We show that any subset A ⊂ N with positive upper Banach density contains the pattern {m,m + [nα], . . . ,m + k[nα]}, for some m ∈ N and n = p − 1 for some prime p, where α ∈ R\Q. Making use for the Furstenberg Correspondence Principle, we do this by proving an associated recurrence result in ergodic theory along the shifted primes. We also prove the convergence result for the associated averag...

The principle of the holography information states that in a theory quantum gravity copy all available on Cauchy slice is also near boundary slice. This redundancy already present at low energy. In context AdS/CFT correspondence, this can be translated into statement about dual conformal field theory. We carry out translation and demonstrate holds bilocal holography.

In the mid-1960's two quite separate but fundamental questions in capital theory were first debated in this Journal. On the one hand, the original paper by Levhari (1965) gave rise to the widely cited series of papers published jointly in November, 1966, as "Paradoxes in Capital Theory: A Symposium," which has since spawned dozens of articles and several books.1 This debate now constitutes a cr...

Simultaneous learning of multiple functions is one of the fundamental issues not only to design intelligent robots but also to understand human’s cognitive developmental process since we, human, do so in our daily lives but we do not know how to do. Drawing an analogy to the well-known bias in child language development, we propose the mutual exclusivity selection principle (μX principle) for l...

This paper describes the present state of an attempt at understanding the quantum behaviour of microphysics in terms of a nondifferentiable space-time continuum having fractal (i.e., scale-dependent) properties. The fundamental principle upon which we rely is that of scale relativity, which generalizes to scale transformations Einstein’s principle of relativity. After having related the fractal...

In Latin America and the Caribbean (LAC) region, geophysical, meteorological hydrological disasters are increasing every year. With significantly limited resources, these countries naturally forced to absorb lessons from disasters. One of fundamental activities during this learning task remains need standardize forensic reporting process. Like all academic disciplines, engineering is exceptiona...

In this paper, we investigate a novel implication of the non-negligible spacetime curvature at large distances when its effects are expressed in terms suitably modified form Heisenberg uncertainty relations. Specifically, establish one-to-one correspondence between principle and Standard Model Extension (SME), string-theoretical effective field theory that accounts for both explicit spontaneous...

2,3,7,8-tetrachlorodibenzo-p-dioxin (tcdd) is a by-product o f t he trichlorophenol (herbicide) production and is also produced through a variety of combustion processes. it appears that tcdd is a ubiquitous chemical, particularly in industrialised countries, and the liver is the target organ of its toxicity. the prominent hepatotoxic effect of tcdd is progressive centrilobular necrosis. the is...