Volume estimates for sections of certain convex bodies

This paper deals with volume estimates for hyperplane sections of the simplex and for m‐codimensional sections of powers of m‐dimensional Euclidean balls. In the first part we consider sections through the centroid of the n‐dimensional regular simplex. We state a volume formula and give a lower bound for the volume of sections through the centroid. In the second part we study the extremal volumes of m‐codimensional sections “perpendicular” to of unit balls in the space for all . We give volume formulas and use them to show that the normal vector (1, 0, …, 0) yields the minimal volume. Furthermore we give an upper bound for the ‐dimensional volumes for natural numbers . This bound is asymptotically attained for the normal vector as .     

实时三维超声心动图与640层CT定量评价冠心病患者左心室容积及收缩功能的对比研究

目的应用实时三维超声心动图（RT-3DE）和640层CT（640- MSCT）定量评价左心室容积和收缩功能,探讨两种方法测值的相关性及在左心功能评价中的应用价值。方法选择临床或冠状动脉造影确诊为冠心病的患者42例,分别行RT-3DE和640- MSCT心脏增强（分别采用自动法和手动法）检查,测量指标包括：左心室舒张末期容积（LVEDV）、左心室收缩末期容积（LVESV）、左心室每搏输出量（LVSV）和左心室射血分数（LVEF）。将两种方法各测量值的结果进行比较。结果（1）RT-3DE测得左心容积及功能指标与640- MSCT （自动、手动两种方法）测值（LVEDV、LVESV、LVSV及LVEF）间相关性较好（P＜0.01）;（2）640- MSCT与RT-3DE左心室容积与心功能测值之间差别在于：LVEDV、LVESV两项指标640- MSCT测值均高于RT-3DE测值（P＜0.05）,LVSV值640- MSCT测值稍高于RT-3DE测值（P＞0.05）,而LVEF值640- MSCT测值稍低于RT-3DE测值（P＞0.05）。结论640- MSCT与RT-3DE在评价冠心病患者左心容积及功能方面高度相关,RT-3DE可推荐为临床首选影像学检查;根据不同患者的病情和各自特点,将640- MSCT与RT-3DE结合使用,可提高临床的影像学诊断率,为临床提供更多的诊疗信息。     

Tamari lattices and noncrossing partitions in type B

The usual, or type A_n, Tamari lattice is a partial order on , the triangulations of an (n+3)-gon. We define a partial order on , the set of centrally symmetric triangulations of a (2n+2)-gon. We show that it is a lattice, and that it shares certain other nice properties of the A_n Tamari lattice, and therefore that it deserves to be considered the B_n Tamari lattice. We also define a bijection between and the noncrossing partitions of type B_n defined by Reiner.     

环的B-稳定正则理想

研究了正则理想是B-稳定的充分和必要条件,并且证明环R的正则理想I是B-稳定的当且仅当对任意的有限生成投射右R-模A,如果A₁和A₂是A的有限生成子模且满足A₁≌A₂,A₁=A₁I以及A₂=A₂I,则存在一个有限生成子模B,使得A=A₁（?）B=A₂（?）B;当且仅当对任意的幂等元e,f∈I,eR≌fR蕴含eR/（eR∩fR）≌fR/（eR∩fR）;当且仅当对任意的a∈1+I,存在一个幂等元e∈I,使得a-e∈∪（R）并且aR∩eR=0.进而构造了相关的例子.     

一般环之分式环

本文给出一般环R之分式环△^-1R的构造和△^-R的理想的一些性质,推广了现有中外教科书的结论．证明了（1）△^-1R中理想有且仅有形式△^-1I,其中△3R．（2）如果P是R的素理想,且△∩P=Ф,则△^-1P是△^-1R的素理想,且θ^-1（△^-1P）=P。     

The K°-relation on the Congruence Lattice of a Regular Semigroup with an Inverse Transversal

Let S be a regular semigroup with an inverse transversal S° and C(S) the congruence lattice of S. A relation K° on C(S) is introduced as follows: if ρ, θ∈ C(S), then we say that ρ and θ are K°-related if Ker ρ° = Ker θ° , where ρ° = ρ|S°. Expressions for the least and the greatest congruences in the same K°-class as ρ are provided. A number of equivalent conditions for K° being a congruence are given.     

A conjecture on bipartite graphical regular representations

In this paper we are concerned with the classification of the finite groups admitting a bipartite DRR and a bipartite GRR.First, we find a natural obstruction that prevents a finite group from admitting a bipartite GRR. Then we give a complete classification of the finite groups satisfying this natural obstruction and hence not admitting a bipartite GRR. Based on these results and on some extensive computer computations, we state a conjecture aiming to give a complete classification of the finite groups admitting a bipartite GRR.Next, we prove the existence of bipartite DRRs for most of the finite groups not admitting a bipartite GRR found in this paper. Actually, we prove a much stronger result: we give an asymptotic enumeration of the bipartite DRRs over these groups. Again, based on these results and on some extensive computer computations, we state a conjecture aiming to give a complete classification of the finite groups admitting a bipartite DRR.