图和有向图的测地数

对于图G（或者有向图D）内的任意两点u和υ,u-υ测地线是指在u和υ之间的最短路（或者从u到υ）.I（u,υ）表示位于一条u-υ测地线上所有点的集合,对于S（U∣）V（G）,I（S）表示所有I（u,υ）的并,这里u,υ∈S.图G（或者有向图D）的测地数g（G）（g（D））是使J（S）=V（G）（J（S）=V（D））的最小点集S的基数.定义G的所有定向图中测地数的最小值为G的下测地数,即g-（G）=min{g（D）：D是G的定向图）;定义G的所有定向图中测地数的最大值为G的上测地数,即g＋（G）=max{g（D）：D是G的定向图）.本文的主要目的是研究G V H 的上、下测地数,此外,文章给出了g（G）=g（G×P3）的一个充分必要条件.     

图的下测地数和上测地数

对于图G(或有向图D)内的任意两点u和v,u—v测地线是指在u和v之间(或从u到v)的最短路．I(u,v)表示位于u—v测地线上所有点的集合,对于S(?)V(G)(或V(D)),I(S)表示所有I(u,v)的并,这里u,v∈S．G(或D)的测地数g(G)(或g(D))是使I(S)=V(G)(或I(S)=V(D))的点集S的最小基数．G的下测地数g~-(G)=min{g(D)：D是G的定向图},G的上测地数g~ (G)=max{g(D)：D是G的定向图}．对于u∈V(G)和v∈V(H),G_u H_v表示在u和v之间加一条边所得的图．本文主要研究图G_u H_v的测地数和上(下)测地数．     

对偶扩张代数的Frobenius态射和固定点代数

设A是由箭图Q和关系I所确定的代数,D(A)是代数A的对偶扩张代数, 对应的箭图Q*和关系I*由Q和I决定．本文证明:带关系箭图(Q*,I*)的自同构由带关系箭图(Q,I)的自同构决定;D(A)的Frobenius态射由A的Frobenius态射完全决定;代数D(A)的固定点代数同构于相应的代数A的固定点代数与A°P的固定点代数的张量积,特别地,当Q为单的箭图时,代数D(A)的固定点代数同构于代数A的固定点代数的对偶扩张代数．     

删失数据的光滑乘积限估计的渐近性质

在删失数据的模型下，对于光滑未知的分布函数Ｆ０，文中提出了光滑化的方法去估计Ｆ０，得到了光滑ＰＬ估计Ｆｎ，并建立了Ｆｎ在Ｄ（－∞，Ｔ），Ｔ＜ＴＦ上的弱收敛和强相合的结果．同时也获得了光滑ＰＬ过程的强逼近和重对数律．     

An Upper Bound for the w-Weak Global Dimension of Pullbacks

Let R be a commutative ring with identity and I0 an ideal of R.We introduce and study the c-weak global dimension c-w.gl.dim(R/I0) of the factor ring R/I0.Let T be a w-linked extension of R,and we also introduce the wR-weak global dimension wR-w.gl.dim(T) of T.We show that the ring T with wR-w.gl.dim(T) =0 is exactly a field and the ring T with wR-w.gl.dim(T) ≤ 1 is exactly a PwRMD.As an application,we give an upper bound for the w-weak global dimension of a Cartesian square (RDTF,M).More precisely,if T is w-linked over R,then w-w.gl.dim(R) ≤ max{wR-w.gl.dim(T) + w-fdR T,c-w.gl.dim(D) + w-fdn D}.Furthermore,for a Milnor square (RDTF,M),we obtain w-w.gl.dim(R) ≤ max{wR-w.gl.dim(T) + w-fdR T,w-w.gl.dim(D) + w-fdR D}.     

Agreeable domains

An integral domain D with quotient field K is defined to be agreeable if for each fractional ideal F of D[X] with F C K[X] there exists 0 = s ε D with sF C D[X]. D is agreeable ? D satisfies property (*) (for 0 ^ f(X) G K[X], there exists 0 = s ε D so that f(X)g(X) ε D[X] for g(X) ε K[X] implies that sg(X) ε D[X]) &; D[X] is an almost principal domain, i.e., for each nonzero ideal I of D[X] with IK[X] = K[X], there exists f(X) ε I and 0 = s ε D with sI C (f(X)). If D is Noetherian or integrally closed, then D is agreeable. A number of other characterizations of agreeable domains are given as are a number of stability properties. For example, if D is agreeable, so is ?^αD_{P α} and for a pair of domains D?D′ with a [DD:′]≠0, D is agreeable?D′ is agreeable. Results on agreeable domains are used to give an alternative treatment of Querre's characterization of divisorial ideals in integrally closed polynomial rings. Finally, the various characterizations of D being agreeable are considered for polynomial rings in several variables.     

Optimum Extrapolated Alternating Direction Implicit Schemes in the Presence of Singular Matrices

This paper shows how Extrapolated Alternating Direction Implicit(E.A.D.I.) methods can be used for the numerical solution ofLaplace's equation under Neumann boundary conditions. E.A.D.I.methods are applied with the Douglas set of parameters and optimumE.A.D.I. schemes are given.     

On Chebychev Acceleration Procedures for Alternating Direction Iterative Methods

The solution of large sparse systems of linear equations arising,for example, from the numerical solution of elliptic partialdifferential equations is considered, with reference to theacceleration technique commonly known as Chebychev acceleration.In particular its application to alternating direction iterative(A.D.I.) methods is compared with the more standard techniquessuch as successive overrelaxation. It is conjectured that inmost circumstances a suitable A.D.I. strategy is that of applyingChebychev semiiteration to an A.D.I. process with a single A.D.I.parameter. It is shown that under general conditions this procedure maysometimes produce faster convergence than the usual multiparameterA.D.I. procedure.     

Comparing symbolic powers of edge ideals of weighted oriented graphs

Journal of Algebraic Combinatorics - Let D be a weighted oriented graph and I(D) be its edge ideal. If D contains an induced odd cycle of length $$2n+1$$ , under certain condition, we show that $$...     

Über das Anwachsen der Lösungen linearer Differentialgleichungen mit rationalen Koeffizienten in Winkelräumen

Let z=∞ be the only irregular singular point of the linear differential equation $$(D)w^{(n)} + P_{n - 1} (z)w^{(n - 1)} + \cdots + P_o (z)w = 0$$ with rational coefficients p_j(z). If w is a multivalent and irregular solution of (D), we define the index I(τr,W), τ ∈ (0,1), of a branch W of w in the plane cut along a half ray. If r→∞, I(τr,W) possesses a finite number of aymptotic directions being exactly the asymptotic directions of the points z with maximal possible modulus of W(z). It follows that each branch W is of mean type σ(W)=|d|/λ in each sector containing an asymptotic direction of I. The possible values of the order of growth λ=λ(W)<∞ and the constant d are given by the PUISEUX-diagram of (D).     

关于Malcev代数的幂零性

We investigate the nilpotence of a Malcev algebra M and of its standard enveloping Lie algebra L(M)=M D(M, M). The main result shows that an ideal A of M is nilpotent in M if and only if the corresponding ideal Ⅰ(A) = A D(A, M)is nilpotent in L(M).     

Separation properties of induced I(L)-topological spaces

The concept of induced I(L)-topological spaces has been introduced by Kubiak (Ph.D. Thesis, UAM, Poznan, 1985) and independently by Wang (Kexue Tongbao 34 (5) (1989) 333). In this paper, the separation properties in the sense of Hutton–Reilly of induced I(L)-topological spaces are investigated. The main result of the paper is a characterization of L-topological spaces by means of the appropriate Hutton–Reilly separation properties of its induced I(L)-topological space.     

曲线上微分算子环及其上的模

我们首先讨论了解析不可约曲线Ｘ／ｋ上微分算子环的右模Ｄ（（ｘ），Ｉ）的性质及应用，然后讨论曲线上微分算子环的有限维向量空间模和ｈｏｌｏｎｏｍｉｃ模．     

半群K(n,r)中的幂等生成元

设Singn是由一个n元集上的所有奇异变换所构成的奇异变换半群，I是由Singn中一些亏数为1的幂等元组成的集合，Howie利用有向图证明了：I是Singn的一个生成集当且仅当与其相应的有向图D（I）是强连通的完全图，本文利用多重有向图将这一结果推广到Singn的每个理想K（,r)上。     

The construction of hopscotch methods for parabolic and elliptic equations in two space dimensions with a mixed derivative

Hopscotch, a fast finite difference technique, is used to solve parabolic and elliptic equations in two space dimensions with a mixed derivative. The method is compared numerically with existing alternating direction implicit (A.D.I.) and locally one dimensional (L.O.D.) methods for simple problems.Douglas and Gunn's A.D.I. method is both simplified and improved by reformulating it as a hopscotch method.     

Intermediate rings between D+I And K [y1,…,yt]

Let R = k [y₁,…,y_t] be an affine domain (where k is a field) having krull dimension =n>0. Let I be a nonzero proper ideal of R and D be a subring of K. In section 1 we determine necessary and sufficient conditions in order that (S,R) is a 'lying over pair' where S = D+I. In section 2 we chaaracterize when S is a Maximal non-Noetherian subring of R. Further we determine when S is a maximal subring of R.     

Numerical Solution of the Robin Problem by Extrapolated A. D. I. Methods

In this paper the Robin problem for elliptic equations is consideredand its numerical integration by several variants of the Extrapolatedform of the Alternating Direction Implicit (E.A.D.I.) methodsis discussed. A comparison among the E.A.D.I. variants includedhere as well as those studied in an earlier paper is carriedout.     

Some pseudovariety joins involvinglocally trivial semigroups

This paper is concerned with the computation of pseudovariety joins involving the pseudovariety L I of locally trivial semigroups. We compute, in particular, the join of L I with any subpseudovariety of CR(m in circle)N, the Mal’cev product of the pseudovariety of completely regular semigroups and the pseudovariety of nilpotent semigroups. Similar studies are conducted for the pseudovarieties K, D and N, where K (resp. D) is the pseudovariety of all semigroups S such that eS=e (resp. Se=e ) for each idempotent e of S .     

A New Generalization of a Theorem of Jung for the Orthogonality Equation

The main result of this paper states as follows: Assume that for a closed ball D @ 0 and with center at the origin, a mapping T : D M D satisfies $$ T(0) = 0\ \hbox{and}\ \vert \langle Tx, Ty \rangle - \langle x, y \rangle \vert \leq \varepsilon \eqno (1) $$ for some 0 h l < min { 1/4, d 2 /17} and for all x , y ] D . Then, there exists an isometry I : D M D with $$ \vert Tx - Ix \vert \le \left\{ {\matrix{ {13\sqrt \varepsilon } \hfill &{{\rm for}\; d     

Some Pseudovariety Joins InvolvingLocally Trivial Semigroups

This paper is concerned with the computation of pseudovariety joins involving the pseudovariety L I of locally trivial semigroups. We compute, in particular, the join of L I with any subpseudovariety of CR(m in circle)N, the Mal'cev product of the pseudovariety of completely regular semigroups and the pseudovariety of nilpotent semigroups. Similar studies are conducted for the pseudovarieties K, D and N, where K (resp. D) is the pseudovariety of all semigroups S such that eS=e (resp. Se=e ) for each idempotent e of S . May 5, 1999