“Finite Groups with Quasinormal Subgroups of Prince Power Order”一文的一点注记

用F (G)代替F(G),将文"FiniteGroupswithQuasinormalSubgroupsofPrimePowerOrder,ActaMathHun gar89(4),2000,321-326"一文中的主要定理的可解性的假设去除,从而推广了该文的结论。

BTZ Quasinormal Frequencies as Poles of Green’s Function

Based on the well known fact that the quasinormal frequencies are the poles of the frequency domain Green’s function we describe a method that allows us to calculate exactly the quasinormal frequencies of the Klein-Gordon field moving in the three-dimensional rotating Bañados-Teitelboim-Zanelli black hole. These quasinormal frequencies are already published and widely explored in several applications, but we use this example to expound the proposed method of computation. We think that the described procedure can be useful to calculate exactly the quasinormal frequencies of classical fields propagating in other backgrounds. Furthermore, we compare with previous results and discuss some related facts.

A Note on s-quasinormally Embedded and c-supplemented Subgroups of Finite Groups

In this paper the influence of s-quasinormally embedded and c-supplemented subgroups on the p-nilpotency of finite groups is investigate and some recent results are generalized.

Asymptotic quasinormal modes of scalar field in a gravity's rainbow

In the framework of the gravity＇s rainbow, the asymptotic quasinormal modes of the modified Schwarzschild black holes undergoing a scalar perturbation are investigated. By using the monodromy method, we analytically calculated the asymptotic quasinormal frequencies, which depend on not only the mass parameter of the black hole, but also the particle＇s energy of the perturbation field. Meanwhile, the real parts of the asymptotic quasinormal modes can be expressed as TH In 3, which is consistent with Hod＇s conjecture. In addition, for the quantum corrected black hole, the area spacing is independent of the particle＇s energy, even though the area itself depends on the particle＇s energy. And that, by relating the area spectrum to loop quantum gravity, the Barbero-Immirzi parameter is given and it remains the same as from the usual black hole.

Quasinormal modes of the scalar field in five-dimensional Lovelock black hole spacetime

In this paper, using the third-order WKB approximation, we investigate the quasinormal frequencies of the scalar field in the background of a five-dimensional Lovelock black hole. We find that the ultraviolet correction to Einstein theory in the Lovelock theory makes the scalar field decay more slowly and oscillate more quickly, and the cosmological constant makes the scalar field decay more slowly and oscillate more slowly in the Lovelock black hole background.

Jordanian Canonical Form of Quasinormal Operator

An operator on a Hilbert space is said to have (SI) decomposition if it is similar to the orthogonal direct sum of some (SI) operators. In this paper, we prove that every operator, which is similar to a quasinormal operator, has (SI)decomposition if and only if it is similar to D ( 0≤j<N λjS), where D is a diagonaloperator, λj is a positive number, N is a natural number or ∞, and S is the unilateral shift.

Dirac Quasinormal Modes of Reissner-Ndstrom Black Hole Surrounded by Quintessence

Using the third-order WKB approximation, we evaluate the quasinormal frequencies of massless Dirac field perturbation around a Reissner Nordstrom black hole surrounded by a static and spherically symmetric quintessence. We study the variation of quasinormal frequencies with the quintessential state parameter ε, the total angular momentum number ｜k｜, the charge Q, and the overtone number n changes, respectively. Moreover, from the results we obtained, we find that the massless Dirac field damps more slowly due to the presence of quintessence.

Object Picture of Electromagnetic Quasinormal Ringing for a Stringy Black Hole

We investigate the evolution of an electromagnetic field in the spacetime of a stringy black hole.The objectpicture of the quasinormal ringing has been obtained by the finite difference method.Compared with a Schwarzschildblack hole,the results show that the electromagnetic field damps more slowly for a stringy black hole.

Quasinormal Modes of a Noncommutative-Geometry-Inspired Schwarzschild Black Hole

The quasinormal modes（QNMs） of massless scalar field perturbation in a noncommutative-geometry-inspired Schwarzschild black hole spacetime are studied using the third-order Wentzel-Kramers-Brillouin approximative approach. The result shows that the noncommutative parameter plays an important role for the quasinormal（QNM） frequencies.

Quasinormal Modes of Phantom Scalar Perturbation in Background of Reissner-Nordstrom Black Hole

We have investigated the quasinormal modes （QNMs） of phantom scalar perturbation in a Reissner Nordstr6m （RN） background. We find that the dependence of Q, NMs on the mass of the field for the phantom perturbation is totally different from that of usual massive perturbation. However, we obtain the same critical value of the overtone number for an angular quantum number from which the mass will begin to have a reverse effect on the real part of QNM frequencies and the perturbation-independent relation between the Q, NMs and the second order thermodynamic phase transition.

Quasinormal Modes of a Noncommutative-Geometry-Inspired Schwarzschild Black Hole: Gravitational, Electromagnetic and Massless Dirac Perturbations

In our previous work [Chin. Phys. Lett. 35（2018） 010410], the quasinormal modes of massless scalar field perturbation in a noncommutative-geometry-inspired Schwarzschild black hole spacetime are studied using the third-order Wentzel–Kramers–Brillouin approximative approach. In this study, we extend the work to the cases of gravitational, electromagnetic and massless Dirac perturbations. The result further confirms that the noncommutative parameter plays an important role for the quasinormal frequencies.

Quasinormal modes of a stationary axisymmetric EMDA black hole

The massless scalar quasiaormal modes （QNMs） of a stationary axisymmetric Einstein-Maxwell dilato-axioa （EMDA） black hole are calculated numerically using the continued fraction method first proposed by Leaver. The fundamental quasinormal frequencies （slowly damped QNMs） are obtained and the peculiar behaviours of them are studied. It is shown that these frequencies depend on the dilaton parameter D, the rotational parameter a, the multiple moment l and the azimuthal number m, and have the same values with other authors at the Schwarzschild and Kerr limit.

Phase Transition and Quasinormal Modes for Spherical Black Holes in 5D Gauss–Bonnet Gravity

We study the quasinormal modes（QNMs） of massless scalar perturbations to probe the van der Waals like SBH/LBH phase transition of anti-de Sitter black holes in five-dimensional（5D） Gauss–Bonnet gravity. It is found that the signature of this SBH/LBH phase transition is detected when the slopes of the QNMs frequency change drastically and differently in small and large black holes near the critical point. The obtained results further support that the QNMs can be a dynamic probe to investigate the thermodynamic properties in black holes.

Quasinormal modes and isospectrality of Bardeen(Anti-)de Sitter black holes

Black holes(BHs)exhibiting coordinate singularities but lacking essential singularities throughout the spacetime are referred to as regular black holes(RBHs).The initial formulation of RBHs was presented by Bardeen,who considered the Einstein equation coupled with a nonlinear electromagnetic field.In this study,we investigate the gravitational perturbations,including the axial and polar sectors,of the Bardeen(Anti-)de Sitter black holes.We derive the master equations with source terms for both axial and polar perturbations and subsequently compute the quasinormal modes(QNMs)through numerical methods.For the Bardeen de Sitter black hole,we employ the 6thorder WKB approach.The numerical results reveal that the isospectrality is broken in this case.Conversely,the QNM frequencies are calculated using the HH method for the Bardeen Anti-de Sitter black hole.

Quasinormal modes and ringdown waveforms of a Frolov black hole

In this paper we investigate scalar perturbation over a Frolov black hole(BH), which is a regular BH induced by the quantum gravity effect. The quasinormal frequencies of a scalar field always consistently reside in the lower half-plane, and the time-domain evolution of the field demonstrates a decaying behavior, with the late-time tail exhibiting a power-law pattern. These observations collectively suggest the stability of a Frolov BH against scalar perturbation.Additionally, our study reveals that the quantum gravity effect leads to slower decay modes. For the case of the angular quantum number l = 0, the oscillation exhibits non-monotonic behavior with the quantum gravity parameter α_(0). However, once l ≥ 1, the angular quantum number surpasses the influence of the quantum gravity effect.

Probing the Bardeen-Kiselev black hole with the cosmological constant caused by Einstein equations coupled with nonlinear electrodynamics using quasinormal modes and greybody bounds

In this work,we investigate a static and spherically symmetric Bardeen-Kiselev black hole(BH)with the cosmological constant,which is a solution of the Einstein-non-linear Maxwell field equations.We compute the quasinormal frequencies for the Bardeen-Kiselev BH with the cosmological constant due to electromagnetic and gravitational perturbations.By varying the BH parameters,we discuss the behavior of both real and imaginary parts of the BH quasinormal frequencies and compare these frequencies with the Reissner-Nordström-de Sitter BH surrounded by quintessence(RN-dSQ).Interestingly,it is shown that the responses of the Bardeen-Kiselev BH with the cosmological constant and the RN-dSQ under electromagnetic perturbations are different when the charge parameter q,the state parameter w and the normalization factor c are varied;however,for the gravitational perturbations,the responses of the Bardeen-Kiselev BH with the cosmological constant and the RN-dSQ are different only when the charge parameter q is varied.Therefore,compared with the gravitational perturbations,the electromagnetic perturbations can be used to understand nonlinear and linear electromagnetic fields in curved spacetime separately.Another interesting observation is that,due to the presence of Kiselev quintessence,the electromagnetic perturbations around the Bardeen-Kiselev BH with the cosmological constant damps faster and oscillates slowly;for the gravitational perturbations,the quasinormal mode decays slowly and oscillates slowly.We also study the reflection and transmission coefficients along with the absorption cross section in the Bardeen-Kiselev BH with the cosmological constant;it is shown that the transmission coefficients will increase due to the presence of Kiselev quintessence.

Massless Dirac perturbations of black holes in f(Q)gravity:quasinormal modes and a weak deflection angle

This article considers a static and spherical black hole(BH)in f(Q)gravity.f(Q)gravity is the extension of symmetric teleparallel general relativity,where both curvature and torsion are vanishing and gravity is described by nonmetricity.In this study,we investigate the possible implications of quasinormal mode(QNM)modified Hawking spectra and deflection angles generated by the model.The Wentzel–Kramers–Brillouin method is used to solve the equations of motion for massless Dirac perturbation fields and explore the impact of the nonmetricity parameter(Q_(0)).Based on the QNM computation,we can ensure that the BH is stable against massless Dirac perturbations and as Q_(0)increases the oscillatory frequency of the mode decreases.We then discuss the weak deflection angle in the weak field limit approximation.We compute the deflection angle up to the fourth order of approximation and show how the nonmetricity parameter affects it.We find that the Q_(0)parameter reduces the deflection angle.

对称群S_(4)中的S-拟正规嵌入子群和几乎SS-嵌入子群研究

为探讨四次对称群S_(4)的所有S-拟正规子群、S-拟正规嵌入子群和几乎SS-嵌入子群,结合置换的计算方法,利用其定义和相关引理得出了相应的结果。结果显示:S_(4)的S-拟正规子群为N_(1),K_(4),A_(4),S_(4);S_(4)的S-拟正规嵌入子群有N_(1),N_(11),N_(12),N_(13),N_(14),K_(4),N_(26),N_(27),N_(28),A_(4),S_(4);S_(4)的几乎SS-嵌入子群有N_(1),N_(2),N_(3),N_(4),N_(5),N_(6),N_(7),N_(11),N_(12),N_(13),N_(14),K_(4),N_(22),N_(23),N_(24),N_(25),N_(26),N_(27),N_(28),A_(4),S_(4)。

SS-拟正规子群对有限群p-超可解性的影响

设G为有限群,若存在B≤G使得G=HB,且对任意p∈π(B),P∈Sy1_( p)(B),都有HP=PH,则称子群H在G中SS-拟正规.利用极小阶反例法,讨论某些p-子群SS-拟正规的有限群结构,得到p-超可解群的若干充分条件,推广了p-超可解性的部分结果.

带磁荷规则黑洞的有质量标量场似正规模

利用三阶WKB近似方法,探究了非线性电动力学中带有磁荷的规则黑洞的似正规模.分别讨论这类带有磁荷的规则黑洞中的Bardeen-class黑洞、Hayward-class黑洞和New-class黑洞,在有质量标量场扰动下的似正规模,分析标量场质量对似正规模频率的影响.结果表明,随着扰动标量场质量的增加,黑洞时空的振荡频率变快,但振荡的衰减速度则变慢,这说明似正规模在大质量场的粒子衰减较慢些.此外,研究发现,随着标量场质量的变化,似正规模频率的实部与虚部之间呈近乎线性的变化关系.