Polishing is considered as the last and most important step in the manufacturing of optical components. Computer control polishing (CCP) methods are usually used to polish complex surfaces. In this method, material removal is controlled at each point, depending on error at that point. In contact polishing mechanism, tool feed rate is often controlled to eliminate local errors. It means that the higher the tool feed rate, the lower the material removal would be and vice versa. Tool influence function (TIF), which is defined as the instantaneous material removal under the polishing tool for a given tool motion, is the most important parameter in CCP and its predictability during the polishing process leads to reliable result. In this study, a new SPHERICAL tool which can polish complex surfaces by using a 3-axis CNC machine is presented. Because of SPHERICAL geometry of both tool and work piece, tool, material removal rate is variable because of changing the angle between tool axis and surface normal vector which leads to variation of relative speed. Tool influence function which depends on tool engagement’s angle was modeled based on Preston equation. Moreover, the simulation is modeled based on discretization of tool path. To evaluate the methodology, some polishing experimental tests were performed. The experimental results show that a 130 mm SPHERICAL convex lens with initial surface roughness of 1.114 micrometer for PV was decreased to 395 nm for PV using the CCP method developed in this study.

In this research article, new fuzzy K-algebras, namely, SPHERICAL fuzzy K-algebras and (∈ , ∈ ∨ q)-SPHERICAL fuzzy K-algebras are constructed. Certain properties of these SPHERICAL fuzzy K-structures are investigated. The behavior of SPHERICAL fuzzy K-algebras under homomorphism is characterized. The SPHERICAL fuzzy K-algebra with thresholds is also delineated.

Theory and experiment of a SPHERICAL probe-fed conformal antenna with a parasitic element mounted on a SPHERICAL multilayer structure are presented in this paper. Rigorous mathematical Method of Moments (MoMs) for analyzing various radiating SPHERICAL structures is presented in this paper by using Dyadic Green's Functions (DGFs) in conjunction with Mixed Potential Integral Equation (MPIE) formulation. Linear Rao-Wilton-Glisson (RWG) triangular basis functions are applied in MPIE formulation. Current distributions on coaxial probe and conformal radiating elements are computed by using spatial domain Dyadic Green's Function (DGF) and its asymptotic approximation. A prototype of such an antenna is fabricated and tested. The effect of the parasitic element on the input impedance and radiation patterns of the antenna is investigated. It is shown that the antenna characteristics are improved significantly with the presence of the conducting parasitic element. Good agreement is achieved between the results obtained from the proposed methods and the measurement results.

A SPHERICAL fuzzy set is an advanced extension of classical fuzzy set in which it has an added advantage to deal with a wider sense of applicability in uncertain situations. In this paper, regular SPHERICAL fuzzy graphs and totally regular SPHERICAL fuzzy graphs are introduced. A necessary and sufficient condition for regular SPHERICAL fuzzy graphs is given. Some properties of regular and totally regular SPHERICAL fuzzy graphs are studied.

This paper presents an analytical solution for two-dimensional conductive heat transfer in SPHERICAL composite pressure vessels. The vessels are in a SPHERICAL shape and fibers are winded in circumferential direction. The vessel is made of one-layer reinforced composite material. The analytical solution is obtained under the general boundary conditions which consist of convection, conduction and radiation inside/outside of vessel. The heat transfer equation for orthotropic conduction in SPHERICAL coordinates is derived and solved using separation of variables method based on the Legendre and Euler functions. Here, the effect of fiber's angle on heat conduction in orthotropic SPHERICAL pressure vessels is investigated in detail. These results can be used extensively for analyzing the thermal stress in this kind of vessels.

In this paper, we propose to extend the hierarchical bivariate Hermite Interpolant to the SPHERICAL case. Let T be an arbitrary SPHERICAL triangle of the unit sphere S and let u be a function defined over the triangle T. For kϵN, we consider a Hermite SPHERICAL Interpolant problem Hk defined by some data scheme Dk (u) and which admits a unique solution pk in the space Bnk (T) of homogeneous Bernstein-Bezier polynomials of degree nk=2 k (resp. nk=2k+1) defined on T. We discuss the case when the data scheme Dr(u) are nested, i.e., Dr-1 (u) ÌDr(u) for all 1£r£k. This, give a recursive formulae to compute the polynomialpk. Moreover, this decomposition give a new basis for the space Bnk (T), which are the hierarchical structure. The method is illustrated by a simple numerical example.