共查询到20条相似文献,搜索用时 62 毫秒
1.
Tom M. Apostol 《Journal of Number Theory》1982,15(1):14-24
An elementary proof is given of the author's transformation formula for the Lambert series relating Gp(e2πiτ) to Gp(e2πiAτ), where p > 1 is an odd integer and is a general modular substitution. The method extends Sczech's argument for treating Dedekind's function , and uses Carlitz's formula expressing generalized Dedekind sums in terms of Eulerian functions. 相似文献
2.
Jean-Louis Nicolas 《Journal of Number Theory》1983,17(3):375-388
Let φ be the Euler's function. A question of Rosser and Schoenfeld is answered, showing that there exists infinitely many n such that , where γ is the Euler's constant. More precisely, if Nk is the product of the first k primes, it is proved that, under the Riemann's hypothesis, holds for any k ≥ 2, and, if the Riemann's hypothesis is false this inequality holds for infinitely many k, and is false for infinitely many k. 相似文献
3.
S. Ihara 《Journal of multivariate analysis》1974,4(1):74-87
The message m = {m(t)} is a Gaussian process that is to be transmitted through the white Gaussian channel with feedback: . Under the average power constraint, , we construct causally the optimal coding, in the sense that the mutual information It(m, Y) between the message m and the channel output Y (up to t) is maximized. The optimal coding is presented by , where and A(s) is a positive function such that . 相似文献
4.
Christian Gros 《European Journal of Operational Research》1978,2(5):368-376
For a vector-valued function f, Sup f and Inf f are defined from the Yu's domination theory and the Pareto's efficiency. A notion of conjugate is proposed for convex vector-valued function, this construction gives once more the usual conjugate function: when the function f is scalar. Then, this concept is used to write the Fenchel's problem in convex multiple objective optimization and to prove the associated duality theorem. 相似文献
5.
Let , let , where g2 and g3 are coefficients of the elliptic curve: Y2 = 4X3 ? g2X ? g3 over a finite field and Δ = g23 ? 27g32 and let . Then the p-adic cohomology theory will be applied to compute explicitly the zeta matrices of the elliptic curves, induced by the pth power map on the free -module . Main results are; Theorem 1.1: X2dY and YdX are basis elements for ; Theorem 1.2: YdX, X2dY, Y?1dX, Y?2dX and XY?2dX are basis elements for , where is a lifting of X, and all the necessary recursive formulas for this explicit computation are given. 相似文献
6.
Carsten Thomassen 《Journal of Combinatorial Theory, Series B》1982,33(2):137-160
Some basic results on duality of infinite graphs are established and it is proven that a block has a dual graph if and only if it is planar and any two vertices are separated by a finite edge cut. Also, the graphs having predual graphs are characterized completely and it is shown that if is a dual and predual graph of G, then G and can be represented as geometric dual graphs. The uniqueness of dual graphs is investigated, in particular, Whitney's 2-isomorphism theorem is extended to infinite graphs. Finally, infinite minimal cuts in dual graphs are studied and the characterization (in terms of planarity and separation properties) of the graphs having dual graphs satisfying conditions on the infinite cuts, as well, is included. 相似文献
7.
In this paper we give fast algorithms for generating all maximal independent sets of three special classes of graphs—interval, circular-arc, and chordal graphs. The worst-case running times of our algorithms are O(n2 + β) for interval and circular-arc graphs, and for chordal graphs, where n, e, and α are the numbers of vertexes, edges, and maximal independent sets of a graph, and β is the sum of the numbers of vertexes of all maximal independent sets. Our algorithms compare favorably with the fastest known algorithm for general graphs which has a worst-case running time of . 相似文献
8.
R.A. Maller 《Stochastic Processes and their Applications》1978,8(2):171-179
Let Xi be iidrv's and Sn=X1+X2+…+Xn. When EX21<+∞, by the law of the iterated logarithm for some constants αn. Thus the r.v. is a.s.finite when δ>0. We prove a rate of convergence theorem related to the classical results of Baum and Katz, and apply it to show, without the prior assumption EX21<+∞ that EYh<+∞ if and only if for 0<h<1 and δ> , whereas whenever h>0 and . 相似文献
9.
The spaces in the title are associated to a fixed representing measure m for a fixed character on a uniform algebra. It is proved that the set of representing measures for that character which are absolutely continuous with respect to m is weakly relatively compact if and only if each m-negligible closed set in the maximal ideal space of L∞ is contained in an m-negligible peak set for H∞. J. Chaumat's characterization of weakly relatively compact subsets in therefore remains true, and is complete, under the first conditions. In this paper we also give a direct proof. From this we obtain that has the Dunford-Pettis property. 相似文献
10.
Detlef Wille 《Journal of Combinatorial Theory, Series B》1978,25(2):143-150
For functions f : D → Rk where D is a finite set and Rk = {0,1,… k} we define complementary and self-complementary functions. De Bruijn's generalization of Polya's theorem gives a formula for the number of non-isomorphic self-complementary functions . We consider the special cases of generalized graphs and m-placed relations. Among other results we prove that the number of non-isomorphic self-complementary relations over 2n elements is equal to the number of non-isomorphic self-complementary graphs with 4n + 1 points. 相似文献
11.
《Journal of Functional Analysis》1987,73(1):122-134
Let Ω denote a connected and open subset of n. The existence of n commuting self-adjoint operators H1,…, Hn on such that each Hj is an extension of (acting on is shown to be equivalent to the existence of a measure μ on n such that f → tf (the Fourier transform of f) is unitary from onto Ω. It is shown that the support of μ can be chosen as a subgroup of n iff H1,…, Hn can be chosen such that the unitary groups generated by H1,…, Hn act multiplicatively on . This happens iff Ω (after correction by a null set) forms a system of representatives for the quotient of n by some subgroup, i.e., iff Ω is essentially a fundamental domain. 相似文献
12.
13.
Loren D. Pitt 《Journal of multivariate analysis》1978,8(1):45-54
For Gaussian vector fields {X(t) ∈ Rn:t ∈ Rd} we describe the covariance functions of all scaling limits Y(t) = limα↓0 B?1(α) X(αt) which can occur when B(α) is a d × d matrix function with B(α) → 0. These matrix covariance functions are found to be homogeneous in the sense that for some matrix L and each α > 0, . Processes with stationary increments satisfying (1) are further analysed and are found to be natural generalizations of Lévy's multiparameter Brownian motion. 相似文献
14.
Didier Robert 《Journal of Functional Analysis》1982,45(1):74-94
Let . Under suitable conditions we prove that is a pseudodifferential operator whose symbol has an asymptotic: . More general pseudodifferential operator's classes are also considered. We apply this result to study the semi-classical behaviour of the spectrum of Hv as h → 0. So, we improve recent results obtained by J. Chazarain and by the author in collaboration with B. Helffer. Furthermore we give a precise meaning to the formal development considered in B. Grammaticos and A. Voros' work (Ann. Physics123 (1979), 359–380). 相似文献
15.
Peter Frankl 《Journal of Combinatorial Theory, Series A》1983,34(1):41-45
For a family of subsets of an n-set X we define the trace of it on a subset Y of X by T(Y) = {F∩Y:F?}. We say that (m,n) → (r,s) if for every with | we can find a Y?X|Y| = s such that |T(Y)| ? r. We give a unified proof for results of Bollobàs, Bondy, and Sauer concerning this arrow function, and we prove a conjecture of Bondy and Lovász saying , which generalizes Turán's theorem on the maximum number of edges in a graph not containing a triangle. 相似文献
16.
Norman Levinson 《Journal of Mathematical Analysis and Applications》1976,54(2):390-401
Using summability it is shown that defines an entire function in the s-plane. Its asymptotic nature is found and a functional equation relating it to the series , Im p = γ > 0,is obtained where p = β + iγ are the nontrivial zeros of Riemann's zeta-function. 相似文献
17.
The Fréchet distance between two multivariate normal distributions having means μX, μY and covariance matrices ΣX, ΣY is shown to be given by . The quantity d0 given by is a natural metric on the space of real covariance matrices of given order. 相似文献
18.
A caterpillar is a tree which metamorphoses into a path when its cocoon of endpoints is removed. The number of nonisomorphic caterpillars with n+4 points is . This neat formula is proved in two ways: first, as a special case of an application of Pólya's enumeration theorem which counts graphs with integer-weighted points; secondly, by an appropriate labeling of the lines of the caterpillar. 相似文献
19.
Witold Lipski 《Discrete Mathematics》1978,21(3):253-259
Let Sπ be the length of a shortest sequence of positive integers which contains every Y ?{1,…,n} as a subsequence of |Y| consecutive terms. We give the following asymptotic estimation: . The upper bound is derived constructively. 相似文献
20.
We consider an extremal problem for directed graphs which is closely related to Turán's theorem giving the maximum number of edges in a graph on n vertices which does not contain a complete subgraph on m vertices. For an integer n?2, let Tn denote the transitive tournament with vertex set Xn={1,2,3,…,n} and edge set {(i,j):1?i<j?n}. A subgraph H of Tn is said to be m-locally unipathic when the restriction of H to each m element subset of Xn consisting of m consecutive integers is unipathic. We show that the maximum number of edges in a m-locally unipathic subgraph of Tn is ( where n= q(m?1+r and . As is the case with Turán's theorem, the extremal graphs for our problem are complete multipartite graphs. Unlike Turán's theorem, the part sizes will not be uniform. The proof of our principal theorem rests on a combinatorial theory originally developed to investigate the rank of partially ordered sets. 相似文献