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Sample records for binary bell polynomials

  1. Application of the Binary Bell Polynomials Method to the Dissipative (2+1)-Dimensional AKNS Equation

    International Nuclear Information System (INIS)

    Liu Na; Liu Xi-Qiang

    2012-01-01

    Based on the binary Bell polynomials, the bilinear representation, bilinear Bäcklund transformation and the Lax pair for the dissipative (2+1)-dimensional Ablowitz—Kaup—Newell—Segur (AKNS) equation are obtained. Moreover, the infinite conservation laws are also derived

  2. Binary Bell polynomial application in generalized (2+1)-dimensional KdV equation with variable coefficients

    International Nuclear Information System (INIS)

    Zhang Yi; Wei Wei-Wei; Cheng Teng-Fei; Song Yang

    2011-01-01

    In this paper, we apply the binary Bell polynomial approach to high-dimensional variable-coefficient nonlinear evolution equations. Taking the generalized (2+1)-dimensional KdV equation with variable coefficients as an illustrative example, the bilinear formulism, the bilinear Bäcklund transformation and the Lax pair are obtained in a quick and natural manner. Moreover, the infinite conservation laws are also derived. (general)

  3. 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.

  4. 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.

  5. Integrability of an extended (2+1)-dimensional shallow water wave equation with Bell polynomials

    International Nuclear Information System (INIS)

    Wang Yun-Hu; Chen Yong

    2013-01-01

    We investigate the extended (2+1)-dimensional shallow water wave equation. The binary Bell polynomials are used to construct bilinear equation, bilinear Bäcklund transformation, Lax pair, and Darboux covariant Lax pair for this equation. Moreover, the infinite conservation laws of this equation are found by using its Lax pair. All conserved densities and fluxes are given with explicit recursion formulas. The N-soliton solutions are also presented by means of the Hirota bilinear method. (general)

  6. 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

  7. 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] ...

  8. On the evaluation at $(-\\iota,\\iota)$ of the Tutte polynomial of a binary matroid

    NARCIS (Netherlands)

    Pendavingh, R.A.

    2014-01-01

    Vertigan has shown that if $M$ is a binary matroid, then $|T_M(-\\iota,\\iota)|$, the modulus of the Tutte polynomial of $M$ as evaluated in $(-\\iota, \\iota)$, can be expressed in terms of the bicycle dimension of $M$. In this paper, we describe how the argument of the complex number

  9. 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.

  10. On the evaluation at $(-\\iota,\\iota)$ of the Tutte polynomial of a binary matroid

    NARCIS (Netherlands)

    Pendavingh, R.A.

    2012-01-01

    Vertigan has shown that if $M$ is a binary matroid, then $|T_M(-\\iota,\\iota)|$, the modulus of the Tutte polynomial of $M$ as evaluated in $(-\\iota, \\iota)$, can be expressed in terms of the bicycle dimension of $M$. In this paper, we exactly determine $T_M(-\\iota,\\iota)$, and show how to evaluate

  11. Compact Bell inequalities for multipartite experiments

    OpenAIRE

    Wu, Yu-Chun; Żukowski, Marek; Chen, Jing-Ling; Guo, Guang-Can

    2013-01-01

    A method for construction of the multipartite Clauser-Horne-Shimony-Holt (CHSH) type Bell inequalities, for the case of local binary observables, is presented. The standard CHSH-type Bell inequalities can be obtained as special cases. A unified framework to establish all kinds of CHSH-type Bell inequalities by increasing step by step the number of observers is given. As an application, compact Bell inequalities, for eight observers, involving just four correlation functions are proposed. They...

  12. 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...... 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.......For any nonzero elementcof a general finite fieldGF(q), it is shown that the polynomials(x - c)^i, i = 0,1,2,cdots, have the "weight-retaining" property that any linear combination of these polynomials with coefficients inGF(q)has Hamming weight at least as great as that of the minimum degree...

  13. 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.

  14. 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.

  15. 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

  16. Bitwise Bell-inequality violations for an entangled state involving 2N ions

    International Nuclear Information System (INIS)

    Pope, D.T.; Milburn, G.J.

    2004-01-01

    Following on from previous work [J.-A ring . Larsson, Phys. Rev. A 67, 022108 (2003)], Bell inequalities based on correlations between binary digits are considered for a particular entangled state involving 2N trapped ions. These inequalities involve applying displacement operations to half of the ions and then measuring correlations between pairs of corresponding bits in the binary representations of the number of center-of-mass phonons of N particular ions. It is shown that the state violates the inequalities and thus displays nonclassical correlations. It is also demonstrated that it violates a Bell inequality when the displacements are replaced by squeezing operations

  17. On tight multiparty Bell inequalities for many settings

    OpenAIRE

    Zukowski, Marek

    2006-01-01

    A derivation method is given which leads to a series of tight Bell inequalities for experiments involving N parties, with binary observables, and three possible local settings. The approach can be generalized to more settings. Ramifications are presented.

  18. 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...

  19. Generalized Bell-inequality experiments and computation

    Energy Technology Data Exchange (ETDEWEB)

    Hoban, Matty J. [Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT (United Kingdom); Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford OX1 3QD (United Kingdom); Wallman, Joel J. [School of Physics, The University of Sydney, Sydney, New South Wales 2006 (Australia); Browne, Dan E. [Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT (United Kingdom)

    2011-12-15

    We consider general settings of Bell inequality experiments with many parties, where each party chooses from a finite number of measurement settings each with a finite number of outcomes. We investigate the constraints that Bell inequalities place upon the correlations possible in local hidden variable theories using a geometrical picture of correlations. We show that local hidden variable theories can be characterized in terms of limited computational expressiveness, which allows us to characterize families of Bell inequalities. The limited computational expressiveness for many settings (each with many outcomes) generalizes previous results about the many-party situation each with a choice of two possible measurements (each with two outcomes). Using this computational picture we present generalizations of the Popescu-Rohrlich nonlocal box for many parties and nonbinary inputs and outputs at each site. Finally, we comment on the effect of preprocessing on measurement data in our generalized setting and show that it becomes problematic outside of the binary setting, in that it allows local hidden variable theories to simulate maximally nonlocal correlations such as those of these generalized Popescu-Rohrlich nonlocal boxes.

  20. Generalized Bell-inequality experiments and computation

    International Nuclear Information System (INIS)

    Hoban, Matty J.; Wallman, Joel J.; Browne, Dan E.

    2011-01-01

    We consider general settings of Bell inequality experiments with many parties, where each party chooses from a finite number of measurement settings each with a finite number of outcomes. We investigate the constraints that Bell inequalities place upon the correlations possible in local hidden variable theories using a geometrical picture of correlations. We show that local hidden variable theories can be characterized in terms of limited computational expressiveness, which allows us to characterize families of Bell inequalities. The limited computational expressiveness for many settings (each with many outcomes) generalizes previous results about the many-party situation each with a choice of two possible measurements (each with two outcomes). Using this computational picture we present generalizations of the Popescu-Rohrlich nonlocal box for many parties and nonbinary inputs and outputs at each site. Finally, we comment on the effect of preprocessing on measurement data in our generalized setting and show that it becomes problematic outside of the binary setting, in that it allows local hidden variable theories to simulate maximally nonlocal correlations such as those of these generalized Popescu-Rohrlich nonlocal boxes.

  1. 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

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

    Science.gov (United States)

    van de Graaf, Robert C; Nicolai, Jean-Philippe A

    2005-11-01

    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 century. Recently, an even earlier account of Bell's palsy was found, as observed by Cornelis Stalpart van der Wiel (1620-1702) from The Hague, The Netherlands in 1683. Because our current knowledge of the history of Bell's palsy before Bell is limited to a few documents, it is interesting to discuss Stalpart van der Wiel's description and determine its additional value for the history of Bell's palsy. It is concluded that Cornelis Stalpart van der Wiel was the first to record Bell's palsy in 1683. His manuscript provides clues for future historical research.

  3. 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 ...

  4. 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 ...

  5. Proposed experiment to test fundamentally binary theories

    Science.gov (United States)

    Kleinmann, Matthias; Vértesi, Tamás; Cabello, Adán

    2017-09-01

    Fundamentally binary theories are nonsignaling theories in which measurements of many outcomes are constructed by selecting from binary measurements. They constitute a sensible alternative to quantum theory and have never been directly falsified by any experiment. Here we show that fundamentally binary theories are experimentally testable with current technology. For that, we identify a feasible Bell-type experiment on pairs of entangled qutrits. In addition, we prove that, for any n , quantum n -ary correlations are not fundamentally (n -1 ) -ary. For that, we introduce a family of inequalities that hold for fundamentally (n -1 ) -ary theories but are violated by quantum n -ary correlations.

  6. 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)

  7. 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 ...

  8. 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.

  9. excess molar volumes, and refractive index of binary mixtures

    African Journals Online (AJOL)

    Preferred Customer

    type polynomial equation to derive the binary coefficients and estimate the standard ... prepared for each system, and their densities and absolute viscosities were .... divided arbitrarily into three types, namely, chemical, physical, and structural.

  10. 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 ...

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

    KAUST Repository

    Lin, Sian-Jheng; Al-Naffouri, Tareq Y.; Han, Yunghsiang S.; Chung, Wei-Ho

    2016-01-01

    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

  12. Orthogonal polynomials

    CERN Document Server

    Freud, Géza

    1971-01-01

    Orthogonal Polynomials contains an up-to-date survey of the general theory of orthogonal polynomials. It deals with the problem of polynomials and reveals that the sequence of these polynomials forms an orthogonal system with respect to a non-negative m-distribution defined on the real numerical axis. Comprised of five chapters, the book begins with the fundamental properties of orthogonal polynomials. After discussing the momentum problem, it then explains the quadrature procedure, the convergence theory, and G. Szegő's theory. This book is useful for those who intend to use it as referenc

  13. 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.

  14. Bell's Palsy

    Science.gov (United States)

    ... or paralysis. Bell's palsy is named for Sir Charles Bell, a 19th century Scottish surgeon who described ... confirm diagnosis of the disorder. Generally, a physician will examine the individual for upper and lower facial ...

  15. 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 ...

  16. 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.

  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. Experimental test of Bell`s inequalities using angular correlation of compton-scattered annihilation photons

    Energy Technology Data Exchange (ETDEWEB)

    Osuch, S.; Popkiewicz, M.; Szeflinski, Z.; Wilhelmi, Z. [Warsaw Univ., Inst. of Experimental Physics, Warsaw (Poland)

    1995-12-31

    The Bell`s inequality has been experimentally tested using angular correlation of Compton-scattered photons from annihilation of positrons emitted from {sup 22}Na source. The result shows a better agreement with the quantum mechanics predictions rather than with the Bell`s inequality. 7 refs, 5 figs, 1 tab.

  19. 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

    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

  20. Covariance Bell inequalities

    Science.gov (United States)

    Pozsgay, Victor; Hirsch, Flavien; Branciard, Cyril; Brunner, Nicolas

    2017-12-01

    We introduce Bell inequalities based on covariance, one of the most common measures of correlation. Explicit examples are discussed, and violations in quantum theory are demonstrated. A crucial feature of these covariance Bell inequalities is their nonlinearity; this has nontrivial consequences for the derivation of their local bound, which is not reached by deterministic local correlations. For our simplest inequality, we derive analytically tight bounds for both local and quantum correlations. An interesting application of covariance Bell inequalities is that they can act as "shared randomness witnesses": specifically, the value of the Bell expression gives device-independent lower bounds on both the dimension and the entropy of the shared random variable in a local model.

  1. 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

  2. Looking for symmetric Bell inequalities

    OpenAIRE

    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 e...

  3. Irreducible multivariate polynomials obtained from polynomials in ...

    Indian Academy of Sciences (India)

    Hall, 1409 W. Green Street, Urbana, IL 61801, USA. E-mail: Nicolae. ... Theorem A. If we write an irreducible polynomial f ∈ K[X] as a sum of polynomials a0,..., an ..... This shows us that deg ai = (n − i) deg f2 for each i = 0,..., n, so min k>0.

  4. 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.......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...

  5. Discrete-time state estimation for stochastic polynomial systems over polynomial observations

    Science.gov (United States)

    Hernandez-Gonzalez, M.; Basin, M.; Stepanov, O.

    2018-07-01

    This paper presents a solution to the mean-square state estimation problem for stochastic nonlinear polynomial systems over polynomial observations confused with additive white Gaussian noises. The solution is given in two steps: (a) computing the time-update equations and (b) computing the measurement-update equations for the state estimate and error covariance matrix. A closed form of this filter is obtained by expressing conditional expectations of polynomial terms as functions of the state estimate and error covariance. As a particular case, the mean-square filtering equations are derived for a third-degree polynomial system with second-degree polynomial measurements. Numerical simulations show effectiveness of the proposed filter compared to the extended Kalman filter.

  6. Stability analysis of polynomial fuzzy models via polynomial fuzzy Lyapunov functions

    OpenAIRE

    Bernal Reza, Miguel Ángel; Sala, Antonio; JAADARI, ABDELHAFIDH; Guerra, Thierry-Marie

    2011-01-01

    In this paper, the stability of continuous-time polynomial fuzzy models by means of a polynomial generalization of fuzzy Lyapunov functions is studied. Fuzzy Lyapunov functions have been fruitfully used in the literature for local analysis of Takagi-Sugeno models, a particular class of the polynomial fuzzy ones. Based on a recent Taylor-series approach which allows a polynomial fuzzy model to exactly represent a nonlinear model in a compact set of the state space, it is shown that a refinemen...

  7. 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

  8. 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.)

  9. 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.

  10. Looking for symmetric Bell inequalities

    Energy Technology Data Exchange (ETDEWEB)

    Bancal, Jean-Daniel; Gisin, Nicolas [Group of Applied Physics, University of Geneva, 20 rue de l' Ecole-de Medecine, CH-1211 Geneva 4 (Switzerland); Pironio, Stefano, E-mail: jean-daniel.bancal@unige.c [Laboratoire d' Information Quantique, Universite Libre de Bruxelles (Belgium)

    2010-09-24

    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.

  11. Multipartite omnidirectional generalized Bell inequality

    Energy Technology Data Exchange (ETDEWEB)

    Nagata, Koji [Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 305-701 (Korea, Republic of)

    2007-10-26

    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.

  12. 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.

  13. 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

  14. 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.

  15. Multipartite omnidirectional generalized Bell inequality

    OpenAIRE

    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 ...

  16. 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.

  17. 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

  18. 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....

  19. 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.

  20. 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)

  1. 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’.

  2. 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

  3. 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.

  4. On generalized Fibonacci and Lucas polynomials

    Energy Technology Data Exchange (ETDEWEB)

    Nalli, Ayse [Department of Mathematics, Faculty of Sciences, Selcuk University, 42075 Campus-Konya (Turkey)], E-mail: aysenalli@yahoo.com; Haukkanen, Pentti [Department of Mathematics, Statistics and Philosophy, 33014 University of Tampere (Finland)], E-mail: mapehau@uta.fi

    2009-12-15

    Let h(x) be a polynomial with real coefficients. We introduce h(x)-Fibonacci polynomials that generalize both Catalan's Fibonacci polynomials and Byrd's Fibonacci polynomials and also the k-Fibonacci numbers, and we provide properties for these h(x)-Fibonacci polynomials. We also introduce h(x)-Lucas polynomials that generalize the Lucas polynomials and present properties of these polynomials. In the last section we introduce the matrix Q{sub h}(x) that generalizes the Q-matrix whose powers generate the Fibonacci numbers.

  5. Stabilisation of discrete-time polynomial fuzzy systems via a polynomial lyapunov approach

    Science.gov (United States)

    Nasiri, Alireza; Nguang, Sing Kiong; Swain, Akshya; Almakhles, Dhafer

    2018-02-01

    This paper deals with the problem of designing a controller for a class of discrete-time nonlinear systems which is represented by discrete-time polynomial fuzzy model. Most of the existing control design methods for discrete-time fuzzy polynomial systems cannot guarantee their Lyapunov function to be a radially unbounded polynomial function, hence the global stability cannot be assured. The proposed control design in this paper guarantees a radially unbounded polynomial Lyapunov functions which ensures global stability. In the proposed design, state feedback structure is considered and non-convexity problem is solved by incorporating an integrator into the controller. Sufficient conditions of stability are derived in terms of polynomial matrix inequalities which are solved via SOSTOOLS in MATLAB. A numerical example is presented to illustrate the effectiveness of the proposed controller.

  6. Soliton interactions and Bäcklund transformation for a (2+1)-dimensional variable-coefficient modified Kadomtsev-Petviashvili equation in fluid dynamics

    Science.gov (United States)

    Xiao, Zi-Jian; Tian, Bo; Sun, Yan

    2018-01-01

    In this paper, we investigate a (2+1)-dimensional variable-coefficient modified Kadomtsev-Petviashvili (mKP) equation in fluid dynamics. With the binary Bell-polynomial and an auxiliary function, bilinear forms for the equation are constructed. Based on the bilinear forms, multi-soliton solutions and Bell-polynomial-type Bäcklund transformation for such an equation are obtained through the symbolic computation. Soliton interactions are presented. Based on the graphic analysis, Parametric conditions for the existence of the shock waves, elevation solitons and depression solitons are given, and it is shown that under the condition of keeping the wave vectors invariable, the change of α(t) and β(t) can lead to the change of the solitonic velocities, but the shape of each soliton remains unchanged, where α(t) and β(t) are the variable coefficients in the equation. Oblique elastic interactions can exist between the (i) two shock waves, (ii) two elevation solitons, and (iii) elevation and depression solitons. However, oblique interactions between (i) shock waves and elevation solitons, (ii) shock waves and depression solitons are inelastic.

  7. EPR and Bell Locality

    OpenAIRE

    Norsen, Travis

    2004-01-01

    A new formulation of the EPR argument is presented, one which uses John Bell's mathematically precise local causality condition in place of the looser locality assumption which was used in the original EPR paper and on which Niels Bohr seems to have based his objection to the EPR argument. The new formulation of EPR bears a striking resemblance to Bell's derivation of his famous inequalities. The relation between these two arguments -- in particular, the role of EPR as part one of Bell's two-...

  8. Better polynomials for GNFS

    OpenAIRE

    Bai , Shi; Bouvier , Cyril; Kruppa , Alexander; Zimmermann , Paul

    2016-01-01

    International audience; The general number field sieve (GNFS) is the most efficient algo-rithm known for factoring large integers. It consists of several stages, the first one being polynomial selection. The quality of the selected polynomials can be modelled in terms of size and root properties. We propose a new kind of polynomials for GNFS: with a new degree of freedom, we further improve the size property. We demonstrate the efficiency of our algorithm by exhibiting a better polynomial tha...

  9. Alexander Graham Bell: Teacher of the Deaf.

    Science.gov (United States)

    Bruce, Robert V.

    The lecture on Alexander Graham Bell by Dr. Robert V. Bruce, the author of a biography of Bell, focuses on Bell's association with the Clarke School for the Deaf in Massachusetts. Noted are Bell's employment by the school at 25 years of age and the preceding period during which Bell taught elocution at a boys' school in Scotland and used his…

  10. 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)

  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. 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. Investigation on some thermophysical properties of poly(ethylene glycol) binary mixtures at different temperatures

    International Nuclear Information System (INIS)

    Moosavi, Mehrdad; Motahari, Ahmad; Omrani, Abdollah; Rostami, Abbas Ali

    2013-01-01

    Highlights: ► Measuring densities and viscosities for binary mixtures of PEG + water or alcohols. ► Finding excess molar volume, refractive index and coefficient of thermal expansion. ► Estimating binary coefficients using Redlich–Kister polynomial equation. ► Deducing excess Gibbs free energy of activation and other activation parameters. ► Correlation of viscosity data with Grunberg–Nissan and Tamura–Kurata equations. -- Abstract: Densities ρ and viscosities η for the binary mixtures of poly(ethylene glycol) + water, + 1,2-ethanediol, + 1,3-propanediol, + 1,4-butanediol over the entire concentration range were determined at temperatures (298.15 to 308.15) K with 5 K interval. The experimental data were used to calculate the excess molar volume V m E , coefficient of thermal expansion α, excess coefficient of thermal expansion α E , excess Gibbs free energy of activation ΔG ∗E , and other activation parameters (i.e., ΔG ∗ ,ΔH ∗ ,ΔS ∗ ). The values of excess properties were fitted to Redlich–Kister polynomial equation to estimate the binary coefficients. The excess refractive index n E and electronic polarizability α e of PEG + water binary mixtures were also determined from the experimental values of refractive indices. The viscosity data were correlated with Grunberg–Nissan and Tamura–Kurata equations. Moreover, the Prigogine–Flory–Patterson theory has been used to correlate the excess molar volumes of the studied mixtures

  14. 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.

  15. 78 FR 65178 - Airworthiness Directives; Bell Helicopter Textron Canada (Bell) Helicopters

    Science.gov (United States)

    2013-10-31

    ... the TCAA AD, and we do not require you to provide an affected cap for rework to Bell Tennessee nor... assembly, ensuring that the rework has been done. Related Service Information Bell has issued ASB No. 206L... or rework the cap assembly by following the instructions depicted in Figure 3 of ASB 206L-04-129 or...

  16. 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...

  17. FFT Algorithm for Binary Extension Finite Fields and Its Application to Reed–Solomon Codes

    KAUST Repository

    Lin, Sian Jheng; Al-Naffouri, Tareq Y.; Han, Yunghsiang S.

    2016-01-01

    Recently, a new polynomial basis over binary extension fields was proposed, such that the fast Fourier transform (FFT) over such fields can be computed in the complexity of order O(n lg(n)), where n is the number of points evaluated in FFT

  18. 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...... extend Thomassen’s technique to the Tutte polynomial and as a consequence, deduce a density result for roots of the Tutte polynomial. This partially answers a conjecture of Jackson and Sokal. Finally, we refocus our attention on the chromatic polynomial and investigate the density of chromatic roots...

  19. Information-Dispersion-Entropy-Based Blind Recognition of Binary BCH Codes in Soft Decision Situations

    Directory of Open Access Journals (Sweden)

    Yimeng Zhang

    2013-05-01

    Full Text Available A method of blind recognition of the coding parameters for binary Bose-Chaudhuri-Hocquenghem (BCH codes is proposed in this paper. We consider an intelligent communication receiver which can blindly recognize the coding parameters of the received data stream. The only knowledge is that the stream is encoded using binary BCH codes, while the coding parameters are unknown. The problem can be addressed on the context of the non-cooperative communications or adaptive coding and modulations (ACM for cognitive radio networks. The recognition processing includes two major procedures: code length estimation and generator polynomial reconstruction. A hard decision method has been proposed in a previous literature. In this paper we propose the recognition approach in soft decision situations with Binary-Phase-Shift-Key modulations and Additive-White-Gaussian-Noise (AWGN channels. The code length is estimated by maximizing the root information dispersion entropy function. And then we search for the code roots to reconstruct the primitive and generator polynomials. By utilizing the soft output of the channel, the recognition performance is improved and the simulations show the efficiency of the proposed algorithm.

  20. 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

  1. Bell Discourse in Russian Culture

    Directory of Open Access Journals (Sweden)

    Элеонора Р Лассан

    2014-12-01

    Full Text Available The article focuses on the symbolic meaning of Russian ringing of bell in the Russian discourse. According to Lotman’s definition of symbol, it has dual nature: an invariant essence and its modification in relation to the cultural context. The article introduces informative and linguistic modifications of the bell topic in the Russian poetic discourse of the 19th, the 20th and the beginning of the 21st century. The author of the article provides the detailed analysis of such discursive descriptions of bell ringing as the ringing of church bells and alarm . The author arrives at the conlusion that the alarm topic prevails in contemporary poetry and this indicates the state of public dissatisfaction. In the 19th and the 20th centuries lexemes the ringing of church bells and alarm were used literally, but in the 21st century lexeme alarm acquires metaphorical meaning of call for blood.

  2. 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 ...

  3. 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.].

  4. Polynomial Heisenberg algebras

    International Nuclear Information System (INIS)

    Carballo, Juan M; C, David J Fernandez; Negro, Javier; Nieto, Luis M

    2004-01-01

    Polynomial deformations of the Heisenberg algebra are studied in detail. Some of their natural realizations are given by the higher order susy partners (and not only by those of first order, as is already known) of the harmonic oscillator for even-order polynomials. Here, it is shown that the susy partners of the radial oscillator play a similar role when the order of the polynomial is odd. Moreover, it will be proved that the general systems ruled by such kinds of algebras, in the quadratic and cubic cases, involve Painleve transcendents of types IV and V, respectively

  5. Bell Inequalities for Complex Networks

    Science.gov (United States)

    2015-10-26

    AFRL-AFOSR-VA-TR-2015-0355 YIP Bell Inequalities for Complex Networks Greg Ver Steeg UNIVERSITY OF SOUTHERN CALIFORNIA LOS ANGELES Final Report 10/26...performance report PI: Greg Ver Steeg Young Investigator Award Grant Title: Bell Inequalities for Complex Networks Grant #: FA9550-12-1-0417 Reporting...October 20, 2015 Final Report for “Bell Inequalities for Complex Networks” Greg Ver Steeg Abstract This effort studied new methods to understand the effect

  6. Polynomial optimization : Error analysis and applications

    NARCIS (Netherlands)

    Sun, Zhao

    2015-01-01

    Polynomial optimization is the problem of minimizing a polynomial function subject to polynomial inequality constraints. In this thesis we investigate several hierarchies of relaxations for polynomial optimization problems. Our main interest lies in understanding their performance, in particular how

  7. 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

  8. 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...

  9. 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.

  10. 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.

  11. 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…

  12. 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.

  13. 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"2r) 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)

  14. 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.

  15. Vortices and polynomials: non-uniqueness of the Adler–Moser polynomials for the Tkachenko equation

    International Nuclear Information System (INIS)

    Demina, Maria V; Kudryashov, Nikolai A

    2012-01-01

    Stationary and translating relative equilibria of point vortices in the plane are studied. It is shown that stationary equilibria of any system containing point vortices with arbitrary choice of circulations can be described with the help of the Tkachenko equation. It is also obtained that translating relative equilibria of point vortices with arbitrary circulations can be constructed using a generalization of the Tkachenko equation. Roots of any pair of polynomials solving the Tkachenko equation and the generalized Tkachenko equation are proved to give positions of point vortices in stationary and translating relative equilibria accordingly. These results are valid even if the polynomials in a pair have multiple or common roots. It is obtained that the Adler–Moser polynomial provides non-unique polynomial solutions of the Tkachenko equation. It is shown that the generalized Tkachenko equation possesses polynomial solutions with degrees that are not triangular numbers. (paper)

  16. Bell inequalities for the simplest exclusivity graph

    OpenAIRE

    Sadiq, Muhamad; Badziag, Piotr; Bourennane, Mohamed; Cabello, Adan

    2011-01-01

    Which is the simplest logical structure for which there is quantum nonlocality? We show that there are only three bipartite Bell inequalities with quantum violation associated with the simplest graph of relationships of exclusivity with a quantum-classical gap. These are the most elementary logical Bell inequalities. We show that the quantum violation of some well-known Bell inequalities is related to them. We test the three Bell inequalities with pairs of polarization-entangled photons and r...

  17. Microscopic and macroscopic bell inequalities

    International Nuclear Information System (INIS)

    Santos, E.

    1984-01-01

    The Bell inequalities, being derived for micro-systems, cannot be tested by (macroscopic) experiments without additional assumptions. A macroscopic definition of local realism is proposed which might be the starting point for deriving Bell inequalities testable without auxiliary assumptions. (orig.)

  18. Boole and Bell inequality

    International Nuclear Information System (INIS)

    Michielsen, K.; De Raedt, H.; Hess, K.

    2011-01-01

    We discuss the relation between Bell's and Boole's inequality. We apply both to the analysis of measurement results in idealized Einstein-Podolsky-Rosen-Bohm experiments. We present a local realist model that violates Bell's and Boole's inequality due to the absence of Boole's one-to-one correspondence between the two-valued variables of the mathematical description and the two-valued measurement results.

  19. 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.

  20. 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.

  1. 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

  2. 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.

    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

  3. Stochastic Estimation via Polynomial Chaos

    Science.gov (United States)

    2015-10-01

    AFRL-RW-EG-TR-2015-108 Stochastic Estimation via Polynomial Chaos Douglas V. Nance Air Force Research...COVERED (From - To) 20-04-2015 – 07-08-2015 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Stochastic Estimation via Polynomial Chaos ...This expository report discusses fundamental aspects of the polynomial chaos method for representing the properties of second order stochastic

  4. A New Generalisation of Macdonald Polynomials

    Science.gov (United States)

    Garbali, Alexandr; de Gier, Jan; Wheeler, Michael

    2017-06-01

    We introduce a new family of symmetric multivariate polynomials, whose coefficients are meromorphic functions of two parameters ( q, t) and polynomial in a further two parameters ( u, v). We evaluate these polynomials explicitly as a matrix product. At u = v = 0 they reduce to Macdonald polynomials, while at q = 0, u = v = s they recover a family of inhomogeneous symmetric functions originally introduced by Borodin.

  5. Special polynomials associated with some hierarchies

    International Nuclear Information System (INIS)

    Kudryashov, Nikolai A.

    2008-01-01

    Special polynomials associated with rational solutions of a hierarchy of equations of Painleve type are introduced. The hierarchy arises by similarity reduction from the Fordy-Gibbons hierarchy of partial differential equations. Some relations for these special polynomials are given. Differential-difference hierarchies for finding special polynomials are presented. These formulae allow us to obtain special polynomials associated with the hierarchy studied. It is shown that rational solutions of members of the Schwarz-Sawada-Kotera, the Schwarz-Kaup-Kupershmidt, the Fordy-Gibbons, the Sawada-Kotera and the Kaup-Kupershmidt hierarchies can be expressed through special polynomials of the hierarchy studied

  6. Nondestructive identification of the Bell diagonal state

    International Nuclear Information System (INIS)

    Jin Jiasen; Yu Changshui; Song Heshan

    2011-01-01

    We propose a scheme for identifying an unknown Bell diagonal state. In our scheme the measurements are performed on the probe qubits instead of the Bell diagonal state. The distinct advantage is that the quantum state of the evolved Bell diagonal state ensemble plus probe states will still collapse on the original Bell diagonal state ensemble after the measurement on probe states; i.e., our identification is quantum state nondestructive. How to realize our scheme in the framework of cavity electrodynamics is also shown.

  7. Obstructions to Bell CMB experiments

    Science.gov (United States)

    Martin, Jérôme; Vennin, Vincent

    2017-09-01

    We present a general and systematic study of how a Bell experiment on the cosmic microwave background could be carried out. We introduce different classes of pseudo-spin operators and show that, if the system is placed in a two-mode squeezed state as inflation predicts, they all lead to a violation of the Bell inequality. However, we also discuss the obstacles that one faces in order to realize this program in practice and show that they are probably insurmountable. We suggest alternative methods that could reveal the quantum origin of cosmological structures without relying on Bell experiments.

  8. 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.

  9. A Summation Formula for Macdonald Polynomials

    Science.gov (United States)

    de Gier, Jan; Wheeler, Michael

    2016-03-01

    We derive an explicit sum formula for symmetric Macdonald polynomials. Our expression contains multiple sums over the symmetric group and uses the action of Hecke generators on the ring of polynomials. In the special cases {t = 1} and {q = 0}, we recover known expressions for the monomial symmetric and Hall-Littlewood polynomials, respectively. Other specializations of our formula give new expressions for the Jack and q-Whittaker polynomials.

  10. 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

  11. Quantum correlations in connected multipartite Bell experiments

    International Nuclear Information System (INIS)

    Tavakoli, Armin

    2016-01-01

    Bell experiments measure correlations between outcomes of a number of observers measuring on a shared physical state emitted from a single source. Quantum correlations arising in such Bell experiments have been intensively studied over the last decades. Much less is known about the nature of quantum correlations arising in network structures beyond Bell experiments. Such networks can involve many independent sources emitting states to observers in accordance with the network configuration. Here, we will study classical and quantum correlations in a family of networks which can be regarded as compositions of several independent multipartite Bell experiments connected together through a central node. For such networks we present tight Bell-type inequalities which are satisfied by all classical correlations. We study properties of the violations of our inequalities by probability distributions arising in quantum theory. (paper)

  12. 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.)

  13. 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...

  14. A new semidefinite programming relaxation for cycles in binary matroids and cuts in graphs

    NARCIS (Netherlands)

    Gouveia, J.; Laurent, M.; Parrilo, P.; Thomas, R.

    2012-01-01

    The theta bodies of a polynomial ideal are a series of semidefinite programming relaxations of the convex hull of the real variety of the ideal. In this paper we construct the theta bodies of the vanishing ideal of cycles in a binary matroid. Applied to cuts in graphs, this yields a new hierarchy of

  15. Alexander Graham Bell (170th birthday anniversary

    Directory of Open Access Journals (Sweden)

    V. P. Samokhin

    2017-01-01

    Full Text Available A brief overview of the main works and achievements of Alexander Graham Bell, an educated teacher for the hard of hearing and public figure, author of 30 US patents, is mainly given in the field of telephony and sound recording and reproduction. Biographical information about the Bell family, as well as some interesting facts from his life and activities are given. Scotsman by birth, A. Bell from his youthful years was carried away by the acoustic features of the human voice apparatus and devoted his entire life to teaching the deaf to the perception of oral speech. The first success in this field Bell reached, opening a private school for the deaf in Boston. Bell's creation of the phone was the result of his attempts to facilitate communication with the hard-of-hearing and led to the development of mass communications technology around the world. Alexander Bell is also known for his achievements in the design of hydroplanes, hydrofoils and as one of the founders of the popular magazine National Geographic. He was awarded many honorable awards and academic titles.

  16. 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...

  17. 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

  18. The Legacy of Dr. Bell.

    Science.gov (United States)

    Breunig, H. Latham

    1990-01-01

    This article describes the family of Alexander Graham Bell, including research and therapeutic work in speech and hearing impairments spanning three generations. Bell's life and discoveries are discussed, including the formation of the American Association for the Promotion of Teaching of Speech to the Deaf, whose history and organization are…

  19. 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...

  20. 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)

  1. 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

  2. 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.

  3. Reconciliation with non-binary species trees.

    Science.gov (United States)

    Vernot, Benjamin; Stolzer, Maureen; Goldman, Aiton; Durand, Dannie

    2008-10-01

    Reconciliation extracts information from the topological incongruence between gene and species trees to infer duplications and losses in the history of a gene family. The inferred duplication-loss histories provide valuable information for a broad range of biological applications, including ortholog identification, estimating gene duplication times, and rooting and correcting gene trees. While reconciliation for binary trees is a tractable and well studied problem, there are no algorithms for reconciliation with non-binary species trees. Yet a striking proportion of species trees are non-binary. For example, 64% of branch points in the NCBI taxonomy have three or more children. When applied to non-binary species trees, current algorithms overestimate the number of duplications because they cannot distinguish between duplication and incomplete lineage sorting. We present the first algorithms for reconciling binary gene trees with non-binary species trees under a duplication-loss parsimony model. Our algorithms utilize an efficient mapping from gene to species trees to infer the minimum number of duplications in O(|V(G) | x (k(S) + h(S))) time, where |V(G)| is the number of nodes in the gene tree, h(S) is the height of the species tree and k(S) is the size of its largest polytomy. We present a dynamic programming algorithm which also minimizes the total number of losses. Although this algorithm is exponential in the size of the largest polytomy, it performs well in practice for polytomies with outdegree of 12 or less. We also present a heuristic which estimates the minimal number of losses in polynomial time. In empirical tests, this algorithm finds an optimal loss history 99% of the time. Our algorithms have been implemented in NOTUNG, a robust, production quality, tree-fitting program, which provides a graphical user interface for exploratory analysis and also supports automated, high-throughput analysis of large data sets.

  4. 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.

  5. Fermionic formula for double Kostka polynomials

    OpenAIRE

    Liu, Shiyuan

    2016-01-01

    The $X=M$ conjecture asserts that the $1D$ sum and the fermionic formula coincide up to some constant power. In the case of type $A,$ both the $1D$ sum and the fermionic formula are closely related to Kostka polynomials. Double Kostka polynomials $K_{\\Bla,\\Bmu}(t),$ indexed by two double partitions $\\Bla,\\Bmu,$ are polynomials in $t$ introduced as a generalization of Kostka polynomials. In the present paper, we consider $K_{\\Bla,\\Bmu}(t)$ in the special case where $\\Bmu=(-,\\mu'').$ We formula...

  6. Relations between Möbius and coboundary polynomials

    NARCIS (Netherlands)

    Jurrius, R.P.M.J.

    2012-01-01

    It is known that, in general, the coboundary polynomial and the Möbius polynomial of a matroid do not determine each other. Less is known about more specific cases. In this paper, we will investigate if it is possible that the Möbius polynomial of a matroid, together with the Möbius polynomial of

  7. Matrix product formula for Macdonald polynomials

    Science.gov (United States)

    Cantini, Luigi; de Gier, Jan; Wheeler, Michael

    2015-09-01

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

  8. 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)

  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. 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)

  11. 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)

  12. Do bells affect behaviour and heart rate variability in grazing dairy cows?

    Directory of Open Access Journals (Sweden)

    Julia Johns

    Full Text Available 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.

  13. 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

  14. Bell's Palsy

    Science.gov (United States)

    ... have been linked to Bell's palsy include the virus that causes: Cold sores and genital herpes (herpes simplex) Chickenpox and shingles (herpes zoster) Infectious mononucleosis (Epstein-Barr) Cytomegalovirus infections Respiratory illnesses (adenovirus) German measles (rubella) ...

  15. Better Bell-inequality violation by collective measurements

    International Nuclear Information System (INIS)

    Liang, Y.-C.; Doherty, Andrew C.

    2006-01-01

    The standard Bell-inequality experiments test for violation of local realism by repeatedly making local measurements on individual copies of an entangled quantum state. Here we investigate the possibility of increasing the violation of a Bell inequality by making collective measurements. We show that the nonlocality of bipartite pure entangled states, quantified by their maximal violation of the Bell-Clauser-Horne inequality, can always be enhanced by collective measurements, even without communication between the parties. For mixed states we also show that collective measurements can increase the violation of Bell inequalities, although numerical evidence suggests that the phenomenon is not common as it is for pure states

  16. 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)

  17. [Bell and his palsy].

    Science.gov (United States)

    van Gijn, Jan; Gijselhart, Joost P

    2011-01-01

    Unlike his eponymous fame suggests, Sir Charles Bell (1774-1842) was an anatomist, draughtsman and surgeon rather than purely a physiologist. He was born and educated in Edinburgh but spent most of his working life in London (1804 to 1836). It was there he started a School of Anatomy, alongside a fledgling surgical practice, just as his elder brother John had done in Edinburgh. In 1814 he joined the surgical staff at the Middlesex Hospital. In 1810 he surmised from occasional animal experiments that the anterior and posterior spinal roots differed in function. Yet it was left to the Frenchman Magendie to identify that these functions were motor and sensory: a discovery that induced Bell into an ungentlemanly feud. Bell also slightly erred on the functions of the trigeminal and facial nerve, but his description of the features of idiopathic facial palsy is unrivalled.

  18. 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)

  19. 78 FR 51123 - Airworthiness Directives; Bell Helicopter Textron

    Science.gov (United States)

    2013-08-20

    ...-0734; Directorate Identifier 2012-SW-080-AD] RIN 2120-AA64 Airworthiness Directives; Bell Helicopter...). SUMMARY: We propose to supersede an existing airworthiness directive (AD) for Bell Helicopter Textron (Bell) Model 222, 222B, 222U, 230, and 430 helicopters. The existing AD currently requires inspecting...

  20. Vertex models, TASEP and Grothendieck polynomials

    International Nuclear Information System (INIS)

    Motegi, Kohei; Sakai, Kazumitsu

    2013-01-01

    We examine the wavefunctions and their scalar products of a one-parameter family of integrable five-vertex models. At a special point of the parameter, the model investigated is related to an irreversible interacting stochastic particle system—the so-called totally asymmetric simple exclusion process (TASEP). By combining the quantum inverse scattering method with a matrix product representation of the wavefunctions, the on-/off-shell wavefunctions of the five-vertex models are represented as a certain determinant form. Up to some normalization factors, we find that the wavefunctions are given by Grothendieck polynomials, which are a one-parameter deformation of Schur polynomials. Introducing a dual version of the Grothendieck polynomials, and utilizing the determinant representation for the scalar products of the wavefunctions, we derive a generalized Cauchy identity satisfied by the Grothendieck polynomials and their duals. Several representation theoretical formulae for the Grothendieck polynomials are also presented. As a byproduct, the relaxation dynamics such as Green functions for the periodic TASEP are found to be described in terms of the Grothendieck polynomials. (paper)

  1. Bell inequalities for random fields

    Energy Technology Data Exchange (ETDEWEB)

    Morgan, Peter [Physics Department, Yale University, CT 06520 (United States)

    2006-06-09

    The assumptions required for the derivation of Bell inequalities are not satisfied for random field models in which there are any thermal or quantum fluctuations, in contrast to the general satisfaction of the assumptions for classical two point particle models. Classical random field models that explicitly include the effects of quantum fluctuations on measurement are possible for experiments that violate Bell inequalities.

  2. Bell inequalities for random fields

    OpenAIRE

    Morgan, Peter

    2004-01-01

    The assumptions required for the derivation of Bell inequalities are not usually satisfied for random fields in which there are any thermal or quantum fluctuations, in contrast to the general satisfaction of the assumptions for classical two point particle models. Classical random field models that explicitly include the effects of quantum fluctuations on measurement are possible for experiments that violate Bell inequalities.

  3. On the Laurent polynomial rings

    International Nuclear Information System (INIS)

    Stefanescu, D.

    1985-02-01

    We describe some properties of the Laurent polynomial rings in a finite number of indeterminates over a commutative unitary ring. We study some subrings of the Laurent polynomial rings. We finally obtain two cancellation properties. (author)

  4. A heuristic algorithm for computing the Poincar\\'e series of the invariants of binary forms

    OpenAIRE

    Djoković, Dragomir Ž.

    2006-01-01

    We propose a heuristic algorithm for fast computation of the Poincar\\'{e} series $P_n(t)$ of the invariants of binary forms of degree $n$, viewed as rational functions. The algorithm is based on certain polynomial identities which remain to be proved rigorously. By using it, we have computed the $P_n(t)$ for $n\\le30$.

  5. Violation of Bell's Inequality Using Continuous Variable Measurements

    Science.gov (United States)

    Thearle, Oliver; Janousek, Jiri; Armstrong, Seiji; Hosseini, Sara; Schünemann Mraz, Melanie; Assad, Syed; Symul, Thomas; James, Matthew R.; Huntington, Elanor; Ralph, Timothy C.; Lam, Ping Koy

    2018-01-01

    A Bell inequality is a fundamental test to rule out local hidden variable model descriptions of correlations between two physically separated systems. There have been a number of experiments in which a Bell inequality has been violated using discrete-variable systems. We demonstrate a violation of Bell's inequality using continuous variable quadrature measurements. By creating a four-mode entangled state with homodyne detection, we recorded a clear violation with a Bell value of B =2.31 ±0.02 . This opens new possibilities for using continuous variable states for device independent quantum protocols.

  6. 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.

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

    KAUST Repository

    Ait-Haddou, Rachid; Goldman, Ron

    2015-01-01

    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.

  8. 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....

  9. Bell, group and tangle

    International Nuclear Information System (INIS)

    Solomon, A. I.

    2010-01-01

    The 'Bell' of the title refers to bipartite Bell states, and their extensions to, for example, tripartite systems. The 'Group' of the title is the Braid Group in its various representations; while 'Tangle' refers to the property of entanglement which is present in both of these scenarios. The objective of this note is to explore the relation between Quantum Entanglement and Topological Links, and to show that the use of the language of entanglement in both cases is more than one of linguistic analogy.

  10. Density of Real Zeros of the Tutte Polynomial

    DEFF Research Database (Denmark)

    Ok, Seongmin; Perrett, Thomas

    2018-01-01

    The Tutte polynomial of a graph is a two-variable polynomial whose zeros and evaluations encode many interesting properties of the graph. In this article we investigate the real zeros of the Tutte polynomials of graphs, and show that they form a dense subset of certain regions of the plane. This ....... This is the first density result for the real zeros of the Tutte polynomial in a region of positive volume. Our result almost confirms a conjecture of Jackson and Sokal except for one region which is related to an open problem on flow polynomials.......The Tutte polynomial of a graph is a two-variable polynomial whose zeros and evaluations encode many interesting properties of the graph. In this article we investigate the real zeros of the Tutte polynomials of graphs, and show that they form a dense subset of certain regions of the plane...

  11. Density of Real Zeros of the Tutte Polynomial

    DEFF Research Database (Denmark)

    Ok, Seongmin; Perrett, Thomas

    2017-01-01

    The Tutte polynomial of a graph is a two-variable polynomial whose zeros and evaluations encode many interesting properties of the graph. In this article we investigate the real zeros of the Tutte polynomials of graphs, and show that they form a dense subset of certain regions of the plane. This ....... This is the first density result for the real zeros of the Tutte polynomial in a region of positive volume. Our result almost confirms a conjecture of Jackson and Sokal except for one region which is related to an open problem on flow polynomials.......The Tutte polynomial of a graph is a two-variable polynomial whose zeros and evaluations encode many interesting properties of the graph. In this article we investigate the real zeros of the Tutte polynomials of graphs, and show that they form a dense subset of certain regions of the plane...

  12. 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....

  13. Optimization over polynomials : Selected topics

    NARCIS (Netherlands)

    Laurent, M.; Jang, Sun Young; Kim, Young Rock; Lee, Dae-Woong; Yie, Ikkwon

    2014-01-01

    Minimizing a polynomial function over a region defined by polynomial inequalities models broad classes of hard problems from combinatorics, geometry and optimization. New algorithmic approaches have emerged recently for computing the global minimum, by combining tools from real algebra (sums of

  14. Review of ϕ3 measurements at Belle

    International Nuclear Information System (INIS)

    Červenkov, Daniel

    2016-01-01

    One of the main goals of the Belle experiment (and the upcoming Belle II experiment) is to measure parameters of electro-weak CP violation (CPV). A useful way to parametrize CPV is through the use of unitarity triangles. A brief introduction tounitarity triangle measurements of CP violation is presented, followed by a summary of recent results from the Belle experiment concerning measurements of the least well constrained angle of the standard unitarity triangle — ϕ_3/γ

  15. Plasma Fibrinogen in Patients With Bell Palsy.

    Science.gov (United States)

    Zhao, Hua; Zhang, Xin; Tang, Yinda; Li, Shiting

    2016-10-01

    To determine the plasma fibrinogen level in patients with Bell palsy and explore the significances of it in Bell palsy. One hundred five consecutive patients with facial paralysis were divided into 3 groups: group I (Bell palsy), group II (temporal bone fractures), and group III (facial nerve schwannoma). In addition, 22 volunteers were defined as control group. Two milliliters fasting venous blood from elbow was collected, and was evaluated by CA-7000 Full-Automatic Coagulation Analyzer. The plasma fibrinogen concentration was significantly higher in the group of patients with Bell palsy (HB IV-VI) than that in the control group (P 0.05); similarly, there was also no marked difference between group III and control group (P >0.05). In group I, the plasma fibrinogen levels became higher with the HB grading increase. The plasma fibrinogen level of HB-VI was highest. Plasma fibrinogen has an important clinical meaning in Bell palsy, which should be used as routine examination items. Defibrinogen in treatment for patients with high plasma fibrinogen content also should be suggested.

  16. Parallel multigrid smoothing: polynomial versus Gauss-Seidel

    International Nuclear Information System (INIS)

    Adams, Mark; Brezina, Marian; Hu, Jonathan; Tuminaro, Ray

    2003-01-01

    Gauss-Seidel is often the smoother of choice within multigrid applications. In the context of unstructured meshes, however, maintaining good parallel efficiency is difficult with multiplicative iterative methods such as Gauss-Seidel. This leads us to consider alternative smoothers. We discuss the computational advantages of polynomial smoothers within parallel multigrid algorithms for positive definite symmetric systems. Two particular polynomials are considered: Chebyshev and a multilevel specific polynomial. The advantages of polynomial smoothing over traditional smoothers such as Gauss-Seidel are illustrated on several applications: Poisson's equation, thin-body elasticity, and eddy current approximations to Maxwell's equations. While parallelizing the Gauss-Seidel method typically involves a compromise between a scalable convergence rate and maintaining high flop rates, polynomial smoothers achieve parallel scalable multigrid convergence rates without sacrificing flop rates. We show that, although parallel computers are the main motivation, polynomial smoothers are often surprisingly competitive with Gauss-Seidel smoothers on serial machines

  17. Parallel multigrid smoothing: polynomial versus Gauss-Seidel

    Science.gov (United States)

    Adams, Mark; Brezina, Marian; Hu, Jonathan; Tuminaro, Ray

    2003-07-01

    Gauss-Seidel is often the smoother of choice within multigrid applications. In the context of unstructured meshes, however, maintaining good parallel efficiency is difficult with multiplicative iterative methods such as Gauss-Seidel. This leads us to consider alternative smoothers. We discuss the computational advantages of polynomial smoothers within parallel multigrid algorithms for positive definite symmetric systems. Two particular polynomials are considered: Chebyshev and a multilevel specific polynomial. The advantages of polynomial smoothing over traditional smoothers such as Gauss-Seidel are illustrated on several applications: Poisson's equation, thin-body elasticity, and eddy current approximations to Maxwell's equations. While parallelizing the Gauss-Seidel method typically involves a compromise between a scalable convergence rate and maintaining high flop rates, polynomial smoothers achieve parallel scalable multigrid convergence rates without sacrificing flop rates. We show that, although parallel computers are the main motivation, polynomial smoothers are often surprisingly competitive with Gauss-Seidel smoothers on serial machines.

  18. 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

  19. Vírus varicela zoster em paralisia de Bell: estudo prospectivo Varicella zoster virus in Bell's palsy: a prospective study

    Directory of Open Access Journals (Sweden)

    Mônica Alcantara de Oliveira Santos

    2010-06-01

    Full Text Available Embora a paralisia de Bell seja o tipo mais frequente de paralisia facial periférica,sua causa ainda é objeto de inúmeros questionamentos. A reativação do vírus varicela zoster tem sido considerada uma das principais causas da paralisia de Bell, porém, os poucos trabalhos que estudam a prevalência do VVZ como agente etiológico da PB são japoneses, o que determina características geográficas e populacionais bastante díspares de nossa população. OBJETIVOS: Verificar a frequência do vírus varicela zoster em saliva de indivíduos com PB, pela técnica de PCR. MATERIAL E MÉTODO: Estudo prospectivo com 171 pacientes com PFP, sendo 120 pacientes portadores de paralisia de Bell, com até uma semana de evolução, sem uso prévio de drogas antivirais. O grupo controle foi composto de 20 adultos sadios. Nestes indivíduos foram coletadas três amostras de saliva em semanas consecutivas, para pesquisa de DNA viral pela técnica de PCR. RESULTADOS: O vírus varicela zoster foi encontrado em amostras de saliva de dois pacientes com paralisia de Bell (1,7%. Nenhum vírus foi identificado no grupo controle. CONCLUSÃO: Foi verificada frequência de 1,7% para vírus varicela zoster em amostras de saliva de pacientes com paralisia de Bell, pela técnica de PCR.Although Bell's palsy is the major cause of acute peripheral facial palsy, its pathogenesis remains unknown. Reactivation of the varicella zoster virus has been implicated as one of the main causes of Bell's palsy, however, studies which investigate the varicella zoster virus reactivation in Bell's palsy patients are mostly Japanese and, therefore, personal and geographic characteristics are quite different from our population. AIMS: To determine varicella zoster virus frequency in saliva samples from patients with Bell's palsy, using PCR. MATERIAL AND METHOD: One hundred seventy one patients with acute peripheral facial palsy were prospectively enrolled in this study. One hundred twenty

  20. 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.

  1. Bell Correlations in a Many-Body System with Finite Statistics

    Science.gov (United States)

    Wagner, Sebastian; Schmied, Roman; Fadel, Matteo; Treutlein, Philipp; Sangouard, Nicolas; Bancal, Jean-Daniel

    2017-10-01

    A recent experiment reported the first violation of a Bell correlation witness in a many-body system [Science 352, 441 (2016)]. Following discussions in this Letter, we address here the question of the statistics required to witness Bell correlated states, i.e., states violating a Bell inequality, in such experiments. We start by deriving multipartite Bell inequalities involving an arbitrary number of measurement settings, two outcomes per party and one- and two-body correlators only. Based on these inequalities, we then build up improved witnesses able to detect Bell correlated states in many-body systems using two collective measurements only. These witnesses can potentially detect Bell correlations in states with an arbitrarily low amount of spin squeezing. We then establish an upper bound on the statistics needed to convincingly conclude that a measured state is Bell correlated.

  2. Efficient computation of Laguerre polynomials

    NARCIS (Netherlands)

    A. Gil (Amparo); J. Segura (Javier); N.M. Temme (Nico)

    2017-01-01

    textabstractAn efficient algorithm and a Fortran 90 module (LaguerrePol) for computing Laguerre polynomials . Ln(α)(z) are presented. The standard three-term recurrence relation satisfied by the polynomials and different types of asymptotic expansions valid for . n large and . α small, are used

  3. 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

  4. 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

  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. 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.

  7. Limitation on Bell's inequality

    Energy Technology Data Exchange (ETDEWEB)

    Buonomano, V [Universidade Estadual de Campinas (Brazil). Inst. de Matematica

    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).

  8. Alexander Graham Bell (170th birthday anniversary)

    OpenAIRE

    V. P. Samokhin; K. V. Meshcherinova

    2017-01-01

    A brief overview of the main works and achievements of Alexander Graham Bell, an educated teacher for the hard of hearing and public figure, author of 30 US patents, is mainly given in the field of telephony and sound recording and reproduction. Biographical information about the Bell family, as well as some interesting facts from his life and activities are given. Scotsman by birth, A. Bell from his youthful years was carried away by the acoustic features of the human voice apparatus and dev...

  9. Need for higher order polynomial basis for polynomial nodal methods employed in LWR calculations

    International Nuclear Information System (INIS)

    Taiwo, T.A.; Palmiotti, G.

    1997-01-01

    The paper evaluates the accuracy and efficiency of sixth order polynomial solutions and the use of one radial node per core assembly for pressurized water reactor (PWR) core power distributions and reactivities. The computer code VARIANT was modified to calculate sixth order polynomial solutions for a hot zero power benchmark problem in which a control assembly along a core axis is assumed to be out of the core. Results are presented for the VARIANT, DIF3D-NODAL, and DIF3D-finite difference codes. The VARIANT results indicate that second order expansion of the within-node source and linear representation of the node surface currents are adequate for this problem. The results also demonstrate the improvement in the VARIANT solution when the order of the polynomial expansion of the within-node flux is increased from fourth to sixth order. There is a substantial saving in computational time for using one radial node per assembly with the sixth order expansion compared to using four or more nodes per assembly and fourth order polynomial solutions. 11 refs., 1 tab

  10. Boxing with Bell

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    2000-04-01

    When Protech Mining moved onto a greenfields site near Ermelo in mid-November last year to start work on the establishment of a box cut for an underground bituminous coal and anthracite mine for Delta Colliery, the company could not have foreseen the difficulties it was to encounter from the unusually high rainfall which fell, almost without abatement, from the time the first sod was turned. Production at the so called Mooiplants mine will commence in March 2001. Mining will take place at a maximum depth of 47 m and coal will be extracted from underground by two conveyor belts and stockpiled. Bell B40 CM mining trucks and an 18 Bell B20 articulated dump truck will be in the haulage fleet. 3 photos.

  11. Experimental Bell-inequality violation without the postselection loophole

    International Nuclear Information System (INIS)

    Lima, G.; Vallone, G.; Chiuri, A.; Cabello, A.; Mataloni, P.

    2010-01-01

    We report on an experimental violation of the Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequality using energy-time-entangled photons. The experiment is not free of the locality and detection loopholes but is the first violation of the Bell-CHSH inequality using energy-time entangled photons which is free of the postselection loophole described by Aerts et al. [Phys. Rev. Lett. 83, 2872 (1999)].

  12. Bell-type inequalities embedded in the subgraph of graph states

    International Nuclear Information System (INIS)

    Hsu, L.-Y.

    2006-01-01

    We investigate the Bell-type inequalities of graph states. In this paper, Bell-type inequalities can be derived based on two kinds of the associated subgraphs of the graph states. First, the star subgraphs lead to the maximal violation of the modified Seevinck-Svetlichny inequalities. Second, cycle subgraphs lead to maximal violation of Bell-type inequalities. As a result, once the associated graph of a graph state is given, the corresponding Bell operators can be immediatedly determined using stabilizing generators. In the above Bell-type inequalities, two measurement settings for each party are required

  13. Two-party Bell inequalities derived from combinatorics via triangular elimination

    International Nuclear Information System (INIS)

    Avis, David; Imai, Hiroshi; Ito, Tsuyoshi; Sasaki, Yuuya

    2005-01-01

    We establish a relation between the two-party Bell inequalities for two-valued measurements and a high-dimensional convex polytope called the cut polytope in polyhedral combinatorics. Using this relation, we propose a method, triangular elimination, to derive tight Bell inequalities from facets of the cut polytope. This method gives two hundred million inequivalent tight Bell inequalities from currently known results on the cut polytope. In addition, this method gives general formulae which represent families of infinitely many Bell inequalities. These results can be used to examine general properties of Bell inequalities

  14. 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

  15. 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.

  16. Testing locality at colliders via Bell's inequality?

    International Nuclear Information System (INIS)

    Abel, S.A.; Dreiner, H.; Dittmar, M.

    1992-01-01

    We consider a measurement of correlated spins at LEP and show that it does not constitute a general test of local-realistic theories via Bell's inequality. The central point of the argument is that such tests, where the spins of two particles are inferred from a scattering distribution, can be described by a local hidden variable theory. We conclude that with present experimental techniques it is not possible to test locality via Bell's inequality at a collider experiment. Finally we suggest an improved fixed-target experiment as a viable test of Bell's inequality. (orig.)

  17. 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.

  18. 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

  19. Generalized Pseudospectral Method and Zeros of Orthogonal Polynomials

    Directory of Open Access Journals (Sweden)

    Oksana Bihun

    2018-01-01

    Full Text Available Via a generalization of the pseudospectral method for numerical solution of differential equations, a family of nonlinear algebraic identities satisfied by the zeros of a wide class of orthogonal polynomials is derived. The generalization is based on a modification of pseudospectral matrix representations of linear differential operators proposed in the paper, which allows these representations to depend on two, rather than one, sets of interpolation nodes. The identities hold for every polynomial family pνxν=0∞ orthogonal with respect to a measure supported on the real line that satisfies some standard assumptions, as long as the polynomials in the family satisfy differential equations Apν(x=qν(xpν(x, where A is a linear differential operator and each qν(x is a polynomial of degree at most n0∈N; n0 does not depend on ν. The proposed identities generalize known identities for classical and Krall orthogonal polynomials, to the case of the nonclassical orthogonal polynomials that belong to the class described above. The generalized pseudospectral representations of the differential operator A for the case of the Sonin-Markov orthogonal polynomials, also known as generalized Hermite polynomials, are presented. The general result is illustrated by new algebraic relations satisfied by the zeros of the Sonin-Markov polynomials.

  20. 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)

  1. Fitting the Fractional Polynomial Model to Non-Gaussian Longitudinal Data

    Directory of Open Access Journals (Sweden)

    Ji Hoon Ryoo

    2017-08-01

    Full Text Available As in cross sectional studies, longitudinal studies involve non-Gaussian data such as binomial, Poisson, gamma, and inverse-Gaussian distributions, and multivariate exponential families. A number of statistical tools have thus been developed to deal with non-Gaussian longitudinal data, including analytic techniques to estimate parameters in both fixed and random effects models. However, as yet growth modeling with non-Gaussian data is somewhat limited when considering the transformed expectation of the response via a linear predictor as a functional form of explanatory variables. In this study, we introduce a fractional polynomial model (FPM that can be applied to model non-linear growth with non-Gaussian longitudinal data and demonstrate its use by fitting two empirical binary and count data models. The results clearly show the efficiency and flexibility of the FPM for such applications.

  2. Quantum dialogue without information leakage based on the entanglement swapping between any two Bell states and the shared secret Bell state

    International Nuclear Information System (INIS)

    Ye, Tian-Yu; Jiang, Li-Zhen

    2014-01-01

    In order to avoid the risk of information leakage during the information mutual transmission between two authorized participants, i.e. Alice and Bob, a quantum dialogue protocol based on the entanglement swapping between any two Bell states and the shared secret Bell state is proposed. The proposed protocol integrates the ideas of block transmission, two-step transmission and unitary operation encoding together using the Bell states as the information carriers. Besides the entanglement swapping between any two Bell states, a shared secret Bell state is also used to overcome the information leakage problem, which not only makes Bob aware of the prepared initial state but also is used for Bob's encoding and entanglement swapping. Security analysis shows that the proposed protocol can resist the general active attacks from an outside eavesdropper Eve. Moreover, the relation between the maximal amount of information Eve can gain and the detection probability is derived. (paper)

  3. 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.

  4. 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.

  5. Thermophysical properties of binary mixtures of triethoxysilane, methyltriethoxysilane, vinyltriethoxysilane and 3-mercaptopropyltriethoxysilane with ethylbenzene at various temperatures

    International Nuclear Information System (INIS)

    Zhang, Yindi; Dong, Hong; Wu, Chuan; Yu, Lijiao

    2014-01-01

    Highlights: • Values of ρ and n D of binary mixtures containing organosilicon compounds at different temperatures were measured. • α, V m E , V ¯ i E,∞ , (n 2 ) E , R m and ΔR m were studied. • The excess molar volumes, excess squared refraction indices and the deviations in molar refractions were negative. - Abstract: The density and refractive index were determined for binary mixtures of triethoxysilane, methyltriethoxysilane, vinyltriethoxysilane and 3-mercaptopropyltriethoxysilane with ethylbenzene at different temperatures (T = 288.15, 298.15, 308.15, 318.15 and 328.15 K) and atmospheric pressure using a DMA4500 and RXA170 combined system. The excess molar volume (V m E ), partial excess volume at infinite dilution (V ¯ i E,∞ ), isobaric coefficient of thermal expansion (α), excess squared refraction indices [(n 2 ) E ], Lorentz–Lorenz molar refraction (R m ) and the deviation in molar refraction (ΔR m ) have been calculated using this data. The results have been incorporated into the Redlich–Kister equation and used to estimate the binary interaction parameter and standard deviation. In addition, the excess molar volume (V m E ) was calculated and correlated using the Legendre polynomials. The value of partial excess volume at infinite dilution (V ¯ i E,∞ ) for these binary systems at different temperatures was calculated from either the adjustable parameters of Redlich–Kister smoothing equation or the Legendre polynomials. The isobaric coefficient of thermal expansion (α) of the binary systems was estimated using the temperature dependence of the densities. The results indicate that the excess molar volumes, excess squared refraction indices and the deviations in molar refractions at each temperature were negative. These phenomena are a result of a number of factors including: the partial interstitial accommodation effect, disruption in the orientational order of the pure components and steric structure

  6. Polynomial sequences generated by infinite Hessenberg matrices

    Directory of Open Access Journals (Sweden)

    Verde-Star Luis

    2017-01-01

    Full Text Available We show that an infinite lower Hessenberg matrix generates polynomial sequences that correspond to the rows of infinite lower triangular invertible matrices. Orthogonal polynomial sequences are obtained when the Hessenberg matrix is tridiagonal. We study properties of the polynomial sequences and their corresponding matrices which are related to recurrence relations, companion matrices, matrix similarity, construction algorithms, and generating functions. When the Hessenberg matrix is also Toeplitz the polynomial sequences turn out to be of interpolatory type and we obtain additional results. For example, we show that every nonderogative finite square matrix is similar to a unique Toeplitz-Hessenberg matrix.

  7. 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.

  8. ["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.

  9. Near-Optimal and Explicit Bell Inequality Violations

    NARCIS (Netherlands)

    Buhrman, H.; Regev, O.; Scarpa, G.; de Wolf, R.

    2011-01-01

    Bell inequality violations correspond to behavior of entangled quantum systems that cannot be simulated classically. We give two new two-player games with Bell inequality violations that are stronger, fully explicit, and arguably simpler than earlier work.The first game is based on the Hidden

  10. Hexagonal pixel detector with time encoded binary readout

    International Nuclear Information System (INIS)

    Hoedlmoser, H.; Varner, G.; Cooney, M.

    2009-01-01

    The University of Hawaii is developing continuous acquisition pixel (CAP) detectors for vertexing applications in lepton colliding experiments such as SuperBelle or ILC. In parallel to the investigation of different technology options such as MAPS or SOI, both analog and binary readout concepts have been tested. First results with a binary readout scheme in which the hit information is time encoded by means of a signal shifting mechanism have recently been published. This paper explains the hit reconstruction for such a binary detector with an emphasis on fake hit reconstruction probabilities in order to evaluate the rate capability in a high background environment such as the planned SuperB factory at KEK. The results show that the binary concept is at least comparable to any analog readout strategy if not better in terms of occupancy. Furthermore, we present a completely new binary readout strategy in which the pixel cells are arranged in a hexagonal grid allowing the use of three independent output directions to reduce reconstruction ambiguities. The new concept uses the same signal shifting mechanism for time encoding, however, in dedicated transfer lines on the periphery of the detector, which enables higher shifting frequencies. Detailed Monte Carlo simulations of full size pixel matrices including hit and BG generation, signal generation, and data reconstruction show that by means of multiple signal transfer lines on the periphery the pixel can be made smaller (higher resolution), the number of output channels and the data volume per triggered event can be reduced dramatically, fake hit reconstruction is lowered to a minimum and the resulting effective occupancies are less than 10 -4 . A prototype detector has been designed in the AMS 0.35μm Opto process and is currently under fabrication.

  11. The strong Bell inequalities: A proposed experimental test

    Science.gov (United States)

    Fry, Edward S.

    1994-01-01

    All previous experimental tests of Bell inequalities have required additional assumptions. The strong Bell inequalities (i.e. those requiring no additional assumptions) have never been tested. An experiment has been designed that can, for the first time, provide a definitive test of the strong Bell inequalities. Not only will the detector efficiency loophole be closed; but the locality condition will also be rigorously enforced. The experiment involves producing two Hg-199 atoms by a resonant Raman dissociation of a mercury dimer ((199)Hg2) that is in an electronic and nuclear spin singlet state. Bell inequalities can be tested by measuring angular momentum correlations between the spin one-half nuclei of the two Hg-199 atoms. The method used to make these latter measurements will be described.

  12. BellTest and CHSH experiments with more than two settings

    Energy Technology Data Exchange (ETDEWEB)

    Basoalto, R M; Percival, I C [Department of Physics, Queen Mary University of London, Mile End Road, London E1 4NS (United Kingdom)

    2003-07-04

    Strong nonlocality allows signals faster than light. Weak nonlocality is a statistical property of classical events for which there is no realistic local theory. This requires the violation of at least one general Bell inequality. The theory of ideal quantum measurements predicts weak nonlocality but not strong nonlocality. Bell experiment here refers to any experiment designed to demonstrate weak nonlocality. BellTest is a computer program generally available on the Web to help planning and analysis of such Bell experiments. In Mode 1 it obtains general Bell inequalities. In Mode 2 it tests for their violation. We describe its use, with some new results for illustration.

  13. 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)

  14. 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?

  15. 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)

  16. Cosmographic analysis with Chebyshev polynomials

    Science.gov (United States)

    Capozziello, Salvatore; D'Agostino, Rocco; Luongo, Orlando

    2018-05-01

    The limits of standard cosmography are here revised addressing the problem of error propagation during statistical analyses. To do so, we propose the use of Chebyshev polynomials to parametrize cosmic distances. In particular, we demonstrate that building up rational Chebyshev polynomials significantly reduces error propagations with respect to standard Taylor series. This technique provides unbiased estimations of the cosmographic parameters and performs significatively better than previous numerical approximations. To figure this out, we compare rational Chebyshev polynomials with Padé series. In addition, we theoretically evaluate the convergence radius of (1,1) Chebyshev rational polynomial and we compare it with the convergence radii of Taylor and Padé approximations. We thus focus on regions in which convergence of Chebyshev rational functions is better than standard approaches. With this recipe, as high-redshift data are employed, rational Chebyshev polynomials remain highly stable and enable one to derive highly accurate analytical approximations of Hubble's rate in terms of the cosmographic series. Finally, we check our theoretical predictions by setting bounds on cosmographic parameters through Monte Carlo integration techniques, based on the Metropolis-Hastings algorithm. We apply our technique to high-redshift cosmic data, using the Joint Light-curve Analysis supernovae sample and the most recent versions of Hubble parameter and baryon acoustic oscillation measurements. We find that cosmography with Taylor series fails to be predictive with the aforementioned data sets, while turns out to be much more stable using the Chebyshev approach.

  17. 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.

  18. 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.

  19. A possible loophole in the theorem of Bell.

    Science.gov (United States)

    Hess, K; Philipp, W

    2001-12-04

    The celebrated inequalities of Bell are based on the assumption that local hidden parameters exist. When combined with conflicting experimental results, these inequalities appear to prove that local hidden parameters cannot exist. This contradiction suggests to many that only instantaneous action at a distance can explain the Einstein, Podolsky, and Rosen type of experiments. We show that, in addition to the assumption that hidden parameters exist, Bell tacitly makes a variety of other assumptions that contribute to his being able to obtain the desired contradiction. For instance, Bell assumes that the hidden parameters do not depend on time and are governed by a single probability measure independent of the analyzer settings. We argue that the exclusion of time has neither a physical nor a mathematical basis but is based on Bell's translation of the concept of Einstein locality into the language of probability theory. Our additional set of local hidden variables includes time-like correlated parameters and a generalized probability density. We prove that our extended space of local hidden variables does not permit Bell-type proofs to go forward.

  20. Device-independent randomness generation from several Bell estimators

    Science.gov (United States)

    Nieto-Silleras, Olmo; Bamps, Cédric; Silman, Jonathan; Pironio, Stefano

    2018-02-01

    Device-independent randomness generation and quantum key distribution protocols rely on a fundamental relation between the non-locality of quantum theory and its random character. This relation is usually expressed in terms of a trade-off between the probability of guessing correctly the outcomes of measurements performed on quantum systems and the amount of violation of a given Bell inequality. However, a more accurate assessment of the randomness produced in Bell experiments can be obtained if the value of several Bell expressions is simultaneously taken into account, or if the full set of probabilities characterizing the behavior of the device is considered. We introduce protocols for device-independent randomness generation secure against classical side information, that rely on the estimation of an arbitrary number of Bell expressions or even directly on the experimental frequencies of measurement outcomes. Asymptotically, this results in an optimal generation of randomness from experimental data (as measured by the min-entropy), without having to assume beforehand that the devices violate a specific Bell inequality.

  1. 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

  2. On polynomial solutions of the Heun equation

    International Nuclear Information System (INIS)

    Gurappa, N; Panigrahi, Prasanta K

    2004-01-01

    By making use of a recently developed method to solve linear differential equations of arbitrary order, we find a wide class of polynomial solutions to the Heun equation. We construct the series solution to the Heun equation before identifying the polynomial solutions. The Heun equation extended by the addition of a term, -σ/x, is also amenable for polynomial solutions. (letter to the editor)

  3. 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.

  4. Measurement and adjustment of dumb-bells for 9-cell TESLA cavity

    International Nuclear Information System (INIS)

    Xu Wencan; Quan Shengwen; Hao Jiankui; Jiang Tao; Zhang Baocheng; Zhao Kui

    2008-01-01

    Correct Dumb-bells are very important to make sure the right field flatness, frequency of TM010 mode and length of 9-cell TESLA cavity. The shape of the dumb-bells will be wrong due to deep drawing, machining and EB welding. Then, the dumb-bells should be adjusted after iris and stiffness welding according to the mechanical and microwave measurement. Peking University has set up facilities for measuring and correcting the dumb-bells. This paper discusses the method of measuring and correcting the dumb-bells. (authors)

  5. 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.

  6. 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)

  7. Colouring and knot polynomials

    International Nuclear Information System (INIS)

    Welsh, D.J.A.

    1991-01-01

    These lectures will attempt to explain a connection between the recent advances in knot theory using the Jones and related knot polynomials with classical problems in combinatorics and statistical mechanics. The difficulty of some of these problems will be analysed in the context of their computational complexity. In particular we shall discuss colourings and groups valued flows in graphs, knots and the Jones and Kauffman polynomials, the Ising, Potts and percolation problems of statistical physics, computational complexity of the above problems. (author). 20 refs, 9 figs

  8. Towards Loophole-Free Optical Bell Test of CHSH Inequality

    Science.gov (United States)

    Tan, Yong-gang; Li, Hong-wei

    2016-09-01

    Bell test had been suggested to end the long-standing debate on the EPR paradox, while the imperfections of experimental devices induce some loopholes in Bell test experiments and hence the assumption of local reality by EPR cannot be excluded with current experimental results. In optical Bell test experiments, the locality loophole can be closed easily, while the attempt of closing detection loophole requires very high efficiency of single photon detectors. Previous studies showed that the violation of Clauser-Horne-Shimony-Holt (CHSH) inequality with maximally entangled states requires the detection efficiency to be higher than 82.8 %. In this paper, we raise a modified CHSH inequality that covers all measurement events including the efficient and inefficient detections in the Bell test and prove that all local hidden models can be excluded when the inequality is violated. We find that, when non-maximally entangled states are applied to the Bell test, the lowest detection efficiency for violation of the present inequality is 66.7 %. This makes it feasible to close the detection loophole and the locality loophole simultaneously in optical Bell test of CHSH inequality.

  9. 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

  10. 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 ...

  11. Bell inequalities under non-ideal conditions

    OpenAIRE

    Especial, João N. C.

    2012-01-01

    Bell inequalities applicable to non-ideal EPRB experiments are critical to the interpretation of experimental Bell tests. In this article it is shown that previous treatments of this subject are incorrect due to an implicit assumption and new inequalities are derived under general conditions. Published experimental evidence is reinterpreted under these results and found to be entirely compatible with local-realism, both, when experiments involve inefficient detection, if fair-sampling detecti...

  12. 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.

  13. Beat characteristics and beat maps of the King Seong-deok Divine Bell

    Science.gov (United States)

    Kim, Seock-Hyun; Lee, Chi-Wook; Lee, Jang-Moo

    2005-03-01

    King Seong-deok Divine Bell is the second oldest bell in Korea. The bell is considered to have the best sound quality among Korean bells. The beat phenomenon is one of the most important characteristics for the sound of the King Seong-deok Divine Bell. In this study, the relationships between the modal parameters and the peculiar beat phenomena of the bell are investigated. It is theoretically proved from the beat characteristics that the sound might indeed be heard differently depending on the listening positions. The beat map method is introduced to visualize the beat distribution properties. It is shown that the beat maps can be drawn with a theoretical model based on the modal data of the bell. Using the beat maps of the King Seong-deok Divine Bell, it is investigated why clear and unclear beats, large and small amplitudes of the vibrations are repeated periodically along the circumference of the bell. Furthermore, the effect of the striking position on the beat distribution property is examined systematically.

  14. Belle status and prospects

    International Nuclear Information System (INIS)

    Hara, Takanori

    2003-01-01

    We review the current status and the future perspectives of the Belle experiment and KEKB asymmetric e + e - collider. Thanks to many efforts of Belle collaborators and KEKB accelerator staffs, we could accumulate a 41.8 fb -1 data by the end of 2001 (more than 80 fb -1 data by the end of summer, 2002), also the KEKB recorded the highest peak luminosity (7.35 x 10 33 cm -2 s -1 ) in the world. Furthermore, the Super KEKB project is being proposed not only to extract the CP violation parameters and moduluses of the CKM matrix with high accuracy, but also to search for B rare decays and explore beyond the Standard Model

  15. Self-guided method to search maximal Bell violations for unknown quantum states

    Science.gov (United States)

    Yang, Li-Kai; Chen, Geng; Zhang, Wen-Hao; Peng, Xing-Xiang; Yu, Shang; Ye, Xiang-Jun; Li, Chuan-Feng; Guo, Guang-Can

    2017-11-01

    In recent decades, a great variety of research and applications concerning Bell nonlocality have been developed with the advent of quantum information science. Providing that Bell nonlocality can be revealed by the violation of a family of Bell inequalities, finding maximal Bell violation (MBV) for unknown quantum states becomes an important and inevitable task during Bell experiments. In this paper we introduce a self-guided method to find MBVs for unknown states using a stochastic gradient ascent algorithm (SGA), by parametrizing the corresponding Bell operators. For three investigated systems (two qubit, three qubit, and two qutrit), this method can ascertain the MBV of general two-setting inequalities within 100 iterations. Furthermore, we prove SGA is also feasible when facing more complex Bell scenarios, e.g., d -setting d -outcome Bell inequality. Moreover, compared to other possible methods, SGA exhibits significant superiority in efficiency, robustness, and versatility.

  16. Factoring polynomials over arbitrary finite fields

    NARCIS (Netherlands)

    Lange, T.; Winterhof, A.

    2000-01-01

    We analyse an extension of Shoup's (Inform. Process. Lett. 33 (1990) 261–267) deterministic algorithm for factoring polynomials over finite prime fields to arbitrary finite fields. In particular, we prove the existence of a deterministic algorithm which completely factors all monic polynomials of

  17. 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

  18. 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.

  19. A Determinant Expression for the Generalized Bessel Polynomials

    Directory of Open Access Journals (Sweden)

    Sheng-liang Yang

    2013-01-01

    Full Text Available Using the exponential Riordan arrays, we show that a variation of the generalized Bessel polynomial sequence is of Sheffer type, and we obtain a determinant formula for the generalized Bessel polynomials. As a result, the Bessel polynomial is represented as determinant the entries of which involve Catalan numbers.

  20. A generalization of the Bernoulli polynomials

    Directory of Open Access Journals (Sweden)

    Pierpaolo Natalini

    2003-01-01

    Full Text Available A generalization of the Bernoulli polynomials and, consequently, of the Bernoulli numbers, is defined starting from suitable generating functions. Furthermore, the differential equations of these new classes of polynomials are derived by means of the factorization method introduced by Infeld and Hull (1951.

  1. 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.

  2. 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...

  3. 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.

  4. The Bells' Capture note TH-3054-CERN

    Energy Technology Data Exchange (ETDEWEB)

    Hartouni, Ed P. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

    2014-01-29

    This document revisits the paper by M. Bell and J. S. Bell “Capture of Cooling Electrons by Cool Protons” TH-3054-CERN (March 30, 1981). I expand the treatment to include e+e- capture.

  5. Testing Bell's inequalities

    International Nuclear Information System (INIS)

    Aspect, A.; Ecole Normale Superieure, 75 - Paris

    1991-01-01

    Testing Bell's inequalities described in the paper 'On the Einstein-Podolsky-Rosen paradox' the conclusions were extremely clear and completely convincing, but there was something special about this paper: it led to two contradictory conclusions. The first part showed that EPR correlations predicted by quantum mechanics are so strong that one can hardly avoid the conclusion that quantum mechanics should be completed by some supplementary parameters (the so-called 'hidden-variables'). But the second part demonstrated that the hidden-variables description in fact contradicts some predictions of quantum mechanics, which is to say both theories predict different results. At the end of the sixties, there was no experimental result to answer the question. The contradiction discovered by John Bell is so subtle that it was necessary to design and build specific experiments. The problems of such experiments are discussed. (R.P.) 7 refs., 4 figs

  6. On Multiple Interpolation Functions of the -Genocchi Polynomials

    Directory of Open Access Journals (Sweden)

    Jin Jeong-Hee

    2010-01-01

    Full Text Available Abstract Recently, many mathematicians have studied various kinds of the -analogue of Genocchi numbers and polynomials. In the work (New approach to q-Euler, Genocchi numbers and their interpolation functions, "Advanced Studies in Contemporary Mathematics, vol. 18, no. 2, pp. 105–112, 2009.", Kim defined new generating functions of -Genocchi, -Euler polynomials, and their interpolation functions. In this paper, we give another definition of the multiple Hurwitz type -zeta function. This function interpolates -Genocchi polynomials at negative integers. Finally, we also give some identities related to these polynomials.

  7. 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)

  8. Common questions about Bell palsy.

    Science.gov (United States)

    Albers, Janet R; Tamang, Stephen

    2014-02-01

    Bell palsy is an acute affliction of the facial nerve, resulting in sudden paralysis or weakness of the muscles on one side of the face. Testing patients with unilateral facial paralysis for diabetes mellitus or Lyme disease is not routinely recommended. Patients with Lyme disease typically present with additional manifestations, such as arthritis, rash, or facial swelling. Diabetes may be a comorbidity of Bell palsy, but testing is not needed in the absence of other indications, such as hypertension. In patients with atypical symptoms, magnetic resonance imaging with contrast enhancement can be used to rule out cranial mass effect and to add prognostic value. Steroids improve resolution of symptoms in patients with Bell palsy and remain the preferred treatment. Antiviral agents have a limited role, and may improve outcomes when combined with steroids in patients with severe symptoms. When facial paralysis is prolonged, surgery may be indicated to prevent ocular desiccation secondary to incomplete eyelid closure. Facial nerve decompression is rarely indicated or performed. Physical therapy modalities, including electrostimulation, exercise, and massage, are neither beneficial nor harmful.

  9. 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)

  10. Bell automation system on STM32F4 Discovery board

    OpenAIRE

    Božović, Denis

    2017-01-01

    A bell automation system is a device, the aim of which is to maximize the automation of bell ringing and thus release from duty the person in charge of it. The modern way of life and forms of employment generally make it difficult for human bell-ringers to carry out the task as they did for centuries. In this thesis it is explained what can be expected of the bell automation system in the regions of Slovenia, and why it is desirable that it supports certain functionalities. Using as an exampl...

  11. The modified Gauss diagonalization of polynomial matrices

    International Nuclear Information System (INIS)

    Saeed, K.

    1982-10-01

    The Gauss algorithm for diagonalization of constant matrices is modified for application to polynomial matrices. Due to this modification the diagonal elements become pure polynomials rather than rational functions. (author)

  12. 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…

  13. Numerical Simulation of Polynomial-Speed Convergence Phenomenon

    Science.gov (United States)

    Li, Yao; Xu, Hui

    2017-11-01

    We provide a hybrid method that captures the polynomial speed of convergence and polynomial speed of mixing for Markov processes. The hybrid method that we introduce is based on the coupling technique and renewal theory. We propose to replace some estimates in classical results about the ergodicity of Markov processes by numerical simulations when the corresponding analytical proof is difficult. After that, all remaining conclusions can be derived from rigorous analysis. Then we apply our results to seek numerical justification for the ergodicity of two 1D microscopic heat conduction models. The mixing rate of these two models are expected to be polynomial but very difficult to prove. In both examples, our numerical results match the expected polynomial mixing rate well.

  14. The Real "Toll" of A. G. Bell: Lessons about Eugenics

    Science.gov (United States)

    Greenwald, Brian H.

    2009-01-01

    Historian Brian Greenwald offers a revisionist interpretation of Bell. He reviews Bell's role and influence within the American eugenics movement and shows that Bell had the respect of the most prominent American eugenicists. His intimate knowledge of deafness, from personal experience with his mother and wife and from his studies of deaf people…

  15. 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 ...

  16. [Bell's palsy and facial pain associated with toxocara infection].

    Science.gov (United States)

    Bachtiar, Arian; Auer, Herbert; Finsterer, Josef

    2012-10-01

    Toxocarosis involving cranial nerves is extremely rare and almost exclusively concerns the optic nerve. Toxocarosis involving the seventh cranial nerve has not been reported. A 33y male developed left-sided Bell's palsy two days after left-sided otalgia 6y before. Despite extensive diagnostic work-up at that time the cause of Bell's palsy remained unknown. During the following years Bell's palsy slightly improved but retromandibular pain remained almost unchanged and he developed enlarged lymph nodes along the jugular veins, submandibularly, and in the trigonum caroticum. Re-evaluation 6y later revealed an increased titer of serum antibodies against Toxocara canis and a positive Westernblot for Toxocara canis ES-antigen. Despite absent eosinophilia in the serum, toxocarosis was diagnosed and a therapy with albendazole initiated, with benefit for retromandibular pain, but hardly for Bell's palsy or enlarged lymph nodes. CSF investigations after albendazole revealed a positive Westernblot for antibodies against toxocara but absent pleocytosis or eosinophilia, and negative PCR for Toxocara canis. Visceral larva migrans due to Toxocara canis may be associated with Bell's palsy, retromandibular pain, and lymphadenopathy. A causal relation between Bell's palsy and the helminthosis remains speculative. Adequate therapy years after onset of the infestation may be of limited benefit.

  17. 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)

  18. A companion matrix for 2-D polynomials

    International Nuclear Information System (INIS)

    Boudellioua, M.S.

    1995-08-01

    In this paper, a matrix form analogous to the companion matrix which is often encountered in the theory of one dimensional (1-D) linear systems is suggested for a class of polynomials in two indeterminates and real coefficients, here referred to as two dimensional (2-D) polynomials. These polynomials arise in the context of 2-D linear systems theory. Necessary and sufficient conditions are also presented under which a matrix is equivalent to this companion form. (author). 6 refs

  19. 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.

  20. 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.

  1. Global sensitivity analysis by polynomial dimensional decomposition

    Energy Technology Data Exchange (ETDEWEB)

    Rahman, Sharif, E-mail: rahman@engineering.uiowa.ed [College of Engineering, The University of Iowa, Iowa City, IA 52242 (United States)

    2011-07-15

    This paper presents a polynomial dimensional decomposition (PDD) method for global sensitivity analysis of stochastic systems subject to independent random input following arbitrary probability distributions. The method involves Fourier-polynomial expansions of lower-variate component functions of a stochastic response by measure-consistent orthonormal polynomial bases, analytical formulae for calculating the global sensitivity indices in terms of the expansion coefficients, and dimension-reduction integration for estimating the expansion coefficients. Due to identical dimensional structures of PDD and analysis-of-variance decomposition, the proposed method facilitates simple and direct calculation of the global sensitivity indices. Numerical results of the global sensitivity indices computed for smooth systems reveal significantly higher convergence rates of the PDD approximation than those from existing methods, including polynomial chaos expansion, random balance design, state-dependent parameter, improved Sobol's method, and sampling-based methods. However, for non-smooth functions, the convergence properties of the PDD solution deteriorate to a great extent, warranting further improvements. The computational complexity of the PDD method is polynomial, as opposed to exponential, thereby alleviating the curse of dimensionality to some extent.

  2. Polynomial asymptotic stability of damped stochastic differential equations

    Directory of Open Access Journals (Sweden)

    John Appleby

    2004-08-01

    Full Text Available The paper studies the polynomial convergence of solutions of a scalar nonlinear It\\^{o} stochastic differential equation\\[dX(t = -f(X(t\\,dt + \\sigma(t\\,dB(t\\] where it is known, {\\it a priori}, that $\\lim_{t\\rightarrow\\infty} X(t=0$, a.s. The intensity of the stochastic perturbation $\\sigma$ is a deterministic, continuous and square integrable function, which tends to zero more quickly than a polynomially decaying function. The function $f$ obeys $\\lim_{x\\rightarrow 0}\\mbox{sgn}(xf(x/|x|^\\beta = a$, for some $\\beta>1$, and $a>0$.We study two asymptotic regimes: when $\\sigma$ tends to zero sufficiently quickly the polynomial decay rate of solutions is the same as for the deterministic equation (when $\\sigma\\equiv0$. When $\\sigma$ decays more slowly, a weaker almost sure polynomial upper bound on the decay rate of solutions is established. Results which establish the necessity for $\\sigma$ to decay polynomially in order to guarantee the almost sure polynomial decay of solutions are also proven.

  3. Polynomial meta-models with canonical low-rank approximations: Numerical insights and comparison to sparse polynomial chaos expansions

    International Nuclear Information System (INIS)

    Konakli, Katerina; Sudret, Bruno

    2016-01-01

    The growing need for uncertainty analysis of complex computational models has led to an expanding use of meta-models across engineering and sciences. The efficiency of meta-modeling techniques relies on their ability to provide statistically-equivalent analytical representations based on relatively few evaluations of the original model. Polynomial chaos expansions (PCE) have proven a powerful tool for developing meta-models in a wide range of applications; the key idea thereof is to expand the model response onto a basis made of multivariate polynomials obtained as tensor products of appropriate univariate polynomials. The classical PCE approach nevertheless faces the “curse of dimensionality”, namely the exponential increase of the basis size with increasing input dimension. To address this limitation, the sparse PCE technique has been proposed, in which the expansion is carried out on only a few relevant basis terms that are automatically selected by a suitable algorithm. An alternative for developing meta-models with polynomial functions in high-dimensional problems is offered by the newly emerged low-rank approximations (LRA) approach. By exploiting the tensor–product structure of the multivariate basis, LRA can provide polynomial representations in highly compressed formats. Through extensive numerical investigations, we herein first shed light on issues relating to the construction of canonical LRA with a particular greedy algorithm involving a sequential updating of the polynomial coefficients along separate dimensions. Specifically, we examine the selection of optimal rank, stopping criteria in the updating of the polynomial coefficients and error estimation. In the sequel, we confront canonical LRA to sparse PCE in structural-mechanics and heat-conduction applications based on finite-element solutions. Canonical LRA exhibit smaller errors than sparse PCE in cases when the number of available model evaluations is small with respect to the input

  4. Polynomial meta-models with canonical low-rank approximations: Numerical insights and comparison to sparse polynomial chaos expansions

    Energy Technology Data Exchange (ETDEWEB)

    Konakli, Katerina, E-mail: konakli@ibk.baug.ethz.ch; Sudret, Bruno

    2016-09-15

    The growing need for uncertainty analysis of complex computational models has led to an expanding use of meta-models across engineering and sciences. The efficiency of meta-modeling techniques relies on their ability to provide statistically-equivalent analytical representations based on relatively few evaluations of the original model. Polynomial chaos expansions (PCE) have proven a powerful tool for developing meta-models in a wide range of applications; the key idea thereof is to expand the model response onto a basis made of multivariate polynomials obtained as tensor products of appropriate univariate polynomials. The classical PCE approach nevertheless faces the “curse of dimensionality”, namely the exponential increase of the basis size with increasing input dimension. To address this limitation, the sparse PCE technique has been proposed, in which the expansion is carried out on only a few relevant basis terms that are automatically selected by a suitable algorithm. An alternative for developing meta-models with polynomial functions in high-dimensional problems is offered by the newly emerged low-rank approximations (LRA) approach. By exploiting the tensor–product structure of the multivariate basis, LRA can provide polynomial representations in highly compressed formats. Through extensive numerical investigations, we herein first shed light on issues relating to the construction of canonical LRA with a particular greedy algorithm involving a sequential updating of the polynomial coefficients along separate dimensions. Specifically, we examine the selection of optimal rank, stopping criteria in the updating of the polynomial coefficients and error estimation. In the sequel, we confront canonical LRA to sparse PCE in structural-mechanics and heat-conduction applications based on finite-element solutions. Canonical LRA exhibit smaller errors than sparse PCE in cases when the number of available model evaluations is small with respect to the input

  5. Emissões otoacústicas por produtos de distorção na paralisia de Bell Distortion product otoacustic emissions in Bell's palsy

    Directory of Open Access Journals (Sweden)

    Cristiane A. Kasse

    2002-10-01

    Full Text Available Introdução: O núcleo do nervo facial e do núcleo olivar superior são conectados por fibras, desta forma uma lesão nesta conecção poderia interferir na função das células ciliadas externas, alterando o exame de emissão otoacústica por produtos de distorção (EOAPD. Objetivo: Observar a possibilidade da paralisia de Bell afetar a função das células ciliadas externas através da EOAPD. Forma do Estudo: Prospectivo clínico. Material e Método: Quarenta pacientes com paralisia de Bell foram comparados com 69 pacientes normais (grupo controle, usando EOAPD. Resultados: Os pacientes com paralisia de Bell e EOAPD alterados foram de 17,5% e no grupo controle de 7,2%, sem diferença estatística entre os valores. Não se observou também uma correlação entre o reflexo estapediano e o grau da paralisia facial com a EOAPD. Conclusão: Não observamos correlação entre EOAPD e a paralisia de Bell.Introduction: The facial nucleus and olivar nucleus are connected with fibers, then a lesion in this conection could interfer in the outer cell function changing the result of otoacoustic emission product distortion test (DPOE. Objective: To observe the possibility of Bell's palsy affect the function of outer hair cells, using the DPOE test. Study Design: Prospective clinical. Material and Method: Forty patients with Bell's palsy were compared with 69 patients without symptons (control group using DPOE. Results: The patients with Bell's palsy without DPOE response were 17.5% and in the control group, 7.2%, without statistical difference between them. We did not observe a correlation with stapedium reflex and degree of palsy and DPOE. Conclusion: There was no correlation with Bell's palsy and DPOE.

  6. Bell's inequality without alternative settings

    International Nuclear Information System (INIS)

    Cabello, Adan

    2003-01-01

    A suitable generalized measurement described by a 4-element positive operator-valued measure (POVM) on each particle of a two-qubit system in the singlet state is, from the point of view of Einstein, Podolsky, and Rosen's (EPR's) criterion of elements of reality, equivalent to a random selection between two alternative projective measurements. It is shown that an EPR-experiment with a fixed POVM on each particle provides a violation of Bell's inequality without requiring local observers to choose between the alternatives. This approach could be useful for designing a loophole-free test of Bell's inequality

  7. 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.

  8. 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

  9. 2-variable Laguerre matrix polynomials and Lie-algebraic techniques

    International Nuclear Information System (INIS)

    Khan, Subuhi; Hassan, Nader Ali Makboul

    2010-01-01

    The authors introduce 2-variable forms of Laguerre and modified Laguerre matrix polynomials and derive their special properties. Further, the representations of the special linear Lie algebra sl(2) and the harmonic oscillator Lie algebra G(0,1) are used to derive certain results involving these polynomials. Furthermore, the generating relations for the ordinary as well as matrix polynomials related to these matrix polynomials are derived as applications.

  10. 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 of the Cremer type correspond to parameters at the boundary of ahyperbolic component of the Mandelbrot set. In this paper we concentrate onthe main cardioid component. We investigate the differences between two-sided(i.e. alternating) and one-sided parabolic perturbations.In the two-sided case, we prove...... 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...

  11. 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.

  12. 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.

  13. Topological quantum information, virtual Jones polynomials and Khovanov homology

    International Nuclear Information System (INIS)

    Kauffman, Louis H

    2011-01-01

    In this paper, we give a quantum statistical interpretation of the bracket polynomial state sum 〈K〉, the Jones polynomial V K (t) and virtual knot theory versions of the Jones polynomial, including the arrow polynomial. We use these quantum mechanical interpretations to give new quantum algorithms for these Jones polynomials. In those cases where the Khovanov homology is defined, the Hilbert space C(K) of our model is isomorphic with the chain complex for Khovanov homology with coefficients in the complex numbers. There is a natural unitary transformation U:C(K) → C(K) such that 〈K〉 = Trace(U), where 〈K〉 denotes the evaluation of the state sum model for the corresponding polynomial. We show that for the Khovanov boundary operator ∂:C(K) → C(K), we have the relationship ∂U + U∂ = 0. Consequently, the operator U acts on the Khovanov homology, and we obtain a direct relationship between the Khovanov homology and this quantum algorithm for the Jones polynomial. (paper)

  14. Generating optimal states for a homodyne Bell test

    International Nuclear Information System (INIS)

    Daffer, S.; Knight, P.L.

    2005-01-01

    Full text: We present a protocol that produces a conditionally prepared state that can be used for a Bell test based on homodyne detection. Based on the results of Munro, the state is near-optimal for Bell inequality violations based on quadrature-phase homodyne measurements that use correlated photon-number states. The scheme utilizes the Gaussian entanglement distillation protocol of Eisert et. al. and uses only beam splitters and photodetection to conditionally prepare a non-Gaussian state from a source of two-mode squeezed states with low squeezing parameter, permitting a loophole-free test of Bell inequalities. (author)

  15. 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.

  16. The simulation library of the Belle II software system

    Science.gov (United States)

    Kim, D. Y.; Ritter, M.; Bilka, T.; Bobrov, A.; Casarosa, G.; Chilikin, K.; Ferber, T.; Godang, R.; Jaegle, I.; Kandra, J.; Kodys, P.; Kuhr, T.; Kvasnicka, P.; Nakayama, H.; Piilonen, L.; Pulvermacher, C.; Santelj, L.; Schwenker, B.; Sibidanov, A.; Soloviev, Y.; Starič, M.; Uglov, T.

    2017-10-01

    SuperKEKB, the next generation B factory, has been constructed in Japan as an upgrade of KEKB. This brand new e+ e- collider is expected to deliver a very large data set for the Belle II experiment, which will be 50 times larger than the previous Belle sample. Both the triggered physics event rate and the background event rate will be increased by at least 10 times than the previous ones, and will create a challenging data taking environment for the Belle II detector. The software system of the Belle II experiment is designed to execute this ambitious plan. A full detector simulation library, which is a part of the Belle II software system, is created based on Geant4 and has been tested thoroughly. Recently the library has been upgraded with Geant4 version 10.1. The library is behaving as expected and it is utilized actively in producing Monte Carlo data sets for various studies. In this paper, we will explain the structure of the simulation library and the various interfaces to other packages including geometry and beam background simulation.

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

    Indian Academy of Sciences (India)

    Meromorphic functions; Nevanlinna theory; logarithmic order; uniqueness problem; difference-differential polynomial. Abstract. 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 ...

  18. 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.

  19. Statistical measure of ensemble non reproducibility and correction to Bell's inequality

    International Nuclear Information System (INIS)

    Khrennikov, A.

    2000-01-01

    In this work it has been analysed the proof of Bell's inequality and demonstrate that this inequality is related to one particular model of probability theory, namely Kolmogorov measure-theoretical axiomatic, 1933. It was found a (numerical) statistical correction to Bell's inequality. Such an additional term ε φ on the right-hand side of Bell's inequality can be considered as a probability invariant of a quantum state φ. This is a measure of non reproducibility of hidden variables in different runs of experiments. Experiments to verify Bell's inequality can be considered as just experiments to estimate the constant ε φ . It seems that Bell's inequality could not be used as a crucial reason to deny local realism

  20. Generic Bell inequalities for multipartite mulit-dimensional systems

    International Nuclear Information System (INIS)

    Son, W.; Lee, J.; Kim, M.S.

    2005-01-01

    Full text: We present generic Bell inequalities for multipartite multi-dimensional systems. They utilize the set of measurements, which are coincident with the generalized version of Greenberger, Horne and Zeilinger (GHZ) paradox. The inequalities that must be satisfied by any local realistic theories are violated by quantum mechanics for even-dimensional multipartite systems. It is also shown that the maximal violation of the inequality is obtained by the generalized GHZ state, which is true multi-body nonseparable state. As a special case for the multipartite two-dimensional systems, it can be shown that the inequality agrees with Bell-Mermin version of inequality. Large sets of variants are shown to naturally emerge from the generic Bell inequalities. We will discuss the particular variants of Bell inequalities that are violated for all the systems including odd-dimensional multipartite systems. Interestingly the variants can be reduced into the Clauser-Horne-Shimony-Holt (CHSH) inequality as well as Ardehali inequality. (author)

  1. 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.

  2. 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....

  3. 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

  4. Imaging characteristics of Zernike and annular polynomial aberrations.

    Science.gov (United States)

    Mahajan, Virendra N; Díaz, José Antonio

    2013-04-01

    The general equations for the point-spread function (PSF) and optical transfer function (OTF) are given for any pupil shape, and they are applied to optical imaging systems with circular and annular pupils. The symmetry properties of the PSF, the real and imaginary parts of the OTF, and the modulation transfer function (MTF) of a system with a circular pupil aberrated by a Zernike circle polynomial aberration are derived. The interferograms and PSFs are illustrated for some typical polynomial aberrations with a sigma value of one wave, and 3D PSFs and MTFs are shown for 0.1 wave. The Strehl ratio is also calculated for polynomial aberrations with a sigma value of 0.1 wave, and shown to be well estimated from the sigma value. The numerical results are compared with the corresponding results in the literature. Because of the same angular dependence of the corresponding annular and circle polynomial aberrations, the symmetry properties of systems with annular pupils aberrated by an annular polynomial aberration are the same as those for a circular pupil aberrated by a corresponding circle polynomial aberration. They are also illustrated with numerical examples.

  5. 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.

  6. Polynomial selection in number field sieve for integer factorization

    Directory of Open Access Journals (Sweden)

    Gireesh Pandey

    2016-09-01

    Full Text Available The general number field sieve (GNFS is the fastest algorithm for factoring large composite integers which is made up by two prime numbers. Polynomial selection is an important step of GNFS. The asymptotic runtime depends on choice of good polynomial pairs. In this paper, we present polynomial selection algorithm that will be modelled with size and root properties. The correlations between polynomial coefficient and number of relations have been explored with experimental findings.

  7. Bell violation in the sky

    Science.gov (United States)

    Choudhury, Sayantan; Panda, Sudhakar; Singh, Rajeev

    2017-02-01

    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 comment

  8. Bell violation in the sky

    International Nuclear Information System (INIS)

    Choudhury, Sayantan; Panda, Sudhakar; Singh, Rajeev

    2017-01-01

    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 comment

  9. 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

  10. 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

  11. 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.

  12. 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)

  13. Remarks on determinants and the classical polynomials

    International Nuclear Information System (INIS)

    Henning, J.J.; Kranold, H.U.; Louw, D.F.B.

    1986-01-01

    As motivation for this formal analysis the problem of Landau damping of Bernstein modes is discussed. It is shown that in the case of a weak but finite constant external magnetic field, the analytical structure of the dispersion relations is of such a nature that longitudinal waves propagating orthogonal to the external magnetic field are also damped, contrary to normal belief. In the treatment of the linearized Vlasov equation it is found convenient to generate certain polynomials by the problem at hand and to explicitly write down expressions for these polynomials. In the course of this study methods are used that relate to elementary but fairly unknown functional relationships between power sums and coefficients of polynomials. These relationships, also called Waring functions, are derived. They are then used in other applications to give explicit expressions for the generalized Laguerre polynomials in terms of determinant functions. The properties of polynomials generated by a wide class of generating functions are investigated. These relationships are also used to obtain explicit forms for the cumulants of a distribution in terms of its moments. It is pointed out that cumulants (or moments, for that matter) do not determine a distribution function

  14. Translationally invariant multipartite Bell inequalities involving only two-body correlators

    International Nuclear Information System (INIS)

    Tura, J; B Sainz, A; Acín, A; Lewenstein, M; Augusiak, R; Vértesi, T

    2014-01-01

    Bell inequalities are natural tools that allow one to certify the presence of nonlocality in quantum systems. The known constructions of multipartite Bell inequalities contain, however, correlation functions involving all observers, making their experimental implementation difficult. The main purpose of this work is to explore the possibility of witnessing nonlocality in multipartite quantum states from the easiest-to-measure quantities, that is, the two-body correlations. In particular, we determine all three- and four-partite Bell inequalities constructed from one- and two-body expectation values that obey translational symmetry, and show that they reveal nonlocality in multipartite states. Also, by providing a particular example of a five-partite Bell inequality, we show that nonlocality can be detected from two-body correlators involving only nearest neighbours. Finally, we demonstrate that any translationally invariant Bell inequality can be maximally violated by a translationally invariant state and the same set of observables at all sites. We provide a numerical algorithm allowing one to seek for maximal violation of a translationally invariant Bell inequality. 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)

  15. Disentanglement, Bell-nonlocality violation and teleportation capacity of the decaying tripartite states

    Energy Technology Data Exchange (ETDEWEB)

    Hu, Ming-Liang, E-mail: mingliang0301@163.com

    2012-09-15

    Dynamics of disentanglement as measured by the tripartite negativity and Bell nonlocality as measured by the extent of violation of the multipartite Bell-type inequalities are investigated in this work. It is shown definitively that for the initial three-qubit Greenberger-Horne-Zeilinger (GHZ) or W class state preparation, the Bell nonlocality suffers sudden death under the influence of thermal reservoirs. Moreover, all the Bell-nonlocal states are useful for nonclassical teleportation, while there are entangled states that do not violate any Bell-type inequalities, but still yield nonclassical teleportation fidelity. - Highlights: Black-Right-Pointing-Pointer Comparison of different aspects of quantum correlations. Black-Right-Pointing-Pointer Robustness of the initial tripartite GHZ and W class states against decoherence. Black-Right-Pointing-Pointer Bell-nonlocality sudden death under the influence of thermal reservoir. Black-Right-Pointing-Pointer A nonzero minimum tripartite negativity is needed for nonclassical teleportation. Black-Right-Pointing-Pointer All the Bell-nonlocal states yield nonclassical teleportation fidelity.

  16. General quantum polynomials: irreducible modules and Morita equivalence

    International Nuclear Information System (INIS)

    Artamonov, V A

    1999-01-01

    In this paper we continue the investigation of the structure of finitely generated modules over rings of general quantum (Laurent) polynomials. We obtain a description of the lattice of submodules of periodic finitely generated modules and describe the irreducible modules. We investigate the problem of Morita equivalence of rings of general quantum polynomials, consider properties of division rings of fractions, and solve Zariski's problem for quantum polynomials

  17. Multiple Meixner polynomials and non-Hermitian oscillator Hamiltonians

    OpenAIRE

    Ndayiragije, François; Van Assche, Walter

    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. Followi...

  18. Multivariable biorthogonal continuous--discrete Wilson and Racah polynomials

    International Nuclear Information System (INIS)

    Tratnik, M.V.

    1990-01-01

    Several families of multivariable, biorthogonal, partly continuous and partly discrete, Wilson polynomials are presented. These yield limit cases that are purely continuous in some of the variables and purely discrete in the others, or purely discrete in all the variables. The latter are referred to as the multivariable biorthogonal Racah polynomials. Interesting further limit cases include the multivariable biorthogonal Hahn and dual Hahn polynomials

  19. 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.

  20. 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.

  1. The finite Fourier transform of classical polynomials

    OpenAIRE

    Dixit, Atul; Jiu, Lin; Moll, Victor H.; Vignat, Christophe

    2014-01-01

    The finite Fourier transform of a family of orthogonal polynomials $A_{n}(x)$, is the usual transform of the polynomial extended by $0$ outside their natural domain. Explicit expressions are given for the Legendre, Jacobi, Gegenbauer and Chebyshev families.

  2. Bell's inequalities for three-qubit entangled states with white noise

    International Nuclear Information System (INIS)

    Chang, Jinho; Kwon, Younghun

    2009-01-01

    We consider three-qubit entangled states classified by Acin et al. and evaluate Bell's inequalities for them when the white noise exists, which may be a real situation for the experiment of the Bells inequality to three-qubit entangled states. We obtain the maximum violation for the Bell inequality in each case and find the condition for exceeding the classical limit. And we observe that even when there would exist quite amount of white noise, some of three-qubit entangled states(for example 2b, 3a, 3b-I, 3b-II and 3b-III types) might show the violation of the Bell inequality.

  3. Belle II silicon vertex detector

    Energy Technology Data Exchange (ETDEWEB)

    Adamczyk, K. [H. Niewodniczanski Institute of Nuclear Physics, Krakow 31-342 (Poland); Aihara, H. [Department of Physics, University of Tokyo, Tokyo 113-0033 (Japan); Angelini, C. [Dipartimento di Fisica, Università di Pisa, I-56127 Pisa (Italy); INFN Sezione di Pisa, I-56127 Pisa (Italy); Aziz, T.; Babu, V. [Tata Institute of Fundamental Research, Mumbai 400005 (India); Bacher, S. [H. Niewodniczanski Institute of Nuclear Physics, Krakow 31-342 (Poland); Bahinipati, S. [Indian Institute of Technology Bhubaneswar, Satya Nagar (India); Barberio, E.; Baroncelli, Ti.; Baroncelli, To. [School of Physics, University of Melbourne, Melbourne, Victoria 3010 (Australia); Basith, A.K. [Indian Institute of Technology Madras, Chennai 600036 (India); Batignani, G. [Dipartimento di Fisica, Università di Pisa, I-56127 Pisa (Italy); INFN Sezione di Pisa, I-56127 Pisa (Italy); Bauer, A. [Institute of High Energy Physics, Austrian Academy of Sciences, 1050 Vienna (Austria); Behera, P.K. [Indian Institute of Technology Madras, Chennai 600036 (India); Bergauer, T. [Institute of High Energy Physics, Austrian Academy of Sciences, 1050 Vienna (Austria); Bettarini, S. [Dipartimento di Fisica, Università di Pisa, I-56127 Pisa (Italy); INFN Sezione di Pisa, I-56127 Pisa (Italy); Bhuyan, B. [Indian Institute of Technology Guwahati, Assam 781039 (India); Bilka, T. [Faculty of Mathematics and Physics, Charles University, 121 16 Prague (Czech Republic); Bosi, F. [INFN Sezione di Pisa, I-56127 Pisa (Italy); Bosisio, L. [Dipartimento di Fisica, Università di Trieste, I-34127 Trieste (Italy); INFN Sezione di Trieste, I-34127 Trieste (Italy); and others

    2016-09-21

    The Belle II experiment at the SuperKEKB collider in Japan is designed to indirectly probe new physics using approximately 50 times the data recorded by its predecessor. An accurate determination of the decay-point position of subatomic particles such as beauty and charm hadrons as well as a precise measurement of low-momentum charged particles will play a key role in this pursuit. These will be accomplished by an inner tracking device comprising two layers of pixelated silicon detector and four layers of silicon vertex detector based on double-sided microstrip sensors. We describe herein the design, prototyping and construction efforts of the Belle-II silicon vertex detector.

  4. Bell's Palsy (For Kids)

    Science.gov (United States)

    ... palsy was named after a Scottish doctor, Sir Charles Bell, who studied the two facial nerves that ... who focuses on how the nervous system works — will do a test called electromyography (say: eh-lek- ...

  5. Algebraic limit cycles in polynomial systems of differential equations

    International Nuclear Information System (INIS)

    Llibre, Jaume; Zhao Yulin

    2007-01-01

    Using elementary tools we construct cubic polynomial systems of differential equations with algebraic limit cycles of degrees 4, 5 and 6. We also construct a cubic polynomial system of differential equations having an algebraic homoclinic loop of degree 3. Moreover, we show that there are polynomial systems of differential equations of arbitrary degree that have algebraic limit cycles of degree 3, as well as give an example of a cubic polynomial system of differential equations with two algebraic limit cycles of degree 4

  6. From sequences to polynomials and back, via operator orderings

    Energy Technology Data Exchange (ETDEWEB)

    Amdeberhan, Tewodros, E-mail: tamdeber@tulane.edu; Dixit, Atul, E-mail: adixit@tulane.edu; Moll, Victor H., E-mail: vhm@tulane.edu [Department of Mathematics, Tulane University, New Orleans, Louisiana 70118 (United States); De Angelis, Valerio, E-mail: vdeangel@xula.edu [Department of Mathematics, Xavier University of Louisiana, New Orleans, Louisiana 70125 (United States); Vignat, Christophe, E-mail: vignat@tulane.edu [Department of Mathematics, Tulane University, New Orleans, Louisiana 70118, USA and L.S.S. Supelec, Universite d' Orsay (France)

    2013-12-15

    Bender and Dunne [“Polynomials and operator orderings,” J. Math. Phys. 29, 1727–1731 (1988)] showed that linear combinations of words q{sup k}p{sup n}q{sup n−k}, where p and q are subject to the relation qp − pq = ı, may be expressed as a polynomial in the symbol z=1/2 (qp+pq). Relations between such polynomials and linear combinations of the transformed coefficients are explored. In particular, examples yielding orthogonal polynomials are provided.

  7. Connection coefficients between Boas-Buck polynomial sets

    Science.gov (United States)

    Cheikh, Y. Ben; Chaggara, H.

    2006-07-01

    In this paper, a general method to express explicitly connection coefficients between two Boas-Buck polynomial sets is presented. As application, we consider some generalized hypergeometric polynomials, from which we derive some well-known results including duplication and inversion formulas.

  8. A Novel Multiparty Quantum Secret Sharing Scheme of Secure Direct Communication Based on Bell States and Bell Measurements

    International Nuclear Information System (INIS)

    Shi Run-Hua; Huang Liu-Sheng; Yang Wei; Zhong Hong

    2011-01-01

    We present a novel quantum secret sharing scheme of secure direct communication and analyze its security. This scheme takes Einstein—Podolsky—Rosen (EPR) pairs in Bell states as quantum resources. In order to obtain the direct communication message, all agents only need to perform Bell measurements, not to perform any local unitary operation. The total efficiency in this scheme approaches 100% as the classical information exchanged is unnecessary except for the eavesdropping checks. (general)

  9. Experimental EPR-steering using Bell-local states

    Science.gov (United States)

    Saunders, D. J.; Jones, S. J.; Wiseman, H. M.; Pryde, G. J.

    2010-11-01

    The concept of `steering' was introduced in 1935 by Schrödinger as a generalization of the EPR (Einstein-Podolsky-Rosen) paradox. It has recently been formalized as a quantum-information task with arbitrary bipartite states and measurements, for which the existence of entanglement is necessary but not sufficient. Previous experiments in this area have been restricted to an approach that followed the original EPR argument in considering only two different measurement settings per side. Here we demonstrate experimentally that EPR-steering occurs for mixed entangled states that are Bell local (that is, that cannot possibly demonstrate Bell non-locality). Unlike the case of Bell inequalities, increasing the number of measurement settings beyond two-we use up to six-significantly increases the robustness of the EPR-steering phenomenon to noise.

  10. 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…

  11. A remark on the use of Bell inequalities

    OpenAIRE

    Geurdes, J. F

    2009-01-01

    In the present paper it is demonstrated that Bell's expression for local hidden variable correlation allows one to derive the quantum correlation. This raises questions about the use of Bell inequalities in experiments. In the paper a CHSH violating example is given based solely on the locality arguments of the model.

  12. Electron entanglement near a superconductor and Bell inequalities

    Indian Academy of Sciences (India)

    In the case of energy filters, Bell-inequality checks constitute a definite probe of entanglement. We formulate Bell-type inequalities in terms of current–current cross-correlations associated with contacts with varying magnetization orientations. We find maximal violation (as in photons) when a superconductor is the particle ...

  13. Violation of Bell-type inequality in single-neutron interferometry

    International Nuclear Information System (INIS)

    Hasegawa, Y.; Badurek, G.; Baron, M.; Rauch, H.; Loidl, R.

    2003-01-01

    Full text: We present an interferometric experiment with single spin-1/2 neutrons to demonstrate the violation of Bell-type inequality. The total wave function of neutrons is described by a two-dimensional Hilbert space. Appropriate combinations of the direction of the spin analysis and the position of the phase shifter allow to demonstrate the violation of the Bell-type inequality. The discussions are given on the violation of the Bell-type inequality in terms of beam polarizations and an entanglement-induced correlation in our experiment. (author)

  14. 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

  15. Diffusion Coefficient Calculations With Low Order Legendre Polynomial and Chebyshev Polynomial Approximation for the Transport Equation in Spherical Geometry

    International Nuclear Information System (INIS)

    Yasa, F.; Anli, F.; Guengoer, S.

    2007-01-01

    We present analytical calculations of spherically symmetric radioactive transfer and neutron transport using a hypothesis of P1 and T1 low order polynomial approximation for diffusion coefficient D. Transport equation in spherical geometry is considered as the pseudo slab equation. The validity of polynomial expansionion in transport theory is investigated through a comparison with classic diffusion theory. It is found that for causes when the fluctuation of the scattering cross section dominates, the quantitative difference between the polynomial approximation and diffusion results was physically acceptable in general

  16. On Roots of Polynomials and Algebraically Closed Fields

    Directory of Open Access Journals (Sweden)

    Schwarzweller Christoph

    2017-10-01

    Full Text Available In this article we further extend the algebraic theory of polynomial rings in Mizar [1, 2, 3]. We deal with roots and multiple roots of polynomials and show that both the real numbers and finite domains are not algebraically closed [5, 7]. We also prove the identity theorem for polynomials and that the number of multiple roots is bounded by the polynomial’s degree [4, 6].

  17. 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)

  18. 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

  19. q-analogue of the Krawtchouk and Meixner orthogonal polynomials

    International Nuclear Information System (INIS)

    Campigotto, C.; Smirnov, Yu.F.; Enikeev, S.G.

    1993-06-01

    The comparative analysis of Krawtchouk polynomials on a uniform grid with Wigner D-functions for the SU(2) group is presented. As a result the partnership between corresponding properties of the polynomials and D-functions is established giving the group-theoretical interpretation of the Krawtchouk polynomials properties. In order to extend such an analysis on the quantum groups SU q (2) and SU q (1,1), q-analogues of Krawtchouk and Meixner polynomials of a discrete variable are studied. The total set of characteristics of these polynomials is calculated, including the orthogonality condition, normalization factor, recurrent relation, the explicit analytic expression, the Rodrigues formula, the difference derivative formula and various particular cases and values. (R.P.) 22 refs.; 2 tabs

  20. Correlations in star networks: from Bell inequalities to network inequalities

    International Nuclear Information System (INIS)

    Tavakoli, Armin; Renou, Marc Olivier; Gisin, Nicolas; Brunner, Nicolas

    2017-01-01

    The problem of characterizing classical and quantum correlations in networks is considered. Contrary to the usual Bell scenario, where distant observers share a physical system emitted by one common source, a network features several independent sources, each distributing a physical system to a subset of observers. In the quantum setting, the observers can perform joint measurements on initially independent systems, which may lead to strong correlations across the whole network. In this work, we introduce a technique to systematically map a Bell inequality to a family of Bell-type inequalities bounding classical correlations on networks in a star-configuration. Also, we show that whenever a given Bell inequality can be violated by some entangled state ρ , then all the corresponding network inequalities can be violated by considering many copies of ρ distributed in the star network. The relevance of these ideas is illustrated by applying our method to a specific multi-setting Bell inequality. We derive the corresponding network inequalities, and study their quantum violations. (paper)

  1. Skew-orthogonal polynomials and random matrix theory

    CERN Document Server

    Ghosh, Saugata

    2009-01-01

    Orthogonal polynomials satisfy a three-term recursion relation irrespective of the weight function with respect to which they are defined. This gives a simple formula for the kernel function, known in the literature as the Christoffel-Darboux sum. The availability of asymptotic results of orthogonal polynomials and the simple structure of the Christoffel-Darboux sum make the study of unitary ensembles of random matrices relatively straightforward. In this book, the author develops the theory of skew-orthogonal polynomials and obtains recursion relations which, unlike orthogonal polynomials, depend on weight functions. After deriving reduced expressions, called the generalized Christoffel-Darboux formulas (GCD), he obtains universal correlation functions and non-universal level densities for a wide class of random matrix ensembles using the GCD. The author also shows that once questions about higher order effects are considered (questions that are relevant in different branches of physics and mathematics) the ...

  2. Some properties of generalized self-reciprocal polynomials over finite fields

    Directory of Open Access Journals (Sweden)

    Ryul Kim

    2014-07-01

    Full Text Available Numerous results on self-reciprocal polynomials over finite fields have been studied. In this paper we generalize some of these to a-self reciprocal polynomials defined in [4]. We consider some properties of the divisibility of a-reciprocal polynomials and characterize the parity of the number of irreducible factors for a-self reciprocal polynomials over finite fields of odd characteristic.

  3. Self-testing protocols based on the chained Bell inequalities

    International Nuclear Information System (INIS)

    Šupić, I; Augusiak, R; Salavrakos, A; Acín, A

    2016-01-01

    Self-testing is a device-independent technique based on non-local correlations whose aim is to certify the effective uniqueness of the quantum state and measurements needed to produce these correlations. It is known that the maximal violation of some Bell inequalities suffices for this purpose. However, most of the existing self-testing protocols for two devices exploit the well-known Clauser–Horne–Shimony–Holt Bell inequality or modifications of it, and always with two measurements per party. Here, we generalize the previous results by demonstrating that one can construct self-testing protocols based on the chained Bell inequalities, defined for two devices implementing an arbitrary number of two-output measurements. On the one hand, this proves that the quantum state and measurements leading to the maximal violation of the chained Bell inequality are unique. On the other hand, in the limit of a large number of measurements, our approach allows one to self-test the entire plane of measurements spanned by the Pauli matrices X and Z. Our results also imply that the chained Bell inequalities can be used to certify two bits of perfect randomness. (paper)

  4. Polynomial algorithms for the Maximal Pairing Problem: efficient phylogenetic targeting on arbitrary trees

    Directory of Open Access Journals (Sweden)

    Stadler Peter F

    2010-06-01

    Full Text Available Abstract Background The Maximal Pairing Problem (MPP is the prototype of a class of combinatorial optimization problems that are of considerable interest in bioinformatics: Given an arbitrary phylogenetic tree T and weights ωxy for the paths between any two pairs of leaves (x, y, what is the collection of edge-disjoint paths between pairs of leaves that maximizes the total weight? Special cases of the MPP for binary trees and equal weights have been described previously; algorithms to solve the general MPP are still missing, however. Results We describe a relatively simple dynamic programming algorithm for the special case of binary trees. We then show that the general case of multifurcating trees can be treated by interleaving solutions to certain auxiliary Maximum Weighted Matching problems with an extension of this dynamic programming approach, resulting in an overall polynomial-time solution of complexity (n4 log n w.r.t. the number n of leaves. The source code of a C implementation can be obtained under the GNU Public License from http://www.bioinf.uni-leipzig.de/Software/Targeting. For binary trees, we furthermore discuss several constrained variants of the MPP as well as a partition function approach to the probabilistic version of the MPP. Conclusions The algorithms introduced here make it possible to solve the MPP also for large trees with high-degree vertices. This has practical relevance in the field of comparative phylogenetics and, for example, in the context of phylogenetic targeting, i.e., data collection with resource limitations.

  5. 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.

  6. on the performance of Autoregressive Moving Average Polynomial

    African Journals Online (AJOL)

    Timothy Ademakinwa

    Distributed Lag (PDL) model, Autoregressive Polynomial Distributed Lag ... Moving Average Polynomial Distributed Lag (ARMAPDL) model. ..... Global Journal of Mathematics and Statistics. Vol. 1. ... Business and Economic Research Center.

  7. 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

  8. Volumetric properties of binary mixtures of N-ethylformamide with tetrahydrofuran, 2-butanone, and ethylacetate from T = (293.15 to 313.15) K

    International Nuclear Information System (INIS)

    Gadžurić, Slobodan; Nikolić, Aleksandar; Vraneš, Milan; Jović, Branislav; Damjanović, Marko; Dožić, Sanja

    2012-01-01

    Highlights: ► Densities of N-ethylformamide mixtures with ketones and esters were measured. ► Excess molar volumes were fitted to Redlich–Kister polynomial equation. ► Excess molar volumes are negative in the whole mole fraction range. ► Increase of the temperature has influence on N-ethylformamide self-association. ► Complex formation between the components was not observed. - Abstract: Densities of binary liquid mixtures of N-ethylformamide (NEF) with tetrahydrofuran (THF), 2-butanone (B), and ethylacetate (EA) were measured at temperatures from (293.15 to 313.15) K and at atmospheric pressure over the whole composition range. Excess molar volumes, V E , have been obtained from values of the experimental density and were fitted to the Redlich–Kister polynomial equation. The V E values for all three mixtures are negative over the entire composition and temperature ranges. The V E values become more negative as the temperature increases for all binary mixtures studied. Other volumetric properties, such as isobaric thermal expansion coefficients, partial molar volumes, apparent molar volumes, partial molar excess volumes and excess thermal expansions have been calculated.

  9. Symmetric functions and orthogonal polynomials

    CERN Document Server

    Macdonald, I G

    1997-01-01

    One of the most classical areas of algebra, the theory of symmetric functions and orthogonal polynomials has long been known to be connected to combinatorics, representation theory, and other branches of mathematics. Written by perhaps the most famous author on the topic, this volume explains some of the current developments regarding these connections. It is based on lectures presented by the author at Rutgers University. Specifically, he gives recent results on orthogonal polynomials associated with affine Hecke algebras, surveying the proofs of certain famous combinatorial conjectures.

  10. 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.

  11. 77 FR 31725 - Safety Zone; Belle Pass Dredge Operations, Belle Pass, Mile Marker 1.0 to Mile Marker (−0.2...

    Science.gov (United States)

    2012-05-30

    ... Environmental Health Risks and Safety Risks. This rule is not an economically significant rule and does not create an environmental risk to health or risk to safety that may disproportionately affect children. 11...-AA00 Safety Zone; Belle Pass Dredge Operations, Belle Pass, Mile Marker 1.0 to Mile Marker (-0.2), Port...

  12. 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.

  13. Polynomially Riesz elements | Živković-Zlatanović | Quaestiones ...

    African Journals Online (AJOL)

    A Banach algebra element ɑ ∈ A is said to be "polynomially Riesz", relative to the homomorphism T : A → B, if there exists a nonzero complex polynomial p(z) such that the image Tp ∈ B is quasinilpotent. Keywords: Homomorphism of Banach algebras, polynomially Riesz element, Fredholm spectrum, Browder element, ...

  14. Bell Operator Method to Classify Local Realistic Theories

    International Nuclear Information System (INIS)

    Nagata, Koji

    2010-01-01

    We review the historical fact of multipartite Bell inequalities with an arbitrary number of settings. An explicit local realistic model for the values of a correlation function, given in a two-setting Bell experiment (two-setting model), works only for the specific set of settings in the given experiment, but cannot construct a local realistic model for the values of a correlation function, given in a continuous-infinite settings Bell experiment (infinite-setting model), even though there exist two-setting models for all directions in space. Hence, the two-setting model does not have the property that the infinite-setting model has. Here, we show that an explicit two-setting model cannot construct a local realistic model for the values of a correlation function, given in an M-setting Bell experiment (M-setting model), even though there exist two-setting models for the M measurement directions chosen in the given M-setting experiment. Hence, the two-setting model does not have the property that the M-setting model has. (general)

  15. 77 FR 64439 - Airworthiness Directives; Bell Helicopter Textron Canada (Bell) Model Helicopters

    Science.gov (United States)

    2012-10-22

    ... unsafe condition for the Bell Model 430 helicopters. Discrepancies in the processing and display of air... pilot and copilot electronic attitude direction indicators airspeed indicators; [cir] Leak testing the... and responsibilities among the various levels of government. For the reasons discussed, I certify this...

  16. Symmetric integrable-polynomial factorization for symplectic one-turn-map tracking

    International Nuclear Information System (INIS)

    Shi, Jicong

    1993-01-01

    It was found that any homogeneous polynomial can be written as a sum of integrable polynomials of the same degree which Lie transformations can be evaluated exactly. By utilizing symplectic integrators, an integrable-polynomial factorization is developed to convert a symplectic map in the form of Dragt-Finn factorization into a product of Lie transformations associated with integrable polynomials. A small number of factorization bases of integrable polynomials enable one to use high order symplectic integrators so that the high-order spurious terms can be greatly suppressed. A symplectic map can thus be evaluated with desired accuracy

  17. Verifying atom entanglement schemes by testing Bell's inequality

    International Nuclear Information System (INIS)

    Angelakis, D.G.; Knight, P.L.; Tregenna, B.; Munro, W.J.

    2001-01-01

    Recent experiments to test Bell's inequality using entangled photons and ions aimed at tests of basic quantum mechanical principles. Interesting results have been obtained and many loopholes could be closed. In this paper we want to point out that tests of Bell's inequality also play an important role in verifying atom entanglement schemes. We describe as an example a scheme to prepare arbitrary entangled states of N two-level atoms using a leaky optical cavity and a scheme to entangle atoms inside a photonic crystal. During the state preparation no photons are emitted, and observing a violation of Bell's inequality is the only way to test whether a scheme works with a high precision or not. (orig.)

  18. Polynomial fuzzy model-based approach for underactuated surface vessels

    DEFF Research Database (Denmark)

    Khooban, Mohammad Hassan; Vafamand, Navid; Dragicevic, Tomislav

    2018-01-01

    The main goal of this study is to introduce a new polynomial fuzzy model-based structure for a class of marine systems with non-linear and polynomial dynamics. The suggested technique relies on a polynomial Takagi–Sugeno (T–S) fuzzy modelling, a polynomial dynamic parallel distributed compensation...... surface vessel (USV). Additionally, in order to overcome the USV control challenges, including the USV un-modelled dynamics, complex nonlinear dynamics, external disturbances and parameter uncertainties, the polynomial fuzzy model representation is adopted. Moreover, the USV-based control structure...... and a sum-of-squares (SOS) decomposition. The new proposed approach is a generalisation of the standard T–S fuzzy models and linear matrix inequality which indicated its effectiveness in decreasing the tracking time and increasing the efficiency of the robust tracking control problem for an underactuated...

  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. Technique for image interpolation using polynomial transforms

    NARCIS (Netherlands)

    Escalante Ramírez, B.; Martens, J.B.; Haskell, G.G.; Hang, H.M.

    1993-01-01

    We present a new technique for image interpolation based on polynomial transforms. This is an image representation model that analyzes an image by locally expanding it into a weighted sum of orthogonal polynomials. In the discrete case, the image segment within every window of analysis is

  1. Bell's inequalities and physical reality

    International Nuclear Information System (INIS)

    Chylinski, Z.

    1985-01-01

    Bell's theory proves the nonlocal character of quantum mechanics alien to the theory of relativity, which shows how essential were the objections of Einstein against quantum mechanics. Since the experiment on Bell's inequalities favours quantum mechanics, this forces one to revise the notion of physical reality. According to Heisenberg one should distinguish between the quantum-potential reality of relations and the classical-actual reality of events. The hypothesis of internal space-time put forward in previous papers supplies the geometrical framework of such a philosophy. Consequently, relations between the constituents of isolated systems precede the space-time events, which fact essentially modifies the meaning of quantum nonlocality and the physical reality itself. 19 refs. (author)

  2. Okounkov's BC-Type Interpolation Macdonald Polynomials and Their q=1 Limit

    NARCIS (Netherlands)

    Koornwinder, T.H.

    2015-01-01

    This paper surveys eight classes of polynomials associated with A-type and BC-type root systems: Jack, Jacobi, Macdonald and Koornwinder polynomials and interpolation (or shifted) Jack and Macdonald polynomials and their BC-type extensions. Among these the BC-type interpolation Jack polynomials were

  3. Complex Polynomial Vector Fields

    DEFF Research Database (Denmark)

    Dias, Kealey

    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...

  4. Classical correlations, Bell inequalities, and communication complexity

    Energy Technology Data Exchange (ETDEWEB)

    Wilms, Johannes; Alber, Gernot [Institut fuer Angewandte Physik, Technische Universitaet Darmstadt, D-64289 Darmstadt (Germany); Percival, Ian C. [Department of Physics, Univ. of London (United Kingdom)

    2007-07-01

    A computer program is presented which is capable of exploring generalizations of Bell-type inequalities for arbitrary numbers of classical inputs and outputs. Thereby, polytopes can be described which represent classical local realistic theories, classical theories without signaling, or classical theories with explicit signaling. These latter polytopes may also be of interest for exploring basic problems of communication complexity. As a first application the influence of non-perfect detectors is discussed in simple Bell experiments.

  5. 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

  6. Connect the Book. Always Inventing: A Photobiography of Alexander Graham Bell

    Science.gov (United States)

    Brodie, Carolyn S.

    2004-01-01

    Cell phones, video phones, voice messaging?one wonders what Alexander Graham Bell would have thought about the many venues today for electronic communication with one another. Bell's March 10, 1876 invention is now 128 years old, but there is no doubt that Bell's "talking machine" changed the world. This article presents a brief review of the…

  7. Excess Molar Volumes and Viscosities of Binary Mixture of Diethyl Carbonate+Ethanol at Different Temperatures

    Institute of Scientific and Technical Information of China (English)

    MA Peisheng; LI Nannan

    2005-01-01

    The purpose of this work was to report excess molar volumes and dynamic viscosities of the binary mixture of diethyl carbonate (DEC)+ethanol. Densities and viscosities of the binary mixture of DEC+ethanol at temperatures 293.15 K-343.15 K and atmospheric pressure were determined over the entire composition range. Densities of the binary mixture of DEC+ethanol were measured by using a vibrating U-shaped sample tube densimeter. Viscosities were determined by using Ubbelohde suspended-level viscometer. Densities are accurate to 1.0×10-5 g·cm-3, and viscosities are reproducible within ±0.003 mPa·s. From these data, excess molar volumes and deviations in viscosity were calculated. Positive excess molar volumes and negative deviations in viscosity for DEC+ethanol system are due to the strong specific interactions.All excess molar vo-lumes and deviations in viscosity fit to the Redlich-Kister polynomial equation.The fitting parameters were presented,and the average deviations and standard deviations were also calculated.The errors of correlation are very small.It proves that it is valuable for estimating densities and viscosities of the binary mixture by the correlated equation.

  8. 77 FR 30232 - Airworthiness Directives; Bell Helicopter Textron Helicopters

    Science.gov (United States)

    2012-05-22

    ...-0530; Directorate Identifier 2011-SW-075-AD] RIN 2120-AA64 Airworthiness Directives; Bell Helicopter Textron Helicopters AGENCY: Federal Aviation Administration (FAA), DOT. ACTION: Notice of proposed rulemaking (NPRM). SUMMARY: We propose to adopt a new airworthiness directive (AD) for Bell Helicopter...

  9. Discriminants and functional equations for polynomials orthogonal on the unit circle

    International Nuclear Information System (INIS)

    Ismail, M.E.H.; Witte, N.S.

    2000-01-01

    We derive raising and lowering operators for orthogonal polynomials on the unit circle and find second order differential and q-difference equations for these polynomials. A general functional equation is found which allows one to relate the zeros of the orthogonal polynomials to the stationary values of an explicit quasi-energy and implies recurrences on the orthogonal polynomial coefficients. We also evaluate the discriminants and quantized discriminants of polynomials orthogonal on the unit circle

  10. Contributions to fuzzy polynomial techniques for stability analysis and control

    OpenAIRE

    Pitarch Pérez, José Luis

    2014-01-01

    The present thesis employs fuzzy-polynomial control techniques in order to improve the stability analysis and control of nonlinear systems. Initially, it reviews the more extended techniques in the field of Takagi-Sugeno fuzzy systems, such as the more relevant results about polynomial and fuzzy polynomial systems. The basic framework uses fuzzy polynomial models by Taylor series and sum-of-squares techniques (semidefinite programming) in order to obtain stability guarantees...

  11. Peripheral facial weakness (Bell's palsy).

    Science.gov (United States)

    Basić-Kes, Vanja; Dobrota, Vesna Dermanović; Cesarik, Marijan; Matovina, Lucija Zadro; Madzar, Zrinko; Zavoreo, Iris; Demarin, Vida

    2013-06-01

    Peripheral facial weakness is a facial nerve damage that results in muscle weakness on one side of the face. It may be idiopathic (Bell's palsy) or may have a detectable cause. Almost 80% of peripheral facial weakness cases are primary and the rest of them are secondary. The most frequent causes of secondary peripheral facial weakness are systemic viral infections, trauma, surgery, diabetes, local infections, tumor, immune disorders, drugs, degenerative diseases of the central nervous system, etc. The diagnosis relies upon the presence of typical signs and symptoms, blood chemistry tests, cerebrospinal fluid investigations, nerve conduction studies and neuroimaging methods (cerebral MRI, x-ray of the skull and mastoid). Treatment of secondary peripheral facial weakness is based on therapy for the underlying disorder, unlike the treatment of Bell's palsy that is controversial due to the lack of large, randomized, controlled, prospective studies. There are some indications that steroids or antiviral agents are beneficial but there are also studies that show no beneficial effect. Additional treatments include eye protection, physiotherapy, acupuncture, botulinum toxin, or surgery. Bell's palsy has a benign prognosis with complete recovery in about 80% of patients, 15% experience some mode of permanent nerve damage and severe consequences remain in 5% of patients.

  12. 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...

  13. 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.

  14. 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.

  15. 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

  16. Typical Werner states satisfying all linear Bell inequalities with dichotomic measurements

    Science.gov (United States)

    Luo, Ming-Xing

    2018-04-01

    Quantum entanglement as a special resource inspires various distinct applications in quantum information processing. Unfortunately, it is NP-hard to detect general quantum entanglement using Bell testing. Our goal is to investigate quantum entanglement with white noises that appear frequently in experiment and quantum simulations. Surprisingly, for almost all multipartite generalized Greenberger-Horne-Zeilinger states there are entangled noisy states that satisfy all linear Bell inequalities consisting of full correlations with dichotomic inputs and outputs of each local observer. This result shows generic undetectability of mixed entangled states in contrast to Gisin's theorem of pure bipartite entangled states in terms of Bell nonlocality. We further provide an accessible method to show a nontrivial set of noisy entanglement with small number of parties satisfying all general linear Bell inequalities. These results imply typical incompleteness of special Bell theory in explaining entanglement.

  17. Linear operator pencils on Lie algebras and Laurent biorthogonal polynomials

    International Nuclear Information System (INIS)

    Gruenbaum, F A; Vinet, Luc; Zhedanov, Alexei

    2004-01-01

    We study operator pencils on generators of the Lie algebras sl 2 and the oscillator algebra. These pencils are linear in a spectral parameter λ. The corresponding generalized eigenvalue problem gives rise to some sets of orthogonal polynomials and Laurent biorthogonal polynomials (LBP) expressed in terms of the Gauss 2 F 1 and degenerate 1 F 1 hypergeometric functions. For special choices of the parameters of the pencils, we identify the resulting polynomials with the Hendriksen-van Rossum LBP which are widely believed to be the biorthogonal analogues of the classical orthogonal polynomials. This places these examples under the umbrella of the generalized bispectral problem which is considered here. Other (non-bispectral) cases give rise to some 'nonclassical' orthogonal polynomials including Tricomi-Carlitz and random-walk polynomials. An application to solutions of relativistic Toda chain is considered

  18. 77 FR 68055 - Airworthiness Directives; Bell Helicopter Textron Helicopters

    Science.gov (United States)

    2012-11-15

    ... Airworthiness Directives; Bell Helicopter Textron Helicopters AGENCY: Federal Aviation Administration (FAA), DOT. ACTION: Final rule. SUMMARY: We are adopting a new airworthiness directive (AD) for Bell Helicopter Textron (BHT) Model 412, 412EP, and 412CF helicopters. This AD requires a repetitive inspection of the...

  19. 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.

  20. 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

  1. Effect of temperature on density, sound velocity, and their derived properties for the binary systems glycerol with water or alcohols

    International Nuclear Information System (INIS)

    Negadi, Latifa; Feddal-Benabed, Badra; Bahadur, Indra; Saab, Joseph; Zaoui-Djelloul-Daouadji, Manel; Ramjugernath, Deresh; Negadi, Amina

    2017-01-01

    Highlights: • Densities (ρ) and sound velocities (u) for glycerol, +water, +methanol, or +ethanol systems were measured. • The derived properties (excess molar volume, isentropic compressibility and deviation in isentropic compressibility) were calculated. • The Redlich–Kister polynomial was used to fit the experimental results. - Abstract: Densities and sound velocities of three binary systems containing glycerol + (water, methanol, or ethanol) have been measured over the entire composition range at temperatures ranging from (283.15 to 313.15) K in 10 K intervals, at atmospheric pressure. A vibrating u-tube densimeter and sound velocity analyzer (Anton Paar DSA 5000M) was used for the measurements. Thermodynamic properties were derived from the measured data, viz. excess molar volume, isentropic compressibility, and deviation in isentropic compressibility. The property data were correlated with the Redlich-Kister polynomial. In all cases, the excess molar volumes and deviation in isentropic compressibility are negative over the entire composition range for all binary mixtures studied and become increasingly negative with an increase in the temperature. These properties provide important information about different interactions that take place between like-like, like-unlike and unlike-unlike molecules in the mixtures.

  2. 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

  3. On Some Extensions of Szasz Operators Including Boas-Buck-Type Polynomials

    Directory of Open Access Journals (Sweden)

    Sezgin Sucu

    2012-01-01

    Full Text Available This paper is concerned with a new sequence of linear positive operators which generalize Szasz operators including Boas-Buck-type polynomials. We establish a convergence theorem for these operators and give the quantitative estimation of the approximation process by using a classical approach and the second modulus of continuity. Some explicit examples of our operators involving Laguerre polynomials, Charlier polynomials, and Gould-Hopper polynomials are given. Moreover, a Voronovskaya-type result is obtained for the operators containing Gould-Hopper polynomials.

  4. On associated polynomials and decay rates for birth-death processes

    NARCIS (Netherlands)

    van Doorn, Erik A.

    2001-01-01

    We consider sequences of orthogonal polynomials 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. In particular, we relate the supports of the

  5. On associated polynomials and decay rates for birth-death processes

    NARCIS (Netherlands)

    van Doorn, Erik A.

    2003-01-01

    We consider sequences of orthogonal polynomials and pursue the question of how (partial) knowledge of the orthogonalizing measure for the associated polynomials can lead to information about the orthogonalizing measure for the original polynomials. In particular, we relate the supports of the two

  6. Bell-inequality tests with macroscopic entangled states of light

    Energy Technology Data Exchange (ETDEWEB)

    Stobinska, M. [Max Planck Institute for the Science of Light, Erlangen (Germany); Institute for Theoretical Physics II, Erlangen-Nuernberg University, Erlangen (Germany); Sekatski, P.; Gisin, N. [Group of Applied Physics, University of Geneva, Geneva (Switzerland); Buraczewski, A. [Faculty of Electronics and Information Technology, Warsaw University of Technology, Warsaw (Poland); Leuchs, G. [Max Planck Institute for the Science of Light, Erlangen (Germany); Institute for Optics, Information and Photonics, Erlangen-Nuernberg University, Erlangen (Germany)

    2011-09-15

    Quantum correlations may violate the Bell inequalities. Most experimental schemes confirming this prediction have been realized in all-optical Bell tests suffering from the detection loophole. Experiments which simultaneously close this loophole and the locality loophole are highly desirable and remain challenging. An approach to loophole-free Bell tests is based on amplification of the entangled photons (i.e., on macroscopic entanglement), for which an optical signal should be easy to detect. However, the macroscopic states are partially indistinguishable by classical detectors. An interesting idea to overcome these limitations is to replace the postselection by an appropriate preselection immediately after the amplification. This is in the spirit of state preprocessing revealing hidden nonlocality. Here, we examine one of the possible preselections, but the presented tools can be used for analysis of other schemes. Filtering methods making the macroscopic entanglement useful for Bell tests and quantum protocols are the subject of an intensive study in the field nowadays.

  7. The EPR paradox, Bell's inequality, and the question of locality

    Science.gov (United States)

    Blaylock, Guy

    2010-01-01

    Most physicists agree that the Einstein-Podolsky-Rosen-Bell paradox exemplifies much of the strange behavior of quantum mechanics, but argument persists about what assumptions underlie the paradox. To clarify what the debate is about, we employ a simple and well-known thought experiment involving two correlated photons to help us focus on the logical assumptions needed to construct the EPR and Bell arguments. The view presented in this paper is that the minimal assumptions behind Bell's inequality are locality and counterfactual definiteness but not scientific realism, determinism, or hidden variables as are often suggested. We further examine the resulting constraints on physical theory with an illustration from the many-worlds interpretation of quantum mechanics—an interpretation that we argue is deterministic, local, and realist but that nonetheless violates the Bell inequality.

  8. Loopholes in Bell inequality tests of local realism

    International Nuclear Information System (INIS)

    Larsson, Jan-Åke

    2014-01-01

    Bell inequalities are intended to show that local realist theories cannot describe the world. A local realist theory is one where physical properties are defined prior to and independent of measurement, and no physical influence can propagate faster than the speed of light. Quantum-mechanical predictions for certain experiments violate the Bell inequality while a local realist theory cannot, and this shows that a local realist theory cannot give those quantum-mechanical predictions. However, because of unexpected circumstances or ‘loopholes’ in available experiment tests, local realist theories can reproduce the data from these experiments. This paper reviews such loopholes, what effect they have on Bell inequality tests, and how to avoid them in experiment. Avoiding all these simultaneously in one experiment, usually called a ‘loophole-free’ or ‘definitive’ Bell test, remains an open task, but is very important for technological tasks such as device-independent security of quantum cryptography, and ultimately for our understanding of the world. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell’s theorem’. (review article)

  9. Some Polynomials Associated with the r-Whitney Numbers

    Indian Academy of Sciences (India)

    26

    Abstract. In the present article we study three families of polynomials associated with ... [29, 39] for their relations with the Bernoulli and generalized Bernoulli polynomials and ... generating functions in a similar way as in the classical cases.

  10. 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 ...

  11. Bells against palsy.

    Science.gov (United States)

    Williams, J D; Lehman, R

    1988-01-01

    A technique is described in which "jingle bells" are sutured in three positions on the face at the points of maximum excursion of the facial musculature when stimulated by a Hilger nerve stimulator set at 2 mA. The procedure is used to monitor movement of the facial nerve while the surgeon dissects the nerve in the cerebellopontine angle and internal auditory canal.

  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. On Bell correlations for the phase space of two entangled light modes

    International Nuclear Information System (INIS)

    Leonhardt, U.

    1993-01-01

    Bell's sign anticorrelations were studied for the phase space of two entangled light modes (or harmonic oscillators). States with the same symmetry as in Bell's example approach the anticorrelation function of the original Einstein-Podolsky-Rosen state as a universal limit for strong correlations. A Bell inequality is not violated. (orig.)

  14. Density, viscosity, isothermal (vapour + liquid) equilibrium, excess molar volume, viscosity deviation, and their correlations for chloroform + methyl isobutyl ketone binary system

    International Nuclear Information System (INIS)

    Clara, Rene A.; Gomez Marigliano, Ana C.; Solimo, Horacio N.

    2007-01-01

    Density and viscosity measurements for pure chloroform and methyl isobutyl ketone at T = (283.15, 293.15, 303.15, and 313.15) K as well as for the binary system {x 1 chloroform + (1 - x 1 ) methyl isobutyl ketone} at the same temperatures were made over the whole concentration range. The experimental results were fitted to empirical equations, which permit the calculation of these properties over the whole concentration and temperature ranges studied. Data of the binary mixture were further used to calculate the excess molar volume and viscosity deviation. The (vapour + liquid) equilibrium (VLE) at T = 303.15 K for this binary system was also measured in order to calculate the activity coefficients and the excess molar Gibbs energy. This binary system shows no azeotrope and negative deviations from ideal behaviour. The excess or deviation properties were fitted to the Redlich-Kister polynomial relation to obtain their coefficients and standard deviations

  15. Conference on Commutative rings, integer-valued polynomials and polynomial functions

    CERN Document Server

    Frisch, Sophie; Glaz, Sarah; Commutative Algebra : Recent Advances in Commutative Rings, Integer-Valued Polynomials, and Polynomial Functions

    2014-01-01

    This volume presents a multi-dimensional collection of articles highlighting recent developments in commutative algebra. It also includes an extensive bibliography and lists a substantial number of open problems that point to future directions of research in the represented subfields. The contributions cover areas in commutative algebra that have flourished in the last few decades and are not yet well represented in book form. Highlighted topics and research methods include Noetherian and non- Noetherian ring theory as well as integer-valued polynomials and functions. Specific topics include: ·    Homological dimensions of Prüfer-like rings ·    Quasi complete rings ·    Total graphs of rings ·    Properties of prime ideals over various rings ·    Bases for integer-valued polynomials ·    Boolean subrings ·    The portable property of domains ·    Probabilistic topics in Intn(D) ·    Closure operations in Zariski-Riemann spaces of valuation domains ·    Stability of do...

  16. Local models violating Bell's inequality by time delays

    International Nuclear Information System (INIS)

    Scalera, G.C.

    1984-01-01

    The performance of ensemble averages is neither a sufficient nor a necessary condition to avoid Bell's inequality violations characteristic of nonergodic systems. Slight modifications of a local nonergodic logical model violating Bell's inequality produce a stochastic model exactly fitting the quantum-mechanical correlation function. From these considerations is appears evident that the last experiments on the existence of local hidden variables are not conclusive

  17. 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

  18. Violation of a Bell-like inequality in neutron-interferometer experiments

    International Nuclear Information System (INIS)

    Hasegawa, Yuji; Badurek, Gerald; Rauch, Helmut; Loidl, Rudolf; Baron, Matthias

    2003-01-01

    We report an interferometric experiment with spin-1/2 neutrons to demonstrate the violation of a Bell-like inequality. The total wave function of neutrons is described by a tensor product Hilbert space. Appropriate combinations of the direction of the spin analysis and the position of the phase shifter allow to demonstrate the violation of the Bell-like inequality. The discussions are presented on the violation of the Bell-like inequality in terms of quantum contextuality and an entanglement-induced correlation in our experiment. (author)

  19. Silicon micro-vertex detector for Belle II

    International Nuclear Information System (INIS)

    Mohanty, Gagan

    2013-01-01

    The Belle experiment at the KEK B-factory is Japan provided the landmark experimental confirmation of CP violation mechanism within the standard model that led to the physics Nobel prize in 2008. In its second phase, called Belle II, it would seek for the holy-grail of new physics using rare decays of B and D mesons and tau leptons as a probe, in complimentary to the direct searches carried out with the LHC experiments. An important component of this upgrade is to replace the innermost subdetector, namely the silicon micro-vertex detector (SVD). The new SVD will, like the old one, consist of four layers of double-sided silicon strip detector, but made from 6âĂİ wafers and located at higher radii as a novel, two-layer DEPFET pixel detector will be inserted very dose to the beam- pipe. Starting with the physics motivation, we discuss the design concept, fabrication and the Indian contributions toward the Belle II SVD. (author)

  20. On the significance of bell's inequality for hidden-variable theories

    International Nuclear Information System (INIS)

    De Baere, W.

    1984-01-01

    It is explicitly shown that Bell's derivation of the generalized Bell inequality and its subsequent interpretation depend on an implicit hypothesis concerning the reproducibility of some set of hidden variables in different runs of the same experiment

  1. 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 ...

  2. Dual exponential polynomials and linear differential equations

    Science.gov (United States)

    Wen, Zhi-Tao; Gundersen, Gary G.; Heittokangas, Janne

    2018-01-01

    We study linear differential equations with exponential polynomial coefficients, where exactly one coefficient is of order greater than all the others. The main result shows that a nontrivial exponential polynomial solution of such an equation has a certain dual relationship with the maximum order coefficient. Several examples illustrate our results and exhibit possibilities that can occur.

  3. Tripartite states' Bell-nonlocality sudden death in an environmental spin chain

    International Nuclear Information System (INIS)

    Liu Benqiong; Shao Bin; Zou Jian

    2010-01-01

    The tripartite nonlocality is investigated by the extent of violation of the Bell inequality in a three-qubit system coupled to an environmental Ising spin chain. In the weak-coupling region, we show that the tripartite Bell-inequality violations can be fully destroyed in a finite time under decoherence induced by the coupling with the spin environment. In addition, how the environment affects the Bell-nonlocality sudden death is demonstrated.

  4. Diagnosis and management of patients with Bell's palsy.

    Science.gov (United States)

    Mooney, Tracy

    Bell's palsy (idiopathic facial paralysis) is the most common cause of acute unilateral facial nerve paralysis. Although it is usually a self-limiting condition, it can be distressing for the patient. Many people who experience one-sided facial paralysis fear that it is a symptom of stroke. However, there are subtle differences between Bell's palsy and stroke. This article discusses potential causes of the condition and identifies the differences between Bell's palsy and stroke. In addition, appropriate strategies for the care of patients with the condition are suggested. Management includes antiviral medication, corticosteroid therapy, eye care, botulinum toxin type A injection, physiotherapy, surgery and acupuncture. Psychological and emotional care of these patients is also important because any facial disability caused by facial nerve paralysis can result in anxiety and stress.

  5. Experimental verification of a new Bell-type inequality

    Science.gov (United States)

    Zhao, Jia-Qiang; Cao, Lian-Zhen; Yang, Yang; Li, Ying-De; Lu, Huai-Xin

    2018-05-01

    Arpan Das et al. proposed a set of new Bell inequalities (Das et al., 2017 [16]) for a three-qubit system and claimed that each inequality within this set is violated by all generalized Greenberger-Horne-Zeilinger (GGHZ) states. We investigate experimentally the new inequalities in the three-photon GGHZ class states. Since the inequalities are symmetric under the identical particles system, we chose one Bell-type inequality from the set arbitrarily. The experimental data well verified the theoretical prediction. Moreover, the experimental results show that the amount of violation of the new Bell inequality against locality realism increases monotonically following the increase of the tangle of the GGHZ state. The most profound physical essence revealed by the results is that the nonlocality of GGHZ state correlate with three tangles directly.

  6. 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.

  7. Polynomial fuzzy observer designs: a sum-of-squares approach.

    Science.gov (United States)

    Tanaka, Kazuo; Ohtake, Hiroshi; Seo, Toshiaki; Tanaka, Motoyasu; Wang, Hua O

    2012-10-01

    This paper presents a sum-of-squares (SOS) approach to polynomial fuzzy observer designs for three classes of polynomial fuzzy systems. The proposed SOS-based framework provides a number of innovations and improvements over the existing linear matrix inequality (LMI)-based approaches to Takagi-Sugeno (T-S) fuzzy controller and observer designs. First, we briefly summarize previous results with respect to a polynomial fuzzy system that is a more general representation of the well-known T-S fuzzy system. Next, we propose polynomial fuzzy observers to estimate states in three classes of polynomial fuzzy systems and derive SOS conditions to design polynomial fuzzy controllers and observers. A remarkable feature of the SOS design conditions for the first two classes (Classes I and II) is that they realize the so-called separation principle, i.e., the polynomial fuzzy controller and observer for each class can be separately designed without lack of guaranteeing the stability of the overall control system in addition to converging state-estimation error (via the observer) to zero. Although, for the last class (Class III), the separation principle does not hold, we propose an algorithm to design polynomial fuzzy controller and observer satisfying the stability of the overall control system in addition to converging state-estimation error (via the observer) to zero. All the design conditions in the proposed approach can be represented in terms of SOS and are symbolically and numerically solved via the recently developed SOSTOOLS and a semidefinite-program solver, respectively. To illustrate the validity and applicability of the proposed approach, three design examples are provided. The examples demonstrate the advantages of the SOS-based approaches for the existing LMI approaches to T-S fuzzy observer designs.

  8. Relevant multi-setting tight Bell inequalities for qubits and qutrits

    International Nuclear Information System (INIS)

    Deng Dongling; Zhou Zisui; Chen Jingling

    2009-01-01

    In the celebrated paper [D. Collins, N. Gisin, J. Phys. A Math. Gen. 37 (2004) 1775], Collins and Gisin presented for the first time a three-setting Bell inequality (here we call it CG inequality for simplicity) which is relevant to the Clauser-Horne-Shimony-Holt (CHSH) inequality. Inspired by their brilliant ideas, we obtained some multi-setting tight Bell inequalities, which are relevant to the CHSH inequality and the CG inequality. Moreover, we generalized the method in the paper [J.L. Chen, D.L. Deng, Phys. Rev. A 79 (2009) 012115] to construct Bell inequality for qubits to higher dimensional system. Based on the generalized method, we present, for the first time, a three-setting tight Bell inequality for two qutrits, which is maximally violated by nonmaximally entangled states and relevant to the Collins-Gisin-Linden-Massar-Popescu inequality.

  9. 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.

  10. Significant-Loophole-Free Test of Bell's Theorem with Entangled Photons.

    Science.gov (United States)

    Giustina, Marissa; Versteegh, Marijn A M; Wengerowsky, Sören; Handsteiner, Johannes; Hochrainer, Armin; Phelan, Kevin; Steinlechner, Fabian; Kofler, Johannes; Larsson, Jan-Åke; Abellán, Carlos; Amaya, Waldimar; Pruneri, Valerio; Mitchell, Morgan W; Beyer, Jörn; Gerrits, Thomas; Lita, Adriana E; Shalm, Lynden K; Nam, Sae Woo; Scheidl, Thomas; Ursin, Rupert; Wittmann, Bernhard; Zeilinger, Anton

    2015-12-18

    Local realism is the worldview in which physical properties of objects exist independently of measurement and where physical influences cannot travel faster than the speed of light. Bell's theorem states that this worldview is incompatible with the predictions of quantum mechanics, as is expressed in Bell's inequalities. Previous experiments convincingly supported the quantum predictions. Yet, every experiment requires assumptions that provide loopholes for a local realist explanation. Here, we report a Bell test that closes the most significant of these loopholes simultaneously. Using a well-optimized source of entangled photons, rapid setting generation, and highly efficient superconducting detectors, we observe a violation of a Bell inequality with high statistical significance. The purely statistical probability of our results to occur under local realism does not exceed 3.74×10^{-31}, corresponding to an 11.5 standard deviation effect.

  11. Solutions of interval type-2 fuzzy polynomials using a new ranking method

    Science.gov (United States)

    Rahman, Nurhakimah Ab.; Abdullah, Lazim; Ghani, Ahmad Termimi Ab.; Ahmad, Noor'Ani

    2015-10-01

    A few years ago, a ranking method have been introduced in the fuzzy polynomial equations. Concept of the ranking method is proposed to find actual roots of fuzzy polynomials (if exists). Fuzzy polynomials are transformed to system of crisp polynomials, performed by using ranking method based on three parameters namely, Value, Ambiguity and Fuzziness. However, it was found that solutions based on these three parameters are quite inefficient to produce answers. Therefore in this study a new ranking method have been developed with the aim to overcome the inherent weakness. The new ranking method which have four parameters are then applied in the interval type-2 fuzzy polynomials, covering the interval type-2 of fuzzy polynomial equation, dual fuzzy polynomial equations and system of fuzzy polynomials. The efficiency of the new ranking method then numerically considered in the triangular fuzzy numbers and the trapezoidal fuzzy numbers. Finally, the approximate solutions produced from the numerical examples indicate that the new ranking method successfully produced actual roots for the interval type-2 fuzzy polynomials.

  12. Tinjauan Anatomi Klinik dan Manajemen Bell's Palsy

    OpenAIRE

    Nur Mujaddidah

    2017-01-01

    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 sti...

  13. Arbitrarily complete Bell-state measurement using only linear optical elements

    Energy Technology Data Exchange (ETDEWEB)

    Grice, W. P. [Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Tennessee (United States)

    2011-10-15

    A complete Bell-state measurement is not possible using only linear-optic elements, and most schemes achieve a success rate of no more than 50%, distinguishing, for example, two of the four Bell states but returning degenerate results for the other two. It is shown here that the introduction of a pair of ancillary entangled photons improves the success rate to 75%. More generally, the addition of 2{sup N}-2 ancillary photons yields a linear-optic Bell-state measurement with a success rate of 1-1/2{sup N}.

  14. 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

  15. 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

  16. An overview on polynomial approximation of NP-hard problems

    Directory of Open Access Journals (Sweden)

    Paschos Vangelis Th.

    2009-01-01

    Full Text Available The fact that polynomial time algorithm is very unlikely to be devised for an optimal solving of the NP-hard problems strongly motivates both the researchers and the practitioners to try to solve such problems heuristically, by making a trade-off between computational time and solution's quality. In other words, heuristic computation consists of trying to find not the best solution but one solution which is 'close to' the optimal one in reasonable time. Among the classes of heuristic methods for NP-hard problems, the polynomial approximation algorithms aim at solving a given NP-hard problem in poly-nomial time by computing feasible solutions that are, under some predefined criterion, as near to the optimal ones as possible. The polynomial approximation theory deals with the study of such algorithms. This survey first presents and analyzes time approximation algorithms for some classical examples of NP-hard problems. Secondly, it shows how classical notions and tools of complexity theory, such as polynomial reductions, can be matched with polynomial approximation in order to devise structural results for NP-hard optimization problems. Finally, it presents a quick description of what is commonly called inapproximability results. Such results provide limits on the approximability of the problems tackled.

  17. For whom bell toils: medical imaging by telephone.

    Science.gov (United States)

    Kuhfeld, A W

    1991-01-01

    The use of the induction balance, which was invented by Alexander Graham Bell to cancel out line interference on his telephone, to determine the location of bullets inside the human body is discussed. Experiments conducted to locate a bullet in the body of US President Garfield, who had been shot by an assassin in 1881, are described. The trials on Garfield were unsuccessful, but the approach was later perfected by Bell.

  18. Constructing general partial differential equations using polynomial and neural networks.

    Science.gov (United States)

    Zjavka, Ladislav; Pedrycz, Witold

    2016-01-01

    Sum fraction terms can approximate multi-variable functions on the basis of discrete observations, replacing a partial differential equation definition with polynomial elementary data relation descriptions. Artificial neural networks commonly transform the weighted sum of inputs to describe overall similarity relationships of trained and new testing input patterns. Differential polynomial neural networks form a new class of neural networks, which construct and solve an unknown general partial differential equation of a function of interest with selected substitution relative terms using non-linear multi-variable composite polynomials. The layers of the network generate simple and composite relative substitution terms whose convergent series combinations can describe partial dependent derivative changes of the input variables. This regression is based on trained generalized partial derivative data relations, decomposed into a multi-layer polynomial network structure. The sigmoidal function, commonly used as a nonlinear activation of artificial neurons, may transform some polynomial items together with the parameters with the aim to improve the polynomial derivative term series ability to approximate complicated periodic functions, as simple low order polynomials are not able to fully make up for the complete cycles. The similarity analysis facilitates substitutions for differential equations or can form dimensional units from data samples to describe real-world problems. Copyright © 2015 Elsevier Ltd. All rights reserved.

  19. A note on the zeros of Freud-Sobolev orthogonal polynomials

    Science.gov (United States)

    Moreno-Balcazar, Juan J.

    2007-10-01

    We prove that the zeros of a certain family of Sobolev orthogonal polynomials involving the Freud weight function e-x4 on are real, simple, and interlace with the zeros of the Freud polynomials, i.e., those polynomials orthogonal with respect to the weight function e-x4. Some numerical examples are shown.

  20. 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.

  1. 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.

  2. Stable piecewise polynomial vector fields

    Directory of Open Access Journals (Sweden)

    Claudio Pessoa

    2012-09-01

    Full Text Available Let $N={y>0}$ and $S={y<0}$ be the semi-planes of $mathbb{R}^2$ having as common boundary the line $D={y=0}$. Let $X$ and $Y$ be polynomial vector fields defined in $N$ and $S$, respectively, leading to a discontinuous piecewise polynomial vector field $Z=(X,Y$. This work pursues the stability and the transition analysis of solutions of $Z$ between $N$ and $S$, started by Filippov (1988 and Kozlova (1984 and reformulated by Sotomayor-Teixeira (1995 in terms of the regularization method. This method consists in analyzing a one parameter family of continuous vector fields $Z_{epsilon}$, defined by averaging $X$ and $Y$. This family approaches $Z$ when the parameter goes to zero. The results of Sotomayor-Teixeira and Sotomayor-Machado (2002 providing conditions on $(X,Y$ for the regularized vector fields to be structurally stable on planar compact connected regions are extended to discontinuous piecewise polynomial vector fields on $mathbb{R}^2$. Pertinent genericity results for vector fields satisfying the above stability conditions are also extended to the present case. A procedure for the study of discontinuous piecewise vector fields at infinity through a compactification is proposed here.

  3. FPGA based algorithms for data reduction at Belle II

    Energy Technology Data Exchange (ETDEWEB)

    Muenchow, David; Gessler, Thomas; Kuehn, Wolfgang; Lange, Jens Soeren; Liu, Ming; Spruck, Bjoern [II. Physikalisches Institut, Universitaet Giessen (Germany)

    2011-07-01

    Belle II, the upgrade of the existing Belle experiment at Super-KEKB in Tsukuba, Japan, is an asymmetric e{sup +}e{sup -} collider with a design luminosity of 8.10{sup 35}cm{sup -2}s{sup -1}. At Belle II the estimated event rate is {<=}30 kHz. The resulting data rate at the Pixel Detector (PXD) will be {<=}7.2 GB/s. This data rate needs to be reduced to be able to process and store the data. A region of interest (ROI) selection is based upon two mechanisms. a.) a tracklet finder using the silicon strip detector and b.) the HLT using all other Belle II subdetectors. These ROIs and the pixel data are forwarded to an FPGA based Compute Node for processing. Here a VHDL based algorithm on FPGA with the benefit of pipelining and parallelisation will be implemented. For a fast data handling we developed a dedicated memory management system for buffering and storing the data. The status of the implementation and performance tests of the memory manager and data reduction algorithm is presented.

  4. Experimental violation of multipartite Bell inequalities with trapped ions.

    Science.gov (United States)

    Lanyon, B P; Zwerger, M; Jurcevic, P; Hempel, C; Dür, W; Briegel, H J; Blatt, R; Roos, C F

    2014-03-14

    We report on the experimental violation of multipartite Bell inequalities by entangled states of trapped ions. First, we consider resource states for measurement-based quantum computation of between 3 and 7 ions and show that all strongly violate a Bell-type inequality for graph states, where the criterion for violation is a sufficiently high fidelity. Second, we analyze Greenberger-Horne-Zeilinger states of up to 14 ions generated in a previous experiment using stronger Mermin-Klyshko inequalities, and show that in this case the violation of local realism increases exponentially with system size. These experiments represent a violation of multipartite Bell-type inequalities of deterministically prepared entangled states. In addition, the detection loophole is closed.

  5. 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

  6. Recent approaches for bell pepper seed vigor testing

    Directory of Open Access Journals (Sweden)

    Marcos Altomani Neves Dias

    2014-08-01

    Full Text Available Seed vigor is a major attribute in the determination of whether a seed lot can be commercialized. Different physiological tests are used to assess seed vigor and are generally based on different concepts, which could lead to variable interpretations, particularly when comparing lots presenting different vigor levels. This study was conducted to compare the different approaches used to evaluate bell pepper seed vigor and verify the applicability of the Seed Vigor Imaging System (SVIS for this purpose. The experiment was performed using four seed lots of bell pepper hybrids in two periods, and the evaluations involved germination, seedling emergence, seedling emergence speed index, saturated salt accelerated aging and image analysis. The use of seedling imaging analysis by SVISis a new approach for bell pepper seed vigor evaluation. Both the software and traditional tests provided sufficient information for seed vigor analysis, enabling the segregation of the analyzed seed lots. Thus, the new method fulfills the requirement for an efficient, rapid, cost-effective and standardized method that allows comparisons among laboratories and avoids human influence on the interpretation of the results. SVIS can be considered a feasible option to be included in quality assurance programs of the bell pepper seed industry.

  7. Bell's palsy: aetiology, clinical features and multidisciplinary care.

    Science.gov (United States)

    Eviston, Timothy J; Croxson, Glen R; Kennedy, Peter G E; Hadlock, Tessa; Krishnan, Arun V

    2015-12-01

    Bell's palsy is a common cranial neuropathy causing acute unilateral lower motor neuron facial paralysis. Immune, infective and ischaemic mechanisms are all potential contributors to the development of Bell's palsy, but the precise cause remains unclear. Advancements in the understanding of intra-axonal signal molecules and the molecular mechanisms underpinning Wallerian degeneration may further delineate its pathogenesis along with in vitro studies of virus-axon interactions. Recently published guidelines for the acute treatment of Bell's palsy advocate for steroid monotherapy, although controversy exists over whether combined corticosteroids and antivirals may possibly have a beneficial role in select cases of severe Bell's palsy. For those with longstanding sequaelae from incomplete recovery, aesthetic, functional (nasal patency, eye closure, speech and swallowing) and psychological considerations need to be addressed by the treating team. Increasingly, multidisciplinary collaboration between interested clinicians from a wide variety of subspecialties has proven effective. A patient centred approach utilising physiotherapy, targeted botulinum toxin injection and selective surgical intervention has reduced the burden of long-term disability in facial palsy. 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. Electronic computer prediction of the type of the crystallization reaction of binary compounds on the base of electronic structure of components

    International Nuclear Information System (INIS)

    Kutolin, S.A.; Kotyukov, V.I.

    1979-01-01

    Presented are the criteria permitting to predict distectic and peritectic reactions of crystallization in narrow and wide regions of homogeneity of Asub(n)Bsub(m) binary compounds. Criteria are found as a result of identification of the crystallization reaction type for one hundred of known binary compounds. Predicting function arguments are Chebishev coefficients whose polynomials describe energy distribution of s-, p-, d-atoms of bands of corresponding compound components in condensed state and also Fermi energy atate in compound components and a content. Prediction relative error of distectic (peritectic) crystallization reaction is 6%, for wide homogeneity region - not more than 12 rel.% (for narrow - up to 1 at%). Presented are the prediction results for the most part of A 3 B and AB 3 binary compounds as well as the rare earth compounds of various composition

  9. Computing Galois Groups of Eisenstein Polynomials Over P-adic Fields

    Science.gov (United States)

    Milstead, Jonathan

    The most efficient algorithms for computing Galois groups of polynomials over global fields are based on Stauduhar's relative resolvent method. These methods are not directly generalizable to the local field case, since they require a field that contains the global field in which all roots of the polynomial can be approximated. We present splitting field-independent methods for computing the Galois group of an Eisenstein polynomial over a p-adic field. Our approach is to combine information from different disciplines. We primarily, make use of the ramification polygon of the polynomial, which is the Newton polygon of a related polynomial. This allows us to quickly calculate several invariants that serve to reduce the number of possible Galois groups. Algorithms by Greve and Pauli very efficiently return the Galois group of polynomials where the ramification polygon consists of one segment as well as information about the subfields of the stem field. Second, we look at the factorization of linear absolute resolvents to further narrow the pool of possible groups.

  10. Fast beampattern evaluation by polynomial rooting

    Science.gov (United States)

    Häcker, P.; Uhlich, S.; Yang, B.

    2011-07-01

    Current automotive radar systems measure the distance, the relative velocity and the direction of objects in their environment. This information enables the car to support the driver. The direction estimation capabilities of a sensor array depend on its beampattern. To find the array configuration leading to the best angle estimation by a global optimization algorithm, a huge amount of beampatterns have to be calculated to detect their maxima. In this paper, a novel algorithm is proposed to find all maxima of an array's beampattern fast and reliably, leading to accelerated array optimizations. The algorithm works for arrays having the sensors on a uniformly spaced grid. We use a general version of the gcd (greatest common divisor) function in order to write the problem as a polynomial. We differentiate and root the polynomial to get the extrema of the beampattern. In addition, we show a method to reduce the computational burden even more by decreasing the order of the polynomial.

  11. Belle monte-carlo production on the Amazon EC2 cloud

    International Nuclear Information System (INIS)

    Sevior, Martin; Fifield, Tom; Katayama, Nobuhiko

    2010-01-01

    The Belle II experiment which aims to increase the Luminosity of the KEKB collider by a factor of 50 will search for physics beyond the Standard Model through precision measurements and the investigation of rare processes in Flavour physics. The expected data rate is comparable to a current era LHC experiment with commensurate computing needs. Incorporating commercial cloud computing, such as that provided by the Amazon Elastic Compute Cloud (EC2) into the Belle II computing model may provide a lower Total Cost of Ownership for the Belle II computing solution. To investigate this possibility, we have created a system to conduct the complete Belle Monte Carlo simulation chain on EC2 to benchmark the cost and performance of the service. This paper will describe how this was achieved in addition to the drawbacks and costs of large-scale Monte Carlo production on EC2.

  12. Belle monte-carlo production on the Amazon EC2 cloud

    Energy Technology Data Exchange (ETDEWEB)

    Sevior, Martin; Fifield, Tom [University of Melbourne, School of Physics, Victoria 3010 Australia (Australia); Katayama, Nobuhiko, E-mail: msevior@gmail.co, E-mail: fifieldt@unimelb.edu.a, E-mail: nobu.katayama@kek.j [High Energy Accelerator Research Organisation (KEK), Tsukuba (Japan)

    2010-04-01

    The Belle II experiment which aims to increase the Luminosity of the KEKB collider by a factor of 50 will search for physics beyond the Standard Model through precision measurements and the investigation of rare processes in Flavour physics. The expected data rate is comparable to a current era LHC experiment with commensurate computing needs. Incorporating commercial cloud computing, such as that provided by the Amazon Elastic Compute Cloud (EC2) into the Belle II computing model may provide a lower Total Cost of Ownership for the Belle II computing solution. To investigate this possibility, we have created a system to conduct the complete Belle Monte Carlo simulation chain on EC2 to benchmark the cost and performance of the service. This paper will describe how this was achieved in addition to the drawbacks and costs of large-scale Monte Carlo production on EC2.

  13. Increased risk of peripheral arterial occlusive disease in patients with Bell's palsy using population data.

    Directory of Open Access Journals (Sweden)

    Li-Syue Liou

    Full Text Available This population-based cohort study investigated the risk of developing peripheral arterial occlusive disease (PAOD in patients with Bell's palsy.We used longitudinal claims data of health insurance of Taiwan to identify 5,152 patients with Bell's palsy newly diagnosed in 2000-2010 and a control cohort of 20,608 patients without Bell's palsy matched by propensity score. Incidence and hazard ratio (HR of PAOD were assessed by the end of 2013.The incidence of PAOD was approximately 1.5 times greater in the Bell's palsy group than in the non-Bell's palsy controls (7.75 vs. 4.99 per 1000 person-years. The Cox proportional hazards regression analysis measured adjusted HR was 1.54 (95% confidence interval (CI = 1.35-1.76 for the Bell's palsy group compared to the non-Bell's palsy group, after adjusting for sex, age, occupation, income and comorbidities. Men were at higher risk of PAOD than women in the Bell's palsy group, but not in the controls. The incidence of PAOD increased with age in both groups, but the Bell's palsy group to control group HR of PAOD decreased as age increased. The systemic steroid treatment reduced 13% of PAOD hazard for Bell's palsy patients, compared to those without the treatment, but not significant.Bell's palsy appears to be associated with an increased risk of developing PAOD. Further pathophysiologic, histopathology and immunologic research is required to explore the underlying biologic mechanism.

  14. Acoustic and thermodynamic properties of binary mixtures of 1-nonanol with o-xylene, m-xylene, p-xylene, ethylbenzene and mesitylene at T = (298.15 and 308.15) K

    International Nuclear Information System (INIS)

    Rani, Ruman; Bhatia, Subhash C.

    2013-01-01

    Highlights: ► The values of densities and speeds of sound were measured for the binary mixtures at 298.15 and 308.15 K. ► Maximum deviations in excess functions were observed for binary mixtures of 1-nonanol with p-xylene. ► Calculated excess and deviation functions were fitted to the Redlich–Kister polynomial. ► The results analysed in terms of molecular interactions and structural effects. -- Abstract: Densities, ρ, and speeds of sound, u, of binary liquid mixtures of 1-nonanol with o-xylene, m-xylene, p-xylene, ethylbenzene and mesitylene have been measured over the entire range of composition at T = (298.15 and 308.15) K and at atmospheric pressure. Using these results, the values of the excess molar volume, V E , isentropic compressibility, κ S , molar isentropic compressibility, K S,m , excess molar isentropic compressibility, K S,m E , deviations of the speed of sound, u D , and excess partial molar volume, V ¯ m,i E,0 , and excess partial molar isentropic compressibility, K ¯ m,i E,0 at infinite dilution, have been calculated. The calculated excess and deviation functions have been fitted to the Redlich–Kister polynomial equations and the results analysed in terms of molecular interactions

  15. A significant-loophole-free test of Bell's theorem with entangled photons

    Science.gov (United States)

    Giustina, Marissa; Versteegh, Marijn A. M.; Wengerowsky, Sören; Handsteiner, Johannes; Hochrainer, Armin; Phelan, Kevin; Steinlechner, Fabian; Kofler, Johannes; Larsson, Jan-Åke; Abellán, Carlos; Amaya, Waldimar; Mitchell, Morgan W.; Beyer, Jörn; Gerrits, Thomas; Lita, Adriana E.; Shalm, Lynden K.; Nam, Sae Woo; Scheidl, Thomas; Ursin, Rupert; Wittmann, Bernhard; Zeilinger, Anton

    2017-10-01

    John Bell's theorem of 1964 states that local elements of physical reality, existing independent of measurement, are inconsistent with the predictions of quantum mechanics (Bell, J. S. (1964), Physics (College. Park. Md). Specifically, correlations between measurement results from distant entangled systems would be smaller than predicted by quantum physics. This is expressed in Bell's inequalities. Employing modifications of Bell's inequalities, many experiments have been performed that convincingly support the quantum predictions. Yet, all experiments rely on assumptions, which provide loopholes for a local realist explanation of the measurement. Here we report an experiment with polarization-entangled photons that simultaneously closes the most significant of these loopholes. We use a highly efficient source of entangled photons, distributed these over a distance of 58.5 meters, and implemented rapid random setting generation and high-efficiency detection to observe a violation of a Bell inequality with high statistical significance. The merely statistical probability of our results to occur under local realism is less than 3.74×10-31, corresponding to an 11.5 standard deviation effect.

  16. Guts of surfaces and the colored Jones polynomial

    CERN Document Server

    Futer, David; Purcell, Jessica

    2013-01-01

    This monograph derives direct and concrete relations between colored Jones polynomials and the topology of incompressible spanning surfaces in knot and link complements. Under mild diagrammatic hypotheses, we prove that the growth of the degree of the colored Jones polynomials is a boundary slope of an essential surface in the knot complement. We show that certain coefficients of the polynomial measure how far this surface is from being a fiber for the knot; in particular, the surface is a fiber if and only if a particular coefficient vanishes. We also relate hyperbolic volume to colored Jones polynomials. Our method is to generalize the checkerboard decompositions of alternating knots. Under mild diagrammatic hypotheses, we show that these surfaces are essential, and obtain an ideal polyhedral decomposition of their complement. We use normal surface theory to relate the pieces of the JSJ decomposition of the  complement to the combinatorics of certain surface spines (state graphs). Since state graphs have p...

  17. Computing Tutte polynomials of contact networks in classrooms

    Science.gov (United States)

    Hincapié, Doracelly; Ospina, Juan

    2013-05-01

    Objective: The topological complexity of contact networks in classrooms and the potential transmission of an infectious disease were analyzed by sex and age. Methods: The Tutte polynomials, some topological properties and the number of spanning trees were used to algebraically compute the topological complexity. Computations were made with the Maple package GraphTheory. Published data of mutually reported social contacts within a classroom taken from primary school, consisting of children in the age ranges of 4-5, 7-8 and 10-11, were used. Results: The algebraic complexity of the Tutte polynomial and the probability of disease transmission increases with age. The contact networks are not bipartite graphs, gender segregation was observed especially in younger children. Conclusion: Tutte polynomials are tools to understand the topology of the contact networks and to derive numerical indexes of such topologies. It is possible to establish relationships between the Tutte polynomial of a given contact network and the potential transmission of an infectious disease within such network

  18. Magic moments with John Bell

    Energy Technology Data Exchange (ETDEWEB)

    Bertlmann, Reinhold A.

    2015-07-15

    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.

  19. 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

  20. Cosmic Bell Test: Measurement Settings from Milky Way Stars

    Science.gov (United States)

    Handsteiner, Johannes; Friedman, Andrew S.; Rauch, Dominik; Gallicchio, Jason; Liu, Bo; Hosp, Hannes; Kofler, Johannes; Bricher, David; Fink, Matthias; Leung, Calvin; Mark, Anthony; Nguyen, Hien T.; Sanders, Isabella; Steinlechner, Fabian; Ursin, Rupert; Wengerowsky, Sören; Guth, Alan H.; Kaiser, David I.; Scheidl, Thomas; Zeilinger, Anton

    2017-02-01

    Bell's theorem states that some predictions of quantum mechanics cannot be reproduced by a local-realist theory. That conflict is expressed by Bell's inequality, which is usually derived under the assumption that there are no statistical correlations between the choices of measurement settings and anything else that can causally affect the measurement outcomes. In previous experiments, this "freedom of choice" was addressed by ensuring that selection of measurement settings via conventional "quantum random number generators" was spacelike separated from the entangled particle creation. This, however, left open the possibility that an unknown cause affected both the setting choices and measurement outcomes as recently as mere microseconds before each experimental trial. Here we report on a new experimental test of Bell's inequality that, for the first time, uses distant astronomical sources as "cosmic setting generators." In our tests with polarization-entangled photons, measurement settings were chosen using real-time observations of Milky Way stars while simultaneously ensuring locality. Assuming fair sampling for all detected photons, and that each stellar photon's color was set at emission, we observe statistically significant ≳7.31 σ and ≳11.93 σ violations of Bell's inequality with estimated p values of ≲1.8 ×10-13 and ≲4.0 ×10-33, respectively, thereby pushing back by ˜600 years the most recent time by which any local-realist influences could have engineered the observed Bell violation.

  1. High-visibility time-bin entanglement for testing chained Bell inequalities

    Science.gov (United States)

    Tomasin, Marco; Mantoan, Elia; Jogenfors, Jonathan; Vallone, Giuseppe; Larsson, Jan-Åke; Villoresi, Paolo

    2017-03-01

    The violation of Bell's inequality requires a well-designed experiment to validate the result. In experiments using energy-time and time-bin entanglement, initially proposed by Franson in 1989, there is an intrinsic loophole due to the high postselection. To obtain a violation in this type of experiment, a chained Bell inequality must be used. However, the local realism bound requires a high visibility in excess of 94.63% in the time-bin entangled state. In this work, we show how such a high visibility can be reached in order to violate a chained Bell inequality with six, eight, and ten terms.

  2. 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 ...

  3. Has Bell's inequality a general meaning for hidden-variable theories

    International Nuclear Information System (INIS)

    Lochak, G.

    1976-01-01

    The proof given by J. S. Bell of an inequality between mean values of measurement results which, according to him, would be characteristic of any local hidden-parameter theory, is analyzed. It is shown that Bell's proof is based upon a hypothesis already contained in von Neumann's famous theorem: It consists in the admission that hidden values of parameters must obey the same statistical laws as observed values. This hypothesis contradicts in advance well known and certainly correct statistical relations in measurement results: one must therefore reject the type of theory considered by Bell, and his inequality has no general meaning

  4. Beat map drawing method for large oriental bell based on operational deflection shape method

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Joong Hyeok; Kim, Seock Hyun [Dept. of Advanced Mechanical Engineering, Kangwon National University, Chuncheon (Korea, Republic of); Park, In Seok [TB Tires Development 1 Team, R and D Center, Kumho Tire, Yongin (Korea, Republic of)

    2016-10-15

    Oriental bells produce a peculiar sound in the form of beats, which are periodic repetitions of strong and weak sounds. A beating sound with a proper period gives the illusion of the bell being alive and breathing. To produce a good beating sound, appropriate modal parameters are required for beat tuning after casting the bell. Conventionally, modal parameters were extracted using frequency response functions of the excitation and response signals. However, a large oriental bell is usually struck by a heavy wooden hammer and hence, only the response signal can be measured. In this study, we extract the modal parameters using the response signal only and employ the data to predict the beat properties of the bell sound. Finally, the validity of the predicted beat properties is experimentally verified for a large oriental bell.

  5. Evaluating the Performance of Polynomial Regression Method with Different Parameters during Color Characterization

    Directory of Open Access Journals (Sweden)

    Bangyong Sun

    2014-01-01

    Full Text Available The polynomial regression method is employed to calculate the relationship of device color space and CIE color space for color characterization, and the performance of different expressions with specific parameters is evaluated. Firstly, the polynomial equation for color conversion is established and the computation of polynomial coefficients is analysed. And then different forms of polynomial equations are used to calculate the RGB and CMYK’s CIE color values, while the corresponding color errors are compared. At last, an optimal polynomial expression is obtained by analysing several related parameters during color conversion, including polynomial numbers, the degree of polynomial terms, the selection of CIE visual spaces, and the linearization.

  6. Exponential time paradigms through the polynomial time lens

    NARCIS (Netherlands)

    Drucker, A.; Nederlof, J.; Santhanam, R.; Sankowski, P.; Zaroliagis, C.

    2016-01-01

    We propose a general approach to modelling algorithmic paradigms for the exact solution of NP-hard problems. Our approach is based on polynomial time reductions to succinct versions of problems solvable in polynomial time. We use this viewpoint to explore and compare the power of paradigms such as

  7. The asymmetric facial skin perfusion distribution of Bell's palsy discovered by laser speckle imaging technology.

    Science.gov (United States)

    Cui, Han; Chen, Yi; Zhong, Weizheng; Yu, Haibo; Li, Zhifeng; He, Yuhai; Yu, Wenlong; Jin, Lei

    2016-01-01

    Bell's palsy is a kind of peripheral neural disease that cause abrupt onset of unilateral facial weakness. In the pathologic study, it was evidenced that ischemia of facial nerve at the affected side of face existed in Bell's palsy patients. Since the direction of facial nerve blood flow is primarily proximal to distal, facial skin microcirculation would also be affected after the onset of Bell's palsy. Therefore, monitoring the full area of facial skin microcirculation would help to identify the condition of Bell's palsy patients. In this study, a non-invasive, real time and full field imaging technology - laser speckle imaging (LSI) technology was applied for measuring facial skin blood perfusion distribution of Bell's palsy patients. 85 participants with different stage of Bell's palsy were included. Results showed that Bell's palsy patients' facial skin perfusion of affected side was lower than that of the normal side at the region of eyelid, and that the asymmetric distribution of the facial skin perfusion between two sides of eyelid is positively related to the stage of the disease (P Bell's palsy patients, and we discovered that the facial skin blood perfusion could reflect the stage of Bell's palsy, which suggested that microcirculation should be investigated in patients with this neurological deficit. It was also suggested LSI as potential diagnostic tool for Bell's palsy.

  8. Radiation Hardness Study of CsI(Tl) Crystals for Belle II Calorimeter

    CERN Document Server

    Matvienko, D V; Sedov, E V; Shwartz, B A

    2017-01-01

    The Belle II calorimeter (at least, its barrel part) consists of CsI(Tl) scintillation crystals which have been used at the Belle experiment. We perform the radiation hardness study of some typical Belle crystals and conclude their light output reductions are acceptable for Belle II experiment where the absorption dose can reach 10 krad during the detector operation. CsI(Tl) crystals have high stablity and low maintenance cost and are considered as possible option for the calorimeter of the future Super-Charm-Tau factory (SCT) in Novosibirsk. Our study demonstrates sufficiently high radiation hardness of CsI(Tl) crystals for SCT conditions.

  9. New Bäcklund transformations and new multisoliton solutions for the (3 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation

    International Nuclear Information System (INIS)

    Na, Liu

    2015-01-01

    In this paper, the (3 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation is studied with the Bell polynomial technique, the gauge transformation and the three-wave method. With the aid of the Bell polynomial technique, its bilinear form and the bilinear Bäcklund transformations, a Lax pair is obtained. Moreover, a new Bäcklund transformation is constructed via applying a gauge transformation to the Bäcklund transformation in bilinear form. Furthermore, multisoliton solutions are also obtained by applying the standard Hirota bilinear and three-wave method. (paper)

  10. Sufficiency of Bell's conditions

    Energy Technology Data Exchange (ETDEWEB)

    Gutkowski, D; Masotto, G [Istituto di Matematica della Universita di Palermo (Italy); Valdes, M V

    1979-04-11

    It is shown that, if the results of measurements of spin components of two-spin one-half particles coupled to a singlet state with respect to n=3 directions satisfy Bell's conditions, then these results are compatible with a local hidden-variable theory. The previous statement is extended to the case n=4.

  11. Nonrecurrence and Bell-like inequalities

    Science.gov (United States)

    Danforth, Douglas G.

    2017-12-01

    The general class, Λ, of Bell hidden variables is composed of two subclasses ΛR and ΛN such that ΛR⋃ΛN = Λ and ΛR∩ ΛN = {}. The class ΛN is very large and contains random variables whose domain is the continuum, the reals. There are an uncountable infinite number of reals. Every instance of a real random variable is unique. The probability of two instances being equal is zero, exactly zero. ΛN induces sample independence. All correlations are context dependent but not in the usual sense. There is no "spooky action at a distance". Random variables, belonging to ΛN, are independent from one experiment to the next. The existence of the class ΛN makes it impossible to derive any of the standard Bell inequalities used to define quantum entanglement.

  12. Update on managing Bell's palsy.

    Science.gov (United States)

    2008-07-01

    Each year in the UK, around 1 in 5,000 people develops Bell's palsy--idiopathic unilateral lower motor neurone facial weakness of rapid onset. Of those who are not treated, about 16% end up with permanent moderate to severe weakness, which can result in facial dysfunction and disfigurement, and psychological difficulties. There has been longstanding controversy about what, if any, treatment should be given, with potential alternatives including corticosteroids, antiviral drugs, acupuncture and physiotherapy. We last reviewed this condition in 2006, indicating that "published trials on the efficacy of drug treatments have been poor and no firm conclusions can be drawn about the benefit of any single drug", and "it is unclear what place, if any, acupuncture and physiotherapy have in the management of patients with Bell's palsy". Here we update our conclusions in the light of recently published evidence.

  13. 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 ...

  14. Volumetric and viscometric properties of binary and ternary mixtures of 1-butyl-3-methylimidazolium tetrafluoroborate, monoethanolamine and water

    International Nuclear Information System (INIS)

    Yin, Yaran; Zhu, Chunying; Ma, Youguang

    2016-01-01

    Highlights: • Densities and viscosities of [Bmim][BF 4 ] + MEA + H 2 O solutions were measured. • Volumetric and viscometric properties were deduced from experimental results. • Intermolecular interactions were analysed by volumetric and viscometric properties. - Abstract: Densities and viscosities of binary {[Bmim][BF 4 ] + H 2 O}, {[Bmim][BF 4 ] + MEA}, (MEA + H 2 O) and ternary mixtures {[Bmim][BF 4 ] + MEA + H 2 O} were measured at T = (293.15–333.15) K. The volumetric and viscometric properties, such as excess molar volume V E , viscosity deviation Δη, and excess Gibbs energy of activation of viscous flow ΔG ∗E for all mixtures, and apparent molar volume, excess partial molar volume and Grunberg-Nissan interaction parameter G 12 for binary mixtures, were deduced from experimental results, and the intermolecular interactions in solutions were also analysed. The excess molar volumes were correlated using the Redlich-Kister polynomial equation for binary mixtures, and Singh et al. equation for the ternary mixture with corresponding binary parameters. The viscosities of binary and ternary solutions were respectively fitted by Jouyban-Acree equation and its extended equation at each measurement temperature, the correlated values are in good agreement with the corresponding experimental data.

  15. Increased risk of Bell palsy in patients with migraine: a nationwide cohort study.

    Science.gov (United States)

    Peng, Kuan-Po; Chen, Yung-Tai; Fuh, Jong-Ling; Tang, Chao-Hsiun; Wang, Shuu-Jiun

    2015-01-13

    To evaluate the association between migraine and Bell palsy and to examine the effects of age, sex, migraine subtype, and comorbid risk factors for Bell palsy. This nationwide cohort study was conducted using data from the Taiwan National Health Insurance Research Database. Subjects aged 18 years or older with neurologist-diagnosed migraine from 2005 to 2009 were included. A nonheadache age- and propensity score-matched control cohort was selected for comparison. All subjects were followed until the end of 2010, death, or the occurrence of a Bell palsy event. Cox proportional hazards regression was used to calculate the adjusted hazard ratios and 95% confidence intervals to compare the risk of Bell palsy between groups. Both cohorts (n = 136,704 each) were followed for a mean of 3.2 years. During the follow-up period, 671 patients (424,372 person-years) in the migraine cohort and 365 matched control subjects (438,677 person-years) were newly diagnosed with Bell palsy (incidence rates, 158.1 and 83.2/100,000 person-years, respectively). The adjusted hazard ratio for Bell palsy was 1.91 (95% confidence interval, 1.68-2.17; p Bell palsy remained significant in sensitivity analyses, and tests of interaction failed to reach significance in all subgroup analyses. Migraine is a previously unidentified risk factor for Bell palsy. The association between these 2 conditions suggests a linked disease mechanism, which is worthy of further exploration. © 2014 American Academy of Neurology.

  16. Violation of a Bell-like inequality in single-neutron interferometry.

    Science.gov (United States)

    Hasegawa, Yuji; Loidl, Rudolf; Badurek, Gerald; Baron, Matthias; Rauch, Helmut

    2003-09-04

    Non-local correlations between spatially separated systems have been extensively discussed in the context of the Einstein, Podolsky and Rosen (EPR) paradox and Bell's inequalities. Many proposals and experiments designed to test hidden variable theories and the violation of Bell's inequalities have been reported; usually, these involve correlated photons, although recently an experiment was performed with (9)Be(+) ions. Nevertheless, it is of considerable interest to show that such correlations (arising from quantum mechanical entanglement) are not simply a peculiarity of photons. Here we measure correlations between two degrees of freedom (comprising spatial and spin components) of single neutrons; this removes the need for a source of entangled neutron pairs, which would present a considerable technical challenge. A Bell-like inequality is introduced to clarify the correlations that can arise between observables of otherwise independent degrees of freedom. We demonstrate the violation of this Bell-like inequality: our measured value is 2.051 +/- 0.019, clearly above the value of 2 predicted by classical hidden variable theories.

  17. Near-equilibrium dumb-bell-shaped figures for cohesionless small bodies

    Science.gov (United States)

    Descamps, Pascal

    2016-02-01

    In a previous paper (Descamps, P. [2015]. Icarus 245, 64-79), we developed a specific method aimed to retrieve the main physical characteristics (shape, density, surface scattering properties) of highly elongated bodies from their rotational lightcurves through the use of dumb-bell-shaped equilibrium figures. The present work is a test of this method. For that purpose we introduce near-equilibrium dumb-bell-shaped figures which are base dumb-bell equilibrium shapes modulated by lognormal statistics. Such synthetic irregular models are used to generate lightcurves from which our method is successfully applied. Shape statistical parameters of such near-equilibrium dumb-bell-shaped objects are in good agreement with those calculated for example for the Asteroid (216) Kleopatra from its dog-bone radar model. It may suggest that such bilobed and elongated asteroids can be approached by equilibrium figures perturbed be the interplay with a substantial internal friction modeled by a Gaussian random sphere.

  18. 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.

  19. 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)

  20. 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....

  1. 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.

  2. Thermodynamic reassessment of the neodymium–gold binary system

    Energy Technology Data Exchange (ETDEWEB)

    Moustaine, D., E-mail: mostainedris@gmail.com; Mahdouk, K.

    2016-07-15

    Phase relationships in Nd–Au binary system have been thermodynamically assessed by means of the CALPHAD technique through Thermo–Calc software package based on the experiment information of phase equilibria and thermodynamic properties from the published literature data. The excess Gibbs energy functions of the solution phases including liquid, fcc-A1, bcc-A2, and dhcp were formulated with Redlich–Kister polynomial functions. The two–sublattice energy model was employed to describe the Nd{sub 14}Au{sub 51} phase which exhibits a homogeneity range. The intermetallic compounds Nd{sub 2}Au, NdAu, Nd{sub 3}Au{sub 4}, Nd{sub 17}Au{sub 36}, and NdAu{sub 6} were treated as stoichiometric phases. A set of self-consistent thermodynamic parameters formulating the Gibbs energy of various phases in the Nd–Au binary system were then obtained. A much better agreement was achieved between the calculated results and the reported experimental data. - Highlights: • The Nd–Au has been re-assessed using the latest experimental results. • The intermetallic compound Nd{sub 14}Au{sub 51} was treated by a two–sublattice model. • The errors of related modelling presented in previous articles have been modified. • A self–consistent thermodynamic description of the Nd–Au system was obtained.

  3. Strong violations of Bell-type inequalities for path-entangled number states

    International Nuclear Information System (INIS)

    Wildfeuer, Christoph F.; Dowling, Jonathan P.; Lund, Austin P.

    2007-01-01

    We show that nonlocal correlation experiments on the two spatially separated modes of a maximally path-entangled number state may be performed. They lead to a violation of a Clauser-Horne Bell inequality for any finite photon number N. We also present an analytical expression for the two-mode Wigner function of a maximally path-entangled number state and investigate a Clauser-Horne-Shimony-Holt Bell inequality for such a state. We test other Bell-type inequalities. Some are violated by a constant amount for any N

  4. Testing bell inequality at experiments of high energy physics

    International Nuclear Information System (INIS)

    Hao Xiqing; Li Xueqian; Ke Hongwei; Ding Yibing; Shen Pengnian

    2010-01-01

    Besides using the laser beam, it is very tempting to directly testify the Bell inequality at high energy experiments where the spin correlation is exactly what the original Bell inequality investigations. In this work, we follow the proposal raised in literature and use the successive decays J/ψ →γηc →Λ(Λ-bar)→pπ - (p-bar)π + to testify the Bell inequality. Our goal is twofold, namely, we first make a Monte-Carlo simulation of the processes based on the quantum field theory (QFT). Since the underlying theory is QFT, it implies that we pre-admit the validity of quantum picture. Even though the QFT is true, we need to find how big the database should be, so that we can clearly show deviations of the correlation from the Bell inequality determined by the local hidden variable theory. There have been some critiques on the proposed method, so in the second part, we suggest some improvements which may help to remedy the ambiguities indicated by the critiques. It may be realized at an updated facility of high energy physics, such as BES III. (authors)

  5. FFT Algorithm for Binary Extension Finite Fields and Its Application to Reed–Solomon Codes

    KAUST Repository

    Lin, Sian Jheng

    2016-08-15

    Recently, a new polynomial basis over binary extension fields was proposed, such that the fast Fourier transform (FFT) over such fields can be computed in the complexity of order O(n lg(n)), where n is the number of points evaluated in FFT. In this paper, we reformulate this FFT algorithm, such that it can be easier understood and be extended to develop frequency-domain decoding algorithms for (n = 2(m), k) systematic Reed-Solomon (RS) codes over F-2m, m is an element of Z(+), with n-k a power of two. First, the basis of syndrome polynomials is reformulated in the decoding procedure so that the new transforms can be applied to the decoding procedure. A fast extended Euclidean algorithm is developed to determine the error locator polynomial. The computational complexity of the proposed decoding algorithm is O(n lg(n-k)+(n-k)lg(2)(n-k)), improving upon the best currently available decoding complexity O(n lg(2)(n) lg lg(n)), and reaching the best known complexity bound that was established by Justesen in 1976. However, Justesen\\'s approach is only for the codes over some specific fields, which can apply Cooley-Tukey FFTs. As revealed by the computer simulations, the proposed decoding algorithm is 50 times faster than the conventional one for the (2(16), 2(15)) RS code over F-216.

  6. p-adic probability interpretation of Bell's inequality

    International Nuclear Information System (INIS)

    Khrennikov, A.

    1995-01-01

    We study the violation of Bell's inequality using a p-adic generalization of the theory of probability. p-adic probability is introduced as a limit of relative frequencies but this limit exists with respect to a p-adic metric. In particular, negative probability distributions are well defined on the basis of the frequency definition. This new type of stochastics can be used to describe hidden-variables distributions of some quantum models. If the hidden variables have a p-adic probability distribution, Bell's inequality is not valid and it is not necessary to discuss the experimental violations of this inequality. ((orig.))

  7. Reply to Comment on ‘What Bell did’

    International Nuclear Information System (INIS)

    Maudlin, Tim W

    2014-01-01

    First, let me express my appreciation to Professor Werner for his discussion of my paper. These are quite contentious and fiercely disputed questions, and the only way to make progress in resolving these disputes is to make a good faith effort to present the arguments clearly and explicitly. Only once things are pinned down on paper with some precision can a proper analysis proceed. Werner’s willingness to do this means progress can be made. There are some important points on which Werner and I agree. We agree that neither Einstein nor Bell presuppose determinism in framing their arguments, so the conclusions of those arguments cannot be avoided simply by adopting indeterminism. We even largely agree on what Bell thought he proved. For example, we agree that Bell did not take his theorem to refute determinism or ‘hidden variables’. Werner even seems to concede that Bell himself thought that he had proven the necessity for any theory that reproduces the predictions of the quantum formalism—or more generally any theory that predicts violations of his inequality for pairs of experiments done at space-like separation—to be non-local (in a particular sense of ‘non-local’). Agreement on this much is already a tremendous amount of progress, and I do not wish to undervalue it

  8. Polynomial chaos functions and stochastic differential equations

    International Nuclear Information System (INIS)

    Williams, M.M.R.

    2006-01-01

    The Karhunen-Loeve procedure and the associated polynomial chaos expansion have been employed to solve a simple first order stochastic differential equation which is typical of transport problems. Because the equation has an analytical solution, it provides a useful test of the efficacy of polynomial chaos. We find that the convergence is very rapid in some cases but that the increased complexity associated with many random variables can lead to very long computational times. The work is illustrated by exact and approximate solutions for the mean, variance and the probability distribution itself. The usefulness of a white noise approximation is also assessed. Extensive numerical results are given which highlight the weaknesses and strengths of polynomial chaos. The general conclusion is that the method is promising but requires further detailed study by application to a practical problem in transport theory

  9. 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.

  10. 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.

  11. Bernoulli numbers and polynomials from a more general point of view

    International Nuclear Information System (INIS)

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

    2000-01-01

    In this work it is applied the method of generating function, to introduce new forms of Bernoulli numbers and polynomials, which are exploited to derive further classes of partial sums involving generalized many index many variable polynomials. Analogous considerations are developed for the Euler numbers and polynomials [it

  12. Generalizations of an integral for Legendre polynomials by Persson and Strang

    NARCIS (Netherlands)

    Diekema, E.; Koornwinder, T.H.

    2012-01-01

    Persson and Strang (2003) evaluated the integral over [−1,1] of a squared odd degree Legendre polynomial divided by x2 as being equal to 2. We consider a similar integral for orthogonal polynomials with respect to a general even orthogonality measure, with Gegenbauer and Hermite polynomials as

  13. The "Belles" Are Back

    Science.gov (United States)

    Hamilton, Kendra

    2009-01-01

    The "Bennett Belle." The words conjure an image that is genteel, old-fashioned--hats and gloves, brown-skinned women in flowing white dresses beaming as they take that final walk to graduation. The Bennett College for Women campus certainly reinforces the image, with its broad, tree-shaded lawns and quadrangle and its historic buildings--fully 15…

  14. 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.

  15. Eye aberration analysis with Zernike polynomials

    Science.gov (United States)

    Molebny, Vasyl V.; Chyzh, Igor H.; Sokurenko, Vyacheslav M.; Pallikaris, Ioannis G.; Naoumidis, Leonidas P.

    1998-06-01

    New horizons for accurate photorefractive sight correction, afforded by novel flying spot technologies, require adequate measurements of photorefractive properties of an eye. Proposed techniques of eye refraction mapping present results of measurements for finite number of points of eye aperture, requiring to approximate these data by 3D surface. A technique of wave front approximation with Zernike polynomials is described, using optimization of the number of polynomial coefficients. Criterion of optimization is the nearest proximity of the resulted continuous surface to the values calculated for given discrete points. Methodology includes statistical evaluation of minimal root mean square deviation (RMSD) of transverse aberrations, in particular, varying consecutively the values of maximal coefficient indices of Zernike polynomials, recalculating the coefficients, and computing the value of RMSD. Optimization is finished at minimal value of RMSD. Formulas are given for computing ametropia, size of the spot of light on retina, caused by spherical aberration, coma, and astigmatism. Results are illustrated by experimental data, that could be of interest for other applications, where detailed evaluation of eye parameters is needed.

  16. 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…

  17. Postselection-Loophole-Free Bell Test Over an Installed Optical Fiber Network.

    Science.gov (United States)

    Carvacho, Gonzalo; Cariñe, Jaime; Saavedra, Gabriel; Cuevas, Álvaro; Fuenzalida, Jorge; Toledo, Felipe; Figueroa, Miguel; Cabello, Adán; Larsson, Jan-Åke; Mataloni, Paolo; Lima, Gustavo; Xavier, Guilherme B

    2015-07-17

    Device-independent quantum communication will require a loophole-free violation of Bell inequalities. In typical scenarios where line of sight between the communicating parties is not available, it is convenient to use energy-time entangled photons due to intrinsic robustness while propagating over optical fibers. Here we show an energy-time Clauser-Horne-Shimony-Holt Bell inequality violation with two parties separated by 3.7 km over the deployed optical fiber network belonging to the University of Concepción in Chile. Remarkably, this is the first Bell violation with spatially separated parties that is free of the postselection loophole, which affected all previous in-field long-distance energy-time experiments. Our work takes a further step towards a fiber-based loophole-free Bell test, which is highly desired for secure quantum communication due to the widespread existing telecommunication infrastructure.

  18. Learning Read-constant Polynomials of Constant Degree modulo Composites

    DEFF Research Database (Denmark)

    Chattopadhyay, Arkadev; Gavaldá, Richard; Hansen, Kristoffer Arnsfelt

    2011-01-01

    Boolean functions that have constant degree polynomial representation over a fixed finite ring form a natural and strict subclass of the complexity class \\textACC0ACC0. They are also precisely the functions computable efficiently by programs over fixed and finite nilpotent groups. This class...... is not known to be learnable in any reasonable learning model. In this paper, we provide a deterministic polynomial time algorithm for learning Boolean functions represented by polynomials of constant degree over arbitrary finite rings from membership queries, with the additional constraint that each variable...

  19. Quantum Locality, Rings a Bell?: Bell's Inequality Meets Local Reality and True Determinism

    Science.gov (United States)

    Sánchez-Kuntz, Natalia; Nahmad-Achar, Eduardo

    2018-01-01

    By assuming a deterministic evolution of quantum systems and taking realism into account, we carefully build a hidden variable theory for Quantum Mechanics (QM) based on the notion of ontological states proposed by 't Hooft (The cellular automaton interpretation of quantum mechanics, arXiv:1405.1548v3, 2015; Springer Open 185, https://doi.org/10.1007/978-3-319-41285-6, 2016). We view these ontological states as the ones embedded with realism and compare them to the (usual) quantum states that represent superpositions, viewing the latter as mere information of the system they describe. Such a deterministic model puts forward conditions for the applicability of Bell's inequality: the usual inequality cannot be applied to the usual experiments. We build a Bell-like inequality that can be applied to the EPR scenario and show that this inequality is always satisfied by QM. In this way we show that QM can indeed have a local interpretation, and thus meet with the causal structure imposed by the Theory of Special Relativity in a satisfying way.

  20. Simple and tight monogamy relations for a class of Bell inequalities

    Science.gov (United States)

    Augusiak, Remigiusz

    2017-01-01

    Physical principles constrain the way nonlocal correlations can be distributed among distant parties in a Bell-type experiment. These constraints are usually expressed by monogamy relations that bound the amount of Bell inequality violation observed by a set of parties by the violation observed by a different set of parties. Here we show that the no-signaling principle yields simple and tight monogamy relations for an important class of bipartite and multipartite Bell inequalities. We also link these trade-offs to the guessing probability—a key quantity in device-independent information processing.

  1. Violation of Bell-type inequality in single-neutron interferometry: quantum contextuality

    International Nuclear Information System (INIS)

    Hasegawa, Y.; Loidl, R.; Badurek, G.; Baron, M.; Rauch, H.

    2004-01-01

    We report a single-neutron optical experiment to demonstrate the violation of a Bell-like inequality. Entanglement is achieved between the degrees of freedom for a single particle. The total wave function of the neutron is described in a tensor product Hilbert space. A Bell-like inequality is derived not by a non-locality but by a contextuality. Joint measurements of the spinor and the path properties lead to the violation of a Bell-like inequality. Manipulation of the wavefunction in one Hilbert space influences the result of the measurement in the other Hilbert space

  2. 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.

  3. A Geometrical Approach to Bell's Theorem

    Science.gov (United States)

    Rubincam, David Parry

    2000-01-01

    Bell's theorem can be proved through simple geometrical reasoning, without the need for the Psi function, probability distributions, or calculus. The proof is based on N. David Mermin's explication of the Einstein-Podolsky-Rosen-Bohm experiment, which involves Stern-Gerlach detectors which flash red or green lights when detecting spin-up or spin-down. The statistics of local hidden variable theories for this experiment can be arranged in colored strips from which simple inequalities can be deduced. These inequalities lead to a demonstration of Bell's theorem. Moreover, all local hidden variable theories can be graphed in such a way as to enclose their statistics in a pyramid, with the quantum-mechanical result lying a finite distance beneath the base of the pyramid.

  4. Index files for Belle II - very small skim containers

    Science.gov (United States)

    Sevior, Martin; Bloomfield, Tristan; Kuhr, Thomas; Ueda, I.; Miyake, H.; Hara, T.

    2017-10-01

    The Belle II experiment[1] employs the root file format[2] for recording data and is investigating the use of “index-files” to reduce the size of data skims. These files contain pointers to the location of interesting events within the total Belle II data set and reduce the size of data skims by 2 orders of magnitude. We implement this scheme on the Belle II grid by recording the parent file metadata and the event location within the parent file. While the scheme works, it is substantially slower than a normal sequential read of standard skim files using default root file parameters. We investigate the performance of the scheme by adjusting the “splitLevel” and “autoflushsize” parameters of the root files in the parent data files.

  5. Gd-DTPA enhanced MR imaging in Bell's palsy

    International Nuclear Information System (INIS)

    Matsumoto, Yasushi; Kawamura, Yuji; Yanagihara, Naoaki; Sadamoto, Masanori; Sadamoto, Kazuhiko.

    1991-01-01

    Magnetic resonance imaging (MRI) was carried out in 27 patients with Bell's palsy. T1-weighted spin-echo images (TR500/TE25-34) were taken before and after the intravenous administration of Gd-DTPA (0.1 mmol/kg) with 0.5T superconductive MRI. There was significant enhancement at the geniculate ganglion and the horizontal segment of the involved facial nerve in 22 patients (81.5%) and at the vertical segment in 20 (74.1%). Enhancement at the meatal fundus was seen in only 4 patients (14.9%) and at the labyrinthine segment in 8 (29.6%). These results corroborate other evidence that the geniculate ganglion is involved most frequently in Bell's palsy. In addition, the enhancement of the proximal portion, i.e. the meatal fundus and the labyrinthine segment of the nerve, although not common, noted in this study may be important in the diagnosis and treatment of Bell's palsy. (author)

  6. Complex centers of polynomial differential equations

    Directory of Open Access Journals (Sweden)

    Mohamad Ali M. Alwash

    2007-07-01

    Full Text Available We present some results on the existence and nonexistence of centers for polynomial first order ordinary differential equations with complex coefficients. In particular, we show that binomial differential equations without linear terms do not have complex centers. Classes of polynomial differential equations, with more than two terms, are presented that do not have complex centers. We also study the relation between complex centers and the Pugh problem. An algorithm is described to solve the Pugh problem for equations without complex centers. The method of proof involves phase plane analysis of the polar equations and a local study of periodic solutions.

  7. Differential recurrence formulae for orthogonal polynomials

    Directory of Open Access Journals (Sweden)

    Anton L. W. von Bachhaus

    1995-11-01

    Full Text Available Part I - By combining a general 2nd-order linear homogeneous ordinary differential equation with the three-term recurrence relation possessed by all orthogonal polynomials, it is shown that sequences of orthogonal polynomials which satisfy a differential equation of the above mentioned type necessarily have a differentiation formula of the type: gn(xY'n(x=fn(xYn(x+Yn-1(x. Part II - A recurrence formula of the form: rn(xY'n(x+sn(xY'n+1(x+tn(xY'n-1(x=0, is derived using the result of Part I.

  8. 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

  9. Facial palsy in Melkersson-Rosenthal syndrome and Bell's palsy: familial history and recurrence tendency.

    Science.gov (United States)

    Sun, Baochun; Zhou, Chengyong; Han, Zeli

    2015-02-01

    The aim of this study was to compare genetic predilection and recurrence tendency between facial palsy in Melkersson-Rosenthal syndrome (MRS) and Bell's palsy We carried out an investigation on patients with facial palsy in MRS and those with Bell's palsy who visited the outpatient department in our hospital between February 2009 and February 2013. They were asked about familial history and whether it was the first episode, with the results recorded and compared. There were 16 patients with facial palsy in MRS and 860 patients with Bell's palsy involved in the study. Familial history was positive in 5 of 16 patients (31.3%) with facial palsy in MRS and 56 of 860 patients (6.5%) with Bell's palsy (P palsy in MRS and 88 of 860 cases (10.2%) with Bell's palsy had a history of facial palsy in the past (P Bell's palsy, facial palsy in MRS has an obvious genetic predilection and recurrence tendency. © The Author(s) 2014.

  10. Considering a non-polynomial basis for local kernel regression problem

    Science.gov (United States)

    Silalahi, Divo Dharma; Midi, Habshah

    2017-01-01

    A common used as solution for local kernel nonparametric regression problem is given using polynomial regression. In this study, we demonstrated the estimator and properties using maximum likelihood estimator for a non-polynomial basis such B-spline to replacing the polynomial basis. This estimator allows for flexibility in the selection of a bandwidth and a knot. The best estimator was selected by finding an optimal bandwidth and knot through minimizing the famous generalized validation function.

  11. 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.

  12. Distribution of Bell-inequality violation versus multiparty-quantum-correlation measures

    Science.gov (United States)

    Sharma, Kunal; Das, Tamoghna; Sen (de), Aditi; Sen, Ujjwal

    Violation of a Bell inequality guarantees the existence of quantum correlations in a shared quantum state. A pure bipartite quantum state, having nonvanishing quantum correlation, always violates a Bell inequality. Such correspondence is absent for multipartite pure quantum states in the case of multipartite correlation function Bell inequalities with two settings at each site. We establish a connection between the monogamy of Bell-inequality violation and multiparty quantum correlations for shared multisite quantum states. We believe that the relation is generic, as it is true for a number of different multisite measures that are defined from radically different perspectives. Precisely, we quantify the multisite-quantum-correlation content in the states by generalized geometric measure, a genuine multisite entanglement measure, as well as three monogamybased multiparty-quantum-correlation measures, viz., 3-tangle, quantum-discord score, and quantum-work-deficit score. We find that generalized Greenberger-Horne-Zeilinger states and another single-parameter family of states, which we refer to as the special Greenberger-Horne-Zeilinger states, have the status of extremal states in such relations.

  13. Game, cloud architecture and outreach for The BIG Bell Test

    Science.gov (United States)

    Abellan, Carlos; Tura, Jordi; Garcia, Marta; Beduini, Federica; Hirschmann, Alina; Pruneri, Valerio; Acin, Antonio; Marti, Maria; Mitchell, Morgan

    The BIG Bell test uses the input from the Bellsters, self-selected human participants introducing zeros and ones through an online videogame, to perform a suite of quantum physics experiments. In this talk, we will explore the videogame, the data infrastructure and the outreach efforts of the BIG Bell test collaboration. First, we will discuss how the game was designed so as to eliminate possible feedback mechanisms that could influence people's behavior. Second, we will discuss the cloud architecture design for scalability as well as explain how we sent each individual bit from the users to the labs. Also, and using all the bits collected via the BIG Bell test interface, we will show a data analysis on human randomness, e.g. are younger Bellsters more random than older Bellsters? Finally, we will talk about the outreach and communication efforts of the BIG Bell test collaboration, exploring both the social media campaigns as well as the close interaction with teachers and educators to bring the project into classrooms.

  14. Bell's Inequality for a System Composed of Particles with Different Spins

    International Nuclear Information System (INIS)

    Moradi, Shahpoor

    2009-01-01

    For two particles with different spins, we derive the Bell's inequality. The inequality is investigated for two systems combining spin-1 and spin-1/2; spin-1/2 and spin-3/2. We show that for these states Bell's inequality is violated.

  15. NMR analog of Bell's inequalities violation test

    International Nuclear Information System (INIS)

    Souza, A M; Oliveira, I S; Sarthour, R S; Magalhaes, A; Teles, J; Azevedo, E R de; Bonagamba, T J

    2008-01-01

    In this paper, we present an analog of Bell's inequalities violation test for N qubits to be performed in a nuclear magnetic resonance (NMR) quantum computer. This can be used to simulate or predict the results for different Bell's inequality tests, with distinct configurations and a larger number of qubits. To demonstrate our scheme, we implemented a simulation of the violation of the Clauser, Horne, Shimony and Holt (CHSH) inequality using a two-qubit NMR system and compared the results to those of a photon experiment. The experimental results are well described by the quantum mechanics theory and a local realistic hidden variables model (LRHVM) that was specifically developed for NMR. That is why we refer to this experiment as a simulation of Bell's inequality violation. Our result shows explicitly how the two theories can be compatible with each other due to the detection loophole. In the last part of this work, we discuss the possibility of testing some fundamental features of quantum mechanics using NMR with highly polarized spins, where a strong discrepancy between quantum mechanics and hidden variables models can be expected

  16. The computation of bond percolation critical polynomials by the deletion–contraction algorithm

    International Nuclear Information System (INIS)

    Scullard, Christian R

    2012-01-01

    Although every exactly known bond percolation critical threshold is the root in [0,1] of a lattice-dependent polynomial, it has recently been shown that the notion of a critical polynomial can be extended to any periodic lattice. The polynomial is computed on a finite subgraph, called the base, of an infinite lattice. For any problem with exactly known solution, the prediction of the bond threshold is always correct for any base containing an arbitrary number of unit cells. For unsolved problems, the polynomial is referred to as the generalized critical polynomial and provides an approximation that becomes more accurate with increasing number of bonds in the base, appearing to approach the exact answer. The polynomials are computed using the deletion–contraction algorithm, which quickly becomes intractable by hand for more than about 18 bonds. Here, I present generalized critical polynomials calculated with a computer program for bases of up to 36 bonds for all the unsolved Archimedean lattices, except the kagome lattice, which was considered in an earlier work. The polynomial estimates are generally within 10 −5 –10 −7 of the numerical values, but the prediction for the (4,8 2 ) lattice, though not exact, is not ruled out by simulations. (paper)

  17. Solving the interval type-2 fuzzy polynomial equation using the ranking method

    Science.gov (United States)

    Rahman, Nurhakimah Ab.; Abdullah, Lazim

    2014-07-01

    Polynomial equations with trapezoidal and triangular fuzzy numbers have attracted some interest among researchers in mathematics, engineering and social sciences. There are some methods that have been developed in order to solve these equations. In this study we are interested in introducing the interval type-2 fuzzy polynomial equation and solving it using the ranking method of fuzzy numbers. The ranking method concept was firstly proposed to find real roots of fuzzy polynomial equation. Therefore, the ranking method is applied to find real roots of the interval type-2 fuzzy polynomial equation. We transform the interval type-2 fuzzy polynomial equation to a system of crisp interval type-2 fuzzy polynomial equation. This transformation is performed using the ranking method of fuzzy numbers based on three parameters, namely value, ambiguity and fuzziness. Finally, we illustrate our approach by numerical example.

  18. Impact adding bifurcation in an autonomous hybrid dynamical model of church bell

    Science.gov (United States)

    Brzeski, P.; Chong, A. S. E.; Wiercigroch, M.; Perlikowski, P.

    2018-05-01

    In this paper we present the bifurcation analysis of the yoke-bell-clapper system which corresponds to the biggest bell "Serce Lodzi" mounted in the Cathedral Basilica of St Stanislaus Kostka, Lodz, Poland. The mathematical model of the system considered in this work has been derived and verified based on measurements of dynamics of the real bell. We perform numerical analysis both by direct numerical integration and path-following method using toolbox ABESPOL (Chong, 2016). By introducing the active yoke the position of the bell-clapper system with respect to the yoke axis of rotation can be easily changed and it can be used to probe the system dynamics. We found a wide variety of periodic and non-periodic solutions, and examined the ranges of coexistence of solutions and transitions between them via different types of bifurcations. Finally, a new type of bifurcation induced by a grazing event - an "impact adding bifurcation" has been proposed. When it occurs, the number of impacts between the bell and the clapper is increasing while the period of the system's motion stays the same.

  19. Excess molar volume and viscosity deviation for binary mixtures of γ-butyrolactone with dimethyl sulfoxide

    International Nuclear Information System (INIS)

    Krakowiak, Joanna; Śmiechowski, Maciej

    2017-01-01

    Highlights: • Densities and viscosities of DMSO-GBL binary liquid mixtures were measured. • The volumetric parameters and excess quantities were obtained. • Ab initio calculations were performed for single molecules and dimers in the studied mixture. • The interactions in solutions are weaker than in pure solvents. - Abstract: The densities of binary liquid mixtures of dimethyl sulfoxide and γ-butyrolactone at (293.15, 298.15, 303.15 and 313.15) K and viscosity at T = 298.15 K have been measured at atmospheric pressure over the entire range of concentration. From these data the excess molar volumes V E at (293.15, 298.15, 303.15 and 313.15) K and the viscosity deviation, the excess entropy, and the excess Gibbs energy of activation for viscous flow at T = 298.15 K have been determined. These data were mathematically represented by the Redlich-Kister polynomial. Partial and apparent molar volumes have been calculated for better understanding of the interactions in the binary systems. The obtained data indicate the lack of specific interactions between unlike molecules, which seem to be a little weaker as compared to the interactions in pure solvents.

  20. Color and illuminance level of lighting can modulate willingness to eat bell peppers.

    Science.gov (United States)

    Hasenbeck, Aimee; Cho, Sungeun; Meullenet, Jean-François; Tokar, Tonya; Yang, Famous; Huddleston, Elizabeth A; Seo, Han-Seok

    2014-08-01

    Food products are often encountered under colored lighting, particularly in restaurants and retail stores. However, relatively little attention has been paid to whether the color of ambient lighting can affect consumers' motivation for consumption. This study aimed to determine whether color (Experiment 1) and illuminance level (Experiment 2) of lighting can influence consumers' liking of appearance and their willingness to eat bell peppers. For red, green, and yellow bell peppers, yellow and blue lighting conditions consistently increased participants' liking of appearance the most and the least, respectively. Participants' willingness to consume bell peppers increased the most under yellow lighting and the least under blue lighting. In addition, a dark condition (i.e. low level of lighting illuminance) decreased liking of appearance and willingness to eat the bell peppers compared to a bright condition (i.e. high level of lighting illuminance). Our findings demonstrate that lighting color and illuminance level can influence consumers' hedonic impression and likelihood to consume bell peppers. Furthermore, the influences of color and illuminance level of lighting appear to be dependent on the surface color of bell peppers. © 2013 Society of Chemical Industry.

  1. A high-order q-difference equation for q-Hahn multiple orthogonal polynomials

    DEFF Research Database (Denmark)

    Arvesú, J.; Esposito, Chiara

    2012-01-01

    A high-order linear q-difference equation with polynomial coefficients having q-Hahn multiple orthogonal polynomials as eigenfunctions is given. The order of the equation coincides with the number of orthogonality conditions that these polynomials satisfy. Some limiting situations when are studie....... Indeed, the difference equation for Hahn multiple orthogonal polynomials given in Lee [J. Approx. Theory (2007), ), doi: 10.1016/j.jat.2007.06.002] is obtained as a limiting case....

  2. 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

  3. Experimental violation of a Bell's inequality with efficient detection.

    Science.gov (United States)

    Rowe, M A; Kielpinski, D; Meyer, V; Sackett, C A; Itano, W M; Monroe, C; Wineland, D J

    2001-02-15

    Local realism is the idea that objects have definite properties whether or not they are measured, and that measurements of these properties are not affected by events taking place sufficiently far away. Einstein, Podolsky and Rosen used these reasonable assumptions to conclude that quantum mechanics is incomplete. Starting in 1965, Bell and others constructed mathematical inequalities whereby experimental tests could distinguish between quantum mechanics and local realistic theories. Many experiments have since been done that are consistent with quantum mechanics and inconsistent with local realism. But these conclusions remain the subject of considerable interest and debate, and experiments are still being refined to overcome 'loopholes' that might allow a local realistic interpretation. Here we have measured correlations in the classical properties of massive entangled particles (9Be+ ions): these correlations violate a form of Bell's inequality. Our measured value of the appropriate Bell's 'signal' is 2.25 +/- 0.03, whereas a value of 2 is the maximum allowed by local realistic theories of nature. In contrast to previous measurements with massive particles, this violation of Bell's inequality was obtained by use of a complete set of measurements. Moreover, the high detection efficiency of our apparatus eliminates the so-called 'detection' loophole.

  4. 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.

  5. Testing the structure of multipartite entanglement with Bell inequalities.

    Science.gov (United States)

    Brunner, Nicolas; Sharam, James; Vértesi, Tamás

    2012-03-16

    We show that the rich structure of multipartite entanglement can be tested following a device-independent approach. Specifically we present Bell inequalities for distinguishing between different types of multipartite entanglement, without placing any assumptions on the measurement devices used in the protocol, in contrast with usual entanglement witnesses. We first address the case of three qubits and present Bell inequalities that can be violated by W states but not by Greenberger-Horne-Zeilinger states, and vice versa. Next, we devise 'subcorrelation Bell inequalities' for any number of parties, which can provably not be violated by a broad class of multipartite entangled states (generalizations of Greenberger-Horne-Zeilinger states), but for which violations can be obtained for W states. Our results give insight into the nonlocality of W states. The simplicity and robustness of our tests make them appealing for experiments.

  6. ANALYTICAL SOLUTION OF THE K-TH ORDER AUTONOMOUS ORDINARY DIFFERENTIAL EQUATION

    Directory of Open Access Journals (Sweden)

    Ronald Orozco López

    2017-04-01

    Full Text Available The main objective of this paper is to find the analytical solution of the autonomous equation y(k = f (y and prove its convergence using autonomous polynomials of order k, define here in addition of the formula of Faá di Bruno for composition of functions and Bell polynomials. Autonomous polynomials of order k are defined in terms of the boundary values of the equation. Also special values of autonomous polynomials of order 1 are given.

  7. H∞ Control of Polynomial Fuzzy Systems: A Sum of Squares Approach

    Directory of Open Access Journals (Sweden)

    Bomo W. Sanjaya

    2014-07-01

    Full Text Available This paper proposes the control design ofa nonlinear polynomial fuzzy system with H∞ performance objective using a sum of squares (SOS approach. Fuzzy model and controller are represented by a polynomial fuzzy model and controller. The design condition is obtained by using polynomial Lyapunov functions that not only guarantee stability but also satisfy the H∞ performance objective. The design condition is represented in terms of an SOS that can be numerically solved via the SOSTOOLS. A simulation study is presented to show the effectiveness of the SOS-based H∞ control designfor nonlinear polynomial fuzzy systems.

  8. Zeros and logarithmic asymptotics of Sobolev orthogonal polynomials for exponential weights

    Science.gov (United States)

    Díaz Mendoza, C.; Orive, R.; Pijeira Cabrera, H.

    2009-12-01

    We obtain the (contracted) weak zero asymptotics for orthogonal polynomials with respect to Sobolev inner products with exponential weights in the real semiaxis, of the form , with [gamma]>0, which include as particular cases the counterparts of the so-called Freud (i.e., when [phi] has a polynomial growth at infinity) and Erdös (when [phi] grows faster than any polynomial at infinity) weights. In addition, the boundness of the distance of the zeros of these Sobolev orthogonal polynomials to the convex hull of the support and, as a consequence, a result on logarithmic asymptotics are derived.

  9. Classical counterexamples to Bell's inequalities

    International Nuclear Information System (INIS)

    Orlov, Yuri F.

    2002-01-01

    This paper shows that a classical system containing a conventional yes/no decision-making component can behave like a quantum system of spin measurements in many ways (although it lacks a wave function) when, in principle, there are no deterministic decision procedures to govern the decision making, and when probabilistic decision procedures consistent with the system are introduced. Most notably, the system violates Bell's inequalities. Moreover, since the system is simple and macroscopic, its similarities to quantum systems arguably provide an insight into quantum mechanics and, in particular, EPR experiments. Thus, from the qualitative correspondences, decisions↔quantum measurements and the impossibility of deterministic decision procedures↔quantum noncommutativity, we conclude that the violation of Bell's inequalities in quantum mechanics does not require the existence of an unknown nonclassical nonlocality. It can merely be a result of local noncommutativity combined with nonlocalities of the classical type. The proposed classical decision-making system is a nonquantum theoretical construct possessing complementarity features in Bohr's sense

  10. Bell-type quantum field theories

    International Nuclear Information System (INIS)

    Duerr, Detlef; Goldstein, Sheldon; Tumulka, Roderich; Zanghi, Nino

    2005-01-01

    In his paper (1986 Beables for quantum field theory Phys. Rep. 137 49-54) John S Bell proposed how to associate particle trajectories with a lattice quantum field theory, yielding what can be regarded as a vertical bar Ψ vertical bar 2 -distributed Markov process on the appropriate configuration space. A similar process can be defined in the continuum, for more or less any regularized quantum field theory; we call such processes Bell-type quantum field theories. We describe methods for explicitly constructing these processes. These concern, in addition to the definition of the Markov processes, the efficient calculation of jump rates, how to obtain the process from the processes corresponding to the free and interaction Hamiltonian alone, and how to obtain the free process from the free Hamiltonian or, alternatively, from the one-particle process by a construction analogous to 'second quantization'. As an example, we consider the process for a second quantized Dirac field in an external electromagnetic field. (topical review)

  11. 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.

  12. Self-testing properties of Gisin's elegant Bell inequality

    Science.gov (United States)

    Andersson, Ole; Badzi&aogo; g, Piotr; Bengtsson, Ingemar; Dumitru, Irina; Cabello, Adán

    2017-09-01

    An experiment in which the Clauser-Horne-Shimony-Holt inequality is maximally violated is self-testing (i.e., it certifies in a device-independent way both the state and the measurements). We prove that an experiment maximally violating Gisin's elegant Bell inequality is not similarly self-testing. The reason can be traced back to the problem of distinguishing an operator from its complex conjugate. We provide a complete and explicit characterization of all scenarios in which the elegant Bell inequality is maximally violated. This enables us to see exactly how the problem plays out.

  13. Bell's "Theorem": loopholes vs. conceptual flaws

    Science.gov (United States)

    Kracklauer, A. F.

    2017-12-01

    An historical overview and detailed explication of a critical analysis of what has become known as Bell's Theorem to the effect that, it should be impossible to extend Quantum Theory with the addition of local, real variables so as to obtain a version free of the ambiguous and preternatural features of the currently accepted interpretations is presented. The central point on which this critical analysis, due originally to Edwin Jaynes, is that Bell incorrectly applied probabilistic formulas involving conditional probabilities. In addition, mathematical technicalities that have complicated the understanding of the logical or mathematical setting in which current theory and experimentation are embedded, are discussed. Finally, some historical speculations on the sociological environment, in particular misleading aspects, in which recent generations of physicists lived and worked are mentioned.

  14. Some Results on the Independence Polynomial of Unicyclic Graphs

    Directory of Open Access Journals (Sweden)

    Oboudi Mohammad Reza

    2018-05-01

    Full Text Available Let G be a simple graph on n vertices. An independent set in a graph is a set of pairwise non-adjacent vertices. The independence polynomial of G is the polynomial I(G,x=∑k=0ns(G,kxk$I(G,x = \\sum\

  15. BELÉM E A BELLE ÉPOQUE DA BORRACHA

    Directory of Open Access Journals (Sweden)

    Geraldo Mártires Coelho

    2016-12-01

    Full Text Available O artigo discute a história e a vida de Belém na passagem do século XIX para o século XX, marcada por um conjunto de elementos sociais, intelectuais e artísticos que refletiam as influências da cultura e da sociedade europeia, principalmente francesa, do período. Em termos de Brasil, esse processo se verificou em Belém e no Rio de Janeiro: era a chamada Belle Époque. Cultivou-se o gosto pelo que vinha da Europa, o que podia ser visto na maneira de se vestir das elites locais e na vida social que levavam em Belém. A literatura, a pintura e a música, cultuadas por essas mesmas elites, faziam da cidade um grande centro de vida intelectual e artística. É preciso, no entanto, observar que a Belle Époque faz parte de um processo maior, o da mundialização da cultura.   PALAVRAS-CHAVE: Belém; Belle Époque; Mundialização da cultura.     ABSTRACT This article treats the history and life of Belem (capital city of Para State/Brazil during the passage from XIX to XX century that was marked by a set of social, intellectual and artistic elements, which reflected the influences from European culture and society, especially the French one in such period. In terms of Brazil, that process was seen in Belem and Rio de Janeiro; it was called Belle Époque. It was cultivated a taste to whatever came from Europe, what could be seen on the dressing fashion of the local elites and the social live they had in Belem. Literature, painting and music, idolised by the same elite made the city a huge centre of intellectual and artistic life. However, it is needed to consider that Belle Époque is part of a bigger process, the globalization one.   KEY WORDS: Belém; Belle Époque; Culture globalization.   RESUMEN  El artículo discute la historia de la vida de Belém en la pasaje del siglo XIX para el siglo XX, marcada por un conjunto de elementos sociales, intelectuales y artísticos que reflejaban las influencias de la cultura y de la sociedad

  16. The Clinical Study about Honilirls Placenta Herbal Acupuncture on Bell's Palsy

    Directory of Open Access Journals (Sweden)

    Lee Chae-Woo

    2005-12-01

    Full Text Available Objectives : This study has been designed and performed to identify the effect on Bell's palsy according to the injection of herbal medicine induced from the Hominis Placenta. Methods : We measured the facial palsy changes of the patients who were admitted for Bell's palsy in the Oriental Medical hospital of Dongeui medical center from 03-01-2004 to 07-31-2004. Bell's palsy patients were divided into two groups. One group(A group was injected with Hominis Placenta herbal acupuncture. The other group(B group was injected with normal saline. Then effects of these treatment was evaluated by Yanagihara's unweighted grading system. Results : A group was marked more higher than B group in treatment outcome. we discovered that it is significant differences between two groups after 4 week. Conclusions : These results provided that A group is more effective than B group. For clearly proving the effect of Hominis Placenta herbal acupuncture on Bell's palsy, it is need more sample's number and more treatment's duration.

  17. Limit cycles bifurcating from the periodic annulus of cubic homogeneous polynomial centers

    Directory of Open Access Journals (Sweden)

    Jaume Llibre

    2015-10-01

    Full Text Available We obtain an explicit polynomial whose simple positive real roots provide the limit cycles which bifurcate from the periodic orbits of any cubic homogeneous polynomial center when it is perturbed inside the class of all polynomial differential systems of degree n.

  18. Polynomial Poisson algebras: Gel'fand-Kirillov problem and Poisson spectra

    OpenAIRE

    Lecoutre, César

    2014-01-01

    We study the fields of fractions and the Poisson spectra of polynomial Poisson algebras.\\ud \\ud First we investigate a Poisson birational equivalence problem for polynomial Poisson algebras over a field of arbitrary characteristic. Namely, the quadratic Poisson Gel'fand-Kirillov problem asks whether the field of fractions of a Poisson algebra is isomorphic to the field of fractions of a Poisson affine space, i.e. a polynomial algebra such that the Poisson bracket of two generators is equal to...

  19. 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

  20. 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.

  1. Bell Canyon test summary report

    International Nuclear Information System (INIS)

    Christensen, C.L.; Peterson, E.W.

    1981-04-01

    The Bell Canyon Test was an in situ evaluation of the ability of a cement grout plug to seal boreholes. It consisted of a 2-m-long, 20-cm-diameter grout plug in an anhydrite formation at a depth of 1370 m, directly above an aquifer that provided a 12.4 MPa (1800 psi) differential pressure. The aquifer had a production capability of 38,000 l/day (240 bbl/day, 10 4 gal/day). The observed leakage after plug installation was 0.6 l/day, which is equivalent to a 50 microdarcy flow path assuming all flow occurred through the plug cross-sectional area. Laboratory results and analysis of field data indicate that the bulk of the flow occurred through a microstructure at the interface between the plug and the host rock. The Bell Canyon Test demonstrated that a plug could be formulated, emplaced, and tested under actual conditions and provide acceptable performance. When these results are related to the WIPP performance assessment models, they provide additional confidence that borehole plugging can be accomplished satisfactorily. The Bell Canyon results can also be used as basis for future activities in the generic repository sealing program for similar emplacements and performance assessment evaluations. If the observed leakage rates are not acceptable at other sites, the BCT results would indicate that the first step in improving such emplacements should deal with improved bonding of the plug to the rock at these sites. The results obtained from the BCT, when coupled with results from long-term durability assessments, form a plug performance data basis for repository designers at other proposed waste repository sites

  2. 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 topology, and a set of analytic invariants, describing the geometry. Conversely, given admissible combinatorial and analytic data sets, we show using surgery the existence of a unique monic and centred polynomial vector field realizing the given invariants. This is the content of the Structure Theorem......, the main result of the paper. This result is an extension and refinement of Douady et al. (Champs de vecteurs polynomiaux sur C. Unpublished manuscript) classification of the structurally stable polynomial vector fields. We further review some general concepts for completeness and show that vector fields...

  3. Maximal violation of Bell's inequalities for algebras of observables in tangent spacetime regions

    International Nuclear Information System (INIS)

    Summers, S.J.; Werner, R.

    1988-01-01

    We continue our study of Bell's inequalities and quantum field theory. It is shown in considerably broader generality than in our previous work that algebras of local observables corresponding to complementary wedge regions maximally violate Bell's inequality in all normal states. Pairs of commuting von Neumann algebras that maximally violate Bell's inequalities in all normal states are characterized. Algebras of local observables corresponding to tangent double cones are shown to maximally violate Bell's inequalities in all normal states in dilatation-invariant theories, in free quantum field models, and in a class of interacting models. Further, it is proven that such algebras are not split in any theory with an ultraviolet scaling limit

  4. Random polynomials and expected complexity of bisection methods for real solving

    DEFF Research Database (Denmark)

    Emiris, Ioannis Z.; Galligo, André; Tsigaridas, Elias

    2010-01-01

    , and by Edelman and Kostlan in order to estimate the real root separation of degree d polynomials with i.i.d. coefficients that follow two zero-mean normal distributions: for SO(2) polynomials, the i-th coefficient has variance (d/i), whereas for Weyl polynomials its variance is 1/i!. By applying results from....... The second part of the paper shows that the expected number of real roots of a degree d polynomial in the Bernstein basis is √2d ± O(1), when the coefficients are i.i.d. variables with moderate standard deviation. Our paper concludes with experimental results which corroborate our analysis....

  5. Thermodynamic properties of (tetradecane + benzene, + toluene, + chlorobenzene, + bromobenzene, + anisole) binary mixtures at T = (298.15, 303.15, and 308.15) K

    International Nuclear Information System (INIS)

    Mutalik, Venkatesh; Manjeshwar, Lata S.; Sairam, Malladi; Aminabhavi, Tejraj M.

    2006-01-01

    Density ρ, viscosity η, and refractive index n D , values for (tetradecane + benzene, + toluene, + chlorobenzene, + bromobenzene, + anisole) binary mixtures over the entire range of mole fraction have been measured at temperatures (298.15, 303.15, and 308.15) K at atmospheric pressure. The speed of sound u has been measured at T = 298.15 K only. Using these data, excess molar volume V E , deviations in viscosity Δη, Lorentz-Lorenz molar refraction ΔR, speed of sound Δu, and isentropic compressibility Δk s have been calculated. These results have been fitted to the Redlich and Kister polynomial equation to estimate the binary interaction parameters and standard deviations. Excess molar volumes have exhibited both positive and negative trends in many mixtures, depending upon the nature of the second component of the mixture. For the (tetradecane + chlorobenzene) binary mixture, an incipient inversion has been observed. Calculated thermodynamic quantities have been discussed in terms of intermolecular interactions between mixing components

  6. O(N) symmetries, sum rules for generalized Hermite polynomials and squeezed states

    International Nuclear Information System (INIS)

    Daboul, Jamil; Mizrahi, Salomon S

    2005-01-01

    Quantum optics has been dealing with coherent states, squeezed states and many other non-classical states. The associated mathematical framework makes use of special functions as Hermite polynomials, Laguerre polynomials and others. In this connection we here present some formal results that follow directly from the group O(N) of complex transformations. Motivated by the squeezed states structure, we introduce the generalized Hermite polynomials (GHP), which include as particular cases, the Hermite polynomials as well as the heat polynomials. Using generalized raising operators, we derive new sum rules for the GHP, which are covariant under O(N) transformations. The GHP and the associated sum rules become useful for evaluating Wigner functions in a straightforward manner. As a byproduct, we use one of these sum rules, on the operator level, to obtain raising and lowering operators for the Laguerre polynomials and show that they generate an sl(2, R) ≅ su(1, 1) algebra

  7. Genealogy of John and Charles Bell: their relationship with the children of Charles Shaw of Ayr.

    Science.gov (United States)

    Kaufman, M

    2005-11-01

    The Reverend William Bell had six children who survived infancy. Two of his sons entered the legal profession and two other sons became distinguished anatomists and surgeons--John Bell, said for 20 years to have been the leading operating surgeon in Britain and throughout the world--and Sir Charles Bell, possibly the most distinguished anatomist and physiologist of his day. Information is not known about the fifth son or their sister. Charles Shaw, a lawyer of Ayr, had four sons and two daughters who survived infancy. Two of his sons, John and Alexander, became anatomists and later surgeons at the Middlesex Hospital, and both worked closely with Charles Bell at the Great Windmill Street School of Anatomy. His third son entered the law and his fourth son became a distinguished soldier. The two daughters of Charles Shaw married into the Bell family: Barbara married George Joseph Bell and Marion married Mr (later Sir) Charles Bell.

  8. Euler polynomials and identities for non-commutative operators

    Science.gov (United States)

    De Angelis, Valerio; Vignat, Christophe

    2015-12-01

    Three kinds of identities involving non-commutating operators and Euler and Bernoulli polynomials are studied. The first identity, as given by Bender and Bettencourt [Phys. Rev. D 54(12), 7710-7723 (1996)], expresses the nested commutator of the Hamiltonian and momentum operators as the commutator of the momentum and the shifted Euler polynomial of the Hamiltonian. The second one, by Pain [J. Phys. A: Math. Theor. 46, 035304 (2013)], links the commutators and anti-commutators of the monomials of the position and momentum operators. The third appears in a work by Figuieira de Morisson and Fring [J. Phys. A: Math. Gen. 39, 9269 (2006)] in the context of non-Hermitian Hamiltonian systems. In each case, we provide several proofs and extensions of these identities that highlight the role of Euler and Bernoulli polynomials.

  9. Aerogel RICH for the Belle II forward PID

    Energy Technology Data Exchange (ETDEWEB)

    Nishida, S., E-mail: shohei.nishida@kek.jp [High Energy Accelerator Research Organization (KEK), Tsukuba (Japan); Adachi, I. [High Energy Accelerator Research Organization (KEK), Tsukuba (Japan); Hamada, N. [Toho University, Funabashi (Japan); Hara, K. [High Energy Accelerator Research Organization (KEK), Tsukuba (Japan); Iijima, T. [Nagoya University, Nagoya (Japan); Iwata, S.; Kakuno, H. [Tokyo Metropolitan University, Hachioji (Japan); Kawai, H. [Chiba University, Chiba (Japan); Korpar, S.; Krizan, P. [Jozef Stefan Institute, Ljubljana (Slovenia); Ogawa, S. [Toho University, Funabashi (Japan); Pestotnik, R.; Ŝantelj, L.; Seljak, A. [Jozef Stefan Institute, Ljubljana (Slovenia); Sumiyoshi, T. [Tokyo Metropolitan University, Hachioji (Japan); Tabata, M. [Japan Aerospace Exploration Agency (JAXA), Sagamihara (Japan); Tahirovic, E. [Jozef Stefan Institute, Ljubljana (Slovenia); Yoshida, K. [Tokyo Metropolitan University, Hachioji (Japan); Yusa, Y. [Niigata University, Niigata (Japan)

    2014-12-01

    The Belle II spectrometer, a follow up of the very successful Belle experiment, is under construction at the SuperKEKB electron–positron collider at KEK in Japan. For the PID system in the forward region of the spectrometer, a proximity focusing ring-imaging Cherenkov (RICH) counter with an aerogel radiator is being developed. The counter will provide a 4σ separation of pions and kaons up to momenta of 4 GeV/c. For the position sensitive photon sensor, a 144-channel Hybrid Avalanche Photo-Detector (HAPD) has been developed with Hamamatsu Photonics K.K. The readout electronics is based on the custom developed ASIC. The design of the components is currently being finalized and part of their mass production have already started. Herein, we report the final design of the counter and a prototype test conducted with test beams at DESY. - Highlights: • We are constructing a RICH counter with aerogel radiator for Belle II. • Beam test for the prototype Aerogel RICH shows its good performance. • The effect of the neutron irradiation of the photodetector is examined.

  10. Trigger Timing Module for SVD2 upgrade at Belle

    International Nuclear Information System (INIS)

    Chang, M.C.; Gao, Z.W.; Guo, Y.N.; Kawasaki, T.; Ueno, K.; Velikzhanin, Y.S.

    2003-01-01

    We have developed a Trigger Timing Module (TTM2) for the control and readout electronics (CORE) of the upgraded Silicon Vertex Detector (SVD2) for use in the BELLE experiment. Eleven Trigger Timing Modules located at one VME-crate provide timing and strobe signals for the SVD2 CORE electronics and make communication between SVD2 and Global Decision Logic of the BELLE data acquisition system. The main motivation to make a new TTM design is to avoid glitches

  11. On integral and finite Fourier transforms of continuous q-Hermite polynomials

    International Nuclear Information System (INIS)

    Atakishiyeva, M. K.; Atakishiyev, N. M.

    2009-01-01

    We give an overview of the remarkably simple transformation properties of the continuous q-Hermite polynomials H n (x vertical bar q) of Rogers with respect to the classical Fourier integral transform. The behavior of the q-Hermite polynomials under the finite Fourier transform and an explicit form of the q-extended eigenfunctions of the finite Fourier transform, defined in terms of these polynomials, are also discussed.

  12. 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.

  13. The association of Varicella zoster virus reactivation with Bell's palsy in children.

    Science.gov (United States)

    Abdel-Aziz, Mosaad; Azab, Noha A; Khalifa, Badwy; Rashed, Mohammed; Naguib, Nader

    2015-03-01

    Bell's palsy is considered the most common cause of facial nerve paralysis in children. Although different theories have been postulated for its diagnosis, reactivation of the Varicella zoster virus (VZV) has been implicated as one of the causes of Bell's palsy. The aim of the study was to evaluate the association of Varicella-zoster virus infection with Bell's palsy and its outcome in children. A total of 30 children with Bell's palsy were recruited and were assayed for evidence of VZV infection. The severity of facial nerve dysfunction and the recovery rate were evaluated according to House-Brackmann Facial Nerve Grading Scale (HB FGS). Paired whole blood samples from all patients were obtained at their initial visit and 3 weeks later, and serum samples were analyzed for VZV IgG and IgM antibodies using ELISA. A significantly higher percentage of Bell's palsy patients were seropositive for VZV IgM antibodies than controls (36.6% of patients vs 10% of controls) while for VZV IgG antibodies the difference was statistically nonsignificant. HB FGS in Bell's palsy patients with serologic evidence of VZV recent infection or reactivation showed a statistiacally significant less cure rate than other patients. VZV reactivation may be an important cause of acute peripheral facial paralysis in children. The appropriate diagnosis of VZV reactivation should be done to improve the outcome and the cure rate by the early use of antiviral treatment. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.

  14. HERPES SIMPLEX VIRUS IN SALIVA OF PATIENTS WITH BELL'S PALSY

    Directory of Open Access Journals (Sweden)

    M.H. Harirchian

    2008-04-01

    Full Text Available Acute idiopathic peripheral facial paralysis (Bell's palsy is the most common disorder of the facial nerve. Most patients recover completely, although some have permanent disfiguring facial weakness. Many studies have attempted to identify an infectious etiology for this disease. Although the cause of Bell's palsy remains unknown, recent studies suggest a possible association with Herpes Simplex Virus-1(HSV-1 infection. In this case-control study we investigated the presence of DNA of HSV in the saliva of 26 patients with Bells palsy in first and second weeks of disorder compared to normal population who were matched in sex, age, as well as history of diabetes mellitus, hypertension and labial herpes. In the case group 3 and 7 patients had positive polymerase chain reaction (PCR for HSV in first and second weeks of disease respectively compared to 4 in controls. It means that there was not any relationship between Bell's palsy and HSV in saliva either in first or in second week. Two and 6 of positive results from the sample of first and second weeks were from patients with severe (grade 4-6 Bell's palsy. Although the positive results were more in second week in patient group and more in severe palsies, but a significant relationship between Bell's palsy or its severity and positive PCR for HSV was not detected (P >0.05.

  15. 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.

  16. On the dynamics of StemBells: Microbubble-conjugated stem cells for ultrasound-controlled delivery

    Science.gov (United States)

    Kokhuis, Tom J. A.; Naaijkens, Benno A.; Juffermans, Lynda J. M.; Kamp, Otto; van der Steen, Antonius F. W.; Versluis, Michel; de Jong, Nico

    2017-07-01

    The use of stem cells for regenerative tissue repair is promising but hampered by the low number of cells delivered to the site of injury. To increase the delivery, we propose a technique in which stem cells are linked to functionalized microbubbles, creating echogenic complex dubbed StemBells. StemBells are highly susceptible to acoustic radiation force which can be employed after injection to push the StemBells locally to the treatment site. To optimally benefit from the delivery technique, a thorough characterization of the dynamics of StemBells during ultrasound exposure is needed. Using high-speed optical imaging, we study the dynamics of StemBells as a function of the applied frequency from which resonance curves were constructed. A theoretical model, based on a modified Rayleigh-Plesset type equation, captured the experimental resonance characteristics and radial dynamics in detail.

  17. Some inequalities for the Bell numbers

    Indian Academy of Sciences (India)

    Feng Qi

    2017-08-19

    Aug 19, 2017 ... Bell number determinant; product; inequality; generating function; derivative; absolutely monotonic function; completely monotonic func- tion; logarithmically absolutely monotonic function; logarithmically completely monotonic function; Stirling number of the second kind; induction; Faà di Bruno formula;.

  18. Families of superintegrable Hamiltonians constructed from exceptional polynomials

    International Nuclear Information System (INIS)

    Post, Sarah; Tsujimoto, Satoshi; Vinet, Luc

    2012-01-01

    We introduce a family of exactly-solvable two-dimensional Hamiltonians whose wave functions are given in terms of Laguerre and exceptional Jacobi polynomials. The Hamiltonians contain purely quantum terms which vanish in the classical limit leaving only a previously known family of superintegrable systems. Additional, higher-order integrals of motion are constructed from ladder operators for the considered orthogonal polynomials proving the quantum system to be superintegrable. (paper)

  19. Raising and Lowering Operators for Askey-Wilson Polynomials

    Directory of Open Access Journals (Sweden)

    Siddhartha Sahi

    2007-01-01

    Full Text Available In this paper we describe two pairs of raising/lowering operators for Askey-Wilson polynomials, which result from constructions involving very different techniques. The first technique is quite elementary, and depends only on the ''classical'' properties of these polynomials, viz. the q-difference equation and the three term recurrence. The second technique is less elementary, and involves the one-variable version of the double affine Hecke algebra.

  20. Rehabilitation of Bells' palsy from a multi-team perspective.

    Science.gov (United States)

    Hultcrantz, Malou

    2016-01-01

    Conclusions Defectively healed facial paralysis causes difficulties to talk and eat, involuntary spasms (synkinesis), and cosmetic deformities which can give rise both to severe psychological and physical trauma. A team consisting of Ear-Nose-Throat specialists, Plastic surgeons and Physiotherapists can offer better care, treatment and outcome for patients suffering from Bells' palsy. Objectives Patients suffering from Bells' palsy from all ENT hospitals in Sweden and the University Hospital in Helsinki has been included. Methods Results have been drawn and statistically processed for different outcomes from a prospective, double blind cross over study. Results from a pilot surgical study and therapeutic results from physiotherapy studies have been included. Ideas concerning different kinds of surgery will be reviewed and the role of physiotherapy discussed. Results According to common results, treatment with Prednisolone enhances the recovery rate and should, if possible, be used early in the course. Sunnybrook grading at 1 month after onset most accurately predicts non-recovery at 12 months in Bells' palsy and a risk factor curve will be presented in order to predict outcome and selection of patients for undergoing facial surgery. This report is focusing on how to handle patients with Bells' palsy from a multi-rehabilitation team point of view, and what will be recommended to provide these patients with the best clinical and surgical help.