Related papers: Self-similar power transforms in extrapolation pro…
In this paper we consider asymptotic expansions for a class of sequences of symmetric functions of many variables. Applications to classical and free probability theory are discussed.
Some aspects of asymptotic freedom are discussed in the context of a simple two-particle non-relativisitic confining potential model. In this model asymptotic freedom follows from the similarity of the free-particle and bound state radial…
When dealing with control systems, it is useful and even necessary to assess the performance of underlying transfer functions. The functions may or may not be linear, may or may not be even monotonic. In addition, they may have structural…
In this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations. Under the mild assumption that the so-called characteristic function of our system is completely…
Generalized power asymptotic expansions of solutions to differential equations that depend on parameters are investigated. The changing nature of these expansions as the parameters of the model cross critical values is discussed. An…
A transition from asymmetric to symmetric patterns in time-dependent extended systems is described. It is found that one dimensional cellular automata, started from fully random initial conditions, can be forced to evolve into complex…
Finding self-similarity is a key step for understanding the governing law behind complex physical phenomena. Traditional methods for identifying self-similarity often rely on specific models, which can introduce significant bias. In this…
In this two-part study we develop a general approach to the design and analysis of exact penalty functions for various optimal control problems, including problems with terminal and state constraints, problems involving differential…
A transformed auto-correlation method is presented here, where a received signal is transformed based on a priori reflecting model, and then the transformed signal is cross-correlated to its original one. If the model is correct, after…
Asymptotic expansions are presented for the moments of bound states in one-dimensional anharmonic potentials. The results are derived by using the SAFE method and include only the first non-zero wave-related correction to the familiar…
We establish formulas for the constant factor in several asymptotic estimates related to the distribution of integer and polynomial divisors. The formulas are then used to approximate these factors numerically.
In this paper, adaptive set-point regulation controllers for discrete-time nonlinear systems are constructed. The system to be controlled is assumed to have a parametric uncertainty, and an excitation signal is used in order to obtain the…
Optimization software enables the solution of problems with millions of variables and associated parameters. These parameters are, however, often uncertain and represented with an analytical description of the parameter's distribution or…
Explicit analytic expressions are derived for the effective-range function for the case when the interaction is represented by a sum of the short-range square-well and long-range Coulomb potentials. These expressions are then transformed…
A general analytical method is developed for describing crossover phenomena of arbitrary nature. The method is based on the algebraic self-similar renormalization of asymptotic series, with control functions defined by crossover conditions.…
Extending classical results on polytopal approximation of convex bodies, we derive asymptotic formulas for the weighted approximation of smooth convex functions by piecewise affine convex functions as the number of their facets tends to…
We study the Cowling approximation by analytical means as applied to a system of linear differential equations arising from models of non-radial stellar pulsation. We consider various asymptotic cases, including those of high harmonic…
We exploit the properties of a sequence of functions that approximate the divisor functions and combine them with an analytical formula of a delta-like sequence to give a new proof of a theorem of Gronwall on the asymptotic of the divisor…
We classify the local asymptotic behavior of positive singular solutions to a class of subcritical sixth order equations on the punctured ball. Initially, using a version of the integral moving spheres technique, we prove that solutions are…
We develop an asymptotic analysis of target fluxes in the three-dimensional (3D) narrow capture problem. The latter concerns a diffusive search process in which the targets are much smaller than the size of the search domain. The small…