Canonical expressions are representative of implicative propositions upto renaming of variables. In this paper we explore, using a Monte-Carlo approach, the model of canonical expressions in order to confirm the paradox that says that asymptotically almost all classical theorems are intuitionistic.
Asymptotic homogenization is used to systematically derive reduced-order macroscopic models of conductive behavior in spirally wound layered materials in which the layers have very different conductivities. The problem is motivated by the need for simplified models of the electrical and thermal behavior of lithium-ion cells, accounting for the high...
The Muskat problem, which models the flow of immiscible viscous fluids in a porous medium, has been studied extensively in recent years from a number of perspectives. While most studies have focused on harmonic analysis techniques in the graphical setting, the formation of topological singularities makes it desirable to have a notion of weak soluti...
Published in Biometrical journal. Biometrische Zeitschrift
Skewed distributions and inferences concerning quantiles are common in the health and social science researches. And most standard simultaneous inference procedures require the normality assumption. For example, few methods exist for comparing the medians of independent samples or quantiles of several distributions in general. To our knowledge, the...
Published in Lobachevskii Journal of Mathematics
AbstractThe article investigates the two point boundary-value problem for a singularly perturbed linear in homogeneous ordinary differential equation of the second order on a segment with a turning point and interior layer. The aim of the study is to construct a uniform asymptotic expansion of the solution of the two point problem with an arbitrary...
Published in Frontiers in Bioengineering and Biotechnology
Organoids are three-dimensional multicellular tissue constructs. When cultured in vitro, they recapitulate the structure, heterogeneity, and function of their in vivo counterparts. As awareness of the multiple uses of organoids has grown, e.g. in drug discovery and personalised medicine, demand has increased for low-cost and efficient methods of pr...
Published in Acta Mechanica et Automatica
The article is concerned with the analysis of the problem for a concentrated line load moving at a constant speed along the surface of a pre-stressed, incompressible, isotropic elastic half-space, within the framework of the plane-strain assumption. The focus is on the near-critical regimes, when the speed of the load is close to that of the surfac...
Published in Lobachevskii Journal of Mathematics
AbstractThe article investigates the Robin boundary-value problem for a linear inhomogeneous ordinary differential equation of the second order on a segment with a small parameter at the highest derivative of the unknown function. The aim of the study is to construct a uniform asymptotic expansion of the solution of the Roben problem with an arbitr...
Published in Lobachevskii Journal of Mathematics
AbstractAn arbitrary compact-support initial datum for the Korteweg–de Vries equation asymptotically splits into solitons and a radiation tail, moving in opposite direction. We give a simple method to predict the number and amplitudes of resulting solitons and some integral characteristics of the tail using only conservation laws.
Published in Lobachevskii Journal of Mathematics
AbstractThe article studies the asymptotic behavior of the solutions of a singularly perturbed three boundary value problems on an interval. The object of the study is a linear inhomogeneous ordinary differential equation of the second order with a small parameter with the highest derivative of the unknown function. The singularities of the problem...
