Results 81 to 90 of about 18,239 (195)

Arithmetic Properties of Bernoulli–Padé Numbers and Polynomials

Journal of Number Theory, 2002
Let \(r,s\) be nonnegative integers. The authors define rational numbers \(B_n^{(r,s)}\), the \(n\)th Bernoulli-Padé numbers of order \((r,s)\), by the formula \[ \frac{(-1)^sr!s!t^{r+s+1}}{(r+s)!(r+s+1)!(Q^{(r,s)}(t)e^t- P^{(r,s)}(t))} = \sum_{n=0}^\infty B_n^{(r,s)}\frac{t^n}{n!}, \] where \(P^{(r,s)}(t)\) and \(Q^{(r,s)}(t)\) are polynomials (given ...
Dilcher, Karl, Louise, Louise
openaire   +2 more sources

C∞‐Structures for Liénard Equations and New Exact Solutions to a Class of Klein–Gordon Equations

Mathematical Methods in the Applied Sciences, Volume 49, Issue 4, Page 2795-2822, 15 March 2026.
ABSTRACT Liénard equations are analyzed using the recent theory of 𝒞∞‐structures. For each Liénard equation, a 𝒞∞‐structure is determined by using a Lie point symmetry and a 𝒞∞‐symmetry. Based on this approach, a novel method for integrating these equations is proposed, which consists in solving sequentially two completely integrable Pfaffian equations.
Beltrán de la Flor, Adrián Ruiz, Concepción Muriel   +2 more
wiley   +1 more source

PearSAN: A Machine Learning Method for Inverse Design Using Pearson Correlated Surrogate Annealing

Advanced Optical Materials, Volume 14, Issue 10, 13 March 2026.
A machine learning–assisted inverse design framework is introduced to overcome the curse of dimensionality in complex nanophotonic design problems. By leveraging Pearson‐correlated surrogate annealing (PearSAN) method within a generative latent space, rapid convergence toward optimal thermophotovoltaic metasurface designs is achieved, enabling precise ...
Michael Bezick, Blake A. Wilson, Vaishnavi Iyer, Yuheng Chen, Vladimir M. Shalaev, Sabre Kais, Alexander V. Kildishev, Brad Lackey, Alexandra Boltasseva   +8 more
wiley   +1 more source

q-Bernoulli numbers and q-Bernoulli polynomials revisited

Advances in Difference Equations, 2011
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.
Kim Taekyun, Lee Byungje, Ryoo Cheon
doaj  

On the Values of the Weighted 𝑞-Zeta and 𝐿-Functions

Discrete Dynamics in Nature and Society, 2011
Recently, the modified 𝑞-Bernoulli numbers and polynomials are introduced in (D. V. Dolgy et al., in press). These numbers are valuable to study the weighted 𝑞-zeta and 𝐿-functions.
T. Kim, S. H. Lee, Hyeon-Ho Han, C. S. Ryoo   +3 more
doaj   +1 more source

Some congruences involving generalized Bernoulli numbers and Bernoulli polynomials

Acta Arithmetica
Let $[x]$ be the integral part of $x$, $n>1$ be a positive integer and $χ_n$ denote the trivial Dirichlet character modulo $n$. In this paper, we use an identity established by Z. H. Sun to get congruences of $T_{m,k}(n)=\sum_{x=1}^{[n/m]}\frac{χ_n(x)}{x^k}\left(\bmod n^{r+1}\right)$ for $r\in \{1,2\}$, any positive integer $m $ with $n \equiv \pm 1
Li, Ni, Ma, Rong
openaire   +2 more sources

Duals of Bernoulli Numbers and Polynomials and Euler Number and Polynomials

, 2015
A sequence inverse relationship can be defined by a pair of infinite inverse matrices. If the pair of matrices are the same, they define a dual relationship. Here presented is a unified approach to construct dual relationships via pseudo-involution of Riordan arrays.
He, Tian-Xiao, Zheng, Jinze
openaire   +2 more sources

Some Identities of Bernoulli Numbers and Polynomials Associated with Bernstein Polynomials

Advances in Difference Equations, 2010
We investigate some interesting properties of Bernstein polynomials associated with boson p-adic integrals on Zp.
Kim T., Kim M.-S., Lee B., Ryoo C.-S.
openaire   +5 more sources

On the Modified q-Bernoulli Numbers of Higher Order with Weight

Abstract and Applied Analysis, 2012
The purpose of this paper is to give some properties of the modified q-Bernoulli numbers and polynomials of higher order with weight. In particular, by using the bosonic p-adic q-integral on ℤp, we derive new identities of q-Bernoulli numbers and ...
T. Kim, J. Choi, Y.-H. Kim, S.-H. Rim
doaj   +1 more source

Identities on the k-ary Lyndon words related to a family of zeta functions

, 2016
The main aim of this paper is to investigate and introduce relations between the numbers of k-ary Lyndon words and unified zeta-type functions which was defined by Ozden et al [15, p. 2785].
Kucukoglu, Irem, Simsek, Yilmaz
core