A smoothing trust region filter algorithm for nonsmooth least squares problems

We propose a smoothing trust region filter algorithm for nonsmooth nonconvex least squares problems. We present convergence theorems of the proposed algorithm to a Clarke stationary point or a global minimizer of the objective function under certain conditions. Preliminary numerical experiments show the efficiency of the proposed algorithm for finding zeros of a system of polynomial equations with high degrees on the sphere and solving differential variational inequalities.     

Sell through a local retailer or operate your own store? Channel structure and risk analysis

Either a company store or a local retailer can be used to establish a sales channel. For high-value products with an existing competing brand, this choice represents a crucial decision a brand-named manufacturer must make for a new market. Under the burden of high operating costs, a weak local retailer may find it difficult to sustain and using it may hurt the manufacturer’s chance to successfully establish the channel. We consider a chain-to-chain competition model comprising two manufacturers and two retailers, in which one retailer may be unable to continue its operation because of high financing costs. We identify a threshold policy for the manufacturers to select the channel structure. Interestingly, we find that channel integration is not always better. Without the consideration of contract termination risk, the manufacturer will bear the operating expenses when its opportunity cost is low or the retailer’s financing cost is sufficiently high. In equilibrium, the manufacturers will choose either (decentralized, decentralized) or (integrated, integrated) channel structure. However, when the termination risk is considered, the equilibrium channel structure would be more likely (integrated, integrated) or (integrated, decentralized).     

儿童额叶癫痫临床和长程视频脑电图特征

目的通过对46例儿童额叶癫痫患儿的临床表现、长程视频脑电图（VEEG）特点进行分析,提高对儿童额叶癫痫的认识。方法收集2008年12月至2014年8月儿科门诊及住院确诊的46例儿童额叶癫痫病例的资料,回顾性分析其临床表现、VEEG及神经影像学等特征。结果本组患儿发病年龄最小11个月,最大15岁。46例患儿共监测到临床发作258次,明确临床发作34例,14.7%仅于清醒期发作,61.8%仅在睡眠期发作,23.5%在清醒、睡眠中均有发作;临床发作形式包括额叶失神、局部阵挛发作、偏转性强直、姿势性强直、过度运动性自动症、口咽自动症、发声、发笑发作、临床下放电和自主神经性发作等。73.9%患儿记录到发作间期额叶为主的癫痫样放电,63.0%患儿记录到发作期额叶为主的癫痫样放电。结论儿童额叶癫痫临床发作频繁、短暂,以睡眠期发作为主,临床表现复杂多样,易漏诊;长程VEEG可监测到儿童额叶癫痫发作期临床及异常脑电图表现,可提供明确诊断率。     

Frobenius morphisms and representations of algebras

By introducing Frobenius morphisms on algebras and their modules over the algebraic closure of the finite field of elements, we establish a relation between the representation theory of over and that of the -fixed point algebra over . More precisely, we prove that the category    mod- of finite-dimensional -modules is equivalent to the subcategory of finite-dimensional -stable -modules, and, when is finite dimensional, we establish a bijection between the isoclasses of indecomposable -modules and the -orbits of the isoclasses of indecomposable -modules. Applying the theory to representations of quivers with automorphisms, we show that representations of a modulated quiver (or a species) over can be interpreted as -stable representations of the corresponding quiver over . We further prove that every finite-dimensional hereditary algebra over is Morita equivalent to some , where is the path algebra of a quiver over and is induced from a certain automorphism of . A close relation between the Auslander-Reiten theories for and is established. In particular, we prove that the Auslander-Reiten (modulated) quiver of is obtained by ``folding" the Auslander-Reiten quiver of . Finally, by taking Frobenius fixed points, we are able to count the number of indecomposable representations of a modulated quiver over with a given dimension vector and to generalize Kac's theorem for all modulated quivers and their associated Kac-Moody algebras defined by symmetrizable generalized Cartan matrices.

     

Fréchet approach in second-order optimization

We state a certain second-order sufficient optimality condition for functions defined in infinite-dimensional spaces by means of generalized Fréchet’s approach to second-order differentiability. Moreover, we show that this condition generalizes a certain second-order condition obtained in finite-dimensional spaces.     

带干扰的多险种风险模型

由于保险公司风险经营规模不断扩大,用单一险种的模型来描述风险过程存在局限性,本文讨论了带干扰多险种风险模型,应用鞅论方法,得出伦德伯格不等式和最终破产概率公式。     

Browder spectra of upper-triangular operator matrices

Let be a 2×2 upper triangular operator matrix acting on the Hilbert space H⊕K. In this paper, for given operators A and B, we prove that

     

Indirect adaptive fuzzy observer and controller design based on interval type-2 T-S fuzzy model

This paper presents the design scheme of the indirect adaptive fuzzy observer and controller based on the interval type-2 (IT2) T-S fuzzy model. The nonlinear systems can be well approximated by IT2 T-S fuzzy model, in which the fuzzy rules’ antecedents are interval type-2 fuzzy sets and consequents are linear state equations. The proposed IT2 T-S fuzzy model is a combination of IT2 fuzzy system and T-S fuzzy model, and also inherits the benefits of type-2 fuzzy logic systems, which is able to directly handle uncertainties and can minimize the effects of uncertainties in rule-based fuzzy system. These characteristics can improve the accuracy of the system modeling and reduce the number of system rules. The proposed method using feedback control, adaptive laws, and on-line object parameters are adjusted to ensure observation error bounded. In addition, using Lyapunov synthesis approach and Lipschitz condition, the stability analysis is conducted. The simulation results show that the proposed method can handle unpredicted disturbance and data uncertainties very well in advantage of the effectiveness of observation and control.     

Strong solution of backward stochastic partial differential equations in C 2 domains

This paper is concerned with the strong solution to the Cauchy–Dirichlet problem for backward stochastic partial differential equations of parabolic type. Existence and uniqueness theorems are obtained, due to an application of the continuation method under fairly weak conditions on variable coefficients and C ² domains. The problem is also considered in weighted Sobolev spaces which allow the derivatives of the solutions to blow up near the boundary. As applications, a comparison theorem is obtained and the semi-linear equation is discussed in the C ² domain.