Related papers: $delta$-Quasi Cauchy Sequences
We establish the asymptotic regularity and the $\Delta$-convergence of the sequence constructed by the alternating projections to closed convex sets in a CAT($\kappa$) space with $\kappa > 0$. Furthermore, the strong convergence of the…
We explore a notion of pseudofinite dimension, introduced by Hrushovski and Wagner, on an infinite ultraproduct of finite structures. Certain conditions on pseudofinite dimension are identified that guarantee simplicity or supersimplicity…
We define and study classes of smooth functions which are less regular than Gevrey functions. To that end we introduce two-parameter dependent sequences which do not satisfy Komatsu's condition (M.2)', which implies stability under…
In this work, a mode of convergence for measurable functions is introduced. A related notion of Cauchy sequence is given and it is proved that this notion of convergence is complete in the sense that Cauchy sequences converge. Moreover, the…
If $f$ is a Henstock--Kurzweil integrable function on the real line, the Alexiewicz norm of $f$ is $\|f\|=\sup_I|\int_I f|$ where the supremum is taken over all intervals $I\subset\R$. Define the translation $\tau_x$ by $\tau_xf(y)=f(y-x)$.…
We investigate the Cauchy problem for a semilinear spatio--temporal fractional diffusion equation with a time-dependent forcing term: \[ \partial_t^\alpha u + (-\Delta)^{\mathsf{s}} u = |u|^p + t^{\sigma}\,\mathbf{w}(x), \quad (t,x) \in…
We study the interplay between additivity (as in the Cauchy functional equation), subadditivity and linearity. We obtain automatic continuity results in which additive or subadditive functions, under minimal regularity conditions, are…
A generalized definition of superpotential has proposed, which connects two one-dimensional potentials $V_{1}$ and $V_{2}$ with discrete energy spectra completely and where: 1) energy of factorization equals to arbitrary level of spectrum…
We analyse the quantum backflow effect and extend it, as a limiting constraint to its spatial extent, for scattering situations in the presence of a purely transmitting discontinuous jump-defect. Analytical and numerical comparisons are…
We first define Pseudo-Calabi flow, as {equation*} {{aligned}{{\partial \varphi}\over {\partial t}}&= -f(\varphi), \triangle_varphi f(\varphi) &= S(\varphi) - \ul S.{aligned}. \end{equation*} Then we prove the well-posedness of this flow…
In this paper, our primary objective is to study a possible decomposition of an approximately convex sequence. For a given $\varepsilon>0$; a sequence $\big<u_n\big>_{n=0}^{\infty}$ is said to be $\varepsilon$-convex, if for any…
We introduce a generalization of sequential compactness using barriers on $\omega$ extending naturally the notion introduced in [W. Kubi\'{s} and P. Szeptycki, On a topological Ramsey theorem, \emph{Canad. Math. Bull.}, 66 (2023),…
Recently, in Axioms 10(2): 119 (2021), a nonclassical first-order theory T of sets and functions has been introduced as the collection of axioms we have to accept if we want a foundational theory for (all of) mathematics that is not weaker…
This paper is inspired by the paper of Leonetti, Russo and Somaglia [\textit{Dense lineability and spaceability in certain subsets of $\ell_\infty$.} Bull. London Math. Soc., 55: 2283--2303 (2023)] and the lineability problems raised…
We establish quantitative compactness estimates for finite difference schemes used to solve nonlinear conservation laws. These equations involve a flux function $f(k(x,t),u)$, where the coefficient $k(x,t$ is $BV$-regular and may exhibit…
For a discrete function $f\left( x\right) $ on a discrete set, the finite difference can be either forward and backward. However, we observe that if $ f\left( x\right) $ is a sum of two functions $f\left( x\right) =f_{1}\left( x\right)…
In 2011, the theory of $\mathcal I^K$-convergence gets birth as an extension of the concept of $\mathcal{I}^*$-convergence of sequences of real numbers. $\mathcal I^K$-limit points and $\mathcal I^K$-cluster points of functions are…
A branching process $Z$ is said to be non conservative if it hits $\infty$ in a finite time with positive probability. It is well known that this happens if and only if the branching mechanism $\varphi$ of $Z$ satisfies…
New corrections to the equation of motion and total collapsing time of an empty spherical cavity immersed in an infinite incompressible medium are proposed on the assumption of a non-uniform density. The dimensionless number quantifying the…
In 1976, Rauzy studied two complexity functions, $\underline{\beta}$ and $\overline{\beta}$, for infinite sequences over a finite alphabet. The function $\underline{\beta}$ achieves its maximum precisely for Borel normal sequences, while…