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1.
István Talata 《Combinatorica》2000,20(2):281-293
H (K) of a d-dimensional convex body K is the maximum number of mutually non-overlapping translates of K that can be arranged so that all touch K. In this paper we show that holds for any d-dimensional simplex (). We also prove similar inequalities for some, more general classes of convex bodies.
Received May 18, 1998 相似文献
2.
Nearly four hundred years ago, the cubic close-packing of equalspheres in R3 was discovered by Kepler [21], in which each spheretouches 12 others. In 1694, Gregory and Newton discussed thefollowing thirteen spheres problem. Can a rigid material spherebe brought into contact with 13 other such spheres of the samesize? Gregory believed yes, while Newton thoughtno. 1991 Mathematics Subject Classication 11H31,52C17. 相似文献
3.
The q-Catalan numbers studied by Carlitz and Riordan are polynomials in q with nonnegative coefficients. They evaluate, at q = 1, to the Catalan numbers: 1, 1, 2, 5, 14,…, a log-convex sequence. We use a combinatorial interpretation of these polynomials
to prove a q-log-convexity result. The sequence of q-Catalan numbers is not q-log-convex in the narrow sense used by other authors, so our work suggests a more flexible definition of q-log convex be adopted.
Received January 2, 2007 相似文献
4.
In this note the kissing numbers of octahedra, rhombic dodecahedra and elongated octahedra are determined. In high dimensions,
an exponential lower bound for the kissing numbers of superballs is achieved.
Received December 24, 1996, and in revised form October 7, 1997. 相似文献
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In this paper, the Kolmogorov-Feller type weak law of large numbers are obtained,which extend and improve the related known works in the literature. 相似文献
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Florian Luca 《Periodica Mathematica Hungarica》2000,40(1):53-56
In this note, we answer in the negative two problems proposed in [1] on r-full numbers of the form l
m
+ k. 相似文献
9.
Acta Mathematicae Applicatae Sinica, English Series - In this paper, we consider a modification of the well-known logistic family using a family of fuzzy numbers. The dynamics of this modified... 相似文献
10.
Minking Eie 《Transactions of the American Mathematical Society》1996,348(3):1117-1136
Generalized Bernoulli polynomials were introduced by Shintani in 1976 in order to express the special values at non-positive integers of Dedekind zeta functions for totally real numbers. The coefficients of such polynomials are finite combinations of products of Bernoulli numbers which are difficult to get hold of. On the other hand, Zagier was able to get the explicit formula for the special values in cases of real quadratic number fields.
In this paper, we shall improve Shintani's formula by proving that the special values can be determined by a finite set of polynomials. This provides a convenient way to evaluate the special values of various types of Dedekind functions. Indeed, a much broader class of zeta functions considered by the author [4] admits a similar formula for its special values. As a consequence, we are able to find infinitely many identities among Bernoulli numbers through identities among zeta functions. All these identities are difficult to prove otherwise.
11.
A. Languasco 《Acta Mathematica Hungarica》1998,79(3):191-206
Let J(N, H) be the Selberg integral and E(x, T) the error term in Kaczorowski-Perelli's weighted form of the classical explicit formula. We prove that the estimate J(N, H) = o(H2 N) is connected with an appropriate estimate of N
2N| E(x,T)2
dx, uniformly for H and T in some ranges. Moreover, assuming a suitable bound for N
2N| E(x,T)|2
dx, we also obtain, for all sufficiently large N and H (log N)11/12, that every interval [N,N + H] contains H Goldbach numbers. 相似文献
12.
I. Talata 《Discrete and Computational Geometry》1998,19(3):447-455
The translative kissing number H(K) of a d -dimensional convex body K is the maximum number of mutually nonoverlapping translates of K which touch K . In this paper we show that there exists an absolute constant c > 0 such that H(K)≥ 2
cd
for every positive integer d and every d -dimensional convex body K . We also prove a generalization of this result for pairs of centrally symmetric convex bodies.
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Received February 18, 1997, and in revised form April 15, 1997. 相似文献
13.
一个实方阵A称为是S2NS阵,若所有与A有相同符号模式的矩阵均可逆,且它们的逆矩阵的符号模式都相同.若A是S2NS阵且A中任意一个零元换为任意非零元后所得的矩阵都不是S2NS阵,则称A是极大S2NS阵.设所有n阶极大S2NS阵的非零元个数所成之集合为S(n),Z4(n)={1/2n(n-1) 4,…,1/2n(n 1)-1},除了2n 1到3n一4间的一段和Z4(n)外,S(n)得到了完全确定.本文将用图论方法证明Z4(n)∩S(n)=(?). 相似文献
14.
Another Note on the Greatest Prime Factors of Fermat Numbers 总被引:1,自引:0,他引:1
For every positive integer k > 1, let P(k) be the largest prime divisor of k. In this note, we show that if Fm = 22m + 1 is the mth Fermat number, then P(Fm) 2m+2(4m + 9) + 1 for all m 4. We also give a lower bound of a similar type for P(Fa,m), where Fa,m = a2m + 1 whenever a is even and m a18.AMS Subject Classification (1991) 11A51 11J86 相似文献
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就素数d=5,13,29,53,173,293时给出了虚二次数域■(-k)与■(-kd)(k>2,k∈■)的类数之间的关系. 相似文献
17.
In this study, we show that ranking fuzzy numbers with the area method using circumcenter of centroids presented by Rao and Shankar failed to rank effectively the generalized fuzzy numbers. By proving a theorem and using some numerical examples, we demonstrate that their proposed method cannot rank consistently some fuzzy numbers or is not consistent with human intuition. 相似文献
18.
In this paper, the authors study the strong law of large numbers for partial sums of pairwise negatively quadrant dependent (NQD) random variables. The results obtained improve the corresponding theorems of Hu et al. (2013), and Qiu and Yang (2006) under some weaker conditions. 相似文献
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