Let us suppose we are given a combinatorially embedded factor ψy. In [9], the main result was the description of semi-Jacobi, Hamilton random variables. We show that there exists a quasi-embedded and free elliptic, non-parabolic subalgebra. The goal of the present article is to derive Hausdorff, contraeverywhere left-ordered, maximal functors. It was Einstein who first asked whether analyticall...

In this paper we give a detailed description of the random wavelet series representation of real-valued linear fractional stable sheet introduced in [2]. By using this representation, in the case where the sample paths are continuous, an anisotropic uniform and quasi-optimal modulus of continuity of these paths is obtained as well as an upper bound for their behavior at infinity and around the ...

In this paper, the concept of fuzzy automata normed linear structure spaces is introduced and suitable examples are provided. ;The ;concepts of fuzzy automata $alpha$-open sphere, fuzzy automata $mathscr{N}$-locally compact spaces, fuzzy automata $mathscr{N}$-Hausdorff spaces are also discussed. Some properties related with to fuzzy automata normed linear structure spaces and fuzzy automata $ma...

The complexity (quasi-metric) space was introduced in [23] to study complexity analysis of programs. Recently, it was introduced in [22] the dual complexity (quasi-metric) space, as a subspace of the function space [0,+∞)ω. Several quasi-metric properties of the complexity space were obtained via the analysis of its dual. We here show that the structure of a quasi-normed semilinear space provid...

In this paper, we introduce the Hausdorff operator associated with Opdam--Cherednik transform and study boundedness of in various Lebesgue spaces. particular, prove spaces, grand quasi-Banach spaces that are transform. Also, give necessary sufficient conditions for these

For a closed subset K of a compact metric space A possessing an α-regular measure μ with μ(K) > 0, we prove that whenever s > α, any sequence of weighted minimal Riesz s-energy configurations ωN = {x i,N} N i=1 on K (for ‘nice’ weights) is quasi-uniform in the sense that the ratios of its mesh norm to separation distance remain bounded as N grows large. Furthermore, if K is an α-rectifiable com...

In this paper we introduce measurable expanding random systems, develop the thermodynamical formalism and establish, in particular, exponential decay of correlations and analyticity of the expected pressure although the spectral gap property does not hold. This theory is then used to investigate fractal properties of conformal random systems. We prove a Bowen’s formula and develop the multifrac...

When testing that a sample of n points in the unit hypercube [0, 1] comes from a uniform distribution, the Kolmogorov–Smirnov and the Cramér–von Mises statistics are simple and well-known procedures. To encompass these measures of uniformity, Hickernell introduced the so-called generalized Lp-discrepancies. These discrepancies can be used in numerical integration through Monte Carlo and quasi–M...

In this paper, we answer a question by Krasinkiewicz, Reńska and Sobolewski by constructing countable connected Hausdorff and Urysohn spaces as quotient spaces of bunches of arcs in the plane. We also consider a generalization of graphs by allowing vertices to be continua and replacing edges by not necessarily connected sets. We require only that two “vertices” be in the same quasi-component of...