We analyse multivalued stochastic differential equations driven by semimartingales. Such equations are understood as the corresponding multivalued stochastic integral equations. Under suitable conditions, it is shown that the considered multivalued stochastic differential equation admits at least one solution. Then we prove that the set of all solutions is closed and bounded., Marek T. Malinowski, Ravi P. Agarwal., and Obsahuje bibliografii
A subgroup H of a finite group G is said to be ss-supplemented in G if there exists a subgroup K of G such that G = HK and H ∩ K is s-permutable in K. In this paper, we first give an example to show that the conjecture in A.A. Heliel’s paper (2014) has negative solutions. Next, we prove that a finite group G is solvable if every subgroup of odd prime order of G is ss-supplemented in G, and that G is solvable if and only if every Sylow subgroup of odd order of G is ss-supplemented in G. These results improve and extend recent and classical results in the literature., Jiakuan Lu, Yanyan Qiu., and Obsahuje seznam literatury
We present new sharp embedding theorems for mixed-norm analytic spaces in pseudoconvex domains with smooth boundary. New related sharp results in minimal bounded homogeneous domains in higher dimension are also provided. Last domains we consider are domains which are direct generalizations of the well-studied so-called bounded symmetric domains in Cn. Our results were known before only in the very particular case of domains of such type in the unit ball. As in the unit ball case, all our proofs are heavily based on nice properties of the r-lattice. Some results of this paper can be also obtained in some unbounded domains, namely tubular domains over symmetric cones., Romi F. Shamoyan, Olivera R. Mihić., and Obsahuje seznam literatury
In this paper we present some theoretical results about the irreducibility of the Laplacian matrix ordered by the Reverse Cuthill-McKee (RCM) algorithm. We consider undirected graphs with no loops consisting of some connected components. RCM is a well-known scheme for numbering the nodes of a network in such a way that the corresponding adjacency matrix has a narrow bandwidth. Inspired by some properties of the eigenvectors of a Laplacian matrix, we derive some properties based on row sums of a Laplacian matrix that was reordered by the RCM algorithm. One of the theoretical results serves as a basis for writing an easy MATLAB code to detect connected components, by using the function “symrcm” of MATLAB. Some examples illustrate the theoretical results., Francisco Pedroche, Miguel Rebollo, Carlos Carrascosa, Alberto Palomares., and Obsahuje seznam literatury
We study the arithmetic properties of hyperelliptic curves given by the affine equation y^{2} = x^{n} + a by exploiting the structure of the automorphism groups. We show that these curves satisfy Lang’s conjecture about the covering radius (for some special covering maps)., Kevser Aktaş, Hasan Şenay., and Obsahuje seznam literatury
Let µ_{n-1}(G) be the algebraic connectivity, and let µ_{1}(G) be the Laplacian spectral radius of a k-connected graph G with n vertices and m edges. In this paper, we prove that {\mu _{n - 1}}(G) \geqslant \frac{{2n{k^2}}}{{(n(n - 1) - 2m)(n + k - 2) + 2{k^2}}} , with equality if and only if G is the complete graph Kn or Kn − e. Moreover, if G is non-regular, then {\mu _1}(G) < 2\Delta - \frac{{2(n\Delta - 2m){k^2}}}{{2(n\Delta - 2m)({n^2} - 2n + 2k) + n{k^2}}} , where ▵ stands for the maximum degree of G. Remark that in some cases, these two inequalities improve some previously known results., Xiaodan Chen, Yaoping Hou., and Obsahuje seznam literatury
Let $G$ be a finite group $G$, $K$ a field of characteristic $p\geq17$ and let $U$ be the group of units in $KG$. We show that if the derived length of $U$ does not exceed $4$, then $G$ must be abelian., Dishari Chaudhuri, Anupam Saikia., and Obsahuje bibliografické odkazy
Let G be a finite group. The intersection graph ΔG of G is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper nontrivial subgroups of G, and two distinct vertices X and Y are adjacent if X ∩ Y ≠ 1, where 1 denotes the trivial subgroup of order 1. A question was posed by Shen (2010) whether the diameters of intersection graphs of finite non-abelian simple groups have an upper bound. We answer the question and show that the diameters of intersection graphs of finite non-abelian simple groups have an upper bound 28. In particular, the intersection graph of a finite non-abelian simple group is connected., Xuanlong Ma., and Obsahuje seznam literatury
A positive integer n is called a square-free number if it is not divisible by a perfect square except 1. Let p be an odd prime. For n with (n, p) = 1, the smallest positive integer f such that n^{f} ≡ 1 (mod p) is called the exponent of n modulo p. If the exponent of n modulo p is p − 1, then n is called a primitive root mod p. Let A(n) be the characteristic function of the square-free primitive roots modulo p. In this paper we study the distribution \sum\limits_{n \leqslant x} {A(n)A(n + 1)} and give an asymptotic formula by using properties of character sums., Huaning Liu, Hui Dong., and Obsahuje seznam literatury
We prove that the one-parameter group of holomorphic automorphisms induced on a strictly geometrically bounded domain by a biholomorphism with a model domain is parabolic. This result is related to the Greene-Krantz conjecture and more generally to the classification of domains having a non compact automorphisms group. The proof relies on elementary estimates on the Kobayashi pseudo-metric., François Berteloot, Ninh Van Thu., and Obsahuje seznam literatury