On Polynomial Functions over Finite Commutative Rings

Let R be an arbitrary finite commutative local ring. In this paper, we obtain a necessary and sufficient condition for a function over R to be a polynomial function. Before this paper, necessary and sufficient conditions for a function to be a polynomial function over some special finite commutative local rings were obtained.     

Single Qubit and Its Universal Logic Gate Made of a Heisenberg Spin Cluster with Five Particles

We investigate an anisotropic Heisenberg spin cluster with five particles controlled by a time-dependent magnetic field. With the algebraic dynamical method, we obtain the exact analytical solution to the time dependent Schr6dinger equation. Based on the analytical solution, it is shown that the system can be used as a universal single qubit logic gate controlled by the strength and frequency of the magnetic field, and the six special single qubit logic gates can be realized physically. We also discuss the anti-decoherence property of the qubit and its logic gates resulted from particle coupling effect and collectivity of the cluster.     

核糖体失活蛋白的应用研究进展

核糖体失活蛋白(ribosome-inactivating proteins,RIPs)是一类广泛存在于高等植物中能抑制核糖体翻译功能的毒蛋白.本文就核糖体失活蛋白在抗病毒、抗真菌、抗昆虫、抗肿瘤及艾滋病等方面的研究进展及应用作一综述.     

Periodic solutions for a Lotka–Volterra mutualism system with several delays

In the present paper, a Lotka–Volterra type mutualism system with several delays is studied. Some new and interesting sufficient conditions are obtained for the global existence of positive periodic solutions of the mutualism system. Our method is based on Mawhin’s coincidence degree and novel estimation techniques for the a priori bounds of unknown solutions. Our results are different from the existing ones such as those in of Yang et al. [F. Yang, D. Jiang, A. Ying, Existence of positive solution of multidelays facultative mutualism system, J. Eng. Math. 3 (2002) 64–68] and Chen et al. [F. Chen, J. Shi, X. Chen, Periodicity in a Lotka–Volterra facultative mutualism system with several delays, J. Eng. Math. 21 (3) (2004) 403–409].     

超子中子星性质的温度效应

从相对论平均场理论出发,考虑核子、超子和介子的相互作用,研究了温度对中子星组成粒子、状态方程和中子星质量等的影响.发现温度越高,超子在中子星内部出现时的重子数密度越低.当密度较高时,中子星的核心区主要由超子组成,即中子星转变成以奇异粒子为主要成分的超子星,并且这种转变受到温度的影响,温度越高,转变密度越低.由于超子的出现,中子星核心高密度区域的状态方程,对于不同温度,差别不大,所以有限温度中子星的最大质量都在1.8M_⊙附近.这与观测结果相符.     

Ruthenium-catalyzed regioselective synthesis of 2-substituted indoles via ring-opening of epoxides by anilines

Anilines react with epoxides in dioxane at 180°C in the presence of a catalytic amount of a ruthenium catalyst along with tin(II) chloride to afford 2-substituted indoles in moderate to good yields.     

Determination of ultra-trace gold in natural water by graphite furnace atomic absorption spectrophotometry after in situ enrichment with thiol cotton fiber

A simple method of determining ultra-trace Au in natural water was presented by using graphite furnace atomic absorption spectrophotometry (GFAAS) after in situ enrichment with thiol cotton fiber (TCF). The sample solution was adjusted to pH 1.5-2.0 with HCl, then the water sample was passed through a column packed with 0.10-0.20 g TCF and the flow rate was controlled at 20-40 ml min⁻¹. The effects of interferences, such as complexing and oxidizing agents and other elements adsorbed on TCF were overcome by chemical treatments prior to the desorption of Au. The adsorbed Au was adsorbed with 2.0 ml hot acid, then it was extracted with 1.00 ml methyl isobutylketone (MIBK). For a 5 l water sample, the detection limit of Au is 0.02 ng l⁻¹. The relative standard deviation (R.S.D.) for the determination of 1.44 ng l⁻¹ Au was 9.4%.The method was applied to determine ultra-trace Au both in suspended phase and soluble phase in natural water, the concentrations of total Au in natural water samples range from 0.51 to 67.82 ng l⁻¹. The recovery of added 0.50-6.00 ng l⁻¹ Au was 80-95%. The method is useful in prospecting for Au deposits by means of hydrogeochemical methods. The enrichment is carried out in the field, and then the determination of Au is completed later in the laboratory.     

New Kamenev-type oscillation criteria for second-order nonlinear differential equations with damping

Some new oscillation criteria are established for the nonlinear damped differential equation (r(t)y′)′+p(t)y′+q(t)f(y)=0 that are different from most known ones in the sense that they are based on a class of new functions Φ(t,s,r) defined in the sequel. Our results are sharper than some previous results which can be seen by the examples at the end of this paper.     

On Romanoff's constant

In 1934, Romanoff proved that there are a positive proportion natural numbers which can be expressed as the sum of a prime and a power of 2. In this paper, a quantitative version of this theorem is given. We show that the proportion is larger than 0.0868 and for a positive proportion of odd integers the number of such representations is between 1 and 16.