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In this paper, we propose some algorithms for analytical solution construction to nonlinear polynomial partial differential equations with constant function coefficients. These schemes are based on one-(single), two- (double) or three-…
Fractional action-like variational problems have recently gained importance in studying dynamics of nonconservative systems. In this note we address multi-dimensional fractional action-like problems of the calculus of variations.
We characterise piecewise Boolean domains, that is, those domains that arise as Boolean subalgebras of a piecewise Boolean algebra. This leads to equivalent descriptions of the category of piecewise Boolean algebras: either as piecewise…
The paper gives some criteria for partial sums of rational number sequences to be not rational functions and to be not algebraic functions. As an application, we study partial sums of some famous rational number sequences in mathematical…
Within the study of uncertain dynamical systems, iterated random functions are a key tool. There, one samples a family of functions according to a stationary distribution. Here, we introduce an extension, where one sample functions…
Fractional analysis is applied to describe classical dynamical systems. Fractional derivative can be defined as a fractional power of derivative. The infinitesimal generators {H, .} and L=G(q,p) \partial_q+F(q,p) \partial_p, which are used…
We show that a problem on minimal periods of solutions of Lipschitz functional differential equations is closely related to the unique solvability of the periodic problem for linear functional differential equations. Sharp bounds for…
Fractional Brownian motion belongs to a class of long memory Gaussian processes that can be represented as linear functionals of an infinite dimensional Markov process. This representation leads naturally to: - An efficient algorithm to…
We develop a Fourier analysis for a generalization of the class of periodic functions, often referred to as $(\theta, T)$-periodic functions, and prove several properties and inequalities related to the Fourier transform, including a type…
In this paper we discuss approximation of partially smooth functions. The problem arises naturally in the study of laminated currents.
In this paper, we study almost periodic solutions for semilinear stochastic differential equations driven by L\'{e}vy noise with exponential dichotomy property. Under suitable conditions on the coefficients, we obtain the existence and…
In this paper, we first propose a new concept of almost periodic time scales, a new definition of almost automorphic functions on almost periodic time scales, and study some their basic properties. Then we prove a result ensuring the…
We investigate the use of piecewise linear systems, whose coefficient matrix is a piecewise constant function of the solution itself. Such systems arise, for example, from the numerical solution of linear complementarity problems and in the…
Partial zeta functions of algebraic varieties over finite fields generalize the classical zeta function by allowing each variable to be defined over a possibly different extension field of a fixed finite field. Due to this extra variation…
We obtain a complete description of the Riesz measures of almost periodic subharmonic functions with at most of linear growth on the complex plane; as a consequence we get a complete description of zero sets for the class of entire…
We examine "partition zeta functions" analogous to the Riemann zeta function but summed over subsets of integer partitions. We prove an explicit formula for a family of partition zeta functions already shown to have nice properties -- those…
In the theory of neutral differential equations with pulse influence (neutral impulsive differential equations), there are many unsolved problems related to certain results in the theory of integral and integro-differential equations. In…
It is proved that the unital Banach algebra of almost periodic functions of several variables with Bohr-Fourier spectrum in a given additive semigroup is an Hermite ring. The same property holds for the Wiener algebra of functions that in…
In this note we classify quasi-sum production functions with constant elasticity of production with respect to any factor of production and with proportional marginal rate of substitution.
It is shown that a piecewise linear function can be represented as a Max-Min polynomial of its linear components.