scholarly journals Exact asymptotic behavior of magnetic stripe domain arrays

2013 ◽  
Vol 87 (6) ◽  
Author(s):  
Tom H. Johansen ◽  
Alexey V. Pan ◽  
Yuri M. Galperin
Keyword(s):  
Asymptotic Behavior ◽  
Stripe Domain ◽  
Exact Asymptotic Behavior

scholarly journals Existence and Exact Asymptotic Behavior of Positive Solutions for a Fractional Boundary Value Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Habib Mâagli ◽  
Noureddine Mhadhebi ◽  
Noureddine Zeddini
Keyword(s):  
Asymptotic Behavior ◽  
Continuous Function ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Exact Asymptotic Behavior ◽  
Nonnegative Continuous Function

We establish the existence and uniqueness of a positive solution for the fractional boundary value problem , with the condition , where , and is a nonnegative continuous function on that may be singular at or .

Exact asymptotic behavior near the boundary to the solution for singular nonlinear Dirichlet problems

2009 ◽  
Vol 71 (9) ◽  
pp. 4137-4150 ◽  
Author(s):  
Sonia Ben Othman ◽  
Habib Mâagli ◽  
Syrine Masmoudi ◽  
Malek Zribi
Keyword(s):  
Asymptotic Behavior ◽  
Dirichlet Problems ◽  
Exact Asymptotic Behavior

Asymptotic Behavior of The Unique Solution to a Singular Elliptic Problem With Nonlinear Convection Term And Singular Weight

2008 ◽  
Vol 8 (2) ◽  
Author(s):  
Zhijun Zhang
Keyword(s):  
Asymptotic Behavior ◽  
Local Solution ◽  
Variation Theory ◽  
Convection Term ◽  
Unique Classical Solution ◽  
Nonlinear Convection ◽  
Comparison Functions ◽  
Exact Asymptotic Behavior ◽  
Nonlinear Convection Term ◽  
Singular Dirichlet Problem

AbstractBy Karamata regular variation theory, we first derived the exact asymptotic behavior of the local solution to the problem -φʹʹ(s) = g(φ(s)), φ(s) > 0, s ∈ (0, a) and φ(0) = 0. Then, by a perturbation method and constructing comparison functions, we derived the exact asymptotic behavior of the unique classical solution near the boundary to a singular Dirichlet problem -Δu = b(x)g(u) + λ|▽u|

scholarly journals FULLY DISCRETE ADAPTIVE METHODS FOR A BLOW-UP PROBLEM

2004 ◽  
Vol 14 (10) ◽  
pp. 1425-1450 ◽  
Author(s):  
CRISTINA BRÄNDLE ◽  
PABLO GROISMAN ◽  
JULIO D. ROSSI
Keyword(s):  
Asymptotic Behavior ◽  
Positive Solutions ◽  
Blow Up ◽  
Numerical Study ◽  
Adaptive Methods ◽  
Fully Discrete ◽  
Adaptive Procedures ◽  
Exact Asymptotic Behavior ◽  
Blow Up Rate ◽  
Continuous Problem

We present adaptive procedures in space and time for the numerical study of positive solutions to the following problem: [Formula: see text] with p,m>0. We describe how to perform adaptive methods in order to reproduce the exact asymptotic behavior (the blow-up rate and the blow-up set) of the continuous problem.

scholarly journals ON THE QUANTUM INVARIANT FOR THE BRIESKORN HOMOLOGY SPHERES

2005 ◽  
Vol 16 (06) ◽  
pp. 661-685 ◽  
Author(s):  
KAZUHIRO HIKAMI
Keyword(s):  
Asymptotic Behavior ◽  
Irreducible Representation ◽  
Fundamental Group ◽  
Modular Form ◽  
Quantum Invariant ◽  
Exact Asymptotic Behavior ◽  
Chern Simons ◽  
Eichler Integrals ◽  
Limiting Value ◽  
Modular Property

We study an exact asymptotic behavior of the Witten–Reshetikhin–Turaev SU(2) invariant for the Brieskorn homology spheres Σ(p1, p2, p3) by use of properties of the modular form following a method proposed by Lawrence and Zagier. Key observation is that the invariant coincides with a limiting value of the Eichler integral of the modular form with weight 3/2. We show that the Casson invariant is related to the number of the Eichler integrals which do not vanish in a limit τ → N ∈ ℤ. Correspondingly there is a one-to-one correspondence between the non-vanishing Eichler integrals and the irreducible representation of the fundamental group, and the Chern–Simons invariant is given from the Eichler integral in this limit. It is also shown that the Ohtsuki invariant follows from a nearly modular property of the Eichler integral, and we give an explicit form in terms of the L-function.

KAZHDAN CONSTANTS FOR SLn(ℤ)

2005 ◽  
Vol 15 (05n06) ◽  
pp. 971-995 ◽  
Author(s):  
MARTIN KASSABOV
Keyword(s):  
Asymptotic Behavior ◽  
Cayley Graph ◽  
Upper Bound ◽  
Spectral Gap ◽  
Abelian Groups ◽  
Working Time ◽  
Generating Set ◽  
Replacement Algorithm ◽  
Exact Asymptotic Behavior ◽  
Product Replacement

In this article we improve the known Kazhdan constant for SL n(ℤ) with respect to the generating set of the elementary matrices. We prove that the Kazhdan constant is bounded from below by [Formula: see text], which gives the exact asymptotic behavior of the Kazhdan constant, as n goes to infinity, since [Formula: see text] is an upper bound. We can use this bound to improve the bounds for the spectral gap of the Cayley graph of SL n(𝔽p) and for the working time of the product replacement algorithm for abelian groups.

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