Báo cáo toán học: "A Remark on the Dirichlet Problem" pdf

... vanishes on pluripolar sets. The function U (μ, h) plays a crucial role in solving the Dirichlet problem. 3. The Comparison Principle for  E p + B a loc In order to prove the main theorem, in ... Pluripotential Theory, Oxford, 1990. 13. Y. Xing, Complex Monge-Ampere measures of pluriharmonic functions with bounded values near the boundary, Cand. J. Math. 52 (2000) 1085–1100. A...

Ngày tải lên: 06/08/2014, 05:20

... the condition nP(|X 1 | > η n ) ≤ c(log n) ε 0 , 0 < ε 0 < 1 in theorem 1.1 of [12]. Remark 1.4. If EX 2 < ∞, then X is in the domain of attraction of the normal law. Therefore, the ... weights. On the other hand, by the Theorem 1 of Schatte [3], Equation (3) fails for weight d k = 1. The optimal weight sequence remains unknown. The purpose of this article is t...

Ngày tải lên: 20/06/2014, 21:20

Ngày tải lên: 05/08/2014, 15:21

... f λ (q) is the generating function for the entries of the column corresponding to the λ-cycles. The dimension of the column-span of our table is therefore equal to dim F n , and the proposition is ... preceeding lemma, the N th entry of the column corresponding to the λ-cycles is equal to the number of nonnegative integer solutions to the equation λ 1 x 1 + ···+ λ k x...

Ngày tải lên: 07/08/2014, 06:20

... information on Maple) implementation of the downhill simplex function optimization method (see [13] for a good description of the method and a C implementation) to the maximize the expression. This ... (3) When conditioning on the event C P 0 , the random graphs of the resulting probability space may contain edges only from within the edges that connect vertices of differen...

Ngày tải lên: 07/08/2014, 06:20

... k>,ifthere are no solutions to the equation x 1 + ···+ x k = y 1 + ···+ y  in A. Denote by SF n k, the number of (k, )-sum-free subsets of [1,n]. Since the set of 1 the electronic journal ... x) =4 1+ln +1 2 (k − )( +1) . Combining the above inequalities with (10), the result follows. Let us conclude this note with some further remarks on the range of k and  satisfy...

Ngày tải lên: 07/08/2014, 06:20

... bounded, then the height distribution concentrates on two consecutive points. 3 Derivation of Results We establish the five parts of Theorem 2. Since the analysis involves a routine use of the saddle ... 1wewrite  A/b 0 (···)=  ∞ 0 (···)−  ∞ A/b (···), evaluate the first integral exactly and use Laplace’s method on the second integral. Now f  (u) < 0 for u ≥ A/b and the...

Ngày tải lên: 07/08/2014, 06:20

... several directions. They conjectured that if |G| > |Aut(G)| and the action of Aut(G)onG has no singleton orbits, then (G) = 2. Though there are graphs for which this fails 1 , the idea that ... define the class Π P k to consist of all languages L for which L ∈ Σ P k .Above, the notation · , · refers to some canonical pairing function. With these definitions, NP = Σ P 1 ,coNP=Π P 1...

Ngày tải lên: 07/08/2014, 06:22

... relation is derived for the rank (over most fields) of the set-inclusion matrices on a finite ground set. Given a finite set X of say v elements, let W = W t,k (v) be the (0,1)-matrix of inclusions for ... A note on the ranks of set-inclusion matrices D. de Caen Department of Mathematics and Statistics Queen’s University Kingston, Ontario, Canada K7L 3N6 decaen@mast.queensu.ca Submit...

Ngày tải lên: 07/08/2014, 06:22

... stationary dis- tribution is the desired distribution. The transitions of the chain consist of selecting a vertex uniformly at random and modifying the configuration only at the chosen vertex. The ... bounds on the mixing time of this modified dynamics imply bounds on the mixing time of the original Glauber dynamics. (See the remark at the end of Section 3 for a disc...

Ngày tải lên: 07/08/2014, 06:22