Results 91 to 100 of about 1,563 (216)

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

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

Anharmonic polynomial generalizations of the numbers of Bernoulli and Euler [PDF]

Transactions of the American Mathematical Society, 1922
We consider twelve infinite systems of polynomials in z which for z = 1 degenerate either to the numbers of Bernoulli or Euler, or to others simply dependent upon these. The first part proceeds from the definition of anharmonic polynomials to the specific twelve systems discussed; the second presents an adaptation of the symbolic calculus of Blissard ...
openaire   +1 more source

A New Approach to -Bernoulli Numbers and -Bernoulli Polynomials Related to -Bernstein Polynomials

Advances in Difference Equations, 2010
We present a new generating function related to the -Bernoulli numbers and -Bernoulli polynomials. We give a new construction of these numbers and polynomials related to the second-kind Stirling numbers and -Bernstein polynomials.
Açikgöz Mehmet, Erdal Dilek, Araci Serkan   +2 more
doaj  

A new family of q-Bernstein polynomials: probabilistic viewpoint

Arab Journal of Basic and Applied Sciences
In this paper, we introduce a new class of polynomials, called probabilistic q-Bernstein polynomials, alongside their generating function. Assuming [Formula: see text] is a random variable satisfying moment conditions, we use the generating function of ...
Ayse Karagenc, Mehmet Acikgoz, Serkan Araci   +2 more
doaj   +1 more source

Deep Spatially Varying Coefficient Model for Interpolation of Non‐Stationary Meteorological Data

Environmetrics, Volume 37, Issue 6, September 2026.
ABSTRACT In spatial statistics, the spatially varying coefficient model (SVCM) is widely applied in the analysis and interpolation of non‐stationary spatial data. By incorporating spatially varying coefficients, the model can capture spatial heterogeneity and provide an attractive interpretation of response‐covariate associations.
Tong Wu, Nan Chen, Zhi‐Sheng Ye
wiley   +1 more source

Identities associated with Milne–Thomson type polynomials and special numbers

Journal of Inequalities and Applications, 2018
The purpose of this paper is to give identities and relations including the Milne–Thomson polynomials, the Hermite polynomials, the Bernoulli numbers, the Euler numbers, the Stirling numbers, the central factorial numbers, and the Cauchy numbers.
Yilmaz Simsek, Nenad Cakic
doaj   +1 more source

Some Identities of Ordinary and Degenerate Bernoulli Numbers and Polynomials

, 2019
In this paper, we investigate some identities on Bernoulli numbers and polynomials and those on degenerate Bernoulli numbers and polynomials arising from certain p-adic invariant integrals on Z p .
Dmitry V. Dolgy, Dae San Kim, Jongkyum Kwon, Taekyun Kim   +3 more
core   +1 more source

Dose Optimization Design for Randomized Phase II Trials With Toxicity and Efficacy Endpoints

Pharmaceutical Statistics, Volume 25, Issue 5, September/October 2026.
ABSTRACT Several study designs for identifying optimal biological dose (OBD) have been proposed for phase I, II, and I/II clinical trials, considering toxicity and efficacy of anticancer drugs, especially molecular‐targeted therapies and immune checkpoint inhibitors.
Ryuta Tabata, Tomohiro Ohigashi, Takashi Sozu   +2 more
wiley   +1 more source

Evaluation of cauchy polynomials via degenerate r-Stirling numbers

Mathematical and Computer Modelling of Dynamical Systems
In this paper, within the framework of unsigned degenerate [Formula: see text]-Stirling numbers, we establish connections among Cauchy polynomials, degenerate Bernoulli polynomials, and degenerate hyperharmonic numbers.
Zhuoyu Chen, Yuankui Ma, Taekyun Kim, Dae San Kim, Yanan Hei   +4 more
doaj   +1 more source