Phase transitions and positive definite couplings

The method of infrared bounds is extended to a large class of nearest neighbour interactions in classical spin systems. Temperature controlled bounds on fluctuations follow whenever the coupling function is a positive definite kernel. Existence of phase transitions is demonstrated for the RP ^Nmodel for d3.     

Jacobi elliptic functions and change of variable in a convolution

We solve the functional equation

The many limits of mixed means

The sequences introduced by Carlson (1971) are variants of the Gauss arithmetic geometric sequences (which have been elegantly discussed by D. A. Cox (1984, 1985)). Given (complex)a ₀,b ₀ we define

On an application of Hall's representatives theorem to a finite geometry problem

It is well-known thatn points not belonging to a hyperplane determine at leastn hyperplanes. The possible configurations of hyperplanes in the case when the number of hyperplanes is equal ton are known, too. In this paper we obtain these results by means of Hall's representatives theorem. The setting is that of a finite geometry.     

A proof of Freud's conjecture for exponential weights

LetW (x) be a function nonnegative inR, positive on a set of positive measure, and such that all power moments ofW ²(x) are finite. Let {p _n (W ²;x)} ₀ denote the sequence of orthonormal polynomials with respect to the weightW ²(x), and let {A _n } ₁ and {B _n } ₁ denote the coefficients in the recurrence relation

The gap between monotone and non-monotone circuit complexity is exponential

A. A. Razborov has shown that there exists a polynomial time computable monotone Boolean function whose monotone circuit complexity is at leastn ^{c losn} . We observe that this lower bound can be improved to exp(cn ^1/6–o(1)). The proof is immediate by combining the Alon—Boppana version of another argument of Razborov with results of Grötschel—Lovász—Schrijver on the Lovász — capacity, of a graph.     

Localization of a theorem of Ambos-Spies and the strong anti-splitting property

LetA be an r.e. nonrecursive set. We sayA has thestrong antisplitting property if there exists an r.e. setB with 0< _T B< _T A such that ifA ₁ A ₂=A andA ₁A ₂=0 thenA _{1 T} B impliesA _{1 T} 0 andB _T A ₁ impliesA _{1 T} A. It is shown that below any high r.e. degree there exists an r.e. set with the strong antisplitting property. The main ingredient of the proof is a localization of Ambos-Spies' result that the cup or cap theorem fails forW-degrees.Research partially supported by N.U.S. Grant RP 85/83 (Singapore).     

Y2O3薄膜处理对3Cr25Ni7N合金的抗高温氧化性能的影响

采用电沉积-热解法在3Cr25Ni7N合金表面制备了Y2O3薄膜,并研究了薄膜处理对合金在1000℃空气中的抗高温氧化性能的影响。氧化动力学曲线、SEM及XRD分析结果表明,Y2O3薄膜处理使合金表面氧化膜以尖晶石结构为主,氧化膜致密,有效地抑制了Cr2O3的挥发反应,且氧化膜与基体的附着性好,因此合金在高温下的抗氧化性能得到提高,这与氧化钇薄膜在较低温度下抗高温氧化性能提高的机制是不同的。在不同温度下,Y2O3薄膜处理均可以有效提高合金的抗高温氧化性能。     

淫羊藿根与叶活性成分的分析和比较

采用细胞膜色谱法（ＣＭＣ）筛选，并结合离体药理实验确定主要活性成分，利用高效液相色谱法分析比较了淫羊藿根与叶中的活性成分及其差异性．色谱条件为Ｋｒｏｍａｓｉｌ ＯＤＳ 柱（１５０ ｍｍ× ４．６ ｍｍ．Ｉ．Ｄ ）流动相甲醇－水（７０：３０，Ｖ：Ｖ）；检测波长２７０ｎｍ。筛选发现淫羊藿根中的两个有效成分ＹＹＨ－２１４和ＹＹＨ－２１６对血管有较强的舒张作用，表明活性成分在ＣＭＣ模型体系中的保留特性与药理作用之间存在良好的相关性。在此色谱条件下淫羊藿叶未检测到这两种活性成分．