In this article, we studied δ-almost Yamabe solitons within the framework of paracontact metric manifolds. First, we proved that for a paracontact metric manifold M , if a paracontact metric g represents a δ-almost Yamabe soliton associated with the potential vector field Z being an infinitesimal contact transformation, then Z is Killing, and if the potential vector field Z is collinear with ξ, then the manifold M is K -paracontact. Next, if we take a K -paracontact metric manifold admitting δ-almost Yamabe soliton with the potential vector field Z parallel to the characteristic vector field and with constant scalar curvature then either the scalar curvature will vanish or g becomes a δ-Yamabe soliton under a certain condition. We established some results on K -paracontact manifolds admitting δ-almost gradient Yamabe solitons. Moreover, we consider a (k, µ)-paracontact metric manifold admitting a non-trivial δ-almost gradient Yamabe soliton. We have shown that the potential vector field Z is parallel to ξ. We have also discussed δ-almost gradient Yamabe solitons on the para-Sasakian manifold. Finally, we consider a para-cosymplectic manifold with a δ-almost Yamabe soliton. In the end, we construct two examples of K -paracontact metric manifolds with δ-almost Yamabe soliton.

In this paper, we focus on the Timoshenko viscoelastic system associated with a nonlinear term. The general stability is established by means of the energy method under the assumption of equal speeds, leading to an energy decay rate that includes exponential and polynomial stabilities as particular cases. Our results improve and generalize previous findings in the literature.

A numerical semigroup S is coated with odd elements (Coe-semigroup), if {x − 1, x + 1} ⊆ S for all odd elements x in S. In this note, we will study this kind of numerical semigroup. In particular, we are interested in the study of the Frobenius number, gender and embedding dimension of a numerical semigroup of this type.

This research paper aims to investigate the properties of almost generalized Ƶ-solitons and almost gradient generalized Ƶ-solitons on perfect fluid spacetimes within f(r, T)-gravity. Initially, we derive some properties of the potential vector field associated with the almost gradient generalized Ƶ-solitons. Furthermore, we explore the characteristics of almost generalized Ƶ-solitons in various specific categories of perfect fluid spacetimes in f(r, T)-gravity, including dust fluid and dark fluid.

Let R be a commutative unital ring and N be a submodule of an R-module M. We show that: 1) the semiprime radical is an invariant on submodules generated by the ascending chain of envelopes of a given submodule; 2) for rings that satisfy the radical formula, ⟨EM (0)⟩ is an idempotent radical leading to a torsion theory whose torsion class has nil R-modules and the torsion-free class has reduced R-modules; and, 3) Noetherian uniserial modules satisfy the semiprime radical formula and their semiprime radical is a nil module.

In this paper, we document a new tractable method to solve nonlinear classes of partial differential equations subject to initial-values. The method involves a detailed transformation procedure, underpinned by the Lie pint symmetries of the one dimensional heat transfer equation. We illustrate the approach with the famous Burgers’ equation, Potential Burgers’ equation and the Hamilton-Jacobi-Bellman equation. This approach identifies new solutions of these nonlinear equations, which enhances our comprehension of its analytical properties and solution behaviour.

A partially ordered ring (R, ≤) with negative squares is a partially ordered ring in which for some element a ∈ R, a 2 < 0. In this paper, we study this class of partially ordered rings. It is shown that, for instance, for a totally ordered field K, the complex field C = K(i) over K, where i 2 = −1, has a directed partial order with negative squares if and only if K is not algebraic over ℚ.

In this paper, we present some sets of geometric conditions that ensure the umbilicity of linear Weingarten hypersurfaces immersed in an Einstein manifold satisfying standard curvature constraints which, in particular, are verified by a Riemannian space with constant sectional curvature. Our methodology relies as an application of maximum principles involving concepts of convergence to zero at infinity and polynomial volume growth, both of them related to complete noncompact Riemannian manifolds.

We present a characterization of effective descent morphisms in the lax comma category Ord//X when X is a locally complete ordered set, as well as in the antisymmetric setting.

This study investigates the invariance properties of the time-fractional stochastic potential-KdV (FSP-KdV) equation, intending to enhance our understanding of the dynamics associated with nonlinear photon and optical soliton propagation. The application of the Lie group analysis method enables the derivation of vector fields and symmetry reductions for the equation. Additionally, employing power series theory, the paper systematically constructs explicit power series solutions, offering a detailed derivation. The resulting wave propagation patterns of these solutions are depicted along the x-axis at various temporal instances. Finally, lever-aging a new conservation theorem, the study formulates two distinct conservation laws for the equation, presenting comprehensive and detailed derivations for each.