The purpose of this article is to deal with uniqueness problem with truncated multiplicities for meromorphic mappings in several complex variables. We obtain a degeneracy theorem of meromorphic mappings without taking...The purpose of this article is to deal with uniqueness problem with truncated multiplicities for meromorphic mappings in several complex variables. We obtain a degeneracy theorem of meromorphic mappings without taking account of multiplicities of order 〉 k in counting functions and a uniqueness theorem for meromorphic mappings sharing 2n ＋ 2（n ≥ 2） hyperplanes in general position, which improve and extend some earlier work.展开更多
The aim of the paper is to deal with the algebraic dependence and uniqueness problem for meromorphic mappings by using the new second main theorem with different weights involved the truncated counting functions,and s...The aim of the paper is to deal with the algebraic dependence and uniqueness problem for meromorphic mappings by using the new second main theorem with different weights involved the truncated counting functions,and some interesting uniqueness results are obtained under more general and weak conditions where the moving hyperplanes in general position are partly shared by mappings from Cn into PN(C),which can be seen as the improvements of previous well-known results.展开更多
By making use of the differential inequalities, in this paper we study the uniqueness of solutions of the two kinds of the singularly perturbed boundary value problems for the nonlinear third order ordinary differenti...By making use of the differential inequalities, in this paper we study the uniqueness of solutions of the two kinds of the singularly perturbed boundary value problems for the nonlinear third order ordinary differential equation with a small parameter ε>0: where i=1, 2; a(?)(ε), β(ε) and γ(ε) are functions defined on (0, ε_o], while ε_o>0 is a constant.This paper is the continuation of our works [4, 6].展开更多
In this work, we present final solving Millennium Prize Problems formulated by Clay Math. Inst., Cambridge. A new uniform time estimation of the Cauchy problem solution for the Navier-Stokes equations is provided. We ...In this work, we present final solving Millennium Prize Problems formulated by Clay Math. Inst., Cambridge. A new uniform time estimation of the Cauchy problem solution for the Navier-Stokes equations is provided. We also describe the loss of smoothness of classical solutions for the Navier-Stokes equations.展开更多
The analytic properties of the scattering amplitude are discussed, and a representation of the potential is obtained using the scattering amplitude. A uniform time estimation of the Cauchy problem solution for the Nav...The analytic properties of the scattering amplitude are discussed, and a representation of the potential is obtained using the scattering amplitude. A uniform time estimation of the Cauchy problem solution for the Navier-Stokes equations is provided. The paper also describes the time blowup of classical solutions for the Navier-Stokes equations by the smoothness assumption.展开更多
Existence and uniqueness conditions for nonnegative solutions to initial value prob- lems of general sublinear-linear differential equations are obtained.They extend the uniqueness theorem due to H.Murakami~[6] and th...Existence and uniqueness conditions for nonnegative solutions to initial value prob- lems of general sublinear-linear differential equations are obtained.They extend the uniqueness theorem due to H.Murakami~[6] and the main results of H.G.Kaper and M.K.Kwong~[4].展开更多
This paper deals with discerete phenomena in uniqueness in the Cauchy problemsum from i?j=0 to n （i?j/0）aijuxixj+sum from i=0 to n（i/0）biuxi+cu=0,x0>0, u（0,x1,…,xn）=ux0（0,x1,…,xn） =0We prove that the prob...This paper deals with discerete phenomena in uniqueness in the Cauchy problemsum from i?j=0 to n （i?j/0）aijuxixj+sum from i=0 to n（i/0）biuxi+cu=0,x0>0, u（0,x1,…,xn）=ux0（0,x1,…,xn） =0We prove that the problem only has trivial solutions in the neighbourhood of the origin, if bo（0）-Z sum from i=1 to n（i/1）（2ai + 1）λi≠0,λi>0 being the square roots of the eigenvalues of the product of matrices(?2aoo/?xi?xi（0）(i?j=i,….?and （aif（0））ii?f….,and ai being the arbitrarily non-negative integers.展开更多
This article deals with the Riemann-Hilbert boundary value problem for quasilinear mixed （elliptic- hyperbolic） complex equations of first order with degenerate rank 0. Firstly, we give the representation theorem an...This article deals with the Riemann-Hilbert boundary value problem for quasilinear mixed （elliptic- hyperbolic） complex equations of first order with degenerate rank 0. Firstly, we give the representation theorem and prove the uniqueness of solutions for the boundary value problem. Afterwards, by using the method of successive iteration, the existence and estimates of solutions for the boundary value problem are verified. The above problem possesses the important applications to the Tricomi problem of mixed type equations of second order. In this article, the proof of HSlder continuity of a singular double integer is very difficult and interesting as in this Section 4 below.展开更多
Unique shortest vector problem(uSVP)plays an important role in lattice based cryptography.Many cryptographic schemes based their security on it.For the cofidence of those applications,it is essential to clarify the co...Unique shortest vector problem(uSVP)plays an important role in lattice based cryptography.Many cryptographic schemes based their security on it.For the cofidence of those applications,it is essential to clarify the complex-ity of uSVP with different parameters.However,proving the NP-hardness of usVP appears quite hard.To the state of the art,we are even not able to prove the NP-hardness of usVP with constant parameters.In this work,we gave a lower bound for the hardness of usVP with constant parameters,i.e.we proved that uSVP is at least as hard as gap shortest vector problem(GapSVP)with gap of O(√n/log(n)),which is in NP n coAM.Unlike previous works,our reduction works for paramters in a bigger range,especially when the constant hidden by the big-O in GapsVP is smallerthan1.展开更多
In this paper,we consider the following problem {-Δu（x）＋u（x）=λ（u^p（x）＋h（x））,x∈R^N,u（x）∈h^1（R^N）,u（x）〉0,x∈R^N,（＊）where λ 〉 0 is a parameter,p =（N＋2）/（N—2）.We will prove that there exi...In this paper,we consider the following problem {-Δu（x）＋u（x）=λ（u^p（x）＋h（x））,x∈R^N,u（x）∈h^1（R^N）,u（x）〉0,x∈R^N,（＊）where λ 〉 0 is a parameter,p =（N＋2）/（N—2）.We will prove that there exists a positive constant 0 〈 A＊ 〈 ＋00such that（＊） has a minimal positive solution for λ∈（0,λ＊）,no solution for λ 〉 λ＊,a unique solution for λ = λ＊.Furthermore,（＊） possesses at least two positive solutions when λ∈（0,λ＊） and 3 ≤ N ≤ 5.For N ≥ 6,under some monotonicity conditions of h we show that there exists a constant 0 〈λ＊＊ 〈 λ＊ such that problem（＊）possesses a unique solution for λ∈（0,λ＊＊）.展开更多
In this paper the inverse problem of determining the source term, which is independent of the time variable, of a linear, uniformly-parabolic equation is investigated. The uniqueness of the inverse problem is proved u...In this paper the inverse problem of determining the source term, which is independent of the time variable, of a linear, uniformly-parabolic equation is investigated. The uniqueness of the inverse problem is proved under mild assumptions by using the orthogonality method and an elimination method. The existence of the inverse problem is proved by means of the theory of solvable operators between Banach spaces; moreover, the continuous dependence on measurement of the solution to the inverse problem is also proved.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.11401291 and 11461042)
文摘The purpose of this article is to deal with uniqueness problem with truncated multiplicities for meromorphic mappings in several complex variables. We obtain a degeneracy theorem of meromorphic mappings without taking account of multiplicities of order 〉 k in counting functions and a uniqueness theorem for meromorphic mappings sharing 2n ＋ 2（n ≥ 2） hyperplanes in general position, which improve and extend some earlier work.
基金supported by the Fund of China Scholarship Council(No.201806360222)。
文摘The aim of the paper is to deal with the algebraic dependence and uniqueness problem for meromorphic mappings by using the new second main theorem with different weights involved the truncated counting functions,and some interesting uniqueness results are obtained under more general and weak conditions where the moving hyperplanes in general position are partly shared by mappings from Cn into PN(C),which can be seen as the improvements of previous well-known results.
基金Project supported by the National Natural Science Foundation of China.
文摘By making use of the differential inequalities, in this paper we study the uniqueness of solutions of the two kinds of the singularly perturbed boundary value problems for the nonlinear third order ordinary differential equation with a small parameter ε>0: where i=1, 2; a(?)(ε), β(ε) and γ(ε) are functions defined on (0, ε_o], while ε_o>0 is a constant.This paper is the continuation of our works [4, 6].
基金the Ministry of Education and Science of the Republic of Kazakhstan for a grant
文摘In this work, we present final solving Millennium Prize Problems formulated by Clay Math. Inst., Cambridge. A new uniform time estimation of the Cauchy problem solution for the Navier-Stokes equations is provided. We also describe the loss of smoothness of classical solutions for the Navier-Stokes equations.
基金the Ministry of Education and Science of the Republic of Kazakhstan for a grant
文摘The analytic properties of the scattering amplitude are discussed, and a representation of the potential is obtained using the scattering amplitude. A uniform time estimation of the Cauchy problem solution for the Navier-Stokes equations is provided. The paper also describes the time blowup of classical solutions for the Navier-Stokes equations by the smoothness assumption.
文摘Existence and uniqueness conditions for nonnegative solutions to initial value prob- lems of general sublinear-linear differential equations are obtained.They extend the uniqueness theorem due to H.Murakami~[6] and the main results of H.G.Kaper and M.K.Kwong~[4].
文摘This paper deals with discerete phenomena in uniqueness in the Cauchy problemsum from i?j=0 to n （i?j/0）aijuxixj+sum from i=0 to n（i/0）biuxi+cu=0,x0>0, u（0,x1,…,xn）=ux0（0,x1,…,xn） =0We prove that the problem only has trivial solutions in the neighbourhood of the origin, if bo（0）-Z sum from i=1 to n（i/1）（2ai + 1）λi≠0,λi>0 being the square roots of the eigenvalues of the product of matrices(?2aoo/?xi?xi（0）(i?j=i,….?and （aif（0））ii?f….,and ai being the arbitrarily non-negative integers.
基金Supported in part by the National Natural Science Foundation of China under Grant No.11021161 and 10928102973 Program of China under Grant No.2011CB80800+2 种基金Chinese Academy of Sciences under Grant No.kjcx-yw-s7project grant of "Center for Research and Applications in Plasma Physics and Pulsed Power Technology,PBCT-Chile-ACT 26"Direcci'on de Programas de Investigaci'on,Universidad de Talca,Chile
文摘This article deals with the Riemann-Hilbert boundary value problem for quasilinear mixed （elliptic- hyperbolic） complex equations of first order with degenerate rank 0. Firstly, we give the representation theorem and prove the uniqueness of solutions for the boundary value problem. Afterwards, by using the method of successive iteration, the existence and estimates of solutions for the boundary value problem are verified. The above problem possesses the important applications to the Tricomi problem of mixed type equations of second order. In this article, the proof of HSlder continuity of a singular double integer is very difficult and interesting as in this Section 4 below.
基金This work is funded by National Natural Science Foundation of China(Grants No.62172405).
文摘Unique shortest vector problem(uSVP)plays an important role in lattice based cryptography.Many cryptographic schemes based their security on it.For the cofidence of those applications,it is essential to clarify the complex-ity of uSVP with different parameters.However,proving the NP-hardness of usVP appears quite hard.To the state of the art,we are even not able to prove the NP-hardness of usVP with constant parameters.In this work,we gave a lower bound for the hardness of usVP with constant parameters,i.e.we proved that uSVP is at least as hard as gap shortest vector problem(GapSVP)with gap of O(√n/log(n)),which is in NP n coAM.Unlike previous works,our reduction works for paramters in a bigger range,especially when the constant hidden by the big-O in GapsVP is smallerthan1.
基金supported by the National Natural Science Foundation of China(No.11201132)Scientific Research Foundation for Ph.D of Hubei University of Technology(No.BSQD12065)supported by the Science Research Project of Hubei Provincial Department of education(No.d200614001)
文摘In this paper,we consider the following problem {-Δu（x）＋u（x）=λ（u^p（x）＋h（x））,x∈R^N,u（x）∈h^1（R^N）,u（x）〉0,x∈R^N,（＊）where λ 〉 0 is a parameter,p =（N＋2）/（N—2）.We will prove that there exists a positive constant 0 〈 A＊ 〈 ＋00such that（＊） has a minimal positive solution for λ∈（0,λ＊）,no solution for λ 〉 λ＊,a unique solution for λ = λ＊.Furthermore,（＊） possesses at least two positive solutions when λ∈（0,λ＊） and 3 ≤ N ≤ 5.For N ≥ 6,under some monotonicity conditions of h we show that there exists a constant 0 〈λ＊＊ 〈 λ＊ such that problem（＊）possesses a unique solution for λ∈（0,λ＊＊）.
文摘In this paper the inverse problem of determining the source term, which is independent of the time variable, of a linear, uniformly-parabolic equation is investigated. The uniqueness of the inverse problem is proved under mild assumptions by using the orthogonality method and an elimination method. The existence of the inverse problem is proved by means of the theory of solvable operators between Banach spaces; moreover, the continuous dependence on measurement of the solution to the inverse problem is also proved.
