The issue of the ”eternal return” is examined from the perspective of the topology of spacetime. Constraints on dynamical laws for the periodic evolution of a system or universe are highlighted. Using a Fourier series expansion, an infinite set of simultaneous linear equations is formulated for the periodic evolution of a system/universe. PACS: 05.70.-a, 05.90.+m, 04.20.Jb, 04.20.Gz

The status of exponential scalar potentials in supergravity is reviewed, and updated. One version of N=8 D=4 supergravity with a positive exponential potential, obtainable from a ‘non-compactification’ of M-theory, is shown to have an accelerating cosmological solution that realizes ‘eternal quintessence’.

Models of eternal inflation predict a stochastic self-similar geometry of the universe at very large scales and allow existence of points that never thermalize. I explore the fractal geometry of the resulting spacetime, using coordinate-independent quantities. The formalism of stochastic inflation can be used to obtain the fractal dimension of the set of eternally inflating points (the “eternal...

Let G(V,E) be a graph with p vertices and q edges. A graph G is said to have an odd mean labeling if there exists a function f : V (G) → {0, 1, 2,...,2q - 1} satisfying f is 1 - 1 and the induced map f* : E(G) → {1, 3, 5,...,2q - 1} defined by f*(uv) = (f(u) + f(v))/2 if f(u) + f(v) is evenf*(uv) = (f(u) + f(v) + 1)/2 if f(u) + f(v) is odd is a bijection. A graph that admits an odd mean labelin...

Subdivision rules have traditionally been designed to generate smooth surfaces from polygonal meshes. In this paper we propose to employ subdivision rules as a polygonal modeling tool, specifically to add additional level of detail to meshes. However, existing subdivision schemes have several undesirable properties making them ill suited for polygonal modeling. In this paper we propose a genera...

the main aim of this study was to identify and present indicators and standards necessary for security management of sport facilities. these standards were recognized via a set of interviews and questionnaires through delphi method. the revised questionnaire of panteza et al. (2003) with 0.89 of reliability and interviews were used to collect data. the subjects were selected from purposeful sam...

Given a dilation matrix A : Z d → Z d , and G a complete set of coset representatives of 2π(A −− Z d /Z d), we consider polynomial solutions M to the equation g∈G M (ξ + g) = 1 with the constraints that M ≥ 0 and M (0) = 1. We prove that the full class of such functions can be generated using polynomial convolution kernels. Trigonometric polynomials of this type play an important role as symbol...