Related papers: On the Functions Generated by the General Purpose …
One of the basic principles of Approximation Theory is that the quality of approximations increase with the smoothness of the function to be approximated. Functions that are smooth in certain subdomains will have good approximations in…
computable functions are defined by abstract finite deterministic algorithms on many-sorted algebras. We show that there exist finite universal algebraic specifications that specify uniquely (up to isomorphism) (i) all abstract computable…
In a previous paper, we provided a formal definition for the concept of computational irreducibility (CIR), i.e. the fact for a function f from N to N that it is impossible to compute f(n) without following approximately the same path than…
For a real c\`{a}dl\`{a}g function f and a positive constant c we find another c\`{a}dl\`{a}g function, which has the smallest total variation pos- sible among all functions uniformly approximating f with accuracy c/2. The solution is…
We present numerical techniques based on generalized functions adapted to nonlinear calculations. They concern main numerical engineering problems ruled by-or issued from-nonlinear equations of continuum mechanics. The aim of this text is…
Using first principles from inference, we design a set of functionals for the purposes of \textit{ranking} joint probability distributions with respect to their correlations. Starting with a general functional, we impose its desired…
The single particle Green's function provides valuable information on the momentum and energy-resolved spectral properties for a strongly correlated system. In large-scale numerical calculations using quantum Monte Carlo (QMC), dynamical…
Computation of (approximate) polynomials common factors is an important problem in several fields of science, like control theory and signal processing. While the problem has been widely studied for scalar polynomials, the scientific…
We establish conditions under which a continuous time reservoir computer, such as a leaky integrator echo state network, admits a generalised synchronisation $f$ between between the source dynamics and reservoir dynamics. We show that…
Recent years witness the tremendous success of generative adversarial networks (GANs) in synthesizing photo-realistic images. GAN generator learns to compose realistic images and reproduce the real data distribution. Through that, a…
Mustafa and Sims [12] introduced the notion of $G$-metric as a possible generalization of usual notion of a metric space. The author generalized the notion of G-metric to more than three variables and introduced the concept of Generalized…
This paper serves as a bridge between quantum computing and analogical modeling (a general theory for predicting categories of behavior in varying contexts). Since its formulation in the early 1980s, analogical modeling has been…
The concept of generalized functions taking values in a differentiable manifold is extended to a functorial theory. We establish several characterization results which allow a global intrinsic formulation both of the theory of…
Multidimensional Continued Fraction Algorithms are generalizations of the Euclid algorithm and find iteratively the gcd of two or more numbers. They are defined as linear applications on some subcone of $\mathbb{R}^d$. We consider…
A uniform approach to computing with infinite objects like real numbers, tuples of these, compacts sets, and uniformly continuous maps is presented. In work of Berger it was shown how to extract certified algorithms working with the signed…
We study the analog of power series expansions on the Sierpinski gasket, for analysis based on the Kigami Laplacian. The analog of polynomials are multiharmonic functions, which have previously been studied in connection with Taylor…
Generative Adversarial Networks (GAN) have received wide attention in the machine learning field for their potential to learn high-dimensional, complex real data distribution. Specifically, they do not rely on any assumptions about the…
Many different types of fractional calculus have been proposed, which can be organised into some general classes of operators. For a unified mathematical theory, results should be proved in the most general possible setting. Two important…
A new classification of real functions and other related real objects defined within a compact interval is proposed. The scope of the classification includes normal real functions and distributions in the sense of Schwartz, referred to…
G\"ahler ([4],[5]) introduced and investigated the notion of 2-metric spaces and 2-normed spaces in sixties. These concepts are inspired by the notion of area in two dimensional Euclidean space. In this paper, we choose a fundamentally…