New solvable lattice models in three dimensions

In this paper we establish a remarkable connection between two seemingly unrelated topics in the area of solvable lattice models. The first is the Zamolodchikov model, which is the only nontrivial model on a three-dimen-sional lattice so far solved. The second is the chiral Potts model on the square lattice and its generalization associated with theU _q(sl(n)) algebra, which is of current interest due to its connections with high-genus algebraic curves and with representations of quantum groups at roots of unity. We show that this last sl(n)-generalized chiral Potts model can be interpreted as a model on a threedimensional simple cubic lattice consisting ofn square-lattice layers with anN- valued (N2) spin at each site. Further, in theN=2 case this three-dimen-sional model reduces (after a modification of the boundary conditions) to the Zamolodchikov model we mentioned above.     

On the -rank Artin Conjecture

We assume the generalized Riemann hypothesis and prove an asymptotic formula for the number of primes for which can be generated by given multiplicatively independent numbers. In the case when the given numbers are primes, we express the density as an Euler product and apply this to a conjecture of Brown-Zassenhaus (J. Number Theory 3 (1971), 306-309). Finally, in some examples, we compare the densities approximated with the natural densities calculated with primes up to .

     

Optimum conditions for transformed Panax ginseng hairy roots in flask culture

Panax ginseng hairy roots were transformed by Agrobacterium rhizogenes KTCT 2744. They showed an active branching pattern and fast growth in hormone-free medium, and good growth at 23°C, pH 5.8, 1/2 MS medium, and 3% sucrose. Sucrose provided the highest growth among seven carbon sources tested. Six complex media were also tested. In the combined sugar study, hairy roots grew better on sucrose without glucose or fructose than with glucose or fructose. In the 1/2 MS basal medium, 30 mM in nitrogen and 0.62 mM phosphate salt concentration was the optimum. The growth ratio was maximal at an inoculum size of 0.4% (w/v). Crude saponin and polysaccharide levels were also measured.     

On completely multiplicative functions whose values are roots of unity

Summary We prove that if a complex valued completely multiplicative function F and a positive integer ℓ≦5 satisfy the condition F(N) = U_ℓ, where U_ℓ is the set of all ℓ-th roots of unity, then {F(n+1) F(n) ∣ nε N} = U_ℓ.     

Extended Jury criterion

In this paper,algebraic criteria are established to determine whether or not a real coefficient polynomial has one or two pairs of conjugate complex roots whose moduli are equal to 1 and the other roots have moduli less than 1 directly from its coefficients.The form and the function of the criteria are similar to those of the Jury criterion which can be used to determine whether or not all the moduli of the roots of a real coefficient polynomial are less than 1.     

Double roots of power series and related matters

For a given collection of distinct arguments , multiplicities and a real interval containing zero, we are interested in determining the smallest for which there is a power series with coefficients in , and roots of order respectively. We denote this by . We describe the usual form of the extremal series (we give a sufficient condition which is also necessary when the extremal series possesses at least non-dependent coefficients strictly inside , where is 1 or 2 as is real or complex). We focus particularly on , the size of the smallest double root of a power series lying on a given ray (of interest in connection with the complex analogue of work of Boris Solomyak on the distribution of the random series ). We computed the value of for the rationals in of denominator less than fifty. The smallest value we encountered was . For the one-sided intervals and the corresponding smallest values were and .

     

Lipids ofGlycyrrhiza glabra roots

A petroleum ether extract ofGlycyrrhiza glabra L. roots was investigated. The extract contains 70% neutral lipids and 30% polar lipids. Hydrocarbons, sterols esters, triacylglycerols, free fatty acids, free sterols, and diacylglycerols were identified. The fatty acid contents of all of the acyl-containing lipids were determined. Fourteen fatty acids were identified; the 18 2 fatty acid prevails among the unsaturated acids, and the 16 0 acid prevails among the saturated acids.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 367–370, February, 1995.     

Fibrous Roots of Cimicifuga Are at Risk of Hepatotoxicity

The cause of liver damage by using black cohosh preparation has been concerned but remains unclear. After a preliminary investigation, the black cohosh medicinal materials sold in the market were adulterated with Asian cohosh (Cimicifuga) without removing the fibrous roots. The safety of Cimicifuga rhizome and fibrous roots is unknown and has not been reported. Therefore, in this paper, the rhizome and fibrous roots of Cimicifuga dahurica (Turcz.) Maxim (C. dahurica) were completely separated, extracted with 70% ethanol, and freeze-dried to obtain crude rhizome extract (RC) and fibrous roots extract (FRC). UHPLC-Q-TOF-MS was used to identify 39 compounds in the rhizome and fibrous roots of Cimicifuga, mainly saponins and phenolic acids. In the L-02 cytotoxicity experiment, the IC₅₀ of fibrous roots (1.26 mg/mL) was slightly lower than that of rhizomes (1.417 mg/mL). In the 90-day sub-chronic toxicity study, the FRC group significantly increased the level of white blood cells, ALP, ALT, AST, BILI and CHOL (p < 0.05); large area of granular degeneration and balloon degeneration occurred in liver tissue; and the expression of p-NF-kB in the nucleus increased in a dose-dependent manner. Overall, Fibrous roots of Cimicifuga are at risk of hepatotoxicity and should be strictly controlled and removed during the processing.     

银行存款模型及应用分析

近年来,越来越多的国际知名企业都认识到了从原始数据中寻找规律对决策管理的重要性.一些顶尖级的银行产品企业,象IBM,Oracle,Informix和Sybase等,已经开发了许多用于银行数据挖掘的软件产品,并为国际上的一些著明银行建立了高精度的统计模型以支持银行管理.存款是银行评价业绩的一项重要指标.建立高精度的存款模型有利于银行的日常资金管理,能提高银行的资金利用率,降低成本等.本文以国内某大城市两大银行的实际业务数据为背景,给出了银行存款模型的建立过程,并分析了模型的应用.本文的一些有趣结果对时间序列建模有一定的启示.