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...

The ancient Gamow liquid drop model of nuclear energies has had a renewed life as an interesting problem in the calculus of variations: Find a set Ω ⊂ R3 with given volume A that minimizes the sum of its surface area and its Coulomb self energy. A ball minimizes the former and maximizes the latter, but the conjecture is that a ball is always a minimizer—when there is a minimizer. Even the exist...

In this work, we study an approximate control problem for the heat equation, with a nonstandard but rather natural restriction on the solution. It is well known that approximate controllability holds. On the other hand, the total mass of the solutions of the uncontrolled system is constant in time. Therefore, it is natural to analyze whether approximate controllability holds supposing the total...

A force-velocity relationship in overarm throwing was determined using ball weights varying from 0.2 to 0.8 kg. Seven experienced handball players were filmed at 240 frames per second. Velocity of joints of the upper extremity and ball together with the force on the ball were derived from the data. A statistically significant negative relationship between force and maximal ball velocity, as wel...

objecttive(s): despite the poor mechanical properties of hydroxyapatite, its unique biological properties leads we think about study on improving its properties rather than completely replacing it with other biomaterials. accordingly, in this study we introduced hydroxyapatite reinforced with hardystonite as a novel bio-nanocompositeand evaluate its in-vitro bioactivity with the aim of developi...