Ω-CONVERGENCE AND Ω-COMPACTNESS OF THE TOPOLOGICAL SPACES

1　 - Convergence of the TopologicalSpaces　　 Definition 1　 Assume (X,T) is a topologicalspace,the subset family {An∶ n∈ N } 2 X,x0 ∈X.If for any open neighborhood Ux0 of x0 ,thereexists a positive M much that An Ux0 ,for n>M,then call {An∶ n∈ N }isΩ - converges to x0 ,or thesubsetfamily{An∶n∈N}isΩ- convergence.　　 Definition2　Assume(X,T) is a topologicalspace and {xn∶ n∈ N }is a sequence of X.If forx0∈ X and any open neighborhood Ux0 of x0 ,thereexists a positive …     

Focusing of Spherical Nonlinear Pulses for Nonlinear Wave Equations Ⅲ. Subcritical Case

IntroductionConsider the following initial value problem inR1++3={t>0, x∈R3}: ( t2-Δx)ε+ F1( tε p1-1 t+ε), tθε q1-1 tθε) = 0( t2- 4Δx)θε+ F2( tε p2-1 tε, tθε q2-1 tθε) = 0ε t=0=εJ+1U0r,r -ε r0 tε t=0=εJU1r,r -ε r0θε t=0=εJ+1V0r,r -ε 2r0 tθε t=0=εJV1r,r -ε 2r0(1)where r= x with x=(x1,x2,x3)∈R3, r0>0,and 1相似文献   

一类二阶拟线性退缩抛物方程的第一边值问题

本文研究了如下形式的拟线性退缩抛物方程u/t=a(u,x,t)~2u/x~2+b(x,t)u/x+c(u,x,t)的第一边值问题,式中 a(u,x,t),b(x,t),c(u,x,t)适当光滑,且 a(u,x,t)≥0。我们证明了属于 W_2~1∩C~α解的存在性。     

NUMERICAL SIMULATION OF SINGLE-GROUP, STEADY STATE AND ISOTROPIC NEUTRON TRANSPORT EQUATION IN DIFFUSIVE REGIMES

The single-group,steadystate,isotropic for mofthe neutron transport equationis given by[1]Ω·+σtI-σsPψ(x,Ω)=q(x,Ω)(x,Ω)∈D×Sψ(x,Ω)=g(x,Ω)x∈Din={x∈D,γ(x)·Ω<0(1)whereσtis the total cross section,σSis the scatteringcross section,andψ(x,Ω)is the angular flux to bedeter mined for all pointsx∈D,D Rn(n=2,3)and all possible travel directionsΩ,ΩS(Sis a u-nit disk or a unit sphere),γ(x)denotes the out wardunit nor mal atx∈D,Idenotes the identity opera-tor,the operator…     

一类含参二阶三点边值问题正解的存在性及多解性

考虑含参二阶三点边值问题u″+λg(t)f(u)=0,00是参数;0<α<1;0<η<1是给定的实数;g∈C([0,1],[0,∞]);非线性项f满足:f∈C((0,∞),(0,∞),且f0∶=li mf(uu)∈[0,∞],f∞∶=li mf(uu)∈[0,∞].在f0,f∞取不同值的各种情形下,用锥上的不动点定理得到了问题(1)正解存在,多解性和不存在的结论及相应的参数λ的取值范围.     

Picard Approximation of Fixed Points of Nonexpansive Mappings

LetXbeaBanachspaceandCbeaconvexsubsetofX .T :X→Cisanonexpansivemapping ,thatis ,Tx -Ty ≤x - y forallx ,y∈X .Now ,westudythefollowingiterativeprocessforx0 ,un∈C ,xn 1=Snxn, ( 1 )whereSn =αn0 I αn1T αn2 T2 … αnkTk γnun,andαni≥ 0 ,0 <α≤αn     

二阶多点边值问题三个正解的存在性

利用一个新的不动点定理,得到了二阶非线性n-点边值问题:u″(t) f(t,u(t))=0,t∈(0,1)u′(0)=∑n-2i=1biu′(ξi),u(1)=∑ki=1aiu(ξi)-∑n-2i=k 1aiu(ξi)至少存在三个正解的一个充分条件,其中0<ξ1<ξ2<…<ξn-2<1,ai,bi∈[0,∞)且满足0<∑ki=1ai-∑n-2i=k 1ai<1,∑n-2i=1bi<1。     

关于圆合成的注记

设Ω是一个环,在Ω上引入二元运算a。b=a+b+ab,a,b∈Ω称为环Ω的圆合成.容易验证在圆合成下(Ω,0)是一个半群,环Ω中的零元素成为(Ω,0)的单位元,因而(Ω,0)是有壹半群.同样,容易看出(Ω,0)的一切拟正则元作成(Ω,0)的子群.我们以 S 记这个子群.McCoy.N.H 在[1]中断言 S 是 Abel 群.作者用反例说明这种论断是不对的.考虑模2整数域 Z_2上的二阶全阵环(Z_2)_2,它由16个元素组成.用     

UNIQUENESS FOR SOLUTIONS OF NONHOMOGENEOUS A -HARMONIC EQUATIONS WITH VERY WEAK BOUNDARY VALUES

LetΩ be a bounded domain in Rn.We consid-er the quasilinear elliptic second order equationdiv A(x,u) =B(x,u) (1 )where A∶ Ω×Rn→Rn and B∶ Ω×Rn→R are func-tions satisfying the usual measurability conditions(Carathodory conditions) and,for1 0whenever h1≠ h2 (4)　　　 |B(x,h) |≤β|h|p -1(5)for almostevery x∈ Ω and all h,h1…     

A NEW APPROACH FOR PREDICTING DYNAMIC BEHAVIOR OF EXTRA-HIGH SPEED DIGITAL VALVE

Nomenclaturet- Time( s)μ0 - Permeability of air( H/ m)μ- Permeability of the material ( H/ m)U- Voltage( V)I- Circuit current ( A)R- Circuit resistance( Ω)N- Number of coil turnx- Plunger displacement ( m)x- Plunger speedΦ - Magnetic flux ( Wb)B- Magnetic flux density( T)H - Magnetic filed ( A/ m)M- Mass of moving parts( kg)Fmag- Magnetic force( N)Fspring- Spring setting force( N)Fc- Viscidity resistance ( N)Fhyd- Reaction force causedby the flowing oil( N)L- Inductance ( …