24 Housing and Urban Development 1 2012-04-01 2012-04-01 false Formula allocation. 92.50 Section 92.50 Housing and Urban Development Office of the Secretary, Department of Housing and Urban Development HOME INVESTMENT PARTNERSHIPS PROGRAM Allocation Formula § 92.50 Formula allocation....
A Quick Guide to Readability Formulas.
ERIC Educational Resources Information Center
Cramer, Eugene H.
1978-01-01
Six of the most widely used readability scales are briefly reviewed and their original source cited: the Dale-Chall Readability Formula, the Flesch "Reading Ease" Formula, the Fog Index, the Fry Readability Graph, the SMOG Grading Plan, and the Spache Readability Formula. (SJL)
Code of Federal Regulations, 2010 CFR
2010-07-01
... 28 Judicial Administration 1 2010-07-01 2010-07-01 false Formula grants. 38.2 Section 38.2 Judicial Administration DEPARTMENT OF JUSTICE EQUAL TREATMENT FOR FAITH-BASED ORGANIZATIONS § 38.2 Formula... cooperative agreement funded by a formula or block grant from the Department. As used in this section,...
27 CFR 24.196 - Formula required.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula required. 24.196... OF THE TREASURY LIQUORS WINE Production of Special Natural Wine § 24.196 Formula required. Before producing any special natural wine, the proprietor shall receive approval of the formula by which it is...
27 CFR 20.101 - Drafting formulas.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Drafting formulas. 20.101... OF THE TREASURY LIQUORS DISTRIBUTION AND USE OF DENATURED ALCOHOL AND RUM Formulas and Statements of Process Approval Policies § 20.101 Drafting formulas. (a) In preparing Form 5150.19, the...
27 CFR 24.201 - Formula required.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula required. 24.201... OF THE TREASURY LIQUORS WINE Production of Agricultural Wine § 24.201 Formula required. Before producing any agricultural wine, the proprietor shall obtain an approval of the formula and process by...
15 CFR 923.110 - Allocation formula.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 15 Commerce and Foreign Trade 3 2010-01-01 2010-01-01 false Allocation formula. 923.110 Section... Grants § 923.110 Allocation formula. (a) As required by subsection 306(a), the Secretary may make grants...) Allocation formula factors and weighting. Each State eligible to receive a financial assistance award...
7 CFR 251.7 - Formula adjustments.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 4 2010-01-01 2010-01-01 false Formula adjustments. 251.7 Section 251.7 Agriculture... GENERAL REGULATIONS AND POLICIES-FOOD DISTRIBUTION THE EMERGENCY FOOD ASSISTANCE PROGRAM § 251.7 Formula adjustments. Formula adjustments. (a) Commodity adjustments. The Department will make annual adjustments...
10 CFR 455.31 - Allocation formulas.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 10 Energy 3 2010-01-01 2010-01-01 false Allocation formulas. 455.31 Section 455.31 Energy... § 455.31 Allocation formulas. (a) Financial assistance for conducting technical assistance programs for... this section. (c) The allocation factor (K) shall be determined by the formula: EC14NO91.086 where,...
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula. 26.31 Section 26... States From Areas Other Than Puerto Rico and the Virgin Islands § 26.31 Formula. (a) The amount of excise.... The formula shall be as follows: (1) Multiply the total excise taxes collected on rum brought into...
25 CFR 273.31 - Distribution formula.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 25 Indians 1 2010-04-01 2010-04-01 false Distribution formula. 273.31 Section 273.31 Indians... formula. (a) Funds shall be distributed to eligible contractors based upon the number of eligible Indian... formula. (b) The Assistant Secretary may make exceptions to the provisions of paragraph (a) of...
24 CFR 574.130 - Formula allocations.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 24 Housing and Urban Development 3 2010-04-01 2010-04-01 false Formula allocations. 574.130... URBAN DEVELOPMENT COMMUNITY FACILITIES HOUSING OPPORTUNITIES FOR PERSONS WITH AIDS Formula Entitlements § 574.130 Formula allocations. (a) Data sources. HUD will allocate funds based on the number of cases...
27 CFR 24.211 - Formula required.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula required. 24.211... OF THE TREASURY LIQUORS WINE Production of Other Than Standard Wine § 24.211 Formula required. The proprietor who desires to produce wine other than standard wine shall first obtain approval of the formula...
Code of Federal Regulations, 2010 CFR
2010-04-01
... Denaturation § 19.452 Formulas. Spirits shall be denatured in accordance with formulas as authorized in 27 CFR... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formulas. 19.452 Section 19.452 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT...
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula. 20.91 Section 20... TREASURY LIQUORS DISTRIBUTION AND USE OF DENATURED ALCOHOL AND RUM Formulas and Statements of Process § 20.91 Formula. (a) Each article made with specially denatured spirits shall be made in accordance...
Code of Federal Regulations, 2010 CFR
2010-01-01
... 5 Administrative Personnel 3 2010-01-01 2010-01-01 false Formulas. 1315.17 Section 1315.17 Administrative Personnel OFFICE OF MANAGEMENT AND BUDGET OMB DIRECTIVES PROMPT PAYMENT § 1315.17 Formulas. (a) Rebate formula. (1) Agencies shall determine credit card payment dates based on an analysis of the...
The Funding of Community Colleges: Formulas & Governance
ERIC Educational Resources Information Center
Mullin, Christopher M.; Honeyman, David S.
2008-01-01
This study identified governing state entities charged with the development of a funding formula for community colleges. Analysis of the data revealed that 40 states utilized a funding formula. Twenty-one states had a "Higher Education" entity with governing control of the formula, 5 states had a "Community College" entity with distinct funding…
Algebraic Formulas for Areas between Curves.
ERIC Educational Resources Information Center
Gabai, Hyman
1982-01-01
Korean secondary school students preparing for college learn about a simple algebraic formula for area bounded by a parabola and line. The approach does not seem well-known among American students. It is noted that, while the formula derivations rely on integration, algebra students could use the formulas without proofs. (MP)
Exponential Formulae and Effective Operations
NASA Technical Reports Server (NTRS)
Mielnik, Bogdan; Fernandez, David J. C.
1996-01-01
One of standard methods to predict the phenomena of squeezing consists in splitting the unitary evolution operator into the product of simpler operations. The technique, while mathematically general, is not so simple in applications and leaves some pragmatic problems open. We report an extended class of exponential formulae, which yield a quicker insight into the laboratory details for a class of squeezing operations, and moreover, can be alternatively used to programme different type of operations, as: (1) the free evolution inversion; and (2) the soft simulations of the sharp kicks (so that all abstract results involving the kicks of the oscillator potential, become realistic laboratory prescriptions).
[Infant formulas and soy protein-based formulas: current data].
Bocquet, A; Bresson, J L; Briend, A; Chouraqui, J P; Darmaun, D; Dupont, C; Frelut, M L; Ghisolfi, J; Goulet, O; Putet, G; Rieu, D; Turck, D; Vidailhet, M
2001-11-01
For many years soy bean-based formulas (SBBF) were the only dietary product used for infants with cow's milk intolerance. At the present time, their place in infant nutrition is reduced as a result of the availability of new dietary products without lactose and/or cow's milk proteins and the recognition of soy bean protein allergy. There is no evidence that SBBF have any efficiency in infant colic. SBBF have no indication in the prevention of allergy, nor in premature infants' nutrition. Their main indication is the feeding of infants of vegetarian parents who do not want to use cow's milk products. Studies have shown that SBBF contain large quantities of phytoestrogens, particularly isoflavone. Because of experimental data suggesting a possible deleterious effect of phytoestrogens on the neuroendocrine maturation, the reduction of their content in SBBF must be considered. PMID:11760676
Formulaic Language in Alzheimer’s Disease
Bridges, Kelly Ann; Van Lancker Sidtis, Diana
2013-01-01
Background Studies of productive language in Alzheimer’s disease (AD) have focused on formal testing of syntax and semantics but have directed less attention to naturalistic discourse and formulaic language. Clinical observations suggest that individuals with AD retain the ability to produce formulaic language long after other cognitive abilities have deteriorated. Aims This study quantifies production of formulaic expressions in the spontaneous speech of individuals with AD. Persons with early- and late-onset forms of the disease were compared. Methods & Procedures Conversational language samples of individuals with early- (n = 5) and late-onset (n = 6) AD and healthy controls (n = 5) were analyzed to determine whether formulaic language, as measured by the number of words in formulaic expressions, differs between groups. Outcomes & Results Results indicate that individuals with AD, regardless of age of onset, used significantly more formulaic expressions than healthy controls. The early- and late-onset AD groups did not differ on formulaic language measures. Conclusions These findings contribute to a dual process model of cerebral function, which proposes differing processing principles for formulaic and novel expressions. In this model, subcortical areas, which remain intact into late in the progression of Alzheimer’s disease, play an important role in the production of formulaic language. Applications to clinical practice include identifying preserved formulaic language and providing informed counseling to patient and family. PMID:24187417
Cottingham formula and nucleon polarisabilities
NASA Astrophysics Data System (ADS)
Gasser, J.; Hoferichter, M.; Leutwyler, H.; Rusetsky, A.
2015-08-01
The difference between the electromagnetic self-energies of proton and neutron can be calculated with the Cottingham formula, which expresses the self-energies as an integral over the electroproduction cross sections - provided the nucleon matrix elements of the current commutator do not contain a fixed pole. We show that, under the same proviso, the subtraction function occurring in the dispersive representation of the virtual Compton forward scattering amplitude is determined by the cross sections. The representation in particular leads to a parameter-free sum rule for the nucleon polarisabilities. We evaluate the sum rule for the difference between the electric polarisabilities of proton and neutron by means of the available parameterisations of the data and compare the result with experiment.
Cosmological parallax-distance formula
NASA Astrophysics Data System (ADS)
Singal, Ashok K.
2015-09-01
The standard cosmological parallax-distance formula, as found in the literature, including text-books and reference books on cosmology, requires a correction. This correction stems from the fact that in the standard text-book derivation it has been ignored that any chosen baseline in a gravitationally bound system does not partake in the cosmological expansion. Though the correction is available in the literature for some time, the text-books still continue to use the older, incorrect formula, and its full implications are not yet fully realized. Apart from providing an alternate correct, closed-form expression that is more suitable and convenient for computations for certain limiting cases of FRW () world models, we also demonstrate how one can compute parallax distance for the currently favored flat-space accelerating-universe (, ) cosmologies. Further, we show that the correction in parallax distance at large redshifts could amount to a factor of three or even more. Moreover, even in an infinite universe the parallax distance does not increase indefinitely with redshift and that even the farthest possible observable point may have a finite parallax angle, a factor that needs to be carefully taken into account when using distant objects as the background field against which the parallax of a foreground object is to be measured. Some other complications that could arise in parallax measurements of a distant source, like that due to the deflection of incoming light by the gravitation field of the Sun and other planetary bodies in the solar system, are pointed out.
27 CFR 26.225 - Previously approved formulas.
Code of Federal Regulations, 2010 CFR
2010-04-01
... formulas. 26.225 Section 26.225 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE... Formulas for Products From the Virgin Islands § 26.225 Previously approved formulas. Any formula approved... voluntarily surrendered. Any person holding such a formula is not required to submit a new formula. If...
27 CFR 26.55 - Previously approved formulas.
Code of Federal Regulations, 2010 CFR
2010-04-01
... formulas. 26.55 Section 26.55 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE... Formulas for Products From Puerto Rico § 26.55 Previously approved formulas. Any formula approved on Form... surrendered. Any person holding such a formula is not required to submit a new formula. If an approved...
Rainfall intensity-duration-frequency formulas.
Chen, C.-L.
1983-01-01
A new general rainfall intensity-duration-frequency formula is presented, utilizing a method similar to, but more accurate than one previously developed. The previously developed formula was based on the average depth-duration ratio of about 40% and the mean depth-frequency ratio of 1.48. It is shown that this formula is only a particular form of the writer's more general formulation. -from Author
Efficient formulas for efficiency correction of cumulants
NASA Astrophysics Data System (ADS)
Kitazawa, Masakiyo
2016-04-01
Formulas connecting cumulants of particle numbers observed with efficiency losses with the original ones are derived based on the binomial model. These formulas can be applied to quantities given by a linear combination of particle numbers observed with different efficiencies in a compact form. Compared with the presently suggested ones based on factorial moments, these formulas would drastically reduce the numerical cost for the efficiency corrections when the order of the cumulant and the number of different efficiencies are large. The efficiency correction with realistic pT-dependent efficiency would be carried out with the aid of these formulas.
Zheng, Xiao-yong; Cao, Dong-sheng; Ye, Fa-qing; Xiang, Zheng
2014-01-01
Traditional Chinese medicine (TCM) has unique therapeutic effects for complex chronic diseases. However, for the lack of an effective systematic approach, the research progress on the effective substances and pharmacological mechanism of action has been very slow. In this paper, by incorporating network biology, bioinformatics and chemoinformatics methods, an integrated approach was proposed to systematically investigate and explain the pharmacological mechanism of action and effective substances of TCM. This approach includes the following main steps: First, based on the known drug targets, network biology was used to screen out putative drug targets; Second, the molecular docking method was used to calculate whether the molecules from TCM and drug targets related to chronic kidney diseases (CKD) interact or not; Third, according to the result of molecular docking, natural product-target network, main component-target network and compound-target network were constructed; Finally, through analysis of network characteristics and literature mining, potential effective multi-components and their synergistic mechanism were putatively identified and uncovered. Bu-shen-Huo-xue formula (BSHX) which was frequently used for treating CKD, was used as the case to demonstrate reliability of our proposed approach. The results show that BSHX has the therapeutic effect by using multi-channel network regulation, such as regulating the coagulation and fibrinolytic balance, and the expression of inflammatory factors, inhibiting abnormal ECM accumulation. Tanshinone IIA, rhein, curcumin, calycosin and quercetin may be potential effective ingredients of BSHX. This research shows that the integration approach can be an effective means for discovering active substances and revealing their pharmacological mechanisms of TCM. PMID:24598793
Preclinical assessment of infant formula.
Lönnerdal, Bo
2012-01-01
Infant formulas are the sole or predominant source of nutrition for many infants and are fed during a sensitive period of development and may therefore have short- and long-term consequences for infant health. Preclinical safety assessment therefore needs to include both short-term and long-term studies in animals. It is recommended that procedures are instituted by which experts may serve as independent scientists for companies developing novel products, without having their integrity compromised, and later serve the legislative institutions. A two-level assessment approach to determine the potential toxicity of a novel ingredient, its metabolites, and their effects in the matrix on developing organ systems has been suggested by IOM. This appears reasonable, as novel ingredients can be of different levels of concern. The use of modern methods in genomics and proteomics should be considered in these evaluation processes as well as novel methods to evaluate outcomes, including metabolomics and molecular techniques to assess the microbiome. PMID:22699767
Using Programmable Calculators to Evaluate Complicated Formulas.
ERIC Educational Resources Information Center
Snover, Stephen L.; Spikell, Mark A.
The application of the programmable calculator to evaluating complicated formulas is illustrated by considering the formula for finding the area of any triangle when only the lengths of the three sides are known. Other advantages of the programmable calculator are discussed such as freeing the student to explore more challenging problems and…
How to Save Money on Infant Formula
... months. Here are some ways you can save money on infant formula . ... Here are a few ways to save money on infant formula: DO NOT buy just one type of baby bottle at first. Try a few different types to see which kind ...
Code of Federal Regulations, 2011 CFR
2011-07-01
... 28 Judicial Administration 1 2011-07-01 2011-07-01 false Formula grants. 38.2 Section 38.2 Judicial Administration DEPARTMENT OF JUSTICE EQUAL TREATMENT FOR FAITH-BASED ORGANIZATIONS § 38.2 Formula grants. (a) Religious organizations are eligible, on the same basis as any other organization, to participate in any Department program for which...
Body surface area formulae: an alarming ambiguity
Redlarski, Grzegorz; Palkowski, Aleksander; Krawczuk, Marek
2016-01-01
Body surface area (BSA) plays a key role in several medical fields, including cancer chemotherapy, transplantology, burn treatment and toxicology. BSA is often a major factor in the determination of the course of treatment and drug dosage. A series of formulae to simplify the process have been developed. Because easy-to-identify, yet general, body coefficient results of those formulae vary considerably, the question arises as to whether the choice of a particular formula is valid and safe for patients. Here we show that discrepancies between most of the known BSA formulae can reach 0.5 m2 for the standard adult physique. Although many previous studies have demonstrated that certain BSA formulae provide an almost exact fit with the patients examined, all of these studies have been performed on a limited and isolated group of people. Our analysis presents a broader perspective, considering 25 BSA formulae. The analysis revealed that the choice of a particular formula is a difficult task. Differences among calculations made by the formulae are so great that, in certain cases, they may considerably affect patients’ mortality, especially for people with an abnormal physique or for children. PMID:27323883
10 CFR 905.33 - Extension formula.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 10 Energy 4 2013-01-01 2013-01-01 false Extension formula. 905.33 Section 905.33 Energy DEPARTMENT OF ENERGY ENERGY PLANNING AND MANAGEMENT PROGRAM Power Marketing Initiative § 905.33 Extension formula. (a) The amount of power to be extended to an existing customer shall be determined according...
10 CFR 905.33 - Extension formula.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 10 Energy 4 2014-01-01 2014-01-01 false Extension formula. 905.33 Section 905.33 Energy DEPARTMENT OF ENERGY ENERGY PLANNING AND MANAGEMENT PROGRAM Power Marketing Initiative § 905.33 Extension formula. (a) The amount of power to be extended to an existing customer shall be determined according...
10 CFR 905.33 - Extension formula.
Code of Federal Regulations, 2012 CFR
2012-01-01
... 10 Energy 4 2012-01-01 2012-01-01 false Extension formula. 905.33 Section 905.33 Energy DEPARTMENT OF ENERGY ENERGY PLANNING AND MANAGEMENT PROGRAM Power Marketing Initiative § 905.33 Extension formula. (a) The amount of power to be extended to an existing customer shall be determined according...
10 CFR 905.33 - Extension formula.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 10 Energy 4 2010-01-01 2010-01-01 false Extension formula. 905.33 Section 905.33 Energy DEPARTMENT OF ENERGY ENERGY PLANNING AND MANAGEMENT PROGRAM Power Marketing Initiative § 905.33 Extension formula. (a) The amount of power to be extended to an existing customer shall be determined according...
10 CFR 905.33 - Extension formula.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 10 Energy 4 2011-01-01 2011-01-01 false Extension formula. 905.33 Section 905.33 Energy DEPARTMENT OF ENERGY ENERGY PLANNING AND MANAGEMENT PROGRAM Power Marketing Initiative § 905.33 Extension formula. (a) The amount of power to be extended to an existing customer shall be determined according...
40 CFR 74.26 - Allocation formula.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 40 Protection of Environment 16 2010-07-01 2010-07-01 false Allocation formula. 74.26 Section 74.26 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) AIR PROGRAMS (CONTINUED) SULFUR DIOXIDE OPT-INS Allowance Calculations for Combustion Sources § 74.26 Allocation formula. (a)...
38 CFR 9.12 - Reinsurance formula.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 38 Pensions, Bonuses, and Veterans' Relief 1 2010-07-01 2010-07-01 false Reinsurance formula. 9.12 Section 9.12 Pensions, Bonuses, and Veterans' Relief DEPARTMENT OF VETERANS AFFAIRS SERVICEMEMBERS' GROUP LIFE INSURANCE AND VETERANS' GROUP LIFE INSURANCE § 9.12 Reinsurance formula. The allocation...
Lewis Carroll's Formula for Calendar Calculating.
ERIC Educational Resources Information Center
Spitz, Herman H.
1993-01-01
This paper presents Lewis Carroll's formula for mentally calculating the day of the week of a given date. The paper concludes that such formulas are too complex for individuals of low intelligence to learn by themselves, and thus "idiots savants" who perform such calendar calculations must be using other systems. (JDD)
Alternative Derivations for the Poisson Integral Formula
ERIC Educational Resources Information Center
Chen, J. T.; Wu, C. S.
2006-01-01
Poisson integral formula is revisited. The kernel in the Poisson integral formula can be derived in a series form through the direct BEM free of the concept of image point by using the null-field integral equation in conjunction with the degenerate kernels. The degenerate kernels for the closed-form Green's function and the series form of Poisson…
A Choice of a New Funding Formula
ERIC Educational Resources Information Center
Hancock, Kenneth
2008-01-01
This report examines the fiscal neutrality of three funding formulas that have been proposed to replace the current funding formula for Oklahoma's common schools in an attempt to have greater equity in the distribution of funds to the various districts. Using data from SY-03 to SY-07, calculations of state aid for the 540- districts and fiscal…
27 CFR 5.26 - Formula requirements.
Code of Federal Regulations, 2014 CFR
2014-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2014-04-01 2014-04-01 false Formula requirements. 5.26 Section 5.26 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY ALCOHOL LABELING AND ADVERTISING OF DISTILLED SPIRITS Formulas § 5.26...
27 CFR 5.26 - Formula requirements.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2011-04-01 2011-04-01 false Formula requirements. 5.26 Section 5.26 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT... requirements. (a) General. An approved formula is required to blend, mix, purify, refine, compound, or...
27 CFR 5.26 - Formula requirements.
Code of Federal Regulations, 2012 CFR
2012-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2012-04-01 2012-04-01 false Formula requirements. 5.26 Section 5.26 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT... requirements. (a) General. An approved formula is required to blend, mix, purify, refine, compound, or...
27 CFR 5.26 - Formula requirements.
Code of Federal Regulations, 2013 CFR
2013-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2013-04-01 2013-04-01 false Formula requirements. 5.26 Section 5.26 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY ALCOHOL LABELING AND ADVERTISING OF DISTILLED SPIRITS Formulas § 5.26...
Body surface area formulae: an alarming ambiguity.
Redlarski, Grzegorz; Palkowski, Aleksander; Krawczuk, Marek
2016-01-01
Body surface area (BSA) plays a key role in several medical fields, including cancer chemotherapy, transplantology, burn treatment and toxicology. BSA is often a major factor in the determination of the course of treatment and drug dosage. A series of formulae to simplify the process have been developed. Because easy-to-identify, yet general, body coefficient results of those formulae vary considerably, the question arises as to whether the choice of a particular formula is valid and safe for patients. Here we show that discrepancies between most of the known BSA formulae can reach 0.5 m(2) for the standard adult physique. Although many previous studies have demonstrated that certain BSA formulae provide an almost exact fit with the patients examined, all of these studies have been performed on a limited and isolated group of people. Our analysis presents a broader perspective, considering 25 BSA formulae. The analysis revealed that the choice of a particular formula is a difficult task. Differences among calculations made by the formulae are so great that, in certain cases, they may considerably affect patients' mortality, especially for people with an abnormal physique or for children. PMID:27323883
Funding the Formula Adequately in Oklahoma
ERIC Educational Resources Information Center
Hancock, Kenneth
2015-01-01
This report is a longevity, simulational study that looks at how the ratio of state support to local support effects the number of school districts that breaks the common school's funding formula which in turns effects the equity of distribution to the common schools. After nearly two decades of adequately supporting the funding formula, Oklahoma…
Formulas for sediment porosity and settling velocity
Technology Transfer Automated Retrieval System (TEKTRAN)
The formulas of Komura (1963) and Han et al. (1981) for the initial porosity of sediment deposits were tested using data sets collected in different countries and regions. It was found that Komura’s formula slightly underestimates the dry density for sand and gravel deposits and overestimates those ...
Review of "Weighted Student Formula Yearbook 2009"
ERIC Educational Resources Information Center
Baker, Bruce
2009-01-01
The new "Weighted Student Formula Yearbook 2009" from the Reason Foundation provides a simple framework for touting the successes of states and urban school districts that grant greater fiscal autonomy to schools. The report defines the Weighted Student Formula (WSF) reform extremely broadly, presenting a variety of reforms under the WSF umbrella.…
Formulas in Physics Have a "Standard" Form
ERIC Educational Resources Information Center
Moelter, Matthew J.; Jackson, Martin
2012-01-01
We discuss the importance of the ordering of symbols in physics formulas and identify implicit conventions that govern the "standard" form for how formulas are written and interpreted. An important part of writing and reading this form is understanding distinctions among constants, parameters, and variables. We delineate these conventions and…
The health implications of soy infant formula
Technology Transfer Automated Retrieval System (TEKTRAN)
Soy formula (SF) has been fed to millions of infants worldwide. It has been shown to promote growth and development as well as milk-based formula (MF) does. Controversy has developed over the adequacy and safety of SF. Most concerns are based on in vivo and in vitro data that raise the possibility o...
ERIC Educational Resources Information Center
Goedhart, Martin; van Duin, Yvonne
Structural formulas give professional chemists information about physical and chemical properties of corresponding compounds. In chemistry education at secondary schools, structural formulas are introduced in the context of chemical bonding. Structural formulas are not introduced as representations of the properties of chemical compounds. This…
A ``fractal'' modification of Torricelli's formula
NASA Astrophysics Data System (ADS)
Maramathas, Athanasios J.; Boudouvis, Andreas G.
2010-03-01
A modification is proposed of Torricelli’s (1608-1647) formula for the velocity of water discharging from a small hole at the bottom of a large tank filled with fractal solid material. The new formula takes proper account of the mechanical energy losses due to flow in the solid matrix, thus expanding the area of validity of the classical Torricelli’s formula. Moreover, it offers a convenient alternative to Darcy’s law for estimating the discharge rate from an aquifer. The new formula was derived from laboratory experiments, with a low-Reynolds number discharge flow (Darcian flow). It was tested in a natural karst aquifer where the flow is non-Darcian, at Almiros spring on the island of Crete (Greece). In both cases, the predictive capability of the modified formula is established.
Consistent Numerical Expressions for Precession Formulae.
NASA Astrophysics Data System (ADS)
Soma, M.
The precession formulae by Lieske et al. (1977) have been used since 1984 for calculating apparent positions and reducing astrometric observations of celestial objects. These formulae are based on the IAU (1976) Astronomical Constants, some of which deviate from their recently determined values. They are also derived using the secular variations of the ecliptic pole from Newcomb's theory, which is not consistent with the recent planetary theories. Accordingly Simon et al. (1994) developed new precession formulae using the recently determined astronomical constants and also being based on the new planetary theory VSOP87. There are two differing definitions of the ecliptic: ecliptic in the inertial sense and ecliptic in the rotating sense (Standish 1981). The ecliptic given by the VSOP87 theory is that in the inertial sense, but the value for obliquity Simon et al. used is the obliquity in the rotating sense. Therefore their precession formulae has inconsistency. This paper gives corrections for consistent precession formulae.
The Lichnerowicz-Weitzenboeck formula and superconductivity
Vargas-Paredes, Alfredo A.; Doria, Mauro M.; Neto, Jose Abdala Helayeel
2013-01-15
We derive the Lichnerowicz-Weitzenboeck formula for the two-component order parameter superconductor, which provides a twofold view of the kinetic energy of the superconductor. For the one component order parameter superconductor we review the connection between the Lichnerowicz-Weitzenboeck formula and the Ginzburg-Landau theory. For the two-component case we claim that this formula opens a venue to describe inhomogeneous superconducting states intertwined by spin correlations and charged dislocation. In this case the Lichnerowicz-Weitzenboeck formula displays local rotational and electromagnetic gauge symmetry (SU(2) Circled-Times U(1)) and relies on local commuting momentum and spin operators. The order parameter lives in a space with curvature and torsion described by Elie Cartan geometrical formalism. The Lichnerowickz-Weitzenboeck formula leads to first order differential equations that are a three-dimensional version of the Seiberg-Witten equations.
The Processing on Different Types of English Formulaic Sequences
ERIC Educational Resources Information Center
Qian, Li
2015-01-01
Formulaic sequences are found to be processed faster than their matched novel phrases in previous studies. Given the variety of formulaic types, few studies have compared processing on different types of formulaic sequences. The present study explored the processing among idioms, speech formulae and written formulae. It has been found that in…
27 CFR 17.137 - Formulas disapproved for drawback.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formulas disapproved for... NONBEVERAGE PRODUCTS Formulas and Samples Approval of Formulas § 17.137 Formulas disapproved for drawback. A formula may be disapproved for drawback either because it does not prescribe appropriate ingredients...
27 CFR 21.52 - Formula No. 27.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 27. 21.52... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.52 Formula No. 27. (a) Formula. To every 100 gallons of alcohol add:...
27 CFR 21.45 - Formula No. 20.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 20. 21.45... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.45 Formula No. 20. (a) Formula. To every 100 gallons of alcohol add:...
27 CFR 21.44 - Formula No. 19.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 19. 21.44... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.44 Formula No. 19. (a) Formula. To every 100 gallons of alcohol add:...
27 CFR 21.54 - Formula No. 27-B.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 27-B. 21.54... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.54 Formula No. 27-B. (a) Formula. To every 100 gallons of alcohol add:...
27 CFR 21.36 - Formula No. 3-B.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 3-B. 21.36... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.36 Formula No. 3-B. (a) Formula. To every 100 gallons of alcohol add:...
27 CFR 17.122 - Amended or revised formulas.
Code of Federal Regulations, 2010 CFR
2010-04-01
... formulas. 17.122 Section 17.122 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE... NONBEVERAGE PRODUCTS Formulas and Samples § 17.122 Amended or revised formulas. Except as provided in this section, amended or revised formulas are considered to be new formulas and shall be numbered...
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 4. 21.38... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.38 Formula No. 4. (a) Formula. To every 100 gallons of alcohol, or to...
27 CFR 21.24 - Formula No. 20.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 20. 21.24... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Completely Denatured Alcohol Formulas § 21.24 Formula No. 20. (a) Formula. To every 100 gallons of ethyl alcohol of not less than 195...
27 CFR 20.115 - Ink general-use formula.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Ink general-use formula..., DEPARTMENT OF THE TREASURY LIQUORS DISTRIBUTION AND USE OF DENATURED ALCOHOL AND RUM Formulas and Statements of Process General-Use Formulas § 20.115 Ink general-use formula. Ink general-use formula is...
27 CFR 25.56 - Filing of formulas.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Filing of formulas. 25.56... OF THE TREASURY LIQUORS BEER Miscellaneous Provisions Formulas § 25.56 Filing of formulas. (a) What are the general requirements for filing a formula? (1) You must file your formula in writing....
27 CFR 21.46 - Formula No. 22.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 22. 21.46... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.46 Formula No. 22. (a) Formula. To every 100 gallons of alcohol add:...
27 CFR 21.70 - Formula No. 39-A.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 39-A. 21.70... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.70 Formula No. 39-A. (a) Formula. To every 100 gallons of alcohol add:...
27 CFR 24.127 - Adoption of formulas.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Adoption of formulas. 24... Establishment § 24.127 Adoption of formulas. The adoption of approved formulas by a successor proprietor will be... formulas for adoption by formula number, name of product, and date of approval. The application...
27 CFR 24.127 - Adoption of formulas.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2011-04-01 2011-04-01 false Adoption of formulas. 24... Establishment § 24.127 Adoption of formulas. The adoption of approved formulas by a successor proprietor will be... formulas for adoption by formula number, name of product, and date of approval. The application...
27 CFR 24.127 - Adoption of formulas.
Code of Federal Regulations, 2014 CFR
2014-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2014-04-01 2014-04-01 false Adoption of formulas. 24... Establishment § 24.127 Adoption of formulas. The adoption of approved formulas by a successor proprietor will be... formulas for adoption by formula number, name of product, and date of approval. The application...
27 CFR 24.127 - Adoption of formulas.
Code of Federal Regulations, 2013 CFR
2013-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2013-04-01 2013-04-01 false Adoption of formulas. 24... Establishment § 24.127 Adoption of formulas. The adoption of approved formulas by a successor proprietor will be... formulas for adoption by formula number, name of product, and date of approval. The application...
27 CFR 24.127 - Adoption of formulas.
Code of Federal Regulations, 2012 CFR
2012-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2012-04-01 2012-04-01 false Adoption of formulas. 24... Establishment § 24.127 Adoption of formulas. The adoption of approved formulas by a successor proprietor will be... formulas for adoption by formula number, name of product, and date of approval. The application...
27 CFR 21.55 - Formula No. 28-A.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 28-A. 21.55... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.55 Formula No. 28-A. (a) Formula. To every 100 gallons of alcohol add:...
27 CFR 21.67 - Formula No. 38-D.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 38-D. 21.67... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.67 Formula No. 38-D. (a) Formula. To every 100 gallons of alcohol add:...
27 CFR 21.66 - Formula No. 38-C.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 38-C. 21.66... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.66 Formula No. 38-C. (a) Formula. To every 100 gallons of alcohol add:...
27 CFR 21.64 - Formula No. 37.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 37. 21.64... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.64 Formula No. 37. (a) Formula. To every 100 gallons of alcohol add:...
Wang, Xuezong; Liu, Ting; Gao, Ningyang; Ding, Daofang; Duan, Tieli; Cao, Yuelong; Zheng, Yuxin
2014-01-01
Objective. The aim of this study is to systematically evaluate the evidence whether traditional Chinese herbal patches (TCHPs) for osteoarthritis (OA) are effective and safe and analyze their medication patterns. Methods. A systematic literature search was performed using all the possible Medical Subject Headings (MeSH) and keywords from January 1979 to July 2013. Both randomized controlled trials (RCTs) and observational studies were included. Estimated effects were analyzed using mean difference (MD) or relative risk (RR) with 95% confidence intervals (CI) and meta-analysis. Results. 86 kinds of TCHPs were identified. RCTs and controlled clinical trials (CCTs) which were mostly of low quality favored TCHPs for local pain and dysfunction relief. TCHPs, compared with diclofenac ointment, had significant effects on global effectiveness rate (RR = 0.50; 95% CI (0.29, 0.87)). Components of formulae were mainly based on the compounds “Xiao Huo Luo Dan” (Minor collateral-freeing pill) and “Du Huo Ji Sheng Tang” (Angelicae Pubescentis and Loranthi decoction). Ten kinds of adverse events (AEs), mainly consisting of itching and/or local skin rashes, were identified after 3-4 weeks of follow-up. Conclusions. TCHPs have certain evidence in improving global effectiveness rate for OA; however, more rigorous studies are warranted to support their use. PMID:24527043
The Parisi Formula has a Unique Minimizer
NASA Astrophysics Data System (ADS)
Auffinger, Antonio; Chen, Wei-Kuo
2015-05-01
In 1979, Parisi (Phys Rev Lett 43:1754-1756, 1979) predicted a variational formula for the thermodynamic limit of the free energy in the Sherrington-Kirkpatrick model, and described the role played by its minimizer. This formula was verified in the seminal work of Talagrand (Ann Math 163(1):221-263, 2006) and later generalized to the mixed p-spin models by Panchenko (Ann Probab 42(3):946-958, 2014). In this paper, we prove that the minimizer in Parisi's formula is unique at any temperature and external field by establishing the strict convexity of the Parisi functional.
Simple formula for estimating airplane ceilings
NASA Technical Reports Server (NTRS)
Diehl, Walter S
1922-01-01
The aeronautical engineer often has occasion to estimate the absolute ceiling of an airplane for which a detailed performance calculation is out of the question. In such cases it is customary to use either empirical performance charts or formulae. The performance charts given in several of the recent works on aeronautics are satisfactory so long as the airplane under consideration does not depart too far from the average in its characteristics. The formulae, with one exception, are no better. Given here is that exception, with indications of which terms of the formula may be neglected without seriously affecting the results, thus simplifying the task.
Shafiee Nahrkhalaji, Saeedeh; Lotfi, Ahmad Reza; Koosha, Mansour
2016-10-01
The present study aims to reveal some facts concerning first language ([Formula: see text] and second language ([Formula: see text] spoken-word processing in unbalanced proficient bilinguals using behavioral measures. The intention here is to examine the effects of auditory repetition word priming and semantic priming in first and second languages of these bilinguals. The other goal is to explore the effects of attention manipulation on implicit retrieval of perceptual and conceptual properties of spoken [Formula: see text] and [Formula: see text] words. In so doing, the participants performed auditory word priming and semantic priming as memory tests in their [Formula: see text] and [Formula: see text]. In a half of the trials of each experiment, they carried out the memory test while simultaneously performing a secondary task in visual modality. The results revealed that effects of auditory word priming and semantic priming were present when participants processed [Formula: see text] and [Formula: see text] words in full attention condition. Attention manipulation could reduce priming magnitude in both experiments in [Formula: see text]. Moreover, [Formula: see text] word retrieval increases the reaction times and reduces accuracy on the simultaneous secondary task to protect its own accuracy and speed. PMID:26643309
Some Simple Computational Formulas for Multiple Regression
ERIC Educational Resources Information Center
Aiken, Lewis R., Jr.
1974-01-01
Short-cut formulas are presented for direct computation of the beta weights, the standard errors of the beta weights, and the multiple correlation coefficient for multiple regression problems involving three independent variables and one dependent variable. (Author)
How to Save Money on Infant Formula
... use a different liner with each feeding, which costs more. If your baby needs special formula because ... see if your insurance will help cover the cost. Not all health plans offer this coverage, but ...
Generalized Doppler Formula in a Nonstatic Universe
ERIC Educational Resources Information Center
Gross, Peter G.
1977-01-01
Derives the general Doppler formula in a nonstatic universe using assumptions of special relativity, homogeneity and isotropy of the universe. Examples of applications to physical cosmology are given. (SL)
A Summation Formula for Macdonald Polynomials
NASA Astrophysics Data System (ADS)
de Gier, Jan; Wheeler, Michael
2016-03-01
We derive an explicit sum formula for symmetric Macdonald polynomials. Our expression contains multiple sums over the symmetric group and uses the action of Hecke generators on the ring of polynomials. In the special cases {t = 1} and {q = 0}, we recover known expressions for the monomial symmetric and Hall-Littlewood polynomials, respectively. Other specializations of our formula give new expressions for the Jack and q-Whittaker polynomials.
Parametric Improper Integrals, Wallis Formula and Catalan Numbers
ERIC Educational Resources Information Center
Dana-Picard, Thierry; Zeitoun, David G.
2012-01-01
We present a sequence of improper integrals, for which a closed formula can be computed using Wallis formula and a non-straightforward recurrence formula. This yields a new integral presentation for Catalan numbers.
27 CFR 26.54 - Filing and disposition of formulas.
Code of Federal Regulations, 2010 CFR
2010-04-01
... BUREAU, DEPARTMENT OF THE TREASURY LIQUORS LIQUORS AND ARTICLES FROM PUERTO RICO AND THE VIRGIN ISLANDS Formulas for Products From Puerto Rico § 26.54 Filing and disposition of formulas. Formulas required...
A Connection Formula for the q-Confluent Hypergeometric Function
NASA Astrophysics Data System (ADS)
Morita, Takeshi
2013-07-01
We show a connection formula for the q-confluent hypergeometric functions {}_2ϕ_1(a,b;0;q,x). Combining our connection formula with Zhang's connection formula for {}_2ϕ_0(a,b;-;q,x), we obtain the connection formula for the q-confluent hypergeometric equation in the matrix form. Also we obtain the connection formula of Kummer's confluent hypergeometric functions by taking the limit qto 1^{-} of our connection formula.
Bellco Formula Domus Home Care System.
Trewin, Elizabeth
2004-01-01
There are certain characteristics in a dialysis machine that would be desirable for use in home and limited care environments. These features relate to safety, ease of use, consideration of physical space, and reliability. The Bellco Formula Domus Home Care System was designed to meet all these requirements. Bellco's philosophy of patient treatment centers on global biocompatibility. This is evident in the design of the Formula Domus Home Care System. It has the smallest hydraulic fluid pathway of any dialysis machine on the market. Formula is capable of preparing ultrapure dialysate. The ultrafiltration measurement mechanism, the patented Coriolis flow meter, measures the mass of the dialysate, not the volume. For this reason it is the only dialysis machine that detects actual backfiltration, not just the theoretical possibility of it based on transmembrane pressure. The Coriolis flow meter also ensures that dialysate flow is a true single pass. The operator interface is a single window operating control. It is possible to select up to 14 different languages. There is an online help key to assist patients with troubleshooting. Programmable start-up and shutdown times save time for the patient. Formula is the only dialysis machine to offer a backup battery feature. Formula is capable of communicating with any software available. The focus on global biocompatibility ensures the best quality dialysis treatments for a population of patients who will likely remain on dialysis for a longer period of time than conventional dialysis patients. PMID:15043621
ERIC Educational Resources Information Center
Rose, Heather; Sonstelie, Jon; Weston, Margaret
2012-01-01
In his 2012-13 budget Governor Brown proposed a new system for allocating state revenue among California school districts. By all accounts the current system is complex and opaque. In contrast, the proposed system--a weighted pupil funding formula--is simple and transparent. Using the PPIC School Finance Model, we compare how this formula would…
A simplification of the Kovarik formula
NASA Astrophysics Data System (ADS)
Chen, Yan-Ni; Du, Hong-Ke; Pang, Yong-Feng
2007-07-01
Let P,Q be two idempotents on a Hilbert space. Z.V. Kovarik (Z.V. Kovarik, Similarity and interpolation between projectors, Acta Sci. Math. (Szeged) 39 (1977) 341-351) showed that when P+Q-I is invertible, the formula K(P,Q)=P(P+Q-I)-2Q gives the only idempotent such that , , where and denote the nullspace and the range of a bounded linear operator T on a Hilbert space, respectively. This formula was later extended to the context of Banach algebras and used in 1983 by J. Esterle to show that two homotopic idempotents may always be connected by a polynomial idempotent valued path. In the present paper, we give a simplification of Kovarik's original formula and one natural generalization of it.
Mass formula for quasi-black holes
Lemos, Jose P. S.; Zaslavskii, Oleg B.
2008-12-15
A quasi-black hole, either nonextremal or extremal, can be broadly defined as the limiting configuration of a body when its boundary approaches the body's quasihorizon. We consider the mass contributions and the mass formula for a static quasi-black hole. The analysis involves careful scrutiny of the surface stresses when the limiting configuration is reached. It is shown that there exists a strict correspondence between the mass formulas for quasi-black holes and pure black holes. This perfect parallelism exists in spite of the difference in derivation and meaning of the formulas in both cases. For extremal quasi-black holes the finite surface stresses give zero contribution to the total mass. This leads to a very special version of Abraham-Lorentz electron in general relativity in which the total mass has pure electromagnetic origin in spite of the presence of bare stresses.
Ewens sampling formulae with and without selection
NASA Astrophysics Data System (ADS)
Huillet, Thierry
2007-09-01
We shall first consider the random Dirichlet partitioning of the interval into n fragments at temperature [theta]>0. Using calculus for Dirichlet integrals, pre-asymptotic versions of the Ewens sampling formulae from finite Dirichlet partitions follow up. From these preliminaries, straightforward proofs of the usual sampling formulae from random proportions with Poisson-Dirichlet (PD)([gamma]) distribution can be obtained, while considering the Kingman limit n[NE pointing arrow][infinity], [theta][south east arrow]0, with n[theta]=[gamma]>0. In this manuscript, the Gibbs version of the Dirichlet partition with symmetric selection is considered. By use of similar series expansion calculus for Dirichlet integrals, closed-form expressions of Ewens sampling formulae in the presence of selection are obtained; special types of Bell polynomials are shown to be involved.
27 CFR 21.41 - Formula No. 13-A.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 13-A. 21.41 Section 21.41 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.41 Formula No....
27 CFR 21.40 - Formula No. 12-A.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 12-A. 21.40 Section 21.40 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.40 Formula No....
27 CFR 21.47 - Formula No. 23-A.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 23-A. 21.47 Section 21.47 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.47 Formula No....
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 1. 21.32 Section 21.32 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.32 Formula No. 1....
27 CFR 21.59 - Formula No. 32.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 32. 21.59 Section 21.59 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.59 Formula No. 32....
27 CFR 21.57 - Formula No. 30.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 30. 21.57 Section 21.57 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.57 Formula No. 30....
27 CFR 21.62 - Formula No. 35-A.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 35-A. 21.62 Section 21.62 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.62 Formula No....
27 CFR 21.41 - Formula No. 13-A.
Code of Federal Regulations, 2012 CFR
2012-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2012-04-01 2012-04-01 false Formula No. 13-A. 21.41 Section 21.41 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.41 Formula No....
27 CFR 21.57 - Formula No. 30.
Code of Federal Regulations, 2013 CFR
2013-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2013-04-01 2013-04-01 false Formula No. 30. 21.57 Section 21.57 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY ALCOHOL FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.57 Formula No. 30....
27 CFR 21.41 - Formula No. 13-A.
Code of Federal Regulations, 2013 CFR
2013-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2013-04-01 2013-04-01 false Formula No. 13-A. 21.41 Section 21.41 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY ALCOHOL FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.41 Formula No....
27 CFR 21.59 - Formula No. 32.
Code of Federal Regulations, 2013 CFR
2013-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2013-04-01 2013-04-01 false Formula No. 32. 21.59 Section 21.59 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY ALCOHOL FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.59 Formula No. 32....
27 CFR 21.59 - Formula No. 32.
Code of Federal Regulations, 2012 CFR
2012-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2012-04-01 2012-04-01 false Formula No. 32. 21.59 Section 21.59 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.59 Formula No. 32....
27 CFR 21.62 - Formula No. 35-A.
Code of Federal Regulations, 2013 CFR
2013-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2013-04-01 2013-04-01 false Formula No. 35-A. 21.62 Section 21.62 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY ALCOHOL FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.62 Formula No....
27 CFR 21.62 - Formula No. 35-A.
Code of Federal Regulations, 2012 CFR
2012-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2012-04-01 2012-04-01 false Formula No. 35-A. 21.62 Section 21.62 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.62 Formula No....
27 CFR 21.57 - Formula No. 30.
Code of Federal Regulations, 2012 CFR
2012-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2012-04-01 2012-04-01 false Formula No. 30. 21.57 Section 21.57 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.57 Formula No. 30....
27 CFR 21.40 - Formula No. 12-A.
Code of Federal Regulations, 2013 CFR
2013-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2013-04-01 2013-04-01 false Formula No. 12-A. 21.40 Section 21.40 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY ALCOHOL FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.40 Formula No....
27 CFR 21.48 - Formula No. 23-F.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2011-04-01 2011-04-01 false Formula No. 23-F. 21.48 Section 21.48 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.48 Formula No....
27 CFR 21.69 - Formula No. 39.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2011-04-01 2011-04-01 false Formula No. 39. 21.69 Section 21.69 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.69 Formula No. 39....
27 CFR 21.63 - Formula No. 36.
Code of Federal Regulations, 2012 CFR
2012-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2012-04-01 2012-04-01 false Formula No. 36. 21.63 Section 21.63 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.63 Formula No. 36....
27 CFR 21.69 - Formula No. 39.
Code of Federal Regulations, 2014 CFR
2014-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2014-04-01 2014-04-01 false Formula No. 39. 21.69 Section 21.69 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY ALCOHOL FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.69 Formula No. 39....
27 CFR 21.48 - Formula No. 23-F.
Code of Federal Regulations, 2014 CFR
2014-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2014-04-01 2014-04-01 false Formula No. 23-F. 21.48 Section 21.48 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY ALCOHOL FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.48 Formula No....
27 CFR 21.23 - Formula No. 19.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 19. 21.23... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Completely Denatured Alcohol Formulas § 21.23 Formula No. 19. To every 100 gallons of ethyl alcohol of not less than 160 proof add:...
24 CFR 990.110 - Operating fund formula.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 24 Housing and Urban Development 4 2010-04-01 2010-04-01 false Operating fund formula. 990.110... DEVELOPMENT THE PUBLIC HOUSING OPERATING FUND PROGRAM Purpose, Applicability, Formula, and Definitions § 990.110 Operating fund formula. (a) General formula. (1) The amount of annual contributions...
27 CFR 24.81 - Filing of formulas.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Filing of formulas. 24.81... OF THE TREASURY LIQUORS WINE Administrative and Miscellaneous Provisions Formulas § 24.81 Filing of formulas. The proprietor shall on each formula filed designate all ingredients and, if required,...
27 CFR 17.126 - Formulas for intermediate products.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formulas for intermediate... NONBEVERAGE PRODUCTS Formulas and Samples § 17.126 Formulas for intermediate products. (a) The manufacturer shall submit a formula on TTB Form 5154.1 for each self-manufactured ingredient made with...
27 CFR 21.22 - Formula No. 18.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 18. 21.22... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Completely Denatured Alcohol Formulas § 21.22 Formula No. 18. To every 100 gallons of ethyl alcohol of not less than 160 proof add:...
7 CFR 761.205 - Computing the formula allocation.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 7 Agriculture 7 2013-01-01 2013-01-01 false Computing the formula allocation. 761.205 Section 761... Farm Loan Programs Funds to State Offices § 761.205 Computing the formula allocation. (a) The formula... funds for a loan program that the National Office allocates to a State Office. formula...
7 CFR 761.205 - Computing the formula allocation.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 7 Agriculture 7 2014-01-01 2014-01-01 false Computing the formula allocation. 761.205 Section 761... Farm Loan Programs Funds to State Offices § 761.205 Computing the formula allocation. (a) The formula... funds for a loan program that the National Office allocates to a State Office. formula...
7 CFR 761.205 - Computing the formula allocation.
Code of Federal Regulations, 2012 CFR
2012-01-01
... 7 Agriculture 7 2012-01-01 2012-01-01 false Computing the formula allocation. 761.205 Section 761... Farm Loan Programs Funds to State Offices § 761.205 Computing the formula allocation. (a) The formula... funds for a loan program that the National Office allocates to a State Office. formula...
27 CFR 21.53 - Formula No. 27-A.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 27-A. 21.53 Section 21.53 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.53 Formula No....
Formula Estimation of Cross-Validated Multiple Correlation.
ERIC Educational Resources Information Center
Schmitt, Neal
A review of cross-validation shrinkage formulas is presented which focuses on the theoretical and practical problems in the use of various formulas. Practical guidelines for use of both formulas and empirical cross-validation are provided. A comparison of results using these formulas in a range of situations is then presented. The result of these…
27 CFR 21.68 - Formula No. 38-F.
Code of Federal Regulations, 2013 CFR
2013-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2013-04-01 2013-04-01 false Formula No. 38-F. 21.68 Section 21.68 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY ALCOHOL FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.68 Formula No....
27 CFR 21.75 - Formula No. 40-A.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2011-04-01 2011-04-01 false Formula No. 40-A. 21.75 Section 21.75 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.75 Formula No....
27 CFR 21.71 - Formula No. 39-B.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2011-04-01 2011-04-01 false Formula No. 39-B. 21.71 Section 21.71 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.71 Formula No....
27 CFR 21.49 - Formula No. 23-H.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2011-04-01 2011-04-01 false Formula No. 23-H. 21.49 Section 21.49 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.49 Formula No....
27 CFR 21.74 - Formula No. 40.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2011-04-01 2011-04-01 false Formula No. 40. 21.74 Section 21.74 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.74 Formula No. 40....
27 CFR 21.63 - Formula No. 36.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2011-04-01 2011-04-01 false Formula No. 36. 21.63 Section 21.63 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.63 Formula No. 36....
27 CFR 21.76 - Formula No. 40-B.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2011-04-01 2011-04-01 false Formula No. 40-B. 21.76 Section 21.76 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.76 Formula No....
27 CFR 21.48 - Formula No. 23-F.
Code of Federal Regulations, 2013 CFR
2013-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2013-04-01 2013-04-01 false Formula No. 23-F. 21.48 Section 21.48 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY ALCOHOL FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.48 Formula No....
27 CFR 21.48 - Formula No. 23-F.
Code of Federal Regulations, 2012 CFR
2012-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2012-04-01 2012-04-01 false Formula No. 23-F. 21.48 Section 21.48 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.48 Formula No....
27 CFR 21.59 - Formula No. 32.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2011-04-01 2011-04-01 false Formula No. 32. 21.59 Section 21.59 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.59 Formula No. 32....
27 CFR 21.62 - Formula No. 35-A.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2011-04-01 2011-04-01 false Formula No. 35-A. 21.62 Section 21.62 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.62 Formula No....
27 CFR 21.40 - Formula No. 12-A.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2011-04-01 2011-04-01 false Formula No. 12-A. 21.40 Section 21.40 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.40 Formula No....
27 CFR 21.47 - Formula No. 23-A.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2011-04-01 2011-04-01 false Formula No. 23-A. 21.47 Section 21.47 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.47 Formula No....
27 CFR 21.41 - Formula No. 13-A.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2011-04-01 2011-04-01 false Formula No. 13-A. 21.41 Section 21.41 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.41 Formula No....
27 CFR 21.57 - Formula No. 30.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2011-04-01 2011-04-01 false Formula No. 30. 21.57 Section 21.57 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.57 Formula No. 30....
Code of Federal Regulations, 2011 CFR
2011-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2011-04-01 2011-04-01 false Formula No. 1. 21.32 Section 21.32 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.32 Formula No. 1....
27 CFR 21.48 - Formula No. 23-F.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 23-F. 21.48 Section 21.48 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.48 Formula No....
27 CFR 21.69 - Formula No. 39.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 39. 21.69 Section 21.69 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.69 Formula No. 39....
Gaussian quadrature formulae for arbitrary positive measures.
Fernandes, Andrew D; Atchley, William R
2006-01-01
We present computational methods and subroutines to compute Gaussian quadrature integration formulas for arbitrary positive measures. For expensive integrands that can be factored into well-known forms, Gaussian quadrature schemes allow for efficient evaluation of high-accuracy and -precision numerical integrals, especially compared to general ad hoc schemes. In addition, for certain well-known density measures (the normal, gamma, log-normal, Student's t, inverse-gamma, beta, and Fisher's F) we present exact formulae for computing the respective quadrature scheme. PMID:19455218
Lewis Carroll's formula for calendar calculating.
Spitz, H H
1994-03-01
One of the extraordinary skills occasionally displayed by individuals of low intelligence (so-called idiots savants) is the ability to name, within seconds, the day of the week for any given date, sometimes over a range of centuries. A number of scholarly papers contain references to formulas that can be used in making this calculation, but none cites one of the earliest published methods, that of Lewis Carroll. However, formulas such as Carroll's are too complex to be self-taught by idiots savants and, consequently, cannot account for their remarkable performance. Alternative explanatory hypotheses were briefly discussed. PMID:8192906
Lead content of milk and infant formula
Walker, B.
1980-03-01
Survey report:A survey to determine the lead content of early infant food sources was conducted in Washington, D.C. Samples were collected from various lots of national brands of infant formula and evaporated milk, cartons of nonfat dry milk, containers of homogenized cow's milk, and human milk. Mean concentrations of lead in infant formula, evaporated milk, nonfat dry milk, fresh cow's milk, and human milk were 0.135 g/ml, 0.03 g/ml, 0.01 g/ml, 0.53 g/ml, and 0.02 g/ml respectively. (2 references, 2 tables)
Pesin's Entropy Formula for Systems Between and
NASA Astrophysics Data System (ADS)
Tian, Xueting
2014-09-01
In this article we give a new observation of Pesin's entropy formula, motivated from Mañé's proof of (Ergod Theory Dyn Sys 1:95-102, 1981). Let be a compact Riemann manifold and be a diffeomorphism on . If is an -invariant probability measure which is absolutely continuous relative to Lebesgue measure and nonuniformly-Hlder-continuous(see Definition 1.1), then we have Pesin's entropy formula, i.e., the metric entropy satisfies where are the Lyapunov exponents at with respect to Nonuniformly-H lder-continuous is a new notion from probabilistic perspective weaker than
Empirical formula of crustal torsional oscillations
NASA Astrophysics Data System (ADS)
Sotani, Hajime
2016-02-01
Crustal torsional oscillations depend on not only crust properties but also the stellar mass and radius. Thus, one could extract stellar information by identifying the observed frequencies of stellar oscillations with the crustal torsional oscillations. Owing to the confinement of torsional oscillations inside the crust region of neutron stars, we successfully derive an empirical formula for the fundamental crustal torsional oscillations as a function of the stellar mass, radius, the so-called slope parameter of the nuclear symmetry energy, and the angular index of oscillations, with which one can estimate the frequencies with high accuracy. This empirical formula could be valuable in both the astrophysics and nuclear physics communities.
Semiclassical trace formulas for noninteracting identical particles
NASA Astrophysics Data System (ADS)
Sakhr, Jamal; Whelan, Niall D.
2003-06-01
We extend the Gutzwiller trace formula to systems of noninteracting identical particles. The standard relation for isolated orbits does not apply since the energy of each particle is separately conserved causing the periodic orbits to occur in continuous families. The identical nature of the particles also introduces discrete permutational symmetries. We exploit the formalism of Creagh and Littlejohn [Phys. Rev. A 44, 836 (1991)], who have studied semiclassical dynamics in the presence of continuous symmetries, to derive many-body trace formulas for the full and symmetry-reduced densities of states. Numerical studies of the three-particle cardioid billiard are used to explicitly illustrate and test the results of the theory.
Connection formulas for thermal density functional theory
NASA Astrophysics Data System (ADS)
Pribram-Jones, A.; Burke, K.
2016-05-01
The adiabatic connection formula of ground-state density functional theory relates the correlation energy to a coupling-constant integral over a purely potential contribution, and is widely used to understand and improve approximations. The corresponding formula for thermal density functional theory is cast as an integral over temperatures instead, ranging upward from the system's physical temperature. We also show how to relate different correlation components to each other, either in terms of temperature or coupling-constant integrations. We illustrate our results on the uniform electron gas.
Razminia, Mansour; Trivedi, Atul; Molnar, Janos; Elbzour, Monther; Guerrero, Mayra; Salem, Yasser; Ahmed, Aziz; Khosla, Sandeep; Lubell, David L
2004-12-01
Mean arterial pressure (MAP) has traditionally been derived from systolic and diastolic pressures, weighted 1/3 systolic and 2/3 diastolic. No correction is made for the increasing time dominance of systole with increasing heart rates. In a previous study, we developed a new and more accurate heart rate-corrected MAP formula from central aorta pressure determinations in a large number of patients: MAP = DP + [0.33 + (HR x 0.0012)] x [PP] where SP and DP are systolic and diastolic pressure and HR is heart rate. The current study validates the new MAP formula in the same patient at increasing paced heart rates. A central aorta catheter was used to obtain computer-determined systolic, diastolic, and MAP in 12 patients. Values were obtained at baseline and then at increasing right atrial paced heart rates. The new and standard MAP formula-derived values were compared with computer-determined values. The new formula showed a much closer correlation with the computer-derived values for MAP. Standard MAP calculations for MAP can easily be improved by inclusion of a heart rate factor. PMID:15558774
Implementing Gilbert's PIP Formula in the Workplace.
ERIC Educational Resources Information Center
Cardinale, Loretta A.
Gilbert (1978) developed a Potential for Improving Performance (PIP) formula based on worth, value, and cost. Worth related the value of a performance to its cost. The PIP related the worth of exemplary performance to the worth of average performance. This offered an opportunity for improvement by making appropriate changes through training or…
25 CFR 273.31 - Distribution formula.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 25 Indians 1 2011-04-01 2011-04-01 false Distribution formula. 273.31 Section 273.31 Indians BUREAU OF INDIAN AFFAIRS, DEPARTMENT OF THE INTERIOR INDIAN SELF-DETERMINATION AND EDUCATION ASSISTANCE ACT PROGRAM EDUCATION CONTRACTS UNDER JOHNSON-O'MALLEY ACT Funding Provisions § 273.31...
24 CFR 574.130 - Formula allocations.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 24 Housing and Urban Development 3 2011-04-01 2010-04-01 true Formula allocations. 574.130 Section 574.130 Housing and Urban Development Regulations Relating to Housing and Urban Development (Continued) OFFICE OF ASSISTANT SECRETARY FOR COMMUNITY PLANNING AND DEVELOPMENT, DEPARTMENT OF HOUSING AND...
24 CFR 92.50 - Formula allocation.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 24 Housing and Urban Development 1 2010-04-01 2010-04-01 false Formula allocation. 92.50 Section 92.50 Housing and Urban Development Office of the Secretary, Department of Housing and Urban... previous fiscal year, are metropolitan cities, urban counties, or consortia approved under § 92.101;...
Nevada's College Funding Formula under Attack
ERIC Educational Resources Information Center
Black Issues in Higher Education, 2005
2005-01-01
Community College of Southern Nevada (CCSN) President Richard Carpenter has criticized the state's college funding formula, saying it penalizes southern Nevada students--particularly minorities. Carpenter said he hopes lawmakers will alter a complex equation that leads to a discrepancy in funding between CCSN and other institutions, including…
Code of Federal Regulations, 2014 CFR
2014-01-01
...) Rebate formula. (1) Agencies shall determine credit card payment dates based on an analysis of the total... offered by the card issuer with the corresponding daily basis points of the government's Current Value of Funds (CVF) rate. If the basis points offered by the card issuer are greater than the daily basis...
Code of Federal Regulations, 2013 CFR
2013-01-01
...) Rebate formula. (1) Agencies shall determine credit card payment dates based on an analysis of the total... offered by the card issuer with the corresponding daily basis points of the government's Current Value of Funds (CVF) rate. If the basis points offered by the card issuer are greater than the daily basis...
Adolescent Formula Literature and Its Promiscuous Progeny.
ERIC Educational Resources Information Center
Stanek, Lou Willett
This paper discusses the history and effect of popular culture generally and of the adolescent formula novel specifically. Seven primary characteristics of art as popular culture are that the work is accessible, easy to understand, conventional in form, not shocking in content, expressive of common and appropriate values, relative to some element…
The Economic Vitality Formula of Success
ERIC Educational Resources Information Center
Konopnicki, Patrick M.
2012-01-01
An economic vitality formula of success can be accomplished by creating partnerships between local career and technical education (CTE), and workforce development and economic development entities. Student industry certifications; dynamic partnerships; programs and projects focused on science, technology, engineering, and mathematics (STEM); and…
Code of Federal Regulations, 2013 CFR
2013-07-01
... 28 Judicial Administration 1 2013-07-01 2013-07-01 false Formula grants. 38.2 Section 38.2... grants. (a) Religious organizations are eligible, on the same basis as any other organization, to... religious character or affiliation. As used in this section, “program” refers to a grant, contract,...
Trinomial Formula, Pascal- and Sierpinski-Pyramid
ERIC Educational Resources Information Center
Zeitler, H.
2002-01-01
Stimulated by a picture of a Sierpinski-pyramid and an article by Stewart, students were asked about a connection between this pyramid and the well-known trinomial formula. The results of all the work done with students are presented in this note. (Contains 8 figures.)
Beyond the Formula: Students Becoming Writers.
ERIC Educational Resources Information Center
Dobler, Judith
To become writers, students must see themselves as writers and be treated as writers by their teachers. Students need to find the motivation to go beyond formulas, to grapple with messy, often inchoate ideas, to find their own particular angle of vision. What rhetoricians call "invention" or "discovery" is difficult to pin down. Without a system…
27 CFR 19.348 - Formula requirements.
Code of Federal Regulations, 2012 CFR
2012-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2012-04-01 2012-04-01 false Formula requirements. 19.348 Section 19.348 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU... 5100.51 as provided in §§ 5.26 and 5.27 of this chapter before a proprietor may: (a) Blend, mix,...
27 CFR 19.348 - Formula requirements.
Code of Federal Regulations, 2014 CFR
2014-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2014-04-01 2014-04-01 false Formula requirements. 19.348 Section 19.348 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY ALCOHOL DISTILLED SPIRITS PLANTS Processing of Distilled Spirits Filing...
27 CFR 19.348 - Formula requirements.
Code of Federal Regulations, 2013 CFR
2013-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2013-04-01 2013-04-01 false Formula requirements. 19.348 Section 19.348 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY ALCOHOL DISTILLED SPIRITS PLANTS Processing of Distilled Spirits Filing...
27 CFR 19.348 - Formula requirements.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2011-04-01 2011-04-01 false Formula requirements. 19.348 Section 19.348 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU... 5100.51 as provided in §§ 5.26 and 5.27 of this chapter before a proprietor may: (a) Blend, mix,...
Quantification of prebiotics in commercial infant formulas.
Sabater, Carlos; Prodanov, Marin; Olano, Agustín; Corzo, Nieves; Montilla, Antonia
2016-03-01
Since breastfeeding is not always possible, infant formulas (IFs) are supplemented with prebiotic oligosaccharides, such as galactooligosaccharides (GOS) and/or fructooligosaccharides (FOS) to exert similar effects to those of the breast milk. Nowadays, a great number of infant formulas enriched with prebiotics are disposal in the market, however there are scarce data about their composition. In this study, the combined use of two chromatographic methods (GC-FID and HPLC-RID) for the quantification of carbohydrates present in commercial infant formulas have been used. According to the results obtained by GC-FID for products containing prebiotics, the content of FOS, GOS and GOS/FOS was in the ranges of 1.6-5.0, 1.7-3.2, and 0.08-0.25/2.3-3.8g/100g of product, respectively. HPLC-RID analysis allowed quantification of maltodextrins with degree of polymerization (DP) up to 19. The methodology proposed here may be used for routine quality control of infant formula and other food ingredients containing prebiotics. PMID:26471520
27 CFR 5.26 - Formula requirements.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula requirements. 5.26 Section 5.26 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT... Supplemental or Form 5110.38 shall remain in effect until revoked, superseded, or voluntarily surrendered....
Universal fitting formulae for baryon oscillation surveys
NASA Astrophysics Data System (ADS)
Blake, Chris; Parkinson, David; Bassett, Bruce; Glazebrook, Karl; Kunz, Martin; Nichol, Robert C.
2006-01-01
The next generation of galaxy surveys will attempt to measure the baryon oscillations in the clustering power spectrum with high accuracy. These oscillations encode a preferred scale which may be used as a standard ruler to constrain cosmological parameters and dark energy models. In this paper we present simple analytical fitting formulae for the accuracy with which the preferred scale may be determined in the tangential and radial directions by future spectroscopic and photometric galaxy redshift surveys. We express these accuracies as a function of survey parameters such as the central redshift, volume, galaxy number density and (where applicable) photometric redshift error. These fitting formulae should greatly increase the efficiency of optimizing future surveys, which requires analysis of a potentially vast number of survey configurations and cosmological models. The formulae are calibrated using a grid of Monte Carlo simulations, which are analysed by dividing out the overall shape of the power spectrum before fitting a simple decaying sinusoid to the oscillations. The fitting formulae reproduce the simulation results with a fractional scatter of 7 per cent (10 per cent) in the tangential (radial) directions over a wide range of input parameters. We also indicate how sparse-sampling strategies may enhance the effective survey area if the sampling scale is much smaller than the projected baryon oscillation scale.
Stability and Equity in Education Finance Formulas.
ERIC Educational Resources Information Center
Fox, William; Murray, Matthew; Price, Patricia A.
2002-01-01
Examines the effectiveness of new funding formula included in major education reform legislation passed by the Tennessee legislature in early 1990s. Finds unanticipated outcomes. For example, while the variance in per-pupil spending among districts is smaller than before the legislation, the gap between the per-pupil spending of one-third of the…
Effects of neurological damage on production of formulaic language
Sidtis, D.; Canterucci, G.; Katsnelson, D.
2014-01-01
Early studies reported preserved formulaic language in left hemisphere damaged subjects and reduced incidence of formulaic expressions in the conversational speech of stroke patients with right hemispheric damage. Clinical observations suggest a possible role also of subcortical nuclei. This study examined formulaic language in the spontaneous speech of stroke patients with left, right, or subcortical damage. Four subjects were interviewed and their speech samples compared to normal speakers. Raters classified formulaic expressions as speech formulae, fillers, sentence stems, and proper nouns. Results demonstrated that brain damage affected novel and formulaic language competence differently, with a significantly smaller proportion of formulaic expressions in subjects with right or subcortical damage compared to left hemisphere damaged or healthy speakers. These findings converge with previous studies that support the proposal of a right hemisphere/subcortical circuit in the management of formulaic expressions, based on a dual-process model of language incorporating novel and formulaic language use. PMID:19382014
Vongsavan, Kadkao; Rirattanapong, Praphasri; Surarit, Rudee
2016-03-01
Dental caries are a major public health problem worldwide. The aim of this study was to compare the effects of children's follow-on instant powdered cow's milk formula, buffalo milk formula and a chicken-based formula on microhardness of bovine enamel with artificial caries-like lesions. Forty bovine teeth were each placed in acrylic blocks and the enamel surfaces were polished to create flat 5 x 5 millimeter surfaces. The teeth surfaces were then demineralized using 0.1M lactic acid (pH 4.5) to achieve an enamel microhardness of 35-65 Vickers Hardness Numbers (VHN). All specimens were then randomly allocated into one of 4 groups (n=10/group). For remineralization, each group was soaked in a different kind of milk formula for 2 hours at 37°C except group 1 which was a negative control (artificial saliva) group. Group 2 was soaked in Murrah™ buffalo milk formula (a positive control ), group 3 in S-26-Promil-Gold™ (cow's milk formula) and group 4 in a chicken-based formula (Siriraj Hospital, Mahidol University). The microhardness of the specimens was then measured again. Data were analyzed using a one-way ANOVA and paired t-test with a 95% confidence interval. After exposure to the formula, the mean VHN for each study group was significantly higher (paired t-test, p < 0.05) except for group 1 (p = 0.345). The mean VHN for the the Murrah™ buffalo milk formula, the chicken-based formula and the S-26-Promil-Gold™ formula group were not significantly different from each other (one-way ANOVA, p > 0.05). In conclusion, S-26-Promil-Gold™ follow-on cow milk formula, Murrah™ buffalo milk formula and the chicken-based formula all increased bovine enamel microhardness after soaking for 2 hours. PMID:27244971
Matrix product formula for Macdonald polynomials
NASA Astrophysics Data System (ADS)
Cantini, Luigi; de Gier, Jan; Wheeler, Michael
2015-09-01
We derive a matrix product formula for symmetric Macdonald polynomials. Our results are obtained by constructing polynomial solutions of deformed Knizhnik-Zamolodchikov equations, which arise by considering representations of the Zamolodchikov-Faddeev and Yang-Baxter algebras in terms of t-deformed bosonic operators. These solutions are generalized probabilities for particle configurations of the multi-species asymmetric exclusion process, and form a basis of the ring of polynomials in n variables whose elements are indexed by compositions. For weakly increasing compositions (anti-dominant weights), these basis elements coincide with non-symmetric Macdonald polynomials. Our formulas imply a natural combinatorial interpretation in terms of solvable lattice models. They also imply that normalizations of stationary states of multi-species exclusion processes are obtained as Macdonald polynomials at q = 1.
Semiclassical trace formulas for noninteracting identical particles.
Sakhr, Jamal; Whelan, Niall D
2003-06-01
We extend the Gutzwiller trace formula to systems of noninteracting identical particles. The standard relation for isolated orbits does not apply since the energy of each particle is separately conserved causing the periodic orbits to occur in continuous families. The identical nature of the particles also introduces discrete permutational symmetries. We exploit the formalism of Creagh and Littlejohn [Phys. Rev. A 44, 836 (1991)], who have studied semiclassical dynamics in the presence of continuous symmetries, to derive many-body trace formulas for the full and symmetry-reduced densities of states. Numerical studies of the three-particle cardioid billiard are used to explicitly illustrate and test the results of the theory. PMID:16241332
Inclusion probability with dropout: an operational formula.
Milot, E; Courteau, J; Crispino, F; Mailly, F
2015-05-01
In forensic genetics, a mixture of two or more contributors to a DNA profile is often interpreted using the inclusion probabilities theory. In this paper, we present a general formula for estimating the probability of inclusion (PI, also known as the RMNE probability) from a subset of visible alleles when dropouts are possible. This one-locus formula can easily be extended to multiple loci using the cumulative probability of inclusion. We show that an exact formulation requires fixing the number of contributors, hence to slightly modify the classic interpretation of the PI. We discuss the implications of our results for the enduring debate over the use of PI vs likelihood ratio approaches within the context of low template amplifications. PMID:25559642
Pizzetti Formulae for Stiefel Manifolds and Applications
NASA Astrophysics Data System (ADS)
Coulembier, Kevin; Kieburg, Mario
2015-10-01
Pizzetti's formula explicitly shows the equivalence of the rotation invariant integration over a sphere and the action of rotation invariant differential operators. We generalize this idea to the integrals over real, complex, and quaternion Stiefel manifolds in a unifying way. In particular, we propose a new way to calculate group integrals and try to uncover some algebraic structures which manifest themselves for some well-known cases like the Harish-Chandra integral. We apply a particular case of our formula to an Itzykson-Zuber integral for the coset . This integral naturally appears in the calculation of the two-point correlation function in the transition of the statistics of the Poisson ensemble and the Gaussian orthogonal ensemble in random matrix theory.
A flood-flow formula for Connecticut
Bigwood, B.L.; Thomas, M.P.
1955-01-01
A study of the frequency and magnitude of floods within the Connecticut area is contained in this report. Annual flood discharges for 44 stream-gaging stations whose records range in length from l0 to 40 years are presented and a regional flood-frequency relationship developed based upon the ratios of all floods to the mean annual flood at each of these locations. Definition of this curve for floods of larger recurrence intervals is based upon historical studies of extraordinary floods which have occurred within the area. For ungaged areas, the mean annual flood value may be determined by use of a flood-flow formula based upon the topographic characteristics of drainage area and basin slope. The development of this formula also is included.
Some inversion formulas for the cone transform
NASA Astrophysics Data System (ADS)
Terzioglu, Fatma
2015-11-01
Several novel imaging applications have lead recently to a variety of Radon type transforms, where integration is made over a family of conical surfaces. We call them cone transforms (in 2D they are also called V-line or broken ray transforms). Most prominently, they are present in the so called Compton camera imaging that arises in medical diagnostics, astronomy, and lately in homeland security applications. Several specific incarnations of the cone transform have been considered separately. In this paper, we address the most general (and overdetermined) cone transform, obtain integral relations between cone and Radon transforms in {{{R}}}n, and a variety of inversion formulas. In many applications (e.g., in homeland security), the signal to noise ratio is very low. So, if overdetermined data is collected (as in the case of Compton imaging), attempts to reduce the dimensionality might lead to essential elimination of the signal. Thus, our main concentration is on obtaining formulas involving overdetermined data.
Average prime-pair counting formula
NASA Astrophysics Data System (ADS)
Korevaar, Jaap; Riele, Herman Te
2010-04-01
Taking r>0 , let π_{2r}(x) denote the number of prime pairs (p, p+2r) with p≤ x . The prime-pair conjecture of Hardy and Littlewood (1923) asserts that π_{2r}(x)˜ 2C_{2r} {li}_2(x) with an explicit constant C_{2r}>0 . There seems to be no good conjecture for the remainders ω_{2r}(x)=π_{2r}(x)- 2C_{2r} {li}_2(x) that corresponds to Riemann's formula for π(x)-{li}(x) . However, there is a heuristic approximate formula for averages of the remainders ω_{2r}(x) which is supported by numerical results.