Related papers: Non Standard Analysis as a Functor, as Local, as I…
A new summation method is introduced to convert a relatively wide family of infinite sums and local expansions into integrals. The integral representations yield global information such as analytic continuability, position of singularities,…
We demonstrate that any full and faithful $*$-functor between approximable categories of locally finite coarse spaces induces a coarse embedding between the underlying spaces. Furthermore, we establish a general characterisation of such…
We present a systematic study on a class of nonlocal integral functionals for functions defined on a bounded domain and the naturally induced function spaces. The function spaces are equipped with a seminorm depending on finite differences…
A previously established correspondence between definite-parity real functions and inner analytic functions is generalized to real functions without definite parity properties. The set of inner analytic functions that corresponds to the set…
We study the multifractal analysis of self-similar measures arising from random homogeneous iterated function systems. Under the assumption of the uniform strong separation condition, we see that this analysis parallels that of the…
This paper studies optimal estimation of large-dimensional nonlinear factor models. The key challenge is that the observed variables are possibly nonlinear functions of some latent variables where the functional forms are left unspecified.…
In this paper, we highlight a new computational aspect of Nonstandard Analysis relating to higher-order computability theory. In particular, we prove that the Gandy-Hyland functional equals a primitive recursive functional involving…
This thesis concerns embeddings and self-embeddings of foundational structures in both set theory and category theory. The first part of the work on models of set theory consists in establishing a refined version of Friedman's theorem on…
Functional depth is used for ranking functional observations from most outlying to most typical. The ranks produced by functional depth have been proposed as the basis for functional classifiers, rank tests, and data visualization…
A natural connection between rational functions of several real or complex variables, and subspace collections is explored. A new class of function, superfunctions, are introduced which are the counterpart to functions at the level of…
We prove that any noetherian quasi-excellent scheme of characteristic zero admits a strong desingularization which is functorial with respect to all regular morphisms. We show that as an easy formal consequence of this result one obtains…
Generalized analytic functions over generalized analytic manifolds are build from sums of convergent real power series with non-negative real exponents (and some well-ordering condition on the support). In a paper by Mart\'in-Villaverde,…
This paper studies normalisation by evaluation for typed lambda calculus from a categorical and algebraic viewpoint. The first part of the paper analyses the lambda definability result of Jung and Tiuryn via Kripke logical relations and…
We introduce the concept of topological finite-determinacy for germs of analytic functions within a fixed ideal $I$, which provides a notion of topological finite-determinacy of functions with non-isolated singularities. We prove the…
A new measure of non-classical correlations is introduced and characterized. It tests the ability of using a state {\rho} of a composite system AB as a probe for a quantum illumination task [e.g. see S. Lloyd, Science 321, 1463 (2008)], in…
In this paper the concept of $\mathbb{F}$-functorial of a finite group was introduced. These functorials have many properties of the Fitting subgroup of a soluble group and the generalized Fitting subgroup of a finite group. It was shown…
Submodular set functions are undoubtedly among the most important building blocks of combinatorial optimization. Somewhat surprisingly, continuous counterparts of such functions have also appeared in an analytic line of research where they…
In the present paper, we first describe the principal basis of non-integral geometry. Non-integral geometry is a new field of generalized function (distribution) theory where the effects breaking the symmetry of integration measure have…
These lecture notes, to be completed in a later version, offer a short and rigorous introduction to Nostandard Analysis, mainly aimed to reach to a presentation of the basics of Loeb integration, and in particular, Loeb measures. The…
We reinterpret various properties of Noetherian local rings via the existence of some $n$-ary numerical function satisfying certain uniform bounds. We provide such characterizations for seminormality, weak normality, generalized…