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Abstract: In this paper, we generalize the classical primal–dual logarithmic barrier method for linear optimization to convex quadratic optimization over symmetric cone by using Euclidean Jordan algebras. The symmetrization of the search directions used in this paper is based on the Nesterov–Todd scaling scheme, and only full Nesterov–Todd step is used at each iteration. We derive the iteration bound that matches the currently best known iteration bound for small-update methods, namely, . Some preliminary numerical results are provided to demonstrate the computational performance of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: A mathematical model of the evaporation system in the form of a state space model with multiple time delays is constructed. On this basis, an optimal control of an industrial-scale alumina evaporation process is obtained, where the objective is to find a control such that the specific quality of the sodium aluminate solution control is met with the least energy usage and the constraints on the state and the control are satisfied. Then, a numerical algorithm is developed for solving this optimal control problem. It is applied to study the optimal control of a practical alumina evaporation process and the results obtained are highly satisfactory. [Copyright &y& Elsevier]

Abstract: In this paper, we study a (weak) vector equilibrium principle with capacity constraints of arcs and common arcs in some different paths. We obtain some necessary and sufficient conditions for a (weak) vector minimum cost flow. By virtue of a (weak) Δ-equilibrium principle, we also derive some necessary and sufficient conditions for a weak vector equilibrium flow. [Copyright &y& Elsevier]

Abstract: In this paper, three kinds of well-posedness for set optimization are first introduced. By virtue of a generalized Gerstewitz’s function, the equivalent relations between the three kinds of well-posedness and the well-posedness of three kinds of scalar optimization problems are established, respectively. Then, sufficient and necessary conditions of well-posedness for set optimization problems are obtained by using a generalized forcing function, respectively. Finally, various criteria and characterizations of well-posedness are given for set optimization problems. [Copyright &y& Elsevier]

Abstract: In this paper, the notions of higher order weak contingent epiderivative and higher order weak adjacent epiderivative for a set-valued map are defined. By virtue of higher order weak adjacent (contingent) epiderivatives and Henig efficiency, we introduce a higher order Mond–Weir type dual problem and a higher order Wolfe type dual problem for a constrained set-valued optimization problem (SOP) and discuss the corresponding weak duality, strong duality and converse duality properties. We also establish higher order Kuhn–Tucker type necessary and sufficient optimality conditions for (SOP). [Copyright &y& Elsevier]

Abstract: In this paper, we consider a class of the optimal state feedback control problems involving switched systems with state jumps. The planning time horizon is subdivided into subintervals, where the breakpoints are called the re-setting times. One system is used during each subinterval with a piecewise state feedback control form. The re-setting time, the feedback gain matrices and the heights of the state jumps at the re-setting times are considered as decision variables. It is shown, through a time scaling transform, that this class of optimal control problems is equivalent to an optimal parameter selection problem, where the varying re-setting time points are mapped into fixed time points. The gradient formula of the transformed cost function is derived. With this gradient formula, the optimal parameter selection problem can be solved as a nonlinear optimization problem, and the optimal control software MISER 3.3 can be used. Two illustrative examples are solved using the proposed method. [Copyright &y& Elsevier]

Abstract: We report on the growth of Co–Mn–Ge thin films on various substrates using low-temperature molecular beam epitaxy. The magnetic and transport properties of the films were investigated. The close-to-stoichiometric Co2MnGe film grown on GaAs(100) shows ferromagnetism and exhibits anomalous Hall effects at room temperature. The irreversibility of zero-field-cooled and field-cooled measurements suggests the formation of superparamagnetic clusters. On the other hand, the growth of Co2MnGe films on Ge buffer layer and Si(100) substrate is found to be unsuitable due to the degraded crystal qualities with weak magnetization signals. [Copyright &y& Elsevier]

Abstract: Using variational analysis, in terms of the Clarke normal cone, we consider super-efficiency of vector optimization in Banach spaces. We establish some characterizations for super-efficiency. In particular, dropping the assumption that the ordering cone has a bounded base, we extend a result in Borwein and Zhuang [J.M. Borwein, D. Zhuang, Super-efficiency in vector optimization, Trans. Amer. Math. Soc. 338 (1993) 105–122] to the nonconvex setting. [Copyright &y& Elsevier]

Abstract: In this paper, we establish the existence of the optimal control for an optimal control problem where the state of the system is defined by a variational inequality problem with monotone type mappings. Moreover, as an application, we get several existence results of an optimal control for the optimal control problem where the system is defined by a quasilinear elliptic variational inequality problem with an obstacle. [Copyright &y& Elsevier]

Abstract: The American option pricing problem is originally formulated as a stochastic optimal stopping time problem. It is also equivalent to a variational inequality problem or a complementarity problem involving the Black–Scholes partial differential operator. In this paper, the corresponding variational inequality problem is discretized by using a fitted finite volume method. Based on the discretized form, an algorithm is developed by applying augmented Lagrangian method (ALM) to the valuation of the American option. Convergence properties of ALM are considered. By empirical numerical experiments, we conclude that ALM is more effective than penalty method and Lagrangian method, and comparable with the projected successive overrelaxation method (PSOR). Furthermore, numerical results show that ALM is more robust in terms of computation time under changes in market parameters: interest rate and volatility. [Copyright &y& Elsevier]

Abstract: We report the growth of Cr1−δ Te films on (100) GaAs substrates using ZnTe buffer layers by solid-source molecular-beam epitaxial technique. RHEED patterns indicate a clear structural change during the initial stages of deposition. Temperature-dependent magnetization results reveal that different NiAs-related phases of Cr1−δ Te can be obtained at different substrate temperatures. By varying the film thickness, a metastable zinc blende structure of CrTe could be obtained at lower substrate temperature. [Copyright &y& Elsevier]

This paper presents a numerical method for the approximation of viscosity solutions to a Hamilton–Jacobi–Bellman (HJB) equation governing a class of optimal feedback control problems. The first-order HJB equation is first perturbed by adding a diffusion term with a singular perturbation parameter. The time and spatial variables in the resulting equation are then discretized respectively by an implicit modified method of characteristics and the alternating direction (AD) scheme. We show that the AD procedure''s perturbation error is virtually negligible due to the small perturbation parameter. And the efficient AD scheme can be applied to our HJB equation without generating splitting error. Numerical results, performed to verify the usefulness of the method, show that the method gives accurate approximate solutions to both of the control and the state variables. [Copyright &y& Elsevier]

In this paper, we establish two theorems of alternative with generalized subconvexlikeness. We introduce two dual models for a generalized fractional programming problem. Theorems of alternative are then applied to establish duality theorems and a saddle-point type optimality condition. [Copyright &y& Elsevier]

In this paper, several kinds of invariant monotone maps and generalized invariant monotone maps are introduced. Some examples are given which show that invariant monotonicity and generalized invariant monotonicity are proper generalizations of monotonicity and generalized monotonicity. Relationships between generalized invariant monotonicity and generalized invexity are established. Our results are generalizations of those presented by Karamardian and Schaible. [ABSTRACT FROM AUTHOR]

In this paper, we study generalized minimax inequalities in a Hausdorff topological vector space, in which the minimization and the maximization of a two-variable set-valued mapping are alternatively taken in the sense of vector optimization. We establish two types of minimax inequalities by employing a nonlinear scalarization function and its strict monotonicity property. Our results are obtained under weaker convexity assumptions than those existing in the literature. Several examples are given to illustrate our results. [Copyright &y& Elsevier]

Self-organized Ge/Si quantum dots (QD's) in strained Si/Ge short-period superlattices are studied by Raman scattering under hydrostatic pressure excited in-resonance and off-resonance with the confined Ge-like E1 transition of Ge using 488 and 514.5 nm lines from an argon-ion laser and 632.8 nm line from a He–Ne laser. The Raman spectra of Ge–Ge, Si–Ge and Si-2TA modes of the QD's were obtained as a function of pressure in the range of 1–70 kbar. Our results show that the mode Gru¨neisen parameter of the Ge–Ge phonon mode in QD's is found to be γ=0.81±0.01, which is smaller than that of the bulk Ge. We observe resonance effects with the confined Ge-like E1 transition and the pressure coefficient of this resonating electronic transition obtained is ∼5±1 meV kbar−1. [Copyright &y& Elsevier]

In this paper we define the vertex-cover polynomial Ψ(G,τ) for a graph G. The coefficient of τr in this polynomial is the number of vertex covers V′ of G with |V′|=r. We develop a method to calculate Ψ(G,τ). Motivated by a problem in biological systematics, we also consider the mappings f from {1, 2,…,m} into the vertex set V(G) of a graph G, subject to f−1(x)∪f−1(y)≠∅ for every edge xy in G. Let F(G,m) be the number of such mappings f. We show that F(G,m) can be determined from Ψ(G,τ). [Copyright &y& Elsevier]

Abstract: T.R. Gulati and Divya Agarwal pointed out that the statement: and imply , on line 4 of page 208 of [X.M. Yang, X.Q. Yang and K.L. Teo, Appl. Math. Lett. 18 (2005) 205–208], is erroneous since is obtained letting . Here is a simple proof that . [Copyright &y& Elsevier]

Abstract: In this paper, we develop two discretization algorithms with a cutting plane scheme for solving combined semi-infinite and semi-definite programming problems, i.e., a general algorithm when the parameter set is a compact set and a typical algorithm when the parameter set is a box set in the m-dimensional space. We prove that the accumulation point of the sequence points generated by the two algorithms is an optimal solution of the combined semi-infinite and semi-definite programming problem under suitable assumption conditions. Two examples are given to illustrate the effectiveness of the typical algorithm. [Copyright &y& Elsevier]

Abstract: We propose a transistor model that incorporates multiple storage elements within a single transistor device. This device is thus smaller in size compared to the magnetoresistive random access memory (MRAM) with the same number of storage bits. The device model can function in both the current as well as voltage detection mode. Simulations were carried out at higher temperature, taking into consideration the spread of electron density above the Fermi level. We found that linear detection of conductance variation with the stored binary value can be achieved for a 3-bit storage device up to a temperature of 350 K. [Copyright &y& Elsevier]

Abstract: We present a self-consistent model of spin transport in a ferromagnetic (FM)–semiconductor (SC)–FM trilayer structure with interfacial barriers at the FM–SC boundaries. The SC layer consists of a highly doped n2+ AlGaAs–GaAs 2DEG while the interfacial resistance is modeled as delta potential (δ) barriers. The self-consistent scheme combines a ballistic model of spin-dependent transmission across the δ-barriers, and a drift-diffusion model within the bulk of the trilayer. The interfacial resistance (R I) values of the two junctions were found to be asymmetric despite the symmetry of the trilayer structure. Transport characteristics such as the asymmetry in R I, spin-injection efficiency and magnetoresistance (MR) are calculated as a function of bulk conductivity σ s and spin-diffusion length (SDL) within the SC layer. In general a large σ s tends to improve all three characteristics, while a long SDL improves the MR ratio but reduces the spin-injection efficiency. These trends may be explained in terms of conductivity mismatch and spin accumulation either at the interfacial zones or within the bulk of the SC layer. [Copyright &y& Elsevier]

Abstract: We present a design for spin injection from a ferromagnetic (FM)-nonmagnetic (NM) bilayer into a semiconductor (SC) layer. This device consists of a left bilayer injector, the SC layer and a right bilayer collector. The FM has a much smaller cross-sectional area (A) compared to the device. This increases the spin-dependent resistance as a fraction of the total device resistance and reduces the effect of conductivity mismatch which suppresses spin-injection efficiency. The NM layer is required as a buffer to contain the spreading resistance (RSP) that arises from the discontinuity of A. With Ni80Fe20/Cu as the bilayers, and GaAs as the SC, our computation yields a spin-injection efficiency of 20% for doping density ND of 1018cm-3, which rises to 30% for . [Copyright &y& Elsevier]

Abstract: We present a theoretical model to study spin injection (η) through a quantum dot system sandwiched by two ferromagnetic contacts. The effect of contact magnetization on η was studied using Green''s function descriptions of the density of states. Green''s function models have the advantages that coherent effects of temperature, electron occupation in the QD, and lead perturbation on the state wave function and hence the current can be formally included in the calculations. In addition, self-consistent treatment of current with applied electrochemical potential or lead conductivity, a necessary step which has not been considered in previous works, has also been implemented in our model. [Copyright &y& Elsevier]