Principal components analysis is a well-known statistical method in dealing with large dependent data sets. It is also used in functional data for both purposes of data reduction as well as variation representation. On the other hand “handwriting” is one of the objects, studied in various statistical fields like pattern recognition and shape analysis. Considering time as the argument, the handwriting would be an infinite dimensional data; a functional object. In this paper we try to use thefunctional principal components analysis(FPCA) to the Persian handwriting data, analyzing the word Mehrwhich is the Persian term for Love.

By applying finite difference formula to time discretization and the cubic B-SPLINEs for spatial variable, a numerical method for solving the inverse system of Burgers equations is presented. Also, the convergence analysis and stability for this problem are investigated and the order of convergence is obtained. By using two test problems, the accuracy of presented method is verified. Additionally, obtained numerical results of the cubic B-SPLINE method are compared to trigonometric cubic B-SPLINE method, exponential cubic Bspline method and radial basis function method. Implementation simplicity and less computational cost are the main advantages of proposed scheme compared to previous proposals.

This article considers a nonlinear inverse problem of the Ostrovsky–Burgers equation by using noisy data. Two B-SPLINEs with different levels, the quintic B-SPLINE and septic B-SPLINE, are used to study this problem. For both B-SPLINEs, the stability and convergence analysis are calculated, and results show that an excellent estimation of the unknown functions of the nonlinear inverse problem.

In this article, the Charged System Search (CSS) algorithm is utilized for structural shape optimization that aims to minimize weight of a plane structure under stress constraints. Also, the Isogeometric Analysis (IA) is employed in order to analyze the structure. In the IA method, Non Uniform Rational BSpline (NURBS) basis functions are used for approximation and interpolation of the displacement field as well as modeling geometry of the structure. Coordinates of the NURBS control points, that construct the geometry, can be considered as the design variables of the shape optimization problem. In earlier studies in structural shape optimization using the Finite Element (FE) method, boundaries of the structure were made by NURBS and the finite element discretization changed when the boundaries were modified in every iteration of the optimization process. As it mentioned, when the IA method is used the geometry is constructed by NURBS, therefore, contrary to using the FE method, the need for remeshing of the domain is eliminated and the computational cost will be remarkably decreased. In this paper, the IA method is briefly reviewed for analysis of the plane-stress elasticity problems. Also, the CSS formulation is derived based on physics laws for shape optimization problems. A few examples are presented to demonstrate the performance of the method and the results are compared when the Sequential Quadratic Programming (SQP) is used as a mathematical based method for structural shape optimization.

Free-form surfaces are usually described using the relationships of parametric surfaces such as Bezier, BSpline and NURBS. The computer-aided design systems use NURBS to describe complex (complicated) geometries. Free-form surfaces known as complex (complicated) surfaces are widely used in a variety of industries such as ship-building and molding, inspection of these surfaces is therefore of high importance (very important). Considering that measured free-form surfaces and design models are located in two different coordinate systems, finding the similarity of free-form surfaces and placing them in an identical coordinates system is necessary to compare these surfaces, this process is called localization. This paper introduces a feature and curvature based method for the automatic localization and comparison of free-form surfaces for inspection with coordinate measuring machine (CMM). This method localizes the measurement surface to the design model through two steps. The first step is general localization which is accomplished based on the relation and similarity between curvatures of free-form surfaces and zoning these surfaces to concave, convex and saddle areas. The second step is fine localization based on genetic algorithm which considers correspondence in the form of point to point. The simulation results show that the localization accuracy of the proposed method for the 50 × 50 mm aluminum workpiece of was about 0. 02 mm, which is 56 percent less than the value obtained from the iterative closest point method.