Theoretical characterization of the chemical bonds of some three-membered ring compounds through QTAIM theory

Structural Chemistry - In this paper, we investigate the nature of the carbonyl and the intraring C–C, C–N, C–O, N–N, O–O and N–O bonds of cyclopropanone and the...     

Evaluation of thermal stability of enalapril maleate tablets using thermogravimetry and differential scanning calorimetry

Differential scanning calorimetry (DSC) and thermogravimetry (TG) were used in order to evaluate the thermal stability of an enalapril maleate formulation packaged in two types of packaging, polyvinyl chloride/aluminum blister and aluminum strip. Enalapril and the excipients employed in the formulation were also evaluated by TG and DSC. Tablets were analyzed before and after storage in an acclimatized room at 40 °C and relative humidity of 75 % for 90 days. The DSC and TG results were compared with the results of dosage of enalapril and related compounds obtained by high-performance liquid chromatography. These results indicate an occurrence of chemical interaction between enalapril maleate and the excipients during its storage. After storage, it was observed that the enalapril content reduced and the predominant degradation product was diketopiperazine for both types of packaging. The predominance of diketopiperazine could be related to the absence of sodium bicarbonate in the tablets, alkalinizing agent employed in the thermal stabilization of the drug.     

Voltammetric sensor based on magnetic particles modified composite electrode for determination of triamterene in biological sample

Some diuretic substances are controlled and monitored by the World Anti-Doping Agency as prohibited substances for use by athletes, such as triamterene (TRT). Thus, this work describes a voltammetric method based on graphite-epoxy composite electrode modified by tosyl-functionalized magnetic particles (GECE/MPs-To) for determination of TRT diuretic in urine sample. The TRT presented an oxidation peak at +1.24 V at GECE/MPs-To with irreversible behavior. Controlled potential electrolysis of the TRT at +1.26 V indicated the two electrons are transferred during amine group oxidation and the main product was identified by LC-MS/MS. The anodic peak current is 25 % higher at the modified electrode, suggesting that TRT is adsorbed on the magnetic particles. Using optimized conditions by using multivariate optimization of the parameters inherent of the square wave voltammetry, a calibration curve was constructed with a linear relationship for TRT from 0.500 to 99.8 μmol L^?1. The limits of detection and quantification were 1.47 and 4.91?×?10^?7 mol L^?1, respectively. The proposed method was applied to urine sample and validated by LC-MS/MS technique where the values found and compared between the two techniques showed no significant difference at 95 % confidence.     

Cohomology relative to a system of closed forms on the torus

To a system of closed one‐forms on the torus, we associate a differential complex and compute the induced cohomology groups provided that a related matrix satisfies a Diophantine condition.     

On Weak and Strong Convergence of the Projected Gradient Method for Convex Optimization in Real Hilbert Spaces

This work focuses on convergence analysis of the projected gradient method for solving constrained convex minimization problems in Hilbert spaces. We show that the sequence of points generated by the method employing the Armijo line search converges weakly to a solution of the considered convex optimization problem. Weak convergence is established by assuming convexity and Gateaux differentiability of the objective function, whose Gateaux derivative is supposed to be uniformly continuous on bounded sets. Furthermore, we propose some modifications in the classical projected gradient method in order to obtain strong convergence. The new variant has the following desirable properties: the sequence of generated points is entirely contained in a ball with diameter equal to the distance between the initial point and the solution set, and the whole sequence converges strongly to the solution of the problem that lies closest to the initial iterate. Convergence analysis of both methods is presented without Lipschitz continuity assumption.     

Cutting and packing problems for irregular objects with continuous rotations: mathematical modelling and non-linear optimization

We further improve our methodology for solving irregular packing and cutting problems. We deal with an accurate representation of objects bounded by circular arcs and line segments and allow their continuous rotations and translations within rectangular and circular containers. We formulate a basic irregular placement problem which covers a wide spectrum of packing and cutting problems. We provide an exact non-linear programming (NLP) model of the problem, employing ready-to-use phi-functions. We develop an efficient solution algorithm to search for local optimal solutions for the problem in a reasonable time. The algorithm reduces our problem to a sequence of NLP subproblems and employs optimization procedures to generate starting feasible points and feasible subregions. Our algorithm allows us to considerably reduce the number of inequalities in NLP subproblems. To show the benefits of our methodology we give computational results for a number of new challenger and the best known benchmark instances.     

On finite groups with automorphisms whose fixed points are Engel

The main result of the paper is the following theorem. Let q be a prime, n a positive integer, and A an elementary abelian group of order q². Suppose that A acts coprimely on a finite group G and assume that for each \({a \in A^{\#}}\) every element of C_G(a) is n-Engel in G. Then the group G is k-Engel for some \({\{n,q\}}\)-bounded number k.     

The real symmetric matrices of odd order with a P-set of maximum size

Suppose that A is a real symmetric matrix of order n. Denote by m_A(0) the nullity of A. For a nonempty subset α of {1, 2,..., n}, let A(α) be the principal submatrix of A obtained from A by deleting the rows and columns indexed by α. When m_A(α)(0) = m_A(0)+|α|, we call α a P-set of A. It is known that every P-set of A contains at most ?n/2? elements. The graphs of even order for which one can find a matrix attaining this bound are now completely characterized. However, the odd case turned out to be more difficult to tackle. As a first step to the full characterization of these graphs of odd order, we establish some conditions for such graphs G under which there is a real symmetric matrix A whose graph is G and contains a P-set of size (n ? 1)/2.     

Nonsymmetric and symmetric fractional calculi on arbitrary nonempty closed sets

We introduce a nabla, a delta, and a symmetric fractional calculus on arbitrary nonempty closed subsets of the real numbers. These fractional calculi provide a study of differentiation and integration of non‐integer order on discrete, continuous, and hybrid settings. Main properties of the new fractional operators are investigated and some fundamental results presented, illustrating the interplay between discrete and continuous behaviors. Copyright © 2015 John Wiley & Sons, Ltd.