This work is devoted to the study of modified Laguerre matrix polynomials. Hypergeometric matrix function representations, integral representation and an explicit expression for the modified Laguerre matrix polynomials are investigated. Finally, identities for power series for the modified Laguerre matrix polynomials are derived.

The main aim of this paper is to introduce a new kind of Legendre matrix polynomials. Hypergeometric matrix representation of these matrix polynomials is given. The convergence properties and the integral form for the Legendre matrix polynomials are derived. The Legendre matrix differential equation of second order is established. Subsequently, Rodrigues formula, orthogonality property, matrix recurrence relation and types of generating matrix functions are then developed for the Legendre matrix polynomials. Furthermore, general families of bilinear and bilateral generating matrix functions for these matrix polynomials are obtained and their applications are presented. Finally, the composite Legendre matrix polynomials is introduced.

This paper deals with the study of the generalized hypergeometric matrix function and obtain some of its properties. We rephrase some results from the previous(earlier) works that will be used in this study. We get the hypergeometric matrix function representation, matrix differential equation, generating matrix functions, bilinear generating matrix functions, matrix recurrence relations, finite summation formulas and related results for the Konhauser matrix polynomials given in [34]. Finally, we give some important results involving properties of Mittag-Leffler and Bessel-Maitland matrix functions as applications.

The present study details the binding process of clofazimine to hen egg white lysozyme (HEWL) using spectroscopy, dynamic light scattering (DLS), transmission electron microscopy (TEM) and molecular docking techniques. Clofazimine binds to the protein with binding constant (Kb) in the order of 1.57x104 at 298K. Binding process is spontaneous and exothermic. Molecular docking results suggested the involvement of hydrogen bonding and hydrophobic interactions in the binding process. Bacterial cell lytic activity in the presence of clofazimine was increased to more than 40% of the value obtained with HEWL only. Interaction of the drug with HEWL induced ordered secondary structure in the protein and molecular compaction. Clofazimine also effectively inhibited the SDS induced amyloid formation in HEWL and caused disaggregation of preformed fibrils, reinforcing the notion that there is involvement of hydrophobic interactions and hydrogen bonding in the binding process of clofazimine with HEWL and clofazimine destabilizes the mature fibrils. Further, transmission electron microscope (TEM) images confirmed that fibrillar species were absent in the samples where amyloid induction was performed in the presence of clofazimine. As clofazimine is a drug less explored for the inhibition of fibril formation of the proteins, this study reports the inhibition of SDS induced amyloid formation of HEWL by clofazimine, which will help in the development of clofazimine related molecules as the treatment for amyloidosis.

Herein,we report a newwet-synthesismethod to separate somewater-soluble chiral silver nanoclusterswith high yield. The cluster materialwas obtained by the reduction of silver nitrate with NaBH4 in the presence of three ligands L-penicillamine(L-pen), D-penicillamine (D-pen) and racemicmixture of penicillamine (rac-pen), functioning as capping ligand. For characterizing all silver cluster samples, the particle size was assessed by transmission electron microscopy (TEM) and powder X-ray diffraction (XRD) and their average chemical formula was determined from thermogravimetric analysis (TGA) and elemental analysis (EA). The particles sizes of all three clusters are 2.1 ± 0.2 nm. The optical properties of the sampleswere studied by four different methods: UV-vis spectroscopy, Fourier transform infrared spectroscopy (FTIR), photoluminescence spectroscopy (PL) and circular dichroism (CD) spectroscopy. The spectra are dominated by the typical and intense plasmonpeak at 486nmaccompanied by asmall shoulder at 540nm. Infraredspectroscopywasmeasured for the free ligand and protected silver nanoclusters, where the disappearance of the S-H vibrational band (2535 e2570cm1) inthe silver nanoclusters confirmed anchoringof ligandto the cluster surface through the sulfur atom.PL studies yieldedthefluorescentpropertiesof the samples.Themainfocus of thiswork,however, lies in the chirality of theparticles. Forall silverclustersCDspectrawere recorded.While for clusters cappedwithone of the two enantiomers (D- or L-form) typical CD spectrawere observed, no significant signalswere detected for a racemic ligandmixture. Furthermore, silver clusters showquite large asymmetry factors (up to 3104) in comparison tomost other ligand protected clusters. These large factors and bands in the visible range of the spectrumsuggest a strong chiral induction fromthe ligand to themetal core. Textural features of the prepared silver nanoclusters were investigated using nitrogen adsorption-desorption at 196 C. Specific surface area SBET, pore volume and average pore diameter were calculated.

An analysis has been carried out to study a problem of the natural convective boundary-layer flow of a nanofluid past a non-linear stretching surface with convective boundary condition in the presence of yield stress in porous media. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The local similarity solutions are obtained by using an efficient numerical shooting technique with a fourth-order Runge–Kutta scheme (MATLAB package). The results corresponding to the dimensionless temperature profiles and the reduced Nusselt number, Sherwood number and skin friction coefficient are displayed graphically for various pertinent parameters. It was found that Nusselt number ( Re − 1 = 2 x Nu x ) and Sherwood number ( Re − 1 = 2 x Sh x ) is a decreasing function of the yield stress parameter Ω and the porous media parameter ξ , while the skin friction coefficient ( Re 1 = 2 x C f ) is an increasing function of the yield stress parameter Ω and the porous media parameter ξ

An analysis has been carried out to study a problem of the natural convective boundary-layer flow of a nanofluid past a non-linear stretching surface with convective boundary condition in the presence of yield stress in porous media. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The local similarity solutions are obtained by using an efficient numerical shooting technique with a fourth-order Runge–Kutta scheme (MATLAB package). The results corresponding to the dimensionless temperature profiles and the reduced Nusselt number, Sherwood number and skin friction coefficient are displayed graphically for various pertinent parameters. It was found that Nusselt number ( Re − 1 = 2 x Nu x ) and Sherwood number ( Re − 1 = 2 x Sh x ) is a decreasing function of the yield stress parameter Ω and the porous media parameter ξ , while the skin friction coefficient ( Re 1 = 2 x C f ) is an increasing function of the yield stress parameter Ω and the porous media parameter ξ

tVery small platinum nanoclusters have been synthesized by reduction of H2PtCl6·6H2O salt with NaBH4in the presence and absence of water-soluble l-cysteine ligand. The synthesized platinum clusters weresupported over anatase titanium dioxide (TiO2) by 1% wt/wt. The spectroscopic properties of Ptn(l-Cys)mclusters were studied by UV–vis spectroscopy and Fourier transform infrared spectroscopy (FTIR) andits chemical structure were determined by thermogravimetric analysis (TGA) and elemental analysis.The particle sizes of supported and non-supported platinum clusters were characterized by transmis-sion electron microscopy (TEM) and powder X-ray diffraction analysis. As well as their specific surfaceareas were determined using nitrogen adsorption/desorption measurements, pore volume and averagepore diameter were also calculated. Finally, oxidation of styrene is used as a simple model reaction todemonstrate that these systems exhibit the potential to be used as heterogeneous catalysts. The dopedmonodisperse platinum clusters (1% Ptn(l-Cys)m/TiO2) catalyst exhibited the highest catalytic activityand selectivity (100% benzaldehyde) in oxidation of styrene. The non-doped platinum clusters (Ptn(l-Cys)m) showed more catalytic activity than doped polydisperse platinum clusters (1% Pt/TiO2). Hydrogenperoxide was used as oxidizing agent, which exhibited stronger oxidation potential than oxygen gas.The unique atom-packing structure and electronic properties of Ptn(l-Cys)mnanoclusters (∼1 nm) arerationalized to be responsible for their extraordinary catalytic activity observed in oxidation of styrene.

Herein, we report the synthesis and characterization of some water-soluble thiol monolayer protected platinum nanoclusters (PtNCs).The cluster material obtained by the reduction of the corresponding metal salt with NaBH4 in presence of water-soluble ligands, L-glutathione (L-GSH) reduced, N-acetyl-L-cysteine (NALC) and L-penicillamine (L-Pen), acting as capping ligands. Platinum nanoclusters with around 1 nm sizes were isolated and characterized by transmission electron microscopy (TEM) and thermogravimetric analysis (TGA). The optical properties of the samples were studied by UV–vis spectroscopy. Fourier transform infrared spectroscopy (FTIR) was measured for the free ligands and protected PtNCs where the disappearance of the S

H vibrational band (2535–2570 cm
1) in the platinum nanoclusters confirmed anchoring of ligand to the cluster surface through the sulfur atom. Textural features of the obtained cluster catalysts were investigated using nitrogen adsorption-desorption at
196 C. Specific surface area SBET, pore volume and average pore diameter were calculated. The prepared clusters were used to load size selected platinum clusters onto Degussa TiO2 P25 to create photocatalysts absorb the visible light. The resulting materials showed high photocatalytic activity in decomposition of methylene blue dye (MB) after irradiation by solar light.

Vibrational contribution to the thermodynamics of nanosized precipitates: vacancy-copper clusters in bcc-Fe