The objective of this paper is to define and introduce a new type of nano semi-open set which called nano -open set as a strong form of nano semi-open set which is related to nano closed sets in nano topological spaces. In this paper, we find all forms of the family of nano -open sets in term of upper and lower approximations of sets and we can easily find nano -open sets and they are a gate to more study.  Several types of nano open sets are known, so we study relationship between the nano -open sets with the other known types of nano open sets in nano topological spaces. The Operators such as nano -interior and nano -closure are the part of this paper.

In this research, we introduce and study the concept of fibrewise bitopological spaces. We generalize some fundamental results from fibrewise topology into fibrewise bitopological space. We also introduce the concepts of fibrewise closed bitopological spaces,(resp., open, locally sliceable and locally sectionable). We state and prove several propositions concerning with these concepts. On the other hand, we extend separation axioms of ordinary bitopology into fibrewise setting. The separation axioms we extend are called fibrewise pairwise T_0 spaces, fibrewise pairwise T_1 spaces, fibrewise pairwise R_0 spaces, fibrewise pairwise Hausdorff spaces, fibrewise pairwise functionally Hausdorff spaces, fibrewise pairwise regular spaces, fibrewise

The main purpose of this paper is to introduce a some concepts in fibrewise totally topological space which are called fibrewise totally mapping, fiberwise totally closed mapping, fibrewise weakly totally closed mapping, fibrewise totlally perfect mapping fibrewise almost totally perfect mapping. Also the concepts as totally adherent point, filter, filter base, totally converges to a subset, totally directed toward a set, totally rigid, totally-H-set, totally Urysohn space, locally totally-QHC totally topological space are introduced and the main concept in this paper is fibrewise totally perfect mapping in totally top

     The concept of separation axioms constitutes a key role in general topology and all generalized forms of topologies. The present authors continued the study of gpα-closed sets by utilizing this concept, new separation axioms, namely gpα-regular and gpα-normal spaces are studied and established their characterizations. Also, new spaces namely gpα-T_k  for k = 0, 1, 2 are studied.

Chemotherapy is one of the most efficient methods for treating cancer patients. Chemotherapy aims to eliminate cancer cells as thoroughly as possible. Delivering medications to patients’ bodies through various methods, either oral or intravenous is part of the chemotherapy process. Different cell-kill hypotheses take into account the interactions of the expansion of the tumor volume, external drugs, and the rate of their eradication. For the control of drug usage and tumor volume, a model based smooth super-twisting control (MBSSTC) is proposed in this paper. Firstly, three nonlinear cell-kill mathematical models are considered in this work, including the log-kill, Norton-Simon, and hypotheses subject to parametric uncertainties and exo

         Continuous functions are novel concepts in topology. Many topologists contributed to the theory of continuous functions in topology. The present authors continued the study on continuous functions by utilizing the concept of gpα-closed sets in topology and introduced the concepts of weakly, subweakly and almost continuous functions. Further, the properties of these functions are established.

Data hiding is the process of encoding extra information in an image by making small modification to its pixels. To be practical, the hidden data must be perceptually invisible yet robust to common signal processing operations. This paper introduces a scheme for hiding a signature image that could be as much as 25% of the host image data and hence could be used both in digital watermarking as well as image/data hiding. The proposed algorithm uses orthogonal discrete wavelet transforms with two zero moments and with improved time localization called discrete slantlet transform for both host and signature image. A scaling factor ? in frequency domain control the quality of the watermarked images. Experimental results of signature image

The main purpose of this article is to study the soft LC-spaces as soft spaces in which every soft Lindelöf subset of  is soft closed. Also, we study the weak  forms of soft LC-spaces and we discussed their relationships with soft LC-spaces as well as among themselves.

The concept of strong soft  pre-open set was initiated by Biswas and Parsanann.We utilize this notion to study several characterizations and properties of this set. We investigate the relationships between this set and other types of soft open sets. Moreover, the properties of the strong soft  pre-interior and closure are discussed. Furthermore, we define a new concept by using strong soft  pre-closed that we denote as locally strong soft  pre-closed, in which several results are obtained. We establish a new type of soft pre-open set, namely soft  pre-open. Also, we continue to study pre-  soft open set and discuss the relationships among all these sets. Some counter examples are given to show some relations