相关论文: Nonstandard Analysis - A Simplified Approach

This article employs techniques from convex analysis to present characterizations of (maximal) $n-$monotonicity, similar to the well-established characterizations of (maximal) monotonicity found in the existing literature. These…

In a minimal extension of the Standard Model, in which new neutral fermions have been introduced, we show that the requirement of vanishing anomalies fixes the hypercharges of all fermions uniquely. This naturally leads to electric charge…

We introduce a category-theoreticabstraction of a syntax with auxiliary functions, called an admissiblemonad morphism. Relying on an abstract form of structural recursion,we then design generic tools to construct admissible monad…

In traditional thermodynamical and statistical-mechanical approaches one has (some) detailed knowledge of the principles governing the microdynamics of a system. However in many instances we may not have a Hamiltonian or good information…

The complexity of biomolecular interactions necessitates advanced methodologies to accurately capture their behavior in solution. In this work, we focus on monoclonal antibodies and adopt a multi-scale coarse-graining strategy for their…

The differences between the $N=0$ and $N=1$ standard models are emphasized in formulating their short distance extension. We sketch methods to reproduce many of the small numbers in the model in terms of scale ratios, applying see-saw like…

The standard model of particle physics represents the cornerstone of our understanding of the microscopic world. In these lectures we review its contents and structure, with a particular emphasis on the central role played by symmetries and…

A characterization of the general linear equation in standard form admitting a maximal symmetry algebra is obtained in terms of a simple set of conditions relating the coefficients of the equation. As a consequence, it is shown that in its…

In a recent work, arXiv:2503.05884, we proposed a unified notion of nonclassicality that applies to arbitrary processes in quantum theory, including individual quantum states, measurements, channels, set of these, etc. This notion is…

This paper consists of a description of the variety of two dimensional associative algebras within the framework of Nonstandard Analysis. By decomposing each algebra in A^2 as sum of a Jordan algebra and a Lie algebra, we calculate the…

We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows the for the generation of…

We determine and use a minimal set of numerical simulations to create a simplified model for the spectral response of nanoantennae with respect to their geometric and modeling parameters. The simplified model is then used to rapidly obtain…

We extend for the second time the Nonstandard Analysis by adding the left monad closed to the right, and right monad closed to the left, while besides the pierced binad (we introduced in 1998) we add now the unpierced binad - all these in…

This paper presents an algorithmic method to study structural properties of nonlinear control systems in dependence of parameters. The result consists of a description of parameter configurations which cause different control-theoretic…

We review a collection of models of random simplicial complexes together with some of the most exciting phenomena related to them. We do not attempt to cover all existing models, but try to focus on those for which many important results…

Using molecular dynamics simulations we study the temperature-density phase diagram of a simple model system of particles in two dimensions. In addition to translational degrees of freedom, each particle has two internal states and…

We will present the benefits of using methods of non-standard analysis in dynamic projective geometry. One major application will be the desingulariazation of geometric constructions.

The purpose of this letter is threefold : (i) to derive, in the framework of a new parametrization, some compact formulas of energy averages for the electrostatic interaction within an (nl)N configuration, (ii) to describe a new generating…

In the work, we derive exact analytic expressions for $(3+N)$-flavor neutrino oscillation probabilities in an arbitrary matter potential in term of matrix elements and eigenvalues of the Hamiltonian. With the analytic expressions, we…

The purpose of the present paper is to clarify, as far as it is possible, the overall picture of experimental results in the field of non-conventional phenomena in nuclear matter published in scientific literature, accumulated in the last…