Bounds of the Ideal Class Numbers of Real Quadratic Function Fields

The theory of continued fractions of functions is used to give a lower bound for class numbers h(D) of general real quadratic function fields K=k(D)over k=Fq(T)．For five series of real quadratic function fields K,the bounds of h(D)are given more explicitly,e．g.,if D=F^2 C．then h(D)≥degF／degP;if D=(SG)^2 cS．then h(D)≥degS／degP;if D=(A^m a)^2 A,then h(D)≥degA／degP,where P is an irreducible polynomial splitting in K,c∈Fq．In addition,three types of quadratic function fields K are found to have ideal class numbers bigger than one．     

四次循环域类数模2的幂的同余公式

设K=k（√θ）是实四次循环域,k是其二次子域,K^-=k（√-θ）是相应的虚四次循环域．把K,k和K^-的类数分别记为hK,hk和kK^-,本文通过研究p-adic L-函数,得到了相对类数h^-=hK／hk和h^--=hK^-／hk的模2的幂的同余公式．     

On Generic Well-posedness of Restricted Chebyshev Center Problems in Banach Spaces

Let B （resp. K, BC,KC） denote the set of all nonempty bounded （resp. compact, bounded convex, compact convex） closed subsets of the Banach space X, endowed with the Hausdorff metric, and let G be a nonempty relatively weakly compact closed subset of X. Let B° stand for the set of all F ∈B such that the problem （F, G） is well-posed. We proved that, if X is strictly convex and Kadec, the set KC ∩ B° is a dense Gδ-subset of KC ／ G. Furthermore, if X is a uniformly convex Banach space, we will prove more, namely that the set B ／B° （resp. K ／ B°, BC ／B°, KC ／ B°） is a-porous in B （resp. K,BC, KC）. Moreover, we prove that for most （in the sense of the Baire category） closed bounded subsets G of X, the set K ／ B° is dense and uncountable in K.     

供应链中的MQ(t)/Gj/∞排队群

本文研究由一个非时齐Poisson到达过程驱动的多个MQ(t)／Gj／∞型排队系统．当一个K型到达发生时(K(?){1,…,m}),对每一个j∈K,顾客按批量QjK进入排队系统j,(Q1K,…,QmK)是相依的随机向量．我们导出了联合队长过程和联合输出过程的多变量母函数,并给出各排队系统之间的相关性分析．这些结果为非时齐供应链分析提供了理论依据     

具有剩余寿命的M/G/1/K排队模型非负解的存在唯一性

研究了以剩余寿命作为增补变量的M／G／1／K排队模型．利用泛函分析中线性算子半群的积分半群理论讨论了该模型的瞬态解的存在唯一性问题．     

剩余寿命增补变量法在排队模型M/GI/1/K中的应用

本文尝试用剩余寿命作为增补变量，建立了经典排队模型M／GI／1／K的密度演化方程，并应用递归的方法得到了模型队长平稳分布的精确解．     

AUTOMORPHISMS OF PSL_2~±(K) OVER ANY SKEW FIELD K

<正> Let K be a skew field and Z its center.The multiplicative groups of non-zero elementsof K and Z are denoted respectively by K~* and Z~*.Denote by GL_2(K)the group of all2×2 invertible matrices over K,by SL_2(K)the group generated by all elementary transve-ctions (?) and (?)λ,μ∈K and by SL_2~±(K)the group generated by all invo-lutions in GL_2(K).We know that if -1 belongs to the commutator subgroup of K~*,thenSL_2~±(K)=SL_2(K);otherwise,SL_2~±(K)can be obtained from SL_2(K)by adjoining anyinvolution to SL_2(K) (cf.[2],p.62).Denote the factor group of GL_2(K)and SL_2~±(K)modulo their centers respectively by PGL_2(K)and PSL_2~±(K).Of course,PSL_2~±(K)can be     

特殊值l—群的l—同态象及l—扩张性

本研究了特殊值l-群的一类特殊的l-同态象及l-扩张闭性。在非超Archimedean的条件下，证明了l-群G是特殊值的当且仅当对于G的每个闭l-理想K，G／K与K均是特殊值的。     

运动水平平板上混合对流的群论分析

本文用变换群理论对运动水平平板混合对流边界层流动的动量、能量和浓度扩散方程进行了分析，得到了与X4/(7-5n)成正比的壁面温度分布和浓度分布，同时壁面运动速度正比于X(3-n)／(7-5n)时存在相似性解．导出了相似性解方程，用四阶Runge－Kutta方法进行了计算，给出了Pr＝0．72　和Sc，K1，K2，K3参数下的速度、温度和浓度分布，得出了各参数对流场、温度场的影响。     

弱Galois扩张与反Smash积

本文对（H,K）-余模代数A，讨论了弱Galois扩张A／C，证明了k的每个自由二次扩张是弱Galois扩张．并利用反Smash积＃op（K，A）与K－余不变子代数C之间的Morita联系讨论A的投射性、Galois扩张及其传递性．     

Centralizers of Certain Matrices Relative to the Operation Related to A K-Loop

With respect to the binary operation A ? B = AB²A on the set m₂(K) of all 2 × 2 matrices over an arbitrary field K, we determine the centralizer of each element A of m₂(K).     

Divisible groups that are brauer groups ∗

Throughour this paper G denotes an abelian divisible torsion group. It is not unreasonable to conjecture that such a G must occur as the Brauer group B(K) of some field K. Some evidence to support this conjecture is provided in [3]; it is proved there that if G is countable then G ? B(K) for some K algebraic over the rational field Q [3, Theorem 2]. In this note we provide still more evidence in support of htis conjecture.     

An integral basis for algebraic fields

Let A be a principal ideal domain, K be the quotient field of A, and let L be a cubic extension of K. In this paper we establish the existence of a special type of integral basis of the field L over K which is a generalization of the integral basis of Voronoi for cubic extensions of the field Q of rational numbers.Translated from Matematicheskie Zametki, Vol. 13, No. 2, pp. 229–234, February, 1973.     

Remarks on unit indices of imaginary abelian number fields

Let K be an imaginary abelian number field. We determine the unit index of K of certain type whose conductor is a product of two or three prime powers. As a consequence we construct some counterexamples to Satz 29 in Hasse's monograph [2].     

关于Q(4k~(2n)+1)的理想类群的循环子群

设ｄ,ａ,ｋ,ｎ是适合４ｋ２ｎ＋１＝ｄａ２,ｋ＞１,ｎ＞２,ｄ无平方因子的正整数;又设Ｃ（Ｋ）和ｈ（Ｋ）分别是实二次域Ｋ的理想类群和类数．本文证明了：当ａ＜０．５ｋ０．５６ｎ时,则ｈ（ｋ）＝０（ｍｏｄｎ）和Ｃ（Ｋ）必有ｎ阶循环子群．     

Identities of representations of nilpotent lie algebras

Lret N be a nilpotent of class 2 Lie algebra with one-dimensional centre C = Kc over an infinite field K and let p : N → End_k:(V) be a representation of N in a vector space V such that p(c) is invertible in End_k(V). We find a basis for the identities of the representation p. As consequences we obtain a basis for all the weak polynomial identities of the pair (M₂:(K), s1₂(K)) over an infinite field K of characteristic 2 and describe the identities of the regular representation of Lie algebras related with the Weyl algebra and its tensor powers.     

Frobenius Partitions in Extraspecial Groups

Let K be a field and G be the group of the upper unitriangular (n + 2) × ( n + 2) K-matrices with nonzero entries only in the first row and in the last column. Then G has a normal subgroup N with a complement H which are K-vector spaces respectively of dimensions n + 1 and n. In the present paper we show that the orbit of H under a group of automorphisms of G together with N, forms a partition of G, provided that there exists a commutative (possibly nonassociative) division algebra of dimension n + 1 over K. This algebra exists when K is a finite field.     

Verlinde模性范畴上的Casimir数及其应用

本文计算了秩为n+1的一类特殊的Verlinde模性范畴L的Casimir数,计算结果表明该Casimir数为2n+4.作为应用,由Higman定理知域K上的Grothendieck代数Gr(L)_Z K是半单代数当且仅当2n+4在域K中不为零.这也给出了第二类型n+1次Dickson多项式E_(n+1)(X)在K[X]中无重因式的一个等价刻画.如果2n+4在域K中为零,借助于Dickson多项式的有关因式分解定理,本文完全给出了Grothendieck代数Gr(L)_Z K的Jacobson根.     

Dedekind zeta-functions and Dedekind sums

In this paper we use Dedekind zeta functions of two real quadratic number fields at -1 to denote Dedekind sums of high rank. Our formula is different from that of Siegel’s. As an application, we get a polynomial representation of ζK(-1): ζK(-1) = 1/45(26n³ -41n± 9),n = ±2(mod 5), where K = Q(√5q), prime q = 4n² + 1, and the class number of quadratic number field K2 = Q(vq) is 1.     

On Normal Integral Bases

in this paper, let K = Q ( ) be an abelian number field,where mi's are distinct square-free integers and Gal (K/Q ) (Z/2Z )n+1, and let k Q(M). When k is imaginary or k is real and has a unit of norm -1, we give a necessaryand sufficient condition for K/k to have a normal integral basis.