A Generalization of Ritz-Variational Method for Solving a Class of Fractional Optimization Problems

This paper presents an approximate method for solving a class of fractional optimization problems with multiple dependent variables with multi-order fractional derivatives and a group of boundary conditions. The fractional derivatives are in the Caputo sense. In the presented method, first, the given optimization problem is transformed into an equivalent variational equality; then, by applying a special form of polynomial basis functions and approximations, the variational equality is reduced to a simple linear system of algebraic equations. It is demonstrated that the derived linear system has a unique solution. We get an approximate solution for the initial optimization problem by solving the final linear system of equations. The choice of polynomial basis functions provides a method with such flexibility that all initial and boundary conditions of the problem can be easily imposed. We extensively discuss the convergence of the method and, finally, present illustrative test examples to demonstrate the validity and applicability of the new technique.     

Alkylation of aromatic amines by tert-enamides: Direct access to protected aminals

Reaction of aromatic amines with tertiary enamides was performed in n-hexane in the presence of acetic acid as an inexpensive and green catalyst at room temperature. This protocol provides the protected aminals through Markovnikov addition reaction with high to excellent yields and regiospecificity. In addition, this procedure was expanded for the synthesis of aminals from commercially available sulfa drugs such as sulfathiazole and sulfabenzamide.     

Electrochemical Oxidation of Desipramine Drug in the Presence of 4,6‐Dimethylpyrimidine‐2‐thiol Nucleophile in Aqueous Acidic Medium

Electrochemical oxidation of desipramine (DES) has been studied in the presence of 4,6‐dimethylpyrimidine‐2‐thiol (DMPT) as nucleophile in acidic medium by means of cyclic voltammetry, controlled‐potential electrolysis and spectroscopic data, as diagnostic techniques. Voltammetric studies of electro‐oxidation of desipramine were realized in a range of pH 1.0 to 8.0 in the absence and presence of DMPT. The results indicate the participation of the product of electrochemical oxidation of desipramine in the reaction with DMPT with ECEC electrochemical mechanism. However, the voltammetry and coulometry results imply existence of a catalytic (EC′) electrochemical mechanism in parallel with ECEC electrochemical mechanism. The product has been characterized by IR, ¹H NMR, ¹³C NMR and MS methods.     

Dimension group of a non-negative integer irreducible matrix

In this paper we are concerned with a non-negative integer and irreducible matrix $A:{\mathbb{Z}}^d\to {\mathbb{Z}}^d$. The main contribution is to prove that if the matrix satisfies certain spectral and algebraic constraints, the cone:$C=\{v\in {\mathbb{Z}}^d/\exists n⩾0\mathrm{and}{A}^{n}v⩾0\}\subset {\mathbb{Z}}^d$is defined by linear maps ${\varphi }_0\text{,}\dots \text{,}{\varphi }_{k-1}:{\mathbb{Z}}^d\to \mathbb{R}$, in the sense that v ∈ C is equivalent to, ϕ_l(v) ⩾ 0 for all l = 0, … , k − 1 (where k is the index of cyclicity of the irreducible matrix). This result allows us to characterize the dimension group generated by the matrix, it is a subgroup of ${\mathbb{R}}^k$ endowed with an order induced by the positive cone of ${\mathbb{R}}^k$.     

High-resolution surface-plasmon imaging in air and in water: V(z) curve and operating conditions

We present what are believed to be the first images obtained with a far-field high-resolution scanning surface-plasmon microscope in an aqueous medium. Measurements of V(z), the output response of the microscope, versus defocus z give a signature of the surface-plasmon propagation. V(z) is strongly conditioned by the laser beam diameter and the objective's numerical aperture, and we show how the operating mode (in air and in water) must be chosen to maximize the surface-plasmon field and to minimize diffraction (edge) effects.     

Dynamic analysis of a flexible slider–crank mechanism with clearance

In this paper we are interested in the study of the dynamic behavior of a planar flexible slider–crank mechanism with clearance. Simulation and experimental tests were carried out for this goal. For the simulation tests, we have built the model under the software ADAMS. We used a contact model based on the so called Impact-function. An experimental set-up was designed and built to achieve some experimental validations. The presented results show that, in the presence of clearance, the mechanism responses were greatly influenced. The motion is characterized by the occurrence of three phases: a free motion, a continuous contact motion and an impact motion. In this paper, both the case of the mechanism with rigid link and the case with flexible link were studied. It is shown that in the presence of clearance, the coupler flexibility has a role of suspension for the mechanism.     

An efficient multistep iteration scheme for systems of nonlinear algebraic equations associated with integral equations

The aim of this research is to present a new iterative procedure in approximating nonlinear system of algebraic equations with applications in integral equations as well as partial differential equations (PDEs). The presented scheme consists of several steps to reach a high rate of convergence and also an improved index of efficiency. The theoretical parts are furnished, and several computational tests mainly arising from practical problems are given to manifest its applicability.     

Sensitivity analysis of inefficient units in data envelopment analysis

One important issue in DEA which has been studied by many DEA researchers is the sensitivity of the results of an analysis to perturbations in the data.This paper develops a procedure for performing a sensitivity analysis of the inefficient decision making units (DMUs). The procedure yields an exact “Necessary Change Region” in which the efficiency score of a specific inefficient DMU changes to a defined efficiency score.In what follows, we identify a new frontier, and prove the efficiency score of each arbitrary unit on it which is defined as the efficiency score.