THE CONJUGATE POINTS OF CP^∞ AND THE ZEROES OF BERGMAN KERNEL

Two points of the infinite dimensional complex projective space CP∞ with homogeneous coordinates a = （a0, a1, a2, ） and b = （b0, b1, b2, ）, respectively, are conjugate if and only if they are complex orthogonal, i.e., ab = ∞∑j=0 ajbj = 0. For a complete ortho-normal system φ（t） = （φ0（t）, φ1（t）, φ2（t）, ） of L2H（D）, the space of the holomorphic and absolutely square integrable functions in the bounded domain D of Cn, φ（t）, t ∈ D, is considered as the homogeneous coordinate of a point in CP∞. The correspondence t →φ（t） induces a holomorphic imbedding ιφ ： D → CP∞. It is proved that the Bergman kernel K（t, v） of D equals to zero for the two points t and v in D if and only if their image points under ιφ are conjugate points of CP∞.     

A Remark on Concircularly Flat Totally Real Minimal Submanifolds in CP^n

Let M be a concircularly fiat totally real minimal submanifold in CP4. The infimum Vm of the volume V （M） of M is obtained, also the necessary and sufficient conditions of ＂V（M）=Vm＂ is given.     

Invariant algebraic curves and rational first integrals of holomorphic foliations in CP(2)

In this paper, using the tools of algebraic geometry we provide sufficient conditions for a holomor-phic foliation in CP(2) to have a rational first integral. Moreover, we obtain an upper bound of the degrees of invariant algebraic curves of a holomorphic foliation in CP(2). Then we use these results to prove that any holomorphic foliation of degree 2 does not have cubic limit cycles.     

量子代数${\cal U}_q(f(K,H))$的量子伴随作用

Let H = uq（sl（2）） or u（sl（2））. By means of the standard basis of polynomial algebras, the Glebsch-Gordan formula and quantum Clebsch-Gordan formula are proved by a unified method, and the explicit formula of the decomposition of V（1）^n into the direct sum of simple modules is given in this paper.     

量子代数${\cal U}_q(f(K,H))$的量子伴随作用

The aim of this paper is to study the adjoint action for the quantum algebra Uq（f（K, H））, which is a natural generalization of quantum algebra Uq（sl2） and is regarded as a class of generalized Weyl algebra..The structure theorem of its locally finite subalgebra F（Uq（f（K, H））） is given.     

本刊英文版Vol.21(2005),No.4论文摘要(英文)

Suppose that G is a finite group and D（G） the double algebra of G. For a given subgroup H of G, there is a sub-Hopf algebra D（G; H） of D（G）. This paper gives the concrete construction of a D（G; H）-invariant subspace AH in field algebra of G-spin model and proves that if H is a normal subgroup of G, then AH is Galois closed.     

因子拟适当半群(英文)

In this paper,we investigate a class of factorisable IC quasi-adequate semigroups,so-called,factorisable IC quasi-adequate semigroups of type-（H,I）.Some characterizations of factorisable IC quasi-adequate semigroups of type-（H,I） are obtained.In particular,we prove that any IC quasi-adequate semigroup has a factorisable IC quasi-adequate subsemigroups of type-（H,I） and a band of cancellative monoids.     

[αCP（a）∪βCP（b）]^-中的一类特殊整谱图

图G是一个简单，图G的补图记为G^-，如果G的谱完全由整数组成，就称G是整谱图，鸡尾酒会图G=CP（n）=K2n-nK2（K2n是完全图）.本文确定了当μ1^-=ab＋1时，图类[αCP（a）∪βCP（b）]^-中的所有整谱图.     

完全图的Cantesian积的L(2,1)-圆标定

For positive integers j and k with j ≥ k, an L（j, k）-labeling of a graph G is an assignment of nonnegative integers to V（G） such that the difference between labels of adjacent vertices is at least j, and the difference between labels of vertices that are distance two apart is at least k. The span of an L（j, k）-labeling of a graph G is the difference between the maximum and minimum integers it uses. The λj, k-number of G is the minimum span taken over all L（j, k）-labelings of G. An m-（j, k）-circular labeling of a graph G is a function f ： V（G） →{0, 1, 2,..., m - 1} such that ｜f（u） - f（v）｜m ≥ j if u and v are adjacent; and ｜f（u） - f（v）｜m 〉 k ifu and v are at distance two, where ｜x｜m = min{｜xl｜, m-｜x｜}. The minimum integer m such that there exists an m-（j, k）-circular labeling of G is called the σj,k-number of G and is denoted by σj,k（G）. This paper determines the σ2,1-number of the Cartesian product of any three complete graphs.     

$L^p(K)$中RBF神经网络的系统识别问题

L^p approximation problems in system identification with RBF neural networks are investigated. It is proved that by superpositions of some functions of one variable in L^ploc（R）, one can approximate continuous functionals defined on a compact subset of L^P（K） and continuous operators from a compact subset of L^p1 （K1） to a compact subset of L^p2 （K2）. These results show that if its activation function is in L^ploc（R） and is not an even polynomial, then this RBF neural networks can approximate the above systems with any accuracy.     

The stability of RDDE\ddot x(t) + p_1 (t)\dot x(t) + q_1 (t)x(t) + p_2 (t)\dot x(t - r(t)) + q_2 (t)x(t - r(t)) = O

In this paper, the author considered the stability of zero solution of linear RDDE $$\begin{gathered} \ddot x(t) + p_1 (t)\dot x(t) + q_1 (t)x(t) + p_2 (t)\dot x(t - r(t)) + q_2 (t)x(t - r(t)) = O, \hfill \\ \ddot x(t) + p_1 (t)\dot x(t) + q_1 (t)x(t) + p_2 (t)\dot x(t - r(t)) = O \hfill \\ \end{gathered} $$ using Liapunov-Razumikhin functional and transformations and obtained some sufficient conditions for the stability of Eqs.(1) and (2). These results are suitable both for boundedp _i (t),q _i (t) andr(t).i=1,2.     

关于数论函数方程φ(x_1…x_(n-1)x_n)=m(φ(x_1)+…+φ(x_(n-1))+φ(x_n))

运用Euler函数的性质证明了:当n>1时,方程φ(x_1…x_(n-1)x_n)=m(φ(x_1)+…+φ(x_(n-1))+φ(x_n))仅有有限多组正整数解(x_1,…,x_(n-1),x_n),得到了这些解都满足max{x_1,…,x_(n-1),x_n}≤2m⁴(n-1)4(n-1)²n2n².     

Gal(E/F)与Gal(L(E)/L(F))的同构

Let E be a field of finite extension of a perfect field F. We show that Gal(E/F) is isomorphic to Gal(L(E)/L(F)).     

On the functional equation f(x+g(y))-f(y+g(y))=f(x)-f(y) on groups

We solve the equation

On the functional equation $$f(x+y)=f(x)+f(y)$$f(x+y)=f(x)+f(y)

Monatshefte für Mathematik - An extension of the linearity of the continuous solutions of the functional equation $$f(x+y)=f(x)+f(y)$$ to measurable functions is presented.     

Vector subdivision schemes in (Lp(Rs))r(1 ≤ p ≤∞) spaces

The purpose of this paper is to investigate the refinement equations of the form ψ(x) = ∑α∈Zs a(α)ψ(Mx - α), x ∈ Rs,where the vector of functions ψ=(ψ1,…,ψr)T is in (Lp(Rs))r, 1≤p≤∞,a(α),α∈Zs,is a finitely supported sequence of r × r matrices called the refinement mask, and M is an s × s integer matrix suchthat lim n→∞ M-n = 0. In order to solve the refinement equation mentioned above, we start with a vectorof compactly supported functions ψ0 ∈ (Lp(Rs))r and use the iteration schemes fn := Qnaψ0,n = 1,2,…,where Qa is the linear operator defined on (Lp(Rs))r given by Qaψ:= ∑α∈Zs a(α)ψ(M·- α),ψ∈ (Lp(Rs))r. This iteration scheme is called a subdivision scheme or cascade algorithm. In this paper, we characterize the Lp-convergence of subdivision schemes in terms of the p-norm joint spectral radius of a finite collection of somelinear operators determined by the sequence a and the set B restricted to a certain invariant subspace, wherethe set B is a complete set of representatives of the distinct cosets of the quotient group Zs/MZs containing 0.     

On the Diophantine system $$f(z)\,{=}\,f(x)f(y)\,{=}\,f(u) f(v)$$

We show that the Diophantine system

$$\begin{aligned} f(z)=f(x)f(y)=f(u)f(v) \end{aligned}$$

has infinitely many nontrivial positive integer solutions for \(f(X)=X^2-1\), and infinitely many nontrivial rational solutions for \(f(X)=X^2+b\) with nonzero integer b.

     

Radiation effects of poly(vinylidene fluoride) (PVDF) (I)

The relationship between the crystallinity of poly (vinylidene fluoride) (PVDF) and electron radiation effects is studied with differential scanning calorimeter and X-ray diffraction. The form of crystal of PVDF is not changed. In the low dose zone (lower than 400 kGy), the crystallinity of PVDF increases slightly with the increase of absorbed dose, and then decreases slowly, whereas the decrease of the crystallinity is accelerated with the increase of the absorbed dose in high dose zone. Gel and Sol properties of irradiated samples of PVDF are also studied with extraction of N, N-dimethyl formamide. In a low dose range, it fits Charlesby-Pinner formula very well; however, with the increase of the dose, it begins to deviate from this formula because of the obstruction of the crystalline region of PVDF.     

A set of maps from K to EndA(l2(A)) isomorphic to EndA(K)(l2(A(K))). Applikations

Let A be a C^*-algebra, K be a compact space, A(K) be the C^*-algebra of all continuous maps from K into A, 1₂(A) be the standard countably generated Hilbert A-module. We investigate a set of maps from K into End_A(1₂(A)), which is isomorphic to End_A(K)(1₂(A(K))). We describe the subsets which are isomorphic to End_fA(K) ^*(1₂(A(K))). GL_A(K)(1₂(A(K))) and GL_fA(K) ^*(1₂(A(K))), respectively. As an application we deduce a criterion for the self-duality of 1₂(A) in the commutative case.