Related papers: Space and Family
Galaxies represent the visible fabric of the Universe and there has been considerable progress recently in both observational and theoretical studies. The underlying goal is to understand the present-day diversity of galaxy forms, masses…
We study links between first-order formulas and arbitrary properties for families of theories, classes of structures and their isomorphism types. Possibilities for ranks and degrees for formulas and theories with respect to given properties…
We note that in general there exist two basic aspects in any branch of physics, including cosmology - one dealing with the attributes of basic constituents and forces of nature, the other dealing with how structures arise from them and how…
In this article, we present what we believe to be a simple way to motivate the use of Hilbert spaces in quantum mechanics. To achieve this, we study the way the notion of dimension can, at a very primitive level, be defined as the…
Graph compositions generalize both integer compositions and partitions of a finite set. We develop formulas, generating functions and recurrence relations for composition counting functions for several families of graphs.
Six families of generalized hypergeometric series in a variable $x$ and an arbitrary number of parameters are considered. Each of them is indexed by an integer $n$. Linear recurrence relations in $n$ relate these functions and their product…
We introduce and analyze a new geometric structure on topological surfaces generalizing the complex structure. To define this so called higher complex structure we use the punctual Hilbert scheme of the plane. The moduli space of higher…
In this paper will be introduced large, probably complete family of complex base systems, which are 'proper' - for each point of the space there is a representation which is unique for all but some zero measure set. The condition defining…
In this paper, we study the topology associated to the fractal manifold model. It turns out that this topology is actually a family of topologies that gives to the fractal manifold a structure of variable topological space. Additionally, we…
In [1] we defined a new kind of space called 'structured space' which locally resembles, near each of its points, some algebraic structure. We noted in the conclusion of the cited paper that the maps $f_s$ and $h$, which are of great…
The possibility of obtaining an open set of regular cosmological models is discussed. Cylindrical stiff perfect fluid cosmologies are studied in detail. The condition for geodesic completeness is easy to check. A large family of…
We consider the set of all 2-step recurrences (difference equations) that are given by linear fractional maps. These give birational maps of the plane. We determine the degree growth of these birational maps. We find the all the maps in…
We perceive the world through images formed by scattering. The ability to interpret scattering data mathematically has opened to our scrutiny the constituents of matter, the building blocks of life, and the remotest corners of the universe.…
In this paper, we extend the work of Andrews, Beck and Hopkins by considering partitions and compositions with bounded gaps between each pair of consecutive parts. We show that both their generating functions and two matrices determined by…
The origin of the large scale structure in the universe - galaxies, quasars, clusters, voids, sheets - is one of the most important questions in cosmology. One can show that some non-thermal energy density fluctuations must have been…
The nature of the change in perspective that accompanies the proposal of a unified physical theory deriving from the single dimension of time is elaborated. On expressing a temporal interval in a multi-dimensional form, via a direct…
Recently various phenomenological implications of the existence of extra space-time dimensions have been investigated. In this letter, we construct a model with realistic fermion mass hierarchy with (large) extra dimensions beyond the usual…
A dilatation structure is a concept in between a group and a differential structure. In this article we study fundamental properties of dilatation structures on metric spaces. This is a part of a series of papers which show that such a…
In this paper we analyze the geometric structure and properties of a certain class of subsets of $\Bbb R^d$, known in the literature as 1-multicones, and here simply called multicones, which are quite natural generalizations of the…
We try to understand how particles acquire mass in general, and in particular, how they acquire mass in the standard model and beyond.