In this paper, we investigate scenarios in which the power of a transcendental entire function of weight two shares a value with its differential-difference polynomial. Our results extend and generalize recent findings by Adud and Chakraborty.

In this article, we study covariant derivatives of polynomial structures for semi-tangent bundles with respect to the projectable vector field's complete and horizontal lifts. The aim of this work is to analyze tensor structures in the semi-tangent bundle by examining the lifts of some projectable symmetric linear connections that were not previously calculated.

The aim of this paper is to study some specific classes of Threshold schemes. Our study is based on modular arithmetic and equivalence classes modulo a prime number. For this purpose we construct a secret sharing scheme by using these classes. This scheme is efficient by means of security.

For an ideal $\frak a$ in a Noetherian ring $R$ contained in the Jacobson radical of $R$, it is shown that if $M$ is a finitely generated $\mathfrak a$-relative Cohen-Macaulay $R$-module, then $\operatorname{Ann}_R(H_{\frak a}^{{\rm cd} (\frak a, M)}(M))= \operatorname{Ann}_R(M)$. As an application of this result, we show that if $M$ is a finitely generated $\frak a$-relative Cohen-Macaulay filtered $R$-module with the cohomological dimension filtration $\mathcal{M} =\{M_i\}_{0\leq i \leq c}$, then for each $0\leq i \leq c$, $\operatorname{Ann}_R(H_{\frak a}^i(M))=\operatorname{Ann}_R (M_i/M_{i-1})$, where $c={\rm cd} (\frak a, M)$. These generalize the main results of [Theorem 3.3] and [Theorem 2.11]. Also, we shall provide some new characterizations of the attached primes of top local cohomology module $H_{\frak a}^{{\rm cd} (\frak a, M)}(M)$ and give a short proof of the main results of [Theorem 2.2] and Theorem 2.7]. Finally, it is shown that if $M$ and $N$ are arbitrary $R$-modules (not necessarily finitely generated) such that $\operatorname{Att}_R(M)\subseteq\operatorname{Att}_R(N)$, then ${\rm cd}(\frak a, R/\operatorname{Ann}_R(M))\leq{\rm cd}(\frak a, R/\operatorname{Ann}_R(N)).$

In this work, we consider a one-dimensional piezoelectric beam model with magnetic effects in the presence of a delay term acting on the two equations. The existence and uniqueness of solutions to the system are proved by the semigroup theory. We demonstrate the system's exponential stability using the energy method and multiplier techniques. Under a suitable assumption on the weight of the delay that the damping effect through two equations is strong enough to stabilize the system even in the presence of a time delay. Furthermore, our result does not depend on any relationship between system parameters.

Present investigation is concerned with the propagation of obliquely incident water waves by a pulsating line source in presence of a fixed nearly vertical rigid cliff, submerged in deep water, assuming the surface tension effect at the free surface. For the perfectly vertical cliff, it's effect on the source is similar to another source located at the image point of the main source regarding to the vertical cliff. However, because of the bended figure of the cliff, there will be extra effects. Assuming the surface tension effect at the free surface, these effects have been obtained up to first order term to the wave amplitude at infinity ($A_{1}$) and the velocity potential ($\phi_{1}$) for deep water by employing a simplified perturbation theory followed by an adequate Havelock's expansion of water wave potential. Considering the two particular shapes of the nearly vertical cliff viz.(i) $c(y)=y\exp(-\lambda y)$ and (ii) $c(y)=\alpha\sin\beta y$, these corrections are also found interms of the integrals involving the shape function of the cliff in presence of surface tension at the free surface. Neglecting the effect of surface tension at the free surface, the approximate solution of the corresponding problem can be found. The solution of the corresponding two dimensional problem can also be derived by a known substitution.

In this study, we obtain explicit forms of the sum of entries, the maximum column sum matrix norm, the maximum row sum matrix norm, Euclidean norm, eigenvalues and determinant of k-circulant matrix with the generalized third-order Jacobsthal numbers. We also study the spectral norm of this k-circulant matrix.

In this paper we show that the welded tangloids show us even macroscopic objects and their dynamics can be characterized by EQFTs. It may also require inclusion of scattering cluster quasiparticles for accurate description, for example in far-from equilibrium processes, because time-dependent dynamics strongly matters.

In this paper, we study left invariant Randers metric $F$ on six-dimensional nilpotent Lie group $\mathcal{N}_{6,11}$ with Lie algebra $\mathfrak{n}_{6,11}.$ We compute Levi-civita connection, Riemann curvature tensor, sectional curvature, Ricci curvature and scalar curvature on $(\mathcal{N}_{6,11},F)$. Moreover, we classify simply connected six-dimensional nilpotent Lie groups equipped with $(\alpha,\beta)$-metrics of Douglas and Berwald type defined by left-invariant Riemannian metric and left-invariant vector field. We also compute S-curvature and flag curvature. At the end it is also proved that $(\mathcal{N}_{6,11},F)$ can neither be naturally reductive nor Ricci-quadratic.

This paper is mainly concerned with the characterization of finite order transcendental entire solutions of some systems of trinomial functional equations where the equations involve $k$-th order derivatives and shifts of the functions. Our results are the generalizations of recent results given by Gao, and Liu-Yang. Moreover, we also discuss the existence of transcendental entire solutions of one differential difference equation which has not been discussed earlier in the literature. To demonstrate the precision and applicability of our findings we exhibit a series of examples.

This work explores the stability and existence of a class of fractional Langevin inclusions with impulsive and time delay effects involving $\psi$-Hilfer derivative. We establish the existence conditions for solutions using the Covitz-Nadler fixed-point theorem. The Picard operator method and a recently developed generalized Gronwall inequality are employed in Ulam stability analysis. We provide a thorough example to illustrate the applicability of our theoretical results.

The positive stabilization problem for a class of fractional conformable linear systems in which the state takes non-negative values when the initial conditions are non-negative is addressed in this paper. Furthermore, the finite-horizon linear quadratic optimal control problem with non-negative state constraints ($FLQ^+$) is studied for continuous-time positive linear fractional systems. Necessary and sufficient conditions are proven so that the $FLQ$-optimal control given by the standard fractional inear quadratic problem is also optimal for $FLQ^+$. Then, sufficient conditions are established for the positivity of the $FLQ$-optimal closed-loop system.

In the domain of Riemannian Geometry, we explore $*$-$\eta$-Ricci-Yamabe soliton on a Riemannian manifold $(G^3, g)$. Initially, we establish that if the metric $g$ of $G^3$ constitutes a $*$-$\eta$-Ricci-Yamabe soliton, then $G^3$ is necessarily Einstein, when the soliton vector field $V$ is contact. Additionally, we investigated that the Riemannian manifold $(G^3, g),$ accommodates a gradient almost $*$-$\eta$-Ricci-Yamabe soliton, concluding that it must be Einstein with a consistent scalar curvature $r=-6.$ The associated functions of the $*$-$\eta$-Ricci soliton are characterized by $\alpha=1$ and $\beta=0.$