The no-zero-divisor division algebra of highest possible dimension over the reals is taken as a model for various physical and mathematical phenomena mostly related to the Four Color Conjecture. A geometric form of associativity is the common thread.

This article explores the concept of life-space intervention, and proposes four dimensions of a single, unified life-space: The physical dimension, where young people’s lives unfold; the mental dimension, reflecting how young people make sense of their life-space; the relational dimension, assigning ‘space’ to young people’s relationships; and, the virtual dimension, constituted by technology-b...

In this paper we discuss dimension-theoretical properties of rational maps on the Riemann sphere. In particular, we study existence and uniqueness of generalized physical measures for several classes of maps including hyperbolic, parabolic, non-recurrent and Topological Collet-Eckmann maps. These measures have the property that their typical points have maximal Hausdorff dimension. On the other...

Theoretical advances toward a purely meshless framework for analysis of the generalized fractal dimension, with applications to turbulence, are considered. The key basic theoretical idea is the formulation of the probability density function of the minimum distance to the nearest part of the flow feature of interest, e.g. a turbulent interface, from any location randomly chosen within a referen...

Predicting the sawability of the dimension stone is one of the most important factors involved in production planning. Moreover, this factor can be used as an important criterion in the cost estimation and planning of the stone plants. The main purpose for carrying out this work was to rank the sawability of the dimension stone using the PROMETHEE method. In this research work, four important p...

‎In this paper we give an upper bound for Noetherian dimension of all injective modules with Krull dimension on arbitrary rings‎. ‎In particular‎, ‎we also give an upper bound for Noetherian dimension of all Artinian modules on Noetherian duo rings.

Material components for the nuclear fusion and the advanced nuclear fi ssion reactors are exposed to high levels of radiation energy, high temperature, and high thermo-mechanical stresses. Radiation damage is inherently a multiscale phenomenon, with interactions encompassing time scales from femto-seconds to years and length scales from subnanometer to meters. In this study, multiscale modeling...

Dimensionality is one of the most important properties of complex physical systems. However, only recently this concept has been considered in the context of complex networks. In this paper we further develop the previously introduced definitions of dimension in complex networks by presenting a new method to characterize the dimensionality of individual nodes. The methodology consists in obtain...