Results 61 to 70 of about 203,104 (277)

Generalized q-Euler Numbers and Polynomials of Higher Order and Some Theoretic Identities

Journal of Inequalities and Applications, 2010
We give a new construction of the q-Euler numbers and polynomials of higher order attached to Dirichlet's character χ. We derive some theoretic identities involving the generalized q-Euler numbers and polynomials of higher order.
T. Kim, Y. H. Kim
doaj   +1 more source

Some formulas related to Euler's product expansion for cosine function [PDF]

Notes on Number Theory and Discrete Mathematics
In this paper, we derive by using elementary methods some continued fractions, certain identities involving derivatives of tan x, several expressions for log cosh x and an identity for π², from a series expansion of tan x, which gives the product ...
Taekyun Kim, Dae San Kim
doaj   +1 more source

On Stirling numbers and Euler sums

Journal of Computational and Applied Mathematics, 1997
In this paper, we propose another yet generalization of Stirling numbers of the first kind for noninteger values of their arguments. We discuss the analytic representations of Stirling numbers through harmonic numbers, the generalized hypergeometric function and the logarithmic beta integral.
openaire   +2 more sources

Microscale Mapping of Fiber Strain and Damage in Composite Wrinkled Laminates Using Computed Tomography Assisted Wide‐Angle X‐Ray Scattering

Advanced Science, EarlyView.
This study combines full‐field tomography with diffraction mapping to quantify radial (ε002$\varepsilon _{002}$) and axial (ε100$\varepsilon _{100}$) lattice strain in wrinkled carbon‐fiber specimens for the first time. Radial microstrain gradients (−14.5 µεMPa$\varepsilon \mathrm{MPa}$−1) are found to signal damage‐prone zones ahead of failure, which ...
Hoang Minh Luong, James Trevarthen, Igor Dolbnya, Wadwan Singhapong, Nicholas Pilato, Richard Butler, Jiraphant Srisuriyachot, Alexander J. G. Lunt   +7 more
wiley   +1 more source

A Research on a Certain Family of Numbers and Polynomials Related to Stirling Numbers, Central Factorial Numbers, and Euler Numbers

Journal of Applied Mathematics, 2013
Recently, many mathematicians have studied different kinds of the Euler, Bernoulli, and Genocchi numbers and polynomials. In this paper, we give another definition of polynomials Ũn(x).
J. Y. Kang, C. S. Ryoo
doaj   +1 more source

Mild Focal Cooling Decouples Dendrites to Reconfigure Cortical Output

Advanced Science, EarlyView.
Mild cooling of the cortical surface selectively modulates apical dendritic excitability, plasticity, and somato‐dendritic coupling, while uncoupling these effects from basal dendrites, and reshapes apical‐driven responses in barrel cortex during whisker touch.
Meisam Habibi Matin, Shulan Xiao, Krishna Jayant   +2 more
wiley   +1 more source

Inherently Disordered Auxetic Metamaterials

Advanced Science, EarlyView.
Inherently disordered auxetic metamaterials based on random chiral Delaunay triangulations are designed and investigated using numerical simulations and experimental tests. These disordered frameworks exhibit orthotropic behavior and a large negative Poisson's ratio (ca.
Matteo Montanari, Reza Moghimimonfared, Andrea Spaggiari, Luke Mizzi   +3 more
wiley   +1 more source

Laguerre-Type Bernoulli and Euler Numbers and Related Fractional Polynomials

Mathematics
We extended the classical Bernoulli and Euler numbers and polynomials to introduce the Laguerre-type Bernoulli and Euler numbers and related fractional polynomials.
Paolo Emilio Ricci, Rekha Srivastava, Diego Caratelli   +2 more
doaj   +1 more source

On the Symmetric Properties of Higher-Order Twisted q-Euler Numbers and Polynomials

Advances in Difference Equations, 2010
In 2009, Kim et al. gave some identities of symmetry for the twisted Euler polynomials of higher-order, recently. In this paper, we extend our result to the higher-order twisted q-Euler numbers and polynomials.
Sun-Jung Lee, Seog-Hoon Rim, Jeong-Hee Jin, Eun-Jung Moon   +3 more
doaj   +1 more source

A Note on Type 2 Degenerate q-Euler Polynomials

Mathematics, 2019
Recently, type 2 degenerate Euler polynomials and type 2 q-Euler polynomials were studied, respectively, as degenerate versions of the type 2 Euler polynomials as well as a q-analog of the type 2 Euler polynomials.
Taekyun Kim, Dae San Kim, Han Young Kim, Sung-Soo Pyo   +3 more
doaj   +1 more source