Abstract:
This paper examines Chinese residents’ experience in learning English in the 3-D virtual world of Second Life (SL). With an introduction to the current English as a Second Language (ESL) education in China, ESL students’ demand for practice, I analyzed an online BBS created and maintained by Chinese SL residents and conducted interviews in SL to argue that there is an urgent need among Chinese ESL learners to practice their English with native English speakers and SL can function as a platform to allow Chinese ESL learners practice with residents from all over the world with help and support provided by their online learning communities such as BBS or SL friends groups.

Abstract:
In this paper, the analytic solutions to constrained optimal control problems are considered. A novel approach based on canonical duality theory is developed to derive the analytic solution of this problem by reformulating a constrained optimal control problem into a global optimization problem. A differential flow is presented to deduce some optimality conditions for solving global optimizations, which can be considered as an extension and a supplement of the previous results in canonical duality theory. Some examples are given to illustrate the applicability of our results.

Abstract:
In this paper, we consider the nonlinear fractional Schr\"odinger equations with Hartree type nonlinearity. We obtain the existence of standing waves by studying the related constrained minimization problems by applying the concentration-compactness principle. Via symmetric decreasing rearrangements, we also show that the standing waves, up to a translations and phases, are positive symmetric nonincreasing functions. Moreover, we prove that the set of minimizers is a stable set for the initial value problem of the equations, that is, a solution whose initial data is near the set will remain near it for all time.

Abstract:
This paper presents a global optimization method for solving general nonlinear programming problems subjected to box constraints. Regardless of convexity or nonconvexity, by introducing a differential flow on the dual feasible space, a set of complete solutions to the original problem is obtained, and criteria for global optimality and existence of solutions are given. Our theorems improve and generalize recent known results in the canonical duality theory. Applications to a class of constrained optimal control problems are discussed. Particularly, an analytical form of the optimal control is expressed. Some examples are included to illustrate this new approach. 1. Introduction In this paper, we consider the following general box constrained nonlinear programming problem (the primal problem in short): where is a feasible space, are two given vectors, and is twice continuously differentiable in . Here, we discuss the primal problem involving nonconvexity or convexity in the objective function. Problem (1.1) appears in many applications, such as engineering design, phase transitions, chaotic dynamics, information theory, and network communication [1, 2]. Particularly, if and , the problem leads to one of the fundamental problems in combinatorial optimization, namely, the integer programming problem [3]. By the fact that the feasible space is a closed convex subset of , the primal problem has at least one global minimizer. When is a convex programming problem, a global minimizer can be obtained by many well-developed nonlinear optimization methods based on the Karush-Kuhn-Tucker (or simply KKT ) optimality theory [4]. However, for with nonconvexity in the objective function, traditional KKT theory and direct methods can only be used for solving to local optimality. So, our interest will be mainly in the case of being nonconvex on in this paper. For special cases of minimizing a nonconvex quadratic function subject to box constraints, much effort and progress have been made on locating the global optimal solution based on the canonical duality theory by Gao (see [5–7] for details). As indicated in [8], the key step of the canonical duality theory is to introduce a canonical dual function, but commonly used methods are not guaranteed to construct it since the general form of the objective function given in (1.1). Thus, there has been comparatively little work in global optimality for general cases. Inspired and motivated by these facts, a differential flow for constructing the canonical dual function is introduced and a new approach to solve the general

Abstract:
Directed cell migration mediates physiological and pathological processes. In particular, immune cell trafficking in tissues is crucial for inducing immune responses and is coordinated by multiple environmental cues such as chemoattractant gradients. Although the chemotaxis mechanism has been extensively studied, how cells integrate multiple chemotactic signals for effective trafficking and positioning in tissues is not clearly defined. Results from previous neutrophil chemotaxis experiments and modeling studies suggested that ligand-induced homologous receptor desensitization may provide an important mechanism for cell migration in competing chemoattractant gradients. However, the previous mathematical model is oversimplified to cell gradient sensing in one-dimensional (1-D) environment. To better understand the receptor desensitization mechanism for chemotactic navigation, we further developed the model to test the role of homologous receptor desensitization in regulating both cell gradient sensing and migration in different configurations of chemoattractant fields in two-dimension (2-D). Our results show that cells expressing normal desensitizable receptors preferentially orient and migrate toward the distant gradient in the presence of a second local competing gradient, which are consistent with the experimentally observed preferential migration of cells toward the distant attractant source and confirm the requirement of receptor desensitization for such migratory behaviors. Furthermore, our results are in qualitative agreement with the experimentally observed cell migration patterns in different configurations of competing chemoattractant fields.

Abstract:
Capsicum red pigment extracted from the dry pepper is a kind of high-quality natural dye which has anticancer and cosmetic properties. First, Qiu North spicy was selected as the experimental objects by comparising the peel meal rate and relative amount of pigment of Fructus capsici, Qian chilli 2, and Qiu North spicy. Then, before extracting paprika dye, sodium hydroxide was used to eliminate the piquancy. Capsicum red pigment was extracted in Soxhlet extractor with 95% ethanol. The elution condition of column chromatographic separation was obtained by thin-layer chromatography, and the purity of capsicum red pigment was identified by methods of infrared spectrum(IR). Finally, the color value of capsicum red pigment was determined by spectrophotometer with 460nm. Results showed that the optimal process: Concentration of peppery removal agent (sodium hydroxide) was 10%, the holding temperature was 80????, solid-liquid ratio was 1:20 (g/ml), the extraction time was 120min and the times of extraction were twice. Eluent of silica gel column chromatography separation consisted of petroleum ether and 90% ethanol with the volume ratio of 2:1. The color value of capsicum red pigment (E1cm 1%460nm) could reach to 125 and 2.88% of yield could be gained. The process was good to extract and purify capsicum red dye whose stability was high at neutral and weak acid solution.

Abstract:
We use the natural $SU(3)\times U(1)$ global symmetry of the gauge-fermion interaction sector of the standard model to discuss the fermion mass hierarchy problem. The $SU(3)$ sixtet and triplet Higgs are introduced. The Yukawa sector is partially symmetric. The smaller the symmetry of a Yukawa term, the smaller its coupling constant. The mass hierarchy is a combined effect of smaller coupling constants and smaller VEVs. There is a bunch of pseudo-goldstone bosons which obtains their masses mainly from the small explicit breaking terms in the Higgs potential.

Abstract:
The tree level diagonalization of a neutrino mass matrix with both Majorana and Dirac masses is discussed in a general context. Flavor changing neutral currents in such models are inevitable. Rephasing invariant quantities characterizing CP violation in FCNC Fermion-Higgs interactions are identified. At the one loop level, the mass eigenstates become an impure Majorana type. The possibility of a significant change in the mass spectrum for the left-handed neutrinos is explored, with an example of two species of neutrinos. Neutrino oscillations with impure Majorana neutrinos are also discussed.

Abstract:
Assuming the small entries in the mass matrices are produced by fermion-scalar loops, we calculate the anomalous dipole moments of the leptons and quarks. The top quark appears in all the loops as the mass seed. When comparing the results with experimental data, including electric and magnetic dipole moments, and radiative transition rates, we obtain the mass limits which are typically larger than .1 TeV for the relevant neutral scalars, and 70 TeV for the relevant lepto-quarks. We then discuss the $P-\bar P$ mixing with a toy model. Rates of the known mixings require the masses of some neutral scalars to be large.

Abstract:
Cascade global symmetry and multi-vacuum expectation values are combined to produce an {\bf initial} texture of the quark mass matrices. Required corrections to the initial texture zeros ({\bf ITZ)} are all at the order of $10^{-3}m_t$ or less. The possibility of {\bf radiative corrections} as the source of the complete mass matrices is briefly discussed.