#### Sample records for castagnoli formula

1. Makeham's Formula

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...

2. Makeham's Formula

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. Breastfeeding vs. Formula Feeding

... 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 ...

4. Infant formulas - overview

... 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. ...

5. Manipulation with Formulae

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:

6. Excel 2013 formulas

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

7. Prebiotics in infant formula

Vandenplas, Yvan; De Greef, Elisabeth; Veereman, Gigi

2014-01-01

The gastrointestinal microbiota of breast-fed babies differ from classic standard formula fed infants. While mother's milk is rich in prebiotic oligosaccharides and contains small amounts of probiotics, standard infant formula doesn’t. Different prebiotic oligosaccharides are added to infant formula: galacto-oligosaccharides, fructo-oligosaccharide, polydextrose, and mixtures of these. There is evidence that addition of prebiotics in infant formula alters the gastrointestinal (GI) microbiota ...

8. SOME DUAL KINEMATIC FORMULAS

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. Machin's Formula and Pi

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.

10. Excel2003 Formulas

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

11. THE ROSENBLUTH FORMULA

Yennie, D.R.

1963-06-15

The Rosenbluth formula, defined as the theoretical expression for the differential cross section for electronproton scattering under one-photon- exchange, is discussed. Electron-proton amd positron-proton scattering are compared using the formula. Some possible corrections to the Rosenbluth formula are discussed. The effects of nonelectromagnetic interactions and two-photon- exchange, with the possibility of Regge pole behavior, are also discussed. (R.E.U.)

12. China's Formula,Go!

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. Selected Baking Formulas.

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…

14. Formula misasi?! / Sten Soomlais

Soomlais, Sten

2008-01-01

Formula Student on kõrgkoolide masinaehituse ja/või autotehnika tudengite meeskondade vaheline iga-aastane tootearendusvõistlus, mis kujutab endast väikese vormelauto projekteerimist, ehitamist ja võidusõitmist ringrajal. Lisa: Formula Student Eestis

15. Perfect IFG-formulas

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.

16. Formulas as programs

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

17. Infant formulas - overview

... rice starch. They are usually needed only for infants with reflux who are not gaining weight or who are very uncomfortable. Formulas for premature and low-birth-weight infants have extra calories and minerals to meet the ...

18. Abbott Infant Formula Recall

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

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

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

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. Electromagnetic shielding formulae

This addendum to an earlier collection of electromagnetic shielding formulae (TRITA-EPP-75-27) contains simple transfer matrices suitable for calculating the quasistatic shielding efficiency for multiple transverse-field and axial-field cylindrical and spherical shields, as well as for estimating leakage fields from long coaxial cables and the normal-incidence transmission of a plane wave through a multiple plane shield. The differences and similarities between these cases are illustrated by means of equivalent circuits and transmission line analogies. The addendum also includes a discussion of a possible heuristic improvement of some shielding formulae. (author)

3. Formula Student 2012

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...

4. The Formula Essay Reconsidered

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. Chen's inversion formula

An alternative view is presented of the Chen's generalization of a formula of classic algebraic number theory, based on the Mellin transformation and Reimann's zeta function. The advantages of the Mellin transform, as a method with a primary role in asymptotic analysis, are outlined. 10 refs

6. Research Timeline: Formulaic language

Wray, Alison

2013-01-01

Creating a timeline for formulaic language is far from simple, because several partially independent lines of research have contributed to the emerging picture. Each exhibits cycles of innovation and consolidation over time: domains take a leading role in developing new knowledge and then fall back, while another area comes to the fore. Thus, some…

7. Mesh Distance Formulae

Pertel, Michael J.

1992-01-01

A table of useful summation formulae are derived, together with a Mathematica package for producing them. The distance distribution in mesh routing networks is derived. The mean and variance of the distance distribution are computed. A program for computing the distance distribution of any mesh is presented.

Peters, Elke; Pauwels, Paul

2015-01-01

This paper reports on a classroom-based study that explored the effect of explicit, vocabulary-focused instruction on English as a Foreign Language (EFL) students’ recognition, cued output and spontaneous use of academic formulaic sequences (FS). In addition, the study aimed to shed some light on which type of classroom activity might be most beneficial. Data were collected among second-year EFL business students (L1 = Dutch) in a classroom-based experiment during students’ regular English cl...

9. Formulas of Revised MRP

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.

10. Overview: Infant Formula and Fluorosis

... 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 ...

11. Cronobacter Illness and Infant Formula

... 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 ...

12. On the cable expansion formula

Liu, Qihou

2008-01-01

In this paper, a generalized version of Morton's formula is proved. Using this formula, one can write down the colored Jones polynomials of cabling of an knot in terms of the colored Jones polynomials of the original knot.

13. Bryant J. correction formula

For the practical application of the method proposed by J. Bryant, the authors carried out a series of small corrections, related with the bottom, the dead time of the detectors and channels, with the resolution time of the coincidences, with the accidental coincidences, with the decay scheme and with the gamma efficiency of the beta detector beta and the beta efficiency beta of the gamma detector. The calculation of the correction formula is presented in the development of the present report, being presented 25 combinations of the probability of the first existent state at once of one disintegration and the second state at once of the following disintegration. (Author)

Peherstorfer, Franz

2008-12-01

First we discuss briefly our former characterization theorem for positive interpolation quadrature formulas (abbreviated qf), provide an equivalent characterization in terms of Jacobi matrices, and give links and applications to other qf, in particular to Gauss-Kronrod quadratures and recent rediscoveries. Then for any polynomial t_n which generates a positive qf, a weight function (depending on n ) is given with respect to which t_n is orthogonal to mathbb{P}_{n-1} . With the help of this result an asymptotic representation of the quadrature weights is derived. In general the asymptotic behaviour is different from that of the Gaussian weights. Only under additional conditions do the quadrature weights satisfy the so-called circle law. Corresponding results are obtained for positive qf of Radau and Lobatto type.

15. Multiple Commutator Formulas

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...

16. Quadrature formulas for Fourier coefficients

Bojanov, Borislav; Petrova, Guergana

2009-09-01

We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node formula for the Fourier-Tchebycheff coefficients given by Micchelli and Sharma and construct new Gaussian formulas for the Fourier coefficients of a function, based on the values of the function and its derivatives.

17. Quadrature formulas for Fourier coefficients

Bojanov, Borislav

2009-09-01

We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node formula for the Fourier-Tchebycheff coefficients given by Micchelli and Sharma and construct new Gaussian formulas for the Fourier coefficients of a function, based on the values of the function and its derivatives. © 2009 Elsevier B.V. All rights reserved.

18. On generalized averaged Gaussian formulas

Spalevic, Miodrag M.

2007-09-01

We present a simple numerical method for constructing the optimal (generalized) averaged Gaussian quadrature formulas which are the optimal stratified extensions of Gauss quadrature formulas. These extensions exist in many cases in which real positive Kronrod formulas do not exist. For the Jacobi weight functions w(x)equiv w^{(alpha,beta)}(x)D(1-x)^alpha(1+x)^beta ( alpha,beta>-1 ) we give a necessary and sufficient condition on the parameters alpha and beta such that the optimal averaged Gaussian quadrature formulas are internal.

19. Discontinuity formulas for multiparticle amplitudes

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

20. Discontinuity formulas for multiparticle amplitudes

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.

1. Algebraic Proofs over Noncommutative Formulas

Tzameret, Iddo

2010-01-01

We study possible formulations of algebraic propositional proof systems operating with noncommutative formulas. We observe that a simple formulation gives rise to systems at least as strong as Frege---yielding a semantic way to define a Cook-Reckhow (i.e., polynomially verifiable) algebraic analogue of Frege proofs, different from that given in [BIKPRS96,GH03]. We then turn to an apparently weaker system, namely, polynomial calculus (PC) where polynomials are written as ordered formulas ("PC over ordered formulas", for short). This is an algebraic propositional proof system that operates with noncommutative polynomials in which the order of products in all monomials respects a fixed linear order on the variables, and where proof-lines are written as noncommutative formulas. We show that the latter proof system is strictly stronger than resolution, polynomial calculus and polynomial calculus with resolution (PCR) and admits polynomial-size refutations for the pigeonhole principle and the Tseitin's formulas. We...

2. Poetic grounds of epic formulae

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

3. A note on generalized averaged Gaussian formulas

Spalevic, Miodrag

2007-11-01

We have recently proposed a very simple numerical method for constructing the averaged Gaussian quadrature formulas. These formulas exist in many more cases than the real positive Gauss?Kronrod formulas. In this note we try to answer whether the averaged Gaussian formulas are an adequate alternative to the corresponding Gauss?Kronrod quadrature formulas, to estimate the remainder term of a Gaussian rule.

4. Trace formulae for arithmetical systems

For quantum problems on the pseudo-sphere generated by arithmetic groups there exist special trace formulae, called trace formulae for Hecke operators, which permit the reconstruction of wave functions from the knowledge of periodic orbits. After a short discussion of this subject, the Hecke operators trace formulae are presented for the Dirichlet problem on the modular billiard, which is a prototype of arithmetical systems. The results of numerical computations for these semiclassical type relations are in good agreement with the directly computed eigenfunctions. (author) 23 refs.; 2 figs

5. APPLICABILITY OF SEDIMENT TRANSPORT FORMULAS

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.

6. Generalized Klein-Nishina formula

Krajewska, K; Kamiński, J Z

2015-01-01

The generalized Klein-Nishina formula for Compton scattering of charged particles by a finite train of pulses is derived in the framework of quantum electrodynamics. The formula also applies to classical Thomson scattering provided that frequencies of generated radiation are smaller that the cut-off frequency. The validity of the formula for incident pulses of different durations is illustrated by numerical examples. The positions of the well-resolved Compton peaks, with the clear labeling by integer orders, opens up the possibility of the precise diagnostics of properties of relativistically intense, short laser pulses. This includes their peak intensity, the carrier-envelope phase, and their polarization properties.

7. New approach to mass formulas

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

8. CHY formula and MHV amplitudes

Du, Yi-jian; Wu, Yong-shi

2016-01-01

In this paper, we study the relation between the Cachazo-He-Yuan (CHY) formula and the maximal-helicity-violating (MHV) amplitudes of Yang-Mills and gravity in four dimensions. We prove that only one special rational solution of the scattering equations found by Weinzierl support the MHV amplitudes. Namely, localized at this solution, the integrated CHY formula reproduces the Parke-Taylor formula for Yang-Mills amplitudes as well as the Hodges formula for gravitational amplitudes. This is achieved by developing techniques, in a manifestly M\\"obius covariant formalism, to explicitly compute relevant reduced Pfaffians/determinants. We observe and prove two interesting properties (or identities), which facilitate the computations. We also check that all the other $(n-3)!-1$ solutions to the scattering equations do not support the MHV amplitudes, and prove analytically that this is indeed true for the other special rational solution proposed by Weinzierl, that actually supports the anti-MHV amplitudes.

9. FDA Abbott Infant Formula Recall

U.S. Department of Health & Human Services — On September 22, 2010, Abbott issued a voluntary recall of certain Similac powdered infant formula after identifying a common warehouse beetle (both larvae and...

10. Summation formulae on trigonometric functions

Wang, Xin; Zheng, De-Yin

2007-11-01

Trigonometric sums over the angles equally distributed on the upper half plane are investigated systematically. Their generating functions and explicit formulae are established through the combination of the formal power series method and partial fraction decompositions.

11. On generalizations of Verlinde's formula

Bántay, P

2000-01-01

It is shown that traces of mapping classes of finite order may be expressed by Verlinde-like formulae. The 3D topological argument is explained, and the resulting trace identities for modular matrix elements are presented.

12. An energy loss straggling formula

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.))

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

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

14. A recursion formula for Bayesian probabilities

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.

15. Shuffle product formulas of multiple zeta values

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.

16. 27 CFR 25.57 - Formula information.

2010-04-01

... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula information. 25.57... OF THE TREASURY LIQUORS BEER Miscellaneous Provisions Formulas § 25.57 Formula information. (a) Ingredient information. (1) For each formula you must list each separate ingredient and the specific...

17. 24 CFR 92.50 - Formula allocation.

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...

18. 27 CFR 19.378 - Formula requirements.

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....

19. Matched Formulas and Backdoor Sets

Stefan Szeider

2008-09-01

Full Text Available We demonstrate hardness results for the detection of small backdoor sets with respect to base classes Mr of CNF formulas with maximum deficiency ≤ r (M0 is the class of matched formulas. One of the results applies also to a wide range of base classes with added ‘empty clause detection’ as recently considered by Dilkina, Gomes, and Sabharwal. We obtain the hardness results in the framework of parameterized complexity, considering the upper bound on the size of smallest backdoor sets as the parameter. Furthermore we compare the generality of the parameters maximum deficiency and the size of a smallest Mr-backdoor set.

20. Geometric formula for prism deflection

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.

1. Betatron Tune Determination: Interpolation Formulas

Fabre, Ignacio

2015-01-01

In order to obtain accurate estimations of the betatron tune, interpolation formulas have been derived that give estimates that approaches the real tune as $1/N^2$ and $1/N^4$ for signals of constant amplitude. In this document interpolation formulas for signals with exponential decaying amplitudes are derived, and its errors are analyzed as a function of the input signal size and the decay constant. We obtain the same scaling law of $1/N^2$ for the case of constant amplitude, and an improvement over the previous methods in the case of decaying amplitude. Lower boundaries for the errors were observed, and methods for surpass this were analyzed.

2. Orbifold techniques in degeneration formulas

Abramovich, Dan

2011-01-01

We give an approach for relative and degenerate Gromov--Witten invariants, inspired by that of Jun Li but replacing predeformable maps by transversal maps to a twisted target. The main advantage is a significant simplification in the definition of the obstruction theory. We reprove in our language the degeneration formula, extending it to the orbifold case.

3. Recurrence Formulas for Fibonacci Sums

2008-01-01

In this article we present a new recurrence formula for a finite sum involving the Fibonacci sequence. Furthermore, we state an algorithm to compute the sum of a power series related to Fibonacci series, without the use of term-by-term differentiation theorem

4. CHY formula and MHV amplitudes

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.

5. Formulas for determining rotational constants

Guelachvili, G.

This document is part of Subvolume B Linear Triatomic Molecules', Part 9, of Volume 20 Molecular Constants mostly from Infrared Spectroscopy' of Landolt-Börnstein Group II Molecules and Radicals'. Part of the introduction, it states formulas for determining rotational constants, band center, band origin, and quadrupole coupling. Specific comments relate to BHO (HBO) and COS (OCS).

6. Error estimates for quadrature formulas

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.

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

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)

8. The Callias index formula revisited

Gesztesy, Fritz

2016-01-01

These lecture notes aim at providing a purely analytical and accessible proof of the Callias index formula. In various branches of mathematics (particularly, linear and nonlinear partial differential operators, singular integral operators, etc.) and theoretical physics (e.g., nonrelativistic and relativistic quantum mechanics, condensed matter physics, and quantum field theory), there is much interest in computing Fredholm indices of certain linear partial differential operators. In the late 1970’s, Constantine Callias found a formula for the Fredholm index of a particular first-order differential operator (intimately connected to a supersymmetric Dirac-type operator) additively perturbed by a potential, shedding additional light on the Fedosov-Hörmander Index Theorem. As a byproduct of our proof we also offer a glimpse at special non-Fredholm situations employing a generalized Witten index.

9. Strategic Consolidation under Formula Apportionment

Buettner, Thiess; Riedel, Nadine; Runkel, Marco

2008-01-01

This paper argues that profit-shifting activities of multi-jurisdictional enterprises (MJE) are maintained under a tax system of consolidation and formula apportionment (FA). A theoretical model discusses how an MJE can exploit its impact on the definition of the consolidated group strategically. The analysis shows that the MJE will run individual affiliates as separate un-consolidated firms for tax purposes if intra-group tax-rate differences, and thereby potential gains from profit-shifting...

10. Analyzing Walksat on random formulas

Coja-Oghlan, Amin

2011-01-01

Let F be a uniformly distributed random k-SAT formula with n variables and m clauses. We prove that the Walksat algorithm from Papadimitriou (FOCS 1991)/Schoning (FOCS 1999) finds a satisfying assignment of F in polynomial time w.h.p. if m/n0. This is an improvement by a factor of $\\Theta(k)$ over the best previous analysis of Walksat from Coja-Oghlan, Feige, Frieze, Krivelevich, Vilenchik (SODA 2009).

11. Hydrolyzed Formula for Every Infant?

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

2016-01-01

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

12. Discretization formulas for unstructured grids

Baumeister, Kenneth J.

1988-01-01

The Galerkin weighted residual technique using linear triangular weight functions is employed to develop finite difference formula in cartesian coordinates for the Laplacian operator, first derivative operators and the function for unstructured triangular grids. The weighted residual coefficients associated with the weak formulation of the Laplacian operator are shown to agree with the Taylor series approach on a global average. In addition, a simple algorithm is presented to determine the Voronoi (finite difference) area of an unstructured grid.

13. How to Save Money on Infant Formula

... gov/ency/patientinstructions/000805.htm How to Save Money on Infant Formula To use the sharing features ... ways you can save money on infant formula . Money-Saving Ideas Here are a few ways to ...

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

... 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 ...

15. A Wald-like Formula for Energy

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.

16. Simple and Clear Proofs of Stirling's Formula

Niizeki, Shozo; Araki, Makoto

2010-01-01

The purpose of our article is to show two simpler and clearer methods of proving Stirling's formula than the traditional and conventional ones. The distinction of our method is to use the simple trapezoidal formula.

17. Lefschetz Formulae for p-Adic Groups

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.

18. Some results on numerical divided difference formulas

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.

19. Formulaic speech in disorders of language

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.

20. Analogues of a transformation formula of Ramanujan

Dixit, Atul

2009-01-01

We derive two new analogues of a transformation formula of Ramanujan involving the Gamma and Riemann zeta functions present in the Lost Notebook. Both involve infinite series consisting of Hurwitz zeta functions and yield modular relations. As a special case of the first formula, we obtain an identity involving polygamma functions given by Andrew P. Guinand and as a limiting case of the second formula, we derive the transformation formula of Ramanujan.

1. Some practical Runge-Kutta formulas

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''

2. Formula Approaches for Market Access Negotiations

2002-01-01

Most of the large tariff reductions achieved in multilateral trade negotiations have involved tariff-cutting formulas such as the ‘Swiss’ formula. Wide variations in initial tariff rates between active participants, however, call for new approaches under the Doha Development Agenda. This Paper surveys a range of formula options and examines both targeted and flexible applications of the Swiss formula that target tariff escalation and peaks, and would allow policymakers to directly target how ...

3. A dimensionally continued Poisson summation formula

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...

4. On an improved effective range formula

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)

5. 10 CFR 905.33 - Extension formula.

2010-01-01

... 10 Energy 4 2010-01-01 2010-01-01 false Extension formula. 905.33 Section 905.33 Energy DEPARTMENT... 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...

6. 28 CFR 38.2 - Formula grants.

2010-07-01

... 28 Judicial Administration 1 2010-07-01 2010-07-01 false Formula grants. 38.2 Section 38.2 Judicial Administration DEPARTMENT OF JUSTICE EQUAL TREATMENT FOR FAITH-BASED ORGANIZATIONS § 38.2 Formula... cooperative agreement funded by a formula or block grant from the Department. As used in this section,...

7. 25 CFR 273.31 - Distribution formula.

2010-04-01

... 25 Indians 1 2010-04-01 2010-04-01 false Distribution formula. 273.31 Section 273.31 Indians... 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...

8. 15 CFR 923.110 - Allocation formula.

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...

9. 27 CFR 26.31 - Formula.

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...

10. 27 CFR 20.91 - Formula.

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...

11. The Verlinde formula for Higgs bundles

Andersen, Jørgen Ellegaard; Pei, Du

2016-01-01

We propose and prove the Verlinde formula for the quantization of the Higgs bundle moduli spaces and stacks for any simple and simply-connected group. This generalizes the equivariant Verlinde formula for the case of $SU(n)$ proposed previously by the second and third author. We further establish a Verlinde formula for the quantization of parabolic Higgs bundle moduli spaces and stacks.

12. Relations Among Some Fuzzy Entropy Formulae

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.

13. AN EXTREMAL APPROACH TO BIRKHOFF QUADRATURE FORMULAS

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.

14. Kac formulas for the extended Virasoro algebras

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)

15. 27 CFR 24.196 - Formula required.

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...

16. 7 CFR 251.7 - Formula adjustments.

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...

17. 27 CFR 24.201 - Formula required.

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...

18. 27 CFR 24.211 - Formula required.

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...

19. 24 CFR 574.130 - Formula allocations.

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...

20. Rice formulas and Gaussian waves

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.

1. Whiteness formula in CIELAB uniform color space

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.

2. Cottingham formula and nucleon polarisabilities

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.)

3. Multidimensional Datawarehouse with Combination Formula

Warnars, Spits

2010-01-01

Multidimensional in data warehouse is a compulsion and become the most important for information delivery, without multidimensional Multidimensional in data warehouse is a compulsion and become the most important for information delivery, without multidimensional datawarehouse is incomplete. Multidimensional give ability to analyze business measurement in many different ways. Multidimensional is also synonymous with online analytical processing (OLAP). By using some concepts in datawarehouse like slice-dice,drill down and roll up will increase the ability of multidimensional datawarehouse. The research question and the discussing for this paper are how much deepest the multidimensional ability from each fact table in datawarehouse. By using the statistic combination formula we try to explore the combination that can be yielded from each dimension in hypercubes, the entire of dimensi combination, minimum combination and maximum combination.

4. Cottingham formula and nucleon polarisabilities

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.)

5. Black hole interior mass formula

We argue by explicit computations that, although the area product, horizon radii product, entropy product, and irreducible mass product of the event horizon and Cauchy horizon are universal, the surface gravity product, the surface temperature product and the Komar energy product of the said horizons do not seem to be universal for Kerr-Newman black hole spacetimes. We show the black hole mass formula on the Cauchy horizon following the seminal work by Smarr [Phys Rev Lett 30:71 (1973), Phys Rev D 7:289 (1973)] for the outer horizon. We also prescribe the four laws of black hole mechanics for the inner horizon. A new definition of the extremal limit of a black hole is discussed. (orig.)

6. Cosmological parallax-distance formula

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.

7. Welfare Effects of Tariff Reduction Formulas

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. No single formula dominates for all conditions. The ranking of the three tools depends on the degree of product differentiation in the industry, and the achieved reduction in the average tariff....

8. Mathematical Formula Search using Natural Language Queries

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.

9. Elements and formulae of special relativity

Guggenheim, E A

2013-01-01

Elements and Formulae of Special Relativity presents elements and formulas of the theory of special relativity and covers topics ranging from kinematics and propagation of light to mechanics of single bodies, hydrodynamics, and thermodynamics. Vector operators, electromagnetic fields, electrodynamics, and statistical mechanics are also explored. This book is comprised of 13 chapters and begins by introducing the reader to the kinematics of special relativity, paying particular attention to formulas required for transformations between two frames of reference. Attention then turns to the propag

10. Developing a Weighted Collection Development Allocation Formula

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 ...

11. Rotational Crofton formulae for flagged intrinsic volumes

Auneau, Jeremy Michel

integration is over all sections containing the fixed point origo. Our main result is a local stereological analogue to the well-known Crofton formula. More precisely, we derive geometric formulae that relate new flagged intrinsic volumes of a set with the flagged intrinsic volumes of its sections, . The...... development of a potential local stereological analogue of the famous principal kinematic formula is also discussed....

12. A General Framework for Probabilistic Characterizing Formulae

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...

13. The fringe capacitance formula of microstructures

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)

14. Column Holdup Formula of Soil Solute Transport

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.

15. Poincare's relativistic Doppler-Fizeau formula

Pierseaux, Yves

2006-01-01

We deduce from Poincare's ellipsoidal wavefronts a relativistic Doppler-Fizeau formula that is not the same as 1905 Einstein's one. Longitudinally, Einstein's formula and Poincare's formula are the same. The question of an experimental test is connected with the possibility or the impossibility of directly measuring the relativistic transverse effect. Hasselkamp's 1978 experiment becomes a crucial experiment because Poincare's relativistic kinematics predicts an expansion of sapce directly co...

16. Non-Commutative Q-Binomial Formula

Nalci, Sengul; Pashaev, Oktay

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 s...

17. Superfluid Kubo Formulas from Partition Function

Chapman, Shira; Oz, Yaron

2014-01-01

Linear response theory relates hydrodynamic transport coefficients to equilibrium retarded correlation functions of the stress-energy tensor and global symmetry currents in terms of Kubo formulas. Some of these transport coefficients are non-dissipative and affect the fluid dynamics at equilibrium. We present an algebraic framework for deriving Kubo formulas for such thermal transport coefficients by using the equilibrium partition function. We use the framework to derive Kubo formulas for all such transport coefficients of superfluids, as well as to rederive Kubo formulas for various normal fluid systems.

18. A rotational integral formula for intrinsic volumes

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...

19. Rotational versions of the Crofton formula

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....

20. AN ANALYTICAL REFLECTION OF FORMULAIC LANGUAGE

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.

1. Efficient formulas for efficiency correction of cumulants

Kitazawa, Masakiyo

2016-01-01

We derive formulas which connect cumulants of particle numbers observed with efficiency losses with the original ones based on the binomial model. These formulas can describe the case with multiple efficiencies in a compact form. Compared with the presently suggested ones based on factorial moments, these formulas would drastically reduce the numerical cost for efficiency corrections when the order of the cumulant and the number of different efficiencies are large. The efficiency correction with realistic $p_T$-dependent efficiency would be carried out with the aid of these formulas.

2. Luescher formula for GKP string

Basso, B

2011-01-01

We investigate finite-size corrections to anomalous dimensions of large-spin twist-two operators in the planar maximally supersymmetric Yang-Mills theory. We develop a framework for analysis of these corrections, that is complementary to the conventional spin-chain approach, by making use of the hole rather than the magnon picture. From the dual string theory perspective where the large-spin operator is identified with the Gubser-Klebanov-Polyakov (GKP) string, our approach is equivalent to constructing the first Luescher correction to the energy of the GKP string by incorporating the contribution of virtual excitations propagating on it. It allows us to propose a formula that controls a particular class of large-spin corrections to the twist-two anomalous dimension and holds at any value of the coupling constant. Compared to wrapping corrections computed with magnons propagating on the spin chain, the finite-size corrections that are encoded in our formalism start at a lower loop level. Our formalism thus ca...

3. Preclinical assessment of infant formula.

Lönnerdal, Bo

2012-01-01

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

4. 27 CFR 20.101 - Drafting formulas.

2010-04-01

... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Drafting formulas. 20.101 Section 20.101 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT... Process Approval Policies § 20.101 Drafting formulas. (a) In preparing Form 5150.19, the...

5. Formula Approaches for Market Access Negotiations

J.F. François (Joseph); W. Martin (William)

2002-01-01

textabstractMost of the large tariff reductions achieved in multilateral trade negotiations have involved tariff-cutting formulas such as the "Swiss" formula. However, wide variations in initial tariff rates between active participants call for new approaches under the Doha Development Agenda. This

6. Emergence String and Mass Formulas of Hadrons

Chang, Yi-Fang

2011-01-01

Assume that hadrons are formed from the emergence string. Usual string should possess two moving states: oscillation and rotation, so we propose corresponding potential and the equation of the emergence string, whose energy spectrum is namely the GMO mass formula and its modified accurate mass formula. These are some relations between the string and observable experimental data.

7. Borromean surgery formula for the Casson invariant

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...

8. A Choice of a New Funding Formula

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. 40 CFR 74.26 - Allocation formula.

2010-07-01

... 40 Protection of Environment 16 2010-07-01 2010-07-01 false Allocation formula. 74.26 Section 74.26 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) AIR PROGRAMS (CONTINUED) SULFUR DIOXIDE OPT-INS Allowance Calculations for Combustion Sources § 74.26 Allocation formula. (a)...

10. 38 CFR 9.12 - Reinsurance formula.

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...

11. Design Formula for Breakage of Tetrapods

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...

12. How to Save Money on Infant Formula

... months. Here are some ways you can save money on infant formula . ... Here are a few ways to save money on infant formula: DO NOT buy just one type of baby bottle at first. Try a few different types to see which kind ...

13. The health implications of soy infant formula

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...

14. 27 CFR 5.26 - Formula requirements.

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...

15. Calculating the Greeks by Cubature formulas

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.

16. A Short Proof of Krattenthaler Formulas

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.

17. The propositional formula checker HeerHugo

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

18. Sample size: from formulae to concepts - II

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

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. Lewis Carroll's Formula for Calendar Calculating.

Spitz, Herman H.

1993-01-01

This paper presents Lewis Carroll's formula for mentally calculating the day of the week of a given date. The paper concludes that such formulas are too complex for individuals of low intelligence to learn by themselves, and thus "idiots savants" who perform such calendar calculations must be using other systems. (JDD)

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

There exists rare integration formulas over quaternions due to the noncommutativity of quarternions multiplication. 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

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

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.

3. The Lichnerowicz-Weitzenboeck formula and superconductivity

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.

4. Menemukan Formula Sinematografi Seni Pertunjukan

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

5. Effect of individual components of soy formula and cows milk formula on zinc bioavailability

Zinc absorption from human milk, cows milk formulas, and soy formulas was studied in human adults by a radioisotope technique using 65Zn and whole body counting. Individual dietary components were investigated for effects on zinc absorption. Phytate was found to have a strong inhibitory effect on zinc absorption; addition of phytate to cows milk formula (yielding a phytate concentration similar to that of soy formula) resulted in a decrease in zinc absorption from 31 to 16% similar to the absorption for soy formula (14%). Carbohydrate source, calcium, and zinc levels of the diet did not affect zinc absorption significantly. Iron supplementation of cows milk formula decreased zinc absorption from 24 to 18% although this decrease was not found to be significant (p less than 0.1). Absorption of zinc from a whey-adjusted cows milk formula was higher (31%) than from a nonmodified cows milk formula (22%). Increasing the zinc supplementation level in cows milk formula but not in soy formula increased zinc absorption to approximate that from breast milk. It is suggested that reduction of phytate content of soy formula may be a more effective avenue of modification than increased level of zinc supplementation

6. 27 CFR 21.66 - Formula No. 38-C.

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:...

7. 27 CFR 21.70 - Formula No. 39-A.

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:...

8. 27 CFR 21.68 - Formula No. 38-F.

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:...

9. 27 CFR 21.55 - Formula No. 28-A.

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:...

10. 27 CFR 21.58 - Formula No. 31-A.

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:...

11. 27 CFR 21.62 - Formula No. 35-A.

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:...

12. 27 CFR 21.67 - Formula No. 38-D.

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:...

13. 27 CFR 21.69 - Formula No. 39.

2010-04-01

... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 39. 21.69... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.69 Formula No. 39. (a) Formula. To every 100 gallons of alcohol add:...

14. 27 CFR 24.127 - Adoption of formulas.

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...

15. 27 CFR 20.115 - Ink general-use formula.

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...

16. 27 CFR 21.38 - Formula No. 4.

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...

17. 27 CFR 21.39 - Formula No. 6-B.

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:...

18. 27 CFR 21.34 - Formula No. 2-C.

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:...

19. 27 CFR 21.35 - Formula No. 3-A.

2010-04-01

... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 3-A. 21.35... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.35 Formula No. 3-A. (a) Formula. To every 100 gallons of alcohol add:...

20. 27 CFR 21.46 - Formula No. 22.

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:...

1. 27 CFR 21.44 - Formula No. 19.

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:...

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

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:...

3. 27 CFR 21.32 - Formula No. 1.

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:...

4. 27 CFR 21.52 - Formula No. 27.

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:...

5. 27 CFR 21.45 - Formula No. 20.

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:...

6. 27 CFR 21.50 - Formula No. 25.

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:...

7. 27 CFR 21.37 - Formula No. 3-C.

2010-04-01

... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 3-C. 21.37... OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM Specially Denatured Spirits Formulas and Authorized Uses § 21.37 Formula No. 3-C. (a) Formula. To every 100 gallons of alcohol add:...

8. 27 CFR 21.42 - Formula No. 17.

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:...

9. 27 CFR 21.36 - Formula No. 3-B.

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:...

10. 27 CFR 21.24 - Formula No. 20.

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...

11. 27 CFR 21.43 - Formula No. 18.

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...

12. Overtopping of Berm Breakwaters Extension of Overtopping Formula

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...

13. 27 CFR 21.63 - Formula No. 36.

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:...

14. 27 CFR 21.56 - Formula No. 29.

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:...

15. 27 CFR 21.60 - Formula No. 33.

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:...

16. 27 CFR 21.61 - Formula No. 35.

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:...

17. 27 CFR 21.57 - Formula No. 30.

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:...

18. 27 CFR 21.59 - Formula No. 32.

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:...

19. 27 CFR 21.64 - Formula No. 37.

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:...

20. 27 CFR 21.48 - Formula No. 23-F.

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:...

1. 27 CFR 21.53 - Formula No. 27-A.

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:...

2. 27 CFR 21.51 - Formula No. 25-A.

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:...

3. 27 CFR 21.40 - Formula No. 12-A.

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:...

4. 27 CFR 21.54 - Formula No. 27-B.

2010-04-01

... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Formula No. 27-B. 21.54... 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:...

5. 27 CFR 21.41 - Formula No. 13-A.

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:...

6. Fundamental formulas of physics, v.1

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

7. Analogues of Euler and Poisson Summation Formulae

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.

8. Correction to Moliere's formula for multiple scattering

The semiclassical correction to Moliere's formula for multiple scattering is derived. The consideration is based on the scattering amplitude obtained with the first semiclassical correction taken into account for an arbitrary localized but not spherically symmetric potential. Unlike the leading term, the correction to Moliere's formula contains the target density n and thickness L not only in the combination nL (areal density). Therefore, this correction can be referred 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 range of applicability of Moliere's formula

9. Ricci Curvature and Bochner Formulas for Martingales

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...

10. Approximate formulas for moderately small eikonal amplitudes

Kisselev, A V

2015-01-01

The eikonal approximation for moderately small scattering amplitudes is considered. With the purpose of using for their numerical estimations, the formulas are derived which contain no Bessel functions, and, hence, no rapidly oscillating integrands. To obtain these formulas, the improper integrals of the first kind which contain products of the Bessel functions J_0(z) are studied. The expression with four functions J_0(z) is generalized. The expressions for the integrals with the product of five and six Bessel functions J_0(z) are also found. The known formula for the improper integral with two functions J_nu(z) is generalized for non-integer nu.

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

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

12. The local index formula in noncommutative geometry

These notes present a partial account of the local index theorem in non-commutative geometry discovered by Alain Connes and Henri Moscovici. It includes Elliptic partial differential operators, cyclic homology theory, Chern characters, homotopy invariants and the index formulas

13. Newton Binomial Formulas in Schubert Calculus

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.

14. Towards a realistic neutrino mass formula

Królikowski, W

2006-01-01

A new option of parameter constraint is described for the recently proposed neutrino mass formula involving primarily three free parameters. The option implies the vanishing of a part of mass formula for the lowest mass neutrino, the part which may - in an intuitive model - be identified with its formal "intrinsic selfenergy". However, its actual mass induced then by another part of mass formula is considerable. In this option, our neutrino mass formula predicts all three neutrino masses as m_1 \\sim 2.5 x 10^{-3} eV, m_2 \\sim 9.3 x 10^{-3} eV and m_3 \\sim 5.0 x 10^{-2} eV, when two experimental estimates \\Delta m^2_{21} \\sim 8.0 x 10^{-5} eV^2 and \\Delta m^2_{32} \\sim 2.4 x 10^{-3} eV^2 are applied as an input.

15. Traction Control System for Formula Student Electric

Houf, Z.; Čeřovský, Z.; Hlinovský, V.

This paper deals with design of traction control of Formula Student Electric Car. There will introduced new conception of formula traction system and its application to the Formula car. In next season we would like to use 2 motors, each of them will be directly connected to its wheel. This solution needs precise control of them to provide high dynamics and great ability to ride curves in high speeds. Using the same torque on each wheel brings problem when one of wheel loss the traction ability. Some slip could happen and the unexpected lateral movement becomes. There will described the mathematic model of formula car. To reduce slips etc. we will publish the theoretical algorithm that reduces or increases torques on rear wheels to stabilize the car. There will be described what states have to be measured and evaluated. Also places where the sensors will be placed will be shown.

16. "Formula Student" / Malle Jürves

Jürves, Malle, 1950-

2008-01-01

Tehnikakõrgkooli ja tehnikaülikooli tudengite 17-liikmeline võiskond osales tänavu suvel Inglismaal Silverstone'i ringrajakompleksis peetaval tootearendusvõistlusel "Formula Student" omaehitatud vormelautoga

17. A note on Marino-Vafa formula

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.

18. FORMULAS OF TENSION OF CONTINUOUS ROLLING PROCESS

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.

19. Formula One’s Financial Crisis

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

20. A Delayed Black and Scholes Formula I

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...

1. Some formulae for double Clausenian functions

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....

2. A proof of image Euler Number formula

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.

3. Supplementation of prebiotics in infant formula

Močić Pavić A; Hojsak I

2014-01-01

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) an...

4. Macdonald formula for curves with planar singularities

Maulik, Davesh

2011-01-01

We generalize Macdonald's formula for the cohomology of Hilbert schemes of points on a curve from smooth curves to curves with planar singularities: we relate the cohomology of the Hilbert schemes to the cohomology of the compactified Jacobian of the curve. The new formula is a consequence of a stronger identity between certain perverse sheaves defined by a family of curves satisfying mild conditions, whose proof makes an essential use of Ng\\^o's support theorem for compactified Jacobians.

5. A product formula and combinatorial field theory

Horzela, A; Duchamp, G H E; Penson, K A; Solomon, A I

2004-01-01

We treat the problem of normally ordering expressions involving the standard boson operators a, a* where [a,a*]=1. We show that a simple product formula for formal power series - essentially an extension of the Taylor expansion - leads to a double exponential formula which enables a powerful graphical description of the generating functions of the combinatorial sequences associated with such functions - in essence, a combinatorial field theory. We apply these techniques to some examples related to specific physical Hamiltonians.

6. Parametric Improper Integrals, Wallis Formula and Catalan Numbers

Dana-Picard, Thierry; Zeitoun, David G.

2012-01-01

We present a sequence of improper integrals, for which a closed formula can be computed using Wallis formula and a non-straightforward recurrence formula. This yields a new integral presentation for Catalan numbers.

7. Supplementation of prebiotics in infant formula

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

8. Connected formulas for amplitudes in standard model

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.

9. Utility of predicted creatinine clearance using MDRD formula compared with other predictive formulas in Nigerian patients

Abefe Sanusi

2009-01-01

Full Text Available The new predictive formula generated during the study of Modification of Diet in Renal Disease (MDRD to estimate the glomerular filtration rate in chronic kidney disease (CKD patients was found to be superior to existing predictive formulas in all races including black Americans. We had previously published a study evaluating and comparing 5 predictive formulas and their applicability in Nigerian CKD patients and normal subjects. The existing data from this study were re-analyzed and the 5 previous formulas compared with the MDRD formula. All the pre-dictive formulas including the MDRD formula correlated significantly with measured creatinine clearance in CKD subjects and controls. Correlation Coefficient, (r ranged between 0.908-0.968 and Coefficient of Determination, (r 2 , ranged between 0.826-0.936. There was also good corre-lation between the measured and predicted CrCl in healthy state, though the r and r 2 values were weaker (0.718-0.957 and (0.516-0.916. Specifically, MDRD formula was only superior to Jelliffe and Gates and not so to Cockcroft and Gault, Hull, and Mawer equations in CRF. MDRD formula yielded r= 0.93 and r 2 = 0.86 and the values for Cockcroft and Gault, Hull and Mawer ranged between 0.96-0.97 and 0.93-0.94 respectively. In conclusion, MDRD formula, though useful and applicable was not superior to existing formulas. Cockcroft and Gault equation can still be used due to the ease of recall and its high correlation coefficient in health and disease states.

10. Semi-empirical formulas for sputtering yield

When charged particles, electrons, light and so on are irradiated on solid surfaces, the materials are lost from the surfaces, and this phenomenon is called sputtering. In order to understand sputtering phenomenon, the bond energy of atoms on surfaces, the energy given to the vicinity of surfaces and the process of converting the given energy to the energy for releasing atoms must be known. The theories of sputtering and the semi-empirical formulas for evaluating the dependence of sputtering yield on incident energy are explained. The mechanisms of sputtering are that due to collision cascade in the case of heavy ion incidence and that due to surface atom recoil in the case of light ion incidence. The formulas for the sputtering yield of low energy heavy ion sputtering, high energy light ion sputtering and the general case between these extreme cases, and the Matsunami formula are shown. At the stage of the publication of Atomic Data and Nuclear Data Tables in 1984, the data up to 1983 were collected, and about 30 papers published thereafter were added. The experimental data for low Z materials, for example Be, B and C and light ion sputtering data were reported. The combination of ions and target atoms in the collected sputtering data is shown. The new semi-empirical formula by slightly adjusting the Matsunami formula was decided. (K.I.)

11. Bellco Formula Domus Home Care System.

Trewin, Elizabeth

2004-01-01

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

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

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…

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

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.

14. Sum formulas for reductive algebraic groups

Andersen, Henning Haahr; Kulkarni, Upendra

2008-01-01

\\supset V^1 \\cdots \\supset V^r = 0$. The sum of the positive terms in this filtration satisfies a well known sum formula. If$T$denotes a tilting module either for$G$or$U_q$then we can similarly filter the space$\\Hom_G(V,T)$, respectively$\\Hom_{U_q}(V,T)$and there is a sum formula for the positive...... terms here as well. We give an easy and unified proof of these two (equivalent) sum formulas. Our approach is based on an Euler type identity which we show holds without any restrictions on$p$or$l$. In particular, we get rid of previous such restrictions in the tilting module case.... 15. From Pauli Matrices to Quantum Ito Formula 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 16. Langlands Program, Trace Formulas, and their Geometrization Frenkel, Edward 2012-01-01 The Langlands Program relates Galois representations and automorphic representations of reductive algebraic groups. The trace formula is a powerful tool in the study of this connection and the Langlands Functoriality Conjecture. After giving an introduction to the Langlands Program and its geometric version, which applies to curves over finite fields and over the complex field, I give a survey of my recent joint work with Robert Langlands and Ngo Bao Chau (arXiv:1003.4578 and arXiv:1004.5323) on a new approach to proving the Functoriality Conjecture using the trace formulas, and on the geometrization of the trace formulas. In particular, I discuss the connection of the latter to the categorification of the Langlands correspondence. 17. Universal fitting formulae for baryon oscillation surveys Blake, C; Bassett, B; Glazebrook, K; Kunz, M; Nichol, R C; Blake, Chris; Parkinson, David; Bassett, Bruce; Glazebrook, Karl; Kunz, Martin; Nichol, Robert C. 2006-01-01 The next generation of galaxy surveys will attempt to measure the baryon oscillations in the clustering power spectrum with high accuracy. These oscillations encode a preferred scale which may be used as a standard ruler to constrain cosmological parameters and dark energy models. In this paper we present simple analytical fitting formulae for the accuracy with which the preferred scale may be determined in the tangential and radial directions by future spectroscopic and photometric galaxy redshift surveys. We express these accuracies as a function of survey parameters such as the central redshift, volume, galaxy number density and (where applicable) photometric redshift error. These fitting formulae should greatly increase the efficiency of optimizing future surveys, which requires analysis of a potentially vast number of survey configurations and cosmological models. The formulae are calibrated using a grid of Monte Carlo simulations, which are analyzed by dividing out the overall shape of the power spectru... 18. Move! Eat better: try the FIT formula CERN Medical Service 2013-01-01 In the physics world, some formulas lead to a Nobel prize. In the world of health and physical activity, the Medical Service also has a winning formula... FIT (physical activity) = Frequency x Intensity x Time Frequency = more than 3 times per week. Intensity = physical activity which slightly increases your heart rate and breathing rate. Time = more than 30 minutes (per session). As part of our Move! Eat better campaign, the Medical Service is still offering the use of a pedometer (available on loan from the infirmary), which is a really useful tool to help you reach the winning FIT formula. Interested in borrowing a CERN pedometer? Click here! 19. 24 CFR 905.10 - Capital Fund formula (CFF). 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... 20. 24 CFR 990.110 - Operating fund formula. 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... 1. 27 CFR 21.23 - Formula No. 19. 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:... 2. 27 CFR 21.22 - Formula No. 18. 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:... 3. Magnetic Moment Formulas of Baryons Determined by Quantum Numbers 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. 4. Accurate formulas for the penalty caused by interferometric crosstalk Rasmussen, Christian Jørgen; Liu, Fenghai; Jeppesen, Palle 2000-01-01 New simple formulas for the penalty caused by interferometric crosstalk in PIN receiver systems and optically preamplified receiver systems are presented. They are more accurate than existing formulas.......New simple formulas for the penalty caused by interferometric crosstalk in PIN receiver systems and optically preamplified receiver systems are presented. They are more accurate than existing formulas.... 5. Identifying a framework for graphing formulas from expert strategies 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 6. Generalization of the Macdonald formula for Hall-Littlewood polynomials Klostermann, Inka 2011-01-01 We study the Gaussent-Littelmann formula for Hall-Littlewood polynomials and we develop combinatorial tools to describe the formula in a purely combinatorial way for type A_n. Furthermore, we show by using these tools that the Gaussent-Littelmann formula and the well-known Macdonald formula for Hall-Littlewood polynomials for type A_n are the same. 7. 7 CFR 761.205 - Computing the formula allocation. 2010-01-01 ... 7 Agriculture 7 2010-01-01 2010-01-01 false Computing the formula allocation. 761.205 Section 761... Funds to State Offices § 761.205 Computing the formula allocation. (a) The formula allocation for FO or... program that the National Office allocates to a State Office. formula allocation = (amount available... 8. Gaussian quadrature formulae for arbitrary positive measures. Fernandes, Andrew D; Atchley, William R 2006-01-01 We present computational methods and subroutines to compute Gaussian quadrature integration formulas for arbitrary positive measures. For expensive integrands that can be factored into well-known forms, Gaussian quadrature schemes allow for efficient evaluation of high-accuracy and -precision numerical integrals, especially compared to general ad hoc schemes. In addition, for certain well-known density measures (the normal, gamma, log-normal, Student's t, inverse-gamma, beta, and Fisher's F) we present exact formulae for computing the respective quadrature scheme. PMID:19455218 9. Gaussian Quadrature Formulae for Arbitrary Positive Measures William R. Atchley 2006-01-01 Full Text Available We present computational methods and subroutines to compute Gaussian quadrature integration formulas for arbitrary positive measures. For expensive integrands that can be factored into well-known forms, Gaussian quadrature schemes allow for efficient evaluation of high-accuracy and -precision numerical integrals, especially compared to general ad hoc schemes. In addition, for certain well-known density measures (the normal, gamma, log-normal, Student’s t, inversegamma, beta, and Fisher’s F we present exact formulae for computing the respective quadrature scheme. 10. Pesin's Entropy Formula for Systems Between and Tian, Xueting 2014-09-01 In this article we give a new observation of Pesin's entropy formula, motivated from Mañé's proof of (Ergod Theory Dyn Sys 1:95-102, 1981). Let be a compact Riemann manifold and be a diffeomorphism on . If is an -invariant probability measure which is absolutely continuous relative to Lebesgue measure and nonuniformly-Hlder-continuous(see Definition 1.1), then we have Pesin's entropy formula, i.e., the metric entropy satisfies where are the Lyapunov exponents at with respect to Nonuniformly-H lder-continuous is a new notion from probabilistic perspective weaker than 11. Vacuum engineering, calculations, formulas, and solved exercises Berman, Armand 1992-01-01 This book was written with two main objectives in mind-to summarize and organize the vast material of vacuum technology in sets of useful formulas, and to provide a collection of worked out exercises showing how to use these formulas for solving technological problems. It is an ideal reference source for those with little time to devote to a full mathematical treatment of the many problems issued in vacuum practice, but who have a working knowledge of the essentials of vacuum technology, elementary physics, and mathematics. This time saving book employs a problem-solving approach throughout, p 12. Mathematical formulas for industrial and mechanical engineering Kadry, Seifedine 2014-01-01 Mathematical Formulas For Industrial and Mechanical Engineering serves the needs of students and teachers as well as professional workers in engineering who use mathematics. The contents and size make it especially convenient and portable. The widespread availability and low price of scientific calculators have greatly reduced the need for many numerical tables that make most handbooks bulky. However, most calculators do not give integrals, derivatives, series and other mathematical formulas and figures that are often needed. Accordingly, this book contains that information in an easy way to 13. Temporal formulas in Serbian oral epic songs Perić Dragoljub Ž. 2013-01-01 Full Text Available This paper seeks to present time as one of the most important parameters in epic songs, shown in the example of temporal formulas. Time also represents the principle of organizing section sequences in the song (linear, successive and chronological, or discontinuous and retrospective. The paper further examines the temporal formulas in a broad and a narrow sense, with regard to whether the temporal markers refer to the narrative shifts in the development of the story, or to some archaic meanings related to expressions which mark the determinants of real time (year and its parts, days of the week, time of the day, etc.. 14. Analytical opacity formulas for low Z plasmas 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. 15. Inductance calculations working formulas and tables 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 16. CRC standard mathematical tables and formulae Zwillinger, Daniel 2002-01-01 New in the 31st edition:Game theory and voting powerHeuristic search techniquesQuadratic fieldsReliabilityRisk analysis and decision rulesA table of solutions to Pell's equationA table of irreducible polynomials in Z2[x]An interpretation of powers of 10A collection of ""proofs without words""Representations of groups of small orderCounting principlesTesselations and tilings…and much more!An indispensable, up-to-date resource, CRC Standard Mathematical Tables and Formulae, 31st Edition makes it effortless to find the equations, tables, and formulae you need most often. 17. On Combinatorial Formulas for Macdonald Polynomials Lenart, Cristian 2008-01-01 A recent breakthrough in the theory of (type A) Macdonald polynomials is due to Haglund, Haiman and Loehr, who exhibited a combinatorial formula for these polynomials in terms of a pair of statistics on fillings of Young diagrams. Ram and Yip gave a formula for the Macdonald polynomials of arbitrary type in terms of so-called alcove walks; these originate in the work of Gaussent-Littelmann and of the author with Postnikov on discrete counterparts to the Littelmann path model. In this paper, w... 18. COMPARISON BETWEEN FORMULAS OF MAXIMUM SHIP SQUAT 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. Efficient computation of the Zassenhaus formula 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. 20. Validation of a new formula for mean arterial pressure calculation: the new formula is superior to the standard formula. Razminia, Mansour; Trivedi, Atul; Molnar, Janos; Elbzour, Monther; Guerrero, Mayra; Salem, Yasser; Ahmed, Aziz; Khosla, Sandeep; Lubell, David L 2004-12-01 Mean arterial pressure (MAP) has traditionally been derived from systolic and diastolic pressures, weighted 1/3 systolic and 2/3 diastolic. No correction is made for the increasing time dominance of systole with increasing heart rates. In a previous study, we developed a new and more accurate heart rate-corrected MAP formula from central aorta pressure determinations in a large number of patients: MAP = DP + [0.33 + (HR x 0.0012)] x [PP] where SP and DP are systolic and diastolic pressure and HR is heart rate. The current study validates the new MAP formula in the same patient at increasing paced heart rates. A central aorta catheter was used to obtain computer-determined systolic, diastolic, and MAP in 12 patients. Values were obtained at baseline and then at increasing right atrial paced heart rates. The new and standard MAP formula-derived values were compared with computer-determined values. The new formula showed a much closer correlation with the computer-derived values for MAP. Standard MAP calculations for MAP can easily be improved by inclusion of a heart rate factor. PMID:15558774 1. A mild Ito formula for SPDEs Da Prato, Giuseppe; Jentzen, Arnulf; Roeckner, Michael 2010-01-01 This article introduces a certain class of stochastic processes, which we suggest to call mild Ito processes, and a new - somehow mild - Ito type formula for such processes. Examples of mild Ito processes are mild solutions of SPDEs and their numerical approximation processes. 2. On Kreĭn’s formula 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 3. Perturbative Semiclassical Trace Formulae for Harmonic Oscillators Møller-Andersen, Jakob; Ögren, Magnus 2015-01-01 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... 4. A universal formula for network functions 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... 5. Calculation of the CIPW norm: New formulas 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. 6. Index formulae for subspaces of Krein spaces Dijksma, A; Gheondea, A 1996-01-01 For a subspace S of a Krein space K and an arbitrary fundamental decomposition K = K-[+]K+ of K, we prove the index formula k(-)(S) + dim(S-perpendicular to boolean AND K-+) = k(+)(S-perpendicular to)+ dim(S boolean AND K-), were k(+/-)(S) stands for the positive/negative signature of S. The differe 7. An ISU(3) hadron mass formula 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) 8. Diffusion Processes and the Ewens Sampling Formula 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. 9. A weak kernel formula for Bessel functions 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. Universal fitting formulae for baryon oscillation surveys

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

2006-01-01

The next generation of galaxy surveys will attempt to measure the baryon oscillations in the clustering power spectrum with high accuracy. These oscillations encode a preferred scale which may be used as a standard ruler to constrain cosmological parameters and dark energy models. In this paper we present simple analytical fitting formulae for the accuracy with which the preferred scale may be determined in the tangential and radial directions by future spectroscopic and photometric galaxy redshift surveys. We express these accuracies as a function of survey parameters such as the central redshift, volume, galaxy number density and (where applicable) photometric redshift error. These fitting formulae should greatly increase the efficiency of optimizing future surveys, which requires analysis of a potentially vast number of survey configurations and cosmological models. The formulae are calibrated using a grid of Monte Carlo simulations, which are analysed by dividing out the overall shape of the power spectrum before fitting a simple decaying sinusoid to the oscillations. The fitting formulae reproduce the simulation results with a fractional scatter of 7 per cent (10 per cent) in the tangential (radial) directions over a wide range of input parameters. We also indicate how sparse-sampling strategies may enhance the effective survey area if the sampling scale is much smaller than the projected baryon oscillation scale.