With simple and undirected connected graph Φ, the Schultz and modified Schultz polynomials are defined as  and , respectively, where the summation is taken over all unordered pairs of distinct vertices in V(Φ), where V(Φ) is the vertex set of Φ, degu  is the degree of vertex u and d(v,u) is the ordinary distance between v and u, u≠v. In this study, the Shultz distance, modified Schultz distance, the polynomial, index, and average for both have been generalized, and this generalization has been applied  to some special graphs.

Thin films of CuPc of various thicknesses (150,300 and 450) nm have been deposited using pulsed laser deposition technique at room temperature. The study showed that the spectra of the optical absorption of the thin films of the CuPc  are two bands of absorption one in the visible region at about 635 nm, referred to as Q-band, and the second in ultra-violet region where B-band is located at 330 nm. CuPc thin films were found to have direct band gap with values around (1.81 and 3.14 (eV respectively. The vibrational studies were carried out using Fourier transform infrared spectroscopy (FT-IR). Finally, From open and closed aperture Z-scan data non-linear absorption coefficient and non-linear refractive index have been calculated res

Assume that G is a finite group and X = tG where t is non-identity element with t3 = 1. The simple graph with node set being X such that a, b ∈ X, are adjacent if ab-1 is an involution element, is called the A4-graph, and designated by A4(G, X). In this article, the construction of A4(G, X) is analyzed for G is the twisted group of Lie type 3D4(3).

     The linear instability and nonlinear stability analyses are performed for the model of bidispersive local thermal non-equilibrium flow. The effect of local thermal non-equilibrium on the onset of convection in a bidispersive porous medium of Darcy type is investigated.  The temperatures in the macropores and micropores are allowed to be different. The effects of various interaction parameters on the stability of the system are discussed. In particular, the effects of the porosity modified conductivity ratio parameters,  and , with the int

We study in this paper the composition operator of induced by the function ?(z)=sz+t where , and We characterize the normal composition operator C? on Hardy space H2 and other related classes of operators. In addition to that we study the essential normality of C? and give some other partial results which are new to the best of our knowledge.

     The increased food requirement puts intense pressure on the agriculture community to grow more from the same resources resulting in people leaving the farming business. This happened not exclusively due to the industrial pressure to produce more but to the lack of technology adoption among growers. The use of the sensor in agriculture is not new, but its adoption among agriculture producers is a challenge for industry and scientists. This study aimed to determine sensors used in agricultural fields with challenges and prospects. The study found that sensors have successfully been used at the industry level with highly skilled labor; however, their adoption is challenging in rural agriculture systems due to the lack of a support

     Let G be a finite group and X be a G-conjugacy of elements of order 3. The A4-graph of G is a simple graph with vertex set X and two vertices x,yÎX are linked if x≠ y and xy^-1 is an involution element. This paper aims to investigate  the A4-graph properties for the monster  Held group He.

This research –paper tack les some of matters relating to marriageability of the young man who has not attained discretion. the aim of this study is to highlight the religious precepts concerned. the religious missive to this effect reads; ''all praise be to Allah ,lord of the world ;I witness that  there is no god but Allah, the sole and only, to him all creation is attributed. He taught man with pen, and all that he does not know, so exalted is he, and I witness that Mohammed is his servant and messenger, the master of all messengers and the seal of all prophets who was entrusted with a message of march to all mankind. May the blessings of Allah be to him, his household and companions. Until the day of Judgement. "this missive i