We construct a family of vertex transitive graphs on a left loop structure of order 2q2 where q is a power of a prime such that q equivalent to 1 mod 4. The graphs are of diameter 2. The smallest of these graphs is isomorphic to the Hoffman-Singleton graph.
We present a comprehensive analysis of the existence and regularity of distributional solutions for a given class of nonlinear degenerate elliptic equations. The equations under consideration contain singular gradient lower order terms and are related to the L(m )data, where the exponent m satisfies 1 < m < d/p(-). To deal with this problem, we use a functional framework that includes Lebesgue-Sobolev spaces with variable exponents. Our findings provide valuable additions to the previous research discussed in Nonlinear degenerate p(x)-Laplacian equation with singular gradient and lower order term (2023) by H. Khelifi and M. A. Zouatini.
The statistical convergence in a topological space is constrained in this study up to order alpha, where alpha is an element of (0, 1). A fresh group of open covers (namely s-gamma covers) and an entirely novel category of denseness (namely s-denseness) are proposed using this notion of s-convergence, which has been used to study various topological aspects of s-density. It has been revealed that the class of s-gamma coverings falls somewhere between the class of gamma covers and the class of s-gamma covers. The influence of s-gamma covers in topological games and selection principles are also investigated.
Under weak conditions on the diffusion coefficients, we prove existence theorems of weak solutions for some nonlinear nonlocal elliptic problems. Our approach is based on the Schauder fixed point theorem combined with an approximation technique. We also give uniqueness results and an example to support them.
Inspired by the work that Professor Janusz R. Prajs did on homogeneous metric continua in his paper (2010) and the version of his work for Hausdorff continua with the uniform property of Effros done by this author, we introduce a new set function, & wp;, and present properties of it.
Projective special unitary groups PSU(5, q), where q4-q3 + q2-q + 1 (5, q + 1) is a prime, is uniquely determined by its order and the size of one conjugacy class.
Let L(H) denote the algebra of all bounded linear operators on a complex infinite dimensional Hilbert space H. For A, B is an element of L(H), the generalized derivation 6A,B and the multiplication operator MA,B are defined on L(H) by 6A,B(X) = AX-XB and MA,B(X) = AXB. In this paper, we give a characterization of bounded operators A and B such that the range of MA,B is closed. We present some sufficient conditions for 6A,B to have closed range. Some related results are also given.
This paper presents several numerical radii and norm inequalities for Hilbert space operators. These inequalities improve some earlier related inequalities. For an operator A, we prove that omega 2(A) <= ||A*A + AA* 1 ((1-t)A*A +tAA* 2 2R-((1-t)(A*A)1/2 + (AA*)1/2)2)|| where R = max{t, 1-t} and 0 <= t <= 1.
Given a metric continuum X and a positive integer n, Fn(X) denotes the hyperspace of all nonempty subsets of X with at most n points endowed with the Hausdorff metric. For K E Fn(X), Fn(K,X) denotes the set of elements of Fn(X) containing K and FnK (X) denotes the quotient space obtained from Fn(X) by shrinking Fn(K, X) to one point set. Given a map f : X-* Y between continua, fn: Fn(X)-* Fn(Y) denotes the induced map defined by fn(A) = f(A). Let K E Fn(X), we shall consider the induced map in the natural way fn,K : FnK (X)-* F f(K) n (Y ). In this paper we consider the maps f, fn, fn,K for some K E Fn(X) and fn,K for each K E Fn(X); and we study relationship between them for the following classes of maps: homeomorphisms, monotone, confluent, light and open maps.
The purpose of this paper is to study the commutative pseudomeadows, the structure which is defined in the same way as commutative meadows, except that the existence of a multiplicative identity is not required. We extend the characterization of finite commutative meadows, given by I. Bethke, P. Rodenburg, and A. Sevenster in their paper (2015), to the case of commutative pseudomeadows with finitely many idempotents. We also extend the well-known characterization of general commutative meadows as the subdirect products of fields to the case of commutative pseudomeadows. Finally, we investigate localizations of commutative pseudomeadows.
We consider the Golomb and the Kirch topologies in the set of natural numbers. Among other results, we show that while with the Kirch topology every arithmetic progression is aposyndetic, in the Golomb topology only for those arithmetic progressions $P(a,b)$ with the property that every prime number that divides $a$ also divides $b$, it follows that being connected, being Brown, being totally Brown, and being aposyndetic are all equivalent. This characterizes the arithmetic progressions which are aposyndetic in the Golomb space.
We prove that several classical Banach space properties are equivalent to separability for the class of Lipschitz-free spaces, including Corson's property (C), Talponen's countable separation property, or being a Gateaux differentiability space. On the other hand, we single out more general properties where this equivalence fails. In particular, the question whether the duals of nonseparable Lipschitz-free spaces have a weak & lowast; sequentially compact ball is undecidable in ZFC. Finally, we provide an example of a nonseparable dual Lipschitz-free space that fails the Radon-Nikodym property.
