Radical of submodules and symmetric algebra

A prime ideal of the symmetric algebra of an R-module N is associated to every prime submodule M ?N and this assignment is then used to obtain a new characterization of the radical of a submodule. Several applications of these results are also included.     

Effect of pH, temperature and solvent mole ratio on solubility of disodium 5′-guanylate in water + ethanol system

Solubility of disodium 5′-guanylate in water + ethanol binary solvent mixtures was determined by a gravimetric method in the temperature range from 283.15 K to 323.15 K, pH range from 8 to 10 and at different water/ethanol mole ratios. The effects of pH, temperature and water/ethanol mole ratio on the solubility were investigated in detail. The modified Apelblat model and the combined nearly ideal binary solvent (CNIBS)/Redlich-Kister model were selected to correlate the experimental data. The results showed that the experimental data was satisfactorily correlated by the (CNIBS)/Redlich-Kister model, but for the modified Apelblat model, the correlation was not so satisfactory in some cases.     

Resonant-Mie-scattering of aggregates of phosphomolybdate and papaverine for measuring activities and screening inhibitors of cyclic nucleotide phosphodiesterase isozymes

A resonant-light-scattering (RLS) method was proposed to quantify phosphate for screening inhibitors of isozymes of cyclic nucleotide phosphodiesterase (PDE). In acidified mixtures of phosphate, papaverine and molybdate, there were aggregates exhibiting micrometre sizes, no absorbance peaks over 360 nm but strong RLS peaks at 392 nm; Mie scattering thus accounted for the RLS signals. When papaverine was added before molybdate to acidified samples of phosphate, RLS signals at 392 nm were stable from 5 to 25 min since the addition of molybdate; after optimization, phosphate from 0.40 to 3.60 μM was quantifiable. This RLS method tolerated 60 mg L⁻¹ proteins besides common PDE inhibitors and dimethyl sulfoxide in acidified samples of phosphate; the integration of this RLS method with the coupled action of a phosphomonoesterase on PDE product was thus rational to measure PDE activities without the removal of proteins in samples. By quantifying activities of a truncated mutant of human PDE4B2 via this RLS method, Michaelis–Menten constant, inhibition constants of rolipram, papaverine and theophylline varied over three magnitudes and were consistent with those estimated by an improved malachite green assay of phosphate, respectively. Hence, this novel RLS method was promising for screening inhibitors of PDE isozymes.     

(λ,μ)-模糊子环和理想的进一步讨论

在(λ,μ)-模糊子群的基础上,进一步刻画了(λ,μ)-模糊子环和理想.详细讨论了(λ,μ)-模糊子环和理想的性质,以及它们与截集的关系,给出了相应结论.     

A note on powers in finite fields

The study of solutions to polynomial equations over finite fields has a long history in mathematics and is an interesting area of contemporary research. In recent years, the subject has found important applications in the modelling of problems from applied mathematical fields such as signal analysis, system theory, coding theory and cryptology. In this connection, it is of interest to know criteria for the existence of squares and other powers in arbitrary finite fields. Making good use of polynomial division in polynomial rings over finite fields, we have examined a classical criterion of Euler for squares in odd prime fields, giving it a formulation that is apt for generalization to arbitrary finite fields and powers. Our proof uses algebra rather than classical number theory, which makes it convenient when presenting basic methods of applied algebra in the classroom.     

二项式系数幂和序列在模p2下的几个性质

利用同余理论和多项式理论研究二项式系数幂和序列在模p2下的同余性质,得到了一些非平凡结果.为进一步研究二项式系数幂和序列的多项式递推公式提供有利的工具.     

关于Smarandache素数列及其它的行列式

对任意正整数n≥2,Smarandache下素数列{pp(n))定义为小于或等于n的最大素数;而Smarandache上素数列{Pp(n))表示大于或等于n的最小素数.本文的主要目的是利用初等方法研究Smarandache素数列的性质,并得到由Smarandache素数列组成的行列式的一些性质.