In this paper,we study the uniqueness of positive solutions to the following semilinear equations{-Δu=λ|x|^(α)ue^(u^(2)),in B_(1),u=0,onδB_(1)ueu2;in B_(1);u=0;on@B_(1);whereλ>0,α>-2;B_(1)denotes the unit ...In this paper,we study the uniqueness of positive solutions to the following semilinear equations{-Δu=λ|x|^(α)ue^(u^(2)),in B_(1),u=0,onδB_(1)ueu2;in B_(1);u=0;on@B_(1);whereλ>0,α>-2;B_(1)denotes the unit disk in R^(2):By delicate and relatively complicated computation of radial solutions to the above equation and the asymptotic expansion of solutions near the boundary of B_(1),the uniqueness of positive solutions is obtained.The results of this paper extend the uniqueness result for the semilinear equation with critical exponential growth in CHEN et al.(2022)to the case that includes a Henon term.展开更多
This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic diff...This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.展开更多
Microorganisms can colonize the surface of microplastics(MPs)to form a distinctive microbiome,known as a“plastisphere”which is regarded as an anthropogenic niche for microbial growth.However,bacterial community asse...Microorganisms can colonize the surface of microplastics(MPs)to form a distinctive microbiome,known as a“plastisphere”which is regarded as an anthropogenic niche for microbial growth.However,bacterial community assembly in virgin and aging MP plastispheres across different habitats is poorly understood.This study aims to assess the variations in bacterial community assembly across different niches and habitats with an in situ ex-periment,in which constructed forest wetland(FW),natural lake wetland(LW),and lotus pond wetland(LP)were habitats,and plastispheres of virgin and aging low-density polyethylene(LDPE)MPs,as well as surround-ing wetland soils were niches.Significant niche-related differences in bacterial communities were observed,with lower diversity and enrichment of potential plastic-degrading bacteria in the plastisphere than in the soil bacterial communities.Furthermore,habitat-related differences exerted a more pronounced influence on the beta-diversity patterns of the bacterial communities.The linear regression analyses indicated that the local species pool con-tributed more to bacterial community assembly in the LW wetland,whereas the relative abundance of species was the primary factor in the LP wetland.The null model analysis indicated that plastisphere bacterial communi-ties were predominantly driven by the stochastic process,with a more deterministic assembly observed in the LP wetland and soil bacterial communities.Additionally,the primary ecological process shaping plastisphere com-munities shifted from drift in the virgin LDPE to homogenising dispersal in the aging LDPE.This study provides new insights into the fate and ecological impacts of MPs in wetlands,thereby facilitating the effective regulations of plastic pollution.展开更多
Interfacial superconductivity(IS)has been a topic of intense interest in condensed matter physics,due to its unique properties and exotic photoelectrical performance.However,there are few reports about IS systems cons...Interfacial superconductivity(IS)has been a topic of intense interest in condensed matter physics,due to its unique properties and exotic photoelectrical performance.However,there are few reports about IS systems consisting of two insulators.Here,motivated by the emergence of an insulator-metal transition in type-Ⅲ heterostructures and the superconductivity in some“special”two-dimensional(2D)semiconductors via electron doping,we predict that the 2D heterostructure SnSe_(2)/PtTe_(2) is a model system for realizing IS by using firstprinciples calculations.Our results show that due to slight but crucial interlayer charge transfer,SnSe_(2)/PtTe_(2) turns to be a type-Ⅲ heterostructure with metallic properties and shows a superconducting transition with the critical temperature(T_(c))of 3.73 K.Similar to the enhanced electron–phonon coupling(EPC)in the electrondoped SnSe_(2) monolayer,the IS in the SnSe_(2)/PtTe_(2) heterostructure mainly originates from the metallized SnSe_(2) layer.Furthermore,we find that its superconductivity is sensitive to tensile lattice strain,forming a domeshaped superconducting phase diagram.Remarkably,at 7%biaxial tensile strain,the superconducting T_(c) can increase more than twofold(8.80 K),resulting from softened acoustic phonons at the𝑀point and enhanced EPC strength.Our study provides a concrete example for realizing IS in type-Ⅲ heterostructures,which waits for future experimental verification.展开更多
Background:To determine whether initiating a glucagon-like peptide-1 receptor agonist(GLP-1 RA)within 3 months of type 2 diabetes(T2DM)diagnosis alters the subsequent risk of overall and site-specific cancer and wheth...Background:To determine whether initiating a glucagon-like peptide-1 receptor agonist(GLP-1 RA)within 3 months of type 2 diabetes(T2DM)diagnosis alters the subsequent risk of overall and site-specific cancer and whether this association differs by baseline body-mass index(BMI).Methods:This retrospective cohort study used electronic health records from the TriNetX U.S.research network.Adults aged 20 years or older diagnosed with T2DM between 2016 and 2024 were included if they received any hypoglycemic agents within 3 months before and after diagnosis.Following 1:1 propensity score matching,both the GLP-1 RA user and non-user groups included 183,264 patients.The study outcome was defined as a diagnosis of malignant neoplasms.Hazard ratios(HRs)for overall and site-specific cancer risk were estimated using Cox proportional hazards models.Kaplan–Meier analysis and stratified analysis by BMI were performed.Results:Early GLP-1 RA use demonstrated a modest but significant association with reduced overall cancer risk(HR 0.93;95%CI:0.90–0.96).Reduced risks were noted for cancers of the digestive(HR 0.81),respiratory(HR 0.66),and female genital(HR 0.87)systems.In stratified analysis,benefits were more pronounced in patients with BMI≥30,particularly for pancreatic and colorectal cancers.Conclusion:Early initiation of GLP-1 receptor agonists in patients with diagnosed T2DM was associated with a modest reduction in overall cancer risk,particularly among individuals with obesity.These findings highlight the dual metabolic and oncologic value of prompt GLP-1 RA therapy.展开更多
Burgers equation in random environment is studied. In order to give the exact solutions of random Burgers equation, we only consider the Wick-type stochastic Burgers equation which is the perturbation of the Burgers e...Burgers equation in random environment is studied. In order to give the exact solutions of random Burgers equation, we only consider the Wick-type stochastic Burgers equation which is the perturbation of the Burgers equation with variable coefficients by white noise W（t）=Bt, where Bt is a Brown motion. The auto-Baecklund transformation and stochastic soliton solutions of the Wick-type stochastic Burgers equation are shown by the homogeneous balance and Hermite transform. The generalization of the Wick-type stochastic Burgers equation is also studied.展开更多
This paper establishes the Razumikhin-type theorem on stability for neutral stochastic functional differential equations with unbounded delay. To overcome difficulties from unbounded delay, we develop several differen...This paper establishes the Razumikhin-type theorem on stability for neutral stochastic functional differential equations with unbounded delay. To overcome difficulties from unbounded delay, we develop several different techniques to investigate stability. To show our idea clearly, we examine neutral stochastic delay differential equations with unbounded delay and linear neutral stochastic Volterra unbounded-delay-integro-differential equations.展开更多
The stability of stochastic functional differential equation with Markovian switching was studied by several authors,but there was almost no work on the stability of the neutral stochastic functional differential equa...The stability of stochastic functional differential equation with Markovian switching was studied by several authors,but there was almost no work on the stability of the neutral stochastic functional differential equations with Markovian switching.The aim of this article is to close this gap.The authors establish Razumikhin-type theorem of the neutral stochastic functional differential equations with Markovian switching,and those without Markovian switching.展开更多
This paper considers the problem of delay-dependent exponential stability in mean square for stochastic systems with polytopic-type uncertainties and time-varying delay. Applying the descriptor model transformation an...This paper considers the problem of delay-dependent exponential stability in mean square for stochastic systems with polytopic-type uncertainties and time-varying delay. Applying the descriptor model transformation and introducing free weighting matrices, a new type of Lyapunov-Krasovskii functional is constructed based on linear matrix inequalities （LMIs）, and some new delay-dependent criteria are obtained. These criteria include the delay-independent/rate- dependent and delay-dependent/rate-independent exponential stability criteria. These new criteria are less conservative than existing ones. Numerical examples demonstrate that these new criteria are effective and are an improvement over existing ones.展开更多
The existence and uniqueness of solutions to backward stochastic differential equations with jumps and with unbounded stopping time as terminal under the non_Lipschitz condition are obtained. The convergence of soluti...The existence and uniqueness of solutions to backward stochastic differential equations with jumps and with unbounded stopping time as terminal under the non_Lipschitz condition are obtained. The convergence of solutions and the continuous dependence of solutions on parameters are also derived. Then the probabilistic interpretation of solutions to some kinds of quasi_linear elliptic type integro_differential equations is obtained.展开更多
In this paper, the Razumikhin approach is applied to the study of both p-th moment and almost sure stability on a general decay for a class of impulsive stochastic functional differential systems with Markovian switch...In this paper, the Razumikhin approach is applied to the study of both p-th moment and almost sure stability on a general decay for a class of impulsive stochastic functional differential systems with Markovian switching. Based on the Lyapunov-Razumikhin methods, some sufficient conditions are derived to check the stability of impulsive stochastic functional differential systems with Markovian switching. One numerical example is provided to demonstrate the effectiveness of the results.展开更多
Modeling log-mortality rates on O-U type processes and forecasting life expectancies are explored using U.S. data. In the classic Lee-Carter model of mortality, the time trend and the age-specific pattern of mortality...Modeling log-mortality rates on O-U type processes and forecasting life expectancies are explored using U.S. data. In the classic Lee-Carter model of mortality, the time trend and the age-specific pattern of mortality over age group are linear, this is not the feature of mortality model. To avoid this disadvantage, O-U type processes will be used to model the log-mortality in this paper. In fact, this model is an AR(1) process, but with a nonlinear time drift term.Based on the mortality data of America from Human Mortality database(HMD), mortality projection consistently indicates a preference for mortality with O-U type processes over those with the classical Lee-Carter model. By means of this model, the low bounds of mortality rates at every age are given. Therefore, lengthening of maximum life expectancies span is estimated in this paper.展开更多
In the paper, perturbed stochastic Volterra Equations with noise terms driven by series of independent scalar Wiener processes are considered. In the study, the resolvent approach to the equations under consideration ...In the paper, perturbed stochastic Volterra Equations with noise terms driven by series of independent scalar Wiener processes are considered. In the study, the resolvent approach to the equations under consideration is used. Sufficient conditions for the existence of strong solution to the class of perturbed stochastic Volterra Equations of convolution type are given. Regularity of stochastic convolution is supplied, as well.展开更多
In this paper we prove the pathwise uniqueness of a kind of two-parameter Volterra type stochastic differential equations under the coefficients satisfy the non-Lipschitz conditions. We use a martingale formula in ste...In this paper we prove the pathwise uniqueness of a kind of two-parameter Volterra type stochastic differential equations under the coefficients satisfy the non-Lipschitz conditions. We use a martingale formula in stead of Ito formula, which leads to simplicity the process of proof and extends the result to unbounded coefficients case.展开更多
BACKGROUND Type Ⅱ diabetes mellitus(T2DM)has been associated with increased risk of colon cancer(CC)and worse prognosis in patients with metastases.The effects of T2DM on postoperative chemoresistance rate(CRR)and lo...BACKGROUND Type Ⅱ diabetes mellitus(T2DM)has been associated with increased risk of colon cancer(CC)and worse prognosis in patients with metastases.The effects of T2DM on postoperative chemoresistance rate(CRR)and long-term disease-free survival(DFS)and overall survival(OS)in patients with stage Ⅲ CC who receive curative resection remain controversial.AIM To investigate whether T2DM or glycemic control is associated with worse postoperative survival outcomes in stage Ⅲ CC.METHODS This retrospective cohort study included 278 patients aged 40-75 years who underwent surgery for stage Ⅲ CC from 2018 to 2021.Based on preoperative T2DM history,the patients were categorized into non-DM(n=160)and DM groups(n=118).The latter was further divided into well-controlled(n=73)and poorly controlled(n=45)groups depending on the status of glycemic control.DFS,OS,and CRR were compared between the groups and Cox regression analysis was used to identify risk factors.RESULTS Patients in the DM and non-DM groups demonstrated similar DFS,OS,and CRR(DFS:72.03%vs 78.75%,P=0.178;OS:81.36%vs 83.12%,P=0.638;CRR:14.41%vs 7.5%,P=0.063).Poorly controlled DM was associated with a significantly worse prognosis and higher CRR than well-controlled DM(DFS:62.22%vs 78.07%,P=0.021;OS:71.11%vs 87.67%,P=0.011;CRR:24.40%vs 8.22%,P=0.015).High preoperative fasting plasma glucose[DFS:Hazard ratio(HR)=2.684,P<0.001;OS:HR=2.105,P=0.019;CRR:HR=2.214,P=0.005]and glycosylated hemoglobin levels(DFS:HR=2.344,P=0.006;OS:HR=2.119,P=0.021;CRR:HR=2.449,P=0.009)indicated significantly poor prognosis and high CRR,while T2DM history did not(DFS:HR=1.178,P=0.327;OS:HR=0.933,P=0.739;CRR:HR=0.997,P=0.581).CONCLUSION Increased preoperative fasting plasma glucose and glycosylated hemoglobin levels,but not T2DM history,were identified as risk factors associated with poor postoperative outcomes and high CRR in patients with stage Ⅲ CC.展开更多
This paper mainly tends to utilize Razumikhin-type theorems to investigate p-th moment stability for a class of stochastic switching nonlinear systems with delay. Based on the Lyapunov-Razumik- hin methods, some suffi...This paper mainly tends to utilize Razumikhin-type theorems to investigate p-th moment stability for a class of stochastic switching nonlinear systems with delay. Based on the Lyapunov-Razumik- hin methods, some sufficient conditions are derived to check the stability of stochastic switching nonlinear systems with delay. One numerical example is provided to demonstrate the effectiveness of the results.展开更多
For Duffle-Epstein type Backward Stochastic Differential Equations, the comparison theorem is proved. Based on the comparison theorem, by monotone iterative technique, the existence of the minimal and maximal solution...For Duffle-Epstein type Backward Stochastic Differential Equations, the comparison theorem is proved. Based on the comparison theorem, by monotone iterative technique, the existence of the minimal and maximal solutions of the equations are proved.展开更多
BACKGROUND Transforming growth factor-β(TGF-β)superfamily plays an important role in tumor progression and metastasis.Activin A receptor type 1C(ACVR1C)is a TGF-βtype I receptor that is involved in tumorigenesis th...BACKGROUND Transforming growth factor-β(TGF-β)superfamily plays an important role in tumor progression and metastasis.Activin A receptor type 1C(ACVR1C)is a TGF-βtype I receptor that is involved in tumorigenesis through binding to dif-ferent ligands.AIM To evaluate the correlation between single nucleotide polymorphisms(SNPs)of ACVR1C and susceptibility to esophageal squamous cell carcinoma(ESCC)in Chinese Han population.METHODS In this hospital-based cohort study,1043 ESCC patients and 1143 healthy controls were enrolled.Five SNPs(rs4664229,rs4556933,rs77886248,rs77263459,rs6734630)of ACVR1C were assessed by the ligation detection reaction method.Hardy-Weinberg equilibrium test,genetic model analysis,stratified analysis,linkage disequi-librium test,and haplotype analysis were conducted.RESULTS Participants carrying ACVR1C rs4556933 GA mutant had significantly decreased risk of ESCC,and those with rs77886248 TA mutant were related with higher risk,especially in older male smokers.In the haplotype analysis,ACVR1C Trs4664229Ars4556933Trs77886248Crs77263459Ars6734630 increased risk of ESCC,while Trs4664229Grs4556933Trs77886248Crs77263459Ars6734630 was associated with lower susceptibility to ESCC.CONCLUSION ACVR1C rs4556933 and rs77886248 SNPs were associated with the susceptibility to ESCC,which could provide a potential target for early diagnosis and treatment of ESCC in Chinese Han population.展开更多
This paper develops a Smolyak-type sparse-grid stochastic collocation method(SGSCM) for uncertainty quantification of nonlinear stochastic dynamic equations.The solution obtained by the method is a linear combination ...This paper develops a Smolyak-type sparse-grid stochastic collocation method(SGSCM) for uncertainty quantification of nonlinear stochastic dynamic equations.The solution obtained by the method is a linear combination of tensor product formulas for multivariate polynomial interpolation.By choosing the collocation point sets to coincide with cubature point sets of quadrature rules,we derive quadrature formulas to estimate the expectations of the solution.The method does not suffer from the curse of dimensionality in the sense that the computational cost does not increase exponentially with the number of input random variables.Numerical analysis of a nonlinear elastic oscillator subjected to a discretized band-limited white noise process demonstrates the computational efficiency and accuracy of the developed method.展开更多
The current research aims to implement the numerical resultsfor the Holling third kind of functional response delay differential modelutilizing a stochastic framework based on Levenberg-Marquardt backpropagationneural...The current research aims to implement the numerical resultsfor the Holling third kind of functional response delay differential modelutilizing a stochastic framework based on Levenberg-Marquardt backpropagationneural networks (LVMBPNNs). The nonlinear model depends uponthree dynamics, prey, predator, and the impact of the recent past. Threedifferent cases based on the delay differential system with the Holling 3^(rd) type of the functional response have been used to solve through the proposedLVMBPNNs solver. The statistic computing framework is provided byselecting 12%, 11%, and 77% for training, testing, and verification. Thirteennumbers of neurons have been used based on the input, hidden, and outputlayers structure for solving the delay differential model with the Holling 3rdtype of functional response. The correctness of the proposed stochastic schemeis observed by using the comparison performances of the proposed and referencedata-based Adam numerical results. The authentication and precision ofthe proposed solver are approved by analyzing the state transitions, regressionperformances, correlation actions, mean square error, and error histograms.展开更多
基金Supported by the Natural Science Foundation of China(12571122,12061010)。
文摘In this paper,we study the uniqueness of positive solutions to the following semilinear equations{-Δu=λ|x|^(α)ue^(u^(2)),in B_(1),u=0,onδB_(1)ueu2;in B_(1);u=0;on@B_(1);whereλ>0,α>-2;B_(1)denotes the unit disk in R^(2):By delicate and relatively complicated computation of radial solutions to the above equation and the asymptotic expansion of solutions near the boundary of B_(1),the uniqueness of positive solutions is obtained.The results of this paper extend the uniqueness result for the semilinear equation with critical exponential growth in CHEN et al.(2022)to the case that includes a Henon term.
基金Supported by the National Natural Science Foundation of China(12001074)the Research Innovation Program of Graduate Students in Hunan Province(CX20220258)+1 种基金the Research Innovation Program of Graduate Students of Central South University(1053320214147)the Key Scientific Research Project of Higher Education Institutions in Henan Province(25B110025)。
文摘This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.
基金supported by Shanghai Municipal Natural Science Foundation,China(No.21ZR1446800)the National Natural Science Foundation of China(No.41877425)the Fundamental Research Funds for the Central Universities(No.226-2024-00052)。
文摘Microorganisms can colonize the surface of microplastics(MPs)to form a distinctive microbiome,known as a“plastisphere”which is regarded as an anthropogenic niche for microbial growth.However,bacterial community assembly in virgin and aging MP plastispheres across different habitats is poorly understood.This study aims to assess the variations in bacterial community assembly across different niches and habitats with an in situ ex-periment,in which constructed forest wetland(FW),natural lake wetland(LW),and lotus pond wetland(LP)were habitats,and plastispheres of virgin and aging low-density polyethylene(LDPE)MPs,as well as surround-ing wetland soils were niches.Significant niche-related differences in bacterial communities were observed,with lower diversity and enrichment of potential plastic-degrading bacteria in the plastisphere than in the soil bacterial communities.Furthermore,habitat-related differences exerted a more pronounced influence on the beta-diversity patterns of the bacterial communities.The linear regression analyses indicated that the local species pool con-tributed more to bacterial community assembly in the LW wetland,whereas the relative abundance of species was the primary factor in the LP wetland.The null model analysis indicated that plastisphere bacterial communi-ties were predominantly driven by the stochastic process,with a more deterministic assembly observed in the LP wetland and soil bacterial communities.Additionally,the primary ecological process shaping plastisphere com-munities shifted from drift in the virgin LDPE to homogenising dispersal in the aging LDPE.This study provides new insights into the fate and ecological impacts of MPs in wetlands,thereby facilitating the effective regulations of plastic pollution.
基金supported by the National Key R&D Program of China (Grant Nos.2022YFA1403103 and 2019YFA0308603)the National Natural Science Foundation of China (Grant No.12304167)the Shandong Provincial Natural Science Foundation of China (Grant No.ZR2023QA020)。
文摘Interfacial superconductivity(IS)has been a topic of intense interest in condensed matter physics,due to its unique properties and exotic photoelectrical performance.However,there are few reports about IS systems consisting of two insulators.Here,motivated by the emergence of an insulator-metal transition in type-Ⅲ heterostructures and the superconductivity in some“special”two-dimensional(2D)semiconductors via electron doping,we predict that the 2D heterostructure SnSe_(2)/PtTe_(2) is a model system for realizing IS by using firstprinciples calculations.Our results show that due to slight but crucial interlayer charge transfer,SnSe_(2)/PtTe_(2) turns to be a type-Ⅲ heterostructure with metallic properties and shows a superconducting transition with the critical temperature(T_(c))of 3.73 K.Similar to the enhanced electron–phonon coupling(EPC)in the electrondoped SnSe_(2) monolayer,the IS in the SnSe_(2)/PtTe_(2) heterostructure mainly originates from the metallized SnSe_(2) layer.Furthermore,we find that its superconductivity is sensitive to tensile lattice strain,forming a domeshaped superconducting phase diagram.Remarkably,at 7%biaxial tensile strain,the superconducting T_(c) can increase more than twofold(8.80 K),resulting from softened acoustic phonons at the𝑀point and enhanced EPC strength.Our study provides a concrete example for realizing IS in type-Ⅲ heterostructures,which waits for future experimental verification.
基金financial support fromthe Chung Shan Medical University Hospital,Taiwan(CSH-2022-A-009).
文摘Background:To determine whether initiating a glucagon-like peptide-1 receptor agonist(GLP-1 RA)within 3 months of type 2 diabetes(T2DM)diagnosis alters the subsequent risk of overall and site-specific cancer and whether this association differs by baseline body-mass index(BMI).Methods:This retrospective cohort study used electronic health records from the TriNetX U.S.research network.Adults aged 20 years or older diagnosed with T2DM between 2016 and 2024 were included if they received any hypoglycemic agents within 3 months before and after diagnosis.Following 1:1 propensity score matching,both the GLP-1 RA user and non-user groups included 183,264 patients.The study outcome was defined as a diagnosis of malignant neoplasms.Hazard ratios(HRs)for overall and site-specific cancer risk were estimated using Cox proportional hazards models.Kaplan–Meier analysis and stratified analysis by BMI were performed.Results:Early GLP-1 RA use demonstrated a modest but significant association with reduced overall cancer risk(HR 0.93;95%CI:0.90–0.96).Reduced risks were noted for cancers of the digestive(HR 0.81),respiratory(HR 0.66),and female genital(HR 0.87)systems.In stratified analysis,benefits were more pronounced in patients with BMI≥30,particularly for pancreatic and colorectal cancers.Conclusion:Early initiation of GLP-1 receptor agonists in patients with diagnosed T2DM was associated with a modest reduction in overall cancer risk,particularly among individuals with obesity.These findings highlight the dual metabolic and oncologic value of prompt GLP-1 RA therapy.
文摘Burgers equation in random environment is studied. In order to give the exact solutions of random Burgers equation, we only consider the Wick-type stochastic Burgers equation which is the perturbation of the Burgers equation with variable coefficients by white noise W（t）=Bt, where Bt is a Brown motion. The auto-Baecklund transformation and stochastic soliton solutions of the Wick-type stochastic Burgers equation are shown by the homogeneous balance and Hermite transform. The generalization of the Wick-type stochastic Burgers equation is also studied.
基金Supported by NSFC (11001091)Chinese UniversityResearch Foundation (2010MS129)
文摘This paper establishes the Razumikhin-type theorem on stability for neutral stochastic functional differential equations with unbounded delay. To overcome difficulties from unbounded delay, we develop several different techniques to investigate stability. To show our idea clearly, we examine neutral stochastic delay differential equations with unbounded delay and linear neutral stochastic Volterra unbounded-delay-integro-differential equations.
基金Sponsored by HUST Foundation(0125011017)the National NSFC under grant(70671047)
文摘The stability of stochastic functional differential equation with Markovian switching was studied by several authors,but there was almost no work on the stability of the neutral stochastic functional differential equations with Markovian switching.The aim of this article is to close this gap.The authors establish Razumikhin-type theorem of the neutral stochastic functional differential equations with Markovian switching,and those without Markovian switching.
基金supported by the National Natural Science Foundation of China (No.60525303, 60604004, 60704009) Natural Science Foundationof Hebei Province, China (No.F2005000390, F2006000270)
文摘This paper considers the problem of delay-dependent exponential stability in mean square for stochastic systems with polytopic-type uncertainties and time-varying delay. Applying the descriptor model transformation and introducing free weighting matrices, a new type of Lyapunov-Krasovskii functional is constructed based on linear matrix inequalities （LMIs）, and some new delay-dependent criteria are obtained. These criteria include the delay-independent/rate- dependent and delay-dependent/rate-independent exponential stability criteria. These new criteria are less conservative than existing ones. Numerical examples demonstrate that these new criteria are effective and are an improvement over existing ones.
文摘The existence and uniqueness of solutions to backward stochastic differential equations with jumps and with unbounded stopping time as terminal under the non_Lipschitz condition are obtained. The convergence of solutions and the continuous dependence of solutions on parameters are also derived. Then the probabilistic interpretation of solutions to some kinds of quasi_linear elliptic type integro_differential equations is obtained.
文摘In this paper, the Razumikhin approach is applied to the study of both p-th moment and almost sure stability on a general decay for a class of impulsive stochastic functional differential systems with Markovian switching. Based on the Lyapunov-Razumikhin methods, some sufficient conditions are derived to check the stability of impulsive stochastic functional differential systems with Markovian switching. One numerical example is provided to demonstrate the effectiveness of the results.
基金Supported by National Social Science Fund of China(17BTJ023)
文摘Modeling log-mortality rates on O-U type processes and forecasting life expectancies are explored using U.S. data. In the classic Lee-Carter model of mortality, the time trend and the age-specific pattern of mortality over age group are linear, this is not the feature of mortality model. To avoid this disadvantage, O-U type processes will be used to model the log-mortality in this paper. In fact, this model is an AR(1) process, but with a nonlinear time drift term.Based on the mortality data of America from Human Mortality database(HMD), mortality projection consistently indicates a preference for mortality with O-U type processes over those with the classical Lee-Carter model. By means of this model, the low bounds of mortality rates at every age are given. Therefore, lengthening of maximum life expectancies span is estimated in this paper.
文摘In the paper, perturbed stochastic Volterra Equations with noise terms driven by series of independent scalar Wiener processes are considered. In the study, the resolvent approach to the equations under consideration is used. Sufficient conditions for the existence of strong solution to the class of perturbed stochastic Volterra Equations of convolution type are given. Regularity of stochastic convolution is supplied, as well.
基金Foundation item: Hubei University Youngth Foundations (099206).
文摘In this paper we prove the pathwise uniqueness of a kind of two-parameter Volterra type stochastic differential equations under the coefficients satisfy the non-Lipschitz conditions. We use a martingale formula in stead of Ito formula, which leads to simplicity the process of proof and extends the result to unbounded coefficients case.
基金Supported by the Leading Innovation Specialist Support Program of Guangdong Provincethe Science and Technology Planning Project of Ganzhou,No.202101074816the National Natural Science Foundation of China,No.82260501.
文摘BACKGROUND Type Ⅱ diabetes mellitus(T2DM)has been associated with increased risk of colon cancer(CC)and worse prognosis in patients with metastases.The effects of T2DM on postoperative chemoresistance rate(CRR)and long-term disease-free survival(DFS)and overall survival(OS)in patients with stage Ⅲ CC who receive curative resection remain controversial.AIM To investigate whether T2DM or glycemic control is associated with worse postoperative survival outcomes in stage Ⅲ CC.METHODS This retrospective cohort study included 278 patients aged 40-75 years who underwent surgery for stage Ⅲ CC from 2018 to 2021.Based on preoperative T2DM history,the patients were categorized into non-DM(n=160)and DM groups(n=118).The latter was further divided into well-controlled(n=73)and poorly controlled(n=45)groups depending on the status of glycemic control.DFS,OS,and CRR were compared between the groups and Cox regression analysis was used to identify risk factors.RESULTS Patients in the DM and non-DM groups demonstrated similar DFS,OS,and CRR(DFS:72.03%vs 78.75%,P=0.178;OS:81.36%vs 83.12%,P=0.638;CRR:14.41%vs 7.5%,P=0.063).Poorly controlled DM was associated with a significantly worse prognosis and higher CRR than well-controlled DM(DFS:62.22%vs 78.07%,P=0.021;OS:71.11%vs 87.67%,P=0.011;CRR:24.40%vs 8.22%,P=0.015).High preoperative fasting plasma glucose[DFS:Hazard ratio(HR)=2.684,P<0.001;OS:HR=2.105,P=0.019;CRR:HR=2.214,P=0.005]and glycosylated hemoglobin levels(DFS:HR=2.344,P=0.006;OS:HR=2.119,P=0.021;CRR:HR=2.449,P=0.009)indicated significantly poor prognosis and high CRR,while T2DM history did not(DFS:HR=1.178,P=0.327;OS:HR=0.933,P=0.739;CRR:HR=0.997,P=0.581).CONCLUSION Increased preoperative fasting plasma glucose and glycosylated hemoglobin levels,but not T2DM history,were identified as risk factors associated with poor postoperative outcomes and high CRR in patients with stage Ⅲ CC.
文摘This paper mainly tends to utilize Razumikhin-type theorems to investigate p-th moment stability for a class of stochastic switching nonlinear systems with delay. Based on the Lyapunov-Razumik- hin methods, some sufficient conditions are derived to check the stability of stochastic switching nonlinear systems with delay. One numerical example is provided to demonstrate the effectiveness of the results.
基金Supported by Science and Technology Development Foundation of Shanghai Education Commission(No.02JG05044)
文摘For Duffle-Epstein type Backward Stochastic Differential Equations, the comparison theorem is proved. Based on the comparison theorem, by monotone iterative technique, the existence of the minimal and maximal solutions of the equations are proved.
基金Supported by The National Natural Science Foundation of China,No.82350127 and No.82241013the Shanghai Natural Science Foundation,No.20ZR1411600+2 种基金the Shanghai Shenkang Hospital Development Center,No.SHDC2020CR4039the Bethune Ethicon Excellent Surgery Foundation,No.CESS2021TC04Xuhui District Medical Research Project of Shanghai,No.SHXH201805.
文摘BACKGROUND Transforming growth factor-β(TGF-β)superfamily plays an important role in tumor progression and metastasis.Activin A receptor type 1C(ACVR1C)is a TGF-βtype I receptor that is involved in tumorigenesis through binding to dif-ferent ligands.AIM To evaluate the correlation between single nucleotide polymorphisms(SNPs)of ACVR1C and susceptibility to esophageal squamous cell carcinoma(ESCC)in Chinese Han population.METHODS In this hospital-based cohort study,1043 ESCC patients and 1143 healthy controls were enrolled.Five SNPs(rs4664229,rs4556933,rs77886248,rs77263459,rs6734630)of ACVR1C were assessed by the ligation detection reaction method.Hardy-Weinberg equilibrium test,genetic model analysis,stratified analysis,linkage disequi-librium test,and haplotype analysis were conducted.RESULTS Participants carrying ACVR1C rs4556933 GA mutant had significantly decreased risk of ESCC,and those with rs77886248 TA mutant were related with higher risk,especially in older male smokers.In the haplotype analysis,ACVR1C Trs4664229Ars4556933Trs77886248Crs77263459Ars6734630 increased risk of ESCC,while Trs4664229Grs4556933Trs77886248Crs77263459Ars6734630 was associated with lower susceptibility to ESCC.CONCLUSION ACVR1C rs4556933 and rs77886248 SNPs were associated with the susceptibility to ESCC,which could provide a potential target for early diagnosis and treatment of ESCC in Chinese Han population.
基金the Scientific Research Foundation of State Education Ministry for the Returned Overseas Scholars(No.14Z102050011)
文摘This paper develops a Smolyak-type sparse-grid stochastic collocation method(SGSCM) for uncertainty quantification of nonlinear stochastic dynamic equations.The solution obtained by the method is a linear combination of tensor product formulas for multivariate polynomial interpolation.By choosing the collocation point sets to coincide with cubature point sets of quadrature rules,we derive quadrature formulas to estimate the expectations of the solution.The method does not suffer from the curse of dimensionality in the sense that the computational cost does not increase exponentially with the number of input random variables.Numerical analysis of a nonlinear elastic oscillator subjected to a discretized band-limited white noise process demonstrates the computational efficiency and accuracy of the developed method.
基金This research received funding support from the NSRF via the Program Management Unit for Human Resources&Institutional Development,Research and Innovation[Grant Number B05F650018].
文摘The current research aims to implement the numerical resultsfor the Holling third kind of functional response delay differential modelutilizing a stochastic framework based on Levenberg-Marquardt backpropagationneural networks (LVMBPNNs). The nonlinear model depends uponthree dynamics, prey, predator, and the impact of the recent past. Threedifferent cases based on the delay differential system with the Holling 3^(rd) type of the functional response have been used to solve through the proposedLVMBPNNs solver. The statistic computing framework is provided byselecting 12%, 11%, and 77% for training, testing, and verification. Thirteennumbers of neurons have been used based on the input, hidden, and outputlayers structure for solving the delay differential model with the Holling 3rdtype of functional response. The correctness of the proposed stochastic schemeis observed by using the comparison performances of the proposed and referencedata-based Adam numerical results. The authentication and precision ofthe proposed solver are approved by analyzing the state transitions, regressionperformances, correlation actions, mean square error, and error histograms.
