Elastic stability and the zero moment condition

1971 ◽  
Vol 1 (1) ◽  
pp. 19-28 ◽  
Author(s):  
Roger L. Fosdick
Keyword(s):  
Elastic Stability ◽  
Moment Condition ◽  
Zero Moment

HYPERGEOMETRIC BERNOULLI POLYNOMIALS AND APPELL SEQUENCES

2008 ◽  
Vol 04 (05) ◽  
pp. 767-774 ◽  
Author(s):  
ABDUL HASSEN ◽  
HIEU D. NGUYEN
Keyword(s):  
Generating Function ◽  
Hypergeometric Series ◽  
Bernoulli Polynomials ◽  
Moment Condition ◽  
Classical Counterpart ◽  
Equivalent Definition ◽  
Appell Sequences ◽  
Zero Moment ◽  
Complete Analogy

There are two analytic approaches to Bernoulli polynomials Bn(x): either by way of the generating function zexz/(ez - 1) = ∑ Bn(x)zn/n! or as an Appell sequence with zero mean. In this article, we discuss a generalization of Bernoulli polynomials defined by the generating function zN exz/(ez - TN-1(z)), where TN(z) denotes the Nth Maclaurin polynomial of ez, and establish an equivalent definition in terms of Appell sequences with zero moments in complete analogy to their classical counterpart. The zero-moment condition is further shown to generalize to Bernoulli polynomials generated by the confluent hypergeometric series.

Non-Classical Problems in the Theory of Elastic Stability

2001 ◽  
Author(s):  
Isaac Elishakoff ◽  
Yiwei Li ◽  
James H. Starnes, Jr
Keyword(s):  
Elastic Stability

Elastic stability of high dose neutron irradiated spinel

1995 ◽  
Author(s):  
Z Li ◽  
S K Chan ◽  
F A Garner
Keyword(s):  
Elastic Stability ◽  
High Dose

scholarly journals Variable Anisotropic Hardy Spaces with Variable Exponents

2021 ◽  
Vol 9 (1) ◽  
pp. 65-89
Author(s):  
Zhenzhen Yang ◽  
Yajuan Yang ◽  
Jiawei Sun ◽  
Baode Li
Keyword(s):  
Hardy Spaces ◽  
Variable Exponent ◽  
Atomic Decomposition ◽  
Integral Operators ◽  
Moment Condition ◽  
Variable Exponents ◽  
Hölder Continuous ◽  
Multi Level ◽  
The Moment ◽  
Variable Anisotropy

Abstract Let p(·) : ℝ n → (0, ∞] be a variable exponent function satisfying the globally log-Hölder continuous and let Θ be a continuous multi-level ellipsoid cover of ℝ n introduced by Dekel et al. [12]. In this article, we introduce highly geometric Hardy spaces Hp (·)(Θ) via the radial grand maximal function and then obtain its atomic decomposition, which generalizes that of Hardy spaces Hp (Θ) on ℝ n with pointwise variable anisotropy of Dekel et al. [16] and variable anisotropic Hardy spaces of Liu et al. [24]. As an application, we establish the boundedness of variable anisotropic singular integral operators from Hp (·)(Θ) to Lp (·)(ℝ n ) in general and from Hp (·)(Θ) to itself under the moment condition, which generalizes the previous work of Bownik et al. [6] on Hp (Θ).

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