Solvability and Hypoellipticity for Operate Lm&mu|on the Heisenberg Group Hn
In this paper ,explicit fundament solution um for partial differential oprator Lmμ on the Heisenberg group Hn is given .By using this um,the solvability and teh hypoellipticity for operator Lmμ are studied.
In this paper,we consider the boundary value problems of higher order ordinary differentinal equations.By using the monotone iterative technique, some existence and uniqueness theorms for solutions are obtained.
In this paper,we give an asymptotic estimation of the eigenfrequencies of a one dimensional thenoelastic system with one end stress damping.It is shown that this kind of boundry stress feedback can improve arbitrarily thr decay rate of teh higher eigenfrequencies.The Legendre spectral method is used to compute the eigenvalues of teh damped operator.Numerical results confirms teh theoretical estimations.
In this paper ,the join of two trees with a regular monoid is explicitly described .
In this paper,we define the Herz spaces and weak Herz spaces on spaces of homogeneous type and study teh properties of some sublinear operators on these spaces .
We wii study teh finite element method for compressible flow of contamination from nuclear in porous media,in which both of molecular diffusion and dispersion are considered.The mathematical model is a coupled quasilinear syetem of parabolic equations about pressure,temperature,brine and radionuclide.Starting from teh primitive model ,finite element scheme based on teh method of characterristics is estabilishe and analysed.Some new estimates about elliptic projection are given,a modified tachnique is proposed to establish teh evolution inequlity for pressure error,the optimal error estimate in L∞ （J；H1（Ω））is proved.
The homogeneous balance method is very effective to seek for solitary wave solution of nonliear evolution equations. in this paper we will give three kinds of important applictions of homogenceous balance method;1)to find new exact solutions for nonlinear evolution equaton;2)to seek for Backlund transformation and Lax parirs of nonlinear evolution ;3)to give symmetry reduction and similarity solution of nonlinear evolution equation .
in this paper,a generalized Gaussian integral method is established to take calculation of intergral for decomposion coefficients of the scaling function transform in the Daubechies wavelet theory.By using teh resolution level increases.After taht,an explicit formula of reconstruction of functions based on teh scaling function transform is deduced out.and some expressions are displayed to functional,differential and integral operations of functions.it is found that this method is powerful to solve for soulutions of strong nonlinear problems.finally,an example of a two-point boundary value problem with strong nonliearity is given to show the efficiency of teh method.
in this paper a class of singular perturbation of nonlocal boundary value problems for elliptic partial differentail equations of hingher order is considered by using teh differential inequalities,the uniformly valid asymptotic expansion of solution is obtained .
IN THIS paper,we consider a class of irrational rumber which can be approximated by rational number at most exponental order,Applications are given in partial differential equation and dynamical systems.
a class of runge-kutta methods charaterized only by two parameters RKs(μ,δ) is given so taht all s-stage runge-kutta methods with distinct abscissas in the interval [0,1],if consisistent of order at less 2s-1 ,are recovered as special cases .for these methods both a-stability or algebraic stability are all equivalent to the condition μ≧,this criteria is an improvement of a famous result by burrage ([3],theorem 4.6.11).based on the methods of this class arbitrarily high order exponentially fitted methods are offered which are algebraically stable and therefore suitable for integration with a large stepsize for fast decaying components of stiff systems.
in this paper ,we give that a jordan block Jm(λ) has square -rooting matrices if and only if m=11 or λ≠0,Jm(λ) has exactly two square-rooting matrices:：±A，where a1 = c , a2 = 1/2c , a3 = -1/8c3 ,… ,
ak = -(a2ak-1+a3ak-2+…+ak-2a3+ak-1a2)/2a1 ,… (k=3,4,…,m), c2 = λ.
in this paper we study the coexistence of two species in competitive systems by using the theory of cone and order in banach spaces,and obtain that two species in competitive systems can attain unique a coexistence under certain conditions.
Ｉｎ ｔｈｉｓ ｐａｐｅｒ，Ｔｈｅ Ｗｕ-ｄｉｆｆｅｒｅｎｔｉａｌ ｃｈａｒａｃｔｅｒｉｓｔｉｃ ｓｅｔ ａｌｇｏｒｉｔｈｍ ｆｏｒ ｃｏｍｐｕｔａｔｉｏｎｓ ｓｙｍｍｅｔｒｉｅｓ ｏｆ ｐａｒｔｉａｌ ｄｉｆｆｅｒｅｎｔｉａｌ ｅｑｕａｔｉｏｎｓ（ＰＤＥｓ） ａｎｄ ｔｈｅ ｕｎｉｔｅｄ ｔｈｅｏｒｅｔｉｃ ｆｒａｍｅｗｏｒｋ ｆｏｒ ｄｅｔｅｒｍｉｎａｔｉｏｎ ｏｆ ｃｌａｓｓｉｃａｌ ａｎｄ ｎｏｎｃｌａｓｓｉｃａｌ ｓｙｍｍｅｔｒｉｅｓ ｏｆ ＰＤＥｓ ａｒｅ ｐｕｔ ｆｏｒｗａｒｄｅｄ．Ｔｈｅ ａｌｇｏｒｉｔｈｍ ａｌｗａｙｓ ｙｉｅｌｄ ａｌｌ Ｄｅｔｅｒｍｉｎｉｎｇ ｅｑｕａｔｉｎｓ （Ｄ．Ｅｓ） ｏｆ ｓｙｍｍｅｔｒｙ ｏｆ ｔｈｅ ｃｏｎｓｉｄｅｒｉｎｇ ＰＤＥｓ ａｎｄ ｍａｋｅｓ ｔｈｅ“ｓｕｐｅｒｌａｒｇｅｓｃａｌｅ”Ｄ．Ｅｓ ｅｑｕｉｖａｌｅｎｔｌｙ ｒｅｄｕｃｅ ｔｏ“ｓｍａｌｌｅｒｓｃａｌｅ” ｓｅｔ ｏｆ ｄｉｆｆｅｒｅｎｔｉａｌ ｅｑｕａｉｔｏｎｓ ａｎｄ ｔｈｅｒｅｆｏｒｅ ｓｉｇｎｉｆｉｃａｎｔｌｙ ｄｅｃｒｅａｓｅ ｔｈｅ ｃｏｍｐｕｔａｔｉｏｎａｌ ｅｆｆｏｒｔｓ ｏｆ ｓｏｌｖｉｎｇ Ｄ．Ｅｓ．Ａｌsｏ ａ ｐｒｉｎｃｉｐｌｅ ｏｆ Ｍｅｃｈａｎｉｃａｌ ｓｙｍｍｅｔｒｙ ｃｏｍｐｕｔｉｎｇ ａｎｄ ｔｅｓｔｉｎｇ ｏｆ ＰＤＥｓ＇ｓｙｍｍｅｔｒｙ ｉｓ ｇｉｖｅｎ．Ａｓ ａｎ ａｐｐｌｉｃａｔｉｏｎ ｏｆ ｏｕｒ ａｌｇｏｒｉｔｈｍ，ｃｏｍｐｌｅｔｅｌｙ ｎｏｎｃｌａｓｓｉｃａｌ ｓｙｍｍｅｔｒｉｅｓ ｏｆ Ｂｕｒｇｅｒｓ ｅｑｕａｔｉｏｎ ａｒｅ ｃａｌｃｕｌａｔｅｄ．
Ｉｎ ｔｈｉｓ ｐａｐｅｒ，ｗｅ ｇｉｖｅ ａ ｌｏｗｅｒ ｂｏｕｎｄ ｆｏｒ ｔｈｅ ｍｏｄｕｌｕｓ ｏｆ ａｎａｌｙｔｉｃ ｆｕｎｃｔｉｏｎｓ ｗｈｉｃｈ ｈａｖｅ ｚｅｒｏｓ ｉｓ |z|＜R； ｔｈｅ ｃｏｒｏｌｌａｒｙ ｅｘｔｅｎｄｓ Ｔｈｍ．１ ｏｆ ［４］ ｉｎ ｓｕｃｈ ａ ｗａｙｔｈａｔ ｏｎｅ ｃａｎ ｅａｓIｌｙ ｄｅｄｕｃｅ ｔｈｅ ｒｅｓｕｌｔｓ ｏｆ［５］ ａｂｏｕｔ ｄｉｖｉｓｉｏｎ ｉｎ ｗｅｉｇｈｔｅｄ ａｌｇｅｂｒａｓ ｏｆ ａｎａｌｙｔｉｃ ｆｕｎｃｔｉｏｎｓ ｏｎ ｔｈｅ ｕｎｉｔ ｄｉｓｃ．
Ｉｎ ｔｈｉｓ ｐａｐｅｒ，ｗｅ ｈａｖｅ ｐｒｏｖｅｄ ｔｈａｔ ｔｈｅ ｓｔａｔｉｓｔｉｃａｌｌｙ ｓｅｌｆ-ｓｉｍｉｌａｒ ｓｅｔ ｉｓ ｇｅｎｅｒａｔｅｄ ｂｙ ａ ｃｏｌｌｅｃｔｉｏｎ ｏｆ ｒａｎｄｏｍ ｃｏｎｔｒａｃｔｉｏｎ ｏｐｅｒａｔｏｒｓ｛fσ，σ∈D｝，ｗｈｅｒｅ fσ ｉｓａ ｒａｎｄｏｍ ｅｌｅｍｅｎｔｓ ｆｒｏｍ ｐｒｏｂａｂｉｌｉｔｙ ｓｐａｃｅ（Ω，，P） ｔｏ ｃｏｎ（E），ａｎｄ ｃｏｎ（E） ｄｅｎｏｔｅｓ ａｌｌ ｃｏｎｔｒａｃｔｉｏｎ ｏｐｅｒａｔｏｒｓ ｆｒｏｍ ｃｏｍｐｌｅｔｅ ｓｅｐａｒａｂｌｅ ｍｅｔｒｉｃ ｓｐａｃｅEｔｏE．
Ｂｙ ｍｅａｎｓ ｏｆ ｔｈｅ Ｉｎｖｅｒｓｅ Ｏｐｅｒａｔｏｒ Ｍｅｔｈｏｄ， ｔｈｅ ａｐｐｒｏｘｉｍａｔｅ ａｎａｌｙｔｉｃ ｓｏｌｕｔｉｏｎ ｆｏｒ ｔｈｅ ｍａｔｈｅｍａｔｉｃａｌ ｍｏｄｅｌ ｏｆ ｔｈｅ ｐａｃｋｅｄ ｂｅｄ ｃａｔａｌｙｔｉｃ ｒｅａｃｔｏｒ （ｉ．ｅ．ａｋｉｎｄ ｏｆ ｓｔｒｏｎｇ ｎｏｎｌｉｎｅｒ ｐａｒｔｉａｌ ｄｉｆｆｅｒｅｎｔｉａｌ ｅｑｕａｔｉｏｎｓ ｗｉｔｈ ｉｎｉｔｉａｌ-ｂｏｕｎｄａｒｙ ｖａｌｕｅ ｐｒｏｂｌｅｍｓ） ａｒｅ ｓｔｕｄｉｅｄ．Ａ ｎｅｗ ｔｅｃｈｎｉｑｕｅ，ｗｈｉｃｈ ｒｅｐｌａｃｅｓ‘ｔｈｅ ａｒｉｔｈｍｅｔｉｃ ｍｅａｎ ｏｆ ｔｈｅ ｐａｒｔｉａｌ ｓｏｌｕｔｉｏｎｓ’ｂｙ ‘ｔｈｅ ｇｅｏｍｅｔｒｙ ｍｅａｎ ｏｆ ｔｈｅ ｐａｒｔｉａｌ ｓｏｌｕｔｉｏｎｓ’， ｉｓ ｐｕｔ ｆｏｒｗａｒｄ． Ｔｈｅ ｔｅｃｈｎｉｑｕｅ ｌｅｄｓ ｔｈａｔ ｔｈｅ ａｐｐｏｘｉｍａｔｅ ａｎａｌｙｔｉｃ ｓｏｌｕｔｉｏｎｓ ａｒｅ ｇｉｖｅｎ ｒｅａｓｏｎａｂｌｙ．
Ｔｈｅ ｐａｐｅｒ ｓｔｕｄｉｅｓ ｔｈｅ ｒａｎｄｏｍ ｐｏｗｅｒ ｓｅｒｉｅｓ ｏｆ ｇｅｎｅｒａｌ ｅｎｏｕｇｈ，ａｎｄ ｐｒｏｖｅｓ ｔｈａｔ ｔｈｅ ｒａｎｄｏｍ ｐｏｗｅｒ ｓｅｒｉｅｓ ｏｆ ｆｉｎｉｔｅ ｏｒｄｅｒ ｄｏ ｎｏｔ ｈａｖｅ ａｌｍｏｓｔ ｓｕｒｅｌｙ ｄｅｆｉｃｉｅｎｔ ｆｕｎｃｔｉｏｎ．
Wish all the best wishes for youRecommendationWish all the best wishes for youRecommendation