A Minty variational principle for set optimization

Extremal problems are studied involving an objective function with values in (order) complete lattices of sets generated by so-called set relations. Contrary to the popular paradigm in vector optimization, the solution concept for such problems, introduced by F. Heyde and A. Löhne, comprises the attainment of the infimum as well as a minimality property. The main result is a Minty type variational inequality for set optimization problems which provides a sufficient optimality condition under lower semicontinuity assumptions and a necessary condition under appropriate generalized convexity assumptions. The variational inequality is based on a new Dini directional derivative for set-valued functions which is defined in terms of a “lattice difference quotient.” A residual operation in a lattice of sets replaces the inverse addition in linear spaces. Relationships to families of scalar problems are pointed out and used for proofs. The appearance of improper scalarizations poses a major difficulty which is dealt with by extending known scalar results such as Diewert's theorem to improper functions.     

A duality principle in weighted Sobolev spaces on the real line

An embedding inequality of Sobolev type is characterized in the paper with help of a duality principle and boundedness criteria for the Hardy–Steklov integral operator in weighted Lebesgue spaces.     

New geometric properties of Banach spaces

In this paper, we introduce new geometric properties as generalizations of p‐uniform smoothness and q‐uniform convexity of Banach spaces. Furthermore, using generalized Beckner's inequality, we characterize the properties in terms of norm inequalities. As an application, we consider the duality relation.     

Uzawa-like methods for numerical modeling of unsteady viscoplastic Bingham medium flows

The Uzawa-like algorithm is implemented for two-dimensional flows of viscoplastic fluids. The rheological model employed is the ideal Bingham model. As a test the lid-driven square-cavity benchmark problem is considered. The results for the steady-state problem are faithfully reproduced as compared to those in the literature for the shape and location of the yield surface. The proposed method is very successful at capturing both yielded and unyielded regions.     

基于ARM和nRF905组网的智能家居系统设计

针对家居中电器种类和数目繁多且分散于各室造成控制不便,提出了一种利用nRF905射频模块实现无线通信的智能家居控制系统。系统对射频数据传输协议进行了设计,给出了室内多个微控制器的组网方案。用户通过手机短信或万能遥控器把对家电的控制信号发送至基于ARM平台搭建的主控中心,再由主控中心发送至若干个通信节点或智能插座,万能遥控器通过射频信号实现对家电的近距离遥控,手机通过GSM通信实现对家电的远程遥控。通信节点基于STC89C52RC单片机设计,能够实现对多种红外家电的控制并具备安防报警功能,智能插座则用于控制非遥控家电。实验表明,该系统可使网络中各节点、插座得到有效的控制,数据传输稳定、功能丰富、可扩展性强,具备较高的应用价值。     

Enzyme-free and DNA-based universal platform for the construction of various logic devices based on graphene oxide and G-quadruplex

In the fields of biocomputing and biomolecular, DNA molecules are applicable to be regarded as data of logical computing platform that uses elaborate logic gates to perform a variety of tasks. Graphene oxide (GO) is a type of novel nanomaterial, which brings new research focus to materials science and biosensors due to its special selectivity and excellent quenching ability. G-quadruplex as a unique DNA structure stimulates the intelligent application of DNA assembly on the strength of its exceptional binding activity. In this paper, we report a universal logic device assisted with GO and G-quadruplex under an enzyme-free condition. Integrated with the quenching ability of GO to the TAMRA (fluorophore, Carboxytetramethylrhodamine) and the enhancement of fluorescence intensity produced by the peculiar binding of G-quadruplex to the NMM (N-methylmesoporphyrin IX), a series of basic binary logic gates (AND. OR. INHIBIT. XOR) have been designed and verified through biological experiments. Given the modularity and programmability of this strategy, two advanced logic gates (half adder and half subtractor) were realized on the basis of the same work platform. The fluorescence signals generated from different input combinations possessed satisfactory results, which provided proof of feasibility. We believe that the proposed universal logical platform that operates at the nanoscale is expected to be utilized for future applications in molecular computing as well as disease diagnosis.     

Cohen–Macaulayness of monomial ideals and symbolic powers of Stanley–Reisner ideals

We present criteria for the Cohen–Macaulayness of a monomial ideal in terms of its primary decomposition. These criteria allow us to use tools of graph theory and of linear programming to study the Cohen–Macaulayness of monomial ideals which are intersections of prime ideal powers. We can characterize the Cohen–Macaulayness of the second symbolic power or of all symbolic powers of a Stanley–Reisner ideal in terms of the simplicial complex. These characterizations show that the simplicial complex must be very compact if some symbolic power is Cohen–Macaulay. In particular, all symbolic powers are Cohen–Macaulay if and only if the simplicial complex is a matroid complex. We also prove that the Cohen–Macaulayness can pass from a symbolic power to another symbolic powers in different ways.     

Extrapolation of weights revisited: New proofs and sharp bounds

We use an appropriate factorization of the Ap weights to give another proof of the extrapolation theorem of Rubio de Francia. It provides sharp bounds in terms of the Ap-constant of the weights. Then we extend the result to more general settings including off-diagonal and partial range extrapolation. Among the applications, we prove by iteration a multivariable extrapolation theorem and give a sharp bound for Calderón-Zygmund operators on Lp(w) for weights in Aq (q<p).     

Homogenization of the Signorini boundary‐value problem in a thick junction and boundary integral equations for the homogenized problem

We consider a mixed boundary‐value problem for the Poisson equation in a thick junction Ω_ε which is the union of a domain Ω₀ and a large number of ε—periodically situated thin cylinders. The non‐uniform Signorini conditions are given on the lateral surfaces of the cylinders. The asymptotic analysis of this problem is done as ε→0, i.e. when the number of the thin cylinders infinitely increases and their thickness tends to zero. We prove a convergence theorem and show that the non‐uniform Signorini boundary conditions are transformed in the limiting variational inequalities in the region that is filled up by the thin cylinders as ε→0. The convergence of the energy integrals is proved as well. The existence and uniqueness of the solution to this non‐standard limit problem is established. This solution can be constructed by using a penalty formulation and successive iteration. For some subclass, these problems can be reduced to an obstacle problem in Ω₀ and an appropriate postprocessing. The equations in Ω₀ finally are also treated with boundary integral equations. Copyright © 2010 John Wiley & Sons, Ltd.