This paper is a natural continuation of Krylov (2020), where strong Markov processes are constructed in time inhomogeneous setting with Borel measurable uniformly bounded and nondegenerate diffusion drift Ld+1(Rd+1). Here we study some properties these such as higher summability Green’s functions, maximum principle for related transport equations irregular coefficients, boundedness resolvent op...

In this paper, we define and study the notion of the real-valued functions on a frame $L$. We show that $F(L) $, consisting of all frame homomorphisms from the power set of $mathbb{R}$ to a frame $ L$, is an $f$-ring, as a generalization of all functions from a set $X$ into $mathbb R$. Also, we show that $F(L) $ is isomorphic to a sub-$f$-ring of $mathcal{R}(L)$, the ring of real-valued continu...

We apply the averaging theory of first, second and third order to the class of generalized polynomial Liénard differential equations. Our main result shows that for any n, m ≥ 1 there are differential equations of the form ẍ+f(x)ẋ+g(x) = 0, with f and g polynomials of degree n and m respectively, having at least [(n + m− 1)/2] limit cycles, where [·] denotes the integer part function.

In this paper we present some results on summability of oneand multi-dimensional Walsh-, Walsh-Kaczmarzand Vilenkin-Fourier series and on the dyadic and Vilenkin derivative. The Fejér and Cesàro summability methods are investigated. We will prove that the maximal operator of the summability means is bounded from the martingale Hardy space Hp to Lp (p > p0). For p = 1 we obtain a weak type inequ...

We study the 1D extended Hubbard model with a weak repulsive short-range interaction in the non-half-filled band case, using non-perturbative Renormalization Group methods and Ward Identities. At the critical temperature, T = 0, the response functions have anomalous power-law decay with multiplicative logarithmic corrections. The critical exponents, the susceptibility and the Drude weight verif...

Here, in this article, we introduce and systematically investigate the ideas of deferred weighted statistical Riemann integrability summability for sequences functions. We begin by proving an inclusion theorem that establishes a relation between these two potentially useful concepts. also state prove Korovkin-type approximation theorems involving algebraic test functions using our proposed conc...

Some integral properties of zonal spherical functions, hypergeometric functions and invariant polynomials are studied for real normed division algebras.

A general theorem is proved which deduces from a Tauberian condition Ti for a summability method, Tauberian condition Ti for the summability method. Recent results of MeyerKönig and Tietz and of Stieglitz are special cases.