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.

In this paper we show that if ? Xi is monotonically T2-space then each Xi is monotonically T2-space, too. Moreover, we show that if ? Xi is monotonically normal space then each Xi is monotonically normal space, too. Among these results we give a new proof to show that the monotonically T2-space property and monotonically normal space property are hereditary property and topologically property and give an example of T2-space but not monotonically T2-space.

It is shown that if a subset of a topological space (χ, τ) is δ-semi.closed, then it is semi.closed. By use this fact, we introduce the concept regularity of a topological space (χ, τ) via δ-semi.open sets. Many properties and results were investigated and studied. In addition we study some maps that preserve the δ-semi.regularity of spaces.

Skull image separation is one of the initial procedures used to detect brain abnormalities. In an MRI image of the brain, this process involves distinguishing the tissue that makes up the brain from the tissue that does not make up the brain. Even for experienced radiologists, separating the brain from the skull is a difficult task, and the accuracy of the results can vary quite a little from one individual to the next. Therefore, skull stripping in brain magnetic resonance volume has become increasingly popular due to the requirement for a dependable, accurate, and thorough method for processing brain datasets. Furthermore, skull stripping must be performed accurately for neuroimaging diagnostic systems since neither no

In this paper, we shall introduce a new kind of Perfect (or proper) Mappings, namely ω-Perfect Mappings, which are strictly weaker than perfect mappings. And the following are the main results: (a) Let f : X→Y be ω-perfect mapping of a space X onto a space Y, then X is compact (Lindeloff), if Y is so. (b) Let f : X→Y be ω-perfect mapping of a regular space X onto a space Y. then X is paracompact (strongly paracompact), if Y is so paracompact (strongly paracompact). (c) Let X be a compact space and Y be a p*-space then the projection p : X×Y→Y is a ω-perfect mapping. Hence, X×Y is compact (paracompact, strongly paracompact) if and only if Y is so.

Most companies use social media data for business. Sentiment analysis automatically gathers analyses and summarizes this type of data. Managing unstructured social media data is difficult. Noisy data is a challenge to sentiment analysis. Since over 50% of the sentiment analysis process is data pre-processing, processing big social media data is challenging too. If pre-processing is carried out correctly, data accuracy may improve. Also, sentiment analysis workflow is highly dependent. Because no pre-processing technique works well in all situations or with all data sources, choosing the most important ones is crucial. Prioritization is an excellent technique for choosing the most important ones. As one of many Multi-Criteria Decision Mak

R. Vasuki [1] proved fixed point theorems for expansive mappings in Menger spaces. R. Gujetiya and et al [2] presented an extension of the main result of Vasuki, for four expansive mappings in Menger space. In this article, an important lemma is given to prove that the iteration sequence is Cauchy under suitable condition in Menger probabilistic G-metric space (shortly, MPGM-space). And then, used to obtain three common fixed point theorems for expansive type mappings.

The aim of this paper is to examine cases of deletion not dependent on linguistic context. Perlmutter (1971) claims that any sentence other than an imperative¹ in which there is an S that does not contain a subject in the surface structure is ungrammatical. Dillon (1978) counts elliptical sentences such as ^ Beg your pardon² as grammatically incomplete (and hence as strictly ungrammatical). Such statements are, however, not without problems for reasons that will be given below.

The effect of Low-Level Laser (LLL) provided by green semiconductor laser with an emission wavelength of 532 nm on of human blood of people with brain and prostate cancer has been investigated. The effect of LLL on white blood cell (WBC), NEUT, LYMPH and MONO have been considered. Platelet count (PLT) has also been considered in this work. 2 ml of blood sample were irradiating by a green laser of the dose of 4.8 J/cm2. The results suggest a potential effect of LLL on WBC, PLT, NEUT, LYMPH, and MONO of people with brain and prostate cancer Key words: white blood cell , platelet , low-level laser therapy