Background: Accurate estimation of the glomerular filtration rate (GFR) and staging of chronic kidney disease (CKD) are important. Currently, there is no research on the differences in several estimated GFR equations ...Background: Accurate estimation of the glomerular filtration rate (GFR) and staging of chronic kidney disease (CKD) are important. Currently, there is no research on the differences in several estimated GFR equations for staging CKD in a large sample of centenarians. Thus, this study aimed to investigate the differences in CKD staging with the most commonly used equations and to analyze sources of discrepancy. Methods: A total of 966 centenarians were enrolled in this study from June 2014 to December 2016 in Hainan province, China. The GFR with the Modification of Diet in Renal Disease (MDRD), Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) and Berlin Initiative Study 1 (BIS1) equations were estimated. Agreement between these equations was investigated with the k statistic and Bland-Altman plots. Sources of discrepancy were investigated by partial correlation analysis. Results: The k values of the MDRD and CKD-EPI equations, MDRD and BIS1 equations, and CKD-EPI and BIS1 equations were 0.610, 0.253, and 0.381, respectively. Serum creatinine (Scr) explained 10.96%, 41.60% and 17.06% of the variability in these three comparisons, respectively. Serum uric acid (SUA) explained 3.65% and 5.43% of the variability in the first 2 comparisons, respectively. Gender was associated with significant differences in these 3 comparisons (P<0.001). Conclusions: The strengths of agreement between the MDRD and CKD-EPI equations were substantial, but those between the MDRD and BIS 1 equations and the CKD-EPI and BIS 1 equations were fair. The difference in CKD staging of the first 2 comparisons strongly depended on Scr, SUA and gender, and that of CKD-EPI and BIS1 equations strongly depended on Scr and gender. The incidence at various stages of CKD staging was quite different. Thus, a new equation that is more suitable for the elderly needs to be built in the future.展开更多
This paper is mainly concerned with the solutions to both forward and backward mean-field stochastic partial differential equation and the corresponding optimal control problem for mean-field stochastic partial differ...This paper is mainly concerned with the solutions to both forward and backward mean-field stochastic partial differential equation and the corresponding optimal control problem for mean-field stochastic partial differential equation. The authors first prove the continuous dependence theorems of forward and backward mean-field stochastic partial differential equations and show the existence and uniqueness of solutions to them. Then they establish necessary and sufficient optimality conditions of the control problem in the form of Pontryagin’s maximum principles. To illustrate the theoretical results, the authors apply stochastic maximum principles to study the infinite-dimensional linear-quadratic control problem of mean-field type. Further, an application to a Cauchy problem for a controlled stochastic linear PDE of mean-field type is studied.展开更多
In a recent article(Commun. Theor. Phys. 67(2017) 207), three(2+1)-dimensional equations — KP equation, cylindrical KP equation and spherical KP equation, have been reduced to the same Kd V equation by using differen...In a recent article(Commun. Theor. Phys. 67(2017) 207), three(2+1)-dimensional equations — KP equation, cylindrical KP equation and spherical KP equation, have been reduced to the same Kd V equation by using different transformation of variables, respectively. In this short note, by adding an adjustment item to original transformation, three more general transformation of variables corresponding to above three equations have been given.Substituting the solutions of the Kd V equation into our transformation of variables, more new exact solutions of the three(2+1)-dimensional equations can be obtained.展开更多
In 1805, Thomas Young was the first to propose an equation(Young’s equation) to predict the value of the equilibrium contact angle of a liquid on a solid. On the basis of our predecessors, we further clarify that the...In 1805, Thomas Young was the first to propose an equation(Young’s equation) to predict the value of the equilibrium contact angle of a liquid on a solid. On the basis of our predecessors, we further clarify that the contact angle in Young’s equation refers to the super-nano contact angle. Whether the equation is applicable to nanoscale systems remains an open question. Zhu et al. [College Phys. 4 7(1985)] obtained the most simple and convenient approximate formula, known as the Zhu–Qian approximate formula of Young’s equation. Here, using molecular dynamics simulation, we test its applicability for nanodrops. Molecular dynamics simulations are performed on argon liquid cylinders placed on a solid surface under a temperature of 90 K, using Lennard–Jones potentials for the interaction between liquid molecules and between a liquid molecule and a solid molecule with the variable coefficient of strength a. Eight values of a between 0.650 and 0.825 are used. By comparison of the super-nano contact angles obtained from molecular dynamics simulation and the Zhu–Qian approximate formula of Young’s equation, we find that it is qualitatively applicable for nanoscale systems.展开更多
Based on the Hirota bilinear operators and their generalized bilinear derivatives, we formulate two new(2+1)-dimensional nonlinear partial differential equations, which possess lumps. One of the new nonlinear differen...Based on the Hirota bilinear operators and their generalized bilinear derivatives, we formulate two new(2+1)-dimensional nonlinear partial differential equations, which possess lumps. One of the new nonlinear differential equations includes the generalized Calogero-Bogoyavlenskii-Schiff equation and the generalized BogoyavlenskyKonopelchenko equation as particular examples, and the other has the same bilinear form with different Dp-operators.A class explicit lump solutions of the new nonlinear differential equation is constructed by using the Hirota bilinear approaches. A specific case of the presented lump solution is plotted to shed light on the charateristics of the lump.展开更多
We present some exact integrability cases of the extended Liénard equation y′′+ f(y)(y′)n +k(y)(y′)m + g(y)y′+ h(y) = 0, with n > 0 and m > 0 arbitrary constants, while f(y), k(y), g(y), and h(y) are a...We present some exact integrability cases of the extended Liénard equation y′′+ f(y)(y′)n +k(y)(y′)m + g(y)y′+ h(y) = 0, with n > 0 and m > 0 arbitrary constants, while f(y), k(y), g(y), and h(y) are arbitrary functions. The solutions are obtained by transforming the equation Liénard equation to an equivalent first kind first order Abel type equation given bydv/dy= f(y)v3-n+ k(y)v3-m+ g(y)v2+ h(y)v3, with v = 1/y′.As a first step in our study we obtain three integrability cases of the extended quadratic-cubic Liénard equation,corresponding to n = 2 and m = 3, by assuming that particular solutions of the associated Abel equation are known. Under this assumption the general solutions of the Abel and Liénard equations with coefficients satisfying some differential conditions can be obtained in an exact closed form. With the use of the Chiellini integrability condition, we show that if a particular solution of the Abel equation is known, the general solution of the extended quadratic cubic Liénard equation can be obtained by quadratures. The Chiellini integrability condition is extended to generalized Abel equations with g(y) ≡ 0 and h(y) ≡ 0, and arbitrary n and m, thus allowing to obtain the general solution of the corresponding Liénard equation. The application of the generalized Chiellini condition to the case of the reduced Riccati equation is also considered.展开更多
The tunneling current in a graphene nanoribbon tunnel field effect transistor(GNR-TFET) has been quantum mechanically modeled. The tunneling current in the GNR-TFET was compared based on calculations of the Dirac-like...The tunneling current in a graphene nanoribbon tunnel field effect transistor(GNR-TFET) has been quantum mechanically modeled. The tunneling current in the GNR-TFET was compared based on calculations of the Dirac-like equation and Schrodinger’s equation. To calculate the electron transmittance, a numerical approach-namely the transfer matrix method(TMM)-was employed and the Launder formula was used to compute the tunneling current. The results suggest that the tunneling currents that were calculated using both equations have similar characteristics for the same parameters, even though they have different values. The tunneling currents that were calculated by applying the Dirac-like equation were lower than those calculated using Schrodinger’s equation.展开更多
This is a survey on the strong uniqueness of the solutions to stochastic partial differential equations (SPDEs) related to two measure-valued processes: superprocess and Fleming-Viot process which are given as rescali...This is a survey on the strong uniqueness of the solutions to stochastic partial differential equations (SPDEs) related to two measure-valued processes: superprocess and Fleming-Viot process which are given as rescaling limits of population biology models. We summarize recent results for Konno-Shiga-Reimers1 and Mytnik's SPDEs, and their related distribution-function-valued SPDEs.展开更多
This article is devoted to the study of fully nonlinear stochastic Hamilton-Jacobi (HJ) equations for the optimal stochastic control problem of ordinary differential equations with random coefficients. Under the stand...This article is devoted to the study of fully nonlinear stochastic Hamilton-Jacobi (HJ) equations for the optimal stochastic control problem of ordinary differential equations with random coefficients. Under the standard Lipschitz continuity assumptions on the coefficients, the value function is proved to be the unique viscosity solution of the associated stochastic HJ equation.展开更多
This article attempts to give a short survey of recent progress on a class of elementary stochastic partial differential equations (for example, stochastic heat equations) driven by Gaussian noise of various covarianc...This article attempts to give a short survey of recent progress on a class of elementary stochastic partial differential equations (for example, stochastic heat equations) driven by Gaussian noise of various covariance structures. The focus is on the existence and uniqueness of the classical (square integrable) solution (mild solution, weak solution). It is also concerned with the Feynman-Kac formula for the solution;Feynman-Kac formula for the moments of the solution;and their applications to the asymptotic moment bounds of the solution. It also briefly touches the exact asymptotics of the moments of the solution.展开更多
Considered here is the periodic Cauchy problem for an integrable Hunter-Saxton equation with a dispersive term. Firstly, we derive a precise blow-up criterion of strong solutions to the equation. Secondly, sufficient ...Considered here is the periodic Cauchy problem for an integrable Hunter-Saxton equation with a dispersive term. Firstly, we derive a precise blow-up criterion of strong solutions to the equation. Secondly, sufficient conditions guaranteeing the development of breaking waves in finite time are demonstrated by applying some conservative quantities and the method of characteristics, respectively. Finally, the exact blow-up rate is determined.展开更多
A non-local abstract Cauchy problem with a singular integral is studied, which is a closed system of two evolution equations for a real-valued function and a function-valued function. By proposing an appropriate Banac...A non-local abstract Cauchy problem with a singular integral is studied, which is a closed system of two evolution equations for a real-valued function and a function-valued function. By proposing an appropriate Banach space, the well-posedness of the evolution system is proved under some boundedness and smoothness conditions on the coefficient functions. Furthermore, an isomorphism is established to extend the result to a partial integro-differential equation with a singular convolution kernel, which is a generalized form of the stationary Wigner equation. Our investigation considerably improves the understanding of the open problem concerning the well-posedness of the stationary Wigner equation with in ow boundary conditions.展开更多
The main purpose of this paper is to obtain the wave solutions of conformable time fractional Boussinesq–Whitham–Broer–Kaup equation arising as a model of shallow water waves. For this aim, the authors employed aux...The main purpose of this paper is to obtain the wave solutions of conformable time fractional Boussinesq–Whitham–Broer–Kaup equation arising as a model of shallow water waves. For this aim, the authors employed auxiliary equation method which is based on a nonlinear ordinary differential equation. By using conformable wave transform and chain rule, a nonlinear fractional partial differential equation is converted to a nonlinear ordinary differential equation. This is a significant impact because neither Caputo definition nor Riemann–Liouville definition satisfies the chain rule. While the exact solutions of the fractional partial derivatives cannot be obtained due to the existing drawbacks of Caputo or Riemann–Liouville definitions, the reliable solutions can be achieved for the equations defined by conformable fractional derivatives.展开更多
The path independence of additive functionals for stochastic differential equations (SDEs) driven by the G-Brownian motion is characterized by the nonlinear partial differential equations. The main result generalizes ...The path independence of additive functionals for stochastic differential equations (SDEs) driven by the G-Brownian motion is characterized by the nonlinear partial differential equations. The main result generalizes the existing ones for SDEs driven by the standard Brownian motion.展开更多
Boreal forests are important carbon sinks and have tremendous potential to mitigate climate change. Aboveground biomass of Siberian larch(Larix sibirica Ledeb.) stands in the Altay Mountains, Northwest China was studi...Boreal forests are important carbon sinks and have tremendous potential to mitigate climate change. Aboveground biomass of Siberian larch(Larix sibirica Ledeb.) stands in the Altay Mountains, Northwest China was studied and allometric equations that are related to the biomass of aboveground components using diameter at breast height(DBH) or both DBH and height(H) as independent variables for L. sibirica trees were derived in this paper. A linear simultaneous equation system by using either DBH or both DBH and H(DBH&H) indices, was used to ensure additivity of the biomass of individual tree components, and was fitted for L. sibirica. Model performance was validated using the jackknifing test. Results indicate that the goodness-of-fit for the regressions was lowest for the needles(R~2 ranging from 0.696 to 0.756), and highest for the stem wood(R~2 ranging from 0.984 to 0.997) and the aggregated biomass components(R~2 ranging from 0.994 to 0.995). The coefficient of determination for each component was only marginally improved in terms of model fit and performance in the biomass equations that used DBH&H as the independent variables compared to that used DBH as the independent variable, and needles yielded an even worse fit. Stem biomass accounted for the largest proportion(87%) of the aboveground biomass. Based on the additive equations that used DBH as the single predicitor in this study, the mean aboveground carbon stock density and the carbon storage values of L. sibirica forests were 74.07 Mg C/hm~2 and 30.69 Tg C, respectively, in the Altay Mountains. Empirical comparisons of published equations for the same species growing in the Altay Mountains of Mongolia were also presented. The mean aboveground carbon stock density estimated for L. sibirica forests was higher in the Chinese Altay Mountains than in the Mongolian Altay Mountains(66.00 Mg C/hm~2).展开更多
For solid-fluid interaction,one of the phase-density equations in diffuse interface models is degenerated to a“0=0”equation when the volume fraction of a certain phase takes the value of zero or unity.This is becaus...For solid-fluid interaction,one of the phase-density equations in diffuse interface models is degenerated to a“0=0”equation when the volume fraction of a certain phase takes the value of zero or unity.This is because the conservative variables in phasedensity equations include volume fractions.The degeneracy can be avoided by adding an artificial quantity of another material into the pure phase.However,nonphysical waves,such as shear waves in fluids,are introduced by the artificial treatment.In this paper,a transport diffuse interface model,which is able to treat zero/unity volume fractions,is presented for solid-fluid interaction.In the proposed model,a new formulation for phase densities is derived,which is unrelated to volume fractions.Consequently,the new model is able to handle zero/unity volume fractions,and nonphysical waves caused by artificial volume fractions are prevented.One-dimensional and two-dimensional numerical tests demonstrate that more accurate results can be obtained by the proposed model.展开更多
This paper considers a class of discontinuous Galerkin method,which is constructed by Wong-Zakai approximation with the orthonormal Fourier basis,for numerically solving nonautonomous Stratonovich stochastic delay dif...This paper considers a class of discontinuous Galerkin method,which is constructed by Wong-Zakai approximation with the orthonormal Fourier basis,for numerically solving nonautonomous Stratonovich stochastic delay differential equations.We prove that the discontinuous Galerkin scheme is strongly convergent:globally stable and analogously asymptotically stable in mean square sense.In addition,this method can be easily extended to solve nonautonomous Stratonovich stochastic pantograph differential equations.Numerical tests indicate that the method has first-order and half-order strong mean square convergence,when the diffusion term is without delay and with delay,respectively.展开更多
In this paper,we show the existence of weak solutions for a higher order nonlinear elliptic equation.Our main method is to show that the evolution operator satis es the xed point theorem for Banach semilattice.
The purpose of this paper is to propose a synthesis method of parametric sensitivity constrained linear quadratic (SCLQ) controller for an uncertain linear time invariant (LTI) system. System sensitivity to parameter ...The purpose of this paper is to propose a synthesis method of parametric sensitivity constrained linear quadratic (SCLQ) controller for an uncertain linear time invariant (LTI) system. System sensitivity to parameter variation is handled through an additional quadratic trajectory parametric sensitivity term in the standard LQ criterion to be minimized. The main purpose here is to find a suboptimal linear quadratic control taking explicitly into account the parametric uncertainties. The paper main contribution is threefold: 1) A descriptor system approach is used to show that the underlying singular linear-quadratic optimal control problem leads to a non-standard Riccati equation. 2) A solution to the proposed control problem is then given based on a connection to the so-called Lur'e matrix equations. 3) A synthesis method of multiple parametric SCLQ controllers is proposed to cover the whole parametric uncertainty while degrading as less as possible the intrinsic robustness properties of each local linear quadratic controller. Some examples are presented in order to illustrate the effectiveness of the approach.展开更多
It has been realized that the 4Rs(repair,repopulation,redistribution,and reoxygenation)would affect the result of cell irradiation,and thus radiation treatment.The 4Rs each occurs at different dose rates,usually very ...It has been realized that the 4Rs(repair,repopulation,redistribution,and reoxygenation)would affect the result of cell irradiation,and thus radiation treatment.The 4Rs each occurs at different dose rates,usually very low dose rates.Depending on the dose rate used for treatment,the corresponding R should be included in the linear-quadratic equation(LQ)and biological effective dose(BED)calculation.For low dose rate brachytherapy(LDR)especially permanent implant,all the 4Rs should be included in LQ for BED calculation.The 4Rs,especially repair and repopulation,play a critical role in dose fractionation.Various dose fractionation schemes such as hyperfractionation and hypofractionation are determined in consideration of the 4Rs.Stereotactic radiation therapy uses hypofractionation with high fractional doses and combine with high accuracy target localization techniques to achieve high local control rates compared to conventional dose fractionation schemes.The 4Rs have been taken into account for LDR and permanent implant.Recently,LQ for permanent implant brachytherapy has been modified to include all the 4Rs for gynecological malignancy 131 Cs permanent implants.Including the 4Rs in radiation therapy has significantly improved the effectiveness and efficiency of radiation therapy for cancer treatment.展开更多
基金National Key R&D Program of China (No.2016YFC1305500)Key Research and Development Program of Hainan (Nos.ZDYF2016135 and ZDYF2017095)+2 种基金the National Natural Science Foundation of China (Nos.61471399,61671479,and 81670663)the National Key Research and Development Program (No. 2016YFC1305404)the Joint Funds of National Natural Science Foundation of China and Henan province (No.U1604284).
文摘Background: Accurate estimation of the glomerular filtration rate (GFR) and staging of chronic kidney disease (CKD) are important. Currently, there is no research on the differences in several estimated GFR equations for staging CKD in a large sample of centenarians. Thus, this study aimed to investigate the differences in CKD staging with the most commonly used equations and to analyze sources of discrepancy. Methods: A total of 966 centenarians were enrolled in this study from June 2014 to December 2016 in Hainan province, China. The GFR with the Modification of Diet in Renal Disease (MDRD), Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) and Berlin Initiative Study 1 (BIS1) equations were estimated. Agreement between these equations was investigated with the k statistic and Bland-Altman plots. Sources of discrepancy were investigated by partial correlation analysis. Results: The k values of the MDRD and CKD-EPI equations, MDRD and BIS1 equations, and CKD-EPI and BIS1 equations were 0.610, 0.253, and 0.381, respectively. Serum creatinine (Scr) explained 10.96%, 41.60% and 17.06% of the variability in these three comparisons, respectively. Serum uric acid (SUA) explained 3.65% and 5.43% of the variability in the first 2 comparisons, respectively. Gender was associated with significant differences in these 3 comparisons (P<0.001). Conclusions: The strengths of agreement between the MDRD and CKD-EPI equations were substantial, but those between the MDRD and BIS 1 equations and the CKD-EPI and BIS 1 equations were fair. The difference in CKD staging of the first 2 comparisons strongly depended on Scr, SUA and gender, and that of CKD-EPI and BIS1 equations strongly depended on Scr and gender. The incidence at various stages of CKD staging was quite different. Thus, a new equation that is more suitable for the elderly needs to be built in the future.
基金supported by the National Natural Science Foundation of China(Nos.11871121,11471079,11301177)the Natural Science Foundation of Zhejiang Province for Distinguished Young Scholar(No.LR15A010001).
文摘This paper is mainly concerned with the solutions to both forward and backward mean-field stochastic partial differential equation and the corresponding optimal control problem for mean-field stochastic partial differential equation. The authors first prove the continuous dependence theorems of forward and backward mean-field stochastic partial differential equations and show the existence and uniqueness of solutions to them. Then they establish necessary and sufficient optimality conditions of the control problem in the form of Pontryagin’s maximum principles. To illustrate the theoretical results, the authors apply stochastic maximum principles to study the infinite-dimensional linear-quadratic control problem of mean-field type. Further, an application to a Cauchy problem for a controlled stochastic linear PDE of mean-field type is studied.
基金Supported by the National Natural Science Foundation of China under Grant No.11771381.
文摘In a recent article(Commun. Theor. Phys. 67(2017) 207), three(2+1)-dimensional equations — KP equation, cylindrical KP equation and spherical KP equation, have been reduced to the same Kd V equation by using different transformation of variables, respectively. In this short note, by adding an adjustment item to original transformation, three more general transformation of variables corresponding to above three equations have been given.Substituting the solutions of the Kd V equation into our transformation of variables, more new exact solutions of the three(2+1)-dimensional equations can be obtained.
基金the National Natural Science Foundation of China(Grant No.11072242)the Key Scientific Studies Program of Hebei Province Higher Education Institute,China(Grant No.ZD2018301)Cangzhou National Science Foundation,China(Grant No.177000001).
文摘In 1805, Thomas Young was the first to propose an equation(Young’s equation) to predict the value of the equilibrium contact angle of a liquid on a solid. On the basis of our predecessors, we further clarify that the contact angle in Young’s equation refers to the super-nano contact angle. Whether the equation is applicable to nanoscale systems remains an open question. Zhu et al. [College Phys. 4 7(1985)] obtained the most simple and convenient approximate formula, known as the Zhu–Qian approximate formula of Young’s equation. Here, using molecular dynamics simulation, we test its applicability for nanodrops. Molecular dynamics simulations are performed on argon liquid cylinders placed on a solid surface under a temperature of 90 K, using Lennard–Jones potentials for the interaction between liquid molecules and between a liquid molecule and a solid molecule with the variable coefficient of strength a. Eight values of a between 0.650 and 0.825 are used. By comparison of the super-nano contact angles obtained from molecular dynamics simulation and the Zhu–Qian approximate formula of Young’s equation, we find that it is qualitatively applicable for nanoscale systems.
基金the National Natural Science Foundation of China under Grant Nos.11775146 and 11472177National Science Foundation under Grant No.DMS-1664561.
文摘Based on the Hirota bilinear operators and their generalized bilinear derivatives, we formulate two new(2+1)-dimensional nonlinear partial differential equations, which possess lumps. One of the new nonlinear differential equations includes the generalized Calogero-Bogoyavlenskii-Schiff equation and the generalized BogoyavlenskyKonopelchenko equation as particular examples, and the other has the same bilinear form with different Dp-operators.A class explicit lump solutions of the new nonlinear differential equation is constructed by using the Hirota bilinear approaches. A specific case of the presented lump solution is plotted to shed light on the charateristics of the lump.
文摘We present some exact integrability cases of the extended Liénard equation y′′+ f(y)(y′)n +k(y)(y′)m + g(y)y′+ h(y) = 0, with n > 0 and m > 0 arbitrary constants, while f(y), k(y), g(y), and h(y) are arbitrary functions. The solutions are obtained by transforming the equation Liénard equation to an equivalent first kind first order Abel type equation given bydv/dy= f(y)v3-n+ k(y)v3-m+ g(y)v2+ h(y)v3, with v = 1/y′.As a first step in our study we obtain three integrability cases of the extended quadratic-cubic Liénard equation,corresponding to n = 2 and m = 3, by assuming that particular solutions of the associated Abel equation are known. Under this assumption the general solutions of the Abel and Liénard equations with coefficients satisfying some differential conditions can be obtained in an exact closed form. With the use of the Chiellini integrability condition, we show that if a particular solution of the Abel equation is known, the general solution of the extended quadratic cubic Liénard equation can be obtained by quadratures. The Chiellini integrability condition is extended to generalized Abel equations with g(y) ≡ 0 and h(y) ≡ 0, and arbitrary n and m, thus allowing to obtain the general solution of the corresponding Liénard equation. The application of the generalized Chiellini condition to the case of the reduced Riccati equation is also considered.
基金supported by Hibah Penelitian Berbasi Kompetensi 2018 RISTEKDIKTI Republic of Indonesia.
文摘The tunneling current in a graphene nanoribbon tunnel field effect transistor(GNR-TFET) has been quantum mechanically modeled. The tunneling current in the GNR-TFET was compared based on calculations of the Dirac-like equation and Schrodinger’s equation. To calculate the electron transmittance, a numerical approach-namely the transfer matrix method(TMM)-was employed and the Launder formula was used to compute the tunneling current. The results suggest that the tunneling currents that were calculated using both equations have similar characteristics for the same parameters, even though they have different values. The tunneling currents that were calculated by applying the Dirac-like equation were lower than those calculated using Schrodinger’s equation.
基金SUST startup fund 28/Y01286120, NSF of Ningxia (2018AAC03245), NSFC (11771018)First-Class Disciplines Foundation Ningxia (NXYLXK2017B09).
文摘This is a survey on the strong uniqueness of the solutions to stochastic partial differential equations (SPDEs) related to two measure-valued processes: superprocess and Fleming-Viot process which are given as rescaling limits of population biology models. We summarize recent results for Konno-Shiga-Reimers1 and Mytnik's SPDEs, and their related distribution-function-valued SPDEs.
基金the National Science and Engineering Research Council of Canada (NSERC)the start-up funds from the University of Calgary.
文摘This article is devoted to the study of fully nonlinear stochastic Hamilton-Jacobi (HJ) equations for the optimal stochastic control problem of ordinary differential equations with random coefficients. Under the standard Lipschitz continuity assumptions on the coefficients, the value function is proved to be the unique viscosity solution of the associated stochastic HJ equation.
基金an NSERC grant and a startup fund of University of Alberta.
文摘This article attempts to give a short survey of recent progress on a class of elementary stochastic partial differential equations (for example, stochastic heat equations) driven by Gaussian noise of various covariance structures. The focus is on the existence and uniqueness of the classical (square integrable) solution (mild solution, weak solution). It is also concerned with the Feynman-Kac formula for the solution;Feynman-Kac formula for the moments of the solution;and their applications to the asymptotic moment bounds of the solution. It also briefly touches the exact asymptotics of the moments of the solution.
基金Supported by the National Natural Science Foundation of China (Grant No. 11561059)Tianshui Normal University ‘QinglanTalents’ Project.
文摘Considered here is the periodic Cauchy problem for an integrable Hunter-Saxton equation with a dispersive term. Firstly, we derive a precise blow-up criterion of strong solutions to the equation. Secondly, sufficient conditions guaranteeing the development of breaking waves in finite time are demonstrated by applying some conservative quantities and the method of characteristics, respectively. Finally, the exact blow-up rate is determined.
基金National Natural Science Foundation of China (Grant Nos. 1167103& 91630130, 91434201, 11421101).
文摘A non-local abstract Cauchy problem with a singular integral is studied, which is a closed system of two evolution equations for a real-valued function and a function-valued function. By proposing an appropriate Banach space, the well-posedness of the evolution system is proved under some boundedness and smoothness conditions on the coefficient functions. Furthermore, an isomorphism is established to extend the result to a partial integro-differential equation with a singular convolution kernel, which is a generalized form of the stationary Wigner equation. Our investigation considerably improves the understanding of the open problem concerning the well-posedness of the stationary Wigner equation with in ow boundary conditions.
文摘The main purpose of this paper is to obtain the wave solutions of conformable time fractional Boussinesq–Whitham–Broer–Kaup equation arising as a model of shallow water waves. For this aim, the authors employed auxiliary equation method which is based on a nonlinear ordinary differential equation. By using conformable wave transform and chain rule, a nonlinear fractional partial differential equation is converted to a nonlinear ordinary differential equation. This is a significant impact because neither Caputo definition nor Riemann–Liouville definition satisfies the chain rule. While the exact solutions of the fractional partial derivatives cannot be obtained due to the existing drawbacks of Caputo or Riemann–Liouville definitions, the reliable solutions can be achieved for the equations defined by conformable fractional derivatives.
文摘The path independence of additive functionals for stochastic differential equations (SDEs) driven by the G-Brownian motion is characterized by the nonlinear partial differential equations. The main result generalizes the existing ones for SDEs driven by the standard Brownian motion.
基金financially supported by the National High-Tech Research and Development Plan of China(2013AA122003).
文摘Boreal forests are important carbon sinks and have tremendous potential to mitigate climate change. Aboveground biomass of Siberian larch(Larix sibirica Ledeb.) stands in the Altay Mountains, Northwest China was studied and allometric equations that are related to the biomass of aboveground components using diameter at breast height(DBH) or both DBH and height(H) as independent variables for L. sibirica trees were derived in this paper. A linear simultaneous equation system by using either DBH or both DBH and H(DBH&H) indices, was used to ensure additivity of the biomass of individual tree components, and was fitted for L. sibirica. Model performance was validated using the jackknifing test. Results indicate that the goodness-of-fit for the regressions was lowest for the needles(R~2 ranging from 0.696 to 0.756), and highest for the stem wood(R~2 ranging from 0.984 to 0.997) and the aggregated biomass components(R~2 ranging from 0.994 to 0.995). The coefficient of determination for each component was only marginally improved in terms of model fit and performance in the biomass equations that used DBH&H as the independent variables compared to that used DBH as the independent variable, and needles yielded an even worse fit. Stem biomass accounted for the largest proportion(87%) of the aboveground biomass. Based on the additive equations that used DBH as the single predicitor in this study, the mean aboveground carbon stock density and the carbon storage values of L. sibirica forests were 74.07 Mg C/hm~2 and 30.69 Tg C, respectively, in the Altay Mountains. Empirical comparisons of published equations for the same species growing in the Altay Mountains of Mongolia were also presented. The mean aboveground carbon stock density estimated for L. sibirica forests was higher in the Chinese Altay Mountains than in the Mongolian Altay Mountains(66.00 Mg C/hm~2).
基金the National Natural Science Foundation of China(Nos.11702029,11771054,U1730118,91852207,and 11801036)the China Postdoctoral Science Foundation(No.2016M600967).
文摘For solid-fluid interaction,one of the phase-density equations in diffuse interface models is degenerated to a“0=0”equation when the volume fraction of a certain phase takes the value of zero or unity.This is because the conservative variables in phasedensity equations include volume fractions.The degeneracy can be avoided by adding an artificial quantity of another material into the pure phase.However,nonphysical waves,such as shear waves in fluids,are introduced by the artificial treatment.In this paper,a transport diffuse interface model,which is able to treat zero/unity volume fractions,is presented for solid-fluid interaction.In the proposed model,a new formulation for phase densities is derived,which is unrelated to volume fractions.Consequently,the new model is able to handle zero/unity volume fractions,and nonphysical waves caused by artificial volume fractions are prevented.One-dimensional and two-dimensional numerical tests demonstrate that more accurate results can be obtained by the proposed model.
基金the National Natural Science Foundation of China(No.11671343).
文摘This paper considers a class of discontinuous Galerkin method,which is constructed by Wong-Zakai approximation with the orthonormal Fourier basis,for numerically solving nonautonomous Stratonovich stochastic delay differential equations.We prove that the discontinuous Galerkin scheme is strongly convergent:globally stable and analogously asymptotically stable in mean square sense.In addition,this method can be easily extended to solve nonautonomous Stratonovich stochastic pantograph differential equations.Numerical tests indicate that the method has first-order and half-order strong mean square convergence,when the diffusion term is without delay and with delay,respectively.
基金The Key Project of Jilin University of Finance and Economics(2018Z02)and the NSF(11701209)of China.
文摘In this paper,we show the existence of weak solutions for a higher order nonlinear elliptic equation.Our main method is to show that the evolution operator satis es the xed point theorem for Banach semilattice.
文摘The purpose of this paper is to propose a synthesis method of parametric sensitivity constrained linear quadratic (SCLQ) controller for an uncertain linear time invariant (LTI) system. System sensitivity to parameter variation is handled through an additional quadratic trajectory parametric sensitivity term in the standard LQ criterion to be minimized. The main purpose here is to find a suboptimal linear quadratic control taking explicitly into account the parametric uncertainties. The paper main contribution is threefold: 1) A descriptor system approach is used to show that the underlying singular linear-quadratic optimal control problem leads to a non-standard Riccati equation. 2) A solution to the proposed control problem is then given based on a connection to the so-called Lur'e matrix equations. 3) A synthesis method of multiple parametric SCLQ controllers is proposed to cover the whole parametric uncertainty while degrading as less as possible the intrinsic robustness properties of each local linear quadratic controller. Some examples are presented in order to illustrate the effectiveness of the approach.
文摘It has been realized that the 4Rs(repair,repopulation,redistribution,and reoxygenation)would affect the result of cell irradiation,and thus radiation treatment.The 4Rs each occurs at different dose rates,usually very low dose rates.Depending on the dose rate used for treatment,the corresponding R should be included in the linear-quadratic equation(LQ)and biological effective dose(BED)calculation.For low dose rate brachytherapy(LDR)especially permanent implant,all the 4Rs should be included in LQ for BED calculation.The 4Rs,especially repair and repopulation,play a critical role in dose fractionation.Various dose fractionation schemes such as hyperfractionation and hypofractionation are determined in consideration of the 4Rs.Stereotactic radiation therapy uses hypofractionation with high fractional doses and combine with high accuracy target localization techniques to achieve high local control rates compared to conventional dose fractionation schemes.The 4Rs have been taken into account for LDR and permanent implant.Recently,LQ for permanent implant brachytherapy has been modified to include all the 4Rs for gynecological malignancy 131 Cs permanent implants.Including the 4Rs in radiation therapy has significantly improved the effectiveness and efficiency of radiation therapy for cancer treatment.