The importance of topology as a tool in preference theory is what motivates this study in which we characterize topologies generating by digraphs. In this paper, we generalized the notions of rough set concepts using two topological structures generated by out (resp. in)-degree sets of vertices on general digraph. New types of topological rough sets are initiated and studied using new types of topological sets. Some properties of topological rough approximations are studied by many propositions.

Two homopolymeric and three copolymeric additives for base oil were synthesized using octyl acrylate (OA) and tert-butyl acrylamide (TBA) monomers. The two additives named P1 and P2 are the homopolymers of TBA and OA, respectively, whereas copolymeric additives named Co1, Co2, and Co3 were synthesized by varying the ratios of TBA:OA as 1:3, 3:1 and 1:1, respectively. The prepared polymers were characterized by Fourier Transform Infrared (FTIR). Based on the solubility of synthesized polymers in base oil and reactivity ratios of TBA/OA copolymer (0.222, 0.434) calculated by Fineman-Ross method, P2, Co1, Co2 and Co3 were selected to evaluate their performance as pour point depressant (PPD), viscosity improver (VII), and anticorrosion addit

This paper contains an equivalent statements of a pre-  space, where  are considered subsets of with the product topology. An equivalence relation between the preclosed set  and a pre-  space, and a relation between a pre-  space and the preclosed set  with some conditions on a function  are found. In addition, we have proved that the graph  of  is preclosed in if  is a pre-  space, where the equivalence relation  on  is open.

     On the other hand, we introduce the definition of a pre-stable ( pre-stable) set by depending on the concept of a pre-neighborhood, where we get that every stable set is pre-stable. Moreover, we obtain that

This work aims to provide a statistical analysis of metal removal during the Magnetic Abrasive Finishing process (MAF) and find out the mathematical model which describes the relationship between the process parameters and metal removal, also estimate the impact of the parameters on metal removal. In this study, the single point incremental forming was used to form the truncated cone made of low carbon steel (1008-AISI) based on the Z-level tool path. Then the finishing was accomplished using a magnetic abrasive process based on the Box-Behnken design of the experiment using Minitab 17 software was used to finish the surface of the formed truncated cone. The influences of different parameters (feed rate, machining step s

Abstract

This research’s goal is to  restore and to revive the jurisprudence of  Mother of Believers (Um alMuaamineen) “Um Salmah” "may God bless her", and to highlight her outstanding assimilation and understanding of religion and her conscious thought.  The current research is a comparative scientific theoretical study  represented in the comparison of  jurisprudence of “Um Salamah” with Hadiths  of  fasting  and pilgrimage rules as well as the duration  mentioned in jurisprudence  of  for doctrines( 4 schools of thought )to identify these hadiths with the inclusion and discussion of their evidence.

The current research included two topics: the first one is to identify and introduce

In our research, we dealt with one of the most important issues of linguistic studies of the Holy Qur’an, which is the words that are close in meaning, which some believe are synonyms, but in the Arabic language they are not considered synonyms because there are subtle differences between them. Synonyms in the Arabic language are very few, rather rare, and in the Holy Qur’an they are completely non-existent. And how were these words, close in meaning, translated in the translation of the Holy Qur’an by Almir Kuliev into the Russian language.

              يتكون الانحدار المقسم من عدة أقسام تفصل بينها نقاط انتماء مختلفة، فتظهر حالة عدم التجانس الناشئة من عملية فصل الأقسام ضمن عينة البحث. ويهتم هذا البحث في تقدير موقع نقطة التغيير بين الأقسام وتقدير معلمات الأنموذج، واقتراح طريقة تقدير حصينة ومقارنتها مع بعض الطرائق المستعملة في الانحدار الخطي المقسم. وقد تم استعمال أحد الطرائق التقليدية (طريقة Muggeo) لإيجاد مقدرات الإمكان الأعظم بالأسلوب الت

Segmented regression consists of several sections separated by different points of membership, showing the heterogeneity arising from the process of separating the segments within the research sample. This research is concerned with estimating the location of the change point between segments and estimating model parameters, and proposing a robust estimation method and compare it with some other methods that used in the segmented regression. One of the traditional methods (Muggeo method) has been used to find the maximum likelihood estimator in an iterative approach for the model and the change point as well. Moreover, a robust estimation method (IRW method) has used which depends on the use of the robust M-estimator technique in

Rheological instrument is one of the basic analytical measurements for diagnosing the properties of polymers fluids to be used in any industry. In this research polycarbonate was chosen because of its importance in many areas and possesses several distinct properties.
Two kinds of rheometers devices were used at different range of temperatures from 220 ˚C-300 ˚C to characterize the rheological technique of melted polycarbonate (Makrolon 2805) by a combination of different investigating techniques. We compared the results of the linear (oscillatory) method with the non-linear (steady-state) method; the former method provided the storage and the loss modulus of melted polycarbonate, and presented the Cox-Merz model as well. One of the