Related papers: On growth in an abstract plane
In this paper I present a kind of proof for classical Euclidean geometric problems which relies on both synthetic and analytic geometry. Using the elementary tools of polynomial algebra and multivariate calculus we manage to reduce the…
We briefly review the properties of radially growing interfaces and their connection to biological growth. We focus on simplified models which result from the abstraction of only considering domain growth and not the interface curvature.…
In this article we prove lower and upper bounds for class numbers of algebraic curves defined over finite fields. These bounds turn out to be better than most of the previously known bounds obtained using combinatorics. The methods used in…
In the hyperbolic plane there are infinite regular lattices. From a fix vertex of a lattice tree graphs can be constructed recursively to the next layers with edges of the lattice. In this article we examine the properties of the growing of…
We discuss a general growth curve including several parameters, whose choice leads to a variety of models including the classical cases of Malthusian, Richards, Gompertz, Logistic and some their generalizations. The advantage is to obtain a…
We study growth and complexity of \'etale groupoids in relation to growth of their convolution algebras. As an application, we construct simple finitely generated algebras of arbitrary Gelfand-Kirillov dimension $\ge 2$ and simple finitely…
We present a new and compelling approach to the efficient solution of important computational problems that arise in the context of abstract argumentation. Our approach makes known algorithms defined for restricted fragments generally…
Generalized Bargmann representations which are based on generalized coherent states are considered. The growth of the corresponding analytic functions in the complex plane is studied. Results about the overcompleteness or undercompleteness…
By recasting metrical geometry in a purely algebraic setting, both Euclidean and non-Euclidean geometries can be studied over a general field with an arbitrary quadratic form. Both an affine and a projective version of this new theory are…
Accretion of mineralized thin wall-like structures via localized growth along their edges is observed in a range of physical and biological systems ranging from molluscan and brachiopod shells to carbonate-silica composite precipitates. To…
Surface growth, by association or dissociation of material on the boundaries of a body, is ubiquitous in both natural and engineering systems. It is the fundamental mechanism by which biological materials grow, starting from the level of a…
We develop a theory of vector-valued heights and intersections defined relative to finitely generated extensions K/k. These generalize both number field and geometric heights. When k is Q or F_p, or when a non-isotriviality condition holds,…
The architecture has its basis in a dialectic search of new choices of representation. We deal with the form on the contemporary architecture under two approaches: expression and content. We examine how mathematical principles based on…
Argumentation frameworks, consisting of arguments and an attack relation representing conflicts, are fundamental for formally studying reasoning under conflicting information. We use methods from mathematical logic, specifically…
There is no field with only one element, yet there is a well-defined notion of what projective geometry over such a field means. This notion is familiar to experts and plays an interesting role behind the scenes in combinatorics and…
In this text, we prove the existence of an asymptotic growth rate of the number of dominating sets (and variants) on finite rectangular grids, when the dimensions of the grid grow to infinity. Moreover, we provide, for each of the variants,…
Biological entities are inherently dynamic. As such, various ecological disciplines use mathematical models to describe temporal evolution. Typically, growth curves are modelled as sigmoids, with the evolution modelled by ordinary…
This is a survey of some recent results concerning polynomial inequalities and polynomial approximation of functions in the complex plane. The results are achieved by the application of methods and techniques of modern geometric function…
We consider finite range Gibbs fields and provide a purely combinatorial proof of the exponential tree decay of semi--invariants, supposing that the logarithm of the partition function can be expressed as a sum of suitable local functions…
We study product sets of finite arithmetic progressions of polynomials over a finite field. We prove a lower bound for the size of the product set, uniform in a wide range of parameters. We apply our results to resolve the function field…