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...
Complex Polynomial Vector Fields
DEFF Research Database (Denmark)
The two branches of dynamical systems, continuous and discrete, correspond to the study of differential equations (vector fields) and iteration of mappings respectively. In holomorphic dynamics, the systems studied are restricted to those described by holomorphic (complex analytic) functions...... or meromorphic (allowing poles as singularities) functions. There already exists a well-developed theory for iterative holomorphic dynamical systems, and successful relations found between iteration theory and flows of vector fields have been one of the main motivations for the recent interest in holomorphic...... vector fields. Since the class of complex polynomial vector fields in the plane is natural to consider, it is remarkable that its study has only begun very recently. There are numerous fundamental questions that are still open, both in the general classification of these vector fields, the decomposition...
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...
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...
Polynomial Vector Fields in One Complex Variable
DEFF Research Database (Denmark)
Branner, Bodil
In recent years Adrien Douady was interested in polynomial vector fields, both in relation to iteration theory and as a topic on their own. This talk is based on his work with Pierrette Sentenac, work of Xavier Buff and Tan Lei, and my own joint work with Kealey Dias.......In recent years Adrien Douady was interested in polynomial vector fields, both in relation to iteration theory and as a topic on their own. This talk is based on his work with Pierrette Sentenac, work of Xavier Buff and Tan Lei, and my own joint work with Kealey Dias....
Enumeration of Combinatorial Classes of Single Variable Complex Polynomial Vector Fields
DEFF Research Database (Denmark)
Dias, Kealey
A vector field in the space of degree d monic, centered single variable complex polynomial vector fields has a combinatorial structure which can be fully described by a combinatorial data set consisting of an equivalence relation and a marked subset on the integers mod 2d-2, satisfying certain...
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.
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...
Space complexity in polynomial calculus
Czech Academy of Sciences Publication Activity Database
Filmus, Y.; Lauria, M.; Nordström, J.; Ron-Zewi, N.; Thapen, Neil
2015-01-01
Roč. 44, č. 4 (2015), s. 1119-1153 ISSN 0097-5397 R&D Projects: GA AV ČR IAA100190902; GA ČR GBP202/12/G061 Institutional support: RVO:67985840 Keywords : proof complexity * polynomial calculus * lower bounds Subject RIV: BA - General Mathematics Impact factor: 0.841, year: 2015 http://epubs.siam.org/doi/10.1137/120895950
Invariant hyperplanes and Darboux integrability of polynomial vector fields
International Nuclear Information System (INIS)
Zhang Xiang
2002-01-01
This paper is composed of two parts. In the first part, we provide an upper bound for the number of invariant hyperplanes of the polynomial vector fields in n variables. This result generalizes those given in Artes et al (1998 Pac. J. Math. 184 207-30) and Llibre and Rodriguez (2000 Bull. Sci. Math. 124 599-619). The second part gives an extension of the Darboux theory of integrability to polynomial vector fields on algebraic varieties
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.
Automorphisms of Algebras and Bochner's Property for Vector Orthogonal Polynomials
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.
Schur Stability Regions for Complex Quadratic Polynomials
Cheng, Sui Sun; Huang, Shao Yuan
2010-01-01
Given a quadratic polynomial with complex coefficients, necessary and sufficient conditions are found in terms of the coefficients such that all its roots have absolute values less than 1. (Contains 3 figures.)
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.
On the existence of polynomial Lyapunov functions for rationally stable vector fields
DEFF Research Database (Denmark)
Leth, Tobias; Wisniewski, Rafal; Sloth, Christoffer
2018-01-01
This paper proves the existence of polynomial Lyapunov functions for rationally stable vector fields. For practical purposes the existence of polynomial Lyapunov functions plays a significant role since polynomial Lyapunov functions can be found algorithmically. The paper extents an existing result...... on exponentially stable vector fields to the case of rational stability. For asymptotically stable vector fields a known counter example is investigated to exhibit the mechanisms responsible for the inability to extend the result further....
Interpretation of stream programs: characterizing type 2 polynomial time complexity
Férée , Hugo; Hainry , Emmanuel; Hoyrup , Mathieu; Péchoux , Romain
2010-01-01
International audience; We study polynomial time complexity of type 2 functionals. For that purpose, we introduce a first order functional stream language. We give criteria, named well-founded, on such programs relying on second order interpretation that characterize two variants of type 2 polynomial complexity including the Basic Feasible Functions (BFF). These charac- terizations provide a new insight on the complexity of stream programs. Finally, we adapt these results to functions over th...
Explicitly solvable complex Chebyshev approximation problems related to sine polynomials
Freund, Roland
1989-01-01
Explicitly solvable real Chebyshev approximation problems on the unit interval are typically characterized by simple error curves. A similar principle is presented for complex approximation problems with error curves induced by sine polynomials. As an application, some new explicit formulae for complex best approximations are derived.
Localization of periodic orbits of polynomial vector fields of even degree by linear functions
Energy Technology Data Exchange (ETDEWEB)
Starkov, Konstantin E. [CITEDI-IPN, Av. del Parque 1310, Mesa de Otay, Tijuana, BC (Mexico)] e-mail: konst@citedi.mx
2005-08-01
This paper is concerned with the localization problem of periodic orbits of polynomial vector fields of even degree by using linear functions. Conditions of the localization of all periodic orbits in sets of a simple structure are obtained. Our results are based on the solution of the conditional extremum problem and the application of homogeneous polynomial forms of even degrees. As examples, the Lanford system, the jerky system with one quadratic monomial and a quartically perturbed harmonic oscillator are considered.
Localization of periodic orbits of polynomial vector fields of even degree by linear functions
International Nuclear Information System (INIS)
Starkov, Konstantin E.
2005-01-01
This paper is concerned with the localization problem of periodic orbits of polynomial vector fields of even degree by using linear functions. Conditions of the localization of all periodic orbits in sets of a simple structure are obtained. Our results are based on the solution of the conditional extremum problem and the application of homogeneous polynomial forms of even degrees. As examples, the Lanford system, the jerky system with one quadratic monomial and a quartically perturbed harmonic oscillator are considered
Existence of 121 limit cycles in a perturbed planar polynomial Hamiltonian vector field of degree 11
International Nuclear Information System (INIS)
Wang, S.; Yu, P.
2006-01-01
In this article, a systematic procedure has been explored to studying general Z q -equivariant planar polynomial Hamiltonian vector fields for the maximal number of closed orbits and the maximal number of limit cycles after perturbation. Following the procedure by taking special consideration of Z 12 -equivariant vector fields of degree 11, the maximal of 99 closed orbits are obtained under a well-defined coefficient group. Consequently, perturbation parameter control in limit cycle computation leads to the existence of 121 limit cycles in the perturbed Hamiltonian vector field, which gives rise to the lower bound of Hilbert number of 11th-order systems as H(11) ≥ 11 2 . Two conjectures are proposed regarding the maximal number of closed orbits for equivariant polynomial Hamiltonian vector fields and the maximal number of limit cycles bifurcated from the well defined Hamiltonian vector fields after perturbation
Design and Use of a Learning Object for Finding Complex Polynomial Roots
Benitez, Julio; Gimenez, Marcos H.; Hueso, Jose L.; Martinez, Eulalia; Riera, Jaime
2013-01-01
Complex numbers are essential in many fields of engineering, but students often fail to have a natural insight of them. We present a learning object for the study of complex polynomials that graphically shows that any complex polynomials has a root and, furthermore, is useful to find the approximate roots of a complex polynomial. Moreover, we…
Squeezed states and Hermite polynomials in a complex variable
International Nuclear Information System (INIS)
Ali, S. Twareque; Górska, K.; Horzela, A.; Szafraniec, F. H.
2014-01-01
Following the lines of the recent paper of J.-P. Gazeau and F. H. Szafraniec [J. Phys. A: Math. Theor. 44, 495201 (2011)], we construct here three types of coherent states, related to the Hermite polynomials in a complex variable which are orthogonal with respect to a non-rotationally invariant measure. We investigate relations between these coherent states and obtain the relationship between them and the squeezed states of quantum optics. We also obtain a second realization of the canonical coherent states in the Bargmann space of analytic functions, in terms of a squeezed basis. All this is done in the flavor of the classical approach of V. Bargmann [Commun. Pure Appl. Math. 14, 187 (1961)
Complex and real Hermite polynomials and related quantizations
International Nuclear Information System (INIS)
Cotfas, Nicolae; Gazeau, Jean Pierre; Gorska, Katarzyna
2010-01-01
It is known that the anti-Wick (or standard coherent state) quantization of the complex plane produces both canonical commutation rule and quantum spectrum of the harmonic oscillator (up to the addition of a constant). In this work, we show that these two issues are not necessarily coupled: there exists a family of separable Hilbert spaces, including the usual Fock-Bargmann space, and in each element in this family there exists an overcomplete set of unit-norm states resolving the unity. With the exception of the Fock-Bargmann case, they all produce non-canonical commutation relation whereas the quantum spectrum of the harmonic oscillator remains the same up to the addition of a constant. The statistical aspects of these non-equivalent coherent state quantizations are investigated. We also explore the localization aspects in the real line yielded by similar quantizations based on real Hermite polynomials.
International Nuclear Information System (INIS)
Cairo, Laurent; Llibre, Jaume
2007-01-01
We classify all the global phase portraits of the cubic polynomial vector fields of Lotka-Volterra type having a rational first integral of degree 2. For such vector fields there are exactly 28 different global phase portraits in the Poincare disc up to a reversal of sense of all orbits
Differential Galois theory and non-integrability of planar polynomial vector fields
Acosta-Humánez, Primitivo B.; Lázaro, J. Tomás; Morales-Ruiz, Juan J.; Pantazi, Chara
2018-06-01
We study a necessary condition for the integrability of the polynomials vector fields in the plane by means of the differential Galois Theory. More concretely, by means of the variational equations around a particular solution it is obtained a necessary condition for the existence of a rational first integral. The method is systematic starting with the first order variational equation. We illustrate this result with several families of examples. A key point is to check whether a suitable primitive is elementary or not. Using a theorem by Liouville, the problem is equivalent to the existence of a rational solution of a certain first order linear equation, the Risch equation. This is a classical problem studied by Risch in 1969, and the solution is given by the "Risch algorithm". In this way we point out the connection of the non integrability with some higher transcendent functions, like the error function.
Predicting beta-turns in proteins using support vector machines with fractional polynomials.
Elbashir, Murtada; Wang, Jianxin; Wu, Fang-Xiang; Wang, Lusheng
2013-11-07
β-turns are secondary structure type that have essential role in molecular recognition, protein folding, and stability. They are found to be the most common type of non-repetitive structures since 25% of amino acids in protein structures are situated on them. Their prediction is considered to be one of the crucial problems in bioinformatics and molecular biology, which can provide valuable insights and inputs for the fold recognition and drug design. We propose an approach that combines support vector machines (SVMs) and logistic regression (LR) in a hybrid prediction method, which we call (H-SVM-LR) to predict β-turns in proteins. Fractional polynomials are used for LR modeling. We utilize position specific scoring matrices (PSSMs) and predicted secondary structure (PSS) as features. Our simulation studies show that H-SVM-LR achieves Qtotal of 82.87%, 82.84%, and 82.32% on the BT426, BT547, and BT823 datasets respectively. These values are the highest among other β-turns prediction methods that are based on PSSMs and secondary structure information. H-SVM-LR also achieves favorable performance in predicting β-turns as measured by the Matthew's correlation coefficient (MCC) on these datasets. Furthermore, H-SVM-LR shows good performance when considering shape strings as additional features. In this paper, we present a comprehensive approach for β-turns prediction. Experiments show that our proposed approach achieves better performance compared to other competing prediction methods.
Classification of polynomial integrable systems of mixed scalar and vector evolution equations: I
International Nuclear Information System (INIS)
Tsuchida, Takayuki; Wolf, Thomas
2005-01-01
We perform a classification of integrable systems of mixed scalar and vector evolution equations with respect to higher symmetries. We consider polynomial systems that are homogeneous under a suitable weighting of variables. This paper deals with the KdV weighting, the Burgers (or potential KdV or modified KdV) weighting, the Ibragimov-Shabat weighting and two unfamiliar weightings. The case of other weightings will be studied in a subsequent paper. Making an ansatz for undetermined coefficients and using a computer package for solving bilinear algebraic systems, we give the complete lists of second-order systems with a third-order or a fourth-order symmetry and third-order systems with a fifth-order symmetry. For all but a few systems in the lists, we show that the system (or, at least a subsystem of it) admits either a Lax representation or a linearizing transformation. A thorough comparison with recent work of Foursov and Olver is made
Classification of polynomial integrable systems of mixed scalar and vector evolution equations: I
Energy Technology Data Exchange (ETDEWEB)
Tsuchida, Takayuki [Department of Physics, Kwansei Gakuin University, 2-1 Gakuen, Sanda 669-1337 (Japan); Wolf, Thomas [Department of Mathematics, Brock University, St Catharines, ON L2S 3A1 (Canada)
2005-09-02
We perform a classification of integrable systems of mixed scalar and vector evolution equations with respect to higher symmetries. We consider polynomial systems that are homogeneous under a suitable weighting of variables. This paper deals with the KdV weighting, the Burgers (or potential KdV or modified KdV) weighting, the Ibragimov-Shabat weighting and two unfamiliar weightings. The case of other weightings will be studied in a subsequent paper. Making an ansatz for undetermined coefficients and using a computer package for solving bilinear algebraic systems, we give the complete lists of second-order systems with a third-order or a fourth-order symmetry and third-order systems with a fifth-order symmetry. For all but a few systems in the lists, we show that the system (or, at least a subsystem of it) admits either a Lax representation or a linearizing transformation. A thorough comparison with recent work of Foursov and Olver is made.
Linear precoding based on polynomial expansion: reducing complexity in massive MIMO
Mueller, Axel
2016-02-29
Massive multiple-input multiple-output (MIMO) techniques have the potential to bring tremendous improvements in spectral efficiency to future communication systems. Counterintuitively, the practical issues of having uncertain channel knowledge, high propagation losses, and implementing optimal non-linear precoding are solved more or less automatically by enlarging system dimensions. However, the computational precoding complexity grows with the system dimensions. For example, the close-to-optimal and relatively “antenna-efficient” regularized zero-forcing (RZF) precoding is very complicated to implement in practice, since it requires fast inversions of large matrices in every coherence period. Motivated by the high performance of RZF, we propose to replace the matrix inversion and multiplication by a truncated polynomial expansion (TPE), thereby obtaining the new TPE precoding scheme which is more suitable for real-time hardware implementation and significantly reduces the delay to the first transmitted symbol. The degree of the matrix polynomial can be adapted to the available hardware resources and enables smooth transition between simple maximum ratio transmission and more advanced RZF. By deriving new random matrix results, we obtain a deterministic expression for the asymptotic signal-to-interference-and-noise ratio (SINR) achieved by TPE precoding in massive MIMO systems. Furthermore, we provide a closed-form expression for the polynomial coefficients that maximizes this SINR. To maintain a fixed per-user rate loss as compared to RZF, the polynomial degree does not need to scale with the system, but it should be increased with the quality of the channel knowledge and the signal-to-noise ratio.
Vector bundles on complex projective spaces
Okonek, Christian; Spindler, Heinz
1980-01-01
This expository treatment is based on a survey given by one of the authors at the Séminaire Bourbaki in November 1978 and on a subsequent course held at the University of Göttingen. It is intended to serve as an introduction to the topical question of classification of holomorphic vector bundles on complex projective spaces, and can easily be read by students with a basic knowledge of analytic or algebraic geometry. Short supplementary sections describe more advanced topics, further results, and unsolved problems.
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
Alshamary, Haider Ali Jasim
2016-01-04
© 2015 IEEE. This paper considers the joint maximum likelihood (ML) channel estimation and data detection problem for massive SIMO (single input multiple output) wireless systems. We propose efficient algorithms achieving the exact ML non-coherent data detection, for both constant-modulus constellations and nonconstant-modulus constellations. Despite a large number of unknown channel coefficients in massive SIMO systems, we show that the expected computational complexity is linear in the number of receive antennas and polynomial in channel coherence time. To the best of our knowledge, our algorithms are the first efficient algorithms to achieve the exact joint ML channel estimation and data detection performance for massive SIMO systems with general constellations. Simulation results show our algorithms achieve considerable performance gains at a low computational complexity.
Alshamary, Haider Ali Jasim; Al-Naffouri, Tareq Y.; Zaib, Alam; Xu, Weiyu
2016-01-01
© 2015 IEEE. This paper considers the joint maximum likelihood (ML) channel estimation and data detection problem for massive SIMO (single input multiple output) wireless systems. We propose efficient algorithms achieving the exact ML non-coherent data detection, for both constant-modulus constellations and nonconstant-modulus constellations. Despite a large number of unknown channel coefficients in massive SIMO systems, we show that the expected computational complexity is linear in the number of receive antennas and polynomial in channel coherence time. To the best of our knowledge, our algorithms are the first efficient algorithms to achieve the exact joint ML channel estimation and data detection performance for massive SIMO systems with general constellations. Simulation results show our algorithms achieve considerable performance gains at a low computational complexity.
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....
On the classification of complex vector bundles of stable rank
Indian Academy of Sciences (India)
, the tuples of cohomology classes on a compact, complex manifold, corresponding to the Chern classes of a complex vector bundle of stable rank. This classification becomes more effective on generalized flag manifolds, where the Lie ...
Shyu, H. C.; Reed, I. S.; Truong, T. K.; Hsu, I. S.; Chang, J. J.
1987-01-01
A quadratic-polynomial Fermat residue number system (QFNS) has been used to compute complex integer multiplications. The advantage of such a QFNS is that a complex integer multiplication requires only two integer multiplications. In this article, a new type Fermat number multiplier is developed which eliminates the initialization condition of the previous method. It is shown that the new complex multiplier can be implemented on a single VLSI chip. Such a chip is designed and fabricated in CMOS-Pw technology.
Viewing the Roots of Polynomial Functions in Complex Variable: The Use of Geogebra and the CAS Maple
Alves, Francisco Regis Vieira
2013-01-01
Admittedly, the Fundamental Theorem of Calculus-TFA holds an important role in the Complex Analysis-CA, as well as in other mathematical branches. In this article, we bring a discussion about the TFA, the Rouché's theorem and the winding number with the intention to analyze the roots of a polynomial equation. We propose also a description for a…
Spinor formalism and complex-vector formalism of general relativity
International Nuclear Information System (INIS)
Han-ying, G.; Yong-shi, W.; Gendao, L.
1974-01-01
In this paper, using E. Cartan's exterior calculus, we give the spinor form of the structure equations, which leads naturally to the Newman--Penrose equations. Furthermore, starting from the spinor spaces and the el (2C) algebra, we construct the general complex-vector formalism of general relativity. We find that both the Cahen--Debever--Defrise complex-vector formalism and that of Brans are its special cases. Thus, the spinor formalism and the complex-vector formalism of general relativity are unified on the basis of the uni-modular group SL(2C) and its Lie algebra
Complex vector triads in spinor theory in Minkowski space
International Nuclear Information System (INIS)
Zhelnorovich, V.A.
1990-01-01
It is shown that tensor equations corresponding to the spinor Dirac equations represent a three-dimensional part of four-dimensional vector equations. The equations are formulated in an evidently invariant form in antisymmetric tensor components and in the corresponding components of a complex vector triad. A complete system of relativistically invariant tensor equations is ascertained
Freund, Roland
1988-01-01
Conjugate gradient type methods are considered for the solution of large linear systems Ax = b with complex coefficient matrices of the type A = T + i(sigma)I where T is Hermitian and sigma, a real scalar. Three different conjugate gradient type approaches with iterates defined by a minimal residual property, a Galerkin type condition, and an Euclidian error minimization, respectively, are investigated. In particular, numerically stable implementations based on the ideas behind Paige and Saunder's SYMMLQ and MINRES for real symmetric matrices are proposed. Error bounds for all three methods are derived. It is shown how the special shift structure of A can be preserved by using polynomial preconditioning. Results on the optimal choice of the polynomial preconditioner are given. Also, some numerical experiments for matrices arising from finite difference approximations to the complex Helmholtz equation are reported.
Linear precoding based on polynomial expansion: reducing complexity in massive MIMO
Mueller, Axel; Kammoun, Abla; Bjö rnson, Emil; Debbah, Mé rouane
2016-01-01
By deriving new random matrix results, we obtain a deterministic expression for the asymptotic signal-to-interference-and-noise ratio (SINR) achieved by TPE precoding in massive MIMO systems. Furthermore, we provide a closed-form expression for the polynomial coefficients that maximizes this SINR. To maintain a fixed per-user rate loss as compared to RZF, the polynomial degree does not need to scale with the system, but it should be increased with the quality of the channel knowledge and the signal-to-noise ratio.
A design of a computer complex including vector processors
International Nuclear Information System (INIS)
Asai, Kiyoshi
1982-12-01
We, members of the Computing Center, Japan Atomic Energy Research Institute have been engaged for these six years in the research of adaptability of vector processing to large-scale nuclear codes. The research has been done in collaboration with researchers and engineers of JAERI and a computer manufacturer. In this research, forty large-scale nuclear codes were investigated from the viewpoint of vectorization. Among them, twenty-six codes were actually vectorized and executed. As the results of the investigation, it is now estimated that about seventy percents of nuclear codes and seventy percents of our total amount of CPU time of JAERI are highly vectorizable. Based on the data obtained by the investigation, (1)currently vectorizable CPU time, (2)necessary number of vector processors, (3)necessary manpower for vectorization of nuclear codes, (4)computing speed, memory size, number of parallel 1/0 paths, size and speed of 1/0 buffer of vector processor suitable for our applications, (5)necessary software and operational policy for use of vector processors are discussed, and finally (6)a computer complex including vector processors is presented in this report. (author)
Weak equivalence classes of complex vector bundles
Czech Academy of Sciences Publication Activity Database
Le, Hong-Van
LXXVII, č. 1 (2008), s. 23-30 ISSN 0862-9544 R&D Projects: GA AV ČR IAA100190701 Institutional research plan: CEZ:AV0Z10190503 Keywords : chern classes * complex Grassmannians weak equivalence Subject RIV: BA - General Mathematics
Generalizations of orthogonal polynomials
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.
Community detection in complex networks using proximate support vector clustering
Wang, Feifan; Zhang, Baihai; Chai, Senchun; Xia, Yuanqing
2018-03-01
Community structure, one of the most attention attracting properties in complex networks, has been a cornerstone in advances of various scientific branches. A number of tools have been involved in recent studies concentrating on the community detection algorithms. In this paper, we propose a support vector clustering method based on a proximity graph, owing to which the introduced algorithm surpasses the traditional support vector approach both in accuracy and complexity. Results of extensive experiments undertaken on computer generated networks and real world data sets illustrate competent performances in comparison with the other counterparts.
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
Chen, Sheng; Hong, Xia; Khalaf, Emad F; Alsaadi, Fuad E; Harris, Chris J
2017-12-01
Complex-valued (CV) B-spline neural network approach offers a highly effective means for identifying and inverting practical Hammerstein systems. Compared with its conventional CV polynomial-based counterpart, a CV B-spline neural network has superior performance in identifying and inverting CV Hammerstein systems, while imposing a similar complexity. This paper reviews the optimality of the CV B-spline neural network approach. Advantages of B-spline neural network approach as compared with the polynomial based modeling approach are extensively discussed, and the effectiveness of the CV neural network-based approach is demonstrated in a real-world application. More specifically, we evaluate the comparative performance of the CV B-spline and polynomial-based approaches for the nonlinear iterative frequency-domain decision feedback equalization (NIFDDFE) of single-carrier Hammerstein channels. Our results confirm the superior performance of the CV B-spline-based NIFDDFE over its CV polynomial-based counterpart.
A Chargeless Complex Vector Matter Field in Supersymmetric Scenario
Directory of Open Access Journals (Sweden)
L. P. Colatto
2015-01-01
Full Text Available We construct and study a formulation of a chargeless complex vector matter field in a supersymmetric framework. To this aim we combine two nochiral scalar superfields in order to take the vector component field to build the chargeless complex vector superpartner where the respective field strength transforms into matter fields by a global U1 gauge symmetry. For the aim of dealing with consistent terms without breaking the global U1 symmetry we imposes a choice to the complex combination revealing a kind of symmetry between the choices and eliminates the extra degrees of freedom which is consistent with the supersymmetry. As the usual case the mass supersymmetric sector contributes as a complement to dynamics of the model. We obtain the equations of motion of the Proca’s type field for the chiral spinor fields and for the scalar field on the mass-shell which show the same mass as expected. This work establishes the first steps to extend the analysis of charged massive vector field in a supersymmetric scenario.
Directory of Open Access Journals (Sweden)
R. Krishnamoorthy
2012-05-01
Full Text Available In this paper, a new lossy to lossless image coding scheme combined with Orthogonal Polynomials Transform and Integer Wavelet Transform is proposed. The Lifting Scheme based Integer Wavelet Transform (LS-IWT is first applied on the image in order to reduce the blocking artifact and memory demand. The Embedded Zero tree Wavelet (EZW subband coding algorithm is used in this proposed work for progressive image coding which achieves efficient bit rate reduction. The computational complexity of lower subband coding of EZW algorithm is reduced in this proposed work with a new integer based Orthogonal Polynomials transform coding. The normalization and mapping are done on the subband of the image for exploiting the subjective redundancy and the zero tree structure is obtained for EZW coding and so the computation complexity is greatly reduced in this proposed work. The experimental results of the proposed technique also show that the efficient bit rate reduction is achieved for both lossy and lossless compression when compared with existing techniques.
Nonnegativity of uncertain polynomials
Directory of Open Access Journals (Sweden)
iljak 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.
High frequency vibration analysis by the complex envelope vectorization.
Giannini, O; Carcaterra, A; Sestieri, A
2007-06-01
The complex envelope displacement analysis (CEDA) is a procedure to solve high frequency vibration and vibro-acoustic problems, providing the envelope of the physical solution. CEDA is based on a variable transformation mapping the high frequency oscillations into signals of low frequency content and has been successfully applied to one-dimensional systems. However, the extension to plates and vibro-acoustic fields met serious difficulties so that a general revision of the theory was carried out, leading finally to a new method, the complex envelope vectorization (CEV). In this paper the CEV method is described, underlying merits and limits of the procedure, and a set of applications to vibration and vibro-acoustic problems of increasing complexity are presented.
Reduced-Complexity Deterministic Annealing for Vector Quantizer Design
Directory of Open Access Journals (Sweden)
Ortega Antonio
2005-01-01
Full Text Available This paper presents a reduced-complexity deterministic annealing (DA approach for vector quantizer (VQ design by using soft information processing with simplified assignment measures. Low-complexity distributions are designed to mimic the Gibbs distribution, where the latter is the optimal distribution used in the standard DA method. These low-complexity distributions are simple enough to facilitate fast computation, but at the same time they can closely approximate the Gibbs distribution to result in near-optimal performance. We have also derived the theoretical performance loss at a given system entropy due to using the simple soft measures instead of the optimal Gibbs measure. We use thederived result to obtain optimal annealing schedules for the simple soft measures that approximate the annealing schedule for the optimal Gibbs distribution. The proposed reduced-complexity DA algorithms have significantly improved the quality of the final codebooks compared to the generalized Lloyd algorithm and standard stochastic relaxation techniques, both with and without the pairwise nearest neighbor (PNN codebook initialization. The proposed algorithms are able to evade the local minima and the results show that they are not sensitive to the choice of the initial codebook. Compared to the standard DA approach, the reduced-complexity DA algorithms can operate over 100 times faster with negligible performance difference. For example, for the design of a 16-dimensional vector quantizer having a rate of 0.4375 bit/sample for Gaussian source, the standard DA algorithm achieved 3.60 dB performance in 16 483 CPU seconds, whereas the reduced-complexity DA algorithm achieved the same performance in 136 CPU seconds. Other than VQ design, the DA techniques are applicable to problems such as classification, clustering, and resource allocation.
International Nuclear Information System (INIS)
Pavicic, Mladen; Merlet, Jean-Pierre; McKay, Brendan; Megill, Norman D
2005-01-01
We give a constructive and exhaustive definition of Kochen-Specker (KS) vectors in a Hilbert space of any dimension as well as of all the remaining vectors of the space. KS vectors are elements of any set of orthonormal states, i.e., vectors in an n-dimensional Hilbert space, H n , n≥3, to which it is impossible to assign 1s and 0s in such a way that no two mutually orthogonal vectors from the set are both assigned 1 and that not all mutually orthogonal vectors are assigned 0. Our constructive definition of such KS vectors is based on algorithms that generate MMP diagrams corresponding to blocks of orthogonal vectors in R n , on algorithms that single out those diagrams on which algebraic (0)-(1) states cannot be defined, and on algorithms that solve nonlinear equations describing the orthogonalities of the vectors by means of statistically polynomially complex interval analysis and self-teaching programs. The algorithms are limited neither by the number of dimensions nor by the number of vectors. To demonstrate the power of the algorithms, all four-dimensional KS vector systems containing up to 24 vectors were generated and described, all three-dimensional vector systems containing up to 30 vectors were scanned, and several general properties of KS vectors were found
On the non-hyperbolicity of a class of exponential polynomials
Directory of Open Access Journals (Sweden)
Gaspar Mora
2017-10-01
Full Text Available In this paper we have constructed a class of non-hyperbolic exponential polynomials that contains all the partial sums of the Riemann zeta function. An exponential polynomial been also defined to illustrate the complexity of the structure of the set defined by the closure of the real projections of its zeros. The sensitivity of this set, when the vector of delays is perturbed, has been analysed. These results have immediate implications in the theory of the neutral differential equations.
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
Algebra of Complex Vectors and Applications in Electromagnetic Theory and Quantum Mechanics
Directory of Open Access Journals (Sweden)
Kundeti Muralidhar
2015-08-01
Full Text Available A complex vector is a sum of a vector and a bivector and forms a natural extension of a vector. The complex vectors have certain special geometric properties and considered as algebraic entities. These represent rotations along with specified orientation and direction in space. It has been shown that the association of complex vector with its conjugate generates complex vector space and the corresponding basis elements defined from the complex vector and its conjugate form a closed complex four dimensional linear space. The complexification process in complex vector space allows the generation of higher n-dimensional geometric algebra from (n — 1-dimensional algebra by considering the unit pseudoscalar identification with square root of minus one. The spacetime algebra can be generated from the geometric algebra by considering a vector equal to square root of plus one. The applications of complex vector algebra are discussed mainly in the electromagnetic theory and in the dynamics of an elementary particle with extended structure. Complex vector formalism simplifies the expressions and elucidates geometrical understanding of the basic concepts. The analysis shows that the existence of spin transforms a classical oscillator into a quantum oscillator. In conclusion the classical mechanics combined with zeropoint field leads to quantum mechanics.
Discrete Fourier Transform Analysis in a Complex Vector Space
Dean, Bruce H.
2009-01-01
Alternative computational strategies for the Discrete Fourier Transform (DFT) have been developed using analysis of geometric manifolds. This approach provides a general framework for performing DFT calculations, and suggests a more efficient implementation of the DFT for applications using iterative transform methods, particularly phase retrieval. The DFT can thus be implemented using fewer operations when compared to the usual DFT counterpart. The software decreases the run time of the DFT in certain applications such as phase retrieval that iteratively call the DFT function. The algorithm exploits a special computational approach based on analysis of the DFT as a transformation in a complex vector space. As such, this approach has the potential to realize a DFT computation that approaches N operations versus Nlog(N) operations for the equivalent Fast Fourier Transform (FFT) calculation.
Directory of Open Access Journals (Sweden)
Luckhana Lawtrakul
2009-05-01
Full Text Available The Particle Swarm Optimization (PSO and Support Vector Machines (SVMs approaches are used for predicting the thermodynamic parameters for the 1:1 inclusion complexation of chiral guests with β-cyclodextrin. A PSO is adopted for descriptor selection in the quantitative structure-property relationships (QSPR of a dataset of 74 chiral guests due to its simplicity, speed, and consistency. The modified PSO is then combined with SVMs for its good approximating properties, to generate a QSPR model with the selected features. Linear, polynomial, and Gaussian radial basis functions are used as kernels in SVMs. All models have demonstrated an impressive performance with R2 higher than 0.8.
Colorings of simplicial complexes and vector bundles over Davis-Januszkiewicz spaces
Notbohm, D.R.A.W.
2010-01-01
We show that coloring properties of a simplicial complex K are reflected by splitting properties of a bundle over the associated Davis-Januszkiewicz space whose Chern classes are given by the elementary symmetric polynomials in the generators of the Stanley-Reisner algebra of K. © 2009 The
Dynamical creation of complex vector solitons in spinor Bose-Einstein condensates
International Nuclear Information System (INIS)
Xiong Bo; Gong Jiangbin
2010-01-01
By numerical simulations of the Gross-Pitaevskii mean-field equations, we show that the dynamical creation of stable complex vector solitons in a homogeneous spin-1 Bose-Einstein condensate can be achieved by applying a localized magnetic field for a certain duration, with the initial uniform density prepared differently for the formation of different vector solitons. In particular, it is shown that stable dark-bright-dark vector solitons, dark-bright-bright vector solitons, and other analogous solutions can be dynamically created. It is also found that the peak intensity and the group velocity of the vector solitons thus generated can be tuned by adjusting the applied magnetic field. Extensions of our approach also allow for the creation of vector-soliton chains or the pumping of many vector solitons. The results can be useful for possible vector-soliton-based applications of dilute Bose-Einstein condensates.
DEFF Research Database (Denmark)
Boeriis, Morten; van Leeuwen, Theo
2017-01-01
should be taken into account in discussing ‘reactions’, which Kress and van Leeuwen link only to eyeline vectors. Finally, the question can be raised as to whether actions are always realized by vectors. Drawing on a re-reading of Rudolf Arnheim’s account of vectors, these issues are outlined......This article revisits the concept of vectors, which, in Kress and van Leeuwen’s Reading Images (2006), plays a crucial role in distinguishing between ‘narrative’, action-oriented processes and ‘conceptual’, state-oriented processes. The use of this concept in image analysis has usually focused...
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....
Quantification of complex blood flow using real-time in vivo vector flow ultrasound
DEFF Research Database (Denmark)
Pedersen, Mads Møller; Pihl, Michael Johannes; Haugaard, Per
2010-01-01
A quantitative method for distinguishing complex from non-complex flow patterns in ultrasound is presented. A new commercial BK Medical ultrasound scanner uses the Transverse Oscillation vector flow technique for visualising flow patterns in real-time. In vivo vector flow data of the blood flow...... patterns of the common carotid artery and the carotid bulb were obtained simultaneously as the basis for quantifying complex flow. The carotid bifurcation of two healthy volunteers were scanned. The presence of complex flow patterns from eight cardiac cycles were evaluated by three experts in medical...... for automatic detection of complex flow patterns....
Stable chains and vortex equations on complex vector bundles
International Nuclear Information System (INIS)
Xi Zhang
2004-07-01
In this paper, we study an object on almost Hermitian manifold M consisting of a finite number of J i -holomorphic vector bundles E i over M and homomorphisms φ i :E 1 →E i-1 . We call such an object a J-holomorphic chain. We then prove a Hitchin-Kobayashi correspondence relating the existence of solutions to certain chain vortex equations and an appropriate notion of stability for the corresponding chains. (author)
Monfared, Vahid
2018-03-01
Elastic analysis is analytically presented to predict the behaviors of the stress and displacement components in the cylindrical ring as a unit cell of a complete composite under applied stress in the complex plane using cubic polynomials. This analysis is based on the complex computation of the stress functions in the complex plane and polar coordinates. Also, suitable boundary conditions are considered and assumed to analyze along with the equilibrium equations and bi-harmonic equation. This method has some important applications in many fields of engineering such as mechanical, civil and material engineering generally. One of the applications of this research work is in composite design and designing the cylindrical devices under various loadings. Finally, it is founded that the convergence and accuracy of the results are suitable and acceptable through comparing the results.
Complex blood flow quantification using real-time in vivo vector flow ultrasound
DEFF Research Database (Denmark)
Pedersen, Mads Møller; Pihl, Michael Johannes; Per, Haugaard
A new method to define and quantify complex blood flow is presented. The standard deviations of real-time in vivo vector flow angle estimates are used. Using vector flow ultrasound imaging both carotid bifurcations of two healthy volunteers were scanned. Scanning was performed with a 7.6 MHz linear...... transducer (8670, B-K Medical, Denmark) and a commercial vector flow ultrasound scanner (ProFocus 2202, B-K Medical). Eight video sequences of one cardiac cycle were obtained. In every frame boxes were placed to define the common carotid artery(box1) and the carotid bulb(box2). The standard deviation...... for the vector angle estimates was calculated for each box in every frame. For comparison three ultrasound experts evaluated the presence of complex flow in every box. The trial was blinded. For every sequence the mean standard deviation of the vector angle estimates were calculated for box1 {39...
Vectorization of copper complexes via biocompatible and biodegradable PLGA nanoparticles.
Courant, T; Roullin, V G; Cadiou, C; Delavoie, F; Molinari, M; Andry, M C; Gafa, V; Chuburu, F
2010-04-23
A double emulsion-solvent diffusion approach with fully biocompatible materials was used to encapsulate copper complexes within biodegradable nanoparticles, for which the release kinetics profiles have highlighted their potential use for a prolonged circulating administration.
Vectorization of copper complexes via biocompatible and biodegradable PLGA nanoparticles
Energy Technology Data Exchange (ETDEWEB)
Courant, T; Roullin, V G; Andry, M C [Institut de Chimie Moleculaire de Reims, CNRS UMR 6229, UFR Pharmacie Reims, 51 rue Cognacq-Jay, F-51100 Reims (France); Cadiou, C; Chuburu, F [Institut de Chimie Moleculaire de Reims, CNRS UMR 6229, UFR des Sciences Exactes et Naturelles, Batiment 18-Europol' Agro, BP 1039, F-51687 Reims Cedex 2 (France); Delavoie, F [Laboratoire de Microscopie Electronique Analytique, INSERM UMRS 926, 21 rue Clement Ader, F-51685 Reims Cedex 2 (France); Molinari, M [Laboratoire de Microscopies et d' Etudes des Nanostructures, UFR des Sciences, Universite de Reims Champagne-Ardenne, 21 rue Clement Ader, F-51685 Reims Cedex 2 (France); Gafa, V, E-mail: gaelle.roullin@univ-reims.fr, E-mail: francoise.chuburu@univ-reims.fr [EA4303 ' Inflammation et Immunite de l' Epithelium Respiratoire' , IFR53, UFR de Pharmacie, Universite de Reims Champagne-Ardenne, 51 rue Cognacq-Jay, F-51100 Reims (France)
2010-04-23
A double emulsion-solvent diffusion approach with fully biocompatible materials was used to encapsulate copper complexes within biodegradable nanoparticles, for which the release kinetics profiles have highlighted their potential use for a prolonged circulating administration.
Vectorization of copper complexes via biocompatible and biodegradable PLGA nanoparticles
International Nuclear Information System (INIS)
Courant, T; Roullin, V G; Andry, M C; Cadiou, C; Chuburu, F; Delavoie, F; Molinari, M; Gafa, V
2010-01-01
A double emulsion-solvent diffusion approach with fully biocompatible materials was used to encapsulate copper complexes within biodegradable nanoparticles, for which the release kinetics profiles have highlighted their potential use for a prolonged circulating administration.
Novel redox nanomedicine improves gene expression of polyion complex vector
Directory of Open Access Journals (Sweden)
Kazuko Toh, Toru Yoshitomi, Yutaka Ikeda and Yukio Nagasaki
2011-01-01
Full Text Available Gene therapy has generated worldwide attention as a new medical technology. While non-viral gene vectors are promising candidates as gene carriers, they have several issues such as toxicity and low transfection efficiency. We have hypothesized that the generation of reactive oxygen species (ROS affects gene expression in polyplex supported gene delivery systems. The effect of ROS on the gene expression of polyplex was evaluated using a nitroxide radical-containing nanoparticle (RNP as an ROS scavenger. When polyethyleneimine (PEI/pGL3 or PEI alone was added to the HeLa cells, ROS levels increased significantly. In contrast, when (PEI/pGL3 or PEI was added with RNP, the ROS levels were suppressed. The luciferase expression was increased by the treatment with RNP in a dose-dependent manner and the cellular uptake of pDNA was also increased. Inflammatory cytokines play an important role in ROS generation in vivo. In particular, tumor necrosis factor (TNF-α caused intracellular ROS generation in HeLa cells and decreased gene expression. RNP treatment suppressed ROS production even in the presence of TNF-α and increased gene expression. This anti-inflammatory property of RNP suggests that it may be used as an effective adjuvant for non-viral gene delivery systems.
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.
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 ...
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....
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...
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.
Quantum entanglement via nilpotent polynomials
International Nuclear Information System (INIS)
Mandilara, Aikaterini; Akulin, Vladimir M.; Smilga, Andrei V.; Viola, Lorenza
2006-01-01
We propose a general method for introducing extensive characteristics of quantum entanglement. The method relies on polynomials of nilpotent raising operators that create entangled states acting on a reference vacuum state. By introducing the notion of tanglemeter, the logarithm of the state vector represented in a special canonical form and expressed via polynomials of nilpotent variables, we show how this description provides a simple criterion for entanglement as well as a universal method for constructing the invariants characterizing entanglement. We compare the existing measures and classes of entanglement with those emerging from our approach. We derive the equation of motion for the tanglemeter and, in representative examples of up to four-qubit systems, show how the known classes appear in a natural way within our framework. We extend our approach to qutrits and higher-dimensional systems, and make contact with the recently introduced idea of generalized entanglement. Possible future developments and applications of the method are discussed
Kiessling, Michael Karl-Heinz
2017-10-01
Let z\\in C, let σ ^2>0 be a variance, and for N\\in N define the integrals E_N^{}(z;σ ) := {1/σ } \\int _R\\ (x^2+z^2) e^{-{1/2σ^2 x^2}}{√{2π }}/dx \\quad if N=1, {1/σ } \\int _{R^N} \\prod \\prod \\limits _{1≤ k1. These are expected values of the polynomials P_N^{}(z)=\\prod _{1≤ n≤ N}(X_n^2+z^2) whose 2 N zeros ± i X_k^{}_{k=1,\\ldots ,N} are generated by N identically distributed multi-variate mean-zero normal random variables {X_k}N_{k=1} with co-variance {Cov}_N^{}(X_k,X_l)=(1+σ ^2-1/N)δ _{k,l}+σ ^2-1/N(1-δ _{k,l}). The E_N^{}(z;σ ) are polynomials in z^2, explicitly computable for arbitrary N, yet a list of the first three E_N^{}(z;σ ) shows that the expressions become unwieldy already for moderate N—unless σ = 1, in which case E_N^{}(z;1) = (1+z^2)^N for all z\\in C and N\\in N. (Incidentally, commonly available computer algebra evaluates the integrals E_N^{}(z;σ ) only for N up to a dozen, due to memory constraints). Asymptotic evaluations are needed for the large- N regime. For general complex z these have traditionally been limited to analytic expansion techniques; several rigorous results are proved for complex z near 0. Yet if z\\in R one can also compute this "infinite-degree" limit with the help of the familiar relative entropy principle for probability measures; a rigorous proof of this fact is supplied. Computer algebra-generated evidence is presented in support of a conjecture that a generalization of the relative entropy principle to signed or complex measures governs the N→ ∞ asymptotics of the regime iz\\in R. Potential generalizations, in particular to point vortex ensembles and the prescribed Gauss curvature problem, and to random matrix ensembles, are emphasized.
Stability and special metrics for complex vector bundles with global sections
International Nuclear Information System (INIS)
Xi Zhang
2004-07-01
In this paper, we study one kind of vortex equations on complex vector bundles over almost Hermitian manifolds and prove a Hitchin-Kobayashi type correspondence relating the existence of solutions of these vortex equations to a certain stability condition. (author)
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...
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
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, ...
Ouyang, J; Perrie, W; Allegre, O J; Heil, T; Jin, Y; Fearon, E; Eckford, D; Edwardson, S P; Dearden, G
2015-05-18
Precise tailoring of optical vector beams is demonstrated, shaping their focal electric fields and used to create complex laser micro-patterning on a metal surface. A Spatial Light Modulator (SLM) and a micro-structured S-waveplate were integrated with a picosecond laser system and employed to structure the vector fields into radial and azimuthal polarizations with and without a vortex phase wavefront as well as superposition states. Imprinting Laser Induced Periodic Surface Structures (LIPSS) elucidates the detailed vector fields around the focal region. In addition to clear azimuthal and radial plasmon surface structures, unique, variable logarithmic spiral micro-structures with a pitch Λ ∼1μm, not observed previously, were imprinted on the surface, confirming unambiguously the complex 2D focal electric fields. We show clearly also how the Orbital Angular Momentum(OAM) associated with a helical wavefront induces rotation of vector fields along the optic axis of a focusing lens and confirmed by the observed surface micro-structures.
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...
Polynomial chaos representation of databases on manifolds
Energy Technology Data Exchange (ETDEWEB)
Soize, C., E-mail: christian.soize@univ-paris-est.fr [Université Paris-Est, Laboratoire Modélisation et Simulation Multi-Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-La-Vallée, Cedex 2 (France); Ghanem, R., E-mail: ghanem@usc.edu [University of Southern California, 210 KAP Hall, Los Angeles, CA 90089 (United States)
2017-04-15
Characterizing the polynomial chaos expansion (PCE) of a vector-valued random variable with probability distribution concentrated on a manifold is a relevant problem in data-driven settings. The probability distribution of such random vectors is multimodal in general, leading to potentially very slow convergence of the PCE. In this paper, we build on a recent development for estimating and sampling from probabilities concentrated on a diffusion manifold. The proposed methodology constructs a PCE of the random vector together with an associated generator that samples from the target probability distribution which is estimated from data concentrated in the neighborhood of the manifold. The method is robust and remains efficient for high dimension and large datasets. The resulting polynomial chaos construction on manifolds permits the adaptation of many uncertainty quantification and statistical tools to emerging questions motivated by data-driven queries.
Vector continued fractions using a generalized inverse
International Nuclear Information System (INIS)
Haydock, Roger; Nex, C M M; Wexler, Geoffrey
2004-01-01
A real vector space combined with an inverse (involution) for vectors is sufficient to define a vector continued fraction whose parameters consist of vector shifts and changes of scale. The choice of sign for different components of the vector inverse permits construction of vector analogues of the Jacobi continued fraction. These vector Jacobi fractions are related to vector and scalar-valued polynomial functions of the vectors, which satisfy recurrence relations similar to those of orthogonal polynomials. The vector Jacobi fraction has strong convergence properties which are demonstrated analytically, and illustrated numerically
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
A consensus for the development of a vector model to assess clinical complexity.
Corazza, Gino Roberto; Klersy, Catherine; Formagnana, Pietro; Lenti, Marco Vincenzo; Padula, Donatella
2017-12-01
The progressive rise in multimorbidity has made management of complex patients one of the most topical and challenging issues in medicine, both in clinical practice and for healthcare organizations. To make this easier, a score of clinical complexity (CC) would be useful. A vector model to evaluate biological and extra-biological (socio-economic, cultural, behavioural, environmental) domains of CC was proposed a few years ago. However, given that the variables that grade each domain had never been defined, this model has never been used in clinical practice. To overcome these limits, a consensus meeting was organised to grade each domain of CC, and to establish the hierarchy of the domains. A one-day consensus meeting consisting of a multi-professional panel of 25 people was held at our Hospital. In a preliminary phase, the proponents selected seven variables as qualifiers for each of the five above-mentioned domains. In the course of the meeting, the panel voted for five variables considered to be the most representative for each domain. Consensus was established with 2/3 agreement, and all variables were dichotomised. Finally, the various domains were parametrized and ranked within a feasible vector model. A Clinical Complexity Index was set up using the chosen variables. All the domains were graphically represented through a vector model: the biological domain was chosen as the most significant (highest slope), followed by the behavioural and socio-economic domains (intermediate slope), and lastly by the cultural and environmental ones (lowest slope). A feasible and comprehensive tool to evaluate CC in clinical practice is proposed herein.
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 ...
Vector bundles on complex projective spaces with an appendix by S. I. Gelfand
Okonek, Christian; Spindler, Heinz
1980-01-01
This expository treatment is based on a survey given by one of the authors at the Séminaire Bourbaki in November 1978 and on a subsequent course held at the University of Göttingen. It is intended to serve as an introduction to the topical question of classification of holomorphic vector bundles on complex projective spaces, and can easily be read by students with a basic knowledge of analytic or algebraic geometry. Short supplementary sections describe more advanced topics, further results, and unsolved problems. This is a corrected third printing with an Appendix by S. I. Gelfand. ------ The present book is the first one, within the extensive literature on algebraic vector bundles, to give both a self-contained introduction to the basic methods and an exposition of the current state of the classification theory of algebraic vector bundles over Pn(C). (…) The reviewer thinks that readers should be grateful to the authors for presenting the first detailed, self-contained and systematic textbook on ve...
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.
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...
Lutzomyia umbratilis, the main vector of Leishmania guyanensis, represents a novel species complex?
Scarpassa, Vera Margarete; Alencar, Ronildo Baiatone
2012-01-01
Lutzomyia umbratilis is an important Leishmania guyanensis vector in South America. Previous studies have suggested differences in the vector competence between L. umbratilis populations situated on opposite banks of the Amazonas and Negro Rivers in the central Amazonian Brazil region, likely indicating a species complex. However, few studies have been performed on these populations and the taxonomic status of L. umbratilis remains unclear. Phylogeographic structure was estimated for six L. umbratilis samples from the central Amazonian region in Brazil by analyzing mtDNA using 1181 bp of the COI gene to assess whether the populations on opposite banks of these rivers consist of incipient or distinct species. The genetic diversity was fairly high and the results revealed two distinct clades ( = lineages) with 1% sequence divergence. Clade I consisted of four samples from the left bank of the Amazonas and Negro Rivers, whereas clade II comprised two samples from the right bank of Negro River. No haplotypes were shared between samples of two clades. Samples within clades exhibited low to moderate genetic differentiation (F(ST) = -0.0390-0.1841), whereas samples between clades exhibited very high differentiation (F(ST) = 0.7100-0.8497) and fixed differences. These lineages have diverged approximately 0.22 Mya in the middle Pleistocene. Demographic expansion was detected for the lineages I and II approximately 30,448 and 15,859 years ago, respectively, in the late Pleistocene. The two genetic lineages may represent an advanced speciation stage suggestive of incipient or distinct species within L. umbratilis. These findings suggest that the Amazonas and Negro Rivers may be acting as effective barriers, thus preventing gene flow between populations on opposite sides. Such findings have important implications for epidemiological studies, especially those related to vector competence and anthropophily, and for vector control strategies. In addition, L
Directory of Open Access Journals (Sweden)
Music Temitope OBEMBE
2018-03-01
Full Text Available It has been established that Anopheles gambiae complex sibling species are the major Plasmodium malaria vectors in Africa; however, not all the sibling species transmit the infection. Easier molecular methods, PCR-based assays, have been developed to distinguish the several members of the A. gambiae complex. However, malaria vector research in less developed countries, particularly sub-Saharan Africa, is being hampered by the lack of PCR facilities in laboratories and the cost of carrying out the assay within lack of funding. Hence, the present study was designed to develop a simple identification key, based on an affordable method of polytene chromosome cytotaxonomy, for identifying the major P. falciparum vectors. The Identification Key was successfully used to identify two members of the A. gambiae complex, A. gambiae sensu stricto and A. arabiensis, which are the most potent malaria vectors in Africa; even so, it could not be used to establish the infective and the refractory strains.
Soler, Marta; Feliu, Lidia; Planas, Marta; Ribas, Xavi; Costas, Miquel
2016-08-16
The rich chemical and structural versatility of transition metal complexes provides numerous novel paths to be pursued in the design of molecules that exert particular chemical or physicochemical effects that could operate over specific biological targets. However, the poor cell permeability of metallodrugs represents an important barrier for their therapeutic use. The conjugation between metal complexes and a functional peptide vector can be regarded as a versatile and potential strategy to improve their bioavailability and accumulation inside cells, and the site selectivity of their effect. This perspective lies in reviewing the recent advances in the design of metallopeptide conjugates for biomedical applications. Additionally, we highlight the studies where this approach has been directed towards the incorporation of redox active metal centers into living organisms for modulating the cellular redox balance, as a tool with application in anticancer therapy.
Accuracy and Precision of Plane Wave Vector Flow Imaging for Laminar and Complex Flow In Vivo
DEFF Research Database (Denmark)
Jensen, Jonas; Traberg, Marie Sand; Villagómez Hoyos, Carlos Armando
2017-01-01
In this study, a comparison between velocity fields for a plane wave 2-D vector flow imaging (VFI) method and a computational fluid dynamics (CFD) simulation is made. VFI estimates are obtained from the scan of a flow phantom, which mimics the complex flow conditions in the carotid artery....... Furthermore, the precision of the VFI method is investigated under laminar and complex flow conditions in vivo. The carotid bifurcation of a healthy volunteer was scanned using both fast plane wave ultrasound and magnetic resonance imaging (MRI). The acquired MRI geometry of the bifurcation was used...... difference within 15 %, however, it was 23 % in the external branch. For the in vivo scan, the precision in terms of mean standard deviation (SD) of estimates aligned to the cardiac cycle was highest in the center of the common carotid artery (SD 4.7◦ for angles) and lowest in the external branch and close...
Viral and vector zoonotic exploitation of a homo-sociome memetic complex.
Rupprecht, C E; Burgess, G W
2015-05-01
As most newly characterized emerging infectious diseases are considered to be zoonotic, a modern pre-eminence ascribed within this classification lies clearly within the viral taxonomic realm. In particular, RNA viruses deserve special concern given their documented impact on conservation biology, veterinary medicine and public health, with an unprecedented ability to promote an evolutionary host-pathogen arms race from the ultimate infection and immunity perspective. However, besides the requisite molecular/gross anatomical and physiological bases for infectious diseases to transmit from one host to another, both viral pathogens and their reservoirs/vectors exploit a complex anthropological, cultural, historical, psychological and social suite that specifically defines the phylodynamics within Homo sapiens, unlike any other species. Some of these variables include the ecological benefits of living in groups, decisions on hunting and foraging behaviours and dietary preferences, myths and religious doctrines, health economics, travel destinations, population planning, political decisions on agricultural product bans and many others, in a homo-sociome memetic complex. Taken to an extreme, such complexities elucidate the underpinnings of explanations as to why certain viral zoonoses reside in neglected people, places and things, whereas others are chosen selectively and prioritized for active mitigation. Canine-transmitted rabies serves as one prime example of how a neglected viral zoonosis may transition to greater attention on the basis of renewed advocacy, social media, local champions and vested international community engagement. In contrast, certain bat-associated and arboviral diseases suffer from basic ignorance and perpetuated misunderstanding of fundamental reservoir and vector ecology tenets, translated into failed control policies that only exacerbate the underlying environmental conditions of concern. Beyond applied biomedical knowledge, epidemiological
Steel, Jason C; Cavanagh, Heather M A; Burton, Mark A; Dingwall, Daniel J; Kalle, Wouter H J
2005-06-01
Adenoviral vectors have been commonly used in gene therapy protocols, however the success of their use is often limited by the induction of host immunity to the vector. Following exposure to the adenoviral vector, adenoviral-specific neutralising antibodies are produced which limits further administration. This study examines the efficacy of complexing liposomes to adenovirus for the protection of the adenovirus from neutralising antibodies in an in vitro setting. Dimethyldioctadecylammonium bromide (DDAB)-dioleoyl-l-phosphatidylethanolamine (DOPE) liposomes were bound at varying concentrations to adenovirus to form AL complexes and tested these complexes' ability to prevent adenoviral neutralisation. It is shown that by increasing the concentration of liposomes in the adenoviral-liposome (AL) complexes we can increase the level of immuno-shielding afforded the adenovirus. It is also shown that the increase in liposomal concentration may lead to drawbacks such as increased cytotoxicity and reductions in expression levels.
Directory of Open Access Journals (Sweden)
Andrew F. Heckler
2016-06-01
Full Text Available In experiments including over 450 university-level students, we studied the effectiveness and time efficiency of several levels of feedback complexity in simple, computer-based training utilizing static question sequences. The learning domain was simple vector math, an essential skill in introductory physics. In a unique full factorial design, we studied the relative effects of “knowledge of correct response” feedback and “elaborated feedback” (i.e., a general explanation both separately and together. A number of other factors were analyzed, including training time, physics course grade, prior knowledge of vector math, and student beliefs about both their proficiency in and the importance of vector math. We hypothesize a simple model predicting how the effectiveness of feedback depends on prior knowledge, and the results confirm this knowledge-by-treatment interaction. Most notably, elaborated feedback is the most effective feedback, especially for students with low prior knowledge and low course grade. In contrast, knowledge of correct response feedback was less effective for low-performing students, and including both kinds of feedback did not significantly improve performance compared to elaborated feedback alone. Further, while elaborated feedback resulted in higher scores, the learning rate was at best only marginally higher because the training time was slightly longer. Training time data revealed that students spent significantly more time on the elaborated feedback after answering a training question incorrectly. Finally, we found that training improved student self-reported proficiency and that belief in the importance of the learned domain improved the effectiveness of training. Overall, we found that computer based training with static question sequences and immediate elaborated feedback in the form of simple and general explanations can be an effective way to improve student performance on a physics essential skill
Steel, Jason C; Cavanagh, Heather M A; Burton, Mark A; Kalle, Wouter H J
2004-11-01
Adenoviral vectors have been commonly used in gene therapy protocols but the success of their use is often limited by the induction of host immunity to the vector. Following exposure to the adenoviral vector, adenoviral-specific neutralising antibodies are produced, which limits further administration. This study examines the effectiveness of a novel combination of microspheres and liposomes for the shielding of adenovirus from neutralising antibodies in an in-vitro setting. We show that liposomes are effective in the protection of adenovirus from neutralising antibody and that the conjugation of these complexes to microspheres augments the level of protection. This study further reveals that previously neutralised adenovirus may still be transported into the cell via liposome-cell interactions and is still capable of expressing its genes, making this vector an effective tool for circumvention of the humoral immune response. We also looked at possible side effects of using the complexes, namely increases in cytotoxicity and reductions in transfection efficiency. Our results showed that varying the liposome:adenovirus ratio can reduce the cytotoxicity of the vector as well as increase the transfection efficiency. In addition, in cell lines that are adenoviral competent, transfection efficiencies on par with uncomplexed adenoviral vectors were achievable with the combination vector.
Energy Technology Data Exchange (ETDEWEB)
Miltiadis Alamaniotis; Vivek Agarwal
2014-10-01
This paper places itself in the realm of anticipatory systems and envisions monitoring and control methods being capable of making predictions over system critical parameters. Anticipatory systems allow intelligent control of complex systems by predicting their future state. In the current work, an intelligent model aimed at implementing anticipatory monitoring and control in energy industry is presented and tested. More particularly, a set of support vector regressors (SVRs) are trained using both historical and observed data. The trained SVRs are used to predict the future value of the system based on current operational system parameter. The predicted values are then inputted to a fuzzy logic based module where the values are fused to obtain a single value, i.e., final system output prediction. The methodology is tested on real turbine degradation datasets. The outcome of the approach presented in this paper highlights the superiority over single support vector regressors. In addition, it is shown that appropriate selection of fuzzy sets and fuzzy rules plays an important role in improving system performance.
Non-existence criteria for Laurent polynomial first integrals
Directory of Open Access Journals (Sweden)
Shaoyun Shi
2003-01-01
Full Text Available In this paper we derived some simple criteria for non-existence and partial non-existence Laurent polynomial first integrals for a general nonlinear systems of ordinary differential equations $\\dot x = f(x$, $x \\in \\mathbb{R}^n$ with $f(0 = 0$. We show that if the eigenvalues of the Jacobi matrix of the vector field $f(x$ are $\\mathbb{Z}$-independent, then the system has no nontrivial Laurent polynomial integrals.
Additive and polynomial representations
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
Optimizing structure of complex technical system by heterogeneous vector criterion in interval form
Lysenko, A. V.; Kochegarov, I. I.; Yurkov, N. K.; Grishko, A. K.
2018-05-01
The article examines the methods of development and multi-criteria choice of the preferred structural variant of the complex technical system at the early stages of its life cycle in the absence of sufficient knowledge of parameters and variables for optimizing this structure. The suggested methods takes into consideration the various fuzzy input data connected with the heterogeneous quality criteria of the designed system and the parameters set by their variation range. The suggested approach is based on the complex use of methods of interval analysis, fuzzy sets theory, and the decision-making theory. As a result, the method for normalizing heterogeneous quality criteria has been developed on the basis of establishing preference relations in the interval form. The method of building preferential relations in the interval form on the basis of the vector of heterogeneous quality criteria suggest the use of membership functions instead of the coefficients considering the criteria value. The former show the degree of proximity of the realization of the designed system to the efficient or Pareto optimal variants. The study analyzes the example of choosing the optimal variant for the complex system using heterogeneous quality criteria.
All ASD complex and real 4-dimensional Einstein spaces with Λ≠0 admitting a nonnull Killing vector
Chudecki, Adam
2016-12-01
Anti-self-dual (ASD) 4-dimensional complex Einstein spaces with nonzero cosmological constant Λ equipped with a nonnull Killing vector are considered. It is shown that any conformally nonflat metric of such spaces can be always brought to a special form and the Einstein field equations can be reduced to the Boyer-Finley-Plebański equation (Toda field equation). Some alternative forms of the metric are discussed. All possible real slices (neutral, Euclidean and Lorentzian) of ASD complex Einstein spaces with Λ≠0 admitting a nonnull Killing vector are found.
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)
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....
Quantum Hilbert matrices and orthogonal polynomials
DEFF Research Database (Denmark)
Andersen, Jørgen Ellegaard; Berg, Christian
2009-01-01
Using the notion of quantum integers associated with a complex number q≠0 , we define the quantum Hilbert matrix and various extensions. They are Hankel matrices corresponding to certain little q -Jacobi polynomials when |q|<1 , and for the special value they are closely related to Hankel matrice...
Stochastic Estimation via Polynomial Chaos
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
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.
Multilevel weighted least squares polynomial approximation
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.
DEFF Research Database (Denmark)
Wang, W.; Ishijima, R.; Matsuda, A.
2010-01-01
As an improvement of the intensity correlation used widely in conventional electronic speckle photography, we propose a new technique for displacement measurement based on correlating Stokes-like parameters derivatives for transformed speckle patterns. The method is based on a Riesz transform of ...... are presented that demonstrate the validity and advantage of the proposed pseudo-Stokes vector correlation technique over conventional intensity correlation technique....... of the intensity speckle pattern, which converts the original real-valued signal into a complex signal. In closest analogy to the polarisation of a vector wave, the Stokes-like vector constructed from the spatial derivative of the generated complex signal has been applied for correlation. Experimental results...
Polynomial optimization : Error analysis and applications
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
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
International Nuclear Information System (INIS)
Saber, Ahmed Yousuf; Chakraborty, Shantanu; Abdur Razzak, S.M.; Senjyu, Tomonobu
2009-01-01
This paper presents a modified particle swarm optimization (MPSO) for constrained economic load dispatch (ELD) problem. Real cost functions are more complex than conventional second order cost functions when multi-fuel operations, valve-point effects, accurate curve fitting, etc., are considering in deregulated changing market. The proposed modified particle swarm optimization (PSO) consists of problem dependent variable number of promising values (in velocity vector), unit vector and error-iteration dependent step length. It reliably and accurately tracks a continuously changing solution of the complex cost function and no extra concentration/effort is needed for the complex higher order cost polynomials in ELD. Constraint management is incorporated in the modified PSO. The modified PSO has balance between local and global searching abilities, and an appropriate fitness function helps to converge it quickly. To avoid the method to be frozen, stagnated/idle particles are reset. Sensitivity of the higher order cost polynomials is also analyzed visually to realize the importance of the higher order cost polynomials for the optimization of ELD. Finally, benchmark data sets and methods are used to show the effectiveness of the proposed method. (author)
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...
Polynomials in algebraic analysis
Multarzyński, Piotr
2012-01-01
The concept of polynomials in the sense of algebraic analysis, for a single right invertible linear operator, was introduced and studied originally by D. Przeworska-Rolewicz \\cite{DPR}. One of the elegant results corresponding with that notion is a purely algebraic version of the Taylor formula, being a generalization of its usual counterpart, well known for functions of one variable. In quantum calculus there are some specific discrete derivations analyzed, which are right invertible linear ...
DEFF Research Database (Denmark)
Dridi, Kim; Bjarklev, Anders Overgaard
1999-01-01
An electromagnetic vector-field modle for design of optical components based on the finite-difference-time-domain method and radiation integrals in presented. Its ability to predict the optical electromagnetic dynamics in structures with complex material distribution is demonstrated. Theoretical...
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 ...
International Nuclear Information System (INIS)
Wang Danher; Hevey, Michael; Juompan, Laure Y.; Trubey, Charles M.; Raja, Nicholas U.; Deitz, Stephen B.; Woraratanadharm, Jan; Luo Min; Yu Hong; Swain, Benjamin M.; Moore, Kevin M.; Dong, John Y.
2006-01-01
The Marburg virus (MARV), an African filovirus closely related to the Ebola virus, causes a deadly hemorrhagic fever in humans, with up to 90% mortality. Currently, treatment of disease is only supportive, and no vaccines are available to prevent spread of MARV infections. In order to address this need, we have developed and characterized a novel recombinant vaccine that utilizes a single complex adenovirus-vectored vaccine (cAdVax) to overexpress a MARV glycoprotein (GP) fusion protein derived from the Musoke and Ci67 strains of MARV. Vaccination with the cAdVaxM(fus) vaccine led to efficient production of MARV-specific antibodies in both mice and guinea pigs. Significantly, guinea pigs vaccinated with at least 5 x 10 7 pfu of cAdVaxM(fus) vaccine were 100% protected against lethal challenges by the Musoke, Ci67 and Ravn strains of MARV, making it a vaccine with trivalent protective efficacy. Therefore, the cAdVaxM(fus) vaccine serves as a promising vaccine candidate to prevent and contain multi-strain infections by MARV
Becker, Noémie S; Margos, Gabriele; Blum, Helmut; Krebs, Stefan; Graf, Alexander; Lane, Robert S; Castillo-Ramírez, Santiago; Sing, Andreas; Fingerle, Volker
2016-09-15
The Borrelia burgdorferi sensu lato (s.l.) species complex consists of tick-transmitted bacteria and currently comprises approximately 20 named and proposed genospecies some of which are known to cause Lyme Borreliosis. Species have been defined via genetic distances and ecological niches they occupy. Understanding the evolutionary relationship of species of the complex is fundamental to explaining patterns of speciation. This in turn forms a crucial basis to frame testable hypotheses concerning the underlying processes including host and vector adaptations. Illumina Technology was used to obtain genome-wide sequence data for 93 strains of 14 named genospecies of the B. burgdorferi species complex and genomic data already published for 18 additional strain (including one new species) was added. Phylogenetic reconstruction based on 114 orthologous single copy genes shows that the genospecies represent clearly distinguishable taxa with recent and still ongoing speciation events apparent in Europe and Asia. The position of Borrelia species in the phylogeny is consistent with host associations constituting a major driver for speciation. Interestingly, the data also demonstrate that vector associations are an additional driver for diversification in this tick-borne species complex. This is particularly obvious in B. bavariensis, a rodent adapted species that has diverged from the bird-associated B. garinii most likely in Asia. It now consists of two populations one of which most probably invaded Europe following adaptation to a new vector (Ixodes ricinus) and currently expands its distribution range. The results imply that genotypes/species with novel properties regarding host or vector associations have evolved recurrently during the history of the species complex and may emerge at any time. We suggest that the finding of vector associations as a driver for diversification may be a general pattern for tick-borne pathogens. The core genome analysis presented here
An Elementary Proof of the Polynomial Matrix Spectral Factorization Theorem
Ephremidze, Lasha
2010-01-01
A very simple and short proof of the polynomial matrix spectral factorization theorem (on the unit circle as well as on the real line) is presented, which relies on elementary complex analysis and linear algebra.
Polynomial approximation on polytopes
Totik, Vilmos
2014-01-01
Polynomial approximation on convex polytopes in \\mathbf{R}^d is considered in uniform and L^p-norms. For an appropriate modulus of smoothness matching direct and converse estimates are proven. In the L^p-case so called strong direct and converse results are also verified. The equivalence of the moduli of smoothness with an appropriate K-functional follows as a consequence. The results solve a problem that was left open since the mid 1980s when some of the present findings were established for special, so-called simple polytopes.
International Nuclear Information System (INIS)
Milks, Matthew M; Guise, Hubert de
2005-01-01
The construction of su(2) intelligent states is simplified using a polynomial representation of su(2). The cornerstone of the new construction is the diagonalization of a 2 x 2 matrix. The method is sufficiently simple to be easily extended to su(3), where one is required to diagonalize a single 3 x 3 matrix. For two perfectly general su(3) operators, this diagonalization is technically possible but the procedure loses much of its simplicity owing to the algebraic form of the roots of a cubic equation. Simplified expressions can be obtained by specializing the choice of su(3) operators. This simpler construction will be discussed in detail
Raisin, Sophie; Morille, Marie; Bony, Claire; Noël, Danièle; Devoisselle, Jean-Marie; Belamie, Emmanuel
2017-08-22
In the context of regenerative medicine, the use of RNA interference mechanisms has already proven its efficiency in targeting specific gene expression with the aim of enhancing, accelerating or, more generally, directing stem cell differentiation. However, achievement of good transfection levels requires the use of a gene vector. For in vivo applications, synthetic vectors are an interesting option to avoid possible issues associated with viral vectors (safety, production costs, etc.). Herein, we report on the design of tripartite polyionic complex micelles as original non-viral polymeric vectors suited for mesenchymal stem cell transfection with siRNA. Three micelle formulations were designed to exhibit pH-triggered disassembly in an acidic pH range comparable to that of endosomes. One formulation was selected as the most promising with the highest siRNA loading capacity while clearly maintaining pH-triggered disassembly properties. A thorough investigation of the internalization pathway of micelles into cells with tagged siRNA was made before showing an efficient inhibition of Runx2 expression in primary bone marrow-derived stem cells. This work evidenced PIC micelles as promising synthetic vectors that allow efficient MSC transfection and control over their behavior, from the perspective of their clinical use.
Primitive polynomials selection method for pseudo-random number generator
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.
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...
Polynomial methods in combinatorics
Guth, Larry
2016-01-01
This book explains some recent applications of the theory of polynomials and algebraic geometry to combinatorics and other areas of mathematics. One of the first results in this story is a short elegant solution of the Kakeya problem for finite fields, which was considered a deep and difficult problem in combinatorial geometry. The author also discusses in detail various problems in incidence geometry associated to Paul Erdős's famous distinct distances problem in the plane from the 1940s. The proof techniques are also connected to error-correcting codes, Fourier analysis, number theory, and differential geometry. Although the mathematics discussed in the book is deep and far-reaching, it should be accessible to first- and second-year graduate students and advanced undergraduates. The book contains approximately 100 exercises that further the reader's understanding of the main themes of the book. Some of the greatest advances in geometric combinatorics and harmonic analysis in recent years have been accompl...
Polynomial representations of GLn
Green, James A; Erdmann, Karin
2007-01-01
The first half of this book contains the text of the first edition of LNM volume 830, Polynomial Representations of GLn. This classic account of matrix representations, the Schur algebra, the modular representations of GLn, and connections with symmetric groups, has been the basis of much research in representation theory. The second half is an Appendix, and can be read independently of the first. It is an account of the Littelmann path model for the case gln. In this case, Littelmann's 'paths' become 'words', and so the Appendix works with the combinatorics on words. This leads to the repesentation theory of the 'Littelmann algebra', which is a close analogue of the Schur algebra. The treatment is self- contained; in particular complete proofs are given of classical theorems of Schensted and Knuth.
Polynomial representations of GLN
Green, James A
1980-01-01
The first half of this book contains the text of the first edition of LNM volume 830, Polynomial Representations of GLn. This classic account of matrix representations, the Schur algebra, the modular representations of GLn, and connections with symmetric groups, has been the basis of much research in representation theory. The second half is an Appendix, and can be read independently of the first. It is an account of the Littelmann path model for the case gln. In this case, Littelmann's 'paths' become 'words', and so the Appendix works with the combinatorics on words. This leads to the repesentation theory of the 'Littelmann algebra', which is a close analogue of the Schur algebra. The treatment is self- contained; in particular complete proofs are given of classical theorems of Schensted and Knuth.
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)
Efficient computation of Laguerre polynomials
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
Optimization over polynomials : Selected topics
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
Epidemic spreading and global stability of an SIS model with an infective vector on complex networks
Kang, Huiyan; Fu, Xinchu
2015-10-01
In this paper, we present a new SIS model with delay on scale-free networks. The model is suitable to describe some epidemics which are not only transmitted by a vector but also spread between individuals by direct contacts. In view of the biological relevance and real spreading process, we introduce a delay to denote average incubation period of disease in a vector. By mathematical analysis, we obtain the epidemic threshold and prove the global stability of equilibria. The simulation shows the delay will effect the epidemic spreading. Finally, we investigate and compare two major immunization strategies, uniform immunization and targeted immunization.
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...
Skew-orthogonal polynomials, differential systems and random matrix theory
International Nuclear Information System (INIS)
Ghosh, S.
2007-01-01
We study skew-orthogonal polynomials with respect to the weight function exp[-2V (x)], with V (x) = Σ K=1 2d (u K /K)x K , u 2d > 0, d > 0. A finite subsequence of such skew-orthogonal polynomials arising in the study of Orthogonal and Symplectic ensembles of random matrices, satisfy a system of differential-difference-deformation equation. The vectors formed by such subsequence has the rank equal to the degree of the potential in the quaternion sense. These solutions satisfy certain compatibility condition and hence admit a simultaneous fundamental system of solutions. (author)
Vanishing of Littlewood-Richardson polynomials is in P
Adve, Anshul; Robichaux, Colleen; Yong, Alexander
2017-01-01
J. DeLoera-T. McAllister and K. D. Mulmuley-H. Narayanan-M. Sohoni independently proved that determining the vanishing of Littlewood-Richardson coefficients has strongly polynomial time computational complexity. Viewing these as Schubert calculus numbers, we prove the generalization to the Littlewood-Richardson polynomials that control equivariant cohomology of Grassmannians. We construct a polytope using the edge-labeled tableau rule of H. Thomas-A. Yong. Our proof then combines a saturation...
Borisov, A.
2018-05-01
The current issue of studying the vector velocity field in a cyclone-separator with a screw insert is considered in the article. Modeling of the velocity vector field in SolidWorks was carried out, tangential, axial and radial velocities were investigated. Also, a software and hardware complex was developed that makes it possible to obtain data on the speed inside a cyclone separator. The results of the experiment showed that on flour dusts the efficiency of the cyclone separator in question was more than 99.5%, with an air flow rate of 376 m3 / h, 472 m3 / h and 516 m3 / h, and ΔP less than 600 Pa. The velocity in the inlet branch of the screw insert was 18-20 m / s, and at the exit of the screw insert the airflow velocity is 50-70 m / s.
Zheng, Fangyang
2002-01-01
The theory of complex manifolds overlaps with several branches of mathematics, including differential geometry, algebraic geometry, several complex variables, global analysis, topology, algebraic number theory, and mathematical physics. Complex manifolds provide a rich class of geometric objects, for example the (common) zero locus of any generic set of complex polynomials is always a complex manifold. Yet complex manifolds behave differently than generic smooth manifolds; they are more coherent and fragile. The rich yet restrictive character of complex manifolds makes them a special and interesting object of study. This book is a self-contained graduate textbook that discusses the differential geometric aspects of complex manifolds. The first part contains standard materials from general topology, differentiable manifolds, and basic Riemannian geometry. The second part discusses complex manifolds and analytic varieties, sheaves and holomorphic vector bundles, and gives a brief account of the surface classifi...
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.
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....
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
Directory of Open Access Journals (Sweden)
S. Vukotic
2016-08-01
Full Text Available Digital polynomial-based interpolation filters implemented using the Farrow structure are used in Digital Signal Processing (DSP to calculate the signal between its discrete samples. The two basic design parameters for these filters are number of polynomial-segments defining the finite length of impulse response, and order of polynomials in each polynomial segment. The complexity of the implementation structure and the frequency domain performance depend on these two parameters. This contribution presents estimation formulae for length and polynomial order of polynomial-based filters for various types of requirements including attenuation in stopband, width of transitions band, deviation in passband, weighting in passband/stopband.
An introduction to orthogonal polynomials
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
Hierarchal scalar and vector tetrahedra
International Nuclear Information System (INIS)
Webb, J.P.; Forghani, B.
1993-01-01
A new set of scalar and vector tetrahedral finite elements are presented. The elements are hierarchal, allowing mixing of polynomial orders; scalar orders up to 3 and vector orders up to 2 are defined. The vector elements impose tangential continuity on the field but not normal continuity, making them suitable for representing the vector electric or magnetic field. Further, the scalar and vector elements are such that they can easily be used in the same mesh, a requirement of many quasi-static formulations. Results are presented for two 50 Hz problems: the Bath Cube, and TEAM Problem 7
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
Bannai-Ito polynomials and dressing chains
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.
Birth-death processes and associated polynomials
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
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.
Ye, Congting; Ji, Guoli; Li, Lei; Liang, Chun
2014-01-01
Inverted repeats are present in abundance in both prokaryotic and eukaryotic genomes and can form DNA secondary structures--hairpins and cruciforms that are involved in many important biological processes. Bioinformatics tools for efficient and accurate detection of inverted repeats are desirable, because existing tools are often less accurate and time consuming, sometimes incapable of dealing with genome-scale input data. Here, we present a MATLAB-based program called detectIR for the perfect and imperfect inverted repeat detection that utilizes complex numbers and vector calculation and allows genome-scale data inputs. A novel algorithm is adopted in detectIR to convert the conventional sequence string comparison in inverted repeat detection into vector calculation of complex numbers, allowing non-complementary pairs (mismatches) in the pairing stem and a non-palindromic spacer (loop or gaps) in the middle of inverted repeats. Compared with existing popular tools, our program performs with significantly higher accuracy and efficiency. Using genome sequence data from HIV-1, Arabidopsis thaliana, Homo sapiens and Zea mays for comparison, detectIR can find lots of inverted repeats missed by existing tools whose outputs often contain many invalid cases. detectIR is open source and its source code is freely available at: https://sourceforge.net/projects/detectir.
Efficient modeling of photonic crystals with local Hermite polynomials
International Nuclear Information System (INIS)
Boucher, C. R.; Li, Zehao; Albrecht, J. D.; Ram-Mohan, L. R.
2014-01-01
Developing compact algorithms for accurate electrodynamic calculations with minimal computational cost is an active area of research given the increasing complexity in the design of electromagnetic composite structures such as photonic crystals, metamaterials, optical interconnects, and on-chip routing. We show that electric and magnetic (EM) fields can be calculated using scalar Hermite interpolation polynomials as the numerical basis functions without having to invoke edge-based vector finite elements to suppress spurious solutions or to satisfy boundary conditions. This approach offers several fundamental advantages as evidenced through band structure solutions for periodic systems and through waveguide analysis. Compared with reciprocal space (plane wave expansion) methods for periodic systems, advantages are shown in computational costs, the ability to capture spatial complexity in the dielectric distributions, the demonstration of numerical convergence with scaling, and variational eigenfunctions free of numerical artifacts that arise from mixed-order real space basis sets or the inherent aberrations from transforming reciprocal space solutions of finite expansions. The photonic band structure of a simple crystal is used as a benchmark comparison and the ability to capture the effects of spatially complex dielectric distributions is treated using a complex pattern with highly irregular features that would stress spatial transform limits. This general method is applicable to a broad class of physical systems, e.g., to semiconducting lasers which require simultaneous modeling of transitions in quantum wells or dots together with EM cavity calculations, to modeling plasmonic structures in the presence of EM field emissions, and to on-chip propagation within monolithic integrated circuits
Algebraic invariant curves of plane polynomial differential systems
Tsygvintsev, Alexei
2001-01-01
We consider a plane polynomial vector field P(x,y) dx + Q(x,y) dy of degree m>1. With each algebraic invariant curve of such a field we associate a compact Riemann surface with the meromorphic differential ω = dx/P = dy/Q. The asymptotic estimate of the degree of an arbitrary algebraic invariant curve is found. In the smooth case this estimate has already been found by Cerveau and Lins Neto in a different way.
Cosmographic analysis with Chebyshev polynomials
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.
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.
Directory of Open Access Journals (Sweden)
Yalin Wu
2014-01-01
Full Text Available The temporal complexity of video sequences can be characterized by motion vector map which consists of motion vectors of each macroblock (MB. In order to obtain the optimal initial QP (quantization parameter for the various video sequences which have different spatial and temporal complexities, this paper proposes a simple and high performance initial QP determining method based on motion vector map and temporal complexity to decide an initial QP in given target bit rate. The proposed algorithm produces the reconstructed video sequences with outstanding and stable quality. For any video sequences, the initial QP can be easily determined from matrices by target bit rate and mapped spatial complexity using proposed mapping method. Experimental results show that the proposed algorithm can show more outstanding objective and subjective performance than other conventional determining methods.
Weierstrass method for quaternionic polynomial root-finding
Falcão, M. Irene; Miranda, Fernando; Severino, Ricardo; Soares, M. Joana
2018-01-01
Quaternions, introduced by Hamilton in 1843 as a generalization of complex numbers, have found, in more recent years, a wealth of applications in a number of different areas which motivated the design of efficient methods for numerically approximating the zeros of quaternionic polynomials. In fact, one can find in the literature recent contributions to this subject based on the use of complex techniques, but numerical methods relying on quaternion arithmetic remain scarce. In this paper we propose a Weierstrass-like method for finding simultaneously {\\sl all} the zeros of unilateral quaternionic polynomials. The convergence analysis and several numerical examples illustrating the performance of the method are also presented.
The neighbourhood polynomial of some families of dendrimers
Nazri Husin, Mohamad; Hasni, Roslan
2018-04-01
The neighbourhood polynomial N(G,x) is generating function for the number of faces of each cardinality in the neighbourhood complex of a graph and it is defined as (G,x)={\\sum }U\\in N(G){x}|U|, where N(G) is neighbourhood complex of a graph, whose vertices of the graph and faces are subsets of vertices that have a common neighbour. A dendrimers is an artificially manufactured or synthesized molecule built up from branched units called monomers. In this paper, we compute this polynomial for some families of dendrimer.
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...
Orthogonal Polynomials and Special Functions
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.
k-Means has polynomial smoothed complexity
Arthur, David; Manthey, Bodo; Röglin, Heiko; Spielman, D.A.
2009-01-01
The k-means method is one of the most widely used clustering algorithms, drawing its popularity from its speed in practice. Recently, however, it was shown to have exponential worst-case running time. In order to close the gap between practical performance and theoretical analysis, the k-means
Symmetric functions and orthogonal polynomials
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.
Burtyka, Filipp
2018-01-01
The paper considers algorithms for finding diagonalizable and non-diagonalizable roots (so called solvents) of monic arbitrary unilateral second-order matrix polynomial over prime finite field. These algorithms are based on polynomial matrices (lambda-matrices). This is an extension of existing general methods for computing solvents of matrix polynomials over field of complex numbers. We analyze how techniques for complex numbers can be adapted for finite field and estimate asymptotic complexity of the obtained algorithms.
a Unified Matrix Polynomial Approach to Modal Identification
Allemang, R. J.; Brown, D. L.
1998-04-01
One important current focus of modal identification is a reformulation of modal parameter estimation algorithms into a single, consistent mathematical formulation with a corresponding set of definitions and unifying concepts. Particularly, a matrix polynomial approach is used to unify the presentation with respect to current algorithms such as the least-squares complex exponential (LSCE), the polyreference time domain (PTD), Ibrahim time domain (ITD), eigensystem realization algorithm (ERA), rational fraction polynomial (RFP), polyreference frequency domain (PFD) and the complex mode indication function (CMIF) methods. Using this unified matrix polynomial approach (UMPA) allows a discussion of the similarities and differences of the commonly used methods. the use of least squares (LS), total least squares (TLS), double least squares (DLS) and singular value decomposition (SVD) methods is discussed in order to take advantage of redundant measurement data. Eigenvalue and SVD transformation methods are utilized to reduce the effective size of the resulting eigenvalue-eigenvector problem as well.
Ait-Haddou, Rachid
2015-06-04
We show that the best degree reduction of a given polynomial P from degree n to m with respect to the discrete (Formula presented.)-norm is equivalent to the best Euclidean distance of the vector of h-Bézier coefficients of P from the vector of degree raised h-Bézier coefficients of polynomials of degree m. Moreover, we demonstrate the adequacy of h-Bézier curves for approaching the problem of weighted discrete least squares approximation. Applications to discrete orthogonal polynomials are also presented. © 2015 Springer Science+Business Media Dordrecht
STABILITY SYSTEMS VIA HURWITZ POLYNOMIALS
Directory of Open Access Journals (Sweden)
BALTAZAR AGUIRRE HERNÁNDEZ
2017-01-01
Full Text Available To analyze the stability of a linear system of differential equations ẋ = Ax we can study the location of the roots of the characteristic polynomial pA(t associated with the matrix A. We present various criteria - algebraic and geometric - that help us to determine where the roots are located without calculating them directly.
On Modular Counting with Polynomials
DEFF Research Database (Denmark)
Hansen, Kristoffer Arnsfelt
2006-01-01
For any integers m and l, where m has r sufficiently large (depending on l) factors, that are powers of r distinct primes, we give a construction of a (symmetric) polynomial over Z_m of degree O(\\sqrt n) that is a generalized representation (commonly also called weak representation) of the MODl f...
Global Polynomial Kernel Hazard Estimation
DEFF Research Database (Denmark)
Hiabu, Munir; Miranda, Maria Dolores Martínez; Nielsen, Jens Perch
2015-01-01
This paper introduces a new bias reducing method for kernel hazard estimation. The method is called global polynomial adjustment (GPA). It is a global correction which is applicable to any kernel hazard estimator. The estimator works well from a theoretical point of view as it asymptotically redu...
Congruences concerning Legendre polynomials III
Sun, Zhi-Hong
2010-01-01
Let $p>3$ be a prime, and let $R_p$ be the set of rational numbers whose denominator is coprime to $p$. Let $\\{P_n(x)\\}$ be the Legendre polynomials. In this paper we mainly show that for $m,n,t\\in R_p$ with $m\
Two polynomial division inequalities in
Directory of Open Access Journals (Sweden)
Goetgheluck P
1998-01-01
Full Text Available This paper is a first attempt to give numerical values for constants and , in classical estimates and where is an algebraic polynomial of degree at most and denotes the -metric on . The basic tools are Markov and Bernstein inequalities.
Dirichlet polynomials, majorization, and trumping
International Nuclear Information System (INIS)
Pereira, Rajesh; Plosker, Sarah
2013-01-01
Majorization and trumping are two partial orders which have proved useful in quantum information theory. We show some relations between these two partial orders and generalized Dirichlet polynomials, Mellin transforms, and completely monotone functions. These relations are used to prove a succinct generalization of Turgut’s characterization of trumping. (paper)
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
Mebarek, Naila; Vicente, Rita; Aubert-Pouëssel, Anne; Quentin, Julie; Mausset-Bonnefont, Anne-Laure; Devoisselle, Jean-Marie; Jorgensen, Christian; Bégu, Sylvie; Louis-Plence, Pascale
2015-05-01
Dendritic cells (DCs) are professional antigen-presenting cells that play a critical role in maintaining the balance between immunity and tolerance and, as such are a promising immunotherapy tool to induce immunity or to restore tolerance. The main challenge to harness the tolerogenic properties of DCs is to preserve their immature phenotype. We recently developed polyion complex micelles, formulated with double hydrophilic block copolymers of poly(methacrylic acid) and poly(ethylene oxide) blocks and able to entrap therapeutic molecules, which did not induce DC maturation. In the current study, the intrinsic destabilizing membrane properties of the polymers were used to optimize endosomal escape property of the micelles in order to propose various strategies to restore tolerance. On the first hand, we showed that high molecular weight (Mw) copolymer-based micelles were efficient to favor the release of the micelle-entrapped peptide into the endosomes, and thus to improve peptide presentation by immature (i) DCs. On the second hand, we put in evidence that low Mw copolymer-based micelles were able to favor the cytosolic release of micelle-entrapped small interfering RNAs, dampening the DCs immunogenicity. Therefore, we demonstrate the versatile use of polyionic complex micelles to preserve tolerogenic properties of DCs. Altogether, our results underscored the potential of such micelle-loaded iDCs as a therapeutic tool to restore tolerance in autoimmune diseases. Copyright © 2015 Elsevier B.V. All rights reserved.
Higher-order Multivariable Polynomial Regression to Estimate Human Affective States
Wei, Jie; Chen, Tong; Liu, Guangyuan; Yang, Jiemin
2016-03-01
From direct observations, facial, vocal, gestural, physiological, and central nervous signals, estimating human affective states through computational models such as multivariate linear-regression analysis, support vector regression, and artificial neural network, have been proposed in the past decade. In these models, linear models are generally lack of precision because of ignoring intrinsic nonlinearities of complex psychophysiological processes; and nonlinear models commonly adopt complicated algorithms. To improve accuracy and simplify model, we introduce a new computational modeling method named as higher-order multivariable polynomial regression to estimate human affective states. The study employs standardized pictures in the International Affective Picture System to induce thirty subjects’ affective states, and obtains pure affective patterns of skin conductance as input variables to the higher-order multivariable polynomial model for predicting affective valence and arousal. Experimental results show that our method is able to obtain efficient correlation coefficients of 0.98 and 0.96 for estimation of affective valence and arousal, respectively. Moreover, the method may provide certain indirect evidences that valence and arousal have their brain’s motivational circuit origins. Thus, the proposed method can serve as a novel one for efficiently estimating human affective states.
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Clement Nyamunura Mweya
2013-10-01
Full Text Available Background: The East African region has experienced several Rift Valley fever (RVF outbreaks since the 1930s. The objective of this study was to identify distributions of potential disease vectors in relation to disease epidemics. Understanding disease vector potential distributions is a major concern for disease transmission dynamics. Methods: Diverse ecological niche modelling techniques have been developed for this purpose: we present a maximum entropy (Maxent approach for estimating distributions of potential RVF vectors in un-sampled areas in East Africa. We modelled the distribution of two species of mosquitoes (Aedes aegypti and Culex pipiens complex responsible for potential maintenance and amplification of the virus, respectively. Predicted distributions of environmentally suitable areas in East Africa were based on the presence-only occurrence data derived from our entomological study in Ngorongoro District in northern Tanzania. Results: Our model predicted potential suitable areas with high success rates of 90.9% for A. aegypti and 91.6% for C. pipiens complex. Model performance was statistically significantly better than random for both species. Most suitable sites for the two vectors were predicted in central and northwestern Tanzania with previous disease epidemics. Other important risk areas include western Lake Victoria, northern parts of Lake Malawi, and the Rift Valley region of Kenya. Conclusion: Findings from this study show distributions of vectors had biological and epidemiological significance in relation to disease outbreak hotspots, and hence provide guidance for the selection of sampling areas for RVF vectors during inter-epidemic periods.
Mweya, Clement Nyamunura; Kimera, Sharadhuli Iddi; Kija, John Bukombe; Mboera, Leonard E G
2013-01-01
The East African region has experienced several Rift Valley fever (RVF) outbreaks since the 1930s. The objective of this study was to identify distributions of potential disease vectors in relation to disease epidemics. Understanding disease vector potential distributions is a major concern for disease transmission dynamics. DIVERSE ECOLOGICAL NICHE MODELLING TECHNIQUES HAVE BEEN DEVELOPED FOR THIS PURPOSE: we present a maximum entropy (Maxent) approach for estimating distributions of potential RVF vectors in un-sampled areas in East Africa. We modelled the distribution of two species of mosquitoes (Aedes aegypti and Culex pipiens complex) responsible for potential maintenance and amplification of the virus, respectively. Predicted distributions of environmentally suitable areas in East Africa were based on the presence-only occurrence data derived from our entomological study in Ngorongoro District in northern Tanzania. Our model predicted potential suitable areas with high success rates of 90.9% for A. aegypti and 91.6% for C. pipiens complex. Model performance was statistically significantly better than random for both species. Most suitable sites for the two vectors were predicted in central and northwestern Tanzania with previous disease epidemics. Other important risk areas include western Lake Victoria, northern parts of Lake Malawi, and the Rift Valley region of Kenya. Findings from this study show distributions of vectors had biological and epidemiological significance in relation to disease outbreak hotspots, and hence provide guidance for the selection of sampling areas for RVF vectors during inter-epidemic periods.
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)
Sheffer and Non-Sheffer Polynomial Families
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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.
The finite Fourier transform of classical polynomials
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.
2D-Zernike Polynomials and Coherent State Quantization of the Unit Disc
Energy Technology Data Exchange (ETDEWEB)
Thirulogasanthar, K., E-mail: santhar@gmail.com [Concordia University, Department of Comuter Science and Software Engineering (Canada); Saad, Nasser, E-mail: nsaad@upei.ca [University of Prince Edward Island, Department of mathematics and Statistics (Canada); Honnouvo, G., E-mail: g-honnouvo@yahoo.fr [McGill University, Department of Mathematics and Statistics (Canada)
2015-12-15
Using the orthonormality of the 2D-Zernike polynomials, reproducing kernels, reproducing kernel Hilbert spaces, and ensuring coherent states attained. With the aid of the so-obtained coherent states, the complex unit disc is quantized. Associated upper symbols, lower symbols and related generalized Berezin transforms also obtained. A number of necessary summation formulas for the 2D-Zernike polynomials proved.
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J. Y. Kang
2013-01-01
Full Text Available Recently, many mathematicians have studied different kinds of the Euler, Bernoulli, and Genocchi numbers and polynomials. In this paper, we give another definition of polynomials Ũn(x. We observe an interesting phenomenon of “scattering” of the zeros of the polynomials Ũn(x in complex plane. We find out some identities and properties related to polynomials Ũn(x. Finally, we also derive interesting relations between polynomials Ũn(x, Stirling numbers, central factorial numbers, and Euler numbers.
A Summation Formula for Macdonald Polynomials
de Gier, Jan; Wheeler, Michael
2016-03-01
We derive an explicit sum formula for symmetric Macdonald polynomials. Our expression contains multiple sums over the symmetric group and uses the action of Hecke generators on the ring of polynomials. In the special cases {t = 1} and {q = 0}, we recover known expressions for the monomial symmetric and Hall-Littlewood polynomials, respectively. Other specializations of our formula give new expressions for the Jack and q-Whittaker polynomials.
A New Generalisation of Macdonald Polynomials
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.
Associated polynomials and birth-death processes
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
PLOTNFIT.4TH, Data Plotting and Curve Fitting by Polynomials
International Nuclear Information System (INIS)
Schiffgens, J.O.
1990-01-01
1 - Description of program or function: PLOTnFIT is used for plotting and analyzing data by fitting nth degree polynomials of basis functions to the data interactively and printing graphs of the data and the polynomial functions. It can be used to generate linear, semi-log, and log-log graphs and can automatically scale the coordinate axes to suit the data. Multiple data sets may be plotted on a single graph. An auxiliary program, READ1ST, is included which produces an on-line summary of the information contained in the PLOTnFIT reference report. 2 - Method of solution: PLOTnFIT uses the least squares method to calculate the coefficients of nth-degree (up to 10. degree) polynomials of 11 selected basis functions such that each polynomial fits the data in a least squares sense. The procedure incorporated in the code uses a linear combination of orthogonal polynomials to avoid 'i11-conditioning' and to perform the curve fitting task with single-precision arithmetic. 3 - Restrictions on the complexity of the problem - Maxima of: 225 data points per job (or graph) including all data sets 8 data sets (or tasks) per job (or graph)
Fractional order differentiation by integration with Jacobi polynomials
Liu, Dayan
2012-12-01
The differentiation by integration method with Jacobi polynomials was originally introduced by Mboup, Join and Fliess [22], [23]. This paper generalizes this method from the integer order to the fractional order for estimating the fractional order derivatives of noisy signals. The proposed fractional order differentiator is deduced from the Jacobi orthogonal polynomial filter and the Riemann-Liouville fractional order derivative definition. Exact and simple formula for this differentiator is given where an integral formula involving Jacobi polynomials and the noisy signal is used without complex mathematical deduction. Hence, it can be used both for continuous-time and discrete-time models. The comparison between our differentiator and the recently introduced digital fractional order Savitzky-Golay differentiator is given in numerical simulations so as to show its accuracy and robustness with respect to corrupting noises. © 2012 IEEE.
Fractional order differentiation by integration with Jacobi polynomials
Liu, Dayan; Gibaru, O.; Perruquetti, Wilfrid; Laleg-Kirati, Taous-Meriem
2012-01-01
The differentiation by integration method with Jacobi polynomials was originally introduced by Mboup, Join and Fliess [22], [23]. This paper generalizes this method from the integer order to the fractional order for estimating the fractional order derivatives of noisy signals. The proposed fractional order differentiator is deduced from the Jacobi orthogonal polynomial filter and the Riemann-Liouville fractional order derivative definition. Exact and simple formula for this differentiator is given where an integral formula involving Jacobi polynomials and the noisy signal is used without complex mathematical deduction. Hence, it can be used both for continuous-time and discrete-time models. The comparison between our differentiator and the recently introduced digital fractional order Savitzky-Golay differentiator is given in numerical simulations so as to show its accuracy and robustness with respect to corrupting noises. © 2012 IEEE.
Directory of Open Access Journals (Sweden)
Fernando A Monteiro
Full Text Available BACKGROUND: Triatoma dimidiata is among the main vectors of Chagas disease in Latin America. However, and despite important advances, there is no consensus about the taxonomic status of phenotypically divergent T. dimidiata populations, which in most recent papers are regarded as subspecies. METHODOLOGY AND FINDINGS: A total of 126 cyt b sequences (621 bp long were produced for specimens from across the species range. Forty-seven selected specimens representing the main cyt b clades observed (after a preliminary phylogenetic analysis were also sequenced for an ND4 fragment (554 bp long and concatenated with their respective cyt b sequences to produce a combined data set totalling 1175 bp/individual. Bayesian and Maximum-Likelihood phylogenetic analyses of both data sets (cyt b, and cyt b+ND4 disclosed four strongly divergent (all pairwise Kimura 2-parameter distances >0.08, monophyletic groups: Group I occurs from Southern Mexico through Central America into Colombia, with Ecuadorian specimens resembling Nicaraguan material; Group II includes samples from Western-Southwestern Mexico; Group III comprises specimens from the Yucatán peninsula; and Group IV consists of sylvatic samples from Belize. The closely-related, yet formally recognized species T. hegneri from the island of Cozumel falls within the divergence range of the T. dimidiata populations studied. CONCLUSIONS: We propose that Groups I-IV, as well as T. hegneri, should be regarded as separate species. In the Petén of Guatemala, representatives of Groups I, II, and III occur in sympatry; the absence of haplotypes with intermediate genetic distances, as shown by multimodal mismatch distribution plots, clearly indicates that reproductive barriers actively promote within-group cohesion. Some sylvatic specimens from Belize belong to a different species - likely the basal lineage of the T. dimidiata complex, originated ~8.25 Mya. The evidence presented here strongly supports the proposition
BSDEs with polynomial growth generators
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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.
Introduction to the spectral theory of polynomial operator pencils
Markus, A S
1988-01-01
This monograph contains an exposition of the foundations of the spectral theory of polynomial operator pencils acting in a Hilbert space. Spectral problems for polynomial pencils have attracted a steady interest in the last 35 years, mainly because they arise naturally in such diverse areas of mathematical physics as differential equations and boundary value problems, controllable systems, the theory of oscillations and waves, elasticity theory, and hydromechanics. In this book, the author devotes most of his attention to the fundamental results of Keldysh on multiple completeness of the eigenvectors and associate vectors of a pencil, and on the asymptotic behavior of its eigenvalues and generalizations of these results. The author also presents various theorems on spectral factorization of pencils which grew out of known results of M. G. Kreibreven and Heinz Langer. A large portion of the book involves the theory of selfadjoint pencils, an area having numerous applications. Intended for mathematicians, resea...
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
Codimensions of generalized polynomial identities
International Nuclear Information System (INIS)
Gordienko, Aleksei S
2010-01-01
It is proved that for every finite-dimensional associative algebra A over a field of characteristic zero there are numbers C element of Q + and t element of Z + such that gc n (A)∼Cn t d n as n→∞, where d=PI exp(A) element of Z + . Thus, Amitsur's and Regev's conjectures hold for the codimensions gc n (A) of the generalized polynomial identities. Bibliography: 6 titles.
The Jones polynomial as a new invariant of topological fluid dynamics
International Nuclear Information System (INIS)
Ricca, Renzo L; Liu, Xin
2014-01-01
A new method based on the use of the Jones polynomial, a well-known topological invariant of knot theory, is introduced to tackle and quantify topological aspects of structural complexity of vortex tangles in ideal fluids. By re-writing the Jones polynomial in terms of helicity, the resulting polynomial becomes then function of knot topology and vortex circulation, providing thus a new invariant of topological fluid dynamics. Explicit computations of the Jones polynomial for some standard configurations, including the Whitehead link and the Borromean rings (whose linking numbers are zero), are presented for illustration. In the case of a homogeneous, isotropic tangle of vortex filaments with same circulation, the new Jones polynomial reduces to some simple algebraic expression, that can be easily computed by numerical methods. This shows that this technique may offer a new setting and a powerful tool to detect and compute topological complexity and to investigate relations with energy, by tackling fundamental aspects of turbulence research. (paper)
Computing Tutte polynomials of contact networks in classrooms
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
Directory of Open Access Journals (Sweden)
Xin Yi Ng
2015-01-01
Full Text Available This study concerns an attempt to establish a new method for predicting antimicrobial peptides (AMPs which are important to the immune system. Recently, researchers are interested in designing alternative drugs based on AMPs because they have found that a large number of bacterial strains have become resistant to available antibiotics. However, researchers have encountered obstacles in the AMPs designing process as experiments to extract AMPs from protein sequences are costly and require a long set-up time. Therefore, a computational tool for AMPs prediction is needed to resolve this problem. In this study, an integrated algorithm is newly introduced to predict AMPs by integrating sequence alignment and support vector machine- (SVM- LZ complexity pairwise algorithm. It was observed that, when all sequences in the training set are used, the sensitivity of the proposed algorithm is 95.28% in jackknife test and 87.59% in independent test, while the sensitivity obtained for jackknife test and independent test is 88.74% and 78.70%, respectively, when only the sequences that has less than 70% similarity are used. Applying the proposed algorithm may allow researchers to effectively predict AMPs from unknown protein peptide sequences with higher sensitivity.
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Bing-Jhih Yao
2016-09-01
Full Text Available An adaptive multi-rate wideband (AMR-WB code is a speech codec developed on the basis of an algebraic code-excited linear-prediction (ACELP coding technique, and has a double advantage of low bit rates and high speech quality. This coding technique is widely used in modern mobile communication systems for a high speech quality in handheld devices. However, a major disadvantage is that a vector quantization (VQ of immittance spectral frequency (ISF coefficients occupies a significant computational load in the AMR-WB encoder. Hence, this paper presents a triangular inequality elimination (TIE algorithm combined with a dynamic mechanism and an intersection mechanism, abbreviated as the DI-TIE algorithm, to remarkably improve the complexity of ISF coefficient quantization in the AMR-WB speech codec. Both mechanisms are designed in a way that recursively enhances the performance of the TIE algorithm. At the end of this work, this proposal is experimentally validated as a superior search algorithm relative to a conventional TIE, a multiple TIE (MTIE, and an equal-average equal-variance equal-norm nearest neighbor search (EEENNS approach. With a full search algorithm as a benchmark for search load comparison, this work provides a search load reduction above 77%, a figure far beyond 36% in the TIE, 49% in the MTIE, and 68% in the EEENNS approach.
Li, Liwei; Wang, Bo; Meroueh, Samy O
2011-09-26
The community structure-activity resource (CSAR) data sets are used to develop and test a support vector machine-based scoring function in regression mode (SVR). Two scoring functions (SVR-KB and SVR-EP) are derived with the objective of reproducing the trend of the experimental binding affinities provided within the two CSAR data sets. The features used to train SVR-KB are knowledge-based pairwise potentials, while SVR-EP is based on physicochemical properties. SVR-KB and SVR-EP were compared to seven other widely used scoring functions, including Glide, X-score, GoldScore, ChemScore, Vina, Dock, and PMF. Results showed that SVR-KB trained with features obtained from three-dimensional complexes of the PDBbind data set outperformed all other scoring functions, including best performing X-score, by nearly 0.1 using three correlation coefficients, namely Pearson, Spearman, and Kendall. It was interesting that higher performance in rank ordering did not translate into greater enrichment in virtual screening assessed using the 40 targets of the Directory of Useful Decoys (DUD). To remedy this situation, a variant of SVR-KB (SVR-KBD) was developed by following a target-specific tailoring strategy that we had previously employed to derive SVM-SP. SVR-KBD showed a much higher enrichment, outperforming all other scoring functions tested, and was comparable in performance to our previously derived scoring function SVM-SP.
Polynomial realization of the Uq (sl(3)) Gel'fand-(Weyl)-Zetlin basis
International Nuclear Information System (INIS)
Dobrev, V.K.; Truini, P.
1996-01-01
We give an explicit realization of the U ≡ U q (sl(3)) Gel'fand-(Weyl)-Zetlin (GWZ) basis as polynomial functions in three variables. This realization is obtained in two complementary ways. First we establish a 1-to-1 correspondence between the abstract GWZ basis and explicit polynomials in the quantum subgroup U + of the raising generators. We then use an explicit construction of arbitrary lowest weight (holomorphic) representations of U in terms of three variables on which the generators of U are realized as q-difference operators. Applying the GWZ corresponding polynomials in this realization to the lowest weight vector (the function 1) produces one realization of our GWZ basis. Another realization of the GWZ polynomial basis is found by the explicit diagonalization of the operators of isospin I-circumflex 2 , third component of isospin I-circumflex z , and hypercharge Y-circumflex, in the same realization as q-difference operators. The result is that the eigenvectors can be written in terms of q-hypergeometric polynomials in our three variables. Finally we construct an explicit scalar product (adapting the Shapovalov form to our setting). Using it we prove the orthogonality of our GWZ polynomials for which we use both realizations. This provides a polynomial construction for the orthonormal GWZ basis. We work for generic q, leaving the root of unity case for a following paper. It seems that our results are new also in the classical situation (q=1). (author). 20 refs
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Mok Tik
2014-06-01
Full Text Available This study formulates regression of vector data that will enable statistical analysis of various geodetic phenomena such as, polar motion, ocean currents, typhoon/hurricane tracking, crustal deformations, and precursory earthquake signals. The observed vector variable of an event (dependent vector variable is expressed as a function of a number of hypothesized phenomena realized also as vector variables (independent vector variables and/or scalar variables that are likely to impact the dependent vector variable. The proposed representation has the unique property of solving the coefficients of independent vector variables (explanatory variables also as vectors, hence it supersedes multivariate multiple regression models, in which the unknown coefficients are scalar quantities. For the solution, complex numbers are used to rep- resent vector information, and the method of least squares is deployed to estimate the vector model parameters after transforming the complex vector regression model into a real vector regression model through isomorphism. Various operational statistics for testing the predictive significance of the estimated vector parameter coefficients are also derived. A simple numerical example demonstrates the use of the proposed vector regression analysis in modeling typhoon paths.
Ait-Haddou, Rachid
2015-01-01
We show that the best degree reduction of a given polynomial P from degree n to m with respect to the discrete (Formula presented.)-norm is equivalent to the best Euclidean distance of the vector of h-Bézier coefficients of P from the vector
Current advances on polynomial resultant formulations
Sulaiman, Surajo; Aris, Nor'aini; Ahmad, Shamsatun Nahar
2017-08-01
Availability of computer algebra systems (CAS) lead to the resurrection of the resultant method for eliminating one or more variables from the polynomials system. The resultant matrix method has advantages over the Groebner basis and Ritt-Wu method due to their high complexity and storage requirement. This paper focuses on the current resultant matrix formulations and investigates their ability or otherwise towards producing optimal resultant matrices. A determinantal formula that gives exact resultant or a formulation that can minimize the presence of extraneous factors in the resultant formulation is often sought for when certain conditions that it exists can be determined. We present some applications of elimination theory via resultant formulations and examples are given to explain each of the presented settings.
On characteristic polynomials for a generalized chiral random matrix ensemble with a source
Fyodorov, Yan V.; Grela, Jacek; Strahov, Eugene
2018-04-01
We evaluate averages involving characteristic polynomials, inverse characteristic polynomials and ratios of characteristic polynomials for a N× N random matrix taken from a L-deformed chiral Gaussian Unitary Ensemble with an external source Ω. Relation to a recently studied statistics of bi-orthogonal eigenvectors in the complex Ginibre ensemble, see Fyodorov (2017 arXiv:1710.04699), is briefly discussed as a motivation to study asymptotics of these objects in the case of external source proportional to the identity matrix. In particular, for an associated complex bulk/chiral edge scaling regime we retrieve the kernel related to Bessel/Macdonald functions.
Grid and basis adaptive polynomial chaos techniques for sensitivity and uncertainty analysis
Energy Technology Data Exchange (ETDEWEB)
Perkó, Zoltán, E-mail: Z.Perko@tudelft.nl; Gilli, Luca, E-mail: Gilli@nrg.eu; Lathouwers, Danny, E-mail: D.Lathouwers@tudelft.nl; Kloosterman, Jan Leen, E-mail: J.L.Kloosterman@tudelft.nl
2014-03-01
The demand for accurate and computationally affordable sensitivity and uncertainty techniques is constantly on the rise and has become especially pressing in the nuclear field with the shift to Best Estimate Plus Uncertainty methodologies in the licensing of nuclear installations. Besides traditional, already well developed methods – such as first order perturbation theory or Monte Carlo sampling – Polynomial Chaos Expansion (PCE) has been given a growing emphasis in recent years due to its simple application and good performance. This paper presents new developments of the research done at TU Delft on such Polynomial Chaos (PC) techniques. Our work is focused on the Non-Intrusive Spectral Projection (NISP) approach and adaptive methods for building the PCE of responses of interest. Recent efforts resulted in a new adaptive sparse grid algorithm designed for estimating the PC coefficients. The algorithm is based on Gerstner's procedure for calculating multi-dimensional integrals but proves to be computationally significantly cheaper, while at the same it retains a similar accuracy as the original method. More importantly the issue of basis adaptivity has been investigated and two techniques have been implemented for constructing the sparse PCE of quantities of interest. Not using the traditional full PC basis set leads to further reduction in computational time since the high order grids necessary for accurately estimating the near zero expansion coefficients of polynomial basis vectors not needed in the PCE can be excluded from the calculation. Moreover the sparse PC representation of the response is easier to handle when used for sensitivity analysis or uncertainty propagation due to the smaller number of basis vectors. The developed grid and basis adaptive methods have been implemented in Matlab as the Fully Adaptive Non-Intrusive Spectral Projection (FANISP) algorithm and were tested on four analytical problems. These show consistent good performance
Grid and basis adaptive polynomial chaos techniques for sensitivity and uncertainty analysis
International Nuclear Information System (INIS)
Perkó, Zoltán; Gilli, Luca; Lathouwers, Danny; Kloosterman, Jan Leen
2014-01-01
The demand for accurate and computationally affordable sensitivity and uncertainty techniques is constantly on the rise and has become especially pressing in the nuclear field with the shift to Best Estimate Plus Uncertainty methodologies in the licensing of nuclear installations. Besides traditional, already well developed methods – such as first order perturbation theory or Monte Carlo sampling – Polynomial Chaos Expansion (PCE) has been given a growing emphasis in recent years due to its simple application and good performance. This paper presents new developments of the research done at TU Delft on such Polynomial Chaos (PC) techniques. Our work is focused on the Non-Intrusive Spectral Projection (NISP) approach and adaptive methods for building the PCE of responses of interest. Recent efforts resulted in a new adaptive sparse grid algorithm designed for estimating the PC coefficients. The algorithm is based on Gerstner's procedure for calculating multi-dimensional integrals but proves to be computationally significantly cheaper, while at the same it retains a similar accuracy as the original method. More importantly the issue of basis adaptivity has been investigated and two techniques have been implemented for constructing the sparse PCE of quantities of interest. Not using the traditional full PC basis set leads to further reduction in computational time since the high order grids necessary for accurately estimating the near zero expansion coefficients of polynomial basis vectors not needed in the PCE can be excluded from the calculation. Moreover the sparse PC representation of the response is easier to handle when used for sensitivity analysis or uncertainty propagation due to the smaller number of basis vectors. The developed grid and basis adaptive methods have been implemented in Matlab as the Fully Adaptive Non-Intrusive Spectral Projection (FANISP) algorithm and were tested on four analytical problems. These show consistent good performance both
Colored Kauffman homology and super-A-polynomials
International Nuclear Information System (INIS)
Nawata, Satoshi; Ramadevi, P.; Zodinmawia
2014-01-01
We study the structural properties of colored Kauffman homologies of knots. Quadruple-gradings play an essential role in revealing the differential structure of colored Kauffman homology. Using the differential structure, the Kauffman homologies carrying the symmetric tensor products of the vector representation for the trefoil and the figure-eight are determined. In addition, making use of relations from representation theory, we also obtain the HOMFLY homologies colored by rectangular Young tableaux with two rows for these knots. Furthermore, the notion of super-A-polynomials is extended in order to encompass two-parameter deformations of PSL(2,ℂ) character varieties
The higher rank numerical range of matrix polynomials
Aretaki, Aikaterini; Maroulas, John
2011-01-01
The notion of the higher rank numerical range $\\Lambda_{k}(L(\\lambda))$ for matrix polynomials $L(\\lambda)=A_{m}\\lambda^{m}+...+A_{1}\\lambda+A_{0}$ is introduced here and some fundamental geometrical properties are investigated. Further, the sharp points of $\\Lambda_{k}(L(\\lambda))$ are defined and their relation to the numerical range $w(L(\\lambda))$ is presented. A connection of $\\Lambda_{k}(L(\\lambda))$ with the vector-valued higher rank numerical range $\\Lambda_{k}(A_{0},..., A_{m})$ is a...
Algebraic polynomials with random coefficients
Directory of Open Access Journals (Sweden)
K. Farahmand
2002-01-01
Full Text Available This paper provides an asymptotic value for the mathematical expected number of points of inflections of a random polynomial of the form a0(ω+a1(ω(n11/2x+a2(ω(n21/2x2+…an(ω(nn1/2xn when n is large. The coefficients {aj(w}j=0n, w∈Ω are assumed to be a sequence of independent normally distributed random variables with means zero and variance one, each defined on a fixed probability space (A,Ω,Pr. A special case of dependent coefficients is also studied.
Improved multivariate polynomial factoring algorithm
International Nuclear Information System (INIS)
Wang, P.S.
1978-01-01
A new algorithm for factoring multivariate polynomials over the integers based on an algorithm by Wang and Rothschild is described. The new algorithm has improved strategies for dealing with the known problems of the original algorithm, namely, the leading coefficient problem, the bad-zero problem and the occurrence of extraneous factors. It has an algorithm for correctly predetermining leading coefficients of the factors. A new and efficient p-adic algorithm named EEZ is described. Bascially it is a linearly convergent variable-by-variable parallel construction. The improved algorithm is generally faster and requires less store then the original algorithm. Machine examples with comparative timing are included
Fourier series and orthogonal polynomials
Jackson, Dunham
2004-01-01
This text for undergraduate and graduate students illustrates the fundamental simplicity of the properties of orthogonal functions and their developments in related series. Starting with a definition and explanation of the elements of Fourier series, the text follows with examinations of Legendre polynomials and Bessel functions. Boundary value problems consider Fourier series in conjunction with Laplace's equation in an infinite strip and in a rectangle, with a vibrating string, in three dimensions, in a sphere, and in other circumstances. An overview of Pearson frequency functions is followe
Killings, duality and characteristic polynomials
Álvarez, Enrique; Borlaf, Javier; León, José H.
1998-03-01
In this paper the complete geometrical setting of (lowest order) abelian T-duality is explored with the help of some new geometrical tools (the reduced formalism). In particular, all invariant polynomials (the integrands of the characteristic classes) can be explicitly computed for the dual model in terms of quantities pertaining to the original one and with the help of the canonical connection whose intrinsic characterization is given. Using our formalism the physically, and T-duality invariant, relevant result that top forms are zero when there is an isometry without fixed points is easily proved. © 1998
Orthogonal polynomials and random matrices
Deift, Percy
2000-01-01
This volume expands on a set of lectures held at the Courant Institute on Riemann-Hilbert problems, orthogonal polynomials, and random matrix theory. The goal of the course was to prove universality for a variety of statistical quantities arising in the theory of random matrix models. The central question was the following: Why do very general ensembles of random n {\\times} n matrices exhibit universal behavior as n {\\rightarrow} {\\infty}? The main ingredient in the proof is the steepest descent method for oscillatory Riemann-Hilbert problems.
Introduction to Real Orthogonal Polynomials
1992-06-01
uses Green’s functions. As motivation , consider the Dirichlet problem for the unit circle in the plane, which involves finding a harmonic function u(r...xv ; a, b ; q) - TO [q-N ab+’q ; q, xq b. Orthogoy RMotion O0 (bq :q)x p.(q* ; a, b ; q) pg(q’ ; a, b ; q) (q "q), (aq)x (q ; q), (I -abq) (bq ; q... motivation and justi- fication for continued study of the intrinsic structure of orthogonal polynomials. 99 LIST OF REFERENCES 1. Deyer, W. M., ed., CRC
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
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)
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.
Bayer Demosaicking with Polynomial Interpolation.
Wu, Jiaji; Anisetti, Marco; Wu, Wei; Damiani, Ernesto; Jeon, Gwanggil
2016-08-30
Demosaicking is a digital image process to reconstruct full color digital images from incomplete color samples from an image sensor. It is an unavoidable process for many devices incorporating camera sensor (e.g. mobile phones, tablet, etc.). In this paper, we introduce a new demosaicking algorithm based on polynomial interpolation-based demosaicking (PID). Our method makes three contributions: calculation of error predictors, edge classification based on color differences, and a refinement stage using a weighted sum strategy. Our new predictors are generated on the basis of on the polynomial interpolation, and can be used as a sound alternative to other predictors obtained by bilinear or Laplacian interpolation. In this paper we show how our predictors can be combined according to the proposed edge classifier. After populating three color channels, a refinement stage is applied to enhance the image quality and reduce demosaicking artifacts. Our experimental results show that the proposed method substantially improves over existing demosaicking methods in terms of objective performance (CPSNR, S-CIELAB E, and FSIM), and visual performance.
Fermionic formula for double Kostka polynomials
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...
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.
Tensor calculus in polar coordinates using Jacobi polynomials
Vasil, Geoffrey M.; Burns, Keaton J.; Lecoanet, Daniel; Olver, Sheehan; Brown, Benjamin P.; Oishi, Jeffrey S.
2016-11-01
Spectral methods are an efficient way to solve partial differential equations on domains possessing certain symmetries. The utility of a method depends strongly on the choice of spectral basis. In this paper we describe a set of bases built out of Jacobi polynomials, and associated operators for solving scalar, vector, and tensor partial differential equations in polar coordinates on a unit disk. By construction, the bases satisfy regularity conditions at r = 0 for any tensorial field. The coordinate singularity in a disk is a prototypical case for many coordinate singularities. The work presented here extends to other geometries. The operators represent covariant derivatives, multiplication by azimuthally symmetric functions, and the tensorial relationship between fields. These arise naturally from relations between classical orthogonal polynomials, and form a Heisenberg algebra. Other past work uses more specific polynomial bases for solving equations in polar coordinates. The main innovation in this paper is to use a larger set of possible bases to achieve maximum bandedness of linear operations. We provide a series of applications of the methods, illustrating their ease-of-use and accuracy.
DEFF Research Database (Denmark)
Zhang, Shun; Yang, Yi; Hanson, Steen Grüner
2015-01-01
for the superiority of the proposed PSVC technique, we study the statistical properties of the spatial derivatives of the complex signal representation generated from the Riesz transform. Under the assumption of a Gaussian random process, a theoretical analysis for the pseudo Stokes vector correlation has been...... provided. Based on these results, we show mathematically that PSVC has a performance advantage over conventional intensity-based correlation technique....
Risteski, Ice B.
2010-01-01
In this article, the author discovers a paradox of balancing chemical equations. The many counterexamples illustrate that the considered procedure of balancing chemical equations given in the paper1 is inconsistent. A new complex vector method for paradox resolution is given too. V članku avtor opisuje paradoks pri uravnoteženju kemijskih reakcij. Več primerov dokazuje, da je procedura uravnoteženja kemijskih reakcij v viru1 inkonsistentna. Predstavljena je nova kompleksna vektorska metoda...
International Nuclear Information System (INIS)
Guppy, C.B.
1962-03-01
In the methods adopted in this report transfer functions in the form of the ratio of two polynomials of the complex variable s are derived from sets of laplace transformed simultaneous differential equations. The set of algebraic simultaneous equations are solved using Cramer's Rule and this gives rise to determinants having polynomial elements. It is shown how the determinants are formed when transfer functions are specified. The procedure for finding the polynomial coefficients from a given determinant is fully described. The first method adopted is a direct one and reduces a determinant with first degree polynomial elements to secular form and follows this by an application of the similarity transformation to reduce the determinant to a form from which the polynomial coefficients can be read out directly. The programme is able to solve a single determinant with polynomial elements and this can be used to reduce an eigenvalue problem in the form of a secular determinant to polynomial form if the need arises. A description is given of the way in which the data is to be set out for solution by the programme. A description is also given of a method used in an earlier programme for solving polynomial determinants by curve fitting techniques using Chebyshev Polynomials. In this method determinants with polynomial elements of any degree can be solved. (author)
Polynomials formalism of quantum numbers
International Nuclear Information System (INIS)
Kazakov, K.V.
2005-01-01
Theoretical aspects of the recently suggested perturbation formalism based on the method of quantum number polynomials are considered in the context of the general anharmonicity problem. Using a biatomic molecule by way of example, it is demonstrated how the theory can be extrapolated to the case of vibrational-rotational interactions. As a result, an exact expression for the first coefficient of the Herman-Wallis factor is derived. In addition, the basic notions of the formalism are phenomenologically generalized and expanded to the problem of spin interaction. The concept of magneto-optical anharmonicity is introduced. As a consequence, an exact analogy is drawn with the well-known electro-optical theory of molecules, and a nonlinear dependence of the magnetic dipole moment of the system on the spin and wave variables is established [ru
Computing derivative-based global sensitivity measures using polynomial chaos expansions
International Nuclear Information System (INIS)
Sudret, B.; Mai, C.V.
2015-01-01
In the field of computer experiments sensitivity analysis aims at quantifying the relative importance of each input parameter (or combinations thereof) of a computational model with respect to the model output uncertainty. Variance decomposition methods leading to the well-known Sobol' indices are recognized as accurate techniques, at a rather high computational cost though. The use of polynomial chaos expansions (PCE) to compute Sobol' indices has allowed to alleviate the computational burden though. However, when dealing with large dimensional input vectors, it is good practice to first use screening methods in order to discard unimportant variables. The derivative-based global sensitivity measures (DGSMs) have been developed recently in this respect. In this paper we show how polynomial chaos expansions may be used to compute analytically DGSMs as a mere post-processing. This requires the analytical derivation of derivatives of the orthonormal polynomials which enter PC expansions. Closed-form expressions for Hermite, Legendre and Laguerre polynomial expansions are given. The efficiency of the approach is illustrated on two well-known benchmark problems in sensitivity analysis. - Highlights: • Derivative-based global sensitivity measures (DGSM) have been developed for screening purpose. • Polynomial chaos expansions (PC) are used as a surrogate model of the original computational model. • From a PC expansion the DGSM can be computed analytically. • The paper provides the derivatives of Hermite, Legendre and Laguerre polynomials for this purpose
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
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)
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.
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.
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
Large degree asymptotics of generalized Bessel polynomials
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
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 ...
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.
Laguerre polynomials by a harmonic oscillator
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.
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)
Dual exponential polynomials and linear differential equations
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.
Technique for image interpolation using polynomial transforms
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
Factoring polynomials over arbitrary finite fields
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
Application of polynomial preconditioners to conservation laws
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
On the number of polynomial solutions of Bernoulli and Abel polynomial differential equations
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.
Matrix product formula for Macdonald polynomials
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.
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)
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.
Explicit analytical expression for the condition number of polynomials in power form
Rack, Heinz-Joachim
2017-07-01
In his influential papers [1-3] W. Gautschi has defined and reshaped the condition number κ∞ of polynomials Pn of degree ≤ n which are represented in power form on a zero-symmetric interval [-ω, ω]. Basically, κ∞ is expressed as the product of two operator norms: an explicit factor times an implicit one (the l∞-norm of the coefficient vector of the n-th Chebyshev polynomial of the first kind relative to [-ω, ω]). We provide a new proof, economize the second factor and express it by an explicit analytical formula.
A set of sums for continuous dual q-2-Hahn polynomials
International Nuclear Information System (INIS)
Gade, R. M.
2009-01-01
An infinite set {τ (l) (y;r,z)} r,lisanelementofN 0 of linear sums of continuous dual q -2 -Hahn polynomials with prefactors depending on a complex parameter z is studied. The sums τ (l) (y;r,z) have an interpretation in context with tensor product representations of the quantum affine algebra U q ' (sl(2)) involving both a positive and a negative discrete series representation. For each l>0, the sum τ (l) (y;r,z) can be expressed in terms of the sum τ (0) (y;r,z), continuous dual q 2 -Hahn polynomials, and their associated polynomials. The sum τ (0) (y;r,z) is obtained as a combination of eight basic hypergeometric series. Moreover, an integral representation is provided for the sums τ (l) (y;r,z) with the complex parameter restricted by |zq| -2 -Hahn polynomials.
International Nuclear Information System (INIS)
Liu Chunjie; Wang Dewen; Zhang Zhaoshan; Gao Yabing; Xiong Chengqi; Long Jianyin; Wang Huixin; Peng Ruiyun; Cui Xuemei
2001-01-01
Objective: To observed the efficiency of gene therapy with TGF β1 antisense gene/liposome complexes and adenovirus transfer vector in RPF rats. Methods: TGFβ1 sense and antisense gene expression vectors and adenovirus transfer vector were introduced into rat bronchus by way of intratracheal instillation. Results: At day 1.5 after TGFβ1 sense and antisense gene transfer, PCR amplification using neo gene-specific primer from lung tissue DNA was all positive. After day 5.5, 67% (2/3) of lung tissue DNA was positive. RNA dot blot hybridization indicated that TGFβ1 mRNA content of lung tissue transfected with pMAMneo-antiTGFβ1 gene decreased. Detection of lung hydroxyproline (Hyp) content after day 35 of gene transfer showed that even in lung of rats received pMAMneo-AntiTGFβ1 lipid complexes it raised remarkably (P 9 pfu/ml were instilled into bronchus at 0.5 ml per rat. After day 2 day 6, the lung tissues of all six rats (three per each group )expressed the transfected luciferase gene by luminometer. Conclusion: Cationic lipid-mediated TGFβ1 antisense gene therapy was a simple and easy method. It can slow down the course of pathogenesis of lung fibrosis. Replication-deficient recombinant adenovirus-mediated gene therapy of lung diseases is a good and efficient method
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
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
Coexistence of critical orbit types in sub-hyperbolic polynomial maps
Poirier, Alfredo
1994-01-01
We establish necessary and sufficient conditions for the realization of mapping schemata as post-critically finite polynomials, or more generally, as post-critically finite polynomial maps from a finite union of copies of the complex numbers {\\bf C} to itself which have degree two or more in each copy. As a consequence of these results we prove a transitivity relation between hyperbolic components in parameter space which was conjectured by Milnor.
Quantized vortices in the ideal bose gas: a physical realization of random polynomials.
Castin, Yvan; Hadzibabic, Zoran; Stock, Sabine; Dalibard, Jean; Stringari, Sandro
2006-02-03
We propose a physical system allowing one to experimentally observe the distribution of the complex zeros of a random polynomial. We consider a degenerate, rotating, quasi-ideal atomic Bose gas prepared in the lowest Landau level. Thermal fluctuations provide the randomness of the bosonic field and of the locations of the vortex cores. These vortices can be mapped to zeros of random polynomials, and observed in the density profile of the gas.
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.
Optimal Conformal Polynomial Projections for Croatia According to the Airy/Jordan Criterion
Directory of Open Access Journals (Sweden)
Dražen Tutić
2009-05-01
Full Text Available The paper describes optimal conformal polynomial projections for Croatia according to the Airy/Jordan criterion. A brief introduction of history and theory of conformal mapping is followed by descriptions of conformal polynomial projections and their current application. The paper considers polynomials of degrees 1 to 10. Since there are conditions in which the 1st degree polynomial becomes the famous Mercator projection, it was not considered specifically for Croatian territory. The area of Croatia was defined as a union of national territory and the continental shelf. Area definition data were taken from the Euro Global Map 1:1 000 000 for Croatia, as well as from two maritime delimitation treaties. Such an irregular area was approximated with a regular grid consisting of 11 934 ellipsoidal trapezoids 2' large. The Airy/Jordan criterion for the optimal projection is defined as minimum of weighted mean of Airy/Jordan measure of distortion in points. The value of the Airy/Jordan criterion is calculated from all 11 934 centres of ellipsoidal trapezoids, while the weights are equal to areas of corresponding ellipsoidal trapezoids. The minimum is obtained by Nelder and Mead’s method, as implemented in the fminsearch function of the MATLAB package. Maps of Croatia representing the distribution of distortions are given for polynomial degrees 2 to 6 and 10. Increasing the polynomial degree results in better projections considering the criterion, and the 6th degree polynomial provides a good ratio of formula complexity and criterion value.
DEFF Research Database (Denmark)
Hansen, Kristoffer Lindskov; Udesen, Jesper; Gran, Fredrik
2008-01-01
Conventional ultrasound methods for acquiring color flow images of the blood motion are restricted by a relatively low frame rate and angle dependent velocity estimates. The Plane Wave Excitation (PWE) method has been proposed to solve these limitations. The frame rate can be increased, and the 2-D...... vector velocity of the blood motion can be estimated. The transmitted pulse is not focused, and a full speckle image of the blood can be acquired for each emission. A 13 bit Barker code is transmitted simultaneously from each transducer element. The 2-D vector velocity of the blood is found using 2-D...... speckle tracking between segments in consecutive speckle images. The flow patterns of six bifurcations and two veins were investigated in-vivo. It was shown: 1) that a stable vortex in the carotid bulb was present opposed to other examined bifurcations, 2) that retrograde flow was present...
Eigenvalues of PT-symmetric oscillators with polynomial potentials
International Nuclear Information System (INIS)
Shin, Kwang C
2005-01-01
We study the eigenvalue problem -u''(z) - [(iz) m + P m-1 (iz)]u(z) λu(z) with the boundary condition that u(z) decays to zero as z tends to infinity along the rays arg z = -π/2 ± 2π/(m+2) in the complex plane, where P m-1 (z) = a 1 z m-1 + a 2 z m-2 + . . . + a m-1 z is a polynomial and integers m ≥ 3. We provide an asymptotic expansion of the eigenvalues λ n as n → +∞, and prove that for each real polynomial P m-1 , the eigenvalues are all real and positive, with only finitely many exceptions
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.
Alpay, Daniel
2015-01-01
This is an exercises book at the beginning graduate level, whose aim is to illustrate some of the connections between functional analysis and the theory of functions of one variable. A key role is played by the notions of positive definite kernel and of reproducing kernel Hilbert space. A number of facts from functional analysis and topological vector spaces are surveyed. Then, various Hilbert spaces of analytic functions are studied.
The Integration Order of Vector Autoregressive Processes
DEFF Research Database (Denmark)
Franchi, Massimo
We show that the order of integration of a vector autoregressive process is equal to the difference between the multiplicity of the unit root in the characteristic equation and the multiplicity of the unit root in the adjoint matrix polynomial. The equivalence with the standard I(1) and I(2...
Multilevel weighted least squares polynomial approximation
Haji-Ali, Abdul-Lateef; Nobile, Fabio; Tempone, Raul; Wolfers, Sö ren
2017-01-01
, 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
Polynomials in finite geometries and combinatorics
Blokhuis, A.; Walker, K.
1993-01-01
It is illustrated how elementary properties of polynomials can be used to attack extremal problems in finite and euclidean geometry, and in combinatorics. Also a new result, related to the problem of neighbourly cylinders is presented.
Polynomial analysis of ambulatory blood pressure measurements
Zwinderman, A. H.; Cleophas, T. A.; Cleophas, T. J.; van der Wall, E. E.
2001-01-01
In normotensive subjects blood pressures follow a circadian rhythm. A circadian rhythm in hypertensive patients is less well established, and may be clinically important, particularly with rigorous treatments of daytime blood pressures. Polynomial analysis of ambulatory blood pressure monitoring
Handbook on semidefinite, conic and polynomial optimization
Anjos, Miguel F
2012-01-01
This book offers the reader a snapshot of the state-of-the-art in the growing and mutually enriching areas of semidefinite optimization, conic optimization and polynomial optimization. It covers theory, algorithms, software and applications.
Generalized catalan numbers, sequences and polynomials
KOÇ, Cemal; GÜLOĞLU, İsmail; ESİN, Songül
2010-01-01
In this paper we present an algebraic interpretation for generalized Catalan numbers. We describe them as dimensions of certain subspaces of multilinear polynomials. This description is of utmost importance in the investigation of annihilators in exterior algebras.
About the solvability of matrix polynomial equations
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.
Two polynomial representations of experimental design
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.
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
Stability analysis of polynomial fuzzy models via polynomial fuzzy Lyapunov functions
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...
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)
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)
Relations between Möbius and coboundary polynomials
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
Rahpaya, Sayed Samim; Tsuchiaka, Shinobu; Kishimoto, Mai; Oba, Mami; Katayama, Yukie; Nunomura, Yuka; Kokawa, Saki; Kimura, Takashi; Kobayashi, Atsushi; Kirino, Yumi; Okabayashi, Tamaki; Nonaka, Nariaki; Mekata, Hirohisa; Aoki, Hiroshi; Shiokawa, Mai; Umetsu, Moeko; Morita, Tatsushi; Hasebe, Ayako; Otsu, Keiko; Asai, Tetsuo; Yamaguchi, Tomohiro; Makino, Shinji; Murata, Yoshiteru; Abi, Ahmad Jan; Omatsu, Tsutomu; Mizutani, Tetsuya
2018-05-31
Bovine abortion, diarrhea, and respiratory disease complexes, caused by infectious agents, result in high and significant economic losses for the cattle industry. These pathogens are likely transmitted by various vectors and reservoirs including insects, birds, and rodents. However, experimental data supporting this possibility are scarce. We collected 117 samples and screened them for 44 bovine abortive, diarrheal, and respiratory disease complex pathogens by using Dembo polymerase chain reaction (PCR), which is based on TaqMan real-time PCR. Fifty-seven samples were positive for at least one pathogen, including bovine viral diarrhea virus, bovine enterovirus, Salmonella enterica ser. Dublin, Salmonella enterica ser. Typhimurium, and Neospora caninum ; some samples were positive for multiple pathogens. Bovine viral diarrhea virus and bovine enterovirus were the most frequently detected pathogens, especially in flies, suggesting an important role of flies in the transmission of these viruses. Additionally, we detected the N. caninum genome from a cockroach sample for the first time. Our data suggest that insects (particularly flies), birds, and rodents are potential vectors and reservoirs of abortion, diarrhea, and respiratory infectious agents, and that they may transmit more than one pathogen at the same time.
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.
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.
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.
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
Best polynomial degree reduction on q-lattices with applications to q-orthogonal polynomials
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.
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.].
Best polynomial degree reduction on q-lattices with applications to q-orthogonal polynomials
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.
Directory of Open Access Journals (Sweden)
Le Goff Gilbert
2003-10-01
Full Text Available Abstract Background Members of the Anopheles gambiae complex are amongst the best malaria vectors in the world, but their vectorial capacities vary between species and populations. A large-scale sampling of An. gambiae sensu lato was carried out in various bioclimatic domains of Madagascar. Local abundance of an unexpected member of this complex raised questions regarding its role in malaria transmission. Methods Sampling took place at 38 sites and 2,067 females were collected. Species assessment was performed using a PCR targeting a sequence in the IGS of the rDNA. Analysis focused on the relative prevalence of the species per site, bioclimatic domain and altitude. Infectivity of Anopheles merus was assessed using an ELISA to detect the presence of malarial circumsporozoite protein in the head-thorax. Results Three species were identified: An. gambiae, Anopheles arabiensis and An. merus. The distribution of each species is mainly a function of bioclimatic domains and, to a lesser extent, altitude. An. arabiensis is present in all bioclimatic domains with highest prevalence in sub-humid, dry and sub-arid domains. An. gambiae has its highest prevalence in the humid domain, is in the minority in dry areas, rare in sub-humid and absent in sub-arid domains. An. merus is restricted to the coastal fringe in the south and west; it was in the majority in one southern village. The majority of sites were sympatric for at least two of the species (21/38 and two sites harboured all three species. The role of An. merus as malaria vector was confirmed in the case of two human-biting females, which were ELISA-positive for Plasmodium falciparum. Conclusion Despite the huge environmental (mainly man-made changes in Madagascar, the distribution of An. gambiae and An. arabiensis appears unchanged for the past 35 years. The distribution of An. merus is wider than was previously known, and its effectiveness as a malaria vector has been shown for the first time; this
Newell, Homer E
2006-01-01
When employed with skill and understanding, vector analysis can be a practical and powerful tool. This text develops the algebra and calculus of vectors in a manner useful to physicists and engineers. Numerous exercises (with answers) not only provide practice in manipulation but also help establish students' physical and geometric intuition in regard to vectors and vector concepts.Part I, the basic portion of the text, consists of a thorough treatment of vector algebra and the vector calculus. Part II presents the illustrative matter, demonstrating applications to kinematics, mechanics, and e
Hoffmann, Banesh
1975-01-01
From his unusual beginning in ""Defining a vector"" to his final comments on ""What then is a vector?"" author Banesh Hoffmann has written a book that is provocative and unconventional. In his emphasis on the unresolved issue of defining a vector, Hoffmann mixes pure and applied mathematics without using calculus. The result is a treatment that can serve as a supplement and corrective to textbooks, as well as collateral reading in all courses that deal with vectors. Major topics include vectors and the parallelogram law; algebraic notation and basic ideas; vector algebra; scalars and scalar p
Discrete-time state estimation for stochastic polynomial systems over polynomial observations
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.
Stabilisation of discrete-time polynomial fuzzy systems via a polynomial lyapunov approach
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.
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)
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
Mweya, Clement N; Kimera, Sharadhuli I; Karimuribo, Esron D; Mboera, Leonard E G
2013-07-01
We investigated mosquito sampling techniques with two types of traps and attractants at different time for trapping potential vectors for Rift Valley Fever virus. The study was conducted in six villages in Ngorongoro district in Tanzania from September to October 2012. A total of 1814 mosquitoes were collected, of which 738 were collected by CDC light traps and 1076 by Mosquito Magnet trapping technique. Of the collected mosquitoes, 12.46% (N = 226) were Aedes aegypti and 87.54% (N = 1588) were Culex pipiens complex. More mosquitoes were collected outdoors using Mosquito Magnets baited with octenol attractant, 36.38% (N =660) followed by indoor trapping using CDC light traps without attractant, 29.60% (N = 537). Most of Ae. aegypti mosquitoes were collected outdoor using Mosquito Magnets, 95% (N = 214) whereas Cx. pipiens complex were trapped both indoor using CDC light traps without attractant and outdoors using both CDC light traps baited with carbon dioxide (CO2) sachets and Mosquito Magnets. Analysis on the differences in abundance of mosquitoes trapped by different techniques using Generalized Linear Models was statistically significance at p-value < 0.05 for both species. Three hours mosquito collections show differing patterns in activity, most Ae. aegypti species were collected primarily during the first and last quarters of the day. Cx pipiens complex was active throughout the night, early evening and early morning then decreased markedly during the day time. The results presented in this paper emphasize the possibility of using Mosquito Magnets in order to efficiently capture these potential RVF vectors.
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.
Fast beampattern evaluation by polynomial rooting
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.
Amara Korba, Raouf; Alayat, Moufida Saoucen; Bouiba, Lazhari; Boudrissa, Abdelkarim; Bouslama, Zihad; Boukraa, Slimane; Francis, Frederic; Failloux, Anna-Bella; Boubidi, Saïd Chaouki
2016-08-17
We investigated the ecological differentiation of two members of the Culex pipiens complex, Cx. p. pipiens form pipiens and Cx. p. pipiens form molestus in three sites, El-Kala, M'Sila and Tinerkouk in Algeria. These two forms are the most widespread mosquito vectors in temperate regions exhibiting important behavioural and physiological differences. Nevertheless, this group of potential vectors has been poorly studied, particularly in North Africa. Ten larval populations of Cx. p. pipiens were sampled from various above- and underground habitats in three zones representing the three bioclimatic regions in Algeria. The reproduction characteristics were also investigated in the laboratory to define the rates of autogeny and stenogamy. Identification of Cx. p. pipiens members present in Algeria was achieved using a molecular analysis with the microsatellite CQ11 locus. We detected larvae of Cx. p. pipiens in all areas suggesting that the species is a ubiquitous mosquito well adapted to various environments. To our knowledge, this study provides the first molecular evidence of the presence of the Cx. p. pipiens form molestus and hybrids (molestus/pipiens) in Algeria with a high proportion of molestus form (48.3 %) in comparison with hybrids (36.8 %) and pipiens form (14.9 %). Some unexpected correlations between the proportion of forms pipiens, molestus and hybrids, and mosquito biological characteristics were observed suggesting some epigenetic effects controlling Cx. p. pipiens mating and reproduction. Consequences for pathogen transmission are discussed.
Twisted Polynomials and Forgery Attacks on GCM
DEFF Research Database (Denmark)
Abdelraheem, Mohamed Ahmed A. M. A.; Beelen, Peter; Bogdanov, Andrey
2015-01-01
Polynomial hashing as an instantiation of universal hashing is a widely employed method for the construction of MACs and authenticated encryption (AE) schemes, the ubiquitous GCM being a prominent example. It is also used in recent AE proposals within the CAESAR competition which aim at providing...... in an improved key recovery algorithm. As cryptanalytic applications of our twisted polynomials, we develop the first universal forgery attacks on GCM in the weak-key model that do not require nonce reuse. Moreover, we present universal weak-key forgeries for the nonce-misuse resistant AE scheme POET, which...
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....
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.
Parallel Optimization of Polynomials for Large-scale Problems in Stability and Control
Kamyar, Reza
In this thesis, we focus on some of the NP-hard problems in control theory. Thanks to the converse Lyapunov theory, these problems can often be modeled as optimization over polynomials. To avoid the problem of intractability, we establish a trade off between accuracy and complexity. In particular, we develop a sequence of tractable optimization problems --- in the form of Linear Programs (LPs) and/or Semi-Definite Programs (SDPs) --- whose solutions converge to the exact solution of the NP-hard problem. However, the computational and memory complexity of these LPs and SDPs grow exponentially with the progress of the sequence - meaning that improving the accuracy of the solutions requires solving SDPs with tens of thousands of decision variables and constraints. Setting up and solving such problems is a significant challenge. The existing optimization algorithms and software are only designed to use desktop computers or small cluster computers --- machines which do not have sufficient memory for solving such large SDPs. Moreover, the speed-up of these algorithms does not scale beyond dozens of processors. This in fact is the reason we seek parallel algorithms for setting-up and solving large SDPs on large cluster- and/or super-computers. We propose parallel algorithms for stability analysis of two classes of systems: 1) Linear systems with a large number of uncertain parameters; 2) Nonlinear systems defined by polynomial vector fields. First, we develop a distributed parallel algorithm which applies Polya's and/or Handelman's theorems to some variants of parameter-dependent Lyapunov inequalities with parameters defined over the standard simplex. The result is a sequence of SDPs which possess a block-diagonal structure. We then develop a parallel SDP solver which exploits this structure in order to map the computation, memory and communication to a distributed parallel environment. Numerical tests on a supercomputer demonstrate the ability of the algorithm to
Wolstenholme, E Œ
1978-01-01
Elementary Vectors, Third Edition serves as an introductory course in vector analysis and is intended to present the theoretical and application aspects of vectors. The book covers topics that rigorously explain and provide definitions, principles, equations, and methods in vector analysis. Applications of vector methods to simple kinematical and dynamical problems; central forces and orbits; and solutions to geometrical problems are discussed as well. This edition of the text also provides an appendix, intended for students, which the author hopes to bridge the gap between theory and appl
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)
Wall, Richard J; Roques, Magali; Katris, Nicholas J; Koreny, Ludek; Stanway, Rebecca R; Brady, Declan; Waller, Ross F; Tewari, Rita
2016-06-24
The SAS6-like (SAS6L) protein, a truncated paralogue of the ubiquitous basal body/centriole protein SAS6, has been characterised recently as a flagellum protein in trypanosomatids, but associated with the conoid in apicomplexan Toxoplasma. The conoid has been suggested to derive from flagella parts, but is thought to have been lost from some apicomplexans including the malaria-causing genus Plasmodium. Presence of SAS6L in Plasmodium, therefore, suggested a possible role in flagella assembly in male gametes, the only flagellated stage. Here, we have studied the expression and role of SAS6L throughout the Plasmodium life cycle using the rodent malaria model P. berghei. Contrary to a hypothesised role in flagella, SAS6L was absent during gamete flagellum formation. Instead, SAS6L was restricted to the apical complex in ookinetes and sporozoites, the extracellular invasive stages that develop within the mosquito vector. In these stages SAS6L forms an apical ring, as we show is also the case in Toxoplasma tachyzoites. The SAS6L ring was not apparent in blood-stage invasive merozoites, indicating that the apical complex is differentiated between the different invasive forms. Overall this study indicates that a conoid-associated apical complex protein and ring structure is persistent in Plasmodium in a stage-specific manner.
Nonclassical Orthogonal Polynomials and Corresponding Quadratures
Fukuda, H; Alt, E O; Matveenko, A V
2004-01-01
We construct nonclassical orthogonal polynomials and calculate abscissas and weights of Gaussian quadrature for arbitrary weight and interval. The program is written by Mathematica and it works if moment integrals are given analytically. The result is a FORTRAN subroutine ready to utilize the quadrature.
Intrinsic Diophantine approximation on general polynomial surfaces
DEFF Research Database (Denmark)
Tiljeset, Morten Hein
2017-01-01
We study the Hausdorff measure and dimension of the set of intrinsically simultaneously -approximable points on a curve, surface, etc, given as a graph of integer polynomials. We obtain complete answers to these questions for algebraically “nice” manifolds. This generalizes earlier work done...
Algebraic polynomial system solving and applications
Bleylevens, I.W.M.
2010-01-01
The problem of computing the solutions of a system of multivariate polynomial equations can be approached by the Stetter-Möller matrix method which casts the problem into a large eigenvalue problem. This Stetter-Möller matrix method forms the starting point for the development of computational
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.
Indecomposability of polynomials via Jacobian matrix
International Nuclear Information System (INIS)
Cheze, G.; Najib, S.
2007-12-01
Uni-multivariate decomposition of polynomials is a special case of absolute factorization. Recently, thanks to the Ruppert's matrix some effective results about absolute factorization have been improved. Here we show that with a jacobian matrix we can get sharper bounds for the special case of uni-multivariate decomposition. (author)
On selfadjoint functors satisfying polynomial relations
DEFF Research Database (Denmark)
Agerholm, Troels; Mazorchuk, Volodomyr
2011-01-01
We study selfadjoint functors acting on categories of finite dimen- sional modules over finite dimensional algebras with an emphasis on functors satisfying some polynomial relations. Selfadjoint func- tors satisfying several easy relations, in particular, idempotents and square roots of a sum...
Polynomial Variables and the Jacobian Problem
Indian Academy of Sciences (India)
algebra and algebraic geometry, and ... algebraically, to making the change of variables (X, Y) r--t. (X +p, Y ... aX + bY + p and eX + dY + q are linear polynomials in X, Y. ..... [5] T T Moh, On the Jacobian conjecture and the confipration of roots,.
Function approximation with polynomial regression slines
International Nuclear Information System (INIS)
Urbanski, P.
1996-01-01
Principles of the polynomial regression splines as well as algorithms and programs for their computation are presented. The programs prepared using software package MATLAB are generally intended for approximation of the X-ray spectra and can be applied in the multivariate calibration of radiometric gauges. (author)
Polynomial stabilization of some dissipative hyperbolic systems
Czech Academy of Sciences Publication Activity Database
Ammari, K.; Feireisl, Eduard; Nicaise, S.
2014-01-01
Roč. 34, č. 11 (2014), s. 4371-4388 ISSN 1078-0947 R&D Projects: GA ČR GA201/09/0917 Institutional support: RVO:67985840 Keywords : exponential stability * polynomial stability * observability inequality Subject RIV: BA - General Mathematics Impact factor: 0.826, year: 2014 http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=9924
Polynomial Asymptotes of the Second Kind
Dobbs, David E.
2011-01-01
This note uses the analytic notion of asymptotic functions to study when a function is asymptotic to a polynomial function. Along with associated existence and uniqueness results, this kind of asymptotic behaviour is related to the type of asymptote that was recently defined in a more geometric way. Applications are given to rational functions and…
Characteristic polynomials of linear polyacenes and their ...
Indian Academy of Sciences (India)
Coefficients of characteristic polynomials (CP) of linear polyacenes (LP) have been shown to be obtainable from Pascal's triangle by using a graph factorisation and squaring technique. Strong subspectrality existing among the members of the linear polyacene series has been shown from the derivation of the CP's. Thus it ...
Coherent states for polynomial su(2) algebra
International Nuclear Information System (INIS)
Sadiq, Muhammad; Inomata, Akira
2007-01-01
A class of generalized coherent states is constructed for a polynomial su(2) algebra in a group-free manner. As a special case, the coherent states for the cubic su(2) algebra are discussed. The states so constructed reduce to the usual SU(2) coherent states in the linear limit
Bernoulli Polynomials, Fourier Series and Zeta Numbers
DEFF Research Database (Denmark)
Scheufens, Ernst E
2013-01-01
Fourier series for Bernoulli polynomials are used to obtain information about values of the Riemann zeta function for integer arguments greater than one. If the argument is even we recover the well-known exact values, if the argument is odd we find integral representations and rapidly convergent...
Euler Polynomials, Fourier Series and Zeta Numbers
DEFF Research Database (Denmark)
Scheufens, Ernst E
2012-01-01
Fourier series for Euler polynomials is used to obtain information about values of the Riemann zeta function for integer arguments greater than one. If the argument is even we recover the well-known exact values, if the argument is odd we find integral representations and rapidly convergent series....
Automatic Control Systems Modeling by Volterra Polynomials
Directory of Open Access Journals (Sweden)
S. V. Solodusha
2012-01-01
Full Text Available The problem of the existence of the solutions of polynomial Volterra integral equations of the first kind of the second degree is considered. An algorithm of the numerical solution of one class of Volterra nonlinear systems of the first kind is developed. Numerical results for test examples are presented.
Spectral properties of birth-death polynomials
van Doorn, Erik A.
2015-01-01
We consider sequences of polynomials that are defined by a three-terms recurrence relation and orthogonal with respect to a positive measure on the nonnegative axis. By a famous result of Karlin and McGregor such sequences are instrumental in the analysis of birth-death processes. Inspired by
Spectral properties of birth-death polynomials
van Doorn, Erik A.
We consider sequences of polynomials that are defined by a three-terms recurrence relation and orthogonal with respect to a positive measure on the nonnegative axis. By a famous result of Karlin and McGregor such sequences are instrumental in the analysis of birth-death processes. Inspired by
Optimization of Cubic Polynomial Functions without Calculus
Taylor, Ronald D., Jr.; Hansen, Ryan
2008-01-01
In algebra and precalculus courses, students are often asked to find extreme values of polynomial functions in the context of solving an applied problem; but without the notion of derivative, something is lost. Either the functions are reduced to quadratics, since students know the formula for the vertex of a parabola, or solutions are…
transformation of independent variables in polynomial regression ...
African Journals Online (AJOL)
Ada
preferable when possible to work with a simple functional form in transformed variables rather than with a more complicated form in the original variables. In this paper, it is shown that linear transformations applied to independent variables in polynomial regression models affect the t ratio and hence the statistical ...
Inequalities for a Polynomial and its Derivative
Indian Academy of Sciences (India)
Annual Meetings · Mid Year Meetings · Discussion Meetings · Public Lectures · Lecture Workshops · Refresher Courses · Symposia · Live Streaming. Home; Journals; Proceedings – Mathematical Sciences; Volume 110; Issue 2. Inequalities for a Polynomial and its Derivative. V K Jain. Volume 110 Issue 2 May 2000 pp 137- ...
Integral Inequalities for Self-Reciprocal Polynomials
Indian Academy of Sciences (India)
Annual Meetings · Mid Year Meetings · Discussion Meetings · Public Lectures · Lecture Workshops · Refresher Courses · Symposia · Live Streaming. Home; Journals; Proceedings – Mathematical Sciences; Volume 120; Issue 2. Integral Inequalities for Self-Reciprocal Polynomials. Horst Alzer. Volume 120 Issue 2 April 2010 ...
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...
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...
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.
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.
Phase unwrapping algorithm using polynomial phase approximation and linear Kalman filter.
Kulkarni, Rishikesh; Rastogi, Pramod
2018-02-01
A noise-robust phase unwrapping algorithm is proposed based on state space analysis and polynomial phase approximation using wrapped phase measurement. The true phase is approximated as a two-dimensional first order polynomial function within a small sized window around each pixel. The estimates of polynomial coefficients provide the measurement of phase and local fringe frequencies. A state space representation of spatial phase evolution and the wrapped phase measurement is considered with the state vector consisting of polynomial coefficients as its elements. Instead of using the traditional nonlinear Kalman filter for the purpose of state estimation, we propose to use the linear Kalman filter operating directly with the wrapped phase measurement. The adaptive window width is selected at each pixel based on the local fringe density to strike a balance between the computation time and the noise robustness. In order to retrieve the unwrapped phase, either a line-scanning approach or a quality guided strategy of pixel selection is used depending on the underlying continuous or discontinuous phase distribution, respectively. Simulation and experimental results are provided to demonstrate the applicability of the proposed method.
Boukhalfa-Heniche, Fatima-Zohra; Hernández, Belén; Gaillard, Stéphane; Coïc, Yves-Marie; Huynh-Dinh, Tam; Lecouvey, Marc; Seksek, Olivier; Ghomi, Mahmoud
2004-04-15
Optical spectroscopic techniques such as CD, Raman scattering, and fluorescence imaging allowed us to analyze the complex formation and vectorization of a single-stranded 20-mer phosphorothioate oligodeoxynucleotide with a 15-mer amphipathic peptide at molecular and cellular levels. Different solvent mixtures (methanol and water) and molecular ratios of peptide/oligodeoxynucleotide complexes were tested in order to overcome the problems related to solubility. Optimal conditions for both spectroscopic and cellular experiments were obtained with the molecular ratio peptide/oligodeoxynucleotide equal to 21:4, corresponding to a 7:5 ratio for their respective +/- charge ratio. At the molecular level, CD and Raman spectra were consistent with a alpha-helix conformation of the peptide in water or in a methanol-water mixture. The presence of methanol increased considerably the solubility of the peptide without altering its alpha-helix conformation, as evidenced by CD and Raman spectroscopies. UV absorption melting profile of the oligodeoxynucleotide gave rise to a flat melting profile, corresponding to its random structure in solution. Raman spectra of oligodeoxynucleotide/peptide complexes could only be studied in methanol/water mixture solutions. Drastic changes observed in Raman spectra have undoubtedly shown: (a) the perturbation occurred in the peptide secondary structure, and (b) possible interaction between the lysine residues of the peptide and the oligodeoxynucleotide. At the cellular level, the complex was prepared in a mixture of 10% methanol and 90% cell medium. Cellular uptake in optimal conditions for the oligodeoxynucleotide delivery with low cytotoxicity was controlled by fluorescence imaging allowing to specifically locate the compacted oligonucleotide labeled with fluorescein at its 5'-terminus with the peptide into human glioma cells after 1 h of incubation at 37 degrees C. Copyright 2004 Wiley Periodicals, Inc.
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.
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
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
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.
Contributions to fuzzy polynomial techniques for stability analysis and control
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...
A general U-block model-based design procedure for nonlinear polynomial control systems
Zhu, Q. M.; Zhao, D. Y.; Zhang, Jianhua
2016-10-01
The proposition of U-model concept (in terms of 'providing concise and applicable solutions for complex problems') and a corresponding basic U-control design algorithm was originated in the first author's PhD thesis. The term of U-model appeared (not rigorously defined) for the first time in the first author's other journal paper, which established a framework for using linear polynomial control system design approaches to design nonlinear polynomial control systems (in brief, linear polynomial approaches → nonlinear polynomial plants). This paper represents the next milestone work - using linear state-space approaches to design nonlinear polynomial control systems (in brief, linear state-space approaches → nonlinear polynomial plants). The overall aim of the study is to establish a framework, defined as the U-block model, which provides a generic prototype for using linear state-space-based approaches to design the control systems with smooth nonlinear plants/processes described by polynomial models. For analysing the feasibility and effectiveness, sliding mode control design approach is selected as an exemplary case study. Numerical simulation studies provide a user-friendly step-by-step procedure for the readers/users with interest in their ad hoc applications. In formality, this is the first paper to present the U-model-oriented control system design in a formal way and to study the associated properties and theorems. The previous publications, in the main, have been algorithm-based studies and simulation demonstrations. In some sense, this paper can be treated as a landmark for the U-model-based research from intuitive/heuristic stage to rigour/formal/comprehensive studies.
Brand, Louis
2006-01-01
The use of vectors not only simplifies treatments of differential geometry, mechanics, hydrodynamics, and electrodynamics, but also makes mathematical and physical concepts more tangible and easy to grasp. This text for undergraduates was designed as a short introductory course to give students the tools of vector algebra and calculus, as well as a brief glimpse into these subjects' manifold applications. The applications are developed to the extent that the uses of the potential function, both scalar and vector, are fully illustrated. Moreover, the basic postulates of vector analysis are brou
On the evaluation at $(-\\iota,\\iota)$ of the Tutte polynomial of a binary matroid
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
A polynomial time algorithm for checking regularity of totally normed process algebra
Yang, F.; Huang, H.
2015-01-01
A polynomial algorithm for the regularity problem of weak and branching bisimilarity on totally normed process algebra (PA) processes is given. Its time complexity is O(n 3 +mn) O(n3+mn), where n is the number of transition rules and m is the maximal length of the rules. The algorithm works for
Cohen, Ayala; Nahum-Shani, Inbal; Doveh, Etti
2010-01-01
In their seminal paper, Edwards and Parry (1993) presented the polynomial regression as a better alternative to applying difference score in the study of congruence. Although this method is increasingly applied in congruence research, its complexity relative to other methods for assessing congruence (e.g., difference score methods) was one of the…
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
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.
On the Lorentz degree of a product of polynomials
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.
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.
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 ...
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 ...
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
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.
Approximating Exponential and Logarithmic Functions Using Polynomial Interpolation
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…
Degenerate r-Stirling Numbers and r-Bell Polynomials
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.
Invariance of the global monodromies in families of nondegenerate polynomials in two variables
International Nuclear Information System (INIS)
Son, Pham Tien
2009-07-01
We are interested in a global version of Le-Ramanujam μ-constant theorem for polynomials. We consider an analytic family {f s }, s element of [0, 1], of complex polynomials in two variables, that are Newton non-degenerate. We suppose that the Euler characteristic of a generic fiber is constant, then we show that the global monodromy fibrations of f s are all isomorphic, and that the degree of f s is constant (up to an algebraic automorphism of C 2 ). (author)
DEFF Research Database (Denmark)
2012-01-01
The present invention relates to a compact, reliable and low-cost vector velocimeter for example for determining velocities of particles suspended in a gas or fluid flow, or for determining velocity, displacement, rotation, or vibration of a solid surface, the vector velocimeter comprising a laser...
Amini, Ata; Shrimpton, Paul J; Muggleton, Stephen H; Sternberg, Michael J E
2007-12-01
Despite the increased recent use of protein-ligand and protein-protein docking in the drug discovery process due to the increases in computational power, the difficulty of accurately ranking the binding affinities of a series of ligands or a series of proteins docked to a protein receptor remains largely unsolved. This problem is of major concern in lead optimization procedures and has lead to the development of scoring functions tailored to rank the binding affinities of a series of ligands to a specific system. However, such methods can take a long time to develop and their transferability to other systems remains open to question. Here we demonstrate that given a suitable amount of background information a new approach using support vector inductive logic programming (SVILP) can be used to produce system-specific scoring functions. Inductive logic programming (ILP) learns logic-based rules for a given dataset that can be used to describe properties of each member of the set in a qualitative manner. By combining ILP with support vector machine regression, a quantitative set of rules can be obtained. SVILP has previously been used in a biological context to examine datasets containing a series of singular molecular structures and properties. Here we describe the use of SVILP to produce binding affinity predictions of a series of ligands to a particular protein. We also for the first time examine the applicability of SVILP techniques to datasets consisting of protein-ligand complexes. Our results show that SVILP performs comparably with other state-of-the-art methods on five protein-ligand systems as judged by similar cross-validated squares of their correlation coefficients. A McNemar test comparing SVILP to CoMFA and CoMSIA across the five systems indicates our method to be significantly better on one occasion. The ability to graphically display and understand the SVILP-produced rules is demonstrated and this feature of ILP can be used to derive hypothesis for
Large level crossings of a random polynomial
Directory of Open Access Journals (Sweden)
Kambiz Farahmand
1987-01-01
Full Text Available We know the expected number of times that a polynomial of degree n with independent random real coefficients asymptotically crosses the level K, when K is any real value such that (K2/nÃ¢Â†Â’0 as nÃ¢Â†Â’Ã¢ÂˆÂž. The present paper shows that, when K is allowed to be large, this expected number of crossings reduces to only one. The coefficients of the polynomial are assumed to be normally distributed. It is shown that it is sufficient to let KÃ¢Â‰Â¥exp(nf where f is any function of n such that fÃ¢Â†Â’Ã¢ÂˆÂž as nÃ¢Â†Â’Ã¢ÂˆÂž.
Sparse DOA estimation with polynomial rooting
DEFF Research Database (Denmark)
Xenaki, Angeliki; Gerstoft, Peter; Fernandez Grande, Efren
2015-01-01
Direction-of-arrival (DOA) estimation involves the localization of a few sources from a limited number of observations on an array of sensors. Thus, DOA estimation can be formulated as a sparse signal reconstruction problem and solved efficiently with compressive sensing (CS) to achieve highresol......Direction-of-arrival (DOA) estimation involves the localization of a few sources from a limited number of observations on an array of sensors. Thus, DOA estimation can be formulated as a sparse signal reconstruction problem and solved efficiently with compressive sensing (CS) to achieve...... highresolution imaging. Utilizing the dual optimal variables of the CS optimization problem, it is shown with Monte Carlo simulations that the DOAs are accurately reconstructed through polynomial rooting (Root-CS). Polynomial rooting is known to improve the resolution in several other DOA estimation methods...
On factorization of generalized Macdonald polynomials
International Nuclear Information System (INIS)
Kononov, Ya.; Morozov, A.
2016-01-01
A remarkable feature of Schur functions - the common eigenfunctions of cut-and-join operators from W ∞ - is that they factorize at the peculiar two-parametric topological locus in the space of time variables, which is known as the hook formula for quantum dimensions of representations of U q (SL N ) and which plays a big role in various applications. This factorization survives at the level of Macdonald polynomials. We look for its further generalization to generalized Macdonald polynomials (GMPs), associated in the same way with the toroidal Ding-Iohara-Miki algebras, which play the central role in modern studies in Seiberg-Witten-Nekrasov theory. In the simplest case of the first-coproduct eigenfunctions, where GMP depend on just two sets of time variables, we discover a weak factorization - on a one- (rather than four-) parametric slice of the topological locus, which is already a very non-trivial property, calling for proof and better understanding. (orig.)
Quantum Hurwitz numbers and Macdonald polynomials
Harnad, J.
2016-11-01
Parametric families in the center Z(C[Sn]) of the group algebra of the symmetric group are obtained by identifying the indeterminates in the generating function for Macdonald polynomials as commuting Jucys-Murphy elements. Their eigenvalues provide coefficients in the double Schur function expansion of 2D Toda τ-functions of hypergeometric type. Expressing these in the basis of products of power sum symmetric functions, the coefficients may be interpreted geometrically as parametric families of quantum Hurwitz numbers, enumerating weighted branched coverings of the Riemann sphere. Combinatorially, they give quantum weighted sums over paths in the Cayley graph of Sn generated by transpositions. Dual pairs of bases for the algebra of symmetric functions with respect to the scalar product in which the Macdonald polynomials are orthogonal provide both the geometrical and combinatorial significance of these quantum weighted enumerative invariants.
Polynomial structures in one-loop amplitudes
International Nuclear Information System (INIS)
Britto, Ruth; Feng Bo; Yang Gang
2008-01-01
A general one-loop scattering amplitude may be expanded in terms of master integrals. The coefficients of the master integrals can be obtained from tree-level input in a two-step process. First, use known formulas to write the coefficients of (4-2ε)-dimensional master integrals; these formulas depend on an additional variable, u, which encodes the dimensional shift. Second, convert the u-dependent coefficients of (4-2ε)-dimensional master integrals to explicit coefficients of dimensionally shifted master integrals. This procedure requires the initial formulas for coefficients to have polynomial dependence on u. Here, we give a proof of this property in the case of massless propagators. The proof is constructive. Thus, as a byproduct, we produce different algebraic expressions for the scalar integral coefficients, in which the polynomial property is apparent. In these formulas, the box and pentagon contributions are separated explicitly.
Energy Technology Data Exchange (ETDEWEB)
Li, Jun; Jiang, Bin; Guo, Hua, E-mail: hguo@unm.edu [Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131 (United States)
2013-11-28
A rigorous, general, and simple method to fit global and permutation invariant potential energy surfaces (PESs) using neural networks (NNs) is discussed. This so-called permutation invariant polynomial neural network (PIP-NN) method imposes permutation symmetry by using in its input a set of symmetry functions based on PIPs. For systems with more than three atoms, it is shown that the number of symmetry functions in the input vector needs to be larger than the number of internal coordinates in order to include both the primary and secondary invariant polynomials. This PIP-NN method is successfully demonstrated in three atom-triatomic reactive systems, resulting in full-dimensional global PESs with average errors on the order of meV. These PESs are used in full-dimensional quantum dynamical calculations.
Link polynomial, crossing multiplier and surgery formula
International Nuclear Information System (INIS)
Deguchi, Tetsuo; Yamada, Yasuhiko.
1989-01-01
Relations between link polynomials constructed from exactly solvable lattice models and topological field theory are reviewed. It is found that the surgery formula for a three-sphere S 3 with Wilson lines corresponds to the Markov trace constructed from the exactly solvable models. This indicates that knot theory intimately relates various important subjects such as exactly solvable models, conformal field theories and topological quantum field theories. (author)
Completeness of the ring of polynomials
DEFF Research Database (Denmark)
Thorup, Anders
2015-01-01
Consider the polynomial ring R:=k[X1,…,Xn]R:=k[X1,…,Xn] in n≥2n≥2 variables over an uncountable field k. We prove that R is complete in its adic topology, that is, the translation invariant topology in which the non-zero ideals form a fundamental system of neighborhoods of 0. In addition we pro...
Moments, positive polynomials and their applications
Lasserre, Jean Bernard
2009-01-01
Many important applications in global optimization, algebra, probability and statistics, applied mathematics, control theory, financial mathematics, inverse problems, etc. can be modeled as a particular instance of the Generalized Moment Problem (GMP) . This book introduces a new general methodology to solve the GMP when its data are polynomials and basic semi-algebraic sets. This methodology combines semidefinite programming with recent results from real algebraic geometry to provide a hierarchy of semidefinite relaxations converging to the desired optimal value. Applied on appropriate cones,
Polynomials and identities on real Banach spaces
Czech Academy of Sciences Publication Activity Database
Hájek, Petr Pavel; Kraus, M.
2012-01-01
Roč. 385, č. 2 (2012), s. 1015-1026 ISSN 0022-247X R&D Projects: GA ČR(CZ) GAP201/11/0345 Institutional research plan: CEZ:AV0Z10190503 Keywords : Polynomials on Banach spaces Subject RIV: BA - General Mathematics Impact factor: 1.050, year: 2012 http://www.sciencedirect.com/science/article/pii/S0022247X11006743
Eye aberration analysis with Zernike polynomials
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.
Directory of Open Access Journals (Sweden)
Guillermo E. Alvarado
2013-08-01
Full Text Available Over the last forty years, research has revealed the importance of magma mixing as a trigger for volcanic eruptions, as well as its role in creating the diversity of magma compositions in arcs. Sensitive isotopic and microchemical techniques can reveal subtle evidence of magma mixing in igneous rocks, but more robust statistical techniques for bulk chemical data can help evaluate complex mixing relationships. Polytopic vector analysis (PVA is a multivariate technique that can be used to evaluate suites of samples that are produced by mixing of two or more magma batches. The Papagayo Tuff of the Miocene-Pleistocene Bagaces Formation in northern Costa Rica is associated with a segment of the Central American Volcanic Arc. While this segment of the arc is located on oceanic plateau, recent (<8 Ma ignimbrites bear the chemical signatures of upper continental crust, marking the transition from oceanic to continental crust. The Papagayo Tuff contains banded pumice fragments consistent with one or more episodes of mixing/mingling to produce a single volcanic deposit. The PVA solution for the sample set is consistent with observations from bulk chemistry, microchemistry and petrographic data from the rocks. However, without PVA, the unequivocal identification of the three end-member solution would not have been possible.
Directory of Open Access Journals (Sweden)
Jude Pavillupillai J
2010-11-01
Full Text Available Abstract Background Anopheles subpictus sensu lato, a widespread malaria vector in Asia, is reportedly composed of four sibling species A - D. Mosquitoes morphologically identified as belonging to the Subpictus complex were collected from different locations near the east coast of Sri Lanka, and specific ribosomal DNA sequences determined to validate their taxonomic status. Methods Anopheles subpictus s.l. larvae and blood-fed adults were collected from different locations in the Eastern province and their sibling species status was determined based on published morphological characteristics. DNA sequences of the D3 domain of 28 S ribosomal DNA (rDNA and the internal transcribed spacer -2 (ITS-2 of mosquitoes morphologically identified as An. subpictus sibling species A, B, C and D were determined. Results Phylogenetic analysis based on D3 domain of rDNA resulted in two clades: one clade with mosquitoes identified as An. subpictus species A, C, D and some mosquitoes identified as species B, and another clade with a majority of mosquitoes identified as species B with D3 sequences that were identical to Anopheles sundaicus cytotype D. Analysis of ITS-2 sequences confirmed a close relationship between a majority of mosquitoes identified as An. subpictus B with members of the An. sundaicus complex and others identified as An. subpictus B with An. subpictus s.l. Conclusions The study suggests that published morphological characteristics are not specific enough to identify some members of the Subpictus complex, particularly species B. The sequences of the ITS-2 and D3 domain of rDNA suggest that a majority that were identified morphologically as An. subpictus species B in the east coast of Sri Lanka, and some identified elsewhere in SE Asia as An. subpictus s.l., are in fact members of the Sundaicus complex based on genetic similarity to An. sundaicus s.l. In view of the well-known ability of An. sundaicus s.l. to breed in brackish and fresh water and
Guilfoyle, Richard A.; Smith, Lloyd M.
1994-01-01
A vector comprising a filamentous phage sequence containing a first copy of filamentous phage gene X and other sequences necessary for the phage to propagate is disclosed. The vector also contains a second copy of filamentous phage gene X downstream from a promoter capable of promoting transcription in a bacterial host. In a preferred form of the present invention, the filamentous phage is M13 and the vector additionally includes a restriction endonuclease site located in such a manner as to substantially inactivate the second gene X when a DNA sequence is inserted into the restriction site.
Guilfoyle, R.A.; Smith, L.M.
1994-12-27
A vector comprising a filamentous phage sequence containing a first copy of filamentous phage gene X and other sequences necessary for the phage to propagate is disclosed. The vector also contains a second copy of filamentous phage gene X downstream from a promoter capable of promoting transcription in a bacterial host. In a preferred form of the present invention, the filamentous phage is M13 and the vector additionally includes a restriction endonuclease site located in such a manner as to substantially inactivate the second gene X when a DNA sequence is inserted into the restriction site. 2 figures.
Flowchart Programs, Regular Expressions, and Decidability of Polynomial Growth-Rate
Ben-Amram, Amir M.; Pineles, Aviad
2014-01-01
We present a new method for inferring complexity properties for a class of programs in the form of flowcharts annotated with loop information. Specifically, our method can (soundly and completely) decide if computed values are polynomially bounded as a function of the input; and similarly for the running time. Such complexity properties are undecidable for a Turing-complete programming language, and a common work-around in program analysis is to settle for sound but incomplete solutions. In ...
Levine, Robert
2004-01-01
The cross-product is a mathematical operation that is performed between two 3-dimensional vectors. The result is a vector that is orthogonal or perpendicular to both of them. Learning about this for the first time while taking Calculus-III, the class was taught that if AxB = AxC, it does not necessarily follow that B = C. This seemed baffling. The…
A General Representation Theorem for Integrated Vector Autoregressive Processes
DEFF Research Database (Denmark)
Franchi, Massimo
We study the algebraic structure of an I(d) vector autoregressive process, where d is restricted to be an integer. This is useful to characterize its polynomial cointegrating relations and its moving average representation, that is to prove a version of the Granger representation theorem valid...
Polynomial-time computability of the edge-reliability of graphs using Gilbert's formula
Directory of Open Access Journals (Sweden)
Marlowe Thomas J.
1998-01-01
Full Text Available Reliability is an important consideration in analyzing computer and other communication networks, but current techniques are extremely limited in the classes of graphs which can be analyzed efficiently. While Gilbert's formula establishes a theoretically elegant recursive relationship between the edge reliability of a graph and the reliability of its subgraphs, naive evaluation requires consideration of all sequences of deletions of individual vertices, and for many graphs has time complexity essentially Θ (N!. We discuss a general approach which significantly reduces complexity, encoding subgraph isomorphism in a finer partition by invariants, and recursing through the set of invariants. We illustrate this approach using threshhold graphs, and show that any computation of reliability using Gilbert's formula will be polynomial-time if and only if the number of invariants considered is polynomial; we then show families of graphs with polynomial-time, and non-polynomial reliability computation, and show that these encompass most previously known results. We then codify our approach to indicate how it can be used for other classes of graphs, and suggest several classes to which the technique can be applied.
Mahmood, Zahid; Ning, Huansheng; Ghafoor, AtaUllah
2017-03-24
Wireless Sensor Networks (WSNs) consist of lightweight devices to measure sensitive data that are highly vulnerable to security attacks due to their constrained resources. In a similar manner, the internet-based lightweight devices used in the Internet of Things (IoT) are facing severe security and privacy issues because of the direct accessibility of devices due to their connection to the internet. Complex and resource-intensive security schemes are infeasible and reduce the network lifetime. In this regard, we have explored the polynomial distribution-based key establishment schemes and identified an issue that the resultant polynomial value is either storage intensive or infeasible when large values are multiplied. It becomes more costly when these polynomials are regenerated dynamically after each node join or leave operation and whenever key is refreshed. To reduce the computation, we have proposed an Efficient Key Management (EKM) scheme for multiparty communication-based scenarios. The proposed session key management protocol is established by applying a symmetric polynomial for group members, and the group head acts as a responsible node. The polynomial generation method uses security credentials and secure hash function. Symmetric cryptographic parameters are efficient in computation, communication, and the storage required. The security justification of the proposed scheme has been completed by using Rubin logic, which guarantees that the protocol attains mutual validation and session key agreement property strongly among the participating entities. Simulation scenarios are performed using NS 2.35 to validate the results for storage, communication, latency, energy, and polynomial calculation costs during authentication, session key generation, node migration, secure joining, and leaving phases. EKM is efficient regarding storage, computation, and communication overhead and can protect WSN-based IoT infrastructure.
On the complex oscillation of differential polynomials generated by ...
Indian Academy of Sciences (India)
x := max{0, log x}. Assume that n(r, f ) counts the number of poles of f in |z| ≤ r, each pole according to its multiplicity, and that. ¯n(r, f ) counts the number of distinct poles of f in |z| ≤ r, ignoring the multiplicity. The characteristic function of f is defined by. T (r, f ) := m(r, f ) + N (r, f ), where. N (r, f ) := ∫ r. 0 n(t, f ) − n(0,f) t dt + n(0 ...
Exponential Time Complexity of the Permanent and the Tutte Polynomial
DEFF Research Database (Denmark)
Dell, Holger; Husfeldt, Thore; Marx, Dániel
2014-01-01
bounds are relative to (variants of) the Exponential Time Hypothesis (ETH), which says that the satisfiability of n-variable 3-CNF formulas cannot be decided in time exp(o(n)). We relax this hypothesis by introducing its counting version #ETH; namely, that the satisfying assignments cannot be counted......We show conditional lower bounds for well-studied #P-hard problems: The number of satisfying assignments of a 2-CNF formula with n variables cannot be computed in time exp(o(n)), and the same is true for computing the number of all independent sets in an n-vertex graph. The permanent of an n× n...
Inverse kinematics algorithm for a six-link manipulator using a polynomial expression
International Nuclear Information System (INIS)
Sasaki, Shinobu
1987-01-01
This report is concerned with the forward and inverse kinematics problem relevant to a six-link robot manipulator. In order to derive the kinematic relationships between links, the vector rotation operator was applied instead of the conventional homogeneous transformation. The exact algorithm for solving the inverse problem was obtained by transforming kinematics equations into a polynomial. As shown in test calculations, the accuracies of numerical solutions obtained by means of the present approach are found to be quite high. The algorithm proposed permits to find out all feasible solutions for the given inverse problem. (author)
A Polynomial Estimate of Railway Line Delay
DEFF Research Database (Denmark)
Cerreto, Fabrizio; Harrod, Steven; Nielsen, Otto Anker
2017-01-01
Railway service may be measured by the aggregate delay over a time horizon or due to an event. Timetables for railway service may dampen aggregate delay by addition of additional process time, either supplement time or buffer time. The evaluation of these variables has previously been performed...... by numerical analysis with simulation. This paper proposes an analytical estimate of aggregate delay with a polynomial form. The function returns the aggregate delay of a railway line resulting from an initial, primary, delay. Analysis of the function demonstrates that there should be a balance between the two...
Conditional Density Approximations with Mixtures of Polynomials
DEFF Research Database (Denmark)
Varando, Gherardo; López-Cruz, Pedro L.; Nielsen, Thomas Dyhre
2015-01-01
Mixtures of polynomials (MoPs) are a non-parametric density estimation technique especially designed for hybrid Bayesian networks with continuous and discrete variables. Algorithms to learn one- and multi-dimensional (marginal) MoPs from data have recently been proposed. In this paper we introduce...... two methods for learning MoP approximations of conditional densities from data. Both approaches are based on learning MoP approximations of the joint density and the marginal density of the conditioning variables, but they differ as to how the MoP approximation of the quotient of the two densities...
Itoh, Shoji; Sugihara, Masaaki
2016-01-01
We present a theorem that defines the direction of a preconditioned system for the bi-conjugate gradient (BiCG) method, and we extend it to preconditioned bi-Lanczos-type algorithms. We show that the direction of a preconditioned system is switched by construction and by the settings of the initial shadow residual vector. We analyze and compare the polynomial structures of four preconditioned BiCG algorithms.
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
Parallel multigrid smoothing: polynomial versus Gauss-Seidel
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.
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.
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
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
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
Czech Academy of Sciences Publication Activity Database
Knížek, J.; Tichý, Petr; Beránek, L.; Šindelář, Jan; Vojtěšek, B.; Bouchal, P.; Nenutil, R.; Dedík, O.
2010-01-01
Roč. 7, č. 10 (2010), s. 48-60 ISSN 0974-5718 Grant - others:GA MZd(CZ) NS9812; GA ČR(CZ) GAP304/10/0868 Institutional research plan: CEZ:AV0Z10300504; CEZ:AV0Z10750506 Keywords : polynomial regression * orthogonalization * numerical methods * markers * biomarkers Subject RIV: BA - General Mathematics
Multiple Meixner polynomials and non-Hermitian oscillator Hamiltonians
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...
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].
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.
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
Applications of polynomial optimization in financial risk investment
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.
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 ...
Gamow-Jordan vectors and non-reducible density operators from higher-order S-matrix poles
International Nuclear Information System (INIS)
Bohm, A.; Loewe, M.; Maxson, S.; Patuleanu, P.; Puentmann, C.; Gadella, M.
1997-01-01
In analogy to Gamow vectors that are obtained from first-order resonance poles of the S-matrix, one can also define higher-order Gamow vectors which are derived from higher-order poles of the S-matrix. An S-matrix pole of r-th order at z R =E R -iΓ/2 leads to r generalized eigenvectors of order k=0,1,hor-ellipsis,r-1, which are also Jordan vectors of degree (k+1) with generalized eigenvalue (E R -iΓ/2). The Gamow-Jordan vectors are elements of a generalized complex eigenvector expansion, whose form suggests the definition of a state operator (density matrix) for the microphysical decaying state of this higher-order pole. This microphysical state is a mixture of non-reducible components. In spite of the fact that the k-th order Gamow-Jordan vectors has the polynomial time-dependence which one always associates with higher-order poles, the microphysical state obeys a purely exponential decay law. copyright 1997 American Institute of Physics
Simulation of aspheric tolerance with polynomial fitting
Li, Jing; Cen, Zhaofeng; Li, Xiaotong
2018-01-01
The shape of the aspheric lens changes caused by machining errors, resulting in a change in the optical transfer function, which affects the image quality. At present, there is no universally recognized tolerance criterion standard for aspheric surface. To study the influence of aspheric tolerances on the optical transfer function, the tolerances of polynomial fitting are allocated on the aspheric surface, and the imaging simulation is carried out by optical imaging software. Analysis is based on a set of aspheric imaging system. The error is generated in the range of a certain PV value, and expressed as a form of Zernike polynomial, which is added to the aspheric surface as a tolerance term. Through optical software analysis, the MTF of optical system can be obtained and used as the main evaluation index. Evaluate whether the effect of the added error on the MTF of the system meets the requirements of the current PV value. Change the PV value and repeat the operation until the acceptable maximum allowable PV value is obtained. According to the actual processing technology, consider the error of various shapes, such as M type, W type, random type error. The new method will provide a certain development for the actual free surface processing technology the reference value.
Quadratic polynomial interpolation on triangular domain
Li, Ying; Zhang, Congcong; Yu, Qian
2018-04-01
In the simulation of natural terrain, the continuity of sample points are not in consonance with each other always, traditional interpolation methods often can't faithfully reflect the shape information which lie in data points. So, a new method for constructing the polynomial interpolation surface on triangular domain is proposed. Firstly, projected the spatial scattered data points onto a plane and then triangulated them; Secondly, A C1 continuous piecewise quadric polynomial patch was constructed on each vertex, all patches were required to be closed to the line-interpolation one as far as possible. Lastly, the unknown quantities were gotten by minimizing the object functions, and the boundary points were treated specially. The result surfaces preserve as many properties of data points as possible under conditions of satisfying certain accuracy and continuity requirements, not too convex meantime. New method is simple to compute and has a good local property, applicable to shape fitting of mines and exploratory wells and so on. The result of new surface is given in experiments.
On factorization of generalized Macdonald polynomials
Energy Technology Data Exchange (ETDEWEB)
Kononov, Ya. [Landau Institute for Theoretical Physics, Chernogolovka (Russian Federation); HSE, Math Department, Moscow (Russian Federation); Morozov, A. [ITEP, Moscow (Russian Federation); Institute for Information Transmission Problems, Moscow (Russian Federation); National Research Nuclear University MEPhI, Moscow (Russian Federation)
2016-08-15
A remarkable feature of Schur functions - the common eigenfunctions of cut-and-join operators from W{sub ∞} - is that they factorize at the peculiar two-parametric topological locus in the space of time variables, which is known as the hook formula for quantum dimensions of representations of U{sub q}(SL{sub N}) and which plays a big role in various applications. This factorization survives at the level of Macdonald polynomials. We look for its further generalization to generalized Macdonald polynomials (GMPs), associated in the same way with the toroidal Ding-Iohara-Miki algebras, which play the central role in modern studies in Seiberg-Witten-Nekrasov theory. In the simplest case of the first-coproduct eigenfunctions, where GMP depend on just two sets of time variables, we discover a weak factorization - on a one- (rather than four-) parametric slice of the topological locus, which is already a very non-trivial property, calling for proof and better understanding. (orig.)
Positive trigonometric polynomials and signal processing applications
Dumitrescu, Bogdan
2017-01-01
This revised edition is made up of two parts: theory and applications. Though many of the fundamental results are still valid and used, new and revised material is woven throughout the text. As with the original book, the theory of sum-of-squares trigonometric polynomials is presented unitarily based on the concept of Gram matrix (extended to Gram pair or Gram set). The programming environment has also evolved, and the books examples are changed accordingly. The applications section is organized as a collection of related problems that use systematically the theoretical results. All the problems are brought to a semi-definite programming form, ready to be solved with algorithms freely available, like those from the libraries SeDuMi, CVX and Pos3Poly. A new chapter discusses applications in super-resolution theory, where Bounded Real Lemma for trigonometric polynomials is an important tool. This revision is written to be more appealing and easier to use for new readers. < Features updated information on LMI...
On factorization of generalized Macdonald polynomials
Kononov, Ya.; Morozov, A.
2016-08-01
A remarkable feature of Schur functions—the common eigenfunctions of cut-and-join operators from W_∞ —is that they factorize at the peculiar two-parametric topological locus in the space of time variables, which is known as the hook formula for quantum dimensions of representations of U_q(SL_N) and which plays a big role in various applications. This factorization survives at the level of Macdonald polynomials. We look for its further generalization to generalized Macdonald polynomials (GMPs), associated in the same way with the toroidal Ding-Iohara-Miki algebras, which play the central role in modern studies in Seiberg-Witten-Nekrasov theory. In the simplest case of the first-coproduct eigenfunctions, where GMP depend on just two sets of time variables, we discover a weak factorization—on a one- (rather than four-) parametric slice of the topological locus, which is already a very non-trivial property, calling for proof and better understanding.
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.
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.
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.
Robinson, Gilbert de B
2011-01-01
This brief undergraduate-level text by a prominent Cambridge-educated mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement for Gilbert de B. Robinson's text, which is the result of several years of teaching and learning the most effective methods from discussions with students. Topics include lines and planes, determinants and linear equations, matrices, groups and linear transformations, and vectors and vector spaces. Additional subjects range from conics and quadrics to homogeneous coordinates and projective geom
Geometry of polynomials and root-finding via path-lifting
Kim, Myong-Hi; Martens, Marco; Sutherland, Scott
2018-02-01
Using the interplay between topological, combinatorial, and geometric properties of polynomials and analytic results (primarily the covering structure and distortion estimates), we analyze a path-lifting method for finding approximate zeros, similar to those studied by Smale, Shub, Kim, and others. Given any polynomial, this simple algorithm always converges to a root, except on a finite set of initial points lying on a circle of a given radius. Specifically, the algorithm we analyze consists of iterating where the t k form a decreasing sequence of real numbers and z 0 is chosen on a circle containing all the roots. We show that the number of iterates required to locate an approximate zero of a polynomial f depends only on log\\vert f(z_0)/ρ_\\zeta\\vert (where ρ_\\zeta is the radius of convergence of the branch of f-1 taking 0 to a root ζ) and the logarithm of the angle between f(z_0) and certain critical values. Previous complexity results for related algorithms depend linearly on the reciprocals of these angles. Note that the complexity of the algorithm does not depend directly on the degree of f, but only on the geometry of the critical values. Furthermore, for any polynomial f with distinct roots, the average number of steps required over all starting points taken on a circle containing all the roots is bounded by a constant times the average of log(1/ρ_\\zeta) . The average of log(1/ρ_\\zeta) over all polynomials f with d roots in the unit disk is \
AMDLIBAE, IBM 360 Subroutine Library, Special Function, Polynomials, Differential Equation
International Nuclear Information System (INIS)
Wang, Jesse Y.
1980-01-01
Description of problem or function: AMDLIBAE is a subset of the IBM 360 Subroutine Library at the Applied Mathematics Division at Argonne National Laboratory. This subset includes library categories A-E: Identification/Description: A152S A MPA: Mult. prec. floating point arith. package; B156S A ARSIN: Arcsine, arccosine; B158S A DSIN/DCOS: DP sine, cosine; B159S A DTAN/DCOT: DP tangent, cotangent; B252S A SINH/COSH: Hyperbolic sine, cosine; B353S A ALOG: SP logarithm; B354S A DEXP: DP exponential; B355S A DLOG: DP logarithm; B456S A DCUBRT: DP cube root; B457S A ARGPOWER: X Y ; B458S A ARGFDXPD: DP X Y ; C150S F DQD: Q. D. algorithm applied to a power series; C151S F DCONF1: Eval. cont. fract. Q. D. of power series; C250S F CUBIC: Roots of cubic polynomial equation; C251S F QUARTIC: Roots of quartic polynomial equation; C252S F RSSR: All roots of poly eqs. with real coef.; C253S F POLDRV: Driver for C254S; C254S F CPOLY: Roots arb. poly. Jenkins-Traub algorithm; C353S F1 CLEBSH: Ang. mom. coef. - Clebsch, Racah, Wigner; C365S A ALGAMA: Logarithm of the gamma function; C366S A DGAMMA/DLGAMA: DP gamma and log(gamma) functions; C368S F EONE: Exponential integral E1; C370S F BESJY: Bessel functions J and Y; C371S F BESIK: Bessel functions I and K; C372S F CHIPRB: Chi-square integral; C380S F DRZETA: Long precision zeta, zeta-1 functions; C382S F DCGAM: Long precision complex gamma; C383S A DERF/DERFC: DP error function; C384S F BFJ1: Bessel function J1; C385S F COULMB: Regular Coulomb wave functions; C386S F1 DSGMAL: Coulomb phase shift; C387S F BFJYR: Bessel functions J0,J1,Y0,Y1; C388S F IRCOUL: LP irregular Coulomb wave functions; C389S F GAMIN: Incomplete gamma function; C390S F LQ: Assoc. Legendre functions of 2. kind; C392S A DAERF: Inverse error function; C393S F CDEONE: Modified complex exponential integral; D153S F DROMB: Two-dimensional Romberg quadrature; D153S P DROMBP: Two-dimensional Romberg quadrature; D158S F ANC4: Adap. quad. using 4. order Newton
Directory of Open Access Journals (Sweden)
Tsugio Fukuchi
2014-06-01
Full Text Available The finite difference method (FDM based on Cartesian coordinate systems can be applied to numerical analyses over any complex domain. A complex domain is usually taken to mean that the geometry of an immersed body in a fluid is complex; here, it means simply an analytical domain of arbitrary configuration. In such an approach, we do not need to treat the outer and inner boundaries differently in numerical calculations; both are treated in the same way. Using a method that adopts algebraic polynomial interpolations in the calculation around near-wall elements, all the calculations over irregular domains reduce to those over regular domains. Discretization of the space differential in the FDM is usually derived using the Taylor series expansion; however, if we use the polynomial interpolation systematically, exceptional advantages are gained in deriving high-order differences. In using the polynomial interpolations, we can numerically solve the Poisson equation freely over any complex domain. Only a particular type of partial differential equation, Poisson's equations, is treated; however, the arguments put forward have wider generality in numerical calculations using the FDM.
Thomas, E. G. F.
2012-01-01
This paper deals with the theory of integration of scalar functions with respect to a measure with values in a, not necessarily locally convex, topological vector space. It focuses on the extension of such integrals from bounded measurable functions to the class of integrable functions, proving
Kernel polynomial method for a nonorthogonal electronic-structure calculation of amorphous diamond
International Nuclear Information System (INIS)
Roeder, H.; Silver, R.N.; Drabold, D.A.; Dong, J.J.
1997-01-01
The Kernel polynomial method (KPM) has been successfully applied to tight-binding electronic-structure calculations as an O(N) method. Here we extend this method to nonorthogonal basis sets with a sparse overlap matrix S and a sparse Hamiltonian H. Since the KPM method utilizes matrix vector multiplications it is necessary to apply S -1 H onto a vector. The multiplication of S -1 is performed using a preconditioned conjugate-gradient method and does not involve the explicit inversion of S. Hence the method scales the same way as the original KPM method, i.e., O(N), although there is an overhead due to the additional conjugate-gradient part. We apply this method to a large scale electronic-structure calculation of amorphous diamond. copyright 1997 The American Physical Society
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
Directory of Open Access Journals (Sweden)
Spinner Justin L
2012-12-01
Full Text Available Abstract Background Toxin complex (Tc family proteins were first identified as insecticidal toxins in Photorhabdus luminescens and have since been found in a wide range of bacteria. The genome of Yersinia pestis, the causative agent of bubonic plague, contains a locus that encodes the Tc protein homologues YitA, YitB, YitC, and YipA and YipB. Previous microarray data indicate that the Tc genes are highly upregulated by Y. pestis while in the flea vector; however, their role in the infection of fleas and pathogenesis in the mammalian host is unclear. Results We show that the Tc proteins YitA and YipA are highly produced by Y. pestis while in the flea but not during growth in brain heart infusion (BHI broth at the same temperature. Over-production of the LysR-type regulator YitR from an exogenous plasmid increased YitA and YipA synthesis in broth culture. The increase in production of YitA and YipA correlated with the yitR copy number and was temperature-dependent. Although highly synthesized in fleas, deletion of the Tc proteins did not alter survival of Y. pestis in the flea or prevent blockage of the proventriculus. Furthermore, YipA was found to undergo post-translational processing and YipA and YitA are localized to the outer membrane of Y. pestis. YitA was also detected by immunofluorescence microscopy on the surface of Y. pestis. Both YitA and YipA are produced maximally at low temperature but persist for several hours after transfer to 37°C. Conclusions Y. pestis Tc proteins are highly expressed in the flea but are not essential for Y. pestis to stably infect or produce a transmissible infection in the flea. However, YitA and YipA localize to the outer membrane and YitA is exposed on the surface, indicating that at least YitA is present on the surface when Y. pestis is transmitted into the mammalian host from the flea.
Flat structure and potential vector fields related with algebraic solutions to Painlevé VI equation
Directory of Open Access Journals (Sweden)
Mitsuo Kato
2018-01-01
Full Text Available A potential vector field is a solution of an extended WDVV equation which is a generalization of a WDVV equation. It is expected that potential vector fields corresponding to algebraic solutions of Painlevé VI equation can be written by using polynomials or algebraic functions explicitly. The purpose of this paper is to construct potential vector fields corresponding to more than thirty non-equivalent algebraic solutions.
Differential operators associated with Hermite polynomials
International Nuclear Information System (INIS)
Onyango Otieno, V.P.
1989-09-01
This paper considers the boundary value problems for the Hermite differential equation -(e -x2 y'(x))'+e -x2 y(x)=λe -x2 y(x), (x is an element of (-∞, ∞)) in both the so-called right-definite and left-definite cases based partly on a classical approach due to E.C. Titchmarsh. We then link the Titchmarsh approach with operator theoretic results in the spaces L w 2 (-∞, ∞) and H p,q 2 (-∞, ∞). The results in the left-definite case provide an indirect proof of the completeness of the Hermite polynomials in L w 2 (-∞, ∞). (author). 17 refs
Kaporin, I. E.
2012-02-01
In order to precondition a sparse symmetric positive definite matrix, its approximate inverse is examined, which is represented as the product of two sparse mutually adjoint triangular matrices. In this way, the solution of the corresponding system of linear algebraic equations (SLAE) by applying the preconditioned conjugate gradient method (CGM) is reduced to performing only elementary vector operations and calculating sparse matrix-vector products. A method for constructing the above preconditioner is described and analyzed. The triangular factor has a fixed sparsity pattern and is optimal in the sense that the preconditioned matrix has a minimum K-condition number. The use of polynomial preconditioning based on Chebyshev polynomials makes it possible to considerably reduce the amount of scalar product operations (at the cost of an insignificant increase in the total number of arithmetic operations). The possibility of an efficient massively parallel implementation of the resulting method for solving SLAEs is discussed. For a sequential version of this method, the results obtained by solving 56 test problems from the Florida sparse matrix collection (which are large-scale and ill-conditioned) are presented. These results show that the method is highly reliable and has low computational costs.
Connection coefficients between Boas-Buck polynomial sets
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.
Mathematical Use Of Polynomials Of Different End Periods Of ...
African Journals Online (AJOL)
This paper focused on how polynomials of different end period of random numbers can be used in the application of encryption and decryption of a message. Eight steps were used in generating information on how polynomials of different end periods of random numbers in the application of encryption and decryption of a ...
On the Lorentz degree of a product of polynomials
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
Exponential time paradigms through the polynomial time lens
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
On polynomial selection for the general number field sieve
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.
A Combinatorial Proof of a Result on Generalized Lucas Polynomials
Directory of Open Access Journals (Sweden)
Laugier Alexandre
2016-09-01
Full Text Available We give a combinatorial proof of an elementary property of generalized Lucas polynomials, inspired by [1]. These polynomials in s and t are defined by the recurrence relation 〈n〉 = s〈n-1〉+t〈n-2〉 for n ≥ 2. The initial values are 〈0〉 = 2; 〈1〉= s, respectively.
Animating Nested Taylor Polynomials to Approximate a Function
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…
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\
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.
An introduction to vectors, vector operators and vector analysis
Joag, Pramod S
2016-01-01
Ideal for undergraduate and graduate students of science and engineering, this book covers fundamental concepts of vectors and their applications in a single volume. The first unit deals with basic formulation, both conceptual and theoretical. It discusses applications of algebraic operations, Levi-Civita notation, and curvilinear coordinate systems like spherical polar and parabolic systems and structures, and analytical geometry of curves and surfaces. The second unit delves into the algebra of operators and their types and also explains the equivalence between the algebra of vector operators and the algebra of matrices. Formulation of eigen vectors and eigen values of a linear vector operator are elaborated using vector algebra. The third unit deals with vector analysis, discussing vector valued functions of a scalar variable and functions of vector argument (both scalar valued and vector valued), thus covering both the scalar vector fields and vector integration.
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.
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...
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
Orthogonal polynomials derived from the tridiagonal representation approach
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.
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)
A note on some identities of derangement polynomials.
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.
vs. a polynomial chaos-based MCMC
Siripatana, Adil
2014-08-01
Bayesian Inference of Manning\\'s n coefficient in a Storm Surge Model Framework: comparison between Kalman lter and polynomial based method Adil Siripatana Conventional coastal ocean models solve the shallow water equations, which describe the conservation of mass and momentum when the horizontal length scale is much greater than the vertical length scale. In this case vertical pressure gradients in the momentum equations are nearly hydrostatic. The outputs of coastal ocean models are thus sensitive to the bottom stress terms de ned through the formulation of Manning\\'s n coefficients. This thesis considers the Bayesian inference problem of the Manning\\'s n coefficient in the context of storm surge based on the coastal ocean ADCIRC model. In the first part of the thesis, we apply an ensemble-based Kalman filter, the singular evolutive interpolated Kalman (SEIK) filter to estimate both a constant Manning\\'s n coefficient and a 2-D parameterized Manning\\'s coefficient on one ideal and one of more realistic domain using observation system simulation experiments (OSSEs). We study the sensitivity of the system to the ensemble size. we also access the benefits from using an in ation factor on the filter performance. To study the limitation of the Guassian restricted assumption on the SEIK lter, 5 we also implemented in the second part of this thesis a Markov Chain Monte Carlo (MCMC) method based on a Generalized Polynomial chaos (gPc) approach for the estimation of the 1-D and 2-D Mannning\\'s n coe cient. The gPc is used to build a surrogate model that imitate the ADCIRC model in order to make the computational cost of implementing the MCMC with the ADCIRC model reasonable. We evaluate the performance of the MCMC-gPc approach and study its robustness to di erent OSSEs scenario. we also compare its estimates with those resulting from SEIK in term of parameter estimates and full distributions. we present a full analysis of the solution of these two methods, of the
Constructing general partial differential equations using polynomial and neural networks.
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.
Efficient linear precoding for massive MIMO systems using truncated polynomial expansion
Müller, Axel
2014-06-01
Massive multiple-input multiple-output (MIMO) techniques have been proposed as a solution to satisfy many requirements of next generation cellular systems. One downside of massive MIMO is the increased complexity of computing the precoding, especially since the relatively \\'antenna-efficient\\' regularized zero-forcing (RZF) is preferred to simple maximum ratio transmission. We develop in this paper a new class of precoders for single-cell massive MIMO systems. It is based on truncated polynomial expansion (TPE) and mimics the advantages of RZF, while offering reduced and scalable computational complexity that can be implemented in a convenient parallel fashion. Using random matrix theory we provide a closed-form expression of the signal-to-interference-and-noise ratio under TPE precoding and compare it to previous works on RZF. Furthermore, the sum rate maximizing polynomial coefficients in TPE precoding are calculated. By simulation, we find that to maintain a fixed peruser rate loss as compared to RZF, the polynomial degree does not need to scale with the system, but it should be increased with the quality of the channel knowledge and signal-to-noise ratio. © 2014 IEEE.
Iris's Functional Description using Zernike polynomials
International Nuclear Information System (INIS)
Munnoz, D. P.; Silva Mata, F. J.; Talavera, I.; Hernandez, N.; Augier, A.
2012-01-01
The main goal of this work is the texture representation of the iris original image by means of functional data. The essence of the method consists in obtaining an adjusted vector of coefficients by means of a least square approximation starting from the representation of the original image by the expansion on the two-dimensional Zernike basis. This type of representation provides remarkable advantages regarding other representations e.g. the appreciable reduction of the dimension of the data, the simplification of the general process of the image and those characteristics of the functional data analysis. The carried out experiments demonstrate the feasibility of this approach and they allowed determining the optimal dimension of the coefficients vectors by means of the minimization of the residual errors. To corroborate the effectiveness of this representation, some experiments on identification were carried out on international databases whose initial results are annexed in the work. (Author)
Dynamics of polynomial Chaplygin gas warm inflation
Energy Technology Data Exchange (ETDEWEB)
Jawad, Abdul [COMSATS Institute of Information Technology, Department of Mathematics, Lahore (Pakistan); Chaudhary, Shahid [Sharif College of Engineering and Technology, Department of Mathematics, Lahore (Pakistan); Videla, Nelson [Pontificia Universidad Catolica de Valparaiso, Instituto de Fisica, Valparaiso (Chile)
2017-11-15
In the present work, we study the consequences of a recently proposed polynomial inflationary potential in the context of the generalized, modified, and generalized cosmic Chaplygin gas models. In addition, we consider dissipative effects by coupling the inflation field to radiation, i.e., the inflationary dynamics is studied in the warm inflation scenario. We take into account a general parametrization of the dissipative coefficient Γ for describing the decay of the inflaton field into radiation. By studying the background and perturbative dynamics in the weak and strong dissipative regimes of warm inflation separately for the positive and negative quadratic and quartic potentials, we obtain expressions for the most relevant inflationary observables as the scalar power spectrum, the scalar spectral, and the tensor-to-scalar ratio. We construct the trajectories in the n{sub s}-r plane for several expressions of the dissipative coefficient and compare with the two-dimensional marginalized contours for (n{sub s}, r) from the latest Planck data. We find that our results are in agreement with WMAP9 and Planck 2015 data. (orig.)
Global sensitivity analysis using polynomial chaos expansions
International Nuclear Information System (INIS)
Sudret, Bruno
2008-01-01
Global sensitivity analysis (SA) aims at quantifying the respective effects of input random variables (or combinations thereof) onto the variance of the response of a physical or mathematical model. Among the abundant literature on sensitivity measures, the Sobol' indices have received much attention since they provide accurate information for most models. The paper introduces generalized polynomial chaos expansions (PCE) to build surrogate models that allow one to compute the Sobol' indices analytically as a post-processing of the PCE coefficients. Thus the computational cost of the sensitivity indices practically reduces to that of estimating the PCE coefficients. An original non intrusive regression-based approach is proposed, together with an experimental design of minimal size. Various application examples illustrate the approach, both from the field of global SA (i.e. well-known benchmark problems) and from the field of stochastic mechanics. The proposed method gives accurate results for various examples that involve up to eight input random variables, at a computational cost which is 2-3 orders of magnitude smaller than the traditional Monte Carlo-based evaluation of the Sobol' indices
Global sensitivity analysis using polynomial chaos expansions
Energy Technology Data Exchange (ETDEWEB)
Sudret, Bruno [Electricite de France, R and D Division, Site des Renardieres, F 77818 Moret-sur-Loing Cedex (France)], E-mail: bruno.sudret@edf.fr
2008-07-15
Global sensitivity analysis (SA) aims at quantifying the respective effects of input random variables (or combinations thereof) onto the variance of the response of a physical or mathematical model. Among the abundant literature on sensitivity measures, the Sobol' indices have received much attention since they provide accurate information for most models. The paper introduces generalized polynomial chaos expansions (PCE) to build surrogate models that allow one to compute the Sobol' indices analytically as a post-processing of the PCE coefficients. Thus the computational cost of the sensitivity indices practically reduces to that of estimating the PCE coefficients. An original non intrusive regression-based approach is proposed, together with an experimental design of minimal size. Various application examples illustrate the approach, both from the field of global SA (i.e. well-known benchmark problems) and from the field of stochastic mechanics. The proposed method gives accurate results for various examples that involve up to eight input random variables, at a computational cost which is 2-3 orders of magnitude smaller than the traditional Monte Carlo-based evaluation of the Sobol' indices.
Polynomial Chaos Surrogates for Bayesian Inference
Le Maitre, Olivier
2016-01-06
The Bayesian inference is a popular probabilistic method to solve inverse problems, such as the identification of field parameter in a PDE model. The inference rely on the Bayes rule to update the prior density of the sought field, from observations, and derive its posterior distribution. In most cases the posterior distribution has no explicit form and has to be sampled, for instance using a Markov-Chain Monte Carlo method. In practice the prior field parameter is decomposed and truncated (e.g. by means of Karhunen- Lo´eve decomposition) to recast the inference problem into the inference of a finite number of coordinates. Although proved effective in many situations, the Bayesian inference as sketched above faces several difficulties requiring improvements. First, sampling the posterior can be a extremely costly task as it requires multiple resolutions of the PDE model for different values of the field parameter. Second, when the observations are not very much informative, the inferred parameter field can highly depends on its prior which can be somehow arbitrary. These issues have motivated the introduction of reduced modeling or surrogates for the (approximate) determination of the parametrized PDE solution and hyperparameters in the description of the prior field. Our contribution focuses on recent developments in these two directions: the acceleration of the posterior sampling by means of Polynomial Chaos expansions and the efficient treatment of parametrized covariance functions for the prior field. We also discuss the possibility of making such approach adaptive to further improve its efficiency.
Scattering amplitudes from multivariate polynomial division
Energy Technology Data Exchange (ETDEWEB)
Mastrolia, Pierpaolo, E-mail: pierpaolo.mastrolia@cern.ch [Max-Planck-Institut fuer Physik, Foehringer Ring 6, 80805 Muenchen (Germany); Dipartimento di Fisica e Astronomia, Universita di Padova, Padova (Italy); INFN Sezione di Padova, via Marzolo 8, 35131 Padova (Italy); Mirabella, Edoardo, E-mail: mirabell@mppmu.mpg.de [Max-Planck-Institut fuer Physik, Foehringer Ring 6, 80805 Muenchen (Germany); Ossola, Giovanni, E-mail: GOssola@citytech.cuny.edu [New York City College of Technology, City University of New York, 300 Jay Street, Brooklyn, NY 11201 (United States); Graduate School and University Center, City University of New York, 365 Fifth Avenue, New York, NY 10016 (United States); Peraro, Tiziano, E-mail: peraro@mppmu.mpg.de [Max-Planck-Institut fuer Physik, Foehringer Ring 6, 80805 Muenchen (Germany)
2012-11-15
We show that the evaluation of scattering amplitudes can be formulated as a problem of multivariate polynomial division, with the components of the integration-momenta as indeterminates. We present a recurrence relation which, independently of the number of loops, leads to the multi-particle pole decomposition of the integrands of the scattering amplitudes. The recursive algorithm is based on the weak Nullstellensatz theorem and on the division modulo the Groebner basis associated to all possible multi-particle cuts. We apply it to dimensionally regulated one-loop amplitudes, recovering the well-known integrand-decomposition formula. Finally, we focus on the maximum-cut, defined as a system of on-shell conditions constraining the components of all the integration-momenta. By means of the Finiteness Theorem and of the Shape Lemma, we prove that the residue at the maximum-cut is parametrized by a number of coefficients equal to the number of solutions of the cut itself.
q-Bernoulli numbers and q-Bernoulli polynomials revisited
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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
Generalized Freud's equation and level densities with polynomial potential
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.
Shapes of interacting RNA complexes
DEFF Research Database (Denmark)
Fu, Benjamin Mingming; Reidys, Christian
2014-01-01
Shapes of interacting RNA complexes are studied using a filtration via their topological genus. A shape of an RNA complex is obtained by (iteratively) collapsing stacks and eliminating hairpin loops.This shape-projection preserves the topological core of the RNA complex and for fixed topological...... genus there are only finitely many such shapes. Our main result is a new bijection that relates the shapes of RNA complexes with shapes of RNA structures. This allows to compute the shape polynomial of RNA complexes via the shape polynomial of RNA structures. We furthermore present a linear time uniform...... sampling algorithm for shapes of RNA complexes of fixed topological genus....
A comparison of companion matrix methods to find roots of a trigonometric polynomial
Boyd, John P.
2013-08-01
A trigonometric polynomial is a truncated Fourier series of the form fN(t)≡∑j=0Naj cos(jt)+∑j=1N bj sin(jt). It has been previously shown by the author that zeros of such a polynomial can be computed as the eigenvalues of a companion matrix with elements which are complex valued combinations of the Fourier coefficients, the "CCM" method. However, previous work provided no examples, so one goal of this new work is to experimentally test the CCM method. A second goal is introduce a new alternative, the elimination/Chebyshev algorithm, and experimentally compare it with the CCM scheme. The elimination/Chebyshev matrix (ECM) algorithm yields a companion matrix with real-valued elements, albeit at the price of usefulness only for real roots. The new elimination scheme first converts the trigonometric rootfinding problem to a pair of polynomial equations in the variables (c,s) where c≡cos(t) and s≡sin(t). The elimination method next reduces the system to a single univariate polynomial P(c). We show that this same polynomial is the resultant of the system and is also a generator of the Groebner basis with lexicographic ordering for the system. Both methods give very high numerical accuracy for real-valued roots, typically at least 11 decimal places in Matlab/IEEE 754 16 digit floating point arithmetic. The CCM algorithm is typically one or two decimal places more accurate, though these differences disappear if the roots are "Newton-polished" by a single Newton's iteration. The complex-valued matrix is accurate for complex-valued roots, too, though accuracy decreases with the magnitude of the imaginary part of the root. The cost of both methods scales as O(N3) floating point operations. In spite of intimate connections of the elimination/Chebyshev scheme to two well-established technologies for solving systems of equations, resultants and Groebner bases, and the advantages of using only real-valued arithmetic to obtain a companion matrix with real-valued elements
Directory of Open Access Journals (Sweden)
Sudha Ellison Mathe
2017-08-01
Full Text Available Multiplication in finite fields is used in many applications, especially in cryptography. It is a basic and the most computationally intensive operation from among all such operations. Several systolic multipliers are proposed in the literature that offer low hardware complexity or high speed. In this paper, a bit‐parallel polynomial basis systolic multiplier for generic irreducible polynomials is proposed based on a modified interleaved multiplication method. The hardware complexity and delay of the proposed multiplier are estimated, and a comparison with the corresponding multipliers available in the literature is presented. Of the corresponding multipliers, the proposed multiplier achieves a reduction in the hardware complexity of up to 20% when compared to the best multiplier for m = 163. The synthesis results of application‐specific integrated circuit and field‐programmable gate array implementations of the proposed multiplier are also presented. From the synthesis results, it is inferred that the proposed multiplier achieves low power consumption and low area complexitywhen compared to the best of the corresponding multipliers.
Harmonic sums and polylogarithms generated by cyclotomic polynomials
Energy Technology Data Exchange (ETDEWEB)
Ablinger, Jakob; Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation; Bluemlein, Johannes [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2011-05-15
The computation of Feynman integrals in massive higher order perturbative calculations in renormalizable Quantum Field Theories requires extensions of multiply nested harmonic sums, which can be generated as real representations by Mellin transforms of Poincare-iterated integrals including denominators of higher cyclotomic polynomials. We derive the cyclotomic harmonic polylogarithms and harmonic sums and study their algebraic and structural relations. The analytic continuation of cyclotomic harmonic sums to complex values of N is performed using analytic representations. We also consider special values of the cyclotomic harmonic polylogarithms at argument x=1, resp., for the cyclotomic harmonic sums at N{yields}{infinity}, which are related to colored multiple zeta values, deriving various of their relations, based on the stuffle and shuffle algebras and three multiple argument relations. We also consider infinite generalized nested harmonic sums at roots of unity which are related to the infinite cyclotomic harmonic sums. Basis representations are derived for weight w=1,2 sums up to cyclotomy l=20. (orig.)
Reduced Multivariate Polynomial Model for Manufacturing Costs Estimation of Piping Elements
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Nibaldo Rodriguez
2013-01-01
Full Text Available This paper discusses the development and evaluation of an estimation model of manufacturing costs of piping elements through the application of a Reduced Multivariate Polynomial (RMP. The model allows obtaining accurate estimations, even when enough and adequate information is not available. This situation typically occurs in the early stages of the design process of industrial products. The experimental evaluations show that the approach is capable, with a low complexity, of reducing uncertainties and to predict costs with significant precision. Comparisons with a neural network showed also that the RMP performs better considering a set of classical performance measures with the corresponding lower complexity and higher accuracy.
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
A summation procedure for expansions in orthogonal polynomials
International Nuclear Information System (INIS)
Garibotti, C.R.; Grinstein, F.F.
1977-01-01
Approximants to functions defined by formal series expansions in orthogonal polynomials are introduced. They are shown to be convergent even out of the elliptical domain where the original expansion converges
Skew-orthogonal polynomials and random matrix theory
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 ...
Numerical Simulation of Polynomial-Speed Convergence Phenomenon
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.
Fast parallel computation of polynomials using few processors
DEFF Research Database (Denmark)
Valiant, Leslie; Skyum, Sven
1981-01-01
It is shown that any multivariate polynomial that can be computed sequentially in C steps and has degree d can be computed in parallel in 0((log d) (log C + log d)) steps using only (Cd)0(1) processors....
Guts of surfaces and the colored Jones polynomial
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...
Solving polynomial systems using no-root elimination blending schemes
Barton, Michael
2011-01-01
Searching for the roots of (piecewise) polynomial systems of equations is a crucial problem in computer-aided design (CAD), and an efficient solution is in strong demand. Subdivision solvers are frequently used to achieve this goal; however
Optimal stability polynomials for numerical integration of initial value problems
Ketcheson, David I.; Ahmadia, Aron
2013-01-01
We consider the problem of finding optimally stable polynomial approximations to the exponential for application to one-step integration of initial value ordinary and partial differential equations. The objective is to find the largest stable step
An algebraic approach to the non-symmetric Macdonald polynomial
International Nuclear Information System (INIS)
Nishino, Akinori; Ujino, Hideaki; Wadati, Miki
1999-01-01
In terms of the raising and lowering operators, we algebraically construct the non-symmetric Macdonald polynomials which are simultaneous eigenfunctions of the commuting Cherednik operators. We also calculate Cherednik's scalar product of them
Force prediction in cold rolling mills by polynomial methods
Directory of Open Access Journals (Sweden)
Nicu ROMAN
2007-12-01
Full Text Available A method for steel and aluminium strip thickness control is provided including a new technique for predictive rolling force estimation method by statistic model based on polynomial techniques.
Entanglement entropy and the colored Jones polynomial
Balasubramanian, Vijay; DeCross, Matthew; Fliss, Jackson; Kar, Arjun; Leigh, Robert G.; Parrikar, Onkar
2018-05-01
We study the multi-party entanglement structure of states in Chern-Simons theory created by performing the path integral on 3-manifolds with linked torus boundaries, called link complements. For gauge group SU(2), the wavefunctions of these states (in a particular basis) are the colored Jones polynomials of the corresponding links. We first review the case of U(1) Chern-Simons theory where these are stabilizer states, a fact we use to re-derive an explicit formula for the entanglement entropy across a general link bipartition. We then present the following results for SU(2) Chern-Simons theory: (i) The entanglement entropy for a bipartition of a link gives a lower bound on the genus of surfaces in the ambient S 3 separating the two sublinks. (ii) All torus links (namely, links which can be drawn on the surface of a torus) have a GHZ-like entanglement structure — i.e., partial traces leave a separable state. By contrast, through explicit computation, we test in many examples that hyperbolic links (namely, links whose complements admit hyperbolic structures) have W-like entanglement — i.e., partial traces leave a non-separable state. (iii) Finally, we consider hyperbolic links in the complexified SL(2,C) Chern-Simons theory, which is closely related to 3d Einstein gravity with a negative cosmological constant. In the limit of small Newton constant, we discuss how the entanglement structure is controlled by the Neumann-Zagier potential on the moduli space of hyperbolic structures on the link complement.
Quasi-topological Ricci polynomial gravities
Li, Yue-Zhou; Liu, Hai-Shan; Lü, H.
2018-02-01
Quasi-topological terms in gravity can be viewed as those that give no contribution to the equations of motion for a special subclass of metric ansätze. They therefore play no rôle in constructing these solutions, but can affect the general perturbations. We consider Einstein gravity extended with Ricci tensor polynomial invariants, which admits Einstein metrics with appropriate effective cosmological constants as its vacuum solutions. We construct three types of quasi-topological gravities. The first type is for the most general static metrics with spherical, toroidal or hyperbolic isometries. The second type is for the special static metrics where g tt g rr is constant. The third type is the linearized quasitopological gravities on the Einstein metrics. We construct and classify results that are either dependent on or independent of dimensions, up to the tenth order. We then consider a subset of these three types and obtain Lovelock-like quasi-topological gravities, that are independent of the dimensions. The linearized gravities on Einstein metrics on all dimensions are simply Einstein and hence ghost free. The theories become quasi-topological on static metrics in one specific dimension, but non-trivial in others. We also focus on the quasi-topological Ricci cubic invariant in four dimensions as a specific example to study its effect on holography, including shear viscosity, thermoelectric DC conductivities and butterfly velocity. In particular, we find that the holographic diffusivity bounds can be violated by the quasi-topological terms, which can induce an extra massive mode that yields a butterfly velocity unbound above.
The Combinatorial Rigidity Conjecture is False for Cubic Polynomials
DEFF Research Database (Denmark)
Henriksen, Christian
2003-01-01
We show that there exist two cubic polynomials with connected Julia sets which are combinatorially equivalent but not topologically conjugate on their Julia sets. This disproves a conjecture by McMullen from 1995.......We show that there exist two cubic polynomials with connected Julia sets which are combinatorially equivalent but not topologically conjugate on their Julia sets. This disproves a conjecture by McMullen from 1995....
Discrete-Time Filter Synthesis using Product of Gegenbauer Polynomials
N. Stojanovic; N. Stamenkovic; I. Krstic
2016-01-01
A new approximation to design continuoustime and discrete-time low-pass filters, presented in this paper, based on the product of Gegenbauer polynomials, provides the ability of more flexible adjustment of passband and stopband responses. The design is achieved taking into account a prescribed specification, leading to a better trade-off among the magnitude and group delay responses. Many well-known continuous-time and discrete-time transitional filter based on the classical polynomial approx...
Raising and Lowering Operators for Askey-Wilson Polynomials
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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.
Bounds and asymptotics for orthogonal polynomials for varying weights
Levin, Eli
2018-01-01
This book establishes bounds and asymptotics under almost minimal conditions on the varying weights, and applies them to universality limits and entropy integrals. Orthogonal polynomials associated with varying weights play a key role in analyzing random matrices and other topics. This book will be of use to a wide community of mathematicians, physicists, and statisticians dealing with techniques of potential theory, orthogonal polynomials, approximation theory, as well as random matrices. .
Polynomial fuzzy observer designs: a sum-of-squares approach.
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.
Ratio asymptotics of Hermite-Pade polynomials for Nikishin systems
International Nuclear Information System (INIS)
Aptekarev, A I; Lopez, Guillermo L; Rocha, I A
2005-01-01
The existence of ratio asymptotics is proved for a sequence of multiple orthogonal polynomials with orthogonality relations distributed among a system of m finite Borel measures with support on a bounded interval of the real line which form a so-called Nikishin system. For m=1 this result reduces to Rakhmanov's celebrated theorem on the ratio asymptotics for orthogonal polynomials on the real line.
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)
Lower bounds for the circuit size of partially homogeneous polynomials
Czech Academy of Sciences Publication Activity Database
Le, Hong-Van
2017-01-01
Roč. 225, č. 4 (2017), s. 639-657 ISSN 1072-3374 Institutional support: RVO:67985840 Keywords : partially homogeneous polynomials * polynomials Subject RIV: BA - General Mathematics OBOR OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) https://link.springer.com/article/10.1007/s10958-017-3483-4
Euler Polynomials and Identities for Non-Commutative Operators
De Angelis, V.; Vignat, C.
2015-01-01
Three kinds of identities involving non-commutating operators and Euler and Bernoulli polynomials are studied. The first identity, as given by Bender and Bettencourt, 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, due to J.-C. Pain, links the commutators and anti-commutators of the monomials of the position and momentum operators. The third appears in a work by Fig...
Conference on Commutative rings, integer-valued polynomials and polynomial functions
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...
Imaging characteristics of Zernike and annular polynomial aberrations.
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.
Polynomial asymptotic stability of damped stochastic differential equations
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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.
Probing deformed orbitals with vector A( vector e, e' N)B reactions
International Nuclear Information System (INIS)
Garrido, E.; Caballero, J.A.; Moya de Guerra, E.; Sarriguren, P.; Udias, J.M.
1995-01-01
We present results for response functions and asymmetries in the nuclear reactions 37 vector Ar( vector e, e' n) 36 Ar and 37 vector K( vector e,e' p) 36 Ar at quasifree kinematics. We compare PWIA results obtained using deformed HF wave functions with PWIA and DWIA results obtained assuming a spherical mean field. We show that the complex structure of the deformed orbitals can be probed by coincidence measurements with polarized beam and targets. ((orig.))
International Nuclear Information System (INIS)
Shrock, Robert; Xu Yan
2012-01-01
We present an analysis of the structure and properties of chromatic polynomials P(G pt,m-vector, q) of one-parameter and multi-parameter families of planar triangulation graphs G pt,m-vector , where m-vector = (m 1 ,…,m p ) is a vector of integer parameters. We use these to study the ratio of |P(G pt,m-vector, τ+1)| to the Tutte upper bound (τ − 1) n−5 , where τ=(1+√5)/2 and n is the number of vertices in G pt,m-vector . In particular, we calculate limiting values of this ratio as n → ∞ for various families of planar triangulations. We also use our calculations to analyze zeros of these chromatic polynomials. We study a large class of families G pt,m-vector with p = 1 and p = 2 and show that these have a structure of the form P(G pt,m ,q) = c G pt ,1 λ 1 m + c G pt ,2 λ 2 m + c G pt ,3 λ 3 m for p = 1, where λ 1 = q − 2, λ 2 = q − 3, and λ 3 = −1, and P(G pt,m-vector ,q) =Σ i 1 =1 3 Σ i 2 =1 3 c G pt ,i 1 i 2 λ i 1 m 1 λ i 2 m 2 for p = 2. We derive properties of the coefficients c G pt ,i-vector and show that P(G pt,m-vector ,q) has a real chromatic zero that approaches (1/2)(3+√5) as one or more of the m i → ∞. The generalization to p ⩾ 3 is given. Further, we present a one-parameter family of planar triangulations with real zeros that approach 3 from below as m → ∞. Implications for the ground-state entropy of the Potts antiferromagnet are discussed. (paper)
Okounkov's BC-Type Interpolation Macdonald Polynomials and Their q=1 Limit
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
Bruno, Delia Evelina; Barca, Emanuele; Goncalves, Rodrigo Mikosz; de Araujo Queiroz, Heithor Alexandre; Berardi, Luigi; Passarella, Giuseppe
2018-01-01
In this paper, the Evolutionary Polynomial Regression data modelling strategy has been applied to study small scale, short-term coastal morphodynamics, given its capability for treating a wide database of known information, non-linearly. Simple linear and multilinear regression models were also applied to achieve a balance between the computational load and reliability of estimations of the three models. In fact, even though it is easy to imagine that the more complex the model, the more the prediction improves, sometimes a "slight" worsening of estimations can be accepted in exchange for the time saved in data organization and computational load. The models' outcomes were validated through a detailed statistical, error analysis, which revealed a slightly better estimation of the polynomial model with respect to the multilinear model, as expected. On the other hand, even though the data organization was identical for the two models, the multilinear one required a simpler simulation setting and a faster run time. Finally, the most reliable evolutionary polynomial regression model was used in order to make some conjecture about the uncertainty increase with the extension of extrapolation time of the estimation. The overlapping rate between the confidence band of the mean of the known coast position and the prediction band of the estimated position can be a good index of the weakness in producing reliable estimations when the extrapolation time increases too much. The proposed models and tests have been applied to a coastal sector located nearby Torre Colimena in the Apulia region, south Italy.
Compressive Sensing with Cross-Validation and Stop-Sampling for Sparse Polynomial Chaos Expansions
Energy Technology Data Exchange (ETDEWEB)
Huan, Xun; Safta, Cosmin; Sargsyan, Khachik; Vane, Zachary Phillips; Lacaze, Guilhem; Oefelein, Joseph C.; Najm, Habib N.
2017-07-01
Compressive sensing is a powerful technique for recovering sparse solutions of underdetermined linear systems, which is often encountered in uncertainty quanti cation analysis of expensive and high-dimensional physical models. We perform numerical investigations employing several com- pressive sensing solvers that target the unconstrained LASSO formulation, with a focus on linear systems that arise in the construction of polynomial chaos expansions. With core solvers of l1 ls, SpaRSA, CGIST, FPC AS, and ADMM, we develop techniques to mitigate over tting through an automated selection of regularization constant based on cross-validation, and a heuristic strategy to guide the stop-sampling decision. Practical recommendations on parameter settings for these tech- niques are provided and discussed. The overall method is applied to a series of numerical examples of increasing complexity, including large eddy simulations of supersonic turbulent jet-in-cross flow involving a 24-dimensional input. Through empirical phase-transition diagrams and convergence plots, we illustrate sparse recovery performance under structures induced by polynomial chaos, accuracy and computational tradeoffs between polynomial bases of different degrees, and practi- cability of conducting compressive sensing for a realistic, high-dimensional physical application. Across test cases studied in this paper, we find ADMM to have demonstrated empirical advantages through consistent lower errors and faster computational times.
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.
Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion
International Nuclear Information System (INIS)
Oladyshkin, S.; Nowak, W.
2012-01-01
We discuss the arbitrary polynomial chaos (aPC), which has been subject of research in a few recent theoretical papers. Like all polynomial chaos expansion techniques, aPC approximates the dependence of simulation model output on model parameters by expansion in an orthogonal polynomial basis. The aPC generalizes chaos expansion techniques towards arbitrary distributions with arbitrary probability measures, which can be either discrete, continuous, or discretized continuous and can be specified either analytically (as probability density/cumulative distribution functions), numerically as histogram or as raw data sets. We show that the aPC at finite expansion order only demands the existence of a finite number of moments and does not require the complete knowledge or even existence of a probability density function. This avoids the necessity to assign parametric probability distributions that are not sufficiently supported by limited available data. Alternatively, it allows modellers to choose freely of technical constraints the shapes of their statistical assumptions. Our key idea is to align the complexity level and order of analysis with the reliability and detail level of statistical information on the input parameters. We provide conditions for existence and clarify the relation of the aPC to statistical moments of model parameters. We test the performance of the aPC with diverse statistical distributions and with raw data. In these exemplary test cases, we illustrate the convergence with increasing expansion order and, for the first time, with increasing reliability level of statistical input information. Our results indicate that the aPC shows an exponential convergence rate and converges faster than classical polynomial chaos expansion techniques.
Emerging vector borne diseases – incidence through vectors
Directory of Open Access Journals (Sweden)
Sara eSavic
2014-12-01
Full Text Available Vector borne diseases use to be a major public health concern only in tropical and subtropical areas, but today they are an emerging threat for the continental and developed countries also. Nowdays, in intercontinetal countries, there is a struggle with emerging diseases which have found their way to appear through vectors. Vector borne zoonotic diseases occur when vectors, animal hosts, climate conditions, pathogens and susceptible human population exist at the same time, at the same place. Global climate change is predicted to lead to an increase in vector borne infectious diseases and disease outbreaks. It could affect the range and popultion of pathogens, host and vectors, transmission season, etc. Reliable surveilance for diseases that are most likely to emerge is required. Canine vector borne diseases represent a complex group of diseases including anaplasmosis, babesiosis, bartonellosis, borreliosis, dirofilariosis, erlichiosis, leishmaniosis. Some of these diseases cause serious clinical symptoms in dogs and some of them have a zoonotic potential with an effect to public health. It is expected from veterinarians in coordination with medical doctors to play a fudamental role at primeraly prevention and then treatment of vector borne diseases in dogs. The One Health concept has to be integrated into the struggle against emerging diseases.During a four year period, from 2009-2013, a total number of 551 dog samples were analysed for vector borne diseases (borreliosis, babesiosis, erlichiosis, anaplasmosis, dirofilariosis and leishmaniasis in routine laboratory work. The analysis were done by serological tests – ELISA for borreliosis, dirofilariosis and leishmaniasis, modified Knott test for dirofilariosis and blood smear for babesiosis, erlichiosis and anaplasmosis. This number of samples represented 75% of total number of samples that were sent for analysis for different diseases in dogs. Annually, on avarege more then half of the samples
Scalar potential for the gauged Heisenberg algebra and a non-polynomial antisymmetric tensor theory
International Nuclear Information System (INIS)
D'Auria, R.; Ferrara, S.; Trigiante, M.; Vaula, S.
2005-01-01
We study some issues related to the effective theory of Calabi-Yau compactifications with fluxes in type II theories. At first the scalar potential for a generic electric Abelian gauging of the Heisenberg algebra, underlying all possible gaugings of R-R isometries, is presented and shown to exhibit, in some circumstances, a 'dual' no-scale structure under the interchange of hypermultiplets and vector multiplets. Subsequently a new setting of such theories, when all R-R scalars are dualized into antisymmetric tensors, is discussed. This formulation falls in the class of non-polynomial tensor theories considered long ago by Freedman and Townsend and it may be relevant for the introduction of both electric and magnetic charges
Beheshti, Alireza
2018-03-01
The contribution addresses the finite element analysis of bending of plates given the Kirchhoff-Love model. To analyze the static deformation of plates with different loadings and geometries, the principle of virtual work is used to extract the weak form. Following deriving the strain field, stresses and resultants may be obtained. For constructing four-node quadrilateral plate elements, the Hermite polynomials defined with respect to the variables in the parent space are applied explicitly. Based on the approximated field of displacement, the stiffness matrix and the load vector in the finite element method are obtained. To demonstrate the performance of the subparametric 4-node plate elements, some known, classical examples in structural mechanics are solved and there are comparisons with the analytical solutions available in the literature.
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
Multivariate Local Polynomial Regression with Application to Shenzhen Component Index
Directory of Open Access Journals (Sweden)
Liyun Su
2011-01-01
Full Text Available This study attempts to characterize and predict stock index series in Shenzhen stock market using the concepts of multivariate local polynomial regression. Based on nonlinearity and chaos of the stock index time series, multivariate local polynomial prediction methods and univariate local polynomial prediction method, all of which use the concept of phase space reconstruction according to Takens' Theorem, are considered. To fit the stock index series, the single series changes into bivariate series. To evaluate the results, the multivariate predictor for bivariate time series based on multivariate local polynomial model is compared with univariate predictor with the same Shenzhen stock index data. The numerical results obtained by Shenzhen component index show that the prediction mean squared error of the multivariate predictor is much smaller than the univariate one and is much better than the existed three methods. Even if the last half of the training data are used in the multivariate predictor, the prediction mean squared error is smaller than the univariate predictor. Multivariate local polynomial prediction model for nonsingle time series is a useful tool for stock market price prediction.
Realization of vector fields for quantum groups as pseudodifferential operators on quantum spaces
International Nuclear Information System (INIS)
Chu, Chong-Sun; Zumino, B.
1995-01-01
The vector fields of the quantum Lie algebra are described for the quantum groups GL q (n), SL q (N) and SO q (N) as pseudodifferential operators on the linear quantum spaces covariant under the corresponding quantum group. Their expressions are simple and compact. It is pointed out that these vector fields satisfy certain characteristic polynomial identities. The real forms SU q (N) and SO q (N,R) are discussed in detail
Vectorization of KENO IV code and an estimate of vector-parallel processing
International Nuclear Information System (INIS)
Asai, Kiyoshi; Higuchi, Kenji; Katakura, Jun-ichi; Kurita, Yutaka.
1986-10-01
The multi-group criticality safety code KENO IV has been vectorized and tested on FACOM VP-100 vector processor. At first the vectorized KENO IV on a scalar processor became slower than the original one by a factor of 1.4 because of the overhead introduced by the vectorization. Making modifications of algorithms and techniques for vectorization, the vectorized version has become faster than the original one by a factor of 1.4 and 3.0 on the vector processor for sample problems of complex and simple geometries, respectively. For further speedup of the code, some improvements on compiler and hardware, especially on addition of Monte Carlo pipelines to the vector processor, are discussed. Finally a pipelined parallel processor system is proposed and its performance is estimated. (author)
Directory of Open Access Journals (Sweden)
Jeiczon Jaimes-Dueñez
2015-04-01
Full Text Available Aedes aegypti is the primary vector of the four serotypes of dengue virus (DENV1-4, Chikungunya and yellow fever virus to humans. Previous population genetic studies have revealed a particular genetic structure among the vector populations in the Americas that suggests differences in the ability to transmit DENV. In Colombia, despite its high epidemiologic importance, the genetic population structure and the phylogeographic depiction of Ae. aegypti, as well as its relationship with the epidemiologic landscapes in cities with heterogeneous incidence levels, remains unknown. We conducted a spatiotemporal analysis with the aim of determining the genetic structure and phylogeography of Colombian populations of Ae. aegypti among cities with different eco-epidemiologic characteristics with regard to DENV.Mitochondrial cytochrome oxidase C subunit 1 (COI--NADH dehydrogenase subunit 4 (ND4 genes were sequenced and analyzed from 341 adult mosquitoes collected during 2012 and 2013 in the Colombian cities of Bello, Riohacha and Villavicencio, which exhibit low, medium and high levels of incidence of DENV, respectively. The results demonstrated a low genetic differentiation over time and a high genetic structure between the cities due to changes in the frequency of two highly supported genetic groups. The phylogeographic analyses indicated that one group (associated with West African populations was found in all the cities throughout the sampling while the second group (associated with East African populations was found in all the samples from Bello and in only one sampling from Riohacha. Environmental factors such as the use of chemical insecticides showed a significant correlation with decreasing genetic diversity, indicating that environmental factors affect the population structure of Ae. aegypti across time and space in these cities.Our results suggest that two Ae. aegypti lineages are present in Colombia; one that is widespread and related to a West
Characteristic Polynomials of Sample Covariance Matrices: The Non-Square Case
Kösters, Holger
2009-01-01
We consider the sample covariance matrices of large data matrices which have i.i.d. complex matrix entries and which are non-square in the sense that the difference between the number of rows and the number of columns tends to infinity. We show that the second-order correlation function of the characteristic polynomial of the sample covariance matrix is asymptotically given by the sine kernel in the bulk of the spectrum and by the Airy kernel at the edge of the spectrum. Similar results are g...
Applying Semigroup Property of Enhanced Chebyshev Polynomials to Anonymous Authentication Protocol
Directory of Open Access Journals (Sweden)
Hong Lai
2012-01-01
Full Text Available We apply semigroup property of enhanced Chebyshev polynomials to present an anonymous authentication protocol. This paper aims at improving security and reducing computational and storage overhead. The proposed scheme not only has much lower computational complexity and cost in the initialization phase but also allows the users to choose their passwords freely. Moreover, it can provide revocation of lost or stolen smart card, which can resist man-in-the-middle attack and off-line dictionary attack together with various known attacks.
International Nuclear Information System (INIS)
Nazarov, S A
1999-01-01
We describe a wide class of boundary-value problems for which the application of elliptic theory can be reduced to elementary algebraic operations and which is characterized by the following polynomial property: the sesquilinear form corresponding to the problem degenerates only on some finite-dimensional linear space P of vector polynomials. Under this condition the boundary-value problem is elliptic, and its kernel and cokernel can be expressed in terms of P. For domains with piecewise-smooth boundary or infinite ends (conic, cylindrical, or periodic), we also present fragments of asymptotic formulae for the solutions, give specific versions of general conditional theorems on the Fredholm property (in particular, by modifying the ordinary weighted norms), and compute the index of the operator corresponding to the boundary-value problem. The polynomial property is also helpful for asymptotic analysis of boundary-value problems in thin domains and junctions of such domains. Namely, simple manipulations with P permit one to find the size of the system obtained by dimension reduction as well as the orders of the differential operators occurring in that system and provide complete information on the boundary layer structure. The results are illustrated by examples from elasticity and hydromechanics
Asekunowo, Patrick O; Haque, Rosenani A; Razali, Mohd R; Avicor, Silas W; Wajidi, Mustafa F F
2018-04-25
A series of four benzimidazolium based nitrile-functionalized mononuclear-Ag(I)-N-heterocyclic carbene and binuclear-Ag(I)-N-heterocyclic carbene (Ag(I)-NHC) hexafluorophosphate complexes (5b-8b) were synthesized by reacting the corresponding hexafluorophosphate salts (1b-4b) with Ag 2 O in acetonitrile, respectively. These compounds were characterized by 1 H NMR, 13 C NMR, IR, UV-visible spectroscopic techniques, elemental analyses and molar conductivity. Additionally, 8b was structurally characterized by single crystal X-ray diffraction technique. Preliminary in vitro antibacterial evaluation was conducted for all the compounds against two standard bacteria; gram-positive (Staphylococcus aureus) and gram-negative (Escherichia coli) bacterial strains. Most of the Ag(I)-NHC complexes (5b-8b) showed moderate to good antibacterial activity with MIC values in the range of 12.5-100 μg/mL. Especially, compound 8b exhibited promising anti-Staphylococcus aureus activity with a low MIC value (12.5 μg/mL). However, all the hexafluorophosphate salts (1b-4b) were inactive against the bacteria strains. The preliminary interactive investigation revealed that the most active compound, 8b, could effectively intercalate into DNA to form 8b-DNA complex which shows a better binding ability for DNA (K b = 3.627 × 10 6 ) than the complexes 5b-7b (2.177 × 10 6 , 8.672 × 10 5 and 6.665 × 10 5 , respectively). Nuclease activity of the complexes on plasmid DNA and Aedes albopictus genomic DNA was time-dependent, although minimal. The complexes were larvicidal to the mosquito, with 5b, 6b and 8b being highly active. Developmental progression from the larval to the adult stage was affected by the complexes, progressively being toxic to the insect's development with increasing concentration. These indicate the potential use of these complexes as control agents against bacteria and the dengue mosquito Ae. albopictus. Copyright © 2018 Elsevier Masson SAS. All
Polynomial algebra of discrete models in systems biology.
Veliz-Cuba, Alan; Jarrah, Abdul Salam; Laubenbacher, Reinhard
2010-07-01
An increasing number of discrete mathematical models are being published in Systems Biology, ranging from Boolean network models to logical models and Petri nets. They are used to model a variety of biochemical networks, such as metabolic networks, gene regulatory networks and signal transduction networks. There is increasing evidence that such models can capture key dynamic features of biological networks and can be used successfully for hypothesis generation. This article provides a unified framework that can aid the mathematical analysis of Boolean network models, logical models and Petri nets. They can be represented as polynomial dynamical systems, which allows the use of a variety of mathematical tools from computer algebra for their analysis. Algorithms are presented for the translation into polynomial dynamical systems. Examples are given of how polynomial algebra can be used for the model analysis. alanavc@vt.edu Supplementary data are available at Bioinformatics online.
Nuclear-magnetic-resonance quantum calculations of the Jones polynomial
International Nuclear Information System (INIS)
Marx, Raimund; Spoerl, Andreas; Pomplun, Nikolas; Schulte-Herbrueggen, Thomas; Glaser, Steffen J.; Fahmy, Amr; Kauffman, Louis; Lomonaco, Samuel; Myers, John M.
2010-01-01
The repertoire of problems theoretically solvable by a quantum computer recently expanded to include the approximate evaluation of knot invariants, specifically the Jones polynomial. The experimental implementation of this evaluation, however, involves many known experimental challenges. Here we present experimental results for a small-scale approximate evaluation of the Jones polynomial by nuclear magnetic resonance (NMR); in addition, we show how to escape from the limitations of NMR approaches that employ pseudopure states. Specifically, we use two spin-1/2 nuclei of natural abundance chloroform and apply a sequence of unitary transforms representing the trefoil knot, the figure-eight knot, and the Borromean rings. After measuring the nuclear spin state of the molecule in each case, we are able to estimate the value of the Jones polynomial for each of the knots.
A Formally Verified Conflict Detection Algorithm for Polynomial Trajectories
Narkawicz, Anthony; Munoz, Cesar
2015-01-01
In air traffic management, conflict detection algorithms are used to determine whether or not aircraft are predicted to lose horizontal and vertical separation minima within a time interval assuming a trajectory model. In the case of linear trajectories, conflict detection algorithms have been proposed that are both sound, i.e., they detect all conflicts, and complete, i.e., they do not present false alarms. In general, for arbitrary nonlinear trajectory models, it is possible to define detection algorithms that are either sound or complete, but not both. This paper considers the case of nonlinear aircraft trajectory models based on polynomial functions. In particular, it proposes a conflict detection algorithm that precisely determines whether, given a lookahead time, two aircraft flying polynomial trajectories are in conflict. That is, it has been formally verified that, assuming that the aircraft trajectories are modeled as polynomial functions, the proposed algorithm is both sound and complete.
A probabilistic approach of sum rules for heat polynomials
International Nuclear Information System (INIS)
Vignat, C; Lévêque, O
2012-01-01
In this paper, we show that the sum rules for generalized Hermite polynomials derived by Daboul and Mizrahi (2005 J. Phys. A: Math. Gen. http://dx.doi.org/10.1088/0305-4470/38/2/010) and by Graczyk and Nowak (2004 C. R. Acad. Sci., Ser. 1 338 849) can be interpreted and easily recovered using a probabilistic moment representation of these polynomials. The covariance property of the raising operator of the harmonic oscillator, which is at the origin of the identities proved in Daboul and Mizrahi and the dimension reduction effect expressed in the main result of Graczyk and Nowak are both interpreted in terms of the rotational invariance of the Gaussian distributions. As an application of these results, we uncover a probabilistic moment interpretation of two classical integrals of the Wigner function that involve the associated Laguerre polynomials. (paper)
Local polynomial Whittle estimation of perturbed fractional processes
DEFF Research Database (Denmark)
Frederiksen, Per; Nielsen, Frank; Nielsen, Morten Ørregaard
We propose a semiparametric local polynomial Whittle with noise (LPWN) estimator of the memory parameter in long memory time series perturbed by a noise term which may be serially correlated. The estimator approximates the spectrum of the perturbation as well as that of the short-memory component...... of the signal by two separate polynomials. Including these polynomials we obtain a reduction in the order of magnitude of the bias, but also in‡ate the asymptotic variance of the long memory estimate by a multiplicative constant. We show that the estimator is consistent for d 2 (0; 1), asymptotically normal...... for d ε (0, 3/4), and if the spectral density is infinitely smooth near frequency zero, the rate of convergence can become arbitrarily close to the parametric rate, pn. A Monte Carlo study reveals that the LPWN estimator performs well in the presence of a serially correlated perturbation term...
Synchronization of generalized Henon map using polynomial controller
International Nuclear Information System (INIS)
Lam, H.K.
2010-01-01
This Letter presents the chaos synchronization of two discrete-time generalized Henon map, namely the drive and response systems. A polynomial controller is proposed to drive the system states of the response system to follow those of the drive system. The system stability of the error system formed by the drive and response systems and the synthesis of the polynomial controller are investigated using the sum-of-squares (SOS) technique. Based on the Lyapunov stability theory, stability conditions in terms of SOS are derived to guarantee the system stability and facilitate the controller synthesis. By satisfying the SOS-based stability conditions, chaotic synchronization is achieved. The solution of the SOS-based stability conditions can be found numerically using the third-party Matlab toolbox SOSTOOLS. A simulation example is given to illustrate the merits of the proposed polynomial control approach.
The Kauffman bracket and the Jones polynomial in quantum gravity
International Nuclear Information System (INIS)
Griego, J.
1996-01-01
In the loop representation the quantum states of gravity are given by knot invariants. From general arguments concerning the loop transform of the exponential of the Chern-Simons form, a certain expansion of the Kauffman bracket knot polynomial can be formally viewed as a solution of the Hamiltonian constraint with a cosmological constant in the loop representation. The Kauffman bracket is closely related to the Jones polynomial. In this paper the operation of the Hamiltonian on the power expansions of the Kauffman bracket and Jones polynomials is analyzed. It is explicitly shown that the Kauffman bracket is a formal solution of the Hamiltonian constraint to third order in the cosmological constant. We make use of the extended loop representation of quantum gravity where the analytic calculation can be thoroughly accomplished. Some peculiarities of the extended loop calculus are considered and the significance of the results to the case of the conventional loop representation is discussed. (orig.)
Polynomial chaos expansion with random and fuzzy variables
Jacquelin, E.; Friswell, M. I.; Adhikari, S.; Dessombz, O.; Sinou, J.-J.
2016-06-01
A dynamical uncertain system is studied in this paper. Two kinds of uncertainties are addressed, where the uncertain parameters are described through random variables and/or fuzzy variables. A general framework is proposed to deal with both kinds of uncertainty using a polynomial chaos expansion (PCE). It is shown that fuzzy variables may be expanded in terms of polynomial chaos when Legendre polynomials are used. The components of the PCE are a solution of an equation that does not depend on the nature of uncertainty. Once this equation is solved, the post-processing of the data gives the moments of the random response when the uncertainties are random or gives the response interval when the variables are fuzzy. With the PCE approach, it is also possible to deal with mixed uncertainty, when some parameters are random and others are fuzzy. The results provide a fuzzy description of the response statistical moments.
Real zeros of classes of random algebraic polynomials
Directory of Open Access Journals (Sweden)
K. Farahmand
2003-01-01
Full Text Available There are many known asymptotic estimates for the expected number of real zeros of an algebraic polynomial a0+a1x+a2x2+⋯+an−1xn−1 with identically distributed random coefficients. Under different assumptions for the distribution of the coefficients {aj}j=0n−1 it is shown that the above expected number is asymptotic to O(logn. This order for the expected number of zeros remains valid for the case when the coefficients are grouped into two, each group with a different variance. However, it was recently shown that if the coefficients are non-identically distributed such that the variance of the jth term is (nj the expected number of zeros of the polynomial increases to O(n. The present paper provides the value for this asymptotic formula for the polynomials with the latter variances when they are grouped into three with different patterns for their variances.
Euler polynomials and identities for non-commutative operators
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.
Emerging Vector-Borne Diseases - Incidence through Vectors.
Savić, Sara; Vidić, Branka; Grgić, Zivoslav; Potkonjak, Aleksandar; Spasojevic, Ljubica
2014-01-01
Vector-borne diseases use to be a major public health concern only in tropical and subtropical areas, but today they are an emerging threat for the continental and developed countries also. Nowadays, in intercontinental countries, there is a struggle with emerging diseases, which have found their way to appear through vectors. Vector-borne zoonotic diseases occur when vectors, animal hosts, climate conditions, pathogens, and susceptible human population exist at the same time, at the same place. Global climate change is predicted to lead to an increase in vector-borne infectious diseases and disease outbreaks. It could affect the range and population of pathogens, host and vectors, transmission season, etc. Reliable surveillance for diseases that are most likely to emerge is required. Canine vector-borne diseases represent a complex group of diseases including anaplasmosis, babesiosis, bartonellosis, borreliosis, dirofilariosis, ehrlichiosis, and leishmaniosis. Some of these diseases cause serious clinical symptoms in dogs and some of them have a zoonotic potential with an effect to public health. It is expected from veterinarians in coordination with medical doctors to play a fundamental role at primarily prevention and then treatment of vector-borne diseases in dogs. The One Health concept has to be integrated into the struggle against emerging diseases. During a 4-year period, from 2009 to 2013, a total number of 551 dog samples were analyzed for vector-borne diseases (borreliosis, babesiosis, ehrlichiosis, anaplasmosis, dirofilariosis, and leishmaniasis) in routine laboratory work. The analysis was done by serological tests - ELISA for borreliosis, dirofilariosis, and leishmaniasis, modified Knott test for dirofilariosis, and blood smear for babesiosis, ehrlichiosis, and anaplasmosis. This number of samples represented 75% of total number of samples that were sent for analysis for different diseases in dogs. Annually, on average more then half of the samples
Generalized vector calculus on convex domain
Agrawal, Om P.; Xu, Yufeng
2015-06-01
In this paper, we apply recently proposed generalized integral and differential operators to develop generalized vector calculus and generalized variational calculus for problems defined over a convex domain. In particular, we present some generalization of Green's and Gauss divergence theorems involving some new operators, and apply these theorems to generalized variational calculus. For fractional power kernels, the formulation leads to fractional vector calculus and fractional variational calculus for problems defined over a convex domain. In special cases, when certain parameters take integer values, we obtain formulations for integer order problems. Two examples are presented to demonstrate applications of the generalized variational calculus which utilize the generalized vector calculus developed in the paper. The first example leads to a generalized partial differential equation and the second example leads to a generalized eigenvalue problem, both in two dimensional convex domains. We solve the generalized partial differential equation by using polynomial approximation. A special case of the second example is a generalized isoperimetric problem. We find an approximate solution to this problem. Many physical problems containing integer order integrals and derivatives are defined over arbitrary domains. We speculate that future problems containing fractional and generalized integrals and derivatives in fractional mechanics will be defined over arbitrary domains, and therefore, a general variational calculus incorporating a general vector calculus will be needed for these problems. This research is our first attempt in that direction.
Sparse estimation of polynomial dynamical models
Toth, R.; Hjalmarsson, H.; Rojas, C.R.; Kinnaert, M.
2012-01-01
In many practical situations, it is highly desirable to estimate an accurate mathematical model of a real system using as few parameters as possible. This can be motivated either from appealing to a parsimony principle (Occam's razor) or from the view point of the utilization complexity in terms of
Local polynomial Whittle estimation covering non-stationary fractional processes
DEFF Research Database (Denmark)
Nielsen, Frank
to the non-stationary region. By approximating the short-run component of the spectrum by a polynomial, instead of a constant, in a shrinking neighborhood of zero we alleviate some of the bias that the classical local Whittle estimators is prone to. This bias reduction comes at a cost as the variance is in...... study illustrates the performance of the proposed estimator compared to the classical local Whittle estimator and the local polynomial Whittle estimator. The empirical justi.cation of the proposed estimator is shown through an analysis of credit spreads....
The algebra of Weyl symmetrised polynomials and its quantum extension
International Nuclear Information System (INIS)
Gelfand, I.M.; Fairlie, D.B.
1991-01-01
The Algebra of Weyl symmetrised polynomials in powers of Hamiltonian operators P and Q which satisfy canonical commutation relations is constructed. This algebra is shown to encompass all recent infinite dimensional algebras acting on two-dimensional phase space. In particular the Moyal bracket algebra and the Poisson bracket algebra, of which the Moyal is the unique one parameter deformation are shown to be different aspects of this infinite algebra. We propose the introduction of a second deformation, by the replacement of the Heisenberg algebra for P, Q with a q-deformed commutator, and construct algebras of q-symmetrised Polynomials. (orig.)
Orthogonal polynomials, Laguerre Fock space, and quasi-classical asymptotics
Engliš, Miroslav; Ali, S. Twareque
2015-07-01
Continuing our earlier investigation of the Hermite case [S. T. Ali and M. Engliš, J. Math. Phys. 55, 042102 (2014)], we study an unorthodox variant of the Berezin-Toeplitz quantization scheme associated with Laguerre polynomials. In particular, we describe a "Laguerre analogue" of the classical Fock (Segal-Bargmann) space and the relevant semi-classical asymptotics of its Toeplitz operators; the former actually turns out to coincide with the Hilbert space appearing in the construction of the well-known Barut-Girardello coherent states. Further extension to the case of Legendre polynomials is likewise discussed.
Discrete-Time Filter Synthesis using Product of Gegenbauer Polynomials
Directory of Open Access Journals (Sweden)
N. Stojanovic
2016-09-01
Full Text Available A new approximation to design continuoustime and discrete-time low-pass filters, presented in this paper, based on the product of Gegenbauer polynomials, provides the ability of more flexible adjustment of passband and stopband responses. The design is achieved taking into account a prescribed specification, leading to a better trade-off among the magnitude and group delay responses. Many well-known continuous-time and discrete-time transitional filter based on the classical polynomial approximations(Chebyshev, Legendre, Butterworth are shown to be a special cases of proposed approximation method.
Orthogonal polynomials on the unit circle part 2 spectral theory
Simon, Barry
2013-01-01
This two-part book is a comprehensive overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. A major theme involves the connections between the Verblunsky coefficients (the coefficients of the recurrence equation for the orthogonal polynomials) and the measures, an analog of the spectral theory of one-dimensional Schrödinger operators. Among the topics discussed along the way are the asymptotics of Toeplitz determinants (Szegő's theorems), limit theorems for the density of the zeros of orthogonal po
Orthogonal polynomials on the unit circle part 1 classical theory
2009-01-01
This two-part book is a comprehensive overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. A major theme involves the connections between the Verblunsky coefficients (the coefficients of the recurrence equation for the orthogonal polynomials) and the measures, an analog of the spectral theory of one-dimensional Schrodinger operators. Among the topics discussed along the way are the asymptotics of Toeplitz determinants (SzegÅ‘'s theorems), limit theorems for the density of the zeros of orthogonal po
Gaussian polynomials and content ideal in trivial extensions
International Nuclear Information System (INIS)
Bakkari, C.; Mahdou, N.
2006-12-01
The goal of this paper is to exhibit a class of Gaussian non-coherent rings R (with zero-divisors) such that wdim(R) = ∞ and fPdim(R) is always at most one and also exhibits a new class of rings (with zerodivisors) which are neither locally Noetherian nor locally domain where Gaussian polynomials have a locally principal content. For this purpose, we study the possible transfer of the 'Gaussian' property and the property 'the content ideal of a Gaussian polynomial is locally principal' to various trivial extension contexts. This article includes a brief discussion of the scopes and limits of our result. (author)
M-Polynomial and Related Topological Indices of Nanostar Dendrimers
Directory of Open Access Journals (Sweden)
Mobeen Munir
2016-09-01
Full Text Available Dendrimers are highly branched organic macromolecules with successive layers of branch units surrounding a central core. The M-polynomial of nanotubes has been vastly investigated as it produces many degree-based topological indices. These indices are invariants of the topology of graphs associated with molecular structure of nanomaterials to correlate certain physicochemical properties like boiling point, stability, strain energy, etc. of chemical compounds. In this paper, we first determine M-polynomials of some nanostar dendrimers and then recover many degree-based topological indices.
On the Lojasiewicz exponent at infinity of real polynomials
International Nuclear Information System (INIS)
Ha Huy Vui; Pham Tien Son
2007-07-01
Let f : R n → R be a nonconstant polynomial function. In this paper, using the information from 'the curve of tangency' of f, we provide a method to determine the Lojasiewicz exponent at infinity of f. As a corollary, we give a computational criterion to decide if the Lojasiewicz exponent at infinity is finite or not. Then, we obtain a formula to calculate the set of points at which the polynomial f is not proper. Moreover, a relation between the Lojasiewicz exponent at infinity of f with the problem of computing the global optimum of f is also established. (author)
Synthetic Aperture Vector Flow Imaging
DEFF Research Database (Denmark)
Villagómez Hoyos, Carlos Armando
The main objective of this project was to continue the development of a synthetic aperture vector flow estimator. This type of estimator is capable of overcoming two of the major limitations in conventional ultrasound systems: 1) the inability to scan large region of interest with high temporal......, this thesis showed that novel information can be obtained with vector velocity methods providing quantitative estimates of blood flow and insight into the complexity of the hemodynamics dynamics. This could give the clinician a new tool in assessment and treatment of a broad range of diseases....
Raster images vectorization system
Genytė, Jurgita
2006-01-01
The problem of raster images vectorization was analyzed and researched in this work. Existing vectorization systems are quite expensive, the results are inaccurate, and the manual vectorization of a large number of drafts is impossible. That‘s why our goal was to design and develop a new raster images vectorization system using our suggested automatic vectorization algorithm and the way to record results in a new universal vectorial file format. The work consists of these main parts: analysis...