共查询到20条相似文献,搜索用时 15 毫秒
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Let and be positive integers with . Given a permutation of integers , we consider -consecutive sums of , i.e., for , where we let . What we want to do in this paper is to know the exact value of where denotes the set of all permutations of . In this paper, we determine the exact values of for some particular cases of and . As a corollary of the results, we obtain , and for any . 相似文献
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V. Hoang B. Orcan-Ekmekci M. Radosz H. Yang 《Journal of Differential Equations》2018,264(12):7328-7356
We propose a system of equations with nonlocal flux in two space dimensions which is closely modeled after the 2D Boussinesq equations in a hyperbolic flow scenario. Our equations involve a vorticity stretching term and a non-local Biot-Savart law and provide insight into the underlying intrinsic mechanisms of singularity formation. We prove stable, controlled finite time blowup involving upper and lower bounds on the vorticity up to the time of blowup for a wide class of initial data. 相似文献
4.
We generalize several results on bounded analytic interpolation of Fitzgerald and Horn, which work by majorization by positive
definite kernels, to the cases of several complex variables and operator-valued interpolation. Using a lemma of Kolmogorov,
we complement a simplification due to Szafraniec in the proofs of the theorems.
Received: November 21, 2006. Accepted: August 03, 2007. 相似文献
5.
Grzegorz Banaszak 《Journal of Pure and Applied Algebra》2007,209(1):239-244
For a pair of rings A⊂B satisfying a certain condition (?) we get general imbedding results for Karoubi-Villamayor, homotopy and Quillen K-theories. One important case is when A and B are respectively the henselization and completion of a regular ring of finite type over a field at a prime ideal. 相似文献
6.
Let be a graph with vertices, and let and denote respectively the adjacency matrix and the degree matrix of . Define for any real . The collection of eigenvalues of together with multiplicities are called the -spectrum of . A graph is said to be determined by its -spectrum if all graphs having the same -spectrum as are isomorphic to . We first prove that some graphs are determined by their -spectra for , including the complete graph , the union of cycles, the complement of the union of cycles, the union of copies of and , the complement of the union of copies of and , the path , and the complement of . Setting or , those graphs are determined by - or -spectra. Secondly, when is regular, we show that is determined by its -spectrum if and only if the join () is determined by its -spectrum for . Furthermore, we also show that the join () is determined by its -spectrum for . In the end, we pose some related open problems for future study. 相似文献
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John Bamberg S.P. Glasby Luke Morgan Alice C. Niemeyer 《Journal of Pure and Applied Algebra》2019,223(12):5428-5429
We give a correction to Fig. 1 and supporting text published in the paper: ‘Maximal linear groups induced on the Frattini quotient of a p-group’, J. Pure Appl. Algebra 222 (10) (2018) 2931–2951. 相似文献
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André C. Silva Alan Arroyo R. Bruce Richter Orlando Lee 《Discrete Mathematics》2019,342(11):3201-3207
The crossing number of a graph is the least number of crossings over all possible drawings of . We present a structural characterization of graphs with crossing number one. 相似文献
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Let be a connected graph with edges. An antimagic labeling of is a one-to-one mapping from to such that the vertex sum (i.e., sum of the labels assigned to edges incident to a vertex) for distinct vertices are different. A graph is called antimagic if has an antimagic labeling. It was conjectured by Hartsfield and Ringel that every tree other than is antimagic. The conjecture remains open though it was verified for trees with some constrains. Caterpillars are an important subclass of trees. This paper shows caterpillars with maximum degree 3 are antimagic, which gives an affirmative answer to an open problem of Lozano et al. (2019). 相似文献
10.
In 2009, Kyaw proved that every -vertex connected -free graph with contains a spanning tree with at most 3 leaves. In this paper, we prove an analogue of Kyaw’s result for connected -free graphs. We show that every -vertex connected -free graph with contains a spanning tree with at most 4 leaves. Moreover, the degree sum condition “” is best possible. 相似文献
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To determine the size of -graphs with given graph parameters is an interesting problem. Chvátal and Hanson (JCTB, 1976) gave a tight upper bound of the size of 2-graphs with restricted maximum degree and matching number; Khare (DM, 2014) studied the same problem for linear 3-graphs with restricted matching number and maximum degree. In this paper, we give a tight upper bound of the size of 3-graphs with bounded codegree and matching number. 相似文献
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For a graph , the -dominating graph of has vertices corresponding to the dominating sets of having cardinality at most , where two vertices of are adjacent if and only if the dominating set corresponding to one of the vertices can be obtained from the dominating set corresponding to the second vertex by the addition or deletion of a single vertex. We denote the domination and upper domination numbers of by and , respectively, and the smallest integer for which is connected for all by . It is known that , but constructing a graph such that appears to be difficult.We present two related constructions. The first construction shows that for each integer and each integer such that , there exists a graph such that , and . The second construction shows that for each integer and each integer such that , there exists a graph such that , and . 相似文献
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We show that any orientation of a graph with maximum degree three has an oriented 9-colouring, and that any orientation of a graph with maximum degree four has an oriented 69-colouring. These results improve the best known upper bounds of 11 and 80, respectively. 相似文献
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Laihao Ding Guan-Huei Duh Guanghui Wang Tsai-Lien Wong Jianliang Wu Xiaowei Yu Xuding Zhu 《Discrete Mathematics》2019,342(1):279-284
A graph is -choosable if the following holds: For any list assignment which assigns to each vertex a set of real numbers, and assigns to each edge a set of real numbers, there is a total weighting such that for , and for every edge . This paper proves that if is a connected graph of maximum degree , then is -choosable. 相似文献
15.
This is a short note to complete the paper appeared in Francini et al. (2016) [4], where a rough version of the classical well known Hadamard three-circle theorem for solution of an elliptic PDE in divergence form has been proved. Precisely, instead of circles, the authors obtain a similar inequality in a more complicated geometry. In this paper we clean the geometry and obtain a generalized version of the three-circle inequality for elliptic equation with coefficients with discontinuity of jump type. 相似文献
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An independent broadcast on a connected graph is a function such that, for every vertex of , the value is at most the eccentricity of in , and implies that for every vertex of within distance at most from . The broadcast independence number of is the largest weight of an independent broadcast on . Clearly, is at least the independence number for every connected graph . Our main result implies . We prove a tight inequality and characterize all extremal graphs. 相似文献
17.
List coloring generalizes graph coloring by requiring the color of a vertex to be selected from a list of colors specific to that vertex. One refinement of list coloring, called choosability with separation, requires that the intersection of adjacent lists is sufficiently small. We introduce a new refinement, called choosability with union separation, where we require that the union of adjacent lists is sufficiently large. For , a -list assignment is a list assignment where for all vertices and for all edges . A graph is -choosable if there is a proper coloring for every -list assignment. We explore this concept through examples of graphs that are not -choosable, demonstrating sparsity conditions that imply a graph is -choosable, and proving that all planar graphs are -choosable and -choosable. 相似文献
18.
The present paper deals with impulsive non-autonomous systems with convergence. We show that the structure of the Levinson center of a compact dissipative system is preserved under homomorphism in impulsive convergent systems. Also, we present some criteria of convergence using Lyapunov functions. 相似文献
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To classify the lattice polytopes with a given -polynomial is an important open problem in Ehrhart theory. A complete classification of the Gorenstein simplices whose normalized volumes are prime integers is known. In particular, their -polynomials are of the form , where and are positive integers. In the present paper, a complete classification of the Gorenstein simplices with the above -polynomials will be performed, when is either or , where and are prime integers with . Moreover, we consider the number of Gorenstein simplices, up to unimodular equivalence, with the expected -polynomial. 相似文献
20.
In the two disjoint shortest paths problem ( 2-DSPP), the input is a graph (or a digraph) and its vertex pairs and , and the objective is to find two vertex-disjoint paths and such that is a shortest path from to for , if they exist. In this paper, we give a first polynomial-time algorithm for the undirected version of the 2-DSPP with an arbitrary non-negative edge length function. 相似文献