For a bounded Lipschitz domain Ω, we show the existence of a measurable set D ⊂ ∂Ω of given area such that the first eigenvalue of the Laplacian with Dirichlet conditions on D and Neumann conditions on ∂Ω \D becomes minimal. If Ω is a ball, D will be a spherical cap.

The ball and beam system is one of the most popular laboratory setups for control education. In this paper, we design a fuzzy PD cascade controller for a ball and beam system using Asexual Reproduction Optimization (ARO) technique. The ball & beam system consists of a servo motor, a grooved beam, and a rolling ball. This system utilizes a servo motor to control ball’s position on the beam. Chan...

In this paper, we prove that every metric line in the Poincare ball model of hyperbolic geometry is exactly a classical line of itself. We also proved nonexistence of periodic lines in the Poincare ball model of hyperbolic geometry.

a 50-year-old male underwent a check-up for an insurance company. chest x-ray revealed a large ball-like lesion in the posterior mediastinum. the finding was confirmed by computed tomography (ct) scan (figure 1). the patient was referred to our center, where he had a successful mass removal surgery (figure 2). pathology identified the mass as neurinoma.

Let B1, B2 be balls in finite-dimensional real vector spaces E1, E2, centered around unit length vectors v1, v2 and not containing zero. An element in the tensor product space E1 ⊗ E2 is called B1 ⊗B2-separable if it is contained in the convex conic hull of elements of the form w1 ⊗w2, where w1 ∈ B1, w2 ∈ B2. We study the cone formed by the separable elements in E1⊗E2. We determine the largest ...

In this research, the efficiency of the comminution circuit as well as the efficiency of size classification equipment of the concentrator plant 2 of Sarcheshmeh copper complex was studied. The comminution circuit of this plant includes one SAG mill in a closed circuit with a vibrating screen and one ball mill with a size classification system of hydrocyclone. The goal of this work was to calcu...