Related papers: Constructing nonstandard hulls and Loeb measures i…
Recent Leibniz scholarship has sought to gauge which foundational framework provides the most successful account of the procedures of the Leibnizian calculus (LC). While many scholars (e.g., Ishiguro, Levey) opt for a default Weierstrassian…
Two major difficulties in using default logics are their intractability and the problem of selecting among multiple extensions. We propose an approach to these problems based on integrating nommonotonic reasoning with plausible reasoning…
The integration of the Einstein equations split into the solution of constraints on an initial space like 3 - manifold, an essentially elliptic system, and a system which will describe the dynamical evolution, modulo a choice of gauge. We…
Effects from nonstandard corrections to Newtonian gravity, at large scale, can be investigated using the cosmological structure formation. In particular, it is possible to show if and how a logarithmic correction (as that induced from…
We generalize the standard product integral formalism to incorporate Grassmann valued matrices and show that the resulting supersymmetric product integrals provide a natural framework for describing supersymmetric Wilson Lines and Wilson…
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…
Interior point methods are among the most popular techniques for large scale nonlinear optimization, owing to their intrinsic ability of scaling to arbitrary large problem sizes. Their efficiency has attracted in recent years a lot of…
We study an entropy measure for quantum systems that generalizes the von Neumann entropy as well as its classical counterpart, the Gibbs or Shannon entropy. The entropy measure is based on hypothesis testing and has an elegant formulation…
This article gives some properties of intervals in $\mathbb{R}$ and discusses some problems involving intervals for which the concept of outer measure on $\mathbb{R}$ provides a more efficient solution than an elementary approach. The outer…
An embedding theorem for algebraic systems is presented, basing on a certain old ultrafilter construction. As an application, we outline alternative proofs of some results from the theory of PI algebras, and establish some properties of…
A nonparametric adaptation theory is developed for the construction of confidence intervals for linear functionals. A between class modulus of continuity captures the expected length of adaptive confidence intervals. Sharp lower bounds are…
In this paper we show that the compactness of a Loeb space depends on its cardinality, the nonstandard universe it belongs to and the underlying model of set theory we live in. In section 1 we prove that Loeb spaces are compact under…
Control theory often takes the mathematical model of the to-be-control-led system for granted. In contrast, port-Hamiltonian systems theory bridges the gap between modelling and control for physical systems. It provides a unified framework…
Self-normalized processes are basic to many probabilistic and statistical studies. They arise naturally in the the study of stochastic integrals, martingale inequalities and limit theorems, likelihood-based methods in hypothesis testing and…
In this communication, we examine new formalisms for the construction of the external space when correlating reference wavefunctions built from nonorthogonal determinant expansions. Defining the external space in nonorthogonal approaches is…
We show that bootstrap methods based on the positivity of probability measures provide a systematic framework for studying both synchronous and asynchronous nonequilibrium stochastic processes on infinite lattices. First, we formulate…
Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…
The paper takles a procedure which allow to extend some linear, wave type equations to the study of nonlinear models. More concretely, we present a practical way to generate the largest class of a given form of second order differential…
Self-assembly in natural and synthetic molecular systems can create complex aggregates or materials whose properties and functionality rises from their internal structure and molecular arrangement. The key microscopic features that control…
In the present paper we focus on building simple nonperturbative analytical relativistic models of magnetars. With this purpose in mind we first develop a method for generating exact interior solutions to the static and axisymmetric…