Description of the Real von Neumann Algebras with Abelian Skew-Symmetric Part

In this note we describe (up to isomorphism) the real von Neiman algebras R with Abelian skew-symmetric part , i.e., such that xy-yx=0 for any .     

The Intersection of Opposed Big Cells in The Real Flag Variety of Type G2

We compute the Euler characteristics of the individual connectedcomponents of the intersection of two opposed big cells in thereal flag variety of type G₂, verifying a conjecture of Rietsch[6]. 2000 Mathematical Subject Classification: primary 14M15; secondary20G20.     

Complex Zeros of Algebraic Polynomial with Non-Zero Mean Random Coefficients

In this paper we obtain a formula for the average density of the distribution of complex zeros of an algebraic polynomial with random coefficients. The coefficients are assumed independent identical normally distributed random variables with mean and variance ². The value of the average density for the case of =0 and ²=1 was obtained previously. Some limits of the distribution of the complex zeros are provided using the presented formula.     

Some remarks on the real rank of non-unital C*-algebras

For a non-unital C-algebra , let be the C-algebra obtained from by adjoining an identity. In this paper we show that

where is a locally compact Hausdorff space with .

     

Indivisibility of Class Numbers of Real Quadratic Fields

Let D denote the fundamental discriminant of a real quadratic field, and let h(D) denote its associated class number. If p is prime, then the Cohen and Lenstra Heuristics give a probability that ph(D). If pgt;3 is prime, then subject to a mild condition, we show that

On random algebraic polynomials

This paper provides asymptotic estimates for the expected number of real zeros and -level crossings of a random algebraic polynomial of the form , where are independent standard normal random variables and is a constant independent of . It is shown that these asymptotic estimates are much greater than those for algebraic polynomials of the form .

     

与象电荷有关的能量和互作用力问题

指出与象电荷有关的系统的互能、互作用力和真实电荷系统的互能、互作用力分别相等,自能、有一般分别不等。     

Thiol–ene coupling reaction of fatty acid monomers

The reactivities and reaction rates of the thiol–ene coupling reaction of 2‐ethyl‐(hydroxymethyl)‐1,3‐propanediol trimercapto acetate and 2‐ethyl‐(hydroxymethyl)‐1,3‐propanediol trimercapto propionate with two common unsaturated fatty acid methyl esters (methyl oleate and methyl linoleate) were evaluated. The reactions were monitored with real‐time IR and ¹H NMR, which both showed that the mercapto acetate was more reactive than the mercapto propionate. Both thiols were more prone to add to the monounsaturated methyl oleate than to methyl linoleate, which contained two unconjugated double bonds. According to bond energy calculations, the thiol hydrogen of mercapto acetate was somewhat more difficult to abstract than the hydrogen of mercapto propionate. Consequently, the formed S? C bond in the acetate case was stronger than in the propionate case, and so the equilibrium was more shifted toward the addition products. The real‐time IR measurements also showed that the cis unsaturation in methyl oleate isomerized much more quickly than that in methyl linoleate, and this also had an impact on the overall addition rate of the thiols because a trans unsaturation was more reactive than a cis unsaturation. The higher isomerization rates in the oleate systems, compared with those of the linoleate systems, was suggested to be due to a more restricted rotation along the C? C bond of the reacted unsaturation in linoleate. This study showed the importance of trans unsaturations in obtaining reasonable reaction rates in thiol–ene reactions with fatty acid derivatives. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 6346–6352, 2004