A discontinuous Galerkin method for the Cahn-Hilliard equation

The Cahn-Hilliard equation is modeled to describe the dynamics of phase separation in glass and polymer systems. A priori error estimates for the Cahn-Hilliard equation have been studied by the authors. In order to control accuracy of approximate solutions, a posteriori error estimation of the Cahn-Hilliard equation is obtained by discontinuous Galerkin method.     

The effect of Mn substitution on thermoelectric properties of Ca3MnxCo4−xO9 at low temperatures

The effects of partial substitution of Mn for Co on the thermoelectric properties of Ca₃Mn_xCo_4−xO₉ (x=0, 0.03, 0.9), prepared by sol-gel process, were investigated at the temperatures from 380 K down to 5 K. The results indicate that the substitution of Mn for Co results in increase in thermopower at temperatures >∼80 K, and substantial (23-31% at 300 K) decrease in lattice thermal conductivity in the whole temperature range investigated. The temperature behavior of ZT suggests that Ca₃Mn_xCo_4−xO₉ with light Mn substitution would be a promising candidate for high-temperature thermoelectric applications.     

Repetition rate multipliers for efficient implementation of multiphoton and pump-probe fluorescence microscopy

With the advances in pulsed laser systems, microscopic imaging techniques such as multiphoton and pump-probe fluorescence microscopy have developed into effective tools for investigating intensity and time-resolved phenomena inside biological systems. However, pulsed lasers used in these techniques usually are commercial systems with repetition frequencies of around 80 MHz. While these systems have proven to be adequate for multiphoton and pump-probe microscopic imaging applications, the temporal separation of the laser pulse train (around 12.5 ns) is long compared to the fluorescence lifetimes of many common fluorescence species. In this work, we present the designs of repetition rate multipliers based on passive optical components that can be used to increase the efficiency in multiphoton and pump-probe fluorescence microscopy. Depending on the lifetime of fluorescence molecules under investigation, the passive repetition rate multiplier can increase the duty cycle of multiphoton or pump-probe microscopy up to fourfold.     

功率超声对溶液性质的影响

本文研究了在功率超声作用下，电解质溶液，小分子溶液和大分子溶液的粘度，表面张力和电导率等物理化学性质的变化规律。实验结果表明，在超声波作用下，溶液的粘度和表面张力暂时下降，而电导率长期升高。     

Catalytic Hydrosilylation of Furan, Thiophene, and Pyridine Aldimines

The addition of hydrosilanes (HSiEt₃, HSiMe₂Ph, H₂SiPh₂) to the CH=N bond of heterocyclic azomethines has been studied in the presence of monovalent complexes of rhodium and palladium. The effect on the reaction of the CF₃ group of the aldimines, which were obtained from O-, S-, and N-heteroaromatic aldehydes and 2-trifluoromethylaniline, has been clarified, as were other regularities of the processes being studied. A series of corresponding furans, thiophenes, and pyridine amines has been synthesized.     

Trace cocharacters and the Kronecker products of Schur functions

It follows from the theory of trace identities developed by Procesi and Razmyslov that the trace cocharacters arising from the trace identities of the algebra M_r(F) of r×r matrices over a field F of characteristic zero are given by TC_r,n=∑_λΛr(n)χ^λχ^λ where χ^λχ^λ denotes the Kronecker product of the irreducible characters of the symmetric group associated with the partition λ with itself and Λ_r(n) denotes the set of partitions of n with r or fewer parts, i.e. the set of partitions λ=(λ₁λ_k) with kr. We study the behavior of the sequence of trace cocharacters TC_r,n. In particular, we study the behavior of the coefficient of χ^(ν,n−m) in TC_r,n as a function of n where ν=(ν₁ν_k) is some fixed partition of m and n−mν_k. Our main result shows that such coefficients always grow as a polynomial in n of degree r−1.     

Spreading Code Design Using a Global Optimization Method

The performance of a code division multiple access system depends on the correlation properties of the employed spreading code. Low cross-correlation values between spreading sequences are desired to suppress multiple access interference and to improve bit error performance. An auto-correlation function with a distinct peak enables proper synchronization and suppresses intersymbol interference. However, these requirements contradict each other and a trade-off needs to be established. In this paper, a global two dimensional optimization method is proposed to minimize the out-of-phase average mean-square aperiodic auto-correlation with average mean-square aperiodic cross-correlation being allowed to lie within a fixed region. This approach is applied to design sets of complex spreading sequences. A design example is presented to illustrate the relation between various correlation characteristics. The correlations of the obtained sets are compared with correlations of other known sequences.     

The Exact Hausdorff Measure Function of the Level Sets of Multi-parameter Symmetric Stable Process

In this paper, we investigate the Hausdorff measure for level sets of N-parameter Rd-valued stable processes, and develop a means of seeking the exact Hausdorff measure function for level sets of N-parameter Rd-valued stable processes. We show that the exact Hausdorff measure function of level sets of N-parameter Rd-valued symmetric stable processes of index α is Ф（r） = r^N-d/α （log log l/r）d/α when Nα 〉 d. In addition, we obtain a sharp lower bound for the Hausdorff measure of level sets of general （N, d, α） strictly stable processes.     

Unique continuation along curves and hypersurfaces for second order anisotropic hyperbolic systems with real analytic coefficients

In this paper we prove the following kind of unique continuation property. That is, the zero on each geodesic of the solution in a real analytic hypersurface for second order anisotropic hyperbolic systems with real analytic coefficients can be continued along this curve.