Graph  is a tool that can be used to simplify and solve network problems. Domination is a typical network problem that graph theory is well suited for. A subset of nodes in any network is called dominating if every node is contained in this subset, or is connected to a node in it via an edge. Because of the importance of domination in different areas, variant types of domination have been introduced according to the purpose they are used for. In this paper, two domination parameters the first is the restrained and the second is secure domination have been chosn. The secure domination, and some types of restrained domination in one type of trees is called complete ary tree  are determined.

Let P be a right R-module, where R is a ring with identity. In the present research, a class of modules is described similar to H-μ-supplemented and μ-lifting modules. A module P is called principally H-μ-supplemented if there is a summand L of P such that pR is μ-equivalent to L for every p in P. Additionally, we present an extension of supplemented modules. A module P is considered to be principally μ-supplemented if, for every p in P, pR has a μ-supplement in P. A number of characteristics of these modules are shown, and it is demonstrated that both the Pμ-H-supplemented and Pμ-supplemented modules include the class of principally μ-lifting modules.

Thin a-:H films were grown successfully by fabrication of designated ingot followed by evaporation onto glass slides. A range of growth conditions, Ge contents, dopant concentration (Al and As), and substrate temperature, were employed. Stoichiometry of the thin films composition was confirmed using standard surface techniques. The structure of all films was amorphous. Film composition and deposition parameters were investigated for their bearing on film electrical and optical properties. More than one transport mechanism is indicated. It was observed that increasing substrate temperature, Ge contents, and dopant concentration lead to a decrease in the optical energy gap of those films. The role of the deposition conditions on value

Research Summary

First: the problem of research and its importance

      The teacher's success in facilitating the students' learning and growth according to the educational and educational goals set out, he must identify the problems of discipline of students in the classroom in terms of sources and reasons and types and methods of prevention and treatment and the teacher to remember that success in his teaching and instruction is not completed more fully once he has the information And knowledge of the subject of the lesson, but must understand the dynamics of the group (class group) and master the skills of classroom management, su

Background: Venous leg ulcers (VLUs) affect 1-3% of the population and impose substantial pain-related morbidity, yet vascular pain remains underrecognized in clinical practice and research. Objectives: This narrative review synthesizes current evidence on the pathophysiology, clinical manifestations, and management strategies for VLU-associated pain. Methods: A comprehensive literature search was conducted across PubMed/MEDLINE, Scopus, Embase, and Web of Science (January 2015-July 2025) following SANRA guidelines. Search terms included "vascular pain", "venous leg ulcer", "chronic venous disease" and related terminology. Studies addressing pathophysiology, clinical characteristics, diagnostic approaches, and therapeutic interventi

 A New developed technique to estimate the necessary six elastic constants of homogeneous laminate of special orthotropic properties are presented in this paper for the first time. The new approach utilizes the elasto-static deflection behavior of composite cantilever beam employing the famous theory of Timoshenko. Three extracted strips of the composite plate are tested for measuring the bending deflection at two locations. Each strip is associated to a preferred principal axis and the deflection is measured in two orthogonal planes of the beam domain. A total of five trails of testing is accomplished and the numerical results of the stiffness coefficients are evaluated correctly under the contribution of the macromechanic

Modern statistical techniques offer a range of methodologies for modelling time series data, with conditional and unconditional approaches providing complementary insights that enhance overall model accuracy. This article introduced a modified ARIMA model employing conditional and unconditional parameter estimates. The methodology for the new model based on novel methods is provided. The prediction process, one and two steps ahead, is covered in detail, and a novel algorithm is presented. The best model is picked based on various measurement criteria, such as coefficient of determination (R2), root mean squared error (RMSE), and mean absolute scaled error (MASE). The suggested model is applied to a monthly petrol sales dataset (Jan

Metoclopramide (MCP) ion selective electrodes based on metoclopramide-phosphotungstic acid (MCP-PT) ion pair complex in PVC matrix membrane were constructed. The plasticizers used were tri-butyl phosphate (TBP), di-octyl phenyl phosphonate (DOPP), di-butyl phthalate (DBPH), di-octyl phthalate (DOP), di-butyl phosphate (DBP), bis 2-ethyl hexyl phosphate (BEHP). The sensors based on TBP, DOPP, DBPH and DOP display a fast, stable and linear response with slopes 59.9, 57.7, 57.4, 55.3 mV/decade respectively at pH ranged 2-6. The linear concentration range between 1.0×10^-5 – 1.0×10^-2 M with detection limit 3.0×10^-6 and 4.0×10^-6 M for electrodes using TBP, DOPP and DBPH while e

This article proposes a new strategy based on a hybrid method that combines the gravitational search algorithm (GSA) with the bat algorithm (BAT) to solve a single-objective optimization problem. It first runs GSA, followed by BAT as the second step. The proposed approach relies on a parameter between 0 and 1 to address the problem of falling into local research because the lack of a local search mechanism increases intensity search, whereas diversity remains high and easily falls into the local optimum. The improvement is equivalent to the speed of the original BAT. Access speed is increased for the best solution. All solutions in the population are updated before the end of the operation of the proposed algorithm. The diversification f

The current research aims to identify the perceptual speed of the university students as well as to identify the differences in the level of perceptual speed for the university students according to the variables of (male, female) specialization (scientific, human) university (Baghdad, Mustansiriya). Additionally, the research aims to identify the prevalence of emotional pattern and to identify the relationship between perceptual speed and the emotional patterns among university students. The researcher designed a questionnaire to measure the Emotional Patterns based on Jerome Freedman perspective. As for perceptual speed, the researcher adopted French, Extrom and Price scale (1963), which was tran