Clarke coderivatives of efficient point multifunctions in parametric vector optimization

The paper is devoted to the study of the Clarke/circatangent coderivatives of the efficient point multifunction of parametric vector optimization problems in Banach spaces. We provide inner/outer estimates for evaluating the Clarke/circatangent coderivative of this multifunction in a broad class of conventional vector optimization problems in the presence of geometrical, operator and (finite and infinite) functional constraints. Examples are given for analyzing and illustrating the obtained results.     

Limit cycles for generalized Kukles polynomial differential systems

We study the limit cycles of generalized Kukles polynomial differential systems using averaging theory of first and second order.     

Variational sets: Calculus and applications to nonsmooth vector optimization

We develop elements of calculus of variational sets for set-valued mappings, which were recently introduced in Khanh and Tuan (2008) [1] and [2] to replace generalized derivatives in establishing optimality conditions in nonsmooth optimization. Most of the usual calculus rules, from chain and sum rules to rules for unions, intersections, products and other operations on mappings, are established. Direct applications in stability and optimality conditions for various vector optimization problems are provided.     

Stability of semi-infinite vector optimization problems without compact constraints

This paper is devoted to the continuity of solution maps for perturbation semi-infinite vector optimization problems without compact constraint sets. The sufficient conditions for lower semicontinuity and upper semicontinuity of solution maps under functional perturbations of both objective functions and constraint sets are established. Some examples are given to analyze the assumptions in the main result.     

Convergence of the projected gradient method for quasiconvex multiobjective optimization

We consider the projected gradient method for solving the problem of finding a Pareto optimum of a quasiconvex multiobjective function. We show convergence of the sequence generated by the algorithm to a stationary point. Furthermore, when the components of the multiobjective function are pseudoconvex, we obtain that the generated sequence converges to a weakly efficient solution.     

Characterization of vector strict global minimizers of order 2 in differentiable vector optimization problems under a new approximation method

In this paper, a new approximation method is introduced to characterize a so-called vector strict global minimizer of order 2 for a class of nonlinear differentiable multiobjective programming problems with (F,ρ)-convex functions of order 2. In this method, an equivalent vector optimization problem is constructed by a modification of both the objectives and the constraint functions in the original multiobjective programming problem at the given feasible point. In order to prove the equivalence between the original multiobjective programming problem and its associated F-approximated vector optimization problem, the suitable (F,ρ)-convexity of order 2 assumption is imposed on the functions constituting the considered vector optimization problem.     

Optical properties of a polyethylene dispersion with a luminescent silica prepared by surface grafting of a perylene derivative

A micrometric silica modified with perylene derivative (SiO₂–TES) has been prepared by hydrolysis–condensation reactions between silica and N,N’-bis-(3-triethoxysilylpropyl)-perylene-tetracarboxyldiimide (P-TES) and utilized as filler in LLDPE films together with a compatibilizer. Spectroscopic analyses on SiO₂–TES confirmed the grafting of P-TES on silica, while its amount was determined by thermogravimetric analysis. Solid state NMR provided information about the structure of silicon atoms involved in the condensation of SiO₂ and P-TES that resulted mainly in silicon atoms grafted with bi-dentate anchorages.UV–Vis and fluorescence analyses carried out on P-TES showed the ability of the dye to generate J-type aggregates in apolar solvents. The same analyses on SiO₂–TES revealed the presence of both isolated and aggregated dye molecules grafted on silica surface, while on polymeric dispersions of SiO₂–TES, they have shown only the presence of P-TES aggregates grafted to silica.Thanks to the direct correlation between optical properties (obtained both by UV–Vis and by fluorescence analyses) and the chemical environment of composites, the luminescent silica SiO₂–TES could be used to estimate the filler dispersion extent in different microcomposite polymer materials.     

Surface holonomy for non-abelian 2-bundles via double groupoids

In the context of non-abelian gerbes, we define a cubical version of categorical group 2-bundles with connection over a smooth manifold. We address their two-dimensional parallel transport, study its properties, and construct non-abelian Wilson surface functionals.     

The derivative of global surface-holonomy for a non-abelian gerbe

Starting with a non-abelian gerbe represented by a non-abelian differential cocycle, with values in a given crossed-module, this paper explicitly calculates a formula for the derivative of the associated surface holonomy of squares mapped into the base manifold; with spheres later considered as a special case. While the definitions in this paper used for gerbes, their connections, and the induced holonomy will initially be simplicial, translations into a cubical setting will be provided to aide in explicit coordinate-based calculations. While there are many previously published results on the properties of these non-abelian gerbes, including some calculations of the derivative over a single open set, this paper endeavors to take these local calculations and glue them together across multiple open sets in order to obtain a single expression for the change in surface holonomy with respect to a one-parameter family of squares.     

基于面积灰关联相对贴近度模型的长三角制造业产业升级研究

借助“制造业高级化”产业升级理论, 从结构优度、价值链高度、环境保护程度三个维度构建制造业产业升级评价指标体系。根据TOPSIS思想, 以被评价对象数列和理想方案指标数列两相邻点间围成图形的面积来表征关联系数, 同时采用标准差修正G1组合赋权原理对指标赋权并进一步计算灰关联相对贴近度; 通过引入时间变量并赋予时间序列权重以实现对长三角制造业产业升级动态评价。研究结果显示:2010至2016年间, 上海市排名最高, 江苏省略高于浙江省, 安徽省最低; 安徽省是长三角制造业产业升级的短板。基于上述结论, 给出长三角制造业产业升级的政策建议。