Coloring perfect (K4 − e)-free graphs

This note proves the Strong Perfect Graph Conjecture for (K₄ − e)-free graphs from first principles. The proof directly yields an O(pn²) algorithm for p-coloring a perfect (K₄ − e)-free graph.     

关于拓扑对策中的I~2(K)I(K)问题

证明了如果空间类κ为D-空间类或闭遗传不可约空间类,则I(κ)(∈)κ.这一结果对于κ为D空间类和闭遗传不可约空间类,肯定地回答了I(κ)是否包含I2(κ)问题.     

Classification of spreads ofPG(3, 4)∖PG(3, 2)

We show that the 800 spreads ofPG(3, 4)PG(3, 2) fall into three orbits of sizes 120, 120 and 560, under the action of its automorphism group.     

阿基米德如何求1 1/4 (1/4)~2 (1/4)~3 …

2000多年前的阿基米德,被认为是有史以来的三个最伟大的数学家之一(另外两位是牛顿与高斯).阿基米德在许多方面有杰出的贡献.他在研究无穷递缩等比数列的和1 1/4     

Overgroups of SU(n,K, f) or Ω(n,K, Q) in GL(n,K)

All the overgroups of SU(n, K, f) or (n, K, Q) in GL(n, K) are determined, for arbitrary division rings K and arbitrary forms f or Q with positive Witt indices.     

相关M_p(K)的极值问题

对于R~n中充分光滑的凸体,通过欧式单位球面上的迷向测度,刻画了在T∈SL(n)下M_p(TK)和M_P~*(TK)的最小值问题.同时也得到了M_p(K)M_p~*(K)取得最小值的条件.     

Invertible symmetric 3 × 3 binary matrices and GQ(2, 4)

We reveal an intriguing connection between the set of 27 (disregarding the identity) invertible symmetric 3?×?3 matrices over GF(2) and the points of the generalized quadrangle GQ(2,?4). The 15 matrices with eigenvalue one correspond to a copy of the subquadrangle GQ(2,?2), whereas the 12 matrices without eigenvalues have their geometric counterpart in the associated double-six. The fine details of this correspondence, including the precise algebraic meaning/analogue of collinearity, are furnished by employing the representation of GQ(2,?4) as a quadric in PG(5,?2) of projective index one. An interesting physics application of our findings is also mentioned.     

Models for CR-manifolds of type (1,K) for 3≤K≤7 and their automorphisms

Models similar to the tangent quadric are constructed for surfaces with one-dimensional complex tangent space. It is shown that these models possess the main properties of the tangent quadric. Their groups and algebras of automorphisms are found. Translated fromMatematicheskie Zametki, Vol. 67, No. 3, pp. 452–459, March, 2000.     

弹性问题单元构造中空间M_3(K)维数计算

<正>1引言线弹性方程的解空间是具有对称性质的应力矩阵和位移向量.在Hellinger-Reissner变分形式下,构造稳定的单元是有限元求解弹性问题的关键.其中,通过构造复合单元的方法[1,2,3,4,5]求解弹性问题,这种方法比较复杂.也可以通过用Lagrange乘子重建弹性问题的混合变分形式,对应力空间施加弱对称性,解决线弹性问题[6,7,8,9,10].2002年,Arnold和Winther在[11]构造了一系列稳定的协调三角形单元和刚体运动下的低     

试题研讨(4)

题 1　已知数列 {an}前 n项和为 Sn,若 a1= 2 ,nan 1=Sn n( n 1 ) .( 1 )求数列 {an}的通项公式 ;( 2 )令 Tn =Sn2 n,1当 n为何值时 ,Tn>Tn 1( n∈ N ) ?2若对一切正整数 n,总有 Tn ≤ m,求 m的取值范围 .( 2 0 0 2年苏州市模拟考试题 )命题溯源　求数列的通项公式是数列知识的重要问题 .1 983年高考题中首次出现由递推数列求通项公式的问题 ,连考了三年 ,当时形成了一个热潮 .多年来两类求数列通项公式的问题是常考常新 .一类是已知f ( an,Sn) =0求数列通项 an;另一类是与不等式相关的数列综合题 ,如 1 998年全国高考试卷末题 ,…     

研究K4-同胚图K4(α,1,1,δ,ε,η)色性的一个引理

主要介绍了一个引理，这个引理奠定了K4－同胚图K4（α，1，1，δ，ε，η）色性研究的基础。     

Regularity for weakly (K1, K2)-quasiregular mappings

In this paper, we first give the definition of weakly (K1, K2)-quasiregular mappings, and then by using the Hodge decomposition and the weakly reverse Holder inequality, we obtain their regularity property: For any ql that satisfies 0 < K1n(n+4)/22n+1 × 100n2[23n/2(25n + 1)](n - q1) < 1, there exists p1 = p1(n, q1, K1, K2) > n, such that any (K1, K2)-quasiregular mapping f ∈W(loc)(1,q1)(Ω,Rn) is in fact in W(loc)(1,p1)(Ω,Rn). That is, f is (K1, K2)-quasiregular in the usual sense.     

Automorphisms of PGL_2(K) over Any Skew Field K

<正> Let K be a skew field and Z be its center.The multiplicative groups of non-zero ele-ments of K and Z are denoted by K~* and Z~* respectively.Denote by GL_2(K) the groupof all 2×2 matrices over K and by PGL_2(K) the factor group of GL_2(K) modulo its ce-nter consisting of all elements of the form γI,where γ∈Z~* and I is the 2×2 identitymatrix.If K is commutative or is of characteristic≠0 the automorphisms of PGL_2(K)are already determined.In the present paper,we'll determine the automorphisms of PGL_2(K)     

The Existence of (K 2 × K 6)-Designs

Direct and recursive constructions are established for graph designs for K ₂ × K ₆ grid-blocks. Using these, the existence of graph designs of index one in which the blocks are K ₂ × K ₆ grid-blocks is completely determined: A (K ₂ × K ₆)-design of order v exists if and only if ${v\equiv1\pmod{72}}$ .