Consider the (p,q) simple connected graph . The sum absolute values of the spectrum of quotient matrix of a graph  make up the graph's quotient energy. The objective of this study is to examine the quotient energy of identity graphs and zero-divisor graphs  of commutative rings using group theory, graph theory, and applications. In this study, the identity graphs  derived from the group  and a few classes of zero-divisor graphs  of the commutative ring R are examined.

In this work, the design and implementation of a smart energy metering system has been developed. This system consists of two parts: billing center and a set of distributed smart energy meters. The function of smart energy meter is measuring and calculating the cost of consumed energy according to a multi-tariff scheme. This can be effectively solving the problem of stressing the electrical grid and rising consumer awareness. Moreover, smart energy meter decreases technical losses by improving power factor. The function of the billing center is to issue a consumer bill and contributes in locating the irregularities on the electrical grid (non-technical losses). Moreover, it sends the switch off command in case of the consumer bill is not

In this paper, a sufficient condition for stability of a system of nonlinear multi-fractional order differential equations on a finite time interval with an illustrative example, has been presented to demonstrate our result. Also, an idea to extend our result on such system on an infinite time interval is suggested.

The PbSe alloy was prepared in evacuated quarts tubs by the method of melt quenching from element, the PbSe thin films prepared by thermal evaporation method and deposited at different substrate temperature (Ts) =R.T ,373 and 473K . The thin films that deposited at room temperature (R.T=303)K was annealed at temperature, Ta= R.T, 373 and 473K . By depended on D.C conductivity measurements calculated the density of state (DOS), The density of extended state N(Eext) increases with increasing the Ts and Ta, while the density of localized state N(Eloc) is decreased . We investigated the absorption coefficient (?) that measurement from reflection and transmission spectrum result, and the effect of Ts and Ta on it , also we calculated the tai

            The article describes a certain computation method of -arcs to construct the number of distinct -arcs in  for . In this method, a new approach employed to compute the number of -arcs and the number of distinct arcs respectively. This approach is based on choosing the number of inequivalent classes } of -secant distributions that is the number of 4-secant, 3-secant, 2-secant, 1-secant and 0-secant in each process. The maximum size of -arc that has been constructed by this method is . The new method is a new tool to deal with the programming difficulties that sometimes may lead to programming problems represented by the increasing number of arcs. It is essential to reduce the established number of -arcs in each cons

The study aims to identify the third instar larvae of fly species (Order : Diptera) feeding on carcasses (Fishes and Rabbits). Two families (Calliphoridae and Sarcophagidae), were recorded with highest rate in Calliphoridae species. The following species had been registered in accordance with their prevalence respectively; Calliphora vicina Rob.-Desvoidy, Chrysomya albiceps (Wiedmann), Chrysomy megacephala (Fabricius), Sarcophaga sp. and Lucilia sericata (Meigen). The highest rate has been registered Calliphora vicina during February, November, December and January at rate 100%, the larvae of this fly have not been observed during July, August, September and October. The highest rate of Ch