Related papers: Bigeometric Calculus and its applications
The paper is concerned with b-metric and generalized b-metric spaces. One proves the existence of the completion of a generalized b-metric space and some fixed point results. The behavior of Lipschitz functions on b-metric spaces of…
Interacting systems of particles with generalized statistics are considered on both classical and quantum level. It is shown that all possible quantum states and corresponding processes can be represented in terms of certain specific…
We use the results of AG/0406290 to discuss the counting formulas of network flow polytopes and magic squares, i.e. the formula for the corresponding Ehrhart polynomial in terms of residues. We also discuss a description of the big cells…
In this paper we discuss various connections between geometric discrepancy measures, such as discrepancy with respect to convex sets (and convex sets with smooth boundary in particular), and applications to numerical analysis and…
We give a geometry of interaction model for a typed lambda-calculus endowed with operators for sampling from a continuous uniform distribution and soft conditioning, namely a paradigmatic calculus for higher-order Bayesian programming. The…
Algebraic statistics uses tools from algebra (especially from multilinear algebra, commutative algebra and computational algebra), geometry and combinatorics to provide insight into knotty problems in mathematical statistics. In this survey…
In this paper, some real-world motivated examples are provided illustrating the power of linear algebra tools as the product of matrices, determinants, eigenvalues and eigenvectors. In this sense, some practical applications related to…
In this paper we provide an exhaustive survey of the current state of the mathematics of filtration enlargement and an interpretation of the key results of the literature from the viewpoint of mathematical finance. The emphasis is on…
The Bayesian statistical paradigm provides a principled and coherent approach to probabilistic forecasting. Uncertainty about all unknowns that characterize any forecasting problem -- model, parameters, latent states -- is able to be…
This article provides the role of big idea statisticians in future of Big Data Science. We describe the `United Statistical Algorithms' framework for comprehensive unification of traditional and novel statistical methods for modeling Small…
In Gromov's treatise Partial Differential Relations (volume 9 of Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 1986), a continuous map between Riemannian manifolds is called isometric if it preserves the length of rectifiable…
The primary aim of this chapter is, commemorating the 150th anniversary of Riemann's death, to explain how the idea of {\it Riemann sum} is linked to other branches of mathematics. The materials I treat are more or less classical and…
Starting from pseudometrics and preorders on sets of integers, we extend the focus to sets of finite sequences of integers, in particular sequences of consecutive integers. We outline existing concepts for deriving centred pseudometrics and…
The present work deals with the search of useful physical applications of some generalized groups of metric transformations. We put forward different proposals and focus our attention on the implementation of one of them. Particularly, the…
The space of embedded submanifolds plays an important role in applications such as computational anatomy and shape analysis. We can define two different classes on Riemannian metrics on this space: so-called outer metrics are metrics that…
This is the first paper in a series (of four) designed to show how to use geometric algebras of multivectors and extensors to a novel presentation of some topics of differential geometry which are important for a deeper understanding of…
In this paper, we introduce new spaces of holomorphic functions on the unit ball $\mathbb{B}_{n}$ of $\mathbb{C}^{n}$ generalizing the classical Bergman spaces. The main results include the properties of some operators and integrals…
The concepts of infinity and infinitesimal in mathematics date back to anciens Greek and have always attracted great attention. Very recently, a new methodology has been proposed by Sergeyev for performing calculations with infinite and…
The essentials of fractional calculus according to different approaches that can be useful for our applications in the theory of probability and stochastic processes are established. In addition to this, from this fractional integral one…
In this short note, we present certain generalized versions of the commutator formulas of some natural operators on manifolds, and give some applications.