Random systems of equations in free abelian groups

We study the solvability of random systems of equations on the free abelian group ? ^m of rank m. Denote by SAT(? ^m , k, n) and \(SAT_{\mathbb{Q}^m } (\mathbb{Z}^m ,k,n)\) the sets of all systems of n equations of k unknowns in ? ^m satisfiable in ? ^m and ? ^m respectively. We prove that the asymptotic density \(\rho \left( {SAT_{\mathbb{Q}^m } (\mathbb{Z}^m ,k,n)} \right)\) of the set \(SAT_{\mathbb{Q}^m } (\mathbb{Z}^m ,k,n)\) equals 1 for n ≤ k and 0 for n > k. As regards, SAT(? ^m , k, n) for n < k, some new estimates are obtained for the lower and upper asymptotic densities and it is proved that they lie between (Π _j=k?n+1 ^k ζ(j))^?1 and \(\left( {\tfrac{{\zeta (k + m)}} {{\zeta (k)}}} \right)^n\) , where ξ(s) is the Riemann zeta function. For n ≤ k, a connection is established between the asymptotic density of SAT(? ^m , k, n) and the sums of inverse greater divisors over matrices of full rank. Starting from this result, we make a conjecture about the asymptotic density of SAT(? ^m , n, n). We prove that ρ(SAT(? ^m , k, n)) = 0 for n > k.     

Seasonal variations of the composition,structural features,and antitumor properties of polysaccharides from <Emphasis Type="Italic">Padina pavonica</Emphasis> (Lebanon) as a function of composition

The variation of the polysaccharide composition of the brown alga Padina pavonica from the Mediterranean Sea was studied as a function of the collection season (April–July). It was shown that the principal polysaccharide (8.0-13.3% of dry alga weight) was alginic acid. Its content did not undergo significant changes from April to July. The content of water-soluble polysaccharides (laminarans and fucoidans) was low (<0.3% of dry alga weight). Water-soluble polysaccharides of the studied alga were practically pure fucoidan. The amount of laminarans was insignificant (<0.01% of dry alga weight). The content of fucoidans increased in alga samples from May through July. It was shown that P. pavonica is a promising source of alginic acids, which have a high capacity for gelation, and fucoidans, which exhibit antitumor action against RPMI-7951 human melanoma cells.     

A computational study on the stability–aromaticity correlation of triply N-confused porphyrins: CMMSE-09

The B3LYP density functional theory methodology in conjunction with the 6-31G(d,p) basis set has been used to characterize triply N-confused meso-tetraphenylporphyrins. According to our computations, there is no a direct correlation between stability and aromaticity as already found for non-substituted confused porphyrins. The inclusion of these substituents in the calculations provokes a decrease of the planarity and aromaticity of these macrocycles along with a notable rise of their relative stability with respect to the non-substituted case. Steric repulsions, both among phenyl rings and β atoms in the pyrrolic rings, and among H atoms in the core of the macrocycles, dominate over aromaticity in the establishment of the most stable conformation of each isomer.     

On the stability of the detonation front in tetranitromethane-nitrobenzene and tetranitromethane-nitromethane liquid composite HEs

The stability of the detonation front and the detonation parameters of composite liquid HEs of fueloxidizer type prepared from tetranitromethane, nitrobenzene, and nitromethane are studied using laser interferometry.     

判别分析在数学建模上的应用

本文依据工科数学第十卷（１９９４年８月）数学建模ＭＣＭ—８９问题Ａ的数据，用Ｆｉｓｈｅｒ判别方法建立数学模型，进行分类，识别新样品的类别，其结论与复杂的原解法一致，此方法一般本科生就可以去作，而且没有更多的假设。     

8Mbps数字电视编解码器系统

本文出了８Ｍｂｐｓ数字电视编解码器的硬件实现方案，包括视频、音频信道三个部分，同时给出了样机的测试结果，最后略地介绍了此编解码器的应用情况。     

磁控溅射法制备的高反Ag_5In_5Te_(47)Sb_(33)相变薄膜的光谱性质及短波长静态记录性能

研究了磁控溅射制备的Ａｇ５Ｉｎ５Ｔｅ４７Ｓｂ３３相变薄膜的光谱及短波长静态记录性能。研究结果表明，晶态薄膜反射率较高，并在６００～９００ｎｍ波长范围内，晶态与非晶态的反射率和折射率相差很大。在ＣＤ－Ｅ系统的工作波长７８０ｎｍ处，晶态反射率高达５０％，光学常数为５．３４－１．０ｉ；非晶态反射率为２３％，光学常数为２．５－１．０３ｉ。从这一角度讲，Ａｇ５Ｉｎ５Ｔｅ４７Ｓｂ３３相变薄膜适于做ＣＤ－Ｅ系统的记录介质。另外，采用波长为５１４．４ｎｍ的短波长光学静态记录测试仪对Ａｇ５Ｉｎ５Ｔｅ４７Ｓｂ３３薄膜的记录性能进行了测试，结果表明，这种薄膜短波长记录性能较好，它在较低功率和短脉宽的激光束作用下就可得到较高的反射率对比度。     

Interfacial crack between elastic half-spaces under harmonic loading

A system of boundary integral equations that allows evaluating the displacement and stress fields for an interfacial crack under harmonic loading is presented. Expressions for the integral kernels are obtained. A numerical solution for a penny-shaped crack between steel and aluminum half-spaces under normally incident compression-rarefaction wave is given __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 8, pp. 47–56, July 2007.