Results 71 to 80 of about 101,104 (278)

On the 𝑞-Bernoulli Numbers and Polynomials with Weight 𝜶

Abstract and Applied Analysis, 2011
We present a systemic study of some families of higher-order 𝑞-Bernoulli numbers and polynomials with weight 𝛼. From these studies, we derive some interesting identities on the 𝑞-Bernoulli numbers and polynomials with weight 𝛼.
T. Kim, J. Choi
doaj   +1 more source

Special Numbers and Polynomials Including Their Generating Functions in Umbral Analysis Methods

Axioms, 2018
In this paper, by applying umbral calculus methods to generating functions for the combinatorial numbers and the Apostol type polynomials and numbers of order k, we derive some identities and relations including the combinatorial numbers, the Apostol ...
Yilmaz Simsek
doaj   +1 more source

Compositional Bernoulli numbers

, 2007
16 pages, to appear in Afr.
Blandin, Hector, Diaz, Rafael
openaire   +2 more sources

Scalable High‐Force Zipping Electrostatic Actuators

Advanced Intelligent Systems, EarlyView.
An electrostatic actuator architecture is presented that combines high energy density with forces and strokes suited for wearable soft robotics. By folding patterned thin films into a scalable honeycomb of zipping units, performance becomes tunable through series–parallel design, achieving over 40 N and 28 J/kg.
Fabio Caruso, Amir Firouzeh, Herbert Shea   +2 more
wiley   +1 more source

Some Identities between the Extended -Bernstein Polynomials with Weight and -Bernoulli Polynomials with Weight (,)

Journal of Applied Mathematics, 2013
Using bosonic -adic -integral on , we give some interesting relationships between -Bernoulli numbers with weight (,) and -Bernstein polynomials with weight .
H. Y. Lee, C. S. Ryoo
doaj   +1 more source

Some Identities of Degenerate Bell Polynomials

Mathematics, 2020
The new type degenerate of Bell polynomials and numbers were recently introduced, which are a degenerate version of Bell polynomials and numbers and are different from the previously introduced partially degenerate Bell polynomials and numbers.
Taekyun Kim, Dae San Kim, Han Young Kim, Jongkyum Kwon   +3 more
doaj   +1 more source

Digital Surface‐Enhanced Raman Scattering With Event Counting and Spectrum Learning for Label‐Free Protein Quantification

Advanced Intelligent Systems, EarlyView.
A statistical and machine learning‐assisted surface‐enhanced Raman scattering (SERS) framework is developed for label‐free quantification of low‐abundance analytes, including proteins. Combining digital SERS event counting with binomial regression and an artificial neural network (ANN) trained on full spectra, the approach achieves picomolar detection ...
Eni Kume, James Rice
wiley   +1 more source

An Expression for Bernoulli Numbers [PDF]

Proceedings of the Glasgow Mathematical Association, 1953
In Muir's Theory of Determinants, Vol. III, pp. 232–237, there will be found accounts of papers by H. Nägelsbach, J. Hammond and J. W. L. Glaisher, in which expressions for the Bernoulli numbers are obtained in terms of determinants. In the present paper an expression for Bn will be derived which appears to be new, but which is very like some of those ...
openaire   +2 more sources

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. On the other hand, Zagier was able to
openaire   +1 more source

Influence of Wall Deformation Structure on the Liquid Film Flow Behavior Under Turbulent Conditions

Asia-Pacific Journal of Chemical Engineering, EarlyView.
ABSTRACT To explore the influence of typical wall deformation structure in the scrubbing‐cooling tube on the liquid film, this paper studied the liquid film flow behavior on the riblet walls with representative riblet radii and compared them with the flat wall. Under different liquid film Reynolds numbers (Rel = 8.3 × 103 ~ 3.14 × 104), the liquid film
Qian Liu, Yifei Wang, Jie Zeng, Zongren Pan, Dawei Feng, Guangsuo Yu   +5 more
wiley   +1 more source