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L_p-mixed intersection bodies

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Science china mathematics 2008年第12期51卷 2172-2188页

作者： ZHAO ChangJian department of information and mathematics sciences, College of Science, china jiliang university, hangzhou 310018, china department of information and mathematics sciences College of Science China Jiliang University Hangzhou 310018 China

In this paper the author first introduce a new concept of Lp-dual mixed volumes of star bodies which extends the classical dual mixed volumes. Moreover, we extend the notions of Lp- intersection body to Lp-mixed intersection body. Inequalities for Lp-dual mixed volumes of Lp-mixed intersection bodies are established and the results established here provide new estimates for these type of inequalities.

关键词： L p -dual mixed volumes L p -intersection bodies L p -mixed intersection bodies 52A40

Lp-dual Quermassintegral sums

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Science china mathematics 2007年第9期50卷 1347-1360页

作者： Chang-jian ZHAO department of information and mathematics sciences,College of Science,china jiliang university,hangzhou 310018,china 1. department of information and mathematics sciences College of Science China Jiliang University Hangzhou 310018 China

In this paper,we first introduce a concept of L_p-dual Quermassintegral sum function of convex bodies and establish the polar projection Minkowski inequality and the polar projection Aleksandrov-Fenchel inequality for L_p-dual Quermassintegral ***,by using Lutwak’s width-integral of index i,we establish the L_p-Brunn-Minkowski inequality for the polar mixed projec- tion *** applications,we prove some interrelated results.

关键词： mixed volumes mixed projection bodies dual Quermassintegral sum polar of mixed projection bodies 52A40 53A15

Kerr black hole shadows cast by extraordinary light rays with Weyl corrections

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Science china(Physics,Mechanics & Astronomy) 2024年第5期67卷 18-26页

作者： Songbai Chen jiliang Jing department of Physics Institute of Interdisciplinary StudiesKey Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of EducationSynergetic Innovation Center for Quantum Effects and ApplicationsHunan Normal UniversityChangsha 410081China Center for Gravitation and Cosmology College of Physical Science and TechnologyYangzhou UniversityYangzhou 225009China

We investigate the equation of motion for photons with Weyl corrections in a Kerr black hole spacetime in a small coupling *** results show that Weyl corrections yield phenomena of *** light rays propagating in the spacetime are separated into the ordinary rays and the extraordinary rays,and the propagation of the latter depends on the *** probe the effects of Weyl corrections on the Kerr black hole shadows casted by the extraordinary rays and find that such corrections result in a weak stretching or squeezing in the vertical direction for the black hole ***,we also study the change of the length of the Near-Horizon Extremal Kerr line(NHEK line)with Weyl *** features could help us to understand the electrodynamics with Weyl corrections from black hole shadows.

关键词： correction light stretching

Gravitational wave fluxes on generic orbits in near-extreme Kerr spacetime:Higher spin and large eccentricity

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Science china(Physics,Mechanics & Astronomy) 2024年第11期67卷 16-28页

作者： Changkai Chen jiliang Jing department of Physics Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of EducationSynergetic Innovation Center for Quantum Effects and ApplicationsHunan Normal UniversityChangsha 410081China

To accurately obtain the waveform template of gravitational waves, substantial computational resources and extremely high precision are often required. In a previous study, we employed the confluent Heun function to obtain an exact solution to the Teukolsky equation. This approach allowed us to efficiently and accurately calculate the gravitational wave flux for a particle in circular orbits around a Schwarzschild black hole. Building on this method, we now extend its application to calculate the asymptotic gravitational wave fluxes from a particle in generic orbits around a near-extreme Kerr black hole. Our extended method proves particularly effective in handling computational challenges associated with large eccentricities(e = 0.9), higher spins(a = 0.999), higher harmonic modes, and strong-field regions. The results we obtained significantly outperform those derived from the numerical integration method based on the Mano-Suzuki-Takasugi method.

关键词： gravitational wave fluxes exact solution Teukolsky equation near-extreme Kerr black hole

Energy flux and waveforms by coalescing spinless binary system in effective one-body theory

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Science china(Physics,Mechanics & Astronomy) 2024年第6期67卷 58-68页

作者： Sheng Long Weike Deng jiliang Jing department of Physics Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of EducationSynergetic Innovation Center for Quantum Effects and ApplicationsHunan Normal UniversityChangsha 410081China Center for Gravitation and Cosmology College of Physical Science and TechnologyYangzhou UniversityYangzhou 225009China

We present a study on the energy radiation rate and waveforms of the gravitational wave generated by coalescing spinless binary systems up to the third post-Minkowskian approximation in the effective one-body *** derive an analytical expansion of the null tetrad components of the gravitational perturbed Weyl tensorΨ4in the effective spacetime,we utilize the method proposed by Sasaki et *** this investigation,we discover more general integral formulas that provide a theoretical framework for computing the results in any ***,we successfully compute the energy radiation rate and waveforms of the gravitational wave,which include the results of the Schwarzschild case and the correction terms resulting from the dimensionless parameters a2and a3in the effective metric.

关键词： post-Minkowskian approximation effective one-body theory gravitational waveform template

Comprehensive modeling strategy for thermomechanical tribological behavior analysis of railway vehicle disc brake system

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Friction 2024年第1期12卷 74-94页

作者： Jiabao YIN Chun LU jiliang MO School of Mechanical Engineering Southwest Jiaotong UniversityChengdu 610031China Technology and Equipment of Rail Transit Operation and Maintenance Key Laboratory of Sichuan Province Chengdu 610031China

A comprehensive modeling strategy for studying the thermomechanical tribological behaviors is proposed in this *** wear degradation considering the influence of temperature(T)is predicted by Archard wear model with the help of the UMESHMOTION subroutine and arbitrary Lagrangian–Eulerian(ALE)remeshing *** the proposed method,the thermomechanical tribological behaviors of railway vehicle disc brake system composed of forged steel brake disc and Cu-based powder metallurgy(PM)friction block are studied *** effectiveness of the proposed methodology is validated by experimental test on a self-designed scaled brake test bench from the perspectives of interface temperature,wear degradation,friction noise and vibration,and contact status *** work can provide an effective way for the investigation of thermomechanical tribological behaviors in the engineering field.

关键词： tribological behaviors thermomechanical field wear prediction finite element simulation disc brake system railway vehicle

Bifurcation stabilization of nonlinear systems by dynamic output feedback with application to rotating stall control

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Science china(information sciences) 2012年第1期55卷 200-213页

作者： CHEN PengNian1,QIN HuaShu2,WANG Yong3&HONG YiGuang2 1department of mathematics,china jiliang university,hangzhou 310018,china 2Institute of Systems Science,The Chinese Academy of sciences,Beijing 100080,china 3department of Mechanics,Peking university,Beijing 100871,china 1. department of mathematics China Jiliang University Hangzhou 310018 China2. Institute of Systems Science The Chinese Academy of Sciences Beijing 100080 China3. Department of Mechanics Peking University Beijing 100871 China

The paper deals with the problem of stabilization of stationary bifurcation solutions of nonlinear systems via dynamic output *** is emphasized that the parameter of the system is not directly *** introduce the concepts of uniform observability of the inverse of a function of state and input and N-order-input-to-state bifurcation *** on the concepts,we propose a new method for designing dynamic compensators that guarantee bifurcation stability for the closed-loop *** an example,we apply the general theory to active control of rotating stall in axial flow compressors by designing a stabilizing dynamic compensator for the three-state Moore-Greitzer model with a class of cubic compressor characteristics.

关键词： bifurcation control uniform observability dynamic output feedback rotating stall

Energy flux and waveform of gravitational wave generated by coalescing slow-spinning binary system in effective one-body theory

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Science china(Physics,Mechanics & Astronomy) 2024年第9期67卷 73-83页

作者： Weike Deng Sheng Long jiliang Jing department of Physics Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Educationand Synergetic Innovation Center for Quantum Effects and ApplicationsHunan Normal UniversityChangsha 410081China Center for Gravitation and Cosmology College of Physical Science and TechnologyYangzhou UniversityYangzhou 225009China

We extend our research on the energy flux and waveform characteristics of gravitational waves generated by merging nonspinning binary black holes through self-consistent effective one-body theory to include binary systems with slowly spinning black ***,we decompose the equation for the null tetrad component of the gravitationally perturbed Weyl tensorψ_4~B into radial and angular parts,leveraging the second-order approximation of the rotation parameter ***,we derive an analytical solution for the radial equation and observe that our results are contingent upon the parameters a_(2),a_(3),and a,which represent the second-and third-order correction parameters,***,we calculate the energy flux,the radiation-reaction force and the waveform for the“plus”and“cross”modes of the gravitational waves generated by merging slowly spinning binary black holes.

关键词： post-Minkowskian approximation effective-one-body theory gravitational waveform template

NONTRIVIAL SOLUTION OF A NONLINEAR SECOND-ORDER THREE-POINT BOUNDARY VALUE PROBLEM

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Applied mathematics(A Journal of Chinese Universities) 2007年第1期22卷 37-47页

作者： Li Shuhong Sun Yongping department of mathematics, Lishui university, Lishui 323000,china department of Applied mathematics, Zhejiang Sci-Tec university, hangzhou 310018, china department of Electron and information, Zhejiang university of Media and Communications, hangzhou 310018, china. department of mathematics Lishui University Lishui China department of Applied mathematics Zhejiang Sci-Tec University Hangzhou China department of Electron and information Zhejiang University of Media and Communications Hangzhou China

In this paper, for a second-order three-point boundary value problem u″＋f（t,u）=0,0〈t〈1,au（0）-bu′（0）=0,u（1）-au（η）=0,where η∈ （0, 1）, a, b, α ∈R with a^2 ＋ b^2 〉 0, the existence of its nontrivial solution is studied. The＇conditions on f which guarantee the existence of nontrivial solution are formulated. As an application, some examples to demonstrate the results are given.

关键词： three-point boundary value problem nonlinear alternative of Leray-Schauder, nontrivial solution.