Related papers: Allowable Changes of Variable for Recently Develop…
In this article, we revisit the paper by Kundu et al.~(2024), presenting new results and insights for both identical and non-identical independent random variables. We derive sufficient conditions for preserving the hazard rate and reversed…
Unlike other techniques of causality inference, the use of valid instrumental variables can deal with unobserved sources of both variable errors, variable omissions, and sampling bias, and still arrive at consistent estimates of average…
An approach to reasoning with default rules where the proportion of exceptions, or more generally the probability of encountering an exception, can be at least roughly assessed is presented. It is based on local uncertainty propagation…
Non-Hermitian evolution is mathematically invertible, yet finite dynamic range imposes a sharp operational limit on reversibility. We identify Precision-Induced Irreversibility (PIR): amplification, mode mixing (as warranted by…
A sequence of non-negative integers is exactly realizable as the fixed point counts sequence of a dynamical system if and only if it gives rise to a sequence of non-negative orbit counts. This provides a simple realizability criterion based…
In this note we present a characterisation of all unary and binary patterns that do not only contain variables, but also reversals of their instances. These types of variables were studied recently in either more general or particular…
Override and update are natural constructions for combining partial functions, which arise in various program specification contexts. We use an unexpected connection with combinatorial geometry to provide a complete finite system of…
Natural revision seems so natural: it changes beliefs as little as possible to incorporate new information. Yet, some counterexamples show it wrong. It is so conservative that it never fully believes. It only believes in the current…
The present article discusses the exact observability of the wave equation when the observation subset of the boundary is variable in time. In the one-dimensional case, we prove an equivalent condition for the exact observability, which…
We prove that a condition of boundedness of the maximal function of a singular integral operator, that is known to be sufficient for the continuity of the corresponding integral operator in H\"{o}lder spaces, is actually also necessary in…
For an arbitrary ordinary second order differential equation a test is constructed that checks if this equation is equivalent to Painleve I, II or Painleve III with three zero parameters equations under the substitutions of variables. If it…
This paper offers what seems at first to be a minor technical correction to the current practice of computing indefinite integrals, and introduces the idea of a "Kahanian constant of integration". However, the total impact of this minor…
A new problem is studied, the concept of exactness of a second order nonlinear ordinary differential equations is established. A method is constructed to reduce this class into a first order equations. If the second order equation is not…
We extend de Finetti's (1937) notion of exchangeability to finite and countable sequences of variables, when a subject's beliefs about them are modelled using coherent lower previsions rather than (linear) previsions. We prove…
Along this work we study an indefinite abstract smoothing problem. After establishing necessary and sufficient conditions for the existence of solutions to this problem, the set of admissible parameters is discussed in detail. Then, its…
Finding necessary and sufficient conditions for isomorphism between two semigroups of order-preserving transformations over an infinite domain with restricted range was an open problem in \cite{FHQS}. In this paper, we show a proof strategy…
We examine the notion of anticonfinement and the role it has to play in the singularity analysis of discrete systems. A singularity is said to be anticonfined if singular values continue to arise indefinitely for the forward and backward…
Variational stability, in the sense of local good behavior of optimal values and solutions in problems of optimization under shifts in parameters, is important not only for validating model robustness in practical applications but also for…
We consider a symmetric matrix, the entries of which depend linearly on some parameters. The domains of the parameters are compact real intervals. We investigate the problem of checking whether for each (or some) setting of the parameters,…
We report on a formalization of the change of variables formula in integrals, in the mathlib library for Lean. Our version of this theorem is extremely general, and builds on developments in linear algebra, analysis, measure theory and…