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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,liu kefeng2,& SHEN Ming3 1department of mathematics,zhejiang university,hangzhou 310027,china 2department of mathematics,university of California at Los Angeles,CA 90095,USA 3Center of Mathematical Sciences,zhejiang university,hangzhou 310027,china department of mathematics Zhejiang University Hangzhou China department of mathematics University of California at Los Angeles Los Angeles USA Center of Mathematical Sciences Zhejiang University Hangzhou 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

Global existence of smooth solutions to two-dimensional compressible isentropic Euler equations for Chaplygin gases

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Science china mathematics 2010年第3期53卷 719-738页

作者： kong dexing 1 , liu kefeng 2 & WANG YuZhu 3, 1 department of mathematics, zhejiang university, hangzhou 310027, china 2 department of mathematics, university of California at Los Angeles, CA 90095, USA 3 department of mathematics, Shanghai Jiao Tong university, Shanghai 200248, china department of mathematics Zhejiang University Hangzhou China department of mathematics University of California at Los Angeles Los Angeles USA department of mathematics Shanghai Jiao Tong University Shanghai China

In this paper we investigate the two-dimensional compressible isentropic Euler equations for Chaplygin gases. Under the assumption that the initial data is close to a constant state and the vorticity of the initial velocity vanishes, we prove the global existence of the smooth solution to the Cauchy problem for twodimensional flow of Chaplygin gases.

关键词： Chaplygin gases compressible Euler equations irrotational flow null condition Cauchy problem smooth solution

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 liu kefeng 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 liu 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 kong 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

Symmetry Reduction and Exact Solutions of a Hyperbolic Monge-Ampère Equation

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Chinese Annals of mathematics,Series B 2012年第2期33卷 309-316页

作者： Zhongzhou DONG Yong CHEN dexing kong Zenggui WANG School of mathematics and Information Science Henan Polytechnic UniversityJiaozuo 454003HenanChina Shanghai Key Laboratory of Trustworthy Computing East China Normal UniversityShanghai 200062China Center of Mathematical Sciences Zhejiang UniversityHangzhou 310027China School of mathematics Sciences Liaocheng UniversityLiaocheng 252059ShandongChina

By means of the classical symmetry method, a hyperbolic Monge-Ampere equa- tion is investigated. The symmetry group is studied and its corresponding group invariant solutions are constructed. Based on the associated vector of the obtained symmetry, the authors construct the group-invariant optimal system of the hyperbolic Monge-Ampere equation, from which two interesting classes of solutions to the hyperbolic Monge-Ampere equation are obtained successfully.

关键词： Symmetry reduction Monge-Ampere equation Exact solutions

A predictive model for early recurrence of colorectal-cancer liver metastases based on clinical parameters

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Gastroenterology Report 2021年第3期9卷 241-251,I0002页

作者： Siqi Dai Yao Ye Xiangxing kong Jun Li kefeng Ding department of Colorectal Surgery The Second Affiliated HospitalZhejiang University School of MedicineHangzhouZhejiangP.R.China Cancer Institute(Key Laboratory of Cancer Prevention and Intervention China National Ministry of EducationKey Laboratory of Molecular Biology in Medical SciencesZhejiang ProvinceChina)The Second Affiliated HospitalZhejiang University School of MedicineHangzhouZhejiangP.R.China

Background:The prognosis for patients with colorectal-cancer liver metastases(CRLM)after curative surgery remains poor and shows great *** recurrence,defined as tumor recurrence within 6 months of curative surgery,is associated with poor survival,requiring earlier detection and *** study aimed to develop and validate a bedside model based on clinical parameters to predict early recurrence in CRLM patients and provide insight into post-operative surveillance *** and methods:A total of 202 consecutive CRLM patients undergoing curative surgeries between 2012 and 2019 were retrospectively enrolled and randomly assigned to the training(n=150)and validation(n=52)*** information and radiological,pathological,and laboratory findings were extracted from medical *** factors for early recurrence were identified via a multivariate logistic-regression model to develop a predictive nomogram,which was validated for discrimination,calibration,and clinical ***:Liver-metastases number,lymph-node suspicion,neurovascular invasion,colon/rectum location,albumin and post-operative carcinoembryonic antigen,and carbohydrate antigen 19–9 levels(CA19–9)were independent predictive factors and were used to construct the nomogramfor early recurrence after curative *** area under the curve was 0.866 and 0.792 for internal and external validation,*** model significantly outperformed the clinical risk score and Beppu’s model in our data *** the lift curve,the nomogram boosted the detection rate in post-operative surveillance by two-fold in the top 30%high-risk ***:Our model for early recurrence in CRLM patients after curative surgeries showed superior performance and could aid in the decision-making for selective follow-up strategies.

关键词： colorectal cancer liver metastases early recurrence prediction model post-operative surveillance

Efficacy of rigosertib, a small molecular RAS signaling disrupter for the treatment of KRAS-mutant colorectal cancer

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Cancer Biology & Medicine 2022年第2期19卷 213-228页

作者： Xinyi Zhou Qian Xiao Dongliang Fu Haochen Zhang Yang Tang Jinjie He Yeting Hu Xiangxing kong Fei Teng Xiangrui liu Ying Yuan kefeng Ding department of Colorectal Surgery and Oncology Key Laboratory of Cancer Prevention and InterventionMinistry of Educationthe Second Affiliated Hospital of Zhejiang University School of MedicineHangzhou 310009China department of Medical Oncology Key Laboratory of Cancer Prevention and InterventionMinistry of Educationthe Second Affiliated Hospital of Zhejiang University School of MedicineHangzhou 310009China hangzhou Oncocare Co Ltd Hangzhou 310009China department of Pharmacology Zhejiang University School of MedicineHangzhou 310058China Cancer Center Zhejiang UniversityHangzhou 310009China

Objective:Mutant KRAS,the principal isoform of RAS,plays a pivotal role in the oncogenesis of colorectal cancer by constitutively activating the RAF/MEK/ERK and PI3K/AKT *** targeted therapies are urgently *** investigated whether rigosertib,a benzyl styryl sulfone RAS signaling disruptor,could selectively kill KRAS-mutant colorectal cancer ***:CCK-8 was used to determine the cell ***-derived tumor and cancer cell xenograft models were used to detect the inhibitory efficacy of *** cytometry was used to evaluate the apoptosis and cell cycle *** and cell cycle arrest markers were detected by Western ***-DA was used to determine the reactive oxygen *** staining and Western blot were performed to characterize RAS signaling markers in colorectal cancer tissues and ***:Rigosertib(RGS)exhibited a cytotoxic effect against colorectal cancer cells,which was greater in KRAS-mutant ***,RGS induced mitotic arrest and oxidative stress-dependent apoptosis in KRAS-mutant DLD1 and HCT116 ***,RGS disrupted RAS signaling,and the inhibition of RAS/MEK/ERK was independent of cellular oxidative *** patient-derived xenograft models,the response and tumor inhibition of RGS were significantly higher in the KRAS-mutant subgroup,while p-MEK,p-ERK,and p-AKT levels of RGS-treated tumors were significantly ***,in a KRAS-mutant,chemotherapy-resistant patient-derived xenograft model,RGS showed a stronger therapeutic effect than the combination standard therapy involving fluoropyrimidine+oxaliplatin/irinotecan+***:These data showed that targeting RAS signaling using RGS could be a therapeutic treatment for KRAS-mutant colorectal cancer patients.

关键词： Colorectal cancer KRAS mutation rigosertib therapeutic effect RAS signaling

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 kong 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 2019 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 2019 pandemic.

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