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25 December 1988, Volume 8 Issue 4 Previous Issue    Next Issue

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THE APPROXIMATION PROBLEM OF ALMOST ISOMETRIC OPERATORS BY ISOMETRIC OPERATORS Ding Guanggui Acta mathematica scientia,Series B. 1988, 8 (4):  361-372.  Abstract ( 48 )   RICH HTML PDF (773KB) ( 26 )   Save The strictly (theorized) "equidistant operater" does not come into existence. What can be seen in practice is "almost equidistant" operator. The description of "almost equidistance" is essentially a form of "absolute error", and in this paper we will study the "almost equidistance (isometry)" described by the form of "relative error". Related Articles | Metrics

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EXISTENCE FOR A TWO POINT BOUNDARY VALUE PROBLEM ARISING IN ELECTRODIFFUSION H. B. Thompson Acta mathematica scientia,Series B. 1988, 8 (4):  373-387.  Abstract ( 23 )   RICH HTML PDF (920KB) ( 29 )   Save In this paper, we consider a two point boundary value problem of the form y"=f(x, y, y', y(0), y(1)); y'(0)=0=y'(1), where f:[0,1]×R4n→Rn is continuous. Related Articles | Metrics

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ON UNIFORMLY VALID ESTIMATE OF SOLUTIONS TO SINGULAR PERTURBATION ROBIN BOUNDARY VALUE PROBLEM Wang Huaizhong Zhou Qinde Acta mathematica scientia,Series B. 1988, 8 (4):  389-398.  Abstract ( 41 )   RICH HTML PDF (619KB) ( 31 )   Save In this paper we study the Robin boundary value problem with a small parameter εy"=f(t, y, ω(ε)y', ε), a0y(0) +b0y'(0)=ξ(ε), a1y(1)+b1y'(1)=η(ε), where the function ω(ε) is continuous on ε ≥ 0 with ω(0)=0. Assuming all known functions are suitably smooth, f satisfies Nagumo's condition, fy>0, ai2-bi2≠0, (-1)iaibi ≤ 0 (i=0, 1) and the reduced equation 0=f(t, y, 0, 0) has a solution y(t) (0 ≤ t ≤ 1), we prove the existence and the uniqueness of the solution for the boundary value problem and givo an asymptotic expansion of the solution in the power ε1/2 which is uniformly valid on 0 ≤ t ≤ 1. Related Articles | Metrics

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THE PARSEVAL FORMULA IN THE HARMONIC ANALYSIS FOR OPERATOR AND THE SUPPORT FOR OPERATORS Yu Shumo Acta mathematica scientia,Series B. 1988, 8 (4):  399-407.  Abstract ( 49 )   RICH HTML PDF (547KB) ( 33 )   Save In this paper a harmonic analysis for operators on a homogeneous Banach space on the additional group of real numbers is discussed. Main resu lts are as following: 1. The Parseval formula for integrable operators with respect right translation holds under some conditions; i.e., the Fourier transform for the product of opreator T and T* at zero is equal to the integral for the product of Fourier transform T(γ) and T(γ)* in the strong operator topelogy. 2. The finite support and finite cosupport for any beunded linear operator are both unique except the having Haar measure zero. 3. The following are equivalent:(1) The measurable set M is the supporting set for operator T; (2). The measursble set M is the cosupporting set for T*. Related Articles | Metrics

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CODIMENSION 1 IMMERSIONS OF THE CIRCLE AND SURFACES Li Banghe Acta mathematica scientia,Series B. 1988, 8 (4):  409-419.  Abstract ( 47 )   RICH HTML PDF (705KB) ( 31 )   Save Let f:S1→M2 or M2→N3 be a map, we classify the immersions homotopic to f, where M2 and N3 are arbitrary surface and 3-manifolds respectively. Related Articles | Metrics

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STABILITY OF THE SOLUTION OF THE ITERATED EQUATION ∑i=1n λif(x)=F(x) Zhang Weinian Acta mathematica scientia,Series B. 1988, 8 (4):  421-424.  Abstract ( 52 )   RICH HTML PDF (210KB) ( 36 )   Save This note is a further work of discussion on the iterated equation λif(x)+λ2f2(x)+…λnfn(x)=F(x), following the author's conclusions of the existence and uniqueness of this equation. In this note we prove that the sufficient condition of the stability of the solution is the same one as the uniqueness of the solution (see[4]). Related Articles | Metrics

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A NOTE ON THE ONSET OF MELTING IN A CLASS OF SIMPLE METALS CONDITION ON THE APPLIED BOUNDARY FLUX Colin Rogers, Guo Benyu Acta mathematica scientia,Series B. 1988, 8 (4):  425-430.  Abstract ( 66 )   RICH HTML PDF (340KB) ( 29 )   Save The onset of melting in a class of simple metals is considered for an applied heat flux q0=h0/√t at the boundary. Reduction of the nonlinear problem to a linear canonical form is obtained by a reciprocal transformation. Bounds are obtained on h0 for melting to occur. Related Articles | Metrics

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NONTRIVIAL SOLUTION OF NONLINEAR SCALAR FIELD EQUATIONS WITH STRONG NONLINEARITY Li Gongbao Zhu Xiping Acta mathematica scientia,Series B. 1988, 8 (4):  431-448.  Abstract ( 43 )   RICH HTML PDF (1003KB) ( 35 )   Save In this paper, we use the concentration-compactness prieciple togther with the Mountain Pass Lemma to get the existence of nontrivial solutions of the following scalar field equations with strong nonlinearity -∑i=1N ∂/∂xi(|▽u|p-2 ∂u/∂xi)+a(x)|u|q-2 u=f(x,u),x∈RN,N ≥ 2 u∈E={u∈Lq(RN)|u real,∂u/∂xi∈Lp(RN),1 ≤ i ≤ N}, where 2 ≤ p ≤ q,p=N. Related Articles | Metrics

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UNIQUENESS OF GROUND STATE SOLUTIONS Zhang Liqun Acta mathematica scientia,Series B. 1988, 8 (4):  449-467.  Abstract ( 48 )   RICH HTML PDF (1119KB) ( 42 )   Save In this paper we discuss the uniqueness of ground state solutions of the problem △u+f(u)=0 in Rn u(x)-0 as|x|→∞, where n>2, f(u) satisfies some conditions which ensure the existence of a ground state solution. Related Articles | Metrics

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REDUCTION OF HIERARCHICAL STRUCTURE Li Chuanxiang Acta mathematica scientia,Series B. 1988, 8 (4):  469-479.  Abstract ( 44 )   RICH HTML PDF (618KB) ( 36 )   Save In this paper, we've studied distributing characteristic of the paths in these graphs, put forward an idea of the nested rule on path distribution, and established a lat ice algebric structure of a covering of intervals. On the basis of this, we've established the partition theory and a reducible model of hierarchical structure. Related Articles | Metrics