Results 91 to 100 of about 47,072 (207)

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

A kind of improved bivariate even order Bernoulli-type multiquadric quasi-interpolation operator and its application in two-dimensional coupled Burgers’ equations

Boundary Value Problems
Multiquadric quasi-interpolation is an efficient high-dimensional approximation algorithm. It can directly obtain the approximation term and its derivatives without solving any large-scale linear equations.
Ruifeng Wu
doaj   +1 more source

Some identities of higher-order Bernoulli, Euler and Hermite polynomials arising from umbral calculus [PDF]

, 2013
In this paper, we study umbral calculus to have alternative ways of obtaining our results. That is, we derive some interesting identities of the higher-order Bernoulli, Euler and Hermite polynomials arising from umbral calculus to have alternative ways ...
Dolgy, Dmitry v., Kim, Dae San, Kim, Taekyun, Rim, Seog-Hoon   +3 more
core  

Multivariate Bernoulli polynomials

, 2019
We introduce a multivariate analogue of Bernoulli polynomials and give their fundamental properties: difference and differential relations, symmetry, explicit formula, inversion formula, multiplication theorem, and binomial type formula. Further, we consider a multivariate analogue of the multiple Bernoulli polynomials and give their fundamental ...
openaire   +2 more sources

SINGULARITY OF RANDOM SYMMETRIC MATRICES—A COMBINATORIAL APPROACH TO IMPROVED BOUNDS

Forum of Mathematics, Sigma, 2019
Let $M_{n}$ denote a random symmetric $n\times n$ matrix whose upper-diagonal entries are independent and identically distributed Bernoulli random variables (which take values $1$ and $-1$ with probability $1/2$ each). It is widely conjectured that $M_{n}
ASAF FERBER, VISHESH JAIN
doaj   +1 more source

A new operational matrix based on Bernoulli polynomials [PDF]

, 2014
In this research, the Bernoulli polynomials are introduced. The properties of these polynomials are employed to construct the operational matrices of integration together with the derivative and product.
Kazem, S., Parand, K., Rad, J. A., Shaban, M.   +3 more
core  

Matiyasevich-type identities for hypergeometric Bernoulli polynomials and poly-Bernoulli polynomials

Moscow Journal of Combinatorics and Number Theory, 2019
The author studies on the Matiyasevich-type identities involving hypergeometric Bernoulli polynomials and poly-Bernoulli polynomials. By using binomial theorem, and also generating functions, the author gives some new formulas involving generalization of Matiyasevich's identity, Miki identity which relates two types of convolutions of Bernoulli numbers
openaire   +2 more sources

Some identities of special numbers and polynomials arising from p-adic integrals on Zp $\mathbb{Z}_{p}$

Advances in Difference Equations, 2019
In recent years, studying degenerate versions of various special polynomials and numbers has attracted many mathematicians. Here we introduce degenerate type 2 Bernoulli polynomials, fully degenerate type 2 Bernoulli polynomials, and degenerate type 2 ...
Dae San Kim, Han Young Kim, Sung-Soo Pyo, Taekyun Kim   +3 more
doaj   +1 more source

Generalized Mixed Type Bernoulli-Gegenbauer Polynomials

Kragujevac Journal of Mathematics, 2023
The generalized mixed type Bernoulli-Gegenbauer polynomials of order α >−1/2 are special polynomials obtained by use of the generating function method. These polynomials represent an interesting mixture between two classes of special functions, namely generalized Bernoulli polynomials and Gegenbauer polynomials.
openaire   +3 more sources

Congruences for Bernoulli numbers and Bernoulli polynomials

Discrete Mathematics, 1997
The Bernoulli numbers and polynomials are defined by \(B_0=1\), \(\sum^{n-1}_{k=0}{n\choose k} B_k= 0\) \((n=2,3,\dots)\) and \(B_n(x)= \sum^n_{k=0}{n\choose k} B_{n-k} x^k\), respectively. Two basic congruences for Bernoulli numbers are the Kummer congruences (used in the theory of Fermat's last theorem) and the von Staudt-Clausen theorem. There exist
openaire   +1 more source