We consider degenerate convection-diffusion equations in both one space dimension and several space dimensions.In the first part of this article,we are concerned with the decay rate of solutions of one dimension conve...We consider degenerate convection-diffusion equations in both one space dimension and several space dimensions.In the first part of this article,we are concerned with the decay rate of solutions of one dimension convection diffusion equation.On the other hand,in the second part of this article,we are concerned with a decay rate of derivatives of solution of convection diffusion equation in several space dimensions.展开更多
Let(g_(n))_(n≥1) be a sequence of independent and identically distributed positive random d×d matrices and consider the matrix product G_(n)=g_(n)…g_1.Under suitable conditions,we establish the Berry-Esseen bou...Let(g_(n))_(n≥1) be a sequence of independent and identically distributed positive random d×d matrices and consider the matrix product G_(n)=g_(n)…g_1.Under suitable conditions,we establish the Berry-Esseen bounds on the rate of convergence in the central limit theorem and Cramer-type moderate deviation expansions,for any matrix norm ‖G_(n)‖ of G_(n),its entries G_(n)^(i,j) and its spectral radius ρ(G_(n)).Extended versions of their joint law with the direction of the random walk G_(n)x are also established,where x is a starting point in the unit sphere of R~d.展开更多
The authors consider a class of nonlinear parabolic problems where the lower order term isdepending on a weighted integral of the solution, and address the issues of existence, uniqueness,stationary solutions and in s...The authors consider a class of nonlinear parabolic problems where the lower order term isdepending on a weighted integral of the solution, and address the issues of existence, uniqueness,stationary solutions and in some cases asymptotic behaviour.展开更多
The basic properties of nonlinear ion-acoustic(IA) waves(IAWs), particularly finite amplitude IA rogue waves(IARWs) in a plasma medium(containing pair ions, iso-thermal positrons, and non-thermal electrons) are theore...The basic properties of nonlinear ion-acoustic(IA) waves(IAWs), particularly finite amplitude IA rogue waves(IARWs) in a plasma medium(containing pair ions, iso-thermal positrons, and non-thermal electrons) are theoretically investigated by deriving the nonlinear Schr¨odinger equation(NLSE).The criteria for the modulational instability of IAWs, and the basic features of finite amplitude IARWs are identified.The modulationally stable and unstable regions are determined by the sign of the ratio of the dispersive coefficient to the nonlinear coefficient of NLSE.The latter is analyzed to obtain the region for the existence of the IARWs, which corresponds to the unstable region.The shape of the profile of the rogue waves depends on the non-thermal parameter α and the ratio of electron temperature to positron temperature.It is found that the increase in the value of the non-thermal parameter enhances both the amplitude and width of IARWs, and that the enhancement of electron(positron) temperature reduces(enhances) the amplitude and width of IARWs.It is worth to mention that our present investigation may be useful for understanding the salient features of IARWs in space(viz., upper region of Titan’s atmosphere, cometary comae, and Earth’s ionosphere, etc.)and laboratory(viz., plasma processing reactor and neutral beam sources, etc.) plasmas.展开更多
We study robust notions of good-deal hedging and valuation under combined uncertainty about the drifts and volatilities of asset prices.Good-deal bounds are determined by a subset of risk-neutral pricing measures such...We study robust notions of good-deal hedging and valuation under combined uncertainty about the drifts and volatilities of asset prices.Good-deal bounds are determined by a subset of risk-neutral pricing measures such that not only opportunities for arbitrage are excluded but also deals that are too good,by restricting instantaneous Sharpe ratios.A non-dominated multiple priors approach to model uncertainty(ambiguity)leads to worst-case good-deal bounds.Corresponding hedging strategies arise as minimizers of a suitable coherent risk measure.Good-deal bounds and hedges for measurable claims are characterized by solutions to secondorder backward stochastic differential equations whose generators are non-convex in the volatility.These hedging strategies are robust with respect to uncertainty in the sense that their tracking errors satisfy a supermartingale property under all a-priori valuation measures,uniformly over all priors.展开更多
Let G be a semisimple group over an algebraically closed field of characteristic p > 0. We give a(partly conjectural) closed formula for the character of many indecomposable tilting rational G-modules assuming that...Let G be a semisimple group over an algebraically closed field of characteristic p > 0. We give a(partly conjectural) closed formula for the character of many indecomposable tilting rational G-modules assuming that p is large.展开更多
The chemotaxis-Navier-Stokes system{nt+u・∇n=Δn−∇・(n∇c),ct+u・∇c=Δc−nc,ut+(u・∇)u=Δu+∇P+n∇φ,∇・u=0is considered in a smoothly bounded planar domainΩunder the boundary conditions(∇n−n∇c)・ν=0,c=c,u=0,x∈∂Ω,t>0,wit...The chemotaxis-Navier-Stokes system{nt+u・∇n=Δn−∇・(n∇c),ct+u・∇c=Δc−nc,ut+(u・∇)u=Δu+∇P+n∇φ,∇・u=0is considered in a smoothly bounded planar domainΩunder the boundary conditions(∇n−n∇c)・ν=0,c=c,u=0,x∈∂Ω,t>0,with a given nonnegative constant c_(*).It is shown that if(n_(0),c_(0),u_(0))is sufficiently regular and such that the product||n_(0)||L^(1)(Ω)||c_(0)||^(2)L^(∞)(Ω)is suitably small,an associated initial value problem possesses a bounded classical solution with(n,c,u)|_(t=0)=(n_(0),c_(0),u_(0)).展开更多
Trigonometric integrators for oscillatory linear Hamiltonian differential equations are considered.Under a condition of Hairer&Lubich on the filter functions in the method,a modified energy is derived that is exac...Trigonometric integrators for oscillatory linear Hamiltonian differential equations are considered.Under a condition of Hairer&Lubich on the filter functions in the method,a modified energy is derived that is exactly preserved by trigonometric integrators.This implies and extends a known result on all-time near-conservation of energy.The extension can be applied to linear wave equations.展开更多
This paper is concerned with Bernstein polynomials on k-simploids by which we mean a crossproduct of k lower dimensional simplices. Specifically, we show that if the Bernstein polynomials ofa given function f on a k-s...This paper is concerned with Bernstein polynomials on k-simploids by which we mean a crossproduct of k lower dimensional simplices. Specifically, we show that if the Bernstein polynomials ofa given function f on a k-simploid form a decreasing sequence then f+l, where l is any correspondingtensor product of affine functions. achieves its maximum on the boundary of the k-simploid. Thisextends recent results in [1] for bivariate Bernstein polynomials on triangles. Unlike the approachused in [1] our approach is based on semigroup techniques and the maximum principle for secondorder elliptic operators. Furthermore, we derive analogous results for cube spline surfaces.展开更多
The objective of this paper is to consider the theory of regularity of systems of partial differential equations with Neumann boundary conditions. It complements previous works of the authors for the Dirichlet case. T...The objective of this paper is to consider the theory of regularity of systems of partial differential equations with Neumann boundary conditions. It complements previous works of the authors for the Dirichlet case. This type of problem is motivated by stochastic differential games. The Neumann case corresponds to stochastic differential equations with reflection on boundary of the domain.展开更多
We consider the well-known problem of scheduling n independent tasks nonpreemptivelyon m identical processors with the objective of minimizing the makespan. Coffman, Garey andJohnson described an algorithm MULTIFIT, b...We consider the well-known problem of scheduling n independent tasks nonpreemptivelyon m identical processors with the objective of minimizing the makespan. Coffman, Garey andJohnson described an algorithm MULTIFIT, based on bin-packing, with a worst case performancebetter than the LPT-algorithm. The bound 1.22 obtained by them was claimed by Friesen in1984 that it can be improved to 1.2. In this paper we give a simp1e proof for this bound.展开更多
In this paper we estimate the solutions of homogeneous linear system of differentialequations with unbounded coefficients on the real line R. We also give a necessary and sufficientcondition in order that the linear d...In this paper we estimate the solutions of homogeneous linear system of differentialequations with unbounded coefficients on the real line R. We also give a necessary and sufficientcondition in order that the linear differential operator with unbounded coefficients has a boundedinverse in the scalar case.展开更多
基金Support by the Special Funds of State Major Basic Research Projects(Grant No.1999075107)Innovation Funds of AMSS,CAS of China+1 种基金Support by the Austrian government START-prize project"Nonlinear SchrSdingerQuantum Boltzmann Equations"(Y-137-TEC)
基金Xiao L.acknowledges the support by the Special Funds of State Major Basic Research Projects(Grant No.1999075107) and the Innovation Funds of AMSS,CAS of China.Zhang K.J.acknowledges supportby the Austrian government START-prize project"Nonlinear
基金partially supported by the Natural Science Foundation of China(11271105)a grant from the China Scholarship Council and a Humboldt fellowship of Germany
文摘We consider degenerate convection-diffusion equations in both one space dimension and several space dimensions.In the first part of this article,we are concerned with the decay rate of solutions of one dimension convection diffusion equation.On the other hand,in the second part of this article,we are concerned with a decay rate of derivatives of solution of convection diffusion equation in several space dimensions.
基金The project supported by the China-Germany Cooperation Project under Grant No. 446 CHV 113/231, ＂Quantum information and related mathematical problems＂ and National Natural Science Foundation of China under Grant Nos. 10375038 and 10271081
基金supported by Deutsche Forschungsgemeinschaft (DFG) (Grant No. ME 4473/2-1)the Centre Henri Lebesgue (CHL) (Grant No. ANR-11-LABX-0020-01)National Natural Science Foundation of China (Grants Nos. 11971063, 11731012, 12271062 and 12288201)。
文摘Let(g_(n))_(n≥1) be a sequence of independent and identically distributed positive random d×d matrices and consider the matrix product G_(n)=g_(n)…g_1.Under suitable conditions,we establish the Berry-Esseen bounds on the rate of convergence in the central limit theorem and Cramer-type moderate deviation expansions,for any matrix norm ‖G_(n)‖ of G_(n),its entries G_(n)^(i,j) and its spectral radius ρ(G_(n)).Extended versions of their joint law with the direction of the random walk G_(n)x are also established,where x is a starting point in the unit sphere of R~d.
基金The work of the first author was supported by the NSF under Grant No.DMS-0411403 and Grant No.DMS-0511611The second author acknowledges the support from the Austrian Science Foundation(FWF)under Grant No.Start Y-192Both authors acknowledge support and the inspiring athmosphere at the Johann Radon Institute for Computational and Applied Mathematics(RICAM),Linz,Austria,during the special semester on computational mechanics
基金Project supported by the Swiss National Science Foundation under the contract#20-67618.02.
文摘The authors consider a class of nonlinear parabolic problems where the lower order term isdepending on a weighted integral of the solution, and address the issues of existence, uniqueness,stationary solutions and in some cases asymptotic behaviour.
基金Supported by the Bangladesh Ministry of Science and Technology Fellowship Awardthe Alexander von Humboldt Foundation for a Postdoctoral Fellowship
文摘The basic properties of nonlinear ion-acoustic(IA) waves(IAWs), particularly finite amplitude IA rogue waves(IARWs) in a plasma medium(containing pair ions, iso-thermal positrons, and non-thermal electrons) are theoretically investigated by deriving the nonlinear Schr¨odinger equation(NLSE).The criteria for the modulational instability of IAWs, and the basic features of finite amplitude IARWs are identified.The modulationally stable and unstable regions are determined by the sign of the ratio of the dispersive coefficient to the nonlinear coefficient of NLSE.The latter is analyzed to obtain the region for the existence of the IARWs, which corresponds to the unstable region.The shape of the profile of the rogue waves depends on the non-thermal parameter α and the ratio of electron temperature to positron temperature.It is found that the increase in the value of the non-thermal parameter enhances both the amplitude and width of IARWs, and that the enhancement of electron(positron) temperature reduces(enhances) the amplitude and width of IARWs.It is worth to mention that our present investigation may be useful for understanding the salient features of IARWs in space(viz., upper region of Titan’s atmosphere, cometary comae, and Earth’s ionosphere, etc.)and laboratory(viz., plasma processing reactor and neutral beam sources, etc.) plasmas.
基金the German Science Foundation,Berlin Mathematical School and RTG 1845 for support,and Xiaolu Tan for helpful discussions.
文摘We study robust notions of good-deal hedging and valuation under combined uncertainty about the drifts and volatilities of asset prices.Good-deal bounds are determined by a subset of risk-neutral pricing measures such that not only opportunities for arbitrage are excluded but also deals that are too good,by restricting instantaneous Sharpe ratios.A non-dominated multiple priors approach to model uncertainty(ambiguity)leads to worst-case good-deal bounds.Corresponding hedging strategies arise as minimizers of a suitable coherent risk measure.Good-deal bounds and hedges for measurable claims are characterized by solutions to secondorder backward stochastic differential equations whose generators are non-convex in the volatility.These hedging strategies are robust with respect to uncertainty in the sense that their tracking errors satisfy a supermartingale property under all a-priori valuation measures,uniformly over all priors.
基金G.Lusztig was supported by National Science Foundation of USA(GrantNo.DMS-1303060)by a Simons Fellowship
文摘Let G be a semisimple group over an algebraically closed field of characteristic p > 0. We give a(partly conjectural) closed formula for the character of many indecomposable tilting rational G-modules assuming that p is large.
基金supported by the Sichuan Science and Technology program(Grant No.2021ZYD0008)Sichuan Youth Science and Technology Foundation(Grant No.2021JDTD0024)+3 种基金support of the Deutsche Forschungsgemeinschaft in the context of the project Emergence of structures and advantages in cross-diffusion systems(Project No.411007140,GZ:WI 3707/5-1)supported by the NNSF of China(Grant Nos.11971093,11771045)the Applied Fundamental Research Program of Sichuan Province(Grant No.2020YJ0264)the Fundamental Research Funds for the Central Universities(Grant No.ZYGX2019J096)。
文摘The chemotaxis-Navier-Stokes system{nt+u・∇n=Δn−∇・(n∇c),ct+u・∇c=Δc−nc,ut+(u・∇)u=Δu+∇P+n∇φ,∇・u=0is considered in a smoothly bounded planar domainΩunder the boundary conditions(∇n−n∇c)・ν=0,c=c,u=0,x∈∂Ω,t>0,with a given nonnegative constant c_(*).It is shown that if(n_(0),c_(0),u_(0))is sufficiently regular and such that the product||n_(0)||L^(1)(Ω)||c_(0)||^(2)L^(∞)(Ω)is suitably small,an associated initial value problem possesses a bounded classical solution with(n,c,u)|_(t=0)=(n_(0),c_(0),u_(0)).
文摘Trigonometric integrators for oscillatory linear Hamiltonian differential equations are considered.Under a condition of Hairer&Lubich on the filter functions in the method,a modified energy is derived that is exactly preserved by trigonometric integrators.This implies and extends a known result on all-time near-conservation of energy.The extension can be applied to linear wave equations.
基金This work was partially supported by NATO Grant No.DJ RG 639/84
文摘This paper is concerned with Bernstein polynomials on k-simploids by which we mean a crossproduct of k lower dimensional simplices. Specifically, we show that if the Bernstein polynomials ofa given function f on a k-simploid form a decreasing sequence then f+l, where l is any correspondingtensor product of affine functions. achieves its maximum on the boundary of the k-simploid. Thisextends recent results in [1] for bivariate Bernstein polynomials on triangles. Unlike the approachused in [1] our approach is based on semigroup techniques and the maximum principle for secondorder elliptic operators. Furthermore, we derive analogous results for cube spline surfaces.
文摘The objective of this paper is to consider the theory of regularity of systems of partial differential equations with Neumann boundary conditions. It complements previous works of the authors for the Dirichlet case. This type of problem is motivated by stochastic differential games. The Neumann case corresponds to stochastic differential equations with reflection on boundary of the domain.
基金National Natural Science Founation of ChinaAustrian"Fonds sur Frdorung der wissonachaftlichen Forschung,Project S32/01"
文摘We consider the well-known problem of scheduling n independent tasks nonpreemptivelyon m identical processors with the objective of minimizing the makespan. Coffman, Garey andJohnson described an algorithm MULTIFIT, based on bin-packing, with a worst case performancebetter than the LPT-algorithm. The bound 1.22 obtained by them was claimed by Friesen in1984 that it can be improved to 1.2. In this paper we give a simp1e proof for this bound.
文摘In this paper we estimate the solutions of homogeneous linear system of differentialequations with unbounded coefficients on the real line R. We also give a necessary and sufficientcondition in order that the linear differential operator with unbounded coefficients has a boundedinverse in the scalar case.
