The concept of the order sum graph associated with a finite group based on the order of the group and order of group elements is introduced. Some of the properties and characteristics such as size, chromatic number, domination number, diameter, circumference, independence number, clique number, vertex connectivity, spectra, and Laplacian spectra of the order sum graph are determined. Characterizations of the order sum graph to be complete, perfect, etc. are also obtained.

We used to think of grammar as the bones of the language and vocabulary as the flesh to be added given that language consisted largely of life generated chunks of lexis. This “skeleton image” has been proverbially used to refer to that central feature of lexis named collocation- an idea that for the first 15 years of language study and analysis gave a moment‟s thought to English classroom material and methodology.
The work of John Sinclair, Dave Willis, Ron Carter, Michael McCarthy, Michael Lewis, and many others have all contributed to the way teachers today approach the area of lexis and what it means in the teaching/learning process of the language. This also seems to have incorporated lexical ideas into the teaching mechanis

An energy and exergy thermodynamic analysis using EES program was done for a domestic refrigerator working with R-134a using vapor compression refrigeration cycle. The analysis deals with the system component, i.e. compressor, condenser, evaporator and the expansion device. The analysis depends on the entropy generation minimization approach to improve the refrigerator performance by exploring the optimum design points. These design points were derived from three different theories governing the entropy generation minimization using exergy analyzing method. These theories were first applied to find the optimum balance between the hot inner condenser area and the cold inner evaporator area of the refrigerator and between

A new definition of a graph called Pure graph of a ring denote Pur(R) was presented , where the vertices of the graph represent the elements of R such that there is an edge between the two vertices ???? and ???? if and only if ????=???????? ???????? ????=????????, denoted by pur(R) . In this work we studied some new properties of pur(R) finally we defined the complement of pur(R) and studied some of it is properties

This paper generalizes and improves the results of Margenstren, by proving that the number of -practical numbers  which is defined by   has a lower bound in terms of . This bound is more sharper than Mangenstern bound when  Further general results are given for the existence of -practical numbers, by proving that the interval contains a -practical for all

In this paper, various aspects of smart grids are described. These aspects include the components of smart grids, the detailed functions of the smart energy meters within the smart grids and their effects on increasing the awareness, the advantages and disadvantages of smart grids, and the requirements of utilizing smart grids. To put some light on the difference between smart grids and traditional utility grids, some aspects of the traditional utility grids are covered in this paper as well.

In this study, the antimicrobial properties of newly synthesized Schiff bases (4a-4e) and thiazolidinone compounds (5a-5e) generated from 3,5-dinitrobenzoic acid were assessed. These compounds were obtained by reacting 3,5-dinitrobenzoic acid (1) with ethanol in a few drops of concentrated H2SO4 to produce the ester (2). The acid hydrazide (3), which was produced by treating the ester with hydrazine hydrate, reacted with the proper aldehydes, including 4-bromobenzaldehyde, 4-chlorobenzaldehyde, 4-hydroxybenzaldehyde, 4-methoxybenzaldehyde, and 4-hydroxy-3-methoxybenzaldehyde, respectively, to form Schiff bases (4a-4e). The thiazolidinone compounds (5a-5e) were produced by the cyclocondensation reaction of compounds (4a-4e) with thio

In this study, the antimicrobial properties of newly synthesized Schiff bases (4a-4e) and thiazolidinone compounds (5a-5e) generated from 3,5-dinitrobenzoic acid were assessed. These compounds were obtained by reacting 3,5-dinitrobenzoic acid (1) with ethanol in a few drops of concentrated H2SO4 to produce the ester (2). The acid hydrazide (3), which was produced by treating the ester with hydrazine hydrate, reacted with the proper aldehydes, including 4-bromobenzaldehyde, 4-chlorobenzaldehyde, 4-hydroxybenzaldehyde, 4-methoxybenzaldehyde, and 4-hydroxy-3-methoxybenzaldehyde, respectively, to form Schiff bases (4a-4e). The thiazolidinone compounds (5a-5e) were produced by the cyclocondensation reaction of compounds (4a-4e) with thio

Sorghum cultivation is often accompanied by low field emergence rates and weak seedlings, which may be due to genetic or environmental stress. A factorial experiment was conducted in the spring and fall seasons of 2022 using a randomized complete block design with split-plot arrangement and four replications. Planting dates (spring season: Feb. 15th, Mar. 1st, 15th, and Apr. 1st, 15th; fall season: Jun. 15th, Jul. 1st, 15th, and Aug. 1st, 15th) were allocated to the main plots. Seeds stimulation treatments (35% banana peel extract + 100 mg L-1 citric acid and distilled water soaking treatment only) were allocated to the subplots. The interaction treatment (banana peel extract + citric acid) with the planting date of April 15 showed the high