The theory of general topology view for continuous mappings is general version and is applied for topological graph theory. Separation axioms can be regard as tools for distinguishing objects in information systems. Rough theory is one of map the topology to uncertainty. The aim of this work is to presented graph, continuity, separation properties and rough set to put a new approaches for uncertainty. For the introduce of various levels of approximations, we introduce several levels of continuity and separation axioms on graphs in Gm-closure approximation spaces.

Longitudinal data is becoming increasingly common, especially in the medical and economic fields, and various methods have been analyzed and developed to analyze this type of data.

In this research, the focus was on compiling and analyzing this data, as cluster analysis plays an important role in identifying and grouping co-expressed subfiles over time and employing them on the nonparametric smoothing cubic B-spline model, which is characterized by providing continuous first and second derivatives, resulting in a smoother curve with fewer abrupt changes in slope. It is also more flexible and can pick up on more complex patterns and fluctuations in the data.

The longitudinal balanced data profile was compiled into subgroup

The main purpose of this work is to introduce some types of fuzzy convergence sequences of operators defined on a standard fuzzy normed space (SFN-spaces) and investigate some properties and relationships between these concepts. Firstly, the definition of weak fuzzy convergence sequence in terms of fuzzy bounded linear functional is given. Then the notions of weakly and strongly fuzzy convergence sequences of operators  are introduced and essential theorems related to these concepts are proved. In particular, if ( ) is a strongly fuzzy convergent sequence with a limit  where linear operator from complete standard fuzzy normed space  into a standard fuzzy normed space  then  belongs to the set of all fuzzy bounded linear operators

Summary:

This research revolves around the probing of those whom Ibn Hajar said, "He has a vision", its significance, and the ruling on the connection and transmission to it.  The number of narrators reached fifty-one (51) narrators, among whom it was said, “He has a vision, whether it is definite or possibly. Some of them had a vision and companionship.”They are eleven (11) narrators, And among them were those who had visions and had no company, and their number was twenty-one (21) narrators, and among them were those who had no vision and nor company, and their number is nineteen (19) narrators.
As a result , whoever said about him “has a vision” and has companions, his hadith is connected, even i

This research presents a particular designing strategy for a free form of surfaces, constructed by the lofting design method. The regarded surfaces were created by sliding a B-spline curves (profile curves), in addition to describing an automatic procedure for selective identification of sampling points in reverse engineering applications using Coordinate Measurement Machine. Two models have been implemented from (Ureol material) to represent the different cases of B-spline types to clarify its scope of application. The interior data of the desired surfaces was designed by MATLAB software, which then were transformed to UG-NX9 software for connecting the sections that were designed in MATLAB program and obtaining G-code programs for the

            This research focuses on the characteristics of polyvinyl alcohol and starch polymer blends doping with Rhodamine-B. The polymer blends were prepared using the solution cast method, which comprises 1:1(wt. /wt.).  The polymer blends of PVA and starch with had different ratios of glycerin 0, 25, 30, 35, and 40 % wt. The ratio of 30% wt of glycerin was found to be the most suitable mechanical properties by strength and elasticity. The polymer blend of 1:1 wt ratios of starch/PVA and 30% wt of glycerin were doped with different ratios of Rhoda mine-B dye 0, 1, 2, 3, 4, 5, and 6% wt and the electrical properties of doping biodegradable blends were studied. The ratio of Rhodamine-B 5% wt to the polymer blends showed hi

The best proximity point is a generalization of a fixed point that is beneficial when the contraction map is not a self-map. On other hand, best approximation theorems offer an approximate solution to the fixed point equation . It is used to solve the problem in order to come up with a good approximation. This paper's main purpose is to introduce new types of proximal contraction for nonself mappings in fuzzy normed space and then proved the best proximity point theorem for these mappings. At first, the definition of fuzzy normed space is given. Then the notions of the best proximity point and - proximal admissible in the context of fuzzy normed space are presented. The notion of α ̃–ψ ̃- proximal contractive mapping is introduced.

Hepatocellular carcinoma (HCC) is the third most common cause of cancer-related death. Therefore, it is critical for researchers to understand molecular biology in greater depth.  In several diseases including cancer, abnormal miRNA expression has been linked to apoptosis, proliferation, differentiation, and metastasis. Many miRNAs have been studied in relation to cancer, including miR-122, miR-223, and others. Hepatitis B and C viruses are the most important global risk factors for HCC. This study is intended to test whether serum miRNAs serve as a potential biomarker for both HCC and viral infections HBV and C. The expression of miRNA in 64 serum samples was analyzed by RT-qPCR. Compared to healthy volunteers, HCC patients' sera expre

   In this paper we obtain some statistical approximation results for a general class of maxproduct operators including the paused linear positive operators.

The aim of this paper is to prove some results for equivalence of moduli of smoothnes in approximation theory , we used a"non uniform" modulus of smoothness and the weighted Ditzian –Totik moduli of smoothness in by spline functions ,several results are obtained .For example , it shown that ,for any the inequality , is satisfied ,finally, similar result for chebyshev partition and weighted Ditzian –Totik moduli of smoothness are also obtained.