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.     

Synthesis of cation-exchanged laponite suspensions by laser ablation of microsized-metal particles in liquid

Laser ablation in the liquid technique has been used to synthesize cation-exchanged laponite suspensions. In summary, laser ablation of the microsize-metal powder (Co, Al, and Cu) dispersed in an aqueous solution containing deionized water laponite crystals was carried out using laser beam generated by a single-mode, Q-switched Nd-Yag laser operating at 532 nm with a pulse duration of 5.5 ns and 10 Hz repetition rate. Laser fluence was 0.265 J/cm² for all tests. For all samples, the mass fraction of laponite was 1%. General observations of the prepared samples indicated that an aqueous suspension of 1 wt% laponite retained its free flowing liquid phase characteristics even after aging for several weeks. When bivalent cationic metals (Cu, Co, Al) were ablated in it for about 1 h, even with a small amount of the metal (0.025% and 0.050%) were generated, the suspension became highly viscous and behaved as a shear-thinning and thixotropic material. That is, the suspension gelled strongly when it was allowed to rest. The gels, however, could easily be reverted to a low viscosity liquid with simple shaking. Information from TEM and XRD analysis indicated that such a sol-gel transformation might be due to the charge exchange between the cationic species produced during the laser ablation and the sodium ions in the interlayers of the clay sheets.     

Cellulosic value-added products from sugarcane bagasse

Cellulose - Sugarcane bagasse (SCB) is a major by-product of the sugarcane industry and one of the most common renewable and sustainable cellulosic materials for various industrial...     

Solution to the Neumann problem exterior to a prolate spheroid by radial basis functions

We consider the exterior Neumann problem of the Laplacian with boundary condition on a prolate spheroid. We propose to use spherical radial basis functions in the solution of the boundary integral equation arising from the Dirichlet–to–Neumann map. Our approach is particularly suitable for handling of scattered data, e.g. satellite data. We also propose a preconditioning technique based on domain decomposition method to deal with ill-conditioned matrices arising from the approximation problem.     

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.     

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.     

Determination of neutron temperature in irradiation channels of reactor

The neutron temperature is a characteristic parameter in irradiation channels of reactor. For nuclides which have resonances in the thermal neutron energy range, their Westcott g-factors are different from unity. The values of g-factors and cross-sections of (n, γ) reaction of these nuclides are temperature dependence. The standard energy for tabulation of thermal neutron cross-section (σ₀) is that of room temperature (293.59 K or 20.43 °C), corresponding to a neutron energy 0.0253 eV or to a neutron velocity of 2200 m/s. However, in the irradiation channels of reactor, the temperature is not exact at 20.43 °C. Thus, the temperature at the irradiation position must be known to convert σ₀ to σ(T). A method for determination of the neutron temperature in irradiation channels of Dalat reactor is presented by fitting the thermal neutron spectrum obtained from the calculation using MCNP code.     

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.