Related papers: General position theorem and its applications
The principle of fractal stiffness self-similarity is expanded to encompass structures with several differently-scaled contributors to the total stiffness matrix. The generalized principle is applied to solve the problem of a fractal…
The aim of this paper is to establish some metrical coincidence and common fixed point theorems with an arbitrary relation under an implicit contractive condition which is general enough to cover a multitude of well known contraction…
We develop a general theory for class-sized symmetric systems as a natural extension of symmetric systems with respect to class forcing. In particular, adapting the usual notions of pretameness and tameness for class forcing, we present…
An introductory to generalized parton distributions is given which emphasizes their spectral property and its uses as well as the equivalence of various GPD representations. Furthermore, the status of the theory and phenomenology of hard…
We generalize Hrushovski's group configuration theorem to the case where the type of the configuration is generically stable, without assuming tameness of the ambient theory. The properties of generically stable types, which we recall in…
A theorem of Mandel allows to determine the covector set of an oriented matroid from its set of topes by using the composition condition. We provide a generalization of that result, stating that the covector set of a conditional oriented…
An overview is given of the methods for treating complicated problems without small parameters, when the standard perturbation theory based on the existence of small parameters becomes useless. Such complicated problems are typical of…
We present an introduction to the framework of strongly local Dirichlet forms and discuss connections between the existence of certain generalized eigenfunctions and spectral properties within this framework. The range of applications is…
We show that the existing generalized separation statements including the conventional extremal principle and its extensions differ {in the ways norms on product spaces are defined}. We prove a general separation statement with arbitrary…
A Generalized Kinetic Theory was proposed in order to have the possibility to treat particles which obey a very general statistics. By adopting the same approach, we generalize here the Kinetic Theory of electrons and phonons. Equilibrium…
Generalized Feller theory provides an important analog to Feller theory beyond locally compact state spaces. This is very useful for solutions of certain stochastic partial differential equations, Markovian lifts of fractional processes, or…
We study the general theorem about gravitational lensing which states the relationship between the numbers of images with different parities. Our formulation allows an extension to the nontransparent and singular model.
In the present work we suggest a general covariant theory which can be used to study the stability of any physical system treated geometrically. Stability conditions are connected to the magnitude of the deviation vector. This theory is a…
The objective of this manuscript is to introduce and develop the concept of a generalized $\theta$-parametric metric space-a novel extension that enriches the modern metric fixed point theory. We study of its fundamental properties,…
We construct a theory of distributions in the setting of analysis on post-critically finite self-similar fractals, and on fractafolds and products based on such fractals. The results include basic properties of test functions and…
We present a generalisation of the theory of iterated function systems and associated fractals to the setting of noncommutative geometry. Along the way, we discuss some ideas surrounding locally compact noncommutative metric spaces.
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
The aim of this paper is to construct a fractal with the help of a finite family of generalized F-contraction mappings, a class of mappings more general than contraction mappings, defined in the setup of b-metric space. Consequently, we…
We present an overview of some recent developments in the theory of generalized formal series, grounded in diffeological geometric framework. These constructions aim to offer new tools for understanding infinite-dimensional phenomena in…
Local fractional derivative and integrals are revealed as one of useful tools to deal with everywhere continuous but nowhere differentiable functions in fractal areas ranging from fundamental science to engineering. In this paper, a…