scholarly journals Uniform convergence rate for Birkhoff means of certain uniquely ergodic toral maps

2020 ◽  
pp. 1-26
Author(s):  
SILVIUS KLEIN ◽  
XIAO-CHUAN LIU ◽  
ALINE MELO
Keyword(s):  
Convergence Rate ◽  
Uniform Convergence ◽  
Modulus Of Continuity ◽  
Skew Product ◽  
Dimensional Torus ◽  
One Dimensional ◽  
Arithmetic Properties ◽  
Uniform Convergence Rate ◽  
The One ◽  
Uniquely Ergodic

Abstract We obtain estimates on the uniform convergence rate of the Birkhoff average of a continuous observable over torus translations and affine skew product toral transformations. The convergence rate depends explicitly on the modulus of continuity of the observable and on the arithmetic properties of the frequency defining the transformation. Furthermore, we show that for the one-dimensional torus translation, these estimates are nearly optimal.

scholarly journals Limit of 𝑝-Laplacian obstacle problems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Raffaela Capitanelli ◽  
Maria Agostina Vivaldi
Keyword(s):  
Asymptotic Behavior ◽  
Uniform Convergence ◽  
Explicit Expression ◽  
Positive Measure ◽  
Sufficient Conditions ◽  
Obstacle Problems ◽  
Dimensional Case ◽  
Asymptotic Behavior Of Solutions ◽  
One Dimensional ◽  
The One

AbstractIn this paper, we study asymptotic behavior of solutions to obstacle problems for p-Laplacians as {p\to\infty}. For the one-dimensional case and for the radial case, we give an explicit expression of the limit. In the n-dimensional case, we provide sufficient conditions to assure the uniform convergence of the whole family of the solutions of obstacle problems either for data f that change sign in Ω or for data f (that do not change sign in Ω) possibly vanishing in a set of positive measure.

scholarly journals Well-posedness of the linear heat equation with a second order memory term

2020 ◽  
Vol 34 ◽  
pp. 03011
Author(s):  
Constantin Niţă ◽  
Laurenţiu Emanuel Temereancă
Keyword(s):  
Initial Data ◽  
Heat Equation ◽  
Unique Solution ◽  
Source Term ◽  
Memory Term ◽  
Well Posedness ◽  
Dimensional Torus ◽  
One Dimensional ◽  
Linear Heat ◽  
The One

In this article we prove that the heat equation with a memory term on the one-dimensional torus has a unique solution and we study the smoothness properties of this solution. These properties are related with some smoothness assumptions imposed to the initial data of the problem and to the source term.

A convergence rate in extreme-value theory

1990 ◽  
Vol 27 (03) ◽  
pp. 577-585 ◽  
Author(s):  
A. A. Balkema ◽  
L. De Haan
Keyword(s):  
Convergence Rate ◽  
Extreme Value Theory ◽  
Domain Of Attraction ◽  
Value Theory ◽  
Order Condition ◽  
Underlying Distribution ◽  
Double Exponential ◽  
Uniform Convergence Rate ◽  
The One ◽  
Bounded Below

A uniform convergence rate is determined for maxima of i.i.d. random variables from a distribution in the domain of attraction of the double-exponential distribution. The result is proved under a second-order condition on the underlying distribution parallelling the one given in Smith (1982) for the domain of attraction of the bounded-below and bounded-above families of limit distributions.

scholarly journals Large semigroups of cellular automata

2011 ◽  
Vol 32 (6) ◽  
pp. 1991-2010 ◽  
Author(s):  
YAIR HARTMAN
Keyword(s):  
Cellular Automata ◽  
Field Structure ◽  
The Other ◽  
Entire Space ◽  
Dimensional Torus ◽  
Semigroup Action ◽  
Closed Set ◽  
One Dimensional ◽  
Shift Space ◽  
The One

AbstractIn this article, we consider semigroups of transformations of cellular automata which act on a fixed shift space. In particular, we are interested in two properties of these semigroups which relate to ‘largeness’: first, a semigroup has the ID (infinite is dense) property if the only infinite invariant closed set (with respect to the semigroup action) is the entire space; the second property is maximal commutativity (MC). We shall consider two examples of semigroups: one is spanned by cellular automata transformations that represent multiplications by integers on the one-dimensional torus, and the other one consists of all the cellular automata transformations which are linear (when the symbols set is the ring ℤ/sℤ). It will be shown that these two properties of these semigroups depend on the number of symbols s. The multiplication semigroup is ID and MC if and only if s is not a power of a prime. The linear semigroup over the mentioned ring is always MC but is ID if and only if s is prime. When the symbol set is endowed with a finite field structure (when possible), the linear semigroup is both ID and MC. In addition, we associate with each semigroup which acts on a one-sided shift space a semigroup acting on a two-sided shift space, and vice versa, in a way that preserves the ID and the MC properties.

scholarly journals Convergence Rate of Extremes for the General Error Distribution

2010 ◽  
Vol 47 (3) ◽  
pp. 668-679 ◽  
Author(s):  
Zuoxiang Peng ◽  
Saralees Nadarajah ◽  
Fuming Lin
Keyword(s):  
Convergence Rate ◽  
Uniform Convergence ◽  
Random Sequence ◽  
Extreme Value ◽  
Error Distribution ◽  
Distribution Of The Maximum ◽  
Uniform Convergence Rate ◽  
Independent Identically Distributed ◽  
General Error

Let {Xn, n ≥ 1} be an independent, identically distributed random sequence with each Xn having the general error distribution. In this paper we derive the exact uniform convergence rate of the distribution of the maximum to its extreme value limit.

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