Extension of Operational Matrix Technique for the Solution of Nonlinear System of Caputo Fractional Differential Equations Subjected to Integral Type Boundary Constrains

We extend the operational matrices technique to design a spectral solution of nonlinear fractional differential equations (FDEs). The derivative is considered in the Caputo sense. The coupled system of two FDEs is considered, subjected to more generalized integral type conditions. The basis of our approach is the most simple orthogonal polynomials. Several new matrices are derived that have strong applications in the development of computational scheme. The scheme presented in this article is able to convert nonlinear coupled system of FDEs to an equivalent S-lvester type algebraic equation. The solution of the algebraic structure is constructed by converting the system into a complex Schur form. After conversion, the solution of the resultant triangular system is obtained and transformed back to construct the solution of algebraic structure. The solution of the matrix equation is used to construct the solution of the related nonlinear system of FDEs. The convergence of the proposed method is investigated analytically and verified experimentally through a wide variety of test problems.     

Synthesis of Carbene-Metal-Amido (CMA) Complexes and Their Use as Precatalysts for the Activator-Free,Gold-Catalyzed Addition of Carboxylic Acids to Alkynes

A straightforward synthetic protocol leading to carbene–metal–amido (CMA) complexes (metal=Au, Cu) using a mild base and an environmentally desirable solvent (EtOH) has been explored, with a focus on complexes bearing backbone-substituted N-heterocyclic carbene (NHC) ligands, including BIAN-NHCs (BIAN=bis(imino)acenaphthene). The novel CMAs were structurally characterized, and gold-based CMAs bearing diverse NHCs were screened as simple, Brønsted-basic precatalysts. The readily accessible complexes display high catalytic activity in the intermolecular and intramolecular hydrocarboxylation of internal alkynes and alkynoic acids respectively, while the screening reveals the ancillary ligand effect of NHCs in these catalytic systems.     

Optical Solitons in Fiber Bragg Gratings with Polynomial Law Nonlinearity and Cubic–Quartic Dispersive Reflectivity

Optics and Spectroscopy - Optical solitons with fiber Bragg gratings and polynomial law of nonlinear refractive index are addressed in the paper. The auxiliary equation approach together with an...     

General decay rate for a class of weakly dissipative second‐order systems with memory

In this paper, we study an abstract class of weakly dissipative second‐order systems with finite memory. We establish a new general decay rate for the solution of the system under some appropriate conditions on the memory kernel (relaxation function). Our result improves and generalizes many existing results in the literature. We also give some examples to illustrate our abstract result.     

Dependence of developing magnetic hysteresis characteristics on stages of evolving microstructure in polycrystalline yttrium iron garnet

The microstructure evolution in several polycrystalline yttrium iron garnet samples as a result of a sintering scheme was studied in detail, in parallel with the changes in their magnetic properties. Samples with nanometer sized starting powder were synthesized by employing the High-Energy Ball Milling technique and then sintering toroidal compacts of the milled powder. Nine sintered samples were obtained, each corresponding to a particular sintering from 600 °C to 1400 °C. The samples were characterized for their evolution in crystalline phases, microstructure and magnetic hysteresis-loops parameters. The results showed an increasing tendency of the saturation magnetization and saturation induction with grain size, which is attributed to crystallinity increase and to reduction of demagnetizing fields in the grains. The variation in coercivity could be related to anisotropy field changes within the samples due to grain size changes. In particular, the starting appearance of room temperature ferromagnetic order suggested by the sigmoid-shaped B-H loops seems to be dependent on a sufficient number of large enough magnetic domain-containing grains having been formed in the microstructure. Viewed simultaneously, the hysteresis loops appear to belong to three groups with different magnetism-type dominance, respectively dependent on phase purity and three different groups of grain size distributions.     

Flow Reversal of Fully-Developed Mixed MHD Convection in Vertical Channels

The present analysis is concerned with flow reversal phenomena of the fully-developed laminar combined free and forced MHD convection in a vertical parallel-plate channel. The effect of viscous dissipation is taken into account. Flow reversal adjacent to the cold （or hot） wall is found to exist within the channel as Gr/Re is above （or below） a threshold value. Parameter zones for the occurrence of reversed flow are presented.     

Sintering temperature dependence of room temperature magnetic and dielectric properties of Co0.5Zn0.5Fe2O4 prepared using mechanically alloyed nanoparticles

Co_0.5Zn_0.5Fe₂O₄ nanoparticles were prepared using mechanical alloying (MA) and sintering. The crystallite size, coercivity, retentivity and saturation magnetization were also measured. The frequency dependence of dielectric and the magnetic parameters, namely, real permittivity ε′, loss tanget tan δ, real permeability μ′ and loss factor μ″ were measured at room temperature for samples sintered from 600 to 1000 °C, in the frequency range 10 MHz to 1.0 GHz. The results show that the crystallite size of the resulting products ranges between 16 and 67 nm for as-milled sample and the sample sintered at 1000 °C, respectively. The sample sintered at 1000 °C, measured at room temperature exhibited a saturation magnetization of 37 emu g⁻¹. The values of permittivity remain constant within the measured frequency, but vary with sintering temperature. The permeability values, on the other hand however vary with both the sintering temperature and the frequency, thus, the absolute value of the permeability decreased after the natural resonance frequency.     

Modulating protein structure with fluorous amino acids: increased stability and native-like structure conferred on a 4-helix bundle protein by hexafluoroleucine

There has recently been much interest in exploiting the unusual properties associated with fluorocarbons to modulate the physicochemical properties of proteins. Here we present a detailed investigation into the effect on structure and stability of systematically repacking the hydrophobic core of a model protein with the extensively fluorinated (fluorous) amino acid l-5,5,5,5',5',5'-hexafluoroleucine (hFLeu). The starting point was a 27-residue peptide, alpha(4)-H, that adopts an antiparallel 4-alpha-helix bundle structure, and in which the hydrophobic core comprises six layers of leucine residues introduced at the "a" and "d" positions of the canonical heptad repeat. A series of peptides were synthesized in which the central two (alpha(4)-F(2))(,) four (alpha(4)-F(4)), or all six layers (alpha(4)-F(6)) of the core were substituted hFLeu. The free energy of unfolding increases by 0.3 (kcal/mol)/hFLeu on repacking the central two layers and by an additional 0.12 (kcal/mol)/hFLeu on repacking additional layers, so that alpha(4)-F(6) is approximately 25% more stable than the nonfluorinated protein alpha(4)-H. One-dimensional proton, two-dimensional (1)H-(15)N HSQC, and (19)F NMR spectroscopies were used to examine the effect of fluorination on the conformational dynamics of the peptide. Unexpectedly, increasing the degree of fluorination also appears to result in peptides that possess a more structured backbone and less fluid hydrophobic core. The latter only occurs in alpha(4)-F(4) and alpha(4)-F(6), suggesting that crowding of the hFLeu residues may restrict the amplitude and/or time scales for rotation of the side chains.     

A note on the polynomial decay of a weakly dissipative viscoelastic system

In this note we study an abstract class of weakly dissipative second-order systems with finite memory. We establish the polynomial decay of Rivera, Naso and Vegni for the solution of the system under a very weak condition on the relaxation function.