Several estimates for the convolution function C[f (x)] := x 1 f (y)f (x/y)(dy/y) and its iterates are obtained when f (x) is a suitable number-theoretic error term. We deal with the case of the asymptotic formula for T 0 |ζ(1/2 + it)| 2k dt (k = 1, 2), the general Dirichlet divisor problem, the problem of nonisomorphic Abelian groups of given order, and the Rankin-Selberg convolution. 1. Convo...

COVID-19 reached its fourth year of pandemic since 2020. The repeated waves infections have been driven by multiple factors such as pathological traits variants, diagnostic accuracy, and vaccination conditions. This study revisits analyzes the dynamic processes viral transmission to generate new scientific knowledge. A cascade model from one case another was developed, theoretically analyzed ho...

and Applied Analysis 3 It is worth mentioning that in the absence of the white noise, the existence of a global attractor for 1.3 1.4 was established in 40 . The main contribution of this paper is to extend the method of tail estimates to stochastic retarded LDSs and prove the existence of a random attractor for the infinite dimensional random dynamical system generated by stochastic retarded L...

A family of permutations F of [n] = {1, 2, . . . , n} is (ε, k)-min-wise independent if for every nonempty subset X of at most k elements of [n], and for any x ∈ X, the probability that in a random element π of F , π(x) is the minimum element of π(X), deviates from 1/|X| by at most ε/|X|. This notion can be defined for the uniform case, when the elements of F are picked according to a uniform d...

We consider the problem of designing (or augmenting) an electric power system such that it satisfies the N-k-ε survivability criterion while minimizing total cost. The survivability criterion requires that at least (1− ε) fraction of the total demand can still be met even if any k (or fewer) of the system components fail. We formulate this problem, taking into account both transmission and gene...

Let Xm,ε be the distribution over m bits (X1, . . . , Xm) where the Xi are independent and each Xi equals 1 with probability (1 + ε)/2 and 0 with probability (1 − ε)/2. We consider the smallest value ε∗ of ε such that the distributions Xm,ε and Xm,0 can be distinguished with constant advantage by a function f : {0, 1}m → S which is the product of k functions f1, f2, . . . , fk on disjoint input...

We study the Kolmogorov ε-entropy and the fractal dimension of global attractors for autonomous and nonautonomous equations of mathematical physics. We prove upper estimates for the ε-entropy and fractal dimension of the global attractors of nonlinear dissipative wave equations. Andrey Nikolaevich Kolmogorov discovered applications of notions of information theory in the theory of dynamical sys...

The present article focuses on the evaluation of a first-moment closure model applicable to film cooling flow and heat transfer computations. The present first-moment closure model consists of a higher level of turbulent heat flux modeling in which two additional transport equations for temperature variance kθ and its dissipation rate εθ are ...

A. (Forgive my choice of) Notation. Let G be a complex, connected, semisimple (or reductive) Lie group, T a maximal torus in G, and K the identity component of the fixed points of an involution in G. Equivalently, K is the complexification of a maximal compact subgroup of the identity component of a real form of G. Of course we assume T ⊂ K. We let ΛG denote the lattice of T -characters (the we...

The area of distributed monitoring requires tracking the value of a function of distributed data as new observations are made. An important case is when attention is restricted to only a recent time period, such as the last hour of readings—the sliding window case. In this announcement, we outline a novel paradigm for handling such monitoring problems, which we dub the “forward/backward” approa...