Recently, we have used the SYMMETRIC bracket of vector fields, and developed the notion of the SYMMETRIC derivation. Using this machinery, we have defined the concept of SYMMETRIC CURVATURE. This concept is natural and is related to the notions divergence and Laplacian of vector fields. This concept is also related to the derivations on the algebra of SYMMETRIC forms which has been discussed by the authors. We introduce a new class of geometric vector fields and prove some basic facts about them. We call these vector fields affinewise. By contraction of the SYMMETRIC CURVATURE, we define two new CURVATUREs which have direct relations to the notions of divergence, Laplacian, and the Ricci tensor.

The SYMMETRIC CURVATURE and ASSOCIATED CURVATUREs of a vector bundle E with connection Ñ on a manifold M with connection Ñ were introduced. It is well-known that a total space of semi-Riemannian vector bundle over a semi-Riemannian manifold can be made into a semi-Riemannian manifold. In this case, the relation between CURVATUREs of the Levi-Civita connections of E and M was studied. Here, the relation between SYMMETRIC CURVATUREs of the Levi-Civita connections and their ASSOCIATED CURVATUREs of E and M is studied.

In this study, an analytical method is proposed for determination and minimization of the exit CURVATURE in extrusion dies. The stream lines are determined by using the Bezier formulation. The improved Bezier formulation is achieved by adding some parameters to the stream line equations and the non-uniform velocity field is extracted from the improved Bezier formulation. By defining the exit CURVATURE criteria, the die is optimized, according to the Bezier coefficients and eccentricity values.For verification of the proposed procedure, the exit CURVATURE of some selective dies is calculated by using Abaqus FEM Software. The FEM results show good agreement with the proposed procedure. Finally the extrusion pressure of the dies is calculated, based on the minimum energy consumption criteria, according to the upper-bound method. Then, the estimated pressures, according to the minimum CURVATURE and minimum energy criterion, are compared.

Elastic analysis of a non-homogenous SYMMETRIC shells with arbitrary CURVATURE and variable thickness is considered in the present research. First order Shear Deformation Theory and total potential energy approach is applied for obtaining the governing equations of non-homogenous SYMMETRIC shell. As a special case, the governing equations are rewritten for a cylinder with variable thickness. Analytical method for constant thickness and Perturbation method for variable thickness are used for solving the governing equations and obtaining results. The comparison between classical theory and First order Shear Deformation Theory (FSDT) are illustrated with some numerical results. Non-homogenous material, boundary condition effects, non-uniform pressure, arbitrary CURVATURE with variable thickness are some advantages of current work. Functionally graded material is considered as nonhomogenous material. Gradation is considered for all mechanical properties along the thickness direction based on a power function. Homogenous material and non-homogenous material by difference in non-homogeneity parameter can be studied with the present research. There is some applications of varying thickness shells in industrial like aerospace engineering. We can reach to optimum design of thickness and also some property like high temperature residence by applying non homogenous material.

Background and Objective: Helicobacter pylori (H.pylori) with positive Cytotoxin ASSOCIATED Gene A (CagA) have higher potential for pathogenesis. Cytotoxin ASSOCIATED Gene A (CagA) accelerate the pathogene city of bacteria due to cytotoxin production stimulation. The aim of this study was to determine the prevalence of the anti-CagA antibody among H. pylori infected persons in Golestan province-North of Iran.Materials and Methods: This descriptive study was carried out on 676 H. pylori positive subjects in Golestan province, northern Iran during 2008. Anti CagA antibody were determined in H.pylori positive subjects. Data analyzed by SPSS-16 software and chi-square test.Results: Prevalence of anti CagA in Helicobacter pylori infected cases was 57.7% (390 cases: 179 males and 211 females) (95% CI: 53.9-61.4). According to age the highest and lowest cases of anti CagA antibody were seen in, 15-24 (63.4%) and under 5 years old (26.3%). The level of anti CagA antibody in Sistanian ethnicity group (67.2%) was more than other ethnic group. Anti CagA antibody in Rural area was more than urban regions. Sero prevalence of anti CagA antibody was highest in Minudasht twon (78%), located in East of province in comparison with Bandar Gaz (44%) in west of provinceConclusion: This study showed the prevalence of CagA positive Helicobacter pylori strains in this region is similar to other regions of Iran, Asia and Europe and higher than African population.

With the rapid development of 3D laser scanners, point-based discrete shape modeling is being widely used in many engineering applications, e.g. quality control, reverse engineering, computer graphics and machine vision. Point cloud discrete CURVATURE estimation is considered a basic operation in point cloud operations and is used in many applications related to cloud points. This paper presents a novel method for point clouds surface CURVATURE estimation. One of the key components of point clouds surface CURVATURE calculation is neighbor coordinates of query point. For selecting neighbors, homogeneous neighborhood method is used. This method of choosing neighbors, in addition to the distance, takes into consideration the directional balance by improving the k nearest neighbors. Surface normal vector is estimated by neighbors coordinates. In this paper surface CURVATURE is calculated based on normal vector and homogeneous neighbors coordinates. Surface CURVATURE calculated using the novel method is called umbrella CURVATURE. To evaluate how this method performs, umbrella CURVATURE values are calculated for a number of cloud points and the results are used in some different applications. The results show that the proposed method performs well in point clouds CURVATURE estimation.

The aim of this paper is to analyze the strain components in the direct extrusion process to predict the CURVATURE of the exit product. For this purpose, Riemann mapping theory is used to model the deformation zone and create a one-to-one correspondence between the input and output cross-sections of the die. With the help of the Bezier curves, flow lines are created between these points and then an upper bound solution is obtained for the velocity field. The process pressure and the distribution of the strain components are determined for the square, hexagonal, and rectangular sections using the obtained velocity field. A theoretical method based on the elastic-plastic bending of beams is presented for calculating the CURVATURE of the exit product for the eccentric dies. In this theoretical method, the distribution of stress components and the bending moments is calculated using the specified strain components. In fact, the amount of bending moments indicates the CURVATURE of the exit product. Finally, the presented theoretical model is validated through comparison with the results of the finite element simulation and the previous studies. The results show that Riemann conformal mapping theory and upper bound method can be used to determine the distribution of strain components and predict the CURVATURE of the output product, in addition to estimate the process pressure.

The purpose of this paper is to introduce the concept of a cone SYMMETRIC space and to investigate relationship between (cone) metric spaces and (cone) SYMMETRIC spaces. Among other things, we shall also extend some fixed point results from metric spaces to cone metric spaces (Theorem 3.3), and to SYMMETRIC spaces (Theorems 3.2 and 3.5) under some new contraction conditions.