Groups with Prescribed Systems of Schmidt Subgroups

Siberian Mathematical Journal - A Schmidt (p, q)-group is a Schmidt group G with π(G) = {p, q} and normal Sylow p-subgroup. The N-critical graph ΓNc(G) of a group G is the directed graph...     

广义四元数群的4-度Cayley图

一个有限群称为广义四元数群,若Q4n=〈a,b a2n=1,b2=an,ab=a-1,〉n 3.本文根据广义四元数群Q4p(p为奇素数)中只有两类二元生成子集,且它们在Aut(Q4p)的作用下是传递的.结合具体图形,利用查圈的方法重点地证明了广义四元数群关于这两类二元生成子集的4-度C ay ley图的正规性与正则性,解决了4-度C ay ley图的完全分类问题.     

随机一致超图的关于H-因子的门槛函数

假设H和H（分别是具有h个顶点和n个顶点的r一致超图．我们称一个具有n/h个分支，且每个分支都同构于H的H的生成子图为H的一个H-因子．记α（H） = max{｜E′｜/｜V′｜-1 ｜}，其中的最大值取遍H的所有满足｜V’｜〉1的子超图（V’，E′）．δ（H）表示超图H的最小度．在本文中，我们证明了如果δ（H）〈α（H），那么P=p（n）=n-1／α（H）就是随机超图Hr（n，P）包含．H-因子的一个紧的门槛函数．也就是说，存在两个常数c和C使得对任意P=p（n）=cn-1／α（H），几乎所有的随机超图Hr（n，P）都不包含一个H-因子，对任意P=p（n）=cn-1／α（H），几乎所有的随机超图Hr（n，P）都包含一个H-因子．     

Graphical Frobenius representations

A Frobenius group is a transitive permutation group that is not regular and such that only the identity fixes more than one point. A graphical Frobenius representation (GFR) of a Frobenius group G is a graph whose automorphism group, as a group of permutations of the vertex set, is isomorphic to G. The problem of classifying which Frobenius groups admit a GFR is a natural extension of the classification of groups that have a graphical regular representation (GRR), which occupied many authors from 1958 through 1982. In this paper, we review for graph theorists some standard and deep results about finite Frobenius groups, determine classes of finite Frobenius groups and individual groups that do and do not admit GFRs, and classify those Frobenius groups of order at most 300 having a GFR. Because a Frobenius group, as opposed to a regular permutation group, has a highly restricted structure, the GFR problem emerges as algebraically more complex than the GRR problem. This paper concludes with some further questions and a strong conjecture.     

一类超椭圆曲线的整点个数

设ｎ是大于２的工整数，Ｄ是无平方因子正整数，分别是Ｋ的理想类群和类数．对于正整数ｍ，设ｇｋ（ｍ）是Ｉｘ中阶数等于ｍ的理想类的个数．本文证明了：超椭圆曲线ｆ（ｘ，ｙ）＝Ｄｘ２－４ｙｎ＋１＝０上整数点（ｘ，ｙ）的个数不超过ｍａｘ（８，２１６４Ｐ８１ｇｋ（Ｐ）），其中ｐ是ｎ的奇素因数．     

基于动态利率风险免疫的银行资产负债优化模型

本文以CIR动态久期缺口的免疫条件为约束进行多资产和多负债的利率风险控制,通过建立线性规划模型来进行银行资产的最优配置。本文的创新与特色:一是通过引进随时间变化的动态利率久期参数构造利率风险控制条件,建立了控制利率风险的资产负债优化模型。改变了现有研究忽略利率动态变化、进而忽略平均久期动态变化的弊端。事实上,利率的动态变化必然引起平均久期的变动,忽略利率变动的控制条件是无法高精度地控制资产配置的利率风险的。二是通过以银行资产收益最大为目标函数,以动态利率久期缺口免疫为主要约束条件,辅以监管的流动性约束匹配银行的资产负债,回避了利率风险对银行所有者权益的影响,避免了利率变动对银行资产所有者带来的损害。     

Generalisation of the Viterbi algorithm

The Viterbi algorithm, derived using dynamic programming techniques,is a maximum a posteriori (MAP) decoding method which was developedin the electrical engineering literature to be used in the analysisof hidden Markov models (HMMs). Given a particular HMM, theoriginal algorithm recovers the MAP state sequence underlyingany observation sequence generated from that model. This paperintroduces a generalization of the algorithm to recover, forarbitrary L, the top L most probable state sequences, with specialreference to its use in the area of automatic speech recognition.     

The intersection of Sylow subgroups in finite groups

In Theorem 1, letting p be a prime, we prove: (1) If G=S_n is a symmetric group of degree n, then G contains two Sylow p-subgroups with trivial intersection iff (p, n) ∉ {(3, 3), (2, 2), (2, 4), (2, 8)}, and (2) If H=A_n is an alternating group of degree n, then H contains two Sylow p-subgroups with trivial intersection iff (p, n) ∉ {(3, 3), (2, 4)}. In Theorem 2, we argue that if G is a finite simple non-Abelian group and p is a prime, then G contains a pair of Sylow p-subgroups with trivial intersection. Also we present the corollary which says that if P is a Sylow subgroup of a finite simple non-Abelian group G, then ‖G‖>‖P‖². Supported by RFFR grants Nos. 93-01-01529, 93-01-01501, and 96-01-01893, and by International Science Foundation and Government of Russia grant RPC300. Translated fromAlgebra i Logika, Vol. 35, No. 4, pp. 424–432, July–August, 1996.     

Maximum a Posteriori Sequence Estimation Using Monte Carlo Particle Filters

We develop methods for performing maximum a posteriori (MAP) sequence estimation in non-linear non-Gaussian dynamic models. The methods rely on a particle cloud representation of the filtering distribution which evolves through time using importance sampling and resampling ideas. MAP sequence estimation is then performed using a classical dynamic programming technique applied to the discretised version of the state space. In contrast with standard approaches to the problem which essentially compare only the trajectories generated directly during the filtering stage, our method efficiently computes the optimal trajectory over all combinations of the filtered states. A particular strength of the method is that MAP sequence estimation is performed sequentially in one single forwards pass through the data without the requirement of an additional backward sweep. An application to estimation of a non-linear time series model and to spectral estimation for time-varying autoregressions is described.     

Derivation of Freund - Witten adelic formula for four-point Veneziano amplitudes

On the basis of an analysis on the adelic group (Tate's formula) a regularization is proposed for the divergent infinite product ofp-adic Γ functions: $$\Gamma _p (\alpha ) = \frac{{1 - p^{\alpha - 1} }}{{1 - p^{ - \alpha } }}, p = 2,3,5...,$$ and the adelic formula $$reg\prod\limits_{p = 2}^\infty {\Gamma p(\alpha ) = \frac{{(\zeta \alpha )}}{{\zeta (1 - \alpha )}},} $$ where ζ(α) is the Riemann ζ function, is proved.     

2-(v,6,1)设计的可解区传递自同构群

设G是一个2-（v,6,1）设计的可解区传递自同构群,且G非旗传递,则：（1）v＝91,G=Z91×Zd,这里3|d|12;（2）v=pm,G≤AL（1,pm）,之一成立．其中p≠2．当p＝3时,4|m见且m＞4;当p＞5时,pm≡1（mod30）。     

On the form of homomorphisms into the differential group Ls 1 and their extensibility

Let L_s ¹ (s ∈ ?) be the s-th differential group, that is the set {(x1,…,x_s): x₁ ≠ 0, x_n ∈ K, n =1,2,…,s} (K ∈ {?,?}) together with the group operation which describes the chain rules (up to order s) for C^s-functions with fixed point 0. We consider homomorphisms Φ_s, Φ_s = (f₁,…,f_s) from an abelian group (G,+) into L_s ¹ such that f₁ = 1, f₂ = … = f_p+2 = 0, 0_p+2 ≠ 0 for a fixed, but arbitrary p ≥ 0 such that p + 2 ≤ s (then f_p+2 is necessarily a homomorphism from (G, +) to (K, +). Let l ∈ ? or l = ∞. We present a criterion for the extensibility of Φ_s to a homomorphism Φ_s+l from (G, +) to L_s+1 ¹ (L_∞ ¹, if l = ∞), by proving that such an extension (continuation) exists iff the component functions f_n of Φ_s with s - p ≤ n ≤ min(s - p + l - 1,s) are certain polynomials in f_P+2 (see Theorem 1). We also formulate the problem in the language of truncated formal power series in one indeterminate X over K. The somewhat easier situation f ₁ ≠ 1 will be studied in a separate paper.     

On approximating higher order MAPs with MAPs of order two

We show that the autocorrelation sequence of interarrival times for a Markovian arrival process (MAP) of order two is geometric. We determine the set of feasible values for the autocorrelation decay parameter and the first two or three moments of the interarrival time distribution. A method is derived for matching these parameters to a MAP of order two and some numerical examples are included to illustrate approximating higher dimensional MAPs by two dimensional ones. The numerical examples have helped us pose important questions regarding the significance of correlation in a MAP of order two when it is used as input to a queueing model.     

On the Distribution of Hecke Eigenvalues over Piatetski-Shapiro Prime Twins

Let λ_f(n) be the normalized n-th Fourier coefficient of holomorphic eigenform f for the full modular group and P_c(x) := {p ≤ x | [p~c] prime}, c ∈ R~+. In this paper, we show that for all 0 c 1 the mean value of λ_f(n) in P_c(x) is x log~(-A) x assuming the Riemann Hypothesis. Unconditionally,in the sense of Lebesgue measure, it holds for almost all c ∈(ε, 1-ε).     

函数F(α)=(A~rB~αA~r)~((p+2r)/(α+2r))的最优单调区间

设p>0且A,B是Hilbert空间上两个正算子,Furuta给出若A>B>0,那么对任意r>0,F(α)=(ArBαAr)p+2r/α+2r 是关于α>P单调递减的,但是他指出这个结果在0<α0的条件下并不一定成立.本文给出: (1)如果-1/2-2r,那么F(α)在(-∞,-P-4r]及[p,+∞)上单调递增,并且这两个区间不能扩大; (3)如果r>0,P>0,那么[p,+∞)也是F(α)的最佳单调区间.     

QUASI-PERMUTATION REPRESENTATIONS OF ALTERNATING AND SYMMETRIC GROUPS

The quantities c(G), q(G) and p(G) for finite groups were defined by H. Behravesh. In this article, these quantities for the alternating group An and the symmetric group Sn are calculated. It is shown that c(G) = q(G)=p(G) = n, when G = An or Sn.     

Multipliers of weak type on locally compact Vilenkin groups

Let be a locally compact Vilenkin group with dual group . We give a sufficient condition for to be a multiplier of weak type on . Some applications of our result are given. We also prove that our result is sharp.

     

The classification of flag-transitive Steiner 4-designs

Among the properties of homogeneity of incidence structures flag-transitivity obviously is a particularly important and natural one. Consequently, in the last decades flag-transitive Steinert-designs (i.e. flag-transitive t-(v,k,1) designs) have been investigated, whereas only by the use of the classification of the finite simple groups has it been possible in recent years to essentially characterize all flag-transitive Steiner 2-designs. However, despite the finite simple group classification, for Steiner t-designs with parameters t > 2 such characterizations have remained challenging open problems for about 40 years (cf. [11, p. 147] and [12 p. 273], but presumably dating back to around 1965). The object of the present paper is to give a complete classification of all flag-transitive Steiner 4-designs. Our result relies on the classification of the finite doubly transitive permutation groups and is a continuation of the author's work [20, 21] on the classification of all flag-transitive Steiner 3-designs. 2000 Mathematics Subject Classification. Primary 51E10 . Secondary 05B05 . 20B25     

B值移动平均过程的Strassen重对数律

设 {ε,εt;t∈ Z}是 iid的 B值随机变量序列 ,{ aj;j∈ Z}是一个实数列 ,满足 ∞j=-∞|aj|<∞ .记 Xt= ∞j=-∞ajεt-j,Sn = nt=1Xt.对 p≥ 1 ,本文研究了n-1 -( p/ 2 ) (2 L2 n) -( p/ 2 ) ni=1 ‖ Si‖p 及 n-1 -( p/ 2 ) (2 L2 n) -( p/ 2 ) ni=0 ‖ Sn- Si‖ p的渐进性质 ,使得 Strassen(1 964)及 Chen(1 994)的一些结果得到推广 .     

肾动脉变窄和流-固结构相互作用对非Newton脉动流的影响——一个真实的腹部主动脉和肾动脉模型

研究肾动脉狭窄(RAS)对血液流动和血管壁的影响.根据CT扫描图像,重建腹部主动脉和肾动脉的解剖模型,通过模型的脉动流进行了仿真计算,计算中考虑了流体-固体结构的相互作用(FSI).研究RAS对血管壁剪切应力和位移的影响,RAS使得肾动脉中流量减少,肾素-血管紧缩素系统可能被激活,从而导致严重的高血压.