The interior proximal extragradient method for solving equilibrium problems

In this article we present a new and efficient method for solving equilibrium problems on polyhedra. The method is based on an interior-quadratic proximal term which replaces the usual quadratic proximal term. This leads to an interior proximal type algorithm. Each iteration consists in a prediction step followed by a correction step as in the extragradient method. In a first algorithm each of these steps is obtained by solving an unconstrained minimization problem, while in a second algorithm the correction step is replaced by an Armijo-backtracking linesearch followed by an hyperplane projection step. We prove that our algorithms are convergent under mild assumptions: pseudomonotonicity for the two algorithms and a Lipschitz property for the first one. Finally we present some numerical experiments to illustrate the behavior of the proposed algorithms.     

剩余格与正则剩余格的特征定理

本文进一步研究了具有广泛应用的一类模糊逻辑代数系统——剩余格，并引入了正则剩余格的概念，对剩余格与正则剩余格的定义进行了讨论，给出了剩余格与正则剩余格的特征定理，其中包含剩余格与正则剩余格的等式特征，从而这两个格类都构成簇．本文还讨论了剩余格与正则剩余格公理系统的独立性，以及它们与相近代数结构的关系．     

Optical modes in nanoscale one-dimensional spin chains

The spin chain systems with one-dimensional magnetic ordering are promising candidates for quantum optical devices. This paper shows how the optical excitation can induce various phonon modes in an ideal Cu-O chain at various lengths. The calculation was carried out at different level theories including configuration interaction singles for excited states, density functional theory and second-order Möller-Plesset perturbation. In general, the number of modes increases with chain length due to growing asymmetry of atomic positions when chain exceeds 5 nm. There were, however, only two basic modes: one is associated with the symmetric oscillation of oxygen and another with the asymmetric motion of the same along the chain. At the length below 4.3 nm, the Raman activity of the symmetric mode (440 cm⁻¹) dominates. From analysis of density of states, this mode may be associated with the excitation across the lowest LUMO bands with changing in spin state.     

High yielding microwave-assisted synthesis of tri-substituted 1,3,5-triazines using Pd-catalyzed aryl and heteroarylamination

A rapid and efficient Pd-catalyzed aryl and heteroarylamination under microwave irradiation has been developed for various tri-substituted triazines that can serve as versatile building blocks for both supramolecular and medicinal chemistry research. Particularly valuable features of this method included the short reaction time, good yield, and convenient operation.     

Subwavelength lithography using metallic grating waveguide heterostructure

We present subwavelength periodic gratings achieved by employing a metallic grating waveguide heterostructure (MGWHS). The mask can be designed to make one of its diffraction order (±mth) waves resonate with the surface plasmon wave supported by the MGWHS. With a finite-difference time-domain method, we numerically demonstrate that one-dimensional periodic structure of about 60 nm feature, which is far beyond the diffraction limit, can be patterned with the interference of the 3rd diffraction order waves of the mask at a wavelength of 546 nm. The technique can also be extended to two-dimensional patterns using circularly polarized incidence and for the incidence with an angle θ.     

Inducing anisotropy in bulk Nd-Fe-Co-Al-B nanocrystalline alloys by quenching in magnetic field

We have observed magnetic anisotropy in bulk Nd_55−xCo_xFe₃₀Al₁₀B₅ (x=10, 15 and 20) alloys prepared by copper mold suction casting method with a presence of external magnetic field (quenching field) μ₀H=0.25 T. By changing direction of the measuring field from perpendicular to parallel one in comparison with that of the quenching field, coercive force of the alloys slightly decreases while remanent magnetization and squareness of hysteresis loop increase more clearly. It is also found that the higher Co-concentration in the alloys the larger magnetic anisotropy is induced. The structure analyses manifest nanocrystalline particles embedded in residual amorphous matrix of the alloys. The size of the particles is in range of 10-30 nm and their crystalline phases consist of Nd₂(Fe,Co)₁₄B, Nd₃Co, Nd₃Al, NdAl₂ and Nd.     

Ozonolysis of dipterocarpol and its derivatives

Oxidation of dipterocarpol and its derivatives with ozone gave compounds containing lactone, lactol, alkoxytetrahydrofuran, aldehyde, and methyl ketone fragments in the side chain, as well as 1,2,4-trioxolane fragment in the A ring. The molecular and crystalline structures of dipterocarpol were determined by X-ray analysis.     

Globally solving a nonlinear UAV task assignment problem by stochastic and deterministic optimization approaches

In this paper, we consider a task allocation model that consists of assigning a set of m unmanned aerial vehicles (UAVs) to a set of n tasks in an optimal way. The optimality is quantified by target scores. The mission is to maximize the target score while satisfying capacity constraints of both the UAVs and the tasks. This problem is known to be NP-hard. Existing algorithms are not suitable for the large scale setting. Scalability and robustness are recognized as two main issues. We deal with these issues by two optimization approaches. The first approach is the Cross-Entropy (CE) method, a generic and practical tool of stochastic optimization for solving NP-hard problem. The second one is Branch and Bound algorithm, an efficient classical tool of global deterministic optimization. The numerical results show the efficiency of our approaches, in particular the CE method for very large scale setting.     

The challenge in managing new financial risks: adopting an heuristic or theoretical approach

The financial crisis began with the collapse of Lehman Brothers and the subprime asset backed securities debacle. Credit risk was turned into liquidity risk, resulting in a lack of confidence among financial institutions. In this article, we will propose a way to model liquidity risk and the credit risk in best practices. We will show that liquidity risk is a new type of risk and the current way to deal with it is based solely on observed variables without any theoretical link. We propose an heuristic approach to combine the numerous liquidity risk indicators with a logistic regression for the first time. In regards to credit risk, several articles prove that the best practice is to use an option model to appreciate this risk. We will present our methodology using stochastic diffusion for the interest rate because currently the yield curves aren’t liquid. This approach is more relevant because the basis model in prior publications has a constant interest rate or a forward rate. Both models allow a better understanding of liquidity and credit risks and the further development of research deals with the link between these two financial risks.     

Electron dynamics in modulation p-doped InGaAs/GaAs quantum dots

We investigate the electron dynamics of p-type modulation doped and undoped InGaAs/GaAs quantum dots using up-conversion photoluminescence at low temperature and room temperature. The rise time of the p-doped sample is significantly shorter than that of the undoped at low temperature. With increasing to room temperature the undoped sample exhibits a decreased rise time whilst that of the doped sample does not change. A relaxation mechanism of electron-hole scattering is proposed in which the doped quantum dots exhibit an enhanced and temperature independent relaxation due to excess built-in holes in the valence band of the quantum dots. In contrast, the rise time of the undoped quantum dots decreases significantly at room temperature due to the large availability of holes in the ground state of the valence band. Furthermore, modulation p-doping results in a shorter lifetime due to the presence of excess defects.