Results 91 to 100 of about 33,621 (261)

A New Generating Function for Hermite Polynomials

International Journal of Mathematics and Mathematical Sciences
This paper presents a new generating function of the form gx,t=∑n=0∞tnHnex for Hermite polynomials and reveals its connection with the incomplete gamma function.
Manouchehr Amiri
doaj   +1 more source

An extremal property of Hermite polynomials

Journal of Mathematical Analysis and Applications, 2004
Consider the sequence of the Hermite polynomials \(H_m(x)=(-1)^m e^{x^2}\frac{d^m}{dx^m} \{e^{-x^2}\}\), \((m=0,1,\dots)\), i.e. orthogonal polynomials in \(L_2(\mathbb R,w)\), where \(w(x)=\exp(-x^2)\). The main result of the paper is the following Duffin-Schaeffer type inequality. If \(f\) is a polynomial on \(\mathbb R\) of degree at most \(n\) such
openaire   +2 more sources

A physics‐informed train on synthetic and test on real method for evaluating large language model‐generated safety‐critical traffic scenarios

Computer-Aided Civil and Infrastructure Engineering, EarlyView.
Abstract Corner cases, which are rare and high‐risk scenarios such as safety‐critical behaviors in autonomous vehicle operations, present significant modeling challenges due to their low occurrence probability and limited data availability. Large language models (LLMs) offer new potential for synthesizing such scenarios, but existing evaluation metrics
Mo Jia, Qixiu Cheng, Chengkun Tao, Yetao Hu, Qi Hong, Wenzhe Cheng, Zhiyuan Liu   +6 more
wiley   +1 more source

Calogero-Sutherland-Moser Systems, Ruijsenaars-Schneider-van Diejen Systems and Orthogonal Polynomials

, 2005
The equilibrium positions of the multi-particle classical Calogero-Sutherland-Moser (CSM) systems with rational/trigonometric potentials associated with the classical root systems are described by the classical orthogonal polynomials; the Hermite ...
Odake, S., Sasaki, R.
core   +2 more sources

Bounding hermite matrix polynomials

Mathematical and Computer Modelling, 2004
The main object under investigation is the family of the Hermite matrix orthogonal polynomials \(\{H_n(x,A)\}_{n\geq 0}\), which depends on the matrix parameter \(A\) having all its eigenvalues in the open right half plane. The main result (Theorem 1) states that \[ \| H_{2n}(x,A)\| \leq \frac{(2n+1)!
Emilio Defez, Antonio Hervás, Lucas Jódar, A. Law   +3 more
openaire   +2 more sources

An Inverted Hermite Kolmogorov–Arnold Network Transformer for multi‐point settlement prediction in high‐speed railway bridge piers

Computer-Aided Civil and Infrastructure Engineering, EarlyView.
Abstract Settlement monitoring of high‐speed railway bridge piers (HSR‐BPs) is critical for ensuring construction and operational safety. However, existing methods for BP settlement prediction face three challenges: limited dataset size, inconsistent observation periods across measuring points, and difficulty in synchronizing spatiotemporal ...
Xunqiang Gong, Qi Liang, Hongyu Wang, Tieding Lu, Junjie Liu, Zhiping Chen, Rui Zhang   +6 more
wiley   +1 more source

The Spectral Connection Matrix for Any Change of Basis within the Classical Real Orthogonal Polynomials

Mathematics, 2015
The connection problem for orthogonal polynomials is, given a polynomial expressed in the basis of one set of orthogonal polynomials, computing the coefficients with respect to a different set of orthogonal polynomials.
Tom Bella, Jenna Reis
doaj   +1 more source

Arithmetic sparsity in mixed Hodge settings

Bulletin of the London Mathematical Society, EarlyView.
Abstract Let X$X$ be a smooth irreducible quasi‐projective algebraic variety over a number field K$K$. Suppose X$X$ is equipped with a p$p$‐adic étale local system compatible with an admissible graded‐polarized variation of mixed Hodge structures on the complex analytification of XC$X_{\operatorname{\mathbb {C}}}$.
Kenneth Chung Tak Chiu
wiley   +1 more source

On the deep‐water and shallow‐water limits of the intermediate long wave equation from a statistical viewpoint

Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.
Abstract We study convergence problems for the intermediate long wave (ILW) equation, with the depth parameter δ>0$\delta > 0$, in the deep‐water limit (δ→∞$\delta \rightarrow \infty$) and the shallow‐water limit (δ→0$\delta \rightarrow 0$) from a statistical point of view.
Guopeng Li, Tadahiro Oh, Guangqu Zheng
wiley   +1 more source

Predictable projections of conformal stochastic integrals: an application to Hermite series and to Widder's representation

, 2011
In this article, we study predictable projections of stochastic integrals with respect to the conformal Brownian motion, extending the connection between powers of the conformal Brownian motion and the corresponding Hermite polynomials.
Casserini, Matteo, Delbaen, Freddy
core   +1 more source