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...

Let Y be an E-proximinal (respectively, a strongly proximinal) subspace of X. We prove that Y is (strongly) ball proximinal in X if and only if for any x ∈ X with (x+ Y ) ∩BX 6= ∅, (x+ Y ) ∩BX is (strongly) proximinal in x+Y . Using this characterization and a smart construction, we obtain three Banach spaces Z ⊂ Y ⊂ X such that Z is ball proximinal in X and Y/Z is ball proximinal in X/Z, but Y...

Abstract: The specific rate of breakage is one of the most important factors in evaluation of grinding process especially in ball mill. In this article the effect of ball size and feed size on selection function were investigated using batch grinding circuit on two-iron ore anomaly (B, C) from sangan mine in north of Iran. Eight different monosize fractions were prepared between 2000 and 50...

2. Polya’s urn. Suppose we have an urn containing one red ball and one blue ball. We draw a ball at random from the urn. If it is red, we put the drawn ball plus another red ball into the urn. If it is blue, we put the drawn ball plus another blue ball into the urn. We then repeat this process. At the n-th stage, we draw a ball at random from the urn with n+1 balls, note its color, and put the ...

In the recent study of infinite root systems, fractal patterns of ball packings were observed while visualizing roots in affine space. In fact, the observed fractals are exactly the ball packings described by Boyd and Maxwell. This correspondence is a corollary of a more fundamental result: given a geometric representation of a Coxeter group in Lorentz space, the set of limit directions of weig...