International Monthly Seminar on Time Scales Analysis #8

In this work, we investigate the approximation of spatially nonstationary spatio-temporal GARCH (ST-GARCH) processes by spatially stationary counterparts at fixed locations. This approach enables a localized analysis of complex spatio-temporal volatility structures. Building upon the model's recursive formulation, we establish that the ST-GARCH process can be represented as a sum of random...

Cohen has introduced the notion of strongly $p$-summing and $p$%
-nuclear for linear operators. Many authors have considered these notions by
generalizing in several directions, namely the multilinear, sublinear and
Lipschitz cases. In the same circle of ideas, we will make an extension of
these notions in order to produce the class of Cohen M-strictly Lipschitz $p$-nuclear...

This talk investigates the conditional Hyers–Ulam stability of first-order nonlinear logistic models, both continuous and discrete. Identifying bounds on both the relative size of the perturbation and the initial population size is an important issue for nonlinear Hyers–Ulam stability analysis. Utilizing a novel approach, for h-difference equations we derive explicit expressions for the...

In extreme value theory (EVT), estimating the tail index of heavy-tailed distributions is crucial for understanding rare and extreme events. Traditional estimators such as the Hill and Maximum Likelihood Estimators (MLE) perform well with large samples but struggle
with small sample sizes due to increased bias and variance. In this paper, we introduce a novel estimation technique the...

In this work, we investigate the existence and decay properties of global solutions for a class of second-order evolution equations incorporating memory effects, a nonlinear delay term, and a time-varying weight function. The model reflects realistic dynamics observed in viscoelastic and thermoelastic systems with hereditary characteristics and delayed feedback. Using appropriate energy...

In this work, we introduce a perturbed non-convex sweeping process with a class of subsmooth moving sets depending on the time and the state. In the first result we study the existence of solution and we present some topological properties of the attainable set, the perturbation considered here is an upper semi-continuous set-valued mapping with nonempty closed convex values unnecessarily...

The present presentation investigates the two-dimensional Euler-Boussinesq system with critical fractional dissipation and a general source term, where we assume that the initial data are of Yudovich type.

Delta Dynamic Equations on Time Scales

The paper deals with the following fractional Hardy-Sobolev equation with nonhomogeneous term
\begin{equation}
%\label{eq1}
\begin{cases}
{(-\Delta)}^{s}u-\mu \frac{u}{|x|^{2s}}=|u|^{2_{s}^{*}-2}u+\lambda \frac{u}{|x|^{2s-\alpha}}+f(x),&x\in \Omega,\
u=0&x\in \partial\Omega,
\end{cases}
\end{equation}
being $0<s<1,$ where $\Omega$ is a bounded domain in $\mathbb{R}^{N},\;(N>2s)$...

1. INTRODUCTION
2. PRELIMINARIES
   3.PRODUCT OF TOEPLITZ MATRIX AND kTH-ORDER SLANT TOEPLITZ MATRIX.

Autoregressive (AR) models are fundamental tools in time series analysis, capturing temporal dependencies through lagged observations. While traditional approaches often focus on long-term dynamics, many real-world phenomena—such as high-frequency financial data, climate fluctuations, and energy demand—exhibit behaviors that are best understood at shorter time scales and are often influenced...

In this talk we study the classes of
bounded linear operators $\Phi :\mathcal{L}\left( X,Y\right) \rightarrow \mathcal{L}\left( Z,W\right)$
such that $\left( T_{n}\right) \rightarrow \left( \Phi \left( T_{n}\right) \right) $ maps $l_{p}^{s}\left( X,Y\right) $ into $l_{p}\left( Z,W\right) $,
$l_{p}^{s}\left( X,Y\right) $ into $l_{p}^{s}\left( Z,W\right) $ and $%
l_{p}^{w}\left(...

In this conversation, examines the long-term existence of solutions for a system of weakly coupled equations involving fractional evolution and various nonlinearities. The main focus is on analyzing the relationship between the regularity of initial data, memory terms, and the allowable range of exponents in a specific equation. Using L^p–L^q estimates for solutions of associated linear...

In this work, the uniform stabilization of certain hyperbolic systems with Wentzell boundary conditions is considered, and a uniform energy decay rate for the problem is established, taking into account both internal localized damping and boundary feedback. The exponential stabilization is attained by constructing a new multiplier and using multiplier methods.

In this talk, we shall investigate the validity of the Wirtinger inequality within the framework of time scales, a unified approach to continuous and discrete analysis. By constructing explicit counterexamples, we demonstrate that the classical Wirtinger inequality does not hold universally across all time scales. Motivated by this finding, we propose a reformulation of the inequality by...