Modular Categories and Orbifold Models

In this paper, we try to answer the following question: given a modular tensor category ? with an action of a compact group G, is it possible to describe in a suitable sense the “quotient” category ?/G? We give a full answer in the case when ?=?ℯ? is the category of vector spaces; in this case, ?ℯ?/G turns out to be the category of representation of Drinfeld's double D(G). This should be considered as the category theory analog of the topological identity {pt}/G=BG. This implies a conjecture of Dijkgraaf, Vafa, E. Verlinde and H. Verlinde regarding so-called orbifold conformal field theories: if ? is a vertex operator algebra which has a unique irreducible module, ? itself, and G is a compact group of automorphisms of ?, and some not too restrictive technical conditions are satisfied, then G is finite, and the category of representations of the algebra of invariants, ? ^G , is equivalent as a tensor category to the category of representations of Drinfeld's double D(G). We also get some partial results in the non-holomorphic case, i.e. when ? has more than one simple module. Received: 27 August 2001 / Accepted: 1 March 2002     

Hierarchical visual data mining for large-scale data

Summary  An increasingly important problem in exploratory data analysis and visualization is that of scale; more and more data sets are much too large to analyze using traditional techniques, either in terms of the number of variables or the number of records. One approach to addressing this problem is the development and use of multiresolution strategies, where we represent the data at different levels of abstraction or detail through aggregation and summarization. In this paper we present an overview of our recent and current activities in the development of a multiresolution exploratory visualization environment for large-scale multivariate data. We have developed visualization, interaction, and data management techniques for effectively dealing with data sets that contain millions of records and/or hundreds of dimensions, and propose methods for applying similar approaches to extend the system to handle nominal as well as ordinal data.     

Freezing of a stripe liquid

The existence of a stripe-liquid phase in a layered nickelate, La(1.725)Sr(0.275)NiO(4), is demonstrated through neutron scattering measurements. We show that incommensurate magnetic fluctuations evolve continuously through the charge-ordering temperature, although an abrupt decrease in the effective damping energy is observed on cooling through the transition. The energy and momentum dependence of the magnetic scattering are parametrized with a damped-harmonic-oscillator model describing overdamped spin waves in the antiferromagnetic domains defined instantaneously by charge stripes.     

ICPAQGP2001: Conference summary

I review recent progress in ultrarelativistic nucleus-nucleus collisions, and the connection of this field to modern QCD theory of deconfinement and/or chiral symmetry restoration. The talks at this Conference have shown a convergence of data and theory as far as the CERN SPS investigations at √s = 17 GeV are concerned; the parton-hadron phase boundary seems now located atT = 170 ± 10 MeV. New data from RHIC and direct photon production results from CERN have been shown that point out the field’s future direction: analysis of partonic matter atT > 200 MeV. Astrophysics analysis was shown to be linked crucially to further theoretical progress with non-perturbative QCD.     

Inhomogeneous cosmology with spinning fluid in high-dimensional space-time

We study the evolution of an inhomogeneous cosmology with spinning fluid in high-dimensional space-time. Using the Szekeres class II metric and the energy-momentum tensor derived by Ray and Smalley, we find evolving solutions, including an exponential inflation.     

Focused ion beam fabrication and magneto-electrical transport properties of La0.67Ca0.33MnO3 nanobridge

La_0.67Ca_0.33MnO₃ particle films with an average particle size of ~150 nm were grown on single-crystal silicon substrate using pulsed electron deposition technique and then focused ion beam was introduced to fabricate nanobridge in size of 300 × 900 nm on the particle film. The magneto-transport properties of both samples were studied. For the film, there is only one resistance peak at 182 K in temperature-dependent resistance (R–T) curves, which is far lower than ferromagnetic–paramagnetic transition temperature (T _C) of 250 K. When compared to the film, double peaks were observed in both R–T curves and magnetoresistance dependent on temperature (MR–T) curves of the nanobridge, one peak is at 186 K, which is very close to metal–insulator transition temperature (T _P) of film, the other one is at 250 K, which is close to the T _C of film, and these two peaks caused separately by grain and grain boundary (GB), which demonstrated that the electrical transport behavior of grain was separated from that of GB.     

The optimized preparation and electrochemical properties of LiMn1.95Co0.05O4 and Al2O3-coated LiMn1.95Co0.05O4

Cathode material LiMn_1.95Co_0.05O₄ for lithium ion battery was synthesized via solid state reaction, and calcination temperature and time were investigated, respectively. Thermogravimetry (TG) and differential thermal analysis (DTA) measurements were utilized to determine the calcination temperature of precursor sample. The optimized calcination temperature and time are 850 °C and 15 h. The surface of LiMn_1.95Co_0.05O₄ cathode is coated using Al₂O₃ coating materials. The phase structures, surface morphologies, and element types of the prepared LiMn_1.95Co_0.05O₄ and Al₂O₃-coated LiMn_1.95 Co_0.05O₄ were characterized by X-ray diffraction (XRD), scanning electron microscope (SEM), and energy spectrum analysis (EDS). The 0.5 wt% Al₂O₃-coated compound exhibited better specific capacity and capacity retention than bare sample. The initial discharge capacity was 140.9 mAh/g and capacity retention was 96.7 % after 10 cycles at 0.1 C. Such enhancements are attributed to the presence of a stable Al₂O₃ layer which acts as the interfacial stabilizer on the surface of LiMn_1.95Co_0.05O₄.     

Hydrothermal synthesis of MnO2 nanowires: structural characterizations,optical and magnetic properties

In this paper, 1D single-crystalline MnO₂ nanowires have been successfully synthesized by hydrothermal method using KMnO₄ and (NH₄)₂S₂O₈ as raw materials. X-ray diffraction patterns and high-resolution TEM images reveal pure tetragonal MnO₂ phase with diameters of 15–20 nm. Photoluminescence studies exhibited a strong ultraviolet (UV) emission band at 380 nm, blue emission at 452 nm and an extra weak defect-related green emission at 542 nm. UV–visible spectrophotometery was used to determine the absorption behavior of nanostructured MnO₂ and a direct optical band gap of 2.5 eV was acquired by Davis–Mott model. The magnetic properties of the products have been evaluated using vibrating sample magnetometer, which showed that MnO₂ nanowires exhibited a superparamagnetic behavior at room temperature. The magnetization versus temperature curve of the as-obtained MnO₂ nanowires shows that antiferromagnetic transition temperature is 99 K.     

Preparation and ionic conductivity of composite polymer electrolytes based on hyperbranched star polymer

Hyperbranched star polymer HBPS-(PPEGMA) _x was synthesized by atom transfer radical polymerization (ATRP) using hyperbranched polystyrene (HBPS) as macroinitiator and poly(ethylene glycol) methyl ether methacrylate (PEGMA) as monomer. The structure of the prepared hyperbranched star polymer was characterized by ¹H NMR, ATR-FTIR, and GPC. Polymer electrolytes based on HBPS-(PPEGMA) _x , lithium salt, and/or nano-TiO₂ were prepared. The influences of lithium salt concentration and type, nano-TiO₂ content, and size on ionic conductivity of the obtained polymer electrolytes were investigated. The results showed that the low crystallinity of the prepared polymer electrolyte was caused by the interaction between lithium salt and polymer. The addition of TiO₂ into HBPS-(PPEGMA) _x /LiTFSI improved the ionic conductivity at low temperature. The prepared composite polymer electrolyte showed the highest ionic conductivity of 9?×?10^?5 S cm^?1 at 30 °C when the content of TiO₂ was 15 wt% and the size of TiO₂ was 20 nm.     

奇异积分算子在实与复分析中的应用

本文是一份综合报告,它基于作者的一部份研究工作和他在北京师范大学的五次讲演稿,以奇异分算子作为桥梁联结函数空间的结果和偏微分方程的结果作了阐述,它包括奇次空间上的调和分析,并应用到多复变函数论上,综述了右的结果并提出未解决的问题。