相关论文: Nonstandard Analysis - A Simplified Approach

Studies in nuclear and atomic physics have played an important role in developing our understanding of the Standard Model of electroweak interactions. We review the basic ingredients of the Standard Model, and discuss some key nuclear and…

The paper proves the equivalence of the notions of nondeterministic and deterministic parameter testing for uniform dense hypergraphs of arbitrary order. It generalizes the result previously known only for the case of simple graphs. By a…

Any object on earth has two fundamental properties: it is finite, and it is made of atoms. Structural information about an object can be obtained from diffraction amplitude measurements that account for either one of these traits.…

Semi-supervised anomaly detection is based on the principle that potential anomalies are those records that look different from normal training data. However, in some cases we are specifically interested in anomalies that correspond to high…

We show some non-standard Poincar\'e type estimates in the biparametric setting with appropriate weights. We will derive these results using variants from classical estimates exploiting the interplay between maximal functions and fractional…

In order to apply nonstandard methods to questions of algebraic geometry we continue our investigation from "Enlargements of categories" (Theory Appl. Categ. 14 (2005), No. 16, 357--398) and show how important homotopical constructions…

Within the paradigm of metamaterials and metasurfaces, electromagnetic properties of composite materials can be engineered by shaping or modulating their constituents, so-called meta-atoms. Synthesis and analysis of complex-shape meta-atoms…

Statistically equivalent blocks are not frequently considered in the context of nonparametric two-sample hypothesis testing. Despite the limited exposure, this paper shows that a number of classical nonparametric hypothesis tests can be…

Using a recent alternative to Tarskian semantics for first-order logic, known as $\textit{possibility semantics}$, I introduce an alternative approach to nonstandard analysis that remains within the bounds of \textit{semi-constructive}…

We introduce an object that has obvious similarity to the classical one - the algebra of supersymmetric polynomials. Despite the similarity, the known structure theorems on supersymmetric polynomials do not help in the study of the new…

This paper deals with existence of a nontrivial positive solution to systems of equations involving nontrivial nonhomogeneous terms and critical or subcritical nonlinearities. Via a minimization argument we prove existence of a positive…

This paper deals with $n$-dimensional algebras, over any field, which have only trivial derivation (automorphism) and simple algebras. It is shown that the corresponding sets of algebras are not empty and, in algebraically closed field…

In this article we use our constructions from "Enlargements of Categories" (Theory and Applications of Categories, 14:357-398) to lay down some foundations for the application of A. Robinson's nonstandard methods to modern Algebraic…

We implement a semi-analytic approach for stability analysis, addressing the ongoing uncertainty about stability and structure of neutron star magnetic fields. Applying the energy variational principle, a model system is displaced from its…

Two essential methods, the symmetry analysis and of the singularity analysis, for the study of the integrability of nonlinear ordinary differential equations are discussed. The main similarities and differences of these two different…

The nonlinear supersymmetry of one-dimensional systems is investigated in the context of the quantum anomaly problem. Any classical supersymmetric system characterized by the nonlinear in the Hamiltonian superalgebra is symplectomorphic to…

This library (collection of subroutines) is presented for calculating standard quantities in the decomposition of many-electron matrix elements in atomic structure theory. These quantities include the coefficients of fractional parentage,…

I extend the definitions of schemes relative to monoids with zero - and therefore, toric geometry - to the world of formal schemes. This expands the usual framework to include, for instance, models for Mumford's degenerating Abelian…

I use Supergravity as a test case to study the role and uses of elegance/simplicity in formulating and evaluating physical models, whose sole criterion is of course truth: an observationally verified description of Nature within a certain…

Anomalies are samples that significantly deviate from the rest of the data and their detection plays a major role in building machine learning models that can be reliably used in applications such as data-driven design and novelty…