The Genus Haplophyllum Juss.: Phytochemistry and Bioactivities—A Review

Herein, a comprehensive review is given focusing on the chemical profiles of the essential oils (EOs), non-volatile compounds, ethnobotany, and biological activities of different Haplophyllum (Rutaceae family) species. To gather the relevant data, all the scientific databases, including Scopus, ISI-WOS (Institute of Scientific Information-Web of Science), and PubMed and highly esteemed publishers such as Elsevier, Springer, Taylor and Francis, etc., were systematically retrieved and reviewed. A wide array of valuable groups of natural compounds, e.g., terpenoids, coumarins, alkaloids, lignans, flavonoids, and organic acids have been isolated and subsequently characterized in different organic extracts of a number of Haplophyllum species. In addition, some remarkable antimicrobial, antifungal, anti-inflammatory, anticancer, cytotoxic, antileishmanial, and antialgal effects as well as promising remedial therapeutic properties have been well-documented for some species of the genus Haplophyllum.     

Vibration analysis of piezoelectric nanowires with surface and small scale effects

An analytical model for predicting surface effects on the free transverse vibrations of piezoelectric nanowires (NWs) is developed based on the non-local Euler-Bernoulli beam theory. The governing equation of motion for the piezoelectric NW with consideration of both surface and non-local effects is initially obtained, and the exact expressions for the natural frequencies and the fundamental buckling voltage are derived for simple support conditions. In addition, an explicit relationship between the residual surface tension and the small scale parameter of the piezoelectric NW, in terms of the critical electric potential at which the axial buckling occurs, is offered. Accordingly, a design chart is presented which may assist in experimental characterization of the mechanical properties of piezoelectric NW-based devices.     

Effect of electron phonon interaction on the optical conductivity of zigzag carbon nanotubes

Optical conductivity of a zigzag carbon nanotube is investigated in the context of the Holstein model. Green??s function approach is applied to calculate the optical conductivity as a function of photon frequency, temperature, and electron?Cphonon coupling strength. Based on our results, optical conductivity decreases with electron?Cphonon coupling constant for both metallic and semiconducting carbon nanotubes. Our results show that temperature yields shortening the height of peaks of zigzag CNT optical absorption.     

On the spectral problem for trivariate functions

Using a variational approach applied to generalized Rayleigh functionals, we extend the concepts of singular values and singular functions to trivariate functions defined on a rectangular parallelepiped. We also consider eigenvalues and eigenfunctions for trivariate functions whose domain is a cube. For a general finite-rank trivariate function, we describe an algorithm for computing the canonical polyadic (CP) decomposition, provided that the CP factors are linearly independent in two variables. All these notions are computed using Chebfun3; a part of Chebfun for numerical computing with 3D functions. Application in finding the best rank-1 approximation of trivariate functions is investigated. We also prove that if the function is analytic and two-way orthogonally decomposable (odeco), then the CP values decay geometrically, and optimal finite-rank approximants converge at the same rate.     

Graphs and ranks of monoids

For a finite monoid S, let ν(S) (ν_d(S)) denote the least number n such that there exists a graph (directed graph) Γ of order n with End(Γ)?S. Also let rank(S) be the smallest number of elements required to generate S. In this paper, we use Cayley digraphs of monoids, to connect lower bounds of ν(S) (ν_d(S)) to the lower bounds of rank(S). On the other hand, we connect upper bounds of rank(S) to upper bounds of ν(S) (ν_d(S)).     

The Complex Interior-Boundary method for linear and nonlinear programming with linear constraints

In this paper we develop the Complex method; an algorithm for solving linear programming (LP) problems with interior search directions. The Complex Interior-Boundary method (as the name suggests) moves in the interior of the feasible region from one boundary point to another of the feasible region bypassing several extreme points at a time. These directions of movement are guaranteed to improve the objective function. As a result, the Complex method aims to reach the optimal point faster than the Simplex method on large LP programs. The method also extends to nonlinear programming (NLP) with linear constraints as compared to the generalized-reduced gradient.The Complex method is based on a pivoting operation which is computationally efficient operation compared to some interior-point methods. In addition, our algorithm offers more flexibility in choosing the search direction than other pivoting methods (such as reduced gradient methods). The interior direction of movement aims at reducing the number of iterations and running time to obtain the optimal solution of the LP problem compared to the Simplex method. Furthermore, this method is advantageous to Simplex and other convex programs in regard to starting at a Basic Feasible Solution (BFS); i.e. the method has the ability to start at any given feasible solution.Preliminary testing shows that the reduction in the computational effort is promising compared to the Simplex method.     

An Operational Strategy for Throughput Maximization and Bottleneck Control in an Assembly Line System: By Selection of the Processing Rates

In this paper, an optimal operational strategy is developed to optimize the system utilization while controlling the bottleneck problem in a finite capacity integrated assembly line system (consisting of a set of tandem workstations, a set of inspection stations, a loading station and an unloading station, linked by a set of transporter stations). To develop the proposed operational strategy, a stochastic optimization model is developed for selecting the optimal processing rates of the workstations and the transporter stations, such that the total throughput rate from the system is maximized while the resulting probability of finding either a workstation or a transporter station blocked is sufficiently close to zero.     

Response of Makrofol polycarbonate plastic track detector to 1.1 MeV/N 54 132 Xe-ion

Makrofol polycarbonate plastic track detectors have been exposed to ₅₄ ¹³² Xe -ions of energy 1.1 MeV/N from the cyclotron beam. The bulk etch rate and track etch rate are measured for different temperatures and the activation energies are calculated. The maximum etched track length is compared with the theoretically computed range. The critical energy loss is (dE/dx) _c =5 MeV cm² mg⁻¹ for this detector material.