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1.
A family of Friedrichs models under rank one perturbations hμ(p), p(−π,π]3, μ>0, associated to a system of two particles on the three-dimensional lattice is considered. We prove the existence of a unique eigenvalue below the bottom of the essential spectrum of hμ(p) for all non-trivial values of p under the assumption that hμ(0) has either a threshold energy resonance (virtual level) or a threshold eigenvalue. The threshold energy expansion for the Fredholm determinant associated to a family of Friedrichs models is also obtained.  相似文献   

2.
We consider the problem of the minimum number of Hamiltonian cycles that could be present in a Hamiltonian maximal planar graph on p vertices. In particular, we construct a p-vertex maximal planar graph containing exactly four Hamiltonian cycles for every p ≥ 12. We also prove that every 4-connected maximal planar graph on p vertices contains at least p/(log2 p) Hamiltonian cycles.  相似文献   

3.
Let G be a graph on p vertices with q edges and let r = q ? p = 1. We show that G has at most cycles. We also show that if G is planar, then G has at most 2r ? 1 = o(2r ? 1) cycles. The planar result is best possible in the sense that any prism, that is, the Cartesian product of a cycle and a path with one edge, has more than 2r ? 1 cycles. © Wiley Periodicals, Inc. J. Graph Theory 57: 255–264, 2008  相似文献   

4.
A group in which every element commutes with its endomorphic images is called an “E-group″. If p is a prime number, a p-group G which is an E-group is called a “pE-group″. Every abelian group is obviously an E-group. We prove that every 2-generator E-group is abelian and that all 3-generator E-groups are nilpotent of class at most 2. It is also proved that every infinite 3-generator E-group is abelian. We conjecture that every finite 3-generator E-group should be abelian. Moreover, we show that the minimum order of a non-abelian pE-group is p 8 for any odd prime number p and this order is 27 for p = 2. Some of these results are proved for a class wider than the class of E-groups.  相似文献   

5.
In this paper we study the existence, nonexistence and multiplicity of positive solutions for nonhomogeneous Neumann boundary value problem of the type
where Ω is a bounded domain in with smooth boundary, 1<p<n,Δpu=div(|u|p-2u) is the p-Laplacian operator, , , (x)0 and λ is a real parameter. The proofs of our main results rely on different methods: lower and upper solutions and variational approach.  相似文献   

6.
Paul J. Sanders 《代数通讯》2013,41(3):1309-1333
A sharp bound is derived for the nilpotency class of a regular p-group in terms of its coexponent, and is used to show that the number of groups of order pn with a given fixed coexponent, is independent of n, for p and n sufficiently large. Explicit formulae are calculated in the case of coexponent 3.  相似文献   

7.
In this paper we show that e/n is the sharp threshold for the existence of tight Hamilton cycles in random k ‐uniform hypergraphs, for all k ≥ 4. When k = 3 we show that 1/n is an asymptotic threshold. We also determine thresholds for the existence of other types of Hamilton cycles. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2013  相似文献   

8.
For positive integers r>?, an r‐uniform hypergraph is called an ?‐cycle if there exists a cyclic ordering of its vertices such that each of its edges consists of r consecutive vertices, and such that every pair of consecutive edges (in the natural ordering of the edges) intersect in precisely ? vertices; such cycles are said to be linear when ?=1, and nonlinear when ?>1. We determine the sharp threshold for nonlinear Hamiltonian cycles and show that for all r>?>1, the threshold for the appearance of a Hamiltonian ?‐cycle in the random r‐uniform hypergraph on n vertices is sharp and given by for an explicitly specified function λ. This resolves several questions raised by Dudek and Frieze in 2011.10  相似文献   

9.
We consider a Cauchy problem for a semilinear heat equation
with p>pS where pS is the Sobolev exponent. If u(x,t)=(Tt)−1/(p−1)φ((Tt)−1/2x) for xRN and t[0,T), where φ is a regular positive solution of
(P)
then u is called a backward self-similar blowup solution. It is immediate that (P) has a trivial positive solution κ≡(p−1)−1/(p−1) for all p>1. Let pL be the Lepin exponent. Lepin obtained a radial regular positive solution of (P) except κ for pS<p<pL. We show that there exist no radial regular positive solutions of (P) which are spatially inhomogeneous for p>pL.  相似文献   

10.
Eli Shamir 《Combinatorica》1983,3(1):123-131
A threshold for a graph propertyQ in the scale of random graph spacesG n,p is ap-band across which the asymptotic probability ofQ jumps from 0 to 1. We locate a sharp threshold for the property of having a hamiltonian path.  相似文献   

11.
12.
In this paper it is proved that in the random graph model G(n,p), the property of containing a k ‐regular subgraph, has a sharp threshold for k ≥ 3. It is also shown how to use similar methods to prove, quite easily, the (known fact of) sharpness of having a non empty k ‐core for k ≥ 3. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 42, 509–519, 2013  相似文献   

13.
14.
《代数通讯》2013,41(7):3497-3504
Abstract

In this paper,we present a sharp bound for the nilpotency class of a finite p-group (where p is an odd prime) in terms of its coexponent. As to a powerful p-group,we give the sharp bound for the nilpotency class in terms of its coexponent for arbitrary prime p.  相似文献   

15.
We show that the edges of the complete symmetric directed graph onn vertices can be partitioned into directed cycles (or anti-directed cycles) of lengthn−1 so that any two distinct cycles have exactly one oppositely directed edge in common whenn=p e>3, wherep is a prime ande is a positive integer. When the cycles are anti-directedp must be odd. We then consider the designs which arise from these partitions and investigate their construction. We would like to thank the Mathematics Department of the University of Arizona for their hospitality during January 1979 when this work was begun. Partial support was provided for this research by the Natural Sciences and Engineering Research Council of Canada under Grant A-4792.  相似文献   

16.
We show in Gn.p' that the threshold for δ(G) ? 1 is the threshold for G2G to be Hamiltonian. © 1994 John Wiley & Sons, Inc.  相似文献   

17.
18.
Networks of threshold elements whose inputs are assigned positive and negative (inhibitory) weights and outputs take the values 0 and 1 are considered. A stationary ensemble is defined as a connected subnetwork of a threshold network for which the unit state (1, 1, …, 1) = 1 is stable. The transfer of an ensemble into the state 1 is called switching on. Necessary and sufficient conditions for a network to be an ensemble are given. It is shown that, in the proposed model, the switching on of one of two ensembles having common elements does not necessarily lead to the switching on of the other.  相似文献   

19.
20.
For points x and y in a poset (X, >) let x> p y mean that more linear extensions of the poset have x above y than y above x. It has been known for some time that > p can have cycles when the height of the poset is two or more. Moreover, the smallest posets with a > p cycle have nine points and heights of 2, 3 and 4. We show here that height-1 posets can also have > p cycles. Our smallest example for this phenomenon has 15 points.Research supported through a fellowship from the Center for Advanced Study of the University of Delaware.  相似文献   

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