Within this research, The problem of scheduling jobs on a single machine is the subject of study to minimize the multi-criteria and multi-objective functions. The first problem, minimizing the multi-criteria, which include Total Completion Time, Total Late Work, and Maximum Earliness Time (∑𝐶𝑗, ∑𝑉𝑗, 𝐸𝑚𝑎𝑥), and the second problem, minimizing the multi-objective functions ∑𝐶𝑗 + ∑𝑉𝑗 +𝐸𝑚𝑎𝑥 are the problems at hand in this paper. In this study, a mathematical model is created to address the research problems, and some rules provide efficient (optimal) solutions to these problems. It has also been proven that each optimal solution for ∑𝐶𝑗 + ∑𝑉𝑗 + 𝐸𝑚𝑎𝑥 is an effic

HS Saeed, SS Abdul-Jabbar, SG Mohammed, EA Abed, HS Ibrahem, Solid State Technology, 2020

Throughout this paper we introduce the concept of quasi closed submodules which is weaker than the concept of closed submodules. By using this concept we define the class of fully extending modules, where an R-module M is called fully extending if every quasi closed submodule of M is a direct summand.This class of modules is stronger than the class of extending modules. Many results about this concept are given, also many relationships with other related concepts are introduced.

Throughout this paper R represents commutative ring with identity and M is a unitary left R-module. The purpose of this paper is to investigate some new results (up to our knowledge) on the concept of weak essential submodules which introduced by Muna A. Ahmed, where a submodule N of an R-module M is called weak essential, if N ? P ? (0) for each nonzero semiprime submodule P of M. In this paper we rewrite this definition in another formula. Some new definitions are introduced and various properties of weak essential submodules are considered.

 الأثر V بالنسبة إلى   sinshT و خواصه قد تم دراسته في هذا البحث حيث تم دراسة علاقة الأثر المخلص والاثر المنتهى التولد والاثر المنفصل وربطها بالمؤثرات المتباينة حيث تم بهنة العلاقات التالية ان الاثر اذا وفقط اذا مقاس في حالة كون المؤثر هو عديم القوة وكذلك في حالة كون المؤثر شامل فان الاثر هو منتهي التولد اي ان الغضاء هو منتهي التولد وايضا تم برهن ان الاثر مخلص لكل مؤثر مقيد وك\لك قد تم التحقق من انه لاي مؤثر مقي

A non-zero submodule N of M is called essential if N L for each non-zero submodule L of M. And a non-zero submodule K of M is called semi-essential if K P for each non-zero prime submodule P of M. In this paper we investigate a class of submodules that lies between essential submodules and semi-essential submodules, we call these class of submodules weak essential submodules.

The main goal of this paper is introducing and studying a new concept, which is named H-essential submodules, and we use it to construct another concept called Homessential modules. Several fundamental properties of these concepts are investigated, and other characterizations for each one of them is given. Moreover, many relationships of Homessential modules with other related concepts are studied such as Quasi-Dedekind, Uniform, Prime and Extending modules.

The smart city concept has attracted high research attention in recent years within diverse application domains, such as crime suspect identification, border security, transportation, aerospace, and so on. Specific focus has been on increased automation using data driven approaches, while leveraging remote sensing and real-time streaming of heterogenous data from various resources, including unmanned aerial vehicles, surveillance cameras, and low-earth-orbit satellites. One of the core challenges in exploitation of such high temporal data streams, specifically videos, is the trade-off between the quality of video streaming and limited transmission bandwidth. An optimal compromise is needed between video quality and subsequently, rec

Throughout this paper we introduce the notion of coextending module as a dual of the class of extending modules. Various properties of this class of modules are given, and some relationships between these modules and other related modules are introduced.

     The purpose of this paper is to introduce dual notions of two known concepts which are semi-essential submodules and semi-uniform modules. We call these concepts; cosemi-essential submodules and cosemi-uniform modules respectively. Also, we verify that these concepts form generalizations of two well-known classes; coessential submodules and couniform modules respectively. Some conditions are considered to obtain the equivalence between cosemi-uniform and couniform. Furthermore, the relationships of cosemi-uniform module with other related concepts are studied, and some conditional characterizations of cosemi-uniform modules are investigated.

الاحتفال عام 1999، هي واحدة من المسرحيات السياسية المؤثرة لهارولد بنتر وفيها ينتقد الناس الذين من المفترض أن يكونوا قوات حفظ السلام، ويسميهم بنتر في المسرحية (مستشارو الاستراتيجية)، ويرعون شؤون الآخرين المهمة لأنهم يمثلون السلطة، في حين ان بنتر صورهم في هذه المسرحية كأناس يتكلمون عن أشياء تافهة ولا يهتمون بحالات القمع السياسي، والفقر، وغيرها من القضايا الهامة للناس في العالم. وعلاوة على ذلك، لم يكن لديهم أي

The main objective of this thesis is to study new concepts (up to our knowledge) which are P-rational submodules, P-polyform and fully polyform modules. We studied a special type of rational submodule, called the P-rational submodule. A submodule N of an R-module M is called P-rational (Simply, N≤_prM), if N is pure and Hom_R (M/N,E(M))=0 where E(M) is the injective hull of M. Many properties of the P-rational submodules were investigated, and various characteristics were given and discussed that are analogous to the results which are known in the concept of the rational submodule. We used a P-rational submodule to define a P-polyform module which is contained properly in the polyform module. An R-module M is called P-polyform if every es

A new class of higher derivatives  for harmonic univalent functions defined by a generalized fractional integral operator inside an open unit disk E is the aim of this paper.

Throughout this paper R represents a commutative ring with identity and all R-modules M are unitary left R-modules. In this work we introduce the notion of S-maximal submodules as a generalization of the class of maximal submodules, where a proper submodule N of an R-module M is called S-maximal, if whenever W is a semi essential submodule of M with N ⊊ W ⊆ M, implies that W = M. Various properties of an S-maximal submodule are considered, and we investigate some relationships between S-maximal submodules and some others related concepts such as almost maximal submodules and semimaximal submodules. Also, we study the behavior of S-maximal submodules in the class of multiplication modules. Farther more we give S-Jacobson radical of rings

In this paper the full stable Banach gamma-algebra modules, fully stable Banach gamma-algebra modules relative to ideal are introduced. Some properties and characterizations of these classes of full stability are studied.

Machine scheduling problems (MSP) are     considered as one of the most important classes of combinatorial optimization problems. In this paper, the problem of job scheduling on a single machine is studied to minimize the multiobjective and multiobjective objective function. This objective function is: total completion time, total lead time and maximum tardiness time, respectively, which are formulated as  are formulated. In this study, a mathematical model is created to solve the research problem. This problem can be divided into several sub-problems and simple algorithms have been found to find the solutions to these sub-problems and compare them with efficient solutions. For this problem, some rules that provide efficient solutio

في هذا البحث تم دراسة تأثير متغير الدوران والمتغيرات الأخرى على التدفق التمعجي لسائل سوتربي في قناة غير متماثلة مائلة تحتوي على وسط مسامي مع انتقال الحرارة. في وجود الدوران، تم تطوير النمذجة الرياضية باستخدام المعادلات الاساسية القائمة على نموذج سائل سوتربي. في تحليل التدفق، يتم استخدام افتراضات مثل تقريب طول الموجة الطويلة وانخفاض عدد رينولدز. تم حل المعادلة التفاضلية الاعتيادية غير الخطية الناتجة تح

     A submodule N is called rational in M if ( , E(M))=0, where E(M) is the an injective hull of M. Rational submodules have been studied and discussed by many authors such as H.H. Storrer, H. Khabazian, E. Ghashghaei, A. Hajikarimi, M.S. Abbas and M.S. Nayef. The main objective of this paper is to give a new class of submodules named P-rational submodules. This class is contained properly in the class of rational submodules. Several properties of this concept are introduced. The relationships between this class of submodules and some other related concepts are discussed such as essential and quasi-invertible submodules. Other characterizations of the P-rational submodule analogous to those which is known in the concept of the ratio

In this paper, we introduce and study a new concept named couniform modules, which is a dual notion of uniform modules, where an R-module M is said to be couniform if every proper submodule N of M is either zero or there exists a proper submodule N1 of N such that is small submodule of Also many relationships are given between this class of modules and other related classes of modules. Finally, we consider the hereditary property between R-module M and R-module R in case M is couniform.

        An R-module M is called polyform if every essential submodule of M is rational. The main goal of this paper is to give a new class of modules named P-polyform modules. This class of modules are contained properly in the class of polyform modules. Several properties of this concept are introduced and compared with those which is known in the concept of polyform modules. Another characterization of the definition of P-polyform modules is given as an analogue to that in the concept of polyform modules. So we proved that a module M is P-polyform if and only if M)= 0, for each essential submodule N of M, which is pure in M, and a submodule K of M, with NÍKÍM. The relationships between this class of modules and some other rela

The main goal of this paper is to introduce and study a new concept named d^*-supplemented which can be considered as a generalization of W- supplemented modules and d-hollow module. Also, we introduce a d^*-supplement submodule. Many relationships of d^*-supplemented modules are studied. Especially, we give characterizations of d^*-supplemented modules and relationship between this kind of modules and other kind modules for example every d-hollow (d-local) module is d^*-supplemented and by an example we show that the converse is not true.

The purpose of this paper is to define fuzzy subspaces for fuzzy space of orderings and we prove some results about this definition in which it leads to a lot of new results on fuzzy space of orderings. Also we define the sum and product over such spaces such that: If f = < a1,…,an > and g = < b1,…bm>, their sum and product are f + g = < a1…,an, b1, …, bm> and f × g =. for all a1,…,an,b1,…,bm ? G

in this paper the notion of threshold relations by using resemblance relation are introduced to get a similarity relation from a resemnblance relation R