Using the Burnside ring theoretic methods a new setting and a complete description of the Artin exponent A(G) of finite p-groups was obtained in [4]. In this paper, we compute A(G) for any finite group G – hence providing the global version of [4].

– We investigate global persistence properties for the non-equilibrium critical dynamics of the randomly diluted Ising model. The disorder averaged persistence probability Pc(t) of the global magnetization is found to decay algebraically with an exponent θc that we compute analytically in a dimensional expansion in d = 4− ǫ. Corrections to Markov process are found to occur already at one loop o...

A square is the concatenation of a nonempty word with itself. A word has period p if its letters at distance pmatch. The exponent of a nonempty word is the quotient of its length over its smallest period. In this article we give a proof of the fact that there exists an infinite binary word which contains finitely many squares and simultaneously avoids words of exponent larger than 7/3. Our infi...

A square is the concatenation of a nonempty word with itself. A word has period p if its letters at distance pmatch. The exponent of a nonempty word is the quotient of its length over its smallest period. In this article we give a proof of the fact that there exists an infinite binary word which contains finitely many squares and simultaneously avoids words of exponent larger than 7/3. Our infi...

We consider stochastic dynamical systems operating under synchronization constraints on system events. The system dynamics is represented by a linear vector equation in an idempotent semiring through second-order state transition matrices with both random and constant entries. As the performance measure of interest, the Lyapunov exponent defined as the asymptotic mean growth rate of the system ...

We study the coherent dynamics of globally coupled maps showing macroscopic chaos. With this term we indicate the hydrodynamical-like irregular behaviour of some global observables, with typical times much longer than the times related to the evolution of the single (or microscopic) elements of the system. The usual Lyapunov exponent is not able to capture the essential features of this macrosc...

A new class of kernels for long-run variance and spectral density estimation is developed by exponentiating traditional quadratic kernels. Depending on whether the exponent parameter is allowed to grow with the sample size, we establish different asymptotic approximations to the sampling distribution of the proposed estimators. When the exponent is passed to infinity with the sample size, the n...

In this paper, we study the antipode of a finite-dimensional Hopf algebra H with dual Chevalley property and obtain an annihilation polynomial for antipode. This generalizes old result given by Taft Wilson in 1974. As consequences, show that 1) quasi-exponent is same as exponent its coradical, is, qexp ( ) = exp ⁡ 0 ; 2) ⋊ k 〈 S 2 〉 .

We study the relations between tail order of copulas and hidden regular variation (HRV) on subcones generated by order statistics. Multivariate regular variation (MRV) and HRV deal with extremal dependence of random vectors with Pareto-like univariate margins. Alternatively, if one uses copula to model the dependence structure of a random vector, then upper exponent and tail order functions can...

Taylor's law (TL) states that the variance V of a nonnegative random variable is a power function of its mean M; i.e., V = aM(b). TL has been verified extensively in ecology, where it applies to population abundance, physics, and other natural sciences. Its ubiquitous empirical verification suggests a context-independent mechanism. Sample exponents b measured empirically via the scaling of samp...