In 1841, Delaunay constructed the embedded surfaces of revolution with constant mean curvature (CMC); these unduloids have genus zero and are now known to be the only embedded CMC surfaces with two ends and finite genus. Here, we construct the complete family of embedded CMC surfaces with three ends and genus zero; they are classified using their asymptotic necksizes. We work in a class slightl...

Magnetic abrasive finishing (MAF) is a micromachining process that uses magnetic field and magnetic abrasive particles to conduct the mechanism of material removal in micro-nanometer scales. In this paper, by an experimental method and statistical analysis, the effects of parameters like working gap, work-piece rotational speed and material removal mechanism (injection of abrasive slurry of Al<...

Magnetic abrasive finishing (MAF) is a micromachining process that uses magnetic field and magnetic abrasive particles to conduct the mechanism of material removal in micro-nanometer scales. In this paper, by an experimental method and statistical analysis, the effects of parameters like working gap, work-piece rotational speed and material removal mechanism (injection of abrasive slurry of Al<...

Bending analyses of isotropic, functionally graded, laminated composite, and sandwich beams are carried out using a quasi-3D polynomial shear and normal deformation theory. The most important feature of the proposed theory is that it considers the effects of transverse shear and transverse normal deformations. It accounts for parabolic variations in the strain/stress produced by transverse shea...

The quadrics are all surfaces that can be expressed as a second degree polynomialin x, y and z. We study the Gauss map G of quadric surfaces in the 3-dimensional Euclidean space R^3 with respect to the so called L_1 operator ( Cheng-Yau operator □) acting on the smooth functions defined on the surfaces. For any smooth functions f defined on the surfaces, L_f=tr(P_1o hessf), where P_1 is t...

In the recent work, the reaction mechanism between triphenylphosphine 1, dialkyl acetylenedicarboxylates 2 in the presence of NH-acid, such as 5-aminoindazole 3 were investigated theoretically. Quantum mechanical studies were performed for evaluation of potential energy surfaces of all structures participated in the reaction mechanism both in gas phase and in dichloromethane. The first step of ...

The design of curves and surfaces in C.A.D. systems has many applications in car, plane or ship industry. Because they offer more flexibility, rational functions are often prefered to polynomial functions to modelize curves and surfaces. In this work, several methods to generate rational Bezier curves and surfaces which minimize some functionals are proposed. The functionals measure a technical...