A Combination of Variational and Penalty Methods for Solving a Class of Fractional Optimal Control Problems

This paper develops an approximate method, based on the combination of epsilon penalty and variational methods, for solving a class of multidimensional fractional optimal control problems. The fractional derivative is in the Caputo sense. In the presented method, utilizing the epsilon method, the given optimal control problem transforms into an unconstrained optimization problem; then, the equivalent variational equality is derived for the given unconstrained problem. The variational equality is approximately solved by applying a spectral method.     

A multi-step class of iterative methods for nonlinear systems

In this article, the numerical solution of nonlinear systems using iterative methods are dealt with. Toward this goal, a general class of multi-point iteration methods with various orders is constructed. The error analysis is presented to prove the convergence order. Also, a thorough discussion on the computational complexity of the new iterative methods will be given. The analytical discussion of the paper will finally be upheld through solving some application-oriented problems.     

Target setting in the general combined-oriented CCR model using an interactive MOLP method

The traditional data envelopment analysis (DEA) model does not include a decision maker’s (DM) preference structure while measuring relative efficiency, with no or minimal input from the DM. To incorporate DM’s preference information in DEA, various techniques have been proposed. An interesting method to incorporate preference information, without necessary prior judgment, is the use of an interactive decision making technique that encompasses both DEA and multi-objective linear programming (MOLP). In this paper, we will use Zionts-Wallenius (Z-W) method to reflecting the DM’s preferences in the process of assessing efficiency in the general combined-oriented CCR model. A case study will conducted to illustrate how combined-oriented efficiency analysis can be conducted using the MOLP method.     

The effect of inorganic and organic macromolecular structures on the performance of metallocene polymerization catalysts

After a short comparative analysis of different macromolecular ligands reported in the relevant literature, the presentation will be centered on the results obtained in the authors' laboratory using structurally defined inorganic supports in terms also of their macromolecular structure. Zeolites and mesomorphous silica can link, after proper chemical modification of their surface with MAO, unmodified metallocene complexes through cage entrapment and weak interactions, thus allowing the transfer from the solution to the solid phase. The metallocene complexes in their new phase are characterized by the catalytic behavior in olefin polymerization after activation with MAO. A decrease of productivity is generally observed depending on the type of support. The steric hindrance provided by the support is evidenced by the depression of chain transfer rate with formation of higher molecular weight polymers. Also shape selectivity is observed during copolymerization of ethylene with α‐olefins having variable size. These steric effects are released when going from HY zeolite to MCM silica.     

Boundary Behaviour of Positive Solutions of Second-Order Parabolic Operators with Lower-Order Terms in a Half-Space

In this paper, we study the boundary behaviour of positive solutions of certain parabolic operators with lower order terms in a half-space. Basing on these results, we characterize the Martin boundary and show that any positive solution has an integral representation. We thus generalize to a large class of parabolic operators some results proved by Kaufman, Wu, Mair, and Taylor for the heat equation.     

Ranking efficient DMUs using the Tchebycheff norm

One problem that has been discussed frequently in data envelopment analysis (DEA) literature has been lack of discrimination in DEA applications, in particular when there are insufficient DMUs or the number of inputs and outputs is too high relative to the number of units. This is an additional reason for the growing interest in complete ranking techniques. In this paper a method for ranking extreme efficient decision making units (DMUs) is proposed. The method uses L_∞(or Tchebycheff) Norm, and it seems to have some superiority over other existing methods, because this method is able to remove the existing difficulties in some methods, such as Andersen and Petersen [2] (AP) that it is sometimes infeasible. The suggested model is always feasible.     

Synthesis and characterization of sulfamic acid supported on Fe3O4 nanoparticles: A green,versatile and magnetically separable acidic catalyst for oxidation reactions and Knoevenagel condensation

Sulfamic acid immobilized on diethylenetriamine functionalized Fe₃O₄ nanoparticles (SA‐DETA‐Fe₃O₄) was successfully prepared and characterized by X‐ray diffraction (XRD), Fourier transform infrared spectroscopy (FT‐IR), vibrating sample magnetometer (VSM), thermo gravimetric analysis (TGA), X‐Ray diffraction (XRD) and scanning electron microscopy (SEM). The sulfamic acid was found as a magnetically separable and highly active catalyst for the oxidative coupling thiols, oxidation of sulfides. Furthermore, the SA‐DETA‐Fe₃O₄ showed the high catalytic activity in Knoevenagel condensation of aromatic aldehydes with active methylene compounds (malononitrile and ethyl cynoacetate). The nanosolid catalyst could be easily recovered by a simple magnetic separation and reused for many cycles without deterioration in catalytic activity.     

A compromised multi-objective solution using fuzzy mixed integer goal programming for market-based short-term unit commitment problem

When implementing, the solution of single-objective unit commitment models may be dissatisfactory or inapplicable. This might mainly be due to not considering the secondary conflicting objectives from the policy-making in internal/external environment of generation companies in the developed models. To attain a practical compromised multi-objective solution for the short-term unit commitment in the deregulated hybrid markets, a novel fuzzy mixed integer linear goal programme is developed in which several complementary objectives with lower relative importances are also incorporated. Non-linear characteristic curves of the generating units are approximated through the piece-wise linear functions. The fuzzy approach is proposed to handle the imprecise nature of the goals’ target levels and priorities as well as some critical data. The critical aspects of power systems are considered in the model. The efficiency of the proposed approach is demonstrated using the experimental results inspired by a real case. The applicable nice feature of our model is that it can easily and efficiently be matched with a various line of unit commitment problems.     

Epsilon-Ritz Method for Solving a Class of Fractional Constrained Optimization Problems

In this paper, epsilon and Ritz methods are applied for solving a general class of fractional constrained optimization problems. The goal is to minimize a functional subject to a number of constraints. The functional and constraints can have multiple dependent variables, multiorder fractional derivatives, and a group of initial and boundary conditions. The fractional derivative in the problem is in the Caputo sense. The constrained optimization problems include isoperimetric fractional variational problems (IFVPs) and fractional optimal control problems (FOCPs). In the presented approach, first by implementing epsilon method, we transform the given constrained optimization problem into an unconstrained problem, then by applying Ritz method and polynomial basis functions, we reduce the optimization problem to the problem of optimizing a real value function. The choice of polynomial basis functions provides the method with such a flexibility that initial and boundary conditions can be easily imposed. The convergence of the method is analytically studied and some illustrative examples including IFVPs and FOCPs are presented to demonstrate validity and applicability of the new technique.