Representation type of Jordan algebras

The problem of classification of Jordan bimodules over (non-semisimple) finite dimensional Jordan algebras with respect to their representation type is considered. The notions of diagram of a Jordan algebra and of Jordan tensor algebra of a bimodule are introduced and a mapping Qui is constructed which associates to the diagram of a Jordan algebra J the quiver of its universal associative enveloping algebra S(J). The main results are concerned with Jordan algebras of semi-matrix type, that is, algebras whose semi-simple component is a direct sum of Jordan matrix algebras. In this case, criterion of finiteness and tameness for one-sided representations are obtained, in terms of diagram and mapping Qui, for Jordan tensor algebras and for algebras with radical square equals to 0.     

Efficient on-line algorithms for Euler diagram region computation

Euler diagrams are an accessible and effective visualisation of data involving simple set-theoretic relationships. Sets are represented by closed curves in the plane and often have wellformedness conditions placed on them in order to enhance comprehensibility. The theoretical underpinning for tool support has usually focussed on the problem of generating an Euler diagram from an abstract model. However, the problem of efficient computation of the abstract model from the concrete diagram has not been addressed before, despite this computation being a necessity for computer interpretations of user drawn diagrams. This may be used, together with automated manipulations of the abstract model, for purposes such as semantic information presentation or diagrammatic theorem proving. Furthermore, in interactive settings, the user may update diagrams “on-line” by adding and removing curves, for example, in which case a system requirement is the update of the abstract model (without the necessity of recomputation of the entire abstract model). We define the notion of marked Euler diagrams, together with a method for associating marked points on the diagram with regions in the plane. Utilising these, we provide on-line algorithms which quickly compute the abstract model of a weakly reducible wellformed Euler diagram (constructible as a sequence of additions or removals of curves, keeping a wellformed diagram at each step), and quickly updates both the set of curves in the plane as well as the abstract model according to the on-line operations. Efficiency is demonstrated by comparison with a common, naive algorithm. Furthermore, the methodology enables a straightforward implementation which has subsequently been realised as an application for the user classification domain.     

The study of melting stage of bulk silicon using molecular dynamics simulation

The melting stage of bulk silicon is studied using classical molecular dynamics simulation. The mean square displacement and diffusion coefficient are focused allowing statistics analysis of the dynamics displacement of each atom. Three stages of the melting processes, premelting, accelerated melting and relaxation, are resolved. The structural development is evaluated through the stages by Lindemann index, non-Gaussian parameter and the second neighbor coordination number. The studies emphasize the observation that premelting occurs in the ideal crystal on melting.     

Phase polymorphism of [Ni(DMSO)6](BF4)2 studied by differential scanning calorimetry

The tetrafluoroborate of hexadimethylsulfoxidenickel(II) was synthesized and studied by differential scanning calorimetry. Seven solid phases of [Ni(DMSO)₆](BF₄)₂ were revealed. Specifically, six phase transitions of the first order were detected between the following solid phases: stable KIb → stable KIa at T _C6 = 335 K, metastable KIIb → metastable KIIa at T _C5 = 368 K, metastable KIII → overcooled phase KI at T _C4 = 378 K, metastable KIIa → overcooled phase KI at T _C3 = 396 K, stable KIa → stable KI at T _C2 = 415 K and stable KI → stable K0 at T _C1 = 433 K. [Ni(DMSO)₆](BF₄)₂ begins decomposition at 440 K with loss of one DMSO molecule per formula unit forming [Ni(DMSO)₅](BF₄)₂ (phase L0) which melts next in two steps in the temperature range 550–593 K. From the entropy changes connected both with melting and with phase transitions, it can be concluded that phases KI, overcooled KI and K0 are orientationally dynamically disordered (ODIC) crystals. Stable phases KIb, KIa and metastable phase KIII are ordered solid phases. Metastable phase KIIa and metastable phase KIIb are more or less ordered solid phases.     

Melting and related precursor cooperative phenomena in chemically bonded assemblies

A number of experimental studies of condensed matter assemblies with different types of chemical bonding will provide the focus of this work. Condensed compounds X(CH₃)₄, with X?=?C, Si or Ge, are the first of such assemblies; two phase boundaries in the pressure--temperature plane being studied: melting and a solid phase boundary heralding orientational disordering of molecules still however on a lattice. Secondly, directionally bonded d-electron transition metals such as Ni, Pd and Nb will be treated. Here, melting is the main focus, but the precursor transition is now the separation of a high-temperature ductile solid from a lower temperature mechanically brittle phase. A dislocation-mediated model of these transitions is discussed, leading into the third area of covalently bonded solids graphite and silicon. Here topological defect models again provide the focus; both dislocations and rotation-dislocations now being invoked. Some qualitative suggestions are made to interpret the melting curve of graphite subjected to high pressure.     

Melting curve T_m(p) of sodium under pressure p: transition from a Wigner-like nuclear bcc structure near 30 GPa to lower symmetry states with negative dT_m / d p at higher pressures

It is known experimentally that the melting temperature T _m(p) of Na as a function of pressure p increases with p out to ～20 GPa and then passes through a maximum. Here, we interpret the behavior as passing from classical Wigner-like bcc nuclear structure at low pressures to a structure out to about 60 GPa where the melting is mediated by topological defects.     

Derivative UV-VIS Spectrophotometry for Porphyrins Interactions in Photodynamic Therapy

Derivative spectrophotometry is an analytical technique of great utility for extracting both qualitative and quantitative information from spectra composed of unresolved bands by calculating and plotting one of the mathematical derivatives of a spectral curve. In photodynamic therapy (PDT) by irradiation with light, the porphyrin used as drugs induced DNA cleavage mainly via a Type II (singlet oxygen mediated) mechanism, and more rarely a Type I (radicals mediated) mechanism. In the present paper, it is estimated the distinct interactions between DNA and 5,10,15,20-tetra-sulphonated-phenyl-porphyrin (TSPP) by means of: UV-Vis derivative spectrophotometry coupled with melting point, fluorescence, and polarization fluorescence techniques. An exemplification of TSPP effect on DNA from K562 cells is also discussed.     

CHANGES IN MELTING BEHAVIOR AND MORPHOLOGY ON ANNEALING OF LINEAR AND BRANCHED POLYETHYLENE

Changes in morphology and melting behavior of various types of commercial polyethylenes as a result of annealing were studied using differential scanning calorimetry, transmission electron microscopy, and density measurements. The range of polyethylenes whose densities varied between 0.96 and 0.90 g/cm³ included linear polyethylene (LPE), high-density polyethylene, a 1-octene copolymer traditional linear low density polyethylene, low density polyethylene, and a 1-octene copolymer prepared by Dow's INSITE constrained geometry catalysts technology. Two sets of samples were initially prepared by fast cooling and slow cooling from the melt. Despite an initial lower crystalline content and crystal thickness for the fast cooled (FC) branched polyethylene samples, a higher melting temperature than for the slow cooled (SC) samples was found using a 10°C/min heating rate. In concordance with a recent work, melting–recrystallization processes are held responsible for the anomalous behavior. The annealing treatment consisted of heating the two sets of samples at 1°C/min from room temperature to a temperature located at the start of the endotherm. The thermal treatment stabilizes the crystals through an increase in their thickness, which prevents melting–recrystallization processes from taking place on subsequent heating. A lower melting temperature after annealing was observed for the FC branched polyethylene samples. No such behavior was found for the SC samples and even for the FC LPE sample.     

金属铜的晶体结构与热力学性质的第一性原理计算

基于第一性原理,利用密度泛函理论(DFT)和密度泛函的微扰理论(DFPT),以及广义梯度近似(GGA),研究了过渡金属Cu的晶体结构、能量、电子能带和态密度、声子的能带结构和态密度,以及其在298.15 K下的热容,体积模量,格林艾森参数和体胀系数等热力学函数并与实验值作了对比.通过分析Cu的晶格几何与能量之间的关系,讨论了金属Cu的固-液相变与晶格声子振动能量之间可能的内在联系,首次提出直接得到Cu熔化温度T_m的静力学方法,研究了熔化温度与压强的关系.计算结果与实验值符合较好,明显优于分子动力学模拟的结果.