A Problem in Applied Topology: on the Selection of Cycles for the Flexibility Analysis of Skeletal Structures

A theory of generalized statical bases is developed for usein the flexibility methods as applied to skeletal structuralproblems. It is shown that any maximal linearly independentset of cycles of the integral cycle group of a linear graphmodel of the structure may be used in the formation of a staticalbasis. Such a set of simple cycles is found by embedding thisgraph into a two-dimensional polyhedron. Cell complexes areformed so that the simple cycles bounding the 2-cells correspondto substructures on which a statical basis may be constructed.Two methods are given for the construction of the embeddings.In one a collapsible complex is formed from a union of a setof disks; while in the other the embedding is into an orientablemanifold which is modified to form an admissible complex.     

额尔齐斯河（新疆段）水质评价

对额尔齐斯河1993～1999年的水质污染数据用因子分析的方法进行分析,得到评价额尔齐斯河水质污染的有机污染因子,综合污染因子和金属污染因子,并以此对额尔齐斯河水质污染情况作出较客观的评价。     

向量随机测度关于白噪声的积分的收敛性

本文主要讨论s.i.s.向量随机测度关于白噪声的积分的收敛性,我们得到了如下结果设X是具type2的Banach空间,{Fn}∞n=0是一列被μ所控制的X值s.i.s随机测度,对任意的E∈∑,E[Fn(E)]=0,E‖Fn(E)‖2＜+∞,{Fn(E)}∞n=0是一致W弱可积,且{Fn}∞n=1弱几乎收敛到F0,则(1)对每个n≥0∫FndW是s.i.s向量随机测度;(2)∫FndWwp→∫F0dW.     

Investigation of internal and external potentials acting on benzyl halides dissolved in different nematic solvents

(Molecular Physics, 1994, 83, 309–326)     

Preparation and characterization of poly(butylene terephthalate)/poly(ethylene terephthalate) copolymers via solid‐state and melt polymerization

To increase the T_g in combination with a retained crystallization rate, bis(2‐hydroxyethyl)terephthalate (BHET) was incorporated into poly(butylene terephthalate) (PBT) via solid‐state copolymerization (SSP). The incorporated BHET fraction depends on the miscibility of BHET in the amorphous phase of PBT prior to SSP. DSC measurements showed that BHET is only partially miscible. During SSP, the miscible BHET fraction reacts via transesterification reactions with the mobile amorphous PBT segments. The immiscible BHET fraction reacts by self‐condensation, resulting in the formation of poly(ethylene terephthalate) (PET) homopolymer. ¹H‐NMR sequence distribution analysis showed that self‐condensation of BHET proceeded faster than the transesterification with PBT. SAXS measurements showed an increase in the long period with increasing fraction BHET present in the mixtures used for SSP followed by a decrease due to the formation of small PET crystals. DSC confirmed the presence of separate PET crystals. Furthermore, the incorporation of BHET via SSP resulted in PBT‐PET copolymers with an increased T_g compared to PBT. However, these copolymers showed a poorer crystallization behavior. The modified copolymer chain segments are apparently fully miscible with the unmodified PBT chains in the molten state. Consequently, the crystal growth process is retarded resulting in a decreased crystallization rate and crystallinity. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 882–899, 2007.     

Modelling the velocity of air through beds of cereal grains

The quality of cereal grains in storage will deteriorate toan unacceptable level if they are not kept dry and cool. Tomodel the drying and cooling process, an accurate knowledgeof the airflow distribution is required. In this paper, theequations used to model the air velocity are analysed. To study the flow of air through a typical drying system forstored grain, a two-dimensional rectangular bin is considered,with a single source of air on the bin floor. Two paths ofstudyare undertaken: the first is a linear analysis for low velocities,and following on from this is a nonlinear approach for largervelocities. The linear analysis is used to study a bin witha semi-infinite height, and the drying pattern is studied inthis bin using the air traverse time. Then bins with a finiteheight are analysed: it is shown that, for tall enough bins,the semi-infinite solution is accurate enough. A perturbationanalysis is used to study the semi-infinite bin when the airvelocity is too large for the linear analysis to be accu rate.It is shown that the effect of the nonlinearity is to move theair away from the high-velocity regions towards the areas oflower velocity.     

On a Moving Boundary Problem Aristing in Fluidized Bed Combustion

We consider a model describing the combustion of a coal particlein a fluidized bed, in which attrition plays a dominant role.The model consists of (1) a quasi-linear elliptic equation forthe oxygen concentration, supplemented by boundary conditionson the moving surface representing the burning particle interface,(2) an evolution equation for the carbon consumption, and (3)an equation governing the motion of the interface in terms ofa specified function of the carbon consumption at the interface.We prove a global existence and uniqueness result, togetherwith a priori bounds for the solution; the existence of travellingwaves will also be established.     

Commutators with idempotent values on multilinear polynomials in prime rings

Let R be a prime ring of characteristic different from 2, C its extended centroid, d a nonzero derivation of R, f(x ₁, . . . , x _n ) a multilinear polynomial over C, ρ a nonzero right ideal of R and m > 1 a fixed integer such that

$$\qquad \left ([d(f(r_{1},\ldots ,r_{n})),f(r_{1},\ldots ,r_{n})]\right )^{m}=[d(f(r_{1},\ldots ,r_{n})),f(r_{1},\ldots ,r_{n})] $$

for all r ₁, . . . , r _n ∈ρ. Then either [f(x ₁,…,x _n ),x _n+1]x _n+2 is an identity for ρ or d(ρ)ρ = 0.

     

La0.789Yb0.20Ho0.001Tm0.01F3纳米立方体的溶剂热合成及白色上转换发光性质

采用溶剂热方法制备了La0.789Yb0.20Ho0.001Tm0.01F3纳米立方体,并利用粉末X射线衍射仪、透射电子显微镜和X射线能谱仪表征了其组成、结构和形貌,用荧光分光光度计测量了样品的室温上转换发射光谱,结果表明,样品具有红、绿和蓝色3个发射带,其辐射跃迁分别归属于Tm3+的1G4→3H6(蓝色)和1G4→3...