关于阶乘的Erds-Stewart猜想

摘要:设n是正整数;P_0=1,P_i(i=1,2,…)是第i个素数.本文证明了:方程 n!+1=P_k~aP_(k+1)~b,P_(k-1)0,b>0,仅有解(n,P_k,P_(k+1),a,b)=(1,1,2,1,0),(2,3,5,1,0),(3,5,7,0,1),(4,5,7,2,0),(5,7,11,0,2).上述结果证实了Erds和Stewart提出的一个猜想.     

互连网络的向量图模型

n-超立方体、环网、k元n超立方体、Star网络、煎饼(pancake)网络、冒泡排序(bubble sort)网络、对换树的Cayley图、De Brujin图、Kautz图、Consecutive-d 有向图、循环图以及有向环图等已被广泛地应用做处理机或通信互连网络.这些网络的性能通常通过它们的度、直径、连通度、H...     

Book reviews

Bauer, H., Maßund Integrationstheorie. De Gruyter Lehrbuch, Walter de Gruyter & Co., Berlin, New York, 1990, XVIII, 259 pp, DM 78, —, ISBN 3-11-012773-3 GB, DM 42, —, (ISBN 3-11-012772-5 KT).

?inlar, E. (ed.), Fitzsimmons, P. J., Williams, R. J. (managing eds.), Seminar on Stochastic Processes, 1990. Progress in Probability, Vol. 24, Birkhaüser Boston, Basel, Berlin 1991, VIII + 351 pp., DM 38,—, ISBN 0-8176-3488-6.

Spalt, D. D. (ed.). Rechnen mit dem Unendlichen. Beiträ zur Entwicklung der Nichtstandard Gegenstandes Birkhaüser Verlag Basel, Boston, Berlin, 1990, 243 pp. DM 49.80, ISBN 3-7643-2568-3.     

Representation of consistent recursive rules

This paper develops the recursive model for connective rules (as proposed in V. Cutello, E. Molina, J. Montero, Associativeness versus recursiveness, in: Proceedings of the 26th IEEE International Symposium on Multiple-valued Logic, Santiago de Compostela, Spain, 29–31 May, 1996, pp. 154–159; V. Cutello, E. Molina, J. Montero, Binary operators and connective rules, in: M.H. Smith, M.A. Lee, J. Keller, J. Yen (Eds.), Proceedings of NAFIPS 96, North American Fuzzy Information Processing Society, IEEE Press, Piscataway, NJ, 1996, pp. 46–49), where a particular solution in the Ordered Weighted Averaging (OWA) context (see V. Cutello, J. Montero, Recursive families of OWA operators, in: P.P. Bonissone (Ed.), Proceedings of the Third IEEE Conference on Fuzzy Systems, IEEE Press, Piscataway, NJ, 1994, pp. 1137–1141; V. Cutello, J. Montero, Recursive connective rules, International Journal of Intelligent Systems, to appear) was translated into a more general framework. In this paper, some families of solutions for the key recursive equation are obtained, based upon the general associativity equation as solved by K. Mak (Coherent continuous systems and the generalized functional equation of associativity, Mathematics of Operations Research 12 (1987) 597–625). A context for the representation of families of binary connectives is given, allowing the characterization of key families of connective rules.     

On automorphisms of a distance-regular graph with intersection array {39, 36, 1; 1, 2, 39}

Possible prime-order automorphisms and their fixed-point subgraphs are found for a hypothetical distance-regular graph with intersection array {39, 36, 1; 1, 2, 39}. It is shownthat graphs with intersection arrays {15, 12, 1; 1, 2, 15}, {35, 32, 1; 1, 2, 35}, and {39, 36, 1; 1, 2, 39} are not vertex-symmetric.     

On the Kodaira Dimension of the Moduli Space of K3 Surfaces II

We show that the Kodaira dimension of the moduli space of polarized K3 surfaces of degree 2n in non negative if n = 42, 43, 51, 53, 55, 57, 59, 61, 66, 67, 69, 74, 83, 85, 105, 119 or 133. We use an automorphic form associated with the fake monster Lie algebra constructed by Borcherds.     

最优(m,n,4,1)光正交签名码的进一步结果

为支持高速多址网络中二维图像的传输,Kitayama首次提出码分多址并行图像传输系统的概念.作为码分多址并行图像传输系统的首选光地址码,光正交签名码(OOSPC)是一族具有良好相关性的Hamming重量为k的m×n(0,1)-矩阵.用Θ(m,n,k,λ)表示所有参数为(m,n,k,λ)的OOSPC中码字容量可能的最大值,则称码字容量为Θ(m,n,k,λ)的(m,n,k,λ)-OOSPC是最优的.本文将针对满足下列条件之一的正整数m和n:(1)mn≡8,16(mod 24),gcd(m,n,2)=2,且mn≡16(mod 32)和gcd(m,n,4)=2不同时成立,其中m和n的所有奇素因子均模6余1;(2)mn≡0(mod 24)且gcd(m,n,6)=2,证明Θ(m,n,4,1)=|mn-1/12|,即构造码字容量为|mn-1/12|的最优(m,n,4,1)-OOSPC.     

BOOK REVIEWS

Book reviewed in this article: Textbook of Quantitative Inorganic Analysis, by I. M. Kolthoff, Ph.D., Professor of Analytical Chemistry, University of Minnesota, and E. B. Sandell, Ph.D., Assistant Professor of Analytical Chemistry, University of Minnesota. A Chemical-Technical Dictionary (German-English-French-Russian), by A. W. Mayer. (Translation under direction of B. N. Menschutkin and M. A. Bloch.) Preservice Course in Automotive Mechanics, by James V. Frost, Instructor in Automotive Trades, Brooklyn High School of Automotive Trades, Brooklyn, New York. Automotive Mechanics, in two volumes by Clarence G. Barger Elements of Food Biochemistry, by William H. Peterson, Ph.D., Professor of Biochemistry, University of Wisconsin, Madison, Wisconsin; John T. Skinner, Ph.D., Assistant Chemist, Kentucky Agricultural Experiment Station, Lexington, Kentucky; and Frank M. Strong, Ph.D., Associate Professor of Biochemistry, University of Wisconsin, Madison, Wisconsin. The Chemical Formulary. A Collection of Valuable, Timely, Practical Commercial Formulae and Recipes for Making Thousands of Products in Many Fields of Industry. Volume VI. Editor-in-Chief, H. Bennett. Air Navigation. Flight Preparation Series. Published under the Supervision of the Training Division, Bureau of Aeronautics, U. S. Navy, Part One, Introduction to Earth. Radio—I, Written to Conform to the Pre-induction Training Course in Fundamentals of Radio as Prepared by the War Department, by R. E. Williams, Manager, School Service, Westinghouse Electric and Manufacturing Company, Pittsburgh, Pennsylvania, and Charles A. Scarlott, Editor, Westinghouse Engineer. Minerals, Their Identification, Uses, and How to Collect Them, by Herbert S. Zim, and Elizabeth K. Cooper. Basic Radio Principles, by Maurice Grayle Suffern, Captain, Signal Corps, Army of the United States.     

An interview with Sam C. Saunders

Sam C. Saunders, the son of Elizabeth Cundiff and Winston E. Saunders, was born in Richland, OR, on February 24, 1931. The family moved to La Grande, OR, in 1944, where Sam completed high school and two years at Eastern Oregon College. He then received the BSc degree in Mathematics from the University of Oregon, Eugene, OR, in 1952, and he attended the University of Washington, Seattle, WA, receiving a PhD degree under Z. W. Birnbaum. After graduating, he accepted employment at the Boeing Company in its Mathematical Services Unit and, in 1972, a position as a Full Professor at Washington State University, Pullman, WA, from which he retired in 1996.