Search results for "polynomials"
showing 10 items of 144 documents
Hardware Computation of Moment Functions in a Silicon Retina Using Binary Patterns
2006
International audience; We present in this paper a method for implementing moment functions in a CMOS retina for shape recognition applications. The method is based on the use of binary patterns and it allows the computation of different moment functions such geometric and Zernike moments of any orders by an adequate choice of the binary patterns. The advantages of the method over other methods described in the literature is that it is particularly suitable for the design of a programmable retina circuit where moment functions of different orders are obtained by simply loading the correct binary patterns into the memory devices implemented on the circuit. The moment values computed by the m…
OPTIMIZATIONS FOR TENSORIAL BERNSTEIN–BASED SOLVERS BY USING POLYHEDRAL BOUNDS
2010
The tensorial Bernstein basis for multivariate polynomials in n variables has a number 3n of functions for degree 2. Consequently, computing the representation of a multivariate polynomial in the tensorial Bernstein basis is an exponential time algorithm, which makes tensorial Bernstein-based solvers impractical for systems with more than n = 6 or 7 variables. This article describes a polytope (Bernstein polytope) with a number of faces, which allows to bound a sparse, multivariate polynomial expressed in the canonical basis by solving several linear programming problems. We compare the performance of a subdivision solver using domain reductions by linear programming with a solver using a c…
Convergence and applications of vector rational approximations
1992
The Padé approximants and their generalizations are for many years the matter of intense researchs .Yet , many theoritical problems stay in suspense : problems of exitence and unicity , problems of convergence and acceleration of convergence .The purpose of the present work vas to give answers to such questions .In the first section we take an in terest in vector Padé approximants of matrix series .Conditions of existence and unicity ,results of convergence are given ,as also the link with the theory of Lanczos method for the resolution of linear Systems . We utilize also the vector Padé approximants to provide a simultaneous approximation of a function and its derivative .In the second sec…
Quantizations from reproducing kernel spaces
2012
Abstract The purpose of this work is to explore the existence and properties of reproducing kernel Hilbert subspaces of L 2 ( C , d 2 z / π ) based on subsets of complex Hermite polynomials. The resulting coherent states (CS) form a family depending on a nonnegative parameter s . We examine some interesting issues, mainly related to CS quantization, like the existence of the usual harmonic oscillator spectrum despite the absence of canonical commutation rules. The question of mathematical and physical equivalences between the s -dependent quantizations is also considered.
Investigation of buckling characteristics of cracked variable stiffness composite plates by an eXtended Ritz approach
2021
Abstract Variable Angle Tow (VAT) composite plates are characterized by in-plane variable stiffness properties, which opens to new concepts of stiffness tailoring and optimization to achieve higher structural performance for advanced lightweight structures where damage tolerance consideration are often mandatory. In this paper, a single-domain eXtended Ritz formulation is proposed to study the buckling behaviour of variable stiffness laminated cracked plates. The plate behaviour is described by the first order shear deformation theory whose generalized displacements, namely reference plane translations and rotations, are expressed via suitable admissible trial functions. These consist of a …
The central polynomials of the infinite-dimensional unitary and nonunitary Grassmann algebras
2010
For a fixed field $k$, let $k_0\langle X\rangle$ and $k_1\langle X \rangle$ denote respectively the free nonunitary associative $k$-algebra and the free unitary associative $k$-algebra on the countable set $X=\{x_1, x_2, \ldots\}.$ A polynomial $f\in k_i\langle X\rangle$ is called a central polynomial for an associative algebra $A$ if every evaluation of $f$ on $A$ lies in the center of $A.$ The set of all central polynomials of $A$ is a $T$-space of $k_i\langle X\rangle,$ i.e, a subspace closed under all endomorphisms of $k_i\langle X\rangle.$ In this paper the authors describe the T-space of central polynomials for both the unitary and the nonunitary infinite-dimensional Grassmann algebra…
Graded central polynomials for the matrix algebra of order two
2009
Let K be an infinite integral domain and $A=M_2(K)$ the algebra of $2\times 2$ matrices over $K$. The authors consider the natural $\mathbb{Z}_2$-grading of $A$ obtained by requiring that the diagonal matrices and the off-diagonal matrices are of homogeneous degree $0$ and $1$, respectively. When $K$ is a field, a basis of the graded identities of $A$ was described in [O. M. Di Vincenzo, On the graded identities of $M_{1,1}(E).$ Israel J. Math. 80 (1992), no. 3, 323-–335] in case $\mbox{char}\, K = 0$ and in [P. E. Koshlukov and S. S. de Azevedo, Graded identities for T-prime algebras over fields of positive characteristic. Israel J. Math. 128 (2002), 157-–176] when $K$ is infinite and $\mb…
On the Complexity of the Bernstein Combinatorial Problem
2012
International audience
Exploratory remarks and discussion on a potential program for interlock even more the mathematics and physics
2021
These remarks are endowed with exploratory argumentation for disrupt further discussion and in favor of the in-depth consolidation of a mathematical and physics identification based on 2 key concepts: 1) finite support and 2) a notion of infinite intrinsic to the usage of the complex numbers. General relativity shows up linked to a kind of a Gelfand representation as an approximation of an analog of a hidden Markov Model. This has deep connections with the Stone–Weierstrass theorem and these discussion are an invitation to the physics community to study the physics x mathematics identification in the case of a holding true multiverse hypothesis. Photon in this setup stands to the analog of …
Computational Experiments with the Roots of Fibonacci-like Polynomials as a Window to Mathematics Research
2022
Fibonacci-like polynomials, the roots of which are responsible for a cyclic behavior of orbits of a second-order two-parametric difference equation, are considered. Using Maple and Wolfram Alpha, the location of the largest and the smallest roots responsible for the cycles of period p among the roots responsible for the cycles of periods 2kp (period-doubling) and kp (period-multiplying) has been determined. These purely computational results of experimental mathematics, made possible by the use of modern digital tools, can be used as a motivation for confirmation through not-yet-developed methods of formal mathematics. peerReviewed