Preparation of Papers

We motivate the study of a vector variational inequality by a practical flow equilibrium problem on a network, namely a generalization of the well-known Wardrop equilibrium principle. Both weak and strong forms of the vector variational inequality are discussed and their relationships to a vector optimization problem are established under various convexity assumptions.     

带有背景矢量场的标量场暗能量模型

讨论了带有背景矢量场的动力学标量场作为暗能量在闭宇宙的情形下的演化. 选取适当的标量场势函数后, 在得到的暗能量有效状态方程中, 参数w在红移z≈0.2处可以越过－1, 而且在z≈1.7处宇宙从减速膨胀的状态转变为加速膨胀状态, 这与最近的宇宙学观测相符.     

On the Spectral Multiplicity of Some Volterra Operators in Sobolev Spaces

Mathematical Notes -     

Partition Lattice q-Analogs Related to q-Stirling Numbers

We construct a family of partially ordered sets (posets) that are q-analogs of the set partition lattice. They are different from the q-analogs proposed by Dowling [5]. One of the important features of these posets is that their Whitney numbers of the first and second kind are just the q-Stirling numbers of the first and second kind, respectively. One member of this family [4] can be constructed using an interpretation of Milne [9] for S[n, k] as sequences of lines in a vector space over the Galois field F _q. Another member is constructed so as to mirror the partial order in the subspace lattice.     

A Simple Proof for a Property of the Vector Space Ⅴ Over the Field F

<正> In this paper we'll prove a fundameutal property of the vector space by means of the ex-tension field,i.e.the numbers of the elements of a basis of the vector space V over the field Fequal to the d imensions(V:F).     

Constructive and Destructive Two-Pulse Excitation Investigated with a White-Light Michelson Interferometer

Linear propagation of two pulses through methanol solution of aluminum phthalocyanine chloride is investigated using a modified white-light Michelson interferometer. The observed coherence time of the white light is 6 fs, and the separation between the two-excitation pulses is set to about 10 fs. The excitation is dependent on the phase-relation between the two pulses. We have observed an enhancement of the excitation when the two pulses are in-phase and strong suppression of the excitation when the two pulses are out of phase by π.     

Vector Lattices on a Set of Two Generators

It is proved that the center of an automorphism group Aut(FVL2) of a free vector lattice FVL2 on a set of two free generators is isomorphic to a multiplicative group of positive reals. It is shown that the free vector lattice FVL2 has an isomorphic representation by continuous piecewise linear functions of the real line; as a consequence, the ideal lattice and the root system for rectifying ideals in FVL2 are amply described. Similar results are obtained for a free vector lattice FVL2 _Q 2 generated by two elements over a field of rational numbers.     

The Essential Component of the Solution Set for Vector Equilibrium Problems

In the paper, by using Ky Fan’s section theorem, we obtain an existence theorem for vector equilibrium problems. Motivated by the ideas of Kinoshita and McLennan, we introduce the concept of the essential component of the solution set for vector equilibrium problems, and we prove that there exists at least one essential component of the solution set for every vector equilibrium problem satisfying some conditions. Research was partially supported by the Natural Science Foundation of Guangdong Province, P. R. China.     

Synthesis and characterization of model 3‐miktoarm star copolymers of poly(dimethylsiloxane) and poly(2‐vinylpyridine)

3‐Miktoarm star copolymers, 3μ‐D₂V, with two poly(dimethylsiloxane) (PDMS) and one poly(2‐vinylpyridine) (P2VP) arm, were synthesized by using anionic polymerization–high vacuum techniques and (chloromethylphenylethyl)methyl dichlorosilane, heterofunctional linking agent, with two SiCl groups and one CH₂Cl group. The synthetic strategy involves the selective reaction of the two ? SiCl groups with PDMSOLi living chains, followed by reaction of the remaining chloromethyl group with P2VPLi. Combined molecular characterization results (size exclusion chromatography, membrane osmometry, and ¹H NMR spectroscopy) revealed a high degree of structural and compositional homogeneity. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 614–619, 2006     

Synthesis of A2B star block copolymers from a heterotrifunctional initiator

We described the obtention of A₂B star block copolymers through the use of a new heterotrifunctional initiator. That way, well‐defined (PCL)₂‐arm‐PtBuMA and (PCL)₂‐arm‐PS star block copolymers have been synthesized from a heterotrifunctional initiator bearing two hydroxyl groups able to initiate ROP of CL (with AlEt₃ or Sn(Oct)₂ as coinitiator) and a bromide function able to initiate ATRP of tBuMA or styrene. Firstly, we have proceeded using a sequential process (two‐steps), leading to an intermediate macroinitiator. Secondly, attempt to polymerize these two monomers in a simultaneous process (one‐step), that is directly from the mixture of monomers, initiator, coinitiators, and solvent, has been realized and has shown that some interferences between the two polymerizations occurred, leading to an inhibition of ATRP when Sn(Oct)₂ was used and an unexpected increase in control when AlEt₃ was used as catalyst for the ROP (obtention of well‐defined (PCL)₂‐arm‐PtBuMA with pdi of 1.18). © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1796–1806, 2006