Bell’s theorem states that quantum correlation function of two spins can not be represented as an expectation value of two classical random variables. Spin is described in Bell’s model by a single scalar random variable. We discuss another classical model of spin in which spin is described by a triple of classical random variables. It is shown that in this model the quantum correlation function...

We show that for any variational symmetry of the problem of the calculus of variations on time scales there exists a conserved quantity along the respective EulerLagrange extremals.

The famous theorem of Szemerédi asserts that for every positive integer k and every positive real number ö > 0 there is a positive integer N such that every subset of {1,2,...,AT} of cardinality at least SN contains an arithmetic progression of length k. A second proof of the theorem was given by Furstenberg using ergodic theory, but neither this proof nor Szemerédi's gave anything other than e...

W represents a message. We will often consider that it is the output of the compressor. The encoder receives W and encodes it to X. The encoder puts X into the channel and Y n is the output the decoder receives. Finally, the decoder tries to estimate W through Y . The decoder’s estimate is denoted by Ŵ . Our goal is to understand what kind of encodings are such that Ŵ is the same as W with high...

We use the fact that a projective half-spin representation of Spin 12 has an open orbit to generalize Pfister's result on quadratic forms of dimension 12 in I 3 to orthogonal involutions. In his seminal paper [Pf], Pfister proved strong theorems describing quadratic forms of even dimension ≤ 12 that have trivial discriminant and Clifford invariant, i.e., that are in I 3. His results have been e...

For every N > I we construct a set A of squares such that JA < (4/log 2)N 1 / 3 log N and every nonnegative integer n < N is a sum of four squares belonging to A . Let A be an increasing sequence of nonnegative integers and let A(x) denote the number of elements of A not exceeding x. If every nonnegative integer up to x is a sum of four elements of A, then A(x)4 > x and so A(x) > x 1/4. In 1770...

Banach's contraction principle has been improved and extensively studied on several generalized metric spaces. Recently, complex-valued $S$-metric spaces have been introduced and studied for this purpose. In this paper, we investigate some generalized fixed point results on a complete complex valued $S$-metric space. To do this, we prove some common fixed point (resp. fixed point) theorems usin...