In this paper, we present a Branch and Bound (B&B) algorithm of scheduling (n) jobs on a single machine to minimize the sum total completion time, total tardiness, total earliness, number of tardy jobs and total late work with unequal release dates. We proposed six heuristic methods for account upper bound. Also to obtain lower bound (LB) to this problem we modified a (LB) select from literature, with (Moore algorithm and Lawler's algorithm).  And some dominance rules were suggested. Also, two special cases were derived. Computational experience showed the proposed (B&B) algorithm was effective in solving problems with up to (16) jobs, also the upper bounds and the lower bound were effective in restr

Objective: This study aims to examine how implementing Extensible Business Reporting Language (XBRL) enhances the efficiency and quality of environmental audits and sustainability reporting in eco-friendly universities. Aligned with Sustainable Development Goal 12 (Responsible Consumption and Production), the study emphasizes promoting transparency and precision in sustainability reporting to encourage responsible management of resources within academic institutions.   Theoretical Framework: The importance of our study is evident in the importance of accurate and transparent reports in the development of environmental performance with theories of sustainable reporting and environmental auditing. One of the most important digital

Due to the impact of industrial companies on the ransformations and developments witnessed by the world in general nd Iraq in particular, especially in the industrial and economic Jonrnal spects, the liberalization of internal and external trade, and the idoption of the open market policy in Iraq, which led to the intensification of competition between industrial companies and heir products and services, and the increase and diversity of the Onumber of alternatives Available to the public on the one hand, and he diversity and change of their desires and needs on the other hand, which was reflected in the reality of those companies and heir products or services, especially in light of the great challenges facing companies and the deteriorat

Let R be a commutative ring with identity and let M be a unitary left R-module. The purpose of this paper is to investigate some new results (up to our knowledge) on the concept of semi-essential submodules which introduced by Ali S. Mijbass and Nada K. Abdullah, and we make simple changes to the definition relate with the zero submodule, so we say that a submodule N of an R-module M is called semi-essential, if whenever N ∩ P = (0), then P = (0) for each prime submodule P of M. Various properties of semi-essential submodules are considered.

The pre - equilibrium and equilibrium double differential cross
sections are calculated at different energies using Kalbach Systematic
approach in terms of Exciton model with Feshbach, Kerman and
Koonin (FKK) statistical theory. The angular distribution of nucleons
and light nuclei on 27Al target nuclei, at emission energy in the center
of mass system, are considered, using the Multistep Compound
(MSC) and Multistep Direct (MSD) reactions. The two-component
exciton model with different corrections have been implemented in
calculating the particle-hole state density towards calculating the
transition rates of the possible reactions and follow up the calculation
the differential cross-sections, that include MS

The focus of this research lies in the definition of an important aspect of financial development, which is reflected on the alleviation of poverty in Iraq, namely financial inclusion and then taking the path of achieving a sustainable economy, certainly after reviewing one of the important international experiences in this regard and finally measuring the level of financial inclusion in Iraq and its impact on poverty reduction through the absolute poverty line indicator.

This paper aims to study the quaternary classical continuous optimal control problem consisting of the quaternary nonlinear parabolic boundary value problem, the cost function, and the equality and inequality constraints on the state and the control. Under appropriate hypotheses, it is demonstrated that the quaternary classical continuous optimal control ruling by the quaternary nonlinear parabolic boundary value problem has a quaternary classical continuous optimal control vector that satisfies the equality constraint and inequality state and control constraint. Moreover, mathematical formulation of the quaternary adjoint equations related to the quaternary state equations is discovered, and then the weak form of the quaternary adjoint

Since the property in Islam is based on the principle of succession , "which made ​​you Khalaúv land and raise yourselves above some degree of Iblukm with Atakm The Lord of the fast punishment and it is Forgiving, Merciful " [cattle : 165 ] and human only Mstkhalaf where " God promised you who believe and do good deeds for Istkhalvenhm Normans in the ground as those before them " [Nur : 55 ] , considering that King God alone any talk about having ownership in Islam in the contemporary sense of ownership , containing three rights are:

1- right to dispose of the right of usufruct tenure

2-The concept is ambiguous as long as that man Mstkhalaf does not have the right to dispose

The theory of general topology view for continuous mappings is general version and is applied for topological graph theory. Separation axioms can be regard as tools for distinguishing objects in information systems. Rough theory is one of map the topology to uncertainty. The aim of this work is to presented graph, continuity, separation properties and rough set to put a new approaches for uncertainty. For the introduce of various levels of approximations, we introduce several levels of continuity and separation axioms on graphs in Gm-closure approximation spaces.