In this paper we will investigate some Heuristic methods to solve travelling salesman problem. The discussed methods are Minimizing Distance Method (MDM), Branch and Bound Method (BABM), Tree Type Heuristic Method (TTHM) and Greedy Method (GRM).

The weak points of MDM are manipulated in this paper. The Improved MDM (IMDM) gives better results than classical MDM, and other discussed methods, while the GRM gives best time for 5≤ n ≤500, where n is the number of visited cities.

     The searching process using a binary codebook of combined Block Truncation Coding (BTC) method and Vector Quantization (VQ), i.e. a full codebook search for each input image vector to find the best matched code word in the codebook, requires a long time.   Therefore, in this paper, after designing a small binary codebook, we adopted a new method by rotating each binary code word in this codebook into 90⁰ to 270⁰ step 90⁰ directions. Then, we systematized each code word depending on its angle  to involve four types of binary code books (i.e. Pour when , Flat when  , Vertical when, or Zigzag). The proposed scheme was used for decreasing the time of the coding pro

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.

Introduction: Although soap industry is known from hundreds of years, the development accompanied with this industry was little. The development implied the mechanical equipment and the additive materials necessary to produce soap with the best specifications of shape, physical and chemical properties. Objectives: This research studies the use of vacuum reactive distillation VRD technique for soap production. Methods: Olein and Palmitin in the ratio of 3 to 1 were mixed in a flask with NaOH solution in stoichiometric amount under different vacuum pressures from -0.35 to -0.5 bar. Total conversion was reached by using the VRD technique. The soap produced by the VRD method was compared with soap prepared by the reaction - only method which

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.

     Coronavirus disease (COVID-19), which is caused by SARS-CoV-2, has been announced as a global pandemic by the World Health Organization (WHO), which results in the collapsing of the healthcare systems in several countries around the globe. Machine learning (ML) methods are one of the most utilized approaches in artificial intelligence (AI) to classify COVID-19 images. However, there are many machine-learning methods used to classify COVID-19. The question is: which machine learning method is best over multi-criteria evaluation? Therefore, this research presents benchmarking of COVID-19 machine learning methods, which is recognized as a multi-criteria decision-making (MCDM) problem. In the recent century, the trend of developing

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.

This paper is concerned with introducing and studying the o-space by using out degree system (resp. i-space by using in degree system) which are the core concept in this paper. In addition, the m-lower approximations, the m-upper approximations and ospace and i-space. Furthermore, we introduce near supraopen (near supraclosed) d. g.'s. Finally, the supra-lower approximation, supraupper approximation, supra-accuracy are defined and some of its properties are investigated.

   The aim of this paper is to introduce and study new class of fuzzy function called fuzzy semi pre homeomorphism in a fuzzy topological space by utilizing fuzzy semi pre-open sets. Therefore, some of their characterization has been proved; In addition to that we define, study and develop corresponding to new class of fuzzy semi pre homeomorphism in fuzzy topological spaces using this new class of functions.

Abstract Throughout this paper R represents commutative ring with identity and M is a unitary left R-module, the purpose of this paper is to study a new concept, (up to our knowledge), named St-closed submodules. It is stronger than the concept of closed submodules, where a submodule N of an R-module M is called St-closed (briefly N ≤Stc M) in M, if it has no proper semi-essential extensions in M, i.e if there exists a submodule K of M such that N is a semi-essential submodule of K then N = K. An ideal I of R is called St-closed if I is an St-closed R-submodule. Various properties of St-closed submodules are considered.