We investigate the complete phase diagram of the decoupled world-sheet theory of (P,Q) strings. These theories include 1+1 dimensional super Yang-Mills theory and non-commutative open string theory. We find that the system exhibits a rich fractal phase structure, including a cascade of alternating supergravity, gauge theory, and matrix string theory phases. The cascade proceeds via a series of ...

In this article, I have studied the ultra discrete limit, which is currently studied in soliton theory, from point of view of valuation theory. A quantity obtained after taking the ultra discrete limit should be regarded as non-archimedean valuation, which is related to the p-adic valuation in number theory. The ultra discrete difference-difference equations, whose domain and range are given by...

As well known, the standard central limit theorem plays a fundamental role in BoltzmannGibbs (BG) statistical mechanics. This important physical theory has been generalized by one of us (CT) in 1988 by using the entropy Sq = 1− ∑ i p i q−1 (with q ∈ R) instead of its particular case S1 = SBG = − ∑ i pi ln pi. The theory which emerges is usually referred to as nonextensive statistical mechanics ...

The object of research is the Fučik spectrum for (p,q)-Laplacian operator. In present paper, we are going to introduce notion a non-linear, non-homogeneous operator, which operator through study following eigenvalue boundary problem: {–∆pu–∆qu=λ(u+)p–1–μ(u–)q–1 in Ω, u=0 on ∂Ω, where Ω⊂RN, N≥1 bounded open subset with smooth and λ μ two real parameters. order establish show existence non-trivia...

In this paper we extend the scope of three important results in linear theory absolutely summing operators. The first one was obtained by Bu and Kranz [4] it asserts that a continuous operator between Banach spaces takes almost unconditionally summable sequences into Cohen strongly q-summable for any q≥2, whenever its adjoint is p-summing some p≥1. second them states operators with hilbertian d...

We give new proofs of two basic results in number theory: The law of quadratic reciprocity and the sign of the Gauss sum. We show that these results are encoded in the relation between the discrete Fourier transform and the action of the Weyl element in the Weil representation modulo p, q and pq. 0. Introduction Two basic results due to Gauss are the quadratic reciprocity law and the sign of th...