共查询到20条相似文献,搜索用时 15 毫秒
1.
Amos J. Carpenter 《Numerische Mathematik》1992,62(1):465-482
Summary We investigate the location of the zeros of the normalized generalized Bessel polynomials and the normalized reversed generalized Bessel polynomials. Also, the rate at which these zeros approach certain well-defined curves is investigated. On the basis of numerical computations and graphs, four new conjectures are proposed.Dedicated to Richard S. Varga on the occasion of his sixtieth birthday (October 9, 1988)This research was made possible and supported by a Butler University Fellowship Award 相似文献
2.
The delta function initial condition solution v*(x,t;y) at x = y ≥ 0 of the generalized Feller equation is used to define a generalized Jacobi Theta function \documentclass{article}\pagestyle{empty}\begin{document}$ \Theta (x,t) = \upsilon *(x,t;0) + 2\sum\limits_{n = 1}^\infty {v*(x,t;y_n)} $\end{document} for a sufficiently rapidly increasing and unbounded positive sequence {yy}. It is shown that Θ(x,t) is analytic in each variable in certain regions of the complex x and t planes and that it is a solution of the generalized Feller equation. For those parameters for which this equation reduces to the heat equation, Θ(x,t) reduces to the third Jacobi Theta function. 相似文献
3.
We study the asymptotic behavior of multiple Meixner polynomials of first and second kind, respectively [6]. We use an algebraic function formulation for the solution of the equilibrium problem with constraint to describe their zero distribution. Moreover, analyzing the limiting behavior of the coefficients of the recurrence relations for Multiple Meixner polynomials we obtain the main term of their asymptotics. 相似文献
4.
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An adaptive wavelet-based method is proposed for solving TV(total variation)–Allen–Cahn type models for multi-phase image segmentation. The adaptive algorithm integrates (i) grid adaptation based on a threshold of the sparse wavelet representation of the locally-structured solution; and (ii) effective finite difference on irregular stencils. The compactly supported interpolating-type wavelets enjoy very fast wavelet transforms, and act as a piecewise constant function filter. These lead to fairly sparse computational grids, and relax the stiffness of the nonlinear PDEs. Equipped with this algorithm, the proposed sharp interface model becomes very effective for multi-phase image segmentation. This method is also applied to image restoration and similar advantages are observed. 相似文献
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8.
Ury Passy 《Journal of Optimization Theory and Applications》1972,9(4):221-237
An extension of geometric programming to includegeneralized polynomials, and not onlyPositive polynomials, is described, together with an algorithm and a numerical example. 相似文献
9.
Wen-Gao Long Dan Dai Yu-Tian Li Xiang-Sheng Wang 《Studies in Applied Mathematics》2020,144(2):133-163
We derive uniform asymptotic expansions for polynomials orthogonal with respect to a class of weight functions that are real analytic and behave asymptotically like the Freud weight at infinity. Although the limiting zero distributions are the same as in the Freud cases, the asymptotic expansions are different due to the fact that the weight functions may have a finite or infinite number of zeros on the imaginary axis. To resolve the singularities caused by these zeros, an auxiliary function is introduced in the Riemann–Hilbert analysis. Asymptotic formulas are established in several regions covering the whole complex plane. We take the continuous dual Hahn polynomials as an example to illustrate our main results. Some numerical verifications are also given. 相似文献
10.
Dimitar K. Dimitrov 《Journal of Mathematical Analysis and Applications》2004,299(1):127-132
We prove that the zeros of the polynomials Pm(a) of degree m, defined by Boros and Moll via
11.
Guillermo López Lagomasino 《Constructive Approximation》1989,5(1):199-219
Letd be a finite positive Borel measure on the interval [0, 2] such that >0 almost everywhere; andW
n be a sequence of polynomials, degW
n
=n, whose zeros (w
n
,1,,w
n,n
lie in [|z|1]. Let d
n
<> for eachnN, whered
n
=d/|W
n
(e
i
)|2. We consider the table of polynomials
n,m such that for each fixednN the system
n,m,mN, is orthonormal with respect tod
n
. If
相似文献
12.
M. Mejri 《Journal of Difference Equations and Applications》2013,19(12):1367-1380
We study in detail a q-extension of the generalized Gegenbauer form (functional). We show that it is symmetric H q -semi-classical of class one. The moments and the integral representations are given. 相似文献
13.
Younghong Chen Stephen J. Kirkland Michael Neumann 《Linear and Multilinear Algebra》1995,39(4):325-340
We consider two types of irreducible stochastic matrices —tridiagonal matrices and periodic jacobi matrices —which can be viewed as transition matrices of interval and circular random walks,respcetively. For both types of matrices we give a formula for the group inverse of the associated singular M-matrix. We discuss both the sign patterns and the relative sizes of the entries in these group inverses and apply our results to give qualitative information about random walks on an interval and on a circle. 相似文献
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15.
Asymptotic expansions are given for orthogonal polynomials when the coefficients in the three-term recursion formula generating the orthogonal polynomials form sequences of bounded variation. 相似文献
16.
Shi-Mei Ma 《Applied mathematics and computation》2011,217(22):9297-9301
In this paper we consider a family of generalized Fibonacci-type polynomials. These polynomials have a lot of similar properties to the generalized Jacobsthal-type polynomials. As an extension of the work of Djordjevi? [G.B. Djordjevi?, Mixed convolutions of the Jacobsthal type, Appl. Math. Comput. 186 (2007) 646-651], we give some recurrence relations and identities involving the generalized Fibonacci-type polynomials. 相似文献
17.
We consider associativePI-algebras over a field of characteristic zero. The main goal of the paper is to prove that the codimensions of a verbally
prime algebra [11] are asymptotically equal to the codimensions of theT-ideal generated by some Amitsur's Capelli-type polynomialsE
M,L
*
[1]. We recall that two sequencesa
n,b
nare asymptotically equal, and we writea
n
≃b
n,if and only if lim
n→∞(a
n/b
n)=1.In this paper we prove that
% MathType!End!2!1!, whereG is the Grassmann algebra. These results extend to all verbally primePI-algebras a theorem of A. Giambruno and M. Zaicev [9] giving the asymptotic equality
% MathType!End!2!1! between the codimensions of the matrix algebraM
k(F) and the Capelli polynomials.
The second author is partially supported by grants RFFI 04-01-00739a, E02-2.0-26. 相似文献
18.
Shy-Der Lin 《Applied mathematics and computation》2011,218(4):1330-1341
The main object of this paper is to investigate several general families of hypergeometric polynomials and their associated multiple integral representations. By suitably specializing our main results, the corresponding integral representations are deduced for such familiar classes of hypergeometric polynomials as (for example) the generalized Bedient polynomials and the generalized Cesàro polynomials. Each of the integral representations, which are derived in this paper, may be viewed also as a linearization relationship for the product of two different members of the associated family of hypergeometric polynomials. 相似文献
19.
Richard Fournier 《Journal of Mathematical Analysis and Applications》2008,338(2):1100-1107
We obtain a characterization and conjecture asymptotics of the Bohr radius for the class of complex polynomials in one variable. Our work is based on the notion of bound-preserving operators. 相似文献
20.
We show that uniform asymptotics of orthogonal polynomials on the real line imply uniform asymptotics for all their derivatives.
This is more technically challenging than the corresponding problem on the unit circle. We also examine asymptotics in the
L
2 norm.
Research supported by NSF grant DMS0400446 and US-Israel BSF grant 2004353. 相似文献
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