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91.
92.
We consider quantum field theoretical models inn dimensional space-time given by interaction densities which are bounded functions of an ultraviolet cut-off boson field. Using methods of euclidean Markov field theory and of classical statistical mechanics, we construct the infinite volume imaginary and real time Wightman functions as limits of the corresponding quantities for the space cut-off models. In the physical Hilbert space, the space-time translations are represented by strongly continuous unitary groups and the generator of time translationsH is positive and has a unique, simple lowest eigenvalue zero, with eigenvector , which is the unique state invariant under space-time translations. The imaginary time Wightman functions and the infinite volume vacuum energy density are given as analytic functions of the coupling constant. The Wightman functions have cluster properties also with respect to space translations. 相似文献
93.
Raphael Høegh-Krohn 《Communications in Mathematical Physics》1969,14(3):171-184
We consider a boson field (x) under an interaction of the form
V((x))dx, whereV() is a bounded continuous real function of a real variable . IfV() has a uniformly continuous and bounded first derivative, we prove that the Heisenberg picture field exists as weak limits of the Heisenberg picture fields corresponding to the cut-off interaction. 相似文献
94.
95.
Let H = (V, E) be an r-uniform hypergraph and let A matching M of H is (α, )-perfect if for each F ∈ , at least α|F| vertices of F are covered by M. Our main result is a theorem giving sufficient conditions for an r-uniform hypergraph to have a -perfect matching. As a special case of our theorem we obtain the following result. Let K(n, r) denote the complete r-uniform hypergraph with n vertices. Let t and r be fixed positive integers where t≥r≥2. Then, K(n, r) can be packed with edge-disjoint copies of K(t, r) such that each vertex is incident with only o(n r ?1) unpacked edges. This extends a result of Rödl [9]. 相似文献
96.
Packing 4-Cycles in Eulerian and Bipartite Eulerian Tournaments with an Application to Distances in Interchange Graphs 总被引:1,自引:0,他引:1
Raphael Yuster 《Annals of Combinatorics》2005,9(1):117-124
We prove that every Eulerian orientation of Km,n contains
arc-disjoint directed 4-cycles, improving earlier lower bounds. Combined with a probabilistic argument, this result is used to prove that every regular tournament with n vertices contains
arc-disjoint directed 4-cycles. The result is also used to provide an upper bound for the distance between two antipodal vertices in interchange graphs.Received February 6, 2004 相似文献
97.
98.
We consider the critical nonlinear Schrödinger equation with initial condition in the energy space and study the dynamics of finite time blow-up solutions. In an earlier sequence of papers, the authors established for a certain class of initial data on the basis of dispersive properties in a sharp and stable upper bound on the blow-up rate: .
by exhibiting the dispersive structure in the scaling invariant space for this log-log regime. In addition, we will extend to the pure energy space a dynamical characterization of the solitons among the zero energy solutions.
In an earlier paper, the authors then addressed the question of a lower bound on the blow-up rate and proved for this class of initial data the nonexistence of self-similar solutions, that is,
In this paper, we prove the sharp lower bound
by exhibiting the dispersive structure in the scaling invariant space for this log-log regime. In addition, we will extend to the pure energy space a dynamical characterization of the solitons among the zero energy solutions.
99.
Sandro Bettin Jonathan W. Bober Andrew R. Booker Brian Conrey Min Lee Giuseppe Molteni Thomas Oliver David J. Platt Raphael S. Steiner 《The Ramanujan Journal》2018,45(3):659-681
By using specific subsequences of two different types of generalized Stern polynomials, we obtain several related classes of finite and infinite continued fractions involving a single term \(z^{t^j}\) in their partial numerators, where z is a complex variable and t is a positive integer. This approach is extended to other, sparser, subsequences of Stern polynomials, based on certain Lucas functions; this then leads to further infinite classes of continued fractions. 相似文献
100.
Raphael Loewy 《Journal of Mathematical Analysis and Applications》2010,365(2):570-583
Let K be a proper (i.e., closed, pointed, full convex) cone in Rn. An n×n matrix A is said to be K-primitive if there exists a positive integer k such that ; the least such k is referred to as the exponent of A and is denoted by γ(A). For a polyhedral cone K, the maximum value of γ(A), taken over all K-primitive matrices A, is called the exponent of K and is denoted by γ(K). It is proved that if K is an n-dimensional polyhedral cone with m extreme rays then for any K-primitive matrix A, γ(A)?(mA−1)(m−1)+1, where mA denotes the degree of the minimal polynomial of A, and the equality holds only if the digraph (E,P(A,K)) associated with A (as a cone-preserving map) is equal to the unique (up to isomorphism) usual digraph associated with an m×m primitive matrix whose exponent attains Wielandt's classical sharp bound. As a consequence, for any n-dimensional polyhedral cone K with m extreme rays, γ(K)?(n−1)(m−1)+1. Our work answers in the affirmative a conjecture posed by Steve Kirkland about an upper bound of γ(K) for a polyhedral cone K with a given number of extreme rays. 相似文献