In this paper, for the full Euler system of the isothermal gas, we show that a globally stable supersonic conic shock wave solution does not exist when a uniform supersonic incoming flow hits an infinitely long and cu...In this paper, for the full Euler system of the isothermal gas, we show that a globally stable supersonic conic shock wave solution does not exist when a uniform supersonic incoming flow hits an infinitely long and curved sharp conic body.展开更多
An intrinsic property of almost any physical measuring device is that it makes observations which are slightly blurred in time. The authors consider a nudging-based approach for data assimilation that constructs an ap...An intrinsic property of almost any physical measuring device is that it makes observations which are slightly blurred in time. The authors consider a nudging-based approach for data assimilation that constructs an approximate solution based on a feedback control mechanism that is designed to account for observations that have been blurred by a moving time average. Analysis of this nudging model in the context of the subcritical surface quasi-geostrophic equation shows, provided the time-averaging window is sufficiently small and the resolution of the observations sufficiently fine, that the approximating solution converges exponentially fast to the observed solution over time. In particular,the authors demonstrate that observational data with a small blur in time possess no significant obstructions to data assimilation provided that the nudging properly takes the time averaging into account. Two key ingredients in our analysis are additional boundedness properties for the relevant interpolant observation operators and a non-local Gronwall inequality.展开更多
Abstract Magnetic resonance electrical impedance tomography （MREIT, for short） is a new medical imaging technique developed recently to visualize the cross-section conduc- tivity of biologic tissues. A new MREIT ima...Abstract Magnetic resonance electrical impedance tomography （MREIT, for short） is a new medical imaging technique developed recently to visualize the cross-section conduc- tivity of biologic tissues. A new MREIT image reconstruction method called harmonic Bz algorithm was proposed in 2002 with the measurement of Bz that is a single component of an induced magnetic flux density subject to an injection current. The key idea is to solve a nonlinear integral equation by some iteration process. This paper deals with the convergence analysis as well as the error estimate for noisy input data Bz, which is the practical situation for MREIT. By analyzing the iteration process containing the Laplacian operation on the input magnetic field rigorously, the authors give the error estimate for the iterative solution in terms of the noisy level 6 and the regularizing scheme for determining ABz approximately from the noisy input data. The regularizing scheme for computing the Laplacian from noisy input data is proposed with error analysis. Our results provide both the theoretical basis and the implementable scheme for evaluating the reconstruction accuracy using harmonic Bz algorithm with practical measurement data containing noise.展开更多
In this paper, the authors prove a general Schwarz lemma at the boundary for the holomorphic mapping f between unit balls B and B＇ in separable complex Hilbert spaces H and H＇, respectively. It is found that if the ...In this paper, the authors prove a general Schwarz lemma at the boundary for the holomorphic mapping f between unit balls B and B＇ in separable complex Hilbert spaces H and H＇, respectively. It is found that if the mapping f ∈ C^1＋α at z0 ∈ B with f（zo） = wo ∈ OB＇, then the Fr＆het derivative operator Df（z0） maps the tangent space Tz0（ B^n） to Tw0（ B＇）, the holomorphic tangent space Tz0^（1,0） to Tw0（1,0）（ B＇）,respectively.展开更多
In this paper,the authors study the centered waves for the two-dimensional(2D for short)pseudo-steady supersonic flow with van der Waals gas satisfied Maxwell's law around a sharp corner.In view of the initial val...In this paper,the authors study the centered waves for the two-dimensional(2D for short)pseudo-steady supersonic flow with van der Waals gas satisfied Maxwell's law around a sharp corner.In view of the initial value of the specific volume and the properties of van der Waals gas,the centered waves at the sharp corner are constructed by classification.It is shown that the supersonic incoming flow turns the sharp corner by a centered simple wave or a centered simple wave with right-contact discontinuity or a composite wave(jump-fan,fan-jump or fan-jump-fan),or a combination of waves and constant state.Moreover,the critical angle of the sharp corner corresponding to the appearance of the vacuum phenomenon is obtained.展开更多
The authors obtain an interlacing relation between the Laplacian spectra of a graph G and its subgraph G-U,which is obtained from G by deleting all the vertices in the vertex subset U together with their incident edge...The authors obtain an interlacing relation between the Laplacian spectra of a graph G and its subgraph G-U,which is obtained from G by deleting all the vertices in the vertex subset U together with their incident edges.Also,some applications of this interlacing property are explored and this interlacing property is extended to the edge weighted graphs.展开更多
A dynamic model of schistosoma japonicum transmission is presented that incorporates effects of the prepatent periods of the different stages of schistosoma into Baxbour＇s model. The model consists of four delay diff...A dynamic model of schistosoma japonicum transmission is presented that incorporates effects of the prepatent periods of the different stages of schistosoma into Baxbour＇s model. The model consists of four delay differential equations. Stability of the disease free equilibrium and the existence of an endemic equilibrium for this model are stated in terms of a key threshold parameter. The study of dynamics for the model shows that the endemic equilibrium is globally stable in an open region if it exists and there is no delays, and for some nonzero delays the endemic equilibrium undergoes Hopf bifurcation and a periodic orbit emerges. Some numerical results are provided to support the theoretic results in this paper. These results suggest that prepatent periods in infection affect the prevalence of schistosomiasis, and it is an effective strategy on schistosomiasis control to lengthen in prepatent period on infected definitive hosts by drug treatment （or lengthen in prepatent period on infected intermediate snails by lower water temperature）.展开更多
A new class of Gorenstein algebras Tm,n(A) is introduced,their module categories are described,and all the Gorenstein-projective Tm,n(A)-modules are explicitly determined.
The fluid flows in a variable cross-section duct are nonconservative because of the source term.Recently,the Riemann problem and the interactions of the elementary waves for the compressible isentropic gas in a variab...The fluid flows in a variable cross-section duct are nonconservative because of the source term.Recently,the Riemann problem and the interactions of the elementary waves for the compressible isentropic gas in a variable cross-section duct were studied.In this paper,the Riemann problem for Chaplygin gas flow in a duct with discontinuous cross-section is studied.The elementary waves include rarefaction waves,shock waves,delta waves and stationary waves.展开更多
The quantile estimation methods are proposed for functional-coefficient partially linear regression （FCPLR） model by combining nonparametric and functional-coefficient regression （FCR） model. The local linear sche...The quantile estimation methods are proposed for functional-coefficient partially linear regression （FCPLR） model by combining nonparametric and functional-coefficient regression （FCR） model. The local linear scheme and the integrated method are used to obtain Focal quantile estimators of all unknown functions in the FCPLR model. These resulting estimators are asymptotically normal, but each of them has big variance. To reduce variances of these quantile estimators, the one-step backfitting technique is used to obtain the efficient quantile estimators of all unknown functions, and their asymptotic normalities are derived. Two simulated examples are carried out to illustrate the proposed estimation methodology.展开更多
This paper is concerned with the decay estimate of high-order energy for a class of special time-dependent structural damped systems represented by Fourier multipliers. This model is widely used in the fields of semic...This paper is concerned with the decay estimate of high-order energy for a class of special time-dependent structural damped systems represented by Fourier multipliers. This model is widely used in the fields of semiconductivity, superconductivity, electromagnetic waves, electrolyte and electrode materials, etc.展开更多
In this paper,the authors propose a novel smoothing descent type algorithm with extrapolation for solving a class of constrained nonsmooth and nonconvex problems,where the nonconvex term is possibly nonsmooth.Their al...In this paper,the authors propose a novel smoothing descent type algorithm with extrapolation for solving a class of constrained nonsmooth and nonconvex problems,where the nonconvex term is possibly nonsmooth.Their algorithm adopts the proximal gradient algorithm with extrapolation and a safe-guarding policy to minimize the smoothed objective function for better practical and theoretical performance.Moreover,the algorithm uses a easily checking rule to update the smoothing parameter to ensure that any accumulation point of the generated sequence is an(afne-scaled)Clarke stationary point of the original nonsmooth and nonconvex problem.Their experimental results indicate the effectiveness of the proposed algorithm.展开更多
The authors investigate the influence of a harmonic potential and random perturbations on the nonlinear Schr6dinger equations. The local and global well-posedness are proved with values in the space ∑（R^n）={f E HI...The authors investigate the influence of a harmonic potential and random perturbations on the nonlinear Schr6dinger equations. The local and global well-posedness are proved with values in the space ∑（R^n）={f E HI（R^n）, ｜·｜f ∈ L^2（R^n）}. When the nonlinearity is focusing and L2-supercritical, the authors give sufficient conditions for the solutions to blow up in finite time for both confining and repulsive potential. Especially for the repulsive case, the solution to the deterministic equation with the initial data satisfying the stochastic blow-up condition will also blow up in finite time. Thus, compared with the deterministic equation for the repulsive case, the blow-up condition is stronger on average, and depends on the regularity of the noise. If φ = 0, our results coincide with the ones for the deterministic equation.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11025105,10931007,11101190)the Doctorial Program Foundation of Ministry of Education of China(No.20090091110005)the Natural Science Fundamental Research Project of Jiangsu Colleges(No.10KLB110002)
文摘In this paper, for the full Euler system of the isothermal gas, we show that a globally stable supersonic conic shock wave solution does not exist when a uniform supersonic incoming flow hits an infinitely long and curved sharp conic body.
基金supported by NSF Grants DMS-1418911,DMS-1418928,ONR Grant N00014-15-1-2333the Einstein Stiftung/Foundation-Berlin+1 种基金the Einstein Visiting Fellow Programthe John Simon Guggenheim Memorial Foundation
文摘An intrinsic property of almost any physical measuring device is that it makes observations which are slightly blurred in time. The authors consider a nudging-based approach for data assimilation that constructs an approximate solution based on a feedback control mechanism that is designed to account for observations that have been blurred by a moving time average. Analysis of this nudging model in the context of the subcritical surface quasi-geostrophic equation shows, provided the time-averaging window is sufficiently small and the resolution of the observations sufficiently fine, that the approximating solution converges exponentially fast to the observed solution over time. In particular,the authors demonstrate that observational data with a small blur in time possess no significant obstructions to data assimilation provided that the nudging properly takes the time averaging into account. Two key ingredients in our analysis are additional boundedness properties for the relevant interpolant observation operators and a non-local Gronwall inequality.
基金supported by the National Natural Science Foundation of China(No.91330109)the Research Found for the Doctoral Program of Higher Education of China(No.20110092110018)
文摘Abstract Magnetic resonance electrical impedance tomography （MREIT, for short） is a new medical imaging technique developed recently to visualize the cross-section conduc- tivity of biologic tissues. A new MREIT image reconstruction method called harmonic Bz algorithm was proposed in 2002 with the measurement of Bz that is a single component of an induced magnetic flux density subject to an injection current. The key idea is to solve a nonlinear integral equation by some iteration process. This paper deals with the convergence analysis as well as the error estimate for noisy input data Bz, which is the practical situation for MREIT. By analyzing the iteration process containing the Laplacian operation on the input magnetic field rigorously, the authors give the error estimate for the iterative solution in terms of the noisy level 6 and the regularizing scheme for determining ABz approximately from the noisy input data. The regularizing scheme for computing the Laplacian from noisy input data is proposed with error analysis. Our results provide both the theoretical basis and the implementable scheme for evaluating the reconstruction accuracy using harmonic Bz algorithm with practical measurement data containing noise.
基金supported by the National Natural Science Foundation of China(Nos.11671361,11571256)the Zhejiang Provincial Natural Science Foundation of China(No.LY14A010008)
文摘In this paper, the authors prove a general Schwarz lemma at the boundary for the holomorphic mapping f between unit balls B and B＇ in separable complex Hilbert spaces H and H＇, respectively. It is found that if the mapping f ∈ C^1＋α at z0 ∈ B with f（zo） = wo ∈ OB＇, then the Fr＆het derivative operator Df（z0） maps the tangent space Tz0（ B^n） to Tw0（ B＇）, the holomorphic tangent space Tz0^（1,0） to Tw0（1,0）（ B＇）,respectively.
基金supported by the National Natural Science Foundation of China(No.12171305)。
文摘In this paper,the authors study the centered waves for the two-dimensional(2D for short)pseudo-steady supersonic flow with van der Waals gas satisfied Maxwell's law around a sharp corner.In view of the initial value of the specific volume and the properties of van der Waals gas,the centered waves at the sharp corner are constructed by classification.It is shown that the supersonic incoming flow turns the sharp corner by a centered simple wave or a centered simple wave with right-contact discontinuity or a composite wave(jump-fan,fan-jump or fan-jump-fan),or a combination of waves and constant state.Moreover,the critical angle of the sharp corner corresponding to the appearance of the vacuum phenomenon is obtained.
基金supported by the National Natural Science Foundation of China (No.10731040)the Shanghai Leading Academic Discipline Project (No.S30104)
文摘The authors obtain an interlacing relation between the Laplacian spectra of a graph G and its subgraph G-U,which is obtained from G by deleting all the vertices in the vertex subset U together with their incident edges.Also,some applications of this interlacing property are explored and this interlacing property is extended to the edge weighted graphs.
基金supported by the National Natural Science Foundation of China(Nos.10831003,10925102)the Program of Shanghai Subject Chief Scientist(No.10XD1406200)
文摘A dynamic model of schistosoma japonicum transmission is presented that incorporates effects of the prepatent periods of the different stages of schistosoma into Baxbour＇s model. The model consists of four delay differential equations. Stability of the disease free equilibrium and the existence of an endemic equilibrium for this model are stated in terms of a key threshold parameter. The study of dynamics for the model shows that the endemic equilibrium is globally stable in an open region if it exists and there is no delays, and for some nonzero delays the endemic equilibrium undergoes Hopf bifurcation and a periodic orbit emerges. Some numerical results are provided to support the theoretic results in this paper. These results suggest that prepatent periods in infection affect the prevalence of schistosomiasis, and it is an effective strategy on schistosomiasis control to lengthen in prepatent period on infected definitive hosts by drug treatment （or lengthen in prepatent period on infected intermediate snails by lower water temperature）.
基金Project supported by the National Natural Science Foundation of China (No. 10725104) the Science and Technology Commission of Shanghai Municipality (No. 09XD1402500)
文摘A new class of Gorenstein algebras Tm,n(A) is introduced,their module categories are described,and all the Gorenstein-projective Tm,n(A)-modules are explicitly determined.
基金the National Natural Science Foundation of China(Nos.11371240,11771274)。
文摘The fluid flows in a variable cross-section duct are nonconservative because of the source term.Recently,the Riemann problem and the interactions of the elementary waves for the compressible isentropic gas in a variable cross-section duct were studied.In this paper,the Riemann problem for Chaplygin gas flow in a duct with discontinuous cross-section is studied.The elementary waves include rarefaction waves,shock waves,delta waves and stationary waves.
基金supported by the Zhejiang Provincial Natural Science Foundation of China (No. Y6110662)
文摘The quantile estimation methods are proposed for functional-coefficient partially linear regression （FCPLR） model by combining nonparametric and functional-coefficient regression （FCR） model. The local linear scheme and the integrated method are used to obtain Focal quantile estimators of all unknown functions in the FCPLR model. These resulting estimators are asymptotically normal, but each of them has big variance. To reduce variances of these quantile estimators, the one-step backfitting technique is used to obtain the efficient quantile estimators of all unknown functions, and their asymptotic normalities are derived. Two simulated examples are carried out to illustrate the proposed estimation methodology.
基金supported by the National Natural Science Foundation of China (No.10871175)
文摘This paper is concerned with the decay estimate of high-order energy for a class of special time-dependent structural damped systems represented by Fourier multipliers. This model is widely used in the fields of semiconductivity, superconductivity, electromagnetic waves, electrolyte and electrode materials, etc.
基金supported by the National Natural Science Foundation of China(No.12001144)Zhejiang Provincial Natural Science Foundation of China(No.LQ20A010007)NSF/DMS-2152961。
文摘In this paper,the authors propose a novel smoothing descent type algorithm with extrapolation for solving a class of constrained nonsmooth and nonconvex problems,where the nonconvex term is possibly nonsmooth.Their algorithm adopts the proximal gradient algorithm with extrapolation and a safe-guarding policy to minimize the smoothed objective function for better practical and theoretical performance.Moreover,the algorithm uses a easily checking rule to update the smoothing parameter to ensure that any accumulation point of the generated sequence is an(afne-scaled)Clarke stationary point of the original nonsmooth and nonconvex problem.Their experimental results indicate the effectiveness of the proposed algorithm.
基金supported by the National Natural Science Foundation of China(Nos.11271330,11261023,11461033,11401269)the Jiangxi Provincial Natural Science Foundation of China(No.20142BAB201003)
文摘In this paper, some endpoint estimates for the generalized multilinear fractional integrals Ia,m on the non-homogeneous metric spaces are established.
基金Project supported by the National Natural Science Foundation of China (Nos.10931001 and 10871173)the Educational Science Foundation of Zhejiang (No.Z201017584)the Science Foundation of Zhejiang University of Science and Technology (No.F501108A02)
文摘The authors prove the certain de Leeuw type theorems on some non-convolution operators,and give some applications on certain known results.
基金supported by the National Natural Science Foundation of China (Nos. 10871175,10931007,10901137)the Zhejiang Provincial Natural Science Foundation of China (No. Z6100217)the Specialized ResearchFund for the Doctoral Program of Higher Education (No. 20090101120005)
文摘The authors investigate the influence of a harmonic potential and random perturbations on the nonlinear Schr6dinger equations. The local and global well-posedness are proved with values in the space ∑（R^n）={f E HI（R^n）, ｜·｜f ∈ L^2（R^n）}. When the nonlinearity is focusing and L2-supercritical, the authors give sufficient conditions for the solutions to blow up in finite time for both confining and repulsive potential. Especially for the repulsive case, the solution to the deterministic equation with the initial data satisfying the stochastic blow-up condition will also blow up in finite time. Thus, compared with the deterministic equation for the repulsive case, the blow-up condition is stronger on average, and depends on the regularity of the noise. If φ = 0, our results coincide with the ones for the deterministic equation.
