The aim of this article is to prove certain properties of multiplicative derivations verifying certain algebraic identities on Jordan ideals and semigroup ideals of a 3prime near-ring. The results obtained characterize the relationship between the structure of this type of near-rings admitting this kind of maps. Additionally, we present examples to show that our assumptions imposed on the various theorems cannot be omitted.

In the present paper, we investigate the hypercyclicity of weighted composition operators acting on the space of holomorphic functions on a connected finite-dimensional Stein manifold. Let ψ be a holomorphic self-map on a connected Stein n-manifold Ω and ω ∈ H(Ω) a holomorphic function. We study the hypercyclicity of weighted composition operator Πψ,ω : H(Ω) → H(Ω) defined by Πψ,ω (f ) := ω · (f ◦ ψ) for every f ∈ H(Ω). We prove that Πψ,ω is hypercyclic if and only if ω(p)̸ = 0 at each p ∈ Ω, ψ is univalent without fixed points in Ω, ψ(Ω) is a Runge domain and for every compact holomorphically convex set K ⊂ Ω there is an integer n such that K ∩ ψ[n](K) = ∅ and their union is holomorphically convex.

Let K be a complete, non-trivially valued, ultrametric (or non-archimedean) field. Entries of sequences, infinite series and infinite matrices are in K. In this paper are defined the notions of speed-Maddox spaces over K, where the speed is defined by a sequence μ = {μn} in K with the property 0 < |μn| ↗ ∞, n → ∞. Let λ be another speed in K. The necessary and sufficient conditions for a matrix A would transform all sequences that are λ-convergent to zero over K into the speed-Maddox spaces over K, where the speed is defined by μ.

This article introduces the notion of an NJ-reflexive ring and demonstrates that it is distinct from the concept of a reflexive ring. The class of NJ-reflexive rings contains the class of semicommutative rings, the class of left (right) quasi-duo rings, and the class of J-clean rings but is strictly larger than these classes. Additionally, the article investigates a sufficient condition for NJ-reflexive rings to be left (right) quasi-duo, as well as some conditions for NJ-reflexive rings to be reduced. It also explores extensions of NJreflexive rings and notes that the NJ-reflexive property may not carry over to polynomial extensions.

Let T M be the tangent bundle with the synectic lift on the n-dimensional Riemannian manifold M . The objective of this article is to investigate the properties of Ricci soliton and generalized Ricci-Yamabe soliton structures according to the synectic lift metric on the tangent bundle T M . Furthermore, the properties of the gradient Ricci soliton and the generalized gradient Ricci-Yamabe soliton are also investigated in this article.

In this paper we associate with a given multi-time dynamical system some geometrical objects (such as nonlinear connection or d−torsions) produced by the least squares Hamiltonian naturally attached to this initial PDE system of first order. Possible geometrical interpretations are still an open problem.

Prajapati and Kachhia [10] introduced the concept of functions of bounded fractional differential variation and proposed an open problem whether the class of functions of bounded fractional differential variation on a closed bounded interval is a Banach algebra. We have given a solution to this problem. For a sequence of functions, we have discussed a condition for the convergence of sequence of Caputo fractional derivatives to the Caputo fractional derivative of the limit function. We have proved an additive property of the total fractional differential variation with respect to closed intervals and given an equivalent condition for vanishing of the total fractional differential variation of a function.

Let N be a near-ring and P be a 3-prime ideal of N . This paper introduces a novel concept known as P-homoderivation and investigates the commutativity of the quotient near-ring N /P when N has a P-homoderivation satisfying certain distinction identities. In addition, we extend several known results related to 3-prime near-rings with homoderivations.