It is well known that the wreath product  is the endmorphism monoid of a free S-act with n-generators. If S is a trivial semigroup then  is isomorphic to . The extension  for  to  where  is an independent algebra has been investigated. In particular, we consider  is to be , where  is a free left S-act of n-generators. The eventual goal of this paper is to show that  is an endomorphism monoid of a free left S-act of n-generators and to prove that  is embedded in the wreath product .

Solvents are important components in the pharmaceutical and chemical industries, and they are increasingly being used in catalytic reactions. Solvents have a significant influence on the kinetics and thermodynamics of reactions, and they can significantly change product selectivity. Solvents can influence product selectivity, conversion rates, and reaction rates. However, solvents have received a lot of attention in the field of green chemistry. This is due to the large amount of solvent that is frequently used in a process or formulation, particularly during the purification steps. However, neither the solvent nor the active ingredient in a formulation is directly responsible for the reaction product's composition. Because these ch

This work aims to analyze a three-dimensional discrete-time biological system, a prey-predator model with a constant harvesting amount. The stage structure lies in the predator species. This analysis is done by finding all possible equilibria and investigating their stability. In order to get an optimal harvesting strategy, we suppose that harvesting is to be a non-constant rate. Finally, numerical simulations are given to confirm the outcome of mathematical analysis.

       In this research, we study the classical continuous Mixed optimal control vector problem dominated by couple nonlinear elliptic PDEs. The existence theorem for the unique state vector solution of the considered couple nonlinear elliptic PDEs for a given continuous classical mixed control vector is stated and proved by applying the Minty-Browder theorem under suitable conditions.  Under suitable conditions, the existence theorem of a classical continuous mixed optimal control vector associated with the considered couple nonlinear elliptic PDEs  is stated and proved.

With the shift of narration and the revolution against the traditional methods which were dominated by the authorial intrusion and the single narrative voice, there appeared new forms that go along with the change in methods of narration. Form becomes the representation which equips us to understand more fully aspects of existence outside of art. Form is the objectifying of idea, and its excellence depends upon its appropriateness to the idea.¹ One of the most important approaches to writing fiction is the power of point of view.

In the strategy of 'point of view' lies the secret of art and, as Norman Friedman indicates, it provides a method for distinguishing the possible degrees of authorial extinction in the narrati

Idioms are a very important part of the English language: you are told that if you want to go far (succeed) you should pull your socks up (make a serious effort to improve your behaviour, the quality of your work, etc.) and use your grey matter (brain).1 Learning and translating idioms have always been very difficult for foreign language learners. The present paper explores some of the reasons why English idiomatic expressions are difficult to learn and translate. It is not the aim of this paper to attempt a comprehensive survey of the vast amount of material that has appeared on idioms in Adams and Kuder (1984), Alexander (1984), Dixon (1983), Kirkpatrick (2001), Langlotz (2006), McCarthy and O'Dell (2002), and Wray (2002), among others

Phase change materials are known to be good in use in latent heat thermal energy storage (LHTES) systems, but one of their drawbacks is the slow melting and solidification processes. So that, in this work, enhancing heat transfer of phase change material is studied experimentally for in charging and discharging processes by the addition of high thermal conductive material such as copper in the form of brushes, which were added in both PCM and air sides. The additions of brushes have been carried out with different void fractions (97%, 94% and 90%) and the effect of four different air velocities was tested. The results indicate that the minimum brush void fraction gave the maximum heat transfer in PCM and reduced the time

Background: Several biological factors such as bacterial infections and immunological status are implicated in predisposing individuals to bladder cancer. Bacterial infection of urinary tract has been related to increase the risk of bladder cancer.
Patients and Methods: Resected tumors of a total of 73 patients were obtained under sterile surgical conditions. Biopsy processing samples and culture procedures of biopsy samples were mentioned in the text.
Results: Bacterial growth was observed in 48 biopsy tissues of those patients represent (65.8%) while, 25(34.2%) yielded no growth (negative results). It is obvious that E. coli is the most predominant organisms followed by K. pneumoniae and Ps. Aer

The study included the investigation of fungi which associated with heavy animal's leather (Cows and Buffalos) and light (Sheep’s and Goats )through different processing stages (raw hides ,dehairing ,pickling,chrome tanned and stainning or finished stages)there were 10 genera and 25 species in addition to sterile fungi associated with animal leathers which included Alternaria ,Aspergillus,Cladosporium,Fusarium, Mucor , Penicillium , Rhizopus , and Trichoderma .Aspergillus and Penicillium have observed in all leather samples and different processing stages, and that the first time isolate two genera Helminthosporium , Stemphylium form leather for staining stage.