共查询到20条相似文献,搜索用时 46 毫秒
1.
O.L. Mangasarian 《Linear algebra and its applications》1974,8(1):43-55
Given the iterative scheme xi+1 = BTxi + r where B, T are fixed n×:n real matrices, r a fixed real n-vector and xi a real n-vector we investigate the convergence and monotonicity of schemes of the type , where Sij are n×:n real matrices related to T. The n-vector iterates vi,wi bracket in a certain sense solutions x of x = BTx + r. We also give necessary and sufficient conditions for the monotonicity of the original iterative scheme itself xi+1 = BTxi + r. This leads to monotonici results for classical iterative schemes such as the Jacobi, Gauss-Seidel, and successive overrelaxation methods. 相似文献
2.
Boguslaw Tomaszewski 《Journal of Functional Analysis》1984,55(1):63-67
It is shown, for n ? m ? 1, that there exist inner maps Φ: Bn → Bm with boundary values such that . where σn and σm are the Haar measures on ?Bn and ?Bm, respectively, and A ? Bn is an arbitrary Borel set. 相似文献
3.
Let and be polynomials with real zeros satisfying An?1 = Bn?1 = 0, and let Using the recently proved validity of the van der Waerden conjecture on permanents, some results on the real zeros of H(x) are obtained. These results are related to classical results on composite polynomials. 相似文献
4.
Gideon Nettler 《Journal of Number Theory》1981,13(4):456-462
In a previous paper it was proven that given the continued fractions where the a's and b's are positive integers, then A, B, A ± B, and AB are irrational numbers if for all n sufficiently large, and transcendental numbers if for all n sufficiently large. Using a more direct approach it is proven in this paper that A, B, A ± B, and AB are transcendental numbers if an > bn > an?1(n?1)2 for all n sufficiently large. 相似文献
5.
6.
A regularity result for singular nonlinear elliptic systems in inverse-power weighted Sobolev spaces
P.D Smith 《Journal of Differential Equations》1984,53(2):125-138
The compactness method to weighted spaces is extended to prove the following theorem:Let H2,s1(B1) be the weighted Sobolev space on the unit ball in Rn with norm Let n ? 2 ? s < n. Let u? [H2,s1(B1) ∩ L∞(B1)]N be a solution of the nonlinear elliptic system , are uniformly continuous functions of their arguments and satisfy: . Then there exists an R1, 0 < R1 < 1, and an α, 0 < α < 1, along with a set such that (1) , (2) Ω does not contain the origin; Ω does not contain BR1, (3) is open, (4) u is ; u is LipαBR1. 相似文献
7.
Using results from the theory of B-splines, various inequalities involving the nth order divided differences of a function f with convex nth derivative are proved; notably, , where z is the center of mass . 相似文献
8.
Ramzi May 《Comptes Rendus Mathematique》2003,336(9):731-734
Let be a maximal solution of the Navier–Stokes equations. We prove that u is C∞ on and there exists a constant , which depends only on n, such that if is finite then, for all we have To cite this article: R. May, C. R. Acad. Sci. Paris, Ser. I 336 (2003). 相似文献
9.
Christer Borell 《Journal of Mathematical Analysis and Applications》1973,43(2):419-440
Let ψ be convex with respect to ?, B a convex body in Rn and f a positive concave function on B. A well-known result by Berwald states that (1) if ξ is chosen such that .The main purpose in this paper is to characterize those functions f : B → R+ such that (1) holds. 相似文献
10.
Let Ω = {1, 0} and for each integer n ≥ 1 let (n-tuple) and for all k = 0,1,…,n. Let {Ym}m≥1 be a sequence of i.i.d. random variables such that . For each A in , let TA be the first occurrence time of A with respect to the stochastic process {Ym}m≥1. R. Chen and A.Zame (1979, J. Multivariate Anal. 9, 150–157) prove that if n ≥ 3, then for each element A in , there is an element B in such that the probability that TB is less than TA is greater than . This result is sharpened as follows: (I) for n ≥ 4 and 1 ≤ k ≤ n ? 1, each element A in , there is an element B also in such that the probability that TB is less than TA is greater than ; (II) for n ≥ 4 and 1 ≤ k ≤ n ? 1, each element A = (a1, a2,…,an) in , there is an element C also in such that the probability that TA is less than TC is greater than if n ≠ 2m or n = 2m but ai = ai + 1 for some 1 ≤ i ≤ n?1. These new results provide us with a better and deeper understanding of the fair coin tossing process. 相似文献
11.
J.W Layman 《Journal of Combinatorial Theory, Series A》1985,40(1):161-168
For any prime p, the sequence of Bell exponential numbers Bn is shown to have p ? 1 consecutive values congruent to zero (mod p), beginning with Bm, where (). This is an improvement over previous results on the maximal strings of zero residues of the Bell numbers. Similar results are obtained for the sequence of generalized Bell numbers An generated by . 相似文献
12.
Tomas Schonbek 《Journal of Differential Equations》1985,56(2):290-296
New and more elementary proofs are given of two results due to W. Littman: (1) Let . The estimate cannot hold for all u?C0∞(Q), Q a cube in , some constant C. (2) Let n ? 2, p ≠ 2. The estimate cannot hold for all C∞ solutions of the wave equation □u = 0 in ; all t ?; some function C: → . 相似文献
13.
14.
Marc Malric 《Comptes Rendus Mathematique》2003,336(6):499-504
The Lévy transform of a Brownian motion B is the Brownian motion ; denote by Bn the Brownian motion obtained from B by iterating n times the Lévy transform. We establish that the set of all instants t such that Btn=0 for some n, is a.s. dense in the time-axis . To cite this article: M. Malric, C. R. Acad. Sci. Paris, Ser. I 336 (2003). 相似文献
15.
J.H Michael 《Journal of Mathematical Analysis and Applications》1981,79(1):203-217
We consider the mixed boundary value problem , where Ω is a bounded open subset of n whose boundary Γ is divided into disjoint open subsets Γ+ and Γ? by an (n ? 2)-dimensional manifold ω in Γ. We assume A is a properly elliptic second order partial differential operator on and Bj, for j = 0, 1, is a normal jth order boundary operator satisfying the complementing condition with respect to A on . The coefficients of the operators and Γ+, Γ? and ω are all assumed arbitrarily smooth. As announced in [Bull. Amer. Math. Soc.83 (1977), 391–393] we obtain necessary and sufficient conditions in terms of the coefficients of the operators for the mixed boundary value problem to be well posed in Sobolev spaces. In fact, we construct an open subset of the reals such that, if then for is a Fredholm operator if and only if s ∈ . Moreover, = ?xewx, where the sets x are determined algebraically by the coefficients of the operators at x. If n = 2, x is the set of all reals not congruent (modulo 1) to some exceptional value; if n = 3, x is either an open interval of length 1 or is empty; and finally, if n ? 4, x is an open interval of length 1. 相似文献
16.
Given a polynomial , we calculate a subspace Gp of the linear space 〈X〉 generated by the indeterminates which is minimal with respect to the property (the algebra generated by Gp, and prove its uniqueness. Furthermore, we use this result to characterize the pairs (P,Q) of polynomials P(X1,…,Xn) and Q(X1,…,Xn) for which there exists an isomorphism T:〈X〉 →〈X〉 that “separates P from Q,” i.e., such that for some k(1<k<n) we can write P and Q as and respectively, where . 相似文献
17.
Abraham Boyarsky 《Journal of Mathematical Analysis and Applications》1980,76(2):483-497
Let τ: [0, 1] → [0, 1] possess a unique invariant density . Then given any ? > 0, we can find a density function p such that is the invariant density of the stochastic difference equation xn + 1 = τ(xn) + W, where W is a random variable. It follows that for all starting points . 相似文献
18.
Walter Rudin 《Journal of Functional Analysis》1983,50(1):100-126
Let B be the open unit ball of n, n > 1. Let I (for “inner”) be the set of all u ? H °(B) that have a.e. on the boundary S of B. Aleksandrov proved recently that there exist nonconstant u ? I. This paper strengthens his basic theorem and provides further information about I and the algebra Q generated by I. Let XY be the finite linear span of products xy, x ? X, y ? Y, and let be the norm closure, in L∞ = L∞(S), of X. Some results: set I is dense in the unit ball of H∞(B) in the compact-open topology. On is weak1-dense in does not contain . (When .) Every unimodular is a pointwise limit a.e. of products . The zeros of every in the ball algebra (but not of every H∞-function) can be matched by those of some u ? I, as can any finite number of derivatives at 0 if . However, cannot be bounded in B if u ? I is non-constant. 相似文献
19.
The usual Sobolev inequality in n, n ? 3, asserts that , with Sn being the sharp constant. This paper is concerned, instead, with functions restricted to bounded domains Ω ? n. Two kinds of inequalities are established: (i) If ? = 0 on ?Ω, then with and with . (ii) If ? ≠ 0 on ?Ω, then with . Some further results and open problems in this area are also presented. 相似文献
20.
Let be a real or complex n × n interval matrix. Then it is shown that the Neumann series is convergent iff the sequence {k} converges to the null matrix , i.e., iff the spectral radius of the real comparison matrix constructed in [2] is less than one. 相似文献