Abstract Generalized autoregressive conditionally heteroskedastic (GARCH) processes are widely used for modelling financial returns, with their extremal properties being of interest market risk management. For GARCH( $$p,q$$ p , q ) $$\max (p,q) = 1$$ <...

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...