一类非线性广义样条最佳L_p逼近的光滑性

设L是常系数n阶线性微分算子,m∈N, 0=s_00适当小,v=1,…,r}本文证明了设f∈L_p[0,1],1≤p<∞,那末当n≥2时,存在f的最佳L_p[0,1]逼近样条(?)∈C[0,1]∩φ~*(m,q)。当n≥3时,存在f的最佳L_p[0,1]逼近样条(?)∈C~1[0,1]∩φ~*(m,q)。     

双重时序模型的高阶矩结构

为建立双重时序AR-MA模型的矩估计，除了需要模型平稳解序列的二阶矩结构[10]外，还需要建立平稳解序列的高阶矩结构[2]．设｛Xt｝为AR（1）－MA（q）模型的4阶平稳解序列．木文部分地证明了。｛X~2_t｝的相关结构为某一ARMA（3q，3q—1）型，这为．建立模型参数的矩估计创造了条件.     

用Bcklund变换确定神经传导反应扩散方程的显示精确行波解

文献[1]讨论了反应扩散方程的形如u(x_1,t)=q(x-ct)的行波解.令ξ=x-ct,给出该方程的BackIund变换为q_x=p(q),q_t=-cp(q).显然,p=p(q)∈C~1[0,1]∩C~2(0,1)应满足p((dp)/(dq) c)=-f(q).若c=0,则p=±(-2∫_0~(q(ξ))f(τ)dτ)~(1/2);若c≠0,则必须从方程(dp)/(dq)=-c-f(q)/p,p(0)=p(1)=0,p(q)>0,q∈(0,1)出发寻求传播较快的行波.如果p和f分别为次数m和n的多项式,那么n=2m-1.在m=1和2情形下求得的传播速度与生物物理学家用实验     

关于矩形和斜带模型的反强迫数和反凯库勒数

在苯类化合物的凯库勒结构的研究中引入了反强迫数和反凯库勒数.通过分析矩形和斜带模型苯类化合物的分子图的结构,证明了具有k行l列的矩形R[k,l]和斜带模型Z[k,l]的反凯库勒数是2,R[k,l]的反强迫数是l,Z[k,l]的反强迫数不超过[(l+1)/2],其中[x]表示不超过x的最大整数.     

p -级数域重排特征系统的(C, α)}和

令G_p 为p级数域.在文献[9]中, G.Gát 和 K.Nagy 已经证明p级数域的重排特征系统的(C,1)极大算子是强 (q, q)型(1 α_n f 几乎处处收敛于f.     

m序列的移位相加性

本文用反例说明一般的q(q>2)元m序列不具有移位相加性,指出了文[1]的一个疏忽,证明了移位相加是二元m序列所具有的特性。     

三维长方体[p,q]内的合作系统

设F是三维长方体[p,q]内的合作向量场,且在此长方体内F的奇点仅为p和q.我们证明了[p,q]内的每条正半轨线或者收敛于p,或者收敛于q.此外,如果在[p,q]的边界上除p和q两点外,F的方向均指向[p,q]的内部,则[p,q]内存在唯一的轨道连结p和q.     

NSD随机变量序列的完全收敛性

本文利用NSD随机变量序列的性质、矩不等式及三级数定理,在一定的矩条件下,得到了NSD随机变量序列的完全收敛性.所得结果推广了 Chow与Lai[15,16]与Jajte[17]的独立序列的结果.     

关于一类数学物理反问题的解

本通过构造遗代序列，研究了抛物型偏散分方程的一类反问题的解，并推广了[1]的结果。     

格蕴涵代数的（∈,∈∨q~[k]）-fuzzy LI-理想

运用fuzzy集的思想和方法研究格蕴涵代数的LI-理想.引入了（∈,∈∨q[k]）-fuzzy LI-理想和（∈,∈∨q[k]）-fuzzy格理想的概念,讨论了它们的性质及相互关系.获得了（∈,∈∨q[k]）-fuzzy LI-理想的若干等价刻画;证明了在格H蕴涵代数中（∈,∈∨q[k]）-fuzzy LI-理想和（∈,∈∨q[k]）-fuzzy格理想相互等价的结论.     

ON THE DISTRIBUTION OF VALUES OF RANDOM DIRICHLET SERIES(II)

For certain Dirichlet series almost surely(a.s.)of order(R) ρ∈(0,∞)in the right-halfplane,a.s.every point of the imaginary axis is a Borel point of order ρ+1 and with no finiteexoeptional value.     

三维七元线性码的重量谱与改进的遗传算法

[n,3,7]线性码的重量谱与其差序列是一一对应的。本文改进了[1]结构4的条件（iv),从而得到了不满足链条件的[n,3;7]线性码的差序列的充要条件,并应用改进的遗传算法搜索满足链条件的[n,3;7]线性码的差序列,取得了较好的结果。     

Homology and cohomology with compact supports forq-convex spaces

Summary In this paper we give an elementary proof of basic vanishing properties for homology and cohomology with compact supports of q-complete spaces which follow from the results of H.Hamm [16], [17] and K.-H.Fieseler-L.Kaup [13]. At the same time we obtain new finiteness results for the homology and the cohomology with compact supports in the q-convex case, which is not treated in [16], [17] and [13]. Our work extends to general q-complete spaces recent papers of M.Coltoiu-N.Mihalache [8] and M.Coltoiu [7] which treated the case of Stein spaces (q=0). A typical result is the following: if X is a q-complete space of dimension n, then H_i (X, Z)=0 for i>n+q and H_n+q (X, Z) is free, if X is also purely dimensional and locally a set-theoretic complete intersection, then H _c ⁱ (X, Z)=0 for ic ⁿ –q(X, Z) is free. The vanishing of the cohomology with compact supports for q-complete spaces has as consequence Lefschetz-type theorems for singular spaces (the homology statements) proved by C.Okonek [24] using Goresky-MacPherson stratified Morse theory.     

K-Theory of Free Rings

The object of this article is to establish the following result (Corollary 3.9 below): If R is a regular right noetherian ring and R{X} is the free associative algebra on the set X, then K_n(R) = K_n(R{X}), where K_n refers to the Quillen K-theory. The result can be stated in the equivalent form that H_n(G1(R),Z) = H_n(G1(R{X}),Z). From this result it follows that if F is a free ring without unit, then K_n(F) = 0, whence free rings are acyclic models for Quillen K-theory (3.11 below). This result in turn enables us to complete Anderson's work [1] in identifying the Quillen K-theory [11] and the K-theory proposed by Gersten [7] and Swan [18] for all rings. We also establish that the natural transformation K_n(R) → K_n ^k-v(R) between the Quillen theory and the K-theory of Karoubi and Villamayor is an isomorphism if R is a supercoherent (Definition 1.2) and regular (Definition 1.3) ring. From this result we can gain some information about the K-theory of group rings of free products of groups (Theorem 5.1).     

On an approximation property of Pisot numbers

Let 1<q<2 be a real number, m≥1 be a rational integer and l_m(q)={|P(q)|,P∈Z[X],P(q)≠0,H(P)≤m}, where Z[X] denotes the set of polynomials P with rational integer coefficients and H(P) is the height of P. The value of l_m(q) was determined for many particular Pisot numbers ([3] and [7]). In this paper we determine the infimum and the supremum of the numbers l_m(q) for any fixed m. We also determine the greatest limit point for the case m=1. This revised version was published online in June 2006 with corrections to the Cover Date.     

Towards relative invariants of real symplectic four-manifolds

Let (X, ω, c_X) be a real symplectic four-manifold with real part . Let be a smooth curve such that We construct invariants under deformation of the quadruple (X, ω, c_X, L) by counting the number of real rational J-holomorphic curves which realize a given homology class d, pass through an appropriate number of points and are tangent to L. As an application, we prove a relation between the count of real rational J-holomorphic curves done in [W2] and the count of reducible real rational curves done in [W3]. Finally, we show how these techniques also allow us to extract an integer valued invariant from a classical problem of real enumerative geometry, namely about counting the number of real plane conics tangent to five given generic real conics. Received: March 2005; Revision: September 2005; Accepted: September 2005     

循环矩阵环的局部化

本文的主要结果如下：(1)环R关于其乘法封闭子集S满足左Ore条件当且仅当R[σ1,σ2,…，σt]关于其相应乘法封闭子集S[σ1,σ2,…，σt]满足左Ore条件．(2)若R关于其乘法封闭子集S满足左Ore条件，S^-1 R是R关于S的左分式环，其自然同态为φ：R→S^-1R，则存在环同态φ：R[σ1,σ2,…,σt]→S[σ1,σ2,…,σt]^-1 R[σ1,σ2,…σt]使得(S-1R)[φ（σ1),φ-(σ2),…φ（σt)]≌S[σl，σ2，…，σt]^-1R[σ1,σ2,…σt]。     

Extensions of Modules with ACC on d-annihilators

A unitary right R-module MR satisfies acc on d-annihilators if for every sequence(a_n)_n of elements of R the ascending chain AnnM(a_1)■ AnnM(a_1 a_2)■AnnM(a_1 a_2 a_3)■… of submodules of MR stabilizes. In this paper we first investigate some triangular matrix extensions of modules with acc on d-annihilators. Then we show that under some additional conditions,the Ore extension module M[x]R[x;α,δ]over the Ore extension ring R[x;α,δ] satisfies acc on d-annihilators if and only if the module MR satisfies acc on d-annihilators. Consequently, several known results regarding modules with acc on d-annihilators are extended to a more general setting.     

Chains of function spaces over Euclidian spaces and local fields

The Lipschitz class Lip(K, α) on a local field K is defined in [10], and an equivalent relationship between the Ho&#168;lder type space Cα(K)[9] and Lip(K,α) is given. In this note, we give a “chain of function spaces“ over Euclidian space by defining higher order continuous modulus in R, and point out that there is no need of higher order continuous modulus for describing the chain of function spaces over local fields.     

Generalized epimorphism theorem

LetR[X, Y] be a polynomial ring in two variables over a commutative ringR and letF∈R[X, Y] such thatR[X, Y]/(F)=R[Z] (a polynomial ring in one variable). In this set-up we prove thatR[X, Y]=R[F, G] for someG∈R[X, Y] if eitherR contains a field of characteristic zero orR is a seminormal domain of characteristic zero.