Abstract:
Let $f:E\longrightarrow O$ be a Hurewicz fibration with a fiber space $F_{r_{o}}$ and a lifting function $L_{f}$. The \emph{$Lf-$function} $\Theta_{L_{f}}$ of $f$ is defined by the restriction map of $L_{f}$ on the space $\Omega(O,r_{o})\times F_{r_{o}}\times \{1\}$. The purpose of this paper is to give some results which show the role of $Lf-$functions in finding a fiber homotopically equivalent relation between two fibrations, over a common polyhedron base. Furthermore we will prove the equivalently between our results and Dold's theorem in fiber bundles, over a common suspension base of polyhedron spaces.

Abstract:
The purpose of this paper is to give some solutions for the classification problem in fibration theory by using the homotopy sequences of fibrations (sequences of $n$-th homotopy groups $ \pi_{n}(S,s_{o}) $ of total spaces of fibrations). In particular, to show the role of homotopy sequence of $n$-th homotopy to get the required fiber map in Fadell-Dold theorem such that the restriction of this fiber map on some fiber spaces is a homotopy equivalence.

Abstract:
We define an equivalence relation on a topological space which is acted by topological monoid as a transformation semigroup. Then, we give some results about the -invariant classes for this relation. We also provide a condition for the existence of relative -invariant classes. 1. Introduction The invariance theory is one of the principal concepts in the topological dynamics system, see [1, 2]. In [3], Colonius and Kliemann introduced the concept of a control set which is relatively invariant with respect to a subset of the phase space of the control system. From a more general point of view, the theory of control sets for semigroup actions was developed by San Martin and Tonelli in [4]. In this paper, we define an equivalence relation on a topological space which is acted by topological monoid as a transformation semigroup. Then, we provide the necessary and sufficient conditions for the equivalence classes to be -invariant classes which correspond with the control sets for control systems. Then, we study the -invariant classes for this relation in , in particular, and we provide the conditions for the existence and uniqueness of invariant classes. Throughout this paper, will denote the closure set of a set , and will denote the interior set of and all topological spaces involved Hausdorff. Definition 1.1 (see [2]). Let be a monoid with the identity element and also a topological space. Then, will be called a topological monoid if the multiplication operation of: is continuous mapping from to . Definition 1.2 (see [4]). Let be a topological monoid and a topological space. We say that acts on as a transformation semigroup if there is a continuous map between the product space and satisfying we further require that for all . The triple is called an flow; will denote . In particular, an flow is called phase flow if is a compact space. The orbit of under is the set . For a subset of , denotes the set . And a subset is called an invariant set if and . A control set for on is a subset of which satisfies(1) ,(2)for all ,(3) is a maximal with these properties. Then, we say that a subset , satisfies the no-return condition if for some and , then . Lemma 1.3 (see [5, Zorn's Lemma]). If each chain in a partially ordered set has an upper bound, then there is a maximal element of the set. 2. Invariant Classes Let be an flow. From the action on , we can define the relation ~ on by It is clear that the relation ~ is an equivalence relation, and will denote the set of all equivalence classes induced by ~ on . We observe that for all , and if , then for all . The

Abstract:
We use the concepts of the quasicoincident relation to introduce and investigate some lower separation axioms such as , , , and as well as the regularity axioms and . Further we study some of their properties and the relations among them in the general framework of fuzzy topological spaces. 1. Introduction The fundamental concept of a fuzzy set was introduced by Zadeh in 1965, [1]. Subsequently, in 1968, Chang [2] introduced fuzzy topological spaces (in short, fts). In Chang’s fuzzy topological spaces, each fuzzy set is either open or not. Later on, Chang’s idea was developed by Goguen [3], who replaced the closed interval by a more general lattice L. In 1985, Kubiak [4], and ？ostak [5], in separated works, made topology itself fuzzy besides their dependence on fuzzy sets. In 1991, from a logical point of view, Ying [6] studied Hohles topology and called it fuzzifying topology. This fuzzification opened a rich field for research. As it is well known, the neighborhood structure is not suitable to -topology, and Pu and Liu [7] broke through the classical theory of neighborhood system and established the strong and powerful method of quasicoincident neighborhood system in -topology. Zhang and Xu [8] established the neighborhood structure in fuzzifying topological spaces. Considering the completeness and usefulness of theory of -fuzzy topologies, Fang [9] established -fuzzy quasicoincident neighborhood system in -fuzzy topological spaces and gave a useful tool to study -fuzzy topologies. In ordinary topology, -open sets were introduced and studied by Njastad [10]. Bin Shahna [11], in the same spirit, defined fuzzy -open and fuzzy -closed. Separation is an essential part of fuzzy topology, on which a lot of work has been done. In the framework of fuzzifying topologies, Shen [12], Yue and Fang [13], Li and Shi [14], and Khedr et al. [15] introduced some separation axioms and their separation axioms are discussed on crisp points not on fuzzy points. In 2004, Mahmoud et al. [16] introduced fuzzy semicontinuity and fuzzy semiseparation axioms and examined the validity of some characterization of these concepts. Further, they also defined fuzzy generalized semiopen set and introduced fuzzy separation axioms by using thew semiopen sets concept. In the same paper, the authors also discussed fuzzy semiconnected and fuzzy semicompact spaces and some of their properties. The present paper is organized as follows. It consists of four sections. After this introduction, Section 2 is devoted to some preliminaries. In Section 3, we introduce the notions of some lower

Abstract:
The purpose of this paper is to introduce two novel subclasses and of meromorphic valent functions by using the linear operator . Then we prove the necessary and sufficient conditions for a function in order to be in the new classes. Further we study several important properties such as coefficients inequalities, inclusion properties, the growth and distortion theorems, the radii of meromorphically valent starlikeness, convexity, and subordination properties. We also prove that the results are sharp for a certain subclass of functions.

Abstract:
Breast cancer is the main threat around the world. Estrogen and estrogen
receptors (ER) assume a noteworthy part in breast disease movement and
advancement. Breast cancer is the most pervasive disease in women, every year
more than 200,000 new cases analyzed. Estrogen receptors are expressed in 70%
of all the breast cancer cases, so it is an important target for the treatment
of breast cancer. Anti-estrogen compounds are of significant importance since
it can be used as a therapy for breast cancer. In this review we have
summarized the most important anti-estrogen compounds being used for the
treatment of the breast cancer and their related molecular pathways with the
hope that this will enhance our understanding to these compounds.

Abstract:
Gastric cancer is one of the most common malignancies worldwide. Understanding the molecular nature of gastric cancer is essential
for the development of effective and personalized therapies. Several molecular
signal transduction pathways drive tumorgenesis when deregulated and responded
to different types of therapeutic interventions. The Hippo signaling pathway
has been demonstrated to play a central role in the development and regulation
of tissues and organ size. The deregulation of Hippo signaling leads to a
concurrent combination of uncontrolled cellular proliferation and inhibition of
apoptosis, two key hall marks in cancer development. The molecular nature of
this pathway was first uncovered in Drosophila
melanogaster through genetic screens to identify regulators of cell growth
and cell division. The pathway is strongly conserved in humans, and rendering Drosophila is a suitable and efficient
model system to better understand the molecular nature of this pathway. Current
studies have demonstrated that a variety of deregulated molecules can alter
Hippo signaling, leading to the constitutive activation of the transcriptional
activator YAP or its paralog TAZ. Additionally, the Hippo-signaling pathway
integrates inputs from a number of growth signaling pathways, positioning the
Hippo-signaling pathway in a central role in the regulation of tissue size.
Importantly, deregulated Hippo signaling is frequently observed in human cancers.
YAP is commonly activated in a number of in
vitro and in vivo models of tumorogenesis,
as well as a number of gastric cancers. The common activation of YAP in many different
tumor types and in gastric cancer provides an attractive target for potential
therapeutic intervention. In this review, we appraise the evidence for the
Hippo-signaling pathway as a cancer signaling network, and discuss cancer-relevant
biological functions, potential mechanisms by which Hippo-signaling pathway
activity is altered in cancer and emerging therapeutic strategies.

Abstract:
Modeling human blood components and disorders is a complicated task. Few researchers have attempted to automate the process of detecting anemia in human blood. These attempts have produced satisfactory but not highly accurate results. In this paper, we present an efficient method to estimate hemoglobin value in human blood and detect anemia using microscopic color image data. We have developed a logit regression model using one thousand (1000) blood samples that were collected from Prince George Hospital laboratory. The output results of our model are compared with the results of the same sample set using CELL-DYN 3200 System in Prince George Hospital laboratory, and found to be near identical. These results exceed those reported in the literature. Moreover, the proposed method can be im-plemented in hardware with minimal circuitry and nominal cost.