Considering a minimal number of assumptions and in the context timeless formalism, conditional probabilities are derived for subsequent measurements non-relativistic regime. Only unitary transformations considered with detection processes described by generalized (POVM). One-time unambiguously via Gleason-Bush theorem, including puzzling cases like Wigner's friend scenario where their form unde...

This paper is motivated by a problem that arises in the study of partition functions of antiferromagnetic Potts models, including as a special case the chromatic polynomial. It relies on a theorem of Beraha, Kahane and Weiss, which asserts that the zeros of certain sequences of polynomials approach the curves on which a matrix has two eigenvalues with equal modulus. It is shown that (in general...

Several inequalities of Kahane-Khintchine’s type in certain Orlicz spaces are proved. For this the classical symmetrization technique is used and four basically different methods have been presented. The first two are based on the well-known estimates for subnormal random variables, see [9], the third one is a consequence of a certain Gaussian-Jensen’s majorization technique, see [6], and the f...

I show that the zeros of the chromatic polynomials PG(q) for the generalized theta graphs Θ(s,p) are, taken together, dense in the whole complex plane with the possible exception of the disc |q − 1| < 1. The same holds for their dichromatic polynomials (alias Tutte polynomials, alias Potts-model partition functions) ZG(q, v) outside the disc |q + v| < |v|. An immediate corollary is that the chr...

We study the chromatic polynomials (= zero-temperature antiferromagnetic Potts-model partition functions) PG(q) for m × n rectangular subsets of the square lattice, with m ≤ 8 (free or periodic transverse boundary conditions) and n arbitrary (free longitudinal boundary conditions), using a transfer matrix in the Fortuin-Kasteleyn representation. In particular, we extract the limiting curves of ...

We give a new proof of the Mallows-Sloane bound on the minimum distance of doubly-even self-dual codes. The proof avoids using the Gleason theorem and invariant theory. It is based on a special choice of the polynomial in the conventional linear programming approach.

results a total number of 43 specimens were studied, from which 9 were obtained from patients with metastatic prostate cancer. the expression of five examined genes had no correlation with psa level and gleason score. the expression of amacr decreased in metastatic prostate cancer (p = 0.02). the expression of other genes showed no difference between metastatic and non-metastatic tumors (p > 0....