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Nonlinear vibrations of rotating pretwisted TC4 composite blades reinforced by graphene under transverse two-parameter aerodynamic loads and tip gap airflow 认领 引用
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作者 Hao FENG Yufei ZHANG +2 位作者 Wei ZHANG Biliu ZHOU Asmaa AMER 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2026年第4期290-309,共20页
Titanium-6 aluminum-4 vanadium(TC4),a titanium alloy,exhibits the excellent mechanical properties.The primary resonance and nonlinear vibrations are investigated for a functionally graded Graphene Platelet-Reinforced ... Titanium-6 aluminum-4 vanadium(TC4),a titanium alloy,exhibits the excellent mechanical properties.The primary resonance and nonlinear vibrations are investigated for a functionally graded Graphene Platelet-Reinforced TC4(GPR-TC4)rotating pre-twisted composite blade under the combined transverse two-parameter excitation and axial excitation by using O,U,and X distribution patterns to the composite blades reinforced by the graphene.The GPRTC4 rotating pre-twisted composite blade is modeled as a functionally graded graphene plateletreinforced rotating pre-twisted composite cantilever plate.A new approach is proposed for addressing the transverse aerodynamic loads through the trigonometric series expansion.The steady-state rotational speed is considered with the minor periodic disturbances.The classical plate theory is used to derive the nonlinear governing equation of motion by using von Karman geometric relations,Lagrange equations,and mode functions satisfying the boundary conditions.Two-degreeof-freedom nonlinear ordinary differential equations are obtained to govern the nonlinear vibrations of the GPR-TC4 rotating pre-twisted composite cantilever plate under the multi-parameter excitations.Runge-Kutta method is utilized to analyze the primary resonance and nonlinear dynamics of the GPR-TC4 rotating pre-twisted composite cantilever plate.The results include the amplitude-frequency response curves,waveforms,Poincare maps,2D and 3D bifurcation diagrams,maximum Lyapunov exponent,and phase portraits.This study provides a comprehensive analysis of the nonlinear dynamic responses of the GPR-TC4 rotating pre-twisted composite cantilever plate under varying excitation parameters. 展开更多
关键词 GPR-TC4 Graphene platelet Leakage of airflow Rotating pre-twisted composite blade Transverse two-parameter excitation
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Exact solutions for the transcritical Riemann problem of two-parameter fluids 认领 引用
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作者 Haotong BAI Yixin YANG +2 位作者 Wenjia XIE Dejian LI Mingbo SUN 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2025年第12期2385-2406,共22页
Transcritical and supercritical fluids widely exist in aerospace propulsion systems,such as the coolant flow in the regenerative cooling channels of scramjet engines.To numerically simulate the coolant flow,we must ad... Transcritical and supercritical fluids widely exist in aerospace propulsion systems,such as the coolant flow in the regenerative cooling channels of scramjet engines.To numerically simulate the coolant flow,we must address the challenges in solving Riemann problems(RPs)for real fluids under complex flow conditions.In this study,an exact numerical solution for the one-dimensional RP of two-parameter fluids is developed.Due to the comprehensive resolution of fluid thermodynamics,the proposed solution framework is suitable for all forms of the two-parameter equation of state(EoS).The pressure splitting method is introduced to enable parallel calculation of RPs across multiple grid points.Theoretical analysis demonstrates the isentropic nature of weak waves in two-parameter fluids,ensuring that the same mathematical properties as ideal gas could be applied in Newton's iteration.A series of numerical cases validate the effectiveness of the proposed method.A comparative analysis is conducted on the exact Riemann solutions for the real fluid EoS,the ideal gas EoS,and the improved ideal gas EoS under supercritical and transcritical conditions.The results indicate that the improved one produces smaller errors in the calculation of momentum and energy fluxes. 展开更多
关键词 two-parameter fluid Riemann problem(RP) exact solution supercritical fluid pressure splitting transcritical fluid
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Prestack migration velocity analysis based on simplified two-parameter moveout equation 认领 引用 被引量：3
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作者 陈海峰 李向阳 +2 位作者 钱忠平 宋建军 赵桂玲 《Applied Geophysics》 SCIE CSCD 2016年第1期135-144,220,221,共10页
Stacking velocity V_（C2）,vertical velocity ratio γ_0,effective velocity ratio γ_（eff）,and anisotropic parameter x_（eff） are correlated in the PS-converted-wave（PS-wave） anisotropic prestack Kirchhoff time mi... Stacking velocity V_（C2）,vertical velocity ratio γ_0,effective velocity ratio γ_（eff）,and anisotropic parameter x_（eff） are correlated in the PS-converted-wave（PS-wave） anisotropic prestack Kirchhoff time migration（PKTM） velocity model and are thus difficult to independently determine.We extended the simplified two-parameter（stacking velocity V_（C2） and anisotropic parameter k_（eff）） moveout equation from stacking velocity analysis to PKTM velocity model updating and formed a new four-parameter（stacking velocity V_（C2）,vertical velocity ratio γ_0,effective velocity ratio γ_（eff）,and anisotropic parameter k_（eff）） PS-wave anisotropic PKTM velocity model updating and process flow based on the simplified twoparameter moveout equation.In the proposed method,first,the PS-wave two-parameter stacking velocity is analyzed to obtain the anisotropic PKTM initial velocity and anisotropic parameters;then,the velocity and anisotropic parameters are corrected by analyzing the residual moveout on common imaging point gathers after prestack time migration.The vertical velocity ratio γ_0 of the prestack time migration velocity model is obtained with an appropriate method utilizing the P- and PS-wave stacked sections after level calibration.The initial effective velocity ratio γ_（eff） is calculated using the Thomsen（1999） equation in combination with the P-wave velocity analysis;ultimately,the final velocity model of the effective velocity ratio γ_（eff） is obtained by percentage scanning migration.This method simplifies the PS-wave parameter estimation in high-quality imaging,reduces the uncertainty of multiparameter estimations,and obtains good imaging results in practice. 展开更多
关键词 PS-converted-wave PKTM velocity updating two-parameter moveout equation migration imaging
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Dynamics of Entanglement for a Two-Parameter Class of States in a Qubit-Qutrit System 认领 引用 被引量：2
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作者 魏海瑞 任宝藏 +2 位作者 李涛 华明 邓富国 《Communications in Theoretical Physics》 SCIE CAS CSCD 2012年第6期983-990,共8页
We investigate the dynamics of entanglement for a two-parameter class of states in a hybrid qubit-qutrit system under the influence of various dissipative channels. Our results show that entanglement sudden death （ES... We investigate the dynamics of entanglement for a two-parameter class of states in a hybrid qubit-qutrit system under the influence of various dissipative channels. Our results show that entanglement sudden death （ESD） is a general phenomenon and it usually takes place in a qubit-qutrit system interacting with various noisy channels, not only the ease with dephasing and depolarizing channels observed by others. ESD can only be avoided for some initially entangled states under some particular noisy channels. Moreover, the environment affects the entanglement and the coherence of the system in very different ways. 展开更多
关键词 dynamics of entanglement qubit-qutrit systems a two-parameter class of states dissipative channels entanglement sudden death
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Buckling analysis of shear deformable composite conical shells reinforced by CNTs subjected to combined loading on the two-parameter elastic foundation 认领 引用 被引量：5
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作者 A.H.Sofiyev N.Kuruoglu 《Defence Technology（防务技术）》 SCIE EI CAS CSCD 2022年第2期205-218,共14页
The main objective of this study is to investigate the buckling analysis of CCSs reinforced by CNTs subjected to combined loading of hydrostatic pressure and axial compression resting on the twoparameter elastic found... The main objective of this study is to investigate the buckling analysis of CCSs reinforced by CNTs subjected to combined loading of hydrostatic pressure and axial compression resting on the twoparameter elastic foundation(T-P-EF).It is one of the first attempts to derive the governing equations of the CCSs reinforced with CNTs,based on a generalized first-order shear deformation shell theory(FSDST)which includes shell-foundation interaction.By adopting the extended mixing rule,the effective material properties of CCSs reinforced by CNTs with linear distributions are approximated by introducing some efficiency parameters.Three carbon nanotube distribution in the matrix,i.e.uniform distribution(U)and V and X-types linear distribution are taken into account.The stability equations are solved by using the Galerkin procedure to determine the combined buckling loads(CBLs)of the structure selected here.The numerical illustrations cover CBLs characteristics of CCSs reinforced by CNTs in the presence of the T-P-EF.Finally,a parametric study is carried out to study the influences of the foundation parameters,the volume fraction of carbon nanotubes and the types of reinforcement on the CBLs. 展开更多
关键词 Nanocomposites CNTs Composite conical shells Two-parameter elastic foundations Combined buckling loads Shear deformation shell theories
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Relation between Fresnel transform of input light field and the two-parameter Radon transform of Wigner function of the field 认领 引用 被引量：1
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作者 范洪义 胡利云 《Chinese Physics B》 SCIE EI CAS 2009年第2期611-615,共5页
This paper proves a new theorem on the relationship between optical field Wigner function＇s two-parameter Radon transform and optical Fresnel transform of the field, i.e., when an input field ψ （x＇） propagates th... This paper proves a new theorem on the relationship between optical field Wigner function＇s two-parameter Radon transform and optical Fresnel transform of the field, i.e., when an input field ψ （x＇） propagates through an optical [D （-B） （-C） A] system, the energy density of the output field is equal to the Radon transform of the Wigner function of the input field, where the Radon transform parameters are D, B. It prove this theorem in both spatial-domain and frequency-domain, in the latter case the Radon transform parameters are A, C. 展开更多
关键词 Fresnel transform two-parameter Radon transform Wigner function
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A New Two-Parameter Formula for Rotational Spectra 认领 引用 被引量：1
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作者 Zeng Guo-mo1,2 Liu Wei1 Zhao En-guang21 Department of Physics, Jilin University, Changchun 1300232 Institute of Theoretical Physics, the Chinese Academy of Sciences, P. O. Box 2735, Beijing 100080 《Chinese journal of nuclear physics》 EI 1995年第4期322-327,共6页
A new two-parameter formula for the rotational spectra of well deformed nuclei isproposed. The formula is deduced from experimental level systematics and alternatively fromnuclear hydrodynamics. Comparisons with a gre... A new two-parameter formula for the rotational spectra of well deformed nuclei isproposed. The formula is deduced from experimental level systematics and alternatively fromnuclear hydrodynamics. Comparisons with a great number of rotational spectra of even-even nu-clei in rare-earth and actinides region show that the formula is the best one among all two-pa-rameter formulas. It is pointed out that this formula can be applied to the spin assignment forsuperdeformed band. 展开更多
关键词 Two-parameter formula Rotational spectra Nuclear hydrodynamics
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A GENERAL FORM OF THE INCREMENTS OF A TWO-PARAMETER WIENER PROCESS 认领 引用 被引量：3
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作者 林正炎 陆传荣 《Applied Mathematics(A Journal of Chinese Universities)》 1993年第1期54-63,共10页
In this paper, we consider a general form of the increments for a two-parameter Wiener process. Both the Csorgo-Revesz's increments and a class of the lag increments are the special cases of this general form of i... In this paper, we consider a general form of the increments for a two-parameter Wiener process. Both the Csorgo-Revesz's increments and a class of the lag increments are the special cases of this general form of increments. Our results imply the theorem that have been given by Csorgo and Revesz (1978), and some of their conditions are removed. 展开更多
关键词 Two-parameter Wiener Process Increments.
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BOUNDARY INTEGRAL EQUATIONS FOR BENDING PROBLEM OF REISSNER'S PLATES ONTWO-PARAMETER FOUNDATION 认领 引用
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作者 李正良 周永明 邓安福 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1998年第4期351-359,共9页
Two fundamental solutions for bending problem of Reissner's plates on twoparameter foundation are derived by means of Fouier integral transformation of generalized function in this paper.On the basis of virtual wo... Two fundamental solutions for bending problem of Reissner's plates on twoparameter foundation are derived by means of Fouier integral transformation of generalized function in this paper.On the basis of virtual work principles, three boundary integral equations which fit for arbitrary shapes, loads and boundary conditions of thick plates are presented according to Hu Haichang's theory about Reissner's plates. It provides the fundamental theories for the application of BEM. A numerical example is given for clamped, simply supported and free boundary conditions. The results obtained are satisfactory as compared with the analytical methods. 展开更多
关键词 Reissuer's plate two-parameter foundation fundamental solution boundary integral equation
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BAYESIAN PREDICTION FOR THE TWO-PARAMETER EXPONENTIAL DISTRIBUTION BASED ON TYPE Ⅱ DOUBLY CENSORING 认领 引用
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作者 LiYanling ZhaoXuanmin XieWenxian 《Applied Mathematics(A Journal of Chinese Universities)》 2005年第1期75-84,共10页
The two-parameter exponential distribution is proposed to be an underlying model,and prediction bounds for future observations are obtained by using Bayesian approach.Prediction intervals are derived for unobserved li... The two-parameter exponential distribution is proposed to be an underlying model,and prediction bounds for future observations are obtained by using Bayesian approach.Prediction intervals are derived for unobserved lifetimes in one-sample prediction and two-sample prediction based on type Ⅱ doubly censored samples.A numerical example is given to illustrate the procedures,prediction intervals are investigated via Monte Carlo method,and the accuracy of prediction intervals is presented. 展开更多
关键词 type Ⅱ doubly censoring two-parameter exponential distribution Bayesian prediction,Monte Carlo method.
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Description of Rotational Molecular Spectra by the Two-Parameter Universal Equation 认领 引用
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作者 ZENG Guo-Mo 《Communications in Theoretical Physics》 SCIE CAS 2002年第8期209-212,共4页
The n-power two-parameter universal equation for rotational spectra which we deduced recently is appliedto the description of the rotational bands of several diatomic and tetra-atomic molecules. Excellent agreement wi... The n-power two-parameter universal equation for rotational spectra which we deduced recently is appliedto the description of the rotational bands of several diatomic and tetra-atomic molecules. Excellent agreement withexperimental data can be obtained with small n values. The relation between our equation and the famous Dunhamformula is discussed. 展开更多
关键词 two-parameter equation, diatomic and tetra-atomic molecules, rotational spectra
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A two-parameter multiple shooting method and its application to the natural vibrations of non-prismatic multi-segment beams 认领 引用
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作者 R.HOŁUBOWSKI K.JARCZEWSKA 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2023年第12期2243-2252,共10页
This paper presents an enhanced version of the standard shooting method that enables problems with two unknown parameters to be solved.A novel approach is applied to the analysis of the natural vibrations of Euler-Ber... This paper presents an enhanced version of the standard shooting method that enables problems with two unknown parameters to be solved.A novel approach is applied to the analysis of the natural vibrations of Euler-Bernoulli beams.The proposed algorithm,named as two-parameter multiple shooting method,is a new powerful numerical tool for calculating the natural frequencies and modes of multi-segment prismatic and non-prismatic beams with different boundary conditions.The impact of the axial force and additional point masses is also taken into account.Due to the fact that the method is based directly on the fourth-order ordinary differential equation,the structures do not have to be divided into many small elements to obtain an accurate enough solution,even though the geometry is very complex.To verify the proposed method,three different examples are considered,i.e.,a three-segment non-prismatic beam,a prismatic column subject to non-uniformly distributed compressive loads,and a two-segment beam with an additional point mass.Numerical analyses are carried out with the software MATHEMATICA.The results are compared with the solutions computed by the commercial finite element program SOFiSTiK.Good agreement is achieved,which confirms the correctness and high effectiveness of the formulated algorithm. 展开更多
关键词 two-parameter multiple shooting method two-point boundary value problem natural vibration non-prismatic beam multi-segment beam
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A New Two-Parameter Heteromorphic Elliptic Equation: Properties and Applications 认领 引用 被引量：6
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作者 Zhouhu Wu 《World Journal of Engineering and Technology》 2020年第4期642-657,共16页
The ellipse and the superellipse are both planar closed curves with a double axis of symmetry. Here we show the isoconcentration contour of the simplified two-dimensional advection-diffusion equation from a stable lin... The ellipse and the superellipse are both planar closed curves with a double axis of symmetry. Here we show the isoconcentration contour of the simplified two-dimensional advection-diffusion equation from a stable line source in the center of a wide river. A new two-parameter heteromorphic elliptic equation with a single axis of symmetry is defined. The values of heights, at the point of the maximum width and that of the centroid of the heteromorphic ellipse, are derived through mathematical analysis. Taking the compression coefficient θ = b/a = 1 as the criterion, the shape classification of H-type, Standard-type and W-type for heteromorphic ellipse have been given. The area formula, the perimeter theorem, and the radius of curvature of heteromorphic ellipses, and the geometric properties of the rotating body are subsequently proposed. An illustrative analysis shows that the inner contour curve of a heteromorphic elliptic tunnel has obvious advantages over the multiple- arc splicing cross section. This work demonstrates that the heteromorphic ellipses have extensive prospects of application in all categories of tunnels, liquid transport tanks, aircraft and submarines, bridges, buildings, furniture, and crafts. 展开更多
关键词 Two-Parameter Curve Heteromorphic Ellipse Standard Equation Geometric Properties Engineering Applications
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Empirical Bayes Test for Two-parameter Exponential Distribution under Type-Ⅱ Censored Samples 认领 引用
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作者 WANG Liang SHI Yi-min CHANG Ping 《Chinese Quarterly Journal of Mathematics》 CSCD 2012年第1期54-58,共5页
The empirical Bayes test problem is considered for scale parameter of twoparameter exponential distribution under type-II censored data.By using wavelets estimation method,the EB test function is constructed,of which ... The empirical Bayes test problem is considered for scale parameter of twoparameter exponential distribution under type-II censored data.By using wavelets estimation method,the EB test function is constructed,of which the asymptotic optimality and convergence rates are obtained.Finally,an example concerning the main result is given. 展开更多
关键词 two-parameter exponential distribution wavelets estimation empirical Bayes test asymptotic optimality convergence rates
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ALMOST SURE CONTINUITY OF INFINITE SERIES OF INDEPENDENT TWO-PARAMETER ORNSTEIN-UHLENBECK PROCESSES 认领 引用
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作者 WEN Ji-wei 《Journal of Zhejiang University Science》 2001年第3期14-17,共4页
This study on the conditions for the convergence and almost-sure continuity of infinite series of independent two-parameter Ornstein-Uhlenbeck processes yielded sufficient conditions similar to that for independent on... This study on the conditions for the convergence and almost-sure continuity of infinite series of independent two-parameter Ornstein-Uhlenbeck processes yielded sufficient conditions similar to that for independent one-parameter Ornstein-Uhlenbeck processes. 展开更多
关键词 two-parameter Ornstein-Uhlenbeck processes infinite series almost-sure continuity
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ON MODULI OF NON-DIFFERENTIABILITY FOR A TWO-PARAMETER ORNSTEIN-UHLENBECK PRCESS 认领 引用
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作者 林正炎 《Acta Mathematica Scientia》 SCIE 1996年第S1期85-91,共7页
In the paper, which is a continuation of [2], we establish moduli of non-differentiablity for a two-parameter Ornstein-Uhlenbeck process.
关键词 Moduli of non-differentiablity two-parameter Ornstein-Uhlenbeck process
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Analysis of vibration stability of fluid conveying pipe on the two-parameter foundation with elastic support boundary conditions 认领 引用 被引量：5
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作者 Yongqi Ma Yunxiang You +1 位作者 Ke Chen Aichun Feng 《Journal of Ocean Engineering and Science》 SCIE 2024年第6期616-629,共14页
In this study,the vibration stability of fluid conveying pipe resting on two-parameter foundation is in-vestigated under four different elastic support boundary conditions.The harmonic differential quadrature(HDQ)meth... In this study,the vibration stability of fluid conveying pipe resting on two-parameter foundation is in-vestigated under four different elastic support boundary conditions.The harmonic differential quadrature(HDQ)method is applied to solve the governing vibration equation derived based on Euler–Bernoulli beam theory subject to the elastic foundation and boundary conditions.As a result,a general set of second-order ordinary differential equations emerges,and by appropriately setting the stiffness of the end springs,one can easily study the dynamics of various systems with classical or non-classical bound-ary conditions.The numerical simulations are conducted to study the pipe instability performance with respect to various boundary conditions,elastic support parameters,elastic foundation parameters and fluid mass ratios.The numerical model is validated by comparison with published data.It is found that the elastic support boundary conditions have significant effects on the stability of pipe resting on elas-tic foundation.The pipe stability performance is very sensitive to the two elastic foundation parameters.Larger fluid mass ratio enhances the pipe flutter stability performance but has no effects on the diver-gence. 展开更多
关键词 Vibration stability Two-parameter foundation Elastic support Boundary conditions Harmonic differential quadrature method
Entanglement for a two-parameter class of states in a high-dimension bipartite quantum system 认领 引用 被引量：8
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作者 DI YaoMin LIU SiPing LIU DongDong 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS 2010年第10期1868-1872,共5页
The entanglement for a two-parameter class of states in a high-dimension (m  n,n≥m≥3) bipartite quantum system is discussed.The negativity (N) and the relative entropy of entanglement (Er) are calculated,and the a... The entanglement for a two-parameter class of states in a high-dimension (m  n,n≥m≥3) bipartite quantum system is discussed.The negativity (N) and the relative entropy of entanglement (Er) are calculated,and the analytic expressions are obtained.Finally the relation between the negativity and the relative entropy of entanglement is discussed.The result demonstrates that all PPT states of the two-parameter class of states are separable,and all entangled states are NPT states.Different from the 2 ? n quantum system,the negativity for a two-parameter class of states in high dimension is not always greater than or equal to the relative entropy of entanglement.The more general relation expression is mN/2≥Er. 展开更多
关键词 two-parameter class of states negativity relative entropy of entanglement
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Statistical Analysis of Two-Parameter Generalized BS-Logistic Fatigue Life Distribution 认领 引用 被引量：1
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作者 XU Xiaoling WANG Ronghua GU Beiqing 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2019年第4期1231-1250,共20页
The logarithmic moment estimations of parameters are proposed for two-parameter generalized Birnbaum-Saunders Logistic fatigue life distribution GBS-Logistic(α,β)under the full sample.The precisions of point estimat... The logarithmic moment estimations of parameters are proposed for two-parameter generalized Birnbaum-Saunders Logistic fatigue life distribution GBS-Logistic(α,β)under the full sample.The precisions of point estimations are investigated and compared with other point estimations by Monte-Carlo simulations.The approximate interval estimations of parameters are given by using Taylor expansion,and the precisions of approximate interval estimations are investigated by Monte-Carlo simulations.Finally,several examples show the feasibility of the methods. 展开更多
关键词 Approximate interval estimation point estimation scale parameter shape parameter two-parameter generalized Birnbaum-Saunders Logistic fatigue life distribution
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Factorization of simple modules for certain restricted two-parameter quantum groups 认领 引用
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作者 Min LI Xiuling WANG 《Frontiers of Mathematics in China》 SCIE CSCD 2013年第1期169-190,共22页
We study the representations of the restricted two-parameter quantum groups of types B and G.For these restricted two-parameter quantum groups,we give some explicit conditions which guarantee that a simple module can ... We study the representations of the restricted two-parameter quantum groups of types B and G.For these restricted two-parameter quantum groups,we give some explicit conditions which guarantee that a simple module can be factored as the tensor product of a one-dimensional module with a module that is naturally a module for the quotient by central group-like elements.That is,givenθa primitive eth root of unity,the factorization of simple uθy,θz(g)-modules is possible,if and only if(2(y-z),e)=1 for 9=SO2n+l;(3(y-z),g)=1 for 9=G2. 展开更多
关键词 Hopf algebra Drinfel'd double restricted two-parameter quantumgroup
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