相关论文: Non-linear fractal interpolating functions of one …
Using a generalized cut vertex expansion we introduce the concept of an extended fracture function for the description of semi-inclusive deep inelastic processes in the target fragmentation region. Extended fracture functions are shown to…
Partition functions for non-interacting particles are known to be symmetric functions. It is shown that powerful group-theoretical techniques can be used not only to derive these relationships, but also to significantly simplify calculation…
The study gives a brief overview of existing modifications of the method of functional separation of variables for nonlinear PDEs. It proposes a more general approach to the construction of exact solutions to nonlinear equations of applied…
We describe some new univariate spline quasi-interpolants on uniform partitions of bounded intervals. Then we give some applications to numerical analysis: integration, differentiation and approximation of zeros.
Line integration of generalized functions is studied. Second order partial differential equations with piecewise continuous and generalized variable coefficients over Cayley-Dickson algebras are investigated. Formulas for integrations of…
Fractal geometry deals mainly with irregularity and captures the complexity of a structure or phenomenon. In this article, we focus on the approximation of set-valued functions using modern machinery on the subject of fractal geometry. We…
Let $f$ be a $r\times m$-matrix of holomorphic functions that is generically surjective. We provide explicit integral representation of holomorphic $\psi$ such that $\phi=f\psi$, provided that $\phi$ is holomorphic and annihilates a certain…
Singular functions and, in general, H\"older functions represent conceptual models of nonlinear physical phenomena. The purpose of this survey is to demonstrate the applicability of fractional velocity as a tool to characterize Holder and…
We consider the set of power functions defined on the set of positive real number, and their linear combinations. After recalling some properties of the gamma function, we give two general definitions of derivatives of positive and negative…
We present two observations related to theapplication of linear (LFE) and nonlinear fractional equations (NFE). First, we give the comparison and estimates of the role of the fractional derivative term to the normal diffusion term in a LFE.…
This paper introduces a couple of new time-frequency transforms, designed to adapt their scale to specific features of the analyzed function. Such an adaptation is implemented via so-called focus functions, which control the window scale as…
We establish properties of a new type of fractal which has partial self similarity at all scales. For any collection of iterated functions systems with an associated probability distribution and any positive integer V there is a…
This article presents the construction of a non-affine hypersurface on an $n$-simplex in $\mathbb{R}^n$. Additionally, fractal dimension of the graph of a non-affine multivariate real-valued fractal function is estimated under certain…
In the framework of higher transcendental functions the Wright functions of the second kind have increased their relevance resulting from their applications in probability theory and, in particular, in fractional diffusion processes. Here,…
The interpolation of couples of separable Hilbert spaces with a function parameter is studied. The main properties of the classic interpolation are proved. Some applications to the interpolation of isotropic H\"ormander spaces over a closed…
A spectral decomposition method is used to obtain solutions to a class of nonlinear differential equations. We extend this approach to the analysis of the fractional form of these equations and demonstrate the method by applying it to the…
This article shows that on a closed interval $[a,b]$ a continuous function may be approximated to an arbitrary degree of accuracy using scattered translates of the general multiquadric $(x^2+c^2)^{k-1/2}$.
We undertake a general study of multifractal phenomena for functions. We show that the existence of several kinds of multifractal functions can be easily deduced from an abstract statement, leading to new results. This general approach does…
In the paper we prove several inequalities involving two isotonic linear functionals. We consider inequalities for functions with variable bounds, for Lipschitz and H\" older type functions etc. These results give us an elegant method for…
In this paper we consider the problem of estimation of oscillatory integrals with Mittag-Leffler functions in two variables. The generalisation is that we replace the exponential function with the Mittag-Leffler-type function, to study…