共查询到20条相似文献,搜索用时 31 毫秒
1.
Mustapha Chellali Teresa W. Haynes Stephen T. Hedetniemi Alice McRae 《Discrete Applied Mathematics》2013
A subset S⊆V in a graph G=(V,E) is a [j,k]-set if, for every vertex v∈V?S, j≤|N(v)∩S|≤k for non-negative integers j and k, that is, every vertex v∈V?S is adjacent to at least j but not more than k vertices in S. In this paper, we focus on small j and k, and relate the concept of [j,k]-sets to a host of other concepts in domination theory, including perfect domination, efficient domination, nearly perfect sets, 2-packings, and k-dependent sets. We also determine bounds on the cardinality of minimum [1, 2]-sets, and investigate extremal graphs achieving these bounds. This study has implications for restrained domination as well. Using a result for [1, 3]-sets, we show that, for any grid graph G, the restrained domination number is equal to the domination number of G. 相似文献
2.
Let R be a commutative ring with identity. We will say that an R-module M satisfies the weak Nakayama property, if IM=M, where I is an ideal of R, implies that for any x∈M there exists a∈I such that (a−1)x=0. In this paper, we will study modules satisfying the weak Nakayama property. It is proved that if R is a local ring, then R is a Max ring if and only if J(R), the Jacobson radical of R, is T-nilpotent if and only if every R-module satisfies the weak Nakayama property. 相似文献
3.
Let G=(V,E) be a graph. A subset D⊆V is a dominating set if every vertex not in D is adjacent to a vertex in D. A dominating set D is called a total dominating set if every vertex in D is adjacent to a vertex in D. The domination (resp. total domination) number of G is the smallest cardinality of a dominating (resp. total dominating) set of G. The bondage (resp. total bondage) number of a nonempty graph G is the smallest number of edges whose removal from G results in a graph with larger domination (resp. total domination) number of G. The reinforcement (resp. total reinforcement) number of G is the smallest number of edges whose addition to G results in a graph with smaller domination (resp. total domination) number. This paper shows that the decision problems for the bondage, total bondage, reinforcement and total reinforcement numbers are all NP-hard. 相似文献
4.
Let S be a positively graded polynomial ring over a field of characteristic 0, and I⊂S a proper graded ideal. In this note it is shown that S/I is Golod if ∂(I)2⊂I. Here ∂(I) denotes the ideal generated by all the partial derivatives of elements of I. We apply this result to find large classes of Golod ideals, including powers, symbolic powers, and saturations of ideals. 相似文献
5.
Michel Mandjes Petteri Mannersalo Ilkka Norros Miranda van Uitert 《Stochastic Processes and their Applications》2006
Consider events of the form {Zs≥ζ(s),s∈S}, where Z is a continuous Gaussian process with stationary increments, ζ is a function that belongs to the reproducing kernel Hilbert space R of process Z, and S⊂R is compact. The main problem considered in this paper is identifying the function β∗∈R satisfying β∗(s)≥ζ(s) on S and having minimal R-norm. The smoothness (mean square differentiability) of Z turns out to have a crucial impact on the structure of the solution. As examples, we obtain the explicit solutions when ζ(s)=s for s∈[0,1] and Z is either a fractional Brownian motion or an integrated Ornstein–Uhlenbeck process. 相似文献
6.
We extend some known results on radicals and prime ideals from polynomial rings and Laurent polynomial rings to Z-graded rings, i.e, rings graded by the additive group of integers. The main of them concerns the Brown–McCoy radical G and the radical S, which for a given ring A is defined as the intersection of prime ideals I of A such that A/I is a ring with a large center. The studies are related to some open problems on the radicals G and S of polynomial rings and situated in the context of Koethe’s problem. 相似文献
7.
Mathias Beiglböck Walter SchachermayerBezirgen Veliyev 《Stochastic Processes and their Applications》2012
Every submartingale S of class D has a unique Doob–Meyer decomposition S=M+A, where M is a martingale and A is a predictable increasing process starting at 0. 相似文献
8.
Let T be a tree with s ends and f,g be continuous maps from T to T with f°g=g°f. In this note we show that if there exists a positive integer m≥2 such that gcd(m,l)=1 for any 2≤l≤s and f,g share a periodic point which is a km-periodic point of f for some positive integer k, then the topological entropy of f°g is positive. 相似文献
9.
Alexander J. Diesl Thomas J. Dorsey Shelly Garg Dinesh Khurana 《Journal of Pure and Applied Algebra》2014
Many authors have investigated the behavior of strong cleanness under certain ring extensions. In this note, we investigate the classical problem of lifting idempotents, in order to consolidate and extend these results. Our main result is that if R is a ring which is complete with respect to an ideal I and if x is an element of R whose image in R/I is strongly π-regular, then x is strongly clean in R. This generalizes Theorem 2.1 of Chen and Zhou (2007) [9]. 相似文献
10.
We prove that if for a continuous map f on a compact metric space X, the chain recurrent set, R(f) has more than one chain component, then f does not satisfy the asymptotic average shadowing property. We also show that if a continuous map f on a compact metric space X has the asymptotic average shadowing property and if A is an attractor for f, then A is the single attractor for f and we have A=R(f). We also study diffeomorphisms with asymptotic average shadowing property and prove that if M is a compact manifold which is not finite with dimM=2, then the C1 interior of the set of all C1 diffeomorphisms with the asymptotic average shadowing property is characterized by the set of Ω-stable diffeomorphisms. 相似文献
11.
Let H be a multigraph, possibly with loops, and consider a set S⊆V(H). A (simple) graph G is (H,S)-semi-linked if, for every injective map f:S→V(G), there exists an injective map g:V(H)?S→V(G)?f(S) and a set of |E(H)| internally disjoint paths in G connecting pairs of vertices of f(S)∪g(V(H)?S) for every edge between the corresponding vertices of H. This new concept of (H,S)-semi-linkedness is a generalization of H-linkedness . We establish a sharp minimum degree condition for a sufficiently large graph G to be (H,S)-semi-linked. 相似文献
12.
Given an ideal a⊆R in a (log) Q-Gorenstein F -finite ring of characteristic p>0, we study and provide a new perspective on the test ideal τ(R,at) for a real number t>0. Generalizing a number of known results from the principal case, we show how to effectively compute the test ideal and also describe τ(R,at) using (regular) alterations with a formula analogous to that of multiplier ideals in characteristic zero. We further prove that the F -jumping numbers of τ(R,at) as t varies are rational and have no limit points, including the important case where R is a formal power series ring. Additionally, we obtain a global division theorem for test ideals related to results of Ein and Lazarsfeld from characteristic zero, and also recover a new proof of Skoda's theorem for test ideals which directly mimics the proof for multiplier ideals. 相似文献
13.
Let k be a field of characteristic zero and R a factorial affine k-domain. Let B be an affineR-domain. In terms of locally nilpotent derivations, we give criteria for B to be R-isomorphic to the residue ring of a polynomial ring R[X1,X2,Y] over R by the ideal (X1X2−φ(Y)) for φ(Y)∈R[Y]?R. 相似文献
14.
15.
Let R(G) be the graph obtained from G by adding a new vertex corresponding to each edge of G and by joining each new vertex to the end vertices of the corresponding edge, and Q(G) be the graph obtained from G by inserting a new vertex into every edge of G and by joining by edges those pairs of these new vertices which lie on adjacent edges of G. In this paper, we determine the Laplacian polynomials of R(G) and Q(G) of a regular graph G; on the other hand, we derive formulae and lower bounds of the Kirchhoff index of these graphs. 相似文献
16.
By means of a certain module V and its tensor powers in a finite tensor category, we study a question of whether the depth of a Hopf subalgebra R of a finite-dimensional Hopf algebra H is finite. The module V is the counit representation induced from R to H, which is then a generalized permutation module, as well as a module coalgebra. We show that if in the subalgebra pair either Hopf algebra has finite representation type, or V is either semisimple with R∗ pointed, projective, or its tensor powers satisfy a Burnside ring formula over a finite set of Hopf subalgebras including R, then the depth of R in H is finite. One assigns a nonnegative integer depth to V, or any other H-module, by comparing the truncated tensor algebras of V in a finite tensor category and so obtains upper and lower bounds for depth of a Hopf subalgebra. For example, a relative Hopf restricted module has depth 1, and a permutation module of a corefree subgroup has depth less than the number of values of its character. 相似文献
17.
18.
S. Vanduffel X. Chen J. Dhaene M. Goovaerts L. Henrard R. Kaas 《Journal of Computational and Applied Mathematics》2008
In this paper we investigate the approximations for the distribution function of a sum S of lognormal random variables. These approximations are obtained by considering the conditional expectation E[S∣Λ] of S with respect to a conditioning random variable Λ. 相似文献
19.
We generalize some results of Borwein, Burke, Lewis, and Wang to mappings with values in metric (resp. ordered normed linear) spaces, and we define two classes of monotone mappings between an ordered linear space and a metric space (resp. ordered linear space): K-monotone dominated and cone-to-cone monotone mappings. K-monotone dominated mappings naturally generalize mappings with finite variation (in the classical sense) and K-monotone functions defined by Borwein, Burke and Lewis to mappings with domains and ranges of higher dimensions. First, using results of Veselý and Zají?ek, we show some relationships between these classes. Then, we show that every K-monotone function f:X→R, where X is any Banach space, is continuous outside of a set which can be covered by countably many Lipschitz hypersurfaces. This sharpens a result due to Borwein and Wang. As a consequence, we obtain a similar result for K-monotone dominated and cone-to-cone monotone mappings. Finally, we prove several results concerning almost everywhere differentiability (also in metric and w∗-senses) of these mappings. 相似文献
20.
In this article, it is proved that for any probability law μ over R with finite first moment and a given deterministic time t>0, there exists a gap diffusion with law μ at the prescribed time t. 相似文献