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Sample records for binary bell polynomials

  1. Generalized Bilinear Differential Operators, Binary Bell Polynomials, and Exact Periodic Wave Solution of Boiti-Leon-Manna-Pempinelli Equation

    Directory of Open Access Journals (Sweden)

    Huanhe Dong

    2014-01-01

    Full Text Available We introduce how to obtain the bilinear form and the exact periodic wave solutions of a class of (2+1-dimensional nonlinear integrable differential equations directly and quickly with the help of the generalized Dp-operators, binary Bell polynomials, and a general Riemann theta function in terms of the Hirota method. As applications, we solve the periodic wave solution of BLMP equation and it can be reduced to soliton solution via asymptotic analysis when the value of p is 5.

  2. Degenerate r-Stirling Numbers and r-Bell Polynomials

    Science.gov (United States)

    Kim, T.; Yao, Y.; Kim, D. S.; Jang, G.-W.

    2018-01-01

    The purpose of this paper is to exploit umbral calculus in order to derive some properties, recurrence relations, and identities related to the degenerate r-Stirling numbers of the second kind and the degenerate r-Bell polynomials. Especially, we will express the degenerate r-Bell polynomials as linear combinations of many well-known families of special polynomials.

  3. Bell Polynomials Approach Applied to (2 + 1-Dimensional Variable-Coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada Equation

    Directory of Open Access Journals (Sweden)

    Wen-guang Cheng

    2014-01-01

    Full Text Available The bilinear form, bilinear Bäcklund transformation, and Lax pair of a (2 + 1-dimensional variable-coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada equation are derived through Bell polynomials. The integrable constraint conditions on variable coefficients can be naturally obtained in the procedure of applying the Bell polynomials approach. Moreover, the N-soliton solutions of the equation are constructed with the help of the Hirota bilinear method. Finally, the infinite conservation laws of this equation are obtained by decoupling binary Bell polynomials. All conserved densities and fluxes are illustrated with explicit recursion formulae.

  4. Higher order derivatives of exponential functions and generalized forms of Kampe de Feriet-Bell polynomials

    International Nuclear Information System (INIS)

    Dattoli, G.; Lorenzutta, S.; Cesarano, C.; Sacchetti, D.

    2000-01-01

    Operational methods are used to provide a different point of view on the theory of Kampe' de Feriet-Bell polynomials. The method here proposed can be exploited to simplify the formalism associated with this family of polynomials and may provide advantages in computation. It suggests their extension to classes of multi-index families, whole role in application is discussed [it

  5. Partial list of bipartite Bell inequalities with four binary settings

    International Nuclear Information System (INIS)

    Brunner, Nicolas; Gisin, Nicolas

    2008-01-01

    We give a partial list of 26 tight Bell inequalities for the case where Alice and Bob choose among four two-outcome measurements. All tight Bell inequalities with less settings are reviewed as well. For each inequality we compute numerically the maximal quantum violation, the resistance to noise and the minimal detection efficiency required for closing the detection loophole. Surprisingly, most of these inequalities are outperformed by the CHSH inequality

  6. Fast evaluation of polynomials over binary finite fields and application to side-channel countermeasures

    DEFF Research Database (Denmark)

    Coron, Jean-Sébastien; Roy, Arnab; Vivek, Srinivas

    2015-01-01

    We describe a new technique for evaluating polynomials over binary finite fields. This is useful in the context of anti-DPA countermeasures when an S-box is expressed as a polynomial over a binary finite field. For n-bit S-boxes, our new technique has heuristic complexity O(2n/2/√n) instead of O(2n...... the polynomial corresponding to an S-box. In practice, we can evaluate any 8-bit S-box in 10 non-linear multiplications instead of 16 in the Roy–Vivek paper from CHES 2013, and the DES S-boxes in 4 non-linear multiplications instead of 7. We also evaluate any 4-bit S-box in 2 non-linear multiplications instead...

  7. Polynomials

    Science.gov (United States)

    Apostol, Tom M. (Editor)

    1991-01-01

    In this 'Project Mathematics! series, sponsored by California Institute for Technology (CalTech), the mathematical concept of polynomials in rectangular coordinate (x, y) systems are explored. sing film footage of real life applications and computer animation sequences, the history of, the application of, and the different linear coordinate systems for quadratic, cubic, intersecting, and higher degree of polynomials are discussed.

  8. Ubiquity of synonymity: almost all large binary trees are not uniquely identified by their spectra or their immanantal polynomials

    Science.gov (United States)

    2012-01-01

    Background There are several common ways to encode a tree as a matrix, such as the adjacency matrix, the Laplacian matrix (that is, the infinitesimal generator of the natural random walk), and the matrix of pairwise distances between leaves. Such representations involve a specific labeling of the vertices or at least the leaves, and so it is natural to attempt to identify trees by some feature of the associated matrices that is invariant under relabeling. An obvious candidate is the spectrum of eigenvalues (or, equivalently, the characteristic polynomial). Results We show for any of these choices of matrix that the fraction of binary trees with a unique spectrum goes to zero as the number of leaves goes to infinity. We investigate the rate of convergence of the above fraction to zero using numerical methods. For the adjacency and Laplacian matrices, we show that the a priori more informative immanantal polynomials have no greater power to distinguish between trees. Conclusion Our results show that a generic large binary tree is highly unlikely to be identified uniquely by common spectral invariants. PMID:22613173

  9. Bell numbers, determinants and series

    Indian Academy of Sciences (India)

    In this article, we study Bell numbers and Uppuluri Carpenter numbers. We obtain various expressions and relations between them. These include polynomial recurrences and expressions as determinants of certain matrices of binomial coefficients. Keywords. p-adic series; Bell numbers. 1. Introduction. Bell numbers, Bn [2] ...

  10. Bell numbers, determinants and series

    Indian Academy of Sciences (India)

    In this article, we study Bell numbers and Uppuluri Carpenter numbers. We obtain various expressions and relations between them. These include polynomial recurrences and expressions as determinants of certain matrices of binomial coefficients.

  11. Application of the Polynomial-Based Least Squares and Total Least Squares Models for the Attenuated Total Reflection Fourier Transform Infrared Spectra of Binary Mixtures of Hydroxyl Compounds.

    Science.gov (United States)

    Shan, Peng; Peng, Silong; Zhao, Yuhui; Tang, Liang

    2016-03-01

    An analysis of binary mixtures of hydroxyl compound by Attenuated Total Reflection Fourier transform infrared spectroscopy (ATR FT-IR) and classical least squares (CLS) yield large model error due to the presence of unmodeled components such as H-bonded components. To accommodate these spectral variations, polynomial-based least squares (LSP) and polynomial-based total least squares (TLSP) are proposed to capture the nonlinear absorbance-concentration relationship. LSP is based on assuming that only absorbance noise exists; while TLSP takes both absorbance noise and concentration noise into consideration. In addition, based on different solving strategy, two optimization algorithms (limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) algorithm and Levenberg-Marquardt (LM) algorithm) are combined with TLSP and then two different TLSP versions (termed as TLSP-LBFGS and TLSP-LM) are formed. The optimum order of each nonlinear model is determined by cross-validation. Comparison and analyses of the four models are made from two aspects: absorbance prediction and concentration prediction. The results for water-ethanol solution and ethanol-ethyl lactate solution show that LSP, TLSP-LBFGS, and TLSP-LM can, for both absorbance prediction and concentration prediction, obtain smaller root mean square error of prediction than CLS. Additionally, they can also greatly enhance the accuracy of estimated pure component spectra. However, from the view of concentration prediction, the Wilcoxon signed rank test shows that there is no statistically significant difference between each nonlinear model and CLS. © The Author(s) 2016.

  12. Bell numbers, determinants and series

    Indian Academy of Sciences (India)

    k=0. (−1)k S(n, k). The usual generating functions for Bell numbers and complementary Bell numbers are given by. ∞. ∑ n=0. Bn tn n! = eet −1 and. ∞. ∑ n=0. ˜Bn tn n! = e−et +1. Stirling numbers can .... + 1) + gn−1(m − 1) = mn−1 + Bn(−1)n. Since there are infinitely many such m the required polynomial recurrence follows.

  13. On Generalisation of Polynomials in Complex Plane

    Directory of Open Access Journals (Sweden)

    Maslina Darus

    2010-01-01

    Full Text Available The generalised Bell and Laguerre polynomials of fractional-order in complex z-plane are defined. Some properties are studied. Moreover, we proved that these polynomials are univalent solutions for second order differential equations. Also, the Laguerre-type of some special functions are introduced.

  14. Bell's Palsy

    Science.gov (United States)

    Bell's palsy is the most common cause of facial paralysis. It usually affects just one side of the ... become inflamed. You are most likely to get Bell's palsy if you are pregnant, diabetic or sick with ...

  15. Chebyshev polynomials

    CERN Document Server

    Mason, JC

    2002-01-01

    Chebyshev polynomials crop up in virtually every area of numerical analysis, and they hold particular importance in recent advances in subjects such as orthogonal polynomials, polynomial approximation, numerical integration, and spectral methods. Yet no book dedicated to Chebyshev polynomials has been published since 1990, and even that work focused primarily on the theoretical aspects. A broad, up-to-date treatment is long overdue.Providing highly readable exposition on the subject''s state of the art, Chebyshev Polynomials is just such a treatment. It includes rigorous yet down-to-earth coverage of the theory along with an in-depth look at the properties of all four kinds of Chebyshev polynomials-properties that lead to a range of results in areas such as approximation, series expansions, interpolation, quadrature, and integral equations. Problems in each chapter, ranging in difficulty from elementary to quite advanced, reinforce the concepts and methods presented.Far from being an esoteric subject, Chebysh...

  16. Polynomial Asymptotes

    Science.gov (United States)

    Dobbs, David E.

    2010-01-01

    This note develops and implements the theory of polynomial asymptotes to (graphs of) rational functions, as a generalization of the classical topics of horizontal asymptotes and oblique/slant asymptotes. Applications are given to hyperbolic asymptotes. Prerequisites include the division algorithm for polynomials with coefficients in the field of…

  17. The Translated Dowling Polynomials and Numbers.

    Science.gov (United States)

    Mangontarum, Mahid M; Macodi-Ringia, Amila P; Abdulcarim, Normalah S

    2014-01-01

    More properties for the translated Whitney numbers of the second kind such as horizontal generating function, explicit formula, and exponential generating function are proposed. Using the translated Whitney numbers of the second kind, we will define the translated Dowling polynomials and numbers. Basic properties such as exponential generating functions and explicit formula for the translated Dowling polynomials and numbers are obtained. Convexity, integral representation, and other interesting identities are also investigated and presented. We show that the properties obtained are generalizations of some of the known results involving the classical Bell polynomials and numbers. Lastly, we established the Hankel transform of the translated Dowling numbers.

  18. The Trigonometric Polynomial Like Bernstein Polynomial

    Science.gov (United States)

    2014-01-01

    A symmetric basis of trigonometric polynomial space is presented. Based on the basis, symmetric trigonometric polynomial approximants like Bernstein polynomials are constructed. Two kinds of nodes are given to show that the trigonometric polynomial sequence is uniformly convergent. The convergence of the derivative of the trigonometric polynomials is shown. Trigonometric quasi-interpolants of reproducing one degree of trigonometric polynomials are constructed. Some interesting properties of the trigonometric polynomials are given. PMID:25276845

  19. The Trigonometric Polynomial Like Bernstein Polynomial

    Directory of Open Access Journals (Sweden)

    Xuli Han

    2014-01-01

    Full Text Available A symmetric basis of trigonometric polynomial space is presented. Based on the basis, symmetric trigonometric polynomial approximants like Bernstein polynomials are constructed. Two kinds of nodes are given to show that the trigonometric polynomial sequence is uniformly convergent. The convergence of the derivative of the trigonometric polynomials is shown. Trigonometric quasi-interpolants of reproducing one degree of trigonometric polynomials are constructed. Some interesting properties of the trigonometric polynomials are given.

  20. Orthogonal polynomials

    CERN Document Server

    Szegő, G

    1939-01-01

    The general theory of orthogonal polynomials was developed in the late 19th century from a study of continued fractions by P. L. Chebyshev, even though special cases were introduced earlier by Legendre, Hermite, Jacobi, Laguerre, and Chebyshev himself. It was further developed by A. A. Markov, T. J. Stieltjes, and many other mathematicians. The book by Szegő, originally published in 1939, is the first monograph devoted to the theory of orthogonal polynomials and its applications in many areas, including analysis, differential equations, probability and mathematical physics. Even after all the

  1. After Bell

    International Nuclear Information System (INIS)

    Khrennikov, Andrei

    2017-01-01

    We analyze foundational consequences of recently reported loophole free tests of violation of Bell's inequality. We consider two interpretations of these remarkable experiments. The conventional one is ''Einstein was wrong and Bohr was right, there is spooky action at a distance, quantum realism is incompatible with locality.'' However, in line with discussions in literature during last decade, we show that it is still possible to treat quantum mechanics without appealing to nonlocality or denying realism. We hope that this note will call the attention of experts in quantum foundations and convince them that the case is not closed, so that they should come with their own comments on the status of the final Bell test. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  2. After Bell

    Energy Technology Data Exchange (ETDEWEB)

    Khrennikov, Andrei [International Center for Mathematical Modeling in Physics, Engineering, Economics, and Cognitive Science Linnaeus University, Vaexjoe (Sweden)

    2017-06-15

    We analyze foundational consequences of recently reported loophole free tests of violation of Bell's inequality. We consider two interpretations of these remarkable experiments. The conventional one is ''Einstein was wrong and Bohr was right, there is spooky action at a distance, quantum realism is incompatible with locality.'' However, in line with discussions in literature during last decade, we show that it is still possible to treat quantum mechanics without appealing to nonlocality or denying realism. We hope that this note will call the attention of experts in quantum foundations and convince them that the case is not closed, so that they should come with their own comments on the status of the final Bell test. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  3. On the Atkin Polynomials

    OpenAIRE

    El-Guindy, Ahmad; Ismail, Mourad E. H.

    2013-01-01

    We identify the Atkin polynomials in terms of associated Jacobi polynomials. Our identificationthen takes advantage of the theory of orthogonal polynomials and their asymptotics to establish many new properties of the Atkin polynomials. This shows that co-recursive polynomials may lead to interesting sets of orthogonal polynomials.

  4. Bell's Palsy Treatment

    Science.gov (United States)

    ... Stories Español Eye Health / Eye Health A-Z Bell's Palsy Sections What Is Bell's Palsy? Bell's Palsy Symptoms Bell's Palsy Treatment Bell's Palsy Treatment Leer en Español: Tratamiento de la parálisis ...

  5. Bell's Palsy Symptoms

    Science.gov (United States)

    ... Stories Español Eye Health / Eye Health A-Z Bell's Palsy Sections What Is Bell's Palsy? Bell's Palsy Symptoms Bell's Palsy Treatment Bell's Palsy Symptoms Leer en Español: Síntomas de la parálisis ...

  6. Bell's Palsy (For Teens)

    Science.gov (United States)

    ... Staying Safe Videos for Educators Search English Español Bell's Palsy KidsHealth / For Teens / Bell's Palsy What's in this ... Print en español Parálisis de Bell What Is Bell's Palsy? Bell's palsy is a temporary weakness or paralysis ...

  7. Polynomial weights and code constructions

    DEFF Research Database (Denmark)

    Massey, J; Costello, D; Justesen, Jørn

    1973-01-01

    polynomial included. This fundamental property is then used as the key to a variety of code constructions including 1) a simplified derivation of the binary Reed-Muller codes and, for any primepgreater than 2, a new extensive class ofp-ary "Reed-Muller codes," 2) a new class of "repeated-root" cyclic codes...... that are subcodes of the binary Reed-Muller codes and can be very simply instrumented, 3) a new class of constacyclic codes that are subcodes of thep-ary "Reed-Muller codes," 4) two new classes of binary convolutional codes with large "free distance" derived from known binary cyclic codes, 5) two new classes...... of long constraint length binary convolutional codes derived from2^r-ary Reed-Solomon codes, and 6) a new class ofq-ary "repeated-root" constacyclic codes with an algebraic decoding algorithm....

  8. Irreducible multivariate polynomials obtained from polynomials in ...

    Indian Academy of Sciences (India)

    over K(X)? We provided some methods to construct irreducible multivariate polynomials over an arbi- trary field, starting from arbitrary irreducible polynomials in fewer variables, of which we mention the following two results: Theorem A. If we write an irreducible polynomial f ∈ K[X] as a sum of polynomials a0,..., an ∈ K[X] ...

  9. Irreducible multivariate polynomials obtained from polynomials in ...

    Indian Academy of Sciences (India)

    We provided some methods to construct irreducible multivariate polynomials over an arbi- trary field, starting from arbitrary irreducible polynomials in fewer variables, of which we mention the following two results: Theorem A. If we write an irreducible polynomial f ∈ K[X] as a sum of polynomials a0,..., an ∈ K[X] with deg a0 ...

  10. Computing for Belle

    CERN Multimedia

    CERN. Geneva

    2004-01-01

    2s-1, 10 times as much as we obtain now. This presentation describes Belle's efficient computing operations, struggles to manage large amount of raw and physics data, and plans for Belle computing for Super KEKB/Belle.

  11. Bell's Palsy (For Kids)

    Science.gov (United States)

    ... Staying Safe Videos for Educators Search English Español Bell's Palsy KidsHealth / For Kids / Bell's Palsy What's in this ... usually goes away on its own. What Is Bell's Palsy? Bell's palsy weakens or paralyzes the muscles on ...

  12. Anti-Bell - Refutation of Bell's theorem

    Science.gov (United States)

    Barukčić, Ilija

    2012-12-01

    In general, Albert Einstein as one of "the founding fathers of quantum mechanics" had some problems to accept especially the Copenhagen dominated interpretation of quantum mechanics. Einstein's dissatisfaction with Copenhagen's interpretation of quantum mechanics, the absence of locality and causality within the Copenhagen dominated quantum mechanics lead to the well known Einstein, Podolsky and Rosen thought experiment. According to Einstein et al., the Copenhagen dominated quantum mechanics cannot be regarded as a complete physical theory. The Einstein, Podolsky and Rosen thought experiment was the origin of J. S. Bell's publication in 1964; known as Bell's theorem. Meanwhile, some dramatic violations of Bell's inequality (by so called Bell test experiments) have been reported which is taken as an empirical evidence against local realism and causality at quantum level and as positive evidence in favor of the Copenhagen dominated quantum mechanics. Thus far, Quantum mechanics is still regarded as a "strictly" non-local theory. The purpose of this publication is to refute Bell's original theorem. Thus far, if we accept Bell's theorem as correct, we must accept that +0> = +1. We can derive a logical contradiction out of Bell's theorem, Bell's theorem is refuted.

  13. Improved polynomial remainder sequences for Ore polynomials.

    Science.gov (United States)

    Jaroschek, Maximilian

    2013-11-01

    Polynomial remainder sequences contain the intermediate results of the Euclidean algorithm when applied to (non-)commutative polynomials. The running time of the algorithm is dependent on the size of the coefficients of the remainders. Different ways have been studied to make these as small as possible. The subresultant sequence of two polynomials is a polynomial remainder sequence in which the size of the coefficients is optimal in the generic case, but when taking the input from applications, the coefficients are often larger than necessary. We generalize two improvements of the subresultant sequence to Ore polynomials and derive a new bound for the minimal coefficient size. Our approach also yields a new proof for the results in the commutative case, providing a new point of view on the origin of the extraneous factors of the coefficients.

  14. Chaos, Fractals, and Polynomials.

    Science.gov (United States)

    Tylee, J. Louis; Tylee, Thomas B.

    1996-01-01

    Discusses chaos theory; linear algebraic equations and the numerical solution of polynomials, including the use of the Newton-Raphson technique to find polynomial roots; fractals; search region and coordinate systems; convergence; and generating color fractals on a computer. (LRW)

  15. Branched polynomial covering maps

    DEFF Research Database (Denmark)

    Hansen, Vagn Lundsgaard

    2002-01-01

    A Weierstrass polynomial with multiple roots in certain points leads to a branched covering map. With this as the guiding example, we formally define and study the notion of a branched polynomial covering map. We shall prove that many finite covering maps are polynomial outside a discrete branch...... set. Particular studies are made of branched polynomial covering maps arising from Riemann surfaces and from knots in the 3-sphere. (C) 2001 Elsevier Science B.V. All rights reserved....

  16. Branched polynomial covering maps

    DEFF Research Database (Denmark)

    Hansen, Vagn Lundsgaard

    1999-01-01

    A Weierstrass polynomial with multiple roots in certain points leads to a branched covering map. With this as the guiding example, we formally define and study the notion of a branched polynomial covering map. We shall prove that many finite covering maps are polynomial outside a discrete branch...... set. Particular studies are made of branched polynomial covering maps arising from Riemann surfaces and from knots in the 3-sphere....

  17. Branched polynomial covering maps

    DEFF Research Database (Denmark)

    Hansen, Vagn Lundsgaard

    2002-01-01

    A Weierstrass polynomial with multiple roots in certain points leads to a branched covering map. With this as the guiding example, we formally define and study the notion of a branched polynomial covering map. We shall prove that many finite covering maps are polynomial outside a discrete branch ...

  18. Belle II production system

    Science.gov (United States)

    Miyake, Hideki; Grzymkowski, Rafal; Ludacka, Radek; Schram, Malachi

    2015-12-01

    The Belle II experiment will record a similar quantity of data to LHC experiments and will acquire it at similar rates. This requires considerable computing, storage and network resources to handle not only data created by the experiment but also considerable amounts of simulated data. Consequently Belle II employs a distributed computing system to provide the resources coordinated by the the DIRAC interware. DIRAC is a general software framework that provides a unified interface among heterogeneous computing resources. In addition to the well proven DIRAC software stack, Belle II is developing its own extension called BelleDIRAC. BelleDIRAC provides a transparent user experience for the Belle II analysis framework (basf2) on various environments and gives access to file information managed by LFC and AMGA metadata catalog. By unifying DIRAC and BelleDIRAC functionalities, Belle II plans to operate an automated mass data processing framework named a “production system”. The Belle II production system enables large-scale raw data transfer from experimental site to raw data centers, followed by massive data processing, and smart data delivery to each remote site. The production system is also utilized for simulated data production and data analysis. Although development of the production system is still on-going, recently Belle II has prepared prototype version and evaluated it with a large scale simulated data production. In this presentation we will report the evaluation of the prototype system and future development plans.

  19. Poly-Frobenius-Euler polynomials

    Science.gov (United States)

    Kurt, Burak

    2017-07-01

    Hamahata [3] defined poly-Euler polynomials and the generalized poly-Euler polynomials. He proved some relations and closed formulas for the poly-Euler polynomials. By this motivation, we define poly-Frobenius-Euler polynomials. We give some relations for this polynomials. Also, we prove the relationships between poly-Frobenius-Euler polynomials and Stirling numbers of the second kind.

  20. Coherent orthogonal polynomials

    International Nuclear Information System (INIS)

    Celeghini, E.; Olmo, M.A. del

    2013-01-01

    We discuss a fundamental characteristic of orthogonal polynomials, like the existence of a Lie algebra behind them, which can be added to their other relevant aspects. At the basis of the complete framework for orthogonal polynomials we include thus–in addition to differential equations, recurrence relations, Hilbert spaces and square integrable functions–Lie algebra theory. We start here from the square integrable functions on the open connected subset of the real line whose bases are related to orthogonal polynomials. All these one-dimensional continuous spaces allow, besides the standard uncountable basis (|x〉), for an alternative countable basis (|n〉). The matrix elements that relate these two bases are essentially the orthogonal polynomials: Hermite polynomials for the line and Laguerre and Legendre polynomials for the half-line and the line interval, respectively. Differential recurrence relations of orthogonal polynomials allow us to realize that they determine an infinite-dimensional irreducible representation of a non-compact Lie algebra, whose second order Casimir C gives rise to the second order differential equation that defines the corresponding family of orthogonal polynomials. Thus, the Weyl–Heisenberg algebra h(1) with C=0 for Hermite polynomials and su(1,1) with C=−1/4 for Laguerre and Legendre polynomials are obtained. Starting from the orthogonal polynomials the Lie algebra is extended both to the whole space of the L 2 functions and to the corresponding Universal Enveloping Algebra and transformation group. Generalized coherent states from each vector in the space L 2 and, in particular, generalized coherent polynomials are thus obtained. -- Highlights: •Fundamental characteristic of orthogonal polynomials (OP): existence of a Lie algebra. •Differential recurrence relations of OP determine a unitary representation of a non-compact Lie group. •2nd order Casimir originates a 2nd order differential equation that defines the

  1. Computing at Belle II

    Science.gov (United States)

    Kuhr, Thomas

    2012-12-01

    Belle II, a next-generation B-factory experiment, will search for new physics effects in a data sample about 50 times larger than the one collected by its predecessor, the Belle experiment. To match the advances in accelerator and detector technology, the computing system and the software have to be upgraded as well. The Belle II computing model is presented and an overview of the distributed computing system and the offline software framework is given.

  2. Computing at Belle II

    International Nuclear Information System (INIS)

    Kuhr, Thomas

    2012-01-01

    Belle II, a next-generation B-factory experiment, will search for new physics effects in a data sample about 50 times larger than the one collected by its predecessor, the Belle experiment. To match the advances in accelerator and detector technology, the computing system and the software have to be upgraded as well. The Belle II computing model is presented and an overview of the distributed computing system and the offline software framework is given.

  3. Information-theoretic lengths of Jacobi polynomials

    Energy Technology Data Exchange (ETDEWEB)

    Guerrero, A; Dehesa, J S [Departamento de Fisica Atomica, Molecular y Nuclear, Universidad de Granada, Granada (Spain); Sanchez-Moreno, P, E-mail: agmartinez@ugr.e, E-mail: pablos@ugr.e, E-mail: dehesa@ugr.e [Instituto ' Carlos I' de Fisica Teorica y Computacional, Universidad de Granada, Granada (Spain)

    2010-07-30

    The information-theoretic lengths of the Jacobi polynomials P{sup ({alpha}, {beta})}{sub n}(x), which are information-theoretic measures (Renyi, Shannon and Fisher) of their associated Rakhmanov probability density, are investigated. They quantify the spreading of the polynomials along the orthogonality interval [- 1, 1] in a complementary but different way as the root-mean-square or standard deviation because, contrary to this measure, they do not refer to any specific point of the interval. The explicit expressions of the Fisher length are given. The Renyi lengths are found by the use of the combinatorial multivariable Bell polynomials in terms of the polynomial degree n and the parameters ({alpha}, {beta}). The Shannon length, which cannot be exactly calculated because of its logarithmic functional form, is bounded from below by using sharp upper bounds to general densities on [- 1, +1] given in terms of various expectation values; moreover, its asymptotics is also pointed out. Finally, several computational issues relative to these three quantities are carefully analyzed.

  4. Incomplete q-Chebyshev Polynomials

    OpenAIRE

    Ercan, Elif; Firengiz, Mirac Cetin; Tuglu, Naim

    2016-01-01

    In this paper, we get the generating functions of q-Chebyshev polynomials using operator. Also considering explicit formulas of q-Chebyshev polynomials, we give new generalizations of q-Chebyshev polynomials called incomplete q-Chebyshev polynomials of the first and second kind. We obtain recurrence relations and several properties of these polynomials. We show that there are connections between incomplete q-Chebyshev polynomials and the some well-known polynomials. Keywords: q-Chebyshev poly...

  5. Computing at Belle II

    International Nuclear Information System (INIS)

    Kuhr, Thomas

    2011-01-01

    The next generation B-factory experiment Belle II will collect a huge data sample which is a challenge for the computing system. In this article, the computing model of the Belle II experiment is presented and the core components of the computing system are introduced.

  6. Clay Bells: Edo Inspiration

    Science.gov (United States)

    Wagner, Tom

    2010-01-01

    The ceremonial copper and iron bells at the Smithsonian's National Museum of African Art were the author's inspiration for an interdisciplinary unit with a focus on the contributions various cultures make toward the richness of a community. The author of this article describes an Edo bell-inspired ceramic project incorporating slab-building…

  7. Where Bell Went Wrong

    International Nuclear Information System (INIS)

    Nieuwenhuizen, Th. M.

    2009-01-01

    It is explained on a physical basis how absence of contextuality allows Bell inequalities to be violated, without bringing an implication on locality or realism. Hereto we connect first to the local realistic theory Stochastic Electrodynamics, and then put the argument more broadly. Thus even if Bell Inequality Violation is demonstrated beyond reasonable doubt, it will have no say on local realism.

  8. The Belle II Experiment

    CERN Document Server

    Kahn, J

    2017-01-01

    Set to begin data taking at the end of 2018, the Belle II experiment is the next-generation B-factory experiment hosted at KEK in Tsukuba, Japan. The experiment represents the cumulative effort from the collaboration of experimental and detector physics, computing, and software development. Taking everything learned from the previous Belle experiment, which ran from 1998 to 2010, Belle II aims to probe deeper than ever before into the field of heavy quark physics. By achieving an integrated luminosity of 50 ab−1 and accumulating 50 times more data than the previous experiment across its lifetime, along with a rewritten analysis framework, the Belle II experiment will push the high precision frontier of high energy physics. This paper will give an overview of the key components and development activities that make the Belle II experiment possible.

  9. Bell's palsy and autoimmunity.

    Science.gov (United States)

    Greco, A; Gallo, A; Fusconi, M; Marinelli, C; Macri, G F; de Vincentiis, M

    2012-12-01

    To review our current knowledge of the etiopathogenesis of Bell's palsy, including viral infection or autoimmunity, and to discuss disease pathogenesis with respect to pharmacotherapy. Relevant publications on the etiopathogenesis, clinical presentation, diagnosis and histopathology of Bell's palsy from 1975 to 2012 were analysed. Bell's palsy is an idiopathic peripheral nerve palsy involving the facial nerve. It accounts for 60 to 75% of all cases of unilateral facial paralysis. The annual incidence of Bell's palsy is 15 to 30 per 100,000 people. The peak incidence occurs between the second and fourth decades (15 to 45 years). The aetiology of Bell's palsy is unknown but viral infection or autoimmune disease has been postulated as possible pathomechanisms. Bell's palsy may be caused when latent herpes viruses (herpes simplex, herpes zoster) are reactivated from cranial nerve ganglia. A cell-mediated autoimmune mechanism against a myelin basic protein has been suggested for the pathogenesis of Bell's palsy. Bell's palsy may be an autoimmune demyelinating cranial neuritis, and in most cases, it is a mononeuritic variant of Guillain-Barré syndrome, a neurologic disorder with recognised cell-mediated immunity against peripheral nerve myelin antigens. In Bell's palsy and GBS, a viral infection or the reactivation of a latent virus may provoke an autoimmune reaction against peripheral nerve myelin components, leading to the demyelination of cranial nerves, especially the facial nerve. Given the safety profile of acyclovir, valacyclovir, and short-course oral corticosteroids, patients who present within three days of the onset of symptoms should be offered combination therapy. However it seems logical that in fact, steroids exert their beneficial effect via immunosuppressive action, as is the case in some other autoimmune disorders. It is to be hoped that (monoclonal) antibodies and/or T-cell immunotherapy might provide more specific treatment guidelines in the

  10. Polynomial Graphs and Symmetry

    Science.gov (United States)

    Goehle, Geoff; Kobayashi, Mitsuo

    2013-01-01

    Most quadratic functions are not even, but every parabola has symmetry with respect to some vertical line. Similarly, every cubic has rotational symmetry with respect to some point, though most cubics are not odd. We show that every polynomial has at most one point of symmetry and give conditions under which the polynomial has rotational or…

  11. Weierstrass polynomials for links

    DEFF Research Database (Denmark)

    Hansen, Vagn Lundsgaard

    1997-01-01

    There is a natural way of identifying links in3-space with polynomial covering spaces over thecircle. Thereby any link in 3-space can be definedby a Weierstrass polynomial over the circle. Theequivalence relation for covering spaces over thecircle is, however, completely different from...

  12. Nonnegativity of uncertain polynomials

    Directory of Open Access Journals (Sweden)

    Šiljak Dragoslav D.

    1998-01-01

    Full Text Available The purpose of this paper is to derive tests for robust nonnegativity of scalar and matrix polynomials, which are algebraic, recursive, and can be completed in finite number of steps. Polytopic families of polynomials are considered with various characterizations of parameter uncertainty including affine, multilinear, and polynomic structures. The zero exclusion condition for polynomial positivity is also proposed for general parameter dependencies. By reformulating the robust stability problem of complex polynomials as positivity of real polynomials, we obtain new sufficient conditions for robust stability involving multilinear structures, which can be tested using only real arithmetic. The obtained results are applied to robust matrix factorization, strict positive realness, and absolute stability of multivariable systems involving parameter dependent transfer function matrices.

  13. Special matrices of mathematical physics stochastic, circulant and Bell matrices

    CERN Document Server

    Aldrovandi, R

    2001-01-01

    This book expounds three special kinds of matrices that are of physical interest, centering on physical examples. Stochastic matrices describe dynamical systems of many different types, involving (or not) phenomena like transience, dissipation, ergodicity, nonequilibrium, and hypersensitivity to initial conditions. The main characteristic is growth by agglomeration, as in glass formation. Circulants are the building blocks of elementary Fourier analysis and provide a natural gateway to quantum mechanics and noncommutative geometry. Bell polynomials offer closed expressions for many formulas co

  14. Generalizations of orthogonal polynomials

    Science.gov (United States)

    Bultheel, A.; Cuyt, A.; van Assche, W.; van Barel, M.; Verdonk, B.

    2005-07-01

    We give a survey of recent generalizations of orthogonal polynomials. That includes multidimensional (matrix and vector orthogonal polynomials) and multivariate versions, multipole (orthogonal rational functions) variants, and extensions of the orthogonality conditions (multiple orthogonality). Most of these generalizations are inspired by the applications in which they are applied. We also give a glimpse of these applications, which are usually generalizations of applications where classical orthogonal polynomials also play a fundamental role: moment problems, numerical quadrature, rational approximation, linear algebra, recurrence relations, and random matrices.

  15. Superiority of legendre polynomials to Chebyshev polynomial in ...

    African Journals Online (AJOL)

    In this paper, we proved the superiority of Legendre polynomial to Chebyshev polynomial in solving first order ordinary differential equation with rational coefficient. We generated shifted polynomial of Chebyshev, Legendre and Canonical polynomials which deal with solving differential equation by first choosing Chebyshev ...

  16. Extended biorthogonal matrix polynomials

    Directory of Open Access Journals (Sweden)

    Ayman Shehata

    2017-01-01

    Full Text Available The pair of biorthogonal matrix polynomials for commutative matrices were first introduced by Varma and Tasdelen in [22]. The main aim of this paper is to extend the properties of the pair of biorthogonal matrix polynomials of Varma and Tasdelen and certain generating matrix functions, finite series, some matrix recurrence relations, several important properties of matrix differential recurrence relations, biorthogonality relations and matrix differential equation for the pair of biorthogonal matrix polynomials J(A,B n (x, k and K(A,B n (x, k are discussed. For the matrix polynomials J(A,B n (x, k, various families of bilinear and bilateral generating matrix functions are constructed in the sequel.

  17. On Symmetric Polynomials

    OpenAIRE

    Golden, Ryan; Cho, Ilwoo

    2015-01-01

    In this paper, we study structure theorems of algebras of symmetric functions. Based on a certain relation on elementary symmetric polynomials generating such algebras, we consider perturbation in the algebras. In particular, we understand generators of the algebras as perturbations. From such perturbations, define injective maps on generators, which induce algebra-monomorphisms (or embeddings) on the algebras. They provide inductive structure theorems on algebras of symmetric polynomials. As...

  18. Studies on Bell's theorem

    Science.gov (United States)

    Guney, Veli Ugur

    In this work we look for novel classes of Bell's inequalities and methods to produce them. We also find their quantum violations including, if possible, the maximum one. The Jordan bases method that we explain in Chapter 2 is about using a pair of certain type of orthonormal bases whose spans are subspaces related to measurement outcomes of incompatible quantities on the same physical system. Jordan vectors are the briefest way of expressing the relative orientation of any two subspaces. This feature helps us to reduce the dimensionality of the parameter space on which we do searches for optimization. The work is published in [24]. In Chapter 3, we attempt to find a connection between group theory and Bell's theorem. We devise a way of generating terms of a Bell's inequality that are related to elements of an algebraic group. The same group generates both the terms of the Bell's inequality and the observables that are used to calculate the quantum value of the Bell expression. Our results are published in [25][26]. In brief, Bell's theorem is the main tool of a research program that was started by Einstein, Podolsky, Rosen [19] and Bohr [8] in the early days of quantum mechanics in their discussions about the core nature of physical systems. These debates were about a novel type of physical states called superposition states, which are introduced by quantum mechanics and manifested in the apparent inevitable randomness in measurement outcomes of identically prepared systems. Bell's huge contribution was to find a means of quantifying the problem and hence of opening the way to experimental verification by rephrasing the questions as limits on certain combinations of correlations between measurement results of spatially separate systems [7]. Thanks to Bell, the fundamental questions related to the nature of quantum mechanical systems became quantifiable [6]. According to Bell's theorem, some correlations between quantum entangled systems that involve incompatible

  19. Darboux polynomials and first integrals of natural polynomial Hamiltonian systems

    International Nuclear Information System (INIS)

    Maciejewski, Andrzej J.; Przybylska, Maria

    2004-01-01

    We show that for a natural polynomial Hamiltonian system the existence of a single Darboux polynomial (a partial polynomial first integral) is equivalent to the existence of an additional first integral functionally independent with the Hamiltonian function. Moreover, we show that, in a case when the degree of potential is odd, the system does not admit any proper Darboux polynomial, i.e., the only Darboux polynomials are first integrals

  20. Context-free grammars for several polynomials associated with Eulerian polynomials

    OpenAIRE

    Ma, Shi-Mei; Ma, Jun; Yeh, Yeong-Nan; Zhu, Bao-Xuan

    2016-01-01

    In this paper, we present grammatical descriptions of several polynomials associated with Eulerian polynomials, including q-Eulerian polynomials, alternating run polynomials and derangement polynomials. As applications, we get several convolution formulas involving these polynomials.

  1. Classifying polynomials and identity testing

    Indian Academy of Sciences (India)

    m = nO(log n). [2]. This provides a excellent classification of easy polynomials. Hence, any polynomial that cannot be written as a determinant of a small sized matrix is not easy. A simple counting argument shows that there exist many such polynomials. However, prov- ing an explicitly given polynomial to be hard has.

  2. Chromatic polynomials for simplicial complexes

    DEFF Research Database (Denmark)

    Møller, Jesper Michael; Nord, Gesche

    2016-01-01

    In this note we consider s s -chromatic polynomials for finite simplicial complexes. When s=1 s=1 , the 1 1 -chromatic polynomial is just the usual graph chromatic polynomial of the 1 1 -skeleton. In general, the s s -chromatic polynomial depends on the s s -skeleton and its value at r...

  3. Belle II Software

    International Nuclear Information System (INIS)

    Kuhr, T; Ritter, M

    2016-01-01

    Belle II is a next generation B factory experiment that will collect 50 times more data than its predecessor, Belle. The higher luminosity at the SuperKEKB accelerator leads to higher background levels and requires a major upgrade of the detector. As a consequence, the simulation, reconstruction, and analysis software must also be upgraded substantially. Most of the software has been redesigned from scratch, taking into account the experience from Belle and other experiments and utilizing new technologies. The large amount of experimental and simulated data requires a high level of reliability and reproducibility, even in parallel environments. Several technologies, tools, and organizational measures are employed to evaluate and monitor the performance of the software during development. (paper)

  4. Exact Polynomial Eigenmodes for Homogeneous Spherical 3-Manifolds

    OpenAIRE

    Weeks, Jeffrey R.

    2005-01-01

    Observational data hints at a finite universe, with spherical manifolds such as the Poincare dodecahedral space tentatively providing the best fit. Simulating the physics of a model universe requires knowing the eigenmodes of the Laplace operator on the space. The present article provides explicit polynomial eigenmodes for all globally homogeneous 3-manifolds: the Poincare dodecahedral space S3/I*, the binary octahedral space S3/O*, the binary tetrahedral space S3/T*, the prism manifolds S3/D...

  5. Computationally Efficient Nonlinear Bell Inequalities for Quantum Networks

    Science.gov (United States)

    Luo, Ming-Xing

    2018-04-01

    The correlations in quantum networks have attracted strong interest with new types of violations of the locality. The standard Bell inequalities cannot characterize the multipartite correlations that are generated by multiple sources. The main problem is that no computationally efficient method is available for constructing useful Bell inequalities for general quantum networks. In this work, we show a significant improvement by presenting new, explicit Bell-type inequalities for general networks including cyclic networks. These nonlinear inequalities are related to the matching problem of an equivalent unweighted bipartite graph that allows constructing a polynomial-time algorithm. For the quantum resources consisting of bipartite entangled pure states and generalized Greenberger-Horne-Zeilinger (GHZ) states, we prove the generic nonmultilocality of quantum networks with multiple independent observers using new Bell inequalities. The violations are maximal with respect to the presented Tsirelson's bound for Einstein-Podolsky-Rosen states and GHZ states. Moreover, these violations hold for Werner states or some general noisy states. Our results suggest that the presented Bell inequalities can be used to characterize experimental quantum networks.

  6. Wringing out better Bell inequalities

    International Nuclear Information System (INIS)

    Braunstein, S.L.; Caves, C.M.

    1989-01-01

    Local realism implies constraints on the statistics of two physically separated systems. These constraints, known collectively as Bell inequalities, can be violated by quantum mechanics. We generalize the standard Bell inequalities in two ways: first, by 'chaining' the Clauser-Horne-Shimony-Holt Bell inequality for two-state systems and, second, by formulating information-theoretic Bell inequalities that apply to any pair of systems. (orig.)

  7. Software Development at Belle II

    Science.gov (United States)

    Kuhr, Thomas; Hauth, Thomas

    2015-12-01

    Belle II is a next generation B-factory experiment that will collect 50 times more data than its predecessor Belle. This requires not only a major upgrade of the detector hardware, but also of the simulation, reconstruction, and analysis software. The challenges of the software development at Belle II and the tools and procedures to address them are reviewed in this article.

  8. Lorentz-invariant Bell's inequality

    International Nuclear Information System (INIS)

    Kim, Won Tae; Son, Edwin J.

    2005-01-01

    We study Bell's inequality in relation to the Einstein-Podolsky-Rosen paradox in the relativistic regime. For this purpose, a relativistically covariant analysis is used in the calculation of the Bell's inequality, which results in the maximally violated Bell's inequality in any reference frame

  9. Bell's inequalities for quantum mechanics

    International Nuclear Information System (INIS)

    Andaas, H.E.

    1991-10-01

    Inequalities corresponding to the generalized Bell's inequalities of local realism are derived for the quantum case. The extremal values permitted by these inequalities exceed those allowed by the generalized Bell's inequalities. Quantum predictions for systems of two spin-1/2 particles prepared as mixtures do not violate Bell's inequalities. 15 refs

  10. Additive and polynomial representations

    CERN Document Server

    Krantz, David H; Suppes, Patrick

    1971-01-01

    Additive and Polynomial Representations deals with major representation theorems in which the qualitative structure is reflected as some polynomial function of one or more numerical functions defined on the basic entities. Examples are additive expressions of a single measure (such as the probability of disjoint events being the sum of their probabilities), and additive expressions of two measures (such as the logarithm of momentum being the sum of log mass and log velocity terms). The book describes the three basic procedures of fundamental measurement as the mathematical pivot, as the utiliz

  11. Elizabeth Belle's Birth Story.

    Science.gov (United States)

    Boro, Jessica; Boro, Samuel

    2014-01-01

    In this article, Jessica and Samuel Boro share the story of the birth of their daughter, Elizabeth Belle. With the physical and emotional support of her husband and her doula, this mother was able to cope with a long labor and have the natural birth she wanted. Her husband describes how important the doula was for him.

  12. Multipartite omnidirectional generalized Bell inequality

    International Nuclear Information System (INIS)

    Nagata, Koji

    2007-01-01

    We derive a multipartite generalized Bell inequality which involves the entire range of settings for each of the local observers. Especially, it is applied to show non-local behavior of a six-qubit mixture of Greenberger-Horne-Zeilinger correlations stronger than previous Bell inequalities. For certain noise admixture to the correlations an explicit local realistic model exists in the case of a standard Bell experiment. Bell experiments with many local settings reveal the non-locality of the state. It turns out that the new inequality is more stringent than many other Bell inequalities in the specific quantum state

  13. Looking for symmetric Bell inequalities

    International Nuclear Information System (INIS)

    Bancal, Jean-Daniel; Gisin, Nicolas; Pironio, Stefano

    2010-01-01

    Finding all Bell inequalities for a given number of parties, measurement settings and measurement outcomes is in general a computationally hard task. We show that all Bell inequalities which are symmetric under the exchange of parties can be found by examining a symmetrized polytope which is simpler than the full Bell polytope. As an illustration of our method, we generate 238 885 new Bell inequalities and 1085 new Svetlichny inequalities. We find, in particular, facet inequalities for Bell experiments involving two parties and two measurement settings that are not of the Collins-Gisin-Linden-Massar-Popescu type.

  14. A complete set of multidimensional Bell inequalities

    International Nuclear Information System (INIS)

    Arnault, François

    2012-01-01

    We give a multidimensional generalization of the complete set of Bell-correlation inequalities given by Werner and Wolf (2001 Phys. Rev. A 64 032112) and by Zukowski and Brukner (2002 Phys. Rev. Lett. 88 210401), for the two-dimensional case. Our construction applies to the n-party, two-observable case, where each observable is d-valued. The d d n inequalities obtained involve homogeneous polynomials. They define the facets of a polytope in a complex vector space of dimension d n . We detail the inequalities obtained in the case d = 3 and, from them, we recover known inequalities. We finally explain how the violations of our inequalities by quantum mechanics can be computed and could be observed, when using unitary observables. (paper)

  15. Fast methods for resumming matrix polynomials and Chebyshev matrix polynomials

    International Nuclear Information System (INIS)

    Liang Wanzen; Baer, Roi; Saravanan, Chandra; Shao Yihan; Bell, Alexis T.; Head-Gordon, Martin

    2004-01-01

    Fast and effective algorithms are discussed for resumming matrix polynomials and Chebyshev matrix polynomials. These algorithms lead to a significant speed-up in computer time by reducing the number of matrix multiplications required to roughly twice the square root of the degree of the polynomial. A few numerical tests are presented, showing that evaluation of matrix functions via polynomial expansions can be preferable when the matrix is sparse and these fast resummation algorithms are employed

  16. Approximations of orthogonal polynomials in terms of Hermite polynomials

    NARCIS (Netherlands)

    J.L. López; N.M. Temme (Nico)

    1999-01-01

    textabstractSeveral orthogonal polynomials have limit forms in which Hermite polynomials show up. Examples are limits with respect to certain parameters of the Jacobi and Laguerre polynomials. In this paper we are interested in more details of these limits and we give asymptotic representations of

  17. Nonsymmetric Askey-Wilson polynomials as vector-valued polynomials

    NARCIS (Netherlands)

    Koornwinder, T.H.; Bouzeffour, F.

    2011-01-01

    Nonsymmetric Askey-Wilson polynomials are usually written as Laurent polynomials. We write them equivalently as 2-vector-valued symmetric Laurent polynomials. Then the Dunkl-Cherednik operator of which they are eigenfunctions, is represented as a 2 × 2 matrix-valued operator. As a new result made

  18. Cyclotomy and Cyclotomic Polynomials

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 4; Issue 12. Cyclotomy and Cyclotomic Polynomials - The Story of how Gauss Narrowly Missed Becoming a Philologist. B Sury. General Article Volume 4 Issue 12 December 1999 pp 41-53 ...

  19. Computing the Alexander Polynomial Numerically

    DEFF Research Database (Denmark)

    Hansen, Mikael Sonne

    2006-01-01

    Explains how to construct the Alexander Matrix and how this can be used to compute the Alexander polynomial numerically.......Explains how to construct the Alexander Matrix and how this can be used to compute the Alexander polynomial numerically....

  20. Interpolation and Polynomial Curve Fitting

    Science.gov (United States)

    Yang, Yajun; Gordon, Sheldon P.

    2014-01-01

    Two points determine a line. Three noncollinear points determine a quadratic function. Four points that do not lie on a lower-degree polynomial curve determine a cubic function. In general, n + 1 points uniquely determine a polynomial of degree n, presuming that they do not fall onto a polynomial of lower degree. The process of finding such a…

  1. Selected topics from Belle

    Indian Academy of Sciences (India)

    Tajima Hiroyasu

    rizes the Belle results on the branching fraction measurements. They are in good agree- ment with BaBaR and CLEO, and show a tendency of Br(KK) < Br(π. · π. ) < Br(Kπ). We should note that π. · π0 is ³pure tree, K0π· and K0π0 are ³pure penguin, and KKs contain annihilation and W-exchange. Charge asymmetry due to ...

  2. Alexander graham bell

    CERN Document Server

    Davis, Lynn

    2015-01-01

    The telephone is one invention that changed the world. It was made by Alexander Graham Bell. Kids will read this book and find out more about him, like that his first job was teaching deaf people. They will also learn more about his invention and working with Thomas Watson. Aligned to Common Core Standards and correlated to state standards. Applied to STEM Concepts of Learning Principles. Super Sandcastle is an imprint of Abdo Publishing, a division of ABDO.

  3. Fourier series in orthogonal polynomials

    CERN Document Server

    Osilenker, Boris

    1999-01-01

    This book presents a systematic course on general orthogonal polynomials and Fourier series in orthogonal polynomials. It consists of six chapters. Chapter 1 deals in essence with standard results from the university course on the function theory of a real variable and on functional analysis. Chapter 2 contains the classical results about the orthogonal polynomials (some properties, classical Jacobi polynomials and the criteria of boundedness).The main subject of the book is Fourier series in general orthogonal polynomials. Chapters 3 and 4 are devoted to some results in this topic (classical

  4. Generalized q-Hermite polynomials

    International Nuclear Information System (INIS)

    Berg, C.; Ruffing, A.

    2001-01-01

    We consider two operators A and A + in a Hilbert space of functions on the exponential lattice {q n ,-q n vertical stroke n element of Z}, where 0 0 and that A and A + are ladder operators for the sequence ψ n =(A + ) n ψ 0 . The sequence (ψ n /ψ 0 ) is shown to be a family of orthogonal polynomials, which we identify as symmetrized q-Laguerre polynomials. We obtain in this way a new proof of the orthogonality for these polynomials. When γ=0 the polynomials are the discrete q-Hermite polynomials of type II, studied in several papers on q-quantum mechanics. (Orig.) (orig.)

  5. Complex Polynomial Vector Fields

    DEFF Research Database (Denmark)

    vector fields. Since the class of complex polynomial vector fields in the plane is natural to consider, it is remarkable that its study has only begun very recently. There are numerous fundamental questions that are still open, both in the general classification of these vector fields, the decomposition...... of parameter spaces into structurally stable domains, and a description of the bifurcations. For this reason, the talk will focus on these questions for complex polynomial vector fields.......The two branches of dynamical systems, continuous and discrete, correspond to the study of differential equations (vector fields) and iteration of mappings respectively. In holomorphic dynamics, the systems studied are restricted to those described by holomorphic (complex analytic) functions...

  6. General Reducibility and Solvability of Polynomial Equations ...

    African Journals Online (AJOL)

    General Reducibility and Solvability of Polynomial Equations. ... Unlike quadratic, cubic, and quartic polynomials, the general quintic and higher degree polynomials cannot be solved algebraically in terms of finite number of additions, ... Galois Theory, Solving Polynomial Systems, Polynomial factorization, Polynomial Ring ...

  7. A Characterization of Polynomials

    DEFF Research Database (Denmark)

    Andersen, Kurt Munk

    1996-01-01

    Given the problem:which functions f(x) are characterized by a relation of the form:f[x1,x2,...,xn]=h(x1+x2+...+xn), where n>1 and h(x) is a given function? Here f[x1,x2,...,xn] denotes the divided difference on n points x1,x2,...,xn of the function f(x).The answer is: f(x) is a polynomial of degr...

  8. Bell inequalities and waiting times

    Energy Technology Data Exchange (ETDEWEB)

    Poeltl, Christina; Governale, Michele [School of Chemical and Physical Sciences and MacDiarmid Institute for Advanced Materials and Nanotechnology, Victoria University of Wellington, PO Box 600, Wellington 6140 (New Zealand)

    2015-07-01

    We propose a Bell test based on waiting time distributions for spin entangled electron pairs, which are generated and split in mesoscopic Coulomb blockade structures, denoted as entanglers. These systems have the advantage that quantum point contacts enable a time resolved observation of the electrons occupying the system, which gives access to quantities such as full counting statistics and waiting time distributions. We use the partial waiting times to define a CHSH-Bell test, which is a purely electronic analogue of the test used in quantum optics. After the introduction of the Bell inequality we discuss the findings on the two examples of a double quantum dot and a triple quantum dot. This Bell test allows the exclusion of irrelevant tunnel processes from the statistics normally used for the Bell correlations. This can improve the parameter range for which a violation of the Bell inequality can be measured significantly.

  9. Recurrences of Bell's palsy.

    Science.gov (United States)

    Cirpaciu, D; Goanta, C M; Cirpaciu, M D

    2014-01-01

    Bell's palsy in known as the most common cause of facial paralysis, determined by the acute onset of lower motor neuron weakness of the facial nerve with no detectable cause. With a lifetime risk of 1 in 60 and an annual incidence of 11-40/100,000 population, the condition resolves completely in around 71% of the untreated cases. Clinical trials performed for Bell's palsy have reported some recurrences, ipsilateral or contralateral to the side affected in the primary episode of facial palsy. Only few data are found in the literature. Melkersson-Rosenthal is a rare neuromucocutaneous syndrome characterized by recurrent facial paralysis, fissured tongue (lingua plicata), orofacial edema. We attempted to analyze some clinical and epidemiologic aspects of recurrent idiopathic palsy, and to develop relevant correlations between the existing data in literature and those obtained in this study. This is a retrospective study carried out on a 10-years period for adults and a five-year period for children. A number of 185 patients aged between 4 and 70 years old were analyzed. 136 of them were adults and 49 were children. 22 of 185 patients with Bell's palsy (12%) had a recurrent partial or complete facial paralysis with one to six episodes of palsy. From this group of 22 cases, 5 patients were diagnosed with Melkersson-Rosenthal syndrome. The patients' age was between 4 and 70 years old, with a medium age of 27,6 years. In the group studied, fifteen patients, meaning 68%, were women and seven were men. The majority of patients in our group with more than two facial palsy episodes had at least one episode on the contralateral side. Our study found a significant incidence of recurrences of idiopathic facial palsy. Recurrent idiopathic facial palsy and Melkersson-Rosenthal syndrome is diagnosed more often in young females. Recurrence is more likely to occur in the first two years from the onset, which leads to the conclusion that we should have a follow up of patients

  10. Polynomial intelligent states

    Energy Technology Data Exchange (ETDEWEB)

    Milks, Matthew M; Guise, Hubert de [Department of Physics, Lakehead University, Thunder Bay, ON, P7B 5E1 (Canada)

    2005-12-01

    The construction of su(2) intelligent states is simplified using a polynomial representation of su(2). The cornerstone of the new construction is the diagonalization of a 2 x 2 matrix. The method is sufficiently simple to be easily extended to su(3), where one is required to diagonalize a single 3 x 3 matrix. For two perfectly general su(3) operators, this diagonalization is technically possible but the procedure loses much of its simplicity owing to the algebraic form of the roots of a cubic equation. Simplified expressions can be obtained by specializing the choice of su(3) operators. This simpler construction will be discussed in detail.

  11. Roots of the Chromatic Polynomial

    DEFF Research Database (Denmark)

    Perrett, Thomas

    The chromatic polynomial of a graph G is a univariate polynomial whose evaluation at any positive integer q enumerates the proper q-colourings of G. It was introduced in connection with the famous four colour theorem but has recently found other applications in the field of statistical physics....... In this thesis we study the real roots of the chromatic polynomial, termed chromatic roots, and focus on how certain properties of a graph affect the location of its chromatic roots. Firstly, we investigate how the presence of a certain spanning tree in a graph affects its chromatic roots. In particular we prove...... of certain minor-closed families of graphs. Later, we study the Tutte polynomial of a graph, which contains the chromatic polynomial as a specialisation. We discuss a technique of Thomassen using which it is possible to deduce that the roots of the chromatic polynomial are dense in certain intervals. We...

  12. Non polynomial B-splines

    Science.gov (United States)

    Laksâ, Arne

    2015-11-01

    B-splines are the de facto industrial standard for surface modelling in Computer Aided design. It is comparable to bend flexible rods of wood or metal. A flexible rod minimize the energy when bending, a third degree polynomial spline curve minimize the second derivatives. B-spline is a nice way of representing polynomial splines, it connect polynomial splines to corner cutting techniques, which induces many nice and useful properties. However, the B-spline representation can be expanded to something we can call general B-splines, i.e. both polynomial and non-polynomial splines. We will show how this expansion can be done, and the properties it induces, and examples of non-polynomial B-spline.

  13. Experimental tests of Bell's inequalities

    International Nuclear Information System (INIS)

    Aspect, A.

    1984-01-01

    The author discusses the experiments related to Bell's inequalities. After first introducing Bell's theorem, the author presents a brief review of the experiments carried out between 1970 and 1976. Finally, some details on experiments that are in progress in the Institut d'Optique d'Orsay are given. (Auth.)

  14. Bell's palsy before Bell : Cornelis Stalpart van der Wiel's observation of Bell's palsy in 1683

    NARCIS (Netherlands)

    van de Graaf, RC; Nicolai, JPA

    2005-01-01

    Bell's palsy is named after Sir Charles Bell (1774-1842), who has long been considered to be the first to describe idiopathic facial paralysis in the early 19th century. However, it was discovered that Nicolaus Anton Friedreich (1761-1836) and James Douglas (1675-1742) preceded him in the 18th

  15. Einstein, Bohr, and Bell

    Science.gov (United States)

    Bellac, Michel Le

    2014-11-01

    The final form of quantum physics, in the particular case of wave mechanics, was established in the years 1925-1927 by Heisenberg, Schrödinger, Born and others, but the synthesis was the work of Bohr who gave an epistemological interpretation of all the technicalities built up over those years; this interpretation will be examined briefly in Chapter 10. Although Einstein acknowledged the success of quantum mechanics in atomic, molecular and solid state physics, he disagreed deeply with Bohr's interpretation. For many years, he tried to find flaws in the formulation of quantum theory as it had been more or less accepted by a large majority of physicists, but his objections were brushed away by Bohr. However, in an article published in 1935 with Podolsky and Rosen, universally known under the acronym EPR, Einstein thought he had identified a difficulty in the by then standard interpretation. Bohr's obscure, and in part beyond the point, answer showed that Einstein had hit a sensitive target. Nevertheless, until 1964, the so-called Bohr-Einstein debate stayed uniquely on a philosophical level, and it was actually forgotten by most physicists, as the few of them aware of it thought it had no practical implication. In 1964, the Northern Irish physicist John Bell realized that the assumptions contained in the EPR article could be tested experimentally. These assumptions led to inequalities, the Bell inequalities, which were in contradiction with quantum mechanical predictions: as we shall see later on, it is extremely likely that the assumptions of the EPR article are not consistent with experiment, which, on the contrary, vindicates the predictions of quantum physics. In Section 3.2, the origin of Bell's inequalities will be explained with an intuitive example, then they will be compared with the predictions of quantum theory in Section 3.3, and finally their experimental status will be reviewed in Section 3.4. The debate between Bohr and Einstein goes much beyond a

  16. A decoding method of an n length binary BCH code through (n + 1n length binary cyclic code

    Directory of Open Access Journals (Sweden)

    TARIQ SHAH

    2013-09-01

    Full Text Available For a given binary BCH code Cn of length n = 2 s - 1 generated by a polynomial of degree r there is no binary BCH code of length (n + 1n generated by a generalized polynomial of degree 2r. However, it does exist a binary cyclic code C (n+1n of length (n + 1n such that the binary BCH code Cn is embedded in C (n+1n . Accordingly a high code rate is attained through a binary cyclic code C (n+1n for a binary BCH code Cn . Furthermore, an algorithm proposed facilitates in a decoding of a binary BCH code Cn through the decoding of a binary cyclic code C (n+1n , while the codes Cn and C (n+1n have the same minimum hamming distance.

  17. Clinical practice guideline: Bell's palsy.

    Science.gov (United States)

    Baugh, Reginald F; Basura, Gregory J; Ishii, Lisa E; Schwartz, Seth R; Drumheller, Caitlin Murray; Burkholder, Rebecca; Deckard, Nathan A; Dawson, Cindy; Driscoll, Colin; Gillespie, M Boyd; Gurgel, Richard K; Halperin, John; Khalid, Ayesha N; Kumar, Kaparaboyna Ashok; Micco, Alan; Munsell, Debra; Rosenbaum, Steven; Vaughan, William

    2013-11-01

    Bell's palsy, named after the Scottish anatomist, Sir Charles Bell, is the most common acute mono-neuropathy, or disorder affecting a single nerve, and is the most common diagnosis associated with facial nerve weakness/paralysis. Bell's palsy is a rapid unilateral facial nerve paresis (weakness) or paralysis (complete loss of movement) of unknown cause. The condition leads to the partial or complete inability to voluntarily move facial muscles on the affected side of the face. Although typically self-limited, the facial paresis/paralysis that occurs in Bell's palsy may cause significant temporary oral incompetence and an inability to close the eyelid, leading to potential eye injury. Additional long-term poor outcomes do occur and can be devastating to the patient. Treatments are generally designed to improve facial function and facilitate recovery. There are myriad treatment options for Bell's palsy, and some controversy exists regarding the effectiveness of several of these options, and there are consequent variations in care. In addition, numerous diagnostic tests available are used in the evaluation of patients with Bell's palsy. Many of these tests are of questionable benefit in Bell's palsy. Furthermore, while patients with Bell's palsy enter the health care system with facial paresis/paralysis as a primary complaint, not all patients with facial paresis/paralysis have Bell's palsy. It is a concern that patients with alternative underlying etiologies may be misdiagnosed or have unnecessary delay in diagnosis. All of these quality concerns provide an important opportunity for improvement in the diagnosis and management of patients with Bell's palsy. The primary purpose of this guideline is to improve the accuracy of diagnosis for Bell's palsy, to improve the quality of care and outcomes for patients with Bell's palsy, and to decrease harmful variations in the evaluation and management of Bell's palsy. This guideline addresses these needs by encouraging

  18. Classifying polynomials and identity testing

    Indian Academy of Sciences (India)

    hard to compute [3,4]! Therefore, the solution to. PIT problem has a key role in our attempt to com- putationally classify polynomials. In this article, we will focus on this connection between PIT and polynomial classification. We now formally define arithmetic circuits and the identity testing problem. 1.1 Problem definition.

  19. Polynomial methods in combinatorics

    CERN Document Server

    Guth, Larry

    2016-01-01

    This book explains some recent applications of the theory of polynomials and algebraic geometry to combinatorics and other areas of mathematics. One of the first results in this story is a short elegant solution of the Kakeya problem for finite fields, which was considered a deep and difficult problem in combinatorial geometry. The author also discusses in detail various problems in incidence geometry associated to Paul Erdős's famous distinct distances problem in the plane from the 1940s. The proof techniques are also connected to error-correcting codes, Fourier analysis, number theory, and differential geometry. Although the mathematics discussed in the book is deep and far-reaching, it should be accessible to first- and second-year graduate students and advanced undergraduates. The book contains approximately 100 exercises that further the reader's understanding of the main themes of the book. Some of the greatest advances in geometric combinatorics and harmonic analysis in recent years have been accompl...

  20. Complex Polynomial Vector Fields

    DEFF Research Database (Denmark)

    Dias, Kealey

    The two branches of dynamical systems, continuous and discrete, correspond to the study of differential equations (vector fields) and iteration of mappings respectively. In holomorphic dynamics, the systems studied are restricted to those described by holomorphic (complex analytic) functions...... or meromorphic (allowing poles as singularities) functions. There already exists a well-developed theory for iterative holomorphic dynamical systems, and successful relations found between iteration theory and flows of vector fields have been one of the main motivations for the recent interest in holomorphic...... vector fields. Since the class of complex polynomial vector fields in the plane is natural to consider, it is remarkable that its study has only begun very recently. There are numerous fundamental questions that are still open, both in the general classification of these vector fields, the decomposition...

  1. On the limit from q-Racah polynomials to big q-Jacobi polynomials

    NARCIS (Netherlands)

    Koornwinder, T.H.

    2011-01-01

    A limit formula from q-Racah polynomials to big q-Jacobi polynomials is given which can be considered as a limit formula for orthogonal polynomials. This is extended to a multi-parameter limit with 3 parameters, also involving (q-)Hahn polynomials, little q-Jacobi polynomials and Jacobi polynomials.

  2. Belle II Technical Design Report

    CERN Document Server

    Abe, T; Adamczyk, K; Ahn, S; Aihara, H; Akai, K; Aloi, M; Andricek, L; Aoki, K; Arai, Y; Arefiev, A; Arinstein, K; Arita, Y; Asner, D M; Aulchenko, V; Aushev, T; Aziz, T; Bakich, A M; Balagura, V; Ban, Y; Barberio, E; Barvich, T; Belous, K; Bergauer, T; Bhardwaj, V; Bhuyan, B; Blyth, S; Bondar, A; Bonvicini, G; Bozek, A; Bracko, M; Brodzicka, J; Brovchenko, O; Browder, T E; Cao, G; Chang, M -C; Chang, P; Chao, Y; Chekelian, V; Chen, A; Chen, K -F; Chen, P; Cheon, B G; Chiang, C -C; Chistov, R; Cho, K; Choi, S -K; Chung, K; Comerma, A; Cooney, M; Cowley, D E; Critchlow, T; Dalseno, J; Danilov, M; Dieguez, A; Dierlamm, A; Dillon, M; Dingfelder, J; Dolenec, R; Dolezal, Z; Drasal, Z; Drutskoy, A; Dungel, W; Dutta, D; Eidelman, S; Enomoto, A; Epifanov, D; Esen, S; Fast, J E; Feindt, M; Garcia, M Fernandez; Fifield, T; Fischer, P; Flanagan, J; Fourletov, S; Fourletova, J; Freixas, L; Frey, A; Friedl, M; Fruehwirth, R; Fujii, H; Fujikawa, M; Fukuma, Y; Funakoshi, Y; Furukawa, K; Fuster, J; Gabyshev, N; Cueto, A Gaspar de Valenzuela; Garmash, A; Garrido, L; Geisler, Ch; Gfall, I; Goh, Y M; Golob, B; Gorton, I; Grzymkowski, R; Guo, H; Ha, H; Haba, J; Hara, K; Hara, T; Haruyama, T; Hayasaka, K; Hayashi, K; Hayashii, H; Heck, M; Heindl, S; Heller, C; Hemperek, T; Higuchi, T; Horii, Y; Hou, W -S; Hsiung, Y B; Huang, C -H; Hwang, S; Hyun, H J; Igarashi, Y; Iglesias, C; Iida, Y; Iijima, T; Imamura, M; Inami, K; Irmler, C; Ishizuka, M; Itagaki, K; Itoh, R; Iwabuchi, M; Iwai, G; Iwai, M; Iwasaki, M; Iwasaki, M; Iwasaki, Y; Iwashita, T; Iwata, S; Jang, H; Ji, X; Jinno, T; Jones, M; Julius, T; Kageyama, T; Kah, D H; Kakuno, H; Kamitani, T; Kanazawa, K; Kapusta, P; Kataoka, S U; Katayama, N; Kawai, M; Kawai, Y; Kawasaki, T; Kennedy, J; Kichimi, H; Kikuchi, M; Kiesling, C; Kim, B K; Kim, G N; Kim, H J; Kim, H O; Kim, J -B; Kim, J H; Kim, M J; Kim, S K; Kim, K T; Kim, T Y; Kinoshita, K; Kishi, K; Kisielewski, B; van Dam, K Kleese; Knopf, J; Ko, B R; Koch, M; Kodys, P; Koffmane, C; Koga, Y; Kohriki, T; Koike, S; Koiso, H; Kondo, Y; Korpar, S; Kouzes, R T; Kreidl, Ch; Kreps, M; Krizan, P; Krokovny, P; Krueger, H; Kruth, A; Kuhn, W; Kuhr, T; Kumar, R; Kumita, T; Kupper, S; Kuzmin, A; Kvasnicka, P; Kwon, Y -J; Lacasta, C; Lange, J S; Lee, I -S; Lee, M J; Lee, M W; Lee, S -H; Lemarenko, M; Li, J; Li, W D; Li, Y; Libby, J; Limosani, A; Liu, C; Liu, H; Liu, Y; Liu, Z; Liventsev, D; Virto, A Lopez; Makida, Y; Mao, Z P; Marinas, C; Masuzawa, M; Matvienko, D; Mitaroff, W; Miyabayashi, K; Miyata, H; Miyazaki, Y; Miyoshi, T; Mizuk, R; Mohanty, G B; Mohapatra, D; Moll, A; Mori, T; Morita, A; Morita, Y; Moser, H -G; Martin, D Moya; Mueller, T; Muenchow, D; Murakami, J; Myung, S S; Nagamine, T; Nakamura, I; Nakamura, T T; Nakano, E; Nakano, H; Nakao, M; Nakazawa, H; Nam, S -H; Natkaniec, Z; Nedelkovska, E; Negishi, K; Neubauer, S; Ng, C; Ninkovic, J; Nishida, S; Nishimura, K; Novikov, E; Nozaki, T; Ogawa, S; Ohmi, K; Ohnishi, Y; Ohshima, T; Ohuchi, N; Oide, K; Olsen, S L; Ono, M; Ono, Y; Onuki, Y; Ostrowicz, W; Ozaki, H; Pakhlov, P; Pakhlova, G; Palka, H; Park, H; Park, H K; Peak, L S; Peng, T; Peric, I; Pernicka, M; Pestotnik, R; Petric, M; Piilonen, L E; Poluektov, A; Prim, M; Prothmann, K; Regimbal, K; Reisert, B; Richter, R H; Riera-Babures, J; Ritter, A; Ritter, A; Ritter, M; Roehrken, M; Rorie, J; Rosen, M; Rozanska, M; Ruckman, L; Rummel, S; Rusinov, V; Russell, R M; Ryu, S; Sahoo, H; Sakai, K; Sakai, Y; Santelj, L; Sasaki, T; Sato, N; Sato, Y; Scheirich, J; Schieck, J; Schwanda, C; Schwartz, A J; Schwenker, B; Seljak, A; Senyo, K; Seon, O -S; Sevior, M E; Shapkin, M; Shebalin, V; Shen, C P; Shibuya, H; Shiizuka, S; Shiu, J -G; Shwartz, B; Simon, F; Simonis, H J; Singh, J B; Sinha, R; Sitarz, M; Smerkol, P; Sokolov, A; Solovieva, E; Stanic, S; Staric, M; Stypula, J; Suetsugu, Y; Sugihara, S; Sugimura, T; Sumisawa, K; Sumiyoshi, T; Suzuki, K; Suzuki, S Y; Takagaki, H; Takasaki, F; Takeichi, H; Takubo, Y; Tanaka, M; Tanaka, S; Taniguchi, N; Tarkovsky, E; Tatishvili, G; Tawada, M; Taylor, G N; Teramoto, Y; Tikhomirov, I; Trabelsi, K; Tsuboyama, T; Tsunada, K; Tu, Y -C; Uchida, T; Uehara, S; Ueno, K; Uglov, T; Unno, Y; Uno, S; Urquijo, P; Ushiroda, Y; Usov, Y; Vahsen, S; Valentan, M; Vanhoefer, P; Varner, G; Varvell, K E; Vazquez, P; Vila, I; Vilella, E; Vinokurova, A; Visniakov, J; Vos, M; Wang, C H; Wang, J; Wang, M -Z; Wang, P; Wassatch, A; Watanabe, M; Watase, Y; Weiler, T; Wermes, N; Wescott, R E; White, E; Wicht, J; Widhalm, L; Williams, K M; Won, E; Xu, H; Yabsley, B D; Yamamoto, H; Yamaoka, H; Yamaoka, Y; Yamauchi, M; Yin, Y; Yoon, H; Yu, J; Yuan, C Z; Yusa, Y; Zander, D; Zdybal, M; Zhang, Z P; Zhao, J; Zhao, L; Zhao, Z; Zhilich, V; Zhou, P; Zhulanov, V; Zivko, T; Zupanc, A; Zyukova, O

    2010-01-01

    The Belle detector at the KEKB electron-positron collider has collected almost 1 billion Y(4S) events in its decade of operation. Super-KEKB, an upgrade of KEKB is under construction, to increase the luminosity by two orders of magnitude during a three-year shutdown, with an ultimate goal of 8E35 /cm^2 /s luminosity. To exploit the increased luminosity, an upgrade of the Belle detector has been proposed. A new international collaboration Belle-II, is being formed. The Technical Design Report presents physics motivation, basic methods of the accelerator upgrade, as well as key improvements of the detector.

  3. Application of a composition of generating functions for obtaining explicit formulas of polynomials

    OpenAIRE

    Kruchinin, Vladimir; Kruchinin, Dmitry

    2012-01-01

    Using notions of composita and composition of generating functions we obtain explicit formulas for Chebyshev polynomials, Legendre polynomials, Gegenbauer polynomials, Associated Laguerre polynomials, Stirling polynomials, Abel polynomials, Bernoulli Polynomials of the Second Kind, Generalized Bernoulli polynomials, Euler Polynomials, Peters polynomials, Narumi polynomials, Humbert polynomials, Lerch polynomials and Mahler polynomials.

  4. Bell's inequalities and Kolmogorov's axioms

    Indian Academy of Sciences (India)

    Abstract. After recalling proofs of the Bell inequality based on the assumptions of separability and of noncontextuality, the most general noncontextual contrapositive conditional probabilities consistent with the Aspect experiment are constructed. In general these probabilities are not all positive.

  5. Magic moments with John Bell

    International Nuclear Information System (INIS)

    Bertlmann, Reinhold A.

    2015-01-01

    John Bell, with whom I had a fruitful collaboration and warm friendship, is best known for his seminal work on the foundations of quantum physics, but he also made outstanding contributions to particle physics and accelerator physics

  6. Orthogonal polynomials in transport theories

    International Nuclear Information System (INIS)

    Dehesa, J.S.

    1981-01-01

    The asymptotical (k→infinity) behaviour of zeros of the polynomials gsub(k)sup((m)(ν)) encountered in the treatment of direct and inverse problems of scattering in neutron transport as well as radiative transfer theories is investigated in terms of the amplitude antiwsub(k) of the kth Legendre polynomial needed in the expansion of the scattering function. The parameters antiwsub(k) describe the anisotropy of scattering of the medium considered. In particular, it is shown that the asymptotical density of zeros of the polynomials gsub(k)sup(m)(ν) is an inverted semicircle for the anisotropic non-multiplying scattering medium

  7. Parallel Construction of Irreducible Polynomials

    DEFF Research Database (Denmark)

    Frandsen, Gudmund Skovbjerg

    Let arithmetic pseudo-NC^k denote the problems that can be solved by log space uniform arithmetic circuits over the finite prime field GF(p) of depth O(log^k (n + p)) and size polynomial in (n + p). We show that the problem of constructing an irreducible polynomial of specified degree over GF(p) ...... of polynomials is in arithmetic NC^3. Our algorithm works over any field and compared to other known algorithms it does not assume the ability to take p'th roots when the field has characteristic p....

  8. Sum rules for zeros of polynomials and generalized Lucas polynomials

    Science.gov (United States)

    Ricci, Paolo Emilio

    1993-10-01

    A representation formula in terms of generalized Lucas polynomials of the second kind [see formula (4.3)], for the sum rules Js(i) introduced by Case [J. Math. Phys. 21, 702 (1980)] and studied by Dehesa et al. [J. Math. Phys. 26, 1547 (1985); 26, 2729 (1985)] in order to obtain information about the zeros' distribution of eigenfunctions of a class of ordinary polynomial differential operators, is derived.

  9. Is the bell ringing?

    CERN Multimedia

    Francesco Poppi

    2010-01-01

    During the Nobel prize-winning UA1 experiment, scientists in the control room used to ring a bell if a particularly interesting event had occurred. Today, the “CMS Exotica hotline” routine produces a daily report that lists the exotic events that were recorded the day before.   Display of an event selected by the Exotica routine. Take just a very small fraction of the available data (max. 5%); define the events that you want to keep and set the parameters accordingly; run the Exotica routine and only look at the very few images that the system has selected for you. This is the recipe that a small team of CMS researchers has developed to identify the signals coming from possible new physics processes. “This approach does not replace the accurate data analysis on the whole set of data. However, it is a very fast and effective way to focus on just a few events that are potentially very interesting”, explains Maurizio Pierini (CERN), who developed the...

  10. Polynomial Regressions and Nonsense Inference

    Directory of Open Access Journals (Sweden)

    Daniel Ventosa-Santaulària

    2013-11-01

    Full Text Available Polynomial specifications are widely used, not only in applied economics, but also in epidemiology, physics, political analysis and psychology, just to mention a few examples. In many cases, the data employed to estimate such specifications are time series that may exhibit stochastic nonstationary behavior. We extend Phillips’ results (Phillips, P. Understanding spurious regressions in econometrics. J. Econom. 1986, 33, 311–340. by proving that an inference drawn from polynomial specifications, under stochastic nonstationarity, is misleading unless the variables cointegrate. We use a generalized polynomial specification as a vehicle to study its asymptotic and finite-sample properties. Our results, therefore, lead to a call to be cautious whenever practitioners estimate polynomial regressions.

  11. An introduction to orthogonal polynomials

    CERN Document Server

    Chihara, Theodore S

    1978-01-01

    Assuming no further prerequisites than a first undergraduate course in real analysis, this concise introduction covers general elementary theory related to orthogonal polynomials. It includes necessary background material of the type not usually found in the standard mathematics curriculum. Suitable for advanced undergraduate and graduate courses, it is also appropriate for independent study. Topics include the representation theorem and distribution functions, continued fractions and chain sequences, the recurrence formula and properties of orthogonal polynomials, special functions, and some

  12. Julia Sets of Orthogonal Polynomials

    DEFF Research Database (Denmark)

    Christiansen, Jacob Stordal; Henriksen, Christian; Petersen, Henrik Laurberg

    2018-01-01

    For a probability measure with compact and non-polar support in the complex plane we relate dynamical properties of the associated sequence of orthogonal polynomials fPng to properties of the support. More precisely we relate the Julia set of Pn to the outer boundary of the support, the lled Julia...... set to the polynomial convex hull K of the support, and the Green's function associated with Pn to the Green's function for the complement of K....

  13. Stochastic Estimation via Polynomial Chaos

    Science.gov (United States)

    2015-10-01

    processes. As originally developed by Norbert Weiner, a polynomial chaos represents key properties of a stochastic process through the application of...polynomial chaos method for representing the properties of second order stochastic processes. As originally developed by Norbert Weiner, a...any real or complex functional ][xF in 2L converges to ][xF in the 2L sense with Wiener measure.[3] In the same reference, the orthogonality of

  14. On Modular Counting with Polynomials

    DEFF Research Database (Denmark)

    Hansen, Kristoffer Arnsfelt

    2006-01-01

    For any integers m and l, where m has r sufficiently large (depending on l) factors, that are powers of r distinct primes, we give a construction of a (symmetric) polynomial over Z_m of degree O(\\sqrt n) that is a generalized representation (commonly also called weak representation) of the MODl...... function. We give a detailed study of the case when m has exactly two distinct prime factors, and classify the minimum possible degree for a symmetric representing polynomial....

  15. Scattering theory and orthogonal polynomials

    International Nuclear Information System (INIS)

    Geronimo, J.S.

    1977-01-01

    The application of the techniques of scattering theory to the study of polynomials orthogonal on the unit circle and a finite segment of the real line is considered. The starting point is the recurrence relations satisfied by the polynomials instead of the orthogonality condition. A set of two two terms recurrence relations for polynomials orthogonal on the real line is presented and used. These recurrence relations play roles analogous to those satisfied by polynomials orthogonal on unit circle. With these recurrence formulas a Wronskian theorem is proved and the Christoffel-Darboux formula is derived. In scattering theory a fundamental role is played by the Jost function. An analogy is deferred of this function and its analytic properties and the locations of its zeros investigated. The role of the analog Jost function in various properties of these orthogonal polynomials is investigated. The techniques of inverse scattering theory are also used. The discrete analogues of the Gelfand-Levitan and Marchenko equations are derived and solved. These techniques are used to calculate asymptotic formulas for the orthogonal polynomials. Finally Szego's theorem on toeplitz and Hankel determinants is proved using the recurrence formulas and some properties of the Jost function. The techniques of inverse scattering theory are used to calculate the correction terms

  16. Bannai-Ito polynomials and dressing chains

    OpenAIRE

    Derevyagin, Maxim; Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei

    2012-01-01

    Schur-Delsarte-Genin (SDG) maps and Bannai-Ito polynomials are studied. SDG maps are related to dressing chains determined by quadratic algebras. The Bannai-Ito polynomials and their kernel polynomials -- the complementary Bannai-Ito polynomials -- are shown to arise in the framework of the SDG maps.

  17. A 'missing' family of classical orthogonal polynomials

    International Nuclear Information System (INIS)

    Vinet, Luc; Zhedanov, Alexei

    2011-01-01

    We study a family of 'classical' orthogonal polynomials which satisfy (apart from a three-term recurrence relation) an eigenvalue problem with a differential operator of Dunkl type. These polynomials can be obtained from the little q-Jacobi polynomials in the limit q = -1. We also show that these polynomials provide a nontrivial realization of the Askey-Wilson algebra for q = -1.

  18. Birth-death processes and associated polynomials

    NARCIS (Netherlands)

    van Doorn, Erik A.

    2003-01-01

    We consider birth-death processes on the nonnegative integers and the corresponding sequences of orthogonal polynomials called birth-death polynomials. The sequence of associated polynomials linked with a sequence of birth-death polynomials and its orthogonalizing measure can be used in the analysis

  19. On Multiple Polynomials of Capelli Type

    Directory of Open Access Journals (Sweden)

    S.Y. Antonov

    2016-03-01

    Full Text Available This paper deals with the class of Capelli polynomials in free associative algebra F{Z} (where F is an arbitrary field, Z is a countable set generalizing the construction of multiple Capelli polynomials. The fundamental properties of the introduced Capelli polynomials are provided. In particular, decomposition of the Capelli polynomials by means of the same type of polynomials is shown. Furthermore, some relations between their T -ideals are revealed. A connection between double Capelli polynomials and Capelli quasi-polynomials is established.

  20. Bell's theorem, accountability and nonlocality

    International Nuclear Information System (INIS)

    Vona, Nicola; Liang, Yeong-Cherng

    2014-01-01

    Bell's theorem is a fundamental theorem in physics concerning the incompatibility between some correlations predicted by quantum theory and a large class of physical theories. In this paper, we introduce the hypothesis of accountability, which demands that it is possible to explain the correlations of the data collected in many runs of a Bell experiment in terms of what happens in each single run. Under this assumption, and making use of a recent result by Colbeck and Renner (2011 Nature Commun. 2 411), we then show that any nontrivial account of these correlations in the form of an extension of quantum theory must violate parameter independence. Moreover, we analyze the violation of outcome independence of quantum mechanics and show that it is also a manifestation of nonlocality. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell's theorem’. (paper)

  1. John Bell and the Identical Twins

    CERN Multimedia

    1984-01-01

    A biographical profile of John S.Bell is presented based on extensive interviews the author had with Bell. Bell’s vierws on the quantum theory are presented along with a simple explanation of his idenity.

  2. Bipartite Bell Inequality and Maximal Violation

    International Nuclear Information System (INIS)

    Li Ming; Fei Shaoming; Li-Jost Xian-Qing

    2011-01-01

    We present new bell inequalities for arbitrary dimensional bipartite quantum systems. The maximal violation of the inequalities is computed. The Bell inequality is capable of detecting quantum entanglement of both pure and mixed quantum states more effectively. (general)

  3. Belle Physics at Wayne State

    International Nuclear Information System (INIS)

    Cinabro, David

    2016-01-01

    The major goals of our work on Belle II were to complete our contributions, a 64-channel PIN diode-based radiation monitor, to the precursor detector called Beast II and the electronics for the endcap K-Long/Muon (E-KLM) detector. This was done by Professor Cinabro, Technician Gutierrez, and undergraduate labor supported by US-Japan funds. Professor Bonvicini through US-Japan funds led the development and installation of a beamstrahlung monitor system in the Belle II interaction region. Graduate students Farhat and DiCarlo worked on this. We also worked on charm physics analysis.

  4. The Belle Silicon Vertex Detector

    CERN Document Server

    Kawasaki, T

    2002-01-01

    The Belle Silicon Vertex Detector (SVD) started working from June 1999 at the KEK B-factory experiment. The main purpose of the SVD is to make precise measurements of the B decay vertex position, which are essential for the observation of CP asymmetries. Excellent vertex resolution and a good detection efficiency are required for the SVD. In the present paper, the performance of Belle SVD is reviewed. The upgrade plan for the SVD2, which is under construction and will be installed in summer 2002, is also presented.

  5. Chromatic polynomials of random graphs

    International Nuclear Information System (INIS)

    Van Bussel, Frank; Fliegner, Denny; Timme, Marc; Ehrlich, Christoph; Stolzenberg, Sebastian

    2010-01-01

    Chromatic polynomials and related graph invariants are central objects in both graph theory and statistical physics. Computational difficulties, however, have so far restricted studies of such polynomials to graphs that were either very small, very sparse or highly structured. Recent algorithmic advances (Timme et al 2009 New J. Phys. 11 023001) now make it possible to compute chromatic polynomials for moderately sized graphs of arbitrary structure and number of edges. Here we present chromatic polynomials of ensembles of random graphs with up to 30 vertices, over the entire range of edge density. We specifically focus on the locations of the zeros of the polynomial in the complex plane. The results indicate that the chromatic zeros of random graphs have a very consistent layout. In particular, the crossing point, the point at which the chromatic zeros with non-zero imaginary part approach the real axis, scales linearly with the average degree over most of the density range. While the scaling laws obtained are purely empirical, if they continue to hold in general there are significant implications: the crossing points of chromatic zeros in the thermodynamic limit separate systems with zero ground state entropy from systems with positive ground state entropy, the latter an exception to the third law of thermodynamics.

  6. Orthogonal Polynomials and Special Functions

    CERN Document Server

    Assche, Walter

    2003-01-01

    The set of lectures from the Summer School held in Leuven in 2002 provide an up-to-date account of recent developments in orthogonal polynomials and special functions, in particular for algorithms for computer algebra packages, 3nj-symbols in representation theory of Lie groups, enumeration, multivariable special functions and Dunkl operators, asymptotics via the Riemann-Hilbert method, exponential asymptotics and the Stokes phenomenon. The volume aims at graduate students and post-docs working in the field of orthogonal polynomials and special functions, and in related fields interacting with orthogonal polynomials, such as combinatorics, computer algebra, asymptotics, representation theory, harmonic analysis, differential equations, physics. The lectures are self-contained requiring only a basic knowledge of analysis and algebra, and each includes many exercises.

  7. Plain Polynomial Arithmetic on GPU

    International Nuclear Information System (INIS)

    Haque, Sardar Anisul; Maza, Marc Moreno

    2012-01-01

    As for serial code on CPUs, parallel code on GPUs for dense polynomial arithmetic relies on a combination of asymptotically fast and plain algorithms. Those are employed for data of large and small size, respectively. Parallelizing both types of algorithms is required in order to achieve peak performances. In this paper, we show that the plain dense polynomial multiplication can be efficiently parallelized on GPUs. Remarkably, it outperforms (highly optimized) FFT-based multiplication up to degree 2 12 while on CPU the same threshold is usually at 2 6 . We also report on a GPU implementation of the Euclidean Algorithm which is both work-efficient and runs in linear time for input polynomials up to degree 2 18 thus showing the performance of the GCD algorithm based on systolic arrays.

  8. Thiol/disulphide homeostasis in Bell's palsy as a novel pathogenetic marker.

    Science.gov (United States)

    Babademez, M A; Gul, F; Kale, H; Muderris, T; Bayazit, Y; Ergin, M; Erel, O; Kiris, M

    2017-04-01

    The aim of this study was to investigate the relationship between Bell's palsy and a novel oxidative stress parameter, thiol/disulphide homeostasis. A prospective study evaluating oxidative stress in Bell's palsy. This research took place in the department of Otorhinolaryngology, Ataturk Training and Research Hospital. Totally, 77 patients with Bell's palsy and 38 healthy controls were included in this study. The blood levels of total and native thiol and disulphide activity were assessed, and their levels were compared in the patients and controls. There were statistically significant differences between the patients and controls regarding thiol/disulphide parameters. The mean native thiol and total thiol were significantly lower and disulphide levels were higher in the Bell's palsy than controls. On binary logistic regression analysis, the created model showed 45.3% variation. The cut-off value was 18.95 for disulphides. Native and total thiol levels were low in the Bell's palsy. This metabolic disturbance may have a role in the pathogenesis of Bell's palsy. © 2016 John Wiley & Sons Ltd.

  9. Orthogonal Polynomials and their Applications

    CERN Document Server

    Dehesa, Jesús; Marcellan, Francisco; Francia, José; Vinuesa, Jaime

    1988-01-01

    The Segovia meeting set out to stimulate an intensive exchange of ideas between experts in the area of orthogonal polynomials and its applications, to present recent research results and to reinforce the scientific and human relations among the increasingly international community working in orthogonal polynomials. This volume contains original research papers as well as survey papers about fundamental questions in the field (Nevai, Rakhmanov & López) and its relationship with other fields such as group theory (Koornwinder), Padé approximation (Brezinski), differential equations (Krall, Littlejohn) and numerical methods (Rivlin).

  10. Recursive formula to compute Zernike radial polynomials.

    Science.gov (United States)

    Honarvar Shakibaei, Barmak; Paramesran, Raveendran

    2013-07-15

    In optics, Zernike polynomials are widely used in testing, wavefront sensing, and aberration theory. This unique set of radial polynomials is orthogonal over the unit circle and finite on its boundary. This Letter presents a recursive formula to compute Zernike radial polynomials using a relationship between radial polynomials and Chebyshev polynomials of the second kind. Unlike the previous algorithms, the derived recurrence relation depends neither on the degree nor on the azimuthal order of the radial polynomials. This leads to a reduction in the computational complexity.

  11. Nonlocal interactions and Bell's inequality

    International Nuclear Information System (INIS)

    Garuccio, A.; Selleri, F.

    1976-01-01

    It is shown that natural extensions of the local hidden variable theories to include nonlocal effects still lead to a full validity of Bell's inequality. It is conjectured that the essential point expressed by this inequality is not locality, but the wave-particle dualism

  12. For Whom the Bells Toll

    NARCIS (Netherlands)

    Franklin, Rachel S.; Leeuwen, van Eveline S.

    2018-01-01

    In his presidential address to the Regional Science Association over thirty years ago, William Alonso presented the case for “Five Bell Shapes in Development” and argued that “the developed countries will enter fully in to the realm of the right-hand tail of these curves” (p. 16) and that this

  13. Clinical studies on Bell's palsy

    International Nuclear Information System (INIS)

    Yamada, Yoshio

    1985-01-01

    The purpose of this study was to evaluate the diagnostic value of the salivary gland scintigraphy using sup(99m)Tc-pertechnetate for the prognosis of Bell's palsy. The salivary gland scintigraphy was performed in 40 patients with Bell's palsy and 15 normal subjects. After intravenous injection of 10 mCt of sup(99m)Tc-pertechnetate, sequential scintigrams were taken with a scintillation camera every one minute for 25 minutes. At 15 minutes after injection, both of normal subjects and patients were given ascorbic acid to stimulate the secretion of saliva. By the present method, the time activity curve was examined for the regions of interest over the parotid and submandibular glands and backgrounds. In normal subjects, values of the concentration and excretory ratio between the right and left sides of the parotid and submandibular glands were more than 80%. Some patients with Bell's palsy showed a decreased concentration and/or excretory ratio less than 80% between the normal and affected sides of the parotid glands. This suggests a functional involvement of the facial nerve in the salivary secretion from the parotid glands. On examination within 10 days of the onset of Bell's palsy, 31 cases with complete recovery showed values of the concentration ratio and/or excretory ratio more than 80% between the normal and affected sides of the submandibular glands. In contrast, 9 cases with imcomplete recovery showed low values of the concentration ratio and excretory ratio less than 80%. In the latter, more active treatments such as decompression operation should be considerd in the early stage of the palsy. The salivary scintigraphy using sup(99m)Tc-pertechnetate is more valuable as an early prognostic indicator for Bell's palsy compared with other prognostic tests such as the lid vibration test, the stapedial reflex test, the electrogustometry, the nerve excitability test and the evoked electromyography. (author)

  14. Clusters of Bell's palsy "Surtos" da paralisia de Bell

    Directory of Open Access Journals (Sweden)

    Thiago D. Gonçalves-Coêlho

    1997-01-01

    Full Text Available The idiopathic facial paralysis or Bell's palsy installs abruptly or within a few hours, without any apparent cause. It corresponds to approximately 75% of all peripheral facial palsies. Three theories try to explain its pathogenecity: vascular-ischemic, viral and auto-immune. We reviewed the records of the EMG Sector, Hospital do Servidor Público Estadual (São Paulo, Brazil, from 1985 to 1995 and found 239 cases of Bell's palsy. Data were analysed according to age, gender, seasonal distribution of cases. There was a predominance of cases in the 31 - 60 age bracket (40.59 %. The female gender was responsible to 70.71 % of cases. There was a predominance of cases in winter (31.38 % and autumn (30.13 %, which was statiscally significant. These findings let us to suppose that Bell's palsy predominates in females, in 41-60 years age bracket, and occurs predominantly in cold months. There are groups of clusters throughout temporal distribution of cases and cases are dependent on one each other or on factors affecting them all, which reinforces the infectious hypothesis (there is a rise in the incidence of viral upper respiratory tract infection during cold months.A paralisia facial idiopática ou paralisia de Bell se instala abruptamente ou em algumas horas, sem causa aparente. Corresponde a aproximadamente 75% de todos os casos de paralisia facial. Três teorias tentam explicar sua patogenia: vásculo-isquêmica, autoimune e viral. Nós revisamos os arquivos do Setor de Eletromiografia do Hospital do Servidor Público Estadual (São Paulo de 1985 a 1995, encontrando 239 casos de paralisia de Bell. Dados foram analisados quanto a idade, sexo, distribuição sazonal. Houve predominância dos casos na faixa etária de 31 a 60 anos (40,59 %. O sexo feminino foi responsável por 70,71 % dos casos. Houve predominância de casos no inverno (31,38 % e outono (30,13 %, estatisticamente sigmficante. Estes achados levam-nos a supor que a paralisia de Bell

  15. Global Polynomial Kernel Hazard Estimation

    DEFF Research Database (Denmark)

    Hiabu, Munir; Miranda, Maria Dolores Martínez; Nielsen, Jens Perch

    2015-01-01

    This paper introduces a new bias reducing method for kernel hazard estimation. The method is called global polynomial adjustment (GPA). It is a global correction which is applicable to any kernel hazard estimator. The estimator works well from a theoretical point of view as it asymptotically redu...

  16. Polynomial Regressions and Nonsense Inference

    DEFF Research Database (Denmark)

    Ventosa-Santaulària, Daniel; Rodríguez-Caballero, Carlos Vladimir

    Polynomial specifications are widely used, not only in applied economics, but also in epidemiology, physics, political analysis, and psychology, just to mention a few examples. In many cases, the data employed to estimate such estimations are time series that may exhibit stochastic nonstationary ...

  17. Dirichlet polynomials, majorization, and trumping

    International Nuclear Information System (INIS)

    Pereira, Rajesh; Plosker, Sarah

    2013-01-01

    Majorization and trumping are two partial orders which have proved useful in quantum information theory. We show some relations between these two partial orders and generalized Dirichlet polynomials, Mellin transforms, and completely monotone functions. These relations are used to prove a succinct generalization of Turgut’s characterization of trumping. (paper)

  18. Two polynomial division inequalities in

    Directory of Open Access Journals (Sweden)

    Goetgheluck P

    1998-01-01

    Full Text Available This paper is a first attempt to give numerical values for constants and , in classical estimates and where is an algebraic polynomial of degree at most and denotes the -metric on . The basic tools are Markov and Bernstein inequalities.

  19. Aspects of the Tutte polynomial

    DEFF Research Database (Denmark)

    Ok, Seongmin

    This thesis studies various aspects of the Tutte polynomial, especially focusing on the Merino-Welsh conjecture. We write T(G;x,y) for the Tutte polynomial of a graph G with variables x and y. In 1999, Merino and Welsh conjectured that if G is a loopless 2-connected graph, then T(G;1,1) ≤ max{T(G;2......,0), T(G;0,2)}. The three numbers, T(G;1,1), T(G;2,0) and T(G;0,2) are respectively the numbers of spanning trees, acyclic orientations and totally cyclic orientations of G. First, I extend Negami's splitting formula to the multivariate Tutte polynomial. Using the splitting formula, Thomassen and I found......-Welsh conjecture has a stronger version claiming that the Tutte polynomial is convex on the line segment between (2,0) and (0,2) for loopless 2-connected graphs. Chavez-Lomeli et al. proved that this holds for coloopless paving matroids, and I provide a shorter proof of their theorem. I also prove it for minimally...

  20. Sheffer and Non-Sheffer Polynomial Families

    Directory of Open Access Journals (Sweden)

    G. Dattoli

    2012-01-01

    Full Text Available By using the integral transform method, we introduce some non-Sheffer polynomial sets. Furthermore, we show how to compute the connection coefficients for particular expressions of Appell polynomials.

  1. Tables of properties of airfoil polynomials

    Science.gov (United States)

    Desmarais, Robert N.; Bland, Samuel R.

    1995-01-01

    This monograph provides an extensive list of formulas for airfoil polynomials. These polynomials provide convenient expansion functions for the description of the downwash and pressure distributions of linear theory for airfoils in both steady and unsteady subsonic flow.

  2. Random walk polynomials and random walk measures

    NARCIS (Netherlands)

    van Doorn, Erik A.; Schrijner, Pauline

    1993-01-01

    Random walk polynomials and random walk measures play a prominent role in the analysis of a class of Markov chains called random walks. Without any reference to random walks, however, a random walk polynomial sequence can be defined (and will be defined in this paper) as a polynomial sequence{Pn(x)}

  3. Positive trigonometric polynomials and signal processing applications

    CERN Document Server

    Dumitrescu, Bogdan

    2007-01-01

    Presents the results on positive trigonometric polynomials within a unitary framework; the theoretical results obtained partly from the general theory of real polynomials, partly from self-sustained developments. This book provides information on the theory of sum-of-squares trigonometric polynomials in two parts: theory and applications.

  4. Associated polynomials and birth-death processes

    NARCIS (Netherlands)

    van Doorn, Erik A.

    2001-01-01

    We consider sequences of orthogonal polynomials with positive zeros, and pursue the question of how (partial) knowledge of the orthogonalizing measure for the {\\it associated polynomials} can lead to information about the orthogonalizing measure for the original polynomials, with a view to

  5. Sibling curves of polynomials | Wiggins | Quaestiones Mathematicae

    African Journals Online (AJOL)

    Sibling curves were demonstrated in papers [2, 3] as a novel way to visualize the zeros of complex valued functions. In this paper, we continue the work done in those papers by focusing solely on polynomials. We proceed to prove that the number of sibling curves of a polynomial is the degree of the polynomial. Keywords: ...

  6. Restricted Schur polynomials and finite N counting

    International Nuclear Information System (INIS)

    Collins, Storm

    2009-01-01

    Restricted Schur polynomials have been posited as orthonormal operators for the change of basis from N=4 SYM to type IIB string theory. In this paper we briefly expound the relationship between the restricted Schur polynomials and the operators forwarded by Brown, Heslop, and Ramgoolam. We then briefly examine the finite N counting of the restricted Schur polynomials.

  7. On polynomial and multiplicative radicals | Tumurbat | Quaestiones ...

    African Journals Online (AJOL)

    We show that polynomial and multiplicative radicals in [1] are special cases of radicals defined by means of elements. We scrutinize the way of defining a radical γG by a subset G of polynomials in noncommuting indeterminates. Defining polynomial radicals, Drazin and Roberts [1] required that the set G be closed

  8. Hermite polynomials in asymptotic representations of generalized Bernoulli,Euler, Bessel and Buchholz polynomials

    NARCIS (Netherlands)

    J.L. López; N.M. Temme (Nico)

    1999-01-01

    textabstractThis is a second paper on finite exact representations of certain polynomials in terms of Hermite polynomials. The representations have asymptotic properties and include new limits of the polynomials, again in terms of Hermite polynomials. This time we consider the generalized Bernoulli,

  9. Special polynomials associated with rational solutions of some hierarchies

    NARCIS (Netherlands)

    Kudryashov, Nikolai A.

    2009-01-01

    New special polynomials associated with rational solutions of the Painleve hierarchies are introduced. The Hirota relations for these special polynomials are found. Differential-difference hierarchies to find special polynomials are presented. These formulae allow us to search special polynomials

  10. Bell Palsy and Acupuncture Treatment

    Directory of Open Access Journals (Sweden)

    Betul Battaloglu Ižnanc

    2013-08-01

    A 22-year-old female patient, a midwifery student, had treatment with corticosteroid and antiviral agents as soon as Bell Palsy (BP was diagnosed (House-Breckman stage 6. Six weeks later, patient didn’t recover, while in House-Breckman stage 3, acupuncture was perfomed and local and distal acupoints were used with ears, body and face. Ear acupuncture point was used two times with detection. In the course of six sessions body and face points were stimulated by electroacupuncture. After ten acupuncture treatments, the subjective symptoms and the facial motion on the affected side improved. There was an spotting ecchymosis the ST2 points on. The symmetry of the face is a determinant of facial charm and influences interpersonal attraction for adults, children and pregnant women. Medical options for the sequelae of BP are limited. Acupuncture’s effectively in Bell palsy patients’ should be shown with more clinical and electrophysiological studies.

  11. Bell Inequalities for Complex Networks

    Science.gov (United States)

    2015-10-26

    of hidden variables af- fecting complex systems. Bell inequalities are a famous example of a hidden variable test in quantum physics that provides...methods have demonstrated value on diverse problems including human behavior, language, neuroscience , and gene expression. 1 Objectives The original...dependence in data. This line of work [5, 6] has already been successfully applied in several domains including neuroscience [7, 8], analyzing text [9

  12. Interacting binaries

    CERN Document Server

    Shore, S N; van den Heuvel, EPJ

    1994-01-01

    This volume contains lecture notes presented at the 22nd Advanced Course of the Swiss Society for Astrophysics and Astronomy. The contributors deal with symbiotic stars, cataclysmic variables, massive binaries and X-ray binaries, in an attempt to provide a better understanding of stellar evolution.

  13. A limitation on Bell's inequality

    International Nuclear Information System (INIS)

    Buonomano, V.

    1978-01-01

    It is shown that Bell's Inequality does not characterize all local hidden variable explanations of the polarization correlation experiments. If one considers theories in which a single polarization measurement is not independent of previous particle-polarizer interactions then it is possible to manufacture local hidden variable theories which agree with quantum mechanics for any of the experiments performed to date. A relevant property here is ergodicity, and we can say that Bell's Inequality characterizes all ergodic local hidden variable theories (i.e. all local theories that give the same time and ensemble average) but not all non-ergodic local hidden variable theories. It is further shown that the most physically reasonable class of non-ergodic local hidden variable theories must also satisfy Bell's Inequality. It might be concluded from this article that if one insists on believing in both local hidden variable theories and the polarization correlation experiments supporting quantum mechanics then one must also believe in the existence of a field, medium or ether that permeates space and has relatively stable states (memory)

  14. Polynomial Mappings with Small Degree

    Directory of Open Access Journals (Sweden)

    Jelonek Zbigniew

    2015-06-01

    Full Text Available Let Xn be an affine variety of dimension n and Yn be a quasi-projective variety of the same dimension. We prove that for a quasi-finite polynomial mapping ƒ : Xn → Yn, every non-empty component of the set Yn\\ ƒ (Xn is closed and it has dimension greater or equal to n μ(ƒ, where μ(ƒ is a geometric degree of ƒ. Moreover, we prove that generally, if ƒ : Xn → Yn is any polynomial mapping, then either every non-empty component of the set is of dimension ≥ n μ(ƒ or ƒ contracts a subvariety of dimension ≥ n μ(ƒ + 1.

  15. BSDEs with polynomial growth generators

    Directory of Open Access Journals (Sweden)

    Philippe Briand

    2000-01-01

    Full Text Available In this paper, we give existence and uniqueness results for backward stochastic differential equations when the generator has a polynomial growth in the state variable. We deal with the case of a fixed terminal time, as well as the case of random terminal time. The need for this type of extension of the classical existence and uniqueness results comes from the desire to provide a probabilistic representation of the solutions of semilinear partial differential equations in the spirit of a nonlinear Feynman-Kac formula. Indeed, in many applications of interest, the nonlinearity is polynomial, e.g, the Allen-Cahn equation or the standard nonlinear heat and Schrödinger equations.

  16. Poly-Cauchy and Peters mixed-type polynomials

    OpenAIRE

    Kim, Dae San; Kim, Taekyun

    2013-01-01

    The Peters polynomials are a generalization of Boole polynomials. In this paper, we consider Peters and poly-Cauchy mixed type polynomials and investigate the properties of those polynomials which are derived from umbral calculus. Finally, we give various identities of those polynomials associated with special polynomials.

  17. Evolutionary Design of Polynomial Controller

    OpenAIRE

    R. Matousek; S. Lang; P. Minar; P. Pivonka

    2011-01-01

    In the control theory one attempts to find a controller that provides the best possible performance with respect to some given measures of performance. There are many sorts of controllers e.g. a typical PID controller, LQR controller, Fuzzy controller etc. In the paper will be introduced polynomial controller with novel tuning method which is based on the special pole placement encoding scheme and optimization by Genetic Algorithms (GA). The examples will show the perform...

  18. Space complexity in polynomial calculus

    Czech Academy of Sciences Publication Activity Database

    Filmus, Y.; Lauria, M.; Nordström, J.; Ron-Zewi, N.; Thapen, Neil

    2015-01-01

    Roč. 44, č. 4 (2015), s. 1119-1153 ISSN 0097-5397 R&D Projects: GA AV ČR IAA100190902; GA ČR GBP202/12/G061 Institutional support: RVO:67985840 Keywords : proof complexity * polynomial calculus * lower bounds Subject RIV: BA - General Mathematics Impact factor: 0.841, year: 2015 http://epubs.siam.org/doi/10.1137/120895950

  19. Codimensions of generalized polynomial identities

    International Nuclear Information System (INIS)

    Gordienko, Aleksei S

    2010-01-01

    It is proved that for every finite-dimensional associative algebra A over a field of characteristic zero there are numbers C element of Q + and t element of Z + such that gc n (A)∼Cn t d n as n→∞, where d=PI exp(A) element of Z + . Thus, Amitsur's and Regev's conjectures hold for the codimensions gc n (A) of the generalized polynomial identities. Bibliography: 6 titles.

  20. Bell violation in the sky

    Energy Technology Data Exchange (ETDEWEB)

    Choudhury, Sayantan [Tata Institute of Fundamental Research, Department of Theoretical Physics, Mumbai (India); TIFR, DTP, Mumbai (India); Panda, Sudhakar [Institute of Physics, Bhubaneswar, Odisha (India); Homi Bhabha National Institute, Mumbai (India); Singh, Rajeev [Savitribai Phule Pune University, Department of Physics, Pune (India)

    2017-02-15

    In this work, we have studied the possibility of setting up Bell's inequality violating experiment in the context of cosmology, based on the basic principles of quantum mechanics. First we start with the physical motivation of implementing the Bell inequality violation in the context of cosmology. Then to set up the cosmological Bell violating test experiment we introduce a model independent theoretical framework using which we have studied the creation of new massive particles by implementing the WKB approximation method for the scalar fluctuations in the presence of additional time-dependent mass contribution in the cosmological perturbation theory. Here for completeness we compute the total number density and the energy density of the newly created particles in terms of the Bogoliubov coefficients using the WKB approximation method. Next using the background scalar fluctuation in the presence of a new time-dependent mass contribution, we explicitly compute the expression for the one point and two point correlation functions. Furthermore, using the results for a one point function we introduce a new theoretical cosmological parameter which can be expressed in terms of the other known inflationary observables and can also be treated as a future theoretical probe to break the degeneracy amongst various models of inflation. Additionally, we also fix the scale of inflation in a model-independent way without any prior knowledge of primordial gravitational waves. Also using the input from a newly introduced cosmological parameter, we finally give a theoretical estimate for the tensor-to-scalar ratio in a model-independent way. Next, we also comment on the technicalities of measurements from isospin breaking interactions and the future prospects of newly introduced massive particles in a cosmological Bell violating test experiment. Further, we cite a precise example of this setup applicable in the context of string theory motivated axion monodromy model. Then we

  1. Local realism and the Bell inequality

    International Nuclear Information System (INIS)

    Brody, T.A.

    1989-01-01

    The Bell inequality has generally been interpreted to involve two requirements for its validity: a locality condition and the existence of hidden variables. The Bell inequality could only be satisfied within the framework of a non-local theory. The Pauli exclusion principle bears an evident non-local character, the origins and implications of which cannot be said to be fully understood; nevertheless, it has not given rise to the conceptual confusions that followed in the wake of the Bell inequality. (Author)

  2. 33 CFR 117.424 - Belle River.

    Science.gov (United States)

    2010-07-01

    ... 33 Navigation and Navigable Waters 1 2010-07-01 2010-07-01 false Belle River. 117.424 Section 117... OPERATION REGULATIONS Specific Requirements Louisiana § 117.424 Belle River. The draw of the S70 bridge, mile 23.8 (Landside Route) near Belle River, shall open on signal; except that, from 10 p.m. to 6 a.m...

  3. The Bell's theorem: GHZ states

    International Nuclear Information System (INIS)

    Cereceda Berdiel, J.L.

    1997-01-01

    In this paper we review a striking new version of Bell's theorem discovered some time ago for three spin-1/2 particles and derive explicitly the states leading to a direct (all or nothing) contradiction between the quantum-mechanical and locally realistic prediction. Due to the fact that perfect correlations exist between the spin measurements the resulting contradiction arises without using inequalities. The treatment that follows only presupposes some acquaintance with elementary quantum mechanics. In doing so, we attempt to outline some recent developments in the field of foundations at a level suitable for the early or intermediate part of introductory courses in quantum mechanics. (Author) 15 refs

  4. On Chebyshev Polynomials of Matrices

    Czech Academy of Sciences Publication Activity Database

    Faber, V.; Liesen, J.; Tichý, Petr

    2010-01-01

    Roč. 31, č. 4 (2010), s. 2205-2221 ISSN 0895-4798 R&D Projects: GA AV ČR IAA100300802 Grant - others:GA AV ČR(CZ) M100300901 Institutional research plan: CEZ:AV0Z10300504 Source of funding: I - inštitucionálna podpora na rozvoj VO Keywords : matrix approximation problems * Chebyshev polynomials * complex approximation theory * Krylov subspace methods * Arnoldi's method Subject RIV: BA - General Mathematics Impact factor: 1.725, year: 2010

  5. Clinical practice guideline: Bell's Palsy executive summary.

    Science.gov (United States)

    Baugh, Reginald F; Basura, Gregory J; Ishii, Lisa E; Schwartz, Seth R; Drumheller, Caitlin Murray; Burkholder, Rebecca; Deckard, Nathan A; Dawson, Cindy; Driscoll, Colin; Gillespie, M Boyd; Gurgel, Richard K; Halperin, John; Khalid, Ayesha N; Kumar, Kaparaboyna Ashok; Micco, Alan; Munsell, Debra; Rosenbaum, Steven; Vaughan, William

    2013-11-01

    The American Academy of Otolaryngology-Head and Neck Surgery Foundation (AAO-HNSF) has published a supplement to this issue featuring the new Clinical Practice Guideline: Bell's Palsy. To assist in implementing the guideline recommendations, this article summarizes the rationale, purpose, and key action statements. The 11 recommendations developed encourage accurate and efficient diagnosis and treatment and, when applicable, facilitate patient follow-up to address the management of long-term sequelae or evaluation of new or worsening symptoms not indicative of Bell's palsy. There are myriad treatment options for Bell's palsy; some controversy exists regarding the effectiveness of several of these options, and there are consequent variations in care. In addition, there are numerous diagnostic tests available that are used in the evaluation of patients with Bell's palsy. Many of these tests are of questionable benefit in Bell's palsy. Furthermore, while patients with Bell's palsy enter the health care system with facial paresis/paralysis as a primary complaint, not all patients with facial paresis/paralysis have Bell's palsy. It is a concern that patients with alternative underlying etiologies may be misdiagnosed or have an unnecessary delay in diagnosis. All of these quality concerns provide an important opportunity for improvement in the diagnosis and management of patients with Bell's palsy.

  6. Classifying 50 years of Bell inequalities

    International Nuclear Information System (INIS)

    Rosset, Denis; Gisin, Nicolas; Bancal, Jean-Daniel

    2014-01-01

    Since John S Bell demonstrated the interest of studying linear combinations of probabilities in relation with the EPR paradox in 1964, Bell inequalities have lead to numerous developments. Unfortunately, the description of Bell inequalities is subject to several degeneracies, which make any exchange of information about them unnecessarily hard. Here, we analyze these degeneracies and propose a decomposition for Bell-like inequalities based on a set of reference expressions which is not affected by them. These reference expressions set a common ground for comparing Bell inequalities. We provide algorithms based on finite group theory to compute this decomposition. Implementing these algorithms allows us to set up a compendium of reference Bell-like inequalities, available online at www.faacets.com. This website constitutes a platform where registered Bell-like inequalities can be explored, new inequalities can be compared to previously-known ones and relevant information on Bell inequalities can be added in a collaborative manner. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell’s theorem’. (paper)

  7. Belle-II Experiment Network Requirements

    Energy Technology Data Exchange (ETDEWEB)

    Asner, David [Pacific Northwest National Laboratory (PNNL), Richland, WA (United States); Bell, Greg [ESnet; Carlson, Tim [Pacific Northwest National Laboratory (PNNL), Richland, WA (United States); Cowley, David [Pacific Northwest National Laboratory (PNNL), Richland, WA (United States); Dart, Eli [ESnet; Erwin, Brock [Pacific Northwest National Laboratory (PNNL), Richland, WA (United States); Godang, Romulus [Univ. of South Alabama, Mobile, AL (United States); Hara, Takanori [High Energy Accelerator Research Organization (KEK), Tsukuba (Japan); Johnson, Jerry [Pacific Northwest National Laboratory (PNNL), Richland, WA (United States); Johnson, Ron [Univ. of Washington, Seattle, WA (United States); Johnston, Bill [ESnet; Dam, Kerstin Kleese-van [Pacific Northwest National Laboratory (PNNL), Richland, WA (United States); Kaneko, Toshiaki [High Energy Accelerator Research Organization (KEK), Tsukuba (Japan); Kubota, Yoshihiro [NII; Kuhr, Thomas [Karlsruhe Inst. of Technology (KIT) (Germany); McCoy, John [Pacific Northwest National Laboratory (PNNL), Richland, WA (United States); Miyake, Hideki [High Energy Accelerator Research Organization (KEK), Tsukuba (Japan); Monga, Inder [ESnet; Nakamura, Motonori [NII; Piilonen, Leo [Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States); Pordes, Ruth [Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States); Ray, Douglas [Pacific Northwest National Laboratory (PNNL), Richland, WA (United States); Russell, Richard [Pacific Northwest National Laboratory (PNNL), Richland, WA (United States); Schram, Malachi [Pacific Northwest National Laboratory (PNNL), Richland, WA (United States); Schroeder, Jim [Pacific Northwest National Laboratory (PNNL), Richland, WA (United States); Sevior, Martin [Univ. of Melbourne (Australia); Singh, Surya [Pacific Northwest National Laboratory (PNNL), Richland, WA (United States); Suzuki, Soh [High Energy Accelerator Research Organization (KEK), Tsukuba (Japan); Sasaki, Takashi [High Energy Accelerator Research Organization (KEK), Tsukuba (Japan); Williams, Jim [Indiana Univ., Bloomington, IN (United States)

    2013-05-28

    The Belle experiment, part of a broad-based search for new physics, is a collaboration of ~400 physicists from 55 institutions across four continents. The Belle detector is located at the KEKB accelerator in Tsukuba, Japan. The Belle detector was operated at the asymmetric electron-positron collider KEKB from 1999-2010. The detector accumulated more than 1 ab-1 of integrated luminosity, corresponding to more than 2 PB of data near 10 GeV center-of-mass energy. Recently, KEK has initiated a $400 million accelerator upgrade to be called SuperKEKB, designed to produce instantaneous and integrated luminosity two orders of magnitude greater than KEKB. The new international collaboration at SuperKEKB is called Belle II. The first data from Belle II/SuperKEKB is expected in 2015. In October 2012, senior members of the Belle-II collaboration gathered at PNNL to discuss the computing and neworking requirements of the Belle-II experiment with ESnet staff and other computing and networking experts. The day-and-a-half-long workshop characterized the instruments and facilities used in the experiment, the process of science for Belle-II, and the computing and networking equipment and configuration requirements to realize the full scientific potential of the collaboration's work.

  8. Bell's theorem and the nature of reality

    International Nuclear Information System (INIS)

    Bertlmann, R.A.

    1988-01-01

    We rediscuss the Einstein-Podolsky-Rosen paradox in Bohm's spin version and oppose to it Bohr's controversial point of view. Then we explain Bell's theorem, Bell inequalities and its consequences. We describe the experiment of Aspect, Dalibard and Roger in detail. Finally we draw attention to the nonlocal structure of the underlying theory. 61 refs., 8 tabs. (Author)

  9. Minimax discrimination of quasi-Bell states

    International Nuclear Information System (INIS)

    Kato, Kentaro

    2014-01-01

    An optimal quantum measurement is considered for the so-called quasi-Bell states under the quantum minimax criterion. It is shown that the minimax-optimal POVM for the quasi-Bell states is given by its square-root measurement and is applicable to the teleportation of a superposition of two coherent states

  10. Classifying 50 years of Bell inequalities

    Science.gov (United States)

    Rosset, Denis; Bancal, Jean-Daniel; Gisin, Nicolas

    2014-10-01

    Since John S Bell demonstrated the interest of studying linear combinations of probabilities in relation with the EPR paradox in 1964, Bell inequalities have lead to numerous developments. Unfortunately, the description of Bell inequalities is subject to several degeneracies, which make any exchange of information about them unnecessarily hard. Here, we analyze these degeneracies and propose a decomposition for Bell-like inequalities based on a set of reference expressions which is not affected by them. These reference expressions set a common ground for comparing Bell inequalities. We provide algorithms based on finite group theory to compute this decomposition. Implementing these algorithms allows us to set up a compendium of reference Bell-like inequalities, available online at www.faacets.com. This website constitutes a platform where registered Bell-like inequalities can be explored, new inequalities can be compared to previously-known ones and relevant information on Bell inequalities can be added in a collaborative manner. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell’s theorem’.

  11. Minimax discrimination of quasi-Bell states

    Energy Technology Data Exchange (ETDEWEB)

    Kato, Kentaro [Quantum ICT Research Institute, Tamagawa University, 6-1-1 Tamagawa-gakuen, Machida, Tokyo 194-8610 (Japan)

    2014-12-04

    An optimal quantum measurement is considered for the so-called quasi-Bell states under the quantum minimax criterion. It is shown that the minimax-optimal POVM for the quasi-Bell states is given by its square-root measurement and is applicable to the teleportation of a superposition of two coherent states.

  12. Occupancy Models, Bell-Type Polynomials and Numbers and Applications to Probability.

    Science.gov (United States)

    1983-06-01

    expressed in terms of such ratios. These recurrences bypass the computational difficulties which come from the fact that the numbers themselves (but not the...biisic properties and rec’u-ruees for r(Tr;nj,r) hrld fac) itat( tlair computation . Remark 2.1 . In tesqlin order t.o avoid unnv e!1.bry cui-l i...Sobel, . , Uppuluri, Y.R.R. and Frankowski, K. (71977). Dirichlet distributions- type 1. In S.lected tables in Mathenatical Statistics, Vol.4

  13. A new Arnoldi approach for polynomial eigenproblems

    Energy Technology Data Exchange (ETDEWEB)

    Raeven, F.A.

    1996-12-31

    In this paper we introduce a new generalization of the method of Arnoldi for matrix polynomials. The new approach is compared with the approach of rewriting the polynomial problem into a linear eigenproblem and applying the standard method of Arnoldi to the linearised problem. The algorithm that can be applied directly to the polynomial eigenproblem turns out to be more efficient, both in storage and in computation.

  14. On classical orthogonal polynomials and differential operators

    International Nuclear Information System (INIS)

    Miranian, L

    2005-01-01

    It is well known that the four families of classical orthogonal polynomials (Jacobi, Bessel, Hermite and Laguerre) each satisfy an equation FP n (x) = λ n P n (x), n ≥ 0, for an appropriate second-order differential operator F. In this paper it is shown that any linear differential operator U which has the Jacobi, Bessel, Hermite or Laguerre polynomials as eigenfunctions has to be a polynomial with constant coefficients in the classical second-order operator F

  15. Quantum bounds on Bell inequalities

    Science.gov (United States)

    Pál, Károly F.; Vértesi, Tamás

    2009-02-01

    We have determined the maximum quantum violation of 241 tight bipartite Bell inequalities with up to five two-outcome measurement settings per party by constructing the appropriate measurement operators in up to six-dimensional complex and eight-dimensional real-component Hilbert spaces using numerical optimization. Out of these inequalities 129 have been introduced here. In 43 cases higher-dimensional component spaces gave larger violation than qubits, and in three occasions the maximum was achieved with six-dimensional spaces. We have also calculated upper bounds on these Bell inequalities using a method proposed recently. For all but 20 inequalities the best solution found matched the upper bound. Surprisingly, the simplest inequality of the set examined, with only three measurement settings per party, was not among them, despite the high dimensionality of the Hilbert space considered. We also computed detection threshold efficiencies for the maximally entangled qubit pair. These could be lowered in several instances if degenerate measurements were also allowed.

  16. Model selection for univariable fractional polynomials.

    Science.gov (United States)

    Royston, Patrick

    2017-07-01

    Since Royston and Altman's 1994 publication ( Journal of the Royal Statistical Society, Series C 43: 429-467), fractional polynomials have steadily gained popularity as a tool for flexible parametric modeling of regression relationships. In this article, I present fp_select, a postestimation tool for fp that allows the user to select a parsimonious fractional polynomial model according to a closed test procedure called the fractional polynomial selection procedure or function selection procedure. I also give a brief introduction to fractional polynomial models and provide examples of using fp and fp_select to select such models with real data.

  17. Acceleration of computation of φ-polynomials.

    Science.gov (United States)

    Kaya, Ilhan; Rolland, Jannick

    2013-11-18

    The benefits of making an effective use of impressive computational power offered by multi-core platforms are investigated for the computation of φ-polynomials used in the description of freeform surfaces. Specifically, we devise parallel algorithms based upon the recurrence relations of both Zernike polynomials and gradient orthogonal Q-polynomials and implement these parallel algorithms on Graphical Processing Units (GPUs) respectively. The results show that more than an order of magnitude improvement is achieved in computational time over a sequential implementation if these recurrence-based parallel algorithms are adopted in the computation of the φ-polynomials.

  18. The q-Laguerre matrix polynomials.

    Science.gov (United States)

    Salem, Ahmed

    2016-01-01

    The Laguerre polynomials have been extended to Laguerre matrix polynomials by means of studying certain second-order matrix differential equation. In this paper, certain second-order matrix q-difference equation is investigated and solved. Its solution gives a generalized of the q-Laguerre polynomials in matrix variable. Four generating functions of this matrix polynomials are investigated. Two slightly different explicit forms are introduced. Three-term recurrence relation, Rodrigues-type formula and the q-orthogonality property are given.

  19. Control to Facet for Polynomial Systems

    DEFF Research Database (Denmark)

    Sloth, Christoffer; Wisniewski, Rafael

    2014-01-01

    This paper presents a solution to the control to facet problem for arbitrary polynomial vector fields defined on simplices. The novelty of the work is to use Bernstein coefficients of polynomials for determining certificates of positivity. Specifically, the constraints that are set up...... for the controller design are solved by searching for polynomials in Bernstein form. This allows the controller design problem to be formulated as a linear programming problem. Examples are provided that demonstrate the efficiency of the method for designing controls for polynomial systems....

  20. Orthonormal polynomials in wavefront analysis: analytical solution.

    Science.gov (United States)

    Mahajan, Virendra N; Dai, Guang-ming

    2007-09-01

    Zernike circle polynomials are in widespread use for wavefront analysis because of their orthogonality over a circular pupil and their representation of balanced classical aberrations. In recent papers, we derived closed-form polynomials that are orthonormal over a hexagonal pupil, such as the hexagonal segments of a large mirror. We extend our work to elliptical, rectangular, and square pupils. Using the circle polynomials as the basis functions for their orthogonalization over such pupils, we derive closed-form polynomials that are orthonormal over them. These polynomials are unique in that they are not only orthogonal across such pupils, but also represent balanced classical aberrations, just as the Zernike circle polynomials are unique in these respects for circular pupils. The polynomials are given in terms of the circle polynomials as well as in polar and Cartesian coordinates. Relationships between the orthonormal coefficients and the corresponding Zernike coefficients for a given pupil are also obtained. The orthonormal polynomials for a one-dimensional slit pupil are obtained as a limiting case of a rectangular pupil.

  1. On the Fermionic -adic Integral Representation of Bernstein Polynomials Associated with Euler Numbers and Polynomials

    Directory of Open Access Journals (Sweden)

    Ryoo CS

    2010-01-01

    Full Text Available The purpose of this paper is to give some properties of several Bernstein type polynomials to represent the fermionic -adic integral on . From these properties, we derive some interesting identities on the Euler numbers and polynomials.

  2. Recognition algorithms for binary signed-graphic matroids

    OpenAIRE

    Pitsoulis, Leonidas; Papalamprou, Konstantinos

    2010-01-01

    In this paper we provide two recognition algorithms for the class of signed-graphic matroids along with necessary and sufficient conditions for a matroid to be signed-graphic. Specifically, we provide a polynomial-time algorithm which determines whether a given binary matroid is signed-graphic and an algorithm which determines whether a general matroid given by an independece oracle is binary signed-graphic.

  3. Orthogonal polynomials from Hermitian matrices. II

    Science.gov (United States)

    Odake, Satoru; Sasaki, Ryu

    2018-01-01

    This is the second part of the project "unified theory of classical orthogonal polynomials of a discrete variable derived from the eigenvalue problems of Hermitian matrices." In a previous paper, orthogonal polynomials having Jackson integral measures were not included, since such measures cannot be obtained from single infinite dimensional Hermitian matrices. Here we show that Jackson integral measures for the polynomials of the big q-Jacobi family are the consequence of the recovery of self-adjointness of the unbounded Jacobi matrices governing the difference equations of these polynomials. The recovery of self-adjointness is achieved in an extended ℓ2 Hilbert space on which a direct sum of two unbounded Jacobi matrices acts as a Hamiltonian or a difference Schrödinger operator for an infinite dimensional eigenvalue problem. The polynomial appearing in the upper/lower end of the Jackson integral constitutes the eigenvector of each of the two-unbounded Jacobi matrix of the direct sum. We also point out that the orthogonal vectors involving the q-Meixner (q-Charlier) polynomials do not form a complete basis of the ℓ2 Hilbert space, based on the fact that the dual q-Meixner polynomials introduced in a previous paper fail to satisfy the orthogonality relation. The complete set of eigenvectors involving the q-Meixner polynomials is obtained by constructing the duals of the dual q-Meixner polynomials which require the two-component Hamiltonian formulation. An alternative solution method based on the closure relation, the Heisenberg operator solution, is applied to the polynomials of the big q-Jacobi family and their duals and q-Meixner (q-Charlier) polynomials.

  4. Polynomial solutions of nonlinear integral equations

    Energy Technology Data Exchange (ETDEWEB)

    Dominici, Diego [Department of Mathematics, State University of New York at New Paltz, 1 Hawk Dr. Suite 9, New Paltz, NY 12561-2443 (United States)], E-mail: dominicd@newpaltz.edu

    2009-05-22

    We analyze the polynomial solutions of a nonlinear integral equation, generalizing the work of Bender and Ben-Naim (2007 J. Phys. A: Math. Theor. 40 F9, 2008 J. Nonlinear Math. Phys. 15 (Suppl. 3) 73). We show that, in some cases, an orthogonal solution exists and we give its general form in terms of kernel polynomials.

  5. Laguerre polynomials by a harmonic oscillator

    Science.gov (United States)

    Baykal, Melek; Baykal, Ahmet

    2014-09-01

    The study of an isotropic harmonic oscillator, using the factorization method given in Ohanian's textbook on quantum mechanics, is refined and some collateral extensions of the method related to the ladder operators and the associated Laguerre polynomials are presented. In particular, some analytical properties of the associated Laguerre polynomials are derived using the ladder operators.

  6. Laguerre polynomials by a harmonic oscillator

    International Nuclear Information System (INIS)

    Baykal, Melek; Baykal, Ahmet

    2014-01-01

    The study of an isotropic harmonic oscillator, using the factorization method given in Ohanian's textbook on quantum mechanics, is refined and some collateral extensions of the method related to the ladder operators and the associated Laguerre polynomials are presented. In particular, some analytical properties of the associated Laguerre polynomials are derived using the ladder operators. (paper)

  7. Integral inequalities for self-reciprocal polynomials

    Indian Academy of Sciences (India)

    that is, the coefficients satisfy ak = an−k for k = 0, 1,...,n. We denote the class of self-reciprocal polynomials of order n by Pn. The properties of self-reciprocal polynomials have been studied by several mathemati- cians. We refer to [1–5] and the references given therein. Here, we are concerned with the following interesting ...

  8. Sibling curves of quadratic polynomials | Wiggins | Quaestiones ...

    African Journals Online (AJOL)

    Sibling curves were demonstrated in [1, 2] as a novel way to visualize the zeroes of real valued functions. In [3] it was shown that a polynomial of degree n has n sibling curves. This paper focuses on the algebraic and geometric properites of the sibling curves of real and complex quadratic polynomials. Key words: Quadratic ...

  9. Polynomial solutions of nonlinear integral equations

    International Nuclear Information System (INIS)

    Dominici, Diego

    2009-01-01

    We analyze the polynomial solutions of a nonlinear integral equation, generalizing the work of Bender and Ben-Naim (2007 J. Phys. A: Math. Theor. 40 F9, 2008 J. Nonlinear Math. Phys. 15 (Suppl. 3) 73). We show that, in some cases, an orthogonal solution exists and we give its general form in terms of kernel polynomials

  10. Exceptional polynomials and SUSY quantum mechanics

    Indian Academy of Sciences (India)

    We show that for the quantum mechanical problem which admit classical Laguerre/Jacobi polynomials as solutions for the Schrödinger equations (SE), will also admit exceptional Laguerre/Jacobi polynomials as solutions having the same eigenvalues but with the ground state missing after a modification of the potential.

  11. Topological string partition functions as polynomials

    International Nuclear Information System (INIS)

    Yamaguchi, Satoshi; Yau Shingtung

    2004-01-01

    We investigate the structure of the higher genus topological string amplitudes on the quintic hypersurface. It is shown that the partition functions of the higher genus than one can be expressed as polynomials of five generators. We also compute the explicit polynomial forms of the partition functions for genus 2, 3, and 4. Moreover, some coefficients are written down for all genus. (author)

  12. The Bessel polynomials and their differential operators

    International Nuclear Information System (INIS)

    Onyango Otieno, V.P.

    1987-10-01

    Differential operators associated with the ordinary and the generalized Bessel polynomials are defined. In each case the commutator bracket is constructed and shows that the differential operators associated with the Bessel polynomials and their generalized form are not commutative. Some applications of these operators to linear differential equations are also discussed. (author). 4 refs

  13. Large degree asymptotics of generalized Bessel polynomials

    NARCIS (Netherlands)

    J.L. López; N.M. Temme (Nico)

    2011-01-01

    textabstractAsymptotic expansions are given for large values of $n$ of the generalized Bessel polynomials $Y_n^\\mu(z)$. The analysis is based on integrals that follow from the generating functions of the polynomials. A new simple expansion is given that is valid outside a compact neighborhood of the

  14. Block orthogonal polynomials: I. Definitions and properties

    International Nuclear Information System (INIS)

    Normand, Jean-Marie

    2007-01-01

    Constrained orthogonal polynomials have been recently introduced in the study of the Hohenberg-Kohn functional to provide basis functions satisfying particle number conservation for an expansion of the particle density. More generally, we define block orthogonal (BO) polynomials which are orthogonal, with respect to a first Euclidean inner product, to a given i-dimensional subspace E i of polynomials associated with the constraints. In addition, they are mutually orthogonal with respect to a second Euclidean inner product. We recast the determination of these polynomials into a general problem of finding particular orthogonal bases in an Euclidean vector space endowed with distinct inner products. An explicit two step Gram-Schmidt orthogonalization (G-SO) process to determine these bases is given. By definition, the standard block orthogonal (SBO) polynomials are associated with a choice of E i equal to the subspace of polynomials of degree less than i. We investigate their properties, emphasizing similarities to and differences from the standard orthogonal polynomials. Applications to classical orthogonal polynomials will be given in forthcoming papers

  15. The Medusa Algorithm for Polynomial Matings

    DEFF Research Database (Denmark)

    Boyd, Suzanne Hruska; Henriksen, Christian

    2012-01-01

    The Medusa algorithm takes as input two postcritically finite quadratic polynomials and outputs the quadratic rational map which is the mating of the two polynomials (if it exists). Specifically, the output is a sequence of approximations for the parameters of the rational map, as well as an image...

  16. On the zeros of a polynomial

    Indian Academy of Sciences (India)

    For a polynomial of degree , we have obtained an upper bound involving coefficients of the polynomial, for moduli of its zeros of smallest moduli, and then a refinement of the well-known Eneström–Kakeya theorem (under certain conditions).

  17. Polynomial approximation approach to transient heat conduction ...

    African Journals Online (AJOL)

    This work reports polynomial approximation approach to transient heat conduction in a long slab, long cylinder and sphere with linear internal heat generation. It has been shown that the polynomial approximation method is able to calculate average temperature as a function of time for higher value of Biot numbers.

  18. Orthonormal polynomials in wavefront analysis: error analysis.

    Science.gov (United States)

    Dai, Guang-Ming; Mahajan, Virendra N

    2008-07-01

    Zernike circle polynomials are in widespread use for wavefront analysis because of their orthogonality over a circular pupil and their representation of balanced classical aberrations. However, they are not appropriate for noncircular pupils, such as annular, hexagonal, elliptical, rectangular, and square pupils, due to their lack of orthogonality over such pupils. We emphasize the use of orthonormal polynomials for such pupils, but we show how to obtain the Zernike coefficients correctly. We illustrate that the wavefront fitting with a set of orthonormal polynomials is identical to the fitting with a corresponding set of Zernike polynomials. This is a consequence of the fact that each orthonormal polynomial is a linear combination of the Zernike polynomials. However, since the Zernike polynomials do not represent balanced aberrations for a noncircular pupil, the Zernike coefficients lack the physical significance that the orthonormal coefficients provide. We also analyze the error that arises if Zernike polynomials are used for noncircular pupils by treating them as circular pupils and illustrate it with numerical examples.

  19. Connections between the matching and chromatic polynomials

    Directory of Open Access Journals (Sweden)

    E. J. Farrell

    1992-01-01

    Full Text Available The main results established are (i a connection between the matching and chromatic polynomials and (ii a formula for the matching polynomial of a general complement of a subgraph of a graph. Some deductions on matching and chromatic equivalence and uniqueness are made.

  20. Generating polynomials using function composition | Aichinger ...

    African Journals Online (AJOL)

    We characterize the integral polynomials that can be obtained from x and x2 (or from 1, x, and x3) by using +;-, and function composition. Keywords: Near-rings, integer polynomials, subnear-ring membership problem. Quaestiones Mathematicae 36(2013), 39-46 ...

  1. Exceptional polynomials and SUSY quantum mechanics

    Indian Academy of Sciences (India)

    Abstract. We show that for the quantum mechanical problem which admit classical Laguerre/. Jacobi polynomials as solutions for the Schrödinger equations (SE), will also admit exceptional. Laguerre/Jacobi polynomials as solutions having the same eigenvalues but with the ground state missing after a modification of the ...

  2. Application of polynomial preconditioners to conservation laws

    NARCIS (Netherlands)

    Geurts, Bernardus J.; van Buuren, R.; Lu, H.

    2000-01-01

    Polynomial preconditioners which are suitable in implicit time-stepping methods for conservation laws are reviewed and analyzed. The preconditioners considered are either based on a truncation of a Neumann series or on Chebyshev polynomials for the inverse of the system-matrix. The latter class of

  3. Whiteheadian approach to Bell's correlations

    International Nuclear Information System (INIS)

    Malin, S.

    1988-01-01

    Certain properties of the Bell-type correlations and, in particular, the impossibility of using them to transmit signals faster than light, are investigated from the point of view of the conceptual structure of quantum mechanics and of Whitehead's process philosophy. The collapses of quantum states are shown to correspond to perspectives of different frames of reference on a Whiteheadian process of self creation of actual entities. The analysis suggests a fundamental limitation on the capacity to describe the propagation of influences among the results of measurements at space-like separation. It is further shown that, if Whitehead's framework is modified in a specific way, it accounts very well for the apparent existence of superluminal influences, and for the impossibility of using them for superluminal communication

  4. Polynomials formalism of quantum numbers

    International Nuclear Information System (INIS)

    Kazakov, K.V.

    2005-01-01

    Theoretical aspects of the recently suggested perturbation formalism based on the method of quantum number polynomials are considered in the context of the general anharmonicity problem. Using a biatomic molecule by way of example, it is demonstrated how the theory can be extrapolated to the case of vibrational-rotational interactions. As a result, an exact expression for the first coefficient of the Herman-Wallis factor is derived. In addition, the basic notions of the formalism are phenomenologically generalized and expanded to the problem of spin interaction. The concept of magneto-optical anharmonicity is introduced. As a consequence, an exact analogy is drawn with the well-known electro-optical theory of molecules, and a nonlinear dependence of the magnetic dipole moment of the system on the spin and wave variables is established [ru

  5. Fuzzy Morphological Polynomial Image Representation

    Directory of Open Access Journals (Sweden)

    Chin-Pan Huang

    2010-01-01

    Full Text Available A novel signal representation using fuzzy mathematical morphology is developed. We take advantage of the optimum fuzzy fitting and the efficient implementation of morphological operators to extract geometric information from signals. The new representation provides results analogous to those given by the polynomial transform. Geometrical decomposition of a signal is achieved by windowing and applying sequentially fuzzy morphological opening with structuring functions. The resulting representation is made to resemble an orthogonal expansion by constraining the results of opening to equate adapted structuring functions. Properties of the geometric decomposition are considered and used to calculate the adaptation parameters. Our procedure provides an efficient and flexible representation which can be efficiently implemented in parallel. The application of the representation is illustrated in data compression and fractal dimension estimation temporal signals and images.

  6. Differential expansion for link polynomials

    Science.gov (United States)

    Bai, C.; Jiang, J.; Liang, J.; Mironov, A.; Morozov, A.; Morozov, An.; Sleptsov, A.

    2018-03-01

    The differential expansion is one of the key structures reflecting group theory properties of colored knot polynomials, which also becomes an important tool for evaluation of non-trivial Racah matrices. This makes highly desirable its extension from knots to links, which, however, requires knowledge of the 6j-symbols, at least, for the simplest triples of non-coincident representations. Based on the recent achievements in this direction, we conjecture a shape of the differential expansion for symmetrically-colored links and provide a set of examples. Within this study, we use a special framing that is an unusual extension of the topological framing from knots to links. In the particular cases of Whitehead and Borromean rings links, the differential expansions are different from the previously discovered.

  7. On the number of polynomial solutions of Bernoulli and Abel polynomial differential equations

    Science.gov (United States)

    Cima, A.; Gasull, A.; Mañosas, F.

    2017-12-01

    In this paper we determine the maximum number of polynomial solutions of Bernoulli differential equations and of some integrable polynomial Abel differential equations. As far as we know, the tools used to prove our results have not been utilized before for studying this type of questions. We show that the addressed problems can be reduced to know the number of polynomial solutions of a related polynomial equation of arbitrary degree. Then we approach to these equations either applying several tools developed to study extended Fermat problems for polynomial equations, or reducing the question to the computation of the genus of some associated planar algebraic curves.

  8. Pontine haemorrhage disguised as Bell's palsy.

    Science.gov (United States)

    Karadan, Ummer; Manappallil, Robin George; Jayakrishnan, Chellenton; Supreeth, Ramesh Naga

    2018-02-05

    Isolated facial nerve palsy is a common presentation of Bell's palsy, but rarely seen in pontine lesions. The patient being reported is a middle-aged man who developed isolated facial nerve palsy and was initially treated as Bell's palsy. However, on MRI of the brain, he was found to have pontine haemorrhage. He was managed conservatively and improved. Pontine haemorrhage as an aetiology for isolated facial nerve palsy is a rare scenario, which often goes misdiagnosed and treated as Bell's palsy. © BMJ Publishing Group Ltd (unless otherwise stated in the text of the article) 2018. All rights reserved. No commercial use is permitted unless otherwise expressly granted.

  9. Arabic text classification using Polynomial Networks

    Directory of Open Access Journals (Sweden)

    Mayy M. Al-Tahrawi

    2015-10-01

    Full Text Available In this paper, an Arabic statistical learning-based text classification system has been developed using Polynomial Neural Networks. Polynomial Networks have been recently applied to English text classification, but they were never used for Arabic text classification. In this research, we investigate the performance of Polynomial Networks in classifying Arabic texts. Experiments are conducted on a widely used Arabic dataset in text classification: Al-Jazeera News dataset. We chose this dataset to enable direct comparisons of the performance of Polynomial Networks classifier versus other well-known classifiers on this dataset in the literature of Arabic text classification. Results of experiments show that Polynomial Networks classifier is a competitive algorithm to the state-of-the-art ones in the field of Arabic text classification.

  10. Tutte polynomial in functional magnetic resonance imaging

    Science.gov (United States)

    García-Castillón, Marlly V.

    2015-09-01

    Methods of graph theory are applied to the processing of functional magnetic resonance images. Specifically the Tutte polynomial is used to analyze such kind of images. Functional Magnetic Resonance Imaging provide us connectivity networks in the brain which are represented by graphs and the Tutte polynomial will be applied. The problem of computing the Tutte polynomial for a given graph is #P-hard even for planar graphs. For a practical application the maple packages "GraphTheory" and "SpecialGraphs" will be used. We will consider certain diagram which is depicting functional connectivity, specifically between frontal and posterior areas, in autism during an inferential text comprehension task. The Tutte polynomial for the resulting neural networks will be computed and some numerical invariants for such network will be obtained. Our results show that the Tutte polynomial is a powerful tool to analyze and characterize the networks obtained from functional magnetic resonance imaging.

  11. Matrix product formula for Macdonald polynomials

    International Nuclear Information System (INIS)

    Cantini, Luigi; Gier, Jan de; Michael Wheeler

    2015-01-01

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

  12. Improved polynomial remainder sequences for Ore polynomials☆

    Science.gov (United States)

    Jaroschek, Maximilian

    2013-01-01

    Polynomial remainder sequences contain the intermediate results of the Euclidean algorithm when applied to (non-)commutative polynomials. The running time of the algorithm is dependent on the size of the coefficients of the remainders. Different ways have been studied to make these as small as possible. The subresultant sequence of two polynomials is a polynomial remainder sequence in which the size of the coefficients is optimal in the generic case, but when taking the input from applications, the coefficients are often larger than necessary. We generalize two improvements of the subresultant sequence to Ore polynomials and derive a new bound for the minimal coefficient size. Our approach also yields a new proof for the results in the commutative case, providing a new point of view on the origin of the extraneous factors of the coefficients. PMID:26523087

  13. Resolving capacity of the circular Zernike polynomials.

    Science.gov (United States)

    Svechnikov, M V; Chkhalo, N I; Toropov, M N; Salashchenko, N N

    2015-06-01

    Circular Zernike polynomials are often used for approximation and analysis of optical surfaces. In this paper, we analyse their lateral resolving capacity, illustrating the effects of a lack of approximation by a finite set of polynomials and answering the following questions: What is the minimum number of polynomials that is necessary to describe a local deformation of a certain size? What is the relationship between the number of approximating polynomials and the spatial spectrum of the approximation? What is the connection between the mean-square error of approximation and the number of polynomials? The main results of this work are the formulas for calculating the error of fitting the relief and the connection between the width of the spatial spectrum and the order of approximation.

  14. Block orthogonal polynomials: II. Hermite and Laguerre standard block orthogonal polynomials

    International Nuclear Information System (INIS)

    Normand, Jean-Marie

    2007-01-01

    The standard block orthogonal (SBO) polynomials P i;n (x), 0 ≤ i ≤ n are real polynomials of degree n which are orthogonal with respect to a first Euclidean scalar product to polynomials of degree less than i. In addition, they are mutually orthogonal with respect to a second Euclidean scalar product. Applying the general results obtained in a previous paper, we determine and investigate these polynomials when the first scalar product corresponds to Hermite (resp. Laguerre) polynomials. These new sets of polynomials, which we call Hermite (resp. Laguerre) SBO polynomials, provide a basis of functional spaces well suited for some applications requiring to take into account special linear constraints which can be recast into an Euclidean orthogonality relation

  15. Recurrence relations on the generelizad poly-Genocchi polynomials

    Science.gov (United States)

    Kurt, Burak; Bilgic, Secil

    2017-07-01

    In this work, we introduce and investigate poly-Genocchi numbers and polynomials. We give recurrence relations for the poly-Genocchi numbers. Also, we prove a relation between multi-poly-Genocchi polynomial and multi-poly-Bernoulli polynomial.

  16. Random Constructions in Bell Inequalities: A Survey

    Science.gov (United States)

    Palazuelos, Carlos

    2018-01-01

    Initially motivated by their relevance in foundations of quantum mechanics and more recently by their applications in different contexts of quantum information science, violations of Bell inequalities have been extensively studied during the last years. In particular, an important effort has been made in order to quantify such Bell violations. Probabilistic techniques have been heavily used in this context with two different purposes. First, to quantify how common the phenomenon of Bell violations is; and second, to find large Bell violations in order to better understand the possibilities and limitations of this phenomenon. However, the strong mathematical content of these results has discouraged some of the potentially interested readers. The aim of the present work is to review some of the recent results in this direction by focusing on the main ideas and removing most of the technical details, to make the previous study more accessible to a wide audience.

  17. A general practice approach to Bell's palsy.

    Science.gov (United States)

    Phan, Nga T; Panizza, Benedict; Wallwork, Benjamin

    2016-11-01

    Bell's palsy is characterised by an acute onset of unilateral, lower motor neuron weakness of the facial nerve in the absence of an identifiable cause. Establishing the correct diagnosis is imperative and choosing the correct treatment options can optimise the likelihood of recovery. This article summarises our understanding of Bell's palsy and the evidence-based management options available for adult patients. The basic assessment should include a thorough history and physical examination as the diagnosis of Bell's palsy is based on exclusion. For confirmed cases of Bell's palsy, corticosteroids are the mainstay of treatment and should be initiated within 72 hours of symptom onset. Antiviral therapy in combination with corticosteroid therapy may confer a small benefit and may be offered on the basis of shared decision making. Currently, no recommendations can be made for acupuncture, physical therapy, electrotherapy or surgical decompression because well-designed studies are lacking and available data are of low quality.

  18. Herpes Simplex Virus-1 and Bell's Palsy

    Directory of Open Access Journals (Sweden)

    J Gordon Millichap

    2008-05-01

    Full Text Available The association between herpes simplex virus-1 (HSV-1 infection and Bell palsy was determined in 47 children studied at Children's Hospital at Montefiore, Bronx, NY. Swabs of saliva and conjunctiva were taken for PCR testing.

  19. Telecom Modeling with ChatterBell.

    Energy Technology Data Exchange (ETDEWEB)

    Jrad, Ahmad M.; Kelic, Andjelka

    2017-12-01

    This document provides a description and user manual for the ChatterBell voice telecom modeling and simulation capability. The intended audience consists of network planners and practitioners who wish to use the tool to model a particular voice network and analyze its behavior under varying assumptions and possible failure conditions. ChatterBell is built on top of the N-SMART voice simulation and visualization suite that was developed through collaboration between Sandia National Laboratories and Bell Laboratories of Lucent Technologies. The new and improved modeling and simulation tool has been modified and modernized to incorporate the latest development in the telecom world including the widespread use of VoIP technology. In addition, ChatterBell provides new commands and modeling capabilities that were not available in the N-SMART application.

  20. Bell inequalities resistant to detector inefficiency

    International Nuclear Information System (INIS)

    Massar, Serge; Pironio, Stefano; Roland, Jeremie; Gisin, Bernard

    2002-01-01

    We derive both numerically and analytically Bell inequalities and quantum measurements that present enhanced resistance to detector inefficiency. In particular, we describe several Bell inequalities which appear to be optimal with respect to inefficient detectors for small dimensionality d=2,3,4 and two or more measurement settings at each side. We also generalize the family of Bell inequalities described by Collins et al. [Phys. Rev. Lett. 88, 040404 (2002)] to take into account the inefficiency of detectors. In addition, we consider the possibility for pairs of entangled particles to be produced with probability less than 1. We show that when the pair production probability is small, one should in general use different Bell inequalities than when the pair production probability is high

  1. Exact multi-restricted Schur polynomial correlators

    International Nuclear Information System (INIS)

    Bhattacharyya, Rajsekhar; Koch, Robert de Mello; Stephanou, Michael

    2008-01-01

    We derive a product rule satisfied by restricted Schur polynomials. We focus mostly on the case that the restricted Schur polynomial is built using two matrices, although our analysis easily extends to more than two matrices. This product rule allows us to compute exact multi-point correlation functions of restricted Schur polynomials, in the free field theory limit. As an example of the use of our formulas, we compute two point functions of certain single trace operators built using two matrices and three point functions of certain restricted Schur polynomials, exactly, in the free field theory limit. Our results suggest that gravitons become strongly coupled at sufficiently high energy, while the restricted Schur polynomials for totally antisymmetric representations remain weakly interacting at these energies. This is in perfect accord with the half-BPS (single matrix) results of hep-th/0512312. Finally, by studying the interaction of two restricted Schur polynomials we suggest a physical interpretation for the labels of the restricted Schur polynomial: the composite operator χ R,(r n ,r m ) (Z,X) is constructed from the half BPS 'partons' χ r n (Z) and χ r m (X).

  2. BELLE progress report. 1995 April - 1996 March

    International Nuclear Information System (INIS)

    1996-03-01

    The scientific goals of the BELLE experiment continue to be of great interest. The large number of papers during the past year that identify measurements that can be done with BELLE reflects the considerable interest in the theoretical community in these physics issues. This is also demonstrated by the approval during the past year of two major B physics projects: the BaBar experiment at SLAC and the HERAB experiment at DESY. Both projects have schedules that put them into direct competition with BELLE for the important goal of testing the KM predictions for CP violations in B meson decays. Other projects addressing this physics are planned for the Tevatron collider and have been proposed both for the LHC and RHIC. The BELLE collaboration remains committed to its goal of being the first group to provide conclusive evidence either confirming or refuting the KM model. The year 1995 was an exciting time for the BELLE experiment. All of the major technology choices were finalized and a final detector configuration has been established. Continued R and D has resulted in improved performance expectations for a number of detector subsystems. The procurement of materials for major subsystems is underway and construction of long leadtime items has started. A construction schedule has been established and an integration strategy is being developed. This report describes the status of BELLE with an emphasis on progress since the last LCPAC meeting in January 1995. (J.P.N.). 90 refs

  3. BELLE progress report. 1995 April - 1996 March

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    1996-03-01

    The scientific goals of the BELLE experiment continue to be of great interest. The large number of papers during the past year that identify measurements that can be done with BELLE reflects the considerable interest in the theoretical community in these physics issues. This is also demonstrated by the approval during the past year of two major B physics projects: the BaBar experiment at SLAC and the HERAB experiment at DESY. Both projects have schedules that put them into direct competition with BELLE for the important goal of testing the KM predictions for CP violations in B meson decays. Other projects addressing this physics are planned for the Tevatron collider and have been proposed both for the LHC and RHIC. The BELLE collaboration remains committed to its goal of being the first group to provide conclusive evidence either confirming or refuting the KM model. The year 1995 was an exciting time for the BELLE experiment. All of the major technology choices were finalized and a final detector configuration has been established. Continued R and D has resulted in improved performance expectations for a number of detector subsystems. The procurement of materials for major subsystems is underway and construction of long leadtime items has started. A construction schedule has been established and an integration strategy is being developed. This report describes the status of BELLE with an emphasis on progress since the last LCPAC meeting in January 1995. (J.P.N.). 90 refs.

  4. BellHouse - a collaboration in ceramics

    Science.gov (United States)

    Johnstone, Rupert; Liggins, Felicity; Buontempo, Carlo; Honnor, Seth; Spencer-Mills, Jocelyn; Newton, Paula; Williams, Emily

    2017-04-01

    In the Spring of 2016, the UK-based arts organisation Kaleider and the EU-funded FP7 climate services project EUPORIAS made an International Commission Call inviting artists to submit ideas for playable artworks to be debuted at the EUPORIAS General Assembly at the Met Office in October 2016. We received over 60 applications worldwide and were overwhelmed with the quality of ideas. We commissioned Roop Johnstone from RAMP Ceramics to create his exquisite playable artwork - BellHouse. BellHouse is a playful, interactive sound sculpture that translated the non-verbal communication of the delegates presenting at the EUPORIAS General Assembly into the chimes of 35 bells in an opened sided house. A motion capture system devised by the Met Office Informatics Lab activated striking mechanisms associated with each ceramic bell generating a continuous chiming whilst each speaker at the 250 delegate conference presented their research. BellHouse also invited Met Office scientists to interact with it through their work. Some of our favourite data translated into sound included Mt. Etna's volcanic plumes, the European drought of 1976, the solar wind, 250 years of English and Welsh temperature and precipitation anomalies and reanalysis data based on citizen science. Here we present an exploration of the why and how of BellHouse, outlining some of our reflections on its effectiveness alongside its legacy.

  5. Neck curve polynomials in neck rupture model

    International Nuclear Information System (INIS)

    Kurniadi, Rizal; Perkasa, Yudha S.; Waris, Abdul

    2012-01-01

    The Neck Rupture Model is a model that explains the scission process which has smallest radius in liquid drop at certain position. Old fashion of rupture position is determined randomly so that has been called as Random Neck Rupture Model (RNRM). The neck curve polynomials have been employed in the Neck Rupture Model for calculation the fission yield of neutron induced fission reaction of 280 X 90 with changing of order of polynomials as well as temperature. The neck curve polynomials approximation shows the important effects in shaping of fission yield curve.

  6. More on rotations as spin matrix polynomials

    International Nuclear Information System (INIS)

    Curtright, Thomas L.

    2015-01-01

    Any nonsingular function of spin j matrices always reduces to a matrix polynomial of order 2j. The challenge is to find a convenient form for the coefficients of the matrix polynomial. The theory of biorthogonal systems is a useful framework to meet this challenge. Central factorial numbers play a key role in the theoretical development. Explicit polynomial coefficients for rotations expressed either as exponentials or as rational Cayley transforms are considered here. Structural features of the results are discussed and compared, and large j limits of the coefficients are examined

  7. Small oscillations, Sturm sequences, and orthogonal polynomials

    International Nuclear Information System (INIS)

    Baake, M.

    1986-07-01

    The relation between small oscillations of one-dimensional mechanical systems and the theory of orthogonal polynomials is investigated. It is shown how the polynomials provide a natural tool to determine the eigenfrequencies and eigencoordinates completely, where the existence of a certain two-termed recurrence formula is essential. Physical and mathematical statements are formulated in terms of the recursion coefficients which can directly be obtained from the corresponding secular equation. Several known as well as new results on Sturm sequences and orthogonal polynomials are presented with respect to the treatment of small oscillations. (orig.)

  8. Bell inequalities for graph states

    International Nuclear Information System (INIS)

    Toth, G.; Hyllus, P.; Briegel, H.J.; Guehne, O.

    2005-01-01

    Full text: In the last years graph states have attracted an increasing interest in the field of quantum information theory. Graph states form a family of multi-qubit states which comprises many popular states such as the GHZ states and the cluster states. They also play an important role in applications. For instance, measurement based quantum computation uses graph states as resources. From a theoretical point of view, it is remarkable that graph states allow for a simple description in terms of stabilizing operators. In this contribution, we investigate the non-local properties of graph states. We derive a family of Bell inequalities which require three measurement settings for each party and are maximally violated by graph states. In turn, any graph state violates at least one of the inequalities. We show that for certain types of graph states the violation of these inequalities increases exponentially with the number of qubits. We also discuss connections to other entanglement properties such as the positively of the partial transpose or the geometric measure of entanglement. (author)

  9. Functional Bell inequalities can serve as a stronger entanglement witness than conventional Bell inequalities

    International Nuclear Information System (INIS)

    Sen, Aditi; Sen, Ujjwal; Zukowski, Marek

    2002-01-01

    We consider a Bell inequality for a continuous range of settings of the apparatus at each site. This 'functional' Bell inequality gives a better range of violation for generalized Greenberger, Horne, and Zeilinger states. Also a family of N-qubit bound entangled states violate this inequality for N>5

  10. Bell's palsy before Bell : Evert Jan Thomassen a Thuessink and idiopathic peripheral facial paralysis

    NARCIS (Netherlands)

    van de Graaf, R. C.; IJpma, F. F. A.; Nicolai, J-P A.; Werker, P. M. N.

    2009-01-01

    Bell's palsy is the eponym for idiopathic peripheral facial paralysis. It is named after Sir Charles Bell (1774-1842), who, in the first half of the nineteenth century, discovered the function of the facial nerve and attracted the attention of the medical world to facial paralysis. Our knowledge of

  11. 78 FR 56148 - Airworthiness Directives; Bell Helicopter Textron Canada Limited (Bell) Helicopters

    Science.gov (United States)

    2013-09-12

    ... Textron Canada Limited (Bell) Helicopters AGENCY: Federal Aviation Administration (FAA), DOT. ACTION... service information identified in this AD, contact Bell Helicopter Textron Canada Limited, 12,800 Rue de l... holidays. The AD docket contains this AD, the foreign authority's AD, the economic evaluation, any comments...

  12. 78 FR 34279 - Airworthiness Directives; Bell Helicopter Textron Canada Limited (Bell) Helicopters

    Science.gov (United States)

    2013-06-07

    ... Directives; Bell Helicopter Textron Canada Limited (Bell) Helicopters AGENCY: Federal Aviation Administration... to the ``Mail'' address between 9 a.m. and 5 p.m., Monday through Friday, except Federal holidays... holidays. The AD docket contains this proposed AD, the economic evaluation, any comments received, and...

  13. 78 FR 66252 - Airworthiness Directives; Bell Helicopter Textron Canada Limited (Bell) Helicopters

    Science.gov (United States)

    2013-11-05

    ... Textron Canada Limited (Bell) Helicopters AGENCY: Federal Aviation Administration (FAA), DOT. ACTION... identified in this AD, contact Bell Helicopter Textron Canada Limited, 12,800 Rue de l'Avenir, Mirabel... Operations Office between 9 a.m. and 5 p.m., Monday through Friday, except Federal holidays. The AD docket...

  14. 78 FR 23114 - Airworthiness Directives; Bell Helicopter Textron Canada (Bell) Helicopters

    Science.gov (United States)

    2013-04-18

    ... Textron Canada (Bell) Helicopters AGENCY: Federal Aviation Administration (FAA), DOT. ACTION: Final rule... information identified in this AD, contact Bell Helicopter Textron Canada Limited, 12,800 Rue de l'Avenir... Operations Office between 9 a.m. and 5 p.m., Monday through Friday, except Federal holidays. The AD docket...

  15. 78 FR 65200 - Airworthiness Directives; Bell Helicopter Textron Canada Limited (Bell) Helicopters

    Science.gov (United States)

    2013-10-31

    ... Textron Canada Limited (Bell) Helicopters AGENCY: Federal Aviation Administration (FAA), DOT. ACTION..., contact Bell Helicopter Textron Canada Limited, 12,800 Rue de l'Avenir, Mirabel, Quebec J7J1R4; telephone... Office between 9 a.m. and 5 p.m., Monday through Friday, except Federal holidays. The AD docket contains...

  16. 76 FR 66609 - Airworthiness Directives; Bell Helicopter Textron Canada (Bell) Model 407 and 427 Helicopters

    Science.gov (United States)

    2011-10-27

    ... Textron Canada (Bell) Model 407 and 427 Helicopters AGENCY: Federal Aviation Administration, DOT. ACTION...., Washington, DC 20590, between 9 a.m. and 5 p.m., Monday through Friday, except Federal holidays. You may get the service information identified in this AD from Bell Helicopter Textron Canada Limited, 12,800 Rue...

  17. Beyond Bell's theorem: realism and locality without Bell-type correlations.

    Science.gov (United States)

    De Zela, F

    2017-11-06

    The long-lasting view of entanglement as the characteristic trait of quantum mechanics has been recently challenged by experimental demonstrations of non-quantum entanglement. This motivates a review of the meaning of Bell violations, which have been widely taken to prove the impossibility of a realistic interpretation of quantum mechanics and as a manifestation of its non-local character. This work provides new theoretical evidence for the need of reviewing the meaning of Bell violations, especially when they occur outside the quantum framework. We present a local-realistic model that reproduces quantum predictions concerning Bell tests. We claim that local-realism is fully compatible with correlations that are not of the Bell type and therefore lie outside the scope of Bell's theorem. Most experimental Bell tests involve either spin vectors spanning the Bloch sphere or Stokes vectors spanning the Poincaré sphere. A suitable statistical tool that allows assessing correlations between vectors is given by inner-product-type correlations. Using them, it is possible to reproduce quantum predictions for all Bell states, thereby explaining experimental results of Bell tests within a local-realistic framework.

  18. Orthonormal curvature polynomials over a unit circle: basis set derived from curvatures of Zernike polynomials.

    Science.gov (United States)

    Zhao, Chunyu; Burge, James H

    2013-12-16

    Zernike polynomials are an orthonormal set of scalar functions over a circular domain, and are commonly used to represent wavefront phase or surface irregularity. In optical testing, slope or curvature of a surface or wavefront is sometimes measured instead, from which the surface or wavefront map is obtained. Previously we derived an orthonormal set of vector polynomials that fit to slope measurement data and yield the surface or wavefront map represented by Zernike polynomials. Here we define a 3-element curvature vector used to represent the second derivatives of a continuous surface, and derive a set of orthonormal curvature basis functions that are written in terms of Zernike polynomials. We call the new curvature functions the C polynomials. Closed form relations for the complete basis set are provided, and we show how to determine Zernike surface coefficients from the curvature data as represented by the C polynomials.

  19. Adapted polynomial chaos expansion for failure detection

    International Nuclear Information System (INIS)

    Paffrath, M.; Wever, U.

    2007-01-01

    In this paper, we consider two methods of computation of failure probabilities by adapted polynomial chaos expansions. The performance of the two methods is demonstrated by a predator-prey model and a chemical reaction problem

  20. Transversals of Complex Polynomial Vector Fields

    DEFF Research Database (Denmark)

    Dias, Kealey

    Vector fields in the complex plane are defined by assigning the vector determined by the value P(z) to each point z in the complex plane, where P is a polynomial of one complex variable. We consider special families of so-called rotated vector fields that are determined by a polynomial multiplied...... by rotational constants. Transversals are a certain class of curves for such a family of vector fields that represent the bifurcation states for this family of vector fields. More specifically, transversals are curves that coincide with a homoclinic separatrix for some rotation of the vector field. Given...... a concrete polynomial, it seems to take quite a bit of work to prove that it is generic, i.e. structurally stable. This has been done for a special class of degree d polynomial vector fields having simple equilibrium points at the d roots of unity, d odd. In proving that such vector fields are generic...

  1. Twisted Polynomials and Forgery Attacks on GCM

    DEFF Research Database (Denmark)

    Abdelraheem, Mohamed Ahmed A. M. A.; Beelen, Peter; Bogdanov, Andrey

    2015-01-01

    nonce misuse resistance, such as POET. The algebraic structure of polynomial hashing has given rise to security concerns: At CRYPTO 2008, Handschuh and Preneel describe key recovery attacks, and at FSE 2013, Procter and Cid provide a comprehensive framework for forgery attacks. Both approaches rely...... heavily on the ability to construct forgery polynomials having disjoint sets of roots, with many roots (“weak keys”) each. Constructing such polynomials beyond naïve approaches is crucial for these attacks, but still an open problem. In this paper, we comprehensively address this issue. We propose to use...... in an improved key recovery algorithm. As cryptanalytic applications of our twisted polynomials, we develop the first universal forgery attacks on GCM in the weak-key model that do not require nonce reuse. Moreover, we present universal weak-key forgeries for the nonce-misuse resistant AE scheme POET, which...

  2. Some results for extended Jacobi polynomials

    International Nuclear Information System (INIS)

    Khan, I.A.

    1991-06-01

    In this paper, some contiguous function relations and generating functions have been established for extended Jacobi polynomials. The results obtained here, are of very general nature. (author). 5 refs

  3. Schur Stability Regions for Complex Quadratic Polynomials

    Science.gov (United States)

    Cheng, Sui Sun; Huang, Shao Yuan

    2010-01-01

    Given a quadratic polynomial with complex coefficients, necessary and sufficient conditions are found in terms of the coefficients such that all its roots have absolute values less than 1. (Contains 3 figures.)

  4. Some generating functions of Laguerre polynomials

    Directory of Open Access Journals (Sweden)

    Bidyut Kumar Guha Thakurta

    1987-01-01

    Full Text Available In this note a class of interesting generating relation, which is stated in the form of theorem, involving Laguerre polynomials is derived. Some applications of the theorem are also given here.

  5. On linear equations with general polynomial solutions

    Science.gov (United States)

    Laradji, A.

    2018-04-01

    We provide necessary and sufficient conditions for which an nth-order linear differential equation has a general polynomial solution. We also give necessary conditions that can directly be ascertained from the coefficient functions of the equation.

  6. Handbook on semidefinite, conic and polynomial optimization

    CERN Document Server

    Anjos, Miguel F

    2012-01-01

    This book offers the reader a snapshot of the state-of-the-art in the growing and mutually enriching areas of semidefinite optimization, conic optimization and polynomial optimization. It covers theory, algorithms, software and applications.

  7. Solving Bivariate Polynomial Systems on a GPU

    International Nuclear Information System (INIS)

    Moreno Maza, Marc; Pan Wei

    2012-01-01

    We present a CUDA implementation of dense multivariate polynomial arithmetic based on Fast Fourier Transforms over finite fields. Our core routine computes on the device (GPU) the subresultant chain of two polynomials with respect to a given variable. This subresultant chain is encoded by values on a FFT grid and is manipulated from the host (CPU) in higher-level procedures. We have realized a bivariate polynomial system solver supported by our GPU code. Our experimental results (including detailed profiling information and benchmarks against a serial polynomial system solver implementing the same algorithm) demonstrate that our strategy is well suited for GPU implementation and provides large speedup factors with respect to pure CPU code.

  8. Polynomial analysis of ambulatory blood pressure measurements

    NARCIS (Netherlands)

    Zwinderman, A. H.; Cleophas, T. A.; Cleophas, T. J.; van der Wall, E. E.

    2001-01-01

    In normotensive subjects blood pressures follow a circadian rhythm. A circadian rhythm in hypertensive patients is less well established, and may be clinically important, particularly with rigorous treatments of daytime blood pressures. Polynomial analysis of ambulatory blood pressure monitoring

  9. Rotation of 2D orthogonal polynomials

    Czech Academy of Sciences Publication Activity Database

    Yang, B.; Flusser, Jan; Kautský, J.

    2018-01-01

    Roč. 102, č. 1 (2018), s. 44-49 ISSN 0167-8655 R&D Projects: GA ČR GA15-16928S Institutional support: RVO:67985556 Keywords : Rotation invariants * Orthogonal polynomials * Recurrent relation * Hermite-like polynomials * Hermite moments Subject RIV: JD - Computer Applications, Robotics Impact factor: 1.995, year: 2016 http://library.utia.cas.cz/separaty/2017/ZOI/flusser-0483250.pdf

  10. A Polynomial Estimate of Railway Line Delay

    DEFF Research Database (Denmark)

    Cerreto, Fabrizio; Harrod, Steven; Nielsen, Otto Anker

    2017-01-01

    by numerical analysis with simulation. This paper proposes an analytical estimate of aggregate delay with a polynomial form. The function returns the aggregate delay of a railway line resulting from an initial, primary, delay. Analysis of the function demonstrates that there should be a balance between the two...... remedial measures, supplement and buffer. Numerical analysis of a Copenhagen Sbane line shows that the polynomial function is valid even when theoretical assumptions are violated....

  11. About the solvability of matrix polynomial equations

    OpenAIRE

    Netzer, Tim; Thom, Andreas

    2016-01-01

    We study self-adjoint matrix polynomial equations in a single variable and prove existence of self-adjoint solutions under some assumptions on the leading form. Our main result is that any self-adjoint matrix polynomial equation of odd degree with non-degenerate leading form can be solved in self-adjoint matrices. We also study equations of even degree and equations in many variables.

  12. Integral inequalities for self-reciprocal polynomials

    Indian Academy of Sciences (India)

    Integral inequalities for self-reciprocal polynomials. HORST ALZER. Morsbacher Str. 10, D-51545 Waldbröl, Germany. E-mail: H.Alzer@gmx.de. MS received 14 November 2007. Abstract. Let n ≥ 1 be an integer and let Pn be the class of polynomials P of degree at most n satisfying znP(1/z) = P (z) for all z ∈ C. Moreover, ...

  13. Two polynomial representations of experimental design

    OpenAIRE

    Notari, Roberto; Riccomagno, Eva; Rogantin, Maria-Piera

    2007-01-01

    In the context of algebraic statistics an experimental design is described by a set of polynomials called the design ideal. This, in turn, is generated by finite sets of polynomials. Two types of generating sets are mostly used in the literature: Groebner bases and indicator functions. We briefly describe them both, how they are used in the analysis and planning of a design and how to switch between them. Examples include fractions of full factorial designs and designs for mixture experiments.

  14. Local fibred right adjoints are polynomial

    DEFF Research Database (Denmark)

    Kock, Anders; Kock, Joachim

    2013-01-01

    For any locally cartesian closed category E, we prove that a local fibred right adjoint between slices of E is given by a polynomial. The slices in question are taken in a well known fibred sense......For any locally cartesian closed category E, we prove that a local fibred right adjoint between slices of E is given by a polynomial. The slices in question are taken in a well known fibred sense...

  15. Fast polynomial multiplication on a GPU

    International Nuclear Information System (INIS)

    Maza, Marc Moreno; Pan Wei

    2010-01-01

    We present CUDA implementations of Fast Fourier Transforms over finite fields. This allows us to develop GPU support for dense univariate polynomial multiplication leading to speedup factors in the range 21 - 37 with respect to the best serial C-code available to us, for our largest input data sets. Since dense univariate polynomial multiplication is a core routine in symbolic computation, this is promising result for the integration of GPU support into computer algebra systems.

  16. Many-body orthogonal polynomial systems

    International Nuclear Information System (INIS)

    Witte, N.S.

    1997-03-01

    The fundamental methods employed in the moment problem, involving orthogonal polynomial systems, the Lanczos algorithm, continued fraction analysis and Pade approximants has been combined with a cumulant approach and applied to the extensive many-body problem in physics. This has yielded many new exact results for many-body systems in the thermodynamic limit - for the ground state energy, for excited state gaps, for arbitrary ground state avenges - and are of a nonperturbative nature. These results flow from a confluence property of the three-term recurrence coefficients arising and define a general class of many-body orthogonal polynomials. These theorems constitute an analytical solution to the Lanczos algorithm in that they are expressed in terms of the three-term recurrence coefficients α and β. These results can also be applied approximately for non-solvable models in the form of an expansion, in a descending series of the system size. The zeroth order order this expansion is just the manifestation of the central limit theorem in which a Gaussian measure and hermite polynomials arise. The first order represents the first non-trivial order, in which classical distribution functions like the binomial distributions arise and the associated class of orthogonal polynomials are Meixner polynomials. Amongst examples of systems which have infinite order in the expansion are q-orthogonal polynomials where q depends on the system size in a particular way. (author)

  17. Vector-Valued Jack Polynomials from Scratch

    Directory of Open Access Journals (Sweden)

    Jean-Gabriel Luque

    2011-03-01

    Full Text Available Vector-valued Jack polynomials associated to the symmetric group S_N are polynomials with multiplicities in an irreducible module of S_N and which are simultaneous eigenfunctions of the Cherednik-Dunkl operators with some additional properties concerning the leading monomial. These polynomials were introduced by Griffeth in the general setting of the complex reflections groups G(r,p,N and studied by one of the authors (C. Dunkl in the specialization r=p=1 (i.e. for the symmetric group. By adapting a construction due to Lascoux, we describe an algorithm allowing us to compute explicitly the Jack polynomials following a Yang-Baxter graph. We recover some properties already studied by C. Dunkl and restate them in terms of graphs together with additional new results. In particular, we investigate normalization, symmetrization and antisymmetrization, polynomials with minimal degree, restriction etc. We give also a shifted version of the construction and we discuss vanishing properties of the associated polynomials.

  18. Strong asymptotics for extremal polynomials associated with weights on ℝ

    CERN Document Server

    Lubinsky, Doron S

    1988-01-01

    0. The results are consequences of a strengthened form of the following assertion: Given 0 1. Auxiliary results include inequalities for weighted polynomials, and zeros of extremal polynomials. The monograph is fairly self-contained, with proofs involving elementary complex analysis, and the theory of orthogonal and extremal polynomials. It should be of interest to research workers in approximation theory and orthogonal polynomials.

  19. On the Connection Coefficients of the Chebyshev-Boubaker Polynomials

    Directory of Open Access Journals (Sweden)

    Paul Barry

    2013-01-01

    Full Text Available The Chebyshev-Boubaker polynomials are the orthogonal polynomials whose coefficient arrays are defined by ordinary Riordan arrays. Examples include the Chebyshev polynomials of the second kind and the Boubaker polynomials. We study the connection coefficients of this class of orthogonal polynomials, indicating how Riordan array techniques can lead to closed-form expressions for these connection coefficients as well as recurrence relations that define them.

  20. On the connection coefficients of the Chebyshev-Boubaker polynomials.

    Science.gov (United States)

    Barry, Paul

    2013-01-01

    The Chebyshev-Boubaker polynomials are the orthogonal polynomials whose coefficient arrays are defined by ordinary Riordan arrays. Examples include the Chebyshev polynomials of the second kind and the Boubaker polynomials. We study the connection coefficients of this class of orthogonal polynomials, indicating how Riordan array techniques can lead to closed-form expressions for these connection coefficients as well as recurrence relations that define them.

  1. Beta-integrals and finite orthogonal systems of Wilson polynomials

    International Nuclear Information System (INIS)

    Neretin, Yu A

    2002-01-01

    The integral is calculated and the system of orthogonal polynomials with weight equal to the corresponding integrand is constructed. This weight decreases polynomially, therefore only finitely many of its moments converge. As a result the system of orthogonal polynomials is finite. Systems of orthogonal polynomials related to 5 H 5 -Dougall's formula and the Askey integral is also constructed. All the three systems consist of Wilson polynomials outside the domain of positiveness of the usual weight

  2. Special polynomials associated with rational solutions of some hierarchies

    International Nuclear Information System (INIS)

    Kudryashov, Nikolai A.

    2009-01-01

    New special polynomials associated with rational solutions of the Painleve hierarchies are introduced. The Hirota relations for these special polynomials are found. Differential-difference hierarchies to find special polynomials are presented. These formulae allow us to search special polynomials associated with the hierarchies. It is shown that rational solutions of the Caudrey-Dodd-Gibbon, the Kaup-Kupershmidt and the modified hierarchy for these ones can be obtained using new special polynomials.

  3. New polynomial-based molecular descriptors with low degeneracy.

    Directory of Open Access Journals (Sweden)

    Matthias Dehmer

    Full Text Available In this paper, we introduce a novel graph polynomial called the 'information polynomial' of a graph. This graph polynomial can be derived by using a probability distribution of the vertex set. By using the zeros of the obtained polynomial, we additionally define some novel spectral descriptors. Compared with those based on computing the ordinary characteristic polynomial of a graph, we perform a numerical study using real chemical databases. We obtain that the novel descriptors do have a high discrimination power.

  4. ["Bell-striking" Saying of Acupuncture Therapy].

    Science.gov (United States)

    Zhao, Jing-Sheng

    2017-04-25

    As an analogy, a prototype of "bell-striking" is proposed in the present paper for exploring the basic properties, major elements, and potential mechanisms of acupuncture stimulation. On the strength of analysis on the physiological basis of acupuncture effect, several fundamental aspects of acupuncture are summarized as a) the body-surface stimulating characters, b) general and local effects, and c) triggering the auto-regulative function of the organism, which mimics the "bell-striking" response. Namely, when stroke, bell will chime, otherwise, chiming will not be heard. During analyzing special contents of acupuncture theory, its formative background should not be separated, and it is improper to take, modern medical theory of the human body as the guiding thinking way for researching the ancient Chinese medical literature.

  5. Best polynomial degree reduction on q-lattices with applications to q-orthogonal polynomials

    KAUST Repository

    Ait-Haddou, Rachid

    2015-06-07

    We show that a weighted least squares approximation of q-Bézier coefficients provides the best polynomial degree reduction in the q-L2-norm. We also provide a finite analogue of this result with respect to finite q-lattices and we present applications of these results to q-orthogonal polynomials. © 2015 Elsevier Inc. All rights reserved.

  6. A new class of generalized polynomials associated with Hermite and Bernoulli polynomials

    Directory of Open Access Journals (Sweden)

    M. A. Pathan

    2015-05-01

    Full Text Available In this paper, we introduce a new class of generalized  polynomials associated with  the modified Milne-Thomson's polynomials Φ_{n}^{(α}(x,ν of degree n and order α introduced by  Derre and Simsek.The concepts of Bernoulli numbers B_n, Bernoulli polynomials  B_n(x, generalized Bernoulli numbers B_n(a,b, generalized Bernoulli polynomials  B_n(x;a,b,c of Luo et al, Hermite-Bernoulli polynomials  {_HB}_n(x,y of Dattoli et al and {_HB}_n^{(α} (x,y of Pathan  are generalized to the one   {_HB}_n^{(α}(x,y,a,b,c which is called  the generalized  polynomial depending on three positive real parameters. Numerous properties of these polynomials and some relationships between B_n, B_n(x, B_n(a,b, B_n(x;a,b,c and {}_HB_n^{(α}(x,y;a,b,c  are established. Some implicit summation formulae and general symmetry identities are derived by using different analytical means and applying generating functions. These results extend some known summations and identities of generalized Bernoulli numbers and polynomials

  7. Certain non-linear differential polynomials sharing a non zero polynomial

    Directory of Open Access Journals (Sweden)

    Majumder Sujoy

    2015-10-01

    functions sharing a nonzero polynomial and obtain two results which improves and generalizes the results due to L. Liu [Uniqueness of meromorphic functions and differential polynomials, Comput. Math. Appl., 56 (2008, 3236-3245.] and P. Sahoo [Uniqueness and weighted value sharing of meromorphic functions, Applied. Math. E-Notes., 11 (2011, 23-32.].

  8. Extending a Property of Cubic Polynomials to Higher-Degree Polynomials

    Science.gov (United States)

    Miller, David A.; Moseley, James

    2012-01-01

    In this paper, the authors examine a property that holds for all cubic polynomials given two zeros. This property is discovered after reviewing a variety of ways to determine the equation of a cubic polynomial given specific conditions through algebra and calculus. At the end of the article, they will connect the property to a very famous method…

  9. Clinical Practice Guideline of Acupuncture for Bell's Palsy

    Directory of Open Access Journals (Sweden)

    Xi Wu

    2016-10-01

    Full Text Available Backgroud: Acupuncture is common used for Bell's palsy in clinic, however, recent systematic reviews all shows that there is no sufficient evidence to support the effectiveness of acupuncture for Bell's palsy because ofthe poor quality and heterogeneity. It's urgently necessary to develop a guideline of acupuncture for Bell's palsy based on principles of evidence-based medicine to optimize acupuncture treating, standardize outcomes evaluating and to improve the quality of acupuncture for patients with Bell's palsy under general circumstances.

  10. The probabilistic origin of Bell's inequality

    Science.gov (United States)

    Krenn, Guenther

    1994-01-01

    The concept of local realism entails certain restrictions concerning the possible occurrence of correlated events. Although these restrictions are inherent in classical physics they have never been noticed until Bell showed in 1964 that general correlations in quantum mechanics can not be interpreted in a classical way. We demonstrate how a local realistic way of thinking about measurement results necessarily leads to limitations with regard to the possible appearance of correlated events. These limitations, which are equivalent to Bell's inequality can be easily formulated as an immediate consequence of our discussion.

  11. Time-dependent generalized polynomial chaos

    International Nuclear Information System (INIS)

    Gerritsma, Marc; Steen, Jan-Bart van der; Vos, Peter; Karniadakis, George

    2010-01-01

    Generalized polynomial chaos (gPC) has non-uniform convergence and tends to break down for long-time integration. The reason is that the probability density distribution (PDF) of the solution evolves as a function of time. The set of orthogonal polynomials associated with the initial distribution will therefore not be optimal at later times, thus causing the reduced efficiency of the method for long-time integration. Adaptation of the set of orthogonal polynomials with respect to the changing PDF removes the error with respect to long-time integration. In this method new stochastic variables and orthogonal polynomials are constructed as time progresses. In the new stochastic variable the solution can be represented exactly by linear functions. This allows the method to use only low order polynomial approximations with high accuracy. The method is illustrated with a simple decay model for which an analytic solution is available and subsequently applied to the three mode Kraichnan-Orszag problem with favorable results.

  12. Chemical Reaction Networks for Computing Polynomials.

    Science.gov (United States)

    Salehi, Sayed Ahmad; Parhi, Keshab K; Riedel, Marc D

    2017-01-20

    Chemical reaction networks (CRNs) provide a fundamental model in the study of molecular systems. Widely used as formalism for the analysis of chemical and biochemical systems, CRNs have received renewed attention as a model for molecular computation. This paper demonstrates that, with a new encoding, CRNs can compute any set of polynomial functions subject only to the limitation that these functions must map the unit interval to itself. These polynomials can be expressed as linear combinations of Bernstein basis polynomials with positive coefficients less than or equal to 1. In the proposed encoding approach, each variable is represented using two molecular types: a type-0 and a type-1. The value is the ratio of the concentration of type-1 molecules to the sum of the concentrations of type-0 and type-1 molecules. The proposed encoding naturally exploits the expansion of a power-form polynomial into a Bernstein polynomial. Molecular encoders for converting any input in a standard representation to the fractional representation as well as decoders for converting the computed output from the fractional to a standard representation are presented. The method is illustrated first for generic CRNs; then chemical reactions designed for an example are mapped to DNA strand-displacement reactions.

  13. Multilevel weighted least squares polynomial approximation

    KAUST Repository

    Haji-Ali, Abdul-Lateef

    2017-06-30

    Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required to achieve quasi-optimal approximation in a given polynomial subspace scales, up to a logarithmic factor, linearly in the dimension of this space. However, in many applications, the computation of samples includes a numerical discretization error. Thus, obtaining polynomial approximations with a single level method can become prohibitively expensive, as it requires a sufficiently large number of samples, each computed with a sufficiently small discretization error. As a solution to this problem, we propose a multilevel method that utilizes samples computed with different accuracies and is able to match the accuracy of single-level approximations with reduced computational cost. We derive complexity bounds under certain assumptions about polynomial approximability and sample work. Furthermore, we propose an adaptive algorithm for situations where such assumptions cannot be verified a priori. Finally, we provide an efficient algorithm for the sampling from optimal distributions and an analysis of computationally favorable alternative distributions. Numerical experiments underscore the practical applicability of our method.

  14. 46 CFR 197.330 - PVHO-Closed bells.

    Science.gov (United States)

    2010-10-01

    ... 46 Shipping 7 2010-10-01 2010-10-01 false PVHO-Closed bells. 197.330 Section 197.330 Shipping... GENERAL PROVISIONS Commercial Diving Operations Equipment § 197.330 PVHO—Closed bells. (a) Except as provided in paragraph (b) of this section, each closed bell must meet the requirements of § 197.328 and— (1...

  15. Quantum chaotic dynamics and random polynomials

    International Nuclear Information System (INIS)

    Bogomolny, E.; Bohigas, O.; Leboeuf, P.

    1995-11-01

    The distribution of roots of polynomials of high degree with random coefficients is investigated which, among others, appear naturally in the context of 'quantum chaotic dynamics'. It is shown that under quite general conditions their roots tend to concentrate near the unit circle in the complex plane. In order to further increase this tendency, the particular case of self-inverse random polynomials is studied, and it is shown that for them a finite portion of all roots lies exactly on the unit circle. Correlation functions of these roots are also computed analytically, and compared to the correlations of eigenvalues of random matrices. The problem of ergodicity of chaotic wavefunctions is also considered. Special attention is devoted to the role of symmetries in the distribution of roots of random polynomials. (author)

  16. Markov and Bernstein type inequalities for polynomials

    Directory of Open Access Journals (Sweden)

    Mohapatra RN

    1999-01-01

    Full Text Available In an answer to a question raised by chemist Mendeleev, A. Markov proved that if is a real polynomial of degree , then The above inequality which is known as Markov's Inequality is best possible and becomes equality for the Chebyshev polynomial . Few years later, Serge Bernstein needed the analogue of this result for the unit disk in the complex plane instead of the interval and the following is known as Bernstein's Inequality. If is a polynomial of degree then This inequality is also best possible and is attained for , being a complex number. The above two inequalities have been the starting point of a considerable literature in Mathematics and in this article we discuss some of the research centered around these inequalities.

  17. Dominating Sets and Domination Polynomials of Paths

    Directory of Open Access Journals (Sweden)

    Saeid Alikhani

    2009-01-01

    Full Text Available Let G=(V,E be a simple graph. A set S⊆V is a dominating set of G, if every vertex in V\\S is adjacent to at least one vertex in S. Let 𝒫ni be the family of all dominating sets of a path Pn with cardinality i, and let d(Pn,j=|𝒫nj|. In this paper, we construct 𝒫ni, and obtain a recursive formula for d(Pn,i. Using this recursive formula, we consider the polynomial D(Pn,x=∑i=⌈n/3⌉nd(Pn,ixi, which we call domination polynomial of paths and obtain some properties of this polynomial.

  18. Minimal residual method stronger than polynomial preconditioning

    Energy Technology Data Exchange (ETDEWEB)

    Faber, V.; Joubert, W.; Knill, E. [Los Alamos National Lab., NM (United States)] [and others

    1994-12-31

    Two popular methods for solving symmetric and nonsymmetric systems of equations are the minimal residual method, implemented by algorithms such as GMRES, and polynomial preconditioning methods. In this study results are given on the convergence rates of these methods for various classes of matrices. It is shown that for some matrices, such as normal matrices, the convergence rates for GMRES and for the optimal polynomial preconditioning are the same, and for other matrices such as the upper triangular Toeplitz matrices, it is at least assured that if one method converges then the other must converge. On the other hand, it is shown that matrices exist for which restarted GMRES always converges but any polynomial preconditioning of corresponding degree makes no progress toward the solution for some initial error. The implications of these results for these and other iterative methods are discussed.

  19. 77 FR 36012 - PPL Bell Bend, LLC; Bell Bend Nuclear Power Plant Combined License Application; Notice of Intent...

    Science.gov (United States)

    2012-06-15

    ... by relocating the power block footprint and other plant components. For purposes of developing the... COMMISSION PPL Bell Bend, LLC; Bell Bend Nuclear Power Plant Combined License Application; Notice of Intent... its Bell Bend Nuclear Power Plant (BBNPP) site, located west of the existing Susquehanna Steam...

  20. 78 FR 4465 - PPL Bell Bend, LLC; Combined License Application for Bell Bend Nuclear Power Plant; Exemption

    Science.gov (United States)

    2013-01-22

    ... License Application for Bell Bend Nuclear Power Plant; Exemption 1.0 Background PPL Bell Bend, LLC... Regulations (10 CFR), Subpart C of Part 52, ``Licenses, Certifications, and Approvals for Nuclear Power Plants.'' This reactor is to be identified as Bell Bend Nuclear Power Plant (BBNPP), in Salem County...

  1. 76 FR 81992 - PPL Bell Bend, LLC; Combined License Application for Bell Bend Nuclear Power Plant; Exemption

    Science.gov (United States)

    2011-12-29

    ... License Application for Bell Bend Nuclear Power Plant; Exemption 1.0 Background PPL Bell Bend, LLC... for Nuclear Power Plants.'' This reactor is to be identified as Bell Bend Nuclear Power Plant (BBNPP... based upon the U.S. EPR reference COL (RCOL) application for UniStar's Calvert Cliffs Nuclear Power...

  2. Baby Bell Libraries?--An Update.

    Science.gov (United States)

    Kessler, Jack

    1993-01-01

    Discusses the emerging three-tiered structure (i.e., the "Baby Bells," network nodes, and information marketers) that will assume responsibility for implementing a new national information network and getting networked information to the public. The role of libraries related to networked information is also considered. (EA)

  3. Some inequalities for the Bell numbers

    Indian Academy of Sciences (India)

    Feng Qi

    2017-08-19

    Aug 19, 2017 ... 551. Some inequalities for the Bell numbers. FENG QI1,2,3,∗. 1Institute of Mathematics, Henan Polytechnic University, Jiaozuo City 454010, Henan. Province, China. 2College of Mathematics, Inner Mongolia University for Nationalities, Tongliao City. 028043, Inner Mongolia Autonomous Region, China.

  4. Bell Yung on Music of China.

    Science.gov (United States)

    Campbell, Patricia Shehan

    1995-01-01

    Presents an interview with Bell Yung, a scholar of Chinese music and ethnomusicology. Maintains that world music (music from many nations and cultures) should be taught as early as possible in the schools and at home. Includes two lesson plans for teaching about Chinese music. (CFR)

  5. Delayed facial nerve decompression for Bell's palsy.

    Science.gov (United States)

    Kim, Sang Hoon; Jung, Junyang; Lee, Jong Ha; Byun, Jae Yong; Park, Moon Suh; Yeo, Seung Geun

    2016-07-01

    Incomplete recovery of facial motor function continues to be long-term sequelae in some patients with Bell's palsy. The purpose of this study was to investigate the efficacy of transmastoid facial nerve decompression after steroid and antiviral treatment in patients with late stage Bell's palsy. Twelve patients underwent surgical decompression for Bell's palsy 21-70 days after onset, whereas 22 patients were followed up after steroid and antiviral therapy without decompression. Surgical criteria included greater than 90 % degeneration on electroneuronography and no voluntary electromyography potentials. This study was a retrospective study of electrodiagnostic data and medical chart review between 2006 and 2013. Recovery from facial palsy was assessed using the House-Brackmann grading system. Final recovery rate did not differ significantly in the two groups; however, all patients in the decompression group recovered to at least House-Brackmann grade III at final follow-up. Although postoperative hearing threshold was increased in both groups, there was no significant between group difference in hearing threshold. Transmastoid decompression of the facial nerve in patients with severe late stage Bell's palsy at risk for a poor facial nerve outcome reduced severe complications of facial palsy with minimal morbidity.

  6. Tinjauan Anatomi Klinik dan Manajemen Bell's Palsy

    Directory of Open Access Journals (Sweden)

    Nur Mujaddidah

    2017-07-01

    Full Text Available Bell's Palsy is a peripheral facial nerve weakness (facial nerve with acute onset on one side of the face. This condition causes the inability of the patient to move half of his face consciously (volunter on the affected side. The Bell's Palsy incidence is 20-30 cases out of 100.000 people and accounts for 60-70% of all cases of unilateral facial paralysis. The disease is self-limited, but causes great suffering for patients who are not treated properly. Controversy in the management is still debated, and the cause is still unknown. The underlying hypothesis is ischemic, vascular, viral, bacterial, hereditary, and immunologic. Therapy done so far is to improve facial nerve function and healing process. The management of the therapy used will be closely related to the structure of the anatomy and its functions and associated abnormalities. The modalities of Bell's Palsy therapy are with corticosteroids and antivirals, facial exercises, electrostimulation, physiotherapy and decompression operations. Approximately 80-90% of patients with Bell's palsy recover completely within 6 months, even in 50-60% of cases improved within 3 weeks. Approximately 10% experienced persistent facial muscle asymmetry, and 5% experienced severe sequelae, and 8% of cases were recurrent.

  7. Bell's palsy syndrome: mimics and chameleons.

    Science.gov (United States)

    Fuller, Geraint; Morgan, Cathy

    2016-12-01

    In this article we will explore the mimics and chameleons of Bell's palsy and in addition argue that we should use the term 'Bell's palsy syndrome' to help guide clinical reasoning when thinking about patients with facial weakness. The diagnosis of Bell's palsy can usually be made on clinical grounds without the need for further investigations. This is because the diagnosis is not one of exclusion (despite this being commonly how it is described), a lower motor neurone facial weakness where all alternative causes have been eliminated, but rather a positive recognition of a clinical syndrome, with a number of exclusions, which are described below. This perhaps would be more accurately referred to a 'Bell's palsy syndrome'. Treatment with corticosteroids improves outcome; adding an antiviral probably reduces the rates of long-term complications. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://www.bmj.com/company/products-services/rights-and-licensing/.

  8. Faulkner's Southern belle - myth or reality?

    Directory of Open Access Journals (Sweden)

    Nataša Intihar Klančar

    2011-12-01

    Full Text Available The article deals with heroines of William Faulkner's novels Light in August, Absalom, Absalom!, The Sound and the Fury, The Unvanquished, The Town and his short story "A Rose for Emily". The Southern belle features as a recurring character in Faulkner's fiction, her fragility, modesty, weakness yet strength, beauty, sincerity, generous nature, status and her fall from innocence comprise her central characteristics. Confronted with various expectations of Southern society and with the hardships of war, the belle is faced with many obstacles and challenges. Faulkner's heroines face a wide array of problems that prevent them from being and/or remaining a Southern belle. Let us name a few: Lena's inappropriate social status, Joanna's wrong roots, Mrs. Hightower's inability to fulfill her duties as the minister's wife, Ellen's miserable marriage, Judith's sad love life, Rosa's feelings of inferiority and humiliation, Mrs. Compson's failure as a mother, Caddy's weak rebellion against male convention, Drusilla's male characteristics, Linda's unrequited love and Emily's dark secret, to name a few. Through these characters and their destinies Faulkner shows a decaying South whose position has changed considerably over the years. Can the Southern belle save it? Can she save herself?

  9. Bell inequalities for continuously emitting sources

    Science.gov (United States)

    Knill, Emanuel; Glancy, Scott; Nam, Sae Woo; Coakley, Kevin; Zhang, Yanbao

    2015-03-01

    A common experimental strategy for demonstrating nonclassical correlations is to show violation of a Bell inequality by measuring a continuously emitted stream of entangled photon pairs. The measurements involve the detection of photons by two spatially separated parties. The detection times are recorded and compared to quantify the violation. The violation critically depends on determining which detections are coincident. Because the recorded detection times have "jitter," coincidences cannot be inferred perfectly. In the presence of settings-dependent timing errors, this can allow a local-realistic system to show apparent violation, the so-called "coincidence loophole." Here, we introduce a family of Bell inequalities based on signed, directed distances between the parties' sequences of recorded time tags. Given that the time tags are recorded for synchronized, fixed observation periods and that the settings choices are random and independent of the source, violation of these inequalities unambiguously shows nonclassical correlations violating local realism. Distance-based Bell inequalities are generally useful for two-party configurations where the effective size of the measurement outcome space is large or infinite. We show how to systematically modify the underlying Bell functions to improve the signal-to-noise ratio and to quantify the significance of the violation.

  10. Peripheral nerve involvement in Bell's palsy

    Directory of Open Access Journals (Sweden)

    J. A. Bueri

    1984-12-01

    Full Text Available A group of patients with Bell's palsy were studied in order to disclose the presence of subclinical peripheral nerve involvement. 20 patients, 8 male and 12 female, with recent Bell's palsy as their unique disease were examined, in all cases other causes of polyneuropathy were ruled out. Patients were investigated with CSF examination, facial nerve latencies in the affected and in the sound sides, and maximal motor nerve conduction velocities, as well as motor terminal latencies from the right median and peroneal nerves. CSF laboratory examination was normal in all cases. Facial nerve latencies were abnormal in all patients in the affected side, and they differed significantly from those of control group in the clinically sound side. Half of the patients showed abnormal values in the maximal motor nerve conduction velocities and motor terminal latencies of the right median and peroneal nerves. These results agree with previous reports which have pointed out that other cranial nerves may be affected in Bell's palsy. However, we have found a higher frequency of peripheral nerve involvement in this entity. These findings, support the hypothesis that in some patients Bell's palsy is the component of a more widespread disease, affecting other cranial and peripheral nerves.

  11. Some Inequalities for the Derivative of Polynomials

    Directory of Open Access Journals (Sweden)

    Sunil Hans

    2014-01-01

    Full Text Available If pz=∑υ=0ncυzυ is a polynomial of degree n, having no zeros in z<1, then Aziz (1989 proved maxz=1p′z≤n/2Mα2+Mα+π21/2, where Mα=max1≤k≤npeiα+2kπ/n. In this paper, we consider a class of polynomial Pnμ of degree n, defined as pz=a0+∑υ=μnaυzυ and present certain generalizations of above inequality and some other well-known results.

  12. The chromatic polynomial and list colorings

    DEFF Research Database (Denmark)

    Thomassen, Carsten

    2009-01-01

    We prove that, if a graph has a list of k available colors at every vertex, then the number of list-colorings is at least the chromatic polynomial evaluated at k when k is sufficiently large compared to the number of vertices of the graph.......We prove that, if a graph has a list of k available colors at every vertex, then the number of list-colorings is at least the chromatic polynomial evaluated at k when k is sufficiently large compared to the number of vertices of the graph....

  13. Steroid plus antiviral treatment for Bell's palsy.

    Science.gov (United States)

    Kang, H M; Jung, S Y; Byun, J Y; Park, M S; Yeo, S G

    2015-05-01

    The effectiveness of antiviral agents for the treatment of Bell's palsy is uncertain. We evaluated whether a steroid with an antiviral agent (S + A group) provided better recovery outcomes than a steroid alone (S group) in patients with Bell's palsy. A total of 1342 patients diagnosed with Bell's palsy who visited the Kyung Hee Medical Center in Seoul, Korea, from 2002 to 2012 were included in this study. Patients in the S + A group were treated with prednisolone and antiviral agents (n = 569) and those in the S group with prednisolone alone (n = 773). Outcomes were measured using the House-Brackmann (HB) scale according to age, initial disease severity, electroneurography (ENoG) findings and underlying comorbidities. The rate of recovery (HB grades I and II) with initially severe Bell's palsy (HB grades V and VI) was higher in the S + A than in the S group (P = 0.001). However, the rates of recovery were similar with initially moderate palsy (HB grades II-IV) (P = 0.502). In patients classified according to age and ENoG-determined severity of palsy, the overall recovery rate was higher in the S + A than in the S group, but the differences were not statistically significant (P > 0.05 for both). The recovery rate without diabetes mellitus (DM) and hypertension (HTN) was higher in the S + A group than in the S group (P = 0.031). But in the patients with HTN and DM, the difference in recovery rates between the S + A and S groups was not statistically significant (P = 0.805). Treatment with a steroid plus antiviral agent resulted in significantly higher recovery rates than steroid therapy alone in patients with initially severe Bell's palsy and without either HTN or DM, and a nonsignificant trend towards higher recovery rates in all patients with Bell's palsy in this study. Antiviral agents may therefore help in the treatment of Bell's palsy. © 2014 The Association for the Publication of the Journal of Internal Medicine.

  14. Some Relationships between the Analogs of Euler Numbers and Polynomials

    Directory of Open Access Journals (Sweden)

    Kim T

    2007-01-01

    Full Text Available We construct new twisted Euler polynomials and numbers. We also study the generating functions of the twisted Euler numbers and polynomials associated with their interpolation functions. Next we construct twisted Euler zeta function, twisted Hurwitz zeta function, twisted Dirichlet -Euler numbers and twisted Euler polynomials at non-positive integers, respectively. Furthermore, we find distribution relations of generalized twisted Euler numbers and polynomials. By numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the twisted -Euler polynomials. Finally, we give a table for the solutions of the twisted -Euler polynomials.

  15. Some Relationships between the Analogs of Euler Numbers and Polynomials

    Directory of Open Access Journals (Sweden)

    C. S. Ryoo

    2007-10-01

    Full Text Available We construct new twisted Euler polynomials and numbers. We also study the generating functions of the twisted Euler numbers and polynomials associated with their interpolation functions. Next we construct twisted Euler zeta function, twisted Hurwitz zeta function, twisted Dirichlet l-Euler numbers and twisted Euler polynomials at non-positive integers, respectively. Furthermore, we find distribution relations of generalized twisted Euler numbers and polynomials. By numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the twisted q-Euler polynomials. Finally, we give a table for the solutions of the twisted q-Euler polynomials.

  16. Equivalences of the multi-indexed orthogonal polynomials

    International Nuclear Information System (INIS)

    Odake, Satoru

    2014-01-01

    Multi-indexed orthogonal polynomials describe eigenfunctions of exactly solvable shape-invariant quantum mechanical systems in one dimension obtained by the method of virtual states deletion. Multi-indexed orthogonal polynomials are labeled by a set of degrees of polynomial parts of virtual state wavefunctions. For multi-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson, and Askey-Wilson types, two different index sets may give equivalent multi-indexed orthogonal polynomials. We clarify these equivalences. Multi-indexed orthogonal polynomials with both type I and II indices are proportional to those of type I indices only (or type II indices only) with shifted parameters

  17. Location of zeros of Wiener and distance polynomials.

    Science.gov (United States)

    Dehmer, Matthias; Ilić, Aleksandar

    2012-01-01

    The geometry of polynomials explores geometrical relationships between the zeros and the coefficients of a polynomial. A classical problem in this theory is to locate the zeros of a given polynomial by determining disks in the complex plane in which all its zeros are situated. In this paper, we infer bounds for general polynomials and apply classical and new results to graph polynomials namely Wiener and distance polynomials whose zeros have not been yet investigated. Also, we examine the quality of such bounds by considering four graph classes and interpret the results.

  18. Polynomial regression analysis and significance test of the regression function

    International Nuclear Information System (INIS)

    Gao Zhengming; Zhao Juan; He Shengping

    2012-01-01

    In order to analyze the decay heating power of a certain radioactive isotope per kilogram with polynomial regression method, the paper firstly demonstrated the broad usage of polynomial function and deduced its parameters with ordinary least squares estimate. Then significance test method of polynomial regression function is derived considering the similarity between the polynomial regression model and the multivariable linear regression model. Finally, polynomial regression analysis and significance test of the polynomial function are done to the decay heating power of the iso tope per kilogram in accord with the authors' real work. (authors)

  19. Blind Recognition of Binary BCH Codes for Cognitive Radios

    Directory of Open Access Journals (Sweden)

    Jing Zhou

    2016-01-01

    Full Text Available A novel algorithm of blind recognition of Bose-Chaudhuri-Hocquenghem (BCH codes is proposed to solve the problem of Adaptive Coding and Modulation (ACM in cognitive radio systems. The recognition algorithm is based on soft decision situations. The code length is firstly estimated by comparing the Log-Likelihood Ratios (LLRs of the syndromes, which are obtained according to the minimum binary parity check matrixes of different primitive polynomials. After that, by comparing the LLRs of different minimum polynomials, the code roots and generator polynomial are reconstructed. When comparing with some previous approaches, our algorithm yields better performance even on very low Signal-Noise-Ratios (SNRs with lower calculation complexity. Simulation results show the efficiency of the proposed algorithm.

  20. Orthogonal polynomials of compact simple Lie groups: branching rules for polynomials

    International Nuclear Information System (INIS)

    Nesterenko, M; Patera, J; Szajewska, M; Tereszkiewicz, A

    2010-01-01

    Polynomials in this paper are defined starting from a compact semisimple Lie group. A known classification of maximal, semisimple subgroups of simple Lie groups is used to select the cases to be considered here. A general method is presented and all the cases of rank ≤3 are explicitly studied. We derive the polynomials of simple Lie groups B 3 and C 3 as they are not available elsewhere. The results point to far reaching Lie theoretical connections to the theory of multivariable orthogonal polynomials.

  1. Airy polynomials, three-variable Hermite polynomials and the paraxial wave equation

    International Nuclear Information System (INIS)

    Torre, A

    2012-01-01

    Within the context of an investigation of the potential of functions, which directly or indirectly relate to the Airy functions, to yield solutions of the 2D paraxial wave equation, we consider here the Airy polynomials. We see that appropriate Gaussian-modulated versions of such polynomials, which could in a sense parallel the Hermite–Gaussian wavefunctions of both elegant and standard type, yield, when assumed as initial functions, solutions of the 2D PWE shaping in the form of a complex Gaussian modulation of three-variable Hermite polynomials. A basic characterization of these wavefunctions is provided, having as a touchstone the Hermite–Gaussian wavefunctions. (paper)

  2. Inequalities for a Polynomial and its Derivative

    Indian Academy of Sciences (India)

    Annual Meetings · Mid Year Meetings · Discussion Meetings · Public Lectures · Lecture Workshops · Refresher Courses · Symposia · Live Streaming. Home; Journals; Proceedings – Mathematical Sciences; Volume 110; Issue 2. Inequalities for a Polynomial and its Derivative. V K Jain. Volume 110 Issue 2 May 2000 pp 137- ...

  3. Integral Inequalities for Self-Reciprocal Polynomials

    Indian Academy of Sciences (India)

    Annual Meetings · Mid Year Meetings · Discussion Meetings · Public Lectures · Lecture Workshops · Refresher Courses · Symposia · Live Streaming. Home; Journals; Proceedings – Mathematical Sciences; Volume 120; Issue 2. Integral Inequalities for Self-Reciprocal Polynomials. Horst Alzer. Volume 120 Issue 2 April 2010 ...

  4. Integral inequalities for self-reciprocal polynomials

    Indian Academy of Sciences (India)

    Annual Meetings · Mid Year Meetings · Discussion Meetings · Public Lectures · Lecture Workshops · Refresher Courses · Symposia · Live Streaming. Home; Journals; Proceedings – Mathematical Sciences; Volume 120; Issue 2. Integral Inequalities for Self-Reciprocal Polynomials. Horst Alzer. Volume 120 Issue 2 April 2010 ...

  5. Polynomial stabilization of some dissipative hyperbolic systems

    Czech Academy of Sciences Publication Activity Database

    Ammari, K.; Feireisl, Eduard; Nicaise, S.

    2014-01-01

    Roč. 34, č. 11 (2014), s. 4371-4388 ISSN 1078-0947 R&D Projects: GA ČR GA201/09/0917 Institutional support: RVO:67985840 Keywords : exponential stability * polynomial stability * observability inequality Subject RIV: BA - General Mathematics Impact factor: 0.826, year: 2014 http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=9924

  6. Bernoulli Polynomials, Fourier Series and Zeta Numbers

    DEFF Research Database (Denmark)

    Scheufens, Ernst E

    2013-01-01

    Fourier series for Bernoulli polynomials are used to obtain information about values of the Riemann zeta function for integer arguments greater than one. If the argument is even we recover the well-known exact values, if the argument is odd we find integral representations and rapidly convergent...

  7. Euler Polynomials, Fourier Series and Zeta Numbers

    DEFF Research Database (Denmark)

    Scheufens, Ernst E

    2012-01-01

    Fourier series for Euler polynomials is used to obtain information about values of the Riemann zeta function for integer arguments greater than one. If the argument is even we recover the well-known exact values, if the argument is odd we find integral representations and rapidly convergent series....

  8. D-stability of polynomial matrices

    Czech Academy of Sciences Publication Activity Database

    Henrion, Didier; Bachelier, O.; Šebek, M.

    2001-01-01

    Roč. 74, č. 8 (2001), s. 845-856 ISSN 0020-7179 R&D Projects: GA AV ČR KSK1019101 Institutional research plan: AV0Z1075907 Keywords : polynomial methods * robust control * linear matrix inequalities Subject RIV: BC - Control Systems Theory Impact factor: 0.736, year: 2001

  9. Odd Degree Polynomials on Real Banach Spaces

    Czech Academy of Sciences Publication Activity Database

    Aron, R. M.; Hájek, Petr Pavel

    2007-01-01

    Roč. 11, č. 1 (2007), s. 143-153 ISSN 1385-1292 R&D Projects: GA AV ČR IAA100190502; GA ČR GA201/04/0090 Institutional research plan: CEZ:AV0Z10190503 Keywords : odd degree polynomials * zero sets Subject RIV: BA - General Mathematics Impact factor: 0.356, year: 2007

  10. Quantum Hilbert matrices and orthogonal polynomials

    DEFF Research Database (Denmark)

    Andersen, Jørgen Ellegaard; Berg, Christian

    2009-01-01

    Using the notion of quantum integers associated with a complex number q≠0 , we define the quantum Hilbert matrix and various extensions. They are Hankel matrices corresponding to certain little q -Jacobi polynomials when |q|... of reciprocal Fibonacci numbers called Filbert matrices. We find a formula for the entries of the inverse quantum Hilbert matrix....

  11. Characteristic polynomials of linear polyacenes and their ...

    Indian Academy of Sciences (India)

    Administrator

    Abstract. Coefficients of characteristic polynomials (CP) of linear polyacenes (LP) have been shown to be obtainable from Pascal's triangle by using a graph factorisation and squaring technique. Strong subspectrality existing among the members of the linear polyacene series has been shown from the derivation of the CP's.

  12. Polynomial computation of Hankel singular values

    NARCIS (Netherlands)

    Kwakernaak, H.

    1992-01-01

    A revised and improved version of a polynomial algorithm is presented. It was published by N.J. Young (1990) for the computation of the singular values and vectors of the Hankel operator defined by a linear time-invariant system with a rotational transfer matrix. Tentative numerical experiments

  13. Characteristic polynomials of linear polyacenes and their ...

    Indian Academy of Sciences (India)

    Coefficients of characteristic polynomials (CP) of linear polyacenes (LP) have been shown to be obtainable from Pascal's triangle by using a graph factorisation and squaring technique. Strong subspectrality existing among the members of the linear polyacene series has been shown from the derivation of the CP's. Thus it ...

  14. Coherent states for polynomial su(2) algebra

    International Nuclear Information System (INIS)

    Sadiq, Muhammad; Inomata, Akira

    2007-01-01

    A class of generalized coherent states is constructed for a polynomial su(2) algebra in a group-free manner. As a special case, the coherent states for the cubic su(2) algebra are discussed. The states so constructed reduce to the usual SU(2) coherent states in the linear limit

  15. On zeros of certain Dirichlet polynomials

    OpenAIRE

    BLLACA, KAJTAZ H.

    2015-01-01

    In this article we establish the zero-free region of certain Dirichlet polynomials $L_{F, X}$ arising in approximate functional equation for functions in the Selberg class and we prove an asymptotic formula for the number of zeros of $L_{F, X}$.

  16. Exceptional polynomials and SUSY quantum mechanics

    Indian Academy of Sciences (India)

    Exceptional polynomials and SUSY quantum mechanics. K V S SHIV CHAITANYA1,∗, S SREE RANJANI2,. PRASANTA K PANIGRAHI3, R RADHAKRISHNAN4 and V SRINIVASAN4. 1BITS Pilani, Hyderabad Campus, Jawahar Nagar, Shameerpet Mandal, Hyderabad 500 078, India. 2Faculty of Science and Technology, ...

  17. Deformation Prediction Using Linear Polynomial Functions ...

    African Journals Online (AJOL)

    The predictions are compared with measured data reported in literature and the results are discussed. The computational aspects of implementation of the model are also discussed briefly. Keywords: Linear Polynomial, Structural Deformation, Prediction Journal of the Nigerian Association of Mathematical Physics, Volume ...

  18. Subintegrality, invertible modules and Laurent polynomial extensions

    Indian Academy of Sciences (India)

    Indian Acad. Sci. (Math. Sci.) Vol. 125, No. 2, May 2015, pp. 149–160. c Indian Academy of Sciences. Subintegrality, invertible modules and Laurent polynomial extensions. VIVEK SADHU. Department of Mathematics ...... comments which have improved the exposition. Further, he would like to thank CSIR,. India for financial ...

  19. Error Minimization of Polynomial Approximation of Delta

    Indian Academy of Sciences (India)

    2016-01-27

    Jan 27, 2016 ... The difference between Universal time (UT) and Dynamical time (TD), known as Delta ( ) is tabulated for the first day of each year in the Astronomical Almanac. During the last four centuries it is found that there are large differences between its values for two consecutive years. Polynomial ...

  20. On Arithmetic-Geometric-Mean Polynomials

    Science.gov (United States)

    Griffiths, Martin; MacHale, Des

    2017-01-01

    We study here an aspect of an infinite set "P" of multivariate polynomials, the elements of which are associated with the arithmetic-geometric-mean inequality. In particular, we show in this article that there exist infinite subsets of probability "P" for which every element may be expressed as a finite sum of squares of real…

  1. On the zeros of the classical polynomials

    International Nuclear Information System (INIS)

    Calogero, F.

    1977-01-01

    Some theorems and conjectures concerning the zeros of the classical polynomials (of Hermite, Laguerre and Jacobi) are announced. The theorems, whose proof is not reported, have been obtained from the relationship between the motion of the zeros of special solutions of simple linear partial differential equations (in x and t), and one-dimensional many-body problems. (author)

  2. Hermite polynomials and quasi-classical asymptotics

    Czech Academy of Sciences Publication Activity Database

    Ali, S. T.; Engliš, Miroslav

    2014-01-01

    Roč. 55, č. 4 (2014), 042102 ISSN 0022-2488 R&D Projects: GA ČR GA201/09/0473 Institutional support: RVO:67985840 Keywords : quantization * Hermite polynomials * reproducing kernel Subject RIV: BA - General Mathematics Impact factor: 1.243, year: 2014 http://scitation.aip.org/content/aip/journal/jmp/55/4/10.1063/1.4869325

  3. Polynomial Asymptotes of the Second Kind

    Science.gov (United States)

    Dobbs, David E.

    2011-01-01

    This note uses the analytic notion of asymptotic functions to study when a function is asymptotic to a polynomial function. Along with associated existence and uniqueness results, this kind of asymptotic behaviour is related to the type of asymptote that was recently defined in a more geometric way. Applications are given to rational functions and…

  4. The 6 Vertex Model and Schubert Polynomials

    Directory of Open Access Journals (Sweden)

    Alain Lascoux

    2007-02-01

    Full Text Available We enumerate staircases with fixed left and right columns. These objects correspond to ice-configurations, or alternating sign matrices, with fixed top and bottom parts. The resulting partition functions are equal, up to a normalization factor, to some Schubert polynomials.

  5. Polynomial Vector Fields in One Complex Variable

    DEFF Research Database (Denmark)

    Branner, Bodil

    In recent years Adrien Douady was interested in polynomial vector fields, both in relation to iteration theory and as a topic on their own. This talk is based on his work with Pierrette Sentenac, work of Xavier Buff and Tan Lei, and my own joint work with Kealey Dias....

  6. Nonclassical Orthogonal Polynomials and Corresponding Quadratures

    CERN Document Server

    Fukuda, H; Alt, E O; Matveenko, A V

    2004-01-01

    We construct nonclassical orthogonal polynomials and calculate abscissas and weights of Gaussian quadrature for arbitrary weight and interval. The program is written by Mathematica and it works if moment integrals are given analytically. The result is a FORTRAN subroutine ready to utilize the quadrature.

  7. Indecomposability of polynomials via Jacobian matrix

    International Nuclear Information System (INIS)

    Cheze, G.; Najib, S.

    2007-12-01

    Uni-multivariate decomposition of polynomials is a special case of absolute factorization. Recently, thanks to the Ruppert's matrix some effective results about absolute factorization have been improved. Here we show that with a jacobian matrix we can get sharper bounds for the special case of uni-multivariate decomposition. (author)

  8. transformation of independent variables in polynomial regression ...

    African Journals Online (AJOL)

    Ada

    preferable when possible to work with a simple functional form in transformed variables rather than with a more complicated form in the original variables. In this paper, it is shown that linear transformations applied to independent variables in polynomial regression models affect the t ratio and hence the statistical ...

  9. On an Inequality Concerning the Polar Derivative of a Polynomial

    Indian Academy of Sciences (India)

    Abstract. In this paper, we present a correct proof of an -inequality concerning the polar derivative of a polynomial with restricted zeros. We also extend Zygmund's inequality to the polar derivative of a polynomial.

  10. On the Symmetric Properties for the Generalized Twisted Bernoulli Polynomials

    Directory of Open Access Journals (Sweden)

    Kim Taekyun

    2009-01-01

    Full Text Available We study the symmetry for the generalized twisted Bernoulli polynomials and numbers. We give some interesting identities of the power sums and the generalized twisted Bernoulli polynomials using the symmetric properties for the -adic invariant integral.

  11. On an inequality concerning the polar derivative of a polynomial

    Indian Academy of Sciences (India)

    Abstract. In this paper, we present a correct proof of an -inequality concerning the polar derivative of a polynomial with restricted zeros. We also extend Zygmund's inequality to the polar derivative of a polynomial.

  12. On a Family of Multivariate Modified Humbert Polynomials

    Science.gov (United States)

    Aktaş, Rabia; Erkuş-Duman, Esra

    2013-01-01

    This paper attempts to present a multivariable extension of generalized Humbert polynomials. The results obtained here include various families of multilinear and multilateral generating functions, miscellaneous properties, and also some special cases for these multivariable polynomials. PMID:23935411

  13. Irreducibility results for compositions of polynomials in several ...

    Indian Academy of Sciences (India)

    We obtain explicit upper bounds for the number of irreducible factors for a class of compositions of polynomials in several variables over a given field. In particular, some irreducibility criteria are given for this class of compositions of polynomials.

  14. Recurrence relations for the Cartesian derivatives of the Zernike polynomials.

    Science.gov (United States)

    Stephenson, Philip C L

    2014-04-01

    A recurrence relation for the first-order Cartesian derivatives of the Zernike polynomials is derived. This relation is used with the Clenshaw method to determine an efficient method for calculating the derivatives of any linear series of Zernike polynomials.

  15. A polynomial time algorithm for solving the maximum flow problem in directed networks

    International Nuclear Information System (INIS)

    Tlas, M.

    2015-01-01

    An efficient polynomial time algorithm for solving maximum flow problems has been proposed in this paper. The algorithm is basically based on the binary representation of capacities; it solves the maximum flow problem as a sequence of O(m) shortest path problems on residual networks with nodes and m arcs. It runs in O(m 2 r) time, where is the smallest integer greater than or equal to log B , and B is the largest arc capacity of the network. A numerical example has been illustrated using this proposed algorithm.(author)

  16. Some symmetric identities for the generalized Bernoulli, Euler and Genocchi polynomials associated with Hermite polynomials.

    Science.gov (United States)

    Khan, Waseem A; Haroon, Hiba

    2016-01-01

    In 2008, Liu and Wang established various symmetric identities for Bernoulli, Euler and Genocchi polynomials. In this paper, we extend these identities in a unified and generalized form to families of Hermite-Bernoulli, Euler and Genocchi polynomials. The procedure followed is that of generating functions. Some relevant connections of the general theory developed here with the results obtained earlier by Pathan and Khan are also pointed out.

  17. The generalized Yablonskii-Vorob'ev polynomials and their properties

    International Nuclear Information System (INIS)

    Kudryashov, Nikolai A.; Demina, Maria V.

    2008-01-01

    Rational solutions of the generalized second Painleve hierarchy are classified. Representation of the rational solutions in terms of special polynomials, the generalized Yablonskii-Vorob'ev polynomials, is introduced. Differential-difference relations satisfied by the polynomials are found. Hierarchies of differential equations related to the generalized second Painleve hierarchy are derived. One of these hierarchies is a sequence of differential equations satisfied by the generalized Yablonskii-Vorob'ev polynomials

  18. Weighted inequalities for generalized polynomials with doubling weights.

    Science.gov (United States)

    Joung, Haewon

    2017-01-01

    Many weighted polynomial inequalities, such as the Bernstein, Marcinkiewicz, Schur, Remez, Nikolskii inequalities, with doubling weights were proved by Mastroianni and Totik for the case [Formula: see text], and by Tamás Erdélyi for [Formula: see text]. In this paper we extend such polynomial inequalities to those for generalized trigonometric polynomials. We also prove the large sieve for generalized trigonometric polynomials with doubling weights.

  19. Approximating Exponential and Logarithmic Functions Using Polynomial Interpolation

    Science.gov (United States)

    Gordon, Sheldon P.; Yang, Yajun

    2017-01-01

    This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is…

  20. On the estimation of the degree of regression polynomial

    International Nuclear Information System (INIS)

    Toeroek, Cs.

    1997-01-01

    The mathematical functions most commonly used to model curvature in plots are polynomials. Generally, the higher the degree of the polynomial, the more complex is the trend that its graph can represent. We propose a new statistical-graphical approach based on the discrete projective transformation (DPT) to estimating the degree of polynomial that adequately describes the trend in the plot

  1. Interlacing of zeros of quasi-orthogonal meixner polynomials | Driver ...

    African Journals Online (AJOL)

    ... interlacing of zeros of quasi-orthogonal Meixner polynomials Mn(x;β; c) with the zeros of their nearest orthogonal counterparts Mt(x;β + k; c), l; n ∈ ℕ, k ∈ {1; 2}; is also discussed. Mathematics Subject Classication (2010): 33C45, 42C05. Key words: Discrete orthogonal polynomials, quasi-orthogonal polynomials, Meixner

  2. Commutators with idempotent values on multilinear polynomials in ...

    Indian Academy of Sciences (India)

    Multilinear polynomial; derivations; generalized polynomial identity; prime ring; right ideal. Abstract. Let R be a prime ring of characteristic different from 2, C its extended centroid, d a nonzero derivation of R , f ( x 1 , … , x n ) a multilinear polynomial over C , ϱ a nonzero right ideal of R and m > 1 a fixed integer such that.

  3. On the Lorentz degree of a product of polynomials

    KAUST Repository

    Ait-Haddou, Rachid

    2015-01-01

    In this note, we negatively answer two questions of T. Erdélyi (1991, 2010) on possible lower bounds on the Lorentz degree of product of two polynomials. We show that the correctness of one question for degree two polynomials is a direct consequence of a result of Barnard et al. (1991) on polynomials with nonnegative coefficients.

  4. The quality of zero bounds for complex polynomials.

    Science.gov (United States)

    Dehmer, Matthias; Tsoy, Yury Robertovich

    2012-01-01

    In this paper, we evaluate the quality of zero bounds on the moduli of univariate complex polynomials. We select classical and recently developed bounds and evaluate their quality by using several sets of complex polynomials. As the quality of priori bounds has not been investigated thoroughly, our results can be useful to find optimal bounds to locate the zeros of complex polynomials.

  5. Lowering and raising operators for some special orthogonal polynomials

    NARCIS (Netherlands)

    Koornwinder, T.H.

    2006-01-01

    Abstract: This paper discusses operators lowering or raising the degree but preserving the parameters of special orthogonal polynomials. Results for one-variable classical (q-)orthogonal polynomials are surveyed. For Jacobi polynomials associated with root system BC2 a new pair of lowering and

  6. Multiple Representations and the Understanding of Taylor Polynomials

    Science.gov (United States)

    Habre, Samer

    2009-01-01

    The study of Maclaurin and Taylor polynomials entails the comprehension of various new mathematical ideas. Those polynomials are initially discussed at the college level in a calculus class and then again in a course on numerical methods. This article investigates the understanding of these polynomials by students taking a numerical methods class…

  7. The Gibbs Phenomenon for Series of Orthogonal Polynomials

    Science.gov (United States)

    Fay, T. H.; Kloppers, P. Hendrik

    2006-01-01

    This note considers the four classes of orthogonal polynomials--Chebyshev, Hermite, Laguerre, Legendre--and investigates the Gibbs phenomenon at a jump discontinuity for the corresponding orthogonal polynomial series expansions. The perhaps unexpected thing is that the Gibbs constant that arises for each class of polynomials appears to be the same…

  8. Root and critical point behaviors of certain sums of polynomials

    Indian Academy of Sciences (India)

    Seon-Hong Kim

    2018-04-24

    Apr 24, 2018 ... Introduction. There is an extensive literature concerning roots of sums of polynomials. Many authors. [5–7] have written about these polynomials. Perhaps the most immediate question of sums of polynomials, A+ B = C is: 'given bounds for the roots of A and B, what bounds can be given for the roots of C?' ...

  9. Uniqueness and zeros of q-shift difference polynomials

    Indian Academy of Sciences (India)

    In this paper, we consider the zero distributions of -shift difference polynomials of meromorphic functions with zero order, and obtain two theorems that extend the classical Hayman results on the zeros of differential polynomials to -shift difference polynomials. We also investigate the uniqueness problem of -shift ...

  10. Strong result for real zeros of random algebraic polynomials

    Directory of Open Access Journals (Sweden)

    T. Uno

    2001-01-01

    Full Text Available An estimate is given for the lower bound of real zeros of random algebraic polynomials whose coefficients are non-identically distributed dependent Gaussian random variables. Moreover, our estimated measure of the exceptional set, which is independent of the degree of the polynomials, tends to zero as the degree of the polynomial tends to infinity.

  11. Self-testing of binary observables based on commutation

    DEFF Research Database (Denmark)

    Kaniewski, Jędrzej

    2017-01-01

    We consider the problem of certifying binary observables based on a Bell inequality violation alone, a task known as self-testing of measurements. We introduce a family of commutation-based measures, which encode all the distinct arrangements of two projective observables on a qubit. These quanti......We consider the problem of certifying binary observables based on a Bell inequality violation alone, a task known as self-testing of measurements. We introduce a family of commutation-based measures, which encode all the distinct arrangements of two projective observables on a qubit....... These quantities by construction take into account the usual limitations of self-testing and since they are “weighted” by the (reduced) state, they automatically deal with rank-deficient reduced density matrices. We show that these measures can be estimated from the observed Bell violation in several scenarios...... and the proofs rely only on standard linear algebra. The trade-offs turn out to be tight, and in particular, they give nontrivial statements for arbitrarily small violations. On the other extreme, observing the maximal violation allows us to deduce precisely the form of the observables, which immediately leads...

  12. Status of the Belle SVD detector

    CERN Document Server

    Abe, R; Alimonti, G; Asano, Y; Bakich, A; Banas, E; Bozek, A; Browder, T E; Dragic, J; Everton, C W; Fukunaga, C; Gordon, A; Guler, H; Haba, J; Hara, K; Hara, T; Hastings, N; Hazumi, M; Heenan, E; Higuchi, T; Hojo, T; Ishino, H; Iwai, G; Jalocha, P; Kaneko, J; Kapusta, P; Kawasaki, T; Korotushenko, K; Lange, J; Li, Y; Marlow, D; Matsubara, T; Miyake, H; Moffitt, L; Moloney, G R; Mori, S; Nagashima, Y; Nakadaira, T; Nakamura, T; Natkaniec, Z; Okuno, S; Olsen, S; Ostrowicz, W; Palka, H; Peak, L; Rozanka, M; Ryuko, J; Sevior, M E; Shimada, K; Stanic, S; Sumisawa, K; Stock, R; Swain, S; Tajima, H; Takahashi, S; Tagomori, H; Takasaki, F; Tamura, N; Tanaka, J; Tanaka, M; Taylor, G N; Tomura, T; Trabelsi, K; Tsuboyama, T; Tsujita, Y; Varner, G; Varvell, K E; Watanabe, Y; Yamada, Y; Yamamoto, H; Yokoyama, M; Zhao, H; Zontar, D

    2002-01-01

    The Belle spectrometer was designed for studies of B meson decays at an asymmetric e sup + e sup - collider operating at the UPSILON(4S) resonance. One of its crucial components, a silicon vertex detector (SVD), is placed just outside a cylindrical beryllium beam-pipe. After a year of Belle operation an upgraded version of SVD was installed during the regular summer shut-down. The new SVD follows the same design, with a few important improvements. Rad-soft readout electronics was replaced by rad-tolerant one, allowing for longer lifetime of the detector. A new radiation and temperature monitoring system was developed and implemented. A saw-shaped inner surface was introduced in the beam-pipe to prevent potential synchrotron radiation damage. The upgraded detector started operating successfully in October 2000.

  13. Double dumb-bell calculus in childhood

    Directory of Open Access Journals (Sweden)

    Joshi Prashant

    2009-01-01

    Full Text Available An eight-year old male was admitted with complaints of right scrotal swelling, dysuria and intermittent retention of urine for 10 days. On per-rectal examination, a hard mass was palpable in the posterior urethra. An X-ray (KUB of the abdomen revealed a double dumb-bell calculus at the base of bladder, extending into the posterior urethra. A cystolithotomy via the suprapubic approach was successfully curative.

  14. EPR and Bell's theorem: A critical review

    International Nuclear Information System (INIS)

    Stapp, H.P.

    1991-01-01

    The argument of Einstein, Podolsky, and Rosen is reviewed with attention to logical structure and character of assumptions. Bohr's reply is discussed. Bell's contribution is formulated without use of hidden variables, and efforts to equate hidden variables to realism are critically examined. An alternative derivation of nonlocality that makes no use of hidden variables, microrealism, counterfactual definiteness, or any other assumption alien to orthodox quantum thinking is described in detail, with particular attention to the quartet or broken-square question

  15. Some inequalities for the Bell numbers

    Indian Academy of Sciences (India)

    Feng Qi

    2017-08-19

    Aug 19, 2017 ... 428–431; available online at doi:10.1016/0022-247X(84)90006-4. [16] Qi F, An explicit formula for the Bell numbers in terms of the Lah and Stirling numbers, Mediterr. J. Math. 13(5) (2016) 2795–2800; available online at doi:10.1007/ · s00009-015-0655-7. [17] Qi F, Generalized weighted mean values with ...

  16. Performance of the Belle silicon vertex detector

    CERN Document Server

    Hazumi, M

    2001-01-01

    The performance of the Silicon Vertex Detector (SVD) in the Belle experiment at the KEK B factory is described. The resolution on the distance between B meson vertices is estimated to be 115 sub - sub 2 sub 6 sup + sup 2 sup 4 mu m, which is good enough for the precise measurement of the CP asymmetry in B decays. A plan for the upgrade of the SVD is also mentioned.

  17. Analytic quantum bounds on Bell inequalities

    International Nuclear Information System (INIS)

    Filipp, S.; Svozil, K.

    2005-01-01

    Full text: Can realism be combined with the quantum world? An important tool to investigate in this question are Bell's inequalities and violations thereof - they represent a cornerstone of our present understanding of quantum mechanics and therefore the description of nature. Here we present a simple algebraic method to calculate violations for any measurement arrangements that are maximal in the sense that quantum mechanics does not allow a stronger violation. Having two or more polarization analyzers available and a source producing photon-pairs in arbitrary polarization states Bell-type inequalities tell us which probabilities for measuring the polarization in particular directions are viable in a deterministic theory. Quantum mechanics does not obey these rules, but yields a violation of these inequalities. The questions is to what extent the inequalities are violated. Making use of a min-max principle analytical expressions can be found for the 'fine structure' of the maximal violations of arbitrary Bell-like inequalities, i. e. the upper bound reachable by any state when the analyzers measure in given directions. Knowing these bounds is useful for experimental tests of the validity of quantum mechanics and can serve as a prerequisite to answer the even more pressing question, why no stronger violation has been observed until now. (author)

  18. Cutaneous Sensibility Changes in Bell's Palsy Patients.

    Science.gov (United States)

    Cárdenas Palacio, Carlos Andrés; Múnera Galarza, Francisco Alejandro

    2017-05-01

    Objective Bell's palsy is a cranial nerve VII dysfunction that renders the patient unable to control facial muscles from the affected side. Nevertheless, some patients have reported cutaneous changes in the paretic area. Therefore, cutaneous sensibility changes might be possible additional symptoms within the clinical presentation of this disorder. Accordingly, the aim of this research was to investigate the relationship between cutaneous sensibility and facial paralysis severity in these patients. Study Design Prospective longitudinal cohort study. Settings Tertiary care medical center. Subjects and Methods Twelve acute-onset Bell's palsy patients were enrolled from March to September 2009. In addition, 12 sex- and age-matched healthy volunteers were tested. Cutaneous sensibility was evaluated with pressure threshold and 2-point discrimination at 6 areas of the face. Facial paralysis severity was evaluated with the House-Brackmann scale. Results Statistically significant correlations based on the Spearman's test were found between facial paralysis severity and cutaneous sensitivity on forehead, eyelid, cheek, nose, and lip ( P Bell's palsy patients but not in healthy subjects. Conclusion Such results suggest a possible relationship between the loss of motor control of the face and changes in facial sensory information processing. Such findings are worth further research about the neurophysiologic changes associated with the cutaneous sensibility disturbances of these patients.

  19. Modelling Trends in Ordered Correspondence Analysis Using Orthogonal Polynomials.

    Science.gov (United States)

    Lombardo, Rosaria; Beh, Eric J; Kroonenberg, Pieter M

    2016-06-01

    The core of the paper consists of the treatment of two special decompositions for correspondence analysis of two-way ordered contingency tables: the bivariate moment decomposition and the hybrid decomposition, both using orthogonal polynomials rather than the commonly used singular vectors. To this end, we will detail and explain the basic characteristics of a particular set of orthogonal polynomials, called Emerson polynomials. It is shown that such polynomials, when used as bases for the row and/or column spaces, can enhance the interpretations via linear, quadratic and higher-order moments of the ordered categories. To aid such interpretations, we propose a new type of graphical display-the polynomial biplot.

  20. Describing Quadratic Cremer Point Polynomials by Parabolic Perturbations

    DEFF Research Database (Denmark)

    Sørensen, Dan Erik Krarup

    1996-01-01

    We describe two infinite order parabolic perturbation proceduresyielding quadratic polynomials having a Cremer fixed point. The main ideais to obtain the polynomial as the limit of repeated parabolic perturbations.The basic tool at each step is to control the behaviour of certain externalrays.Polynomials...... the existence of polynomials having an explicitlygiven external ray accumulating both at the Cremer point and at its non-periodicpreimage. We think of the Julia set as containing a "topologists double comb".In the one-sided case we prove a weaker result: the existence of polynomials havingan explicitly given...

  1. Planar Harmonic and Monogenic Polynomials of Type A

    Directory of Open Access Journals (Sweden)

    Charles F. Dunkl

    2016-10-01

    Full Text Available Harmonic polynomials of type A are polynomials annihilated by the Dunkl Laplacian associated to the symmetric group acting as a reflection group on R N . The Dunkl operators are denoted by T j for 1 ≤ j ≤ N , and the Laplacian Δ κ = ∑ j = 1 N T j 2 . This paper finds the homogeneous harmonic polynomials annihilated by all T j for j > 2 . The structure constants with respect to the Gaussian and sphere inner products are computed. These harmonic polynomials are used to produce monogenic polynomials, those annihilated by a Dirac-type operator.

  2. Zernike polynomials for photometric characterization of LEDs

    International Nuclear Information System (INIS)

    Velázquez, J L; Ferrero, A; Pons, A; Campos, J; Hernanz, M L

    2016-01-01

    We propose a method based on Zernike polynomials to characterize photometric quantities and descriptors of light emitting diodes (LEDs) from measurements of the angular distribution of the luminous intensity, such as total luminous flux, BA, inhomogeneity, anisotropy, direction of the optical axis and Lambertianity of the source. The performance of this method was experimentally tested for 18 high-power LEDs from different manufacturers and with different photometric characteristics. A small set of Zernike coefficients can be used to calculate all the mentioned photometric quantities and descriptors. For applications not requiring a great accuracy such as those of lighting design, the angular distribution of the luminous intensity of most of the studied LEDs can be interpolated with only two Zernike polynomials. (paper)

  3. Orthogonal polynomials in neutron transport theory

    Energy Technology Data Exchange (ETDEWEB)

    Dehesa, J.S. (Granada Univ. (Spain). Facultad de Ciencias)

    1982-01-01

    The asymptotic average properties of zeros of the polynomials gsub(k)sup(m) (x), which play a fundamental role in neutron transport and radiative transfer theories, are investigated analytically in terms of the angular expansion coefficients wsub(k) of the scattering kernel for three wide classes of scattering models. In particular it is found that the scattering models of Eccleston-McCormick (J. Nucl. Energy.; 24:23 (1970)), Shultis et al (Nucl. Sci. Eng.; 59:53 (1976)) and Henyey-Greenstein (Astrophys. J.; 93:70 (1941)) belong in one of the above-mentioned classes, and their associated polynomials gsub(k)sup(m) (x) have the same asymptotic density of zeros.

  4. Polynomial chaos representation of databases on manifolds

    Energy Technology Data Exchange (ETDEWEB)

    Soize, C., E-mail: christian.soize@univ-paris-est.fr [Université Paris-Est, Laboratoire Modélisation et Simulation Multi-Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-La-Vallée, Cedex 2 (France); Ghanem, R., E-mail: ghanem@usc.edu [University of Southern California, 210 KAP Hall, Los Angeles, CA 90089 (United States)

    2017-04-15

    Characterizing the polynomial chaos expansion (PCE) of a vector-valued random variable with probability distribution concentrated on a manifold is a relevant problem in data-driven settings. The probability distribution of such random vectors is multimodal in general, leading to potentially very slow convergence of the PCE. In this paper, we build on a recent development for estimating and sampling from probabilities concentrated on a diffusion manifold. The proposed methodology constructs a PCE of the random vector together with an associated generator that samples from the target probability distribution which is estimated from data concentrated in the neighborhood of the manifold. The method is robust and remains efficient for high dimension and large datasets. The resulting polynomial chaos construction on manifolds permits the adaptation of many uncertainty quantification and statistical tools to emerging questions motivated by data-driven queries.

  5. Polynomial structures in one-loop amplitudes

    International Nuclear Information System (INIS)

    Britto, Ruth; Feng Bo; Yang Gang

    2008-01-01

    A general one-loop scattering amplitude may be expanded in terms of master integrals. The coefficients of the master integrals can be obtained from tree-level input in a two-step process. First, use known formulas to write the coefficients of (4-2ε)-dimensional master integrals; these formulas depend on an additional variable, u, which encodes the dimensional shift. Second, convert the u-dependent coefficients of (4-2ε)-dimensional master integrals to explicit coefficients of dimensionally shifted master integrals. This procedure requires the initial formulas for coefficients to have polynomial dependence on u. Here, we give a proof of this property in the case of massless propagators. The proof is constructive. Thus, as a byproduct, we produce different algebraic expressions for the scalar integral coefficients, in which the polynomial property is apparent. In these formulas, the box and pentagon contributions are separated explicitly.

  6. A Deterministic and Polynomial Modified Perceptron Algorithm

    Directory of Open Access Journals (Sweden)

    Olof Barr

    2006-01-01

    Full Text Available We construct a modified perceptron algorithm that is deterministic, polynomial and also as fast as previous known algorithms. The algorithm runs in time O(mn3lognlog(1/ρ, where m is the number of examples, n the number of dimensions and ρ is approximately the size of the margin. We also construct a non-deterministic modified perceptron algorithm running in timeO(mn2lognlog(1/ρ.

  7. Polynomials and identities on real Banach spaces

    Czech Academy of Sciences Publication Activity Database

    Hájek, Petr Pavel; Kraus, M.

    2012-01-01

    Roč. 385, č. 2 (2012), s. 1015-1026 ISSN 0022-247X R&D Projects: GA ČR(CZ) GAP201/11/0345 Institutional research plan: CEZ:AV0Z10190503 Keywords : Polynomials on Banach spaces Subject RIV: BA - General Mathematics Impact factor: 1.050, year: 2012 http://www.sciencedirect.com/science/article/pii/S0022247X11006743

  8. Piecewise polynomial solutions to linear inverse problems

    DEFF Research Database (Denmark)

    Hansen, Per Christian; Mosegaard, K.

    1996-01-01

    We have presented a new algorithm PP-TSVD that computes piecewise polynomial solutions to ill-posed problems, without a priori knowledge about the positions of the break points. In particular, we can compute piecewise constant functions that describe layered models. Such solutions are useful, e.g.......g., in seismological problems, and the algorithm can also be used as a preprocessor for other methods where break points/discontinuities must be incorporated explicitly....

  9. Polynomial Variables and the Jacobian Problem

    Indian Academy of Sciences (India)

    Most readers would be familiar with the technique of shifting the origin to simplify the equation -of a locus. This process is the same as choosing new coordinate axes, ..... 1982 by H Bass, E H Connell and D Wright. Points at Infinity. Let f be a nonzero polynomial in X, Y, and let d = deg (f). Then f can be written in the form f =.

  10. Moments, positive polynomials and their applications

    CERN Document Server

    Lasserre, Jean Bernard

    2009-01-01

    Many important applications in global optimization, algebra, probability and statistics, applied mathematics, control theory, financial mathematics, inverse problems, etc. can be modeled as a particular instance of the Generalized Moment Problem (GMP) . This book introduces a new general methodology to solve the GMP when its data are polynomials and basic semi-algebraic sets. This methodology combines semidefinite programming with recent results from real algebraic geometry to provide a hierarchy of semidefinite relaxations converging to the desired optimal value. Applied on appropriate cones,

  11. Completeness of the ring of polynomials

    DEFF Research Database (Denmark)

    Thorup, Anders

    2015-01-01

    Consider the polynomial ring R:=k[X1,…,Xn]R:=k[X1,…,Xn] in n≥2n≥2 variables over an uncountable field k. We prove that R   is complete in its adic topology, that is, the translation invariant topology in which the non-zero ideals form a fundamental system of neighborhoods of 0. In addition we prove...

  12. Zero sets of polynomials in several variables

    Czech Academy of Sciences Publication Activity Database

    Aron, R. M.; Hájek, Petr Pavel

    2006-01-01

    Roč. 86, č. 6 (2006), s. 561-568 ISSN 0003-889X R&D Projects: GA ČR(CZ) GA201/01/1198; GA ČR(CZ) GA201/04/0090; GA AV ČR(CZ) IAA1019205 Institutional research plan: CEZ:AV0Z10190503 Keywords : polynomial * zero set Subject RIV: BA - General Mathematics Impact factor: 0.341, year: 2006

  13. Trigonometric Polynomials For Estimation Of Spectra

    Science.gov (United States)

    Greenhall, Charles A.

    1990-01-01

    Orthogonal sets of trigonometric polynomials used as suboptimal substitutes for discrete prolate-spheroidal "windows" of Thomson method of estimation of spectra. As used here, "windows" denotes weighting functions used in sampling time series to obtain their power spectra within specified frequency bands. Simplified windows designed to require less computation than do discrete prolate-spheroidal windows, albeit at price of some loss of accuracy.

  14. Detecting Prime Numbers via Roots of Polynomials

    Science.gov (United States)

    Dobbs, David E.

    2012-01-01

    It is proved that an integer n [greater than or equal] 2 is a prime (resp., composite) number if and only if there exists exactly one (resp., more than one) nth-degree monic polynomial f with coefficients in Z[subscript n], the ring of integers modulo n, such that each element of Z[subscript n] is a root of f. This classroom note could find use in…

  15. Bell's palsy: A Case Report and Literature Review

    Directory of Open Access Journals (Sweden)

    Tashika Kushraj

    2014-06-01

    Full Text Available Bell's palsy is considered as a disease of exclusion. It is a form of lower motor neuron paralysis affecting the facial muscles. Rapid onset of paralysis causes panic to the patients. For speedy recovery, correct diagnosis and early treatment are crucial. Here a case of Bell's palsy is reported and the literature on Bell's palsy is reviewed. [Cukurova Med J 2014; 39(3.000: 581-588

  16. Multivariate Krawtchouk Polynomials and Composition Birth and Death Processes

    Directory of Open Access Journals (Sweden)

    Robert Griffiths

    2016-05-01

    Full Text Available This paper defines the multivariate Krawtchouk polynomials, orthogonal on the multinomial distribution, and summarizes their properties as a review. The multivariate Krawtchouk polynomials are symmetric functions of orthogonal sets of functions defined on each of N multinomial trials. The dual multivariate Krawtchouk polynomials, which also have a polynomial structure, are seen to occur naturally as spectral orthogonal polynomials in a Karlin and McGregor spectral representation of transition functions in a composition birth and death process. In this Markov composition process in continuous time, there are N independent and identically distributed birth and death processes each with support 0 , 1 , … . The state space in the composition process is the number of processes in the different states 0 , 1 , … . Dealing with the spectral representation requires new extensions of the multivariate Krawtchouk polynomials to orthogonal polynomials on a multinomial distribution with a countable infinity of states.

  17. Doubling (Dual) Hahn Polynomials: Classification and Applications

    Science.gov (United States)

    Oste, Roy; Van der Jeugt, Joris

    2016-01-01

    We classify all pairs of recurrence relations in which two Hahn or dual Hahn polynomials with different parameters appear. Such couples are referred to as (dual) Hahn doubles. The idea and interest comes from an example appearing in a finite oscillator model [Jafarov E.I., Stoilova N.I., Van der Jeugt J., J. Phys. A: Math. Theor. 44 (2011), 265203, 15 pages, arXiv:1101.5310]. Our classification shows there exist three dual Hahn doubles and four Hahn doubles. The same technique is then applied to Racah polynomials, yielding also four doubles. Each dual Hahn (Hahn, Racah) double gives rise to an explicit new set of symmetric orthogonal polynomials related to the Christoffel and Geronimus transformations. For each case, we also have an interesting class of two-diagonal matrices with closed form expressions for the eigenvalues. This extends the class of Sylvester-Kac matrices by remarkable new test matrices. We examine also the algebraic relations underlying the dual Hahn doubles, and discuss their usefulness for the construction of new finite oscillator models.

  18. Violating Bell inequalities maximally for two d-dimensional systems

    International Nuclear Information System (INIS)

    Chen Jingling; Wu Chunfeng; Oh, C. H.; Kwek, L. C.; Ge Molin

    2006-01-01

    We show the maximal violation of Bell inequalities for two d-dimensional systems by using the method of the Bell operator. The maximal violation corresponds to the maximal eigenvalue of the Bell operator matrix. The eigenvectors corresponding to these eigenvalues are described by asymmetric entangled states. We estimate the maximum value of the eigenvalue for large dimension. A family of elegant entangled states |Ψ> app that violate Bell inequality more strongly than the maximally entangled state but are somewhat close to these eigenvectors is presented. These approximate states can potentially be useful for quantum cryptography as well as many other important fields of quantum information

  19. Emile Galle ja legendaarne Belle Epoque / Kärt Kross

    Index Scriptorium Estoniae

    Kross, Kärt

    2008-01-01

    1811. aastal rajatud Perrier-Jouet shampanjamajast ja shampanjast Belle Epoque, mille lillemotiividega pudeli disainis prantsuse klaasikunstnik Emile Galle (1846-1904). Kunstniku eluloolisi andmeid, loomingust

  20. Solving a binary puzzle

    NARCIS (Netherlands)

    P.H. Utomo (Putranto); R.H. Makarim (Rusydi)

    2017-01-01

    textabstractA Binary puzzle is a Sudoku-like puzzle with values in each cell taken from the set (Formula presented.). Let (Formula presented.) be an even integer, a solved binary puzzle is an (Formula presented.) binary array that satisfies the following conditions: (1) no three consecutive ones and

  1. Eclipsing binaries in open clusters

    DEFF Research Database (Denmark)

    Southworth, John; Clausen, J.V.

    2006-01-01

    Stars: fundamental parameters - Stars : binaries : eclipsing - Stars: Binaries: spectroscopic - Open clusters and ass. : general Udgivelsesdato: 5 August......Stars: fundamental parameters - Stars : binaries : eclipsing - Stars: Binaries: spectroscopic - Open clusters and ass. : general Udgivelsesdato: 5 August...

  2. Aspects of the History of the Nerves: Bell's Theory, the Bell-Magendie Law and Controversy, and Two Forgotten Works by P.W. Lund and D.F. Eschricth

    DEFF Research Database (Denmark)

    Jørgensen, C. Barker

    2003-01-01

    History of nerves, Bell's Idea, Bell-Magendie law, Bell-Magendie controversy, Charles Bell, Francois Magendie, P.W. Lund, D.F. Eschricht, Herbert Mayo, Johannes Müller, Claude Bernard, spinal nerve roots, cranial nerves, recurrent sensitivity......History of nerves, Bell's Idea, Bell-Magendie law, Bell-Magendie controversy, Charles Bell, Francois Magendie, P.W. Lund, D.F. Eschricht, Herbert Mayo, Johannes Müller, Claude Bernard, spinal nerve roots, cranial nerves, recurrent sensitivity...

  3. From $r$-Linearized Polynomial Equations to $r^m$-Linearized Polynomial Equations

    OpenAIRE

    Fernando, Neranga; Hou, Xiang-dong

    2015-01-01

    Let $r$ be a prime power and $q=r^m$. For $0\\le i\\le m-1$, let $f_i\\in \\mathbb{F}_r[x]$ be $q$-linearized and $a_i\\in \\mathbb{F}_q$. Assume that $z\\in \\mathbb{\\bar{F}}_r$ satisfies the equation $\\sum_{i=0}^{m-1}a_if_i(z)^{r^i}=0$, where $\\sum_{i=0}^{m-1}a_if_i^{r_i}\\in \\mathbb{F}_q[x]$ is an $r$-linearized polynomial. It is shown that $z$ satisfies a $q$-linearized polynomial equation with coefficients in $\\mathbb{F}_r$. This result provides an explanation for numerous permutation polynomials...

  4. 78 FR 37158 - Airworthiness Directives; Bell Helicopter Textron Canada (Bell) Model Helicopters

    Science.gov (United States)

    2013-06-20

    ... Textron Canada (Bell) Model Helicopters AGENCY: Federal Aviation Administration (FAA), DOT. ACTION: Notice... through Friday, except Federal holidays. Examining the AD Docket You may examine the AD docket on the....m., Monday through Friday, except Federal holidays. The AD docket contains this proposed AD, the...

  5. 77 FR 64439 - Airworthiness Directives; Bell Helicopter Textron Canada (Bell) Model Helicopters

    Science.gov (United States)

    2012-10-22

    ... Textron Canada (Bell) Model Helicopters AGENCY: Federal Aviation Administration (FAA) DOT. ACTION: Notice...'' address between 9 a.m. and 5 p.m., Monday through Friday, except Federal holidays. Examining The AD Docket... Operations Office between 9 a.m. and 5 p.m., Monday through Friday, except Federal holidays. The AD docket...

  6. 78 FR 4762 - Airworthiness Directives; Bell Helicopter Textron Canada Limited (Bell) Helicopters

    Science.gov (United States)

    2013-01-23

    ... Textron Canada Limited (Bell) Helicopters AGENCY: Federal Aviation Administration (FAA), DOT. ACTION... ``Mail'' address between 9 a.m. and 5 p.m., Monday through Friday, except Federal holidays. Examining the... the Docket Operations Office between 9 a.m. and 5 p.m., Monday through Friday, except Federal holidays...

  7. 78 FR 37152 - Airworthiness Directives; Bell Helicopter Textron Canada Limited (Bell) Helicopters

    Science.gov (United States)

    2013-06-20

    ... Textron Canada Limited (Bell) Helicopters AGENCY: Federal Aviation Administration (FAA), DOT. ACTION... through Friday, except Federal holidays. Examining the AD Docket You may examine the AD docket on the....m., Monday through Friday, except Federal holidays. The AD docket contains this proposed AD, the...

  8. 78 FR 34286 - Airworthiness Directives; Bell Helicopter Textron Canada Limited (Bell) Helicopters

    Science.gov (United States)

    2013-06-07

    ... Textron Canada Limited (Bell) Helicopters AGENCY: Federal Aviation Administration (FAA), DOT. ACTION... to the ``Mail'' address between 9 a.m. and 5 p.m., Monday through Friday, except Federal holidays... holidays. The AD docket contains this proposed AD, the economic evaluation, any comments received, and...

  9. 78 FR 65206 - Airworthiness Directives; Bell Helicopter Textron Canada Limited (Bell) Helicopters

    Science.gov (United States)

    2013-10-31

    ... Textron Canada Limited (Bell) Helicopters AGENCY: Federal Aviation Administration (FAA), DOT. ACTION... Helicopter Textron Canada Limited, 12,800 Rue de l'Avenir, Mirabel, Quebec J7J1R4; telephone (450) 437-2862....m., Monday through Friday, except Federal holidays. The AD docket contains this AD, the foreign...

  10. 78 FR 65202 - Airworthiness Directives; Bell Helicopter Textron Canada Limited (Bell) Helicopters

    Science.gov (United States)

    2013-10-31

    ... Textron Canada Limited (Bell) Helicopters AGENCY: Federal Aviation Administration (FAA), DOT. ACTION... Helicopter Textron Canada Limited, 12,800 Rue de l'Avenir, Mirabel, Quebec J7J1R4; telephone (450) 437-2862.... and 5 p.m., Monday through Friday, except Federal holidays. The AD docket contains this AD, the...

  11. 78 FR 34282 - Airworthiness Directives; Bell Helicopter Textron Canada Limited (Bell) Helicopters

    Science.gov (United States)

    2013-06-07

    ... Textron Canada Limited (Bell) Helicopters AGENCY: Federal Aviation Administration (FAA), DOT. ACTION... holidays. Examining the AD Docket You may examine the AD docket on the Internet at http://www.regulations..., except Federal holidays. The AD docket contains this proposed AD, the economic evaluation, any comments...

  12. 78 FR 34280 - Airworthiness Directives; Bell Helicopter Textron Canada Limited (Bell) Helicopters

    Science.gov (United States)

    2013-06-07

    ... Textron Canada Limited (Bell) Helicopters AGENCY: Federal Aviation Administration (FAA), DOT. ] ACTION..., except Federal holidays. Examining the AD Docket You may examine the AD docket on the Internet at http... through Friday, except Federal holidays. The AD docket contains this proposed AD, the economic evaluation...

  13. 78 FR 34290 - Airworthiness Directives; Bell Helicopter Textron Canada Limited (Bell) Helicopters

    Science.gov (United States)

    2013-06-07

    ... Textron Canada Limited (Bell) Helicopters AGENCY: Federal Aviation Administration (FAA), DOT. ACTION...'' address between 9 a.m. and 5 p.m., Monday through Friday, except Federal holidays. Examining the AD Docket... Operations Office between 9 a.m. and 5 p.m., Monday through Friday, except Federal holidays. The AD docket...

  14. The Belle II Silicon Vertex Detector

    International Nuclear Information System (INIS)

    Friedl, M.; Ackermann, K.; Aihara, H.; Aziz, T.; Bergauer, T.; Bozek, A.; Campbell, A.; Dingfelder, J.; Drasal, Z.; Frankenberger, A.; Gadow, K.; Gfall, I.; Haba, J.; Hara, K.; Hara, T.; Higuchi, T.; Himori, S.; Irmler, C.; Ishikawa, A.; Joo, C.

    2013-01-01

    The KEKB machine and the Belle experiment in Tsukuba (Japan) are now undergoing an upgrade, leading to an ultimate luminosity of 8×10 35 cm −2 s −1 in order to measure rare decays in the B system with high statistics. The previous vertex detector cannot cope with this 40-fold increase of luminosity and thus needs to be replaced. Belle II will be equipped with a two-layer Pixel Detector surrounding the beam pipe, and four layers of double-sided silicon strip sensors at higher radii than the old detector. The Silicon Vertex Detector (SVD) will have a total sensitive area of 1.13m 2 and 223,744 channels—twice as many as its predecessor. All silicon sensors will be made from 150 mm wafers in order to maximize their size and thus to reduce the relative contribution of the support structure. The forward part has slanted sensors of trapezoidal shape to improve the measurement precision and to minimize the amount of material as seen by particles from the vertex. Fast-shaping front-end amplifiers will be used in conjunction with an online hit time reconstruction algorithm in order to reduce the occupancy to the level of a few percent at most. A novel “Origami” chip-on-sensor scheme is used to minimize both the distance between strips and amplifier (thus reducing the electronic noise) as well as the overall material budget. This report gives an overview on the status of the Belle II SVD and its components, including sensors, front-end detector ladders, mechanics, cooling and the readout electronics

  15. The Belle II Silicon Vertex Detector

    Energy Technology Data Exchange (ETDEWEB)

    Friedl, M., E-mail: markus.friedl@oeaw.ac.at [HEPHY – Institute of High Energy Physics, Nikolsdorfer Gasse 18, 1050 Vienna (Austria); Ackermann, K. [MPI Munich, Föhringer Ring 6, 80805 München (Germany); Aihara, H. [University of Tokyo, Department of Physics, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan); Aziz, T. [Tata Institute of Fundamental Research, Experimental High Energy Physics Group, Homi Bhabha Road, Mumbai 400 005 (India); Bergauer, T. [HEPHY – Institute of High Energy Physics, Nikolsdorfer Gasse 18, 1050 Vienna (Austria); Bozek, A. [Institute of Nuclear Physics, Division of Particle Physics and Astrophysics, ul. Radzikowskiego 152, 31 342 Krakow (Poland); Campbell, A. [DESY, Notkestrasse 85, 22607 Hamburg (Germany); Dingfelder, J. [University of Bonn, Department of Physics and Astronomy, Nussallee 12, 53115 Bonn (Germany); Drasal, Z. [Charles University, Institute of Particle and Nuclear Physics, Ke Karlovu 3, 121 16 Praha 2 (Czech Republic); Frankenberger, A. [HEPHY – Institute of High Energy Physics, Nikolsdorfer Gasse 18, 1050 Vienna (Austria); Gadow, K. [DESY, Notkestrasse 85, 22607 Hamburg (Germany); Gfall, I. [HEPHY – Institute of High Energy Physics, Nikolsdorfer Gasse 18, 1050 Vienna (Austria); Haba, J.; Hara, K.; Hara, T. [KEK, 1-1 Oho, Tsukuba, Ibaraki 305-0801 (Japan); Higuchi, T. [University of Tokyo, Kavli Institute for Physics and Mathematics of the Universe, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8583 (Japan); Himori, S. [Tohoku University, Department of Physics, Aoba Aramaki Aoba-ku, Sendai 980-8578 (Japan); Irmler, C. [HEPHY – Institute of High Energy Physics, Nikolsdorfer Gasse 18, 1050 Vienna (Austria); Ishikawa, A. [Tohoku University, Department of Physics, Aoba Aramaki Aoba-ku, Sendai 980-8578 (Japan); Joo, C. [Seoul National University, High Energy Physics Laboratory, 25-107 Shinlim-dong, Kwanak-gu, Seoul 151-742 (Korea, Republic of); and others

    2013-12-21

    The KEKB machine and the Belle experiment in Tsukuba (Japan) are now undergoing an upgrade, leading to an ultimate luminosity of 8×10{sup 35}cm{sup −2}s{sup −1} in order to measure rare decays in the B system with high statistics. The previous vertex detector cannot cope with this 40-fold increase of luminosity and thus needs to be replaced. Belle II will be equipped with a two-layer Pixel Detector surrounding the beam pipe, and four layers of double-sided silicon strip sensors at higher radii than the old detector. The Silicon Vertex Detector (SVD) will have a total sensitive area of 1.13m{sup 2} and 223,744 channels—twice as many as its predecessor. All silicon sensors will be made from 150 mm wafers in order to maximize their size and thus to reduce the relative contribution of the support structure. The forward part has slanted sensors of trapezoidal shape to improve the measurement precision and to minimize the amount of material as seen by particles from the vertex. Fast-shaping front-end amplifiers will be used in conjunction with an online hit time reconstruction algorithm in order to reduce the occupancy to the level of a few percent at most. A novel “Origami” chip-on-sensor scheme is used to minimize both the distance between strips and amplifier (thus reducing the electronic noise) as well as the overall material budget. This report gives an overview on the status of the Belle II SVD and its components, including sensors, front-end detector ladders, mechanics, cooling and the readout electronics.

  16. Arbitrated quantum signature scheme using Bell states

    International Nuclear Information System (INIS)

    Li Qin; Chan, W. H.; Long Dongyang

    2009-01-01

    In an arbitrated quantum signature scheme, the signatory signs the message and the receiver verifies the signature's validity with the assistance of the arbitrator. We present an arbitrated quantum signature scheme using two-particle entangled Bell states similar to the previous scheme using three-particle entangled Greenberger-Horne-Zeilinger states [G. H. Zeng and C. H. Keitel, Phys. Rev. A 65, 042312 (2002)]. The proposed scheme can preserve the merits in the original scheme while providing a higher efficiency in transmission and reducing the complexity of implementation.

  17. Boron Isotope Fractionation in Bell Pepper

    OpenAIRE

    Geilert, Sonja; Vogl, Jochen; Rosner, Martin; Voerkelius, Susanne; Eichert, Thomas

    2015-01-01

    Various plant compartments of a single bell pepper plant were studied to verify the variability of boron isotope composition in plants and to identify possible intra-plant isotope fractionation. Boron mass fractions varied from 9.8 mg/kg in the fruits to 70.0 mg/kg in the leaves. Boron (B) isotope ratios reported as δ11B ranged from -11.0‰ to +16.0‰ (U ≤ 1.9‰, k=2) and showed a distinct trend to heavier δ11B values the higher the plant compartments were located in the plant. A fractionatio...

  18. Increased stroke risk in Bell's palsy patients without steroid treatment.

    Science.gov (United States)

    Lee, C-C; Su, Y-C; Chien, S-H; Ho, H-C; Hung, S-K; Lee, M-S; Chou, P; Chiu, B C-H; Huang, Y-S

    2013-04-01

    To investigate the risk of stroke development following a diagnosis of Bell's palsy in a nationwide follow-up study. Information on Bell's palsy and other factors relevant for stroke was obtained for 433218 eligible subjects without previous stroke who had ambulatory visit in 2004. Of those, 897 patients with Bell's palsy were identified. Over a median 2.9 years of follow-up, 4581 incident strokes were identified. We estimated hazard ratios (HR) and 95% confidence intervals [CI] with Cox proportional hazard models adjusting for age, sex, co-morbidities, and important risk factors. Standardized incidence ratio of stroke amongst patients with Bell's palsy was analyzed. Compared with non-Bell's palsy patients, patients with Bell's palsy had a 2.02-times (95% CI, 1.42-2.86) higher risk of stroke. The adjusted HR of developing stroke for patients with Bell's palsy treated with and without systemic steroid were 1.67 (95% CI, 0.69-4) and 2.10 (95%, 1.40-3.07), respectively. Patients with Bell's palsy carry a higher risk of stroke than the general population. Our data suggest that these patients might benefit from a more intensive stroke prevention therapy and regular follow-up after initial diagnosis. © 2012 The Author(s) European Journal of Neurology © 2012 EFNS.

  19. Eugenics Past and Present: Remembering Buck v. Bell.

    Science.gov (United States)

    Berson, Michael J.; Cruz, Barbara

    2001-01-01

    Provides background information about the eugenics movement. Focuses on eugenics in the United States detailing the case, Buck v. Bell, and eugenics in Germany. Explores the present eugenic movement, focusing on "The Bell Curve," China's one child policy, and the use of eugenic sterilizations in the United States and Canada. Includes…

  20. Quantification of the gene expression of bell peppers ( Capsicum ...

    African Journals Online (AJOL)

    Fruits can be divided into two groups according to the regulatory mechanisms underlying their ripening process. The two ripening processes are climacteric and non-climacteric process; bell peppers are part of the non-climacteric plant groups. Bell peppers are members of the Solanacaea family. The Solanacaea family is ...

  1. 77 FR 42421 - Airworthiness Directives; Bell Helicopter Textron Canada Helicopters

    Science.gov (United States)

    2012-07-19

    ... Textron Canada Helicopters AGENCY: Federal Aviation Administration (FAA), Department of Transportation... (AD) superseding an existing airworthiness directive for Bell Helicopter Textron Canada (Bell) Model... through Friday, except Federal holidays. Examining The AD Docket You may examine the AD docket on the...

  2. 77 FR 18970 - Airworthiness Directives; Bell Helicopter Textron Canada Helicopters

    Science.gov (United States)

    2012-03-29

    ... Directives; Bell Helicopter Textron Canada Helicopters AGENCY: Federal Aviation Administration (FAA), DOT... (AD) for the Bell Helicopter Textron Canada Limited (BHTC) Model 407 helicopters. This proposed AD is... through Friday, except Federal holidays. Examining the AD Docket: You may examine the AD docket on the...

  3. First experimental test of Bell inequalities performed using a non ...

    Indian Academy of Sciences (India)

    This experiment is the first test of Bell inequalities using a non-maximally entangled state and thus represents an important step in the direction of eliminating the detection loophole. Keywords. Bell inequalities; non-locality; EPR. PACS No. 03.65.Bz. The idea that quantum mechanics (QM) could be an incomplete theory, ...

  4. Reconciling local realism and quantum physics: a critique to Bell

    International Nuclear Information System (INIS)

    Claudio Garola.

    1994-01-01

    A Metatheoretical Generalized Principle (MGP) is stated that formalizes an operational non-standard way of looking at the laws of physics. In Quantum Physics MGP leads to the invalidation of Bell's Inequality without renouncing to a minimal form of realism or to locality. Therefore the violation of Bell's Inequality predicted by Quantum Physics does not appear paradoxial if MGP is accepted

  5. Violation of Bell's inequality in neutral kaons system

    Indian Academy of Sciences (India)

    Lett. 83, 1 (1999)) that claimed such a test to be possible. Keywords. Entangled neutral kaons; Bell's inequalities; regenerators. PACS No. 03.65.Ud. Bell's inequality (BI) represents the fact that if one assumes local realism (LR) then the correlation between spatially separated constituents of a bipartite system is bound by 2,.

  6. Exponential operators, generalized polynomials and evolution problems

    International Nuclear Information System (INIS)

    Dattoli, G.; Mancho, A.M.; Quattromini, M.; Torre, A.

    2001-01-01

    The operator (d/dx) χ d/dx plays a central role in the theory of operational calculus. Its exponential form is crucial in problems relevant to solutions of Fokker-Planck and Schroedinger equations. We explore the formal properties of the evolution operators associated to (d/dx) χ d/dx, discuss its link to special forms of Laguerre polynomials and Laguerre-based functions. The obtained results are finally applied to specific problems concerning the solution of Fokker-Planck equations relevant to the beam lifetime in storage rings

  7. Polynomial solutions of the Monge-Ampère equation

    Energy Technology Data Exchange (ETDEWEB)

    Aminov, Yu A [B.Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, Khar' kov (Ukraine)

    2014-11-30

    The question of the existence of polynomial solutions to the Monge-Ampère equation z{sub xx}z{sub yy}−z{sub xy}{sup 2}=f(x,y) is considered in the case when f(x,y) is a polynomial. It is proved that if f is a polynomial of the second degree, which is positive for all values of its arguments and has a positive squared part, then no polynomial solution exists. On the other hand, a solution which is not polynomial but is analytic in the whole of the x, y-plane is produced. Necessary and sufficient conditions for the existence of polynomial solutions of degree up to 4 are found and methods for the construction of such solutions are indicated. An approximation theorem is proved. Bibliography: 10 titles.

  8. Least squares orthogonal polynomial approximation in several independent variables

    International Nuclear Information System (INIS)

    Caprari, R.S.

    1992-06-01

    This paper begins with an exposition of a systematic technique for generating orthonormal polynomials in two independent variables by application of the Gram-Schmidt orthogonalization procedure of linear algebra. It is then demonstrated how a linear least squares approximation for experimental data or an arbitrary function can be generated from these polynomials. The least squares coefficients are computed without recourse to matrix arithmetic, which ensures both numerical stability and simplicity of implementation as a self contained numerical algorithm. The Gram-Schmidt procedure is then utilised to generate a complete set of orthogonal polynomials of fourth degree. A theory for the transformation of the polynomial representation from an arbitrary basis into the familiar sum of products form is presented, together with a specific implementation for fourth degree polynomials. Finally, the computational integrity of this algorithm is verified by reconstructing arbitrary fourth degree polynomials from their values at randomly chosen points in their domain. 13 refs., 1 tab

  9. Explicitly integrable polynomial Hamiltonians and evaluation of Lie transformations

    International Nuclear Information System (INIS)

    Shi, J.; Yan, Y.T.

    1993-01-01

    We have found that any homogeneous polynomial can be written as a sum of integrable polynomials of the same degree, with which each associated polynomial Hamiltonian is integrable, and the associated Lie transformation can be evaluated exactly. An integrable polynomial factorization has thus been developed to convert a sympletic map in the form of a Dragt-Finn factorization into a product of exactly evaluable Lie transformations associated with integrable polynomials. Having a small number of factorization bases of integrable polynomials enables one to consider a factorization with the use of high-order symplectic integrators so that a symplectic map can always be evaluated with the desired accuracy. The results are significant for studying the long-term stability of beams in accelerators

  10. Comparative assessment of freeform polynomials as optical surface descriptions.

    Science.gov (United States)

    Kaya, Ilhan; Thompson, Kevin P; Rolland, Jannick P

    2012-09-24

    Slow-servo single-point diamond turning as well as advances in computer controlled small lap polishing enables the fabrication of freeform optics, or more specifically, optical surfaces for imaging applications that are not rotationally symmetric. Various forms of polynomials for describing freeform optical surfaces exist in optical design and to support fabrication. A popular method is to add orthogonal polynomials onto a conic section. In this paper, recently introduced gradient-orthogonal polynomials are investigated in a comparative manner with the widely known Zernike polynomials. In order to achieve numerical robustness when higher-order polynomials are required to describe freeform surfaces, recurrence relations are a key enabler. Results in this paper establish the equivalence of both polynomial sets in accurately describing freeform surfaces under stringent conditions. Quantifying the accuracy of these two freeform surface descriptions is a critical step in the future application of these tools in both advanced optical system design and optical fabrication.

  11. Polynomials for torus links from Chern-Simons gauge theories

    International Nuclear Information System (INIS)

    Isidro, J.M.; Labastida, J.M.F.; Ramallo, A.V.

    1993-01-01

    Invariant polynomials for torus links are obtained in the framework of the Chern-Simons topological gauge theory. The polynomials are computed as vacuum expectation values on the three-sphere of Wilson line operators representing the Verlinde algebra of the corresponding rational conformal field theory. In the case of the SU(2) gauge theory our results provide explicit expressions for the Jones polynomial as well as for the polynomials associated to the N-state (N>2) vertex models (Akutsu-Wadati polynomials). By means of the Chern-Simons coset construction, the minimal unitary models are analyzed, showing that the corresponding link invariants factorize into two SU(2) polynomials. A method to obtain skein rules from the Chern-Simons knot operators is developed. This procedure yields the eigenvalues of the braiding matrix of the corresponding conformal field theory. (orig.)

  12. Computational Fluid Dynamics Simulation of Dual Bell Nozzle Film Cooling

    Science.gov (United States)

    Braman, Kalen; Garcia, Christian; Ruf, Joseph; Bui, Trong

    2015-01-01

    Marshall Space Flight Center (MSFC) and Armstrong Flight Research Center (AFRC) are working together to advance the technology readiness level (TRL) of the dual bell nozzle concept. Dual bell nozzles are a form of altitude compensating nozzle that consists of two connecting bell contours. At low altitude the nozzle flows fully in the first, relatively lower area ratio, nozzle. The nozzle flow separates from the wall at the inflection point which joins the two bell contours. This relatively low expansion results in higher nozzle efficiency during the low altitude portion of the launch. As ambient pressure decreases with increasing altitude, the nozzle flow will expand to fill the relatively large area ratio second nozzle. The larger area ratio of the second bell enables higher Isp during the high altitude and vacuum portions of the launch. Despite a long history of theoretical consideration and promise towards improving rocket performance, dual bell nozzles have yet to be developed for practical use and have seen only limited testing. One barrier to use of dual bell nozzles is the lack of control over the nozzle flow transition from the first bell to the second bell during operation. A method that this team is pursuing to enhance the controllability of the nozzle flow transition is manipulation of the film coolant that is injected near the inflection between the two bell contours. Computational fluid dynamics (CFD) analysis is being run to assess the degree of control over nozzle flow transition generated via manipulation of the film injection. A cold flow dual bell nozzle, without film coolant, was tested over a range of simulated altitudes in 2004 in MSFC's nozzle test facility. Both NASA centers have performed a series of simulations of that dual bell to validate their computational models. Those CFD results are compared to the experimental results within this paper. MSFC then proceeded to add film injection to the CFD grid of the dual bell nozzle. A series of

  13. John Stewart Bell and twentieth century physics vision and integrity

    CERN Document Server

    Whitaker, Andrew

    2016-01-01

    John Stewart Bell (1928-1990) was one of the most important figures in twentieth-century physics, famous for his work on the fundamental aspects of the century's most important theory, quantum mechanics. While the debate over quantum theory between the supremely famous physicists, Albert Einstein and Niels Bohr, appeared to have become sterile in the 1930s, Bell was able to revive it and to make crucial advances - Bell's Theorem or Bell's Inequalities. He was able to demonstrate a contradiction between quantum theory and essential elements of pre-quantum theory - locality and causality. The book gives a non-mathematical account of Bell's relatively impoverished upbringing in Belfast and his education. It describes his major contributions to quantum theory, but also his important work in the physics of accelerators, and nuclear and elementary particle physics.

  14. Conditions Database for the Belle II Experiment

    Science.gov (United States)

    Wood, L.; Elsethagen, T.; Schram, M.; Stephan, E.

    2017-10-01

    The Belle II experiment at KEK is preparing for first collisions in 2017. Processing the large amounts of data that will be produced will require conditions data to be readily available to systems worldwide in a fast and efficient manner that is straightforward for both the user and maintainer. The Belle II conditions database was designed with a straightforward goal: make it as easily maintainable as possible. To this end, HEP-specific software tools were avoided as much as possible and industry standard tools used instead. HTTP REST services were selected as the application interface, which provide a high-level interface to users through the use of standard libraries such as curl. The application interface itself is written in Java and runs in an embedded Payara-Micro Java EE application server. Scalability at the application interface is provided by use of Hazelcast, an open source In-Memory Data Grid (IMDG) providing distributed in-memory computing and supporting the creation and clustering of new application interface instances as demand increases. The IMDG provides fast and efficient access to conditions data via in-memory caching.

  15. A loophole-free Bell's inequality experiment

    Science.gov (United States)

    Kwiat, Paul G.; Steinberg, Aephraim M.; Chiao, Raymond Y.; Eberhard, Philippe H.

    1994-01-01

    The proof of Nature's nonlocality through Bell-type experiments is a topic of longstanding interest. Nevertheless, no experiments performed thus far have avoided the so-called 'detection loophole,' arising from low detector efficiencies and angular-correlation difficulties. In fact, most, if not all, of the systems employed to date can never close this loophole, even with perfect detectors. In addition, another loophole involving the non-rapid, non-random switching of various parameter settings exists in all past experiments. We discuss a proposal for a potentially loophole-free Bell's inequality experiment. The source of the EPR-correlated pairs consists of two simultaneously-pumped type-2 phase-matched nonlinear crystals and a polarizing beam splitter. The feasibility of such a scheme with current detector technology seems high, and will be discussed. We also present a single-crystal version, motivated by other work presented at this conference. In a separate experiment, we have measured the absolute detection efficiency and time response of four single-photon detectors. The highest observed efficiencies were 70.7 plus or minus 1.9 percent (at 633 nm, with a device from Rockwell International) and 76.4 plus or minus 2.3 percent (at 702 nm, with an EG&G counting module). Possible efficiencies as high as 90 percent were implied. The EG&G devices displayed sub-nanosecond time resolution.

  16. Software Quality Control at Belle II

    Science.gov (United States)

    Ritter, M.; Kuhr, T.; Hauth, T.; Gebard, T.; Kristof, M.; Pulvermacher, C.; Belle Software Group, II

    2017-10-01

    Over the last seven years the software stack of the next generation B factory experiment Belle II has grown to over one million lines of C++ and Python code, counting only the part included in offline software releases. There are several thousand commits to the central repository by about 100 individual developers per year. To keep a coherent software stack of high quality that it can be sustained and used efficiently for data acquisition, simulation, reconstruction, and analysis over the lifetime of the Belle II experiment is a challenge. A set of tools is employed to monitor the quality of the software and provide fast feedback to the developers. They are integrated in a machinery that is controlled by a buildbot master and automates the quality checks. The tools include different compilers, cppcheck, the clang static analyzer, valgrind memcheck, doxygen, a geometry overlap checker, a check for missing or extra library links, unit tests, steering file level tests, a sophisticated high-level validation suite, and an issue tracker. The technological development infrastructure is complemented by organizational means to coordinate the development.

  17. Note on Generating Orthogonal Polynomials and Their Application in Solving Complicated Polynomial Regression Tasks

    Czech Academy of Sciences Publication Activity Database

    Knížek, J.; Tichý, Petr; Beránek, L.; Šindelář, Jan; Vojtěšek, B.; Bouchal, P.; Nenutil, R.; Dedík, O.

    2010-01-01

    Roč. 7, č. 10 (2010), s. 48-60 ISSN 0974-5718 Grant - others:GA MZd(CZ) NS9812; GA ČR(CZ) GAP304/10/0868 Institutional research plan: CEZ:AV0Z10300504; CEZ:AV0Z10750506 Keywords : polynomial regression * orthogonalization * numerical methods * markers * biomarkers Subject RIV: BA - General Mathematics

  18. Open Problems Related to the Hurwitz Stability of Polynomials Segments

    Directory of Open Access Journals (Sweden)

    Baltazar Aguirre-Hernández

    2018-01-01

    Full Text Available In the framework of robust stability analysis of linear systems, the development of techniques and methods that help to obtain necessary and sufficient conditions to determine stability of convex combinations of polynomials is paramount. In this paper, knowing that Hurwitz polynomials set is not a convex set, a brief overview of some results and open problems concerning the stability of the convex combinations of Hurwitz polynomials is then provided.

  19. Recurrence relations and weight functions for approximation by orthonormal polynomials

    International Nuclear Information System (INIS)

    Bisoi, A.K.

    1989-12-01

    The popular three-term recurrence relation is found to be a numerically unstable algorithm for generation of higher order orthogonal polynomials. For stability, a k-term recurrence relation for generating the k th order polynomial is suggested. Instead of assigning equal weight to data points with unspecified errors, the use of the Jacobian weight function is suggested for generating the orthogonal polynomials to effect a closer representation. (author). 6 refs, 1 tab

  20. Vector polynomials for direct analysis of circular wavefront slope data.

    Science.gov (United States)

    Mahajan, Virendra N; Acosta, Eva

    2017-10-01

    In the aberration analysis of a circular wavefront, Zernike circle polynomials are used to obtain its wave aberration coefficients. To obtain these coefficients from the wavefront slope data, we need vector functions that are orthogonal to the gradients of the Zernike polynomials, and are irrotational so as to propagate minimum uncorrelated random noise from the data to the coefficients. In this paper, we derive such vector functions, which happen to be polynomials.

  1. Root and Critical Point Behaviors of Certain Sums of Polynomials

    Indian Academy of Sciences (India)

    13

    There is an extensive literature concerning roots of sums of polynomials. Many papers and books([5], [6],. [7]) have written about these polynomials. Perhaps the most immediate question of sums of polynomials,. A + B = C, is “given bounds for the roots of A and B, what bounds can be given for the roots of C?” By. Fell [3], if ...

  2. Applications of polynomial optimization in financial risk investment

    Science.gov (United States)

    Zeng, Meilan; Fu, Hongwei

    2017-09-01

    Recently, polynomial optimization has many important applications in optimization, financial economics and eigenvalues of tensor, etc. This paper studies the applications of polynomial optimization in financial risk investment. We consider the standard mean-variance risk measurement model and the mean-variance risk measurement model with transaction costs. We use Lasserre's hierarchy of semidefinite programming (SDP) relaxations to solve the specific cases. The results show that polynomial optimization is effective for some financial optimization problems.

  3. 76 FR 27958 - Airworthiness Directives; Bell Helicopter Textron Canada (Bell) Model 206A, 206B, and 206B3...

    Science.gov (United States)

    2011-05-13

    ... Textron Canada (Bell) Model 206A, 206B, and 206B3 Helicopters AGENCY: Federal Aviation Administration (FAA...., Washington, DC 20590, between 9 a.m. and 5 p.m., Monday through Friday, except Federal holidays. You may get the service information identified in this proposed AD from Bell Helicopter Textron Canada Limited, 12...

  4. An Analytic Formula for the A_2 Jack Polynomials

    Directory of Open Access Journals (Sweden)

    Vladimir V. Mangazeev

    2007-01-01

    Full Text Available In this letter I shall review my joint results with Vadim Kuznetsov and Evgeny Sklyanin [Indag. Math. 14 (2003, 451-482] on separation of variables (SoV for the $A_n$ Jack polynomials. This approach originated from the work [RIMS Kokyuroku 919 (1995, 27-34] where the integral representations for the $A_2$ Jack polynomials was derived. Using special polynomial bases I shall obtain a more explicit expression for the $A_2$ Jack polynomials in terms of generalised hypergeometric functions.

  5. Tabulating knot polynomials for arborescent knots

    International Nuclear Information System (INIS)

    Mironov, A; Morozov, A; Morozov, A; Sleptsov, A; Ramadevi, P; Singh, Vivek Kumar

    2017-01-01

    Arborescent knots are those which can be represented in terms of double fat graphs or equivalently as tree Feynman diagrams. This is the class of knots for which the present knowledge is sufficient for lifting topological description to the level of effective analytical formulas. The paper describes the origin and structure of the new tables of colored knot polynomials, which will be posted at the dedicated site (http://knotebook.org). Even if formal expressions are known in terms of modular transformation matrices, the computation in finite time requires additional ideas. We use the ‘family’ approach, suggested in Mironov and Morozov (2015 Nucl. Phys . B 899 395–413), and apply it to arborescent knots in the Rolfsen table by developing a Feynman diagram technique, associated with an auxiliary matrix model field theory. Gauge invariance in this theory helps to provide meaning to Racah matrices in the case of non-trivial multiplicities and explains the need for peculiar sign prescriptions in the calculation of [21]-colored HOMFLY-PT polynomials. (paper)

  6. Positive trigonometric polynomials and signal processing applications

    CERN Document Server

    Dumitrescu, Bogdan

    2017-01-01

    This revised edition is made up of two parts: theory and applications. Though many of the fundamental results are still valid and used, new and revised material is woven throughout the text. As with the original book, the theory of sum-of-squares trigonometric polynomials is presented unitarily based on the concept of Gram matrix (extended to Gram pair or Gram set). The programming environment has also evolved, and the books examples are changed accordingly. The applications section is organized as a collection of related problems that use systematically the theoretical results. All the problems are brought to a semi-definite programming form, ready to be solved with algorithms freely available, like those from the libraries SeDuMi, CVX and Pos3Poly. A new chapter discusses applications in super-resolution theory, where Bounded Real Lemma for trigonometric polynomials is an important tool. This revision is written to be more appealing and easier to use for new readers. < Features updated information on LMI...

  7. Tabulating knot polynomials for arborescent knots

    Science.gov (United States)

    Mironov, A.; Morozov, A.; Morozov, A.; Ramadevi, P.; Singh, Vivek Kumar; Sleptsov, A.

    2017-02-01

    Arborescent knots are those which can be represented in terms of double fat graphs or equivalently as tree Feynman diagrams. This is the class of knots for which the present knowledge is sufficient for lifting topological description to the level of effective analytical formulas. The paper describes the origin and structure of the new tables of colored knot polynomials, which will be posted at the dedicated site (http://knotebook.org). Even if formal expressions are known in terms of modular transformation matrices, the computation in finite time requires additional ideas. We use the ‘family’ approach, suggested in Mironov and Morozov (2015 Nucl. Phys. B 899 395-413), and apply it to arborescent knots in the Rolfsen table by developing a Feynman diagram technique, associated with an auxiliary matrix model field theory. Gauge invariance in this theory helps to provide meaning to Racah matrices in the case of non-trivial multiplicities and explains the need for peculiar sign prescriptions in the calculation of [21]-colored HOMFLY-PT polynomials.

  8. Simulation of aspheric tolerance with polynomial fitting

    Science.gov (United States)

    Li, Jing; Cen, Zhaofeng; Li, Xiaotong

    2018-01-01

    The shape of the aspheric lens changes caused by machining errors, resulting in a change in the optical transfer function, which affects the image quality. At present, there is no universally recognized tolerance criterion standard for aspheric surface. To study the influence of aspheric tolerances on the optical transfer function, the tolerances of polynomial fitting are allocated on the aspheric surface, and the imaging simulation is carried out by optical imaging software. Analysis is based on a set of aspheric imaging system. The error is generated in the range of a certain PV value, and expressed as a form of Zernike polynomial, which is added to the aspheric surface as a tolerance term. Through optical software analysis, the MTF of optical system can be obtained and used as the main evaluation index. Evaluate whether the effect of the added error on the MTF of the system meets the requirements of the current PV value. Change the PV value and repeat the operation until the acceptable maximum allowable PV value is obtained. According to the actual processing technology, consider the error of various shapes, such as M type, W type, random type error. The new method will provide a certain development for the actual free surface processing technology the reference value.

  9. Bell's Palsy in Children (BellPIC): protocol for a multicentre, placebo-controlled randomized trial.

    Science.gov (United States)

    Babl, Franz E; Mackay, Mark T; Borland, Meredith L; Herd, David W; Kochar, Amit; Hort, Jason; Rao, Arjun; Cheek, John A; Furyk, Jeremy; Barrow, Lisa; George, Shane; Zhang, Michael; Gardiner, Kaya; Lee, Katherine J; Davidson, Andrew; Berkowitz, Robert; Sullivan, Frank; Porrello, Emily; Dalziel, Kim Marie; Anderson, Vicki; Oakley, Ed; Hopper, Sandy; Williams, Fiona; Wilson, Catherine; Williams, Amanda; Dalziel, Stuart R

    2017-02-13

    Bell's palsy or acute idiopathic lower motor neurone facial paralysis is characterized by sudden onset paralysis or weakness of the muscles to one side of the face controlled by the facial nerve. While there is high level evidence in adults demonstrating an improvement in the rate of complete recovery of facial nerve function when treated with steroids compared with placebo, similar high level studies on the use of steroids in Bell's palsy in children are not available. The aim of this study is to assess the utility of steroids in Bell's palsy in children in a randomised placebo-controlled trial. We are conducting a randomised, triple-blinded, placebo controlled trial of the use of prednisolone to improve recovery from Bell's palsy at 1 month. Study sites are 10 hospitals within the Australian and New Zealand PREDICT (Paediatric Research in Emergency Departments International Collaborative) research network. 540 participants will be enrolled. To be eligible patients need to be aged 6 months to Bell's palsy to one of the participating hospital emergency departments. Patients will be excluded in case of current use of or contraindications to steroids or if there is an alternative diagnosis. Participants will receive either prednisolone 1 mg/kg/day to a maximum of 50 mg/day or taste matched placebo for 10 days. The primary outcome is complete recovery by House-Brackmann scale at 1 month. Secondary outcomes include assessment of recovery using the Sunnybrook scale, the emotional and functional wellbeing of the participants using the Pediatric Quality of Life Inventory and Child Health Utility 9D Scale, pain using Faces Pain Scale Revised or visual analogue scales, synkinesis using a synkinesis assessment questionnaire and health utilisation costs at 1, 3 and 6 months. Participants will be tracked to 12 months if not recovered earlier. Data analysis will be by intention to treat with primary outcome presented as differences in proportions and an odds ratio

  10. Comparative assessment of orthogonal polynomials for wavefront reconstruction over the square aperture.

    Science.gov (United States)

    Ye, Jingfei; Gao, Zhishan; Wang, Shuai; Cheng, Jinlong; Wang, Wei; Sun, Wenqing

    2014-10-01

    Four orthogonal polynomials for reconstructing a wavefront over a square aperture based on the modal method are currently available, namely, the 2D Chebyshev polynomials, 2D Legendre polynomials, Zernike square polynomials and Numerical polynomials. They are all orthogonal over the full unit square domain. 2D Chebyshev polynomials are defined by the product of Chebyshev polynomials in x and y variables, as are 2D Legendre polynomials. Zernike square polynomials are derived by the Gram-Schmidt orthogonalization process, where the integration region across the full unit square is circumscribed outside the unit circle. Numerical polynomials are obtained by numerical calculation. The presented study is to compare these four orthogonal polynomials by theoretical analysis and numerical experiments from the aspects of reconstruction accuracy, remaining errors, and robustness. Results show that the Numerical orthogonal polynomial is superior to the other three polynomials because of its high accuracy and robustness even in the case of a wavefront with incomplete data.

  11. Relations between zeros of special polynomials associated with the Painleve equations

    International Nuclear Information System (INIS)

    Kudryashov, Nikolai A.; Demina, Maria V.

    2007-01-01

    A method for finding relations of roots of polynomials is presented. Our approach allows us to get a number of relations between the zeros of the classical polynomials as well as the roots of special polynomials associated with rational solutions of the Painleve equations. We apply the method to obtain the relations for the zeros of several polynomials. These are: the Hermite polynomials, the Laguerre polynomials, the Yablonskii-Vorob'ev polynomials, the generalized Okamoto polynomials, and the generalized Hermite polynomials. All the relations found can be considered as analogues of generalized Stieltjes relations

  12. Interacting binary stars

    CERN Document Server

    Sahade, Jorge; Ter Haar, D

    1978-01-01

    Interacting Binary Stars deals with the development, ideas, and problems in the study of interacting binary stars. The book consolidates the information that is scattered over many publications and papers and gives an account of important discoveries with relevant historical background. Chapters are devoted to the presentation and discussion of the different facets of the field, such as historical account of the development in the field of study of binary stars; the Roche equipotential surfaces; methods and techniques in space astronomy; and enumeration of binary star systems that are studied

  13. Binary Masking & Speech Intelligibility

    DEFF Research Database (Denmark)

    Boldt, Jesper

    The purpose of this thesis is to examine how binary masking can be used to increase intelligibility in situations where hearing impaired listeners have difficulties understanding what is being said. The major part of the experiments carried out in this thesis can be categorized as either experime......The purpose of this thesis is to examine how binary masking can be used to increase intelligibility in situations where hearing impaired listeners have difficulties understanding what is being said. The major part of the experiments carried out in this thesis can be categorized as either...... experiments under ideal conditions or as experiments under more realistic conditions useful for real-life applications such as hearing aids. In the experiments under ideal conditions, the previously defined ideal binary mask is evaluated using hearing impaired listeners, and a novel binary mask -- the target...... binary mask -- is introduced. The target binary mask shows the same substantial increase in intelligibility as the ideal binary mask and is proposed as a new reference for binary masking. In the category of real-life applications, two new methods are proposed: a method for estimation of the ideal binary...

  14. Comparing parallel square root method with extended Bell\\'s class ...

    African Journals Online (AJOL)

    ... for simultaneous determination of zeros of polynomial. We synchronize our numerical result as a comparison with result obtained from the q-step parallel square root iteration formula. A significant conclusion is drawn from the results of these two methods. Journal of the Nigerian Association of Mathematical Physics Vol.

  15. Multiparty Quantum Direct Secret Sharing of Classical Information with Bell States and Bell Measurements

    Science.gov (United States)

    Song, Yun; Li, Yongming; Wang, Wenhua

    2018-02-01

    This paper proposed a new and efficient multiparty quantum direct secret sharing (QDSS) by using swapping quantum entanglement of Bell states. In the proposed scheme, the quantum correlation between the possible measurement results of the members (except dealer) and the original local unitary operation encoded by the dealer was presented. All agents only need to perform Bell measurements to share dealer's secret by recovering dealer's operation without performing any unitary operation. Our scheme has several advantages. The dealer is not required to retain any photons, and can further share a predetermined key instead of a random key to the agents. It has high capacity as two bits of secret messages can be transmitted by an EPR pair and the intrinsic efficiency approaches 100%, because no classical bit needs to be transmitted except those for detection. Without inserting any checking sets for detecting the eavesdropping, the scheme can resist not only the existing attacks, but also the cheating attack from the dishonest agent.

  16. The ladder operator normal ordering problem for quantum confined systems and the generalization of the Stirling and Bell numbers

    International Nuclear Information System (INIS)

    Aleixo, A N F; Balantekin, A B

    2010-01-01

    We solve the normal ordering problem for the ladder operators B-hat + and B-hat - for strings in the form (B-hat + r B-hat - s ) n for supersymmetric and shape-invariant potential systems, with r, s and n positive integers. We provide exact and explicit expressions for their normal form N{(B-hat + r B-hat - s ) n }, where N{...} all B-hat - are at the right side, and find that the solution involves an expansion coefficients sequence which, for r, s > 1, corresponds to the generalization, for any shape-invariant potential system, of the classical Stirling and Bell numbers. We show that these numbers are obtained for families of polynomials generated with parameters related to the forms of the supersymmetric partner potentials. We apply the general formalism to Poeschl-Teller, Morse, Scarf and self-similar potential systems.

  17. Bell's palsy before Bell: Evert Jan Thomassen à Thuessink and idiopathic peripheral facial paralysis.

    Science.gov (United States)

    van de Graaf, R C; IJpma, F F A; Nicolai, J-P A; Werker, P M N

    2009-11-01

    Bell's palsy is the eponym for idiopathic peripheral facial paralysis. It is named after Sir Charles Bell (1774-1842), who, in the first half of the nineteenth century, discovered the function of the facial nerve and attracted the attention of the medical world to facial paralysis. Our knowledge of this condition before Bell's landmark publications is very limited and is based on just a few documents. In 1804 and 1805, Evert Jan Thomassen à Thuessink (1762-1832) published what appears to be the first known extensive study on idiopathic peripheral facial paralysis. His description of this condition was quite accurate. He located several other early descriptions and concluded from this literature that, previously, the condition had usually been confused with other afflictions (such as 'spasmus cynicus', central facial paralysis and trigeminal neuralgia). According to Thomassen à Thuessink, idiopathic peripheral facial paralysis and trigeminal neuralgia were related, being different expressions of the same condition. Thomassen à Thuessink believed that idiopathic peripheral facial paralysis was caused by 'rheumatism' or exposure to cold. Many aetiological theories have since been proposed. Despite this, the cold hypothesis persists even today.

  18. Belle DAQ system upgrade at 2001

    CERN Document Server

    Suzuki, S Y; Kim, H W; Kim, H J; Kim, H O; Nakao, M; Won, E; Yamauchi, M

    2002-01-01

    We renewed the data acquisition system for the Belle experiment. Previous data acquisition system, which has been used since December 1998, did not have level 2 trigger facility. To improve the data reduction factor and total throughput, we replaced event builder, online computer farm and the storage system. The event builder and online computer farm are unified into one system. This event building farm uses commodity hardware and newly appended level 2 trigger functionality. This data acquisition system started its operation since last autumn and is very stable. We took 36 fb sup - sup 1 with new DAQ system, it had already overtaken 30 fb sup - sup 1 that is total amount of previous DAQ system.

  19. Data acquisition system for the Belle experiment

    Science.gov (United States)

    Nakao, M.; Yamauchi, M.; Suzuki, S. Y.; Itoh, R.; Fujii, H.

    2000-04-01

    We built a data acquisition system for the Belle experiment at the KEK B-factory. The system is designed to record the signals from the detectors at 500 Hz trigger rate with a less than 10% dead time fraction. A typical event size is 30 kbyte, which corresponds to a data transfer rate of 15 Mbyte/s. Main components are two kinds of detector readout systems, an event builder, an online computer farm and a data storage system. The system has been reliably in operation at the design performance for a half year. We have completed cosmic-ray data taking for 2.5 months and have started physics data taking on Jun. 1, 1999.

  20. Recent results on XYZ States at Belle

    Science.gov (United States)

    Shen, Chengping

    2016-05-01

    Exotic hadronic states beyond the conventional quark model (called charmoniumlike/bottomoniumlike states or XYZ particles) have been sought and many candidates were proposed including glueballs, hybrids, multi-quark states, hadron molecules, etc. Dramatic progress has been made in the study of such exotic hadrons after the running of the B-factories. In this report, I present the most recent results on the XYZ states at Belle, including (1) X states: the first observation of B0 → X(3872)K+π- and evidence for B+ → X(3872)K0 π+; search for the Xb state; (2) Y states: the updated results for the Y(4360) and Y(4660) and cross section measurement of e+e- → K+ K- J/ψ; (3) Z states: the evidence for the Zc(4050)± → π±ψ(2S); search for the Zcs in e+e- → K+ K- J/ψ.

  1. Quantifying Bell nonlocality with the trace distance

    Science.gov (United States)

    Brito, S. G. A.; Amaral, B.; Chaves, R.

    2018-02-01

    Measurements performed on distant parts of an entangled quantum state can generate correlations incompatible with classical theories respecting the assumption of local causality. This is the phenomenon known as quantum nonlocality that, apart from its fundamental role, can also be put to practical use in applications such as cryptography and distributed computing. Clearly, developing ways of quantifying nonlocality is an important primitive in this scenario. Here, we propose to quantify the nonlocality of a given probability distribution via its trace distance to the set of classical correlations. We show that this measure is a monotone under the free operations of a resource theory and, furthermore, that it can be computed efficiently with a linear program. We put our framework to use in a variety of relevant Bell scenarios also comparing the trace distance to other standard measures in the literature.

  2. On Continued Fraction Expansion of Real Roots of Polynomial Systems

    DEFF Research Database (Denmark)

    Mantzaflaris, Angelos; Mourrain, Bernard; Tsigaridas, Elias

    2011-01-01

    We elaborate on a correspondence between the coefficients of a multivariate polynomial represented in the Bernstein basis and in a tensor-monomial basis, which leads to homography representations of polynomial functions that use only integer arithmetic (in contrast to the Bernstein basis) and are...

  3. On polynomial selection for the general number field sieve

    Science.gov (United States)

    Kleinjung, Thorsten

    2006-12-01

    The general number field sieve (GNFS) is the asymptotically fastest algorithm for factoring large integers. Its runtime depends on a good choice of a polynomial pair. In this article we present an improvement of the polynomial selection method of Montgomery and Murphy which has been used in recent GNFS records.

  4. Optimal Approximation of Biquartic Polynomials by Bicubic Splines

    Directory of Open Access Journals (Sweden)

    Kačala Viliam

    2018-01-01

    The goal of this paper is to resolve this problem. Unlike the spline curves, in the case of spline surfaces it is insufficient to suppose that the grid should be uniform and the spline derivatives computed from a biquartic polynomial. We show that the biquartic polynomial coefficients have to satisfy some additional constraints to achieve optimal approximation by bicubic splines.

  5. Classification of complex polynomial vector fields in one complex variable

    DEFF Research Database (Denmark)

    Branner, Bodil; Dias, Kealey

    2010-01-01

    This paper classifies the global structure of monic and centred one-variable complex polynomial vector fields. The classification is achieved by means of combinatorial and analytic data. More specifically, given a polynomial vector field, we construct a combinatorial invariant, describing the top...

  6. A Combinatorial Proof of a Result on Generalized Lucas Polynomials

    Directory of Open Access Journals (Sweden)

    Laugier Alexandre

    2016-09-01

    Full Text Available We give a combinatorial proof of an elementary property of generalized Lucas polynomials, inspired by [1]. These polynomials in s and t are defined by the recurrence relation 〈n〉 = s〈n-1〉+t〈n-2〉 for n ≥ 2. The initial values are 〈0〉 = 2; 〈1〉= s, respectively.

  7. Orthonormal polynomials for elliptical wavefronts with an arbitrary orientation.

    Science.gov (United States)

    Díaz, José A; Navarro, Rafael

    2014-04-01

    We generalize the analytical form of the orthonormal elliptical polynomials for any arbitrary aspect ratio to arbitrary orientation and give expression for them up to the 4th order. The utility of the polynomials is demonstrated by obtaining the expansion up to the 8th order in two examples of an off-axis wavefront exiting from an optical system with a vignetted pupil.

  8. Animating Nested Taylor Polynomials to Approximate a Function

    Science.gov (United States)

    Mazzone, Eric F.; Piper, Bruce R.

    2010-01-01

    The way that Taylor polynomials approximate functions can be demonstrated by moving the center point while keeping the degree fixed. These animations are particularly nice when the Taylor polynomials do not intersect and form a nested family. We prove a result that shows when this nesting occurs. The animations can be shown in class or…

  9. On peculiar properties of generating functions of some orthogonal polynomials

    International Nuclear Information System (INIS)

    Szabłowski, Paweł J

    2012-01-01

    We prove that for |x| ⩽ |t| ≥( t i )/(q) i h n+i ( x|q) =h n (x|t,q) Σ i≥0 (t i )/(q) i h i (x|q), where h n (x|q) and h n (x|t, q) are respectively the so-called q-Hermite and the big q-Hermite polynomials, and (q) n denotes the so-called q-Pochhammer symbol. We prove similar equalities involving big q-Hermite and Al-Salam–Chihara polynomials, and Al-Salam–Chihara and the so-called continuous dual q-Hahn polynomials. Moreover, we are able to relate in this way some other ‘ordinary’ orthogonal polynomials such as, e.g., Hermite, Chebyshev or Laguerre. These equalities give a new interpretation of the polynomials involved and moreover can give rise to a simple method of generating more and more general (i.e. involving more and more parameters) families of orthogonal polynomials. We pose some conjectures concerning Askey–Wilson polynomials and their possible generalizations. We prove that these conjectures are true for the cases q = 1 (classical case) and q = 0 (free case), thus paving the way to generalization of Askey–Wilson polynomials at least in these two cases. (paper)

  10. On an inequality concerning the polar derivative of a polynomial

    Indian Academy of Sciences (India)

    We also extend Zygmund's inequality to the polar derivative of a polynomial. Keywords. Zygmund's inequality; polar derivative; Lp-norm inequalities. 1. Introduction and statement of results. Let P (z) be a polynomial of degreen and let P (z) be its derivative. Then according to the famous result known as Bernstein's inequality ...

  11. Numerical Performances of Two Orthogonal Polynomials in the Tau ...

    African Journals Online (AJOL)

    In this work, efforts are made at comparing the numerical effectiveness of the two most accurate orthogonal polynomials; Chebyshev and Legendre polynomials. Although the two have different weight functions, but they most time give close results especially when they are considered in the same interval. This work has ...

  12. Mathematical Use Of Polynomials Of Different End Periods Of ...

    African Journals Online (AJOL)

    This paper focused on how polynomials of different end period of random numbers can be used in the application of encryption and decryption of a message. Eight steps were used in generating information on how polynomials of different end periods of random numbers in the application of encryption and decryption of a ...

  13. Generalized Freud's equation and level densities with polynomial

    Indian Academy of Sciences (India)

    Home; Journals; Pramana – Journal of Physics; Volume 81; Issue 2. Generalized Freud's equation and level densities with polynomial potential. Akshat Boobna Saugata Ghosh. Research Articles Volume 81 ... Keywords. Orthogonal polynomial; Freud's equation; Dyson–Mehta method; methods of resolvents; level density.

  14. Zeros and uniqueness of Q-difference polynomials of meromorphic ...

    Indian Academy of Sciences (India)

    In this paper, we investigate the value distribution of -difference polynomials of meromorphic function of finite logarithmic order, and study the zero distribution of difference-differential polynomials [ f n ( z ) f ( q z + c ) ] ( k ) and [ f n ( z ) ( f ( q z + c ) − f ( z ) ) ] ( k ) , where () is a transcendental function of zero order.

  15. A case presentation of bilateral simultaneous Bell's palsy.

    Science.gov (United States)

    Kilic, Rahmi; Ozdek, Ali; Felek, Sevim; Safak, M Asim; Samim, Erdal

    2003-01-01

    Bilateral simultaneous facial paralysis is an extremely rare clinical entity. Unlike the unilateral form, bilateral facial paralysis seldom falls into Bell's category. It is most often a special finding in a symptom complex of a systemic disease; many of them are potentially life-threatening, and therefore the condition warrants urgent medical intervention. Lyme disease, Guillian-Barre syndrome, Bell's palsy, leukemia, sarcoidosis, bacterial meningitis, syphilis, leprosy, Moebius syndrome, infectious mononucleosis, and skull fracture are the most common cause of bilateral facial paralysis. Here we present a 16-year-old patient with bilateral simultaneous Bell's palsy.

  16. Migrating the Belle II collaborative services and tools

    Science.gov (United States)

    Braun, N.; Dossett, D.; Dramburg, M.; Frost, O.; Gellrich, A.; Grygier, J.; Hauth, T.; Jahnke-Zumbusch, D.; Knittel, D.; Kuhr, T.; Levonian, S.; Moser, H.-G.; Li, L.; Nakao, N.; Prim, M.; Reest, P. v. d.; Schwenssen, F.; Urquijo, P.; Vennemann, B.

    2017-10-01

    The Belle II collaboration decided in 2016 to migrate its collaborative services and tools into the existing IT infrastructure at DESY. The goal was to reduce the maintenance effort for solutions operated by Belle II members as well as to deploy state-of-art technologies. In addition, some new services and tools were or will be introduced. Planning and migration work was carried out by small teams consisting of experts form Belle II and the involved IT divisions. The migration was successfully accomplished before the KEK computer centre replacement in August 2016.

  17. Official regulations and perceptual aspects of bell ringing

    Directory of Open Access Journals (Sweden)

    Kovačič Mojca

    2017-01-01

    Full Text Available Through the analytical approach of studying official and perception-related discourse on bell ringing I accentuate the complexity of aspects that the sound of church bell presents in contemporary society. I point out the misleading officially defined level of noise nuisance and reveal how, when and why bell ringing is perceived as a positive or negative part of the acoustic environment. The study argues for a holistic approach to the noise nuisance issues, still much underestimated in the official discourse, that co-create our everyday soundscape.

  18. Bell's palsy at high altitude -- an unsuspected finding.

    Science.gov (United States)

    Kumar, K V S Hari; Shijith, K P; Ahmad, F M H

    2016-01-01

    Bell's palsy is a common condition seen in clinical practice. The aetiology of this condition is not clearly defined and neuroimaging is essential to exclude intracranial causes of infra-nuclear facial palsy. We report a young soldier, who presented with Bell's palsy and neuroimaging revealed an unsuspected finding of multiple intracranial calcifications. Detailed evaluation revealed the additional diagnosis of vitamin D deficiency and secondary hyperparathyroidism due to lack of sun exposure at high altitude area. The health care practitioners, looking after the soldiers at high altitude areas should be aware of the measures to prevent vitamin D deficiency. Intracranial calcifications are uncommon in hyperparathyroidism and Bell's palsy.

  19. Reluctant genius Alexander Graham Bell and the passion for invention

    CERN Document Server

    Gray, Charlotte

    2011-01-01

    The popular image of Alexander Graham Bell is that of an elderly American patriarch, memorable only for his paunch, his Santa Claus beard, and the invention of the telephone. In this magisterial reassessment based on thorough new research, acclaimed biographer Charlotte Gray reveals Bell's wide-ranging passion for invention and delves into the private life that supported his genius. The child of a speech therapist and a deaf mother, and possessed of superbly acute hearing, Bell developed an early interest in sound. His understanding of how sound waves might relate to electrical waves enabled h

  20. Quantum communication complexity advantage implies violation of a Bell inequality

    Science.gov (United States)

    Buhrman, Harry; Czekaj, Łukasz; Grudka, Andrzej; Horodecki, Michał; Horodecki, Paweł; Markiewicz, Marcin; Speelman, Florian; Strelchuk, Sergii

    2016-01-01

    We obtain a general connection between a large quantum advantage in communication complexity and Bell nonlocality. We show that given any protocol offering a sufficiently large quantum advantage in communication complexity, there exists a way of obtaining measurement statistics that violate some Bell inequality. Our main tool is port-based teleportation. If the gap between quantum and classical communication complexity can grow arbitrarily large, the ratio of the quantum value to the classical value of the Bell quantity becomes unbounded with the increase in the number of inputs and outputs. PMID:26957600

  1. Improvement of AMGA Python Client Library for Belle II Experiment

    Science.gov (United States)

    Kwak, Jae-Hyuck; Park, Geunchul; Huh, Taesang; Hwang, Soonwook

    2015-12-01

    This paper describes the recent improvement of the AMGA (ARDA Metadata Grid Application) python client library for the Belle II Experiment. We were drawn to the action items related to library improvement after in-depth discussions with the developer of the Belle II distributed computing system. The improvement includes client-side metadata federation support in python, DIRAC SSL library support as well as API refinement for synchronous operation. Some of the improvements have already been applied to the AMGA python client library as bundled with the Belle II distributed computing software. The recent mass Monte- Carlo (MC) production campaign shows that the AMGA python client library is reliably stable.

  2. Observation of Bell Inequality violation in B mesons

    CERN Document Server

    Go, A

    2004-01-01

    A pair of $B^0\\bar B^0$ mesons from $\\Upsilon(4S)$ decay exhibit EPR type non-local particle-antiparticle (flavor) correlation. It is possible to write down Bell Inequality (in the CHSH form: $S\\le2$) to test the non-locality assumption of EPR. Using semileptonic $B^0$ decays of $\\Upsilon(4S)$ at Belle experiment, a clear violation of Bell Inequality in particle-antiparticle correlation is observed: S=2.725+-0.167(stat)+-0.092(syst)

  3. From Bell's inequalities to quantum information: a new quantum revolution

    CERN Multimedia

    CERN. Geneva

    2015-01-01

    In 1964, John Stuart Bell discovered that it is possible to settle the debate experimentally, by testing the famous "Bell's inequalities", and to show directly that the revolutionary concept of entanglement is indeed a reality. 

A long series of experiments closer and closer to the ideal scheme presented by Bell has confirmed that entanglement is indeed "a great quantum mystery", to use the words of Feynman. Based on that concept, a new field of research has emerged, quantum information, where one uses quantum bits, the so-called “qubits”, to encode the information and process it. Entanglement ...

  4. Conditional Density Approximations with Mixtures of Polynomials

    DEFF Research Database (Denmark)

    Varando, Gherardo; López-Cruz, Pedro L.; Nielsen, Thomas Dyhre

    2015-01-01

    Mixtures of polynomials (MoPs) are a non-parametric density estimation technique especially designed for hybrid Bayesian networks with continuous and discrete variables. Algorithms to learn one- and multi-dimensional (marginal) MoPs from data have recently been proposed. In this paper we introduce...... is found. We illustrate and study the methods using data sampled from known parametric distributions, and we demonstrate their applicability by learning models based on real neuroscience data. Finally, we compare the performance of the proposed methods with an approach for learning mixtures of truncated...... basis functions (MoTBFs). The empirical results show that the proposed methods generally yield models that are comparable to or significantly better than those found using the MoTBF-based method....

  5. Kinetic term anarchy for polynomial chaotic inflation

    Science.gov (United States)

    Nakayama, Kazunori; Takahashi, Fuminobu; Yanagida, Tsutomu T.

    2014-09-01

    We argue that there may arise a relatively flat inflaton potential over super-Planckian field values with an approximate shift symmetry, if the coefficients of the kinetic terms for many singlet scalars are subject to a certain random distribution. The inflation takes place along the flat direction with a super-Planckian length, whereas the other light directions can be stabilized by the Hubble-induced mass. The inflaton potential generically contains various shift-symmetry breaking terms, leading to a possibly large deviation of the predicted values of the spectral index and tensor-to-scalar ratio from those of the simple quadratic chaotic inflation. We revisit a polynomial chaotic inflation in supergravity as such.

  6. Dynamic normal forms and dynamic characteristic polynomial

    DEFF Research Database (Denmark)

    Frandsen, Gudmund Skovbjerg; Sankowski, Piotr

    2011-01-01

    We present the first fully dynamic algorithm for computing the characteristic polynomial of a matrix. In the generic symmetric case, our algorithm supports rank-one updates in O(n2logn) randomized time and queries in constant time, whereas in the general case the algorithm works in O(n2klogn......) randomized time, where k is the number of invariant factors of the matrix. The algorithm is based on the first dynamic algorithm for computing normal forms of a matrix such as the Frobenius normal form or the tridiagonal symmetric form. The algorithm can be extended to solve the matrix eigenproblem...... with relative error 2−b in additional O(nlog2nlogb) time. Furthermore, it can be used to dynamically maintain the singular value decomposition (SVD) of a generic matrix. Together with the algorithm, the hardness of the problem is studied. For the symmetric case, we present an Ω(n2) lower bound for rank...

  7. Orthogonal polynomials derived from the tridiagonal representation approach

    Science.gov (United States)

    Alhaidari, A. D.

    2018-01-01

    The tridiagonal representation approach is an algebraic method for solving second order differential wave equations. Using this approach in the solution of quantum mechanical problems, we encounter two new classes of orthogonal polynomials whose properties give the structure and dynamics of the corresponding physical system. For a certain range of parameters, one of these polynomials has a mix of continuous and discrete spectra making it suitable for describing physical systems with both scattering and bound states. In this work, we define these polynomials by their recursion relations and highlight some of their properties using numerical means. Due to the prime significance of these polynomials in physics, we hope that our short expose will encourage experts in the field of orthogonal polynomials to study them and derive their properties (weight functions, generating functions, asymptotics, orthogonality relations, zeros, etc.) analytically.

  8. Higher order branching of periodic orbits from polynomial isochrones

    Directory of Open Access Journals (Sweden)

    B. Toni

    1999-09-01

    Full Text Available We discuss the higher order local bifurcations of limit cycles from polynomial isochrones (linearizable centers when the linearizing transformation is explicitly known and yields a polynomial perturbation one-form. Using a method based on the relative cohomology decomposition of polynomial one-forms complemented with a step reduction process, we give an explicit formula for the overall upper bound of branch points of limit cycles in an arbitrary $n$ degree polynomial perturbation of the linear isochrone, and provide an algorithmic procedure to compute the upper bound at successive orders. We derive a complete analysis of the nonlinear cubic Hamiltonian isochrone and show that at most nine branch points of limit cycles can bifurcate in a cubic polynomial perturbation. Moreover, perturbations with exactly two, three, four, six, and nine local families of limit cycles may be constructed.

  9. Structured matrix based methods for approximate polynomial GCD

    CERN Document Server

    Boito, Paola

    2011-01-01

    Defining and computing a greatest common divisor of two polynomials with inexact coefficients is a classical problem in symbolic-numeric computation. The first part of this book reviews the main results that have been proposed so far in the literature. As usual with polynomial computations, the polynomial GCD problem can be expressed in matrix form: the second part of the book focuses on this point of view and analyses the structure of the relevant matrices, such as Toeplitz, Toepliz-block and displacement structures. New algorithms for the computation of approximate polynomial GCD are presented, along with extensive numerical tests. The use of matrix structure allows, in particular, to lower the asymptotic computational cost from cubic to quadratic order with respect to polynomial degree. .

  10. Multiple Meixner polynomials and non-Hermitian oscillator Hamiltonians

    International Nuclear Information System (INIS)

    Ndayiragije, F; Van Assche, W

    2013-01-01

    Multiple Meixner polynomials are polynomials in one variable which satisfy orthogonality relations with respect to r > 1 different negative binomial distributions (Pascal distributions). There are two kinds of multiple Meixner polynomials, depending on the selection of the parameters in the negative binomial distribution. We recall their definition and some formulas and give generating functions and explicit expressions for the coefficients in the nearest neighbor recurrence relation. Following a recent construction of Miki, Tsujimoto, Vinet and Zhedanov (for multiple Meixner polynomials of the first kind), we construct r > 1 non-Hermitian oscillator Hamiltonians in r dimensions which are simultaneously diagonalizable and for which the common eigenstates are expressed in terms of multiple Meixner polynomials of the second kind. (paper)

  11. Primitive polynomials selection method for pseudo-random number generator

    Science.gov (United States)

    Anikin, I. V.; Alnajjar, Kh

    2018-01-01

    In this paper we suggested the method for primitive polynomials selection of special type. This kind of polynomials can be efficiently used as a characteristic polynomials for linear feedback shift registers in pseudo-random number generators. The proposed method consists of two basic steps: finding minimum-cost irreducible polynomials of the desired degree and applying primitivity tests to get the primitive ones. Finally two primitive polynomials, which was found by the proposed method, used in pseudorandom number generator based on fuzzy logic (FRNG) which had been suggested before by the authors. The sequences generated by new version of FRNG have low correlation magnitude, high linear complexity, less power consumption, is more balanced and have better statistical properties.

  12. Jack polynomial fractional quantum Hall states and their generalizations

    International Nuclear Information System (INIS)

    Baratta, Wendy; Forrester, Peter J.

    2011-01-01

    In the study of fractional quantum Hall states, a certain clustering condition involving up to four integers has been identified. We give a simple proof that particular Jack polynomials with α=-(r-1)/(k+1), (r-1) and (k+1) relatively prime, and with partition given in terms of its frequencies by [n 0 0 (r-1)s k0 r-1 k0 r-1 k...0 r-1 m] satisfy this clustering condition. Our proof makes essential use of the fact that these Jack polynomials are translationally invariant. We also consider nonsymmetric Jack polynomials, symmetric and nonsymmetric generalized Hermite and Laguerre polynomials, and Macdonald polynomials from the viewpoint of the clustering.

  13. A note on some identities of derangement polynomials.

    Science.gov (United States)

    Kim, Taekyun; Kim, Dae San; Jang, Gwan-Woo; Kwon, Jongkyum

    2018-01-01

    The problem of counting derangements was initiated by Pierre Rémond de Montmort in 1708 (see Carlitz in Fibonacci Q. 16(3):255-258, 1978, Clarke and Sved in Math. Mag. 66(5):299-303, 1993, Kim, Kim and Kwon in Adv. Stud. Contemp. Math. (Kyungshang) 28(1):1-11 2018. A derangement is a permutation that has no fixed points, and the derangement number [Formula: see text] is the number of fixed-point-free permutations on an n element set. In this paper, we study the derangement polynomials and investigate some interesting properties which are related to derangement numbers. Also, we study two generalizations of derangement polynomials, namely higher-order and r -derangement polynomials, and show some relations between them. In addition, we express several special polynomials in terms of the higher-order derangement polynomials by using umbral calculus.

  14. Binary effectivity rules

    DEFF Research Database (Denmark)

    Keiding, Hans; Peleg, Bezalel

    2006-01-01

    effectivity rule is regular if it is the effectivity rule of some regular binary SCR. We characterize completely the family of regular binary effectivity rules. Quite surprisingly, intrinsically defined von Neumann-Morgenstern solutions play an important role in this characterization...

  15. Binary colloidal crystals

    NARCIS (Netherlands)

    Christova-Zdravkova, C.G.

    2005-01-01

    Binary crystals are crystals composed of two types of particles having different properties like size, mass density, charge etc. In this thesis several new approaches to make binary crystals of colloidal particles that differ in size, material and charge are reported We found a variety of crystal

  16. Do Bells Affect Behaviour and Heart Rate Variability in Grazing Dairy Cows?

    Science.gov (United States)

    Johns, Julia; Patt, Antonia; Hillmann, Edna

    2015-01-01

    In alpine regions cows are often equipped with bells. The present study investigated the impact of wearing a bell on behaviour and heart rate variability in dairy cows. Nineteen non-lactating Brown-Swiss cows with bell experience were assigned to three different treatments. For 3 days each, cows were equipped with no bell (control), with a bell with inactivated clapper (silent bell) or with a functional bell (functional bell). The bells weighed 5.5 kg and had frequencies between 532 Hz and 2.8 kHz and amplitudes between 90 and 113 dB at a distance of 20 cm. Data were collected on either the first and third or on all 3 days of each treatment. Whereas duration of rumination was reduced with a functional bell and a silent bell compared with no bell, feeding duration was reduced with a silent bell and was intermediate with a functional bell. Head movements were reduced when wearing a silent bell compared with no bell and tended to be reduced when wearing a functional compared to no bell. With a functional bell, lying duration was reduced by almost 4 hours on the third day of treatment compared with the first day with a functional bell and compared with no bell or a silent bell. All additional behavioural measures are consistent with the hypothesis of a restriction in the behaviour of the cows wearing bells, although this pattern did not reach significance. There was no treatment effect on heart rate variability, suggesting that the bells did not affect vago-sympathetic balance. An effect of experimental day was found for only 1 out of 10 behavioural parameters, as shown by a decrease in lying with a functional bell on day 3. The results indicate behavioural changes in the cows wearing a bell over 3 days, without indication of habituation to the bell. Altogether, the behavioural changes suggest that the behaviour of the cows was disturbed by wearing a bell. If long-lasting, these effects may have implications for animal welfare. PMID:26110277

  17. Belle-II High Level Trigger at SuperKEKB

    Science.gov (United States)

    Lee, S.; Itoh, R.; Higuchi, T.; Nakao, M.; Suzuki, S. Y.; Won, E.

    2012-12-01

    A next generation B-factory experiment, Belle II, is now being constructed at KEK in Japan. The upgraded accelerator SuperKEKB is designed to have the maximum luminosity of 8 × 1035 cm-2s-1 that is a factor 40 higher than the current world record. As a consequence, the Belle II detector yields a data stream of the event size ~1 MB at a Level 1 rate of 30 kHz. The Belle II High Level Trigger (HLT) is designed to reduce the Level 1 rate to 1/5 by performing the real time full event reconstruction and by applying the physics level event selection as the software trigger. In this paper, the development of the high level trigger system for Belle II and its performance is discussed.

  18. Quantum nonlocality and reality 50 years of Bell's theorem

    CERN Document Server

    Gao, Shan

    2016-01-01

    Description Contents Resources Courses About the Authors Combining twenty-six original essays written by an impressive line-up of distinguished physicists and philosophers of physics, this anthology reflects some of the latest thoughts by leading experts on the influence of Bell's theorem on quantum physics. Essays progress from John Bell's character and background, through studies of his main work, and on to more speculative ideas, addressing the controversies surrounding the theorem, and investigating the theorem's meaning and its deep implications for the nature of physical reality. Combined, they present a powerful comment on the undeniable significance of Bell's theorem for the development of ideas in quantum physics over the past 50 years. Questions surrounding the assumptions and significance of Bell's work still inspire discussion in the field of quantum physics. Adding to this with a theoretical and philosophical perspective, this balanced anthology is an indispensable volume for students and researc...

  19. NOAA Ship Bell M. Shimada Underway Meteorological Data, Quality Controlled

    Data.gov (United States)

    National Oceanic and Atmospheric Administration, Department of Commerce — NOAA Ship Bell M. Shimada Underway Meteorological Data (delayed ~10 days for quality control) are from the Shipboard Automated Meteorological and Oceanographic...

  20. Do oral steroids aid recovery in children with Bell's palsy?

    Science.gov (United States)

    Ismail, Abdul Qader; Alake, Oluwaseyi; Kallappa, Chetana

    2014-10-01

    There is growing evidence that steroids are not beneficial for treatment of paediatric patients with Bell's palsy. To investigate, we conducted a retrospective longitudinal study examining notes of 100 children, over 12 years coded for facial nerve palsy. Of the 79 diagnosed with Bell's palsy, all recovered, and for 46 patients we had data on interval from onset of symptoms to resolution (median duration in treated group = 5 weeks, range = 39; median duration in untreated group = 6 weeks, range = 11; P = .86). From our results, we conclude that all children with Bell's palsy recovered, with or without steroid treatment, with no statistically significant difference in symptoms duration. Complications of unresolved Bell's palsy can have important long-term functional and psychosocial consequences. Therefore, we need further research on use of steroids in children with complete/severe cases; it would be a shame to omit treatment due to "absence of evidence" rather than "evidence of absence." © The Author(s) 2013.

  1. Vanessa Bell's Photographs: Modernism, the Maternal and the Erotic

    OpenAIRE

    Humm, Maggie

    2002-01-01

    The chapter focuses on Vanessa Bell member of modernism's "first family", proposing that as a painter and photographer, she crossed and recrossed genre boundaries, especially in her child photography, a body of work eroticizing the maternal presence.

  2. Two-setting Bell inequalities for graph states

    International Nuclear Information System (INIS)

    Toth, Geza; Guehne, Otfried; Briegel, Hans J.

    2006-01-01

    We present Bell inequalities for graph states with a high violation of local realism. In particular, we show that there is a basic Bell inequality for every nontrivial graph state which is violated by the state at least by a factor of 2. This inequality needs the measurement of, at most, two operators for each qubit and involves only some of the qubits. We also show that for some families of graph states composite Bell inequalities can be constructed such that the violation of local realism increases exponentially with the number of qubits. We prove that some of our inequalities are facets of the convex polytope containing the many-body correlations consistent with local hidden variable models. Our Bell inequalities are built from stabilizing operators of graph states

  3. Hidden assumptions in the derivation of the theorem of Bell

    International Nuclear Information System (INIS)

    Hess, Karl; Raedt, Hans De; Michielsen, Kristel

    2012-01-01

    John Bell's inequalities have already been considered by Boole in 1862. Boole established a one-to-one correspondence between experimental outcomes and mathematical abstractions of his probability theory. His abstractions are two-valued functions that permit the logical operations AND, OR and NOT and are the elements of an algebra. Violation of the inequalities indicated to Boole an inconsistency of definition of the abstractions and/or the necessity to revise the algebra. It is demonstrated in this paper, that a violation of Bell's inequality by Einstein-Podolsky-Rosen type of experiments can be explained by Boole's ideas. Violations of Bell's inequality also call for a revision of the mathematical abstractions and corresponding algebra. It will be shown that this particular view of Bell's inequalities points toward an incompleteness of quantum mechanics, rather than to any superluminal propagation or influences at a distance.

  4. Characterization of the bell-shaped vibratory angular rate gyro.

    Science.gov (United States)

    Liu, Ning; Su, Zhong; Li, Qing; Fu, MengYin; Liu, Hong; Fan, JunFang

    2013-08-07

    The bell-shaped vibratory angular rate gyro (abbreviated as BVG) is a novel shell vibratory gyroscope, which is inspired by the Chinese traditional bell. It sensitizes angular velocity through the standing wave precession effect. The bell-shaped resonator is a core component of the BVG and looks like the millimeter-grade Chinese traditional bell, such as QianLong Bell and Yongle Bell. It is made of Ni43CrTi, which is a constant modulus alloy. The exciting element, control element and detection element are uniformly distributed and attached to the resonator, respectively. This work presents the design, analysis and experimentation on the BVG. It is most important to analyze the vibratory character of the bell-shaped resonator. The strain equation, internal force and the resonator's equilibrium differential equation are derived in the orthogonal curvilinear coordinate system. When the input angular velocity is existent on the sensitive axis, an analysis of the vibratory character is performed using the theory of thin shells. On this basis, the mode shape function and the simplified second order normal vibration mode dynamical equation are obtained. The coriolis coupling relationship about the primary mode and secondary mode is established. The methods of the signal processing and control loop are presented. Analyzing the impact resistance property of the bell-shaped resonator, which is compared with other shell resonators using the Finite Element Method, demonstrates that BVG has the advantage of a better impact resistance property. A reasonable means of installation and a prototypal gyro are designed. The gyroscopic effect of the BVG is characterized through experiments. Experimental results show that the BVG has not only the advantages of low cost, low power, long work life, high sensitivity, and so on, but, also, of a simple structure and a better impact resistance property for low and medium angular velocity measurements.

  5. Hugh Blairs Lectures on Rhetoric and Belles Lettres

    DEFF Research Database (Denmark)

    Schatz-Jakobsen, Claus

    1989-01-01

    Artiklen nærlæser dekonstruktivt dele af den skotske retorikprofessor Hugh Blairs Lecures on Rhetoric and Belles Lettres (1783) og påviser splittelsen mellem to vidt forskellige retorik- og liltteraturhistoriske interesser, neoklassicistiske vs. romantiske.......Artiklen nærlæser dekonstruktivt dele af den skotske retorikprofessor Hugh Blairs Lecures on Rhetoric and Belles Lettres (1783) og påviser splittelsen mellem to vidt forskellige retorik- og liltteraturhistoriske interesser, neoklassicistiske vs. romantiske....

  6. Characterization of the Bell-Shaped Vibratory Angular Rate Gyro

    Directory of Open Access Journals (Sweden)

    Junfang Fan

    2013-08-01

    Full Text Available The bell-shaped vibratory angular rate gyro (abbreviated as BVG is a novel shell vibratory gyroscope, which is inspired by the Chinese traditional bell. It sensitizes angular velocity through the standing wave precession effect. The bell-shaped resonator is a core component of the BVG and looks like the millimeter-grade Chinese traditional bell, such as QianLong Bell and Yongle Bell. It is made of Ni43CrTi, which is a constant modulus alloy. The exciting element, control element and detection element are uniformly distributed and attached to the resonator, respectively. This work presents the design, analysis and experimentation on the BVG. It is most important to analyze the vibratory character of the bell-shaped resonator. The strain equation, internal force and the resonator's equilibrium differential equation are derived in the orthogonal curvilinear coordinate system. When the input angular velocity is existent on the sensitive axis, an analysis of the vibratory character is performed using the theory of thin shells. On this basis, the mode shape function and the simplified second order normal vibration mode dynamical equation are obtained. The coriolis coupling relationship about the primary mode and secondary mode is established. The methods of the signal processing and control loop are presented. Analyzing the impact resistance property of the bell-shaped resonator, which is compared with other shell resonators using the Finite Element Method, demonstrates that BVG has the advantage of a better impact resistance property. A reasonable means of installation and a prototypal gyro are designed. The gyroscopic effect of the BVG is characterized through experiments. Experimental results show that the BVG has not only the advantages of low cost, low power, long work life, high sensitivity, and so on, but, also, of a simple structure and a better impact resistance property for low and medium angular velocity measurements.

  7. Interpretation of the quantum formalism and Bell's theorem

    International Nuclear Information System (INIS)

    Santos, E.

    1991-01-01

    It is argued that quantum mechanics must be interpreted according to the Copenhagen interpretation. Consequently the formalism must be used in a purely operational way. The relation between realism, hidden variables, and the Bell inequalities is discussed. The proof of impossibility of local hidden-variables theories (Bell theorem) is criticized on the basis that the quantum mechanical states violating local realism are not physically realizable states

  8. Novel Polynomial Basis with Fast Fourier Transform and Its Application to Reed-Solomon Erasure Codes

    KAUST Repository

    Lin, Sian-Jheng

    2016-09-13

    In this paper, we present a fast Fourier transform (FFT) algorithm over extension binary fields, where the polynomial is represented in a non-standard basis. The proposed Fourier-like transform requires O(h lg(h)) field operations, where h is the number of evaluation points. Based on the proposed Fourier-like algorithm, we then develop the encoding/ decoding algorithms for (n = 2m; k) Reed-Solomon erasure codes. The proposed encoding/erasure decoding algorithm requires O(n lg(n)), in both additive and multiplicative complexities. As the complexity leading factor is small, the proposed algorithms are advantageous in practical applications. Finally, the approaches to convert the basis between the monomial basis and the new basis are proposed.

  9. Identification of time-varying neural dynamics from spiking activities using Chebyshev polynomials.

    Science.gov (United States)

    Song Xu; Yang Li; Xudong Wang; Chan, Rosa H M

    2016-08-01

    Neural plasticity, elicited by processes such as development and learning, is an important biological attribute which can be viewed as a time-varying property of the nervous system. In this paper, we investigated the novel use of Chebyshev polynomials to estimate the changes in model parameters efficiently for time-varying dynamical systems with binary inputs and outputs. A forward orthogonal least square (FOLS) algorithm selected the significant model terms. Extensive simulations showed that the proposed algorithm identified the system changes more accurately in comparison with adaptive filter. This approach can be applied to identify not only gradual but also abrupt temporal evolutions of neural dynamics underlying nervous system activity with high sensitivity and accuracy by observing input and output spike trains only.

  10. Communication complexity of distributed computing and a parallel algorithm for polynomial roots

    International Nuclear Information System (INIS)

    Tiwari, P.

    1986-01-01

    The first part of this thesis begins with a discussion of the minimum communication requirements in some distributed networks. The main result is a general technique for determining lower bounds on the communication complexity of problems on various distributed computer networks. This general technique is derived by simulating the general network by a linear array and then using a lower bound on the communication complexity of the problem on the linear array. Applications of this technique yield nontrivial optimal or near-optimal lower bounds on the communication complexity of distinctness, ranking, uniqueness, merging, and triangle detection on a ring, a mesh, and a complete binary tree of processors. A technique similar to the one used in proving the above results, yields interesting graph theoretic results concerning decomposition of a graph into complete bipartite subgraphs. The second part of the this is devoted to the design of a fast parallel algorithm for determining all roots of a polynomial. Given a polynomial rho(z) of degree n with m bit integer coefficients and an integer μ, the author considers the problem of determining all its roots with error less than 2/sup -μ/. It is shown that this problem is in the class NC if rho(z) has all real roots

  11. Corticosteroids for Bell's palsy (idiopathic facial paralysis).

    Science.gov (United States)

    Madhok, Vishnu B; Gagyor, Ildiko; Daly, Fergus; Somasundara, Dhruvashree; Sullivan, Michael; Gammie, Fiona; Sullivan, Frank

    2016-07-18

    Inflammation and oedema of the facial nerve are implicated in causing Bell's palsy. Corticosteroids have a potent anti-inflammatory action that should minimise nerve damage. This is an update of a review first published in 2002 and last updated in 2010. To determine the effectiveness and safety of corticosteroid therapy in people with Bell's palsy. On 4 March 2016, we searched the Cochrane Neuromuscular Specialised Register, the Cochrane Central Register of Controlled Trials (CENTRAL), MEDLINE, EMBASE and LILACS. We reviewed the bibliographies of the randomised trials and contacted known experts in the field to identify additional published or unpublished trials. We also searched clinical trials registries for ongoing trials. Randomised trials and quasi-randomised trials comparing different routes of administration and dosage schemes of corticosteroid or adrenocorticotrophic hormone therapy versus a control group receiving no therapy considered effective for this condition, unless the same therapy was given in a similar way to the experimental group. We used standard Cochrane methodology. The main outcome of interest was incomplete recovery of facial motor function (i.e. residual facial weakness). Secondary outcomes were cosmetically disabling persistent sequelae, development of motor synkinesis or autonomic dysfunction (i.e. hemifacial spasm, crocodile tears) and adverse effects of corticosteroid therapy manifested during follow-up. We identified seven trials, with 895 evaluable participants for this review. All provided data suitable for the primary outcome meta-analysis. One of the trials was new since the last version of this Cochrane systematic review. Risk of bias in the older, smaller studies included some unclear- or high-risk assessments, whereas we deemed the larger studies at low risk of bias. Overall, 79/452 (17%) participants allocated to corticosteroids had incomplete recovery of facial motor function six months or more after randomisation

  12. Workplace cluster of Bell's palsy in Lima, Peru.

    Science.gov (United States)

    Reaves, Erik J; Ramos, Mariana; Bausch, Daniel G

    2014-05-09

    We report on a workplace cluster of Bell's palsy that occurred within a four-month period in 2011 among employees of a three-story office building in Lima, Peru and our investigation to determine the etiology and associated risk factors. An outbreak investigation was conducted to identify possible common infectious or environmental exposures and included patient interviews, reviews of medical records, an epidemiologic survey, serological analysis for IgM and IgG antibodies to putative Bell's palsy-inducing pathogens, and an environmental exposure assessment of the office building. Three cases of Bell's palsy were reported among 65 at-risk employees, attack rate 4.6%. Although two patients had underlying risk factors, there was no clear association or common identifiable risk factor among all cases. Serologic analysis showed no evidence of recent infections, and air and water sample measures of all known chemical or neurotoxins were below maximum allowable concentrations for exposure. An infection spread among workplace employees could not be excluded as a potential cause of this cluster; however, it was unlikely a pathogen commonly associated with individual cases of Bell's palsy. Although a specific etiology was not identified among all cases, we believe this methodology will aid future outbreak investigations of Bell's palsy and a better understanding of its etiology. While environmental assessments may be useful in their ability to ascertain the cause of clusters of Bell's palsy, future investigations should prioritize focus on common infectious etiology.

  13. Effects of Bell Speed and Flow Rate on Evaporation of Water Spray from a Rotary Bell Atomizer

    Directory of Open Access Journals (Sweden)

    Rajan Ray

    2015-05-01

    Full Text Available A phase doppler anemometer (PDA was used to determine the effects of evaporation on water spray for three rotary bell atomizer operational variable parameters: shaping air, bell speed and liquid flow. Shaping air was set at either 200 standard liters per minute (L/min or 300 L/min, bell speed was set to 30, 40 or 50 thousand rotations per minute (krpm and water flow rate was varied between 100, 200 or 300 cubic centimeters per minute (cm3/min. The total evaporation between 22.5 and 37.5 cm from the atomizer (cm3/s was calculated for all the combinations of those variables. Evaporation rate increased with higher flow rate and bell speed but no statistically significant effects were obtained for variable shaping air on interactions between parameters.

  14. vs. a polynomial chaos-based MCMC

    KAUST Repository

    Siripatana, Adil

    2014-08-01

    Bayesian Inference of Manning\\'s n coefficient in a Storm Surge Model Framework: comparison between Kalman lter and polynomial based method Adil Siripatana Conventional coastal ocean models solve the shallow water equations, which describe the conservation of mass and momentum when the horizontal length scale is much greater than the vertical length scale. In this case vertical pressure gradients in the momentum equations are nearly hydrostatic. The outputs of coastal ocean models are thus sensitive to the bottom stress terms de ned through the formulation of Manning\\'s n coefficients. This thesis considers the Bayesian inference problem of the Manning\\'s n coefficient in the context of storm surge based on the coastal ocean ADCIRC model. In the first part of the thesis, we apply an ensemble-based Kalman filter, the singular evolutive interpolated Kalman (SEIK) filter to estimate both a constant Manning\\'s n coefficient and a 2-D parameterized Manning\\'s coefficient on one ideal and one of more realistic domain using observation system simulation experiments (OSSEs). We study the sensitivity of the system to the ensemble size. we also access the benefits from using an in ation factor on the filter performance. To study the limitation of the Guassian restricted assumption on the SEIK lter, 5 we also implemented in the second part of this thesis a Markov Chain Monte Carlo (MCMC) method based on a Generalized Polynomial chaos (gPc) approach for the estimation of the 1-D and 2-D Mannning\\'s n coe cient. The gPc is used to build a surrogate model that imitate the ADCIRC model in order to make the computational cost of implementing the MCMC with the ADCIRC model reasonable. We evaluate the performance of the MCMC-gPc approach and study its robustness to di erent OSSEs scenario. we also compare its estimates with those resulting from SEIK in term of parameter estimates and full distributions. we present a full analysis of the solution of these two methods, of the

  15. Generalized Freud's equation and level densities with polynomial potential

    Science.gov (United States)

    Boobna, Akshat; Ghosh, Saugata

    2013-08-01

    We study orthogonal polynomials with weight $\\exp[-NV(x)]$, where $V(x)=\\sum_{k=1}^{d}a_{2k}x^{2k}/2k$ is a polynomial of order 2d. We derive the generalised Freud's equations for $d=3$, 4 and 5 and using this obtain $R_{\\mu}=h_{\\mu}/h_{\\mu -1}$, where $h_{\\mu}$ is the normalization constant for the corresponding orthogonal polynomials. Moments of the density functions, expressed in terms of $R_{\\mu}$, are obtained using Freud's equation and using this, explicit results of level densities as $N\\rightarrow\\infty$ are derived.

  16. q-Bernoulli numbers and q-Bernoulli polynomials revisited

    Directory of Open Access Journals (Sweden)

    Kim Taekyun

    2011-01-01

    Full Text Available Abstract This paper performs a further investigation on the q-Bernoulli numbers and q-Bernoulli polynomials given by Acikgöz et al. (Adv Differ Equ, Article ID 951764, 9, 2010, some incorrect properties are revised. It is point out that the generating function for the q-Bernoulli numbers and polynomials is unreasonable. By using the theorem of Kim (Kyushu J Math 48, 73-86, 1994 (see Equation 9, some new generating functions for the q-Bernoulli numbers and polynomials are shown. Mathematics Subject Classification (2000 11B68, 11S40, 11S80

  17. Coherent states and Hermite polynomials on quaternionic Hilbert spaces

    Energy Technology Data Exchange (ETDEWEB)

    Thirulogasanthar, K; Krzyzak, A [Department of Computer Science and Software Engineering, Concordia University, 1455 de Maisonneuve Blvd. W, Montreal, Quebec H3G 1M8 (Canada); Honnouvo, G, E-mail: santhar@cs.concordia.c, E-mail: krzyzak@cs.concordia.c, E-mail: g-honnouvo@yahoo.f [Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, Quebec H3A 2K6 (Canada)

    2010-09-24

    Coherent states, similar to the canonical coherent states of the harmonic oscillator, labeled by quaternions are established on the right and left quaternionic Hilbert spaces. On the left quaternionic Hilbert space reproducing kernels are established. As was claimed by Adler and Millard (J. Math. Phys. 1997 38 2117-26) it is proved that these coherent states cannot be realized as a group action on a quaternionic Hilbert space. As an extension of the complex Hermite polynomials, quaternionic Hermite polynomials are defined and these polynomials are associated with an operator as eigenfunctions.

  18. Local polynomial Whittle estimation covering non-stationary fractional processes

    DEFF Research Database (Denmark)

    Nielsen, Frank

    This paper extends the local polynomial Whittle estimator of Andrews & Sun (2004) to fractionally integrated processes covering stationary and non-stationary regions. We utilize the notion of the extended discrete Fourier transform and periodogram to extend the local polynomial Whittle estimator...... to the non-stationary region. By approximating the short-run component of the spectrum by a polynomial, instead of a constant, in a shrinking neighborhood of zero we alleviate some of the bias that the classical local Whittle estimators is prone to. This bias reduction comes at a cost as the variance is in...

  19. Chromatic Polynomials Of Some (m,l-Hyperwheels

    Directory of Open Access Journals (Sweden)

    Julian A. Allagan

    2014-03-01

    Full Text Available In this paper, using a standard method of computing the chromatic polynomial of hypergraphs, we introduce a new reduction theorem which allows us to find explicit formulae for the chromatic polynomials of some (complete non-uniform $(m,l-$hyperwheels and non-uniform $(m,l-$hyperfans. These hypergraphs, constructed through a ``join" graph operation, are some generalizations of the well-known wheel and fan graphs, respectively. Further, we revisit some results concerning these graphs and present their chromatic polynomials in a standard form that involves the Stirling numbers of the second kind.

  20. Automorphisms of Algebras and Bochner's Property for Vector Orthogonal Polynomials

    Science.gov (United States)

    Horozov, Emil

    2016-05-01

    We construct new families of vector orthogonal polynomials that have the property to be eigenfunctions of some differential operator. They are extensions of the Hermite and Laguerre polynomial systems. A third family, whose first member has been found by Y. Ben Cheikh and K. Douak is also constructed. The ideas behind our approach lie in the studies of bispectral operators. We exploit automorphisms of associative algebras which transform elementary vector orthogonal polynomial systems which are eigenfunctions of a differential operator into other systems of this type.