In the paper, we take up a new method to prove a result of value distribution of meromorphic functions: let f be a meromorphic function in , and let , where P is a polynomial. Suppose that all zeros of f have multipli...In the paper, we take up a new method to prove a result of value distribution of meromorphic functions: let f be a meromorphic function in , and let , where P is a polynomial. Suppose that all zeros of f have multiplicity at least , except possibly finite many, and as . Then has infinitely many zeros.展开更多
In this study,we comprehensively investigated charged AdS black holes surrounded by a distinct form of dark matter.In particular,we focused on key elements including the Hawking temperature,quasi-normal modes(QNMs),em...In this study,we comprehensively investigated charged AdS black holes surrounded by a distinct form of dark matter.In particular,we focused on key elements including the Hawking temperature,quasi-normal modes(QNMs),emission rate,and shadow.We first calculated the Hawking temperature,thereby identifying critical values such as the critical radius and maximum temperature of the black hole,essential for determining its phase transition.Further analysis focused on the QNMs of charged AdS black holes immersed in perfect fluid dark matter(PFDM)within the massless scalar field paradigm.Employing the Wentzel-Kramers-Brillouin(WKB)method,we accurately derived the frequencies of these QNMs.Additionally,we conducted a meticulous assessment of how the intensity of the PFDM parameterαinfluences the partial absorption cross sections of the black hole,along with a detailed study of the frequency variation of the energy emission rate.The pivotal role of geodesics in understanding astrophysical black hole characteristics is highlighted.Specifically,we examined the influence of the dark matter parameter on photon evolution by computing the shadow radius of the black hole.Our findings distinctly demonstrate the significant impact of the PFDM parameterαon the boundaries of this shadow,providing crucial insights into its features and interactions.We also provide profound insights into the intricate dynamics between a charged AdS black hole,novel dark matter,and various physical phenomena,elucidating their interplay and contributing valuable knowledge to the understanding of these cosmic entities.展开更多
Aiming at the dynamic multi-attribute decision making problem where the weight of each decision stage and attribute weight are completely unknown and the attribute value is unknown distributed three-parameter interval...Aiming at the dynamic multi-attribute decision making problem where the weight of each decision stage and attribute weight are completely unknown and the attribute value is unknown distributed three-parameter interval grey number,a threeparameter interval grey number dynamic multiattribute grey target decision making method with attribute value following quasi-normal distribution is proposed.Firstly,the position relationship between the“center of gravity”point and the kernel of the threeparameter interval grey number is discussed.According to the characteristicthat the attribute value obeys the quasi-normal distribution,anew weight isgiventothe“centerof gravity”point,and a new distance measure formula of the three-parameter interval grey number is defined.Secondly,according to the principle of maximum entropy,the objective programming model is constructed to determine the stage weight and attributeweight.Then,the schemes aresorted according to thesize of the comprehensive bull's-eye distance Finally an example is given to illustrate the effectiveness of the decision model.展开更多
We model analytically a relativistic problem consisting of two quasi-particles each with mass m in close orbit around a static Schwarzschild black hole with mass M = 1 situated at the center of mass of the system. The...We model analytically a relativistic problem consisting of two quasi-particles each with mass m in close orbit around a static Schwarzschild black hole with mass M = 1 situated at the center of mass of the system. The angular momentum l of the system is taken to be 2. We model the mass density of the orbiting particles as a δ-function and we assume that there are no deformations. To model the system, we apply the second-order differential equation obtained elsewhere for a dynamic thin matter shell on a Schwarzschild background. As it is the case in this paper, the framework on which the equation was obtained is Bodi-Sachs. The only change in the equation is that now the quasi-normal mode parameter represents the particle’s orbital frequency from which we are able to analytically compute the gravitational radiation emitted by the system at null infinity. We note that in a real astrophysical scenario the dynamics of the particles paths will be very dynamic and complicated and that the analytical methods used here will have to be developed further to accommodate that.展开更多
The aim of this paper is to study a class of right pp semigroups, so-called pseudo-C- rpp semigroups. After obtaining some characterizations of pseudo-C-rpp semigroups, we establish a construction of such semigroups i...The aim of this paper is to study a class of right pp semigroups, so-called pseudo-C- rpp semigroups. After obtaining some characterizations of pseudo-C-rpp semigroups, we establish a construction of such semigroups in terms of left normal bands and right C-rpp semigroups. In particular, a special case is considered.展开更多
Methods of finding quasi-normal modes of non-rotating relativistic stars have been well established, however, none of the existing treatments which take spacetime and fluid oscillations fully into account can determin...Methods of finding quasi-normal modes of non-rotating relativistic stars have been well established, however, none of the existing treatments which take spacetime and fluid oscillations fully into account can determine modes of long decay time, e.g., the p and g mode series, or the f modes for stars with low compactness ratio （M/R）. In this paper we show how the quasi-normal modes of long lifetime can be determined through refinements of a treatment originally due to Detweiler and Lindblom. The determination of the p mode series has been argued in the literature to have implication on the life time of gravitational wave sources and stellar stability. In this paper we 1） provide detailed steps in our treatment to facilitate future effort in this direction; 2） correct mistakes in the literature on the formulation; and 3） analyse the accuracy of the quasi-normal mode frequencies obtained and the limitations of the treatment.展开更多
In this paper, we study the gravitational quasi-normal modes（QNMs） for a static R^2 black hole（BH） in Anti-de Sitter（AdS） spacetime. The corresponding master equation of odd parity is derived and the QNMs are ev...In this paper, we study the gravitational quasi-normal modes（QNMs） for a static R^2 black hole（BH） in Anti-de Sitter（AdS） spacetime. The corresponding master equation of odd parity is derived and the QNMs are evaluated by the Horowitz and Hubeny method. Meanwhile the stability of such BH is also discussed through the temporal evolution of the perturbation field. Here we mainly consider the coefficient λ, which is related to the radius of AdS black hole, on the QNMs of the R^2 AdS BH. The results show that the Re（ω） and ｜Im（ω）｜ of the QNMs increase together as ｜λ｜ increases for a given angular momentum number l. That indicates with a larger value of ｜λ｜ the corresponding R^2 AdS BH returns to stable much more quickly. The dynamic evolution of the perturbation field is consistent with the results derived by the Horowitz and Hubeny method. Since in the conformal field theory the QNMs can reflect its approach to equilibrium, so our related results could be referential to studies of the AdS/CFT conjecture. The relationship between λ and the properties of the static R^2 BH might be helpful for the development of R^2 gravitational theory.展开更多
Define the differential operators φ_(n) for n∈N inductively by φ_(1)[f](z)=f(z)and φ_(n+1)[f](z)=f(z)φ_(n)[f](z)+d/daφ_(n)[f](z).For a positive integer k≥2 and a positive number δ,let F be the family of functi...Define the differential operators φ_(n) for n∈N inductively by φ_(1)[f](z)=f(z)and φ_(n+1)[f](z)=f(z)φ_(n)[f](z)+d/daφ_(n)[f](z).For a positive integer k≥2 and a positive number δ,let F be the family of functions f meromorphic on domain D■C such that φ_(k)[f](z)≠0 and|Res(f,a)-j|≥δ for all j∈{0,1,...,k-1}and all simple poles α of f in D.Then F is quasi-normal on D of order 1.展开更多
Considering rank s fields obey first order equation of motion, we study the dynamics of such fields in a 3-dimensionaJ self-duaJ space-like warped AdS3 black hole background. We obtain a Klein-Gordon-like equation for...Considering rank s fields obey first order equation of motion, we study the dynamics of such fields in a 3-dimensionaJ self-duaJ space-like warped AdS3 black hole background. We obtain a Klein-Gordon-like equation for tensor fields. By using gauge constraint and traceless condition, we will find the exact solutions of the equations of motion. Then, we will Compute the quasi-normal modes by imposing appropriate boundary conditions at horizon and infinity.展开更多
From the perturbation around the background spacetimes in the Gauss Bonnet gravity, we find the physical evidence that Ricci fiat AdS black holes and AdS solitons are different physical configurations and stay in diff...From the perturbation around the background spacetimes in the Gauss Bonnet gravity, we find the physical evidence that Ricci fiat AdS black holes and AdS solitons are different physical configurations and stay in different phases, this serves as a strong support to the previous mathematical and thermodynamieal arguments.展开更多
文摘In the paper, we take up a new method to prove a result of value distribution of meromorphic functions: let f be a meromorphic function in , and let , where P is a polynomial. Suppose that all zeros of f have multiplicity at least , except possibly finite many, and as . Then has infinitely many zeros.
基金Supported by the Doctoral Foundation of Zunyi Normal University of China(BS[2022]07,QJJ-[2022]-314)the National Natural Science Foundation of China(12265007)+1 种基金supported by 20230316 and 20240220-SIP-IPN,Mexico,and began this work with permission from IPN for a research stay in Chinapartially supported by the Long-Term Conceptual Development of a University of Hradec Kralove for 2023,issued by the Ministry of Education,Youth,and Sports of the Czech Republic。
文摘In this study,we comprehensively investigated charged AdS black holes surrounded by a distinct form of dark matter.In particular,we focused on key elements including the Hawking temperature,quasi-normal modes(QNMs),emission rate,and shadow.We first calculated the Hawking temperature,thereby identifying critical values such as the critical radius and maximum temperature of the black hole,essential for determining its phase transition.Further analysis focused on the QNMs of charged AdS black holes immersed in perfect fluid dark matter(PFDM)within the massless scalar field paradigm.Employing the Wentzel-Kramers-Brillouin(WKB)method,we accurately derived the frequencies of these QNMs.Additionally,we conducted a meticulous assessment of how the intensity of the PFDM parameterαinfluences the partial absorption cross sections of the black hole,along with a detailed study of the frequency variation of the energy emission rate.The pivotal role of geodesics in understanding astrophysical black hole characteristics is highlighted.Specifically,we examined the influence of the dark matter parameter on photon evolution by computing the shadow radius of the black hole.Our findings distinctly demonstrate the significant impact of the PFDM parameterαon the boundaries of this shadow,providing crucial insights into its features and interactions.We also provide profound insights into the intricate dynamics between a charged AdS black hole,novel dark matter,and various physical phenomena,elucidating their interplay and contributing valuable knowledge to the understanding of these cosmic entities.
基金Supported by Humanities and Social Science Project of Henan Colleges and Universities(2022-ZZJH-067)。
文摘Aiming at the dynamic multi-attribute decision making problem where the weight of each decision stage and attribute weight are completely unknown and the attribute value is unknown distributed three-parameter interval grey number,a threeparameter interval grey number dynamic multiattribute grey target decision making method with attribute value following quasi-normal distribution is proposed.Firstly,the position relationship between the“center of gravity”point and the kernel of the threeparameter interval grey number is discussed.According to the characteristicthat the attribute value obeys the quasi-normal distribution,anew weight isgiventothe“centerof gravity”point,and a new distance measure formula of the three-parameter interval grey number is defined.Secondly,according to the principle of maximum entropy,the objective programming model is constructed to determine the stage weight and attributeweight.Then,the schemes aresorted according to thesize of the comprehensive bull's-eye distance Finally an example is given to illustrate the effectiveness of the decision model.
文摘We model analytically a relativistic problem consisting of two quasi-particles each with mass m in close orbit around a static Schwarzschild black hole with mass M = 1 situated at the center of mass of the system. The angular momentum l of the system is taken to be 2. We model the mass density of the orbiting particles as a δ-function and we assume that there are no deformations. To model the system, we apply the second-order differential equation obtained elsewhere for a dynamic thin matter shell on a Schwarzschild background. As it is the case in this paper, the framework on which the equation was obtained is Bodi-Sachs. The only change in the equation is that now the quasi-normal mode parameter represents the particle’s orbital frequency from which we are able to analytically compute the gravitational radiation emitted by the system at null infinity. We note that in a real astrophysical scenario the dynamics of the particles paths will be very dynamic and complicated and that the analytical methods used here will have to be developed further to accommodate that.
基金Supported by the NSF of Jiangxi Provincethe SF of Education Department of Jiangxi Provincethe SF of Jiangxi Normal University
文摘The aim of this paper is to study a class of right pp semigroups, so-called pseudo-C- rpp semigroups. After obtaining some characterizations of pseudo-C-rpp semigroups, we establish a construction of such semigroups in terms of left normal bands and right C-rpp semigroups. In particular, a special case is considered.
基金supported by the Science Foundation of the Education Department of Hunan Province of China (Grant No. 07c578)in part by the US National Science Foundation NRACthe McDonnell Center for the Space Sciences of the Washington University(Grant No. MCA93S025)
文摘Methods of finding quasi-normal modes of non-rotating relativistic stars have been well established, however, none of the existing treatments which take spacetime and fluid oscillations fully into account can determine modes of long decay time, e.g., the p and g mode series, or the f modes for stars with low compactness ratio （M/R）. In this paper we show how the quasi-normal modes of long lifetime can be determined through refinements of a treatment originally due to Detweiler and Lindblom. The determination of the p mode series has been argued in the literature to have implication on the life time of gravitational wave sources and stellar stability. In this paper we 1） provide detailed steps in our treatment to facilitate future effort in this direction; 2） correct mistakes in the literature on the formulation; and 3） analyse the accuracy of the quasi-normal mode frequencies obtained and the limitations of the treatment.
基金supported by the National Natural Science Foundation of China(Grant Nos.11205254,11178018,11375279,and 11605015)the Fundamental Research Funds for the Central Universities,China(Grant Nos.106112016CDJXY300002 and CDJRC10300003)+1 种基金the Chinese State Scholarship Fund,FAPESP(Grant No.2012/08934-0)the Natural Science Foundation Project of CQ CSTC(Grant No.2011BB0052)
文摘In this paper, we study the gravitational quasi-normal modes（QNMs） for a static R^2 black hole（BH） in Anti-de Sitter（AdS） spacetime. The corresponding master equation of odd parity is derived and the QNMs are evaluated by the Horowitz and Hubeny method. Meanwhile the stability of such BH is also discussed through the temporal evolution of the perturbation field. Here we mainly consider the coefficient λ, which is related to the radius of AdS black hole, on the QNMs of the R^2 AdS BH. The results show that the Re（ω） and ｜Im（ω）｜ of the QNMs increase together as ｜λ｜ increases for a given angular momentum number l. That indicates with a larger value of ｜λ｜ the corresponding R^2 AdS BH returns to stable much more quickly. The dynamic evolution of the perturbation field is consistent with the results derived by the Horowitz and Hubeny method. Since in the conformal field theory the QNMs can reflect its approach to equilibrium, so our related results could be referential to studies of the AdS/CFT conjecture. The relationship between λ and the properties of the static R^2 BH might be helpful for the development of R^2 gravitational theory.
文摘Define the differential operators φ_(n) for n∈N inductively by φ_(1)[f](z)=f(z)and φ_(n+1)[f](z)=f(z)φ_(n)[f](z)+d/daφ_(n)[f](z).For a positive integer k≥2 and a positive number δ,let F be the family of functions f meromorphic on domain D■C such that φ_(k)[f](z)≠0 and|Res(f,a)-j|≥δ for all j∈{0,1,...,k-1}and all simple poles α of f in D.Then F is quasi-normal on D of order 1.
文摘Considering rank s fields obey first order equation of motion, we study the dynamics of such fields in a 3-dimensionaJ self-duaJ space-like warped AdS3 black hole background. We obtain a Klein-Gordon-like equation for tensor fields. By using gauge constraint and traceless condition, we will find the exact solutions of the equations of motion. Then, we will Compute the quasi-normal modes by imposing appropriate boundary conditions at horizon and infinity.
文摘From the perturbation around the background spacetimes in the Gauss Bonnet gravity, we find the physical evidence that Ricci fiat AdS black holes and AdS solitons are different physical configurations and stay in different phases, this serves as a strong support to the previous mathematical and thermodynamieal arguments.
