scholarly journals Hardy Type Asymptotics for Cosine Series in Several Variables with Decreasing Power-Like Coefficients

2016 ◽  
Vol 5 ◽  
pp. 35-51 ◽  
Author(s):  
Victor Kozyakin
Keyword(s):  
Asymptotic Behavior ◽  
Asymptotic Analysis ◽  
Trigonometric Series ◽  
Mathematical Analysis ◽  
Tauberian Theorems ◽  
Abel Transform ◽  
Cosine Series ◽  
Hardy Type ◽  
Several Variables ◽  
Explicit Expressions

The investigation of the asymptotic behavior of trigonometric series near the origin is a prominent topic in mathematical analysis. For trigonometric series in one variable, this problem was exhaustively studied by various authors in a series of publications dating back to the work of G. H. Hardy, 1928. Trigonometric series in several variables have got less attention. The aim of the work is to partially fill this gap by finding the asymptotics of trigonometric series in several variables with the terms, having a form of `one minus the cosine' up to a decreasing power-like factor.The approach developed in the paper is quite elementary and essentially algebraic. It does not rely on the classic machinery of the asymptotic analysis such as slowly varying functions, Tauberian theorems or the Abel transform. However, in our case, it allows obtaining explicit expressions for the asymptotics and extending to the general case of trigonometric series in several variables classical results of G. H. Hardy and other authors known for the case of one variable.

An asymptotic analysis for Hamilton–Jacobi equations with large Hamiltonian drift terms

2017 ◽  
Vol 0 (0) ◽  
Author(s):  
Taiga Kumagai
Keyword(s):  
Asymptotic Behavior ◽  
Euclidean Space ◽  
Asymptotic Analysis ◽  
Open Subset ◽  
Dimensional Euclidean Space ◽  
Asymptotic Behavior Of Solutions ◽  
Two Dimensional ◽  
Jacobi Equations ◽  
Drift Terms

AbstractWe investigate the asymptotic behavior of solutions of Hamilton–Jacobi equations with large Hamiltonian drift terms in an open subset of the two-dimensional Euclidean space. The drift is given by

scholarly journals The Small-Péclet-Number Approximation for Radiative Zones and its Application to Shear Layer Instabilities

2004 ◽  
Vol 215 ◽  
pp. 346-347
Author(s):  
F. Lignières
Keyword(s):  
Asymptotic Behavior ◽  
Thermal Diffusivity ◽  
Asymptotic Analysis ◽  
Shear Layer ◽  
Peclet Number ◽  
Earth Atmosphere ◽  
Hydrodynamic Equations ◽  
The Earth ◽  
Shear Instabilities ◽  
Thermal Diffusivities

Thermal diffusivities within stars are higher by several orders of magnitude than in the earth atmosphere. This particularity of the stellar fluid has subtle effects on the dynamics of stably stratified radiative zones as it contributes to favour some flows and supress others. An asymptotic analysis of hydrodynamic equations for large values of the thermal diffusivity is presented and this results in a simplification of the dynamical effects of the thermal diffusivity. This asymptotic behavior proved to be very useful to understand shear instabilities of Kelvin-Helmholtz type.

scholarly journals The role of the range of dispersal in a nonlocal Fisher-KPP equation: an asymptotic analysis

2020 ◽  
pp. 2050032
Author(s):  
Julien Brasseur
Keyword(s):  
Asymptotic Behavior ◽  
Asymptotic Analysis ◽  
Positive Solution ◽  
Nonlocal Problem ◽  
Type Equation ◽  
Independent Interest ◽  
Kpp Equation ◽  
Open Question

In this paper, we study the asymptotic behavior as [Formula: see text] of solutions [Formula: see text] to the nonlocal stationary Fisher-KPP type equation [Formula: see text] where [Formula: see text] and [Formula: see text]. Under rather mild assumptions and using very little technology, we prove that there exists one and only one positive solution [Formula: see text] and that [Formula: see text] as [Formula: see text] where [Formula: see text]. This generalizes the previously known results and answers an open question raised by Berestycki et al. Our method of proof is also of independent interest as it shows how to reduce this nonlocal problem to a local one. The sharpness of our assumptions is also briefly discussed.

scholarly journals Inequalities of Hardy Type via Superquadratic Functions with General Kernels and Measures for Several Variables on Time Scales

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
H. M. Rezk ◽  
H. A. Abd El-Hamid ◽  
A. M. Ahmed ◽  
Ghada AlNemer ◽  
M. Zakarya
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Minkowski Inequality ◽  
Jensen Inequality ◽  
Hardy Type ◽  
Several Variables ◽  
Special Cases ◽  
Superquadratic Functions

We use the properties of superquadratic functions to produce various improvements and popularizations on time scales of the Hardy form inequalities and their converses. Also, we include various examples and interpretations of the disparities in the literature that exist. In particular, our findings can be seen as refinements of some recent results closely linked to the time-scale inequalities of the classical Hardy, Pólya-Knopp, and Hardy-Hilbert. Some continuous inequalities are derived from the main results as special cases. The essential results will be proved by making use of some algebraic inequalities such as the Minkowski inequality, the refined Jensen inequality, and the Bernoulli inequality on time scales.

A Class of Generalized Hypergeometric Functions in Several Variables

1992 ◽  
Vol 44 (6) ◽  
pp. 1317-1338 ◽  
Author(s):  
Zhimin Yan
Keyword(s):  
Asymptotic Behavior ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Hypergeometric Function ◽  
Unique Solution ◽  
Hypergeometric Functions ◽  
Integral Representations ◽  
Gaussian Hypergeometric Function ◽  
Generalized Hypergeometric Functions ◽  
Several Variables

AbstractWe study a class of generalized hypergeometric functions in several variables introduced by A. Korânyi. It is shown that the generalized Gaussian hypergeometric function is the unique solution of a system partial differential equations. Analogues of some classical results such as Kummer relations and Euler integral representations are established. Asymptotic behavior of generalized hypergeometric functions is obtained which includes some known estimates.

ASYMPTOTIC BEHAVIOR OF THE GINZBURG-LANDAU FUNCTIONAL ON COMPLEX LINE BUNDLES OVER COMPACT RIEMANN SURFACES

1996 ◽  
Vol 08 (03) ◽  
pp. 457-486
Author(s):  
GIANDOMENICO ORLANDI
Keyword(s):  
Asymptotic Behavior ◽  
Asymptotic Analysis ◽  
Chern Class ◽  
Riemann Surfaces ◽  
Line Bundles ◽  
Complex Line ◽  
Ginzburg Landau ◽  
Renormalized Energy ◽  
Compact Riemann Surfaces ◽  
Complex Line Bundles

Motivated by the works of F. Bethuel, H. Brezis, F. Hélein [5] and of F. Bethuel, T. Rivière [6], an asymptotic analysis is carried out for minimizers of the Ginzburg-Landau functional depending on a parameter ε, in the more general case of complex line bundles with prescribed Chern class over compact Riemann surfaces. Such a functional describes a 2-dimensional abelian Higgs model and is also related to phenomena in superconductivity. A suitable renormalized energy is defined which characterizes the singularities (degree one vortices) of the limiting configuration.

scholarly journals Asymptotic Analysis of Plausible Tree Hash Modes for SHA-3

2017 ◽  
pp. 212-239
Author(s):  
Kevin Atighehchi ◽  
Alexis Bonnecaze
Keyword(s):  
Asymptotic Behavior ◽  
Asymptotic Analysis ◽  
Reasonable Assumption ◽  
Resource Usage ◽  
Modes Of Operation ◽  
Software Applications ◽  
Single Tree ◽  
Mode Of Operation ◽  
Different Types

Discussions about the choice of a tree hash mode of operation for a standardization have recently been undertaken. It appears that a single tree mode cannot address adequately all possible uses and specifications of a system. In this paper, we review the tree modes which have been proposed, we discuss their problems and propose solutions. We make the reasonable assumption that communicating systems have different specifications and that software applications are of different types (securing stored content or live-streamed content). Finally, we propose new modes of operation that address the resource usage problem for three representative categories of devices and we analyse their asymptotic behavior.

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