Positivity and continuity of the Lyapounov exponent for shifts on T d with arbitrary frequency vector and real analytic potentiald with arbitrary frequency vector and real analytic potential

2005 ◽  
Vol 96 (1) ◽  
pp. 313-355 ◽  
Author(s):  
J. Bourgain
Keyword(s):  
Frequency Vector ◽  
Lyapounov Exponent ◽  
Real Analytic ◽  
Arbitrary Frequency ◽  
Analytic Potential

Moderate deviations for linear eigenvalue statistics of β-ensembles

2021 ◽  
pp. 2250017
Author(s):  
Fuqing Gao ◽  
Jianyong Mu
Keyword(s):  
Moderate Deviation ◽  
Main Ingredient ◽  
Moderate Deviation Principle ◽  
Uniform Estimates ◽  
Linear Eigenvalue Statistics ◽  
Deviation Principle ◽  
Eigenvalue Statistics ◽  
Real Analytic ◽  
The One ◽  
Analytic Potential

We establish a moderate deviation principle for linear eigenvalue statistics of [Formula: see text]-ensembles in the one-cut regime with a real-analytic potential. The main ingredient is to obtain uniform estimates for the correlators of a family of perturbations of [Formula: see text]-ensembles using the loop equations.

Viscous stability of quasi-periodic tori

2012 ◽  
Vol 34 (1) ◽  
pp. 185-210
Author(s):  
ZHENGUO LIANG ◽  
JUN YAN ◽  
YINGFEI YI
Keyword(s):  
Resonant Frequency ◽  
Viscosity Solutions ◽  
Invariant Torus ◽  
Frequency Vector ◽  
Effective Hamiltonian ◽  
Hölder Exponent ◽  
Hölder Continuous ◽  
Lipschitz Continuous ◽  
Real Analytic ◽  
Uniformly Lipschitz

AbstractThis paper is devoted to the study of $P$-regularity of viscosity solutions $u(x,P)$, $P\in {\Bbb R}^n$, of a smooth Tonelli Lagrangian $L:T {\Bbb T}^n \rightarrow {\Bbb R}$ characterized by the cell equation $H(x,P+D_xu(x,P))=\overline {H}(P)$, where $H: T^* {\Bbb T}^n\rightarrow {\Bbb R}$ denotes the Hamiltonian associated with $L$ and $\overline {H}$ is the effective Hamiltonian. We show that if $P_0$ corresponds to a quasi-periodic invariant torus with a non-resonant frequency, then $D_xu(x,P)$ is uniformly Hölder continuous in $P$ at $P_0$ with Hölder exponent arbitrarily close to $1$, and if both $H$ and the torus are real analytic and the frequency vector of the torus is Diophantine, then $D_xu(x,P)$ is uniformly Lipschitz continuous in $P$ at $P_0$, i.e., there is a constant $C\gt 0$ such that $\|D_xu(\cdot ,P)-D_xu(\cdot ,P_0)\|_{\infty }\le C\|P-P_0\|$ for $\|P-P_0\|\ll 1$. Similar P-regularity of the Peierls barriers associated with $L(x,v)- \langle P,v \rangle $is also obtained.

The Moments of Real Analytic Funtions

2020 ◽  
pp. 112-118 ◽  
Author(s):  
Ricardo Estrada
Keyword(s):  
Real Analytic

scholarly journals Time-Domain Studies of General Dispersive Anisotropic Media by the Complex-Conjugate Pole–Residue Pairs Model

2021 ◽  
Vol 11 (9) ◽  
pp. 3844
Author(s):  
Konstantinos P. Prokopidis ◽  
Dimitrios C. Zografopoulos
Keyword(s):  
Time Domain ◽  
Electromagnetic Wave Propagation ◽  
Frequency Dispersion ◽  
Magnetized Plasma ◽  
Dispersive Media ◽  
Complex Conjugate ◽  
Pole Residue ◽  
Permittivity And Permeability ◽  
Arbitrary Frequency ◽  
Difference Time

A novel finite-difference time-domain formulation for the modeling of general anisotropic dispersive media is introduced in this work. The method accounts for fully anisotropic electric or magnetic materials with all elements of the permittivity and permeability tensors being non-zero. In addition, each element shows an arbitrary frequency dispersion described by the complex-conjugate pole–residue pairs model. The efficiency of the technique is demonstrated in benchmark numerical examples involving electromagnetic wave propagation through magnetized plasma, nematic liquid crystals and ferrites.

On finite sums of periodic functions

2020 ◽  
Vol 27 (2) ◽  
pp. 265-269
Author(s):  
Alexander Kharazishvili
Keyword(s):  
Analytic Function ◽  
Real Line ◽  
Real Analytic Function ◽  
Periodic Functions ◽  
Uniform Limit ◽  
The Real ◽  
Pointwise Limit ◽  
Finite Sums ◽  
Real Analytic

AbstractIt is shown that any function acting from the real line {\mathbb{R}} into itself can be expressed as a pointwise limit of finite sums of periodic functions. At the same time, the real analytic function {x\rightarrow\exp(x^{2})} cannot be represented as a uniform limit of finite sums of periodic functions and, simultaneously, this function is a locally uniform limit of finite sums of periodic functions. The latter fact needs the techniques of Hamel bases.

scholarly journals Modular invariance in finite temperature Casimir effect

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Francesco Alessio ◽  
Glenn Barnich
Keyword(s):  
Partition Function ◽  
Chemical Potential ◽  
Casimir Effect ◽  
Temperature Inversion ◽  
Massless Scalar ◽  
Partition Functions ◽  
Parallel Plates ◽  
Modular Transformations ◽  
Real Analytic ◽  
Set Up

Abstract The temperature inversion symmetry of the partition function of the electromagnetic field in the set-up of the Casimir effect is extended to full modular transformations by turning on a purely imaginary chemical potential for adapted spin angular momentum. The extended partition function is expressed in terms of a real analytic Eisenstein series. These results become transparent after explicitly showing equivalence of the partition functions for Maxwell’s theory between perfectly conducting parallel plates and for a massless scalar with periodic boundary conditions.

40‐MHz high‐frequency vector Doppler imaging for superficial venous valve flow estimation

2020 ◽  
Vol 47 (9) ◽  
pp. 4020-4031
Author(s):  
Hsin Huang ◽  
Pei‐Yu Chen ◽  
Chih‐Chung Huang
Keyword(s):  
High Frequency ◽  
Doppler Imaging ◽  
Frequency Vector ◽  
Venous Valve ◽  
Flow Estimation
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