Levitin–Polyak Well-Posedness of Vector Variational Inequality Problems with Functional Constraints

The Levitin–Polyak well-posedness for a constrained problem guarantees that, for an approximating solution sequence, there is a subsequence which converges to a solution of the problem. In this article, we introduce several types of (generalized) Levitin–Polyak well-posednesses for a vector variational inequality problem with both abstract and functional constraints. Various criteria and characterizations for these types of well-posednesses are given. Relations among these types of well-posednesses are presented.     

Inversion of the phase sequence between the cubic and smectic C phases under pressure

The phase behaviour of a thermotropic cubic mesogen of 1,2-bis(4′-n-tetradecyloxybenzoyl)hydrazine BABH-14 was studied under hydrostatic pressure using a polarising optical microscope equipped with a high-pressure optical cell, and the P–T phase diagram was constructed. BABH-14 shows the Cr–Cub–I transition sequence under atmospheric and lower pressures, but the Cub phase is replaced completely by the high-pressure SmC, SmC(hp), phase under higher pressures. There is a narrow intermediate-pressure region between the low- and high-pressure regions, in which the Cr–SmC(hp)–Cub–I phase sequence is recognised. The SmC(hp)–Cub transition line has a positive slope with pressure and there are two triple points: one is for the Cr, Cub and SmC(hp) phases and the other is for the I, Cub and SmC(hp) phases. Comparing the phase sequence of BABH-14 with those for BABH-8 and -10, the pressure-induced inversion of the phase sequence between the cubic and SmC phases occurs in the BABH-n homologous compounds. Another new phenomenon is the formation of the monotropic cubic phase on cooling in the intermediate- and high-pressure regions, and an intriguing phenomenon of the cubic phase appearing twice, i.e. I–Cub–SmC(hp)– Cub–Cr phase transition, occurs in the intermediate-pressure region.     

Some constructions for block sequences of Steiner quadruple systems with error correcting consecutive unions

In this article, we investigate a block sequence of a Steiner quadruple system which contains the blocks exactly once such that the collection of all blocks together with all unions of two consecutive blocks of the sequence forms an error correcting code with minimum distance four. In particular, we give two recursive constructions and obtain infinitely many such sequences by utilizing individual sequences as starters of the recursions. © 2007 Wiley Periodicals, Inc. J Combin Designs 16: 152–163, 2008     

Φ-强增生映象方程解的具误差迭代序列逼近过程

在任意的实Banach空间中,研究Φ-强增生映象T的方程的解的具误差Ishikawa迭代序列的逼近问题,改进并推广了Chidume CE,Osilike M O中的相关研究结果,使结论更具一般性.     

Kantorovich's type theorems for systems of equations with constant rank derivatives

The famous Newton–Kantorovich hypothesis has been used for a long time as a sufficient condition for the convergence of Newton's method to a solution of an equation. Here we present a “Kantorovich type” convergence analysis for the Gauss–Newton's method which improves the result in [W.M. Häußler, A Kantorovich-type convergence analysis for the Gauss–Newton-method, Numer. Math. 48 (1986) 119–125.] and extends the main theorem in [I.K. Argyros, On the Newton-Kantorovich hypothesis for solving equations, J. Comput. Appl. Math. 169 (2004) 315–332]. Furthermore, the radius of convergence ball is also obtained.     

Die Reaktion von AlCl mit H2O in festem Argon: IR‐matrixspektroskopischer Nachweis von HAl(Cl)OH

The Reaction of AlCl with H₂O in Solid Argon: IR Matrixspectroscopic Detection of HAl(Cl)OH After photolytical activation of AlCl and H₂O in solid argon the molecule HAl(Cl)OH is formed. Structure and bonding is characterized by means of normal coordinate analysis and quantum chemical calculations. The complex AlCl···H₂O formed directly after condensation serves as a model system for the stabilisation of aluminium monohalide in a mixture of toluene and ether.     

相关系数平稳序列的均值和方差的参数估计

文献[1]提出了相关系数平稳过程并讨论了它的参数估计方法,其参数估计值采用了数值迭代法.本文在[1]的基础上对一种特殊的相关系数平稳序列的均值和方差提出一种具体的解决方法,得到了确切的均值和方差的参数估计表达式.     

Analysis of a renormalization group method and normal form theory for perturbed ordinary differential equations

For singular perturbation problems, the renormalization group (RG) method of Chen, Goldenfeld, and Oono [Phys. Rev. E. 49 (1994) 4502–4511] has been shown to be an effective general approach for deriving reduced or amplitude equations that govern the long time dynamics of the system. It has been applied to a variety of problems traditionally analyzed using disparate methods, including the method of multiple scales, boundary layer theory, the WKBJ method, the Poincaré–Lindstedt method, the method of averaging, and others. In this article, we show how the RG method may be used to generate normal forms for large classes of ordinary differential equations. First, we apply the RG method to systems with autonomous perturbations, and we show that the reduced or amplitude equations generated by the RG method are equivalent to the classical Poincaré–Birkhoff normal forms for these systems up to and including terms of , where is the perturbation parameter. This analysis establishes our approach and generalizes to higher order. Second, we apply the RG method to systems with nonautonomous perturbations, and we show that the reduced or amplitude equations so generated constitute time-asymptotic normal forms, which are based on KBM averages. Moreover, for both classes of problems, we show that the main coordinate changes are equivalent, up to translations between the spaces in which they are defined. In this manner, our results show that the RG method offers a new approach for deriving normal forms for nonautonomous systems, and it offers advantages since one can typically more readily identify resonant terms from naive perturbation expansions than from the nonautonomous vector fields themselves. Finally, we establish how well the solution to the RG equations approximates the solution of the original equations on time scales of .     

On the sign changes of coefficients of general Dirichlet series

Under what conditions do the (possibly complex) coefficients of a general Dirichlet series exhibit oscillatory behavior? In this work we invoke Laguerre's Rule of Signs and Landau's Theorem to provide a rather simple answer to this question. Furthermore, we explain how our result easily applies to a multitude of functions.