In this study, structures damage identification method based on changes in the dynamic characteristics
(frequencies) of the structure are examined, stiffness as well as mass matrices of the curved
(in and out-of-plane vibration) beam elements is formulated using Hamilton's principle. Each node
of both of them possesses seven degrees of freedom including the warping degree of freedom. The
curved beam element had been derived based on the Kang and Yoo’s thin-walled curved beam theory
in 1994. A computer program was developing to carry out free vibration analyses of the curved
beam as well as straight beam. Comparing with the frequencies for other researchers using the general
purpose program MATLAB. Fuzzy logic syste

Let Y be a"uniformly convex n-Banach space, M be a nonempty closed convex subset of Y, and S:M→M be adnonexpansive mapping. The purpose of this paper is to study some properties of uniform convex set that help us to develop iteration techniques for1approximationjof"fixed point of nonlinear mapping by using the Mann iteration processes in n-Banachlspace.

Background: To assess the alveolar bone crest level (ABCL) by Cone Beam Computed To-mography (CBCT) and to investigate several variables as predictors for the height of the alveolar bone in adolescents. Materials and methods: Age, sex, and ethnic groups were rec-orded for each patient. CBCT images were used to obtain measurements of the interproximal alveolar bone level from the cementoenamel junction (CEJ) to the alveolar crest. The highest measurement in each sextant was recorded along with any presence of a vertical bone defect or calculus. Results: Total of 720 measurements were recorded for 120 subjects. No vertical bony defects or calculus were observed radiographically. Statistically significant (P< 0.05) differences were observed be

The aim of this paper is to introduces and study the concept of CSO-compact space via the notation of simply-open sets as well as to investigate their relationship to some well known classes of topological spaces and give some of his properties.

     In this paper, we introduce new definitions of the - spaces  namely the    - spaces  Here,  and  are natural numbers that are not necessarily equal, such that . The space  refers to the n-dimensional Euclidean space,  refers to the quaternions set and  refers to the N-dimensional quaternionic space. Furthermore, we establish and prove some properties of their elements. These elements are quaternion-valued N-vector functions defined on , and the  spaces  have never been introduced in this way before.

In this work we explain and discuss new notion of fibrewise topological spaces, calledfibrewise soft ideal topological spaces, Also, we show the notions of fibrewise closed soft ideal topological spaces, fibrewise open soft ideal topological spaces and fibrewise soft near ideal topological spaces.

The method of solving volterra integral equation by using numerical solution is a simple operation but to require many memory space to compute and save the operation. The importance of this equation appeares new direction to solve the equation by using new methods to avoid obstacles. One of these methods employ neural network for obtaining the solution.

This paper presents a proposed method by using cascade-forward neural network to simulate volterra integral equations solutions. This method depends on training cascade-forward neural network by inputs which represent the mean of volterra integral equations solutions, the target of cascade-forward neural network is to get the desired output of this network. Cascade-forward neural

In this paper, the process for finding an approximate solution of nonlinear three-dimensional (3D) Volterra type integral operator equation (N3D-VIOE) in R³ is introduced. The modelling of the majorant function (MF) with the modified Newton method (MNM) is employed to convert N3D-VIOE to the linear 3D Volterra type integral operator equation (L3D-VIOE). The method of trapezoidal rule (TR) and collocation points are utilized to determine the approximate solution of L3D-VIOE by dealing with the linear form of the algebraic system. The existence of the approximate solution and its uniqueness are proved, and illustrative examples are provided to show the accuracy and efficiency of the model.

Mathematical Subject Classificat

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.