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The system of equations for parametric sub-resonant growth of the amplitude of oscillations was obtained. The time of turning point from the growing of the amplitude to the bounded oscillations in the slow variable was found. The comparison…
The main purpose of this paper is to provide an asymptotically optimal test. The proposed statistic is of Neyman-Pearson-type when the parameters are estimated with a particular kind of estimators. It is shown that the proposed estimators…
We construct a new type of convergent, and asymptotic, representations, dyadic expansions. Their convergence is geometric and the region of convergence often extends from infinity down to $0^+$. We show that dyadic expansions are…
In this paper, we study the asymptotic behavior of radial extremal functions to an inequality involving Hardy potential and critical Sobolev exponent. Based on the asymptotic behavior at the origin and the infinity, we shall deduce a strict…
We study maximum-likelihood-type estimation for diffusion processes when the coefficients are nonrandom and observation occurs in nonsynchronous manner. The problem of nonsynchronous observations is important when we consider the analysis…
In general, there is an inverse relation between the degree of localization of a wavefunction of a certain class and its transform representation dictated by the scaling property of the Fourier transform. We report that in the case of…
For arbitrary Borel probability measures on the real line, necessary and sufficient conditions are presented that characterize best purely atomic approximations relative to the classical Levy probability metric, given any number of atoms,…
One of the basic principles of Approximation Theory is that the quality of approximations increase with the smoothness of the function to be approximated. Functions that are smooth in certain subdomains will have good approximations in…
We study the variance of the number of zeroes of a stationary Gaussian process on a long interval. We give a simple asymptotic description under mild mixing conditions. This allows us to characterise minimal and maximal growth. We show that…
In this paper, we study the asymptotic behavior of solutions to a Gas-liquid model with external forces and general pressure law. Under some suitable assumptions on the initial date and $\gamma>1$, if…
We investigate the structure of branching asymptotics appearing in solutions to elliptic edge problems. The exponents in powers of the half-axis variable, logarithmic terms, and coefficients depend on the variables on the edge and may be…
The single-particle spectral functions in asymmetric nuclear matter are computed using the ladder approximation within the theory of finite temperature Green's functions. The internal energy and the momentum distributions of protons and…
A new method, called the method of self-similar approximants, and its recent developments are described. The method is based on the ideas of renormalization group theory and optimal control theory. It allows for the effective extrapolation…
We determine the asymptotic behaviour of (bilateral) obstacle problems for fractional energies in rather general aperiodic settings via Gamma-convergence arguments. As further developments we consider obstacles with random sizes and shapes…
Antonymous functions are real-valued functions on the Stone spectrum of a von Neumann algebra R. They correspond to the self-adjoint operators in R, which are interpreted as observables in quantum physics. Antonymous functions turn out to…
Functional methods like Dyson-Schwinger equations, the nPI effective action formalism, bound state equations and the functional renormalization group are versatile tools to study quantum field theories. They are exact, nonperturbative…
In this paper, we will develop an iterative procedure to determine the detailed asymptotic behaviour of solutions of a certain class of nonlinear vector differential equations which approach a nonlinear sink as time tends to infinity. This…
In this paper, we derive tail approximations of integrals of exponential functions of Gaussian random fields with varying mean functions and approximations of the associated point processes. This study is motivated naturally by multiple…
This paper develops an asymptotic likelihood theory for triangular arrays of stationary Gaussian time series depending on a multidimensional unknown parameter. We give sufficient conditions for the associated sequence of statistical models…
The asymptotic behavior of the molecular continuum wave function has been analyzed within a model of non-overlapping atomic potentials. It is been shown that the representation of the wave function far from a molecule as a plane wave and…