Lang, Kenneth R
1978-01-01
This volume is a reference source of fundamental formulae in physics and astrophysics. In contrast to most of the usual compendia it carefully explains the physical assumptions entering the formulae. All the important results of physical theories are covered: electrodynamics, hydrodynamics, general relativity, atomic and nuclear physics, and so on. Over 2100 formulae are included, and the original papers for the formulae are cited together with papers on modern applications in a bibliography of over 1900 entries. For this new edition, a chapter on space, time, matter and cosmology has been included and the other chapters have been carefully revised.
DEFF Research Database (Denmark)
Astrup Jensen, Bjarne
Makeham's formula is an actuarial formula expressing the present value of a payment stream in terms of its repayments instead of the payments themselves. The formula is largely neglected in the finance literature, but -- as this paper shows -- it has a number of useful applications in fixed income...... analysis. We use Makeham's formula to decompose the return on a bond investment into interest payments, realized capital gains and accrued capital gains for a variety of accounting rules for measuring accruals in order to study the theoretical properties of these accounting rules, their taxation...
Breastfeeding vs. Formula Feeding
... 1- to 2-Year-Old Breastfeeding vs. Formula Feeding KidsHealth > For Parents > Breastfeeding vs. Formula Feeding Print ... a lactation specialist. previous continue All About Formula Feeding Commercially prepared infant formulas are a nutritious alternative ...
Breastfeeding vs. Formula Feeding
... A What's in this article? All About Breastfeeding Breastfeeding Challenges All About Formula Feeding Formula Feeding Challenges Making a Choice en español Lactancia materna versus lactancia artificial Choosing whether to breastfeed or formula feed their ...
Institute of Scientific and Technical Information of China (English)
2008-01-01
<正>An equation which gives a general rule for a particular type of problem is called a formula. Frequently it is convenient to transform a formula,that is,express the formula with a dif- ferent subject.Consider the formula C=2πr;the subject is C.However,if we divide both sides by 2π:
Walkenbach, John
2013-01-01
Maximize the power of Excel 2013 formulas with this must-have Excel reference John Walkenbach, known as ""Mr. Spreadsheet,"" is a master at deciphering complex technical topics and Excel formulas are no exception. This fully updated book delivers more than 800 pages of Excel 2013 tips, tricks, and techniques for creating formulas that calculate, developing custom worksheet functions with VBA, debugging formulas, and much more. Demonstrates how to use all the latest features in Excel 2013 Shows how to create financial formulas and tap into the power of array formulas
... based formulas. These formulas are made with cow's milk protein that has been changed to be more like ... be helpful for infants who have allergies to milk protein and for those with skin rashes or wheezing ...
Vandenplas,Yvan; DE GREEF, Elisabeth; Veereman, Gigi
2014-01-01
The gastrointestinal microbiota of breast-fed babies differ from classic standard formula fed infants. While mother's milk is rich in prebiotic oligosaccharides and contains small amounts of probiotics, standard infant formula doesn’t. Different prebiotic oligosaccharides are added to infant formula: galacto-oligosaccharides, fructo-oligosaccharide, polydextrose, and mixtures of these. There is evidence that addition of prebiotics in infant formula alters the gastrointestinal (GI) microbiota ...
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…
Walkenbach, John
2011-01-01
Everything you need to know about* Mastering operators, error values, naming techniques, and absolute versus relative references* Debugging formulas and using the auditing tools* Importing and exporting XML files and mapping the data to specific cells* Using Excel 2003's rights management feature* Working magic with array formulas* Developing custom formulas to produce the results you needHere's the formula for Excel excellenceFormulas are the lifeblood of spreadsheets, and no one can bring a spreadsheet to life like John Walkenbach. In this detailed reference guide, he delves deeply into unde
Infant feeding: formula, solids.
Barness, L A
1985-04-01
This article discusses and evaluates current formulas, traces their continual improvement (based largely on new information on breast milk composition), and then discusses the question of supplemental feedings.
Institute of Scientific and Technical Information of China (English)
Li Yinghong; Yang Wei
2009-01-01
@@ On the first day of November,when Jenson Button cheered his first Formula I World Championship 2009 at the final race of the season in Abu Dhabi,Chinese young university students were busy preparing for their own Formula event.According to a press conference on October 19,2009 in Beijing,the first Formula SAE-China (FSAE) event has set off,and will be officially launch its final race next year from October 14 to October 17 at Shanghai International Circuit,where will also be the Formula 12010 China stop again in next April.
Tube formula, Berezinians, and Dwork formula
Khudaverdian, Hovhannes M
2007-01-01
We consider an example of tubes of hypersurfaces in Euclidean space and generalise the tube formula to supercase. By this we assign to a point of the hypersurface in superspace a rational characteristic function. Does this rational function appear when we calculate the zeta-function of an arithmetic variety?
Formula misasi?! / Sten Soomlais
Soomlais, Sten
2008-01-01
Formula Student on kõrgkoolide masinaehituse ja/või autotehnika tudengite meeskondade vaheline iga-aastane tootearendusvõistlus, mis kujutab endast väikese vormelauto projekteerimist, ehitamist ja võidusõitmist ringrajal. Lisa: Formula Student Eestis
Mann, Allen L
2008-01-01
IFG logic is a variant of the independence-friendly logic of Hintikka and Sandu. We answer the question: ``Which IFG-formulas are equivalent to ordinary first-order formulas?'' We use the answer to show that the ordinary cylindric set algebra over a structure can be embedded into a reduct of the IFG-cylindric set algebra over the structure.
Vandenplas, Yvan; De Greef, Elisabeth; Veereman, Gigi
2014-01-01
The gastrointestinal microbiota of breast-fed babies differ from classic standard formula fed infants. While mother's milk is rich in prebiotic oligosaccharides and contains small amounts of probiotics, standard infant formula doesn't. Different prebiotic oligosaccharides are added to infant formula: galacto-oligosaccharides, fructo-oligosaccharide, polydextrose, and mixtures of these. There is evidence that addition of prebiotics in infant formula alters the gastrointestinal (GI) microbiota resembling that of breastfed infants. They are added to infant formula because of their presence in breast milk. Infants on these supplemented formula have a lower stool pH, a better stool consistency and frequency and a higher concentration of bifidobacteria in their intestine compared to infants on a non-supplemented standard formula. Since most studies suggest a trend for beneficial clinical effects, and since these ingredients are very safe, prebiotics bring infant formula one step closer to breastmilk, the golden standard. However, despite the fact that adverse events are rare, the evidence on prebiotics of a significant health benefit throughout the alteration of the gut microbiota is limited.
General forecasting correcting formula
2009-01-01
A general forecasting correcting formula, as a framework for long-use and standardized forecasts, is created. The formula provides new forecasting resources and new possibilities for expansion of forecasting including economic forecasting into the areas of municipal needs, middle-size and small-size business and, even, to individual forecasting.
U.S. Department of Health & Human Services — This list includes products subject to recall since September 2010 related to infant formula distributed by Abbott. This list will be updated with publicly available...
U.S. Department of Health & Human Services — This list includes products subject to recall since September 2010 related to infant formula distributed by Abbott. This list will be updated with publicly...
Readability Formulas: Pluses and Minuses.
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)
Geometrization of Trace Formulas
Frenkel, Edward
2010-01-01
Following our joint work arXiv:1003.4578 with Robert Langlands, we make the first steps toward developing geometric methods for analyzing trace formulas in the case of the function field of a curve defined over a finite field. We also suggest a conjectural framework of geometric trace formulas for curves defined over the complex field, which exploits the categorical version of the geometric Langlands correspondence.
Energy Technology Data Exchange (ETDEWEB)
Iwayama, I.; Iwayama, A.
1982-04-10
A fuel formula that includes a homogenous mixture of benzine, aromatic ether oils, perfume and other perfuming agents, as well as the lowest possible aliphatic alcohol as a component solvent, surfactant, and possibly, a soluble pigment that colors the formula an appropriate color. This formula is used as an aromatic fuel for cigarette lights. The ether oils can be musk, amber, camomille, lavender, mint, anise, rose, camphor, and other aromatic oils; the perfuming agents are: geraniol, linalool, menthol, camphor, benzyl or phenetyl alcohols, phenylacetaldehyde, vanillin, coumarin, and so forth; the pigments are: beta-carotene, sudan dyes, etc.; the low aliphatic alcohols are EtOH, iso-PrOH. Example: 70 parts benzine, 10 parts EtOH, 15 parts oxide mezithylene and 5 parts borneol form a clear liquid that has a camphor aroma when it is lit.
The Pico's formula Generalization
Sergiu Cataranciuc; Marina Holban
2007-01-01
The Pico formula generalizations are obtained for area calculation of a polygon P through the determination of special nodes of the network in which this P is placed. The case of the polygon with rational coordinates of its vertexes is examined, as well as the case of the polygon with holes. In the case of three-dimensional space a formula of volume calculation for some polyhedrons, such as prism and tetrahedron is presented. On the basis of theoretic outcomes an algorithm that can be applied...
The Pico's formula Generalization
Directory of Open Access Journals (Sweden)
Sergiu Cataranciuc
2007-04-01
Full Text Available The Pico formula generalizations are obtained for area calculation of a polygon P through the determination of special nodes of the network in which this P is placed. The case of the polygon with rational coordinates of its vertexes is examined, as well as the case of the polygon with holes. In the case of three-dimensional space a formula of volume calculation for some polyhedrons, such as prism and tetrahedron is presented. On the basis of theoretic outcomes an algorithm that can be applied in calculation for areas of plane figure is elaborated.
General correcting formula of forecasting?
2009-01-01
A general correcting formula of forecasting (as a framework for long-use and standardized forecasts) is proposed. The formula provides new forecasting resources and areas of application including economic forecasting.
Analysis of straightening formula
Directory of Open Access Journals (Sweden)
Devadatta M. Kulkarni
1988-01-01
standard bitableaux (or the set of standard monomials in minors gives a free basis for a polynomial ring in a matrix of indeterminates over a field. The straightening formula expresses a nonstandard bitableau as an integral linear cobmbination of standard bitableaux. In this paper we analyse the exchanges in the process of straightening a nonstandard pure tableau of depth two. We give precisely the number of steps required to straighten a given violation of a nonstandard tableau. We also characterise the violation which is eliminated in a single step.
Feynman formulae for evolution semigroups
Directory of Open Access Journals (Sweden)
Ya. A. Butko
2014-01-01
Full Text Available The paper systematically describes an approach to solution of initial and initial-boundary value problems for evolution equations based on the representation of the corresponding evolution semigroups with the help of Feynman formulae. The article discusses some of the methods of constructing Feynman formulae for different evolution semigroups, presents specific examples of solutions of evolution equations. In particular, Feynman formula is obtained for evolution semigroups generated by multiplicative perturbations of generators of some initial semigroups. In this case semigroups on a Banach space of continuous functions defined on an arbitrary metric space are considered; Feynman formulae are constructed with the help of operator families, which are Chernoff equivalent to the initial unperturbed semigroups. The present result generalizes the author's paper \\Feynman formula for semigroups with multiplicative perturbed generators" and some of the results of the joint with O.G. Smolyanov and R.L. Schilling paper \\Lagrangian and Hamiltonian Feynman formulae for some Feller processes and their perturbations". The approach to the construction of Feynman formulae for semigroups with multiplicative and additive perturbed generators is illustrated with examples of the Cauchy problem for the Schrodinger equation, the approximation of transition probabilities of some Markov processes.Further, a wider class of additive and multiplicative perturbations of a particular generator | the Laplace operator | is considered in the paper. And Feynman formula for the solution of the Cauchy problem for a second order parabolic equation with unbounded variable coefficients is proved. In addition, the article describes a method for constructing Feynman formulae for solutions of the Cauchy | Dirichlet problem for parabolic differential equations. The method is also illustrated by a second order parabolic equation with variable coefficients. These results generalize some
Digital Repository of Mathematical Formulae
Howard S. Cohl; McClain, Marjorie A.; Saunders, Bonita V.; Schubotz, Moritz; Williams, Janelle C.
2014-01-01
The purpose of the NIST Digital Repository of Mathematical Formulae (DRMF) is to create a digital compendium of mathematical formulae for orthogonal polynomials and special functions (OPSF) and of associated mathematical data. The DRMF addresses needs of working mathematicians, physicists and engineers: providing a platform for publication and interaction with OPSF formulae on the web. Using MediaWiki extensions and other existing technology (such as software and macro collections developed f...
Quadrature formulas for Fourier coefficients
Bojanov, Borislav
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. © 2009 Elsevier B.V. All rights reserved.
TWO REMARKS ON SCHWARZ FORMULA
Institute of Scientific and Technical Information of China (English)
Ding Xiaqi; Luo Peizhu
2005-01-01
This paper discusses two problems. Firstly the authors give the Schwarz formula for a holomorphic function in unit disc when the boundary value of its real part is in the class H of generalized functions in the sense of Hua. Secondly the authors use the classical Schwarz formula to give a new proof of the zero free region of the Riemann zeta-function.
Algebraic Proofs over Noncommutative Formulas
Tzameret, Iddo
2010-01-01
We study possible formulations of algebraic propositional proof systems operating with noncommutative formulas. We observe that a simple formulation gives rise to systems at least as strong as Frege---yielding a semantic way to define a Cook-Reckhow (i.e., polynomially verifiable) algebraic analogue of Frege proofs, different from that given in [BIKPRS96,GH03]. We then turn to an apparently weaker system, namely, polynomial calculus (PC) where polynomials are written as ordered formulas ("PC over ordered formulas", for short). This is an algebraic propositional proof system that operates with noncommutative polynomials in which the order of products in all monomials respects a fixed linear order on the variables, and where proof-lines are written as noncommutative formulas. We show that the latter proof system is strictly stronger than resolution, polynomial calculus and polynomial calculus with resolution (PCR) and admits polynomial-size refutations for the pigeonhole principle and the Tseitin's formulas. We...
The Formula of Plague Narratives
DEFF Research Database (Denmark)
Christensen, Jørgen Riber
2015-01-01
it is possible to establish a stable formula for plague narratives despite the spread over centuries and in different text types, and to explain this formula and possible variations of it. The initial and tentative hypothesis is that a formulaic narrative structure exists for accounts, both documentary...... and fictional, of epidemics. The samples include: Exodus, History of the Peloponnesian War, Samuel Pepys’ Diary, A Journal of the Plague Year, The Last Man, The Plague in Bergamo, Discipline and Punish: The Birth of the Prison, Doomsday, The Dead Zone, World War Z. An Oral History of the Zombie War, Pandemic...
APPLICABILITY OF SEDIMENT TRANSPORT FORMULAS
Institute of Scientific and Technical Information of China (English)
Chih Ted YANG; Caian HUANG
2001-01-01
The paper provides a comprehensive testing of the applicability of 13 sediment transport formulas under different flow and sediment conditions. The dimensionless parameters used for testing the reliability and sensitivity of formulas are dimensionless particle diameter, relative depth, Froude number, relative shear velocity, dimensionless unit stream power, and sediment concentration. A total of 3,391 sets of laboratory and river data are used in the tests. Engineers may find the test results useful to their selection of formulas under different flow and sediment conditions.
Generalized Klein-Nishina formula
Krajewska, K; Kamiński, J Z
2015-01-01
The generalized Klein-Nishina formula for Compton scattering of charged particles by a finite train of pulses is derived in the framework of quantum electrodynamics. The formula also applies to classical Thomson scattering provided that frequencies of generated radiation are smaller that the cut-off frequency. The validity of the formula for incident pulses of different durations is illustrated by numerical examples. The positions of the well-resolved Compton peaks, with the clear labeling by integer orders, opens up the possibility of the precise diagnostics of properties of relativistically intense, short laser pulses. This includes their peak intensity, the carrier-envelope phase, and their polarization properties.
Energy Technology Data Exchange (ETDEWEB)
Tachibana, Takahiro [Waseda Univ., Tokyo (Japan). Advanced Research Center for Science and Engineering
1997-07-01
Wapstra and Audi`s Table is famous for evaluation of experimental data of atomic nuclear masses (1993/1995 version) which estimated about 2000 kinds of nuclei. The error of atomic mass of formula is 0.3 MeV-0.8 MeV. Four kinds of atomic mass formula: JM (Jaenecke and Masson), TUYY (Tachibana, Uno, Yamada and Yamada), FRDM (Moeller, Nix, Myers and Swiatecki) and ETFSI (Aboussir, Pearson, Dutta and Tondeur) and their properties (number of parameter and error etc.) were explained. An estimation method of theoretical error of mass formula was presented. It was estimated by the theoretical error of other surrounding nuclei. (S.Y.)
Overview: Infant Formula and Fluorosis
... Journal Articles for Community Water Fluoridation Overview: Infant Formula and Fluorosis Recommend on Facebook Tweet Share Compartir ... file Microsoft PowerPoint file Microsoft Word file Microsoft Excel file Audio/Video file Apple Quicktime file RealPlayer ...
FDA Abbott Infant Formula Recall
U.S. Department of Health & Human Services — On September 22, 2010, Abbott issued a voluntary recall of certain Similac powdered infant formula after identifying a common warehouse beetle (both larvae and...
CHY formula and MHV amplitudes
Du, Yi-jian; Wu, Yong-shi
2016-01-01
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 support the MHV amplitudes. Namely, localized at this solution, the integrated CHY formula reproduces the Parke-Taylor formula for Yang-Mills amplitudes as well as the Hodges formula for gravitational amplitudes. This is achieved by developing techniques, in a manifestly M\\"obius 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.
On generalizations of Verlinde's formula
Bántay, P
2000-01-01
It is shown that traces of mapping classes of finite order may be expressed by Verlinde-like formulae. The 3D topological argument is explained, and the resulting trace identities for modular matrix elements are presented.
Quantum computing of semiclassical formulas.
Georgeot, B; Giraud, O
2008-04-01
We show that semiclassical formulas such as the Gutzwiller trace formula can be implemented on a quantum computer more efficiently than on a classical device. We give explicit quantum algorithms which yield quantum observables from classical trajectories, and which alternatively test the semiclassical approximation by computing classical actions from quantum evolution. The gain over classical computation is in general quadratic, and can be larger in some specific cases.
New supplements to infant formulas.
Eshach Adiv, Orly; Berant, Moshe; Shamir, Raanan
2004-12-01
Foods, which, in addition to their nutritional attributes, contain also elements that are considered to be health-promoting, have been termed "functional foods". In this regard, human milk has gained recognition as being the ultimate functional food for infants - by its biological compatibility, nutritional value and the undisputed added value of its health promoting qualities. Intensive research activity has recently evolved in a quest to identify and define the components of human milk that might confer disease-preventing and health-enhancing properties and to determine the instances and clinical conditions in which these factors become particularly important. The outcome of such research would also provide a rationale for advocating the supplementation of commercial infant formulas with such substances. In effect, the body of data accumulated from scientific and clinical studies on nucleotides, probiotics, prebiotics and long-chain polyunsaturated fatty acids in human milk and as additives to infant formula, has become regarded as convincing enough by the infant formula industry so as to launch into the market formulas supplemented with one or more of these factors - in an effort to emulate human milk and its beneficial effects. The following review is intended for the reader to obtain a general idea of the new supplements that have been introduced to infant formulas. We summarize the pertinent experimental and clinical observations concerning each of the supplements, pointing out their potential specific benefits, their possible disadvantages and the issues that still remain unresolved.
Positive Formulas in Intuitionistic and Minimal Logic
de Jongh, D.; Zhao, Z.; Aher, M.; Hole, D.; Jeřábek, E.; Kupke, C.
2015-01-01
In this article we investigate the positive, i.e. ¬,⊥-free formulas of intuitionistic propositional and predicate logic, IPC and IQC, and minimal logic, MPC and MQC. For each formula φ of IQC we define the positive formula φ+ that represents the positive content of φ. The formulas φ and φ+ exhibit t
Two Notes on Numerical Differentiation Formulae
Institute of Scientific and Technical Information of China (English)
ZHENG Hua-sheng
2012-01-01
Some new conclusions on asymptotic properties and inverse problems of numerical differentiation formulae have been drawn in this paper.In the first place,several asymptotic properties of intermediate points of numerical differentiation formulae are presented by using Taylor's formula.And then,based on the ideas of algebraic accuracy,several inverse problems of numerical differentiation formulae are given.
Cubature formulas on combinatorial graphs
Pesenson, Isaac Z
2011-01-01
Many contemporary applications, for example, cataloging of galaxies, document analysis, face recognition, learning theory, image processing, operate with a large amount of data which is often represented as a graph embedded into a high dimensional Euclidean space. The variety of problems arising in contemporary data processing requires development on graphs such topics of the classical harmonic analysis as Shannon sampling, splines, wavelets, cubature formulas. The goal of the paper is to establish cubature formulas on finite combinatorial graphs. The results have direct applications to problems that arise in connection with data filtering, data denoising and data dimension reduction.
Geometric formula for prism deflection
Indian Academy of Sciences (India)
Apoorva G Wagh; Veer Chand Rakhecha
2004-08-01
While studying neutron deflections produced by a magnetic prism, we have stumbled upon a simple `geometric' formula. For a prism of refractive index close to unity, the deflection simply equals the product of the refractive power − 1 and the base-to-height ratio of the prism, regardless of the apex angle. The base and height of the prism are measured respectively along and perpendicular to the direction of beam propagation within the prism. The geometric formula greatly simplifies the optimisation of prism parameters to suit any specific experiment.
Reasoning on Schemata of Formulae
Echenim, Mnacho
2012-01-01
A logic is presented for reasoning on iterated sequences of formulae over some given base language. The considered sequences, or "schemata", are defined inductively, on some algebraic structure (for instance the natural numbers, the lists, the trees etc.). A proof procedure is proposed to relate the satisfiability problem for schemata to that of finite disjunctions of base formulae. It is shown that this procedure is sound, complete and terminating, hence the basic computational properties of the base language can be carried over to schemata.
Zhang, Yong
2016-01-01
In this paper, we develop a rather general way to reduce integrands with polarisation involved in the Cachazo-He-Yuan formulae, such as the reduced Pfaffian and its compactification, as well as the new object for F3 amplitude. We prove that the reduced Pfaffian vanishes unless on a certain set of solutions. It leads us to build up the 4d CHY formulae using spinors, which strains off many useless solutions. The supersymmetrization is straightforward and may provide a hint to understanding ambitwistor string in 4d.
Developing the Vertex Formula Meaningfully
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…
Recurrence Formulas for Fibonacci Sums
Brandao, Adilson J V
2008-01-01
In this article we present a new recurrence formula for a finite sum involving the Fibonacci sequence. Furthermore, we state an algorithm to compute the sum of a power series related to Fibonacci series, without the use of term-by-term differentiation theorem
Blackhole formula and example relativity
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.
The Callias index formula revisited
Gesztesy, Fritz
2016-01-01
These lecture notes aim at providing a purely analytical and accessible proof of the Callias index formula. In various branches of mathematics (particularly, linear and nonlinear partial differential operators, singular integral operators, etc.) and theoretical physics (e.g., nonrelativistic and relativistic quantum mechanics, condensed matter physics, and quantum field theory), there is much interest in computing Fredholm indices of certain linear partial differential operators. In the late 1970’s, Constantine Callias found a formula for the Fredholm index of a particular first-order differential operator (intimately connected to a supersymmetric Dirac-type operator) additively perturbed by a potential, shedding additional light on the Fedosov-Hörmander Index Theorem. As a byproduct of our proof we also offer a glimpse at special non-Fredholm situations employing a generalized Witten index.
Koide's Mass Formula for Neutrinos
Brannen, Carl
2006-05-01
We derive Koide's mass formula as an eigenvector equation. We show that to within current experimental error, the square roots of the masses of the charged leptons follow the simple equation (m^-n)^0.5 = μ1(1 + √2(δ1+ 2nπ/3)) where δ1 is the interesting number .22222204717(48) and μ1 is a constant. Next we generalize the Koide formula to the neutrinos by assuming that the square root of the mass of the smallest neutrino must be taken to be negative. Then masses of the simple form (m^0n)^0.5 = μ0(1 + √2(δ1+ π/12 + 2nπ/3)) where 3;μ0= 3^12 ;μ1, satisfy recent neutrino oscillation measurements close to the centers of the error bars. Finally, we discuss the preon model for the fermions that led to the above discovery.
Analyzing Walksat on random formulas
Coja-Oghlan, Amin
2011-01-01
Let F be a uniformly distributed random k-SAT formula with n variables and m clauses. We prove that the Walksat algorithm from Papadimitriou (FOCS 1991)/Schoning (FOCS 1999) finds a satisfying assignment of F in polynomial time w.h.p. if m/n0. This is an improvement by a factor of $\\Theta(k)$ over the best previous analysis of Walksat from Coja-Oghlan, Feige, Frieze, Krivelevich, Vilenchik (SODA 2009).
Koppelman formulas on flag manifolds
Samuelsson, Håkan
2010-01-01
We construct Koppelman formulas on manifolds of flags in $\\C^N$ for forms with values in any holomorphic line bundle as well as in the tautological vector bundles and their duals. As an application we obtain new explicit proofs of some vanishing theorems of the Bott-Borel-Weil type by solving the corresponding $\\debar$-equation. We also construct reproducing kernels for harmonic $(p,q)$-forms in the case of Grassmannians.
McLean's second variation formula revisited
Lê, Hông Vân; Vanžura, Jiří
2017-03-01
We revisit McLean's second variation formulas for calibrated submanifolds in exceptional geometries, and correct his formulas concerning associative submanifolds and Cayley submanifolds, using a unified treatment based on the (relative) calibration method and Harvey-Lawson's identities.
Infant Formula - Buying, Preparing, Storing, and Feeding
... 000806.htm Infant Formula – Buying, Preparing, Storing, and Feeding To use the sharing features on this page, ... brush to get at hard-to-reach places. Feeding Formula to Baby Here is a guide to ...
Formula Feeding FAQs: Starting Solids and Milk
... Year-Old Formula Feeding FAQs: Starting Solids and Milk KidsHealth > For Parents > Formula Feeding FAQs: Starting Solids ... When can I start giving my baby cow's milk? Before their first birthday, babies still need the ...
Formulaic speech in disorders of language
Directory of Open Access Journals (Sweden)
Diana Sidtis
2014-04-01
Formulaic language studies remain less well recognized in language disorders. Profiles of differential formulaic language abilities in neurological disease have implications for cerebral models of language and for clinical evaluation and treatment of neurogenic language disorders.
Simple and Clear Proofs of Stirling's Formula
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.
Some results on numerical divided difference formulas
Institute of Scientific and Technical Information of China (English)
Wang; Xinghua; Wang; Heyu; Ming-Jun; Lai
2005-01-01
The remainder estimates of numerical divided difference formula are given for the functions of lower and higher smoothness, respectively. Then several divided difference formulas with super-convergence are derived with their remainder expressions.
Lefschetz Formulae for p-Adic Groups
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this paper, Lefschetz formulae for torus actions on p-adic groups are proven.These are similar to comparable formulae for real Lie groups. Applications lie in the realm of dynamical zeta functions.
Solutions of the motivic ADHM recursion formula
Mozgovoy, Sergey
2011-01-01
We give an explicit solution of the ADHM recursion formula conjectured by Chuang, Diaconescu, and Pan. This solution is closely related to the formula for the Hodge polynomials of Higgs moduli spaces conjectured by Hausel and Rodriguez-Villegas. We solve also the twisted motivic ADHM recursion formula. As a byproduct we obtain a conjectural formula for the motives of twisted Higgs moduli spaces, which generalizes the conjecture of Hausel and Rodriguez-Villegas.
A rotational integral formula for intrinsic volumes
DEFF Research Database (Denmark)
Jensen, Eva Bjørn Vedel; Rataj, J.
2008-01-01
A rotational version of the famous Crofton formula is derived. The motivation for deriving the formula comes from local stereology, a new branch of stereology based on sections through fixed reference points. The formula shows how rotational averages of intrinsic volumes measured on sections...
The Verlinde formula for Higgs bundles
Andersen, Jørgen Ellegaard; Pei, Du
2016-01-01
We propose and prove the Verlinde formula for the quantization of the Higgs bundle moduli spaces and stacks for any simple and simply-connected group. This generalizes the equivariant Verlinde formula for the case of $SU(n)$ proposed previously by the second and third author. We further establish a Verlinde formula for the quantization of parabolic Higgs bundle moduli spaces and stacks.
Relations Among Some Fuzzy Entropy Formulae
Institute of Scientific and Technical Information of China (English)
卿铭
2004-01-01
Fuzzy entropy has been widely used to analyze and design fuzzy systems, and many fuzzy entropy formulae have been proposed. For further in-deepth analysis of fuzzy entropy, the axioms and some important formulae of fuzzy entropy are introduced. Some equivalence results among these fuzzy entropy formulae are proved, and it is shown that fuzzy entropy is a special distance measurement.
Concerning Two Formulaic Classes in Computational Combinatorics
Institute of Scientific and Technical Information of China (English)
Leetsch C. HSU
2012-01-01
Here introduced and studied are two formulaic classes consisting of various combinatorial algebraic identities and series summation formulas.The basic ideas include utilizing properly the △-operator and Stirling numbers for some series transformations.A variety of classic formulas and remarkable identities are shown to be the members of the classes.
AN EXTREMAL APPROACH TO BIRKHOFF QUADRATURE FORMULAS
Institute of Scientific and Technical Information of China (English)
Ying-guang Shi
2001-01-01
As we know, a solution of an extremal problem with Hermite interpolation constraints is a system of nodes of corresponding Gaussian Hermite quadrature formula (the so-called Jacobi approach). But this conclusion is violated for a Birkhoff quadrature formula. In this paper an extremal problem with Birkhoff interpolation constraints is discussed, from which a large class of Birkhoff quadrature formulas may be derived.
Bryant J. correction formula; Formula corregida de J. Bryant
Energy Technology Data Exchange (ETDEWEB)
Tejera R, A.; Cortes P, A.; Becerril V, A
1990-03-15
For the practical application of the method proposed by J. Bryant, the authors carried out a series of small corrections, related with the bottom, the dead time of the detectors and channels, with the resolution time of the coincidences, with the accidental coincidences, with the decay scheme and with the gamma efficiency of the beta detector beta and the beta efficiency beta of the gamma detector. The calculation of the correction formula is presented in the development of the present report, being presented 25 combinations of the probability of the first existent state at once of one disintegration and the second state at once of the following disintegration. (Author)
Whiteness formula in CIELAB uniform color space
Institute of Scientific and Technical Information of China (English)
Guoxin He; Mingxun Zhou
2007-01-01
@@ Many attempts have been made to standardize the calculation of whiteness. Whiteness formulas currently in use satisfactorily characterize the appearance of commercial whiteness. However, they have poor correlations with the observers' evaluations, and are often unsuccessful in assessing tinted white samples.A whiteness formula in the CIELAB uniform color space is developed in this paper. Several whiteness formulas are analyzed and compared. The experimental results show that the whiteness formula in the CIELAB uniform color space agrees well with the visual ranking, and it is superior to the CIE whiteness formula and the others in visual correlativity, uniformity and applicability.
A novel mathematical formula for retrieval algorithm
2014-01-01
A method is proposed to retrieve mathematical formula in LaTeX documents. Firstly, we represent the retrieved mathematical formula by binary tree according to its LaTeX description, normalize the structure of the binary tree, and obtain the structure code and then search the mathematical formula table that is named by the structure code and the formula elements of the first two levels of the binary tree in the mathematical formula database. If the table exists, then we search the normalizing ...
Magical Formulae for Market Futures
DEFF Research Database (Denmark)
Garsten, Christina; Sörbom, Adrienne
2016-01-01
, and financial advisors are often savvy in the art of creatively blending the ‘objective facts’ of markets with magical formulae, rites, and imaginaries of the future. This article looks at the World Economic Forum's yearly Davos meeting as a large-scale ritual that engages senior executives of global......Markets are often portrayed as being organized by way of rationalized knowledge, objective reasoning, and the fluctuations of demand and supply. In parallel, and often mixed with this modality of knowledge, magical beliefs and practices are prevalent. Business leaders, management consultants....... By invoking global and regional challenges and risks, discussing possible scenarios and solutions, presenters invoke a sense of urgency and contribute to the articulation of global ‘problems’ and ‘solutions’. It is proposed that the magic of Davos resides to a large extent in the ritualized form...
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.
Multidimensional Datawarehouse with Combination Formula
Warnars, Spits
2010-01-01
Multidimensional in data warehouse is a compulsion and become the most important for information delivery, without multidimensional Multidimensional in data warehouse is a compulsion and become the most important for information delivery, without multidimensional datawarehouse is incomplete. Multidimensional give ability to analyze business measurement in many different ways. Multidimensional is also synonymous with online analytical processing (OLAP). By using some concepts in datawarehouse like slice-dice,drill down and roll up will increase the ability of multidimensional datawarehouse. The research question and the discussing for this paper are how much deepest the multidimensional ability from each fact table in datawarehouse. By using the statistic combination formula we try to explore the combination that can be yielded from each dimension in hypercubes, the entire of dimensi combination, minimum combination and maximum combination.
Cottingham formula and nucleon polarisabilities
Energy Technology Data Exchange (ETDEWEB)
Gasser, J.; Leutwyler, H. [Universitaet Bern, Albert Einstein Center for Fundamental Physics, Institut fuer theoretische Physik, Bern (Switzerland); Hoferichter, M. [Universitaet Bern, Albert Einstein Center for Fundamental Physics, Institut fuer theoretische Physik, Bern (Switzerland); Technische Universitaet Darmstadt, Institut fuer Kernphysik, Darmstadt (Germany); GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, ExtreMe Matter Institute EMMI, Darmstadt (Germany); University of Washington, Institute for Nuclear Theory, Seattle, WA (United States); Rusetsky, A. [Universitaet Bonn, Helmholtz-Institut fuer Strahlen- und Kernphysik (Theorie) and Bethe Center for Theoretical Physics, Bonn (Germany)
2015-08-15
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. (orig.)
Mathematical Formula Search using Natural Language Queries
Directory of Open Access Journals (Sweden)
YANG, S.
2014-11-01
Full Text Available This paper presents how to search mathematical formulae written in MathML when given plain words as a query. Since the proposed method allows natural language queries like the traditional Information Retrieval for the mathematical formula search, users do not need to enter any complicated math symbols and to use any formula input tool. For this, formula data is converted into plain texts, and features are extracted from the converted texts. In our experiments, we achieve an outstanding performance, a MRR of 0.659. In addition, we introduce how to utilize formula classification for formula search. By using class information, we finally achieve an improved performance, a MRR of 0.690.
Welfare Effects of Tariff Reduction Formulas
DEFF Research Database (Denmark)
Guldager, Jan G.; Schröder, Philipp J.H.
. This paper presents a two country intra-industry trade model with heterogeneous firms subject to high and low tariffs. We examine the welfare effects of applying three different tariff reduction formulas proposed in the literature i) a proportional cut, ii) the Swiss formula and iii) a compression formula......WTO negotiations rely on tariff reduction formulas. It has been argued that formula approaches are of increasing importance in trade talks, because of the large number of countries involved, the wider dispersion in initial tariffs (e.g. tariff peaks) and gaps between bound and applied tariff rates....... No single formula dominates for all conditions. The ranking of the three tools depends on the degree of product differentiation in the industry, and the achieved reduction in the average tariff....
[Hypoallergenic milks (HA formulas) in infant nutrition].
Zoppi, G
1993-01-01
According to the definition of the European Scientific Committee for Food, hypoallergenic or hypoantigenic formulas (HA-formulas) are those which contain hydrolysed protein derived both from casein or whey. Soy-based formulas are not comprised in this definition since it has been demonstrated from several years that soy-protein, in several circumstances, may be highly allergenic. Hypoallergenic formulas contain besides hydrolysed protein, carbohydrate and lipid in amount and proportion similar to those indicated by ESPGAN recommendations on adapted formulas. As far as it concerns composition in lipid, recently great attention has been given to optimal supply and ratio of omega 3 and omega 6 fatty acids. Hypoallergenic formulas are therefore suitable for balanced nutrition of suckling infants. Specific indications on prevention of atopic diseases are not treated.
Column Holdup Formula of Soil Solute Transport
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The shortcomings of the present two formulae for describing column holdup are analyzed and deductions are made to find a new formula. The column holdup, Hw, described by the new formula is dimensional,and related to soil solute transport kinesis and column physical properties. Compared with the other two column holdups, Hw is feasible to describe dimensional column holdup during solute transport process. The relationships between Hw and retardation factor, R, in different solute transport boundary conditions are established.
Elements and formulae of special relativity
Guggenheim, E A
2013-01-01
Elements and Formulae of Special Relativity presents elements and formulas of the theory of special relativity and covers topics ranging from kinematics and propagation of light to mechanics of single bodies, hydrodynamics, and thermodynamics. Vector operators, electromagnetic fields, electrodynamics, and statistical mechanics are also explored. This book is comprised of 13 chapters and begins by introducing the reader to the kinematics of special relativity, paying particular attention to formulas required for transformations between two frames of reference. Attention then turns to the propag
Synthesizing Accurate Floating-Point Formulas
Ioualalen, Arnault; Martel, Matthieu
2013-01-01
International audience; Many critical embedded systems perform floating-point computations yet their accuracy is difficult to assert and strongly depends on how formulas are written in programs. In this article, we focus on the synthesis of accurate formulas mathematically equal to the original formulas occurring in source codes. In general, an expression may be rewritten in many ways. To avoid any combinatorial explosion, we use an intermediate representation, called APEG, enabling us to rep...
Reconstruction Formulas for Photoacoustic Sectional Imaging
Elbau, Peter; Schulze, Rainer
2011-01-01
The literature on reconstruction formulas for photoacoustic tomography (PAT) is vast. The various reconstruction formulas differ by used measurement devices and geometry on which the data are sampled. In standard photoacoustic imaging (PAI), the object under investigation is illuminated uniformly. Recently, sectional photoacoustic imaging techniques, using focusing techniques for initializing and measuring the pressure along a plane, appeared in the literature. This paper surveys existing and provides novel exact reconstruction formulas for sectional photoacoustic imaging.
A General Framework for Probabilistic Characterizing Formulae
DEFF Research Database (Denmark)
Sack, Joshua; Zhang, Lijun
2012-01-01
a general method for determining characteristic formulae of behavioral relations for probabilistic automata using fixed-point probability logics. We consider such behavioral relations as simulations and bisimulations, probabilistic bisimulations, probabilistic weak simulations, and probabilistic forward......Recently, a general framework on characteristic formulae was proposed by Aceto et al. It offers a simple theory that allows one to easily obtain characteristic formulae of many non-probabilistic behavioral relations. Our paper studies their techniques in a probabilistic setting. We provide...
Girvin, Mike
2013-01-01
Designed with Excel gurus in mind, this handbook outlines how to create formulas that can be used to solve everyday problems with a series of data values that standard Excel formulas cannot or would be too arduous to attempt. Beginning with an introduction to array formulas, this manual examines topics such as how they differ from ordinary formulas, the benefits and drawbacks of their use, functions that can and cannot handle array calculations, and array constants and functions. Among the practical applications surveyed include how to extract data from tables and unique lists, how to get resu
Relating Turing's Formula and Zipf's Law
Samuelsson, C
1996-01-01
An asymptote is derived from Turing's local reestimation formula for population frequencies, and a local reestimation formula is derived from Zipf's law for the asymptotic behavior of population frequencies. The two are shown to be qualitatively different asymptotically, but nevertheless to be instances of a common class of reestimation-formula-asymptote pairs, in which they constitute the upper and lower bounds of the convergence region of the cumulative of the frequency function, as rank tends to infinity. The results demonstrate that Turing's formula is qualitatively different from the various extensions to Zipf's law, and suggest that it smooths the frequency estimates towards a geometric distribution.
Design Formula for Breakage of Tetrapods
DEFF Research Database (Denmark)
Burcharth, H. F.; Jensen, Jacob Birk; Liu, Z.
1995-01-01
The paper presents a design formula for Tetrapod armour on a 1:1.5 slope exposed to head-on random wave attack. The formula predicts the relative number of broken Tetrapods as function of: the mass of the Tetrapods, the concrete tensile strength and the wave height in front of the structure. Thus......, the formula addresses the observed problem of ensuring structural integrity of the slender types of non-reinforced armour units. The formula is based on results from small scale model tests with load-cell instrumented Tetrapods in which both the static, the quasi-static and the impact proportions of the loads...
Formulas in Physics Have a "Standard" Form
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…
101 ready-to-use Excel formulas
Alexander, Michael
2014-01-01
Mr. Spreadsheet has done it again with 101 easy-to-apply Excel formulas 101 Ready-to-Use Excel Formulas is filled with the most commonly-used, real-world Excel formulas that can be repurposed and put into action, saving you time and increasing your productivity. Each segment of this book outlines a common business or analysis problem that needs to be solved and provides the actual Excel formulas to solve the problem-along with detailed explanation of how the formulas work. Written in a user-friendly style that relies on a tips and tricks approach, the book details how to perform everyday Excel tasks with confidence. 101 Ready-to-Use Excel Formulas is sure to become your well-thumbed reference to solve your workplace problems. The recipes in the book are structured to first present the problem, then provide the formula solution, and finally show how it works so that it can be customized to fit your needs. The companion website to the book allows readers to easily test the formulas and provides visual confirmat...
Body surface area formulae: an alarming ambiguity.
Redlarski, Grzegorz; Palkowski, Aleksander; Krawczuk, Marek
2016-06-21
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.
Formula Approaches for Market Access Negotiations
J.F. François (Joseph); W. Martin (William)
2002-01-01
textabstractMost of the large tariff reductions achieved in multilateral trade negotiations have involved tariff-cutting formulas such as the "Swiss" formula. However, wide variations in initial tariff rates between active participants call for new approaches under the Doha Development Agenda. This
10 CFR 905.33 - Extension formula.
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... an appropriate public process. (d) The formula set forth in paragraph (a) of this section also...
Isomorphic Formulae in Classical Propositional Logic
Dosen, K
2009-01-01
Isomorphism between formulae is defined with respect to categories formalizing equality of deductions in classical propositional logic and in the multiplicative fragment of classical linear propositional logic caught by proof nets. This equality is motivated by generality of deductions. Characterizations are given for pairs of isomorphic formulae, which lead to decision procedures for this isomorphism.
Emergence String and Mass Formulas of Hadrons
Chang, Yi-Fang
2011-01-01
Assume that hadrons are formed from the emergence string. Usual string should possess two moving states: oscillation and rotation, so we propose corresponding potential and the equation of the emergence string, whose energy spectrum is namely the GMO mass formula and its modified accurate mass formula. These are some relations between the string and observable experimental data.
A Short Proof of Krattenthaler Formulas
Institute of Scientific and Technical Information of China (English)
MA Xin Rong
2002-01-01
With an effort to investigate a unified approach to the Lagrange inverse Krattenthaler established operator method we finally found a general pair of inverse relations, called the Krattenthaler formulas. The present paper presents a very short proof of this formula via Lagrange interpolation.Further, our method of proof declares that the Krattenthaler result is unique in the light of Lagrange interpolation.
40 CFR 74.26 - Allocation formula.
2010-07-01
...) SULFUR DIOXIDE OPT-INS Allowance Calculations for Combustion Sources § 74.26 Allocation formula. (a) The Administrator will calculate the annual allowance allocation for a combustion source based on the data... 40 Protection of Environment 16 2010-07-01 2010-07-01 false Allocation formula. 74.26 Section...
Borromean surgery formula for the Casson invariant
DEFF Research Database (Denmark)
Meilhan, Jean-Baptiste Odet Thierry
2008-01-01
It is known that every oriented integral homology 3-sphere can be obtained from S3 by a finite sequence of Borromean surgeries. We give an explicit formula for the variation of the Casson invariant under such a surgery move. The formula involves simple classical invariants, namely the framing, li...
The Lichnerowicz-Weitzenboeck formula and superconductivity
Energy Technology Data Exchange (ETDEWEB)
Vargas-Paredes, Alfredo A.; Doria, Mauro M. [Departamento de Fisica dos Solidos, Universidade Federal do Rio de Janeiro, 21941-972 Rio de Janeiro (Brazil); Neto, Jose Abdala Helayeel [Centro Brasileiro de Pesquisas Fisicas, 22290-160 Rio de Janeiro RJ (Brazil)
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.
A ``fractal'' modification of Torricelli's formula
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.
Approximate formulas for moderately small eikonal amplitudes
Kisselev, A V
2015-01-01
The eikonal approximation for moderately small scattering amplitudes is considered. With the purpose of using for their numerical estimations, the formulas are derived which contain no Bessel functions, and, hence, no rapidly oscillating integrands. To obtain these formulas, the improper integrals of the first kind which contain products of the Bessel functions J_0(z) are studied. The expression with four functions J_0(z) is generalized. The expressions for the integrals with the product of five and six Bessel functions J_0(z) are also found. The known formula for the improper integral with two functions J_nu(z) is generalized for non-integer nu.
Approximate formulas for moderately small eikonal amplitudes
Kisselev, A. V.
2016-08-01
We consider the eikonal approximation for moderately small scattering amplitudes. To find numerical estimates of these approximations, we derive formulas that contain no Bessel functions and consequently no rapidly oscillating integrands. To obtain these formulas, we study improper integrals of the first kind containing products of the Bessel functions J0(z). We generalize the expression with four functions J0(z) and also find expressions for the integrals with the product of five and six Bessel functions. We generalize a known formula for the improper integral with two functions Jυ (az) to the case with noninteger υ and complex a.
Analogues of Euler and Poisson Summation Formulae
Indian Academy of Sciences (India)
Vivek V Rane
2003-08-01
Euler–Maclaurin and Poisson analogues of the summations $\\sum_{a < n ≤ b}(n)f(n), \\sum_{a < n ≤ b}d(n) f(n), \\sum_{a < n ≤ b}d(n)(n) f(n)$ have been obtained in a unified manner, where (()) is a periodic complex sequence; () is the divisor function and () is a sufficiently smooth function on [, ]. We also state a generalised Abel's summation formula, generalised Euler's summation formula and Euler's summation formula in several variables.
Connection formula for thermal density functional theory
Pribram-Jones, Aurora
2015-01-01
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 upwards from the system's physical temperature to infinite temperatures. Several formulas yield one component of the thermal correlation free energy in terms of another, many of which can be expressed either in terms of temperature- or coupling-constant integration. We illustrate with the uniform electron gas.
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.
Institute of Scientific and Technical Information of China (English)
LU; Wenxuan
2006-01-01
Hodge integrals over moduli spaces of curves appear naturally during the localization procedure in computation of Gromov-Witten invariants. A remarkable formula of Marino-Vafa expresses a generation function of Hodge integrals via some combinatorial and algebraic data seemingly unrelated to these apriori algebraic geometric objects. We prove in this paper by directly expanding the formula and estimating the involved terms carefully that except a specific type all the other Hodge integrals involving up to three Hodge classes can be calculated from this formula. This implies that amazingly rich information about moduli spaces and Gromov-Witten invariants is encoded in this complicated formula. We also give some low genus examples which agree with the previous results in literature. Proofs and calculations are elementary as long as one accepts Mumford relations on the reductions of products of Hodge classes.
"Formula Student" / Malle Jürves
Jürves, Malle, 1950-
2008-01-01
Tehnikakõrgkooli ja tehnikaülikooli tudengite 17-liikmeline võiskond osales tänavu suvel Inglismaal Silverstone'i ringrajakompleksis peetaval tootearendusvõistlusel "Formula Student" omaehitatud vormelautoga
FORMULAS OF TENSION OF CONTINUOUS ROLLING PROCESS
Institute of Scientific and Technical Information of China (English)
J.Z. Zhang; X.P. Zhang
2007-01-01
The development of computer controlled continuous rolling process calls for a mathematicalexpression that can express the inequality condition of "constant flow". Tension is the link of thecontinuous rolling process. From the condition of dynamic equilibrium, a differential equation oftension is given out. On the basis of the physical rules established from the industrial practice andexperimental studies, the law of volume constancy, the linear relation of forward slip and tension,the state equation of continuous rolling, the formula of dynamic tension, and the formula of statictension have been obtained. These formulae reflect the functional relations between tensions,thickness, roll velocity, and time in the continuous rolling process. It is implied that the continuousrolling process is a gradually steady, controllable, and measurable dynamic system. An assumptionof predicting the thickness of a steel plate using these tension formulae is also put forward.
Formula One’s Financial Crisis
Institute of Scientific and Technical Information of China (English)
2009-01-01
The global economic slowdown is bad news for F1 auto racing Formula One (Fl), the world’s most expensive sport, faces major changes next season as Fl teams and the sport’s sanctioning body, the International
The strange formula of Dr. Koide
Rivero, A; Rivero, Alejandro; Gsponer, Andre
2005-01-01
We present a short historical and bibliographical review of the lepton mass formula of Yoshio Koide, as well as some speculations on its extensions to quark and neutrino masses, and its possible relations to more recent theoretical developments.
The Metaplectic Casselman-Shalika Formula
McNamara, Peter J
2011-01-01
This paper studies spherical Whittaker functions for central extensions of reductive groups over local fields. We follow the development of Chinta-Offen to produce a metaplectic Casselman-Shalika formula for tame covers of all unramified groups.
A Mass Formula for EYM Solitons
Corichi, A; Sudarsky, D; Corichi, Alejandro; Nucamendi, Ulises; Sudarsky, Daniel
2001-01-01
The recently introduced Isolated Horizon formalism, together with a simple phenomenological model for colored black holes is used to predict a formula for the ADM mass of the solitons of the EYM system in terms of horizon properties of black holes {\\it for all} values of the horizon area. In this note, this formula is tested numerically --up to a large value of the area-- for spherically symmetric solutions and shown to yield the known masses of the solitons.
A product formula and combinatorial field theory
Horzela, A; Duchamp, G H E; Penson, K A; Solomon, A I
2004-01-01
We treat the problem of normally ordering expressions involving the standard boson operators a, a* where [a,a*]=1. We show that a simple product formula for formal power series - essentially an extension of the Taylor expansion - leads to a double exponential formula which enables a powerful graphical description of the generating functions of the combinatorial sequences associated with such functions - in essence, a combinatorial field theory. We apply these techniques to some examples related to specific physical Hamiltonians.
Macdonald formula for curves with planar singularities
Maulik, Davesh
2011-01-01
We generalize Macdonald's formula for the cohomology of Hilbert schemes of points on a curve from smooth curves to curves with planar singularities: we relate the cohomology of the Hilbert schemes to the cohomology of the compactified Jacobian of the curve. The new formula is a consequence of a stronger identity between certain perverse sheaves defined by a family of curves satisfying mild conditions, whose proof makes an essential use of Ng\\^o's support theorem for compactified Jacobians.
A Summation Formula for Macdonald Polynomials
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.
A proof of image Euler Number formula
Institute of Scientific and Technical Information of China (English)
LIN Xiaozhu; SHA Yun; JI Junwei; WANG Yanmin
2006-01-01
Euler Number is one of the most important characteristics in topology. In two- dimension digital images, the Euler characteristic is locally computable. The form of Euler Number formula is different under 4-connected and 8-connected conditions. Based on the definition of the Foreground Segment and Neighbor Number, a formula of the Euler Number computing is proposed and is proved in this paper. It is a new idea to locally compute Euler Number of 2D image.
Supplementation of prebiotics in infant formula
Directory of Open Access Journals (Sweden)
Močić Pavić A
2014-06-01
Full Text Available Ana Močić Pavić, Iva Hojsak Referral Center for Pediatric Gastroenterology and Nutrition, Children's Hospital Zagreb, Zagreb, Croatia Background: In recent years prebiotics have been added to infant formula to make it resemble breast milk more closely and to promote growth and development of beneficial intestinal microbiota. This review aims to present new data on the possible positive effects of prebiotics in infant formula on intestinal microbiota (bifidogenic and lactogenic effect and on clinical outcomes including growth, infections, and allergies. With that aim, a literature search of the Cochrane Central Register of Controlled Trials (CENTRAL, EMBASE, Scopus, PubMed/Medline, Web of Science, and Science Direct in the last 10 years (December 2003 to December 2013 was performed. Results: Altogether 24 relevant studies were identified. It was found that during intervention, prebiotics can elicit a bifidogenic and lactogenic effect. As far as clinical outcomes were concerned, 14 studies investigated the effect of infant formula supplemented with prebiotics on growth and found that there was no difference when compared with non-supplemented infant formula. All available data are insufficient to support prebiotic supplementation in order to reduce risk of allergies and infections. Conclusion: There is currently no strong evidence to recommend routine supplementation of infant formulas with prebiotics. Further well-designed clinical studies with long-term follow-up are needed. Keywords: prebiotics, infant formula, growth, allergy, infections, supplementation
Connected formulas for amplitudes in standard model
He, Song; Zhang, Yong
2017-03-01
Witten's twistor string theory has led to new representations of S-matrix in massless QFT as a single object, including Cachazo-He-Yuan formulas in general and connected formulas in four dimensions. As a first step towards more realistic processes of the standard model, we extend the construction to QCD tree amplitudes with massless quarks and those with a Higgs boson. For both cases, we find connected formulas in four dimensions for all multiplicities which are very similar to the one for Yang-Mills amplitudes. The formula for quark-gluon color-ordered amplitudes differs from the pure-gluon case only by a Jacobian factor that depends on flavors and orderings of the quarks. In the formula for Higgs plus multi-parton amplitudes, the massive Higgs boson is effectively described by two additional massless legs which do not appear in the Parke-Taylor factor. The latter also represents the first twistor-string/connected formula for form factors.
Hypoallergenicity of an extensively hydrolyzed whey formula.
Giampietro, P G; Kjellman, N I; Oldaeus, G; Wouters-Wesseling, W; Businco, L
2001-04-01
Several different protein hydrolysate-based infant formulas have been promoted as hypoallergenic and considered suitable for the dietary management of cow's milk allergy (CMA). Accepting that none of the hydrolysate-based products is completely safe, the American Academy of Pediatrics (AAP) recommends that these formulas should be tested in a double-blind placebo-controlled setting and tolerated by at least 90% of children with proven CMA. In principle, this recommendation is also endorsed by the European Society of Paediatric Gastroenterology and Nutrition (ESPGAN) and the European Society of Paediatric Allergy and Clinical Immunology (ESPACI). In this two-center study, 32 children with proven CMA were tested with the extensive hydrolysate whey formula Nutrilon Pepti, for comparison with Profylac (extensive) and Nan HA (partial) whey hydrolysate products. Skin-prick tests (SPTs) were, respectively, positive to the three hydrolysate formulas in 19%, 15%, and 32% of children. After oral challenge it was concluded that 97% (95% CI: 85-100%) of the children tolerated Nutrilon Pepti, 94% (95% CI: 75-100%) tolerated Profylac, and 64% (95% CI: 37-81%) tolerated Nan HA. This study demonstrates that the extensive hydrolysates Nutrilon Pepti and Profylac are well tolerated in a population of children with proven CMA and that both products can be considered safe for their intended use. This study confirms that a very small number of children react even to extensively hydrolyzed formulas. SPT prior to oral exposure to the hydrolysate-based formulas can indicate whether a child is at risk of showing reactions to the product. Introduction of new products to these children should be carried out under a doctor's supervision. However, the majority of the SPT-positive children did tolerate the two extensively hydrolyzed whey-based formulas tested.
The ATOS[TM] Readability Formula for Books and How It Compares to Other Formulas. Report.
School Renaissance Inst., Inc., Madison, WI.
Readability formulas estimate how difficult text is to read. The resulting "readability level" helps teachers and school librarians match students to appropriate books. Guiding students to appropriate-level books is now easier and more accurate with the ATOS (Advantage-TASA Open Standard) Readability Formula for Books, the new…
Institute of Scientific and Technical Information of China (English)
CHEN CHANG-YUAN
2000-01-01
In this paper, the general formulas and the recurrence formulas for radial matrix elements of N-dimensional isotropic harmonic oscillator are obtained. The relevant results of 2- dimensional and 3- dimensiona] isotropic harmonic oscillators reported in the reference papers are contained in a more general equations derived in this paper as special cases.
Move! Eat better: try the FIT formula
CERN Medical Service
2013-01-01
In the physics world, some formulas lead to a Nobel prize. In the world of health and physical activity, the Medical Service also has a winning formula... FIT (physical activity) = Frequency x Intensity x Time Frequency = more than 3 times per week. Intensity = physical activity which slightly increases your heart rate and breathing rate. Time = more than 30 minutes (per session). As part of our Move! Eat better campaign, the Medical Service is still offering the use of a pedometer (available on loan from the infirmary), which is a really useful tool to help you reach the winning FIT formula. Interested in borrowing a CERN pedometer? Click here!
Explicit formulas for regularized products and series
Jorgenson, Jay; Goldfeld, Dorian
1994-01-01
The theory of explicit formulas for regularized products and series forms a natural continuation of the analytic theory developed in LNM 1564. These explicit formulas can be used to describe the quantitative behavior of various objects in analytic number theory and spectral theory. The present book deals with other applications arising from Gaussian test functions, leading to theta inversion formulas and corresponding new types of zeta functions which are Gaussian transforms of theta series rather than Mellin transforms, and satisfy additive functional equations. Their wide range of applications includes the spectral theory of a broad class of manifolds and also the theory of zeta functions in number theory and representation theory. Here the hyperbolic 3-manifolds are given as a significant example.
Langlands Program, Trace Formulas, and their Geometrization
Frenkel, Edward
2012-01-01
The Langlands Program relates Galois representations and automorphic representations of reductive algebraic groups. The trace formula is a powerful tool in the study of this connection and the Langlands Functoriality Conjecture. After giving an introduction to the Langlands Program and its geometric version, which applies to curves over finite fields and over the complex field, I give a survey of my recent joint work with Robert Langlands and Ngo Bao Chau (arXiv:1003.4578 and arXiv:1004.5323) on a new approach to proving the Functoriality Conjecture using the trace formulas, and on the geometrization of the trace formulas. In particular, I discuss the connection of the latter to the categorification of the Langlands correspondence.
A Generalized Sagnac-Wang-Fizeau formula
Ori, Amos
2016-01-01
We present a special-relativistic analysis of deformable interferometers where counter propagating beams share a common optical path. The optical path is allowed to change rather arbitrarily and need not be stationary. We show that, in the absence of dispersion the phase shift has two contributions. To leading order in $v/c$ one contribution is given by Wang empirical formula for deformable Sagnac interferometers. The second contribution is due to the stretching of the optical path and we give an explicit formula for this stretch term valid to first order in $v/c$. The analysis provides a unifying framework incorporating the Sagnac, Wang and Fizeau effects in a single scheme and gives a rigorous proof of Wang empirical formula.
Flowcharting the Meaning of Logic Formulas
Directory of Open Access Journals (Sweden)
Sabah Al-Fedaghi
2016-10-01
Full Text Available In logic, representation of a domain (e.g., physical reality comprises the things its expressions (formulas refer to and their relationships. Recent research has examined the realm of nonsymbolic representations, especially diagrams. It is claimed that, in general, diagrams have advantages over linguistic descriptions. Current diagrammatic representations of logic formulas do not completely depict their underlying semantics, and they lack a basic static structure that incorporates elementary dynamic features, creating a conceptual gap that can lead to misinterpretation. This paper demonstrates a methodology for mapping the sense of a logic formula and producing diagrams that integrate linguistic conception, truth-values, and meaning and can be used in teaching, communication, and understanding, especially with students specializing in logic representation and reasoning.
Completing the Complete ECC Formulae with Countermeasures
Directory of Open Access Journals (Sweden)
Łukasz Chmielewski
2017-02-01
Full Text Available This work implements and evaluates the recent complete addition formulae for the prime order elliptic curves of Renes, Costello and Batina on an FPGA platform. We implement three different versions:(1 an unprotected architecture; (2 an architecture protected through coordinate randomization; and (3 an architecture with both coordinate randomization and scalar splitting in place. The evaluation is done through timing analysis and test vector leakage assessment (TVLA. The results show that applying an increasing level of countermeasures leads to an increasing resistance against side-channel attacks. This is the ﬁrst work looking into side-channel security issues of hardware implementations of the complete formulae.
Mathematical formulas for industrial and mechanical engineering
Kadry, Seifedine
2014-01-01
Mathematical Formulas For Industrial and Mechanical Engineering serves the needs of students and teachers as well as professional workers in engineering who use mathematics. The contents and size make it especially convenient and portable. The widespread availability and low price of scientific calculators have greatly reduced the need for many numerical tables that make most handbooks bulky. However, most calculators do not give integrals, derivatives, series and other mathematical formulas and figures that are often needed. Accordingly, this book contains that information in an easy way to
Hexa-herbal Chinese formula for eczema
DEFF Research Database (Denmark)
Chang, J.; Jäger, Anna; Heinrich, M.
2014-01-01
Diverse pharmacological activities and reliable clinical performances of Chinese herbal medicines have attracted worldwide attention in terms of its modernization. Here, a hexa-herbal Chinese formula (HHCF) for treating eczema topically has been studied from both chemical and biological perspective...... colonizes the skin of most patients with AD and produces superantigens that could further increase severity of AD via subverting T-regulatory cell activity and inducing corticosteroid resistance. [3] Therefore, activity of the decoctions prepared from mixture and individual medicinal plants of the formula...
CRC standard mathematical tables and formulae
Zwillinger, Daniel
2002-01-01
New in the 31st edition:Game theory and voting powerHeuristic search techniquesQuadratic fieldsReliabilityRisk analysis and decision rulesA table of solutions to Pell's equationA table of irreducible polynomials in Z2[x]An interpretation of powers of 10A collection of ""proofs without words""Representations of groups of small orderCounting principlesTesselations and tilings…and much more!An indispensable, up-to-date resource, CRC Standard Mathematical Tables and Formulae, 31st Edition makes it effortless to find the equations, tables, and formulae you need most often.
Methods of computing Campbell-Hausdorff formula
Sogo, Kiyoshi
2016-11-01
A new method computing Campbell-Hausdorff formula is proposed by using quantum moment-cumulant relations, which is given by Weyl ordering symmetrization of classical moment-cumulant relations. The method enables one to readily use symbolic language software to compute arbitrary terms in the formula, and explicit expressions up to the 6-th order are obtained by the way of illustration. Further the symmetry Codd(A, B) = Codd(B, A), Ceven(A, B) = - Ceven(B, A) is found and proved. The operator differential method by Knapp is also examined for the comparison.
COMPARISON BETWEEN FORMULAS OF MAXIMUM SHIP SQUAT
Directory of Open Access Journals (Sweden)
PETRU SERGIU SERBAN
2016-06-01
Full Text Available Ship squat is a combined effect of ship’s draft and trim increase due to ship motion in limited navigation conditions. Over time, researchers conducted tests on models and ships to find a mathematical formula that can define squat. Various forms of calculating squat can be found in the literature. Among those most commonly used are of Barrass, Millward, Eryuzlu or ICORELS. This paper presents a comparison between the squat formulas to see the differences between them and which one provides the most satisfactory results. In this respect a cargo ship at different speeds was considered as a model for maximum squat calculations in canal navigation conditions.
On the robustness of random Boolean formulae
Energy Technology Data Exchange (ETDEWEB)
Mozeika, Alexander; Saad, David [Non-linearity and Complexity Research Group, Aston University, Birmingham B4 7ET (United Kingdom); Raymond, Jack, E-mail: a.s.mozeika@aston.ac.u, E-mail: d.saad@aston.ac.u [Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay (Hong Kong)
2010-06-01
Random Boolean formulae, generated by a growth process of noisy logical gates are analyzed using the generating functional methodology of statistical physics. We study the type of functions generated for different input distributions, their robustness for a given level of gate error and its dependence on the formulae depth and complexity and the gates used. Bounds on their performance, derived in the information theory literature for specific gates, are straightforwardly retrieved, generalized and identified as the corresponding typical-case phase transitions. Results for error-rates, function-depth and sensitivity of the generated functions are obtained for various gate-type and noise models.
Vacuum engineering, calculations, formulas, and solved exercises
Berman, Armand
1992-01-01
This book was written with two main objectives in mind-to summarize and organize the vast material of vacuum technology in sets of useful formulas, and to provide a collection of worked out exercises showing how to use these formulas for solving technological problems. It is an ideal reference source for those with little time to devote to a full mathematical treatment of the many problems issued in vacuum practice, but who have a working knowledge of the essentials of vacuum technology, elementary physics, and mathematics. This time saving book employs a problem-solving approach throughout, p
The Economic Vitality Formula of Success
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…
Index formulae for subspaces of Krein spaces
Dijksma, A; Gheondea, A
1996-01-01
For a subspace S of a Krein space K and an arbitrary fundamental decomposition K = K-[+]K+ of K, we prove the index formula k(-)(S) + dim(S-perpendicular to boolean AND K-+) = k(+)(S-perpendicular to)+ dim(S boolean AND K-), were k(+/-)(S) stands for the positive/negative signature of S. The differe
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.
A universal formula for network functions
DEFF Research Database (Denmark)
Skelboe, Stig
1975-01-01
A linear electrical network can be described in a convenient way by means of the node equations. This letter presents a universal formula which expresses any network function as the quotient of two determinants. The determinants belong to matrices derived from the indefinite nodal admittance...
Composition formulas in the Weyl calculus
DEFF Research Database (Denmark)
Kobayashi, Toshiyuki; Ørsted, Bent; Pevzner, Michael
2009-01-01
In pseudodifferential analysis, the usual composition formula, which has asymptotic value, extends that valid for differential operators. The one developed here is based instead on the decomposition of symbols (functions in Rn×Rn ) as integral superpositions of homogeneous ones, of degrees lying ...
An Automatic Proof of Euler's Formula
Directory of Open Access Journals (Sweden)
Jun Zhang
2005-05-01
Full Text Available In this information age, everything is digitalized. The encoding of functions and the automatic proof of functions are important. This paper will discuss the automatic calculation for Taylor expansion coefficients, as an example, it can be applied to prove Euler's formula automatically.
Behrndt, Jussi; Snoo, Henk de
2009-01-01
Kreĭn’s formula provides a parametrization of the generalized resolvents and Štraus extensions of a closed symmetric operator with equal possibly infinite defect numbers in a Hilbert space in terms of Nevanlinna families in a parameter space. The aim of this note is to give a simple complete analyti
Detecting Code Smells in Spreadsheet Formulas
Hermans, F.; Pinzger, M.; Van Deursen, A.
2011-01-01
Spreadsheets are used extensively in business processes around the world and just like software, spreadsheets are changed throughout their lifetime causing maintainability issues. This paper adapts known code smells to spreadsheet formulas. To that end we present a list of metrics by which we can de
Several explicit formulae for Bernoulli polynomials
Komatsu, Takao; Pita Ruiz V., Claudio de J.
2016-01-01
We prove several explicit formulae for the $n$-th Bernoulli polynomial $B_{n}(x)$, in which $B_{n}(x)$ is equal to an affine combination of the polynomials $(x-1)^{n}$, $(x-2)^{n}$, $ldots$, $(x-k-1)^{n}$, where $k$ is any fixed positive integer greater or equal than $n$.
Calculation of the CIPW norm: New formulas
Pruseth, Kamal L.
2009-02-01
A completely new set of formulas, based on matrix algebra, has been suggested for the calculation of the CIPW norm for igneous rocks to achieve highly consistent and accurate norms. The suggested sequence of derivation of the normative minerals greatly deviates from the sequence followed in the classical scheme. The formulas are presented in a form convenient for error-free implementation in computer programs. Accurate formulas along with the use of variable molecular weights for CaO and FeO; corrected formula weights for apatite, pyrite and fluorite; and suggested measures to avoid significant rounding off errors to achieve absolute match between the sum of the input weights of the oxides and the sum of the weights of the estimated normative minerals. Using an analogous procedure for determining the oxidation ratios of igneous rocks as used in the SINCLAS system of Verma et al (2002, 2003), the suggested calculation scheme exactly reproduces their results except for apatite for reasons explained in the text, but with a superior match between the totals for about 11,200 analyses representing rocks of a wide range of composition
Calculation of the CIPW norm: New formulas
Indian Academy of Sciences (India)
Kamal L Pruseth
2009-02-01
A completely new set of formulas,based on matrix algebra,has been suggested for the calculation of the CIPW norm for igneous rocks to achieve highly consistent and accurate norms.The suggested sequence of derivation of the normative minerals greatly deviates from the sequence followed in the classical scheme.The formulas are presented in a form convenient for error-free implementation in computer programs.Accurate formulas along with the use of variable molecular weights for CaO and FeO;corrected formula weights for apatite,pyrite and ﬂuorite;and suggested measures to avoid signiﬁcant rounding off errors to achieve absolute match between the sum of the input weights of the oxides and the sum of the weights of the estimated normative minerals.Using an analogous procedure for determining the oxidation ratios of igneous rocks as used in the SINCLAS system of Ver ma et al (2002,2003),the suggested calculation scheme exactly reproduces their results except for apatite for reasons explained in the text,but with a superior match between the totals for about 11,200 analyses representing rocks of a wide range of composition.
The mystery of the strange formulae
Bracken, Tony
2016-10-01
On a recent visit to the Wilhelm Röntgen memorial in Wurzburg, Germany, I noticed two strange trigonometric formulae set in the terrazzo floor at the western entrance to the building that houses Röntgen's X-ray laboratory.
Contradiction and Kant's Formula of Universal Law
Kleingeld, Pauline
2017-01-01
Kant’s most prominent formulation of the Categorical Imperative, known as the Formula of Universal Law (FUL), is generally thought to demand that one act only on maxims that one can will as universal laws without this generating a contradiction. Kant's view is standardly summarized as requiring the
25 CFR 273.31 - Distribution formula.
2010-04-01
... 25 Indians 1 2010-04-01 2010-04-01 false Distribution formula. 273.31 Section 273.31 Indians... ACT PROGRAM EDUCATION CONTRACTS UNDER JOHNSON-O'MALLEY ACT Funding Provisions § 273.31 Distribution... the purpose shall be allotted pro rata in accordance with the distribution method outlined in...
Rowlands, Derek J
2012-01-01
The QT interval on the electrocardiogram is an increasingly important measurement, especially in relation to drug action and interaction. The QT interval varies inversely as the heart rate and numerous rate correction formulae have been proposed. It is difficult to compare the effect of applying different formulae at different heart rates and for different measured QT intervals. A simple graphical display of the results from different formulae is proposed. This display is dependent on the concept of the absolute correction factor. This graphical presentation is useful (a) in comparing the effect of the application of different formulae and (b) in directly reading the correction produced by any individual formula.
Adaptive dispersion formula for index interpolation and chromatic aberration correction.
Li, Chia-Ling; Sasián, José
2014-01-13
This paper defines and discusses a glass dispersion formula that is adaptive. The formula exhibits superior convergence with a minimum number of coefficients. Using this formula we rationalize the correction of chromatic aberration per spectrum order. We compare the formula with the Sellmeier and Buchdahl formulas for glasses in the Schott catalogue. The six coefficient adaptive formula is found to be the most accurate with an average maximum index of refraction error of 2.91 × 10(-6) within the visible band.
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.
Universality of Mixed Action Extrapolation Formulae
Chen, Jiunn-Wei; Walker-Loud, Andre
2009-01-01
Mixed action theories with chirally symmetric valence fermions exhibit very desirable features both at the level of the lattice calculations as well as in the construction and implementation of the low energy mixed action effective field theory. In this work we show that when the mixed action effective field theory is projected onto the valence sector, both the Lagrangian and the extrapolation formulae become universal in form through next to leading order, for all variants of discretization methods used for the sea fermions. This implies that for all sea quark methods which are in the same universality class as QCD, the numerical values of the physical coefficients in the various mixed action chiral Lagrangians will be the same up to perturbative lattice spacing dependent corrections. This allows us to construct a prescription to determine the mixed action extrapolation formulae for a large class of hadronic correlation functions computed in partially quenched chiral perturbation theory at the one-loop level...
Asymptotic sampling formulae for Lambda-coalescents
Berestycki, Julien; Limic, Vlada
2012-01-01
We present a robust method which translates information on the speed of coming down from infinity of a genealogical tree into sampling formulae for the underlying population. We apply these results to population dynamics where the genealogy is given by a Lambda-coalescent. This allows us to derive an exact formula for the asymptotic behavior of the site and allele frequency spectrum and the number of segregating sites, as the sample size tends to infinity. Some of our results hold in the case of a general Lambda-coalescent that comes down from infinity, but we obtain more precise information under a regular variation assumption. In this case, we obtain results of independent interest for the time at which a mutation uniformly chosen at random was generated. This exhibits a phase transition at \\alpha=3/2, where \\alpha \\in(1,2) is the exponent of regular variation.
Message passing for quantified Boolean formulas
Zhang, Pan; Zdeborová, Lenka; Zecchina, Riccardo
2012-01-01
We introduce two types of message passing algorithms for quantified Boolean formulas (QBF). The first type is a message passing based heuristics that can prove unsatisfiability of the QBF by assigning the universal variables in such a way that the remaining formula is unsatisfiable. In the second type, we use message passing to guide branching heuristics of a Davis-Putnam Logemann-Loveland (DPLL) complete solver. Numerical experiments show that on random QBFs our branching heuristics gives robust exponential efficiency gain with respect to the state-of-art solvers. We also manage to solve some previously unsolved benchmarks from the QBFLIB library. Apart from this our study sheds light on using message passing in small systems and as subroutines in complete solvers.
Clause Elimination Procedures for CNF Formulas
Heule, Marijn; Järvisalo, Matti; Biere, Armin
We develop and analyze clause elimination procedures, a specific family of simplification techniques for conjunctive normal form (CNF) formulas. Extending known procedures such as tautology, subsumption, and blocked clause elimination, we introduce novel elimination procedures based on hidden and asymmetric variants of these techniques. We analyze the resulting nine (including five new) clause elimination procedures from various perspectives: size reduction, BCP-preservance, confluence, and logical equivalence. For the variants not preserving logical equivalence, we show how to reconstruct solutions to original CNFs from satisfying assignments to simplified CNFs. We also identify a clause elimination procedure that does a transitive reduction of the binary implication graph underlying any CNF formula purely on the CNF level.
Sum formulas for reductive algebraic groups
DEFF Research Database (Denmark)
Andersen, Henning Haahr; Kulkarni, Upendra
2008-01-01
Let $V$ be a Weyl module either for a reductive algebraic group $G$ or for the corresponding quantum group $U_q$. If $G$ is defined over a field of positive characteristic $p$, respectively if $q$ is a primitive $l$'th root of unity (in an arbitrary field) then $V$ has a Jantzen filtration $V=V^0...... \\supset V^1 \\cdots \\supset V^r = 0$. The sum of the positive terms in this filtration satisfies a well known sum formula. If $T$ denotes a tilting module either for $G$ or $U_q$ then we can similarly filter the space $\\Hom_G(V,T)$, respectively $\\Hom_{U_q}(V,T)$ and there is a sum formula for the positive...
Statics formulas and problems : engineering mechanics 1
Gross, Dietmar; Wriggers, Peter; Schröder, Jörg; Müller, Ralf
2017-01-01
This book contains the most important formulas and more than 160 completely solved problems from Statics. It provides engineering students material to improve their skills and helps to gain experience in solving engineering problems. Particular emphasis is placed on finding the solution path and formulating the basic equations. Topics include: - Equilibrium - Center of Gravity, Center of Mass, Centroids - Support Reactions - Trusses - Beams, Frames, Arches - Cables - Work and Potential Energy - Static and Kinetic Friction - Moments of Inertia.
Two tractable subclasses of minimal unsatisfiable formulas
Institute of Scientific and Technical Information of China (English)
赵希顺; 丁德成
1999-01-01
The minimal unsatisfiability problem is considered of the propositional formulas in CNF which in the case of variables x1,…, xn consist of n+k clauses including x1V…Vxn and （?） -（X1）V…V（?）xn. It is shown that when k≤4 the minimal unsatisfiability problem can be solved in polynomial time.
A Handbook of Essential Mathematical Formulae
Davies, Alan
2005-01-01
Intended for students of mathematics as well as of engineering, physical science, economics, business studies, and computer science, this handbook contains vital information and formulas for algebra, geometry, calculus, numerical methods, and statistics. Comprehensive tables of standard derivatives and integrals, together with the tables of Laplace, Fourier, and Z transforms are included. A spiral binding that allows the handbook to lay flat for easy reference enhances the user-friendly design.
A Generalized Formula to Determine Pythagorean Triples
Mohapatra, Amar Kumar; Prakash, Nupur
2010-01-01
This note proposes a unique solutions to find out the value of x, y and z which satisfies the equation x[superscript 2] + y[superscript 2] = z[superscript 2]. The uniqueness of the proposed formulae is to find the total number of y's and z's at a given value of x. The value of y and z can be calculated by factoring x[superscript 2] or…
Recursive formulae for the multiplicative partition function
Directory of Open Access Journals (Sweden)
Jun Kyo Kim
1999-01-01
Full Text Available For a positive integer n, let f(n be the number of essentially different ways of writing n as a product of factors greater than 1, where two factorizations of a positive integer are said to be essentially the same if they differ only in the order of the factors. This paper gives a recursive formula for the multiplicative partition function f(n.
Lessons in speed from Formula One.
2016-06-22
Could observing a sports team be the key to improving care in a time-critical hospital environment? Nick Evans, writing in Nursing Children and Young People, examines how a collaboration between a Formula One team and the University Hospital of Wales (UHW) generated ideas for clinicians to improve care. What similarities did the neonatal team at UHW spot between the sport and resuscitative care? And what changes did the hospital make following the collaboration?
Formula for a Solution of + (, D) =
Indian Academy of Sciences (India)
Adimurthi; G D Veerappa Gowda
2000-11-01
We study the continuous as well as the discontinuous solutions of Hamilton–Jacobi equation + (, D) = in $\\mathbb{R}^n × \\mathbb{R}_+$ with (, 0)=0(). The Hamiltonian (, ) is assumed to be convex and positively homogeneous of degree one in for each in $\\mathbb{R}$. If is non increasing in , in general, this problem need not admit a continuous viscosity solution. Even in this case we obtain a formula for discontinuous viscosity solutions.
Pocket book of integrals and mathematical formulas
Tallarida, Ronald J
2008-01-01
Convenient Organization of Essential Material so You Can Look up Formulas Fast Containing a careful selection of standard and timely topics, the Pocket Book of Integrals and Mathematical Formulas, Fourth Edition presents many numerical and statistical tables, scores of worked examples, and the most useful mathematical formulas for engineering and scientific applications. This fourth edition of a bestseller provides even more comprehensive coverage with the inclusion of several additional topics, all while maintaining its accessible, clear style and handy size. New to the Fourth Edition An expanded chapter on series that covers many fascinating properties of the natural numbers that follow from number theory New applications such as geostationary satellite orbits and drug kinetics An expanded statistics section that discusses nonlinear regression as well as the normal approximation of the binomial distribution Revised f...
A Hartree-Fock-Bogoliubov mass formula
Samyn, M; Heenen, P H; Pearson, J M; Tondeur, F
2002-01-01
In order to have more reliable predictions of nuclear masses at the neutron drip line, we here go beyond the recent mass formula HFBCS-1 and present a new mass formula, HFB-1, based on the Hartree-Fock-Bogoliubov method. As with the HFBCS-1 mass formula, we use a 10-parameter Skyrme force along with a 4-parameter delta-function pairing force and a 2-parameter phenomenological Wigner term. However, with the original HFBCS-1 Skyrme force (MSk7), the rms error becomes unacceptably large and a new force fit is required. With the isoscalar and isovector effective masses constrained to be equal, the remaining 15 degrees of freedom are fitted to the masses of all the 1754 measured nuclei with A>=16, |N-Z|>2 given in the 1995 Audi-Wapstra compilation. The rms error with respect to the masses of all the 1888 measured nuclei with Z,N>=8 is 0.764 MeV. A complete mass table, HFB-1 (available on the Web), has been constructed, giving all nuclei lying between the two drip lines over the range Z,N>=8 and Z<=120. A compar...
The health implications of soy infant formula.
Badger, Thomas M; Gilchrist, Janet M; Pivik, R Terry; Andres, Aline; Shankar, Kartik; Chen, Jin-Ran; Ronis, Martin J
2009-05-01
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). 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 of estrogenic effects of isoflavones contained in SF. There are few studies of children who were fed SF, and thus insufficient data are available to judge if SF feeding results in clinically significant developmental effects and if there are any long-term health consequences (adverse or beneficial). However, the Arkansas Children's Nutrition Center is conducting a prospective longitudinal study comparing growth, development, and health of breastfed children with formula-fed (SF and MF) children from birth through age 6 y. After 5 y of study, children in all 3 groups (n > 300) are growing and developing within normal limits, and there are no indications of adverse effects in the soy-fed children. Neonatal pig studies comparing SF, MF, and breast milk (BM) have shown diet-specific gene expression profiles in various target tissues. Therefore, although SF differed significantly from BM, MF also differed from BM, and SF differed from MF. Nonetheless, these animals grew and developed normally, and SF piglets had several health benefits (eg, increased bone quality) and no observable adverse effects. Thus, to date, our results suggest that SF supports normal growth and may have advantages in promoting bone development.
ON QUADRATURE FORMULAE FOR SINGULAR INTEGRALS OF ARBITRARY ORDER
Institute of Scientific and Technical Information of China (English)
杜金元
2004-01-01
Some quadrature formulae for the numerical evaluation of singular integrals of arbitrary order are established and both the estimate of remainder and the convergence of each quadrature formula derived here are also given.
A family quantization formula for symplectic manifolds with boundary
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
his paper generalizes the family quantization formula of Zh angto the case of manifolds with boundary. As an application, Tian-Zhang's ana lytic version of the Guillemin-Kalkman-Martin residue formula is generalized to the family case.
The Euler-Maclaurin Formula and Extensions - An Elementary Approach
Gearhart, W. B.; Qian, Maijian
2005-01-01
This note offers a derivation of the Euler-Maclaurin formula that is simple and elementary. In addition, the paper shows that the derivation provides Euler-Maclaurin formulas for a variety of functionals other than the trapezoid rule.
A family of inversion formulas in thermoacoustic tomography
Nguyen, Linh
2009-10-01
We present a family of closed form inversion formulas in thermoacoustic tomography in the case of a constant sound speed. The formulas are presented in both time-domain and frequency-domain versions. As special cases, they imply most of the previously known filtered backprojection type formulas. © 2009 AMERICAN INSTITUTE OF MATHEMATICAL SCIENCES.
7 CFR 761.205 - Computing the formula allocation.
2010-01-01
... 7 Agriculture 7 2010-01-01 2010-01-01 false Computing the formula allocation. 761.205 Section 761..., DEPARTMENT OF AGRICULTURE SPECIAL PROGRAMS GENERAL PROGRAM ADMINISTRATION Allocation of Farm Loan Programs Funds to State Offices § 761.205 Computing the formula allocation. (a) The formula allocation for FO...
p-adic Gauss integrals from the Poison summarizing formula
Prokhorenko, D V
2011-01-01
In the present paper we show how to obtain the well-known formula for Gauss sums and the Gauss reciprocity low from the Poison summarizing formula by using some ideas of renormalization and ergodic theories. We also apply our method to obtain new simple derivation of the standard formula for p-adic Gauss integrals.
Ultradiscrete soliton equations derived from ultradiscrete permanent formulae
Energy Technology Data Exchange (ETDEWEB)
Nakamura, Shinya, E-mail: s-nakamura@moegi.waseda.jp [Major in Pure and Applied Mathematics, Graduate School of Fundamental Science and Engineering, Waseda University, 3-4-1, Okubo, Shinjuku-ku, Tokyo 169-8555 (Japan)
2011-07-22
We propose formulae of ultradiscrete permanent. Utilizing the formulae, ultradiscrete soliton equations and their multi-soliton solutions are obtained by a simple process. Changing variables and parameters of the formulae, we can derive the ultradiscrete Toda, KdV and hungry Lotka-Volterra equations. An extended version of the ultradiscrete hungry Lotka-Volterra equation is also proposed.
27 CFR 21.49 - Formula No. 23-H.
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 23-H. 21.49 Section 21.49 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT... and Authorized Uses § 21.49 Formula No. 23-H. (a) Formula. To every 100 gallons of alcohol add:...
Addition formulae for Abelian functions associated with specialized curves.
Eilbeck, J C; Matsutani, S; Onishi, Y
2011-03-28
We discuss a family of multi-term addition formulae for Weierstrass functions on specialized curves of low genus with many automorphisms, concentrating mostly on the case of genus 1 and 2. In the genus 1 case, we give addition formulae for the equianharmonic and lemniscate cases, and in genus 2 we find some new addition formulae for a number of curves.
27 CFR 24.303 - Formula wine record.
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula wine record. 24..., DEPARTMENT OF THE TREASURY LIQUORS WINE Records and Reports § 24.303 Formula wine record. A proprietor who produces beverage formula wine shall maintain records showing by transaction date the details of...
Aaij, R; Beteta, C Abellán; Adeva, B; Adinolfi, M; Affolder, A; Ajaltouni, Z; Akar, S; Albrecht, J; Alessio, F; Alexander, M; Ali, S; Alkhazov, G; Alvarez Cartelle, P; Alves, A A; Amato, S; Amerio, S; Amhis, Y; An, L; Anderlini, L; Anderson, J; Andreassen, R; Andreotti, M; Andrews, J E; Appleby, R B; Aquines Gutierrez, O; Archilli, F; Artamonov, A; Artuso, M; Aslanides, E; Auriemma, G; Baalouch, M; Bachmann, S; Back, J J; Badalov, A; Baesso, C; Baldini, W; Barlow, R J; Barschel, C; Barsuk, S; Barter, W; Batozskaya, V; Battista, V; Bay, A; Beaucourt, L; Beddow, J; Bedeschi, F; Bediaga, I; Belogurov, S; Belous, K; Belyaev, I; Ben-Haim, E; Bencivenni, G; Benson, S; Benton, J; Berezhnoy, A; Bernet, R; Bettler, M-O; van Beuzekom, M; Bien, A; Bifani, S; Bird, T; Bizzeti, A; Bjørnstad, P M; Blake, T; Blanc, F; Blouw, J; Blusk, S; Bocci, V; Bondar, A; Bondar, N; Bonivento, W; Borghi, S; Borgia, A; Borsato, M; Bowcock, T J V; Bowen, E; Bozzi, C; Brambach, T; Bressieux, J; Brett, D; Britsch, M; Britton, T; Brodzicka, J; Brook, N H; Brown, H; Bursche, A; Busetto, G; Buytaert, J; Cadeddu, S; Calabrese, R; Calvi, M; Calvo Gomez, M; Campana, P; Campora Perez, D; Carbone, A; Carboni, G; Cardinale, R; Cardini, A; Carson, L; Carvalho Akiba, K; Casse, G; Cassina, L; Castillo Garcia, L; Cattaneo, M; Cauet, Ch; Cenci, R; Charles, M; Charpentier, Ph; Chefdeville, M; Chen, S; Cheung, S-F; Chiapolini, N; Chrzaszcz, M; Ciba, K; Cid Vidal, X; Ciezarek, G; Clarke, P E L; Clemencic, M; Cliff, H V; Closier, J; Coco, V; Cogan, J; Cogneras, E; Cogoni, V; Cojocariu, L; Collins, P; Comerma-Montells, A; Contu, A; Cook, A; Coombes, M; Coquereau, S; Corti, G; Corvo, M; Counts, I; Couturier, B; Cowan, G A; Craik, D C; Cruz Torres, M; Cunliffe, S; Currie, R; D'Ambrosio, C; Dalseno, J; David, P; David, P N Y; Davis, A; De Bruyn, K; De Capua, S; De Cian, M; De Miranda, J M; De Paula, L; De Silva, W; De Simone, P; Decamp, D; Deckenhoff, M; Del Buono, L; Déléage, N; Derkach, D; Deschamps, O; Dettori, F; Di Canto, A; Dijkstra, H; Donleavy, S; Dordei, F; Dorigo, M; Dosil Suárez, A; Dossett, D; Dovbnya, A; Dreimanis, K; Dujany, G; Dupertuis, F; Durante, P; Dzhelyadin, R; Dziurda, A; Dzyuba, A; Easo, S; Egede, U; Egorychev, V; Eidelman, S; Eisenhardt, S; Eitschberger, U; Ekelhof, R; Eklund, L; El Rifai, I; Elena, E; Elsasser, Ch; Ely, S; Esen, S; Evans, H-M; Evans, T; Falabella, A; Färber, C; Farinelli, C; Farley, N; Farry, S; Fay, R F; Ferguson, D; Fernandez Albor, V; Ferreira Rodrigues, F; Ferro-Luzzi, M; Filippov, S; Fiore, M; Fiorini, M; Firlej, M; Fitzpatrick, C; Fiutowski, T; Fol, P; Fontana, M; Fontanelli, F; Forty, R; Francisco, O; Frank, M; Frei, C; Frosini, M; Fu, J; Furfaro, E; Gallas Torreira, A; Galli, D; Gallorini, S; Gambetta, S; Gandelman, M; Gandini, P; Gao, Y; García Pardiñas, J; Garofoli, J; Garra Tico, J; Garrido, L; Gaspar, C; Gauld, R; Gavardi, L; Gavrilov, G; Geraci, A; Gersabeck, E; Gersabeck, M; Gershon, T; Ghez, Ph; Gianelle, A; Gianì, S; Gibson, V; Giubega, L; Gligorov, V V; Göbel, C; Golubkov, D; Golutvin, A; Gomes, A; Gotti, C; Grabalosa Gándara, M; Graciani Diaz, R; Granado Cardoso, L A; Graugés, E; Graziani, G; Grecu, A; Greening, E; Gregson, S; Griffith, P; Grillo, L; Grünberg, O; Gui, B; Gushchin, E; Guz, Yu; Gys, T; Hadjivasiliou, C; Haefeli, G; Haen, C; Haines, S C; Hall, S; Hamilton, B; Hampson, T; Han, X; Hansmann-Menzemer, S; Harnew, N; Harnew, S T; Harrison, J; He, J; Head, T; Heijne, V; Hennessy, K; Henrard, P; Henry, L; Hernando Morata, J A; van Herwijnen, E; Heß, M; Hicheur, A; Hill, D; Hoballah, M; Hombach, C; Hulsbergen, W; Hunt, P; Hussain, N; Hutchcroft, D; Hynds, D; Idzik, M; Ilten, P; Jacobsson, R; Jaeger, A; Jalocha, J; Jans, E; Jaton, P; Jawahery, A; Jing, F; John, M; Johnson, D; Jones, C R; Joram, C; Jost, B; Jurik, N; Kaballo, M; Kandybei, S; Kanso, W; Karacson, M; Karbach, T M; Karodia, S; Kelsey, M; Kenyon, I R; Ketel, T; Khanji, B; Khurewathanakul, C; Klaver, S; Klimaszewski, K; Kochebina, O; Kolpin, M; Komarov, I; Koopman, R F; Koppenburg, P; Korolev, M; Kozlinskiy, A; Kravchuk, L; Kreplin, K; Kreps, M; Krocker, G; Krokovny, P; Kruse, F; Kucewicz, W; Kucharczyk, M; Kudryavtsev, V; Kurek, K; Kvaratskheliya, T; La Thi, V N; Lacarrere, D; Lafferty, G; Lai, A; Lambert, D; Lambert, R W; Lanfranchi, G; Langenbruch, C; Langhans, B; Latham, T; Lazzeroni, C; Le Gac, R; van Leerdam, J; Lees, J-P; Lefèvre, R; Leflat, A; Lefrançois, J; Leo, S; Leroy, O; Lesiak, T; Leverington, B; Li, Y; Likhomanenko, T; Liles, M; Lindner, R; Linn, C; Lionetto, F; Liu, B; Lohn, S; Longstaff, I; Lopes, J H; Lopez-March, N; Lowdon, P; Lucchesi, D; Luo, H; Lupato, A; Luppi, E; Lupton, O; Machefert, F; Machikhiliyan, I V; Maciuc, F; Maev, O; Malde, S; Malinin, A; Manca, G; Mancinelli, G; Mapelli, A; Maratas, J; Marchand, J F; Marconi, U; Marin Benito, C; Marino, P; Märki, R; Marks, J; Martellotti, G; Martens, A; Sánchez, A Martín; Martinelli, M; Martinez Santos, D; Martinez Vidal, F; Martins Tostes, D; Massafferri, A; Matev, R; Mathe, Z; Matteuzzi, C; Mazurov, A; McCann, M; McCarthy, J; McNab, A; McNulty, R; McSkelly, B; Meadows, B; Meier, F; Meissner, M; Merk, M; Milanes, D A; Minard, M-N; Moggi, N; Molina Rodriguez, J; Monteil, S; Morandin, M; Morawski, P; Mordà, A; Morello, M J; Moron, J; Morris, A-B; Mountain, R; Muheim, F; Müller, K; Mussini, M; Muster, B; Naik, P; Nakada, T; Nandakumar, R; Nasteva, I; Needham, M; Neri, N; Neubert, S; Neufeld, N; Neuner, M; Nguyen, A D; Nguyen, T D; Nguyen-Mau, C; Nicol, M; Niess, V; Niet, R; Nikitin, N; Nikodem, T; Novoselov, A; O'Hanlon, D P; Oblakowska-Mucha, A; Obraztsov, V; Oggero, S; Ogilvy, S; Okhrimenko, O; Oldeman, R; Onderwater, G; Orlandea, M; Otalora Goicochea, J M; Owen, P; Oyanguren, A; Pal, B K; Palano, A; Palombo, F; Palutan, M; Panman, J; Papanestis, A; Pappagallo, M; Pappalardo, L L; Parkes, C; Parkinson, C J; Passaleva, G; Patel, G D; Patel, M; Patrignani, C; Alvarez, A Pazos; Pearce, A; Pellegrino, A; Pepe Altarelli, M; Perazzini, S; Trigo, E Perez; Perret, P; Perrin-Terrin, M; Pescatore, L; Pesen, E; Petridis, K; Petrolini, A; Picatoste Olloqui, E; Pietrzyk, B; Pilař, T; Pinci, D; Pistone, A; Playfer, S; Plo Casasus, M; Polci, F; Poluektov, A; Polycarpo, E; Popov, A; Popov, D; Popovici, B; Potterat, C; Price, E; Price, J D; Prisciandaro, J; Pritchard, A; Prouve, C; Pugatch, V; Puig Navarro, A; Punzi, G; Qian, W; Rachwal, B; Rademacker, J H; Rakotomiaramanana, B; Rama, M; Rangel, M S; Raniuk, I; Rauschmayr, N; Raven, G; Redi, F; Reichert, S; Reid, M M; Dos Reis, A C; Ricciardi, S; Richards, S; Rihl, M; Rinnert, K; Rives Molina, V; Robbe, P; Rodrigues, A B; Rodrigues, E; Rodriguez Perez, P; Roiser, S; Romanovsky, V; Romero Vidal, A; Rotondo, M; Rouvinet, J; Ruf, T; Ruiz, H; Ruiz Valls, P; Saborido Silva, J J; Sagidova, N; Sail, P; Saitta, B; Salustino Guimaraes, V; Sanchez Mayordomo, C; Sanmartin Sedes, B; Santacesaria, R; Santamarina Rios, C; Santovetti, E; Sarti, A; Satriano, C; Satta, A; Saunders, D M; Savrie, M; Savrina, D; Schiller, M; Schindler, H; Schlupp, M; Schmelling, M; Schmidt, B; Schneider, O; Schopper, A; Schune, M-H; Schwemmer, R; Sciascia, B; Sciubba, A; Seco, M; Semennikov, A; Sepp, I; Serra, N; Serrano, J; Sestini, L; Seyfert, P; Shapkin, M; Shapoval, I; Shcheglov, Y; Shears, T; Shekhtman, L; Shevchenko, V; Shires, A; Silva Coutinho, R; Simi, G; Sirendi, M; Skidmore, N; Skwarnicki, T; Smith, N A; Smith, E; Smith, E; Smith, J; Smith, M; Snoek, H; Sokoloff, M D; Soler, F J P; Soomro, F; Souza, D; De Paula, B Souza; Spaan, B; Sparkes, A; Spradlin, P; Sridharan, S; Stagni, F; Stahl, M; Stahl, S; Steinkamp, O; Stenyakin, O; Stevenson, S; Stoica, S; Stone, S; Storaci, B; Stracka, S; Straticiuc, M; Straumann, U; Stroili, R; Subbiah, V K; Sun, L; Sutcliffe, W; Swientek, K; Swientek, S; Syropoulos, V; Szczekowski, M; Szczypka, P; Szilard, D; Szumlak, T; T'Jampens, S; Teklishyn, M; Tellarini, G; Teubert, F; Thomas, C; Thomas, E; van Tilburg, J; Tisserand, V; Tobin, M; Tolk, S; Tomassetti, L; Tonelli, D; Topp-Joergensen, S; Torr, N; Tournefier, E; Tourneur, S; Tran, M T; Tresch, M; Tsaregorodtsev, A; Tsopelas, P; Tuning, N; Ubeda Garcia, M; Ukleja, A; Ustyuzhanin, A; Uwer, U; Vacca, C; Vagnoni, V; Valenti, G; Vallier, A; Vazquez Gomez, R; Vazquez Regueiro, P; Vázquez Sierra, C; Vecchi, S; Velthuis, J J; Veltri, M; Veneziano, G; Vesterinen, M; Viaud, B; Vieira, D; Vieites Diaz, M; Vilasis-Cardona, X; Vollhardt, A; Volyanskyy, D; Voong, D; Vorobyev, A; Vorobyev, V; Voß, C; Voss, H; de Vries, J A; Waldi, R; Wallace, C; Wallace, R; Walsh, J; Wandernoth, S; Wang, J; Ward, D R; Watson, N K; Websdale, D; Whitehead, M; Wicht, J; Wiedner, D; Wilkinson, G; Williams, M P; Williams, M; Wilschut, H W; Wilson, F F; Wimberley, J; Wishahi, J; Wislicki, W; Witek, M; Wormser, G; Wotton, S A; Wright, S; Wyllie, K; Xie, Y; Xing, Z; Xu, Z; Yang, Z; Yuan, X; Yushchenko, O; Zangoli, M; Zavertyaev, M; Zhang, L; Zhang, W C; Zhang, Y; Zhelezov, A; Zhokhov, A; Zhong, L; Zvyagin, A
The production of the [Formula: see text] state in proton-proton collisions is probed via its decay to the [Formula: see text] final state with the LHCb detector, in the rapidity range [Formula: see text] and in the meson transverse-momentum range [Formula: see text]. The cross-section for prompt production of [Formula: see text] mesons relative to the prompt [Formula: see text] cross-section is measured, for the first time, to be [Formula: see text] at a centre-of-mass energy [Formula: see text] using data corresponding to an integrated luminosity of 0.7 fb[Formula: see text], and [Formula: see text] at [Formula: see text] using 2.0 fb[Formula: see text]. The uncertainties quoted are, in order, statistical, systematic, and that on the ratio of branching fractions of the [Formula: see text] and [Formula: see text] decays to the [Formula: see text] final state. In addition, the inclusive branching fraction of [Formula: see text]-hadron decays into [Formula: see text] mesons is measured, for the first time, to be [Formula: see text], where the third uncertainty includes also the uncertainty on the [Formula: see text] inclusive branching fraction from [Formula: see text]-hadron decays. The difference between the [Formula: see text] and [Formula: see text] meson masses is determined to be [Formula: see text].
Some new addition formulae for Weierstrass elliptic functions.
Eilbeck, J Chris; England, Matthew; Onishi, Yoshihiro
2014-11-08
We present new addition formulae for the Weierstrass functions associated with a general elliptic curve. We prove the structure of the formulae in n-variables and give the explicit addition formulae for the 2- and 3-variable cases. These new results were inspired by new addition formulae found in the case of an equianharmonic curve, which we can now observe as a specialization of the results here. The new formulae, and the techniques used to find them, also follow the recent work for the generalization of Weierstrass functions to curves of higher genus.
The Global Properties of Valid Formulas in Modal Logic K
Institute of Scientific and Technical Information of China (English)
孙吉贵; 程晓春; 等
1996-01-01
Global property is the necessary condition which must be satisfied by the provable formulas.It can help to find out some unprovable formula that does not satisfy some global property before proving it using formal automated reasoning systems,thus the efficiency of the whole system is improved.This paper presents some global properties of valid formulas in modal logic K.Such properties are structure characters of formulas,so they are simple and easy to check.At the same time,some global properties of K unsatisfiable formula set are also given.
The chemical formula of a magnetotactic bacterium.
Naresh, Mohit; Das, Sayoni; Mishra, Prashant; Mittal, Aditya
2012-05-01
Elucidation of the chemical logic of life is one of the grand challenges in biology, and essential to the progress of the upcoming field of synthetic biology. Treatment of microbial cells explicitly as a "chemical" species in controlled reaction (growth) environments has allowed fascinating discoveries of elemental formulae of a few species that have guided the modern views on compositions of a living cell. Application of mass and energy balances on living cells has proved to be useful in modeling of bioengineering systems, particularly in deriving optimized media compositions for growing microorganisms to maximize yields of desired bio-derived products by regulating intra-cellular metabolic networks. In this work, application of elemental mass balance during growth of Magnetospirillum gryphiswaldense in bioreactors has resulted in the discovery of the chemical formula of the magnetotactic bacterium. By developing a stoichiometric equation characterizing the formation of a magnetotactic bacterial cell, coupled with rigorous experimental measurements and robust calculations, we report the elemental formula of M. gryphiswaldense cell as CH(2.06)O(0.13)N(0.28)Fe(1.74×10(-3)). Remarkably, we find that iron metabolism during growth of this magnetotactic bacterium is much more correlated individually with carbon and nitrogen, compared to carbon and nitrogen with each other, indicating that iron serves more as a nutrient during bacterial growth rather than just a mineral. Magnetotactic bacteria have not only invoked some interest in the field of astrobiology for the last two decades, but are also prokaryotes having the unique ability of synthesizing membrane bound intracellular organelles. Our findings on these unique prokaryotes are a strong addition to the limited repertoire, of elemental compositions of living cells, aimed at exploring the chemical logic of life.
Excel formulas and functions for dummies
Bluttman, Ken
2013-01-01
Learn to use Excel for practical, day-to-day calculations Excel is a powerful program with more than 300 built-in functions that can be used to perform an almost infinite number of calculations. This friendly book shows you how to use the 150 most valuable ones in real-world situations: to compare the cost of buying vs. leasing a car, calculate classroom grades, or evaluate investment performance, for example. Another 85 specialized functions are also described. Detailed, step-by-step instructions help you understand how functions work within formulas and how you can use them t
Dirac's monopole, quaternions, and the Zassenhaus formula
Soloviev, Michael A
2016-01-01
Starting from the quaternionic quantization scheme proposed by Emch and Jadczyk for describing the motion of a quantum particle in the magnetic monopole field, we derive an algorithm for finding the differential representation of the star product generated by the quaternionic Weyl correspondence on phase-space functions. This procedure is illustrated by explicit calculation of the star product up to the second order in the Planck constant. Our main tools are an operator analog of the twisted convolution and the Zassenhaus formula for the products of exponentials of noncommuting operators.
Local index formula and twisted spectral triples
Moscovici, Henri
2009-01-01
We prove a local index formula for a class of twisted spectral triples of type III modeled on the transverse geometry of conformal foliations with locally constant transverse conformal factor. Compared with the earlier proof of the untwisted case, the novel aspect resides in the fact that the twisted analogues of the JLO entire cocycle and of its retraction are no longer cocycles in their respective Connes bicomplexes. We show however that the passage to the infinite temperature limit, respectively the integration along the full temperature range against the Haar measure of the positive half-line, has the remarkable effect of curing in both cases the deviations from the cocycle identity.
THE CODIMENSION FORMULA ON AF-COSUBMODULES
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
Let M1,M2 be submodules of analytic Hilbert module X on Ω( Cn) such that M1 M2and dimM1/M2 = k ＜∞.If M2 is an AF-cosubmodule,then the codimension dimM1/M2 of M2 in M1 equals the cardinality of zeros of M2 related to M1 by counting multiplicities.The codimension formula has some interesting applications.In particular,the author calculates out the dimension of Rudin quotient module,which is raised in [14].
Crystal chemical formula for sartorite homologues
DEFF Research Database (Denmark)
Makovicky, Emil; Topa, Dan
2015-01-01
The members of the sartorite homologous series are complex sulfides Me 2+ 8N–16–2X Me 3+ 16+X Me + XS8N+8where Me 2+ is Pb and Me 3+ is As and Sb, whereas Me + is Ag and/or Tl. This paper presents calculation formulae for the homologue order N and for the separate substitution percentages for Tl...
ON IMMERSION FORMULAS FOR SOLITON SURFACES
Directory of Open Access Journals (Sweden)
Alfred Michel Grundland
2016-06-01
Full Text Available This paper is devoted to a study of the connections between three different analytic descriptions for the immersion functions of 2D-surfaces corresponding to the following three types of symmetries: gauge symmetries of the linear spectral problem, conformal transformations in the spectral parameter and generalized symmetries of the associated integrable system. After a brief exposition of the theory of soliton surfaces and of the main tool used to study classical and generalized Lie symmetries, we derive the necessary and sufficient conditions under which the immersion formulas associated with these symmetries are linked by gauge transformations. We illustrate the theoretical results by examples involving the sigma model.
Perturbative Semiclassical Trace Formulae for Harmonic Oscillators
DEFF Research Database (Denmark)
Møller-Andersen, Jakob; Ögren, Magnus
2015-01-01
In this article we extend previous semiclassical studies by including more general perturbative potentials of the harmonic oscillator in arbitrary spatial dimensions. Our starting point is a radial harmonic potential with an arbitrary even monomial perturbation, which we use to study the resulting...... U(D) to O(D) symmetry breaking. We derive the gross structure of the semiclassical spectrum from periodic orbit theory, in the form of a perturbative (ħ → 0) trace formula. We then show how to apply the results to even-order polynomial potentials, possibly including mean-field terms. We have drawn...
Variational formulas of higher order mean curvatures
Xu, Ling
2011-01-01
In this paper, we establish the first variational formula and its Euler-Lagrange equation for the total $2p$-th mean curvature functional $\\mathcal {M}_{2p}$ of a submanifold $M^n$ in a general Riemannian manifold $N^{n+m}$ for $p=0,1,...,[\\frac{n}{2}]$. As an example, we prove that closed complex submanifolds in complex projective spaces are critical points of the functional $\\mathcal {M}_{2p}$, called relatively $2p$-minimal submanifolds, for all $p$. At last, we discuss the relations between relatively $2p$-minimal submanifolds and austere submanifolds in real space forms, as well as a special variational problem.
Dynamics formulas and problems : engineering mechanics 3
Gross, Dietmar; Wriggers, Peter; Schröder, Jörg; Müller, Ralf
2017-01-01
This book contains the most important formulas and more than 190 completely solved problems from Kinetics and Hydrodynamics. It provides engineering students material to improve their skills and helps to gain experience in solving engineering problems. Particular emphasis is placed on finding the solution path and formulating the basic equations. Topics include: - Kinematics of a Point - Kinetics of a Point Mass- Dynamics of a System of Point Masses - Kinematics of Rigid Bodies - Kinetics of Rigid Bodies - Impact - Vibrations - Non-Inertial Reference Frames - Hydrodynamics .
What's in the Bottle? A Review of Infant Formulas.
Green Corkins, Kelly; Shurley, Teresa
2016-09-19
Infant formulas are designed to be a substitute for breast milk. Since they are sole source of nutrition for growing and developing infants, they are highly regulated by the government. All ingredients in infant formulas must be considered "generally recognized as safe." Manufacturers are continually modifying their products to make them more like breast milk. Functional ingredients added to infant formula include long-chain polyunsaturated fatty acids, nucleotides, prebiotics, and probiotics. The most common breast milk substitutes are standard cow's milk-based term infant formulas, which include subcategories of organic and breast milk supplementation, and come in standard dilutions of 19 or 20 calories per ounce. In addition to standard cow's milk-based term infant formulas, there is a line of term infant formulas marketed for signs and symptoms of intolerance. These products include modifications in lactose content, partially hydrolyzed protein, added probiotics, or added rice starch. There are also specialized formulas for medical conditions such as prematurity, gastrointestinal disorders, allergy, disorders of fat metabolism, and renal insufficiency. Infants on specialty formulas should be monitored closely by medical professionals. Formulas come in ready-to-feed, liquid concentrate, and powder forms. Each offers advantages and disadvantages. Each step in the formula mixing process or each manipulation required for the feeding is another opportunity to introduce bacteria to the formula. There are guidelines for preparing formula in institutions. Standard dilution and mixing instructions are different for each formula, so individual recipes are needed. Caregivers should also be educated on proper hygiene when preparing formula at home.
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). 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.
Proximate and elemental analysis of infant formula.
Tanner, J T
1982-11-01
The Nutrient Surveillance Branch has been conducting a survey of infant formula products for Fiscal Year 1981. Each product has been carefully analyzed and the results compared to the label declaration and the minimum-maximum limits specified by the American Academy of Pediatrics' Committee on Nutrition (CON/AAP). Proximate and elemental analyses were made. Protein, fat, ash, and total solids (moisture) were determined by AOAC methods. Osmolality, density, and fatty acids (linoleic) were also determined. Carbohydrates were calculated by difference and caloric content was calculated by using the general Atwater factors. Elemental analysis for Ca, P, Mg, Fe, Zn, Cu, Mn, Na, and K were performed by induction coupled plasma absorption spectroscopy. Chloride was assayed by potentiometric titration with AgNO3. A summary of the findings from the infant formula survey have been compared with CON/AAP recommendations. In general, there were only a few exceptions where the label claims and the CON/AAP requirements were not met. However, in none of these cases was the difference considered to be of public health significance.
Surface diffuseness correction in global mass formula
Wang, Ning; Wu, Xizhen; Meng, Jie
2014-01-01
By taking into account the surface diffuseness correction for unstable nuclei, the accuracy of the macroscopic-microscopic mass formula is further improved. The rms deviation with respect to essentially all the available mass data falls to 298 keV, crossing the 0.3 MeV accuracy threshold for the first time within the mean-field framework. Considering the surface effect of the symmetry potential which plays an important role in the evolution of the "neutron skin" toward the "neutron halo" of nuclei approaching the neutron drip line, we obtain an optimal value of the symmetry energy coefficient J=30.16 MeV. With an accuracy of 258 keV for all the available neutron separation energies and of 237 keV for the alpha-decay Q-values of super-heavy nuclei, the proposed mass formula is particularly important not only for the reliable description of the r-process of nucleosynthesis but also for the study of the synthesis of super-heavy nuclei.
Multilinear Formulas and Skepticism of Quantum Computing
Aaronson, S
2003-01-01
Several researchers, including Leonid Levin, Gerard 't Hooft, and Stephen Wolfram, have argued that quantum mechanics will break down before the factoring of large numbers becomes possible. If this is true, then there should be a natural "Sure/Shor separator" -- that is, a set of quantum states that can account for all experiments performed to date, but not for Shor's factoring algorithm. We propose as a candidate the set of states expressible by a polynomial number of additions and tensor products. Using a recent lower bound on multilinear formula size due to Raz, we then show that states arising in quantum error-correction require n^{Omega(log n)} additions and tensor products even to approximate, which incidentally yields the first superpolynomial gap between general and multilinear formula size of functions. More broadly, we introduce a complexity classification of pure quantum states, and prove many basic facts about this classification. Our goal is to refine vague ideas about a breakdown of quantum mech...
From formulas to cirquents in computability logic
Japaridze, Giorgi
2009-01-01
Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently introduced semantical platform and ambitious program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth which logic has more traditionally been. Its expressions represent interactive computational tasks seen as games played by a machine against the environment, and "truth" is understood as existence of an algorithmic winning strategy. With logical operators standing for operations on games, the formalism of CL is open-ended, and has already undergone series of extensions. This article extends the expressive power of CL in a qualitatively new way, generalizing formulas (to which the earlier languages of CL were limited) to circuit-style structures termed cirquents. The latter, unlike formulas, are able to account for subgame/subtask sharing between different parts of the overall game/task. Among the many advantages offered by this ability is that it allows us to capture, refin...
Recurrence Formulas for the Mie Series
Institute of Scientific and Technical Information of China (English)
SUN Ji-Yu; XIE Hong
2011-01-01
The Mie series has very important applications in electromagnetics (including optics). We employ a formulation for the Mie series which relies more on the derivatives of Legendre polynomials than Bessel functions. Recurrence formulas for derivatives related to Legendre polynomials are derived to realize the Mie series conveniently and to avoid treating special angles.%The Mie series has very important applications in electromagnetics (including optics).We employ a formulation for the Mie series which relies more on the derivatives of Legendre polynomials than Bessel functions.Recurrence formulas for derivatives related to Legendre polynomials are derived to realize the Mie series conveniently and to avoid treating special angles.The series solution for scattering by homogeneous spheres was first obtained by Mie[1] and has been studied by many researchers,[2] including its numerical implementation.[3-5] In the literature,far-field behaviors such as scattering amplitude,absorption,and extinction cross sections have been extensively studied.In contrast,we are interested in the calculation of the near-field behaviors such as the energy flux around small particles.[6-8] In this Letter,we employ a new formulation which relies more on the derivatives of associated Legendre polynomials than Bessel functions.
Around Poisson--Mehler summation formula
Szabłowski, Paweł J
2011-01-01
We study some simple generalizations of the Poisson-Mehler summation formula (PM). In particular we exploit farther, the recently obtained equality {\\gamma}_{m,n}(x,y|t,q) = {\\gamma}_{0,0}(x,y|t,q)Q_{m,n}(x,y|t,q) where {\\gamma}_{m,n}(x,y|t,q) = \\Sigma_{i\\geq0}((t^{i})/([i]_{q}!))H_{i+n}(x|q)H_{m+i}(y|q), {H_{n}(x|q)}_{n\\geq-1} are the so called q-Hermite polynomials and {Q_{m,n}(x,y|t,q)}_{n,m\\geq0} are certain polynomials in x,y of order m+n being rational functions in t and q. We study properties of polynomials Q_{m,n}(x,y|t,q) expressing them with the help the so called Al-Salam--Chihara (ASC) polynomials and using them in expansion of the reciprocal of the right hand side of the Poisson-Mehler formula. We prove also some similar in nature equalities like e.g. the following \\Sigma_{i\\geq0}((t^{i})/([i]_{q}!))H_{n+i}(x|q) = H_{n}(x|t,q)\\Sigma_{i\\geq0}((t^{i})/([i]_{q}!))H_{i}(x|q), where H_{n}(x|t,q) is the so called big q-Hermite polynomial. We prove similar equalities involving big q-Hermite and ASC poly...
Asghari, Sakineh; Qandalee, Mohammad; Sarmadi, Amir Ali
2017-02-01
A direct entry and simple process for the synthesis of [Formula: see text]-spiroiminolactones present in a large number of natural products has been developed. In the first step, the synthesis of parabanic acid derivatives was commenced from the reaction of [Formula: see text]-disubstituted urea and thiourea with oxalyl chloride, then a three-component reaction was carried out with isocyanides, acetylenic esters, and [Formula: see text]-disubstituted parabanic acid derivatives. The method allows the construction of a variety of [Formula: see text]-spiroiminolactone structures in good to high yields starting from readily available precursors. It was found that in the case of [Formula: see text]-diphenyl thioparabanic acid, additional products of [Formula: see text]-dispiroiminolactones have been formed due to the higher electrophilicity of [Formula: see text]-dicarbonyl groups. The structures were fully established using spectroscopic analysis NMR, IR, and Mass spectrometry. The crystal structure of [Formula: see text]-dispiroiminolactone was confirmed from single-crystal X-ray diffraction study.
Unbounded random operators and Feynman formulae
Orlov, Yu. N.; Sakbaev, V. Zh.; Smolyanov, O. G.
2016-12-01
We introduce and study probabilistic interpolations of various quantization methods. To do this, we develop a method for finding the expectations of unbounded random operators on a Hilbert space by averaging (with the help of Feynman formulae) the random one-parameter semigroups generated by these operators (the usual method for finding the expectations of bounded random operators is generally inapplicable to unbounded ones). Although the averaging of families of semigroups generates a function that need not possess the semigroup property, the Chernoff iterates of this function approximate a certain semigroup, whose generator is taken for the expectation of the original random operator. In the case of bounded random operators, this expectation coincides with the ordinary one.
Algebraic properties of the monopole formula
Hanany, Amihay
2016-01-01
The monopole formula provides the Hilbert series of the Coulomb branch for a 3-dimensional N=4 gauge theory. Employing the concept of a fan defined by the matter content, and summing over the corresponding collection of monoids, allows the following: firstly, we provide explicit expressions for the Hilbert series for any gauge group. Secondly, we prove that the order of the pole at t=1 and t=infinity equals the complex or quaternionic dimension of the moduli space, respectively. Thirdly, we determine all bare and dressed BPS monopole operators that are sufficient to generate the entire chiral ring. As an application, we demonstrate the implementation of our approach to computer algebra programs and the applicability to higher rank gauge theories.
Handbook of mathematical formulas and integrals
Jeffrey, Alan
2003-01-01
The updated Handbook is an essential reference for researchers and students in applied mathematics, engineering, and physics. It provides quick access to important formulas, relations, and methods from algebra, trigonometric and exponential functions, combinatorics, probability, matrix theory, calculus and vector calculus, ordinary and partial differential equations, Fourier series, orthogonal polynomials, and Laplace transforms. Many of the entries are based upon the updated sixth edition of Gradshteyn and Ryzhik''s Table of Integrals, Series, and Products and other important reference works.The Third Edition has new chapters covering solutions of elliptic, parabolic and hyperbolic equations and qualitative properties of the heat and Laplace equation.Key Features: * Comprehensive coverage of frequently used integrals, functions and fundamental mathematical results * Contents selected and organized to suit the needs of students, scientists, and engineers * Contains tables of Laplace and Fourier transfor...
Entropy Formulas For Dynamical Systems With Mistakes
Rousseau, Jerome; Zhao, Yun
2010-01-01
We study the recurrence to mistake dynamical balls, that is, dynamical balls that admit some errors and whose proportion of errors decrease tends to zero with the length of the dynamical ball. We prove, under mild assumptions, that the measure-theoretic entropy coincides with the exponential growth rate of return times to mistake dynamical balls and that minimal return times to mistake dynamical balls grow linearly with respect to its length.Moreover we obtain averaged recurrence formula for subshifts of finite type and suspension semiflows. Applications include $\\beta$-transformations, Axiom A flows and suspension semiflows of maps with a mild specification property. In particular we extend some results from [4, 9, 17] for mistake dynamical balls.
Some applications of Rice formulas to waves
Azaïs, Jean-Marc; Wschebor, Mario
2009-01-01
We use Rice's formulas in order to compute the moments of some level functionals which are linked to problems in oceanography and optics. For instance, we consider the number of specular points in one or two dimensions, the number of twinkles, the distribution of normal angle of level curves and the number or the length of dislocations in random wavefronts. We compute expectations and in some cases, also second moments of such functionals. Moments of order greater than one are more involved, but one needs them whenever one wants to perform statistical inference on some parameters in the model or to test the model itself. In some case we are able to use these computations to obtain a Central Limit Theorem.
Algebraic properties of the monopole formula
Hanany, Amihay; Sperling, Marcus
2017-02-01
The monopole formula provides the Hilbert series of the Coulomb branch for a 3-dimensional N=4 gauge theory. Employing the concept of a fan defined by the matter content, and summing over the corresponding collection of monoids, allows the following: firstly, we provide explicit expressions for the Hilbert series for any gauge group. Secondly, we prove that the order of the pole at t = 1 and t → ∞ equals the complex or quaternionic dimension of the moduli space, respectively. Thirdly, we determine all bare and dressed BPS monopole operators that are sufficient to generate the entire chiral ring. As an application, we demonstrate the implementation of our approach to computer algebra programs and the applicability to higher rank gauge theories.
Dipolar interaction and the Manning formula
Directory of Open Access Journals (Sweden)
J. Roberto Mercado-Escalante,
2015-06-01
Full Text Available In this work we want to show that the mathematical model of quantum mechanics, led to its classical approach, is able to reproduce as close macroscopic experimental results captured by the Manning formula, sufficiently verified through their diverse applications in hydraulics. Molecular interaction between the fluid and the wall of the vessel is studied decomposing the Hamiltonian in two parts: free, and interacting. Scaling process is considered from molecular to hydraulic. Participation of the symmetries of Saint-Venant equation in the hydraulic gradient is taken into account. Correlations between different variables are set. The magnitude of scale change is estimated. We conclude that the Compton wavelength induces to the Boussinesq viscosity concept and the characteristic length of the viscous sublayer.
Directory of Open Access Journals (Sweden)
Manuel Aguirre
2010-02-01
Full Text Available En este trabajo, se le da un sentido a la fórmula (formula donde (formula . Nuestra fórmula es una generalización de formulas que aparecen en ([3] y ([4]. En particular cuando m=1 y , l=1 la formula es considerada por ejemplo, por Bollini, Giambiagi y Tiommo para la teoría de regularización analítica en las ecuaciones clásicas de Yan-Mills y sus aplicaciones para el potencial singulars (c.f. [5].In this paper, we give a sense to formula (formula were (formula. Our formula is a generalization of the formulae that appear in ([3] and ([4]. In particular when 1=m and ,1=l the formula is considered for example, by Bollini, Giambiagi and Tiommo for their Theory of analytic regularization in classical Yan-Mills equations and its application for the singular potentials (c.f. [5].
Design formulas of transmission coefficients for permeable breakwaters
Directory of Open Access Journals (Sweden)
Su-xiang ZHANG
2015-10-01
Full Text Available New empirical formulas of the transmission coefficient for permeable breakwaters were suggested based on available experimental data regarding the low-crest structure (LCS, including the permeable rubble mound breakwater and pile-type breakwater. The rationality of the present formulas was verified by their comparison with existing empirical and analytical formulas. Numerical flume results were obtained by solving the modified Boussinessq-type wave equations (MBEs, and a new expression relating the friction coefficient to the relative submerged depth was also derived. Comparative analysis shows that the results of the present formulas agree with the numerical flume results as well as available experimental data, and the present formulas are superior to the existing empirical and analytical expressions in estimating the transmission coefficient. The present formulas can provide references for estimation of the transmission coefficient in engineering practice.
Design formulas of transmission coefficients for permeable breakwaters
Institute of Scientific and Technical Information of China (English)
Su-xiang ZHANG; Xi LI
2014-01-01
Newempirical formulas of the transmission coefficient for permeable breakwaters were suggested based on available experimental data regarding the low-crest structure (LCS), including the permeable rubble mound breakwater and pile-type breakwater. The rationality of the present formulas was verified by their comparison with existing empirical and analytical formulas. Numerical flume results were obtained by solving the modified Boussinessq-type wave equations (MBEs), and a new expression relating the friction coefficientαto the relative submerged depth tsRHwas also derived. Comparative analysis shows that the results of the present formulas agree with the numerical flume results as well as available experimental data, and the present formulas are superior to the existing empirical and analytical expressions in estimating the transmission coefficient. The present formulas can provide references for estimation of the transmission coefficient in engineering practice.
General inverse of Stokes, Vening-Meinesz and Molodensky formulae
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The operator operations between the disturbing potential and the geoidal undulation, the gravity anomaly, the deflection of the vertical are defined based on the relations among the gravity potential, the normal gravity potential and the disturbing potential. With the sphere as the boundary surface, based on the solution of the external boundary value problem for the disturbing potential by the spherical harmonics in the physical geodesy, the general inverse Stokes' formula, the general inverse Vening-Meinesz formula and the general Molodensky's formula are derived from the operator operations defined. The general formulae can get rid of the restriction of the classical formulae only used on the geoid. If the boundary surface is defined as the geoid, the general formulas are degenerated into the classic ones.
Infant Formulas for Food Allergy Treatment and Prevention.
Parekh, Hetu; Bahna, Sami L
2016-04-01
The number of infant formulas intended for food allergy treatment or prevention has been increasing. Some products fulfill the criteria for hypoallergenicity, such as extensively hydrolyzed protein (casein or whey) and synthesized amino acid formulas (elemental diet). Numerous partially hydrolyzed formulas have been derived from bovine milk, soybean, and rice. They are not hypoallergenic and are not recommended for children allergic to the parent protein, yet certain preparations have shown efficacy for allergy prevention. Soybean-derived preparations, although not hypoallergenic, have been tolerated by a majority of children allergic to bovine milk. Studies on the addition of probiotics or prebiotics to infant formulas have shown inconsistent findings. Numerous hypoallergenic formulas or milk substitutes are available for pediatricians to choose for children with food allergy. Caution is needed in prescribing formulas that are erroneously marketed as hypoallergenic.
Asymptotic formulae of two divergent bilateral basic hypergeometric series
Mori, Hironori
2016-01-01
We provide new formulae for the degenerations of the bilateral basic hypergeometric function ${}_1\\psi_1 ( a; b; q, z )$ with using the $q$-Borel-Laplace transformation. These are thought of as the first step to construct connection formulae of $q$-difference equation for ${}_1\\psi_1 ( a; b; q, z )$. Moreover, we show that our formulae have the $q \\to 1 - 0$ limit.
South African Formula One Grand Prix: a dream or nightmare.
2008-01-01
In 2004 a group of South African based companies submitted a bid to the Formula One Management to host a South African Formula One Grand Prix, from 2009 in Cape Town. The group approached the government to establish a public-private partnership, due to the: • escalating hosting and infrastruture development cost, resulting in very few Formula One Grand Prix host countries undertaking hosting without government involvement; and • believe that the economic benefits of hosting the event would st...
An Exponential Lower Bound on OBDD Refutations for Pigeonhole Formulas
Tveretina, Olga; Zantema, Hans
2009-01-01
Haken proved that every resolution refutation of the pigeonhole formula has at least exponential size. Groote and Zantema proved that a particular OBDD computation of the pigeonhole formula has an exponential size. Here we show that any arbitrary OBDD refutation of the pigeonhole formula has an exponential size, too: we prove that the size of one of the intermediate OBDDs is at least $\\Omega(1.025^n)$.
Improvement in a phenomenological formula for ground state binding energies
Gangopadhyay, G
2016-01-01
The phenomenological formula for ground state binding energy derived earlier (International Journal of Modern Physics E {\\bf 20} (2011) 179) has been modified. The parameters have been obtained by fitting the latest available tabulation of experimental values. The major modifications include a new term for pairing and introduction of a new neutron magic number at $N=160$. The new formula reduced the root mean square deviation to 363 keV, a substantial improvement over the previous version of the formula.
Mean size formula of wavelet subdivision tree on Heisenberg group
Institute of Scientific and Technical Information of China (English)
WANG Guo-mao
2008-01-01
The purpose of this paper is to investigate the mean size formula of wavelet packets (wavelet subdivision tree) on Heisenberg group. The formula is given in terms of the p-norm joint spectral radius. The vector refinement equations on Heisenberg group and the subdivision tree on the Heisenberg group are discussed. The mean size formula of wavelet packets can be used to describe the asymptotic behavior of norm of the subdivision tree.
Sherman-Morrison-Woodbury Formula for Linear Integrodifferential Equations
Directory of Open Access Journals (Sweden)
Feng Wu
2016-01-01
Full Text Available The well-known Sherman-Morrison-Woodbury formula is a powerful device for calculating the inverse of a square matrix. The paper finds that the Sherman-Morrison-Woodbury formula can be extended to the linear integrodifferential equation, which results in an unified scheme to decompose the linear integrodifferential equation into sets of differential equations and one integral equation. Two examples are presented to illustrate the Sherman-Morrison-Woodbury formula for the linear integrodifferential equation.
Direct Evidence for Inversion Formula in Multifractal Financial Volatility Measure
Institute of Scientific and Technical Information of China (English)
JIANG Zhi-Qiang; ZHOU Wei-Xing
2009-01-01
The inversion formula for conservative multifractal measures was unveiled mathematically a decade ago, which is however not well tested in real complex systems. We propose to verify the inversion formula using high-frequency 1982 to 1999 and its inverse measure of exit time. Both the direct and inverse measures exhibit nice multifractal nature, whose scaling ranges are not irrelevant. Empirical investigation shows that the inversion formula holds in financial markets.
A resistance formula for coherent multi-barrier structures
Institute of Scientific and Technical Information of China (English)
Zhang Zhi-Chen; Yang Jian-Hong
2007-01-01
Using the Landauer formula and the quantum S-matrix scattering theory, we derive a resistance formula for multi-barrier structure under phase coherent transmission condition. This formula shows that when the transport is coherent, the potential wells of the structure are just like conductors contributing to the overall resistance. And because the resistance formula is derived based on the scattering theory, the barrier resistance will change with the number of scattering centres (i.e. the number of barriers) in the structure.
Cardy-Verlinde Formula of Noncommutative Schwarzschild Black Hole
Directory of Open Access Journals (Sweden)
G. Abbas
2014-01-01
Full Text Available Few years ago, Setare (2006 has investigated the Cardy-Verlinde formula of noncommutative black hole obtained by noncommutativity of coordinates. In this paper, we apply the same procedure to a noncommutative black hole obtained by the coordinate coherent approach. The Cardy-Verlinde formula is entropy formula of conformal field theory in an arbitrary dimension. It relates the entropy of conformal field theory to its total energy and Casimir energy. In this paper, we have calculated the total energy and Casimir energy of noncommutative Schwarzschild black hole and have shown that entropy of noncommutative Schwarzschild black hole horizon can be expressed in terms of Cardy-Verlinde formula.
A Stability Formula for Plastic-Tipped Bullets Part 1: Motivation and Development of New Formula
Courtney, Michael W
2014-01-01
Part 1 of this paper describes a modification of the original Miller twist rule for computing gyroscopic bullet stability that is better suited to plastic-tipped bullets. The original Miller twist rule assumes a bullet of constant density, but it also works well for conventional copper (or gilding metal) jacketed lead bullets because the density of copper and lead are sufficiently close. However, the original Miller twist rule significantly underestimates the gyroscopic stability of plastic-tipped bullets, because the density of plastic is much lower than the density of copper and lead. Here, a new amended formula is developed for the gyroscopic stability of plastic-tipped bullets by substituting the length of just the metal portion for the total length in the $(1 + L^2)$ term of the original Miller twist rule. Part 2 describes experimental testing of this new formula on three plastic-tipped bullets. The new formula is relatively accurate for plastic-tipped bullets whose metal portion has nearly uniform densi...
Directory of Open Access Journals (Sweden)
Sara Rodríguez-Alayza
2016-05-01
Full Text Available Objective: to compare Mondelli’s formula with Obando’s anthropometric formula in order to determine the mesiodistal width of maxillary central incisor. Materials and Methods: 100 adults (50 women were selected. The mesiodistal width of maxillary central incisor was measured. Maximum smile was used for Mondelli’s formula. Inter-alar distance and longitudinal axis of the ear were used for Obando’s formula. Correlations and differences between estimates of both formulas and the actual mesiodistal width of the central incisor were estimated. Results: Obando’s formula presented a strong correlation (r=0.8846 with the mesiodistal width, with no statistically significant differences between the two measures (p>0.05. Mondelli’s formula presented a moderate negative correlation with the mesiodistal width (r=-0.3401 and a statistically significant difference with respect to the mesiodistal width (p<0.0001, in both men and women. Conclusion: Obando’s formula estimated more accurately the mesiodistal width of the central incisor in comparison to Mondelli’s formula in the Peruvian population.
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Thun, R P; Tian, F; Tibbetts, M J; Tikhomirov, V O; Tikhonov, Yu A; Timoshenko, S; Tiouchichine, E; Tipton, P; Tisserant, S; Todorov, T; Todorova-Nova, S; Toggerson, B; Tojo, J; Tokár, S; Tokushuku, K; Tollefson, K; Tomlinson, L; Tomoto, M; Tompkins, L; Toms, K; Topilin, N D; Torrence, E; Torres, H; Torró Pastor, E; Toth, J; Touchard, F; Tovey, D R; Tran, H L; Trefzger, T; Tremblet, L; Tricoli, A; Trigger, I M; Trincaz-Duvoid, S; Tripiana, M F; Triplett, N; Trischuk, W; Trocmé, B; Troncon, C; Trottier-McDonald, M; Trovatelli, M; True, P; Trzebinski, M; Trzupek, A; Tsarouchas, C; Tseng, J C-L; Tsiareshka, P V; Tsionou, D; Tsipolitis, G; Tsirintanis, N; Tsiskaridze, S; Tsiskaridze, V; Tskhadadze, E G; Tsukerman, I I; Tsulaia, V; Tsuno, S; Tsybychev, D; Tudorache, A; Tudorache, V; Tuna, A N; Tupputi, S A; Turchikhin, S; Turecek, D; Turk Cakir, I; Turra, R; Tuts, P M; Tykhonov, A; Tylmad, M; Tyndel, M; Uchida, K; Ueda, I; Ueno, R; Ughetto, M; Ugland, M; Uhlenbrock, M; Ukegawa, F; Unal, G; Undrus, A; Unel, G; Ungaro, F C; Unno, Y; Urbaniec, D; Urquijo, P; Usai, G; Usanova, A; Vacavant, L; Vacek, V; Vachon, B; Valencic, N; Valentinetti, S; Valero, A; Valery, L; Valkar, S; Valladolid Gallego, E; Vallecorsa, S; Valls Ferrer, J A; Van Berg, R; Van Der Deijl, P C; van der Geer, R; van der Graaf, H; Van Der Leeuw, R; van der Ster, D; van Eldik, N; van Gemmeren, P; Van Nieuwkoop, J; van Vulpen, I; van Woerden, M C; Vanadia, M; Vandelli, W; Vanguri, R; Vaniachine, A; Vankov, P; Vannucci, F; Vardanyan, G; Vari, R; Varnes, E W; Varol, T; Varouchas, D; Vartapetian, A; Varvell, K E; Vazeille, F; Vazquez Schroeder, T; Veatch, J; Veloso, F; Veneziano, S; Ventura, A; Ventura, D; Venturi, M; Venturi, N; Venturini, A; Vercesi, V; Verducci, M; Verkerke, W; Vermeulen, J C; Vest, A; Vetterli, M C; Viazlo, O; Vichou, I; Vickey, T; Vickey Boeriu, O E; Viehhauser, G H A; Viel, S; Vigne, R; Villa, M; Villaplana Perez, M; Vilucchi, E; Vincter, M G; Vinogradov, V B; Virzi, J; Vivarelli, I; Vives Vaque, F; Vlachos, S; Vladoiu, D; Vlasak, M; Vogel, A; Vokac, P; Volpi, G; Volpi, M; von der Schmitt, H; von Radziewski, H; von Toerne, E; Vorobel, V; Vorobev, K; Vos, M; Voss, R; Vossebeld, J H; Vranjes, N; Vranjes Milosavljevic, M; Vrba, V; Vreeswijk, M; Vu Anh, T; Vuillermet, R; Vukotic, I; Vykydal, Z; Wagner, W; Wagner, P; Wahrmund, S; Wakabayashi, J; Walder, J; Walker, R; Walkowiak, W; Wall, R; Waller, P; Walsh, B; Wang, C; Wang, C; Wang, F; Wang, H; Wang, H; Wang, J; Wang, J; Wang, K; Wang, R; Wang, S M; Wang, T; Wang, X; Wanotayaroj, C; Warburton, A; Ward, C P; Wardrope, D R; Warsinsky, M; Washbrook, A; Wasicki, C; Watanabe, I; Watkins, P M; Watson, A T; Watson, I J; Watson, M F; Watts, G; Watts, S; Waugh, B M; Webb, S; Weber, M S; Weber, S W; Webster, J S; Weidberg, A R; Weigell, P; Weinert, B; Weingarten, J; Weiser, C; Weits, H; Wells, P S; Wenaus, T; Wendland, D; Weng, Z; Wengler, T; Wenig, S; Wermes, N; Werner, M; Werner, P; Wessels, M; Wetter, J; Whalen, K; White, A; White, M J; White, R; White, S; Whiteson, D; Wicke, D; Wickens, F J; Wiedenmann, W; Wielers, M; Wienemann, P; Wiglesworth, C; Wiik-Fuchs, L A M; Wijeratne, P A; Wildauer, A; Wildt, M A; Wilkens, H G; Will, J Z; Williams, H H; Williams, S; Willis, C; Willocq, S; Wilson, J A; Wilson, A; Wingerter-Seez, I; Winklmeier, F; Wittgen, M; Wittig, T; Wittkowski, J; Wollstadt, S J; Wolter, M W; Wolters, H; Wosiek, B K; Wotschack, J; Woudstra, M J; Wozniak, K W; Wright, M; Wu, M; Wu, S L; Wu, X; Wu, Y; Wulf, E; Wyatt, T R; Wynne, B M; Xella, S; Xiao, M; Xu, D; Xu, L; Yabsley, B; Yacoob, S; Yamada, M; Yamaguchi, H; Yamaguchi, Y; Yamamoto, A; Yamamoto, K; Yamamoto, S; Yamamura, T; Yamanaka, T; Yamauchi, K; Yamazaki, Y; Yan, Z; Yang, H; Yang, H; Yang, U K; Yang, Y; Yanush, S; Yao, L; Yao, W-M; Yasu, Y; Yatsenko, E; Yau Wong, K H; Ye, J; Ye, S; Yen, A L; Yildirim, E; Yilmaz, M; Yoosoofmiya, R; Yorita, K; Yoshida, R; Yoshihara, K; Young, C; Young, C J S; Youssef, S; Yu, D R; Yu, J; Yu, J M; Yu, J; Yuan, L; Yurkewicz, A; Zabinski, B; Zaidan, R; Zaitsev, A M; Zaman, A; Zambito, S; Zanello, L; Zanzi, D; Zaytsev, A; Zeitnitz, C; Zeman, M; Zemla, A; Zengel, K; Zenin, O; Ženiš, T; Zerwas, D; Zevi Della Porta, G; Zhang, D; Zhang, F; Zhang, H; Zhang, J; Zhang, L; Zhang, X; Zhang, Z; Zhao, Z; Zhemchugov, A; Zhong, J; Zhou, B; Zhou, L; Zhou, N; Zhu, C G; Zhu, H; Zhu, J; Zhu, Y; Zhuang, X; Zibell, A; Zieminska, D; Zimine, N I; Zimmermann, C; Zimmermann, R; Zimmermann, S; Zimmermann, S; Zinonos, Z; Ziolkowski, M; Zobernig, G; Zoccoli, A; Zur Nedden, M; Zurzolo, G; Zutshi, V; Zwalinski, L
A likelihood-based discriminant for the identification of quark- and gluon-initiated jets is built and validated using 4.7 fb[Formula: see text] of proton-proton collision data at [Formula: see text] [Formula: see text] collected with the ATLAS detector at the LHC. Data samples with enriched quark or gluon content are used in the construction and validation of templates of jet properties that are the input to the likelihood-based discriminant. The discriminating power of the jet tagger is established in both data and Monte Carlo samples within a systematic uncertainty of [Formula: see text] 10-20 %. In data, light-quark jets can be tagged with an efficiency of [Formula: see text] while achieving a gluon-jet mis-tag rate of [Formula: see text] in a [Formula: see text] range between [Formula: see text] and [Formula: see text] for jets in the acceptance of the tracker. The rejection of gluon-jets found in the data is significantly below what is attainable using a Pythia 6 Monte Carlo simulation, where gluon-jet mis-tag rates of 10 % can be reached for a 50 % selection efficiency of light-quark jets using the same jet properties.
The influence of traditional herbal formulas on cytokine activity.
Burns, J J; Zhao, Lijun; Taylor, Ethan Will; Spelman, Kevin
2010-11-28
Many of the botanical "immunomodulators", a class of herbal medicines widely recognized in traditional medical systems such as Chinese Medicine (TCM) and Ayurvedic Medicine, alter immune function and may offer clinically relevant therapeutics or leads to therapeutics. Many of these traditional remedies are prepared from combinations of medicinal plants which may influence numerous molecular pathways. These effects may differ from the sum of effects from the individual plants and therefore, research demonstrating the effects of the formula is crucial for insights into the effects of traditional remedies. In this review we surveyed the primary literature for research that focused on combinations of medicinal plants and effects on cytokine activity. The results demonstrate that many extracts of herb mixtures have effects on at least one cytokine. The most commonly studies cytokines were IL-4, IL-6, IL-10, TNF and IFN-γ. The majority of the formulas researched derived from TCM. The following formulas had activity on at least three cytokines; Chizukit N, CKBM, Daeganghwal-tang, Food Allergy Formula, Gamcho-Sasim-Tang, Hachimi-jio-gan, Herbkines, Hochuekki, Immune System Formula, Jeo-Dang-Tang, Juzen-taiho-to, Kakkon-to, Kan jang, Mao-Bushi-Saishin-to, MSSM-002, Ninjin-youei-to, PG201, Protec, Qing-huo-bai-du-yin, Qingfu Guanjieshu, Sambucol Active Defense, Seng-fu-tang, Shin-Xiao-Xiang, Tien Hsien, Thuja formula, Unkei-to, Vigconic, Wheeze-relief-formula, Xia-Bai-San, Yangyuk-Sanhwa-Tang, Yi-fey Ruenn-hou, and Yuldahansotang. Of the western based combinations, formulas with Echinacea spp. were common and showed multiple activities. Numerous formulas demonstrated activity on both gene and protein expression. The research demonstrates that the reviewed botanical formulas modulate cytokine activity, although the bulk of the research is in vitro. Therapeutic success using these formulas may be partially due to their effects on cytokines. Further study of phytotherapy on
Effects of Different Fertilizing Formulae on Potato
Directory of Open Access Journals (Sweden)
Giovanna Cucci
Full Text Available Trials conducted on potato fertilization at different rates of nitrogen, phosphorus and potassium have shown that the elements able to influence the marketable tuber yield are nitrogen and phosphorus. The potato dry matter, which reflects other quality aspects such as the specific gravity and the starch content, increases with nitrogen fertilization till 150-200 kg ha-1 of nitrogen; beyond those rates values remain nearly unchanged. Dry matter increases also with the application of phosphorus and at low potassium rates. The objective of the research was to test the effect of different rates of N P K fertilizer on yield and some quality traits of potato. The test was conducted at the Campus of the Agricultural Faculty, Bari University, Italy. It involved the comparison of 6 fertilizing formulae N1 P1 K1, N1 P2 K1, N2 P1 K1, N2 P2 K1, N3 P1 K1, N3 P2 K1, obtained from the factorial combination of three nitrogen levels (N = 100-200-300 kg ha-1 and two phosphorus rates (P2O5 = 50-100 kg ha-1 against an unfertilized control N0P0K0. The dose of potassium was constant for all fertilizing formulae (K2O = 300 kg ha-1. The highest total and marketable yields of tubers per plant have been observed at the two highest fertilizing levels (N3 P1 K1, N3 P2 K1, which are not statistically different so that the best treatments is shown to be N3 P1 K1; the trend was similar for the mean weight of tubers. With the various treatments, no difference was observed in terms of yield of tubers belonging to the two first size classes (< 35mm and 35-55mm; what has increased with the fertilizing levels is the yield of tubers greater than 55 mm. Tuber specific gravity show, as expected, a positive correlation with the dry matter percentage. Both parameters increased shifting from the control to the N2 P2 K1 and decreased at the highest N level, without any difference being observed with the change in the P rate. The highest starch percentage (20.5% was also observed in the
How Spacecraft Fly Spaceflight Without Formulae
Swinerd, Graham
2009-01-01
About half a century ago a small satellite, Sputnik 1, was launched. The satellite did very little other than to transmit a radio signal to announce its presence in orbit. However, this humble beginning heralded the dawn of the Space Age. Today literally thousands of robotic spacecraft have been launched, many of which have flown to far-flung regions of the Solar System carrying with them the human spirit of scientific discovery and exploration. Numerous other satellites have been launched in orbit around the Earth providing services that support our technological society on the ground. How Spacecraft Fly: Spaceflight Without Formulae by Graham Swinerd focuses on how these spacecraft work. The book opens with a historical perspective of how we have come to understand our Solar System and the Universe. It then progresses through orbital flight, rocket science, the hostile environment within which spacecraft operate, and how they are designed. The concluding chapters give a glimpse of what the 21st century may ...
Product formulas for volumes of flow polytopes
Meszaros, Karola
2011-01-01
Intrigued by the product formula prod_{i=1}^{n-2} C_i for the volume of the Chan-Robbins-Yuen polytope CRY_n, where C_i is the ith Catalan number, we construct a family of polytopes P_{m,n}, whose volumes are given by the product \\prod_{i=m+1}^{m+n-2}\\frac{1}{2i+1}{{m+n+i} \\choose {2i}}. The Chan-Robbins-Yuen polytope CRY_n coincides with P_{0,n-1}. Our construction of the polytopes P_{m,n} is an application of a systematic method we develop for expressing volumes of a class of flow polytopes as the number of certain triangular arrays. This method can also be used as a heuristic technique for constructing polytopes with combinatorial volumes. As an illustration of this we construct polytopes whose volumes equal the number of r-ary trees on n internal nodes, \\frac{1}{(r-1)n+1} {{rn} \\choose n}. Using triangular arrays we also express the volumes of flow polytopes as constant terms of formal Laurent series.
Tibetan medicinal formulas used to treat neuropsychiatric disorders
Directory of Open Access Journals (Sweden)
Raquel de Luna Antonio
2012-06-01
Full Text Available Introduction: Men-Tsee-Khang in Dharamsala, India, formally known as the Tibetan Medical and Astrological Institute (TMAI, is dedicated to the teachings and practice of Tibetan medicine, which uses therapeutic agents in multi-ingredient formulas. Aim of the study: The aim of the present study was to identify formulas used at Men-Tsee-Khang for the treatment of neuropsychiatric disorders and to compare the Tibetan usage of particular ingredients with pharmacological data from the scientific database. Methods: Using ethnographic techniques and methods, five physicians were selected, and the interviews were conducted between July 2010 and February 2011. Results: A correlation was observed between central nervous system disorders and rLung, one of the three humors in Tibetan medicine, and 10 formulas used to treat the imbalance of this particular humor were identified. These formulas utilize 61 ingredients, including salts, animal products and plants. The 48 plant species identified in these formulas are traditionally used in Tibetan medicine and are deposited at the Men-Tsee-Khang Herbarium. Each formula treats several symptoms related to rLung imbalance, so the plants may have therapeutic uses distinct from those of the formulas in which they are included. Data from the scientific literature indicate that all of the formulas include ingredients with neuropsychiatric action and corroborate the therapeutic use of 75,6% of the plants. Conclusion: These findings indicate a level of congruence between the therapeutic uses of particular plant species in Tibetan and Western medicines.
40 CFR 1065.630 - 1980 international gravity formula.
2010-07-01
... 40 Protection of Environment 32 2010-07-01 2010-07-01 false 1980 international gravity formula. 1065.630 Section 1065.630 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) AIR... international gravity formula. The acceleration of Earth's gravity, a g, varies depending on your...
Formula Student as Part of a Mechanical Engineering Curriculum
Davies, Huw Charles
2013-01-01
Formula Student (FS) is a multi-university student design competition managed by the UK Institution of Mechanical Engineers. Students are required to demonstrate and prove their creativity and engineering skills through the design, manufacture and financing of a small formula style race car. This paper seeks to explore the educational value that…
Hardy type inequalities in [Formula: see text] with sharp remainders.
Ioku, Norisuke; Ishiwata, Michinori; Ozawa, Tohru
2017-01-01
Sharp remainder terms are explicitly given on the standard Hardy inequalities in [Formula: see text] with [Formula: see text]. Those remainder terms provide a direct and exact understanding of Hardy type inequalities in the framework of equalities as well as of the nonexistence of nontrivial extremals.
Stewart formula and some inequalities for a simplex
Institute of Scientific and Technical Information of China (English)
YANG Shi-guo
2005-01-01
Problems on Stewart formula and inequalities for the areas of the bisection planes of the dihedral angles of a simplex are studied with the theory and method of distance geometry. Stewart formula and some inequalities for the areas of the bisection planes of the dihedral angles of a simplex inare established.
Trace formula for a dielectric microdisk with a point scatterer
Hales, Robert F.M.; Sieber, Martin; Waalkens, Holger
2011-01-01
Two-dimensional dielectric microcavities are of widespread use in microoptics applications. Recently, a trace formula has been established for dielectric cavities which relates their resonance spectrum to the periodic rays inside the cavity. In this paper, we extend this trace formula to a dielectri
24 CFR 92.604 - ADDI allocation formula.
2010-04-01
... 24 Housing and Urban Development 1 2010-04-01 2010-04-01 false ADDI allocation formula. 92.604... Development HOME INVESTMENT PARTNERSHIPS PROGRAM American Dream Downpayment Initiative § 92.604 ADDI allocation formula. (a) General. HUD will provide ADDI funds to participating jurisdictions in...
Mathematically Equivalent, Computationally Non-equivalent Formulas and Software Comprehensibility
2016-06-07
and Software Comprehensibility Marvin J. Goldstein Surface Ship Sonar Department Approved for public release; distribution unlimited Report...equivalent Formulas and Software Comprehensibility 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) Marvin Goldstein...13. SUPPLEMENTARY NOTES NUWC2015 14. ABSTRACT In the development of mathematical software , often the formula that defines the mathematical purpose
27 CFR 26.50 - Formulas for liquors.
2010-04-01
....C. 5232, the formula shall include a statement to that effect. If any product contains liquors made outside of Puerto Rico, the country of origin for each such liquor shall be stated on the formula. These.... If any wine contains liquors made outside of Puerto Rico, the country of origin for each such...
A Simple Approach to the Landau-Zener Formula
Vutha, Amar C.
2010-01-01
The Landau-Zener formula provides the probability of non-adiabatic transitions occurring when two energy levels are swept through an avoided crossing. The formula is derived here in a simple calculation that emphasizes the physics responsible for non-adiabatic population transfer. (Contains 2 figures.)
A general Voronoi summation formula for GL(n,Z)
Miller, Stephen D
2009-01-01
In an earlier paper we derived an analogue of the classical Voronoi summation formula for automorphic forms on GL(3), by using the theory of automorphic distributions. The purpose of the present paper is to apply this theory to derive the analogous formulas for GL(n).
Weighted Plancherel formula on unit ball in R
Institute of Scientific and Technical Information of China (English)
刘建明; 郑维行
1996-01-01
Let / be a function on the unit ball of Rn. For , the action T of SO0 (1, n) on f isdefined by .The invariant Laplacian corresponding to T is calculated, and a family of its eigenfunctions is found out. Then the corresponding Fourier transform is defined and the inversion formula and Plancherel formula are obtained.
The role of infant appetite in extended formula feeding
Syrad, H.; Jaarsveld, C.H.M. van; Wardle, J.; Llewellyn, C.H.
2015-01-01
OBJECTIVE: Parental decision-making around extended formula feeding (12 months+) has not been explored previously. This study tested the hypotheses that extended formula milk use (i) is associated with poorer appetite and (ii) supplements lower food intake. METHODS: Appetite was assessed with the Ch
A FORMULA FOR CALCULATING THE ERRORS OF SUPERCONDUCTING MAGNETIZATION CURVE
Institute of Scientific and Technical Information of China (English)
GUO SHU-QUAN; LIU MENG-LIN; ZHENG DONG-NING; ZHAO BAI-RU
2001-01-01
Because of field inhomogeneity in the magnetization measurement system, large errors may exist in the decreasing field superconducting magnetization curves, but not in the increasing field curves. The physical origin of the large errors is proposed here. A simple formula for calculating the errors is given. This formula is consistent with the experimental data.
Quadrature Formula of Singular Integral Based on Rational Interpolation
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
We construct a quadrature formula of the singular integral with the Chebyshev weight of the second kind by using Lagrange interpolation based on the rational system {1/(x-a1),1/(x-a2),...}, and both the remainder and convergence of the quadrature formula established here are discussed. Our results extend some classical ones.
Formulae for Arithmetic on Genus 2 Hyperelliptic Curves
DEFF Research Database (Denmark)
Lange, Tanja
2005-01-01
The ideal class group of hyperelliptic curves can be used in cryptosystems based on the discrete logarithm problem. In this article we present explicit formulae to perform the group operations for genus 2 curves. The formulae are completely general but to achieve the lowest number of operations w...
Formula for emulsifier for production of emulsion fuels
Energy Technology Data Exchange (ETDEWEB)
Simakawa, K.; Arai, T.; Oseki, O.; Tega, K.; Wakidzaka, A.
1982-05-20
Patent for an emulsifier for preparation of emulsion fuels type v/m (formula provided). This particular formula is utilized to derive emulsion fuels from kerosene, light and heavy oils, etc. The emulsions have water drops of even size and a high thermal stability. When these fuels are used, formation of soot and nitrogen oxides is reduced.
Formulaic Sequences and the Implications for Second Language Learning
Xu, Qi
2016-01-01
The present paper is a review of literature in relation to formulaic sequences and the implications for second language learning. The formulaic sequence is a significant part of our language, and plays an essential role in both first and second language learning. The paper first introduces the definition, classifications, and major features of…
Development of student engineering competitions "STUDENT FORMULA SAE» in Ukraine
Directory of Open Access Journals (Sweden)
Dashchenko A.F.
2015-12-01
Full Text Available The article deals with the direction of the educational level of students in Ukrainian higher technical educational institutions. The advantages and attractiveness of the student engineering competition "Formula Student". The evolution of the development of the Ukrainian engineering team "Formula Student" for example, the team of Odessa National Polytechnic University.
New Formula for Stability of Cube Armoured Roundheads
DEFF Research Database (Denmark)
Maciñeira, Enrique; Burcharth, Hans F.
2009-01-01
The paper presents a new formula for the stability of cube armoured roundheads. The formula is based on physical model tests in Aalborg University which both long crested and short crested waves of different wave steepness were used. The slope of the radius of the head were varied in order...
FORMULA MAKANAN GLIKEMIK TINGGI UNTUK ANAK GIZI KURANG
Directory of Open Access Journals (Sweden)
Uken S. Soetrisno
2012-11-01
Full Text Available High Glycaemic Food Formula For Under Nourished Children.Background: The reported prevalence of undernounshed children is highly increase since economic crisis. Six months food intervention based on skim milk only improved 65% of the undernourished children. Since gastrointestinal tract of such childrents incapable of digesting high molecular weight of carbohydrate and protein, there is a need to develop an easily digested food formula which has high glycaemic index.Objective: to produce high glycaemic index formula using dextrinized carbohydrate and fermented skim milk that is easily digested for undernourished children.Method: Two groups of subjects, each consists of 34 and 33 undernourished children were given either high glycaemic index formula (test group or skim milk formula (control group for 4 months. The food formula compliance, anthropometric measurement, blood and fecal component were analyzed.Results: There were increase in body weight of test group even though not changing their nutritional status based on Z-score. The blood and fecal component data indicated that the high glycaemic formula can be digested well by the undernourished children.Keywords: high glycaemic formula, undernourished
Agostoni, Carlo; Axelsson, Irene; Goulet, Olivier; Koletzko, Berthold; Michaelsen, Kim Fleischerm; Puntis, John; Rieu, Daniel; Rigo, Jacques; Shamir, Raanan; Szajewska, Hania; Turck, Dominique
2006-04-01
This comment by the European Society for Paediatric Gastroenterology Hepatology and Nutrition (ESPGHAN) Committee on Nutrition summarizes available information on the composition and use of soy protein formulae as substitutes for breastfeeding and cows' milk protein formulae as well as on their suitability and safety for supporting adequate growth and development in infants. Soy is a source of protein that is inferior to cows' milk, with a lower digestibility and bioavailability as well as a lower methionine content. For soy protein infant formulae, only protein isolates can be used, and minimum protein content required in the current European Union legislation is higher than that of cows' milk protein infant formulae (2.25 g/100 kcal vs. 1.8 g/100kcal). Soy protein formulae can be used for feeding term infants, but they have no nutritional advantage over cows' milk protein formulae and contain high concentrations of phytate, aluminum, and phytoestrogens (isoflavones), which might have untoward effects. There are no data to support the use of soy protein formulae in preterm infants. Indications for soy protein formulae include severe persistent lactose intolerance, galactosemia, and ethical considerations (e.g., vegan concepts). Soy protein formulae have no role in the prevention of allergic diseases and should not be used in infants with food allergy during the first 6 months of life. If soy protein formulae are considered for therapeutic use in food allergy after the age of 6 months because of their lower cost and better acceptance, tolerance to soy protein should first be established byclinical challenge. There is no evidence supporting the use of soy protein formulae for the prevention or management of infantile colic, regurgitation, or prolonged crying.
Kubo formulas for dispersion in heterogeneous periodic nonequilibrium systems
Guérin, T.; Dean, D. S.
2015-12-01
We consider the dispersion properties of tracer particles moving in nonequilibrium heterogeneous periodic media. The tracer motion is described by a Fokker-Planck equation with arbitrary spatially periodic (but constant in time) local diffusion tensors and drifts, eventually with the presence of obstacles. We derive a Kubo-like formula for the time-dependent effective diffusion tensor valid in any dimension. From this general formula, we derive expressions for the late time effective diffusion tensor and drift in these systems. In addition, we find an explicit formula for the late finite-time corrections to these transport coefficients. In one dimension, we give a closed analytical formula for the transport coefficients. The formulas derived here are very general and provide a straightforward method to compute the dispersion properties in arbitrary nonequilibrium periodic advection-diffusion systems.
Formulaic Language in Second Language Acquisition:A Review
Institute of Scientific and Technical Information of China (English)
YU Xia
2015-01-01
This paper argues for the need of the reappraisal of the formulaic aspect of language in second language acquisition by drawing insights from recent development in applied linguistics, psycholinguistics and corpus linguistics. This library study begins by reviewing the dual-nature view of language in relation to formulaic aspect of language. Then, a brief survey of evidence from corpus linguistics is provided to demonstrate the formulaicity of language. What follows is the discussion of rehearsal and implicit learning vis-a-vis memory from the perspective of psycholinguistics. After that, the role of formulaic language in second lan⁃guage acquisition is examined by taking stock of empirical findings that have accumulated in this area. Finally, by way of conclu⁃sion, how the formulaicity of language can shed light on second/foreign language teaching theory is illustrated.
Cardy formula for charged black holes with anisotropic scaling
Bravo-Gaete, Moises; Hassaine, Mokhtar
2015-01-01
We first observe that for Lifshitz black holes whose only charge is the mass, the resulting Smarr relation is a direct consequence of the Lifshitz Cardy formula. From this observation, we propose to extend the Cardy formula to the case of electrically charged Lifshitz black holes satisfying as well a Smarr relation. The expression of our formula depends on the dynamical exponent, the energy and the charge of the ground state which is played by a magnetically charged soliton obtained through a double Wick rotation. The expression also involves a factor multiplying the chemical potentials which varies in function of the electromagnetic theory considered. This factor is precisely the one that appears in the Smarr formula for charged Lifshitz black holes. We test the validity of this Cardy formula in different situations where electrically Lifshitz charged black holes satisfying a Smarr relation are known. We then extend these results to electrically charged black holes with hyperscaling violation. Finally, an ex...
Formalization for Granular Computing Based on Logical Formulas
Institute of Scientific and Technical Information of China (English)
Lin Yan; Qing Liu
2006-01-01
In order to make formalization for granular computing, some kinds of formulas are constructed on a universe by a logical method. Every formula expresses a property, and can separate a semantic set which consists of all of the objects satisfying the formula. Therefore a granular space on the universe is produced based on the formulas,and the semantic sets separated by the formulas are taken as a formal definition for granules ,and are called abstract granules. Furthermore, it is proved that any specific granule from an extended mathematical system can be formalized into an abstract granule ,the conclusions is obtained that specific granules from approximate spaces and information systems can also be formalized into abstract granules. Based on a granular space and abstract granules, granular computing is defined, which finally realizes the goal of formalization for granular computing.
Multiscale Regional Formula Fertilization Considering Environment Information Incompleteness
Institute of Scientific and Technical Information of China (English)
Qianqian ZHANG; Yan LIANG
2015-01-01
Conventional formula fertilization tends to calculate regional rate of fertilizer application by means of analyzing spatial distribution of regional cultivated land productivity combined with experiment data. However,as environment information of cultivated land is incomplete due to limitation of traditional cultivated land management technology and data acquisition,uncertainty of rate of fertilizer makes it hard to define the interval of formula fertilization and support the regional fertilization task. With the technique of spatial analysis and multiscale uncertainty theory,conventional fertilization can be optimized. Four steps are involved to calculate regional formula fertilization interval based on conventional formula fertilization:( i) To simulate cultivated land productivity according to EGLSN Model,and make it crop target field;( ii) To determine rate of fertilizer according to target field to define cultivated land productivity fertilizer interval and mid-value;( iii) To define region fertilizer interval length and value of region varying with scales as environment information becomes complete gradually;( iv) To apply block fertilizer combined with conventional formula by soil testing. Multiscale optimizing formula fertilization system has been established by using the Arc Engine as a platform to integrate the methods,which is applied in Xinjiang County,Shanxi Province,in order to optimize the existing fertilization formula in study area. It showed that the optimized formula fertilization had more spatial details of productivity than the original one.And the new method is available to support formula fertilization in any region or the block with uncertain environment information. It is therefore concluded that the proposed method has the potential for popularity,which provides a multiscale,multiple-factor and standardized formula fertilization method.
Fundamental formulae for wave-energy conversion.
Falnes, Johannes; Kurniawan, Adi
2015-03-01
The time-average wave power that is absorbed from an incident wave by means of a wave-energy conversion (WEC) unit, or by an array of WEC units-i.e. oscillating immersed bodies and/or oscillating water columns (OWCs)-may be mathematically expressed in terms of the WEC units' complex oscillation amplitudes, or in terms of the generated outgoing (diffracted plus radiated) waves, or alternatively, in terms of the radiated waves alone. Following recent controversy, the corresponding three optional expressions are derived, compared and discussed in this paper. They all provide the correct time-average absorbed power. However, only the first-mentioned expression is applicable to quantify the instantaneous absorbed wave power and the associated reactive power. In this connection, new formulae are derived that relate the 'added-mass' matrix, as well as a couple of additional reactive radiation-parameter matrices, to the difference between kinetic energy and potential energy in the water surrounding the immersed oscillating WEC array. Further, a complex collective oscillation amplitude is introduced, which makes it possible to derive, by a very simple algebraic method, various simple expressions for the maximum time-average wave power that may be absorbed by the WEC array. The real-valued time-average absorbed power is illustrated as an axisymmetric paraboloid defined on the complex collective-amplitude plane. This is a simple illustration of the so-called 'fundamental theorem for wave power'. Finally, the paper also presents a new derivation that extends a recently published result on the direction-average maximum absorbed wave power to cases where the WEC array's radiation damping matrix may be singular and where the WEC array may contain OWCs in addition to oscillating bodies.
Zhang, Shujun; Luo, Jun; Hackenberger, Wesley; Sherlock, Nevin P; Meyer, Richard J; Shrout, Thomas R
2009-05-15
Relaxor based [Formula: see text] ternary single crystals (PIN-PMN-PT) were reported to have broader temperature usage range [Formula: see text] and comparable piezoelectric properties to [Formula: see text] (PMNT) crystals. In this work, the orientation dependent dielectric, piezoelectric and electromechanical properties for PIN-PMN-PT crystals were investigated along [Formula: see text] and [Formula: see text] directions. The electromechanical couplings [Formula: see text] and [Formula: see text] for [Formula: see text] poled crystals were found to be 0.91 and 0.91, respectively, with piezoelectric coefficients [Formula: see text] and [Formula: see text] on the order of 925 and -1420 pC/N. Of particular significance was the mechanical quality factor [Formula: see text] for [Formula: see text] oriented crystals, which was found to be [Formula: see text], much higher than the [Formula: see text] values of [Formula: see text] oriented relaxor-PT crystals [Formula: see text]. The temperature dependence of the piezoelectric properties exhibited good temperature stability up to their ferroelectric phase transition [Formula: see text], indicating [Formula: see text] and [Formula: see text] oriented PIN-PMN-PT are promising materials for transducer applications, with the latter for high power resonant devices where low loss (high [Formula: see text]) was required.
21 CFR 107.230 - Elements of an infant formula recall.
2010-04-01
... 21 Food and Drugs 2 2010-04-01 2010-04-01 false Elements of an infant formula recall. 107.230... (CONTINUED) FOOD FOR HUMAN CONSUMPTION INFANT FORMULA Infant Formula Recalls § 107.230 Elements of an infant formula recall. A recalling firm shall conduct an infant formula recall with the following elements:...
Yang, Yan; Huang, Yuanqiong; Song, Hongjian; Liu, Yuxiu; Wang, Lizhong; Wang, Qingmin
2016-11-01
To study the effect of the variation of fused ring size and substitution on the antiviral activity of [Formula: see text]-carboline alkaloids, four types of structurally novel [Formula: see text]-carboline alkaloids analogues, with indole-fused six- to nine-membered-rings motifs, were designed, synthesized, and evaluated for the inhibition of tobacco mosaic virus (TMV). Bioassay results indicated that most of these analogues had significant anti-TMV activity; especially I-14 (54 [Formula: see text] 3 % at 500 [Formula: see text]g/mL in vitro; 51 [Formula: see text] 2, 45 [Formula: see text] 2, and 42 [Formula: see text] 1 % at 500 [Formula: see text]g/mL in vivo), II-4 (53 [Formula: see text] 1 % at 500 [Formula: see text]g/mL in vitro; 49 [Formula: see text] 2, 57 [Formula: see text] 2, and 48 [Formula: see text] 1 % at 500 [Formula: see text]g/mL in vivo), and II-8 (48 [Formula: see text] 1 % at 500 [Formula: see text]g/mL in vitro; 53 [Formula: see text] 2 %, 56 [Formula: see text] 2 %, and 46 [Formula: see text] 1 % at 500 [Formula: see text]g/mL in vivo), which were more potent vs. TMV than was ribavirin (36 [Formula: see text] 1 % at 500 [Formula: see text]g/mL in vitro; 37 [Formula: see text] 2, 41 [Formula: see text] 2, and 38 [Formula: see text] 1 % at 500 [Formula: see text]g/mL in vivo). The size of the fused ring has important effects on anti-TMV potency, which may be ascribed to conformational differences. The X-ray structures of I-1, I-6, II-8, and III show differing conformational preferences. The most potent compounds can be used as leads for further optimization as antiphytoviral agents.
The effect of lactase and formula reconstitution on milk osmolality.
LENUS (Irish Health Repository)
Malone, A J
2012-02-03
These experiments investigated the reaction rate of lactase on milk lactose by measuring milk osmolality; and explored the effect of formula reconstitution on milk osmolality. The investigations measured milk osmolality with the Fiske Os, freezing-point osmometer. Lactase (Lactaid) incubated with pure lactose solutions established the validity of the method. Lactase was incubated for 24 hours with four reconstituted milk formulas (Milumil, and Cow and Gate Nutrilon Plus, Farley\\'s First Milk, SMA Gold). Milk osmolality increased most rapidly in the first 4 hours after the addition of lactase. The lactase enzyme completed over 90% of the reaction within 12 hours. The milk osmolalities ranged from 487 to 591 mosm\\/kg after 24 hours with 2-4 drops of lactase in 240 ml of formula. A clinical guideline osmolality of 400 mosm\\/kg was reached in 240 ml of formula at 1 to 12 hours depending on the dose of lactase. High milk osmolalities due to prolonged enzyme incubation, or high lactase doses could be reduced to around 400 mosm\\/kg by dilution of 240 ml of formula with an extra 60 ml of water. The initial osmolality of formula after reconstitution by paediatric nurses varied widely and usually exceeded the manufacturer\\'s quoted osmolality. This initial osmolality was a further influence on the final osmolality reached after the addition of lactase. It is concluded that the recommended incubation time for Lactaid of 24 hours is unnecessary as lactase exerts the majority of its effect in less than 12 hours. Adjustment of Lactaid dose and incubation times will maintain milk formula osmolality within standard guidelines. Dilution with extra water will correct inadvertent high enzyme doses and prolonged incubation times. The normal method of reconstituting milk formulas from powder may be unreliable as the manufacturer\\'s quoted osmolality was not reproduced when milk formulas were reconstituted by paediatric nurses.
Combinatorial theory of Macdonald polynomials I: Proof of Haglund's formula
Haglund, J.; Haiman, M.; Loehr, N
2005-01-01
Haglund recently proposed a combinatorial interpretation of the modified Macdonald polynomials H̃μ. We give a combinatorial proof of this conjecture, which establishes the existence and integrality of H̃μ. As corollaries, we obtain the cocharge formula of Lascoux and Schützenberger for Hall–Littlewood polynomials, a formula of Sahi and Knop for Jack's symmetric functions, a generalization of this result to the integral Macdonald polynomials Jμ, a formula for H̃μ in terms of Lascoux–Leclerc–Th...
Revisiting the redistancing problem using the Hopf-Lax formula
Lee, Byungjoon; Darbon, Jérôme; Osher, Stanley; Kang, Myungjoo
2017-02-01
This article presents a fast new numerical method for redistancing objective functions based on the Hopf-Lax formula [1]. The algorithm suggested here is a special case of the previous work in [2] and an extension that applies the Hopf-Lax formula for computing the signed distance to the front. We propose the split Bregman approach to solve the minimization problem as a solution of the eikonal equation obtained from Hopf-Lax formula. Our redistancing procedure is expected to be generalized and widely applied to many fields such as computational fluid dynamics, the minimal surface problem, and elsewhere.
VERIFICATION AND COMPARISON OF FORMULAS FOR BED LOAD TRANSPORT
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Several typical formulas for bed load transport are examinedbased on field data in this paper. It is concluded that, the Einstein formula provides good estimates for the bed load transport rate while other ones predict much lower transport rates. The main reason for the under-prediction is that Dp, the effective diameter of particles, is too large as a representative diameter of the bed material for gravel streams with partially movable bed. Performance of these formulas can be significantly improved if D35 is adopted instead of Dp.
A generalized Allwright formula and the vector Riccati equation
DEFF Research Database (Denmark)
Andersen, Kurt Munk; Sandqvist, Allan
2010-01-01
A classical formula of Allwright on the general solution of a scalar differential equation is generalized to a system of differential equations by means of the Kronecker product.The Allwright formula is connected with the Riccati equation, and in a similar way the generalized formula is connected...... with a special type of a differential system called a vector Riccati equation. Moreover,the classical result that a scalar differential equation is a Riccati equation if and only if its general solution is a fractional linear function of the starting value, is also generalized to a differential system....
A generalized Allwright formula and the vector Riccati equation
Andersen, Kurt Munk
2010-01-01
A classical formula of Allwright on the general solution of a scalar differential equation is generalized to a system of differential equations by means of the Kronecker product.The Allwright formula is connected with the Riccati equation, and in a similar way the generalized formula is connected with a special type of a differential system called a vector Riccati equation. Moreover,the classical result that a scalar differential equation is a Riccati equation if and only if its general solution is a fractional linear function of the starting value, is also generalized to a differential system.
NTP-CERHR monograph on Soy Infant Formula.
2010-09-01
Soy infant formula contains soy protein isolates and is fed to infants as a supplement to or replacement for human milk or cow milk. Soy protein isolates contains estrogenic isoflavones ("phytoestrogens") that occur naturally in some legumes, especially soybeans. Phytoestrogens are non-steroidal, estrogenic compounds. In plants, nearly all phytoestrogens are bound to sugar molecules and these phytoestrogen-sugar complexes are not generally considered hormonally active. Phytoestrogens are found in many food products in addition to soy infant formula, especially soy-based foods such as tofu, soy milk, and in some over-the-counter dietary supplements. Soy infant formula was selected for evaluation by the National Toxicology Program (NTP) because of the: (1)availability of large number of developmental toxicity studies in laboratory animals exposed to the isoflavones found in soy infant formula (namely, genistein) or other soy products, as well as a number of studies on human infants fed soy infant formula, (2)the availability of information on exposures in infants fed soy infant formula, and (3)public concern for effects on infant or child development. The NTP evaluation was conducted through its Center for the Evaluation of Risks to Human Reproduction (CERHR) and completed in September 2010. The results of this soy infant formula evaluation are published in an NTP Monograph. This document contains the NTP Brief on Soy Infant Formula, which presents NTP's opinion on the potential for exposure to soy infant formula to cause adverse developmental effects in humans. The NTP Monograph also contains an expert panel report prepared to assist the NTP in reaching conclusions on soy infant formula. The NTP concluded there is minimal concern for adverse effects on development in infants who consume soy infant formula. This level of concern represents a "2" on the five-level scale of concern used by the NTP that ranges from negligible concern ("1") to serious concern ("5"). This
Correction to the Moliere's formula for multiple scattering
Lee, R N
2008-01-01
The quasiclassical correction to the Moliere's formula for multiple scattering is derived. The consideration is based on the scattering amplitude, obtained with the first quasiclassical correction taken into account for arbitrary localized but not spherically symmetric potential. Unlike the leading term, the correction to the Moliere's formula contains the target density $n$ and thickness $L$ not only in the combination $nL$ (areal density). Therefore, this correction can be reffered to as the bulk density correction. It turns out that the bulk density correction is small even for high density. This result explains the wide region of applicability of the Moliere's formula.
Modification of the Engelund bed-load formula
Institute of Scientific and Technical Information of China (English)
Zhen Meng; Danxun Li; Xingkui Wang
2016-01-01
The classic Engelund bed-load formula involves four oversimplified assumptions concerning the quantity of particles per unit bed area that can be potentially entrained into motion, the probability of sediment being entrained into motion at a given instant, the mean velocity of bed-load motion, and the dimen-sionless incipient shear stress. These four aspects are reexamined in the light of new findings in hydrodynamics, and a modified bed-load formula is then proposed. The modified formula shows promise as being reliable in predicting bed-load transport rates in a wide range of flow intensities.
MENENTUKAN FORMULA PREMI TAHUNAN TIDAK KONSTAN PADA ASURANSI JOINT LIFE
Directory of Open Access Journals (Sweden)
I GEDE BAGUS PASEK SUBADRA
2015-11-01
Full Text Available The aim of this research was to determine the annual premium formula that turns on the joint life insurance. This formula uses the reference insurance contracts of the previous research Insurance Models for Joint Life and Last Survivor Benefits. The first step is to determine the value of mortality tables by using the Table Helligman-pollard. Furthermore, determining the value of a life annuity and single premium. The results of this research was formula to be affected by the changing premium ( with the increase and decrease in constant interest.
Cubature Formula and Interpolation on the Cubic Domain
Institute of Scientific and Technical Information of China (English)
Huiyuan Li; Jiachang Sun; Yuan Xu
2009-01-01
Several cubature formulas on the cubic domains are derived using the dis-crete Fourier analysis associated with lattice tiling, as developed in [10]. The main results consist of a new derivation of the Gaussian type cubature for the product Cheby-shev weight functions and associated interpolation polynomials on [-1,1]2, as well as new results on [-1,1]3. In particular, compact formulas for the fundamental interpo-lation polynomials are derived, based on n3/4 + (n2) nodes of a cubature formula on [-1,1]3.
A simple formula for predicting settling velocity of sediment particles
Directory of Open Access Journals (Sweden)
Song Zhiyao
2008-03-01
Full Text Available Based on the general relationship described by Cheng between the drag coefficient and the Reynolds number of a particle, a new relationship between the Reynolds number and a dimensionless particle parameter is proposed. Using a trial-and-error procedure to minimize errors, the coefficients were determined and a formula was developed for predicting the settling velocity of natural sediment particles. This formula has higher prediction accuracy than other published formulas and it is applicable to all Reynolds numbers less than 2×105.
Sampel Susu Formula dan Praktik Pemberian Air Susu Ibu Eksklusif
Directory of Open Access Journals (Sweden)
Tuti Nuraini
2013-07-01
Full Text Available Cakupan pemberian air susu ibu (ASI eksklusif di Kota Pagar Alam, tahun 2011 sekitar 43% tergolong rendah. Sebaliknya, pemberian susu formula meningkat tiga kali lipat dari 10,3% menjadi 32,5%. Iklan susu formula telah menyentuh bidan swasta dan puskesmas melalui pendekatan produsen susu formula dan pemberian susu formula secara gratis kepada ibu menyusui. Penelitian yang bertujuan mengetahui determinan kegagalan praktik pemberiaan ASI eksklusif di Kota Pagar Alam Provinsi Sumatera Selatan ini menggunakan desain studi unmatching kasus kontrol. Populasi adalah seluruh ibu yang mempunyai bayi berusia 7 _ 12 bulan. Penarikan sampel dilakukan dengan metode proportional random sampling. Variabel terikat praktik adalah pemberian ASI eksklusif, variabel bebas adalah pemberian sampel susu formula. Ibu yang mendapat sampel susu formula dan yang tidak mendapat dukungan tenaga kesehatan berisiko 3,67 dan 4,2 kali lebih besar untuk tidak memberikan ASI eksklusif. The coverage of exclusive breastfeeding in the City of Pagar Alam in 2011 was by 43%. Advertising of infant formula has reached privately practicing midwives or health centers. The approach from infant formula manufacturers to midwives in health centers is by providing free milk formula to nursing mothers to be distributed under the pretext of promotion. The objective of this study is to analyze the determinants of exclusive breastfeeding practice failures in the City of Pagar Alam of South Sumatra Province. The population study with an unmatched case-control design was conducted in the City of Pagar Alam. The population was all breastfeeding mothers who had babies in the city of Pagar Alam of South Sumatra Province. The research subjects are breastfeeding mothers who had babies aged 7 - 12 months who selected with proportional random sampling method. The variables of the study included the dependent variable, i.e, the practice of exclusive breastfeeding, the independent variable, i.e, promotion of
[Rethinking on application of "syndrome differentiation through formula effect assessment"].
Tang, Shi-huan; Yang, Hong-jun; Huang, Lu-qi
2007-03-01
By summarizing the state of application of "syndrome differentiation through formula effect assessment", it was pointed out that several problems exist in this kind of study, mainly the irrational setting of experimental control group, over simplified pharmacodynamic indexes, and negligence of study on "correspondence between drug and disease", etc. The authors proposed accordingly the thinking methods and strategy in the study on "syndrome differentiation through formula effect assessment" should be setting control properly, taken "correspondence between disease and syndrome" as the key point, and to define clearly the criteria for evaluating the efficacy of formula as the premise.
Data Sharing of Mechanical Design Formulas Using Semantic Web Technology
Zhou, Jun; Watanuki, Keiichi
Speed and efficiency are necessary in the field of mechanical design. CAD/CAM/CAE technologies have advanced and attention has also been paid to increasing the efficiency of data sharing and agent processes in the web environment. In this paper, Semantic Web technology is used to enable the sharing of metadata. The metadata consists of design documents and design formulas, with additional semantic information inserted. Mathematical information is expressed by adding metadata into conventional mechanical design formulas using a Resource Description Framework (RDF). The design formulas are later written in MathML (Mathematical Markup Language) for the sake of data sharing. In this way, data sharing and advanced searching is made easy, because the relevant information is made machine readable in the web environment. The calculation of design formulas is made possible using a mathematical processing system, thus increasing the efficiency of mechanical design.
Quantitative thermo-acoustic imaging: An exact reconstruction formula
Ammari, Habib; Jing, Wenjia; Nguyen, Loc
2012-01-01
The quantitative thermo-acoustic imaging is considered in this paper. Given several data sets of electromagnetic data, we first establish an exact formula for the absorption coefficient, which involves derivatives of the given data up to the third order. However, because of the dependence of such derivatives, this formula is unstable in the sense that small measurement noises may cause large errors. Hence, with the presence of noise, the obtained formula, together with noise regularization, provides an initial guess for the true absorption coefficient. We next correct the errors by deriving a reconstruction formula based on the least square solution of an optimal control problem and show that this optimization step reduces the errors occurring.
An Empirical Formula From Ion Exchange Chromatography and Colorimetry.
Johnson, Steven D.
1996-01-01
Presents a detailed procedure for finding an empirical formula from ion exchange chromatography and colorimetry. Introduces students to more varied techniques including volumetric manipulation, titration, ion-exchange, preparation of a calibration curve, and the use of colorimetry. (JRH)
Pesin’s entropy formula for stochastic flows of diffeomorphisms
Institute of Scientific and Technical Information of China (English)
刘培东
1996-01-01
Pesin’s entropy formula relating entropy and Lyapunov exponents within the context of random dynamical systems generated by (discrete or continuous) stochastic flows of diffeomorphisms (including solution flows of stochastic differential equations on manifolds) is proved.
The interactional significance of formulas in autistic language.
Dobbinson, Sushie; Perkins, Mick; Boucher, Jill
2003-01-01
The phenomenon of echolalia in autistic language is well documented. Whilst much early research dismissed echolalia as merely an indicator of cognitive limitation, later work identified particular discourse functions of echolalic utterances. The work reported here extends the study of the interactional significance of echolalia to formulaic utterances. Audio and video recordings of conversations between the first author and two research participants were transcribed and analysed according to a Conversation Analysis framework and a multi-layered linguistic framework. Formulaic language was found to have predictable interactional significance within the language of an individual with autism, and the generic phenomenon of formulaicity in company with predictable discourse function was seen to hold across the research participants, regardless of cognitive ability. The implications of formulaicity in autistic language for acquisition and processing mechanisms are discussed.
A Prebiotic Formula Improves the Gastrointestinal Bacterial Flora in Toddlers
Directory of Open Access Journals (Sweden)
Ya-Ling Chen
2016-01-01
Full Text Available We aimed to investigate the effect of enriched 3-prebiotic formula (including inulin, fructooligosaccharides, and galactooligosaccharides on toddler gut health by measuring fecal microbiota. Our results revealed that the consumption of 3-prebiotic formula three times per day giving total intake of 1.8 g prebiotic ingredients significantly showed the increased number of probiotic Bifidobacterium spp. colonies and the reduced populations of both C. perfringens and total anaerobic bacteria on the fecal bacterial flora in toddlers at 18~36 months. In addition, total organic acids in the fecal samples significantly increased which improves the utilization of bifidus under acidic conditions after consumption of the 3-prebiotic formula. Therefore, using the formula enriched with prebiotic may maintain gut health in toddlers.
An Empirical Formula for Sound Absorption of Fibrous Materials
Institute of Scientific and Technical Information of China (English)
ZHANG Xin-an
2008-01-01
The sound absorption coefficient (SAC) curves of the nonwovens, fabrics, and thick fibrous layers with the frequency in the range of 125-3 200 Hz and cavity distances of 5 cm, 10 cm, 20 cm, 30 cm and 40 cm were measured.Based on analysis, it is found that the SAC is actually in direct proportion to the relative vibration amplitude of the sound wave, resulting in obtaining a mathematical expression showing that the SAC changes with the frequency for a given material. Additionally, a good corresponding relation between the maximal SAC and the permeability of the materials is discovered, thus an empirical formula is established. As a result, a complete SAC formula has been developed. In this formula, the SAC is solely a function of the sound wave frequency and permeability of the material. In comparison with sound absorption spectra of several materials, the calculated results and results measured with the formula coincide well with each other.
The Elusive Universal Post-Mortem Interval Formula
Energy Technology Data Exchange (ETDEWEB)
Vass, Arpad Alexander [ORNL
2011-01-01
The following manuscript details our initial attempt at developing universal post-mortem interval formulas describing human decomposition. These formulas are empirically derived from data collected over the last 20 years from the University of Tennessee's Anthropology Research Facility, in Knoxville, Tennessee, USA. Two formulas were developed (surface decomposition and burial decomposition) based on temperature, moisture, and the partial pressure of oxygen, as being three of the four primary drivers for human decomposition. It is hoped that worldwide application of these formulas to environments and situations not readily studied in Tennessee will result in interdisciplinary cooperation between scientists and law enforcement personnel that will allow for future refinements of these models leading to increased accuracy.
Iterated index formulae for closed geodesics with applications
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
In this paper, various precise iteration equalities and inequalities of Morse indices for the closed geodesics are established. As applications of these formulae, multiplicity results of closed geodesics on some Riemannian manifolds are proved.
The structural elucidation of Eisenstein’s formula
Institute of Scientific and Technical Information of China (English)
HASHIMOTO; Masahiro; KANEMITSU; Shigeru
2010-01-01
In this paper,we shall give a complete structural description of generalizations of the classical Eisenstein formula that expresses the first periodic Bernoulli polynomial as a finite combination of cotangent values,as a relation between two bases of the vector space of periodic Dirichlet series.We shall also determine the limiting behavior of them,giving rise to Gauss’ famous closed formula for the values of the digamma function at rational points on the one hand and elucidation of Eisenstein-Wang’s formulas in the context of Kubert functions on the other.W shall reveal that most of the relevant previous results are the combinations of the generalized Eisenstein formula and the functional equation.
Seiberg-Witten-Floer Homology and Gluing Formulae
Institute of Scientific and Technical Information of China (English)
Alan L. CAREY; Bai Ling WANG
2003-01-01
This paper gives a detailed construction of Seiberg-Witten-Floer homology for a closed oriented 3-manifold with a non-torsion Spinc structure. Gluing formulae for certain 4-dimensional manifolds splitting along an embedded 3-manifold are obtained.
Knowledge Requirements Formula for Interpreters and Interpreting Training
Institute of Scientific and Technical Information of China (English)
高宇婷
2009-01-01
Based on Zhong Weihe's knowledge requirements formula for interpreters:KI=KL+EK+S(P+AP),this paper explains in detail how the different knowledge is used in the course of interpreting and provides some useful strategies in interpreting practice.
Some Infinite Summation Formulae Involving Kampe de Feriet Function
Directory of Open Access Journals (Sweden)
V. L. Deshpande
1971-04-01
Full Text Available Two infinite summation formulae for Kampe de Feriet function have been established and results are generalised by applying operational technique and method of finite mathematical induction. Various special cases are also obtained of which few are known.
On Ruby's solid angle formula and some of its generalizations
Friot, Samuel
2014-01-01
Using the Mellin-Barnes representation, we show that Ruby's solid angle formula and some of its generalizations may be expressed in a compact way in terms of the Appell F4 and Lauricella Fc functions.
Dialogue Recitation and CFL Learners’ Production of Formulaic Expressions
Directory of Open Access Journals (Sweden)
Jia Yang
2016-07-01
Full Text Available This study examined American learners’ spoken production of formulaic expressions in Chinese after receiving ten weeks of instruction comprised of dialogue recitation and question-answer drills. Students’ speech samples were collected through an oral interview test at the end of the instruction period. The results suggested a positive effect of dialogue recitation on learners’ spoken production of formulaic expressions. The follow-up interviews with the selected high-performing and low-performing learners revealed that high performers used more deep mental processing strategies to make associations and elaborations when learning formulaic expressions, whereas low performers tended to remain in the stage of rote memorization and hence had difficulties in the application of the expressions to a new situation. The results indicate that rote memorization offers the time needed to process the new formulaic expression, while association and elaboration provide the chances of long-term retention and the ability of application.
Confirmation of some formulas related to spin coherence time
Orlov, Yuri
2015-01-01
This paper considers two sets of formulas related to a Spin Coherence Time (SCT) case with only vertical oscillations in a purely electric ring, the first derived by the author for the field index m > 0 and the second by Ivan Koop for the field index m = 0. I argue that a continuous transition can exist from one set to the other (contrary to appearances), and assume that a necessary condition for the transition is that both sets of formulas follow from the same equation. I demonstrate that they do follow when one takes into account that the first set of formulas holds only for times much larger than the period of the vertical oscillations. This demonstration confirms the correctness of the formulas and the equation.
NEW WAVE-DEPENDENT FORMULAE FOR SEA SPRAY FLUX AT AIR-SEA INTERFACE
Institute of Scientific and Technical Information of China (English)
SHI Jian; ZHAO Dong-liang; LI Xun-qiang; ZHONG Zhong
2009-01-01
calculated by two kinds of formulae in different wave states show that previous wave-independent spray flux formulae are the special cases of the presented new wave dependent formulae for sea spray flux.
ON CAUCHY-POMPEIU FORMULA FOR FUNCTIONS WITH VALUES IN A UNIVERSAL CLIFFORD ALGEBRA
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
This paper obtains the Cauchy-Pompeiu formula on certain distinguishedboundary for functions with values in a universal Clifford algebra. This formula is just anextension of the Cauchy's integral formula obtained in [11].
[Usefulness of a soy- and oatmeal-based formula in infant nutrition. Nitrogen balance].
del Valle Canseco, F; Villanueva Clift, H; Escobedo, M; Reyes Govea, J; Hernández Nevárez, M C; Briones, J; Muñóz, M de J; Talamás Abbud, A
1980-01-01
A soy flour and oatmeal formula added with vitamins and minerals is presented. Nitrogen balance is carried out in 6 malnourished infants undergoing recovery as compared with a commercial milk formula, finding no significant statistical differences between the two formulas.
There is (still too much aluminium in infant formulas
Directory of Open Access Journals (Sweden)
Burrell Shelle-Ann M
2010-08-01
Full Text Available Abstract Background Infant formulas are sophisticated milk-based feeds for infants which are used as a substitute for breast milk. Historically they are known to be contaminated by aluminium and in the past this has raised health concerns for exposed infants. We have measured the aluminium content of a number of widely used infant formulas to determine if their contamination by aluminium and consequent issues of child health persists. Methods Samples of ready-made milks and powders used to make milks were prepared by microwave digestion of acid/peroxide mixtures and their aluminium content determined by THGA. Results The concentration of aluminium in ready-made milks varied from ca 176 to 700 μg/L. The latter concentration was for a milk for preterm infants. The aluminium content of powders used to make milks varied from ca 2.4 to 4.3 μg/g. The latter content was for a soya-based formula and equated to a ready-to-drink milk concentration of 629 μg/L. Using the manufacturer's own guidelines of formula consumption the average daily ingestion of aluminium from infant formulas for a child of 6 months varied from ca 200 to 600 μg of aluminium. Generally ingestion was higher from powdered as compared to ready-made formulas. Conclusions The aluminium content of a range of well known brands of infant formulas remains high and particularly so for a product designed for preterm infants and a soya-based product designed for infants with cow's milk intolerances and allergies. Recent research demonstrating the vulnerability of infants to early exposure to aluminium serves to highlight an urgent need to reduce the aluminium content of infant formulas to as low a level as is practically possible.
A Prebiotic Formula Improves the Gastrointestinal Bacterial Flora in Toddlers
2016-01-01
We aimed to investigate the effect of enriched 3-prebiotic formula (including inulin, fructooligosaccharides, and galactooligosaccharides) on toddler gut health by measuring fecal microbiota. Our results revealed that the consumption of 3-prebiotic formula three times per day giving total intake of 1.8 g prebiotic ingredients significantly showed the increased number of probiotic Bifidobacterium spp. colonies and the reduced populations of both C. perfringens and total anaerobic bacteria on t...
Nuclear binding energy using semi empirical mass formula
Ankita, Suthar, B.
2016-05-01
In the present communication, semi empirical mass formula using the liquid drop model has been presented. Nuclear binding energies are calculated using semi empirical mass formula with various constants given by different researchers. We also compare these calculated values with experimental data and comparative study for finding suitable constants is added using the error plot. The study is extended to find the more suitable constant to reduce the error.
Smarr formula for Lovelock black holes: A Lagrangian approach
Liberati, Stefano; Pacilio, Costantino
2016-04-01
The mass formula for black holes can be formally expressed in terms of a Noether charge surface integral plus a suitable volume integral, for any gravitational theory. The integrals can be constructed as an application of Wald's formalism. We apply this formalism to compute the mass and the Smarr formula for static Lovelock black holes. Finally, we propose a new prescription for Wald's entropy in the case of Lovelock black holes, which takes into account topological contributions to the entropy functional.
Mass Formulae for Broken Supersymmetry in Curved Space-Time
Ferrara, Sergio
2016-01-01
We derive the mass formulae for ${\\cal N}=1$, $D=4$ matter-coupled Supergravity for broken (and unbroken) Supersymmetry in curved space-time. These formulae are applicable to de Sitter configurations as is the case for inflation. For unbroken Supersymmetry in anti-de Sitter (AdS) one gets the mass relations modified by the AdS curvature. We compute the mass relations both for the potential and its derivative non-vanishing.
The Mehler Formula for the Generalized Clifford-Hermite Polynomials
Institute of Scientific and Technical Information of China (English)
F.BRACKX; N.DE SCHEPPER; K.I.KOU; F.SOMMEN
2007-01-01
The Mehler formula for the Hermite polynomials allows for an integral representation of the one-dimensional Fractional Fourier transform.In this paper,we introduce a multi-dimensional Fractional Fourier transform in the framework of Clifford analysis.By showing that it coincides with the classical tensorial approach we are able to prove Mehler ’s formula for the generalized Clifford –Hermitepolynomials of Cli ord analysis.
Reciprocity and mutual impedance formulas within lossy cavities
Directory of Open Access Journals (Sweden)
F. Gronwald
2005-01-01
Full Text Available We discuss the validity of reciprocity and mutual impedance formulas within lossy cavities. Mutual impedance formulas are well-known from antenna theory and useful to describe the electromagnetic coupling between electromagnetic interference sources and victims. As an example the mutual impedance between two dipole antennas within a lossy rectangular cavity is calculated from a system of coupled Hallén's equations that efficiently is solved by the method of moments.
The aluminium content of infant formulas remains too high
2013-01-01
Background Recent research published in this journal highlighted the issue of the high content of aluminium in infant formulas. The expectation was that the findings would serve as a catalyst for manufacturers to address a significant problem of these, often necessary, components of infant nutrition. It is critically important that parents and other users have confidence in the safety of infant formulas and that they have reliable information to use in choosing a product with a lower content ...
Arthur's invariant trace formula and comparison of inner forms
Flicker, Yuval Z
2016-01-01
This monograph provides an accessible and comprehensive introduction to James Arthur’s invariant trace formula, a crucial tool in the theory of automorphic representations. It synthesizes two decades of Arthur’s research and writing into one volume, treating a highly detailed and often difficult subject in a clearer and more uniform manner without sacrificing any technical details. The book begins with a brief overview of Arthur’s work and a proof of the correspondence between GL(n) and its inner forms in general. Subsequent chapters develop the invariant trace formula in a form fit for applications, starting with Arthur’s proof of the basic, non-invariant trace formula, followed by a study of the non-invariance of the terms in the basic trace formula, and, finally, an in-depth look at the development of the invariant formula. The final chapter illustrates the use of the formula by comparing it for G’ = GL(n) and its inner form G and for functions with matching orbital integrals. Arthur’s Invarian...
On generalization of Kible-Slepian kernel formula
Szabłowski, Paweł J
2010-01-01
We study generalization of Kible-Slepian (K-S) expansion formula in 3 dimensions. The generalization is obtained by replacing in K-S formula Hermite polynomials by q-Hermite ones. If such replacement would lead to non-negativity of values for all allowed values of parameters and for values of variables from certain Cartesian product of compact intervals then we would deal with generalization of 3 dimensional normal distribution. We show that this is not the case. We indicate some values of parameters and some compact set in R^3 of positive measure, such that values of the extension K-S formula are on this set negative. Nevertheless we indicate other applications of so generalized K-S formula, namely we use this formula to sum certain kernels built of Al-Salam-Chihara polynomials for cased that were not considered by other authors. One of such kernels sum up to Askey-Wilson density. Hence we are able to obtain generalization of 2 dimensional Poisson-Mehler formula. We also pose several open questions.
Vanderhoof, Jon; Moore, Nancy; de Boissieu, Delphine
2016-01-01
ABSTRACT Nearly 2% to 3% of infants and children younger than 3 years have confirmed cow's milk protein allergy with multiple clinical presentations including atopic dermatitis (AD), diarrhea, and vomiting/spitting up. Although most infants with cow's milk protein allergy experience clinical improvement with the use of an extensively hydrolyzed (EH) formula, highly sensitive infants may require an amino acid−based formula. In this observational, prospective study, 30 infants (1–12 months of age) with a history of weight loss and persistent allergic manifestations while on an EH formula were provided an amino acid−based formula for 12 weeks. Mean weight gain (z score change) improved +0.43 ± 0.28 (mean ± standard deviation) after the 12-week feeding period. Improvement was observed for many allergic symptoms including significant decreases in AD severity (P = 0.02). These results indicate the new amino acid–based infant formula supported healthy weight gain and improvement in allergic manifestations in infants not responding to EH formulas. PMID:27526059
Directory of Open Access Journals (Sweden)
Jianglong Song
2013-01-01
Full Text Available At the molecular level, it is acknowledged that a TCM formula is often a complex system, which challenges researchers to fully understand its underlying pharmacological action. However, module detection technique developed from complex network provides new insight into systematic investigation of the mode of action of a TCM formula from the molecule perspective. We here proposed a computational approach integrating the module detection technique into a 2-class heterogeneous network (2-HN which models the complex pharmacological system of a TCM formula. This approach takes three steps: construction of a 2-HN, identification of primary pharmacological units, and pathway analysis. We employed this approach to study Shu-feng-jie-du (SHU formula, which aimed at discovering its molecular mechanism in defending against influenza infection. Actually, four primary pharmacological units were identified from the 2-HN for SHU formula and further analysis revealed numbers of biological pathways modulated by the four pharmacological units. 24 out of 40 enriched pathways that were ranked in top 10 corresponding to each of the four pharmacological units were found to be involved in the process of influenza infection. Therefore, this approach is capable of uncovering the mode of action underlying a TCM formula via module analysis.
Assessment on Dietary Melamine Exposure from Tainted Infant Formula
Institute of Scientific and Technical Information of China (English)
XU-DONG JIA; NING LI; ZHU-TIAN WANG; YUN-FENG ZHAO; YONG-NING WU; WEI-XING YAN
2009-01-01
Objective To estimate the dietary melamine exposure in Chinese infants and young children from the consumption of melamine adulterated Sanlu infant formula. Methods Four age groups of infants and young children (3, 6, 12, and 24 months) were chosen as the assessed subjects and the maximum amount of infant formula consumption was estimated based on the recommended usage level in the package insert of Sanlu infant formula and other brands. Melamine was analyzed in 111 Sanlu infant formula samples collected from the markets in Beijing and Gansu province using the LC-MS-MS with a limit of quantification of 0.05 mg/kg. Four levels of melamine concentration were chosen to estimate the dietary intakes, including the mean, median, 90th percentile, and maximum. Results The infants of 3 months had the highest intake of melamine, and with the increase of the age (month), the intake decreased. Based on the median melamine concentration (1 000 mg/kg) as an example, the melamine intakes for the infants of 3, 6, 12, and 24 months were 23.4, 21.4, 15.0, and 8.6 mg/kg bw/d, respectively. Conclusion Dietary melamine intakes from tainted Sanlu infant formula significantly exceeded the TDI level (0.2 mg/kg bw/d) recommended by the WHO Expert Meeting in 2008. However, the present assessment has some limitations including the poor representative samples, the varied melamine concentrations in the adulterated Sanlu infant formula, and other brand infant formula possibly consumed by these infants.
Students' Understanding of Chemical Formulae: A review of empirical research
Taskin, Vahide; Bernholt, Sascha
2014-01-01
The fluent use of the chemical language is a major tool for successfully passing chemistry courses at school or university as well as for working as a chemist, since chemical formulae are both a descriptive and a heuristic tool. However, numerous studies have revealed remarkable difficulties of students with chemical formulae both at school and at university. Although analysed for decades, current studies and practical experiences indicate that the misinterpretation of symbolic representations by students is still an ongoing problem. This review intends not only to summarize but also to categorize students' problems and difficulties when dealing with chemical formulae as reported in empirical studies. For this purpose, two categories of descriptive character were deduced from the empirical data: the type of chemical formulae and the operational activities that were required in the tasks of the studies. All in all, 38 articles were analysed on the basis of these categories. Students' problems and difficulties are then reflected based on three main problem areas: language-based problems, problems due to conceptual understanding, and problems due to inadequate selection and interpretation of formulae. These three areas call for a broader perspective in the interpretation of students' problems and thus lead to a discussion of implications for further research and changes in teaching practice.
Analytical Dielectric Spectrum Formula Based on Representative Frequencies
Institute of Scientific and Technical Information of China (English)
Bo Kong; Ke-xiang Fu; Min-hua Shan; Xiang-yuan Li
2009-01-01
According to experimental data available for the complex refractive index of particular di-electrics, a dielectric spectrum formula is proposed by the least square fitting technique combined with selected natural frequencies. From the dielectric spectrum formula, the spec-tra of optical and dielectric constants can be obtained in the whole frequency region. Three dielectrics, water, ethanol, and toluene, are taken as examples. In the region where the ex-perimental data are available, the spectra of the optical constants calculated by the formula are in good agreement with the real refractive spectrum obtained by Kramers-Kronig (K-K) transform and the experimental imaginary refractive spectrum. In the region where no ex-perimental data are available, the extrapolation of our formula can make predictions. The merits of the present treatment are that we are able to get the uniform spectrum formula, without splitting into different frequency sections, and the analytical form of the dielectric spectra will be useful in the theoretical description of solvation dynamics.
Lönnerdal, Bo
2014-03-01
Human milk contains an abundance of biologically active components that are highly likely to contribute to the short- and long-term benefits of breastfeeding. Many of these components are proteins; this article describes some of these proteins, such as α-lactalbumin, lactoferrin, osteopontin, and milk fat globule membrane proteins. The possibility of adding their bovine counterparts to infant formula is discussed as well as the implications for infant health and development. An important consideration when adding bioactive proteins to infant formula is that the total protein content of formula needs to be reduced, because formula-fed infants have significantly higher concentrations of serum amino acids, insulin, and blood urea nitrogen than do breastfed infants. When reducing the protein content of formula, the amino acid composition of the formula protein becomes important because serum concentrations of the essential amino acids should not be lower than those in breastfed infants. Both the supply of essential amino acids and the bioactivities of milk proteins are dependent on their digestibility: some proteins act only in intact form, others act in the form of larger or small peptides formed during digestion, and some are completely digested and serve as a source of amino acids. The purity of the proteins or protein fractions, potential contaminants of the proteins (such as lipopolysaccharide), as well as the degree of heat processing used during their isolation also need to be considered. It is likely that there will be more bioactive components added to infant formulas in the near future, but guidelines on how to assess their bioactivities in vitro, in animal models, and in clinical studies need to be established. The extent of testing needed is likely going to depend on the degree of complexity of the components and their bioequivalence with the human compounds whose effects they are intended to mimic.
21 CFR 107.260 - Revision of an infant formula recall.
2010-04-01
... 21 Food and Drugs 2 2010-04-01 2010-04-01 false Revision of an infant formula recall. 107.260... (CONTINUED) FOOD FOR HUMAN CONSUMPTION INFANT FORMULA Infant Formula Recalls § 107.260 Revision of an infant... by the infant formula. (b) Carry out additional effectiveness checks, if the agency's audits,...
21 CFR 107.250 - Termination of an infant formula recall.
2010-04-01
... 21 Food and Drugs 2 2010-04-01 2010-04-01 false Termination of an infant formula recall. 107.250... (CONTINUED) FOOD FOR HUMAN CONSUMPTION INFANT FORMULA Infant Formula Recalls § 107.250 Termination of an infant formula recall. The recalling firm may submit a recommendation for termination of the recall...
21 CFR 107.220 - Scope and effect of infant formula recalls.
2010-04-01
... 21 Food and Drugs 2 2010-04-01 2010-04-01 false Scope and effect of infant formula recalls. 107... SERVICES (CONTINUED) FOOD FOR HUMAN CONSUMPTION INFANT FORMULA Infant Formula Recalls § 107.220 Scope and effect of infant formula recalls. (a) The requirements of this subpart apply: (1) When the Food and...
Mineral retention in three-week-old piglets fed goat and cow milk infant formulas
Rutherfurd, S.M.; Darragh, A.J.; Hendriks, W.H.; Prosser, C.G.; Lowry, D.
2006-01-01
Goat milk and cow milk are commonly used in infant formula preparations and, as such, understanding the nutritional characteristics of infant formulas made from these milks is important. In this study, a goat milk infant formula was compared with an adapted (whey-enhanced) cow milk infant formula wi
Comparative study of various intra ocular lens formulae by IOL master
Directory of Open Access Journals (Sweden)
Arikeri Krishna Kishore
2015-11-01
The HAIGIS formula has a better predictability and accuracy. The postoperative hyperopic shift was comparable between HAIGIS and SRK-T formulae the least postoperative hyperopic shift with Haigis formula compared to other formulae. [Int J Res Med Sci 2015; 3(11.000: 3391-3398
An index formula for the extended Heisenberg algebra of Epstein, Melrose and Mendoza
van Erp, Erik
2010-01-01
The extended Heisenberg algebra for a contact manifold contains, as subalgebras, both the Heisenberg algebra as well as the classical pseudodifferential operators. We derive here a formula for the index of Fredholm operators in this extended calculus. This formula incorporates in a single expression the Atiyah-Singer formula for elliptic operators, as well as Boutet de Monvel's Toeplitz index formula.
Conditions for predicting quasistationary states by rearrangement formula
Yamaguchi, Yoshiyuki Y.; Ogawa, Shun
2015-10-01
Predicting the long-lasting quasistationary state for a given initial state is one of central issues in Hamiltonian systems having long-range interaction. A recently proposed method is based on the Vlasov description and uniformly redistributes the initial distribution along contours of the asymptotic effective Hamiltonian, which is defined by the obtained quasistationary state and is determined self-consistently. The method, to which we refer as the rearrangement formula, was suggested to give precise prediction under limited situations. Restricting initial states consisting of a spatially homogeneous part and small perturbation, we numerically reveal two conditions that the rearrangement formula prefers: One is a no Landau damping condition for the unperturbed homogeneous part, and the other comes from the Casimir invariants. Mechanisms of these conditions are discussed. Clarifying these conditions, we validate to use the rearrangement formula as the response theory for an external field, and we shed light on improving the theory as a nonequilibrium statistical mechanics.
Investigating uncertainty in BPR formula parameters: a case study
DEFF Research Database (Denmark)
Manzo, Stefano; Nielsen, Otto Anker; Prato, Carlo Giacomo
uncertainty within the model. The research described in this paper investigated uncertainty in the BPR formula parameters. Within traffic assignment models, the relationship between travel time and traffic flows is commonly described by the BPR formula. The BPR formula works as a link performance function......; given free flow travel time, observed flow and link capacity, it uses parameters to fit the equation to various types of roadways and circumstances. Usually, the values for the parameters are pre-defined, based on assumptions and practice. The present paper describes a work implemented to define the BPR...... on their output highly unreliable. The main consequence of this inherent uncertainty is that modelled traffic flows cannot be expressed as a point estimate, because this would only represent one of the possible outputs generated by the model. Instead, modelled traffic flows are better expressed as a central...
A Gamma Class Formula for Open Gromov-Witten Calculations
Mahowald, Matthew
2016-01-01
For toric Calabi-Yau threefolds, open Gromov-Witten invariants associated to Riemann surfaces with one boundary component can be written as the product of a disk factor and a closed invariant. When the Lagrangian boundary cycle is preserved by the torus action and can be locally described as the fixed locus of an anti-holomorphic involution, we prove a formula that expresses the disk factor in terms of a gamma class and combinatorial data about the image of the Lagrangian cycle in the moment polytope. As a corollary, we construct a generating function for these invariants using Givental's $J$ function. We then verify that this formula encodes the expected invariants obtained from localization by comparing with several examples. Finally, motivated by large $N$ duality, we show that this formula also unexpectedly applies to Lagrangian cycles on $\\mathcal{O}_{\\mathbb{P}^1}(-1,-1)$ constructed from torus knots.
Some reference formulas for the generating functions of canonical transformations
Anselmi, Damiano
2015-01-01
We study some properties of the canonical transformations in classical mechanics and quantum field theory and give a number of practical formulas concerning their generating functions. First, we give a diagrammatic formula for the perturbative expansion of the composition law around the identity map. Then, we propose a standard way to express the generating function of a canonical transformation by means of a certain "componential" map, which obeys the Baker-Campbell-Hausdorff formula. We derive the diagrammatic interpretation of the componential map, work out its relation with the solution of the Hamilton-Jacobi equation and derive its time-ordered version. Finally, we generalize the results to the Batalin-Vilkovisky formalism, where the conjugate variables may have both bosonic and fermionic statistics, and describe applications to quantum field theory.
Modular forms and a generalized Cardy formula in higher dimensions
Shaghoulian, Edgar
2016-06-01
We derive a formula which applies to conformal field theories on a spatial torus and gives the asymptotic density of states solely in terms of the vacuum energy on a parallel plate geometry. The formula follows immediately from global scale and Lorentz invariance, but to our knowledge has not previously been made explicit. It can also be understood from the fact that log Z on T2×Rd -1 transforms as the absolute value of a nonholomorphic modular form of weight d -1 , which we show. The results are extended to theories which violate Lorentz invariance and hyperscaling but maintain a scaling symmetry. The formula is checked for the cases of a free scalar, free Maxwell gauge field, and free N =4 super Yang-Mills. The case of a Maxwell gauge field gives Casimir's original calculation of the electromagnetic force between parallel plates in terms of the entropy of a photon gas.
Some reference formulas for the generating functions of canonical transformations
Energy Technology Data Exchange (ETDEWEB)
Anselmi, Damiano [Universita di Pisa, Dipartimento di Fisica ' ' Enrico Fermi' ' , Pisa (Italy); INFN, Sezione di Pisa, Pisa (Italy)
2016-02-15
We study some properties of the canonical transformations in classical mechanics and quantum field theory and give a number of practical formulas concerning their generating functions. First, we give a diagrammatic formula for the perturbative expansion of the composition law around the identity map. Then we propose a standard way to express the generating function of a canonical transformation by means of a certain ''componential'' map, which obeys the Baker-Campbell-Hausdorff formula. We derive the diagrammatic interpretation of the componential map, work out its relation with the solution of the Hamilton-Jacobi equation and derive its time-ordered version. Finally, we generalize the results to the Batalin-Vilkovisky formalism, where the conjugate variables may have both bosonic and fermionic statistics, and describe applications to quantum field theory. (orig.)
Inversion formula for the growth function of a cancellative monoid
Saito, Kyoji
2012-01-01
We consider any cancellative monoid $M$ equipped with a discrete degree map $deg:M\\to R_{\\ge0}$ and associated generating function $P(t)=\\sum_{m\\in M}t^{deg(m)}$, called the growth function of $M$. We also introduce, using some towers of minimal common multiple sets in $M$, another signed generating function $N(t)$, called the skew-growth function of $M$. We show that these functions satisfy the inversion formula $P(t)N(t)=1$. In case the monoid is the set of positive integers with ordinary product structure and the degree map is logarithm function, using the coordinate change $t=exp(-s)$, the inversion formula turns out to be the Euler product formula for the Riemann's zeta function.
Towards the Cardy formula for hyperscaling violation black holes
Bravo-Gaete, Moises; Hassaine, Mokhtar
2015-01-01
The aim of this paper is to propose a generalized Cardy formula in the case of three-dimensional hyperscaling violation black holes. We first note that for the hyperscaling violation metrics, the scaling of the entropy in term of the temperature (defined as the effective spatial dimensionality divided by the dynamical exponent) depends explicitly on the gravity theory. Starting from this observation, we first explore the case of quadratic curvature gravity theory for which we derive four classes of asymptotically hyperscaling violation black holes. For each solution, we compute their masses as well as those of their soliton counterparts obtained through a double Wick rotation. Assuming that the partition function has a certain invariance involving the effective spatial dimensionality, a generalized Cardy formula is derived. This latter is shown to correctly reproduce the entropy where the ground state is identified with the soliton. Comparing our formula with the one derived in the standard Einstein gravity c...
The Parkland formula under fire: is the criticism justified?
Blumetti, Jennifer; Hunt, John L; Arnoldo, Brett D; Parks, Jennifer K; Purdue, Gary F
2008-01-01
Controversy has continued regarding the practicality and accuracy of the Parkland burn formula since its introduction over 35 years ago. The best guide for adequacy of resuscitation is urine output (UOP) per hour. A retrospective study of patients resuscitated with the Parkland formula was conducted to determine the accuracy (calculated vs. actual volume) based on UOP. A review of burn resuscitation from a single institution over 15 years was conducted. The Parkland formula was defined as fluid resuscitation of 3.7 to 4.3 ml/kg/% total body surface area (TBSA) burn in the first 24 hours. Adequate resuscitation was defined as UOP of 0.5 to 1.0 ml/kg/hr. Over-resuscitation was defined as UOP > 1.0 ml/kg/hr. Patients were stratified according to UOP. Burns more than 19% TBSA were included. Electrical burns, trauma, and children (UOP is the important parameter.
Modular forms and a generalized Cardy formula in higher dimensions
Shaghoulian, Edgar
2015-01-01
We derive a formula which applies to conformal field theories on a spatial torus and gives the asymptotic density of states solely in terms of the vacuum energy on a parallel plate geometry. The formula follows immediately from global scale and Lorentz invariance, but to our knowledge has not previously been made explicit. It can also be understood from the fact that $\\log Z$ on $\\mathbb{T}^2\\times \\mathbb{R}^{d-1}$ is the absolute value of a modular form of weight $1-d$, which we prove. The results are extended to theories which violate Lorentz invariance and hyperscaling but maintain a scaling symmetry. The formula is checked for the cases of a free scalar, free Maxwell gauge field, and free $\\mathcal{N}=4$ super Yang-Mills. The case of a Maxwell gauge field gives Casimir's original calculation of the electromagnetic force between parallel plates in terms of the entropy of a photon gas.
Crosstalk Model and Estimation Formula for VLSI Interconnect Wires
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
We develop an interconnect crosstalk estimation model on the assumption of linearity for CMOS device. First, we analyze the terminal response of RC model on the worst condition from the S field to the time domain. The exact 3 order coefficients in S field are obtained due to the interconnect tree model. Based on this, a crosstalk peak estimation formula is presented. Unlike other crosstalk equations in the literature, this formula is only used coupled capacitance and grand capacitance as parameter. Experimental results show that, compared with the SPICE results, the estimation formulae are simple and accurate. So the model is expected to be used in such fields as layout-driven logic and high level synthesis, performance-driven floorplanning and interconnect planning.
Humanizing infant milk formula to decrease postnatal HIV transmission.
Blais, David R; Altosaar, Illimar
2007-09-01
There are currently no safe methods for feeding babies born from the 16 million HIV-infected women living in resource-constrained countries. Breast milk can transmit HIV, and formula feeding can lead to gastrointestinal illnesses owing to unsanitary conditions and the composition of milk formulations. There is therefore a need to ensure that breast milk substitutes provide optimal health outcomes. Given that the immune properties of several breast milk proteins are known, transgenic food crops could facilitate inexpensive and safe reconstitution of the beneficial breast milk proteome in infant formulae, while keeping the HIV virus at bay. At least seven breast milk immune proteins have already been produced in food crops, and dozens more proteins could potentially be produced if fortified formula proves effective in nursing newborns born to HIV-infected mothers.
New integral formula and its applications to light nucleus reactions
Sun, Xiaojun
2015-01-01
A new integral formula, which has not been compiled in any integral tables or mathematical softwares, is proposed to obtain the analytical energy-angular spectra of the particles that are sequentially emitted from the discrete energy levels of the residual nuclei in the statistical theory of light nucleus reaction (STLN). In the cases of the neutron induced light nucleus reactions, the demonstration of the kinetic energy conservation in the sequential emission processes becomes straightforward thanks to this new integral formula and it is also helpful to largely reduce the volume of file-6 in nuclear reaction databases. Furthermore, taking p+$^9$Be reaction at 18 MeV as an example, this integral formula is extended to calculate the energy-angular spectra of the sequentially emitted neutrons for proton induced light nucleus reactions in the frame of STLN.
Generating function formula of heat transfer in harmonic networks
Saito, Keiji; Dhar, Abhishek
2011-04-01
We consider heat transfer across an arbitrary classical harmonic network connected to two heat baths at different temperatures. The network has N positional degrees of freedom, of which NL are connected to a bath at temperature TL and NR are connected to a bath at temperature TR. We derive an exact formula for the cumulant generating function for heat transfer between the two baths. The formula is valid even for NL≠NR and satisfies the Gallavotti-Cohen fluctuation symmetry. Since harmonic crystals in three dimensions are known to exhibit different regimes of transport such as ballistic, anomalous, and diffusive, our result implies validity of the fluctuation theorem in all regimes. Our exact formula provides a powerful tool to study other properties of nonequilibrium current fluctuations.
Testing Linear Temporal Logic Formulae on Finite Execution Traces
Havelund, Klaus; Rosu, Grigore; Norvig, Peter (Technical Monitor)
2001-01-01
We present an algorithm for efficiently testing Linear Temporal Logic (LTL) formulae on finite execution traces. The standard models of LTL are infinite traces, reflecting the behavior of reactive and concurrent systems which conceptually may be continuously alive. In most past applications of LTL. theorem provers and model checkers have been used to formally prove that down-scaled models satisfy such LTL specifications. Our goal is instead to use LTL for up-scaled testing of real software applications. Such tests correspond to analyzing the conformance of finite traces against LTL formulae. We first describe what it means for a finite trace to satisfy an LTL property. We then suggest an optimized algorithm based on transforming LTL formulae. The work is done using the Maude rewriting system. which turns out to provide a perfect notation and an efficient rewriting engine for performing these experiments.
Some reference formulas for the generating functions of canonical transformations
Anselmi, Damiano
2016-02-01
We study some properties of the canonical transformations in classical mechanics and quantum field theory and give a number of practical formulas concerning their generating functions. First, we give a diagrammatic formula for the perturbative expansion of the composition law around the identity map. Then we propose a standard way to express the generating function of a canonical transformation by means of a certain "componential" map, which obeys the Baker-Campbell-Hausdorff formula. We derive the diagrammatic interpretation of the componential map, work out its relation with the solution of the Hamilton-Jacobi equation and derive its time-ordered version. Finally, we generalize the results to the Batalin-Vilkovisky formalism, where the conjugate variables may have both bosonic and fermionic statistics, and describe applications to quantum field theory.
Families of automorphic forms and the trace formula
Shin, Sug; Templier, Nicolas
2016-01-01
Featuring the work of twenty-three internationally-recognized experts, this volume explores the trace formula, spectra of locally symmetric spaces, p-adic families, and other recent techniques from harmonic analysis and representation theory. Each peer-reviewed submission in this volume, based on the Simons Foundation symposium on families of automorphic forms and the trace formula held in Puerto Rico in January-February 2014, is the product of intensive research collaboration by the participants over the course of the seven-day workshop. The goal of each session in the symposium was to bring together researchers with diverse specialties in order to identify key difficulties as well as fruitful approaches being explored in the field. The respective themes were counting cohomological forms, p-adic trace formulas, Hecke fields, slopes of modular forms, and orbital integrals.
The emotional and practical experiences of formula-feeding mothers.
Fallon, Victoria; Komninou, Sophia; Bennett, Kate M; Halford, Jason C G; Harrold, Joanne A
2016-11-14
The majority of infant-feeding research is focused on identifying mother's reasons for the cessation of breastfeeding. The experience of mothers who choose to use formula is largely overlooked in quantitative designs. This study aimed to describe the emotional and practical experiences of mothers who formula feed in any quantity, and examine whether these experiences would vary among different cohorts of formula-feeding mothers according to prenatal feeding intention and postnatal feeding method. A total of 890 mothers of infants up to 26 weeks of age, who were currently formula feeding in any quantity, were recruited through relevant international social media sites via advertisements providing a link to an online survey. Predictors of emotional experiences included guilt, stigma, satisfaction, and defense as a result of their infant feeding choices. Practical predictor variables included support received from health professionals, respect displayed by their everyday environment, and main sources of infant feeding information. Descriptive findings from the overall sample highlighted a worryingly high percentage of mother's experienced negative emotions as a result of their decision to use formula. Multinomial logit models revealed that negative emotions such as guilt, dissatisfaction, and stigma were directly associated with feeding intention and method. The evidence suggests that the current approach to infant-feeding promotion and support may be paradoxically related to significant issues with emotional well-being. These findings support criticisms of how infant-feeding recommendations are framed by health care professionals and policy makers, and highlight a need to address formula feeding in a more balanced, woman-centered manner.
The mathematics of mosaic analysis. II. Formulae for interacting foci.
Wyman, R J; Salkoff, L
1982-04-01
Mosaic fate mapping requires first a measurement of the frequency of separation (by genotype) of two structures and then a conversion of this frequency of separation to distance (WYMAN and THOMAS 1982). If the genotype of two structures is visible, the frequency of separation (sturt distance) may be directly obtained. If the genotype is not visible (e.g., for behavioral foci) then the frequency of separation (sturt distance) itself must be calculated. The formulae introduced by HOTTA and BENZER (1972) for calculating frequency of separation are appropriate only for a set of mosaics in which each fly has half normal and half mutant tissue. Using these formulae for a set of mosaics with a different fraction of mutant tissue can give enormously incorrect results.--In this paper we use intuitive lines of reasoning to obtain simple formulae for frequencies of separation that are algebraically equal to the more elaborate HOTTA and BENZER (1972) formulae.--We show that when calculating sturt distances, data from a collection of mosaics with a range of malenesses, even if the average maleness is 1/2, cannot be lumped together. We prove that applying any formula appropriate for m = 1/2 to a set of mosaics all of maleness m, and then to a set of maleness 1-m, and then averaging the two results, does give the correct value for sturt distances. In this way all the mapping distances may be obtained.--Another method for locating foci is called "contour mapping". We show that the currently available contour formulae are inaccurate. We suggest that contour maps be drawn using the accurate sturt distances.
The U.S. infant formula industry: is direct-to-consumer advertising unethical or inevitable?
Cutler, Bob D; Wright, Robert F
2002-01-01
Throughout their history, U.S. based infant formula companies have promoted their products as though they required a prescription. This form of marketing is called "ethical" promotion, which focuses on gaining a physician to parent recommendation for a brand of infant formula. Until Nestle's entry into the U.S. infant formula market in 1988, there was little direct-to-consumer promotion of infant formula. This article provides a background on the history of infant formula practices in the United States and then focuses on a descriptive model to explain how mothers' make their infant formula selection. Finally, we offer suggestions for the "ethical" marketers of infant formula.
Testing the Witten-Veneziano Formula on the Lattice
Cichy, Krzysztof; Jansen, Karl; Ottnad, Konstantin; Urbach, Carsten
2015-01-01
In this proceeding contribution we report on a test of the famous Witten-Veneziano formula using lattice techniques. We perform dedicated quenched simulations and apply the spectral projector method to determine the topological susceptibility in pure Yang-Mills theory. In order to compute the relevant meson masses and the flavor singlet decay constant we employ lattice QCD with $N_f=2+1+1$ dynamical Wilson twisted mass fermions. Taking the continuum and the $SU(2)$ chiral limits we find good agreement within uncertainties for both sides of the formula.
The Bajnok-Janik formula and wrapping corrections
Balog, Janos(Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, MTA Lendület Holographic QFT Group, 1525, Budapest 114, P.O.B. 49, Hungary); Hegedus, Arpad
2010-01-01
We write down the simplified TBA equations of the $AdS_5 \\times S^5$ string sigma-model for minimal energy twist-two operators in the sl(2) sector of the model. By using the linearized version of these TBA equations it is shown that the wrapping corrected Bethe equations for these states are identical, up to O(g^8), to the Bethe equations calculated in the generalized L\\"uscher approach (Bajnok-Janik formula). Applications of the Bajnok-Janik formula to relativistic integrable models, the non...
Improved Numerical Generalization of Bethe- Weizsacker Mass Formula
Mavrodiev, Strachimir
2016-01-01
In this paper is presented explicit improved numerical generalization of Bethe-Weizsacker mass formulae which describes the values of measured 2654 nuclear mass in AME2012 nuclear database with accuracy less than 2.2 MeV, starting from the number of protons Z=1 and number of neutrons N=1. In the obtained generazation of the Bethe-Weizsacker formula the influence of magic numbers and boundaries of their influence between them is defined for nine proton (2, 8, 14, 20, 28, 50, 82, 108, 124) and ten neutron (2, 8, 14, 20, 28, 50, 82, 124, 152, 202) magic numbers.
Evaluations of energy coefficients of Bethe-Weizsacker mass formula
Basu, D N
2004-01-01
A mass fit to the liquid drop model is presented. Coefficients of the volume, surface, coulomb, asymmetry and pairing energy terms of the semiemirical Bethe-Weizsacker mass formula have been determined by furnishing best fit to the observed mass excesses. Different sets of the weighting parameters for liquid drop model Bethe-Weizsacker mass formula have been obtained from minimizations of chisquare and mean square deviation. The recent exerimental and estimated mass excesses from Audi-Wapstra-Thibault atomic mass table have been used for the least square fitting procedure. Some implications of the modifications of parameters have been discussed.
Approximate formulas for total cross section for moderately small eikonal
Kisselev, A V
2016-01-01
The eikonal representation for the total cross section is considered. The approximate formulas for a moderately small eikonal are derived. In contrast to the standard eikonal integrals, they contain no Bessel functions, and, hence, no rapidly oscillating integrands. The formulas obtained are applied to numerical evaluations of the total cross section for a number of particular expressions for the eikonal. It is shown that for pure imaginary eikonals the relative error of O(10^(-5)) can be achieved. Also two improper triple integrals are analytically calculated.
Simple formulas for Stirling numbers of the second kind
Low, A. A.; Ho, C. K.
2015-12-01
For large values of k, especially those closer to n, the expression for S(n, k), the Stirling numbers (of the second kind) can become quite cumbersome to deal with. In this paper, we obtained simple formulas for S(n, n - r) for small values of r. Our formulas contain only a combination of r combinatorial terms. As a consequence, our results revealed the fact that our values of S(n, n - r) are indeed far lower than the upper bounds given by Rennie and Dobson.
Customizable Visualizations with Formula-Linked Building Blocks
DEFF Research Database (Denmark)
Kuhail, Mohammad Amin; Lauesen, Søren
different appearance or behavior than what the widgets support. Another approach is to combine primitive graphical elements using traditional programming or visualization toolkits. Traditional programming allows high customizability, but it is time consuming and hard to develop advanced visualizations....... Visualization toolkits allow easier visualization creation in some cases, but customization and interaction are tedious. As an alternative, we developed uVis visualization tool that uses spreadsheet-like formulas to connect building blocks. uVis formulas can refer to building blocks and database tables. We...
Determinantal formulae for the Casimir operators of inhomogeneous Lie algebras
Energy Technology Data Exchange (ETDEWEB)
Campoamor-Stursberg, Rutwig [Dpto. Geometria y Topologia, Fac CC Matematicas, Universidad Complutense de Madrid, Plaza de Ciencias, 3, E-28040 Madrid (Spain)
2006-03-10
Contractions of Lie algebras are combined with the classical matrix method of Gel'fand to obtain matrix formulae for the Casimir operators of inhomogeneous Lie algebras. The method is presented for the inhomogeneous pseudo-unitary Lie algebras Iu(p,q). This procedure is extended to contractions of Iu(p,q) isomorphic to an extension by a derivation of the inhomogeneous special pseudo-unitary Lie algebras Isu(p-1,q), providing an additional analytical method to obtain their invariants. Further, matrix formulae for the invariants of other inhomogeneous Lie algebras are presented.
Reducing Spreadsheet Risk with FormulaDataSleuth
Bekenn, Bill
2008-01-01
A new MS Excel application has been developed which seeks to reduce the risks associated with the development, operation and auditing of Excel spreadsheets. FormulaDataSleuth provides a means of checking spreadsheet formulas and data as they are developed or used, enabling the users to identify actual or potential errors quickly and thereby halt their propagation. In this paper, we will describe, with examples, how the application works and how it can be applied to reduce the risks associated with Excel spreadsheets.
Mass formulae for broken supersymmetry in curved space-time
Energy Technology Data Exchange (ETDEWEB)
Ferrara, Sergio [Theoretical Physics Department, CERN, Geneva (Switzerland); INFN - Laboratori Nazionali di Frascati, Frascati (Italy); Department of Physics and Astronomy, U.C.L.A, Los Angeles, CA (United States); Proeyen, Antoine van [KU Leuven, Institute for Theoretical Physics, Leuven (Belgium)
2016-11-15
We derive the mass formulae for N = 1, D = 4 matter-coupled Supergravity for broken (and unbroken) Supersymmetry in curved space-time. These formulae are applicable to De Sitter configurations as is the case for inflation. For unbroken Supersymmetry in anti-de Sitter (AdS) one gets the mass relations modified by the AdS curvature. We compute the mass relations both for the potential and its derivative non-vanishing. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Vacum Black Hole Mass Formula Is a Vanishing Noether Charge
Institute of Scientific and Technical Information of China (English)
WUXiao－Ning; HUANGChao－Guang; 等
2002-01-01
The Noether current and its variation relation with respect to diffeomorphism invariance of gravitational theories have been derived from the horizontal variation and vertical-horizontal bi-variation of the Lagrangian,respectively.For Einstein's GR in the stationary,axisymmetric black holes,the mass formula in vacuum can be derived from this Noether current although it definitely vanishes.This indicates that the mass formula of black holes is a vanishing Noether charge in this case.The first law of black hole thermodynamics can also be derived from the variation relation of this vanishing Noether current.
As Time Passes Us By: Temporal Dimensions in Formulas
Directory of Open Access Journals (Sweden)
Zlatko Knežević
2016-03-01
Full Text Available In this article, I shall deal with the concept of formula, created by John Cawelti as a means of studying popular culture, mostly literature. Based on a difference between conventions and inventions, this concept promised a lot of change in theoretical dealings with popular culture. However, some changes are needed in its definition, since Cawelti didn't spend a lot of time defining formula's mutation through time as well as its relation to genre, another concept used in popular culture studies. I also investigate in greater depth the aforementioned relation between convention and invention.
Simplified formula for isoparametric quadrilateral element stiffness matrix
Energy Technology Data Exchange (ETDEWEB)
Changlian, X.
1987-02-01
Homogeneous parallelogram and quasi-parallelogram elements are usually used in finite element seismic modeling. Theoretically, the coordinates of element nodes may be arbitrary values on condition that elements are successive and not superposed. Isoparametric quadrilateral elements, whose nodes are presumed to be in laterally uniform distribution, are used so that not only unit stiffness matrix formula is essentially simplified to cut computing time but also finite element method remains flexible enough to be used in complex modeling. Simplified formulae for computing the stiffness matrices in four cases are derived, which, compared with corresponding Gauss integration algorithm, can cut 94-98% computing time.
An algorithm for the Baker-Campbell-Hausdorff formula
Matone, Marco
2015-05-01
A simple algorithm, which exploits the associativity of the BCH formula, and that can be generalized by iteration, extends the remarkable simplification of the BakerCampbell-Hausdorff (BCH) formula, recently derived by Van-Brunt and Visser. We show that if [ X, Y] = uX + vY + cI, [ Y, Z] = wY + zZ + dI, and, consistently with the Jacobi identity, [ X, Z] = mX + nY + pZ + eI, then
The Differential Virial Theorem with Gradient Formulas for the Operators
Finley, James P
2016-01-01
A gradient dependent formula is derived for the spinless one-particle density-matrix operator z from the differential virial theorem. A gradient dependent formula is also derived for a spinless one-particle density-matrix operator that can replace the two operators of the differential virial theorem that arise from the kinetic energy operator. Other operators are also derived that can replace the operators mentioned above in the differential virial theorem; these operators depend on the real part of spinless one-particle density-matrix.
Fluctuation formula for nonreversible dynamics in the thermostated Lorentz gas
Dolowschiák, M.; Kovács, Z.
2002-12-01
We investigate numerically the validity of the Gallavotti-Cohen fluctuation formula in the two- and three-dimensional periodic Lorentz gas subjected to constant electric and magnetic fields and thermostated by the Gaussian isokinetic thermostat. The magnetic field breaks the time reversal symmetry, and by choosing its orientation with respect to the lattice, one can have either a generalized reversing symmetry or no reversibility at all. Our results indicate that the scaling property described by the fluctuation formula may be approximately valid for large fluctuations even in the absence of reversibility.
Testing the Witten-Veneziano formula on the lattice
Energy Technology Data Exchange (ETDEWEB)
Cichy, Krysztof [Frankfurt am Main Univ. (Germany). Inst. fuer Theoretische Physik; DESY Zeuthen (Germany). NIC; Poznan Univ. (Poland). Faculty of Physics; Garcia-Ramos, Elena [DESY Zeuthen (Germany). NIC; Humboldt Univ. Berlin (Germany); Jansen, Karl [DESY Zeuthen (Germany). NIC; Ottnad, Konstantin; Urbach, Carsten [Bonn Univ. (Germany). Institut fuer Strahlen- und Kernphysik and Bethe Center for Theoretical Physics
2015-11-15
In this proceeding contribution we report on a test of the famousWitten-Veneziano formula using lattice techniques. We perform dedicated quenched simulations and apply the spectral projector method to determine the topological susceptibility in pure Yang-Mills theory. In order to compute the relevant meson masses and the flavor singlet decay constant we employ lattice QCD with N{sub f}=2+1+1 dynamical Wilson twisted mass fermions. Taking the continuum and the SU(2) chiral limits we find good agreement within uncertainties for both sides of the formula.
Decay properties of heavier nuclei and mass formula
Energy Technology Data Exchange (ETDEWEB)
Uno, Masahiro [Ministry of Education, Science and Culture, Tokyo (Japan)
2000-03-01
The stabilities of heavy nuclei, including super-heavy elements, are governed by alpha decay and fission. Some exotic types of decay, such as heavy cluster decay, which does not occur so frequently as to govern stability, have been also reported. The half-time estimations of various types of decay are reviewed. And the possibility of decay, mainly in case of heavy cluster decay, is discussed with Q-value obtained from mass formulae as well. Some topics concerning other types of exotic decay are presented. Recent trends in the research on mass formula are reviewed from the historical point of view, to get perspectives of future development. (Yamamoto, A.)
The Parisi formula for mixed p-spin models
Panchenko, Dmitry
2011-01-01
The Parisi formula for the free energy in the Sherrington-Kirkpatrick and mixed p-spin models for even p \\geq 2 was proved in the seminal work of Michel Talagrand, [24]. In this paper we prove the Parisi formula for general mixed p-spin models which also include p-spin interactions for odd p. Most of the ideas used in the paper are well known and can now be combined following a recent proof of the Parisi ultrametricity conjecture in [17].
A New Formula for Front Slope Recession of Berm Breakwaters
DEFF Research Database (Denmark)
Andersen, Thomas Lykke; Burcharth, Hans F.
2010-01-01
The front slope stability of breakwaters with a homogeneous berm was studied in a large number of two dimensional model tests at Aalborg University, Denmark. The results are presented together with a new formula for prediction of the berm recession which is the most important parameter for descri......The front slope stability of breakwaters with a homogeneous berm was studied in a large number of two dimensional model tests at Aalborg University, Denmark. The results are presented together with a new formula for prediction of the berm recession which is the most important parameter...
ψ-Contraction and [Formula: see text]-contraction in Menger probabilistic metric space.
Ma, Pengcheng; Guan, Jinyu; Tang, Yanxia; Xu, Yongchun; Su, Yongfu
2016-01-01
The purpose of this paper is to present the definition of [Formula: see text]-contractive mapping and to discuss the relation of [Formula: see text]-contractive mappings and [Formula: see text]-contractive mappings. Furthermore, the generalized [Formula: see text]-contraction mapping principle has been proved without the uniqueness condition. Meanwhile, the generalized [Formula: see text]-contraction mapping principle has been obtained by using an ingenious method.
An Amended Formula for the Decay of Radioactive Material for Cosmic Times
Carmeli, M; Carmeli, Moshe; Malin, Shimon
1999-01-01
An amended formula for the decay of radioactive material is presented. It is a modification of the standard exponential formula. The new formula applies for long cosmic times that are comparable to the Hubble time. It reduces to the standard formula for short times. It is shown that the material decays faster than expected. The application of the new formula to direct measurements of the age of the Universe and its implications is briefly discussed.
Kavanagh, Katherine F.; Cohen, Roberta J.; Heinig, M. Jane; Dewey, Kathryn G.
2008-01-01
Objective: Formula-fed infants gain weight faster than breastfed infants. This study evaluated whether encouraging formula-feeding caregivers to be sensitive to infant satiety cues would alter feeding practices and reduce infant formula intake and weight gain. Design: Double-blind, randomized educational intervention, with intake and growth…
The Formula for Integration by Parts and Taylor's Formula%分部积分与Taylor公式
Institute of Scientific and Technical Information of China (English)
赵虹; 汤宇
2012-01-01
利用定积分的分部积分法由简到繁的推导得到了微分学中的Taylor公式,从而给出了Taylor公式的另一种证法,并利用这种方法还可得到复变函数或泛函分析中的Taylor公式及某些函数的渐进级数和更广泛的函数展开.%In this paper, we establish Taylor's Formula by using integration by parts, therefore we obtain another proof of Taylor's Formula. We also can obtain Taylor's formula of complex variable and some asymptotic series of function by using integration by parts.
Prevalence of Salmonella spp. in Imported Powered Infant Formula (PIF
Directory of Open Access Journals (Sweden)
RENIS MAÇI
2015-10-01
Full Text Available Salmonella species are well-known long-standing foodborne human pathogen that demonstrate long-term survival in/on dry or low-water activity (aw in foods. Salmonellosis caused by ingestion of contaminated powdered infant formula has been reported nationwide. In recent years, 8 reported outbreaks of Salmonella infection in infants have been linked to the consumption of powdered infant formula. Outbreaks of Salmonellosis due to contaminated PIF are likely to be under-reported nationwide even in Albania. The aim of this study was to investigate the potential existence of Salmonella spp. in canned powdered infant formula in Albania. During two years investigation Salmonella spp was on the focus and was detected in 1 out of 70 analysed samples (1.43%. The strain of Salmonella spp. was biochemically identified by the analytical profile index (API 20 E system and poly A, H, and Vi antiserum. Food safety criteria are laid down in EU regulation “EC No. 2073/2005” for Salmonella spp. in dried infant formula and dried dietary foods for special medical purposes intended for infants. These criterias are transposed to Albanian Legislation. A laboratory-based on food-borne disease surveillance systems is needed in terms of strethening control and reducing the risk of exposure.
A Formula of Average Path Length for Unweighted Networks
Institute of Scientific and Technical Information of China (English)
LIU Chun-Ping; LIU Yu-Rong; HE Da-Ren; ZHU Lu-Jin
2008-01-01
In this paper, based on the adjacency matrix of the network and its powers, the formulas are derived for the shortest path and the average path length, and an effective algorithm is presented. Furthermore, an example is provided to demonstrate the proposed method.
Composite Gauss-Legendre Formulas for Solving Fuzzy Integration
Directory of Open Access Journals (Sweden)
Xiaobin Guo
2014-01-01
Full Text Available Two numerical integration rules based on composition of Gauss-Legendre formulas for solving integration of fuzzy numbers-valued functions are investigated in this paper. The methods' constructions are presented and the corresponding convergence theorems are shown in detail. Two numerical examples are given to illustrate the proposed algorithms finally.
Effective formulas for invariant functions -- case of elementary Reinhardt domains
Pflug, Peter; Zwonek, Wlodzimierz
1996-01-01
In the paper we find effective formulas for the invariant functions, appearing in the theory of several complex variables, of the elementary Reinhardt domains. This gives us the first example of a large family of domains for which the functions are calculated explicitly.
Assay of ghrelin concentration in infant formulas and breast milk
Institute of Scientific and Technical Information of China (English)
Francesco Savino; Elisa Petrucci; Maria Maddalena Lupica; Giuliana Eva Nanni; Roberto Oggero
2011-01-01
AIM: To test if total ghrelin is present in infant formulas. METHODS: Using a radioimmunoassay, we measured total ghrelin concentrations in 19 samples of commercial infant formulas and in 20 samples of human milk. We also determined ghrelin concentration in the serum of infants and lactating mothers. RESULTS: Ghrelin concentrations were significantly higher in artificial milk (2007.1 ± 1725.36 pg/mL) than in human milk (828.17 ± 323.32 pg/mL) (P = 0.005). The mean ghrelin concentration in infant serum (n = 56) was 1115.86 ± 42.89 pg/mL, and was significantly higher (P = 0.023) in formula-fed infants (1247.93 ± 328.07 pg/mL) than in breast-fed infants (1045.7 ± 263.38 pg/mL). The mean serum ghrelin concentration (mean ± SD) in lactating mothers (n = 20) was 1319.18 ± 140.18 pg/mL. CONCLUSION: This study provides evidence that total ghrelin is present in infant formulas. This finding raises diverse questions regarding the uptake, absorp-tion and metabolic effects of this hormone.
Secret Sharing and Secure Computing from Monotone Formulae
DEFF Research Database (Denmark)
Damgård, Ivan Bjerre; Kölker, Jonas; Miltersen, Peter Bro
2012-01-01
We present a construction of log-depth formulae for various threshold functions based on atomic threshold gates of constant size. From this, we build a new family of linear secret sharing schemes that are multiplicative, scale well as the number of players increases and allows to raise a shared...
Two-level convolution formula for nuclear structure function
Ma, Boqiang
1990-05-01
A two-level convolution formula for the nuclear structure function is derived in considering the nucleus as a composite system of baryon-mesons which are also composite systems of quark-gluons again. The results show that the European Muon Colaboration effect can not be explained by the nuclear effects as nucleon Fermi motion and nuclear binding contributions.
The fundamental formulas for vertices of convex hull
Directory of Open Access Journals (Sweden)
Md. Kazi Salimullah
2013-07-01
Full Text Available This paper represents four formulas for solution of convex hull problem. It aims to analyze how many points are vertices out of total input points, how many vertices lie on a horizontal or vertical lines, position of vertices and number of vertices on lower and higher lines(horizontal or vertical.
Matrix formulae and skein relations for cluster algebras from surfaces
Musiker, Gregg
2011-01-01
This paper concerns cluster algebras with principal coefficients A(S,M) associated to bordered surfaces (S,M), and is a companion to a concurrent work of the authors with Schiffler [MSW2]. Given any (generalized) arc or loop in the surface -- with or without self-intersections -- we associate an element of (the fraction field of) A(S,M), using products of elements of PSL_2(R). We give a direct proof that our matrix formulas for arcs and loops agree with the combinatorial formulas for arcs and loops in terms of matchings, which were given in [MSW, MSW2]. Finally, we use our matrix formulas to prove skein relations for the cluster algebra elements associated to arcs and loops. Our matrix formulas and skein relations generalize prior work of Fock and Goncharov [FG1, FG2, FG3], who worked in the coefficient-free case. The results of this paper will be used in [MSW2] in order to show that certain collections of arcs and loops comprise a vector-space basis for A(S,M).
49 CFR 192.105 - Design formula for steel pipe.
2010-10-01
... 49 Transportation 3 2010-10-01 2010-10-01 false Design formula for steel pipe. 192.105 Section 192... for steel pipe. (a) The design pressure for steel pipe is determined in accordance with the following... § 192.113. T=Temperature derating factor determined in accordance with § 192.115. (b) If steel pipe...
The Landauer-Büttiker formula and resonant quantum transport
DEFF Research Database (Denmark)
Cornean, Horia Decebal; Jensen, Arne; Moldoveanu, Valeriu
We give a short presentation of two recent results. The firrst one is a rigorous proof of the Landauer-Büttiker formula, and the second one concerns resonant quantum transport. The detailed results are in [2]. In the last section we present the results of some numerical computations on a model...
Experimental Study on Angeng Formula for Climacteric Syndrome in Rats
Institute of Scientific and Technical Information of China (English)
CHEN Da-shuai; LI Peng-li; TAN Hai-zhi
2014-01-01
Objective:To observe the effect of Angeng Formula on climacteric syndrome in rats. Methods:The ovaries of female SD rats were removed for the establishment of menopausal syndrome rat models. After drug delivery for 30 d, serum sex hormone levels and indexes of uterus, adrenal gland and pituitary were detected. Meanwhile, the effects of drugs on the histopathology of uterus, adrenal gland and pituitary in rats were observed. Results:Angeng Formula could increase the level of estradiol (E2) in castrated rat (P<0.01) and had a tendency to increase the level of progestin (P), lower the level of luteinizing hormone (LH) and follicle-stimulating hormone (FSH) as well as increase the indexes of the uterus and adrenal gland. Moreover, Angeng Formula could improve the pathologic condition of the uterus, adrenal gland and pituitary in castrated rats. Conclusion:Angeng Formula has a therapeutic effect on climacteric syndrome, the mechanism of which might be related with the function of regulating sex hormone.
Pulsed thermal NDT in tables, figures, and formulas
Vavilov, V. P.; Burleigh, D. D.
2015-05-01
Several reviews and summary papers describing the history and the current status of pulsed thermal nondestructive testing (TNDT have been published recently. However, some of the theoretical possibilities cannot easily be implemented in practical applications. This paper contains useful tables and formulas that are illustrated with typical IR thermograms to provide a general overlook of pulsed TNDT.
The Campus-Based Formula. NASFAA Task Force Report
National Association of Student Financial Aid Administrators, 2014
2014-01-01
The primary purpose of the National Association of Student Financial Aid Administrators (NASFAA) Campus-Based Aid Allocation Task Force was to examine the formula by which congressional appropriations for the Federal Supplemental Educational Opportunity Grant (FSEOG), Federal Work-Study (FWS), and Perkins Loan programs are distributed to schools,…
Incidence of Diarrhea in Hospitalized Patients with Standard Enteral Formula
Directory of Open Access Journals (Sweden)
Shabbu Ahmadi bonakdar
2014-10-01
Conclusion: Evaluation of patients receiving Milatech standard formula showed that diarrhea wasn’t seen in hospitalized patients. Diarrhea was reported by the nurses may refer to other diarrhea genic causes including of long length of stay, entral duration or medical side effects or infections.
A second addition formula for continuous q-ultraspherical polynomials
Koornwinder, T.H.
2005-01-01
This paper provides the details of Remark 5.4 in the author's paper "Askey-Wilson polynomials as zonal spherical functions on the SU(2) quantum group", SIAM J. Math. Anal. 24 (1993), 795-813. In formula (5.9) of the 1993 paper a two-parameter class of Askey-Wilson polynomials was expanded as a finit
A Simple Capacity Formula for Correlated Diversity Rayleigh Fading Channels
Institute of Scientific and Technical Information of China (English)
CHENG Xing-qing; SU Shu-chun; LI Dao-ben
2004-01-01
Abstract: The system capacity can be considerably increased if we appropriately exploit the randomness of multipath propagation. A simple average capacity formula is derived for correlated diversity Rayleigh fading channels through linear transformation method.Numerical results that illustrate the effect of correlation parameter and diversity order on the diversitycapacity are also presented.
A note on the Campbell-Hausdorff formula
Veldkamp, F.D.
1980-01-01
In his book (“Lie Algebras,” Interscience, 1962) Jacobson proves the Campbell-Hausdorff formula for formal power series in Lie algebras. In this short note we shall prove it for finite-dimensional Lie groups making use of parts of Jacobson's proof.
The Landauer-Büttiker formula and resonant quantum transport
DEFF Research Database (Denmark)
Cornean, Horia; Jensen, Arne; Moldoveanu, Valeriu
2006-01-01
We give a short presentation of two recent results. The first one is a rigorous proof of the Landauer-Büttiker formula, and the second one concerns resonant quantum transport. The detailed results are in [2]. In the last section we present the results of som numerical computations on a model syst...
27 CFR 21.54 - Formula No. 27-B.
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 27-B. 21.54 Section 21.54 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT... gallon of lavender oil, N.F., and 100 pounds of green soap, U.S.P. Note. The requirements of this...
Invention of the Plane Geometrical Formulae - Part III
Directory of Open Access Journals (Sweden)
Mr. Satish M. Kaple
2014-04-01
Full Text Available In this paper , I have invented the first new type of a scalene quadrilateral and also developed the two new formulae for finding the area of that’s new type of quadrilateral. My finding are based on phthagoras theorem.
Asymptotic Formulae for Multivariate Kantorovich Type Generalized Sampling Series
Institute of Scientific and Technical Information of China (English)
Carlo BARDARO; Ilaria MANTELLINI
2011-01-01
In this paper an asymptotic formula of Voronovskaja type for a multivariate extension of the Kantorovich generalized sampling series is given.Moreover a quantitative version in terms of some moduli of smoothness is established.Finally some particular examples of kernels are discussed,as the Bochner-Riesz kernel and the multivariate splines.
Discussion of the loop formula for the fermionic determinant
Stamatescu, Ion-Olimpiu
2016-01-01
A formula expressing the fermionic determinant (a large order polynomial) as an infinite product of smaller determinants is derived and discussed. These smaller determinants are of a fixed size, independent of the size of the lattice and are indexed by loops of increasing length.
Using Paperclips to Explain Empirical Formulas to Students
Nassiff, Peter; Czerwinski, Wendy A.
2014-01-01
Early in their chemistry education, students learn to do empirical formula calculations by rote without an understanding of the historical context behind them or the reason why their calculations work. In these activities, students use paperclip "atoms", construct a series of simple compounds representing real molecules, and discover,…
A note on the infinitesimal Baker-Campbell-Hausdorff formula
Nishimura, Hirokazu; Takamiya, Hirowaki
2015-01-01
We have studied the infinitesimal Baker-Campbell-Hausdorff formula up to n=4 (Math. Appl. 2 (2013), 61-91). In this note we correct some errors in our calculation for n=4 and presents the calculation for n=5 by using Mathematica.
Applications of an Explicit Formula for the Generalized Euler Numbers
Institute of Scientific and Technical Information of China (English)
Guo Dong LIU; Wen Peng ZHANG
2008-01-01
The authors establish an explicit formula for the generalized Euler Numbers E(x)2n ,and obtain some identities and congruences involving the higher-order Euler numbers, Stirling numbers,the central factorial numbers and the values of the Riemann zeta-function.
Kronecker limit formula for real quadratic number fields(III)
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
For a kind of L-function of the real quadratic number fields, we prove a Kronecker limit formula which generalized a result of Hecke. And taking an example we give an interesting identity on a fundamental unit of such a field.
The usefulness of cystatin C and related formulae in pediatrics.
Filler, Guido; Huang, Shih-Han S; Yasin, Abeer
2012-12-01
Serum creatinine does not share the properties of an ideal marker of glomerular filtration rate (GFR) like inulin, but continues to be the most widely used endogenous marker of GFR. In the search of a better biomarker of GFR, the small molecular weight protein cystatin C has been introduced with features more similar to that of inulin, such as constant production and no non-renal elimination. However,it has not enjoyed widespread use despite its significantly improved diagnostic performance in the detection of impaired GFR and its independence of body composition. A variety of formulae based on either cystatin C or creatinine or both have been developed to estimate GFR. We summarize the currently used methods of GFR measurement, their limitations and analytical errors. The review also summarizes the history, features and the feasibility of cystatin C measurements as well as the most widely used formulae for the estimation of GFR in children. The diagnostic performance of the cystatin C derived eGFR formulae at various levels of GFR is also discussed. An eGFR formula derived from pooled studies analyzing both creatinine and cystatin C, and using a biology-based mathematical approach maybe advantageous.
Determination of the Formula of a Hydrate: A Greener Alternative
Klingshirn, Marc A.; Wyatt, Allison F.; Hanson, Robert M.; Spessard, Gary O.
2008-01-01
We are currently in the process of incorporating green chemistry throughout the chemistry curriculum. In this article we describe how we applied the principles of green chemistry in one of our first-semester general chemistry courses, specifically in relation to the determination of the formula of a hydrate. We utilize a copper hydrate salt that…
75 FR 38797 - Predominantly Black Institutions Formula Grant Program
2010-07-06
... [Federal Register Volume 75, Number 128 (Tuesday, July 6, 2010)] [Notices] [Pages 38797-38798] [FR Doc No: 2010-16376] DEPARTMENT OF EDUCATION [CFDA No. 84.031P] Predominantly Black Institutions... applications for new awards for FY 2010 for the Predominantly Black Institutions Formula Grant Program...
A Poisson type formula for Hardy classes on Heisenberg's group
Directory of Open Access Journals (Sweden)
Lopushansky O.V.
2010-06-01
Full Text Available The Hardy type class of complex functions with infinite many variables defined on the Schrodinger irreducible unitary orbit of reduced Heisenberg group, generated by the Gauss density, is investigated. A Poisson integral type formula for their analytic extensions on an open ball is established. Taylor coefficients for analytic extensions are described by the associatedsymmetric Fock space.
31 CFR Appendix B to Part 356 - Formulas and Tables
2010-07-01
... percentage of the value of the inflation-adjusted principal, in current dollars, for the date on which it is... Equivalent Prices Definitions P = unadjusted or real price per 100 (dollars). Padj = inflation adjusted price.... Formulas for Conversion of Inflation-Protected Security Yields to Equivalent Prices. IV. Computation...
Hydrolyzed infant formula and early β-cell autoimmunity
DEFF Research Database (Denmark)
Knip, Mikael; Åkerblom, Hans K; Becker, Dorothy
2014-01-01
IMPORTANCE: The disease process leading to clinical type 1 diabetes often starts during the first years of life. Early exposure to complex dietary proteins may increase the risk of β-cell autoimmunity in children at genetic risk for type 1 diabetes. Extensively hydrolyzed formulas do not contain ...
The remodeling conjecture and the Faber-Pandharipande formula
Bouchard, Vincent; Marchal, Olivier; Sulkowski, Piotr
2011-01-01
In this note, we prove that the free energies F_g constructed from the Eynard-Orantin topological recursion applied to the curve mirror to C^3 reproduce the Faber-Pandharipande formula for genus g Gromov-Witten invariants of C^3. This completes the proof of the remodeling conjecture for C^3.
The Koppelman-Leray formula on complex Finsler manifolds
Institute of Scientific and Technical Information of China (English)
QIU Chunhui; ZHONG Tongde
2005-01-01
By means of the invariant integral kernel (the Berndtsson kernel), the complex Finsler metric and the non-linear connection associated with the Chern-Finsler connection to research into the integral representation theory on complex Finsler manifolds, theKoppelman and Koppelman-Leray formulas are obtained, and the - -equations are solved.
An extension of the formula for spreading speeds.
Weinberger, Hans F; Zhao, Xiao-Qiang
2010-01-01
A well-known formula for the spreading speed of a discrete-time recursion model is extended to a class of problems for which its validity was previously unknown. These include migration models with moderately fat tails or fat tails. Examples of such models are given.
A Feynman-Kac formula for geometric quantization
Institute of Scientific and Technical Information of China (English)
郭懋正; 钱敏; 王正栋
1996-01-01
The geometric quantization on a homogeneous manifold is studied. For any quantizable function f, the stochastical expression for the unitary group exp(itQ (f)) generated by the quantized operator Q(f) is established. As an application, a Feynman-Kac formula for the compact semisimple Lie group is rederived.
Calderon type reproducing formula on spaces of homogeneous type
Institute of Scientific and Technical Information of China (English)
邓东皋; 韩永生
1995-01-01
By using the Calderon-Zygmund operator theory, a continuous version of the Calderon type reproducing formula associated to a para-accretive function on spaces of homogeneous type is proved. A new characterization of the Besov and Triebel-Lizorkin spaces on spaces of homogeneous type is also obtained.
Probabilistic assignment of formulas to mass peaks in metabolomics experiments
Rogers, Simon; Scheltema, Richard A.; Girolami, Mark; Breitling, Rainer
2009-01-01
Motivation: High-accuracy mass spectrometry is a popular technology for high-throughput measurements of cellular metabolites (metabolomics). One of the major challenges is the correct identification of the observed mass peaks, including the assignment of their empirical formula, based on the measure
DEFF Research Database (Denmark)
Nørrung, Birgit
to the characteristics and physiological state of the organism, the state of the host and the food matrix. The widespread distribution of E. sakazakii suggests that consumption of low numbers in infant formula and follow-on formula by healthy infants and children does not lead to illness. Salmonella and E. sakazakii do....... sakazakii in high-risk infants (pre-term, underweight, immunocompromised), would be to use commercial sterile liquid formula. It is recommended that a Performance Objective (PO) for powdered infant formula and follow-on formula, aiming at very low levels of Salmonella and E. sakazakii (e.g. absence in 1, 10...
Regional variation in infant hypoallergenic formula prescriptions in Australia.
Mullins, Raymond J; Clark, Sunday; Camargo, Carlos A
2010-03-01
There is little information on the regional distribution of food allergy in Australia. We examined the influence of latitude (a marker of sunlight/vitamin D status) on food allergy, as measured by 2007 infant hypoallergenic formula (IHF) prescription rates in children ages 0-2 yrs. Data were compiled from the 52 statistical divisions in mainland Australia plus the island of Tasmania (n=53 observations). Data from the Australian Department of Health and Aging and the Australian Bureau of Statistics were analysed by statistical division. There was significant regional variability in hypoallergenic formula prescription rates (per 100,000 population/yr), with the highest rates in southern Australia (14,406) and the lowest in the north (721), compared with a national average of 4099. Geographical factors (decreasing latitude and increasing longitude) were associated with a higher rate of IHF prescriptions, such that rates were higher in southern vs. northern regions, and in eastern compared with western regions. Controlling for longitude, physician density and markers of socioeconomic status, southern latitudes were associated with higher hypoallergenic formulae prescription rates [beta, -147.98; 95% confidence interval (CI)=-281.83 to -14.14; p=0.03]. Controlling for latitude, physician density and markers of socioeconomic status, eastern longitudes were also associated with higher hypoallergenic formulae prescription rates (beta, 89.69; 95% CI=2.90-176.49; p=0.04). Among young children, hypoallergenic formula prescription rates are more common in the southern and eastern regions of Australia. These data provide support for a possible role of sun exposure/vitamin D status (amongst other potential factors) in the pathogenesis of food allergy.
2013-04-16
... Nutrition (HFS- 850), Food and Drug Administration, 5100 Paint Branch Pkwy, College Park, MD 20740, 240-402..., Drug, and Cosmetic Act (the FD&C Act) (21 U.S.C. 350a(i)) establishes requirements for the nutrient... infant formula, a food that is intended to be the sole source of nutrition for infants and...
The best quadrature formula based on Hermite information for the class KW2[a,b
Institute of Scientific and Technical Information of China (English)
WANG; Xinghua; MI; Xiangjiang
2005-01-01
The best quadrature formula has been found in the following sense: for a function whose norm of the second derivative is bounded by a given constant and the best quadrature formula for the approximate evaluation of integration of that function can minimize the worst possible error if the values of the function and its derivative at certain nodes are known.The best interpolation formula used to get the quadrature formula above is also found.Moreover,we compare the best quadrature formula with the open compound corrected trapezoidal formula by theoretical analysis and stochastic experiments.
A new Leray formula for smooth functions on bounded domains in Cn
Institute of Scientific and Technical Information of China (English)
YAO; Zongyuan(姚宗元); QIU; Chunhui(邱春晖); ZHONG; Chunping
2002-01-01
By means of a new technique of integral representations in Cn given by the authors, we establish a new abstract formula with a vector function W for smooth functions on bounded domains in Cn, which is different from the well-known Leray formula, This new formula eliminates the term that contains the parameter λ from the classical Leray formula, and especially on some domains the uniform estimates for the -equation are very simple. From the new Leray formula, we can obtain correspondingly many new formulas for smooth functions on many domains in Cn, which are different from the classical ones, when we properly select the vector function W.
Trace element status and zinc homeostasis differ in breast and formula-fed piglets
Miousse, Isabelle R; Mason, Andrew Z; Sharma, Neha; Blackburn, Michael L; Badger, Thomas M
2015-01-01
Differences in trace element composition and bioavailability between breast milk and infant formulas may affect metal homeostasis in neonates. However, there is a paucity of controlled studies in this area. Here, piglets were fed soy infant formula (soy), cow’s milk formula (milk), or were allowed to suckle from the sow from PND2 to PND21. Serum iron concentrations were higher in formula-fed compared to breastfed piglets (P supplementation, allows strong causal inference that significant differences in serum zinc after cow’s milk formula compared to soy formula consumption result in compensatory changes in expression of zinc transporters, binding proteins, and zinc-regulated genes. PMID:25179632
A new formula to calculate activity of superoxide dismutase in indirect assays.
Zhang, Chen; Bruins, Marieke E; Yang, Zhi-Qiang; Liu, Shu-Tao; Rao, Ping-Fan
2016-06-15
To calculate superoxide dismutase (SOD) activity rapidly and accurately by indirect SOD assays, a formula based on the ratio of the catalytic speed of SOD to the reaction speed of the indicator with superoxide anion was deduced. The accuracy of this formula was compared with the conventional formula based on inhibition in five indirect SOD assays. The new formula was validated in nearly the entire SOD activity range, whereas the conventional formula was validated only during inhibition of 40-60%. This formula might also be used for the assays of other enzymes.
Analytical Formulas for Short Bunch Wakes in a Flat Dechirper
Energy Technology Data Exchange (ETDEWEB)
Bane, Karl [SLAC National Accelerator Lab., Menlo Park, CA (United States); Stupakov, Gennady [SLAC National Accelerator Lab., Menlo Park, CA (United States); Zagorodnov, Igor [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2016-03-29
We develop analytical models of the longitudinal and transverse wakes, on and off axis for realistic structures, and then compare them with numerical calculations, and generally find good agreement. These analytical "first order" formulas approximate the droop at the origin of the longitudinal wake and of the slope of the transverse wakes; they represent an improvement in accuracy over earlier, "zeroth order" formulas. In example calculations for the RadiaBeam/LCLS dechirper using typical parameters, we find a 16% droop in the energy chirp at the bunch tail compared to simpler calculations. With the beam moved to 200 m from one jaw in one dechiper section, one can achieve a 3 MV transverse kick differential over a 30 m length.
New stopping power formula for intermediate energy electrons.
Gümüş, Hasan
2008-12-01
This study presents a new stopping power (SP) formula for electrons. In the modified Bethe-Bloch SP expression, analytical expressions for the effective charge and effective mean excitation energies (EMEE) of target atoms are used, while for the effective charge of incoming electrons, Sugiyama's semiempirical formula from Peterson and Green is used. An analytical expression for practical SP calculations is obtained using the Bethe approximation and a Thomas-Fermi model of the atom. The calculated results of the SP for electrons in some materials, such as H(2)O, H(2), CO(2), N(2), and O(2), are compared with experimental data, together with Penelope code results and a number of other semiempirical and analytical calculations.
Analysis on formulas of concrete plate under contact explosion
Directory of Open Access Journals (Sweden)
Wang Zheng
2015-01-01
Full Text Available Based on many test data of concrete plates of several thicknesses, this paper presents some new simple engineering formulas for computing critical thickness of scabbing and perforation, the front explosion diameter and the rear scabbing diameter of reinforced concrete plates under contact explosion. For the damage problem of a 20 cm thick concrete target under contact explosion of 1.25 kg TNT charge, the paper gives the numerical simulation results of LS-DYNA software for comparison. The damage zone of concrete plate in numerical simulation is determined by analysis of tension pressure resulted from shock wave reflection on the free boundary. And the numerical simulation results are in basic agreement on the results of these engineering formulas.
Glomerular filtration rate in cows estimated by a prediction formula.
Murayama, Isao; Miyano, Anna; Sato, Tsubasa; Iwama, Ryosuke; Satoh, Hiroshi; Ichijyo, Toshihiro; Sato, Shigeru; Furuhama, Kazuhisa
2014-12-01
To testify the relevance of Jacobsson's equation for estimating bovine glomerular filtration rate (GFR), we prepared an integrated formula based on its equation using clinically healthy dairy (n=99) and beef (n=63) cows, and cows with reduced renal function (n=15). The isotonic, nonionic, contrast medium iodixanol was utilized as a test tracer. The GFR values estimated from the integrated formula were well consistent with those from the standard multisample method in each cow strain, and the Holstein equation prepared by a single blood sample in Holstein dairy cows. The basal reference GFR value in healthy dairy cows was significantly higher than that in healthy beef cows, presumably due to a breed difference or physiological state difference. It is concluded that the validity for the application of Jacobsson's equation to estimate bovine GFR is proven and it can be used in bovine practices.
Screening for Enterobacteriaceae Bacteria in Infant Formula Powder
Institute of Scientific and Technical Information of China (English)
Lu Yan; Qi Feng; Sun Mei-ling; Wang Wei
2012-01-01
A total of 151 infant formula powder samples were tested for the screening of the Enterobacteriaceae bacteria, and it had been contaminated by the conditioned pathogen like Enterobacter sakazakii, Klebsiella pneumoniae, Klebsiella oxytoca, and Enterobacter cloacae. The results showed that six samples were separated Enterobacter sakazakii, 24 samples were separated Enterobacteriaceae by using the traditional validation and real-time fluorescence quantitative PCR. Then the result identified by API20E biochemistry test and VITEC2 identification system. Through the study we concluded the potential safety hazard of the current infant formula powder and should regard Enterobacteriaceae as an indicator to carry out effective management, the neglected mild and discontinuity contamination could be easily found, thus to guarantee the safety of the special group.
The Coulomb Branch Formula for Quiver Moduli Spaces
Manschot, Jan; Sen, Ashoke
2014-01-01
In recent series of works, by translating properties of multi-centered supersymmetric black holes into the language of quiver representations, we proposed a formula that expresses the Hodge numbers of the moduli space of semi-stable representations of quivers with generic superpotential in terms of a set of invariants associated to `single-centered' or `pure-Higgs' states. The distinguishing feature of these invariants is that they are independent of the choice of stability condition. Furthermore they are uniquely determined by the $\\chi_y$-genus of the moduli space. Here, we provide a self-contained summary of the Coulomb branch formula, spelling out mathematical details but leaving out proofs and physical motivations.
Development of process energy intensity formula under different state variables
Institute of Scientific and Technical Information of China (English)
陈光
2004-01-01
In a production process, the actual energy consumption is greatly affected by the production state.Certain processing operations are classified into six states, including normal production, abnormal production,planned overhaul, unplanned overhaul, transitional period from unplanned overhaul to normal production (referred for short as unplanned transition) and transitional period from planned overhaul to normal production (referred for short as planned transition). The article takes the analysis of relationship between different states of a certain processing operation and corresponding energy consumptions as a startup point to develop a process energy intensity formula with variables of operating rate, yielding rate and operating frequency, etc. This process energy intensity formula can be used to analyze effectively the pattern of impact exerted by different state variables on energy consumption.
Systematics of nuclear mass and level density formulas
Energy Technology Data Exchange (ETDEWEB)
Nakamura, Hisashi [Fuji Electric Co. Ltd., Kawasaki, Kanagawa (Japan)
1998-03-01
The phenomenological models of the nuclear mass and level density are close related to each other, the nuclear ground and excited state properties are described by using the parameter systematics on the mass and level density formulas. The main aim of this work is to provide in an analytical framework the improved energy dependent shell, pairing and deformation corrections generalized to the collective enhancement factors, which offer a systematic prescription over a great number of nuclear reaction cross sections. The new formulas are shown to be in close agreement with not only the empirical nuclear mass data but the measured slow neutron resonance spacings, and experimental systematics observed in the excitation energy dependent properties. (author)
Evaluating the accuracy of wear formulae for acetabular cup liners.
Wu, James Shih-Shyn; Hsu, Shu-Ling; Chen, Jian-Horng
2010-02-01
This study proposes two methods for exploring the wear volume of a worn liner. The first method is a numerical method, in which SolidWorks software is used to create models of the worn out regions of liners at various wear directions and depths. The second method is an experimental one, in which a machining center is used to mill polyoxymethylene to manufacture worn and unworn liner models, then the volumes of the models are measured. The results show that the SolidWorks software is a good tool for presenting the wear pattern and volume of a worn liner. The formula provided by Ilchmann is the most suitable for computing liner volume loss, but is not accurate enough. This study suggests that a more accurate wear formula is required. This is crucial for accurate evaluation of the performance of hip components implanted in patients, as well as for designing new hip components.
Thermal switching of the electrical conductivity of Si(111)([Formula
DEFF Research Database (Denmark)
Wells, J W; Kallehauge, Jesper; Hofmann, Ph
2007-01-01
The temperature-dependent surface conductivity of the Si(111)([Formula: see text])Ag surface was measured using a microscopic four-point probe. The conductivity was found to undergo a sharp increase of about three orders of magnitude when the system was heated above about 220 K. This strong...... conductivity change is reversible and attributed to the phase transition which is generally believed to occur on this surface. It is also shown that, in order to find the true surface conductivity, it is necessary to separate it from the contribution of the bulk and space charge layer. In this work......, this is achieved by using a finite-element model. A percolating network of Ag islands on Si(111) was also studied and a much simpler behaviour (compared to that of Si(111)([Formula: see text])Ag) was found. The temperature-dependent conductivity of this system was found to display typical metallic behaviour...
Empirical formulas for description of the fatigue crack growth rate
Energy Technology Data Exchange (ETDEWEB)
Rozumek, D. [Opole University of Technology, Faculty of Mechanical Engineering, Opole (Poland)
2010-02-15
The paper presents the test results obtained for fatigue crack growth in flat specimens subjected to bending. The tests were conducted for different loading amplitudes and different load ratios using the {delta}J parameter. Accuracy of description of the fatigue crack growth rate was tested with use of different empirical formulas. One-side restrained specimens made of 10HNAP steel were tested. In each tested specimen, there was the external notch 5 mm in depth, and the notch rounding radius was {rho}=0.2 mm. The tests were carried out at the fatigue test stand MZGS-100 under loading frequency 28.8 Hz. It has been found that the obtained results depend on the applied empirical formula. (Abstract Copyright [2010], Wiley Periodicals, Inc.)
Hades’ Famous Foals and the Prehistory of Homeric Horse Formulas
Directory of Open Access Journals (Sweden)
Ryan Platte
2014-03-01
Full Text Available This article investigates Hades’ enigmatic Homeric epithet κλυτόπωλος (“of famous foals” in an attempt to identify its origins within the linguistic history of Homeric composition. Through an analysis of the phonetic similarities that κλυτόπωλος shares with other Homeric expressions, it becomes possible to identify a broad network of formulas to which this epithet must be genetically related. Furthermore, analysis of this network as a whole allows insight into the diachronic development of a wide range of Homeric equine formulas, from rather deep Indo-European antiquity to archaic Greece.
Penggunaan Formula Mineral Lokal dalam Ransum Ayam Petelur
Directory of Open Access Journals (Sweden)
Khalil
2010-08-01
Full Text Available A mineral formula composed of three locally available materials: limestone originated from Bukit Kamang of West Sumatra, freshwater oyster shell and bone meal and fortified with micro minerals of Cu, Zn and I was investigated as mineral supplement for diet of laying hens. The experimental diets were: P0 (diet contained of 6% commercial mineral, P1 (diet contained of 6% local mineral, P2 (diet contained of 6% Bukit Kamangs’ limestone and P3 (diet contained of 6% fresh water oyster shell meal. The total of four experimental diets was then fed to 120 laying hens. The hens were divided into 3 groups based on body weight: heavy, medium and light. Each group was subdivided into 4 subgroups in accordance with number of treatments, so that each treatment consisted of 3 replicates containing of 10 hens. Parameters measured included: feed intake, hen-day egg production, feed conversion ratio (FCR, eggshell quality, mineral retention and mineral composition of tibia bone. Data were subjected to statistical analysis using variance analysis in a completely block design with 4 treatments and 3 blocks as replicates The results showed that the egg weight and eggshell qualities were found not significantly difference, but different mineral sources gave significant effect on egg production and bone mineralization. The laying performances and tibia bone weight of chickens fed diet mixed with the local mineral formula were found not significantly different with those fed diet mixed with commercial formula, but significantly better (P<0.05 than those of fed diet mixed with only limestone or oyster shell. Hens fed with diet mixed with Bukit Kamangs’ limestone showed better performances and heavier tibia bone than those fed with diet mixed with oyster shell. It was concluded that the local mineral formula could be used as sole mineral source for laying hens. The nutritive value of Bukit Kamangs’ limestone was better than that of fresh water oyster shell.
Safety of soya-based infant formulas in children.
Vandenplas, Yvan; Castrellon, Pedro Gutierrez; Rivas, Rodolfo; Gutiérrez, Carlos Jimenez; Garcia, Luisa Diaz; Jimenez, Juliana Estevez; Anzo, Anahi; Hegar, Badriul; Alarcon, Pedro
2014-04-28
Soya-based infant formulas (SIF) containing soya flour were introduced almost 100 years ago. Modern soya formulas are used in allergy/intolerance to cows' milk-based formulas (CMF), post-infectious diarrhoea, lactose intolerance and galactosaemia, as a vegan human milk (HM) substitute, etc. The safety of SIF is still debated. In the present study, we reviewed the safety of SIF in relation to anthropometric growth, bone health (bone mineral content), immunity, cognition, and reproductive and endocrine functions. The present review includes cross-sectional, case-control, cohort studies or clinical trials that were carried out in children fed SIF compared with those fed other types of infant formulas and that measured safety. The databases that were searched included PubMed (1909 to July 2013), Embase (1988 to May 2013), LILACS (1990 to May 2011), ARTEMISA (13th edition, December 2012), Cochrane controlled trials register, Bandolier and DARE using the Cochrane methodology. Wherever possible, a meta-analysis was carried out. We found that the anthropometric patterns of children fed SIF were similar to those of children fed CMF or HM. Despite the high levels of phytates and aluminium in SIF, Hb, serum protein, Zn and Ca concentrations and bone mineral content were found to be similar to those of children fed CMF or HM. We also found the levels of genistein and daidzein to be higher in children fed SIF; however, we did not find strong evidence of a negative effect on reproductive and endocrine functions. Immune measurements and neurocognitive parameters were similar in all the feeding groups. In conclusion, modern SIF are evidence-based safety options to feed children requiring them. The patterns of growth, bone health and metabolic, reproductive, endocrine, immune and neurological functions are similar to those observed in children fed CMF or HM.
Computing energy budget within a crop canopy from Penmann's formulae
Indian Academy of Sciences (India)
Mahendra Mohan; K K Srivastava
2001-06-01
The Lhomme's model (1988a), that extended Penmann's formulae to a multi-layer model, is rede-fined as a function of micrometeorological and physiological profiles of crop canopy. The sources and sinks of sensible and latent heat uxes are assumed to lie on a fictitious plane called zero-displacement plane. Algorithms are given to compute sensible and latent heat ux densities. Per-formance of the algorithms is compared with that of earlier algorithms.
Index Formulae for Subspaces of Kreĭn Spaces
Dijksma, Aad; Gheondea, Aurelian
1996-01-01
For a subspace S of a Kreĭn space K and an arbitrary fundamental decomposition K = K-[+]K+ of K, we prove the index formula κ-(S) + dim(S⊥ ∩ K+) = κ+(S⊥) + dim(S ∩ K-), where κ±(S) stands for the positive/negative signature of S. The difference dim(S ∩ K-) - dim(S⊥ ∩ K+), provided it is well defined
Mechanics of materials formulas and problems : engineering mechanics 2
Gross, Dietmar; Wriggers, Peter; Schröder, Jörg; Müller, Ralf
2017-01-01
This book contains the most important formulas and more than 140 completely solved problems from Mechanics of Materials and Hydrostatics. It provides engineering students material to improve their skills and helps to gain experience in solving engineering problems. Particular emphasis is placed on finding the solution path and formulating the basic equations. Topics include: - Stress - Strain - Hooke’s Law - Tension and Compression in Bars - Bending of Beams - Torsion - Energy Methods - Buckling of Bars - Hydrostatics .
Revision of the new formula for book losing rate
Institute of Scientific and Technical Information of China (English)
TANG Zhen-yu; GENG Xiao-bing
2005-01-01
While the amount of book borrowing is overlooked in the calculation of book losing rate in a closed system, there are also other important overlooked elements, factors such as reader groups and the reading timetable in open book stacks. On the basis of concrete evidence, this paper revised a new formula for book losing rate with the purpose of making the estimation in management more objective and more accurate.
Get Ready to Watch F1 Formula Raching in China
Institute of Scientific and Technical Information of China (English)
WeiXing
2002-01-01
In July, construction began on the Shanghai International Motorcycle Race Field. Main construction should be completed in March 2004 and Fl Formula China Championships could be held that year.Located in the suburban Jiading District of Shanghai, the International Motorcycle Race Field will occupy an area of 5.3 square kilometers. It consists of a race area, a business and exhibition area, an entertainment area and a reserved area.
Multi-dimensional versions of a formula of Popoviciu
Institute of Scientific and Technical Information of China (English)
2007-01-01
In this paper, an explicit formulation for multivariate truncated power functions of degree one is given firstly. Based on multivariate truncated power functions of degree one, a formulation is presented which counts the number of non-negative integer solutions of s×(s + 1) linear Diophantine equations and it can be considered as a multi-dimensional versions of the formula counting the number of non-negative integer solutions of ax + by = n which is given by Popoviciu in 1953.
Multi-dimensional versions of a formula of Popoviciu
Institute of Scientific and Technical Information of China (English)
Zhi-qiang XU
2007-01-01
In this paper, an explicit formulation for multivariate truncated power functions of degree one is given firstly. Based on multivariate truncated power functions of degree one, a formulation is presented which counts the number of non-negative integer solutions of s × (s + 1) linear Diophantine equations and it can be considered as a multi-dimensional versions of the formula counting the number of non-negative integer solutions of ax + by = n which is given by Popoviciu in 1953.
Characteristic Formulae for Relations with Nested Fixed Points
Directory of Open Access Journals (Sweden)
Luca Aceto
2012-02-01
Full Text Available A general framework for the connection between characteristic formulae and behavioral semantics is described in [2]. This approach does not suitably cover semantics defined by nested fixed points, such as the n-nested simulation semantics for n greater than 2. In this study we address this deficiency and give a description of nested fixed points that extends the approach for single fixed points in an intuitive and comprehensive way.
Formulas and Asymptotics for the Asymmetric Simple Exclusion Process
Energy Technology Data Exchange (ETDEWEB)
Tracy, Craig A.; Widom, Harold, E-mail: widom@ucsc.edu [University of California, Department of Mathematics (United States)
2011-09-15
This is an expanded version of a series of lectures delivered by the second author in June, 2009. It describes the results of three of the authors' papers on the asymmetric simple exclusion process, from the derivation of exact formulas for configuration probabilities, through Fredholm determinant representation, to asymptotics with step initial condition establishing KPZ universality. Although complete proofs are in general not given, at least the main elements of them are.
Extending generalized Fibonacci sequences and their binet-type formula
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Saeki Osamu
2006-01-01
Full Text Available We study the extension problem of a given sequence defined by a finite order recurrence to a sequence defined by an infinite order recurrence with periodic coefficient sequence. We also study infinite order recurrence relations in a strong sense and give a complete answer to the extension problem. We also obtain a Binet-type formula, answering several open questions about these sequences and their characteristic power series.
On Bosonic Magnetic Flux Operator and Bosonic Faraday Operator Formula
Institute of Scientific and Technical Information of China (English)
FAN Hong-Yi; WANG Tong-Tong; WANG Ji-Suo
2007-01-01
In the literature about mesoscopic Josephson devices the magnetic flux is considered as an operator, the fundamental commutative relation between the magnetic flux operator and the Cooper-pair charge operator is usually preengaged. In this paper we show that such a relation can be deduced from the basic Bose operators' commutative relation through the entangled state representation. The Faraday formula in bosonic form is then equivalent to the second Josephson equation. The current operator equation for LC mesoscopic circuit is also derived.
Mesoscopic formulas of linear and angular momentum fluxes
Fruleux, Antoine; Sekimoto, Ken
2016-07-01
Many approaches of coarse graining have been developed under the names of Cosserat theory or polar-fluid theory for those materials in which some component elements undergo nonaffine deformations, such as elastic materials with inclusions or granular matters. For the complex elements such as living cells, however, the microscopic variables and their dynamics are often unknown, and there has been no systematic theory of coarse graining from the microscales nor the formulas like the Irving-Kirkwood formula that constitutes the macroscopic stress or couple stress in terms of some microscale quantities. We show that, for the quasi-steady states, the coarse-graining procedure must generally provide us with the Cosserat-type balance equations as long as the procedure keeps track of the conservation of linear and angular momenta, and that the fluxes of these conserved quantities should generally be expressed in the Irving-Kirkwood-type formulas, where the interparticle distance or forces and torques should be replaced by those associated to the pair of neighboring coarse-graining volumes. This framework, which refers to no particular microvariables or dynamics, is valid for active complex matters out of equilibrium and with any multibody interactions.
Assessment of the breast volume by a new simple formula
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El-Oteify Mahmoud
2006-01-01
Full Text Available Background: With the recent introduction of improved techniques for plastic surgery of the breast and increased public awareness toward these procedures, plastic surgeons are continuously trying to improve their methods and results to reach perfection. Assessment of the breast volume is an important issue prior to the use of breast implants in any aesthetic or reconstructive breast surgery. Previous methods to measure breast volume have included use of a simple bra and breast cup size, cumbersome fluid displacement, appliances and approximate visual estimation. Objectives: In this work we have tried to develop an easy method for assessment of the breast volume for both the patient and the the surgeon through a simple mathematical formula. Materials and Methods: Fifty two volunteers were included in this study. For every one, general parameters including age, weight and height were recorded. Local breast measurements and water volume displacement were also recorded. Results: The collected data were statistically correlated. Using the analyzed data, the breast volume was calculated through a simple and direct formula on the basis of the breast circumference. Conclusion: Our method has, as its principle, the use of an accurate and simple formula, which is based only on one measurement. This is easy for both the patient and the plastic surgeon. This equation is not only a significant technical advantage for the surgeon, but also provides a universal standardization of the breast volume.
Formula recollection through a NEVER BEFORE SEEN mnemonic technique
Schunicht, Shannon
2009-04-01
While in the Army, Mr. Schunicht was involved in a mid- air collision rendering him unconscious for 3 weeks. Everything had to be re-learned, as nursing actions were reported as having been displayed upon awakening from the extended unconsciousness (19 days). Studies in recovery brought about some pragmatic discoveries to compensate for the residual memory deficits. The most valuable was having each vowel represent a mathematical operation, i.e. ``a'' multiplication implying ``@'',``o'' for division implying ``over'', ``i'' for subtraction implying ``minus'', ``u'' for addition implying ``plus'', and ``e'' implying ``equals''. Most constants and variables are indeed consonants, e.g. ``c'' = ``speed of light'' & ``z'' = ``altitude''. Note, how with this author's mnemonic technique, ANY FORMULA may be algebraically manipulated into a word, or series of words for ease of recollection. Additional letters may be added to the enhance the letter combination's intelligibility, but these additional letters need be consonants only! The transition of complicated formulas into simple acronyms will be shown, as well as those submitted by attendees upon arrival. One common example is the quadratic equation: CAPITAL LETTERS ARE ADDITIONAL CONSONANTS yeS, i buiLD rabbits 4caTS oN 2HaTS (remember Dr. Seuss?) The possibilities of mnemonic technique are limitless as Delta X => 0. With the student's usage, an acronym will become more apropos to the actual formula it actually represents!
Semi-empirical formula for spontaneous fission half life time
Energy Technology Data Exchange (ETDEWEB)
Santhosh, K.P., E-mail: drkpsanthosh@gmail.co [School of Pure and Applied Physics, Kannur University, Payyanur Campus 670 327 (India); Biju, R.K.; Sahadevan, Sabina [P G Department of Physics and Research Centre, Payyanur College, Payyanur 670 327 (India)
2010-01-15
A new semi-empirical formula is proposed for determining the spontaneous fission half lives, which works well for the mass region from {sup 232}Th to {sup 286}114. The computed spontaneous fission half life times are also compared with other semi-empirical formula predictions. The alpha decay half lives are systematically computed for heavy and super heavy region with proton numbers varying from 90<=Z<=122 using Coulomb and Proximity Potential Model. The comparison between computed alpha decay half lives and the present spontaneous fission semi-empirical formula predictions of even-even isotopes with Z=90-122 are studied. It is found that in super heavy region the isotopes {sup 270-274}Ds, {sup 272-278}112, {sup 272-282}114, {sup 274-292}116, {sup 276-298}118, {sup 276-308}120 and {sup 278-314}122 will survive fission and can be synthesized and identified via alpha decay.
The Ryu-Takayanagi Formula from Quantum Error Correction
Harlow, Daniel
2016-01-01
I argue that a version of the quantum-corrected Ryu-Takayanagi formula holds in any quantum error-correcting code. I present this result as a series of theorems of increasing generality, with the final statement expressed in the language of operator-algebra quantum error correction. In AdS/CFT this gives a "purely boundary" interpretation of the formula. I also extend a recent theorem, which established entanglement-wedge reconstruction in AdS/CFT, when interpreted as a subsystem code, to the more general, and I argue more physical, case of subalgebra codes. For completeness, I include a self-contained presentation of the theory of von Neumann algebras on finite-dimensional Hilbert spaces, as well as the algebraic definition of entropy. The results confirm a close relationship between bulk gauge transformations, edge-modes/soft-hair on black holes, and the Ryu-Takayanagi formula. They also suggest a new perspective on the homology constraint, which basically is to get rid of it in a way that preserves the val...
Properties of nuclear matter from macroscopic-microscopic mass formulas
Wang, Ning; Ou, Li; Zhang, Yingxun
2015-01-01
Based on the standard Skyrme energy density functionals together with the extended Thomas-Fermi approach, the properties of symmetric and asymmetric nuclear matter represented in two macroscopic-microscopic mass formulas: Lublin-Strasbourg nuclear drop energy (LSD) formula and Weizs\\"acker-Skyrme (WS*) formula, are extracted through matching the energy per particle of finite nuclei. For LSD and WS*, the obtained incompressibility coefficients of symmetric nuclear matter are $K_\\infty=230 \\pm 11$ MeV and $235\\pm 11$ MeV, respectively. The slope parameter of symmetry energy at saturation density is $L=41.6\\pm 7.6$ MeV for LSD and $51.5\\pm 9.6$ MeV for WS*, respectively, which is compatible with the liquid-drop analysis of Lattimer and Lim [ApJ. \\textbf{771}, 51 (2013)]. The density dependence of the mean-field isoscalar and isovector effective mass, and the neutron-proton effective masses splitting for neutron matter are simultaneously investigated. The results are generally consistent with those from the Skyrm...
Feynman-Kac formula for stochastic hybrid systems.
Bressloff, Paul C
2017-01-01
We derive a Feynman-Kac formula for functionals of a stochastic hybrid system evolving according to a piecewise deterministic Markov process. We first derive a stochastic Liouville equation for the moment generator of the stochastic functional, given a particular realization of the underlying discrete Markov process; the latter generates transitions between different dynamical equations for the continuous process. We then analyze the stochastic Liouville equation using methods recently developed for diffusion processes in randomly switching environments. In particular, we obtain dynamical equations for the moment generating function, averaged with respect to realizations of the discrete Markov process. The resulting Feynman-Kac formula takes the form of a differential Chapman-Kolmogorov equation. We illustrate the theory by calculating the occupation time for a one-dimensional velocity jump process on the infinite or semi-infinite real line. Finally, we present an alternative derivation of the Feynman-Kac formula based on a recent path-integral formulation of stochastic hybrid systems.
Properties of nuclear matter from macroscopic-microscopic mass formulas
Wang, Ning; Liu, Min; Ou, Li; Zhang, Yingxun
2015-12-01
Based on the standard Skyrme energy density functionals together with the extended Thomas-Fermi approach, the properties of symmetric and asymmetric nuclear matter represented in two macroscopic-microscopic mass formulas: Lublin-Strasbourg nuclear drop energy (LSD) formula and Weizsäcker-Skyrme (WS*) formula, are extracted through matching the energy per particle of finite nuclei. For LSD and WS*, the obtained incompressibility coefficients of symmetric nuclear matter are K∞ = 230 ± 11 MeV and 235 ± 11 MeV, respectively. The slope parameter of symmetry energy at saturation density is L = 41.6 ± 7.6 MeV for LSD and 51.5 ± 9.6 MeV for WS*, respectively, which is compatible with the liquid-drop analysis of Lattimer and Lim [4]. The density dependence of the mean-field isoscalar and isovector effective mass, and the neutron-proton effective masses splitting for neutron matter are simultaneously investigated. The results are generally consistent with those from the Skyrme Hartree-Fock-Bogoliubov calculations and nucleon optical potentials, and the standard deviations are large and increase rapidly with density. A better constraint for the effective mass is helpful to reduce uncertainties of the depth of the mean-field potential.
An index formula for perturbed Dirac operators on Lie manifolds
Carvalho, Catarina
2011-01-01
We give an index formula for a class of Dirac operators coupled with unbounded potentials. More precisely, we study operators of the form P := D+ V, where D is a Dirac operators and V is an unbounded potential at infinity on a possibly non-compact manifold M_0. We assume that M_0 is a Lie manifold with compactification denoted M. Examples of Lie manifolds are provided by asymptotically Euclidean or asymptotically hyperbolic spaces. The potential V is required to be invertible outside a compact set K and V^{-1} extends to a smooth function on M\\K that vanishes on all faces of M in a controlled way. Using tools from analysis on non-compact Riemannian manifolds, we show that the computation of the index of P reduces to the computation of the index of an elliptic pseudodifferential operator of order zero on M_0 that is a multiplication operator at infinity. The index formula for P can then be obtained from earlier results. The proof also yields similar index formulas for Callias-type pseudodifferential operators ...
A gluing formula for the analytic torsion on singular spaces
Lesch, Matthias
2012-01-01
We prove a gluing formula for the analytic torsion on non-compact (i.e. singular) riemannian manifolds. Let M= U\\cup M_1, where M_1 is a compact manifold with boundary and U represents a model of the singularity. For general elliptic operators we formulate a criterion, which can be checked solely on U, for the existence of a global heat expansion, in particular for the existence of the analytic torsion in case of the Laplace operator. The main result then is the gluing formula for the analytic torsion. Here, decompositions M=M_1\\cup_W M_2 along any compact closed hypersurface W with M_1, M_2 both non-compact are allowed; however product structure near W is assumed. We work with the de Rham complex coupled to an arbitrary flat bundle F; the metric on F is not assumed to be flat. In an appendix the corresponding algebraic gluing formula is proved. As a consequence we obtain a framework for proving a Cheeger-M\\"uller type Theorem for singular manifolds; the latter has been the main motivation for this work. The ...
Optimum Approximate Solution of Herschel-Bulkley Fluid Formula
Institute of Scientific and Technical Information of China (English)
XU Gui-yun; LIN Xue-dong; ZHANG Yong-zhong
2004-01-01
During calculating the fluid resistence with Herschel-Bulkley formula, the deviation is very large in some regions. In order to decrease the deviation, the optimized parameters of approximate solution are obtained through mathematic analysis and 3-D optimization calculation. In the close region of relative radius of the core flow, the continuity of deviation is determined with the limit methods. By analysis, the results indicate that the deviation in the area around the discontinuous nodes is very large; the deviation is the function of fluid parameters, approximate solution parameters and the relative radius of the core flow. While the fluid parameters keep certain, the 3-D figures of the deviation are drawn. The slice plane is used to seek the extremums of multi-peaks surface; The optimized parameters of approximate formula make the approximate formula in the regions of the certain deviation. The available area of relative radius of the core flow increases by 43.2%. It is more valuable for the calculation of flow resistance in pipe transportation.
Historic records on the commercial production of infant formula.
Obladen, Michael
2014-01-01
Industrialized food production first appeared in 1856, pioneered by Borden in the USA, Liebig in Germany, Nestlé in Switzerland, and Mellin in the UK. Their products differed remarkably and deviated from human and cow's milk, and physicians discussed the importance of minute variations in protein, fat and carbohydrates. Proprietary formulas were free of bacteria, and the companies prospered with mass production, international marketing and aggressive advertising. From 1932 on, medical societies restricted advertising to the laity. In 1939 Williams in Singapore and in 1970 Jelliffe in Jamaica suspected that commercial formula may be increasing infant mortality in the Third World. Breastfeeding continued to decline during the early 20th century, falling in 1970 below 10% in the USA. The Swiss 'Third World Group' and the US 'Infant Formula Action Coalition' linked infant mortality and industry marketing in the Third World. The controversy of 1970-1984 led to the WHO Code, which regulated the advertising and marketing of baby food. This was one of several public health statements contributing to the resurgence of breastfeeding.
Sterol Composition in Infant Formulas and Estimated Intake.
Claumarchirant, Lorena; Matencio, Esther; Sanchez-Siles, Luis Manuel; Alegría, Amparo; Lagarda, María Jesús
2015-08-19
Sterol contents in infant formulas (IFs) from the European market were determined, and their intakes by infants between 0 and 6 months were evaluated. Total animal sterols (mg/100 mL) ranged from 1.71 to 5.46, cholesterol being the main animal sterol (1.46-5.1). In general, cholesterol and desmosterol were lower than the human milk (HM) values indicated by other authors. Total plant sterol (mg/100 mL) ranged from 3.1 to 5.0. β-Sitosterol, the most abundant phytosterol, ranged from 1.82 to 3.01, followed by campesterol (0.72-1.15), stigmasterol (0.27-0.53), and brassicasterol (0.14-0.28). Cholesterol intake (mg/day) ranged from 9 to 51 and plant sterol intake (mg/day) from 19 to 50. The sterol profile of IFs is highly dependent on the type and quantity of fats used in their formula. The use of bovine milk fat and milk fat globule membrane in the IFs can approximate the profile of animal sterols to those found in HM, though cholesterol intakes in breastfed infants are still higher than in formula-fed infants.
Feynman-Kac formula for stochastic hybrid systems
Bressloff, Paul C.
2017-01-01
We derive a Feynman-Kac formula for functionals of a stochastic hybrid system evolving according to a piecewise deterministic Markov process. We first derive a stochastic Liouville equation for the moment generator of the stochastic functional, given a particular realization of the underlying discrete Markov process; the latter generates transitions between different dynamical equations for the continuous process. We then analyze the stochastic Liouville equation using methods recently developed for diffusion processes in randomly switching environments. In particular, we obtain dynamical equations for the moment generating function, averaged with respect to realizations of the discrete Markov process. The resulting Feynman-Kac formula takes the form of a differential Chapman-Kolmogorov equation. We illustrate the theory by calculating the occupation time for a one-dimensional velocity jump process on the infinite or semi-infinite real line. Finally, we present an alternative derivation of the Feynman-Kac formula based on a recent path-integral formulation of stochastic hybrid systems.
On a Reduction Formula for a Kind of Double q-Integrals
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Zhi-Guo Liu
2016-06-01
Full Text Available Using the q-integral representation of Sears’ nonterminating extension of the q-Saalschütz summation, we derive a reduction formula for a kind of double q-integrals. This reduction formula is used to derive a curious double q-integral formula, and also allows us to prove a general q-beta integral formula including the Askey–Wilson integral formula as a special case. Using this double q-integral formula and the theory of q-partial differential equations, we derive a general q-beta integral formula, which includes the Nassrallah–Rahman integral as a special case. Our evaluation does not require the orthogonality relation for the q-Hermite polynomials and the Askey–Wilson integral formula.
The calculating formula for radial matrix elements of a relativistic harmonic oscillator
Institute of Scientific and Technical Information of China (English)
强稳朝
2003-01-01
A universal practical formula is given for calculating an integral which includes two confluent hypergeometric functions, power and exponential functions; then by means of this formula, the expressions of the radial matrix elements for a relativistic harmonic oscillator are given.
About clarification of the formula for determination of intrinsic frequency of horizontal pendulum
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Sarkisyan V. K.
2010-09-01
Full Text Available Using the equation the intrinsic frequency of pendulum is decided. Intrinsic frequency is calculated for a certain pendulum. The verity of formula is confirmed by experiment. The deduced is compared with formulas brought in literature.
Comparison between formulas of rotational band for axially symmetric deformed nuclei
Institute of Scientific and Technical Information of China (English)
WU Xi; LEI Yi-An
2008-01-01
The experimental rotational spectra of the deformed nuclei available in even-even and odd-A nuclei in the rare-earth and actinide regions are systematically analyzed with several rotational spectra formulas,including Bohr-Mottelson's I(I+l)-expansion,Harris'w2-expansion,ab and abc formulas.It is shown that the simple 2-parameter ab formula is much better than the widely used 2-parameter Bohr-Mottelson's AB formula and Harris'αβ formula.The available data of the rotational spectra of both ground-state band in even-even nuclei and one-quaasiparticle band in odd-A nuclei can be conveniently and rather accurately reproduced by ab formula and abc formula.The moment of inertia and the variation with rotational frequency of angular momentum can be satisfactorily reproduced by ab and abc formulas.
Generalizing PFD formulas of IEC 61508 for KooN configurations.
Jahanian, Hamid
2015-03-01
Detailed formulas are given in IEC 61508 for calculating Probability of Failure on Demand for 1oo1, 1oo2, 2oo2, 2oo3 and 1oo3 systems. Simplified PFD formulas are also derived for general k-out-of-n combinations, without incorporating all the elements utilized in IEC 61508 formulas. While there have been other studies on IEC 61508 formulas and the simplified k-out-of-n equations, none have proposed an inclusive generalized form of IEC 61508 formulas to replicate all the specific combinations covered by the standard. This paper uses a detailed analysis to derive a generalized PFD formula based on IEC 61508.6-2011 that can be applied to all k-out-of-n combinations. The proposed formula is verified against both IEC 61508 and the simplified formulas, and its application is demonstrated by a real life example.
Explicit Formulae for the Continued Fraction Convergents of "Square Root of D"
Braza, Peter A.
2010-01-01
The formulae for the convergents of continued fractions are always given recursively rather than in explicit form. This article derives explicit formulae for the convergents of the continued fraction expansions for square roots.
Most Cow's Milk Baby Formulas Don't Up Risk of Type 1 Diabetes
... page: https://medlineplus.gov/news/fullstory_163146.html Most Cow's Milk Baby Formulas Don't Up Risk ... nutrition for babies, a new study suggests that most cow's milk formulas don't increase the risk ...
A change of scale formula for Wiener integrals on abstract Wiener spaces
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Il Yoo
1994-01-01
Full Text Available In this paper we obtain a change of scale formula for Wiener integrals on abstract Wiener spaces. This formula is shown to hold for many classes of functions of interest in Feynman integration theory and quantum mechanics.
Comparison Among Commonly Available Infant Formula Milks in the Iraqi Market
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Ehab Mudher Mikhael MClinPharm
2015-10-01
Full Text Available Breast-feeding is the best method of feeding infants. In some cases, formula milk can be a suitable alternative, so this study aimed to compare the safety and nutritional adequacy of commonly available formula milks in the Iraqi market. An observational study for the commonly available formula milks was conducted in the largest supermarkets of Baghdad, Iraq, during January-March 2015. The macronutrient and micronutrient contents as presented in the label of each type of formula milk was compared with the standard requirement of formula milk according to the European Society for Paediatric Gastroenterology, Hepatology and Nutrition (ESPGHAN guidelines. Dielac formula milk is the commonest formula milk in the Iraqi market, with the lowest price when compared with other formula milks. All infant formula milks (Similac, Guigoz, and S-26 Gold except Dielac have the mandatory contents within the specified ranges, according to the ESPGHAN guidelines. Dielac lacks more than 1 of the major mandatory contents besides lacking all optional contents in its formula. Guigoz formula milk lacks the optional ingredients arachidonic acid, docosahexaenoic acid, and nucleotides. Similac milk was supplemented with a higher-than-specified level of nucleotides, and its l-carnitine contents were not declared. Only S26 Gold formula milk contained all mandatory and optional ingredients within the specified range, according to the ESPGHAN guidelines. In conclusion, no formula milk can resemble breast milk; however, S26 Gold formula milk is the most acceptable formula, and Dielac formula milk is the worst. Therefore, it is recommended that Dielac be withdrawn from the Iraqi market.
Opening and closing formulae in Tswana folktales: A structural and functional analysis
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S. A. Swanepoel
1983-05-01
Full Text Available Opening and closing formulae are acknowledged by many research workers and specialists of folktales. It is therefore a pity that although most researchers have recognized it, here is a tendency to neglect the layout of the structure and the functions played by the formulae. In this discussion attention will be paid to the structure and the various functions of the formulae, because the opening and closing formulae, as a unity, constitute one of the main structural features of folktales.
Comments on the Formulae of Eötvös Corrections for Airborne Gravimetry
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HUANG Motao
2015-01-01
Full Text Available A detailed analysis is made on the different former and existing formulae of Eötvös corrections for airborne gravimetry in view of the inconsistency of their uses by many scholars at home and abroad. A numeral comparison between the different formulae is accomplished. The problems from the use of approximate formulae by our country's scholars are pointed out. And the necessity of using rigorous formulae is emphasized.
Alghali, R.; Kamaruddin, A. F.; Mokhtar, N.
2016-12-01
Introduction: The application of forensic odontology using teeth and bones becomes the most commonly used methods to determine age of unknown individuals. Objective: The aim of this study was to determine the reliability of Malay formula of Demirjian and Malay formula of Cameriere methods in determining the dental age that is closely matched with the chronological age of Malay children in Kepala Batas region. Methodology: This is a retrospective cross-sectional study. 126 good quality dental panoramic radiographs (DPT) of healthy Malay children aged 8-16 years (49 boys and 77 girls) were selected and measured. All radiographs were taken at Dental Specialist Clinic, Advanced Medical and Dental Institute, Universiti Sains Malaysia. The measurements were carried out using new Malay formula of both Demirjian and Cameriere methods by calibrated examiner. Results: The intraclass correlation coefficient (ICC) analysis between the chronological age with Demirjian and Cameriere has been calculated. The Demirjian method has shown a better percentage (91.4%) of ICC compared to Cameriere (89.2%) which also indicates a high association, with good reliability. However, by comparing between Demirjian and Cameriere, it can be concluded that Demirjian has a better reliability. Conclusion: Thus, the results suggested that, modified Demirjian method is more reliable than modified Cameriere method among the population in Kepala Batas region.
Dancis, Jerome
2001-01-01
Students in a freshmen calculus course should become fluent in modeling physical phenomena represented by integrals, in particular geometric formulas for volumes and arc length and physical formulas for work. Describes how to train students to became fluent in such modeling and derivation of standard integral formulas. Indicates that these lessons…
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Oleg V. Bugakov
2015-11-01
Full Text Available Interpretation formulas for conjunctions and particles in the explanatory Ukrainian language dictionary Interpretation formulas for conjunctions and particles in the Ukrainian Language Dictionary are defined. The peculiarities of presenting lexical semantics for these parts of speech in the explanatory part of the dictionary entry are described. The way of presenting interpretation formulas using synonyms is also described.
24 CFR Appendix B to Part 1000 - IHBG Block Grant Formula Mechanisms
2010-04-01
... 24 Housing and Urban Development 4 2010-04-01 2010-04-01 false IHBG Block Grant Formula Mechanisms B Appendix B to Part 1000 Housing and Urban Development Regulations Relating to Housing and Urban... Grant Formula Mechanisms 1. The Indian Housing Block Grant (IHBG) formula consists of two...
2011-06-07
... Collection; Comment Request; Infant Formula Recall Regulations AGENCY: Food and Drug Administration, HHS... on requirements related to the recall of infant formula. DATES: Submit either electronic or written... appropriate, and other forms of information technology. Infant Formula Recall Regulations--21 CFR 107.230,...
37 CFR 1.58 - Chemical and mathematical formulae and tables.
2010-07-01
... Provisions The Application § 1.58 Chemical and mathematical formulae and tables. (a) The specification, including the claims, may contain chemical and mathematical formulae, but shall not contain drawings or flow... mathematical formulae must be encoded to maintain the proper positioning of their characters when displayed...
Using Readability Formulas to Establish the Grade Level Difficulty of Software.
Clariana, Roy B.
1993-01-01
Compared the grade level difficulty obtained from seven readability formulas to student reading levels from two national standardized tests to determine which formulas best determined the readability of computer-based text. Found that the Flesch-Kincaid, FOG, and ARI formulas provided the best estimate of reading grade level of computer-based text…
24 CFR 1000.314 - What is formula current assisted stock?
2010-04-01
... stock? 1000.314 Section 1000.314 Housing and Urban Development Regulations Relating to Housing and Urban... current assisted stock? Formula current assisted stock is current assisted stock as described in § 1000... recipient and are under management as indicated in the Formula Response Form. Formula current assisted...
The KR-20 Reliability Coefficient as a Special Case of a More General Formula.
Smith, Donald M.
The Kuder Richardson-20 Formula is shown to be a special case, where each examinee is given sufficient time to answer each item, of a more general formula where each examinee may not be allowed the necessary time. The formula is extended to allow two scores, knowledge and speed, to be extracted from each examinees test score. Using a sample of 82…
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César Augusto Guevara-Cuéllar
2010-12-01
Full Text Available Introduction: Although the levels of low-density lipoprotein (LDL-C should ideally be determined by beta quantification or enzymatic methods, there are limitations in developing countries. The goal of this study is to compare LDL-C obtained through three formulae (LDL-Cnf with LDL-C obtained through the Friedewald formula (LDL-Cf using LDL-C through enzymatic methods as the most-accepted reference method in clinical practice (LDL-Cr.Methods: A concordance study was carried out in a reference laboratory in Cali, Colombia. The three formulae were (mg/dl: Men with triglycerides under 400 mg/dl: LDL-C = Total Cholesterol (TC - triglycerides (TG /6.5 - 45; men with triglycerides equal to or greater than 400 mg/dl: LDL-C = (TC - (TG / 7 -50 and women: LDL-C = (TC-(TG /6.5 - 70.Results: Three-hundred fifteen values were obtained of which 53% were for women. The mean age and LDL-Cr were 54 years (±15.8 and 112.1 mg/dl (±32.5, respectively. The median (interquartile range, mg/dl of TC, high-density lipoprotein (HDL-C and TG were 204 mg/dl (171-229, 51 mg/dl (41-61, and 156 mg/dl (99-237, respectively. There were no differences between mean values of LDL-Cr and LDL-Cnf (113.48 vs. 112.67 mg/dl; p=0.45. The intraclass correlation coefficient among LDL-Cr and LDL-Cf and LDL-Cnf were high (R=0.93 and 0.92, respectively. The correlation between LDL-Cf and LDL-Cnf was 0.95. There is no difference between the areas under the receiver operating characteristic (ROC curve with the level of LDL-Cr at 160 mg/dl for LDL-Cnf and LDL-Cf. (0.94 vs. 0.93; p=0.27.Conclusion: There is high concordance between LDL-Cf and LDL-Cnf. These formulae could be an alternative when there are limitations to determine LDL-C because of the lack of enzymatic methods or through Friedewald formula due to the absence of HDL-C.
Directory of Open Access Journals (Sweden)
César Augusto Guevara-Amador
2011-01-01
Full Text Available Introduction: Although the levels of low-density lipoprotein (LDL-C should ideally be determined by beta quantification or enzymatic methods, there are limitations in developing countries. The goal of this study is to compare LDL-C obtained through three formulae (LDL-Cnf with LDL-C obtained through the Friedewald formula (LDL-Cf using LDL-C through enzymatic methods as the most-accepted reference method in clinical practice (LDL-Cr. Methods: A concordance study was carried out in a reference laboratory in Cali, Colombia. The three formulae were (mg/dl: Men with triglycerides under 400 mg/dl: LDL-C = Total Cholesterol (TC - triglycerides (TG /6.5 - 45; men with triglycerides equal to or greater than 400 mg/dl: LDL-C = (TC - (TG / 7 -50 and women: LDL-C = (TC-(TG /6.5 - 70. Results: Three-hundred fifteen values were obtained of which 53% were for women. The mean age and LDL-Cr were 54 years (±15.8 and 112.1 mg/dl (±32.5, respectively. The median (interquartile range, mg/dl of TC, high-density lipoprotein (HDL-C and TG were 204 mg/dl (171-229, 51 mg/dl (41-61, and 156 mg/dl (99-237, respectively. There were no differences between mean values of LDL-Cr and LDL-Cnf (113.48 vs. 112.67 mg/dl; p=0.45. The intraclass correlation coefficient among LDL-Cr and LDL-Cf and LDL-Cnf were high (R=0.93 and 0.92, respectively. The correlation between LDL-Cf and LDL-Cnf was 0.95. There is no difference between the areas under the receiver operating characteristic (ROC curve with the level of LDL-Cr at 160 mg/dl for LDL-Cnf and LDL-Cf. (0.94 vs. 0.93; p=0.27. Conclusion: There is high concordance between LDL-Cf and LDL-Cnf. These formulae could be an alternative when there are limitations to determine LDL-C because of the lack of enzymatic methods or through Friedewald formula due to the absence of HDL-C.
Theory of (n) truth degrees of formulas in modal logic and a consistency theorem
Institute of Scientific and Technical Information of China (English)
WANG GuoJun; DUAN QiaoLin
2009-01-01
The theory of (n) truth degrees of formulas is proposed in modal logic for the first time. A consistency theorem is obtained which says that the (n) truth degree of a modality-free formula equals the truth degree of the formula in two-valued propositional logic. Variations of (n) truth degrees of formulas w.r.t. n in temporal logic is investigated. Moreover, the theory of (n) similarity degrees among modal formulas is proposed and the (n) modal logic metric space is derived therefrom which contains the classical logic metric space as a subspace. Finally, a kind of approximate reasoning theory is proposed in modal logic.
The History of Infant Formula: Quality, Safety, and Standard Methods.
Wargo, Wayne F
2016-01-01
Food-related laws and regulations have existed since ancient times. Egyptian scrolls prescribed the labeling needed for certain foods. In ancient Athens, beer and wines were inspected for purity and soundness, and the Romans had a well-organized state food control system to protect consumers from fraud or bad produce. In Europe during the Middle Ages, individual countries passed laws concerning the quality and safety of eggs, sausages, cheese, beer, wine, and bread; some of these laws still exist today. But more modern dietary guidelines and food regulations have their origins in the latter half of the 19th century when the first general food laws were adopted and basic food control systems were implemented to monitor compliance. Around this time, science and food chemistry began to provide the tools to determine "purity" of food based primarily on chemical composition and to determine whether it had been adulterated in any way. Since the key chemical components of mammalian milk were first understood, infant formulas have steadily advanced in complexity as manufacturers attempt to close the compositional gap with human breast milk. To verify these compositional innovations and ensure product quality and safety, infant formula has become one of the most regulated foods in the world. The present paper examines the historical development of nutritional alternatives to breastfeeding, focusing on efforts undertaken to ensure the quality and safety from antiquity to present day. The impact of commercial infant formulas on global regulations is addressed, along with the resulting need for harmonized, fit-for-purpose, voluntary consensus standard methods.
The Physical Meaning of the Titius-Bode Formula
Smirnov, V. A.
It is proposed an special hypothesis of the formation of symmetric objects in space with the help of the interference of standing waves which act in the process of evolution of the primordial gas-dust cloud including the formation of the Solar system, that may be revealed by 11-year cycle of Solar activity in particular. It is used the idea of J.Kepler of the construction of the Solar system, viewed as inscribed and circumscribed Platonic figures, a common measure of which, according to the author, is the length of the standing waves generated by the variable energy sources of the primary cloud. This explains the physical meaning of the Titius-Bode formula. In 1968 S.F.Dermott revealed the foundation of Titius-Bode empiric formula, basing on Theory of Resonance. But in addition to direct statement of existing resonance mechanism of formula T(n)=T(0)*Cn, n=1,2,3,4, physical sense does not come to light. I tried to explain the formation of symmetric figures and space constructions with evident experience of formation of Chladni E. figures, offering the calculation, confirmed by experience of appearance of new space bodies in the nodes of standing waves of primary gas-dust cloud. The interference of standings waves is surely promotes the formation of different figures - such as symmetric galaxies, hexagon vortex at Saturn, and others. Unlike Dermott's theory, our explanation of symmetric formation of planets is a common solution of task for multi bodies interaction, and proposes the version of solution in case with more than two bodies.
The Wald entropy formula and loop quantum gravity
Bodendorfer, Norbert
2013-01-01
We outline how the Wald entropy formula naturally arises in loop quantum gravity based on recently introduced dimension-independent connection variables. The key observation is that in a loop quantization of a generalized gravity theory, the analog of the area operator turns out to measure, morally speaking, the Wald entropy rather than the area. We discuss the explicit example of (higher-dimensional) Lovelock gravity and comment on recent work on finding the correct numerical prefactor of the entropy by comparing it to a semiclassical effective action.
A note on connected formula for form factors
He, Song
2016-01-01
In this note we study the connected prescription, originally derived from Witten's twistor string theory, for tree-level form factors in ${\\cal N}=4$ super-Yang-Mills theory. The construction is based on the recently proposed four-dimensional scattering equations with $n$ massless on-shell states and one off-shell state, which we expect to work for form factors of general operators. To illustrate the universality of the prescription, we propose compact formulas for super form factors with chiral stress-tensor multiplet operator, and bosonic ones with scalar operators ${\\rm Tr}(\\phi^m)$ for arbitrary $m$.
Analytical Formulae for Two of A. H. Stroud's Quadrature Rules
Peterson, J W
2009-01-01
Analytical formulae for the points and weights of two fifth-order quadrature rules for C_3, the 3-cube, are given. The rules, originally formulated by A. H. Stroud in 1967, are discussed in greater detail in terms of both the setup of the basic equations and the method of obtaining their solutions analytically. The primary purpose of this paper is to better document what we feel is a particularly practical quadrature rule (e.g. in finite element calculations) and one for which we felt comprehensive information was scarce.
A generalized spectral radius formula and Olsen's question
DEFF Research Database (Denmark)
Loring, Terry; Shulman, Tatiana
2012-01-01
Let A be a C⁎C⁎-algebra and I be a closed ideal in A. For x∈Ax∈A, its image in A/IA/I is denoted by x˙, and its spectral radius is denoted by r(x)r(x). We prove that max{r(x),‖x˙‖}=inf‖(1+i)−1x(1+i)‖ (where the infimum is taken over all i∈Ii∈I such that 1+i1+i is invertible), which generalizes...... the spectral radius formula of Murphy and West. Moreover if r(x)
A formula for crossing probabilities of critical systems inside polygons
Flores, S. M.; Simmons, J. J. H.; Kleban, P.; Ziff, R. M.
2017-02-01
In this article, we use our results from Flores and Kleban (2015 Commun. Math. Phys. 333 389-434, 2015 Commun. Math. Phys. 333 435-81, 2015 Commun. Math. Phys. 333 597-667, 2015 Commun. Math. Phys. 333 669-715) to generalize known formulas for crossing probabilities. Prior crossing results date back to Cardy’s prediction of a formula for the probability that a percolation cluster in two dimensions connects the left and right sides of a rectangle at the percolation critical point in the continuum limit (Cardy 1992 J. Phys. A: Math. Gen. 25 L201-6). Here, we predict a new formula for crossing probabilities of a continuum limit loop-gas model on a planar lattice inside a 2N-sided polygon. In this model, boundary loops exit and then re-enter the polygon through its vertices, with exactly one loop passing once through each vertex, and these loops join the vertices pairwise in some specified connectivity through the polygon’s exterior. The boundary loops also connect the vertices through the interior, which we regard as a crossing event. For particular values of the loop fugacity, this formula specializes to FK cluster (resp. spin cluster) crossing probabilities of a critical Q-state random cluster (resp. Potts) model on a lattice inside the polygon in the continuum limit. This includes critical percolation as the Q = 1 random cluster model. These latter crossing probabilities are conditioned on a particular side-alternating free/fixed (resp. fluctuating/fixed) boundary condition on the polygon’s perimeter, related to how the boundary loops join the polygon’s vertices pairwise through the polygon’s exterior in the associated loop-gas model. For Q\\in ≤ft\\{2,3,4\\right\\} , we compare our predictions of these random cluster (resp. Potts) model crossing probabilities in a rectangle (N = 2) and in a hexagon (N = 3) with high-precision computer simulation measurements. We find that the measurements agree with our predictions very
Power electronics basics operating principles, design, formulas, and applications
Rozanov, Yuriy; Chaplygin, Evgeny; Voronin, Pavel
2015-01-01
Power Electronics Basics: Operating Principles, Design, Formulas, and Applications provides fundamental knowledge for the analysis and design of modern power electronic devices. This concise and user-friendly resource:Explains the basic concepts and most important terms of power electronicsDescribes the power assemblies, control, and passive components of semiconductor power switchesCovers the control of power electronic devices, from mathematical modeling to the analysis of the electrical processesAddresses pulse-width modulation, power quality control, and multilevel, modular, and multicell
General formulae for f1 -> f2 γ
Lavoura, L.
2003-07-01
At one-loop level the decay f_1 to f_2 γ, where f1 and f2 are two spin-1/2 particles with the same electric charge, is mediated by a boson B and a spin-1/2 fermion F. The boson B may have either spin - interacting with the fermions through the Dirac matrices 1 and γ_5 - or spin 1 - with V+ A and V- A couplings to the fermions. I give general formulae for the one-loop electroweak amplitude of f_1 to f_2 γ in all these cases.
General formulae for f sub 1-> f sub 2 gamma
Lavoura, L
2003-01-01
At one-loop level the decay f sub 1-> f sub 2 gamma, where f sub 1 and f sub 2 are two spin-1/2 particles with the same electric charge, is mediated by a boson B and a spin-1/2 fermion F. The boson B may have either spin 0-interacting with the fermions through the Dirac matrices 1 and gamma sub 5 - or spin 1 - with V+A and V-A couplings to the fermions. I give general formulae for the one-loop electroweak amplitude of f sub 1-> f sub 2 gamma in all these cases. (orig.)
General formulae for f1 --> f2 gamma
Lavoura, L
2003-01-01
At one-loop level the decay f1 --> f2 gamma, where f1 and f2 are two spin-1/2 particles with the same electric charge, is mediated by a boson B and a spin-1/2 fermion F. The boson B may have either spin 0 - interacting with the fermions through Dirac matrices 1 and gamma5 - or spin 1 - with V+A and V-A couplings to the fermions. I give general formulae for the one-loop electroweak amplitude of f1 --> f2 gamma in all these cases.
A note on connected formula for form factors
He, Song; Liu, Zhengwen
2016-12-01
In this note we study the connected prescription, originally derived from Witten's twistor string theory, for tree-level form factors in N = 4 super-Yang-Mills theory. The construction is based on the recently proposed four-dimensional scattering equations with n massless on-shell states and one off-shell state, which we expect to work for form factors of general operators. To illustrate the universality of the prescription, we propose compact formulas for super form factors with chiral stress-tensor multiplet operator, and bosonic ones with scalar operators Tr( ϕ m ) for arbitrary m.
The Schwinger formula revisited II (a mathematical treatment).
Haro Cases, Jaume
2003-01-01
In this paper we study the production of pairs in no-analytic potentials. It is a well-known fact that, when the potential is analytic the average number of produced pairs is exponentially small in ?. On the other hand, when the potential is no-analytic, using the W.K.B. method, we prove that the average number of produced pairs is ?????, where ? is the regularity of the potential and ? is the fine structure constant. Finally, we give a rigorous proof of the Schwinger’s formula.
CKP Hierarchy, Bosonic Tau Function and Bosonization Formulae
Directory of Open Access Journals (Sweden)
Johan W. van de Leur
2012-06-01
Full Text Available We develop the theory of CKP hierarchy introduced in the papers of Kyoto school [Date E., Jimbo M., Kashiwara M., Miwa T., J. Phys. Soc. Japan 50 (1981, 3806-3812] (see also [Kac V.G., van de Leur J.W., Adv. Ser. Math. Phys., Vol. 7, World Sci. Publ., Teaneck, NJ, 1989, 369-406]. We present appropriate bosonization formulae. We show that in the context of the CKP theory certain orthogonal polynomials appear. These polynomials are polynomial both in even and odd (in Grassmannian sense variables.
CKP Hierarchy, Bosonic Tau Function and Bosonization Formulae
van de Leur, Johan W.; Orlov, Alexander Yu.; Shiota, Takahiro
2012-06-01
We develop the theory of CKP hierarchy introduced in the papers of Kyoto school [Date E., Jimbo M., Kashiwara M., Miwa T., J. Phys. Soc. Japan 50 (1981), 3806-3812] (see also [Kac V.G., van de Leur J.W., Adv. Ser. Math. Phys., Vol. 7, World Sci. Publ., Teaneck, NJ, 1989, 369-406]). We present appropriate bosonization formulae. We show that in the context of the CKP theory certain orthogonal polynomials appear. These polynomials are polynomial both in even and odd (in Grassmannian sense) variables.
CKP Hierarchy, Bosonic Tau Function and Bosonization Formulae
van de Leur, Johan W.; Alexander Yu. Orlov; Takahiro Shiota
2011-01-01
We develop the theory of CKP hierarchy introduced in the papers of Kyoto school [Date E., Jimbo M., Kashiwara M., Miwa T., J. Phys. Soc. Japan 50 (1981), 3806-3812] (see also [Kac V.G., van de Leur J.W., Adv. Ser. Math. Phys., Vol. 7, World Sci. Publ., Teaneck, NJ, 1989, 369-406]). We present appropriate bosonization formulae. We show that in the context of the CKP theory certain orthogonal polynomials appear. These polynomials are polynomial both in even and odd (in Grassmannian sense) varia...
Optimal Worst Case Formulas Comparing Cache Memory Associativity
Lennerstad, Håkan; Lundberg, Lars
1995-01-01
Consider an arbitrary program $P$ which is to be executed on a computer with two alternative cache memories. The first cache is set associative or direct mapped. It has $k$ sets and $u$ blocks in each set, this is called a (k,u)$-cache. The other is a fully associative cache with $q$ blocks - a $(1,q)$-cache. We present formulas optimally comparing the performance of a $(k,u)$-cache compared to a $(1,q)$-cache for worst case programs. Optimal mappings of the program variables to the cache blo...
Nonequilibrium Electron Transport Through a Quantum Dot from Kubo Formula
Institute of Scientific and Technical Information of China (English)
L(U) Rong; ZHANG Guang-Ming
2005-01-01
Based on the Kubo formula for an electron tunneling junction, we revisit the nonequilibrium transport properties through a quantum dot. Since the Fermi level of the quantum dot is set by the conduction electrons of the leads, we calculate the electron current from the left side by assuming the quantum dot coupled to the right lead as another side of the tunneling junction, and the other way round is used to calculate the current from the right side. By symmetrizing these two currents, an effective local density states on the dot can be obtained, and is discussed at high and low temperatures, respectively.
Monotonicity Formula and Regularity for General Free Discontinuity Problems
Bucur, Dorin; Luckhaus, Stephan
2014-02-01
We give a general monotonicity formula for local minimizers of free discontinuity problems which have a critical deviation from minimality, of order d - 1. This result allows us to prove partial regularity results (that is closure and density estimates for the jump set) for a large class of free discontinuity problems involving general energies associated to the jump set, as for example free boundary problems with Robin conditions. In particular, we give a short proof to the De Giorgi-Carriero-Leaci result for the Mumford-Shah functional.
On analytic formulas of Feynman propagators in position space
Institute of Scientific and Technical Information of China (English)
ZHANG Hong-Hao; FENG Kai-Xi; QIU Si-Wei; ZHAO An; LI Xue-Song
2010-01-01
We correct an inaccurate result of previous work on the Feynman propagator in position space of a free Dirac field in(3+1)-dimensional spacetime; we derive the generalized analytic formulas of both the scalar Feynman propagator and the spinor Feynman propagator in position space in arbitrary(D+1)-dimensional spacetime; and we further find a recurrence relation among the spinor Feynman propagator in(D+l)-dimensional spacetime and the scalar Feynman propagators in(D+1)-,(D-1)-and(D+3)-dimensional spacetimes.
Empirical formula for the refractive index of freezing brine
DEFF Research Database (Denmark)
Frisvad, Jeppe Revall
2009-01-01
The refractive index of freezing brine is important for example in order to estimate oceanic scattering as sea ice develops. Previously, no simple continuous expression was available for estimating the refractive index of brine at subzero temperatures. I show that extrapolation of the empirical...... formula for the refractive index of seawater by Quan and Fry [Appl. Opt. 34(18), 3477-3480 (1995)] provides a good fit to the refractive index of freezing brine for temperatures above -24 degrees celsius and salinities below 180 parts per thousand....
Notes on an Internal Boundary-Layer Height Formula
Savelyev, Sergiya.; Taylor, Petera.
The derivation of the Panofsky-Dutton internal boundary-layer(IBL) height formula has been revisited. We propose that the upwindroughness length (rather than downwind) should be used in theformula and that a turbulent vertical velocity (w) ratherthan the surface friction velocity (u*) should be considered asthe appropriate scaling for the rate of propagation ofdisturbances into the turbulent flow. A published set ofwind-tunnel and atmospheric data for neutral stratification hasbeen used to investigate the influence of the magnitude ofroughness change on the IBL height.
CRC standard probability and statistics tables and formulae Student ed.
Kokoska, Stephen
2000-01-01
Users of statistics in their professional lives and statistics students will welcome this concise, easy-to-use reference for basic statistics and probability. It contains all of the standardized statistical tables and formulas typically needed plus material on basic statistics topics, such as probability theory and distributions, regression, analysis of variance, nonparametric statistics, and statistical quality control.For each type of distribution the authors supply:?definitions?tables?relationships with other distributions, including limiting forms?statistical parameters, such as variance a
Glasser, Leslie
2011-01-01
Formula unit (or molecular) volume, "V[subscript m]", is related to many thermodynamic and physical properties of materials, so that knowledge of "V[subscript m]" is useful in prediction of such properties for known and even hypothetical materials. The symbol "Z" represents the number of formula units in a crystallographic unit cell; "Z" thus…
Fatty acid composition of human milk and infant formulas
Directory of Open Access Journals (Sweden)
Ivančica Delaš
2005-04-01
Full Text Available The appropriate fatty acid composition of membrane lipids is necessary for structure and function of the developing nervous system. Rapid synthesis of brain tissue occurs during the last trimester of pregnancy and the early postnatal weeks. This synthesis of brain structure involves the formation of complex lipids, many of which contain significant quantities of essential fatty acids and their higher homologs. This study was undertaken to elucidate how fatty acid compositions of available diets for infants meet the requirements for essential fatty acids. Samples of infant formulas, present on the market, as well as milk samples obtained from breast feeding mothers, were extracted by chloroform : methanol mixtures in order to obtain total lipids. Fatty acid methyl esters were prepared and fatty acid composition was revealed by gas chromatography. Special interest was directed to the content of long chain polyunsaturated fatty acids. The results have shown that infant formulas, designed to substitute mothers’ breast milk, contain medium chain fatty acids (C 10:0, C 12:0, along with the other saturated fatty acids, in the amounts acceptable for infants’ energy consumption. Although linoleic acid (C18:2, n-6 was present at the level expected to cover needs for essential fatty acids, most of the tested products did not contain sufficient amounts of long chain polyunsaturated fatty acids, despite the fact that these fatty acids are necessary for undisturbed brain development, ignoring the strong recommendations that they should be used as a supplement in infants’ food.
Formulas of components of citronella oil against mosquitoes (Aedes aegypti).
Hsu, Wey-Shin; Yen, Jui-Hung; Wang, Yei-Shung
2013-01-01
The mosquito Aedes aegypti is an epidemic vector of several diseases such as dengue fever and yellow fever. Several pesticides are used to control the mosquito population. Because of their frequent use, some mosquitoes have developed resistance. In this study, we used the Y-tube olfactometer to test essential oils of Cymbopogon species and screened specific formulas of components as repellents against Ae. aegypti. At 400 μL, the extracted oil of citronella grass (Cymbopogon nardus) and myrcene produced a low-active response by inhibiting mosquito host-seeking activity. Citronella grass, lemon grass (Cymbopogon citratus), citral and myrcene also produced a low-treatment response to repellents, for more potential to affect host-seeking behavior. Furthermore, the mixture of citral, myrcene, and citronellal oil (C:M:Ci = 6:4:1) greatly affected and inhibited host-seeking behavior (76% active response; 26% treatment response with 40 μL; 42.5%, 18% with 400 μL; and 19%, 23% with 1000 μL). As compared with the result for N,N-diethyl-3-methylbenzamide (DEET; 44%, 22% with 400 μL), adjusting the composition formulas of citronella oil had a synergistic effect, for more effective repellent against Ae. aegypti.
The mass formula for an exotic BTZ black hole
Zhang, Baocheng
2016-04-01
An exotic Bañados-Teitelboim-Zanelli (BTZ) black hole has an angular momentum larger than its mass in three dimension (3D), which suggests the possibility that cosmic censorship could be violated if angular momentum is extracted by the Penrose process. In this paper, we propose a mass formula for the exotic BTZ black hole and show no violation of weak cosmic censorship in the gedanken process above by understanding properly its mass formula. Unlike the other black holes, the total energy of the exotic BTZ black hole is represented by the angular momentum instead of the mass, which supports a basic point of view that the same geometry should be determined by the same energy in 3D general relativity whose equation of motion can be given either by normal 3D Einstein gravity or by exotic 3D Einstein gravity. However, only the mass of the exotic black hole is related to the thermodynamics and other forms of energy are "dumb", which is consistent with the earlier thermodynamic analysis about exotic black holes.
The Nutritional Value of Protein-hydrolyzed Formulae.
Agostoni, Carlo; Terracciano, Luigi; Varin, Elena; Fiocchi, Alessandro
2016-01-01
Allergy to cow's milk proteins is a challenging condition in early infancy. Allergic infants may be predisposed to impairments of growth from either the disease itself or the nutritional constraints of the exclusion diet they should follow. Formulae based on extensively hydrolyzed cow's milk proteins are widely used, representing therapy, and constituting 100% nutrient source in the first four to six months of life and half the daily nutrient intake in the second semester of life. In some cases, these products are used also for preventive purposes. Some impairments in growth have been reported for infants using these products, even if mostly limited to the first year of life, with no apparent consequences in either the medium or long term. The macronutrient content of infant formulae based on protein hydrolysates, whichever the source, should carefully be tested not only as far as the optimal utilization of nitrogenous sources but also on the nature and metabolic fate of non-nitrogen caloric sources, represented by carbohydrates and fats, and micronutrients, particularly iron. It is recommended that studies aimed at the allergologic effects of these products also include an appropriate nutritional evaluation to determine their efficiency.
Numerical Simulation of the Flow Field around Generic Formula One
Directory of Open Access Journals (Sweden)
Dang Tienphuc
2016-01-01
Full Text Available The steady Reynolds-Averaged Navier-Stokes (RANS method with the Realizable k turbulence model was used to analyze the flow field around a race car (generic Formula One. This study was conducted using the ANSYS software package. The numerical simulations were conducted at a Reynolds number based on the race car model (14.9×106. The time-averaged velocity field, flow topology, velocity magnitude, static pressure magnitude and vortex regions of the flow fields are presented in this paper. The measurements were performed on the vertical and cross-sectional planes. The results are presented graphically, showing the main characteristics of the flow field around the whole race car, whereas most previous studies only mention the flow field around individual components of race cars. The Realizable k turbulence model results showed consistency with the valuable validation data, which helps to elucidate the flow field around a model generic Formula one race car.
Formula student as part of a mechanical engineering curriculum
Davies, Huw Charles
2013-10-01
Formula Student (FS) is a multi-university student design competition managed by the UK Institution of Mechanical Engineers. Students are required to demonstrate and prove their creativity and engineering skills through the design, manufacture and financing of a small formula style race car. This paper seeks to explore the educational value that derives from the FS activity through a series of semi-structured interviews with key stakeholders. Through the analysis of the interview data, it was found that the FS activity supported development of student skills and competencies in the following areas: use of engineering knowledge to support the application of existing and emerging technology; application of theoretical and practical knowledge to the solution of engineering problems; development of technical and commercial management skills; development of effective interpersonal skills, including communication skills; and demonstration of personal commitment to professional development. In addition, a number of areas for implementing 'good practise' have been identified. The information herein supports educators in their responsibility to help meet the needs of the engineering industry for high quality graduates.
Macro-microscopic mass formulae and nuclear mass predictions
Royer, G.; Guilbaud, M.; Onillon, A.
2010-12-01
Different mass formulae derived from the liquid drop model and the pairing and shell energies of the Thomas-Fermi model have been studied and compared. They include or not the diffuseness correction to the Coulomb energy, the charge exchange correction term, the curvature energy, different forms of the Wigner term and powers of the relative neutron excess I=(N-Z)/A. Their coefficients have been determined by a least square fitting procedure to 2027 experimental atomic masses (G. Audi et al. (2003) [1]). The Coulomb diffuseness correction Z/A term or the charge exchange correction Z/A term plays the main role to improve the accuracy of the mass formula. The Wigner term and the curvature energy can also be used separately but their coefficients are very unstable. The different fits lead to a surface energy coefficient of around 17-18 MeV. A large equivalent rms radius ( r=1.22-1.24 fm) or a shorter central radius may be used. An rms deviation of 0.54 MeV can be reached between the experimental and theoretical masses. The remaining differences come probably mainly from the determination of the shell and pairing energies. Mass predictions of selected expressions have been compared to 161 new experimental masses and the correct agreement allows to provide extrapolations to masses of 656 selected exotic nuclei.
Cardy Formula for 4d SUSY Theories and Localization
Di Pietro, Lorenzo
2016-01-01
We study 4d $\\mathcal{N}=1$ supersymmetric theories on a compact Euclidean manifold of the form $S^1 \\times\\mathcal{M}_3$. Partition functions of gauge theories on this background can be computed using localization, and explicit formulas have been derived for different choices of the compact manifold $\\mathcal{M}_3$. Taking the limit of shrinking $S^1$, we present a general formula for the limit of the localization integrand, derived by simple effective theory considerations, generalizing the result of arXiv:1512.03376. The limit is given in terms of an effective potential for the holonomies around the $S^1$, whose minima determine the asymptotic behavior of the partition function. If the potential is minimized in the origin, where it vanishes, the partition function has a Cardy-like behavior fixed by $\\mathrm{Tr}(R)$, while a nontrivial minimum gives a shift in the coefficient. In all the examples that we consider, the origin is a minimum iff $\\mathrm{Tr}(R) \\leq 0$.
The mass formula for an exotic BTZ black hole
Energy Technology Data Exchange (ETDEWEB)
Zhang, Baocheng, E-mail: zhangbc.zhang@yahoo.com
2016-04-15
An exotic Bañados–Teitelboim–Zanelli (BTZ) black hole has an angular momentum larger than its mass in three dimension (3D), which suggests the possibility that cosmic censorship could be violated if angular momentum is extracted by the Penrose process. In this paper, we propose a mass formula for the exotic BTZ black hole and show no violation of weak cosmic censorship in the gedanken process above by understanding properly its mass formula. Unlike the other black holes, the total energy of the exotic BTZ black hole is represented by the angular momentum instead of the mass, which supports a basic point of view that the same geometry should be determined by the same energy in 3D general relativity whose equation of motion can be given either by normal 3D Einstein gravity or by exotic 3D Einstein gravity. However, only the mass of the exotic black hole is related to the thermodynamics and other forms of energy are “dumb”, which is consistent with the earlier thermodynamic analysis about exotic black holes.
The mass formula for an exotic BTZ black hole
Zhang, Baocheng
2016-01-01
An exotic Banados-Teitelboim-Zanelli (BTZ) black hole has an angular momentum larger than its mass in three dimension (3D), which suggests the possibility that cosmic censorship could be violated if angular momentum is extracted by the Penrose process. In this paper, we propose a mass formula for the exotic BTZ black hole and show no violation of weak cosmic censorship in the gedanken process above by understanding properly its mass formula. Unlike the other black holes, the total energy of the exotic BTZ black hole is represented by the angular momentum instead of the mass, which supports a basic point of view that the same geometry should be determined by the same energy in 3D general relativity whose equation of motion can be given either by normal 3D Einstein gravity or by exotic 3D Einstein gravity. However, only the mass of the exotic black hole is related to the thermodynamics and other forms of energy are "dumb", which is consistent with the earlier thermodynamic analysis about exotic black holes.
Plasticizers in total diet samples, baby food and infant formulae
DEFF Research Database (Denmark)
Petersen, Jens Højslev; Breindahl, T.
2000-01-01
The plasticizers di-n-butylphthalate (DBP), butylbenzylphthalate (BBP), di-2-(ethylhexyl)phthalate (DEHP) and di-2-(ethylhexyl)adipate (DEHA) were analysed in 29 total diet samples, in 11 samples of baby food and in 11 samples of infant formulae. In all of the total diet samples the presence of one...... or more of the plasticizers was demonstrated. Maximum and minimum mean concentrations in the total diet samples were: 0.09-0.19 mg DBP/kg, 0.017-0.019 mg BBP/kg, 0.11-0.18 mg DEHP/kg and 0.13-0.14 mg DEHA/kg. One or more of the phthalates was also found in about 50% of the samples of baby food as well...... as in infant formulae. The calculated mean maximum intakes of the individual compounds from the total diet samples were below 10% of the restrictions proposed by the EU Scientific Committee for Food (SCF), and the spread in individual intakes was considerable. DEHP was the plasticizer determined most...
Pontryagin invariants and integral formulas for Milnor's triple linking number
DeTurck, Dennis; Komendarczyk, Rafal; Melvin, Paul; Shonkwiler, Clayton; Vela-Vick, David Shea
2011-01-01
To each three-component link in the 3-sphere, we associate a geometrically natural characteristic map from the 3-torus to the 2-sphere, and show that the pairwise linking numbers and Milnor triple linking number that classify the link up to link homotopy correspond to the Pontryagin invariants that classify its characteristic map up to homotopy. This can be viewed as a natural extension of the familiar fact that the linking number of a two-component link in 3-space is the degree of its associated Gauss map from the 2-torus to the 2-sphere. When the pairwise linking numbers are all zero, we give an integral formula for the triple linking number analogous to the Gauss integral for the pairwise linking numbers. The integrand in this formula is geometrically natural in the sense that it is invariant under orientation-preserving rigid motions of the 3-sphere, while the integral itself can be viewed as the helicity of a related vector field on the 3-torus.
Brooke, O G; Wood, C; Barley, J
1982-12-01
Energy balance, nitrogen balance, and growth studies were done in 37 preterm infants (20 of very low birthweight) who were fed on expressed breast milk or on one of 3 formulae each of different composition, including a special premature formula and a highly adapted 'humanised' formula. The variability of breast milk composition was such that it would have been difficult to predict the infants' protein and energy intakes under normal nursing conditions. All measured parameters of nutritional performance were best in infants fed on the 'premature' formula and were reflected in greater weight gain, linear growth, and head growth. The nitrogen balance data suggest that the highly adapted formula, which had a protein content comparable with that of mature human milk, contained too little protein for small preterm infants.
Accuracy of Intraocular Lens Power Calculation Formulas for Highly Myopic Eyes
Zhang, Yichi; Liang, Xiao Ying; Liu, Shu; Lee, Jacky W. Y.; Bhaskar, Srinivasan; Lam, Dennis S. C.
2016-01-01
Purpose. To evaluate and compare the accuracy of different intraocular lens (IOL) power calculation formulas for eyes with an axial length (AL) greater than 26.00 mm. Methods. This study reviewed 407 eyes of 219 patients with AL longer than 26.0 mm. The refractive prediction errors of IOL power calculation formulas (SRK/T, Haigis, Holladay, Hoffer Q, and Barrett Universal II) using User Group for Laser Interference Biometry (ULIB) constants were evaluated and compared. Results. One hundred seventy-one eyes were enrolled. The Barrett Universal II formula had the lowest mean absolute error (MAE) and SRK/T and Haigis had similar MAE, and the statistical highest MAE were seen with the Holladay and Hoffer Q formulas. The interquartile range of the Barrett Universal II formula was also the lowest among all the formulas. The Barrett Universal II formulas yielded the highest percentage of eyes within ±1.0 D and ±0.5 D of the target refraction in this study (97.24% and 79.56%, resp.). Conclusions. Barrett Universal II formula produced the lowest predictive error and the least variable predictive error compared with the SRK/T, Haigis, Holladay, and Hoffer Q formulas. For high myopic eyes, the Barrett Universal II formula may be a more suitable choice. PMID:27119018
Accuracy of Intraocular Lens Power Calculation Formulas for Highly Myopic Eyes
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Yichi Zhang
2016-01-01
Full Text Available Purpose. To evaluate and compare the accuracy of different intraocular lens (IOL power calculation formulas for eyes with an axial length (AL greater than 26.00 mm. Methods. This study reviewed 407 eyes of 219 patients with AL longer than 26.0 mm. The refractive prediction errors of IOL power calculation formulas (SRK/T, Haigis, Holladay, Hoffer Q, and Barrett Universal II using User Group for Laser Interference Biometry (ULIB constants were evaluated and compared. Results. One hundred seventy-one eyes were enrolled. The Barrett Universal II formula had the lowest mean absolute error (MAE and SRK/T and Haigis had similar MAE, and the statistical highest MAE were seen with the Holladay and Hoffer Q formulas. The interquartile range of the Barrett Universal II formula was also the lowest among all the formulas. The Barrett Universal II formulas yielded the highest percentage of eyes within ±1.0 D and ±0.5 D of the target refraction in this study (97.24% and 79.56%, resp.. Conclusions. Barrett Universal II formula produced the lowest predictive error and the least variable predictive error compared with the SRK/T, Haigis, Holladay, and Hoffer Q formulas. For high myopic eyes, the Barrett Universal II formula may be a more suitable choice.