Theoretical investigation of magnetic property in paramagnetic neodymium gallium garnet under high magnetic field

The magnetic property in neodymium gallium garnet (NdGaG) is studied by the quantum theory. The ground configuration split states are calculated taking into account the spin–orbit interaction and crystal field effect. Taking account of the Nd–Nd exchange interaction, a good agreement between experimental and theoretical values can be obtained for the variation of the magnetic moment with the external magnetic field under “extreme” conditions (low temperature and high magnetic field). Moreover, the temperature dependence of magnetic moment and the magnetic susceptibility χ is also discussed. Above 30 K, the magnetization (M) shows a linear field (H_e) dependence.     

养殖池塘沉积物的重金属分布及污染特征

浙江省淅西北地区淡水养殖池塘沉积物重金属调查研究表明，养殖池塘沉积物中7种重金属元素分布不均衡，差异也较大，除Hg和Cr元素外，其余重金属元素已大大超过土壤本底值．虽然其实测含量都未超出国家规定的标准值范围，但沉积物中重金属元素对养殖水环境、养殖品种存在的潜在污染与危害值得关注．污染指数评价显示，养殖池塘沉积物中主要污染物质为Cu和Cr，而Hg、Pb污染程度相对较轻．     

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.     

Eigenvalue and stability of singular differential delay systems

The eigenvalue and the stability of singular differential systems with delay are considered. Firstly we investigate some properties of the eigenvalue, then give the exact exponential estimation for the fundamental solution, and finally discuss the necessary and sufficient condition of uniform asymptotic stability.     

Controlled/living polymerization of 2‐(diethylamino)ethyl methacrylate and its block copolymer with tert‐butyl methacrylate by atom transfer radical polymerization

Polymerization of 2‐(diethylamino)ethyl methacrylate (DEAEMA) via homogeneous atom transfer radical polymerization under various reaction conditions is described. The effects of the initiators and solvents were examined. With 1,1,4,7,10,10‐hexamethyl triethylenetetramine/copper(I) chloride/p‐toluenesulfonyl chloride as the ligand/catalyst/initiator system in methanol, poly(DEAEMA) with a polydispersity index as low as 1.07 was synthesized. Kinetic studies demonstrated the polymerization was very well controlled and exhibited the living characteristic of the process. Well‐defined block copolymers of DEAEMA and tert‐butyl methacrylate (tBMA) were successfully synthesized. The copolymers could be synthesized with equally good results by starting with either p(DEAEMA) or p(tBMA) as the macroinitiators. However, only the macroinitiators terminated with chlorine should be used. The corresponding macroinitiators with bromine as a transferable group did not yield well‐defined copolymers. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2688–2695, 2003     

D-N交替法与Schwartz交替法的收敛关系分析

This paper has demonstrated that the Schwartz alternating process must converge if D-N alternating process has converged. Its technique is that the overlapping regions in Schwartz alternating process are considered as independent domains, then Schwartz alternating process could be transformed into D-N alter-nating process. Finally the convergence estimation of Schwartz alternating process could be obtained. The results show that its convergence rate is same as that of D-N alternating process.     

Vassiliev invariants for braids on surfaces

We show that Vassiliev invariants separate braids on a closed oriented surface, and we exhibit a universal Vassiliev invariant for these braids in terms of chord diagrams labeled by elements of the fundamental group of the surface.

     

The Computational Complexity of the Chow Form

We present a bounded probability algorithm for the computation of the Chowforms of the equidimensional components of an algebraic variety. In particular, this gives an alternative procedure for the effective equidimensional decomposition of the variety, since each equidimensional component is characterized by its Chow form. The expected complexity of the algorithm is polynomial in the size and the geometric degree of the input equation system defining the variety. Hence it improves (or meets in some special cases) the complexity of all previous algorithms for computing Chow forms. In addition to this, we clarify the probability and uniformity aspects, which constitutes a further contribution of the paper. The algorithm is based on elimination theory techniques, in line with the geometric resolution algorithm due to M. Giusti, J. Heintz, L. M. Pardo, and their collaborators. In fact, ours can be considered as an extension of their algorithm for zero-dimensional systems to the case of positive-dimensional varieties. The key element for dealing with positive-dimensional varieties is a new Poisson-type product formula. This formula allows us to compute the Chow form of an equidimensional variety from a suitable zero-dimensional fiber. As an application, we obtain an algorithm to compute a subclass of sparse resultants, whose complexity is polynomial in the dimension and the volume of the input set of exponents. As another application, we derive an algorithm for the computation of the (unique) solution of a generic overdetermined polynomial equation system.     

Photoluminescence characteristics of ZnTiO3: Bi nanocrystals

The photoluminescence properties of the Bi³⁺ in sol-gel derived ZnTiO₃ nanocrystals have been investigated. An ultra-violet emission at 360 nm and a visible emission band at 506 nm have been observed, originating from two kinds of emission centers. The former is ascribed to the ³P₁-¹S₀ transition of Bi³⁺ and the latter to the recombination of the electrons with the photo-generated holes trapped in the zinc vacancies. In all cases the latter contribution is predominant.     

Investigating and ordering Quadrilaterals and their analogies in space—problem fields with various aspects

Problem fields with one or two generating problems and possibilities of varying existing problems give a good chance for self-activities of students and can be used for reaching different general aims. In this paper some topics concerning quadrilaterals will be presented. I hope they will animate teachers for more problem orientation in mathematics education. First we will reflect about different types of convex and non-convex quadrilaterals and possibilities of ordering them. Then we focus on middle-quadrilaterals and types of quadrilaterals with special middle-quadrilaterals as well as their logical ordering. Finally we investigate the analogies in space to the parallelogram and its sub-types and order them in the “house of parallelepipeds”.