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.

A dynamical system describes the consequence of the current state of an event or particle in future. The models expressed by functions in the dynamical systems are more often deterministic, but these functions might also be stochastic in some cases. The prediction of the system's behavior in future is studied with the analytical solution of the implicit relations (Differential, Difference equations) and simulations. A discrete-time first order system of equations with quadratic nonlinearity is considered for study in this work. Classical approach of stability analysis using Jury's condition is employed to analyze the system's stability. The chaotic nature of the dynamical system is illustrated by the bifurcation theory. The enhancement o

In this research, the possibility of using waste wooden materials (reed and sawdust) was studied to produce sustainable and thermal insulation lightweight building units , which has economic and environmental advantages. This study is intended to produce light weight building units with low thermal conductivity, so it can be used as partitions to improve the thermal insulation in buildings. Waste wooden materials were used as a partial replacement of natural sand, in different percentages (10, 20, 30, and 40) % . The mix proportions were (1:2.5) (cement: fine aggregate) with w/c of 0.4. The values of 28 days oven dry density ranged between (2060-1693) kg/m³.The thermal conductivity decreased from (0.745 to 0.2

The paper discusses the lack of a uniform definition of politeness due to the constant tension between its universality and language specificity, and argues that some of the theoretical debate could be resolved if the distinction between politeness as a commonsense notion and politeness as a theoretical construct were clearly addressed and acknowledged in the research.

This research aims at shedding light on the concept of insurance awareness and clarifying its role on marketing insurance services of a sample of (100) employees in the National Company for Insurance. Questionnaire is used as a main instrument for collecting data and information from the sample. Their answers were analyzed by using arithmetic means, standard deviation, centesimal weight, and the correlation coefficient ( , F, t) tests .The research reached several conclusions of which:1.The sample member's response to insurance awareness and marketing insurance services factors was in the medium level.2.There was a positive relationship of a moral sign between insurance awareness and marketing insurance services, that correlation coeffic

      Let A, and N  are a semiring ,and  a left A- semimodule, respectively. In this work we will discuss two cases: 

1. The direct summand of π-projective semi module is π-projective, while the direct sum of two π-projective semimodules in general is not π-projective . The details of the proof will be given.
2. We will give a condition under which the direct sum of two π-projective semi modules is π-projective, as well as we also set conditions under which π-projective semi modules are projective.

The study was conducted at research station A, department of field crops, college of agricultural engineering sciences, university of Baghdad during summer 2021 to evaluate the effect of boron and some growth regulators on some growth criteria and yield of soybean crop (cv. shimaa). The experiment  was carried out according to split plots by using randomized complete block design with three replications. The main plots included three concentrations of boron (75, 150 and 225) mg.L^-1, the sub-plots included three levels of growth regulators, spraying kinetin (100 mg. L^-1), spraying ethrel (200 mg.L^-1) and spraying kinetin (100 mg.L^-1) + spraying ethrel (200 mg.L^-1) as

  In this paper we introduce a new class of degree of best algebraic approximation polynomial Α,, for unbounded functions in weighted space Lp,α(X), 1 ∞ .We shall prove direct and converse theorems for best algebraic approximation in terms modulus of smoothness in weighted space

Our goal from this work is to find the linear prediction of the sum of two Poisson process
) ( ) ( ) ( t Y t X t Z + = at the future time 0 ), ( ≥ + τ τ t Z and that is when we know the values of
) (t Z in the past time and the correlation function ) (τ βz

The discussion in this paper gives several theorems and lemmas on the Sums of Squares of  consecutive Carol Numbers. These theorems are proved by using the definition of carol numbers and mathematical induction method. Here the matrix form and the recursive form of sum of squares of  consecutive Carol numbers is also given. The properties of the Carol numbers are also derived.