Pseudospectra of Matrix Polynomials that Are Expressed in Alternative Bases

Spectra and pseudospectra of matrix polynomials are of interest in geometric intersection problems, vibration problems, and analysis of dynamical systems. In this note we consider the effect of the choice of polynomial basis on the pseudospectrum and on the conditioning of the spectrum of regular matrix polynomials. In particular, we consider the direct use of the Lagrange basis on distinct interpolation nodes, and give a geometric characterization of “good” nodes. We also give some tools for computation of roots at infinity via a new, natural, reversal. The principal achievement of the paper is to connect pseudospectra to the well-established theory of Lebesgue functions and Lebesgue constants, by separating the influence of the scalar basis from the natural scale of the matrix polynomial, which allows many results from interpolation theory to be applied. This work was partially funded by the Natural Sciences and Engineering Research Council of Canada, and by the MITACS Network of Centres of Excellence.     

Phase equilibria of binary and ternary polymer solutions using modified UNIQUAC-based local composition model

Journal of Thermal Analysis and Calorimetry - In the present research, a modification on UNIQUAC activity coefficient model was done based on the local composition concept. The model was applied...     

Induced modulational instability in EDFAs in the presence of higher-order nonlinear and dispersive effects

We derive the dispersion equation for erbium doped fiber amplifiers (EDFAs), assuming the supplementary effects of time-derivative nonlinearities including intrapulse Raman scattering and self-steepening incorporated with third order dispersion and product of gain and square of dipole relaxation time parameter, in the extended form of nonlinear Schrödinger equation and investigate their impacts on gain and cut-off frequency of modulational instability (MI) in EDFAs. Also, the influences of those effects on instability of steady-state amplitude, in the form of generation of terahertz pulse train of femtosecond solitons from a weak-modulated signal by induced MI, are numerically simulated and discussed within EDFAs in normalized form.     

Wideband wavelength conversion using double-pass cascaded χ:χ interaction in lossy waveguides

We report the wavelength conversion based on double-pass cascaded nonlinear interaction (χ⁽²⁾:χ⁽²⁾) of sum and difference frequency generation in quasi-phase matched lithium niobate waveguides and compare it with double-pass cascaded second harmonic generation and difference frequency generation with and without waveguide loss. It is shown that the efficiency decreases considerably even for the low-loss waveguide compared to the lossless one especially for long waveguides and to achieve the higher efficiency for the same length, the amount of the extra power to compensate the loss increases. Also, an increased detuning of pump wavelength is proposed to flatten the response with a small efficiency penalty. The detuning- and loss-compensating pump powers can be found using the design diagrams in which the criteria for the design of waveguide length and the assignment of pumps power to obtain the desired efficiency, ripple and bandwidth are presented assuming a 75-nm pump wavelength difference.     

Force field parametrization and molecular dynamics simulation of flexible POSS-linked (NHC; phosphine) Ru catalytic complexes

In recent years, N-heterocyclic carbene (NHC) or phospine groups have been put forward as candidate catalysts ligands for olefin metathesis reactions to be performed using multistep methods. Some of these proposed ligands contain polyhedral oligomeric silsesquioxane (POSS) structures linked to NHC rings by means of alkyl chains. Some important properties for the prediction of catalytic activity, such as the theoretically defined buried volume, are related to the conformational characteristics of these complex ligands that can be studied through molecular dynamics simulations. However, the chemical structure of resulting catalytic complexes usually contains atoms or groups that are not included in the common forcefields used in simulations. In this work we focus on complexes formed by a catalytic metal center (Ru) with both phospine and POSS-linked NHC groups. The central part of the complexes contain atoms and groups that have bonds, bond angles, and torsional angles whose parameters have not been previously evaluated and included in existing force fields. We have performed basic ab initio quantum mechanical calculations based on the density functional theory to obtain energies for this central section. The force field parameters for bonds, bond angles, and torsional angles are then calculated from an analysis of energies calculated for the equilibrium and different locally deformed structures. Nonbonded interactions are also conveniently evaluated. From subsequent molecular dynamics simulations, we have obtained results that illustrate the conformational characteristics most closely connected with the catalytic activity.     

A novel 4H–SiC MESFET with modified channel depletion region for high power and high frequency applications

In this paper, a novel 4H–SiC metal semiconductor field effect transistor (MESFET) with modified depletion region is introduced. The key idea in this work is modifying the depletion region in the channel for improving the electrical performances. The proposed structure consists of upper and lower gates. Also, the lower gate is divided into a number (N) of smaller step-shaped sections. Therefore, we have called the proposed structure multiple-recessed 4H–SiC MESFET (MR-MESFET). DC and RF characteristics of the MR-MESFET structure with various lower gate segments are analyzed by 2D numerical simulation. The simulated results show that as the number of the lower gate sections increases, the channel depletion region is modified and the drain current (I_D) enhances. Also, by increasing the number of the lower gate sections, the breakdown voltage (V_BR) enhances, too. Improvement of the I_D and V_BR leads to a further increase in the output power density of the device. Also, cut-off frequency (f_T), maximum oscillation frequency (f_max), and maximum available gain (MAG) improvements are achieved for the MR-MESFET structure with further number of the lower gate sections. The results show that the MR-MESFET structure with higher number of the lower gate segments has superior electrical characteristics and performances in comparison with the MR-MESFET structure with fewer number of the lower gate sections.     

3-Hydroxy-7,8,9,10-tetrahydro-6H-benzo[c]chromen-6-one and 3-hydroxy-6H-benzo[c]chromen-6-one act as on-off selective fluorescent sensors for Iron (III) under in vitro and ex vivo conditions

Regarding the abundant use of metals for different purposes, it becomes more critical from various scientific and technological perspectives to discover novel agents as selective probes for the detection of specific metals. In our previous studies, we have shown that aqueous solutions of natural urolithins (i.e., hydroxyl-substituted benzo[c]chromen-6-one derivatives) are selective Iron (III) sensors in fluorescence assays. In this study, we have extrapolated these findings to another coumarine compound (i.e., 3-Hydroxy-7,8,9,10-tetrahydro-6H-benzo[c]chromen-6-one) and compared the selective metal binding properties with Urolithin B (i.e., 3-Hydroxy-6H-benzo[c]chromen-6-one). Following the synthesis and structure identification studies, the fluorometric studies pointed out that the lactam group in the structure still persists to be the important scaffold for maintaining selective on-off sensor capacity that renders the compound a selective Iron (III) binding probe. Moreover, for the first time, fluorescence cellular imaging studies concomitant to cytotoxicity assays with the title compounds were also performed and the results displayed the cell-penetrative, safe, and fluorescent detectable characteristics of the compounds in neuroblastoma and glioblastoma cells through servings as intracellular Iron (III) on-off sensors.     

Human health-related properties of chromones: an overview

Abstract

Natural compounds occurring throughout the world are scientifically and practically valuable because of their unique and beneficial properties to control a wide range of disorders in the human body. Chromones are attracting increasing attention as novel therapeutic agents due to their effective bioactivities for human health. Accordingly, the present overview article was designed to scan the biological and pharmacological performance of chromones, including their anti-inflammatory, anticancer, anti-oxidant, and anti-microbial activities.