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Time-periodic solutions of the Einstein's field equations II:geometric singularities

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Science china Mathematics 2010年第6期53卷 1507-1520页

作者： kong dexing1,{2. {3.2.& SHEN Ming3.1department of Mathematics,zhejiang university,hangzhou 3.002.,china 2.6} of Mathematics,university of California at Los Angeles,CA 90095,USA 3.enter of Mathematical Sciences,zhejiang university,hangzhou 3.002.,china 1. department of Mathematics Zhejiang University Hangzhou 310027 China2. Department of Mathematics University of California at Los Angeles Los Angeles CA 90095 USA3. Center of Mathematical Sciences Zhejiang University Hangzhou 310027 China

In this paper,we construct several kinds of new time-periodic solutions of the vacuum Einstein's field equations whose Riemann curvature tensors vanish,keep finite or take the infinity at some points in these space-times,*** singularities of these new time-periodic solutions are investigated and some new physical phenomena are discovered.

关键词： Einstein’s field equations time-periodic solution Riemann curvature tensor singularity event horizon

Time-periodic solutions of the Einstein's field equations Ⅰ:general framework

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Science china Mathematics 2010年第5期53卷 176-193页

作者： kong dexing1 & {2. {3.2.1department of Mathematics,zhejiang university,hangzhou 3.002.,china 2.4} of Mathematics,university of California at Los Angeles,CA 90095,USA

In this paper,we develop a new algorithm to find the exact solutions of the Einstein's field ***-periodic solutions are constructed by using the new *** singularities of the time-periodic solutions are investigated and some new physical phenomena,such as degenerate event horizon and time-periodic event horizon,are *** applications of these solutions in modern cosmology and general relativity are expected.

关键词： Einstein’s field equations time-periodic solution Riemann curvature tensor singularity event horizon

Time-periodic solutions of the Einstein's field equations Ⅲ:physical singularities

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Science china Mathematics 2011年第1期54卷 23-33页

作者： kong dexing {2. {3. SHEN Ming department of Mathematics Zhejiang University Hangzhou 310027 China department of Mathematics University of California at Los Angeles CA 90095 USA Center of Mathematical Sciences Zhejiang University Hangzhou 310027 China

In this paper we construct a new time-periodic solution of the vacuum Einstein's field equations, this solution possesses physical singularities, i.e., the norm of the solution's Riemann curvature tensor takes the infinity at some points. We show that this solution is intrinsically time-periodic and describes a time-periodic universe with the "time-periodic physical singularity". By calculating the Weyl scalars of this solution, we investigate new physical phenomena and analyze new singularities for this universal model.

关键词： Einstein's field equations time-periodic solution geometric singularity physical singularity Weyl scalar

GLOBAL EXISTENCE OF CLASSICAL SOLUTIONS TO THE HYPERBOLIC GEOMETRY FLOW WITH TIME-DEPENDENT DISSIPATION

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Acta Mathematica Scientia 2018年第3期38卷 745-755页

作者： dexing kong Qi {2. School of Mathematical Sciences Zhejiang Universit department of Applied Mathematics College of ScienceZhongyuan University of Technolog

In this article, we investigate the hyperbolic geometry flow with time-dependent dissipation（δ2.gij）/δt2.μ/（（1 ＋ t）λ）（δ gij）/δt=-2.Rij,on Riemann surface. On the basis of the energy method, for 0 〈 λ ≤ 1, μ 〉 λ ＋ 1, we show that there exists a global solution gij to the hyperbolic geometry flow with time-dependent dissipation with asymptotic flat initial Riemann surfaces. Moreover, we prove that the scalar curvature R（t, x） of the solution metric gij remains uniformly bounded.

关键词： Hyperbolic geometry flow time-dependent damping classical solution energy method global existence

A Primal-Dual Hybrid Gradient Algorithm to Solve the LLT Model for Image Denoising

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Numerical Mathematics(Theory,Methods and Applications) 2012年第2期5卷 260-277页

作者： Chunxiao liu dexing {2. Shengfeng Zhu department of Mathematics Hangzhou Normal UniversityHangzhou 310036China department of Mathematics Zhejiang UniversityHangzhouChina

We propose an efficient gradient-type algorithm to solve the fourth-order LLT denoising model for both gray-scale and vector-valued *** on the primal-dual formulation of the original nondifferentiable model,the new algorithm updates the primal and dual variables alternately using the gradient descent/ascent *** examples are provided to demonstrate the superiority of our algorithm.

关键词： LLT model image denoising primal-dual

Suspected Close Contacts as the Pilot Indicator of the Growth Trend of Confirmed Population During the COVID-19 Pandemic: A Simulation Approach

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Infectious Microbes & Diseases 2020年第2期2卷 35-41页

作者： Sisi Huang Anding Zhu Yan wang Yancong Xu Lu Li dexing {2. School of Mathematical Sciences Zhejiang UniversityHangzhou 310027China School of Management Engineering Zhejiang Gongshang UniversityHangzhou 310018China School of Mathematical Sciences Chongqing Normal UniversityChongqing 401331China department of Mathematics Hangzhou Normal UniversityHangzhou 311121China College of Basic Medical Sciences Zhejiang Chinese Medical UniversityHangzhou 310053China

Regarding to the actual situation of the new coronavirus disease 2.19 epidemic,social factors should be taken into account and the increasing growth trend of confirmed populations needs to be explained.A proper model needs to be established,not only to simulate the epidemic,but also to evaluate the future epidemic situation and find a pilot indicator for the *** original susceptible-infectious-recover model is modified into the susceptible-infectious-quarantine-confirm-recover combined with social factors(SIDCRL)model,which combines the natural transmission with social factors such as external interventions and *** numerical simulation method is used to imitate the change curve of the cumulative number of the confirmed cases and the number of cured ***,we investigate the relationship between the suspected close contacts(SCC)and the final outcome of the growth trend of confirmed cases with a simulation *** article selects four representative countries,that is,china,South Korea,Italy,and the United States,and gives separate numerical *** simulation results of the model fit the actual situation of the epidemic development and reasonable predictions are *** addition,it is analyzed that the increasing number of SCC contributes to the epidemic outbreak and the prediction of the United States based on the population of the SCC highlights the importance of external intervention and active prevention *** simulation of the model verifies its reliability and stresses that observable variable SCC can be taken as a pilot indicator of the coronavirus disease 2.19 pandemic.

关键词： COVID-19 SIR model social factors numerical simulation suspected close contacts confirmed case temporary hospital

Application of computer-aided diagnosis of congenital heart disease in four-chamber view of fetal heart basic screening

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Chinese Medical Journal 2022年第24期135卷 3010-3012页

作者： Fangfei Su Xiaoqian Zhang Jijing Han Jingjing wang Lu Li dexing {2. Qingqing Wu department of Ultrasound Beijing Obstetrics and Gynecology HospitalCapital Medical UniversityBeijing 100026China School of Mathematical Sciences Zhejiang UniversityHangzhouZhejiang 310058China department of Obstetrics&Gynecology The Chinese University of Hong KongHong KongChina

To the Editor:Congenital heart disease(CHD)is the most common severe congenital malformation which threatens the health of the fetus and the primary factor of intrauterine *** detection of severe CHD could reduce the neonatal mortality and *** detection rate ranges between 2..0%and 59.7%in the prenatal ultrasonographic examination.^([1])We need to identify new strategies to improve detection rates of CHD ***-learning(DL)-based computer-aided diagnosis(CAD)has been highly and rapidly developed in recent years.

关键词： diagnosis congenital fetal

On the wave catching-up phenomenon in a two-layer nonlinearly elastic composite bar

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On the wave catching-up phenomenon in a two-layer nonlinearl...

Advances in statistical mechanics of rock masses and its engineering applications

2.0}d International Congress of Theoretical and Applied Mechanics

作者： Shoujun Huang Huihui Dai Zhen Chen dexing kong department of Mathematics Anhui Normal University department of Mathematics City University of Hong Kong department of Civil and Environmental Engineering University of MissouriColumbiaUSA department of Engineering Mechanics Dalian University of Technology department of Mathematics Zhejiang University

＜正＞Cracking induced by tensile wave at the free surface of an impacted target is an important issue in impact-resistant design. Here,we explore to use material nonlinearity to undermine the strength of the tensile ...

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Journal of Rock Mechanics and Geotechnical Engineering 2021年第1期13卷 22-45页

作者： Faquan Wu Jie Wu Han Bao Bo Li Zhigang Shan Deheng kong Shaoxing university Shaoxing312000China Rock Innovation(zhejiang)Co. Ltd.Shaoxing312000China School of Highway Chang’an UniversityXi’an710064China Huadong Engineering Co. Ltd.PowerChinaHangzhou311122China department of Geotechnical Engineering College of Civil EngineeringTongji UniversityShanghai200092China

To efficiently link the continuum mechanics for rocks with the structural statistics of rock masses,a theoretical and methodological system called the statistical mechanics of rock masses(SMRM)was developed in the past three *** SMRM,equivalent continuum models of stressestrain relationship,strength and failure probability for jointed rock masses were established,which were based on the geometric probability models characterising the rock mass *** follows the statistical physics,the continuum mechanics,the fracture mechanics and the weakest link hypothesis.A general constitutive model and complete stressestrain models under compressive and shear conditions were also developed as the derivatives of the SMRM *** SMRM calculation system was then developed to provide fast and precise solutions for parameter estimations of rock masses,such as full-direction rock quality designation(RQD),elastic modulus,Coulomb compressive strength,rock mass quality rating,and Poisson’s ratio and shear *** constitutive equations involved in SMRM were integrated into a FLAC3. based numerical module to apply for engineering rock *** is also capable of analysing the complete deformation of rock masses and active reinforcement of engineering rock *** of engineering applications of SMRM were presented,including a rock mass at QBT hydropower station in northwestern china,a dam slope of Zongo II hydropower station in ***,an open-pit mine in {2.,china,an underground powerhouse of Jinping I hydropower station in southwestern china,and a typical circular tunnel in Lanzhou-Chongqing railway,*** applications verified the reliability of the SMRM and demonstrated its applicability to broad engineering issues associated with jointed rock masses.

关键词： Statistical mechanics of rock masses(SMRM) Jointed rock mass Geometric probability model Failure probability Anisotropic constitutive model Engineering parameters