A new hybrid method for solving global optimization problem

In this paper we present a new hybrid method, called the SASP method. The purpose of this method is the hybridization of the simulated annealing (SA) with the descent method, where we estimate the gradient using simultaneous perturbation. Firstly, the new hybrid method finds a local minimum using the descent method, then SA is executed in order to escape from the currently discovered local minimum to a better one, from which the descent method restarts a new local search, and so on until convergence.The new hybrid method can be widely applied to a class of global optimization problems for continuous functions with constraints. Experiments on 30 benchmark functions, including high dimensional functions, show that the new method is able to find near optimal solutions efficiently. In addition, its performance as a viable optimization method is demonstrated by comparing it with other existing algorithms. Numerical results improve the robustness and efficiency of the method presented.     

A two-phase approach for setting targets in DEA with negative data

Conventional DEA models have been introduced to deal with non-negative data. In the real world, in some occasions, we have outputs and/or inputs, which can take negative data. In DEA literature some approaches have been presented for evaluating performance of units, which operate with negative data. In this paper, firstly, we give a brief review of these works, then we present a new additive based approach in this framework. The proposed model is designed to provide a target with non-negative value associated with negative components for each observed unit, failed by other methods. An empirical application in banking is then used to show the applicability of the proposed method and make a comparison with the other approaches in the literature.     

Some results on Ramsey numbers using sumfree sets

Maximal sumfree sets chosen from the non-zero elements of galois group of order 2⁶ (i.e. GF(2⁶)?{0}) are found to be of size 13, 17, 18, 20 and 32 only. This gives a negative result to an investigation which would otherwise have delivered an exact value of the Ramsey number R(3,3,3,3;2).     

A Survey on Existence Results for Boundary Value Problems of Nonlinear Fractional Differential Equations and Inclusions

In this survey paper, we shall establish sufficient conditions for the existence and uniqueness of solutions for various classes of initial and boundary value problem for fractional differential equations and inclusions involving the Caputo fractional derivative. The both cases of convex and nonconvex valued right hand side are considered. The topological structure of the set of solutions is also considered.     

Unreliable M/G/1 retrial queue: monotonicity and comparability

In this paper we investigate the monotonicity properties of an unreliable M/G/1 retrial queue using the general theory of stochastic ordering. We show the monotonicity of the transition operator of the embedded Markov chain relative to the strong stochastic ordering and increasing convex ordering. We obtain conditions of comparability of two transition operators and we obtain comparability conditions of the number of customers in the system. Inequalities are derived for the mean characteristics of the busy period, number of customers served during a busy period, number of orbit busy periods and waiting times. Inequalities are also obtained for some probabilities of the steady-state distribution of the server state. An illustrative numerical example is presented.     

Large Amplitude Motions of Pyruvic Acid (CH3-CO-COOH)

Torsional and rotational spectroscopic properties of pyruvic acid are determined using highly correlated ab initio methods and combining two different theoretical approaches: Second order perturbation theory and a variational procedure in three-dimensions. Four equilibrium geometries of pyruvic acid, Tc, Tt, Ct, and CC, outcome from a search with CCSD(T)-F12. All of them can be classified in the C_s point group. The variational calculations are performed considering the three internal rotation modes responsible for the non-rigidity as independent coordinates. More than 50 torsional energy levels (including torsional subcomponents) are localized in the 406–986 cm⁻¹ region and represent excitations of the ν₂₄ (skeletal torsion) and the ν₂₃ (methyl torsion) modes. The third independent variable, the OH torsion, interacts strongly with ν₂₃. The A₁/E splitting of the ground vibrational state has been evaluated to be 0.024 cm⁻¹ as it was expected given the high of the methyl torsional barrier (338 cm⁻¹). A very good agreement with respect to previous experimental data concerning fundamental frequencies (ν^CAL − ν^EXP ~ 1 cm⁻¹), and rotational parameters (B₀^CAL − B₀^EXP < 5 MHz), is obtained.     

Slant Submanifolds of Almost Contact Metric 3-Structure Manifolds

In this paper we introduce the notion of slant submanifold of an almost contact metric 3-structure manifold. We give some examples and characterize these submanifolds. Moreover, Sasakian slant submanifolds of an almost contact 3-structure manifold are defined and studied. We also establish a sharp inequality including the squared mean curvature and Ricci curvature of a Sasakian slant submanifold.     

Wavelet analysis method for solving linear and nonlinear singular boundary value problems

In this paper, a robust and accurate algorithm for solving both linear and nonlinear singular boundary value problems is proposed. We introduce the Chebyshev wavelets operational matrix of derivative and product operation matrix. Chebyshev wavelets expansions together with operational matrix of derivative are employed to solve ordinary differential equations in which, at least, one of the coefficient functions or solution function is not analytic. Several examples are included to illustrate the efficiency and accuracy of the proposed method.     

A scenario decomposition approach for stochastic production planning in sawmills

This study considers a real world stochastic multi-period, multi-product production planning problem. Motivated by the challenges encountered in sawmill production planning, the proposed model takes into account two important aspects: (i) randomness in yield and in demand; and (ii) set-up constraints. Rather than considering a single source of randomness, or ignoring set-up constraints as is typically the case in the literature, we retain all these characteristics while addressing real life-size instances of the problem. Uncertainties are modelled by a scenario tree in a multi-stage environment. In the case study, the resulting large-scale multi-stage stochastic mixed-integer model cannot be solved by using the mixed-integer solver of a commercial optimization package, such as CPLEX. Moreover, as the production planning model under discussion is a mixed-integer programming model lacking any special structure, the development of decomposition and cutting plane algorithms to obtain good solutions in a reasonable time-frame is not straightforward. We develop a scenario decomposition approach based on the progressive hedging algorithm, which iteratively solves the scenarios separately. CPLEX is then used for solving the sub-problems generated for each scenario. The proposed approach attempts to gradually steer the solutions of the sub-problems towards an implementable solution by adding some penalty terms in the objective function used when solving each scenario. Computational experiments for a real-world large-scale sawmill production planning model show the effectiveness of the proposed solution approach in finding good approximate solutions.     

Photocatalytic Performance of H6P2W18O62/TiO2 Nanocomposite Encapsulated into Beta Zeolite under UV Irradiation in the Degradation of Methyl Orange

In this work, neat and supported H₆P₂W₁₈O₆₂ into nanocage of β‐zeolite were synthesized. However, H₆P₂W₁₈O₆₂ into nanocage of β‐zeolite was synthesized via template synthesis method. In addition, TiO₂ was supported on H₆P₂W₁₈O₆₂/β zeolite by impregnation method. The obtained materials were characterized by XRD, FT‐IR, UV‐Vis, FESEM and EDS techniques. Also, W and Ti contents of the catalyst were determined by ICP and EDS technique. The results reveal that the photocatalyst performance depends on catalyst loading, pH effect, and methyl orange concentration. Photocatalytic degradation of methyl orange follows a pseudo‐first order kinetic. The chemical oxygen demand (COD) experimental proved mineralization of methyl orange. Another reason for degradation and mineralization of methyl orange is the absence of hydrazine at the end of reaction which is one of the photodecolorization products. The plausible mechanism for photodegradation of MO was proposed.