The starting point for this work is an old question of H. Furstenberg. Recall that a Borel probability measure on the torus T = R=Z is called p-invariant if p = , where p(x) def = p x (mod 1) and p def = 1 p . Suppose that is non-atomic, and is simultaneously 2and 3-invariant. Assume also that is ergodic under the joint action of 2; 3. Does it follow that is necessarily Lebesgue measure? In his...

Abstract. A seminal theorem due to Weyl [14] states that if (an) is any sequence of distinct integers, then, for almost every x ∈ R, the sequence (anx) is uniformly distributed modulo one. In particular, for almost every x in the unit interval, the sequence (anx) is uniformly distributed modulo one for every computable sequence (an) of distinct integers. Call such an x UD random. Here it is sho...

In this paper we continue the investigation into the group of algebras with uniformly distributed invariants, U(k’), and its relation to the Schur subgroup S(K), undertaken in [6, 71. We maintain the notation of [6, 71. In the first section we investigate U(K) for a real quadratic field K. We calculate generators of U(K) explicitly. In the second section we investigate U(K) for other real field...

We model two-dimensional crystals by a configuration space in which every admissible configuration is a hard disk configuration and a perturbed version of some triangular lattice with side length one. In this model we show that, under the uniform distribution, expected configurations in a given box are arbitrarily close to some triangular lattice whenever the particle density is chosen sufficie...

The optimal antenna location for maximizing the channel capacity is searched by particle swarm optimizer (PSO). There are two different receiver locations considered in the simulation. The receivers are located with uniform intervals distribution (i) on the tables; (ii) in the whole indoor environment. Numerical results have shown that our proposed method is effect to find the optimal location ...

Pseudo-random number sequences have been used in Monte Carlo methods in wide areas of science and engineer. Recently, quasi-random number sequences having uniform distribution property are used in numerical integrations, particle transport problems, financial problems and so on. Here, I survey on the quasi-random number generation and its applications. At the end, I discuss about the possible i...

An environmentally clean synthesis technique is reported for preparing the green phosphor SrGa2S4:Eu . This method is based on solid state chemical reactions with the use of raw materials: sodium dimethyldithiocarbomate, tetramethylammonium chloride, gallium nitrate, europium nitrate, strontium sulfide and sulfur. The method is shown to produce powders with quasispherical shape, smooth surface ...

Non homogeneous particle distribution is one of the greatest problems in casting Metal Matrix Composites (MMC's). To optimize some of the parameters for uniform particle distribution for batch compocasting the present simulation studies were conducted. The simulation involves visualisation experiments. In the visualisation experiments liquid and semi solid aluminium are replaced by other fluids...

We introduce an elementary argument to the theory of distribution of sequences modulo one.