The unique properties of Gemini surfactants and their variety of applications encouraged many researchers to synthesize more of these compounds. Herein, we constructed new cationic Gemini surfactants by using aromatic spacers with different chain lengths. The critical micelle concentration value for each surfactant was determined using the electrical conductivity measurements. The variety of aggregation behaviors of Gemini surfactants was studied by using atomic force microscopy, which encouraged us to use these surfactants in the preparation of mesoporous silica NPs. Our results indicated that we have succeeded in finding a new soft-template for preparing uniform small size hollow spheres mesoporous silica NPs of a diameter depending on the used surfactant. Moreover, we investigated the effect of pH value on the morphology of the prepared silica, which indicated that using of acidic media resulted in the formation of hollow micro-particles instead of hollow NPs. Furthermore, the anticorrosion efficiency of these surfactants in comparing with cetyltrimethylammonium bromide (CTAB) as a positive control was investigated by monitoring the corrosion rate of iron sheets in 0.5M of hydrochloric acid based on weight loss method. Our results indicated that all the prepared Gemini surfactants possessed higher anti-corrosion efficiency at very low concentrations than CTAB surfactant.

CdS nanoparticles were synthesized by co-precipitation method. Samples were annealed in air for 3hrs in the temperature range of 200-700°C to study the effect of annealing temperature (Ta) on structural, morphological and optical properties of CdS nanoparticles. Monodispersed CdS was UV irradiated to investigate photo-induced changes in the optical properties of the samples. Structural and optical properties were characterized using XRD, HRTEM, UV-vis absorption and FTIR spectroscopy. The increase in average crystallite size from 3 to 23 nm as a result of annealing has been estimated from XRD. Total phase transition at Ta = 300oC from as prepared Cubic to hexagonal CdS structure and to CdSO3 monoclinic structure at Ta = 700oC. Analysis of UV-vis absorption spectra, show remarkable decrease in optical band gap from 3.4 for as prepared to 2.5eV at 500oC with increasing Ta, as a result of enhancement in crystallinity and increase in particle size, which in turn leads to the reduction of quantum confinement effect. UV induced effect on CdS nanoparticles dispersed in double distilled water leads to an increase in the optical band gap (photo-brightening).

The main object of this present paper is to introduce an extended family of Laguerre matrix polynomials and to derive a new class of certain summation formulas with the help of the Lie algebra method using techniques.

In this study, we establish new two-sided inequalities for Tricomi functions. Some special and confluent cases of our main aim are established with the help of the inequalities for hypergeometric functions;_{0}F_{1}.

This work is devoted to the study of some new families of matrix functions which provide a further extension of the extended Bessel matrix functions. In the sequel, some new and interesting properties of these families of k-Bessel matrix functions have been investigated and the connections between k-Bessel matrix functions and k-Laguerre matrix polynomials are indicated in the concluding section of the paper.

This paper is devoted to construct Lie operators associated with Konhauser matrix polynomials of the first kind using Lie group theory. Furthermore, certain generating matrix functions, integral representations, and matrix differential recurrence relations, new and known consequences for Konhauser matrix polynomials are derived and their applications are presented.

This study deals with the convergence properties of Struve matrix functions within the complex analysis. Certain new classes of matrix differential recurrence relations, matrix differential equations, the various families of integral representations and integrals obtained here are believed to be new in the theory of Struve matrix functions, and the several properties of the modified Struve matrix functions are also included. Finally, we investigate the operational rules which yield a different view of the expansion formulae for Struve and modified Struve matrix functions.

The aim of this present paper is to investigate interesting generating matrix relations for generalized Hermite-type matrix polynomials by the application of the Lie group-theoretic method. Based on the Weisner's group theoretic method, we derived some properties for these generalized Hermite-type matrix polynomials. Some applications of the result are also given here.

Mathematical inequalities and other results involving such widely- and extensively-studied special functions of mathematical physics and applied mathematics as (for example) the Bessel, Struve and Lommel functions as well as the associated hypergeometric functions are potentially useful in many seemingly diverse areas of applications, especially in situations in which these functions are involved in solutions of mathematical, physical and engineering problems which can be modeled by ordinary and partial differential equations. With this objective in view, our present investigation is motivated by some open problems involving inequalities for a number of particular forms of the hypergeometric function 1F2(a; b, c; z). Here, in this paper, we apply a novel approach to such problems and obtain presumably new two-sided inequalities for the Struve function, the associated Struve function and the modified Struve function by first investigating inequalities for the general hypergeometric function 1F2(a; b, c; z). We also briefly discuss the analogous new inequalities for the Lommel function under some conditions and constraints. Finally, as special cases of our main results, we deduce several inequalities for the modified Lommel function and the normalized Lommel function.

By using the generating-function method as a starting point, the authors construct several (presumably new) basic (or q-) extensions of the Humbert function. Various potentially useful properties of these q-Humbert functions including (for example) explicit representations, recurrence relations and differential recurrence relations are derived by applying the defining generating functions.