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851.
Walter Benz 《Aequationes Mathematicae》1992,43(2-3):177-182
Summary The following theorem holds true.
Theorem.
Let X be a normed real vector space of dimension 3 and let k > 0 be a fixed real number. Suppose that f: X X and g: X × X are functions satisfying x – y = k f(x) – f(y) = g(x, y)(x – y) for all x, y X. Then there exist elements and t X such that f(x) = x + t for all x X and such that g(x, y) = for all x, y X with x – y = k. 相似文献
852.
Janusz Matkowski 《Aequationes Mathematicae》1992,43(2-3):219-224
Summary In the present note we prove that every functionf: (0, ) [0, ) satisfying the inequalityaf(s) + bf(t) f(as + bt), s, t > 0, for somea andb such that 0 <a < 1 <a + b must be of the formf(t) = f(1)t, (t > 0). This improves our recent result in [2], where the inequality is assumed to hold for alls, t 0, and gives a positive answer to the question raised there.An analogue for functions of several real variables of the above result characterizes concave functions. Conjugate functions and some relations to Hölder's and Minkowski's inequalities are mentioned. 相似文献
853.
Alexander Pott 《Combinatorica》1992,12(1):89-93
In this paper we develop a new method to obtain identities in a group algebraGF(p)G if an abelian difference set of ordern0 (modp) exists inG. We give an explicit formula ifp
2 orp
3 is the exactp-power dividingn. This generalizes the approach of Wilbrink, Arasu and the author. The proof presented here uses some knowledge about field extensions of thep-adic numbers. 相似文献
854.
Thomas Stehling 《Combinatorica》1992,12(4):475-479
We consider the numberN
A
(r) of subgroups of orderp
r
ofA, whereA is a finite Abelianp-group of type =1,2,...,
l
()), i.e. the direct sum of cyclic groups of order ii. Formulas for computingN
A
(r) are well known. Here we derive a recurrence relation forN
A
(r), which enables us to prove a conjecture of P. E. Dyubyuk about congruences betweenN
A
(r) and the Gaussian binomial coefficient
. 相似文献
855.
We show that the maximum number of edges boundingm faces in an arrangement ofn line segments in the plane isO(m
2/3
n
2/3+n(n)+nlogm). This improves a previous upper bound of Edelsbrunner et al. [5] and almost matches the best known lower bound which is (m
2/3
n
2/3+n(n)). In addition, we show that the number of edges bounding anym faces in an arrangement ofn line segments with a total oft intersecting pairs isO(m
2/3
t
1/3+n(t/n)+nmin{logm,logt/n}), almost matching the lower bound of (m
2/3
t
1/3+n(t/n)) demonstrated in this paper.Work on this paper by the first and fourth authors has been partially supported by Office of Naval Research Grant N00014-87-K-0129, by National Science Foundation Grants DCR-83-20085 and CCR-89-01484. Work by the first author has also been supported by an AT&T Bell Laboratories Ph.D. scholarship at New York University and by DIMACS (Center for Discrete Mathematics and Theoretical Computer Science), a National Science Foundation Science and Technology Center (NSF-STC88-09648). Work by the second author has been supported by NSF under Grants CCR-87-14565 and CCR-89-21421. Work by the fourth author has additionally been supported by grants from the U.S.-Israeli Binational Science Foundation, the NCRD (the Israeli National Council for Research and Development) and the Fund for Basic Research in Electronics, Computers and Communication, administered by the Israeli National Academy of Sciences. 相似文献
856.
Harald Luschgy 《Probability Theory and Related Fields》1992,93(1):39-66
Summary Let
(Q) be the statistical experiment based on the observation of an unknown function in the presence of an additive noise process with distributionQ. The (possible) loss of information whenQ is replaced by some other noise distributionP is measured by the deficiency of
(P) relative to
(Q). This deficiency and its relation to the variational distance ofP andQ are studied mainly for Gaussian noise processes. Gaussian diffusion processes and special set-indexed processes are treated in detail.Research supported by a Heisenberg grant of the Deutsche Forschungsgemeinschaft 相似文献
857.
P. Révész 《Probability Theory and Related Fields》1992,93(1):21-37
Summary We say that the discD()R
2, of radius , located around the origin isp-covered in timeT by a Wiener processW(·) if for anyzD() there exists a 0tT such thatW(t) is a point of the disc of radiusp, located aroundz. The supremum of those 's (0) is studied for which,D() isp-covered inT. 相似文献
858.
For each positive integerk, we consider the setA
k
of all ordered pairs [a, b] such that in everyk-graph withn vertices andm edges some set of at mostam+bn vertices meets all the edges. We show that eachA
k
withk2 has infinitely many extreme points and conjecture that, for every positive , it has only finitely many extreme points [a, b] witha. With the extreme points ordered by the first coordinate, we identify the last two extreme points of everyA
k
, identify the last three extreme points ofA
3, and describeA
2 completely. A by-product of our arguments is a new algorithmic proof of Turán's theorem. 相似文献
859.
Jeff Kahn 《Combinatorica》1992,12(4):417-423
Letn(k) be the least size of an intersecting family ofk-sets with cover numberk, and let
k
denote any projective plane of orderk–1.Theorem There is a constant A such that ifH is a random set ofm Aklogk lines from
k
then Pr(H<)0(k).Corollary
If there exists a
k
thenn(k)=O(klogk). These statements were conjectured by P. Erds and L. Lovász in 1973.Supported in part by NSF-DMS87-83558 and AFOSR grants 89-0066, 89-0512 and 90-0008 相似文献
860.
Toeplitz and Hankel type operators on the upper half-plane 总被引:3,自引:0,他引:3
An orthogonal decomposition of admissible wavelets is constructed via the Laguerre polynomials, it turns to give a complete decomposition of the space of square integrable functions on the upper half-plane with the measurey
dxdy. The first subspace is just the weighted Bergman (or Dzhrbashyan) space. Three types of Ha-plitz operators are defined, they are the generalization of classical Toeplitz, small and big Hankel operators respectively. Their boundedness, compactness and Schatten-von Neumann properties are studied.Research was supported by the National Natural Science Foundation of China. 相似文献