共查询到20条相似文献,搜索用时 954 毫秒
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Peter Wolfe 《Journal of Functional Analysis》1980,36(1):105-113
Let Lu be the integral operator defined by where S is the interior of a smooth, closed Jordan curve in the plane, k is a complex number with Re k ? 0, Im k ? 0, and ?2 = (x ?x′)2 + (y ? y′)2. We define , where in the definition of W21(q, S) the derivatives are taken in the sense of distributions. We prove that Lk is a continuous 1-l mapping of L2(q, S) onto W21(q, S). 相似文献
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M Meyniel 《Journal of Combinatorial Theory, Series B》1973,14(2):137-147
In this article we prove that a sufficient condition for an oriented strongly connected graph with n vertices to be Hamiltonian is: (1) for any two nonadjacent vertices x and y. 相似文献
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Juan C. Peral 《Journal of Functional Analysis》1980,36(1):114-145
Let u(x, t) be the solution of utt ? Δxu = 0 with initial conditions . Consider the linear operator . (Here g = 0.) We prove for t fixed the following result. Theorem 1: T is bounded in Lp if and only if . Theorem 2: If the coefficients are variables in C and constant outside of some compact set we get: (a) If n = 2k the result holds for . (b) If n = 2k ? 1, the result is valid for . This result are sharp in the sense that for p such that we prove the existence of in such a way that . Several applications are given, one of them is to the study of the Klein-Gordon equation, the other to the completion of the study of the family of multipliers and finally we get that the convolution against the kernel is bounded in H1. 相似文献
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David Joyce 《Journal of Pure and Applied Algebra》1982,23(1):37-65
The two operations of conjugation in a group, and satisfy certain identities. A set with two operations satisfying these identities is called a quandle. The Wirtinger presentation of the knot group involves only relations of the form y-1xy=z and so may be construed as presenting a quandle rather than a group. This quandle, called the knot quandle, is not only an invariant of the knot, but in fact a classifying invariant of the knot. 相似文献
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Let B be a body in R3 and let S denote the boundary of B. The surface S is described by , where f is an analytic function that is real and positive on (?1, 1) and f(±1) = 0. An algorithm is described for computing the scattered field due to a plane wave incident field, under Leontovich boundary conditions. The Galerkin method of solution used here leads to a block diagonal matrix involving 2M + 1 blocks, each block being of order 2(2N + 1). If, e.g., N = O(M2), the computed scattered field is accurate to within an error bounded by , where C and c are positive constants depending only on f. 相似文献
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Given the linear stationary first-order iterative scheme for the solution of the linear complex system (I ? T)x = c, its extrapolated complex scheme is considered. The problem which is studied and solved is that of determining an optimum value for ω, over the set of complex numbers, such that the extrapolated scheme considered converges asymptotically as fast as possible. 相似文献
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J.E Nymann 《Journal of Number Theory》1975,7(4):406-412
Given a set S of positive integers let denote the number of k-tuples 〈m1, …, mk〉 for which and (m1, …, mk) = 1. Also let denote the probability that k integers, chosen at random from , are relatively prime. It is shown that if P = {p1, …, pr} is a finite set of primes and S = {m : (m, p1 … pr) = 1}, then if k ≥ 3 and where d(S) denotes the natural density of S. From this result it follows immediately that as n → ∞. This result generalizes an earlier result of the author's where and S is then the whole set of positive integers. It is also shown that if S = {p1x1 … prxr : xi = 0, 1, 2,…}, then as n → ∞. 相似文献
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G.F Clements 《Journal of Combinatorial Theory, Series A》1974,17(2):227-244
Let S(n) denote the set of subsets of an n-element set. For an element x of S(n), let Γx and Px denote, respectively, all (|x| ?1)-element subsets of x and all (|x| + 1)-element supersets of x in S(n). Several inequalities involving Γ and P are given. As an application, an algorithm for finding an x-element antichain in S(n) satisfying for all x-element antichains X in S(n) is developed, where YX is the set of all elements of S(n) contained in an element of X. This extends a result of Kleitman [9] who solved the problem in case x is a binomial coefficient. 相似文献
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Let be a finite separable extension, , and the torsion subgroup of . When is an abelian extension is explicitly determined. This information is used to study the structure of . In particular, when am = a ∈ F is explicitly determined. 相似文献
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Let (S,∪) be a finite join-semilattice and (D, ∨, ∧) be a distributive lattice. Let be a map satisfying for each x and y in S. Then for any valuation v on D the following identity holds. where C is the set of all chains in S and l(c) denotes the length of a chain c. Also the theorem can be dualized. 相似文献
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Yuh-Jia Lee 《Journal of Functional Analysis》1982,47(2):153-164
Let (H, B) be an abstract Wiener pair and pt the Wiener measure with variance t. Let a be the class of exponential type analytic functions defined on the complexification [B] of B. For each pair of nonzero complex numbers α, β and f ? a, we define We show that the inverse α,β?1 exists and there exist two nonzero complex numbers α′,β′ such that . Clearly, the Fourier-Wiener transform, the Fourier-Feynman transform, and the Gauss transform are special cases of α,β. Finally, we apply the transform to investigate the existence of solutions for the differential equations associated with the operator c, where c is a nonzero complex number and c is defined by where Δ is the Laplacian and (·, ·) is the pairing. We show that the solutions can be represented as integrals with respect to the Wiener measure. 相似文献
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The positive but unknow coefficient a(y) in the partial differential equation is determined from a mixture of Dirichlet and Neumann data together with the additional specification of the “flux”: . 相似文献
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Milton Rosenberg 《Journal of multivariate analysis》1978,8(2):295-316
Let p, q be arbitrary parameter sets, and let be a Hilbert space. We say that x = (xi)i?q, xi ? , is a bounded operator-forming vector (?Fq) if the Gram matrix 〈x, x〉 = [(xi, xj)]i?q,j?q is the matrix of a bounded (necessarily ≥ 0) operator on , the Hilbert space of square-summable complex-valued functions on q. Let A be p × q, i.e., let A be a linear operator from to . Then exists a linear operator ǎ from (the Banach space) Fq to Fp on (A) = {x:x ? Fq, is p × q bounded on } such that y = ǎx satisfies yj?σ(x) = {space spanned by the xi}, 〈y, x〉 = A〈x, x〉 and . This is a generalization of our earlier [J. Multivariate Anal.4 (1974), 166–209; 6 (1976), 538–571] results for the case of a spectral measure concentrated on one point. We apply these tools to investigate q-variate wide-sense Markov processes. 相似文献
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Hsin Chu 《Journal of Mathematical Analysis and Applications》1982,85(2):566-583
Let X and Y be Banach spaces, ; P is said to be strongly ?-accretive if for some c > 0 and each x,y?X. These mappings constitute a generalization simultaneously of monotone mappings () and accretive mappings (when Y = X). By applying a theorem of 1. Ekeland, it is shown that a localized class of these mappings must be surjective under appropriate geometric assumptions on and continuity assumptions on P. The results generalize two theorems of F. E. Browder and the proofs further refine the methodology for dealing with such mappings. 相似文献
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A generalized Room square of order n and degree k is an array, each cell of which is either empty or contains an unordered k-tuple of a set S, |S| = n, such that each row and each column of the array contains each element of S exactly once and contains each unordered k-tuple of S exactly once. Using a class of Steiner systems and a generalized Room square of order 18 and degree 3 constructed by ad hoc methods, an infinite class of degree 3 squares is constructed. 相似文献