Purpose The primary objective of this article is to study weakly cyclic contracted space-matter tensor under the influence of semi-symmetric metric connection through computational procedure. An important observation regarding spacetime anomalies is obtained in this article. Design/methodology/approach Applying the Frobenius method, non-linear differential equation has been solved through numerical simulation. Findings The study presents the following findings: (1) The observation signifies the existence of high-level energy (or black hole) in the era of cosmological theory. The SSMC developed here can be taken into account, which is the futuristic scope of the present study, for various cosmological models to examine in the context of different energy conditions. (2) Spacetime anomalies are shifted towards the increasing direction of x1. Originality/value The study has been developed newly with the help of a new approach involving numerical simulation.
Purpose We study a Lamé-type viscoelastic system with logarithmic velocity damping and quantify its stabilizing effect. The dissipation is weak near zero (σ(v) ⋅ v ∼|v|4 as |v| → 0) yet becomes stronger than linear for large speeds. Our goal is to prove global well-posedness and quantify the long-time decay of the natural energy. Design/methodology/approach We combine the Faedo–Galerkin scheme, Aubin–Lions compactness, and Minty's monotonicity to construct weak solutions and derive an energy identity. A Lyapunov function adapted to the logarithmic dissipation links the decay of the relaxation kernel g to the mechanical energy, assuming g ≥ 0 is nonincreasing and −g′(t) ≥ ξ(t)g(t) with nonincreasing ξ. Findings We obtain global existence and uniqueness of weak solutions and a general decay estimate E(t)≤Cexp−κ∫0tξ(s)ds. Hence, exponential decay holds when inft≥0 ξ(t) > 0, whereas polynomial rates follow if ξ(t) ∼ c(1 + t)−1. The results clarify the combined role of Lamé ellipticity, hereditary memory, and logarithmic damping in stabilization. Originality/value Prior Lamé–viscoelastic studies used logarithmic terms mainly as sources; here the damping itself is logarithmic. This reveals a distinct stabilization mechanism and unifies exponential and polynomial regimes.
PurposeSince weighted shifts play a vital role in linear dynamics so in 2021 Chan & Sanders considered weighted shift operators on ℓp(Z) that are not hypercyclic and proved that under certain conditions they can be factorized as products of hypercyclic shifts. The purpose of this article is to extend their results to operator weighted shifts on ℓ2(K) by using the concept of generalized shift of higher multiplicity developed herein.Design/methodology/approachTraditionally, an operator T is considered as a shift on a space H if there is some canonical basis for H such that T shifts every basis vector to the immediate next basis vector, maybe with some weight attached to it. This clearly indicates that an operator which is a shift with respect to a basis for H may not remain a shift if the basis is changed. This motivates the definition of a generalized shift operator. We begin with the case of multiplicity one and then extend it to higher finite multiplicity. We then develop the idea so that we can frame conditions under which a bilateral shift can be factorized as product of hypercyclic generalized shifts.FindingsA generalized bilateral backward weighted shift (GBBWS) is defined in terms of a bijection on Z and it is shown that if there are two bijections σ and ρ which generate the same generalized shift, then there exists a unique c such that σ(i) = ρ(i + c) for all integers i. We determine conditions under which the direct sum of generalized shifts is again a generalized shift. We also show that for a uniformly bounded sequence of invertible diagonal operators {Ai} on a separable complex Hilbert space K of finite dimension, if W is bilateral backward weighted shift on ℓ2(K) with weight sequence {Ai} then there exists hypercyclic GBBWS T and P on ℓ2(K) such that W = TP.Originality/valueThe idea of generalized shift of multiplicity one was introduced by Chan & Sanders in 2018. However, we have developed the idea further, particularly extending it to the case of shifts of higher multiplicity. The factorization of shifts as product of hypercyclic shifts was also done by them. We have extended their result to higher dimension, and our approach to the problem is completely different from theirs.
PurposeThis paper introduces a new (q, τ)–balanced growth class of analytic functions in the unit disk, motivated by quantum–deformation computing and scale–dependent geometric analysis. The aim is to develop a geometric framework that simultaneously captures radial growth and angular distortion through finite–scale (q, τ)–deformations.Design/methodology/approachThe proposed class is defined via a nonlinear admissibility condition involving a (q, τ)–deformed logarithmic growth factor. Unlike classical starlike and spiral-like families characterized by half–plane constraints, the new class is governed by a parabolic admissible region incorporating quadratic damping effects. A generalized Jack lemma in the (q, τ)–setting is established and applied to derive a sharp subordination theorem with an explicit dominant mapping. The theoretical analysis is complemented by extremal function techniques and conformal visualization of the dominant mappings.FindingsThe developed approach yields explicit starlikeness radius results together with sharp extremal functions that attain the admissibility boundary. A geometric phase diagram in the parameter space (α, β, q, τ) is obtained, separating regions of full radial coherence, critical transition, and loss of starlikeness. The conformal plots demonstrate how the deformation parameters contract the admissible domain and influence extremal directions. Several known classical results are recovered as limiting cases of the proposed framework.Originality/valueThe paper introduces a novel (q, τ)–balanced growth structure combining quantum–deformation concepts, nonlinear admissibility methods, and geometric function theory within a unified setting. The use of a parabolic admissibility region together with finite–scale logarithmic deformation provides a new perspective on analytic growth phenomena and extends classical starlike theory to a broader nonlocal geometric regime.
PurposeTo describe the structure of a special sort of rings whose non-invertible elements are the sum of a nilpotent and a square-idempotent (which commute one another). Specifically, we consider in-depth and characterize in certain aspects the class of so-called strongly NUS-nil clean rings, that are those rings whose non-units are square-nil clean in the sense that they are a sum of a nilpotent and a square-idempotent that commutes with each other. This class of rings lies properly between the classes of strongly nil clean rings and strongly clean rings.Design/methodology/approachWe develop an original method of proof based on polynomial expressions.FindingsIt is proved the valuable criterion that a ring R is strongly NUS-nil clean if, and only if, a4 - a2 ∈ Nil(R) for every a ∉ U(R). In particular, a ring R with only trivial idempotents is strongly NUS-nil clean if, and only if, R is a local ring with nil Jacobson radical. Some special matrix constructions and group ring extensions will provide us with new sources of examples of strongly NUS-nil clean rings.Originality/valueWe declare that the obtained by us results are absolutely original and do not duplicate other known results.
