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We introduce the notion of $p$-adic asymptotics, or $p$-asymptotics, to the context of finite-index subgroup and subalgebra enumeration. For finitely generated groups and finite-dimensional algebras, we connect these asymptotics with the…

In this paper, we consider the large time asymptotic behavior of solutions to systems of two cubic nonlinear Schr"odinger equations in one space dimension. It turns out that for a system there exists a small solution of which asymptotic…

We obtain the asymptotic expansion of the Voigt functions $K(x,y)$ and $L(x,y)$ for large (real) values of the variables $x$ and $y$, paying particular attention to the exponentially small contributions. A Stokes phenomenon is encountered…

We present a solution of the problem of multiplication of Schwartz distributions by embedding the space of distributions into a differential algebra of generalized functions, called in the paper ``asymptotic function'', similar to but…

This paper completes and partially improves some of the results of [arXiv:0809.5002] about the asymptotic behavior of solutions of linear and nonlinear elliptic equations with singular coefficients via an Almgren type monotonicity formula

In this paper, by using asymptotic expansions of oscillatory integrals with positive real power phase functions in one variable, we obtain asymptotic expansions of oscillatory integrals with phase functions expressed by a product of…

We consider an estimation problem of expected functionals of a general random element that values in a metric space. If the functional forms an explicit function of some unknown parameters, we can estimate it by plugging-in a suitable…

We study operators on a singular manifold, here of conical or edge type, and develop a new general approach of representing asymptotics of solutions to elliptic equations close to the singularities. The idea is to construct so-called…

The main aim of this article is a careful investigation of the asymptotic behavior of zeros of Bernoulli polynomials of the second kind. It is shown that the zeros are all real and simple. The asymptotic expansions for the small, large, and…

We consider composite functions in the elementary algebraic framework. Without any use of the Fourier transform, we find almost periodic orbits which suitably characterizes certain composite functions. In particular, we provide special…

We obtain asymptotic approximations for the probability density function of the product of two correlated normal random variables with non-zero means and arbitrary variances. As a consequence, we deduce asymptotic approximations for the…

In this note, presented as a ``community service", followed by the PhD research of the author, we draw the relation between Casselman's theorem regarding the asymptotic behavior of matrix coefficients of reductive algebraic groups over…

We define for discrete finitely presented groups a new property related to their asymptotic representations. Namely we say that a groups has the property AGA if every almost representation generates an asymptotic representation. We give…

The asymptotic behaviour of partial sums of generalized hypergeometric series of unit argument is investigated.

We survey recent results about asymptotic functions of groups, obtained by the authors in collaboration with J.-C.Birget, V. Guba and E. Rips. We also discuss methods used in the proofs of these results.

In this paper we characterize those positive operators which are asymptotic limits of contractions in strong operator topology or uniform topology. We examine the problem when the asymptotic limits of two contractions coincide.

We develop a theory of multiplicative functions (with values inside or on the unit circle) in arithmetic progressions analogous to the well-known theory of primes in arithmetic progressions.

We define thin and asymptotically scattered metric spaces as asymptotic counterparts of discrete and scattered metric spaces respectively. We characterize asymptotically scattered spaces in terms of prohibited subspaces, and classify thin…

We compute the whole asymptotic expansion of the probability that a large uniform labeled graph is connected, and of the probability that a large uniform labeled tournament is irreducible. In both cases, we provide a combinatorial…

Although approximate Bayesian computation (ABC) has become a popular technique for performing parameter estimation when the likelihood functions are analytically intractable there has not as yet been a complete investigation of the…