Results 41 to 50 of about 2,081 (228)

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

A Note on Bernoulli Numbers and Shintani Generalized Bernoulli Polynomials [PDF]

Transactions of the American Mathematical Society, 1996
Generalized Bernoulli polynomials were introduced by Shintani in 1976 in order to express the special values at non-positive integers of Dedekind zeta functions for totally real numbers. The coefficients of such polynomials are finite combinations of products of Bernoulli numbers which are difficult to get hold of.
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Arithmetical properties of double Möbius-Bernoulli numbers

Open Mathematics, 2019
Given positive integers n, n′ and k, we investigate the Möbius-Bernoulli numbers Mk(n), double Möbius-Bernoulli numbers Mk(n,n′), and Möbius-Bernoulli polynomials Mk(n)(x).
Bayad Abdelmejid, Kim Daeyeoul, Li Yan
doaj   +1 more source

Differentiated Impacts of EU Rural Development Measures: A Finite Mixture Evaluation of Italian Olive Farms

Applied Economic Perspectives and Policy, EarlyView.
ABSTRACT This paper examines the relationship between participation in the EU Rural Development Program and the economic performance of Italian olive farms using a finite‐mixture model with inverse‐probability‐weighted regression adjustment. Based on 2010–2022 FADN panel data, it estimates heterogeneous treatment effects while correcting for selection ...
Francesco Caracciolo, Marilena Furno
wiley   +1 more source

A note on degenerate poly-Bernoulli numbers and polynomials [PDF]

, 2015
In this paper, we consider the degenerate poly-Bernoulli polynomials and present new and explicit formulas for computing them in terms of the degenerate Bernoulli polynomials and Stirling numbers of the second kind.
Dae San Kim, Taekyun Kim
semanticscholar   +1 more source

Physics‐Grounded Probabilistic Bits for Hardware‐Efficient Intelligent Inference and Optimization

Advanced Intelligent Systems, EarlyView.
Si–SiNx interface traps are harnessed as a complementary metal–oxide–semiconductor‐compatible source of controllable randomness for probabilistic bits. Pulse‐width‐programmed stochastic capture converts nanoscale defect dynamics into Boltzmann‐consistent binary outputs, while a physics‐based Simulation Program with Integrated Circuit Emphasis model ...
Dokyoung Lee, Jun‐Young Park, Joon‐Kyu Han, Sungho Kim   +3 more
wiley   +1 more source

A Note on the Modified q-Bernoulli Numbers and Polynomials with Weight α

Abstract and Applied Analysis, 2011
A systemic study of some families of the modified q-Bernoulli numbers and polynomials with weight α is presented by using the p-adic q-integration ℤp.
T. Kim, D. V. Dolgy, S. H. Lee, B. Lee, S. H. Rim   +4 more
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Some applications of degenerate poly-Bernoulli numbers and polynomials [PDF]

Georgian Mathematical Journal, 2015
In this paper, we consider degenerate poly-Bernoulli numbers and polynomials associated with a polylogarithmic function and a p-adic invariant integral on ℤ p {\mathbb{Z}_{p}} .
Dae San Kim, Taekyun Kim
semanticscholar   +1 more source

Improving the Finite Sample Estimation of Average Treatment Effects Using Double/Debiased Machine Learning With Propensity Score Calibration

Journal of Applied Econometrics, EarlyView.
ABSTRACT Double/debiased machine learning (DML) uses for estimating an average treatment effect (ATE) a double‐robust score function that relies on the prediction of nuisance functions, such as the propensity score, which is the probability of treatment assignment given covariates.
Daniele Ballinari, Nora Bearth
wiley   +1 more source

Some identities related to degenerate Bernoulli and degenerate Euler polynomials

Mathematical and Computer Modelling of Dynamical Systems
The aim of this paper is to study degenerate Bernoulli and degenerate Euler polynomials and numbers and their higher-order analogues. We express the degenerate Euler polynomials in terms of the degenerate Bernoulli polynomials and vice versa.
Taekyun Kim, Dae San Kim, Wonjoo Kim, Jongkyum Kwon   +3 more
doaj   +1 more source