Tamkang Journal of Mathematics

Second-order noncanonical mixed type difference equations of unstable type: new oscillation criteria

P. Ganesan — 2024-10-30

This paper is concerned with the oscillatory properties of the second order noncanonical difference equation with a deviating arguments of the form
\begin{equation*}
\Delta(a_n\Delta y_n) = q_ny_{\sigma(n)}.
\end{equation*}
The authors first transform the noncanonical equation into canonical form so that the discrete Kneser theorem can be applied to classify the nonoscillatory solutions into two types. Some new monotonic properties of the nonoscillatory solutions are then obtained, and they are used to eliminate certain type of nonoscillatory solutions. This leads to the development of new oscillation criteria for the equation. The results obtained are new and complement those currently existing in the literature. Examples to illustrate the importance of the main results are also presented.

Riemann solitons on Lorentzian generalized symmetric spaces

Mehdi Jafari — 2024-11-12

In this paper, we classify Riemann solitons on simply-connected 4-dimensional Lorentzian generalized symmetric spaces up to isometry. Then it is
proved which of them is the gradient soliton. Also, we prove none of the potential vector fields of Riemann solitons are Killing vector fields.

Recent advances in metallic Riemannian geometry: a comprehensive review

Bang-Yen Chen — 2024-12-12

Metallic structures, introduced by V. de Spinadel in 2002, opened a new avenue in differential geometry. Building upon this concept, C. E. Hretcanu and M. Crasmareanu laid the foundation for metallic Riemannian manifolds in 2013. The field's rich potential and diverse applications have since attracted significant research efforts, leading to a wealth of valuable insights. This review delves into the latest advances in metallic Riemannian geometry, a rapidly progressing area within the broader field of differential geometry.

Dynamics for a viscoelastic wave equation with nonlocal nonlinear dissipation and logarithmic nonlinearity: blow-up solutions, lifespan estimates and asymptotic stability

Amir Peyravi — 2024-12-27

This paper investigates the instability of a class of wave equations with a non-local nonlinear damping term
\begin{equation*} v_{tt}-\Delta v+(g\ast \Delta v)(t)+\sigma(\|\nabla v\|_{2}^{2})\phi(v_{t})=|v|^{p-2}v\ln|v|^{k},
\end{equation*}
where $(x,t)\in\Omega\times(0,T)$, $\Omega\subset \mathbb{R}^{n}$, $\sigma$ represents the nonlocal coefficient and $\phi$ is the nonlinear damping term. By considering suitable assumptions on the functions $\sigma$ and $\phi$, the exponents $p$ and $k$, the relaxation function $g$ and the initial data, and by making use of differential
inequality technique, we establish the occurrence of finite time blow up of solutions at low and arbitrary high positive initial energy levels. Moreover, lower bounds for the lifespan of solutions are derived in both cases. Asymptotic stability for the solution energy is also investigated by employing the energy perturbation method. This work extends and complements
some previous results in the literature.

Further inequalities for the numerical radius of off-diagonal part of 2 by 2 operator matrices

Mehdi Naimi — 2025-02-25

In this paper, using a refinement of the classical Young inequality, we present some new upper weighted bounds for the numerical radius of $2\times 2$ block matrices, with entries are bounded operators.

Climate change potential impacts on mosquito-borne diseases: a mathematical modelling analysis

Goutam Saha — 2025-03-05

Climate change and global warming have caused catastrophic effects that are already being felt in Bangladesh. The rise in temperature associated with global warming, as well as the broader impacts of climate change, are damaging the planet. These effects are spatial and temporal and have led to unexpected outcomes, such as the coexistence of humans and mosquitoes in regions where it was previously unimaginable. Despite being the smallest animals on earth, mosquitoes are also the deadliest, killing thousands of humans each year. The Culex mosquito, a common type of mosquito in Bangladesh, is easily accessible and poses a significant threat to human health. The transmission of viruses to humans is a significant concern. This article introduces and discusses the LMSEI-SEIR mathematical model, which can help in understanding this process. The disease-free equilibrium point and its stability are presented, and the reproduction number is calculated. To further investigate the implications of this model, a numerical analysis is conducted using MATLAB. The resulting figures can be used to inform future measures aimed at protecting against human fatalities.