共查询到20条相似文献,搜索用时 15 毫秒
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The graph grabbing game is a two-player game on weighted connected graphs where all weights are non-negative. Two players, Alice and Bob, alternately remove a non-cut vertex from the graph (i.e., the resulting graph is still connected) and get the weight assigned to the vertex, where the starting player is Alice. Each player’s aim is to maximize his/her outcome when all vertices have been taken, and Alice wins the game if she gathered at least half of the total weight. Seacrest and Seacrest (2017) proved that Alice has a winning strategy for every weighted tree with even order, and conjectured that the same statement holds for every weighted connected bipartite graph with even order. In this paper, we prove that Alice wins the game on a type of a connected bipartite graph with even order called a -tree. 相似文献
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Aysel Erey 《Discrete Mathematics》2018,341(5):1419-1431
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David Gilat Isaac Meilijson Laura Sacerdote 《Stochastic Processes and their Applications》2018,128(6):1849-1856
For a martingale starting at with final variance , and an interval , let be the normalized length of the interval and let be the normalized distance from the initial point to the lower endpoint of the interval. The expected number of upcrossings of by is at most if and at most otherwise. Both bounds are sharp, attained by Standard Brownian Motion stopped at appropriate stopping times. Both bounds also attain the Doob upper bound on the expected number of upcrossings of for submartingales with the corresponding final distribution. Each of these two bounds is at most , with equality in the first bound for . The upper bound on the length covered by during upcrossings of an interval restricts the possible variability of a martingale in terms of its final variance. This is in the same spirit as the Dubins & Schwarz sharp upper bound on the expected maximum of above , the Dubins & Schwarz sharp upper bound on the expected maximal distance of from , and the Dubins, Gilat & Meilijson sharp upper bound on the expected diameter of . 相似文献
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Tathagata Basak 《Journal of Pure and Applied Algebra》2018,222(10):3036-3042
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We generalize results concerning -semigroups on Banach lattices to a setting of ordered Banach spaces. We prove that the generator of a disjointness preserving -semigroup is local. Some basic properties of local operators are also given. We investigate cases where local operators generate local -semigroups, by using Taylor series or Yosida approximations. As norms we consider regular norms and show that bands are closed with respect to such norms. Our proofs rely on the theory of embedding pre-Riesz spaces in vector lattices and on corresponding extensions of regular norms. 相似文献
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L. Avena O. Blondel A. Faggionato 《Stochastic Processes and their Applications》2018,128(10):3490-3530
We consider random walks in dynamic random environments given by Markovian dynamics on . We assume that the environment has a stationary distribution and satisfies the Poincaré inequality w.r.t. . The random walk is a perturbation of another random walk (called “unperturbed”). We assume that also the environment viewed from the unperturbed random walk has stationary distribution . Both perturbed and unperturbed random walks can depend heavily on the environment and are not assumed to be finite-range. We derive a law of large numbers, an averaged invariance principle for the position of the walker and a series expansion for the asymptotic speed. We also provide a condition for non-degeneracy of the diffusion, and describe in some details equilibrium and convergence properties of the environment seen by the walker. All these results are based on a more general perturbative analysis of operators that we derive in the context of - bounded perturbations of Markov processes by means of the so-called Dyson–Phillips expansion. 相似文献
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The purpose of this note is to show a new series of examples of homogeneous ideals I in for which the containment fails. These ideals are supported on certain arrangements of lines in , which resemble Fermat configurations of points in , see [14]. All examples exhibiting the failure of the containment constructed so far have been supported on points or cones over configurations of points. Apart from providing new counterexamples, these ideals seem quite interesting on their own. 相似文献
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Alexey Ananyevskiy 《Journal of Pure and Applied Algebra》2018,222(10):3195-3218
We provide a cohomological interpretation of the zeroth stable -homotopy group of a smooth curve over an infinite perfect field. We show that this group is isomorphic to the first Nisnevich (or Zariski) cohomology group of a certain sheaf closely related to the first Milnor–Witt K-theory sheaf. This cohomology group can be computed using an explicit Gersten-type complex. We show that if the base field is algebraically closed then the zeroth stable -homotopy group of a smooth curve coincides with the zeroth Suslin homology group that was identified by Suslin and Voevodsky with a relative Picard group. As a consequence we reobtain a version of Suslin's rigidity theorem. 相似文献
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Tutte’s -flow conjecture states that every -edge-connected graph admits a nowhere-zero -flow. In this paper, we characterize all graphs with independence number at most that admit a nowhere-zero -flow. The characterization of -flow verifies Tutte’s -flow conjecture for graphs with independence number at most and with order at least . In addition, we prove that every odd--edge-connected graph with independence number at most admits a nowhere-zero -flow. To obtain these results, we introduce a new reduction method to handle odd wheels. 相似文献
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E. Martínez-Moro A. Piñera-Nicolás I.F. Rúa 《Journal of Pure and Applied Algebra》2018,222(2):359-367
In this work, we study the structure of multivariable modular codes over finite chain rings when the ambient space is a principal ideal ring. We also provide some applications to additive modular codes over the finite field . 相似文献
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Adam Kabela 《Discrete Mathematics》2018,341(3):579-587
Studying the shortness of longest cycles in maximal planar graphs, we improve the upper bound on the shortness exponent of the class of -tough maximal planar graphs presented by Harant and Owens (1995). In addition, we present two generalizations of a similar result of Tká? who considered -tough maximal planar graphs (Tká?, 1996); we remark that one of these generalizations gives a tight upper bound. We fix a problematic argument used in both mentioned papers. 相似文献
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We study solutions of the focusing energy-critical nonlinear heat equation in . We show that solutions emanating from initial data with energy and -norm below those of the stationary solution W are global and decay to zero, via the “concentration-compactness plus rigidity” strategy of Kenig–Merle [33], [34]. First, global such solutions are shown to dissipate to zero, using a refinement of the small data theory and the -dissipation relation. Finite-time blow-up is then ruled out using the backwards-uniqueness of Escauriaza–Seregin–Sverak [17], [18] in an argument similar to that of Kenig–Koch [32] for the Navier–Stokes equations. 相似文献
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We study the Hénon–Lane–Emden conjecture, which states that there is no non-trivial non-negative solution for the Hénon–Lane–Emden elliptic system whenever the pair of exponents is subcritical. By scale invariance of the solutions and Sobolev embedding on , we prove this conjecture is true for space dimension ; which also implies the single elliptic equation has no positive classical solutions in when the exponent lies below the Hardy–Sobolev exponent, this covers the conjecture of Phan–Souplet [22] for . 相似文献
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We investigate the occurrence of Shimura (special) subvarieties in the locus of Jacobians of abelian Galois covers of in and give classifications of families of such covers that give rise to Shimura subvarieties in the Torelli locus inside . Our methods are based on Moonen–Oort works as well as characteristic p techniques of Dwork and Ogus and Monodromy computations. 相似文献
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Let be a prime power and be a positive integer. A subspace partition of , the vector space of dimension over , is a collection of subspaces of such that each nonzero vector of is contained in exactly one subspace in ; the multiset of dimensions of subspaces in is then called a Gaussian partition of . We say that contains a direct sum if there exist subspaces such that . In this paper, we study the problem of classifying the subspace partitions that contain a direct sum. In particular, given integers and with , our main theorem shows that if is a subspace partition of with subspaces of dimension for , then contains a direct sum when has a solution for some integers and belongs to the union of two natural intervals. The lower bound of captures all subspace partitions with dimensions in that are currently known to exist. Moreover, we show the existence of infinite classes of subspace partitions without a direct sum when or when the condition on the existence of a nonnegative integral solution is not satisfied. We further conjecture that this theorem can be extended to any number of distinct dimensions, where the number of subspaces in each dimension has appropriate bounds. These results offer further evidence of the natural combinatorial relationship between Gaussian and integer partitions (when ) as well as subspace and set partitions. 相似文献
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Fares Maalouf 《Journal of Pure and Applied Algebra》2018,222(5):1003-1005
We show that if k is an infinite field, then there exists a subspace of dimension , such that no nonzero member of W has infinitely many zeros. This generalizes a result from a paper by Bergman and Nahlus, and partly answers another question from the same paper. 相似文献
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Haiyang Zhu Lianying Miao Sheng Chen Xinzhong Lü Wenyao Song 《Discrete Mathematics》2018,341(8):2211-2219
Let be the set of all positive integers. A list assignment of a graph is a function that assigns each vertex a list for all . We say that is --choosable if there exists a function such that for all , if and are adjacent, and if and are at distance 2. The list--labeling number of is the minimum such that for every list assignment , is --choosable. We prove that if is a planar graph with girth
and its maximum degree is large enough, then . There are graphs with large enough and having . 相似文献