Results 31 to 40 of about 101,561 (280)
Demonstratio Mathematica, 2022 In this article, the authors present two identities involving products of the Bernoulli numbers, provide four alternative proofs for these two identities, derive two closed-form formulas for the Bernoulli numbers in terms of central factorial numbers of ...
Chen Xue-Yan +3 more
doaj +1 more source
q-Bernoulli Numbers Associated with q-Stirling Numbers
Advances in Difference Equations, 2008 We consider Carlitz q-Bernoulli numbers and q-Stirling numbers of the first and the second kinds. From the properties of q-Stirling numbers, we derive many interesting formulas associated with Carlitz q-Bernoulli numbers. Finally, we will prove βn,q=â
Taekyun Kim
doaj +1 more source
Journal of Number Theory, 1995 The author strengthens the Sylvester-Lipschitz theorem for Bernoulli numbers \(B_m\) as follows: ``For an integer \(a\) and a positive integer \(m\) the number \(a^{[\log_2 m]+1} (a^m- 1)B_m/ m\) is an integer.'' It is noted that in a certain sense this strengthening of the Sylvester- Lipschitz theorem is the best possible.
openaire +2 more sources
Advanced Materials, EarlyView.Stacked nanoflake assembly (SNA) membranes can oscillate autonomously, offering opportunities for soft actuation and energy harvesting. This work uncovers the physical mechanism behind the sustained oscillation of SNA membranes in gradient humidity and identifies three governing dimensionless parameters, enabling rational design for optimizing SNA ...
Zijing Zhang +5 more
wiley +1 more source
Mathematics, 2021 In this paper, we further study the generating function involving a variety of special numbers and ploynomials constructed by the second author. Applying the Mellin transformation to this generating function, we define a new class of zeta type functions,
Daeyeoul Kim, Yilmaz Simsek
doaj +1 more source
A cut-invariant law of large numbers for random heaps
, 2015 Heap monoids equipped with Bernoulli measures are a model of probabilistic asynchronous systems. We introduce in this framework the notion of asynchronous stopping time, which is analogous to the notion of stopping time for classical probabilistic ...
Abbes, Samy
core +2 more sources
Bernoulli Related Polynomials and Numbers [PDF]
Mathematics of Computation, 1979 The polynomials φ n ( x ; a , b ) {\varphi _n}(x;a,b) of degree n defined by the equations \[ Δ a φ n ( x
openaire +3 more sources
Advanced Optical Materials, EarlyView.Molecular crystals must withstand both isotropic and anisotropic stress to function in flexible optoelectronics and high‐pressure devices. In situ high‐pressure single‐crystal X‐ray diffraction coupled with DFT‐D computations reveal how an emissive molecular crystal with interdigitated packing bends elastically at ambient‐pressure and remains ...
Arif H. Dar +10 more
wiley +1 more source
Fully degenerate poly-Bernoulli numbers and polynomials
Open Mathematics, 2016 In this paper, we introduce the new fully degenerate poly-Bernoulli numbers and polynomials and inverstigate some properties of these polynomials and numbers.
Kim Taekyun, Kim Dae San, Seo Jong-Jin
doaj +1 more source
Journal of Inequalities and Applications, 2018 In the present paper, firstly we find a number of poles of generating functions of Bernoulli numbers and associated Euler numbers, denoted by n(a,B) $n ( a,\mathbf{B} ) $ and n(a,E) $n ( a,E ) $, respectively.
Serkan Araci, Mehmet Acikgoz
doaj +1 more source