Viscosity solutions of fully nonlinear parabolic systems

In this paper, we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second-order degenerate parabolic equations and their Cauchy-Dirichlet problem. We prove the existence, uniqueness and continuity of viscosity solution by combining Perron's method with the technique of coupled solutions. The results here generalize those in Proc. London Math. Soc. 63 (1991) 212-240 and Comm. Partial Differential Equations 16 (1991) 1095-1128.     

Characterization of Metallo Bis(terpyridine) Diblock Polymers by Nonaqueous Capillary Zone Electrophoresis

A method of nonaqueous capillary zone electrophoresis (CZE) has been developed to characterize block (co)polymers of poly(ethylene oxide) and poly(styrene) containing metallo bis(terpyridine) complexes as bridging units. Specific CZE separation conditions had to be applied, with barium perchlorate dissolved in N-methylformamide (NMF) as background electrolyte and OV-1701-OH deactivated capillaries. For detection UV absorption was measured at a wavelength of 316 nm. Metallo diblock polymers with molecular weights up to 30,000 Da could be analyzed by the proposed nonaqueous CZE method. Experiments performed with polymeric compounds containing Fe, Ni or Ru as central metal ions showed that their electrophoretic mobilities were independent of the type of metal ion. Therefore, the data on the size of the polymeric compounds could be obtained using just one set of calibration standards. Polydispersities of the samples calculated from the experimental results were in correlation with the polydispersities of the polymers used in the synthesis of the metallo diblock polymers. Several polymeric samples contained metallo mono(terpyridine) complexes as impurities. These by-products could be separated from the main product. With symmetrical diblock polymers only one by-product was detected, while with an asymmetric diblock polymer two types of mono-complexes were found. The amount of the mono-complexes present as impurities was dependent on the type of central metal ion (Ni > Fe >> Ru).     

Linearisation and potential symmetries of certain systems of diffusion equations

We consider systems of two pure one-dimensional diffusion equations that have considerable interest in Soil Science and Mathematical Biology. We construct non-local symmetries for these systems. These are determined by expressing the equations in a partially and wholly conserved form, and then by performing a potential symmetry analysis on those systems that can be linearised. We give several examples of such systems, and in a specific case we show how linearising and hodograph-type mappings can lead to new solutions of the diffusion system.     

一类死区非线性输入系统的自适应模糊控制

针对一类具有死区非线性输入的非线性系统,基于滑模控制的基本原理,利用II型模糊逻辑系统对未知函数进行在线逼近,提出了一种具有监督器的自适应模糊滑模控制方法。该方法通过监督控制器保证闭环系统所有信号有界,并通过引入最优逼近误差的自适应补偿项来消除建模误差的影响。通过理论分析,证明了跟踪误差收敛到零。     

大型稀疏无约束最优化问题的行列修正算法

本文提出了一类适用于大型稀疏最优化问题的简单易行的行列修正算法，获得了新算法的局部超一性收敛性，大量的数值试验表明这是一个较为理想的修正算不。新算法同样可以用来求解大型对称性非线性方程组。     

Crossover from BCS-superconductivity to Bose-condensation

Starting from a model of free Fermions in two dimensions with an arbitrary strong effective interaction, we derive a Ginzburg-Landau theory describing the crossover from BCS-superconductivity to Bose-condensation. We find a smooth crossover from the standard BCS-limit to a Gross-Pitaevski type equation for the order parameter in a Bose superfluid. The mean field transition temperature exhibits a maximum at a coupling strength, where the behaviour crosses over from BCS to Bose like with corresponding values of 2 Δ₀/T_c ≈ 5 which are characteristic for high T_c superconductors.     

无严格互补松驰条件的序列线性方程组新算法

该文通过构造特殊形式的有效集来逼近KKT点处的有效集，给出了一个任意初始点下的序列线性方程组新算法，并证明了该算法在没有严格互补松驰条件的情况下具有全局收敛性和一步超线性收敛性。      

代数构造及在Ramsey理论中的应用

这篇文章在伽罗瓦域上的代数构造和关于一些特定类型图的Ramsey数之间建立了一个关系. 研究了关于伽罗瓦域上的代数构造的方程及方程组的解. 我们得到了一些关于二部图的Ramsey数的新的下界和上界.     

Reducing system of parameters and the Cohen-Macaulay property

Let R be a local ring and let (x ₁, …, x _r) be part of a system of parameters of a finitely generated R-module M, where r < dim_R M. We will show that if (y ₁, …, y _r) is part of a reducing system of parameters of M with (y ₁, …, y _r) M = (x ₁, …, x _r) M then (x ₁, …, x _r) is already reducing. Moreover, there is such a part of a reducing system of parameters of M iff for all primes P ε Supp M ∩ V _R(x ₁, …, x _r) with dim_R R/P = dim_R M − r the localization M _P of M at P is an r-dimensional Cohen-Macaulay module over R _P. Furthermore, we will show that M is a Cohen-Macaulay module iff y _d is a non zero divisor on M/(y ₁, …, y _d−1) M, where (y ₁, …, y _d) is a reducing system of parameters of M (d:= dim_R M).     

Capillary zone electrophoresis of cationic and anionic drugs in methanol

The actual mobilities and dissociation constants of acidic and basic pharmaceuticals were determined in methanol. Actual mobilities were derived from the dependence of the effective mobilities of the analytes on the pH of the methanolic background electrolyte solution (pH(MeOH)). The pKa values of the pharmaceuticals in methanol (pK(a,MeOH)) were calculated by non-linear curve fitting to the measured mobility values. It was found that the shift in pKa value (when compounds were transferred from water to methanol) increased with the acidity of the analyte. The average pKa shift for compounds exhibiting acidic properties in water was ca. 5.5 units, and the shift for basic compounds about 2 units. As was shown for a mixture of beta-blockers, the calculated actual mobilities and pKa values can be utilised in the optimisation of pH conditions for separation. The practical value of the method was illustrated by the analysis of urine samples.