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Sample records for bethe-heitler-schiff formula

  1. Infant formula.

    Science.gov (United States)

    O'Connor, Nina R

    2009-04-01

    Although the American Academy of Pediatrics and the American Academy of Family Physicians recommend breast milk for optimal infant nutrition, many parents still choose formula as an acceptable alternative. The wide variety of available formulas is confusing to parents and physicians, but formulas can be classified according to three basic criteria: caloric density, carbohydrate source, and protein composition. Most infants require a term formula with iron. There is insufficient evidence to recommend supplementation with docosahexaenoic acid or arachidonic acid. Soy formulas are indicated for congenital lactase deficiency and galactosemia, but are not recommended for colic because of insufficient evidence of benefit. Hypoallergenic formulas with extensively hydrolyzed protein are effective for the treatment of milk protein allergy and the prevention of atopic disease in high-risk infants. Antireflux formulas decrease emesis and regurgitation, but have not been shown to affect growth or development. Most infants with reflux require no treatment. Family physicians can use these guidelines to counsel parents about infant formula, countering consumer advertising that is not evidence-based. PMID:19378873

  2. Makeham's Formula

    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...... consequences and their implications for the relation between the yield before tax and the yield after tax. We also show how Makeham's formula produces short-cut expressions for the duration and convexity of a bond and facilitates the analytical calculation of the yield in certain cases....

  3. Makeham's Formula

    DEFF Research Database (Denmark)

    Astrup Jensen, Bjarne

    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...

  4. Breastfeeding vs. Formula Feeding

    Science.gov (United States)

    ... Things to Know About Zika & Pregnancy Breastfeeding vs. Formula Feeding KidsHealth > For Parents > Breastfeeding vs. Formula Feeding ... with a lactation specialist. previous continue All About Formula Feeding Commercially prepared infant formulas are a nutritious ...

  5. Infant formulas - overview

    Science.gov (United States)

    ... based formulas should be used for infants with galactosemia , a rare condition. These formulas can also be ... free formulas: These formulas are also used for galactosemia and for children who can't digest lactose. ...

  6. Manipulation with Formulae

    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:

  7. Excel 2013 formulas

    CERN Document Server

    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

  8. SOME DUAL KINEMATIC FORMULAS

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    In this article, some kinematic formulas for dual quermassintegral of star bodies and for chord power integrals of convex bodies are established by using dual mixed volumes. These formulas are the extensions of the fundamental kinematic formula involving quermassintegral to the case of dual quermassintegral and chord power integrals.

  9. Designing State Aid Formulas

    Science.gov (United States)

    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…

  10. Machin's Formula and Pi

    OpenAIRE

    西山, 豊

    2011-01-01

    This article explains the calculation of Pi historically, focusing on Machin's formula. Archimedes' formula is shown first, followed by Machin's formula using Gregory's formula. Machin's formula makes particularly ingenious use of the tan double and quadruple angle trigonometric addition formulae. The chapter closes with an explanation of Takano's formula.

  11. Excel2003 Formulas

    CERN Document Server

    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

  12. China's Formula,Go!

    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.

  13. Tube formula, Berezinians, and Dwork formula

    CERN Document Server

    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?

  14. Perfect IFG-formulas

    CERN Document Server

    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.

  15. Selected Baking Formulas.

    Science.gov (United States)

    Bogdany, Melvin

    This manual is designed to help baking students learn to use formulas in the preparation of baking products. Tested and proven formulas are, for the most part, standard ones with only slight modifications. The recipes are taken mainly from bakery product manufacturers and are presented in quantities suitable for school-shop use. Each recipe…

  16. Formula misasi?! / Sten Soomlais

    Index Scriptorium Estoniae

    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

  17. Formulas as programs

    NARCIS (Netherlands)

    Apt, K.R.; Bezem, M.A.

    1998-01-01

    We provide here a computational interpretation of first-order logic based on a constructive interpretation of satisfiability w.r.t. a fixed but arbitrary interpretation. In this approach the emph{formulas themselves are emph{programs. This contrasts with the so-called emph{formulas as types approach

  18. Abbott Infant Formula Recall

    Data.gov (United States)

    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...

  19. Geometrization of Trace Formulas

    CERN Document Server

    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.

  20. Contributions to multidimensional quadrature formulas

    International Nuclear Information System (INIS)

    The general objective of this paper is to construct multidimensional quadrature formulas similar to the Gaussian Quadrature Formulas in one dimension. The correspondence between these formulas and orthogonal and nonnegative polynomials is established. One part of the paper considers the construction of multidimensional quadrature formulas using only methods of algebraic geometry, on the other part it is tried to obtain results on quadrature formulas with real nodes and, if possible, with positive weights. The results include the existence of quadrature formulas, information on the number resp. on the maximum possible number of points in the formulas for given polynomial degree N and the construction of formulas. (orig.)

  1. Fuel formula for lighters

    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.

  2. Formula Student 2012

    OpenAIRE

    Escuela Técnica Superior de Ingeniería Industrial

    2012-01-01

    Los integrantes del equipo de la UPCT conducirán el prototipo que ellos mismos han fabricado. La diferencia de estos jóvenes con un piloto profesional de Formula 1 está en que conocen al detalle la composición de cada elemento de su vehículo, porque ellos son los que han diseñado este monoplaza de carreras. En esta edición de la competición Formula Student, los alumnos estuvieron acompañados por Miguel Lucas, profesor asociado que forma parte de los tutores que participan en el proyecto Formu...

  3. 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.

  4. The Formula Essay Reconsidered

    Science.gov (United States)

    Haluska, Jan

    2012-01-01

    Bruce Pirie offers the following criticism about formula essays: "What does a five-paragraph essay teach about writing? It teaches that there are rules, and that those rules take the shape of a preordained form, like a cookie-cutter, into which we can pour ideas and expect them to come out well shaped." He goes on to discredit such essays as being…

  5. Formulas of Revised MRP

    Directory of Open Access Journals (Sweden)

    Alfredo Bregni

    2013-04-01

    innovation to the main process functioning. As a result, the proposed algorithm copes better with demand uncertainty, lowers the system nervousness and also removes the need for continuous forecast adjustments, thereby improving the ease in managing the material flow, allowing the development of new forms of collaboration among different supply chain partners and the creation of new business networks. The algorithm is presented in formulas to describe in detail each procedure step and calculations.

  6. Overview: Infant Formula and Fluorosis

    Science.gov (United States)

    ... Journal Articles for Community Water Fluoridation Overview: Infant Formula and Fluorosis Recommend on Facebook Tweet Share Compartir ... dentist or hygienist to see. Because most infant formulas contain low levels of fluoride, regularly mixing powdered ...

  7. Cronobacter Illness and Infant Formula

    Science.gov (United States)

    ... most at risk. Illnesses Linked to Powdered Infant Formula In some outbreak investigations, Cronobacter was found in ... other sources of this rare sickness. Powdered Infant Formula is Not Sterile Manufacturers report that, using current ...

  8. 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.

  9. Multiple Commutator Formulas

    OpenAIRE

    Hazrat, R.; Zhang, Z.

    2011-01-01

    Let A be a quasi-finite R-algebra (i.e., a direct limit of module finite algebras) with identity. Let I_i, i=0,...,m, be two-sided ideals of A, \\GL_n(A,I_i) the principal congruence subgroup of level I_i in GL_n(A) and E_n(A,I_i) be the relative elementary subgroup of level I_i. We prove a multiple commutator formula [E_n(A,I_0),\\GL_n(A,I_1),& \\GL_n(A, I_2),..., \\GL_n(A, I_m)] = [E_n(A,I_0),E_n(A,I_1),E_n(A, I_2),..., E_n(A, I_m)], which is a broad generalization of the standard commutator fo...

  10. Quadrature formulas for Fourier coefficients

    KAUST Repository

    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.

  11. Discontinuity formulas for multiparticle amplitudes

    International Nuclear Information System (INIS)

    It is shown how discontinuity formulas for multiparticle scattering amplitudes are derived from unitarity and analyticity. The assumed analyticity property is the normal analytic structure, which was shown to be equivalent to the space-time macrocausality condition. The discontinuity formulas to be derived are the basis of multi-particle fixed-t dispersion relations

  12. Discontinuity formulas for multiparticle amplitudes

    Energy Technology Data Exchange (ETDEWEB)

    Stapp, H.P.

    1976-03-01

    It is shown how discontinuity formulas for multiparticle scattering amplitudes are derived from unitarity and analyticity. The assumed analyticity property is the normal analytic structure, which was shown to be equivalent to the space-time macrocausality condition. The discontinuity formulas to be derived are the basis of multi-particle fixed-t dispersion relations.

  13. Algebraic Proofs over Noncommutative Formulas

    CERN Document Server

    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...

  14. Poetic grounds of epic formulae

    Directory of Open Access Journals (Sweden)

    Delić Lidija

    2013-01-01

    Full Text Available The study of oral formulae in the twentieth century had several phases. After the initial - very stimulating and influential - research by M. Parry and A. B. Lord, who focused on the technique of composing the poem and the mnemotechnic function of formulae, the focus at first shifted to the concept of performance (J. M. Foley, and then to the mental text (L. Honko, which introduced into research horizons social, ideological, psychological and mental conditions of improvisation, interaction between the singer and the audience, collective and individual factors of memorising, cultural representation, and the like. Although all the abovementioned aspects undoubtedly determine the structure of a specific variant, it should be kept in mind that formulae transcend concrete improvisations and connect different epic zones, different local traditions and different times. The formula precedes verbal improvisation both chronologically and logically. Therefore - before explaining the repeating of formulae by the needs and nature of improvisation (composition-in-performance or the generating of formulae in specific variants by textualisation of mental text - we must explain the existence of the formula in the first place. This paper seeks to point out the complex system of factors that determine the genesis of formulae. Formulae are regarded as cultural codes, which combine elements from different spheres (the conceptualization of space, time, colour and so on, elements of rituals, customary norms, historical experience, life realities, ethics, etc.. Therefore, their structure is described in terms of hidden knowledge, hidden complexity, frame semantics, the tip of the iceberg, compressed meanings. Meanings “compressed” in the formulae are upgraded with new “income” in every new/concrete realisation (i.e. poem and this is the area where aesthetics rivals poetics. [Projekat Ministarstva nauke Republike Srbije, br. 178011: Serbian Oral Tradition in an

  15. Generalized Klein-Nishina formula

    CERN Document Server

    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.

  16. 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.

  17. New approach to mass formulas

    International Nuclear Information System (INIS)

    The Regge approach to mass formulas is grounded. The main types of interrelations between meson masses are picked out and analysed. The spectrum of vector mesons with the fifth flavour is also evaluated

  18. CHY formula and MHV amplitudes

    CERN Document Server

    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.

  19. FDA Abbott Infant Formula Recall

    Data.gov (United States)

    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...

  20. Infant Formula - Buying, Preparing, Storing, and Feeding

    Science.gov (United States)

    ... page: //medlineplus.gov/ency/patientinstructions/000806.htm Infant Formula – Buying, Preparing, Storing, and Feeding To use the ... using infant formula . Buying, Preparing, and Storing Infant Formula The following tips can help you buy, prepare, ...

  1. A recursion formula for Bayesian probabilities

    NARCIS (Netherlands)

    Nijsse, M

    2003-01-01

    A recursion formula for Bayes' formula is derived. The formula is useful in applications in which diagnoses are added in a stepwise way to predict a criterion. On each step, changes in various diagnostic measures can be easily evaluated.

  2. An energy loss straggling formula

    International Nuclear Information System (INIS)

    The analytical formulae for straggling widths were obtained solving Symon's equations for the second and third order central moments of the straggling distributions in non-relativistic approximation, enabling prediction of peak widths and asymmetry parameters of charged particle energy loss distributions for thick targets. The respective calculations based on these formulae were found to be in good agreement with experimental values for particle energy losses of light ions up to 70% of the nominal projectile energy value. ((orig.))

  3. Quantum computing of semiclassical formulas.

    Science.gov (United States)

    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.

  4. 27 CFR 19.378 - Formula requirements.

    Science.gov (United States)

    2010-04-01

    ... Manufacture of Articles Formulas § 19.378 Formula requirements. An approved formula on TTB Form 5110.38 must be secured for spirits for domestic use or export as provided in 27 CFR 5.26-5.27 before processors... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula requirements....

  5. 24 CFR 92.50 - Formula allocation.

    Science.gov (United States)

    2010-04-01

    ... 24 Housing and Urban Development 1 2010-04-01 2010-04-01 false Formula allocation. 92.50 Section... Development HOME INVESTMENT PARTNERSHIPS PROGRAM Allocation Formula § 92.50 Formula allocation. (a) Jurisdictions eligible for a formula allocation. HUD will provide allocations of funds in amounts determined...

  6. Shuffle product formulas of multiple zeta values

    OpenAIRE

    Li, Zhonghua; Chen QIN

    2016-01-01

    Using the combinatorial description of shuffle product, we prove or reformulate several shuffle product formulas of multiple zeta values, including a general formula of the shuffle product of two multiple zeta values, some restricted shuffle product formulas of the product of two multiple zeta values, and a restricted shuffle product formula of the product of $n$ multiple zeta values.

  7. Reasoning on Schemata of Formulae

    CERN Document Server

    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.

  8. CHY formulae in 4d

    CERN Document Server

    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.

  9. 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.

  10. CHY formula and MHV amplitudes

    Science.gov (United States)

    Du, Yi-Jian; Teng, Fei; Wu, Yong-Shi

    2016-05-01

    In this paper, we study the relation between the Cachazo-He-Yuan (CHY) formula and the maximal-helicity-violating (MHV) amplitudes of Yang-Mills and gravity in four dimensions. We prove that only one special rational solution of the scattering equations found by Weinzierl supports the MHV amplitudes. Namely, localized at this solution, the integrated CHY formula produces the Parke-Taylor formula for MHV Yang-Mills amplitudes as well as the Hodges formula for MHV gravitational amplitudes, with an arbitrary number of external gluons/gravitons. This is achieved by developing techniques, in a manifestly Möbius covariant formalism, to explicitly compute relevant reduced Pfaffians/determinants. We observe and prove two interesting properties (or identities), which facilitate the computations. We also check that all the other ( n - 3)! - 1 solutions to the scattering equations do not support the MHV amplitudes, and prove analytically that this is indeed true for the other special rational solution proposed by Weinzierl, that actually supports the anti-MHV amplitudes. Our results reveal a mysterious feature of the CHY formalism that in Yang-Mills and gravity theory, solutions of scattering equations, involving only external momenta, somehow know about the configuration of external polarizations of the scattering amplitudes.

  11. Error estimates for quadrature formulas

    Energy Technology Data Exchange (ETDEWEB)

    Kalaida, A.F. [Kiev State Univ. (Ukraine)

    1994-06-05

    We construct two-sided polynomials of collocation type of the same order as a given system of basis functions according to a given ordered system of nodes of arbitrary multiplicity and according to a system of nodes displaced to the right (or to the left) at one position. Numerical estimates are given for the remaining terms of the quadrature formulas. 3 refs.

  12. The generalized Euler's formula from Poisson's summation formula and some applications

    International Nuclear Information System (INIS)

    The generalized Euler's formula is derived from Poisson's summation formula. In special cases, it reduces to the ordinary Euler's formula and Walfisz formula in one dimension. As an application, the generalized Euler's formula is used to calculate the expression for the number of quantum states of a single non-relativistic particle in a rectangular three-dimensional box of finite size. (Author)

  13. Blackhole formula and example relativity

    Science.gov (United States)

    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.

  14. Koide's Mass Formula for Neutrinos

    Science.gov (United States)

    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.

  15. The Callias index formula revisited

    CERN Document Server

    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.

  16. Hydrolyzed Formula for Every Infant?

    Science.gov (United States)

    Fleischer, David M; Venter, Carina; Vandenplas, Yvan

    2016-01-01

    Presently, hydrolyzed formulas (HF) are used primarily in infants that cannot be exclusively breastfed, those with cow's milk allergy and for primary prevention of allergic disease, but HFs are increasingly being used worldwide, begging the question if they may be recommended as the optimal choice for all standard-risk, full-term, non-exclusively breastfed infants. Data regarding the nutritional adequacy of modern-day HFs are scarce and lack long-term data suggesting that growth in infants fed HF versus an intact protein formula (IPF) is different. While human breast milk is the optimal source of nutrition for multiple reasons, a 2006 systematic review determined there were no comparable long-term studies regarding prolonged use of HFs versus breastfeeding. Meta-analyses of formula consumption and risk of atopic dermatitis (AD) have found that infants fed partially HF compared to IPF had a lower risk of AD, but there are significant limitations to these studies, making conclusions about the general use of HFs problematic. Costs should be considered in decision-making regarding the choice of the formula, but global comparison of this is difficult given large cost differences in different countries. Despite the issues raised here, the desire to provide concrete recommendations of widespread HF use needs to be balanced carefully in order not to overstate claims of benefit. Long-term studies are needed to investigate the feasibility of HF as a routine feeding option for healthy, standard-risk infants. Because of the paucity of data, routine use of HF as an equivalent option to breastfeeding or IPF cannot be supported at present based on available scientific evidence.

  17. Hydrolyzed Formula for Every Infant?

    Science.gov (United States)

    Fleischer, David M; Venter, Carina; Vandenplas, Yvan

    2016-01-01

    Presently, hydrolyzed formulas (HF) are used primarily in infants that cannot be exclusively breastfed, those with cow's milk allergy and for primary prevention of allergic disease, but HFs are increasingly being used worldwide, begging the question if they may be recommended as the optimal choice for all standard-risk, full-term, non-exclusively breastfed infants. Data regarding the nutritional adequacy of modern-day HFs are scarce and lack long-term data suggesting that growth in infants fed HF versus an intact protein formula (IPF) is different. While human breast milk is the optimal source of nutrition for multiple reasons, a 2006 systematic review determined there were no comparable long-term studies regarding prolonged use of HFs versus breastfeeding. Meta-analyses of formula consumption and risk of atopic dermatitis (AD) have found that infants fed partially HF compared to IPF had a lower risk of AD, but there are significant limitations to these studies, making conclusions about the general use of HFs problematic. Costs should be considered in decision-making regarding the choice of the formula, but global comparison of this is difficult given large cost differences in different countries. Despite the issues raised here, the desire to provide concrete recommendations of widespread HF use needs to be balanced carefully in order not to overstate claims of benefit. Long-term studies are needed to investigate the feasibility of HF as a routine feeding option for healthy, standard-risk infants. Because of the paucity of data, routine use of HF as an equivalent option to breastfeeding or IPF cannot be supported at present based on available scientific evidence. PMID:27336594

  18. Analyzing Walksat on random formulas

    CERN Document Server

    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).

  19. Koppelman formulas on flag manifolds

    CERN Document Server

    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.

  20. Antibiotics, Formula Feeding Might Change Baby's 'Microbiome'

    Science.gov (United States)

    ... nih.gov/medlineplus/news/fullstory_159392.html Antibiotics, Formula Feeding Might Change Baby's 'Microbiome' C-section birth ... microbiomes" are altered by cesarean births, antibiotics and formula feeding. "The microbiome is really important in how ...

  1. A Wald-like Formula for Energy

    OpenAIRE

    Amsel, Aaron J.; Gorbonos, Dan

    2012-01-01

    We present a simple "Wald-like" formula for gravitational energy about a constant curvature background spacetime. The formula is derived following the Abbott-Deser-Tekin approach for the definition of conserved asymptotic charges in higher-derivative gravity.

  2. Simple and Clear Proofs of Stirling's Formula

    Science.gov (United States)

    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.

  3. 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.

  4. Lefschetz Formulae for p-Adic Groups

    Institute of Scientific and Technical Information of China (English)

    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.

  5. 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.

  6. A dimensionally continued Poisson summation formula

    OpenAIRE

    Johnson-McDaniel, Nathan K.

    2010-01-01

    We generalize the standard Poisson summation formula for lattices so that it operates on the level of theta series, allowing us to introduce noninteger dimension parameters (using the dimensionally continued Fourier transform). When combined with one of the proofs of the Jacobi imaginary transformation of theta functions that does not use the Poisson summation formula, our proof of this generalized Poisson summation formula also provides a new proof of the standard Poisson summation formula f...

  7. Some practical Runge-Kutta formulas

    International Nuclear Information System (INIS)

    A new selection is made of the most practical of the many explicit Runge-Kutta formulas of order 4 which have been proposed. A new formula is considered, formulas are modified to improve their quality and efficiency in agreement with improved understanding of the issues, and formulas are derived which permit interpolation. It is possible to do a lot better than the pair of Fehlberg currently regarded as ''best''

  8. On an improved effective range formula

    International Nuclear Information System (INIS)

    A new effective range formula is derived using a conformal mapping variable that incorporates the knowledge of the left-hand cut. Our formula is valid up to higher energies and has good convergence and extrapolation properties. As an illustration, we use the formula for a study of the S and P waves in the n-p scattering. (author)

  9. 10 CFR 905.33 - Extension formula.

    Science.gov (United States)

    2010-01-01

    ... 10 Energy 4 2010-01-01 2010-01-01 false Extension formula. 905.33 Section 905.33 Energy DEPARTMENT... formula. (a) The amount of power to be extended to an existing customer shall be determined according to this formula: Customer Contract Rate of Delivery (CROD) today/total project CROD under contract...

  10. 25 CFR 273.31 - Distribution formula.

    Science.gov (United States)

    2010-04-01

    ... 25 Indians 1 2010-04-01 2010-04-01 false Distribution formula. 273.31 Section 273.31 Indians... formula. (a) Funds shall be distributed to eligible contractors based upon the number of eligible Indian... formula. (b) The Assistant Secretary may make exceptions to the provisions of paragraph (a) of...

  11. 15 CFR 923.110 - Allocation formula.

    Science.gov (United States)

    2010-01-01

    ... 15 Commerce and Foreign Trade 3 2010-01-01 2010-01-01 false Allocation formula. 923.110 Section... Grants § 923.110 Allocation formula. (a) As required by subsection 306(a), the Secretary may make grants...) Allocation formula factors and weighting. Each State eligible to receive a financial assistance award...

  12. 27 CFR 26.31 - Formula.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula. 26.31 Section 26... States From Areas Other Than Puerto Rico and the Virgin Islands § 26.31 Formula. (a) The amount of excise.... The formula shall be as follows: (1) Multiply the total excise taxes collected on rum brought into...

  13. 27 CFR 20.91 - Formula.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula. 20.91 Section 20... TREASURY LIQUORS DISTRIBUTION AND USE OF DENATURED ALCOHOL AND RUM Formulas and Statements of Process § 20.91 Formula. (a) Each article made with specially denatured spirits shall be made in accordance...

  14. 27 CFR 24.196 - Formula required.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula required. 24.196... OF THE TREASURY LIQUORS WINE Production of Special Natural Wine § 24.196 Formula required. Before producing any special natural wine, the proprietor shall receive approval of the formula by which it is...

  15. 7 CFR 251.7 - Formula adjustments.

    Science.gov (United States)

    2010-01-01

    ... 7 Agriculture 4 2010-01-01 2010-01-01 false Formula adjustments. 251.7 Section 251.7 Agriculture... GENERAL REGULATIONS AND POLICIES-FOOD DISTRIBUTION THE EMERGENCY FOOD ASSISTANCE PROGRAM § 251.7 Formula adjustments. Formula adjustments. (a) Commodity adjustments. The Department will make annual adjustments...

  16. 27 CFR 24.201 - Formula required.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula required. 24.201... OF THE TREASURY LIQUORS WINE Production of Agricultural Wine § 24.201 Formula required. Before producing any agricultural wine, the proprietor shall obtain an approval of the formula and process by...

  17. 27 CFR 24.211 - Formula required.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula required. 24.211... OF THE TREASURY LIQUORS WINE Production of Other Than Standard Wine § 24.211 Formula required. The proprietor who desires to produce wine other than standard wine shall first obtain approval of the formula...

  18. 24 CFR 574.130 - Formula allocations.

    Science.gov (United States)

    2010-04-01

    ... 24 Housing and Urban Development 3 2010-04-01 2010-04-01 false Formula allocations. 574.130... URBAN DEVELOPMENT COMMUNITY FACILITIES HOUSING OPPORTUNITIES FOR PERSONS WITH AIDS Formula Entitlements § 574.130 Formula allocations. (a) Data sources. HUD will allocate funds based on the number of cases...

  19. 27 CFR 25.57 - Formula information.

    Science.gov (United States)

    2010-04-01

    ... that covers the production of any beer base used in producing the formula product. If the beer base was... OF THE TREASURY LIQUORS BEER Miscellaneous Provisions Formulas § 25.57 Formula information. (a... content of the flavor; and the point of production at which the flavor was added (that is, before,...

  20. 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.

  1. 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.

  2. 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.

  3. The Verlinde formula for Higgs bundles

    CERN Document Server

    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.

  4. Kac formulas for the extended Virasoro algebras

    International Nuclear Information System (INIS)

    The determination method of the conformal dimension (Kac formula) of the primary fields in the minimal models with c < 1 from the point of G/H picture is generalized. As a result all the known formulas are reproduced. Furthermore the rather general Kac formulas are derived. The connection between the ordinary method and our method is discussed. (author)

  5. 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.

  6. Welfare Effects of Tariff Reduction Formulas

    DEFF Research Database (Denmark)

    Guldager, Jan G.; Schröder, Philipp J.H.

    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....... 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...

  7. Rice formulas and Gaussian waves

    CERN Document Server

    Azaïs, Jean-Marc; Wschebor, Mario

    2011-01-01

    We use Rice's formulas in order to compute the moments of some level functionals which are linked to problems in oceanography and optics: the number of specular points in one and two dimensions, the distribution of the normal angle of level curves and the number 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 cases we are able to use these computations to obtain a Central Limit Theorem.

  8. 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.)

  9. Multidimensional Datawarehouse with Combination Formula

    CERN Document Server

    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.

  10. Preclinical assessment of infant formula.

    Science.gov (United States)

    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.

  11. Cosmological parallax-distance formula

    Science.gov (United States)

    Singal, Ashok K.

    2015-09-01

    The standard cosmological parallax-distance formula, as found in the literature, including text-books and reference books on cosmology, requires a correction. This correction stems from the fact that in the standard text-book derivation it has been ignored that any chosen baseline in a gravitationally bound system does not partake in the cosmological expansion. Though the correction is available in the literature for some time, the text-books still continue to use the older, incorrect formula, and its full implications are not yet fully realized. Apart from providing an alternate correct, closed-form expression that is more suitable and convenient for computations for certain limiting cases of FRW () world models, we also demonstrate how one can compute parallax distance for the currently favored flat-space accelerating-universe (, ) cosmologies. Further, we show that the correction in parallax distance at large redshifts could amount to a factor of three or even more. Moreover, even in an infinite universe the parallax distance does not increase indefinitely with redshift and that even the farthest possible observable point may have a finite parallax angle, a factor that needs to be carefully taken into account when using distant objects as the background field against which the parallax of a foreground object is to be measured. Some other complications that could arise in parallax measurements of a distant source, like that due to the deflection of incoming light by the gravitation field of the Sun and other planetary bodies in the solar system, are pointed out.

  12. 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.

  13. [Hypoallergenic milks (HA formulas) in infant nutrition].

    Science.gov (United States)

    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.

  14. Developing a Weighted Collection Development Allocation Formula

    OpenAIRE

    Bailey, Jeff; Creibaum, Linda

    2015-01-01

    In this session the presenters demonstrated and discussed how to create a spreadsheet‐based library collection development allocation formula to help acquisitions personnel better manage their library’s limited collection development resources. The presenters demonstrated and led participants through Arkansas State University’s process of creating an Excel‐based formula that utilizes criteria relevant to their specific library and institution. Key to the success of this formula is the use of ...

  15. A General Framework for Probabilistic Characterizing Formulae

    DEFF Research Database (Denmark)

    Sack, Joshua; Zhang, Lijun

    2012-01-01

    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 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...

  16. Column Holdup Formula of Soil Solute Transport

    Institute of Scientific and Technical Information of China (English)

    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.

  17. Reconstruction Formulas for Photoacoustic Sectional Imaging

    CERN Document Server

    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.

  18. The fringe capacitance formula of microstructures

    International Nuclear Information System (INIS)

    This paper presents a fringe capacitance formula of microstructures. The formula is derived by curve fitting on ANSYS simulation results. Compared with the ANSYS and experimental results, the deviation is within ±2%. The application to determine the pull-in voltage of an electrostatic micro-beam is demonstrated, which agrees very well with the experimental data. The formula presented is very accurate, yields explicit physical meanings and is applicable to common dimension ranges for MEMS devices. (paper)

  19. 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...... passing through fixed points are related to the geometry of the sectioned object. In particular it is shown how certain weighting factors, appearing in the rotational integral formula, can be expressed in terms of hypergeometric functions. Close connections to geometric tomography will be pointed out...

  20. Rotational versions of the Crofton formula

    DEFF Research Database (Denmark)

    Jensen, Eva B. Vedel

    1995-01-01

    Inspired by recent developments in stereology, rotational versions of the Crofton formula are derived. The first version involves rotation averages of Minkowski functionals. It is shown that for the special case where the Minkowski functional is surface area, the rotation average can be expressed...... in terms of hypergeometric functions. The second rotational version of the Crofton formula solves the `opposite' problem of finding functions with rotation averages equal to the Minkowski functionals. For the case of surface area, hypergeometric functions appear again. The second type of rotational...... Crofton formula has applications in local stereology. As a by-product, a formula involving mixed volumes is found....

  1. AN ANALYTICAL REFLECTION OF FORMULAIC LANGUAGE

    Institute of Scientific and Technical Information of China (English)

    LiuSiping

    2004-01-01

    This paper gives a brief panorama of formulaic language, inwhich some of the author's analytical and critical reflections canbe found. First, a rough review is made of various definitionsand identification of formulaic language, a topic that hasremained unsettled to date (Wray, 2000 ). Among thediversified terminology, my own definition is included as areflection of my understating. Next, transferability ofunanalysed formulae to analytical competence, will follow. Asthis topic has aroused heated discussion, it is very hard to reacha consensus. The last section, under the title of rationale andfunctions, is devoted to various features of formulaic language,which include econornicality, acceptability, dependability, anddifficulty.

  2. Non-Commutative Q-Binomial Formula

    CERN Document Server

    Nalci, Sengul

    2012-01-01

    In this paper, we found new q-binomial formula for Q-commutative operators. Expansion coefficients in this formula are given by q-binomial coefficients with two bases (q,Q), determined by Q-commutative q-Pascal triangle. Our formula generalizes all well-known binomial formulas in the form of Newton, Gauss, symmetrical, non-commutative and Binet-Fibonacci binomials. By our non-commutative q-binomial, we introduce q-analogue of function of two non-commutative variables, which could be used in study of non-commutative q-analytic functions and non- commutative q-traveling waves.

  3. Preclinical assessment of infant formula.

    Science.gov (United States)

    Lönnerdal, Bo

    2012-01-01

    Infant formulas are the sole or predominant source of nutrition for many infants and are fed during a sensitive period of development and may therefore have short- and long-term consequences for infant health. Preclinical safety assessment therefore needs to include both short-term and long-term studies in animals. It is recommended that procedures are instituted by which experts may serve as independent scientists for companies developing novel products, without having their integrity compromised, and later serve the legislative institutions. A two-level assessment approach to determine the potential toxicity of a novel ingredient, its metabolites, and their effects in the matrix on developing organ systems has been suggested by IOM. This appears reasonable, as novel ingredients can be of different levels of concern. The use of modern methods in genomics and proteomics should be considered in these evaluation processes as well as novel methods to evaluate outcomes, including metabolomics and molecular techniques to assess the microbiome. PMID:22699767

  4. Gaussian Integral Formula for Quaternions Based on Class Operator's Formula of Rotation Group

    Institute of Scientific and Technical Information of China (English)

    FAN Hong-Yi; XU Zhi-Hua

    2008-01-01

    There exists rare integration formulas over quaternions due to the noncommutativity of quarternions mult-plication. Based on the class operator's formula of rotation group we derive a Gaussian integral formula for quaternions, which is similar in form to the integration for coherent state's completeness relation.

  5. How to Save Money on Infant Formula

    Science.gov (United States)

    ... or the lowest price. Save formula coupons and free samples, even if you plan to breastfeed. You may decide to supplement with formula a few months from now, and those coupons will save you money. Sign up for newsletters, special programs, and deals ...

  6. The health implications of soy infant formula

    Science.gov (United States)

    Soy formula (SF) has been fed to millions of infants worldwide. It has been shown to promote growth and development as well as milk-based formula (MF) does. Controversy has developed over the adequacy and safety of SF. Most concerns are based on in vivo and in vitro data that raise the possibility o...

  7. The propositional formula checker HeerHugo

    NARCIS (Netherlands)

    Groote, J.F.; Warners, J.P.

    1999-01-01

    HeerHugo is a propositional formula checker that determines whether a given formula is satisfiable or not. Its main ingredient is the branch/merge rule, that is inspired by an algorithm proposed by Staa llmarck, which is protected by a software patent. The algorithm can be interpreted as a breadth f

  8. A Choice of a New Funding Formula

    Science.gov (United States)

    Hancock, Kenneth

    2008-01-01

    This report examines the fiscal neutrality of three funding formulas that have been proposed to replace the current funding formula for Oklahoma's common schools in an attempt to have greater equity in the distribution of funds to the various districts. Using data from SY-03 to SY-07, calculations of state aid for the 540- districts and fiscal…

  9. 38 CFR 9.12 - Reinsurance formula.

    Science.gov (United States)

    2010-07-01

    ... 38 Pensions, Bonuses, and Veterans' Relief 1 2010-07-01 2010-07-01 false Reinsurance formula. 9.12 Section 9.12 Pensions, Bonuses, and Veterans' Relief DEPARTMENT OF VETERANS AFFAIRS SERVICEMEMBERS' GROUP LIFE INSURANCE AND VETERANS' GROUP LIFE INSURANCE § 9.12 Reinsurance formula. The allocation...

  10. Formula Approaches for Market Access Negotiations

    NARCIS (Netherlands)

    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

  11. Emergence String and Mass Formulas of Hadrons

    CERN Document Server

    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.

  12. Formulas in Physics Have a "Standard" Form

    Science.gov (United States)

    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…

  13. 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.

  14. Calculating the Greeks by Cubature formulas

    OpenAIRE

    Teichmann, Josef

    2004-01-01

    We provide cubature formulas for the calculation of derivatives of expected values in the spririt of Terry Lyons and Nicolas Victoir. In financial mathematics derivatives of option prices with respect to initial values, so called Greeks, are of particular importance as hedging parameters. Cubature formulas allow to calculate these quantities very quickly. Simple examples are added to the theoretical exposition.

  15. 40 CFR 74.26 - Allocation formula.

    Science.gov (United States)

    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...

  16. 27 CFR 5.26 - Formula requirements.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula requirements. 5.26 Section 5.26 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS LABELING AND ADVERTISING OF DISTILLED SPIRITS Formulas § 5.26...

  17. 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...

  18. Sample size: from formulae to concepts - II

    Directory of Open Access Journals (Sweden)

    Rakesh R. Pathak

    2013-02-01

    Full Text Available Sample size formulae need some input data or to say it otherwise we need some parameters to calculate sample size. This second part on the formula explanation gives ideas of Z, population size, precision of error, standard deviation, contingency etc which influence sample size. [Int J Basic Clin Pharmacol 2013; 2(1.000: 94-95

  19. 101 ready-to-use Excel formulas

    CERN Document Server

    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...

  20. 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...

  1. 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.

  2. Menemukan Formula Sinematografi Seni Pertunjukan

    Directory of Open Access Journals (Sweden)

    Arif Eko Suprihono

    2013-11-01

    Full Text Available Fokus dari sinematografi untuk seni pertunjukan dimaksudkan untuk diskusi tentang pembuatan pilihanpencahayaan dan kamera saat merekam aktivitas seni pertunjukan di panggung untuk program televisi. Televisiadalah bentuk di mana sesuatu disampaikan, dicapai, atau ditransfer ke sejumlah besar orang. Isu ‘efek’ televisikehilangan program-program yang mengarah perlu diminta tidak hanya dalam hal efek atau kegiatan penontontetapi juga dalam hal kesempatan yang hilang bagi keanekaragaman budaya yang akan diekspresikan pada kreativitastelevisi. Setiap aspek dari televisi menunjukkan ketergantungan pada genre, yang merupakan kelompok kategorisproses diskursif yang transek teks melalui interaksi budaya mereka dengan industri, penonton, dan konteks yanglebih luas. Kita mungkin mulai diskusi dengan memulai dengan contoh tekstual seperti ketoprak humor, wayangkulit, opera van java sebagai praktek industri, pergeseran sejarah, atau kontroversi penonton.Kata kunci: sinematografi , seni pertunjukan, ketoprak humorABSTRACTThe Formula of Performing Arts Cinematography. The focus of cinematography for performing arts is intendedto a discussion about the making of lighting and camera choices when recording performing arts activities on stage for thetelevision programs. Television is the form in which something is conveyed, accomplished, or transferred to a large numberof people. The issues of ‘the effects’ of television miss leading programs needs to be asked not only in terms of effects oraudience activity but also in terms of missing opportunities for cultural diversity to be expressed on television creativities.Every aspect of television exhibits a reliance on genre, which are categorical clusters of discursive processes that transect textsvia their cultural interactions with industries, audiences, and broader contexts. We might begin a discussion by startingwith a textual example such as ketoprak humor, wayang kulit, opera van java as an industrial

  3. 27 CFR 21.66 - Formula No. 38-C.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 38-C. 21.66... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.66 Formula No. 38-C. (a) Formula. To every 100 gallons of alcohol add:...

  4. 27 CFR 21.70 - Formula No. 39-A.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 39-A. 21.70... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.70 Formula No. 39-A. (a) Formula. To every 100 gallons of alcohol add:...

  5. 27 CFR 21.68 - Formula No. 38-F.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 38-F. 21.68... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.68 Formula No. 38-F. (a) Formula. To every 100 gallons of alcohol add:...

  6. 27 CFR 21.55 - Formula No. 28-A.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 28-A. 21.55... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.55 Formula No. 28-A. (a) Formula. To every 100 gallons of alcohol add:...

  7. 27 CFR 21.58 - Formula No. 31-A.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 31-A. 21.58... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.58 Formula No. 31-A. (a) Formula. To every 100 gallons of alcohol add:...

  8. 27 CFR 21.62 - Formula No. 35-A.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 35-A. 21.62... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.62 Formula No. 35-A. (a) Formula. To every 100 gallons of alcohol add:...

  9. 27 CFR 21.67 - Formula No. 38-D.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 38-D. 21.67... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.67 Formula No. 38-D. (a) Formula. To every 100 gallons of alcohol add:...

  10. 27 CFR 24.127 - Adoption of formulas.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Adoption of formulas. 24... Establishment § 24.127 Adoption of formulas. The adoption of approved formulas by a successor proprietor will be... formulas for adoption by formula number, name of product, and date of approval. The application...

  11. 27 CFR 20.115 - Ink general-use formula.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Ink general-use formula..., DEPARTMENT OF THE TREASURY LIQUORS DISTRIBUTION AND USE OF DENATURED ALCOHOL AND RUM Formulas and Statements of Process General-Use Formulas § 20.115 Ink general-use formula. Ink general-use formula is...

  12. 27 CFR 21.38 - Formula No. 4.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 4. 21.38... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.38 Formula No. 4. (a) Formula. To every 100 gallons of alcohol, or to...

  13. 27 CFR 21.39 - Formula No. 6-B.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 6-B. 21.39... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.39 Formula No. 6-B. (a) Formula. To every 100 gallons of alcohol add:...

  14. 27 CFR 21.34 - Formula No. 2-C.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 2-C. 21.34... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.34 Formula No. 2-C. (a) Formula. To every 100 gallons of alcohol add:...

  15. 27 CFR 21.46 - Formula No. 22.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 22. 21.46... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.46 Formula No. 22. (a) Formula. To every 100 gallons of alcohol add:...

  16. 27 CFR 21.44 - Formula No. 19.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 19. 21.44... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.44 Formula No. 19. (a) Formula. To every 100 gallons of alcohol add:...

  17. 27 CFR 21.33 - Formula No. 2-B.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 2-B. 21.33... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.33 Formula No. 2-B. (a) Formula. To every 100 gallons of alcohol add:...

  18. 27 CFR 21.32 - Formula No. 1.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 1. 21.32... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.32 Formula No. 1. (a) Formula. To every 100 gallons of alcohol add:...

  19. 27 CFR 21.52 - Formula No. 27.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 27. 21.52... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.52 Formula No. 27. (a) Formula. To every 100 gallons of alcohol add:...

  20. 27 CFR 21.45 - Formula No. 20.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 20. 21.45... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.45 Formula No. 20. (a) Formula. To every 100 gallons of alcohol add:...

  1. 27 CFR 21.50 - Formula No. 25.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 25. 21.50... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.50 Formula No. 25. (a) Formula. To every 100 gallons of alcohol add:...

  2. 27 CFR 21.42 - Formula No. 17.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 17. 21.42... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.42 Formula No. 17. (a) Formula. To every 100 gallons of alcohol add:...

  3. 27 CFR 21.36 - Formula No. 3-B.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 3-B. 21.36... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.36 Formula No. 3-B. (a) Formula. To every 100 gallons of alcohol add:...

  4. 27 CFR 21.24 - Formula No. 20.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 20. 21.24... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Completely Denatured Alcohol Formulas § 21.24 Formula No. 20. (a) Formula. To every 100 gallons of ethyl alcohol of not less than 195...

  5. 27 CFR 21.43 - Formula No. 18.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 18. 21.43... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.43 Formula No. 18. (a) Formula. To every 100 gallons of alcohol of not...

  6. 27 CFR 21.48 - Formula No. 23-F.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 23-F. 21.48... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.48 Formula No. 23-F. (a) Formula. To every 100 gallons of alcohol add:...

  7. 27 CFR 21.53 - Formula No. 27-A.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 27-A. 21.53... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.53 Formula No. 27-A. (a) Formula. To every 100 gallons of alcohol add:...

  8. 27 CFR 21.51 - Formula No. 25-A.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 25-A. 21.51... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.51 Formula No. 25-A. (a) Formula. To every 100 gallons of alcohol add:...

  9. 27 CFR 21.40 - Formula No. 12-A.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 12-A. 21.40... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.40 Formula No. 12-A. (a) Formula. To every 100 gallons of alcohol add:...

  10. 27 CFR 21.54 - Formula No. 27-B.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 27-B. 21.54... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.54 Formula No. 27-B. (a) Formula. To every 100 gallons of alcohol add:...

  11. 27 CFR 21.41 - Formula No. 13-A.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 13-A. 21.41... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.41 Formula No. 13-A. (a) Formula. To every 100 gallons of alcohol add:...

  12. 27 CFR 21.63 - Formula No. 36.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 36. 21.63... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.63 Formula No. 36. (a) Formula. To every 100 gallons of alcohol add:...

  13. 27 CFR 21.56 - Formula No. 29.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 29. 21.56... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.56 Formula No. 29. (a) Formula. To every 100 gallons of alcohol add:...

  14. 27 CFR 21.60 - Formula No. 33.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 33. 21.60... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.60 Formula No. 33. (a) Formula. To every 100 gallons of alcohol add:...

  15. 27 CFR 21.61 - Formula No. 35.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 35. 21.61... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.61 Formula No. 35. (a) Formula. To every 100 gallons of alcohol add:...

  16. 27 CFR 21.57 - Formula No. 30.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 30. 21.57... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.57 Formula No. 30. (a) Formula. To every 100 gallons of alcohol add:...

  17. 27 CFR 21.59 - Formula No. 32.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 32. 21.59... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.59 Formula No. 32. (a) Formula. To every 100 gallons of alcohol add:...

  18. 27 CFR 21.64 - Formula No. 37.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 37. 21.64... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.64 Formula No. 37. (a) Formula. To every 100 gallons of alcohol add:...

  19. Fundamental formulas of physics, v.1

    CERN Document Server

    1960-01-01

    The republication of this book, unabridged and corrected, fills the need for a comprehensive work on fundamental formulas of mathematical physics. It ranges from simple operations to highly sophisticated ones, all presented most lucidly with terms carefully defined and formulas given completely. In addition to basic physics, pertinent areas of chemistry, astronomy, meteorology, biology, and electronics are also included.This is no mere listing of formulas, however. Mathematics is integrated into text, for the most part, so that each chapter stands as a brief summary or even short textbook of

  20. Approximate formulas for moderately small eikonal amplitudes

    CERN Document Server

    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.

  1. 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.

  2. Ricci Curvature and Bochner Formulas for Martingales

    OpenAIRE

    Haslhofer, Robert; Naber, Aaron

    2016-01-01

    We generalize the classical Bochner formula for the heat flow on M to martingales on the path space PM, and develop a formalism to compute evolution equations for martingales on path space. We see that our Bochner formula on PM is related to two sided bounds on Ricci curvature in much the same manner that the classical Bochner formula on M is related to lower bounds on Ricci curvature. Using this formalism, we obtain new characterizations of bounded Ricci curvature, new gradient estimates for...

  3. [Formula: see text] and [Formula: see text] Spoken Word Processing: Evidence from Divided Attention Paradigm.

    Science.gov (United States)

    Shafiee Nahrkhalaji, Saeedeh; Lotfi, Ahmad Reza; Koosha, Mansour

    2016-10-01

    The present study aims to reveal some facts concerning first language ([Formula: see text] and second language ([Formula: see text] spoken-word processing in unbalanced proficient bilinguals using behavioral measures. The intention here is to examine the effects of auditory repetition word priming and semantic priming in first and second languages of these bilinguals. The other goal is to explore the effects of attention manipulation on implicit retrieval of perceptual and conceptual properties of spoken [Formula: see text] and [Formula: see text] words. In so doing, the participants performed auditory word priming and semantic priming as memory tests in their [Formula: see text] and [Formula: see text]. In a half of the trials of each experiment, they carried out the memory test while simultaneously performing a secondary task in visual modality. The results revealed that effects of auditory word priming and semantic priming were present when participants processed [Formula: see text] and [Formula: see text] words in full attention condition. Attention manipulation could reduce priming magnitude in both experiments in [Formula: see text]. Moreover, [Formula: see text] word retrieval increases the reaction times and reduces accuracy on the simultaneous secondary task to protect its own accuracy and speed. PMID:26643309

  4. A note on Marino-Vafa formula

    Institute of Scientific and Technical Information of China (English)

    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.

  5. Some Simple Computational Formulas for Multiple Regression

    Science.gov (United States)

    Aiken, Lewis R., Jr.

    1974-01-01

    Short-cut formulas are presented for direct computation of the beta weights, the standard errors of the beta weights, and the multiple correlation coefficient for multiple regression problems involving three independent variables and one dependent variable. (Author)

  6. On noetherianity for logical formulas over fields

    OpenAIRE

    Berzins, Aivars

    2008-01-01

    In this paper we consider noetherianity for formulas of propositional and predicate calculus over different fields. Three types of noetherianity are considered: standard noetherianity, logical noetherianity and denumerable noetherianity.

  7. 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

  8. Newton Binomial Formulas in Schubert Calculus

    OpenAIRE

    Cordovez, Jorge; Gatto, Letterio; Santiago, Taise

    2008-01-01

    We prove Newton's binomial formulas for Schubert Calculus to determine numbers of base point free linear series on the projective line with prescribed ramification divisor supported at given distinct points.

  9. 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.

  10. "Formula Student" / Malle Jürves

    Index Scriptorium Estoniae

    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

  11. The Metaplectic Casselman-Shalika Formula

    CERN Document Server

    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.

  12. A Delayed Black and Scholes Formula I

    OpenAIRE

    Mercedes Arriojas; Yaozhong Hu; Salah-Eldin Mohammed; Gyula Pap

    2006-01-01

    In this article we develop an explicit formula for pricing European options when the underlying stock price follows a non-linear stochastic differential delay equation (sdde). We believe that the proposed model is sufficiently flexible to fit real market data, and is yet simple enough to allow for a closed-form representation of the option price. Furthermore, the model maintains the no-arbitrage property and the completeness of the market. The derivation of the option-pricing formula is based...

  13. Some formulae for double Clausenian functions

    DEFF Research Database (Denmark)

    Karlsson, Per W.

    2000-01-01

    For certain third-order hypergeometric functions of two variables, reduction and transformation formulae under various conditions upon the parameters are derived from an Euler integral representation that requires one relation between parameters.......For certain third-order hypergeometric functions of two variables, reduction and transformation formulae under various conditions upon the parameters are derived from an Euler integral representation that requires one relation between parameters....

  14. 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.

  15. Macdonald formula for curves with planar singularities

    CERN Document Server

    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.

  16. A product formula and combinatorial field theory

    CERN Document Server

    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.

  17. 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

  18. Connected formulas for amplitudes in standard model

    CERN Document Server

    He, Song

    2016-01-01

    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.

  19. Bellco Formula Domus Home Care System.

    Science.gov (United States)

    Trewin, Elizabeth

    2004-01-01

    There are certain characteristics in a dialysis machine that would be desirable for use in home and limited care environments. These features relate to safety, ease of use, consideration of physical space, and reliability. The Bellco Formula Domus Home Care System was designed to meet all these requirements. Bellco's philosophy of patient treatment centers on global biocompatibility. This is evident in the design of the Formula Domus Home Care System. It has the smallest hydraulic fluid pathway of any dialysis machine on the market. Formula is capable of preparing ultrapure dialysate. The ultrafiltration measurement mechanism, the patented Coriolis flow meter, measures the mass of the dialysate, not the volume. For this reason it is the only dialysis machine that detects actual backfiltration, not just the theoretical possibility of it based on transmembrane pressure. The Coriolis flow meter also ensures that dialysate flow is a true single pass. The operator interface is a single window operating control. It is possible to select up to 14 different languages. There is an online help key to assist patients with troubleshooting. Programmable start-up and shutdown times save time for the patient. Formula is the only dialysis machine to offer a backup battery feature. Formula is capable of communicating with any software available. The focus on global biocompatibility ensures the best quality dialysis treatments for a population of patients who will likely remain on dialysis for a longer period of time than conventional dialysis patients. PMID:15043621

  20. Funding Formulas for California Schools III: An Analysis of Governor Brown's Weighted Pupil Funding Formula

    Science.gov (United States)

    Rose, Heather; Sonstelie, Jon; Weston, Margaret

    2012-01-01

    In his 2012-13 budget Governor Brown proposed a new system for allocating state revenue among California school districts. By all accounts the current system is complex and opaque. In contrast, the proposed system--a weighted pupil funding formula--is simple and transparent. Using the PPIC School Finance Model, we compare how this formula would…

  1. GENERAL FORMULA AND RECURRENCE FORMULA FOR RADIAL MATRIX ELEMENTS OF N-DIMENSIONAL ISOTROPIC HARMONIC OSCILLATOR

    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.

  2. Explicit formulas for regularized products and series

    CERN Document Server

    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.

  3. From Pauli Matrices to Quantum Ito Formula

    International Nuclear Information System (INIS)

    This paper answers important questions raised by the recent description, by Attal, of a robust and explicit method to approximate basic objects of quantum stochastic calculus on bosonic Fock space by analogues on the state space of quantum spin chains. The existence of that method justifies a detailed investigation of discrete-time quantum stochastic calculus. Here we fully define and study that theory and obtain in particular a discrete-time quantum Ito formula, which one can see as summarizing the commutation relations of Pauli matrices.An apparent flaw in that approximation method is the difference in the quantum Ito formulas, discrete and continuous, which suggests that the discrete quantum stochastic calculus differs fundamentally from the continuous one and is therefore not a suitable object to approximate subtle phenomena. We show that flaw is only apparent by proving that the continuous-time quantum Ito formula is actually a consequence of its discrete-time counterpart

  4. Langlands Program, Trace Formulas, and their Geometrization

    CERN Document Server

    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.

  5. Move! Eat better: try the FIT formula

    CERN Multimedia

    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!

  6. 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.

  7. A non-PSLQ route to BBP-type formulas

    OpenAIRE

    Adegoke, Kunle

    2016-01-01

    BBP-type formulas are usually discovered experimentally, through computer searches. In this paper, however, starting with two simple generators, and hence without doing any computer searches, we derive a wide range of BBP-type formulas in general bases. Many previously discovered BBP-type formulas turn out to be particular cases of the formulas derived here.

  8. 24 CFR 905.10 - Capital Fund formula (CFF).

    Science.gov (United States)

    2010-04-01

    ... 24 Housing and Urban Development 4 2010-04-01 2010-04-01 false Capital Fund formula (CFF). 905.10... DEVELOPMENT THE PUBLIC HOUSING CAPITAL FUND PROGRAM § 905.10 Capital Fund formula (CFF). (a) General. This section describes the formula for allocation of capital funds to PHAs. The formula is referred to as...

  9. 24 CFR 990.110 - Operating fund formula.

    Science.gov (United States)

    2010-04-01

    ... 24 Housing and Urban Development 4 2010-04-01 2010-04-01 false Operating fund formula. 990.110... DEVELOPMENT THE PUBLIC HOUSING OPERATING FUND PROGRAM Purpose, Applicability, Formula, and Definitions § 990.110 Operating fund formula. (a) General formula. (1) The amount of annual contributions...

  10. 27 CFR 21.23 - Formula No. 19.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 19. 21.23... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Completely Denatured Alcohol Formulas § 21.23 Formula No. 19. To every 100 gallons of ethyl alcohol of not less than 160 proof add:...

  11. 27 CFR 21.22 - Formula No. 18.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 18. 21.22... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Completely Denatured Alcohol Formulas § 21.22 Formula No. 18. To every 100 gallons of ethyl alcohol of not less than 160 proof add:...

  12. Magnetic Moment Formulas of Baryons Determined by Quantum Numbers

    OpenAIRE

    Chang, Yi-Fang

    2008-01-01

    We propose that the magnetic moment formulas of baryons may be determined by quantum numbers, and obtain three formulas. This is a new type of magnetic moment formula, and agrees better with the experimental values. It is also similar to corresponding mass formulas of hadrons.

  13. Identifying a framework for graphing formulas from expert strategies

    NARCIS (Netherlands)

    Kop, P; F, Janssen,; Drijvers, Paul; Veenman, M.; van Driel, Jan

    2014-01-01

    Graphing formulas with paper and pen helps learners to connect the algebraic and graphical representation of a function, which is important in learning to read algebraic formulas. To be able to graph formulas, a repertoire of functions that can be instantly visualized by a graph (formula-graphics) i

  14. CRC standard mathematical tables and formulae

    CERN Document Server

    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.

  15. Comments Upon the Mass Oscillation Formulas

    CERN Document Server

    De Leo, S; Rotelli, P

    1999-01-01

    Standard formulas for mass oscillations are based upon the approximation, $t definite momentum, $p$, or, alternatively, with definite energy, $E$. This represents an inconsistent scenario and gives an unjustified factor of two in mass oscillation formulas. Such an ambiguity has been a matter of speculations and mistakes in discussing flavour oscillations. We present a series of results and show how the problem of the factor two in the oscillation length is not a consequence of gedanken experiments, i.e. oscillations in time. The common velocity scenario yields the maximum simplicity and probably the right answer.

  16. Mathematical formulas for industrial and mechanical engineering

    CERN Document Server

    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

  17. Efficient computation of the Zassenhaus formula

    CERN Document Server

    Casas, Fernando; Nadinic, Mladen

    2012-01-01

    A new recursive procedure to compute the Zassenhaus formula up to high order is presented, providing each exponent in the factorization directly as a linear combination of independent commutators and thus containing the minimum number of terms. The recursion can be easily implemented in a symbolic algebra package and requires much less computational effort, both in time and memory resources, than previous algorithms. In addition, by bounding appropriately each term in the recursion, it is possible to get a larger convergence domain of the Zassenhaus formula when it is formulated in a Banach algebra.

  18. 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.

  19. Inductance calculations working formulas and tables

    CERN Document Server

    Grover, Frederick W

    2009-01-01

    This authoritative compilation of formulas and tables simplifies the design of inductors for electrical engineers. It features a single simple formula for virtually every type of inductor, together with tables from which essential numerical factors may be interpolated. Although compiled in the 1940s, before calculators and computers, this book provides fundamental equations that professionals and practitioners can use to produce algorithms for computer programs and spreadsheets.Starting with a survey of general principles, it explains circuits with straight filaments; parallel elements of equa

  20. Analytical opacity formulas for low Z plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Rubiano, J; Rodriguez, R; Gil, J M; Florido, R; Martel, P; Mendoza, M A; Suarez, D [Departamento de FIasica, Universidad de Las Palmas de GC, 35017 Las Palmas de GC (Spain); Minguez, E [Instituto de Fusion Nuclear DENIM. Universidad Politecnica de Madrid, 28019 Madrid (Spain)], E-mail: jgarcia@dfis.ulpgc.es

    2008-05-01

    The accurate computation of radiative opacities is basic in the ICF target physics analysis, in which the radiation is an important feature to determine in detail. For this reason, accurate analytical formulas for giving mean opacities versus temperature and density of the plasma seem to be a useful tool. In this work we analyse some analytical expressions found in the literature for the opacity low Z plasmas in a wide range of temperature and densities. The validity of these formulas for computing the opacity under NLTE conditions is investigated using the new code ABAKO.

  1. Vacuum engineering, calculations, formulas, and solved exercises

    CERN Document Server

    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

  2. Measuring the deviation from the Rutherford formula

    OpenAIRE

    Kuraev, E. A.; Shatnev, M.; Tomasi-Gustafsson, E.

    2009-01-01

    Modern experiments with heavy ion-leptons collisions open the possibility to measure the deviation of cross section of small angles electron(positron)-ion elastic scattering from the Rutherford formula due to multiple virtual photons exchange. The charge asymmetry and the polarization of the scattered leptons are calculated and numerical predictions are given. A generalization to elastic proton-nucleus scattering is discussed.

  3. 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.

  4. On Kreĭn’s formula

    NARCIS (Netherlands)

    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

  5. 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...

  6. 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.

  7. Diffusion Processes and the Ewens Sampling Formula

    OpenAIRE

    Feng, Shui

    2016-01-01

    Crane [Statist. Sci. 31 (2016) 1–19] provides an excellent review of Ewens’ sampling formula (henceforth, ESF), its applications in and connections with various subjects. This note intends to extend the discussion a little bit. The focus will be on nonequilibrium ESF involving diffusion processes, ESF with symmetric selection and asymptotics of ESF. The references listed are by no means exhaustive.

  8. Quantum Mechanical Correspondence of Poisson Integral Formula

    Institute of Scientific and Technical Information of China (English)

    FAN Hong-Yi; JIANG Nian-Quan

    2011-01-01

    In this paper we set up quantum mechanical correspondence of the Poisson integral formula. We show that Poisson kernel function existing in the transformation between the continuum entangled state representation and its induced state, i.e. the number-difference-correlated amplitude entangled state representation.

  9. A weak kernel formula for Bessel functions

    OpenAIRE

    Chai, Jingsong

    2015-01-01

    In this paper, we prove a weak kernel formula of Bessel functions attached to irreducible generic representations of p-adic $GL(n)$. As an application, we show that the Bessel function defined by Bessel distribution coincides with the Bessel function defined via uniqueness of Whittaker models on the open Bruhat cell.

  10. An ISU(3) hadron mass formula

    International Nuclear Information System (INIS)

    A universal mass expression is derived for non-charm hadrons which unites GMO formulae for various multiplets. Mass splitting is achieved via the generators of the 14-parameter ISU(3) group. The spectrum depends on three parameters which vary with the spin. Comparison with particle data shows a nearly linear dependence. (author)

  11. Index formulae for subspaces of Krein spaces

    NARCIS (Netherlands)

    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

  12. Quantification of prebiotics in commercial infant formulas.

    Science.gov (United States)

    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.

  13. Entropy Product Formula for Gravitational Instanton

    CERN Document Server

    Pradhan, Parthapratim

    2016-01-01

    We investigate the entropy product formula for various gravitational instantons. We speculate that due to the mass-independent characteristics of the said instatons they are \\emph{universal} as well as they are \\emph{quantized}. For isolated Euclidean Schwarzschild black hole, these properties simply \\emph{fail}.

  14. The Economic Vitality Formula of Success

    Science.gov (United States)

    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…

  15. Quantification of prebiotics in commercial infant formulas.

    Science.gov (United States)

    Sabater, Carlos; Prodanov, Marin; Olano, Agustín; Corzo, Nieves; Montilla, Antonia

    2016-03-01

    Since breastfeeding is not always possible, infant formulas (IFs) are supplemented with prebiotic oligosaccharides, such as galactooligosaccharides (GOS) and/or fructooligosaccharides (FOS) to exert similar effects to those of the breast milk. Nowadays, a great number of infant formulas enriched with prebiotics are disposal in the market, however there are scarce data about their composition. In this study, the combined use of two chromatographic methods (GC-FID and HPLC-RID) for the quantification of carbohydrates present in commercial infant formulas have been used. According to the results obtained by GC-FID for products containing prebiotics, the content of FOS, GOS and GOS/FOS was in the ranges of 1.6-5.0, 1.7-3.2, and 0.08-0.25/2.3-3.8g/100g of product, respectively. HPLC-RID analysis allowed quantification of maltodextrins with degree of polymerization (DP) up to 19. The methodology proposed here may be used for routine quality control of infant formula and other food ingredients containing prebiotics. PMID:26471520

  16. 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 ...

  17. Average prime-pair counting formula

    Science.gov (United States)

    Korevaar, Jaap; Riele, Herman Te

    2010-04-01

    Taking r>0 , let π_{2r}(x) denote the number of prime pairs (p, p+2r) with p≤ x . The prime-pair conjecture of Hardy and Littlewood (1923) asserts that π_{2r}(x)˜ 2C_{2r} {li}_2(x) with an explicit constant C_{2r}>0 . There seems to be no good conjecture for the remainders ω_{2r}(x)=π_{2r}(x)- 2C_{2r} {li}_2(x) that corresponds to Riemann's formula for π(x)-{li}(x) . However, there is a heuristic approximate formula for averages of the remainders ω_{2r}(x) which is supported by numerical results.

  18. Some consequence relations on propositional formulas

    Directory of Open Access Journals (Sweden)

    Borovčanin Momčilo

    2011-01-01

    Full Text Available Consequence relations on propositional formulas are binary relations on propositional formulas that represent certain types of entailment - formal or semi-formal derivation of conclusion from a certain set of premises. Some of well known examples are classical implication (standard logical entailment, preference relations (i.e. relations that satisfy Reflexivity, Left logical equivalence, Right weakening, And, Or and Cautious monotonicity rational relations (i.e. preference relations that also satisfy rational monotonicity, consequence relations (prime examples are qualitative possibilities and necessities etc. More than two decades various consequence relations are used in automated decision making, product control, risk assessment and so on. The aim of this paper is to give a short overview of the most prominent examples of consequence relations.

  19. Pizzetti Formulae for Stiefel Manifolds and Applications

    Science.gov (United States)

    Coulembier, Kevin; Kieburg, Mario

    2015-10-01

    Pizzetti's formula explicitly shows the equivalence of the rotation invariant integration over a sphere and the action of rotation invariant differential operators. We generalize this idea to the integrals over real, complex, and quaternion Stiefel manifolds in a unifying way. In particular, we propose a new way to calculate group integrals and try to uncover some algebraic structures which manifest themselves for some well-known cases like the Harish-Chandra integral. We apply a particular case of our formula to an Itzykson-Zuber integral for the coset . This integral naturally appears in the calculation of the two-point correlation function in the transition of the statistics of the Poisson ensemble and the Gaussian orthogonal ensemble in random matrix theory.

  20. Formula 47游艇介绍

    Institute of Scientific and Technical Information of China (English)

    黄芳武

    2004-01-01

    最近Formula系列产品中的佼佼者Formula 47因其自身的诸多优点而备受瞩目。Formula公司一直以来都以其产品性能的优良而著称,自60年代Formula创下近海离岸短距离赛跑赢家的纪录以来,公司就一直试图用艇赛来提高游艇速度,但是游艇的速度始终及不上其良好性能,Formula 47似乎在速度上更慢,但这未必是个坏消息。

  1. Inclusion probability with dropout: an operational formula.

    Science.gov (United States)

    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.

  2. Feynman graph derivation of Einstein quadrupole formula

    International Nuclear Information System (INIS)

    The one graviton transition operator, and consequently, the classical energy loss formula for gravitational radiation are derived from the Feynman graphs of helicity +- 2 theories of gravitation. The calculations are done both for the case of electromagnetic and gravitational scattering. The departure of the in and out states from plane waves owing to the long range nature of gravitation is taken into account to improve the Born approximation calculations. This also includes a long range modification of the graviton wave function which is shown to be equivalent to the classical problem of the true light cones deviating logarithmically at large distances from the flat space light cones. The transition from the S-matrix elements calculated graphically to the graviton transition operator is done by using complimentarity of space-time and momentum descriptions. The energy loss formula derived originally by Einstein is shown to be correct. (Auth.)

  3. Matrix product formula for Macdonald polynomials

    International Nuclear Information System (INIS)

    We derive a matrix product formula for symmetric Macdonald polynomials. Our results are obtained by constructing polynomial solutions of deformed Knizhnik–Zamolodchikov equations, which arise by considering representations of the Zamolodchikov–Faddeev and Yang–Baxter algebras in terms of t-deformed bosonic operators. These solutions are generalized probabilities for particle configurations of the multi-species asymmetric exclusion process, and form a basis of the ring of polynomials in n variables whose elements are indexed by compositions. For weakly increasing compositions (anti-dominant weights), these basis elements coincide with non-symmetric Macdonald polynomials. Our formulas imply a natural combinatorial interpretation in terms of solvable lattice models. They also imply that normalizations of stationary states of multi-species exclusion processes are obtained as Macdonald polynomials at q = 1. (paper)

  4. A generalization of exotic options pricing formulae

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    Exotic options, or "path-dependent" options are options whose payoff depends on the behavior of the price of the underlying between 0 and the maturity, rather than merely on the final price of the underlying, such as compound options, reset options and so on. In this paper, a generalization of the Geske formula for compound call options is obtained in the case of time-dependent volatility and time-dependent interest rate by applying martingale methods and the change of numeraire or the change of probability measure. An analytic formula for the reset call options with predetermined dates is also derived in the case by using the same approach. In contrast to partial differential equation (PDE) approach, our approach is simpler.

  5. Clause Elimination Procedures for CNF Formulas

    Science.gov (United States)

    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.

  6. 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.

  7. Recursive formula for arithmetic Asian option prices

    OpenAIRE

    Kyungsub Lee

    2013-01-01

    We derive a recursive formula for arithmetic Asian option prices with finite observation times in semimartingale models. The method is based on the relationship between the risk-neutral expectation of the quadratic variation of the return process and European option prices. The computation of arithmetic Asian option prices is straightforward whenever European option prices are available. Applications with numerical results under the Black-Scholes framework and the exponential L\\'evy model are...

  8. Universal fitting formulae for baryon oscillation surveys

    OpenAIRE

    Blake, Chris; Parkinson, David; Glazebrook, Karl; Bassett, Bruce A.; Kunz, Martin; Nichol, Robert C.

    2006-01-01

    The next generation of galaxy surveys will attempt to measure the baryon oscillations in the clustering power spectrum with high accuracy. These oscillations encode a preferred scale which may be used as a standard ruler to constrain cosmological parameters and dark energy models. In this paper we present simple analytical fitting formulae for the accuracy with which the preferred scale may be determined in the tangential and radial directions by future spectroscopic and photometric galaxy re...

  9. A Handbook of Essential Mathematical Formulae

    CERN Document Server

    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.

  10. A Giambelli formula for even orthogonal Grassmannians

    OpenAIRE

    Skovsted Buch, Anders; Kresch, Andrew; Tamvakis, Harry

    2011-01-01

    Let X be an orthogonal Grassmannian parametrizing isotropic subspaces in an even dimensional vector space equipped with a nondegenerate symmetric form. We prove a Giambelli formula which expresses an arbitrary Schubert class in the classical and quantum cohomology rings of X as a polynomial in certain special Schubert classes. Our analysis reveals a surprising relation between the Schubert calculus on even and odd orthogonal Grassmannians. We also study eta polynomials, a family of polynomial...

  11. A Giambelli formula for isotropic Grassmannians

    OpenAIRE

    Buch, Anders S; Kresch, Andrew; Tamvakis, Harry

    2008-01-01

    Let X be a symplectic or odd orthogonal Grassmannian parametrizing isotropic subspaces in a vector space equipped with a nondegenerate (skew) symmetric form. We prove a Giambelli formula which expresses an arbitrary Schubert class in H^*(X,Z) as a polynomial in certain special Schubert classes. We study theta polynomials, a family of polynomials defined using raising operators whose algebra agrees with the Schubert calculus on X. Furthermore, we prove that theta polynomials are special cases ...

  12. Universal Lie formulas for higher antibrackets

    CERN Document Server

    Manetti, Marco

    2015-01-01

    We prove that the hierachy of higher antibrackets (aka higher Koszul brackets, aka Koszul braces) of a linear operator D on a commutative superalgebra can be defined by some universal formulas involving iterated Nijenhuis-Richardson brackets having as arguments D and the multiplication operators. As a byproduct we can immediately extend higher antibrackets to noncommutative algebras in a way preserving the validity of generalized Jacobi identities.

  13. The Trace Formula of the Spinoriel Amplitude

    OpenAIRE

    Mekhfi, M.

    2009-01-01

    We re express the fermion's probability amplitude as a trace over spinor indices, which formulation surprisingly does not exist in literature. This formulation puts the probabilty amplitude and the the probabilty(squared amplitude) of a given process on equal footing at the compuational level and this is our principal motivation to write the present paper. We test the power of the trace formula in three applications: Calculation of the charge-current of fermions by using symbolic programs, wh...

  14. Pocket book of integrals and mathematical formulas

    CERN Document Server

    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...

  15. A Hartree-Fock-Bogoliubov mass formula

    CERN Document Server

    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...

  16. Overtopping of Berm Breakwaters Extension of Overtopping Formula

    DEFF Research Database (Denmark)

    Andersen, Thomas Lykke; Burcharth, H. F.

    2005-01-01

    ) formula and the present improved formula. However, for a more stable structure and low wave steepness the improved formula performs better. Six different data sets are used to study the validity of the Lykke Andersen & Burcharth (2004) formula, the present improved formula and the CLASH neural network...... model. The present improved formula seems to be the best choice. The CLASH NN-Model performs very well for berm breakwater data sets included in the fitting of the NN-Model, but much worse for those not included. This demonstrates some degree of overlearning of the neural network due to limited data...... the formula is improved so it gives reliable estimates also for more stable structures. The extension of the overtopping formula is based on analysis of front slope stability data from many different data sets. In most cases there is only a small difference between the Lykke Andersen & Burcharth (2004...

  17. The Euler-Maclaurin Formula and Extensions - An Elementary Approach

    Science.gov (United States)

    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.

  18. 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.

  19. A Multidimensional Analogue of the Simpson's Formula of Integral

    CERN Document Server

    Fujii, Kazuyuki

    2009-01-01

    The Simpson's formula is obtained by approximating the integral of a function on some interval by the integral of the quadratic polynomial determined by the function. However, a multidimensional analogue of the formula has not been given as far as we know. In this paper such a formula is given. Our formula is simple and beautiful, so it may be convenient in Mathematics or Mathematical Physics.

  20. The $n$th+1 Prime Number Limit Formulas

    OpenAIRE

    Kawalec, Artur

    2016-01-01

    A new derivation of Golomb's limit formula for generating the $n$th$+1$ prime number is presented. The limit formula is derived by extracting $p_{n+1}$ from Euler's prime product representation of the Riemann zeta function $\\zeta(s)$ in the limit as $s$ approaches infinity. Also, new variations of these limit formulas are explored, such as the logarithm and a half-prime formulas for the $p_{n+1}$.

  1. Counterexamples on Jumarie's two basic fractional calculus formulae

    Science.gov (United States)

    Liu, Cheng-shi

    2015-05-01

    Jumarie proposed a modified Riemann-Liouville derivative definition and gave two basic fractional calculus formulae (u (t) v (t)) (α) =u (α) (t) v (t) + u (t)v (α) (t) and (f (u (t))) (α) = fu‧ u (α) (t) . We give two counterexamples to show that Jumarie's two formulae are not true. Respectively, all results obtained in references by using Jumarie's these two formulae are incorrect. In the end, we give the corresponding formulae.

  2. Infant formula increases bone turnover favoring bone formation

    Science.gov (United States)

    In the first year of life, the major infant food choices have traditionally been breast milk (BM), cow's milk formula (MF), or soy formula (SF). Studies examining the effects of infant formula on early life skeletal development are extremely limited. We have enrolled 120 healthy 6-month-old infants ...

  3. 27 CFR 17.125 - Adoption of formulas and processes.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Adoption of formulas and... NONBEVERAGE PRODUCTS Formulas and Samples § 17.125 Adoption of formulas and processes. (a) Adoption of... of adoption with the appropriate TTB officer. The notice shall be filed with the first claim...

  4. 27 CFR 19.187 - Adoption of formulas.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Adoption of formulas. 19... After Original Qualification § 19.187 Adoption of formulas. (a) Forms 5110.38. The adoption by a... the appropriate TTB officer. The application shall list the formulas for adoption by (1)...

  5. A family of inversion formulas in thermoacoustic tomography

    KAUST Repository

    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.

  6. Illinois' School Funding Formula--A Mathematical and Geometrical Analysis.

    Science.gov (United States)

    Toenjes, Laurence A.

    1982-01-01

    Compares Illinois' funding formula with a mathematical model for resource compensating formulas. Describes the variables used (including district enrollment, wealth, tax effort, and state guaranteed valuation). Uses graphs to illustrate varying equity effects of the formula for K-12, K-8, and high school districts, both statewide and in selected…

  7. p-adic Gauss integrals from the Poison summarizing formula

    CERN Document Server

    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.

  8. 49 CFR 198.13 - Grant allocation formula.

    Science.gov (United States)

    2010-10-01

    ... 49 Transportation 3 2010-10-01 2010-10-01 false Grant allocation formula. 198.13 Section 198.13... PIPELINE SAFETY PROGRAMS Grant Allocation § 198.13 Grant allocation formula. (a) Beginning in calendar year... state agency comments on any proposed changes to the allocation formula. (f) Grants are limited to...

  9. 48 CFR 32.304-3 - Asset formula.

    Science.gov (United States)

    2010-10-01

    ... 48 Federal Acquisition Regulations System 1 2010-10-01 2010-10-01 false Asset formula. 32.304-3... REQUIREMENTS CONTRACT FINANCING Loan Guarantees for Defense Production 32.304-3 Asset formula. (a) Under..., by use of an asset formula, to an amount that does not exceed a specified percentage (90 percent...

  10. 40 CFR 72.95 - Allowance deduction formula.

    Science.gov (United States)

    2010-07-01

    ... 40 Protection of Environment 16 2010-07-01 2010-07-01 false Allowance deduction formula. 72.95... (CONTINUED) PERMITS REGULATION Compliance Certification § 72.95 Allowance deduction formula. The following formula shall be used to determine the total number of allowances to be deducted for the calendar...

  11. 24 CFR 92.604 - ADDI allocation formula.

    Science.gov (United States)

    2010-04-01

    ... 24 Housing and Urban Development 1 2010-04-01 2010-04-01 false ADDI allocation formula. 92.604... allocation formula. (a) General. HUD will provide ADDI funds to participating jurisdictions in amounts determined by the formula described in this section. (b) Allocation to states that are...

  12. 75 FR 32495 - Operating Fund Subsidies Allocation Formula

    Science.gov (United States)

    2010-06-08

    ... URBAN DEVELOPMENT Operating Fund Subsidies Allocation Formula AGENCY: Office of the Chief Information... available to public housing agencies (PHAs) which assistance is determined using a formula approach under...: Operating Fund Subsidies Allocation Formula. OMB Approval Number: 2577-0029. Form Numbers: HUD-52722,...

  13. 45 CFR 1321.37 - Intrastate funding formula.

    Science.gov (United States)

    2010-10-01

    ... 45 Public Welfare 4 2010-10-01 2010-10-01 false Intrastate funding formula. 1321.37 Section 1321... funding formula. (a) The State agency, after consultation with all area agencies in the State, shall develop and use an intrastate funding formula for the allocation of funds to area agencies under this...

  14. 24 CFR 990.200 - Determination of formula amount.

    Science.gov (United States)

    2010-04-01

    ... 24 Housing and Urban Development 4 2010-04-01 2010-04-01 false Determination of formula amount... Subsidy § 990.200 Determination of formula amount. (a) General. The amount of operating subsidy that a PHA is eligible for is the difference between its formula expenses (as calculated under subpart C of...

  15. 42 CFR 51.3 - Formula for determining allotments.

    Science.gov (United States)

    2010-10-01

    ... 42 Public Health 1 2010-10-01 2010-10-01 false Formula for determining allotments. 51.3 Section 51....3 Formula for determining allotments. The Secretary shall make allotments to eligible Systems from amounts apportioned each year under the Act on the basis of a formula prescribed by the Secretary...

  16. 27 CFR 26.197 - Furnishing formula to consignee.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Furnishing formula to... Custody to Internal Revenue Bond § 26.197 Furnishing formula to consignee. Prior to the first shipment... formula covering such spirits to the appropriate TTB officer, and to the proprietor of each...

  17. 24 CFR 570.406 - Formula miscalculation grants.

    Science.gov (United States)

    2010-04-01

    ... 24 Housing and Urban Development 3 2010-04-01 2010-04-01 false Formula miscalculation grants. 570... Grants § 570.406 Formula miscalculation grants. (a) General. Grants under this section will be made to... section. (b) Application. Since the grant is to correct a technical error in the formula amount...

  18. New addition formula for the little $q$-Bessel functions

    OpenAIRE

    Bouzeffour, Fethi

    2013-01-01

    Starting from the addition formula for little $q$-Jacobi polynomials, we derive a new addition formula for the little $q$-Bessel functions. The result is obtained by the use of a limit transition. We also establish a product formula for little $q$-Bessel functions with a positive and symmetric kernel.

  19. A general type of twisted anomaly cancellation formulas

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    For even-dimensional manifolds, we prove some twisted anomaly cancellation formulas which generalize some well-known cancellation formulas. For odd dimensional manifolds, we obtain some modularly invariant characteristic forms by the Chern-Simons transgression and we also get some twisted anomaly cancellation formulas.

  20. 7 CFR 761.205 - Computing the formula allocation.

    Science.gov (United States)

    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...

  1. 27 CFR 21.49 - Formula No. 23-H.

    Science.gov (United States)

    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:...

  2. 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.

  3. Unsatisfiable (k,(4*2^k/k))-CNF formulas

    OpenAIRE

    Gebauer, Heidi

    2008-01-01

    A boolean formula in a conjuctive normal form is called a (k,s)-formula if every clause contains exactly k variables and every variable occurs in at most s clauses. We prove the existence of a (k, 4 * (2^k/k))-CNF formula which is unsatisfiable.

  4. 27 CFR 24.303 - Formula wine record.

    Science.gov (United States)

    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...

  5. The chemical formula of a magnetotactic bacterium.

    Science.gov (United States)

    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.

  6. Infant formula companies battle for breast.

    Science.gov (United States)

    1996-01-01

    The infant formula manufacturer Mead Johnson has filed a lawsuit in Ontario courts against its competitor Ross Abbott for false advertising of its new Similac brand of infant formula. Mead Johnson contends that the Ross Abbott advertisement of Similac as providing benefits similar to mother's milk is false and misleading. Breast feeding specialists agree with Mead Johnson's claim. Yet, one year earlier, Mead Johnson claimed that its infant formula is modeled after mother's milk. The Infant Feeding Action Coalition (INFACT) Canada had complained to the Competition Bureau that called for Mead Johnson to cease its claim. Court documents reveal that both companies disregard the World Health Organization (WHO) International Code of Marketing of Breast Milk Substitutes. This code prohibits manufacturers from advertising directly to pregnant women and mothers. Two Ross Abbott spokespersons have different responses to their advertising practices: increasing emphasis on consumer promotion and support of the principle and objective of the WHO Code. Both companies have sought support of health professionals in Canada. In July 1996 Mead Johnson sent letters to about 7000 clinicians declaring "as someone who cares about infant health and nutrition as much as we do" and "...the most alarming concern is that, although there is no scientific basis for such claims, mothers believe them to be true." Ross Abbott responded to these letters by sending physicians letters declaring "Our business is built on trust, and we assure you that you may trust in Similac Advance and the benefits we have ascribed to it." The two companies will meet again in court on September 30, 1996. PMID:12320465

  7. Generalization of Equatorial Impact-Parameter Formulas for Rotating Bodies

    CERN Document Server

    Graber, James

    2009-01-01

    This paper computes co-rotating and contra-rotating impact-parameter formulas in the plane of symmetry for any plane symmetric and axisymmetric rotating body in all metric theories of gravity, including general relativity. Impact-parameter formulas are useful to compute the appearance of accreting black holes, neutron stars, and other emitting or reflecting matter near a gravitationally compact rotating body. These rotating-body impact-parameter formulas generalize similar impact-parameter formulas for the Kerr case derived by Bardeen and coworkers in 1972, and another general-metric formula for the spherical case published by Bodenner and Will in 2003.

  8. Complexity of Some Problems Concerning 2CNF Formulas

    Institute of Scientific and Technical Information of China (English)

    Hans; Kleine; Büning

    2003-01-01

    In this paper we investigate the complexity of several problems concerning 2CNF formulas. At first, we show that the minimal unsatisfiability problem for 2CNF formulas can be solved in linear time. Then we prove that the problem determining if a 2CNF formula can be transformed to a minimal unsatisfiable formula is also solvable in linear time. Thirdly, we show the polynomial solvability of the satisfiability problem for symmetric monotone formulas in which all clauses has length 2 or ? n - k ( n is the ...

  9. 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.

  10. 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.

  11. Composite Sandwich Design for Formula SAE Monocoque

    OpenAIRE

    Sanchez, Christopher Medina

    2013-01-01

    This paper is an approach in how to design a composite sandwich laminate, that is to be used for an open wheeled race car with a monocoque chassis. The composite sandwich design of the monocoque must be in accordance with the 2013 Formula SAE regulations. The composite sandwich laminate is to be used in a preliminary monocoque design based on the Revolve NTNU’s 2013 student race car, the KA Aquilo R. The composite materials for the monocoque’s sandwich structure are HexPly 6376 and Rohacel...

  12. Dirac's monopole, quaternions, and the Zassenhaus formula

    CERN Document Server

    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.

  13. 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...

  14. Excel formulas and functions for dummies

    CERN Document Server

    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

  15. Personal commentary - Crude oil pricing formulas

    OpenAIRE

    Lajous, Adrian

    2006-01-01

    Almost 21 years ago Pemex introduced spot-related formulas for determining the price of its crude oil exports. Other major players in the international oil market later adopted them and they continue to have a major influence on how oil prices are formed today. This might be a good time to remember the context in which they were originally developed, the objectives and constraints to which they responded and the role they played as part of the overall package of instruments of its commercial ...

  16. 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...

  17. Wald entropy formula and loop quantum gravity

    Science.gov (United States)

    Bodendorfer, N.; Neiman, Y.

    2014-10-01

    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) Lanczos-Lovelock gravity and comment on recent work on finding the correct numerical prefactor of the entropy by comparing it to a semiclassical effective action.

  18. Walfisz-like formula from Poisson's summation formula and some applications

    International Nuclear Information System (INIS)

    Walfiscz-like formula for the number of lattice points of an arbitrary m-dimensional lattice in a hyperellipsoid with given semi-axes is derived from the Poisson's summation formula. Applications to (i) the evaluation of certain lattice sums and (ii) the calculation of the expressions for the density of states of a single non-relativistic particle as well as of a relativistic particle enclosed in a rectangular m-dimensional box of finite size and subject to different boundary conditions are given. (Author)

  19. Around Poisson--Mehler summation formula

    CERN Document Server

    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...

  20. Proximate and elemental analysis of infant formula.

    Science.gov (United States)

    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.

  1. Lovelock gravity and Weyl's tube formula

    International Nuclear Information System (INIS)

    In four space-time dimensions, there are good theoretical reasons for believing that general relativity is the correct geometrical theory of gravity, at least at the classical level. If one admits the possibility of extra space-time dimensions, what would we expect classical gravity to be like? It is often stated that the most natural generalization is Lovelock's theory, which shares many physical properties with general relativity. But there are also key differences and problems. A potentially serious problem is the breakdown of determinism, which can occur when the matrix of coefficients of second time derivatives of the metric degenerates. This can be avoided by imposing inequalities on the curvature. Here it is argued that such inequalities occur naturally if the Lovelock action is obtained from Weyl's formulas for the volume and surface area of a tube. Part of the purpose of this article is to give a treatment of the Weyl tube formula in terminology familiar to relativists and to give an appropriate (straightforward) generalization to a tube embedded in Minkowski space.

  2. Surface diffuseness correction in global mass formula

    International Nuclear Information System (INIS)

    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 α-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

  3. Black-Scholes Formula in Subdiffusive Regime

    Science.gov (United States)

    Magdziarz, Marcin

    2009-08-01

    In the classical approach the price of an asset is described by the celebrated Black-Scholes model. In this paper we consider a generalization of this model, which captures the subdiffusive characteristics of financial markets. We introduce a subdiffusive geometric Brownian motion as a model of asset prices exhibiting subdiffusive dynamics. We find the corresponding fractional Fokker-Planck equation governing the dynamics of the probability density function of the introduced process. We prove that the considered model is arbitrage-free and incomplete. We find the corresponding subdiffusive Black-Scholes formula for the fair prices of European options and show how these prices can be evaluated using Monte-Carlo methods. We compare the obtained results with the classical ones.

  4. Handbook of mathematical formulas and integrals

    CERN Document Server

    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...

  5. Some applications of Rice formulas to waves

    CERN Document Server

    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.

  6. 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.

  7. 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.

  8. Infant Formulas for Food Allergy Treatment and Prevention.

    Science.gov (United States)

    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. [Pediatr Ann. 2016;45(4):e150-e156.]. PMID:27064473

  9. Empirical formula for mass excess of heavy and superheavy nuclei

    Science.gov (United States)

    Manjunatha, H. C.; Chandrika, B. M.; Seenappa, L.

    2016-08-01

    A new empirical formula is proposed for mass excess of heavy and superheavy nuclei in the region Z = 96-129. The parameters of the formula are obtained by making a polynomial fit to the available theoretical and experimental data. The calculated mass excess values are compared with the experimental values and other results of the earlier proposed models such as finite range droplet model (FRDM) and Hartree-Fock-Bogoliubov (HFB) method. Standard deviation of calculated mass excess values for each atomic number is tabulated. The good agreement of present formula with the experiment and other models suggests that the present formula could be used to evaluate the mass excess values of heavy and superheavy nuclei in the region 96 ≤Z ≥129. This formula is a model-independent formula and is first of its kind that produces a mass excess values with the only simple inputs of only Z and A.

  10. General inverse of Stokes, Vening-Meinesz and Molodensky formulae

    Institute of Scientific and Technical Information of China (English)

    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.

  11. Infant Formulas for Food Allergy Treatment and Prevention.

    Science.gov (United States)

    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.

  12. 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.

  13. Improvement in a phenomenological formula for ground state binding energies

    CERN Document Server

    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.

  14. SOME RECURRENCE FORMULAS FOR BOX SPLINES AND CONE SPLINES

    Institute of Scientific and Technical Information of China (English)

    Patrick J. Van Fleet

    2004-01-01

    A degree elevation formula for multivariate simplex splines was given by Micchelli[6] and extended to hold for multivariate Dirichlet splines in [8]. We report similar formulae for multivariate cone splines and box splines. To this end, we utilize a relation due to Dahmen and Micchelli[4] that connects box splines and cone splines and a degree reduction formula given by Cohen, Lyche, and Riesenfeld in [2].

  15. SOME RECURRENCE FORMULAS FOR BOX SPLINES AND CONE SPLINES

    Institute of Scientific and Technical Information of China (English)

    Patrick J. Van Fleet

    2002-01-01

    A degree elevation formula for multivariate simplex splines was given by Micchelli [6] and extended to hold for multivariate Dirichlet splines in [8]. We report similar formulae for multivariate cone splines and box_splines. To this end, we utilize a relation due to Dahmen and Micchelli [4] that connects box splines and cone splines and a degree reduction formula given by Cohen, Lyche, and Riesenfeld in [2].

  16. Incidence of Diarrhea in Hospitalized Patients with Standard Enteral Formula

    OpenAIRE

    Shabbu Ahmadi bonakdar; Mahdieh Pouryazdanpanah; Zahra Ganie Far; Saba Ghazanfari; Abdolreza Norouzy

    2014-01-01

    Introduction: Malnutrition is common in intensive care unit, occurring in (30% to 50%) of hospitalized patients. To prevent malnutrition, nutritionists recommend industrials formula for patients who cannot eat but with functional gastrointestinal track, But due to verbal nurse`s reports standard enteral formula is inducing diarrhea. In this study our purpose is to evaluate the incidence of diarrhea in hospitalized patients with standard Enteral Nutrition (EN) formula intake. Materials and ...

  17. CFT and Logarithmic Corrections of Black Hole Entropy Product Formula

    CERN Document Server

    Pradhan, Parthapratim

    2016-01-01

    We examine the \\emph{effects of CFT} (conformal field theory) on the logarithmic corrections of black hole (BH) entropy product formula of outer horizon and inner horizon by explicitly giving several examples. We also argue that logarithmic corrections of BH entropy product formula when calculated via CFT the formula also should \\emph{not be universal} and it also should \\emph{not be quantized}.

  18. Quantum Schubert polynomials and the Vafa-Intriligator formula

    CERN Document Server

    Kirillov, A N; Kirillov, Anatol N.; Maeno, Toshiaki

    1996-01-01

    We introduce a quantization map and study the quantization of Schubert and Grothendieck polynomials, monomials, elementary and complete polynomials. Our construction is based on the quantum Cauchy identity. As a corollary, we prove the Lascoux-Schützenberger type formula for quantum Schubert polynomials of the flag manifold. Our formula gives a simple method for computation of quantum Schubert polynomials. We also prove the higher genus analog of Vafa-Intriligator's formula for the flag manifold. We introduce the Extended Ehresman-Bruhat order on the symmetric group and prove the equivariant quantum Pieri formula.

  19. 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...... to explore the influence of the geometry on the armour stability. Besides cubes with mass density 2.4 t/m3, cubes with mass density 2.80 t/m3 were used in order to include the effect of mass density in the formula. The damage predictions given by the formula have been compared with prototype hand...

  20. A Dilogarithmic Formula for the Cheeger-Chern-Simons Class

    DEFF Research Database (Denmark)

    Dupont, Johan Louis; Zickert, C.K.

    2005-01-01

    We present a simplification of Neumann's formula in [8] for the universal Cheeger-Chern-Simons class of the second Chern polynomial. Our approach is completely algebraic, and the final formula can be applied directly on a homology class in the bar complex.......We present a simplification of Neumann's formula in [8] for the universal Cheeger-Chern-Simons class of the second Chern polynomial. Our approach is completely algebraic, and the final formula can be applied directly on a homology class in the bar complex....

  1. 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.

  2. Cardy-Verlinde Formula of Noncommutative Schwarzschild Black Hole

    International Nuclear Information System (INIS)

    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

  3. Evaluation of standard liver volume formulae for Chinese adults

    Institute of Scientific and Technical Information of China (English)

    Zheng-Rong Shi; Lu-Nan Yan; Bo Li; Tian-Fu Wen

    2009-01-01

    AIM:To evaluate different standard liver volume (SLV) formula and verify the applicability of the formulae for Chinese adults.METHODS:Data from 70 cases of living donor liver transplantation (LDLT) performed at our transplantation centers between January 2008 and April 2009 were analyzed.SLV was estimated using our recently reported formula [the Chengdu formula:SLV (mL) = 11.5×body weight (kg) + 334] and other reported formulae used for Chinese adults.Actual intraoperative liver volumes were obtained from a review of the patients' medical records.RESULTS:The actual right liver volume was not signifi-cantly different from the estimated right liver volume determined by the Chengdu formula,but was significantly smaller than estimates using the Heinemann,Urata,Vauthey,and Lee formulae (P<0.01),and significantly larger than estimates using the Fan formula (P<0.05).CONCLUSION:The Chengdu formula was demonstrated to be reliable by its application in LDLT.

  4. 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.

  5. A Stability Formula for Plastic-Tipped Bullets Part 1: Motivation and Development of New Formula

    CERN Document Server

    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...

  6. Product formulas for volumes of flow polytopes

    CERN Document Server

    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.

  7. Analytical opacity formulas for ICF elements

    Energy Technology Data Exchange (ETDEWEB)

    Minguez, E. E-mail: minguez@denim.upm.es; Martel, P.; Gil, J.M.; Rubiano, J.G.; Rodriguez, R

    2002-01-01

    Local Thermodynamic Equilibrium (LTE) opacity codes have been developed by the Instituto de Fusion Nuclear (DENIM) during the last years. JIMENA code (Laser and Particle Beams 6 (1998) 265; Laser and Particle Beams 10 (1992) 651) is an opacity code that solves self-consistently, for each temperature and density, the radial Dirac equation with a local spherically symmetrical potential. Very recently we have developed a new opacity code, called ANALOP, that uses an analytical potential (JQSRT 54 (1995) 621), which can include density and temperature effects for atomic data calculations. Opacities are determined with these two codes for selected elements at different plasma conditions. This work is focused on the determination of Rosseland and Planck mean analytical formulas for several single elements used in ICF targets. A scaling law of these mean opacities is given as a function of the plasma parameters: electron temperature and plasma density. These opacities have been tested with numerical results from other codes and with available experimental results.

  8. How Spacecraft Fly Spaceflight Without Formulae

    CERN Document Server

    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 ...

  9. On formula to compute primes and the nth prime

    CERN Document Server

    Kaddoura, Issam

    2012-01-01

    In this paper, we propose a new primality test, and then we employ this test to find a formula for {\\pi} that computes the number of primes within any interval. We finally propose a new formula that computes the nth prime number as well as the next prime for any given number

  10. The role of infant appetite in extended formula feeding

    NARCIS (Netherlands)

    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

  11. 49 CFR 192.105 - Design formula for steel pipe.

    Science.gov (United States)

    2010-10-01

    ... 49 Transportation 3 2010-10-01 2010-10-01 false Design formula for steel pipe. 192.105 Section 192... NATURAL AND OTHER GAS BY PIPELINE: MINIMUM FEDERAL SAFETY STANDARDS Pipe Design § 192.105 Design formula for steel pipe. (a) The design pressure for steel pipe is determined in accordance with the...

  12. A More Intuitive Version of the Lorentz Velocity Addition Formula

    Science.gov (United States)

    Devlin, John F.

    2009-01-01

    The Lorentz velocity addition formula for one-dimensional motion presents a number of problems for beginning students of special relativity. In this paper we suggest a simple rewrite of the formula that is easier for students to memorize and manipulate, and furthermore is more intuitive in understanding the correction necessary when adding…

  13. A Preliminary Analysis of California's New Local Control Funding Formula

    Science.gov (United States)

    Wolf, Rebecca; Sands, Janelle

    2016-01-01

    California recently overhauled its K-12 public education finance system. Enacted in 2013, the Local Control Funding Formula (LCFF) replaced California's 40-year-old funding formula. The LCFF increases district officials' fiscal flexibility; provides more resources to districts serving larger proportions of low-income, English learner (EL), and…

  14. 14 CFR 271.7 - Subsidy payout formula.

    Science.gov (United States)

    2010-01-01

    ... 14 Aeronautics and Space 4 2010-01-01 2010-01-01 false Subsidy payout formula. 271.7 Section 271.7 Aeronautics and Space OFFICE OF THE SECRETARY, DEPARTMENT OF TRANSPORTATION (AVIATION PROCEEDINGS) ECONOMIC... payout formula. (a) Subsidy will be paid by the Department to the air carrier monthly, based on...

  15. Sum formula for SL2 over imaginary quadratic number fields

    NARCIS (Netherlands)

    Lokvenec-Guleska, H.

    2004-01-01

    The subject of this thesis is generalization of the classical sum formula of Bruggeman and Kuznetsov to the upper half-space H3. The derivation of the preliminary sum formula involves computation of the inner product of two specially chosen Poincar´e series in two different ways: the spectral descri

  16. 34 CFR 303.200 - Formula for State allocations.

    Science.gov (United States)

    2010-07-01

    ... 34 Education 2 2010-07-01 2010-07-01 false Formula for State allocations. 303.200 Section 303.200 Education Regulations of the Offices of the Department of Education (Continued) OFFICE OF SPECIAL EDUCATION... TODDLERS WITH DISABILITIES Procedures for Making Grants to States § 303.200 Formula for State...

  17. 45 CFR 1385.8 - Formula for determining allotments.

    Science.gov (United States)

    2010-10-01

    ... 45 Public Welfare 4 2010-10-01 2010-10-01 false Formula for determining allotments. 1385.8 Section 1385.8 Public Welfare Regulations Relating to Public Welfare (Continued) OFFICE OF HUMAN DEVELOPMENT... Formula for determining allotments. The Commissioner will allocate funds appropriated under the Act...

  18. 75 FR 38797 - Predominantly Black Institutions Formula Grant Program

    Science.gov (United States)

    2010-07-06

    ... Predominantly Black Institutions Formula Grant Program ACTION: Notice inviting applications for new awards for fiscal year (FY) 2010; Correction. SUMMARY: On June 21, 2010, we published in the Federal Register (75 FR... Institutions Formula Grant Program (PBI Notice). The PBI Notice incorrectly indicated that this program...

  19. 24 CFR 990.195 - Calculation of formula income.

    Science.gov (United States)

    2010-04-01

    ... communications with the respective PHAs. (e) Inapplicability of 24 CFR 85.25. Formula income is not subject to the provisions regarding program income in 24 CFR 85.25. ... 24 Housing and Urban Development 4 2010-04-01 2010-04-01 false Calculation of formula income....

  20. Quantum mechanical photoncount formula derived by entangled state representation

    Institute of Scientific and Technical Information of China (English)

    Hu Li-Yun; Wang Zi-Sheng; L.C.Kwek; Fan Hong-Yi

    2011-01-01

    By introducing the thermo entangled state representation,we derive four new photocount distribution formulas for a given light field density operator. It is shown that these new formulas,which are convenient to calculate the photocount,can be expressed as integrations over a Laguree-Gaussian function with a characteristic function,Wigner function,Q-function and P-function,respectively.

  1. 40 CFR 1065.630 - 1980 international gravity formula.

    Science.gov (United States)

    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...

  2. 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.

  3. Infant Formula: A Little Knowledge Can Be Dangerous.

    Science.gov (United States)

    Frisby-LaRue, Jeannine

    1982-01-01

    Misuse of infant formula products in third-world countries is discussed with regard to the World Health Organization's International Code of Marketing of Breastmilk Substitutes. The Nestle Company's response to the code is presented and the Infant Formula Action Committee (INFACT) boycott of Nestle products is described. (CM)

  4. APPROVAL OF FORMULA FOR TIME CALCULATION OF FORGOTTEN TEACHING MATERIAL

    Directory of Open Access Journals (Sweden)

    A. Meteshkin

    2010-01-01

    Full Text Available The analysis concerning forgotten by students teaching material in IT is carried out. The formula for time calculation after the expiration of which students’ knowledge remains at the same level is offered. The reliability of calculations performed with the application of the above stated formula is proved experimentally.

  5. 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.

  6. Formulaic Sequences and the Implications for Second Language Learning

    Science.gov (United States)

    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…

  7. Understanding State School Finance Formulas. National Education Association Search.

    Science.gov (United States)

    National Education Association, Washington, DC. Research Div.

    The fourth report in a series on school finance describes how state school finance formulas are differentiated and the calculations used to measure local need, wealth, and effort. The following topics are addressed: (1) criteria for evaluating state school finance programs; (2) origins of state school aid formulas; (3) operation of equalization…

  8. 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.

  9. Counting efficiency formulae for two, three or four photomultiplier systems

    International Nuclear Information System (INIS)

    Counting efficiency formulae as a function of the non-detection probability and the electron distributions for systems with two, three or dour photomultipliers are obtained in this paper. It is assumed that the photocathode electron emission follows the Poisson distribution. The obtained formulae are basic to compute the counting efficiency in liquid scintillation spectrometers

  10. 27 CFR 26.50 - Formulas for liquors.

    Science.gov (United States)

    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...

  11. Trace formula for a dielectric microdisk with a point scatterer

    NARCIS (Netherlands)

    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

  12. 27 CFR 5.28 - Adoption of predecessor's formulas.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Adoption of predecessor's formulas. 5.28 Section 5.28 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS LABELING AND ADVERTISING OF DISTILLED SPIRITS Formulas § 5.28 Adoption...

  13. A simple formula for the thermal pair annihilation line emissivity

    OpenAIRE

    Svensson, Roland; Larsson, Stefan; Poutanen, Juri

    1996-01-01

    We introduce a simple and convenient fitting formula for the thermal annihilation line from pair plasmas in cosmic sources. The fitting formula is accurate to 0.04\\% and is valid at all photon energies and temperatures of interest. The commonly used Gaussian line profile is not a good approximation for broader lines.

  14. Formula Student as Part of a Mechanical Engineering Curriculum

    Science.gov (United States)

    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…

  15. Formulaic Speech in Early Classroom Second Language Development.

    Science.gov (United States)

    Ellis, Rod

    Formulaic speech, expressions learned as unanalyzed wholes and used on particular occasions by native speakers, is contrasted to "grammatical" sentences using novel combinations of words in the second language classroom. The speech produced by three limited English-speaking children in an English program suggests that formulaic speech enables…

  16. 7 CFR 246.16a - Infant formula cost containment.

    Science.gov (United States)

    2010-01-01

    ... 7 Agriculture 4 2010-01-01 2010-01-01 false Infant formula cost containment. 246.16a Section 246..., DEPARTMENT OF AGRICULTURE CHILD NUTRITION PROGRAMS SPECIAL SUPPLEMENTAL NUTRITION PROGRAM FOR WOMEN, INFANTS AND CHILDREN State Agency Provisions § 246.16a Infant formula cost containment. (a) Who must use...

  17. Ernst equation, Fay identities and variational formulas on hyperelliptic curves

    OpenAIRE

    Klein, C.; Korotkin, D.; Shramchenko, V.

    2004-01-01

    We present a unified approach to theta-functional solutions of the stationary axisymmetric Einstein equations in vacuum. Using Fay's trisecant identity and variational formulas on hyperelliptic Riemann surfaces, we establish formulas for the metric functions, the Ernst potential and their derivatives.

  18. 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.

  19. 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.

  20. 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...

  1. Energy-shifting formulae yield reliable reaction and capture probabilities

    International Nuclear Information System (INIS)

    Predictions of energy-shifting formulae for partial reaction and capture probabilities are compared with coupled channels calculations. The quality of the agreement notably improves with increasing mass of the system and/or decreasing mass asymmetry in the heavy-ion collision. The formulae are reliable and useful for circumventing impracticable reaction calculations at low energies

  2. A Simple Approach to the Landau-Zener Formula

    Science.gov (United States)

    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.)

  3. On the construction of general cubature formula by flat extensions

    Science.gov (United States)

    Bucero, Marta Abril; Bajaj, Chandrajit

    2016-01-01

    We describe a new method to compute general cubature formulae. The problem is initially transformed into the computation of truncated Hankel operators with flat extensions. We then analyze the algebraic properties associated to flat extensions and show how to recover the cubature points and weights from the truncated Hankel operator. We next present an algorithm to test the flat extension property and to additionally compute the decomposition. To generate cubature formulae with a minimal number of points, we propose a new relaxation hierarchy of convex optimization problems minimizing the nuclear norm of the Hankel operators. For a suitably high order of convex relaxation, the minimizer of the optimization problem corresponds to a cubature formula. Furthermore cubature formulae with a minimal number of points are associated to faces of the convex sets. We illustrate our method on some examples, and for each we obtain a new minimal cubature formula.

  4. 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.

  5. Cluster radioactivity in trans-tin region using semiempirical formula

    International Nuclear Information System (INIS)

    A semiempirical formula with only three parameters for calculating the logarithm of half-lives of heavy particle emission from a radioactive nucleus is recently proposed. The constants in the formula were obtained by fitting the available data in the trans-actinide region. The suitability of the formula in trans-tin region is studied here. The present study reveals that the semiempirical formula with only three parameters is not agreeing well with other theoretical models in the trans-tin region. Hence, one of the constants proposed earlier which acts a scaling constant is suitably replaced by a quadratic equation. The results are compared with analytical superasymmetric fission model and Shanmugham and Kamalakaran model. The semiempirical formula with new set of constants are found to have a better agreement with the available theoretical results. (author)

  6. BOUNDARY INTEGRAL FORMULA OF ELASTIC PROBLEMS IN CIRCLE PLANE

    Institute of Scientific and Technical Information of China (English)

    DONG Zheng-zhu; LI Shun-cai; YU De-hao

    2005-01-01

    By bianalytic functions, the boundary integral formula of the stress function for the elastic problem in a circle plane is developed. But this integral formula includes a strongly singular integral and can not be directly calculated. After the stress function is expounded to Fourier series, making use of some formulas in generalized functions to the convolutions, the boundary integral formula which does not include strongly singular integral is derived further. Then the stress function can be got simply by the integration of the values of the stress function and its derivative on the boundary. Some examples are given. It shows that the boundary integral formula of the stress function for the elastic problem is convenient.

  7. Formulas for fixing serum sodium: curb your enthusiasm.

    Science.gov (United States)

    Sterns, Richard H

    2016-08-01

    A variety of formulas have been proposed to predict changes in serum sodium concentration. All are based on an experiment done over 50 years ago by Edelman, who derived a formula relating the plasma sodium concentration to isotopically measured body sodium, potassium, and water. Some of these formulas fail because they do not include urinary losses of electrolytes and water. Even those that include these essential variables are not accurate enough for clinical use because it is impractical to adjust calculations to rapid changes in urinary composition, and because the formulas do not account for changes in serum sodium caused by internal exchanges between soluble and bound sodium stores or shifts of water into or out of cells resulting from changes in intracellular organic osmolytes. Nephrologists should curb their enthusiasm for predictive formulas and rely instead on frequent measurements of the serum sodium when correcting hyponatremia and hypernatremia. PMID:27478590

  8. Kubo formulas for dispersion in heterogeneous periodic nonequilibrium systems.

    Science.gov (United States)

    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. PMID:26764628

  9. 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.

  10. Custom Formula-Based Visualizations for Savvy Designers"

    DEFF Research Database (Denmark)

    Kuhail, Mohammad Amin

    . For instance, it would save time and money if a clinician familiar with spreadsheet formulas could refine a visualization (e.g. the lifelines) rather than hiring a programmer. Existing approaches to visualization are one of the two: accessible to savvy designers but limited in customizability, or inaccessible...... and expressive. For instance, chart tools are easy to use, but support only predefined visualizations, while visualization tools support custom visualizations, but require program-like specifications. This thesis presents Uvis, a visualization system that targets savvy designers. With Uvis, designers drag...... and drop visual objects, set the visual object properties with formulas, and see the result immediately. The formulas are declarative and similar to spreadsheet formulas. The formulas compute the property values and can refer to fields, visual properties, functions, etc. This thesis hypothesizes...

  11. Growth and development during the first year of life of infants fed breast-milk, milk formula or soy formula

    Science.gov (United States)

    The adequacy of soy infant formulas to support growth and development is still under debate. The concerns center on the phytochemicals such as isoflavones which are associated with the soy proteins, the sole source of protein in soy infant formulas. To assess growth and development of infants fed br...

  12. 21 CFR 107.230 - Elements of an infant formula recall.

    Science.gov (United States)

    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:...

  13. Physicians, formula companies, and advertising. A historical perspective.

    Science.gov (United States)

    Greer, F R; Apple, R D

    1991-03-01

    The recent advent of new advertising campaigns for infant formulas aimed at the general public via television commercials, newspapers, free formula coupons, and lay periodicals has disrupted a comfortable symbiotic relationship between infant food manufacturers and the medical profession that has endured for more than 50 years. In the late 19th century, physicians were concerned about the advertising claims of these products and generally felt that indications and directions for their use should be the province of the physician. Between 1929 and 1932, the American Medical Association, through its Committee on Foods and "Seal of Acceptance," essentially required the entire formula industry to advertise only to the medical profession. Since 1932, the US formula industry has developed into a $1.6 billion market. In 1988, Nestlé (absent from the US infant formula industry since the 1940s) acquired the Carnation Company and launched an advertising campaign to the general public for its formula products. Bristol Myers/Mead Johnson, in cooperation with Gerber Products Company, quickly followed suit. These actions threaten to once again remove the realm of infant feeding from the exclusive supervision of the medical profession. The new multimedia public advertising campaigns may increase the cost of infant formula to the general public and have a negative impact on the incidence of breast-feeding. In addition, formula advertising campaigns will likely increase the danger of advertising hyperbole and affect the level of financial support by formula companies for scientific meetings, medical research, education, and social events at medical meetings. PMID:1781817

  14. 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.

  15. Recommended formulae and formats for a resonance parameter library

    International Nuclear Information System (INIS)

    It is proposed that a library of neutron resonance parameters be set up, on punched cards and magnetic tape, which will complement the cross section data in the present U.K. Nuclear Data Library. This report gives parametric formulae for the resolved resonance region, based on:- (i) the Breit-Wigner approximation, (ii) other approximations of R-matrix theory and (iii) the formulae of Adler and Adler. In addition, the statistical distributions of the parameters are given. The final section of the report contains the recommended formats for the parameters of the various formulae. (author)

  16. 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.

  17. 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.

  18. Correction to the Moliere's formula for multiple scattering

    CERN Document Server

    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.

  19. 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....

  20. A generalized Allwright formula and the vector Riccati equation

    CERN Document Server

    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.

  1. Hydrolyzed infant formula and early β-cell autoimmunity

    DEFF Research Database (Denmark)

    Knip, Mikael; Åkerblom, Hans K; Becker, Dorothy;

    2014-01-01

    intact proteins. OBJECTIVE: To test the hypothesis that weaning to an extensively hydrolyzed formula decreases the cumulative incidence of diabetes-associated autoantibodies in young children. DESIGN, SETTING, AND PARTICIPANTS: A double-blind randomized clinical trial of 2159 infants with HLA...... no clinically significant differences in the rate of reported adverse events between the 2 groups. CONCLUSIONS AND RELEVANCE: Among infants at risk for type 1 diabetes, the use of a hydrolyzed formula, when compared with a conventional formula, did not reduce the incidence of diabetes-associated autoantibodies...

  2. Cardy-Verlinde Formula of Noncommutative Schwarzschild Black Hole

    OpenAIRE

    Abbas, G.

    2014-01-01

    Few years ago, Setare \\cite{1} has investigated the Cardy-Verlinde formula of non-commutative black hole obtained by non-commutativity of coordinates. In this paper, we apply the same procedure to a non-commutative black hole obtained by the co-ordinate coherent approch. The Cardy-Verlinde formula is entropy formula of conformal field theory in an arbitrary dimension. It relates the entropy of conformal filed theory to its total energy and Casimir energy. In this paper, we have calculated the...

  3. Improving accessibility to mathematical formulas: the Wikipedia Math Accessor

    Science.gov (United States)

    Fuentes Sepúlveda, J.; Ferres, L.

    2012-09-01

    Mathematics accessibility is an important topic for inclusive education. In this paper, we make Wikipedia's repository of mathematical formulas accessible by providing a natural language description of its more than 420,000 formulas using a well-researched sub-language. We also contribute by targeting Spanish speakers, for whom assistive technologies, particularly domain-specific technologies like the one described here, are scarce. Our focus on the semantics of formulas (rather than their visual appearance) allowed us to generate verbalizations with a precision of approximately 80% of understandable descriptions, as shown in an evaluation with sighted users.

  4. VERIFICATION AND COMPARISON OF FORMULAS FOR BED LOAD TRANSPORT

    Institute of Scientific and Technical Information of China (English)

    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.

  5. On the satisfiability of random regular signed SAT formulas

    CERN Document Server

    Laus, Christian

    2011-01-01

    Regular signed SAT is a variant of the well-known satisfiability problem in which the variables can take values in a fixed set V \\subset [0,1], and the `literals' have the form "x \\le a" or "x \\ge a". We answer some open question regarding random regular signed k-SAT formulas: the probability that a random formula is satisfiable increases with |V|; there is a constant upper bound on the ratio m/n of clauses m over variables n, beyond which a random formula is asypmtotically almost never satisfied; for k=2 and V=[0,1], there is a phase transition at m/n=2.

  6. On Ruby's solid angle formula and some of its generalizations

    CERN Document Server

    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.

  7. On Ruby's solid angle formula and some of its generalizations

    Science.gov (United States)

    Friot, Samuel

    2015-02-01

    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.

  8. Iterated index formulae for closed geodesics with applications

    Institute of Scientific and Technical Information of China (English)

    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.

  9. A generalized Lichnerowicz formula, the Wodzicki Residue and Gravity

    OpenAIRE

    Ackermann, Thomas; Tolksdorf, Jürgen

    1995-01-01

    We prove a generalized version of the well-known Lichnerowicz formula for the square of the most general Dirac operator $\\widetilde{D}$\\ on an even-dimensional spin manifold associated to a metric connection $\\widetilde{\

  10. Some Computational Formulas for D-Nörlund Numbers

    OpenAIRE

    Guodong Liu

    2009-01-01

    The author establishes some identities involving the $D$ numbers, Bernoulli numbers, and central factorial numbers of the first kind. A generating function and several computational formulas for $D$ -Nörlund numbers are also presented.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. Application of Erlang Formulae in Next Generation Networks

    Directory of Open Access Journals (Sweden)

    Erik Chromy

    2012-02-01

    Full Text Available The paper deals with the possibility of the Erlang B and Erlang C formula utilization in Next Generation Networks (NGN. Based on the common properties of synchronous and asynchronous networks it is possible the utilization of Erlang formulas also for asynchronous networks. It is possible to describe traffic in NGN networks by calculation of following parameters – loss, link utilization and bandwidth. The second part of this paper deals with the possibility of application of Erlang B formula in contact center. Contact center is one of the many examples of the NGN networks. By application of Erlang B formula in contact center environment it is possible to monitor following important parameters - number of agents, probability of call blocking, utilization of agents and mean number of calls in the system.

  16. The interactional significance of formulas in autistic language.

    Science.gov (United States)

    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. PMID:12945605

  17. A note on the loop formula for the fermionic determinant

    Science.gov (United States)

    Seiler, Erhard; Stamatescu, Ion-Olimpiu

    2016-08-01

    A formula expressing the fermionic determinant 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.

  18. Higher-order corrections to the Grimus-Stockinger formula

    International Nuclear Information System (INIS)

    For the Grimus-Stockinger formula one and the same dimensionless parameter of asymptotic expansion is found by several ways of calculations. This parameter strongly depends on the width of wave packet

  19. Quantum mechanical derivation of the Wallis formula for π

    International Nuclear Information System (INIS)

    A famous pre-Newtonian formula for π is obtained directly from the variational approach to the spectrum of the hydrogen atom in spaces of arbitrary dimensions greater than one, including the physical three dimensions

  20. SU(4), SU(8) mass formulas and weak interactions

    International Nuclear Information System (INIS)

    ss formulas for SU(4) and SU(8) groups were obtained, and are especially very simple for degenerate representations. Also, tensor representations of baryon multiplets are discussed together with some applications to weak decay processes. (U.S.)al

  1. A Prebiotic Formula Improves the Gastrointestinal Bacterial Flora in Toddlers

    Science.gov (United States)

    Chen, Ya-Ling; Liao, Fang-Hsuean

    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 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. PMID:27403155

  2. Asymptotic formula for eigenvalues of one dimensional Dirac system

    Science.gov (United States)

    Ulusoy, Ismail; Penahlı, Etibar

    2016-06-01

    In this paper, we study the spectral problem for one dimensional Dirac system with Dirichlet boundary conditions. By using Counting lemma, we give an asymptotic formulas of eigenvalues of Dirac system.

  3. Thermal inactivation of Enterobacter sakazakii in rehydrated infant formula.

    Science.gov (United States)

    Edelson-Mammel, Sharon G; Buchanan, Robert L

    2004-01-01

    The presence of low levels of Enterobacter sakazakii in dried infant formula have been linked to outbreaks of meningitis, septicemia, and necrotizing enterocolitis in neonates, particularly those who are premature or immunocompromised. In the current study, the ability of 12 strains of E. sakazakii to survive heating in rehydrated infant formula was determined at 58 degrees C with a submerged coil apparatus. The observed D58-values ranged from 30.5 to 591.9 s, with the strains appearing to fall into two distinct heat resistance phenotypes. The z-value of the most heat-resistant strain was 5.6 degrees C. When dried infant formula containing this strain was rehydrated with water preequilibrated to various temperatures, a more than 4-log reduction in E. sakazakii levels was achieved by preparing the formula with water at 70 degrees C or greater. PMID:14717352

  4. Confirmation of some formulas related to spin coherence time

    CERN Document Server

    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.

  5. 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.

  6. ON CAUCHY-POMPEIU FORMULA FOR FUNCTIONS WITH VALUES IN A UNIVERSAL CLIFFORD ALGEBRA

    Institute of Scientific and Technical Information of China (English)

    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].

  7. [Usefulness of a soy- and oatmeal-based formula in infant nutrition. Nitrogen balance].

    Science.gov (United States)

    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.

  8. An implicit spectral formula for generalized linear Schroedinger equations

    International Nuclear Information System (INIS)

    We generalize the semiclassical Bohr–Sommerfeld quantization rule to an exact, implicit spectral formula for linear, generalized Schroedinger equations admitting a discrete spectrum. Special cases include the position-dependent mass Schroedinger equation or the Schroedinger equation for weighted energy. Requiring knowledge of the potential and the solution associated with the lowest spectral value, our formula predicts the complete spectrum in its exact form. (author)

  9. Modified Bethe-Weizsaecker mass formula for hypernuclei

    International Nuclear Information System (INIS)

    The Bethe-Weizsaecker mass formula originally designed to reproduce the gross features of nuclear binding energies for medium and heavy mass nuclei, fails for light nuclei especially away from the line of stability. To alleviate this problem a modified Bethe-Weizsaecker mass formula was suggested which explained the gross features of the binding energy versus neutron number curves of all the elements from Li to Bi

  10. School Finance Reform: Aid Formulas and Equity Objectives

    OpenAIRE

    Duncombe, William; Yinger, John

    1998-01-01

    State education officials have implemented performance standards, but state education aid has not kept up. By focusing on the relationship between spending and property wealth, most existing aid formulas only partially account for cost differences across districts and, thus, fail to fully promote equity in school performance. This paper shows how to estimate comprehensive educational cost indexes that control for school district inefficiency and include them in state aid formulas. It also sim...

  11. Pathwise integrals and Ito-Tanaka Formula for Gaussian processes

    OpenAIRE

    Sottinen, Tommi; Viitasaari, Lauri

    2013-01-01

    We prove the Ito-Tanaka formula and the existence of pathwise stochastic integrals for a wide class of Gaussian processes. Motivated by financial applications, we define the stochastic integrals as forward-type pathwise integrals introduced by F\\"ollmer and as pathwise generalized Lebesgue-Stieltjes integrals introduced by Z\\"ahle. As an application, we illustrate the importance of Ito-Tanaka formula for pricing and hedging of financial derivatives.

  12. 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.

  13. Understanding Model Counting for beta-acyclic CNF-formulas

    OpenAIRE

    Brault-Baron, Johann; Capelli, Florent; Mengel, Stefan

    2015-01-01

    We show that SAT on beta-acyclic CNF-formulas can be solved in polynomial time. In contrast to previous algorithms for other structurally restricted classes of formulas, our algorithm does not proceed by dynamic programming. Instead, it works along an elimination order, solving a weighted version of constraint satisfaction. We give evidence that this deviation from more standard algorithms is no coincidence by showing that it is outside of the framework recently proposed by Saether et al. (SA...

  14. 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.

  15. Nuclear binding energy using semi empirical mass formula

    Science.gov (United States)

    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.

  16. Mass Formulae for Broken Supersymmetry in Curved Space-Time

    CERN Document Server

    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.

  17. 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.

  18. Dahlberg formula: a novel approach for its evaluation

    OpenAIRE

    Maria Christina de Souza Galvão; João Ricardo Sato; Edvaldo Capobiango Coelho

    2012-01-01

    INTRODUCTION: The accurate evaluation of error of measurement (EM) is extremely important as in growth studies as in clinical research, since there are usually quantitatively small changes. In any study it is important to evaluate the EM to validate the results and, consequently, the conclusions. Because of its extreme simplicity, the Dahlberg formula is largely used worldwide, mainly in cephalometric studies. OBJECTIVES: (I) To elucidate the formula proposed by Dahlberg in 1940, evaluating i...

  19. Duality and corrections to the van Royen-Weisskopf formula

    International Nuclear Information System (INIS)

    We propose that duality can be used in conjunction with QCD calculations of the cross section for e+e- → qanti q- to evaluate relativistic and radiative corrections to the leptonic widths of the psi and UPSILON states. We use this method to discuss relativistic corrections to the van Royen-Weisskopf formula for leptonic widths. We also point out that this formula is in error by an important factor 4m2sub(q)/M2sub(n). (orig.)

  20. On the Limitations of Neutrino Emissivity Formula of Iwamoto

    OpenAIRE

    Ghosh, Sanjay K.; Phatak, S. C.; Sahu, Pradip K.

    1993-01-01

    The neutrino emissivity from two and three flavour quark matter is numerically calculated and compared with Iwamoto's formula. We find that the calculated emissivity is smaller than Iwamoto's result by orders of magnitude when $p_{f}(u)+p_{f}(e)-p_{f}(d(s))$ is comparable with the temperature. We attribute it to the severe restriction imposed by momentum conservation on the phase space integral. We obtain an alternate formula for the neutrino emissivity which is valid when the quarks and elec...

  1. Analysis of a Carbon Fibre Rim : Student Formula

    OpenAIRE

    Uyttersprot, Bryan

    2015-01-01

    This master’s thesis is within the context of a formula race competition between universities. The main goal is to replace the modern rims of the TAMK Student Formula car by lighter and more efficient rims. To achieve this goal, important topics such as general rim design, tyre forces, tyre moments, strength of materials, fatigue and mechanical properties of carbon fibre were examined. Carbon fibre was applied because of its decent strength, weight and fatigue characteristics. Two possib...

  2. A next-to-leading Lüscher formula

    International Nuclear Information System (INIS)

    We propose a next-to-leading Lüscher-like formula for the finite-size corrections of the excited states energies in integrable theories. We conjecture the expressions of the corrections for both the energy and the particles’ rapidities by interpreting the excited states as momenta-dependent defects. We check the resulting formulas in some simple relativistic model and conjecture those for the AdS5/CFT4 case

  3. A Prebiotic Formula Improves the Gastrointestinal Bacterial Flora in Toddlers

    OpenAIRE

    Chen, Ya-Ling; Liao, Fang-Hsuean; Lin, Shyh-Hsiang; Chien, Yi-Wen

    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...

  4. Extended Griess algebras and Matsuo-Norton trace formulae

    OpenAIRE

    Yamauchi, Hiroshi

    2012-01-01

    We introduce the Z_2-extended Griess algebra of a vertex operator superalgebra with an involution and derive the Matsuo-Norton trace formulae for the extended Griess algebra based on conformal design structure. We illustrate an application of our formulae by reformulating the one-to-one correspondence between 2A-elements of the Baby-monster simple group and N=1 c=7/10 Virasoro subalgebras inside the Baby-monster vertex operator superalgebra.

  5. On generalization of Kible-Slepian kernel formula

    CERN Document Server

    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.

  6. Arthur's invariant trace formula and comparison of inner forms

    CERN Document Server

    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...

  7. A New Binary BBP-type Formula for $\\sqrt 5\\,\\log\\phi$

    OpenAIRE

    Adegoke, Kunle

    2016-01-01

    Hitherto only a base 5 BBP-type formula is known for $\\sqrt 5\\log\\phi$, where \\mbox{$\\phi=(\\sqrt 5+1)/2$}, the golden ratio, ( i.e. Formula 83 of the April 2013 edition of Bailey's Compendium of \\mbox{BBP-type} formulas). In this paper we derive a new binary BBP-type formula for this constant. The formula is obtained as a particular case of a BBP-type formula for a family of logarithms.

  8. Growth of breast-fed and formula-fed infants.

    Science.gov (United States)

    Ziegler, Ekhard E

    2006-01-01

    Growth and nutrition during infancy are being viewed with renewed interest because of the possibility that they may be linked to cardiovascular and metabolic health in later life. Of particular interest are differences between breast- and formula-fed infants with regard to nutrient intake and growth because breastfeeding has been shown to be associated with a reduced risk of obesity in later life. During the first 6-8 weeks of life there is little difference in growth (gain in weight and length) between breast- and formula-fed infants. However, from about 2 months of age to the end of the first year of life formula-fed infants gain weight and length more rapidly than breast-fed infants. There are no consistent differences in adiposity during the first 4-5 months of life, but during the later part of the first year of life the preponderance of the evidence suggests that breast-fed infants are leaner than formula-fed infants. Formula-fed infants at 4-5 months of age show higher plasma levels of insulin-like growth factor-1 (IGF-1), insulin and certain amino acids than breast-fed infants. Whereas the protein intake of breast-fed infants decreases with age and closely matches the requirements for protein during the early months of life, the protein intake of formula-fed infants exceeds requirements after the first 1-2 months of life. The data are consistent with the hypothesis that differences in protein intake are mainly responsible for differences in growth between breast- and formula-fed infants. Differences in energy intake probably are responsible for differences in adiposity observed in older infants.

  9. 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.

  10. 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.

  11. Analysis of the mass formula dependence of spallation product distribution

    International Nuclear Information System (INIS)

    A new version of a spallation reaction simulation code NUCLEUS has been developed by incorporating the newly revised Uno and Yamada's mass formula. The mass formula dependence of the spallation product distribution has been investigated by comparing the new results with those calculated by the original version which uses the combination of the Cameron's mass formula and the mass table compiled by Wapstra et al. Detailed differences between these two mass formulas are shown in the comparisons of mass excess values. The distributions of spallation products of a uranium target nucleus bombarded by high energy (0.38 - 2.9 GeV) protons have been calculated with the new and original versions of NUCLEUS. The calculated results show that there is no significant discrepancy in the non-fission component of cumulative product yields such as the mass distribution and the number of emitted neutrons but in the fission component Uno and Yamada's mass formula reproduces the measured data obtained from thin foil experiments significantly better, especially in the neutron excess side, than the Cameron's one. (author)

  12. Students' Understanding of Chemical Formulae: A review of empirical research

    Science.gov (United States)

    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.

  13. Orbital magnetism of Bloch electrons I. General formula

    International Nuclear Information System (INIS)

    We derive an exact formula of orbital susceptibility expressed in terms of Bloch wave functions, starting from the exact one-line formula by Fukuyama in terms of Green's functions. The obtained formula contains four contributions: (1) Landau-Peierls susceptibility, (2) interband contribution, (3) Fermi surface contribution, and (4) contribution from occupied states. Except for the Landau-Peierls susceptibility, the other three contributions involve the crystal-momentum derivatives of Bloch wave functions. Physical meaning of each term is clarified. The present formula is simplified compared with those obtained previously by Hebborn et al. Based on the formula, it is seen first of all that diamagnetism from core electrons and Van Vleck susceptibility are the only contributions in the atomic limit. The band effects are then studied in terms of linear combination of atomic orbital treating overlap integrals between atomic orbitals as a perturbation and the itinerant feature of Bloch electrons in solids are clarified systematically for the first time. (author)

  14. Phenomenological formula for alpha-decay half-lives

    International Nuclear Information System (INIS)

    A phenomenological formula is presented for the partial half-life from the Q value for α decay. It is constructed in a conventional way by considering the penetrability of a charged particle in a spherical Coulomb potential. Parameters in the formula are fixed because they are determined by physical constants except for the following three adjustable parameters: the product of the collision frequency of an α particle and the formation probability, N; the distance between the charge radius and the radius of an inner point of the Coulomb barrier, r 0; and the odd-mass hindrance, h 0. The values obtained for the three adjustable parameters are reasonable, in contrast with those of conventional models such as the Viola-Seaborg formula. The root-mean-square deviations from experimental partial half-lives for even-even, odd-A, and odd-odd nuclei are 0.344, 0.740, and 0.940 (in log10), respectively. The obtained formula gives half-lives that are two or three times longer than those obtained using the Viola-Seaborg formula in the superheavy nuclear mass region. (author)

  15. Families of automorphic forms and the trace formula

    CERN Document Server

    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.

  16. A Weizsacker-Bethe type mass formula for hypernuclei

    International Nuclear Information System (INIS)

    Theoretical estimates of hypernuclear binding energies are generally much larger than the empirical value and the disagreement is rather marked for the binding energy of sub(Λ)5He. Here we try to explain the so-called over-binding problem by way of introducing a Weizsacker-Bethe type mass formula used for ordinary nuclei. Using the most recent data on binding energies of hypernuclei, parameters of the hypernuclear mass formula are estimated by fitting a least-square curve as is the usual practice in nuclear physics. Theoretical predictions for hypernuclear binding energies are then made by using the formula as obtained above and results compared with experimental values. Agreement with experiment is found to be rather good and in particular the result obtained for sub(Λ)5He, although slightly larger than the observed value, has shown significant improvement over earlier estimates. (author)

  17. Analytic flux formulas and tables of shielding functions

    Energy Technology Data Exchange (ETDEWEB)

    Wallace, O.J.

    1981-06-01

    Hand calculations of radiation flux and dose rates are often useful in evaluating radiation shielding and in determining the scope of a problem. The flux formulas appropriate to such calculations are almost always based on the point kernel and allow for at most the consideration of laminar slab shields. These formulas often require access to tables of values of integral functions for effective use. Flux formulas and function tables appropriate to calculations involving homogeneous source regions with the shapes of lines, disks, slabs, truncated cones, cylinders, and spheres are presented. Slab shields may be included in most of these calculations, and the effect of a cylindrical shield surrounding a cylindrical source may be estimated. Detector points may be located axially, laterally, or interior to a cylindrical source. Line sources may be tilted with respect to a slab shield. All function tables are given for a wide range of arguments.

  18. 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.)

  19. Dr. Euler's fabulous formula Cures many mathematical ills

    CERN Document Server

    Nahin, Paul J

    2006-01-01

    I used to think math was no fun'Cause I couldn't see how it was doneNow Euler's my heroFor I now see why zeroEquals e[pi] i+1--Paul Nahin, electrical engineer In the mid-eighteenth century, Swiss-born mathematician Leonhard Euler developed a formula so innovative and complex that it continues to inspire research, discussion, and even the occasional limerick. Dr. Euler's Fabulous Formula shares the fascinating story of this groundbreaking formula--long regarded as the gold standard for mathematical beauty--and shows why it still lies at the heart of complex number theory. This book is the seque

  20. Modular forms and a generalized Cardy formula in higher dimensions

    Science.gov (United States)

    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.

  1. The Parkland formula under fire: is the criticism justified?

    Science.gov (United States)

    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.

  2. Inversion formula for the growth function of a cancellative monoid

    CERN Document Server

    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.

  3. Crosstalk Model and Estimation Formula for VLSI Interconnect Wires

    Institute of Scientific and Technical Information of China (English)

    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.

  4. A Gamma Class Formula for Open Gromov-Witten Calculations

    CERN Document Server

    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.

  5. New integral formula and its applications to light nucleus reactions

    CERN Document Server

    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.

  6. Analytic study of the Migdal-Kadanoff recursion formula

    International Nuclear Information System (INIS)

    After proposing lattice gauge field models in which the Migdal renormalization group recursion formulas are exact, we study the recursion formulas analytically. If D is less than 4, it is shown that the effective actions of D-dimensional U(1) lattice gauge models are uniformly driven to the high temperature region no matter how low the initial temperature is. If the initial temperature is large enough, this holds for any D and gauge group G. These are also the cases for the recursion formulas of Kadanoff type. It turns out, however, that the string tension for D=3 obtained by these methods is rather big compared with the one already obtained by Mack, Goepfert and by the present author. The reason is clarified. (orig.)

  7. Analytic flux formulas and tables of shielding functions

    International Nuclear Information System (INIS)

    Hand calculations of radiation flux and dose rates are often useful in evaluating radiation shielding and in determining the scope of a problem. The flux formulas appropriate to such calculations are almost always based on the point kernel and allow for at most the consideration of laminar slab shields. These formulas often require access to tables of values of integral functions for effective use. Flux formulas and function tables appropriate to calculations involving homogeneous source regions with the shapes of lines, disks, slabs, truncated cones, cylinders, and spheres are presented. Slab shields may be included in most of these calculations, and the effect of a cylindrical shield surrounding a cylindrical source may be estimated. Detector points may be located axially, laterally, or interior to a cylindrical source. Line sources may be tilted with respect to a slab shield. All function tables are given for a wide range of arguments

  8. Some reference formulas for the generating functions of canonical transformations

    International Nuclear Information System (INIS)

    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.)

  9. Explorations of two empirical formulas for fermion masses

    International Nuclear Information System (INIS)

    Two empirical formulas for the lepton and quark masses (i.e. Kartavtsev's extended Koide formulas), Kl = (sum lml)/(sum l√(ml))2 = 2/3 and Kq = (sum qmq)/(sum q√(mq))2 = 2/3, are explored in this paper. For the lepton sector, we show that Kl = 2/3, only if the uncertainty of the tauon mass is relaxed to about 2σ confidence level, and the neutrino masses can consequently be extracted with the current experimental data. For the quark sector, the extended Koide formula should only be applied to the running quark masses, and Kq is found to be rather insensitive to the renormalization effects in a large range of energy scales from GeV to 1012 GeV. We find that Kq is always slightly larger than 2/3, but the discrepancy is merely about 5%. (orig.)

  10. Conditions for predicting quasistationary states by rearrangement formula

    Science.gov (United States)

    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.

  11. Some reference formulas for the generating functions of canonical transformations

    Science.gov (United States)

    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.

  12. Some reference formulas for the generating functions of canonical transformations

    CERN Document Server

    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.

  13. Mineral retention in three-week-old piglets fed goat and cow milk infant formulas

    NARCIS (Netherlands)

    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

  14. New double inequalities for g-frames in Hilbert [Formula: see text]-modules.

    Science.gov (United States)

    Xiang, Zhong-Qi

    2016-01-01

    In this work, we establish two types of double inequalities for g-frames in Hilbert [Formula: see text]-modules, which involve scalars [Formula: see text] and [Formula: see text] respectively. It is shown that the results we obtained can immediately lead to the existing corresponding results when taking [Formula: see text]. PMID:27441144

  15. 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

  16. An index formula for the extended Heisenberg algebra of Epstein, Melrose and Mendoza

    CERN Document Server

    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.

  17. 21 CFR 107.260 - Revision of an infant formula recall.

    Science.gov (United States)

    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,...

  18. 21 CFR 107.250 - Termination of an infant formula recall.

    Science.gov (United States)

    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...

  19. 21 CFR 107.220 - Scope and effect of infant formula recalls.

    Science.gov (United States)

    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...

  20. Microbiological assessment and evaluation of rehydration instructions on powdered infant formulas, follow-up formulas, and infant foods in Malaysia.

    Science.gov (United States)

    Abdullah Sani, N; Hartantyo, S H P; Forsythe, S J

    2013-01-01

    A total of 90 samples comprising powdered infant formulas (n=51), follow-up formulas (n=21), and infant foods (n=18) from 15 domestic and imported brands were purchased from various retailers in Klang Valley, Malaysia and evaluated in terms of microbiological quality and the similarity of rehydration instructions on the product label to guidelines set by the World Health Organization. Microbiological analysis included the determination of aerobic plate count (APC) and the presence of Enterobacteriaceae and Cronobacter spp. Isolates of interest were identified using ID 32E (bioMérieux France, Craponne, France). In this study, 87% of powdered infant formulas, follow-up formulas, and infant foods analyzed had an APC below the permitted level of 70°C for formula preparation, as specified by the 2008 revised World Health Organization guidelines. Six brands instructed the use of water at 40 to 55°C, a temperature range that would support the survival and even growth of Enterobacteriaceae. PMID:23141821

  1. The U.S. infant formula industry: is direct-to-consumer advertising unethical or inevitable?

    Science.gov (United States)

    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. PMID:12077809

  2. Formulas giving prime numbers under Cram\\'er's conjecture

    OpenAIRE

    Farhi, Bakir

    2006-01-01

    Under Cram\\'er's conjecture concerning the prime numbers, we prove that for any $x>1$, there exists a real $A=A(x)>1$ for which the formula $[A^{n^x}]$ (where $[]$ denotes the integer part) gives a prime number for any positive integer $n$. Under the same conjecture, we also prove that for any $\\epsilon>0$, there exists a positive real number $B$ for which the formula $[B.{n!}^{2+\\epsilon}]$ gives a prime number for any sufficiently large positive integer $n$.

  3. Reducing Spreadsheet Risk with FormulaDataSleuth

    CERN Document Server

    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.

  4. Comparison of semiempirical formulae for alpha decay half-lives

    International Nuclear Information System (INIS)

    The semiempirical relationships given by Froeman, Wapstra et al., Viola and Seaborg, Hornshoj et al., Taagepera and Nurmia, Keller and Munzel for alpha decay half-lives are compared with experimental results and with a new formula derived by the authors form the fission theory of alpha decay in even-even, odd-even, even-odd and odd-odd nuclei. By taking into consideration the shell effects, the new formula allows one to obtain a better agreement with experimental data, even in the neighbourhood of the magic numbers

  5. 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.

  6. ROLL CAGE DESIGN AND ANALYSIS FOR FORMULA STUDENT RACE CAR

    OpenAIRE

    Shubham Kolhe *, Vrushabh U. Joijode

    2016-01-01

    This paper deals with the Design and Analysis of Roll Cage for the Formula Student Car. In a Formula Student Car the roll cage is one of the main components. It form the structure or the main frame of the vehicle on which other parts like Engine, Steering, and Transmission are mounted. Roll Cage comes under the sprung mass of the Vehicle. There are a lot of forces acting on vehicle in the running condition. These forces are responsible for causing crack initiation and deformation in the vehic...

  7. 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.

  8. Filtrations, factorizations and explicit formulae for harmonic maps

    CERN Document Server

    Svensson, Martin

    2009-01-01

    We use filtrations of the Grassmannian model to produce explicit algebraic formulae for harmonic maps of finite uniton number from a Riemann surface to the unitary group for a general class of factorizations by unitons. We show how these specialize to give explicit formulae for harmonic maps into the special orthogonal and symplectic groups, real, complex and quaternionic Grassmannians, and the spaces SO(2m)/U(m) and Sp(n)/U(n), i.e., all the classical compact Lie groups and their inner symmetric spaces. Our methods also give explicit J_2-holomorphic lifts for harmonic maps into Grassmannians and an explicit Iwasawa decomposition.

  9. 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...... 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...

  10. The Differential Virial Theorem with Gradient Formulas for the Operators

    CERN Document Server

    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.

  11. SPECTRAL DECOMPOSITRION FORMULA FORREGULARIZATION SOLUTION OF ILL-POSED EQUATION

    Institute of Scientific and Technical Information of China (English)

    ShenYunzhong; HsuH.T.

    2003-01-01

    This paper discusses the regularization solution of ill-posed equation with the help of its spectral decomposition formula. It shows that regularization can filter the influence of the high frequency errors which are very sensitive to the parameters to be estimated, and gives a complete derivation of the spectral decomposition formulae of least squares adjustment, rank-deficient adjustment and the regularization solution of ill-posed equation. It also shows the equivalence between the trace of the mean squares error and the expectation of the second norm of estimated parameter's total error.

  12. Improved Numerical Generalization of Bethe- Weizsacker Mass Formula

    CERN Document Server

    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.

  13. Approximate formulas for total cross section for moderately small eikonal

    CERN Document Server

    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.

  14. Analytic formulas for above threshold ionization or detachment plateau spectra

    Science.gov (United States)

    Frolov, M. V.; Manakov, N. L.; Starace, Anthony F.

    2009-11-01

    Closed form analytic formulas are derived in the tunneling limit for both above threshold detachment (ATD) of negative ions and above threshold ionization (ATI) of neutral atoms. These formulas provide a fully quantum justification of the well-known classical three-step scenario for strong field ionization and detachment spectra in the high energy region of the ATI or ATD plateau and also provide analytical insight into how the ATI/ATD rates may be controlled by varying the laser field parameters or by varying the atomic species.

  15. Evaluations of energy coefficients of Bethe-Weizsacker mass formula

    CERN Document Server

    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.

  16. Geometric Product Formula for Charged Accelerating Black Hole

    CERN Document Server

    Pradhan, Parthapratim

    2016-01-01

    We evaluate the geometric product formula i.e. area (or entropy) product formula of outer horizon (${\\cal H}^{+}$) and inner horizon (${\\cal H}^{-}$) for charged accelerating black hole. We find that mass-independent area functional relation of ${\\cal H}^{\\pm}$ for this black hole in terms of black hole charge, acceleration, cosmological constant and \\emph{cosmic string tension} respectively. We also compute the \\emph{Penrose inequality} for this black hole. Finally we compute the specific heat for this BH to determine the local thermodynamic stability of this black hole. Under certain criterion the black hole displayed second order phase transition.

  17. Nuclear shell energies and deformations in atomic mass formula

    International Nuclear Information System (INIS)

    Our group has for several years been studying a method of calculating nuclear shell energies and incorporating them into a mass formula. This method is characterized by the calculation of single-particle levels in an extended spherical Woods-Saxon potential, the extraction of crude shell energy, the refinement of crude shell energy due to residual interactions, and the incorporation into a mass formula. Here, we report the advance of this work focusing especially on nuclear deformations, and give some preliminary results and remarks. (author)

  18. 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.

  19. 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...

  20. 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.)

  1. An algorithm for the Baker-Campbell-Hausdorff formula

    Science.gov (United States)

    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

  2. Testing the Witten-Veneziano formula on the lattice

    International Nuclear Information System (INIS)

    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 Nf=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.

  3. 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.

  4. ψ-Contraction and [Formula: see text]-contraction in Menger probabilistic metric space.

    Science.gov (United States)

    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.

  5. Educational Intervention to Modify Bottle-Feeding Behaviors among Formula-Feeding Mothers in the WIC Program: Impact on Infant Formula Intake and Weight Gain

    Science.gov (United States)

    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…

  6. Hypoallergenic formulas--when, to whom and how long

    DEFF Research Database (Denmark)

    Høst, A; Halken, S

    2004-01-01

    Hypoallergenic formulas are processed by enzymatic hydrolysis of different protein sources such as bovine casein/whey and soy followed by further processing such as heat treatment and/or ultrafiltration, or they are based on amino acid mixtures. The products have been classified according to the ...

  7. 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.

  8. Gauss-Bonnet's Formula and Closed Frenet Frames

    DEFF Research Database (Denmark)

    Røgen, Peter

    1998-01-01

    curves are found using Gauss-Bonnet's theorem after cutting the curve into simple closed sub-curves. If the spherical curve is the tangent indicatrix of a space curve we obtain a new short proof of a formula for integrated torsion presented in an unpublished manuscript by C. Chicone and N.J. Kalton...

  9. 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.

  10. The Campus-Based Formula. NASFAA Task Force Report

    Science.gov (United States)

    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,…

  11. 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...

  12. 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 system...

  13. The pricing kernel and the Black-Scholes formula.

    OpenAIRE

    Molinari, Franco

    2009-01-01

    This note provides an introduction to the pricing kernel methodology for financial derivatives. In order to illustrate the pricing kernel approach we apply it to the Black and Scholes model and obtain the famous Black and Scholes formula for the fair price of an European call option.

  14. 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.

  15. New Formula for Stability of Cube Armoured Roundheads

    DEFF Research Database (Denmark)

    Maciñeira, Enrique; Burcharth, Hans F.

    2007-01-01

    Design of armour for rubble mound breakwater roundheads constitutes in many cases a problem due to the limitation of available data and guidelines. The objective of the paper is to present the results of a comprehensive model test study on the stability of cube armoured roundheads, resulting...... in a new stability formula...

  16. Relativistic bound states: a mass formula for vector mesons

    International Nuclear Information System (INIS)

    In the framework of a relativistic description of two particles bound states, a mass formula for vector mesons considered as quark-antiquark systems bound by harmonic oscillator like forces is proposed. Results in good agreement with experimental values are obtained

  17. 24 CFR 92.454 - Reallocations by formula.

    Science.gov (United States)

    2010-04-01

    ... jurisdiction under 24 CFR 91.520(f) for failure to submit in a timely manner a performance report required by 24 CFR 91.520 that is satisfactory to HUD; and (4) Any HOME funds remitted to HUD under § 92.503(b... 24 Housing and Urban Development 1 2010-04-01 2010-04-01 false Reallocations by formula....

  18. Problem Solvers: Problem--Area beyond the Formula

    Science.gov (United States)

    Dean, Chrystal

    2014-01-01

    In this article, associate professor Chrystal Dean describes how teachers can challenge their upper elementary students' understanding of area beyond a memorized formula. Herein she describes an activity that will show students the "why" behind using A = l × w to solve rectangular area problems. The activity will help deepen…

  19. 45 CFR 87.2 - Formula and block grants.

    Science.gov (United States)

    2010-10-01

    ... the Charitable Choice regulations found at 42 CFR Part 54 and 45 CFR Parts 96, 260, and 1050. (b... CFR Parts 74, 92, and 96. (c) Organizations that receive direct financial assistance from the... 45 Public Welfare 1 2010-10-01 2010-10-01 false Formula and block grants. 87.2 Section 87.2...

  20. 24 CFR 968.310 - Determination of formula amount.

    Science.gov (United States)

    2010-04-01

    .... After a PHA is designated as a mod troubled agency under PHMAP (24 CFR part 901), HUD shall inform the... CFR part 950 (subpart I) which are not determined to be high risk under § 950.135 of this chapter, the... 24 Housing and Urban Development 4 2010-04-01 2010-04-01 false Determination of formula...

  1. 24 CFR 574.110 - Overview of formula allocations.

    Science.gov (United States)

    2010-04-01

    ... approval of a consolidated plan, pursuant to 24 CFR part 91, that covers the assistance to be provided... this part (providing they comply with 24 CFR part 91) for eligible activities that address the housing... 24 Housing and Urban Development 3 2010-04-01 2010-04-01 false Overview of formula...

  2. Enteral nutrition formula selection: current evidence and implications for practice.

    Science.gov (United States)

    Brown, Britta; Roehl, Kelly; Betz, Melanie

    2015-02-01

    Many new enteral nutrition (EN) formulas have been created over the past several decades with a variety of intended uses. Although each is intended to promote improved outcomes, research is often unclear and, in many cases, conflicting. It is important to note that EN products are considered medical foods by the U.S. Food and Drug Administration and therefore do not have to complete premarket review or approval and are not regulated to the same extent as pharmaceuticals. While standard EN formulas are designed to meet the basic macro- and micronutrient requirements of individuals who cannot meet nutrition needs orally, specialty EN products have been developed to exhibit pharmacologic properties, such as immune-enhancing formulas containing arginine, glutamine, nucleotides, and ω-3 fatty acids. With the vast number of products available, rising costs of healthcare, and the drive toward evidence-based practice, it is imperative that clinicians carefully consider research regarding use of specialty formulas, paying close attention to the quality, patient population, clinical end points, and cost to patient and/or facility. PMID:25516537

  3. Modified predictive formula for the electron stopping power

    International Nuclear Information System (INIS)

    We report an improved predictive formula for the electron stopping power (SP) based on an analysis and fit of SPs and electron inelastic mean free paths (IMFPs) calculated from optical data for 37 elemental solids and energies between 200 eV and 30 keV. The formula is a function of energy, density, and IMFP, and is recommended for solids with atomic numbers larger than 6. While the mean deviation between predicted and calculated SPs was 7.25%, larger deviations were found for four additional materials, Li (22.2%), Be (17.9%), graphite (15.3%), and diamond (15.7%). The predictive SP formula can be applied to multicomponent materials. Test comparisons for two compounds, guanine and InSb, showed average deviations of 16.0% and 19.1%, respectively. The improved SP formula is expected to be useful in simulations of electron trajectories in solids with the continuous slowing-down approximation (e.g., in Auger-electron spectroscopy and electron microprobe analysis)

  4. Whole blood viscosity extrapolation formula: Note on appropriateness of units

    Directory of Open Access Journals (Sweden)

    Ezekiel Uba Nwose

    2011-01-01

    Full Text Available Background : A series has recently been done on whole blood viscosity. The first on the series proposed extrapolation chart with conventional reference range. Since the publication, two concerns have been received in personal communications. The first expressed concern over the use of serum proteins values in ′g/L′ instead of ′g/dL′ that was contained in the referenced material. The second enquired on suitability of the formula for determination of blood viscosity at low shear rate. Aim : This work sets out to compare different units-converted-modifications of the extrapolation with a view to develop a statement of comparison and suitability of units. Materials and Methods : The values of haematocrit and serum proteins were used in different unit-conversions on the mathematical formula to derive four modifications, which were compared. Five clinical cases that were specifically tested for whole blood viscosity, and had results for haematocrit and serum proteins were evaluated. The appropriateness of modifications for determination of viscosity at low shear rate was reviewed. Results : Except as modified and used in the series, determination of whole blood viscosity at low shear rate using other unit conversions on the formula yields negative values for all five cases. Conclusion : Given that it is unexpected for blood viscosity level to be zero let alone less, it is logical that negative values are invalid. A formula that gives the least invalid results may be most appropriate. Therefore, extrapolation modification used in the series is most appropriate.

  5. Matrix formulae and skein relations for cluster algebras from surfaces

    CERN Document Server

    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).

  6. 27 CFR 21.79 - Formula No. 44.

    Science.gov (United States)

    2010-04-01

    ... gallons of n-butyl alcohol (b) Authorized uses. (1) As a solvent: 430.Sterilizing and preserving solutions... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 44. 21.79 Section 21.79 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU,...

  7. 27 CFR 21.74 - Formula No. 40.

    Science.gov (United States)

    2010-04-01

    ... gallon of tert-butyl alcohol, and: One and one-half avoirdupois ounces of either (1) brucine alkaloid, (2... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 40. 21.74 Section 21.74 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU,...

  8. 27 CFR 21.71 - Formula No. 39-B.

    Science.gov (United States)

    2010-04-01

    ... and one-half gallons of diethyl phthalate and 1/8 gallon of tert-butyl alcohol. (b) Authorized uses... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 39-B. 21.71 Section 21.71 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU,...

  9. 27 CFR 21.76 - Formula No. 40-B.

    Science.gov (United States)

    2010-04-01

    ...-sixteenth avoirdupois ounce of denatonium benzoate, N.F., and 1/8 gallon of tert-butyl alcohol. (b... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 40-B. 21.76 Section 21.76 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU,...

  10. 27 CFR 21.75 - Formula No. 40-A.

    Science.gov (United States)

    2010-04-01

    ... pound of sucrose octaacetate and 1/8 gallon of tert-butyl alcohol. (b) Authorized uses. (1) As a solvent... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 40-A. 21.75 Section 21.75 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU,...

  11. 27 CFR 21.69 - Formula No. 39.

    Science.gov (United States)

    2010-04-01

    ..., N.F. VII; and 1/8 gallon of tert-butyl alcohol. (b) Authorized uses. (1) As a solvent: 111.Hair and... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 39. 21.69 Section 21.69 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU,...

  12. FORMULAS OF GAUSS-OSTROGRADSKII TYPE ON REAL FINSLER MANIFOLDS

    Institute of Scientific and Technical Information of China (English)

    Li Zhiwei; Zhong Chunping

    2008-01-01

    This article generalizes the formulas of Gauss-Ostrogradskii type for semibasic vector fields from Riemannian manifolds to real Finsler manifolds and obtains some for- mulas of Gauss-Ostrogradskii type for Finsler vector fields which are expressed in terms of the vertical and horizontal derivatives of the Cartan connection in real Finsler manifolds.

  13. Seizing the Moment for Transformation: California's Local Control Funding Formula

    Science.gov (United States)

    Miles, Karen Hawley; Feinberg, Randi

    2014-01-01

    In 2013 California adopted a new funding formula that includes a significant reinvestment in public education after years of budget cuts. The new law allocates funds differently, directing more resources to students with higher needs and providing more local control and greater transparency. This revolutionary change presents California districts…

  14. 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.

  15. General spectral flow formula for fixed maximal domain

    DEFF Research Database (Denmark)

    Booss-Bavnbek, Bernhelm; Zhu, Chaofeng

    2005-01-01

    and symplectic analysis and give a full (and surprisingly short) proof of our General Spectral Flow Formula for the case of fixed maximal domain. As a side result, we establish local stability of weak inner unique continuation property (UCP) and explain its role for parameter dependent spectral theory....

  16. Using Paperclips to Explain Empirical Formulas to Students

    Science.gov (United States)

    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,…

  17. 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.

  18. Update formulas for split-plot and block designs

    NARCIS (Netherlands)

    H. Arnouts (Heidi); P.P. Goos (Peter)

    2009-01-01

    textabstractFor the algorithmic construction of optimal experimental designs, it is important to be able to evaluate small modifications of given designs in terms of the optimality criteria at a low computational cost. This can be achieved by using powerful update formulas for the optimality criteri

  19. Discussion of the loop formula for the fermionic determinant

    CERN Document Server

    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.

  20. A note on the depth formula and vanishing of cohomology

    OpenAIRE

    Sadeghi, Arash

    2012-01-01

    It is proved that if one of the finite modules M and N, over a local ring R, has reducible complexity and has finite Gorenstein dimension then the depth formula holds, provided TorR_i(M,N) = 0 for i>>0. We also study the vanishing of cohomology of a module of finite complete intersection dimension.