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25 September 1992, Volume 12 Issue 3 Previous Issue    Next Issue

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GENERALIZED BIANCHI'S IDENTITIES FOR VARIANT CONSTRAINED SYSTEM Li Ziping Acta mathematica scientia,Series B. 1992, 12 (3):  241-247.  Abstract ( 55 )   RICH HTML PDF (454KB) ( 31 )   Save In this paper the generalized Bianchi's identities for the variant constrained system (GBIVOS) with non-invariant action integral and constraint conditions was derived, and the strong and weak conservation laws for such system was deduced. The preliminary applications of the GBIVCS to the case for some models of field theories was given. The Dirac constraint of such system was discussed. Related Articles | Metrics

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DISTRIBUTED OPTIMAL LOCAL DOUBLE LOOP NETWORK Li Layuan Acta mathematica scientia,Series B. 1992, 12 (3):  248-259.  Abstract ( 87 )   RICH HTML PDF (747KB) ( 37 )   Save A distibuted optimal local double loop(DOLDL) network is presented. Emphasis is laid on the topology and distributed routing algorithms for the DOLDL. On the basis of building an abstract model, a set of definitions and theorems are described and proved. An algorithm which can optimize the double loop networks is presented. The optimal values of the topologic parameters for the DOLDL have been obtained by the algorithm, and these numer. cal results are analyzed, The study shows that the bounds of the optimal diameter (d) and average hop distance (a) for this class of networks are 「√3N-2」 ≤ d ≤ 「√3N+1」 and, (5N/9(N-1))(√3N-1.8) < a < (5N/9(N-1))·(√3N-0.23) respectively (N is the number of nodes in the network. 「3 ≤ N ≤ 104). A class of the distributed routing algorithms for the DOLDL and the implementation procedure of an adaptive fault-tolerant algorithm are proposed. The correctness of the algorithm has been also verified by simulating. Related Articles | Metrics

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NEW GENERALIZED FUNCTIONSIN NONSTANDARD FRAMEWORK Li Banghe, Li Yaqing Acta mathematica scientia,Series B. 1992, 12 (3):  260-269.  Abstract ( 72 )   RICH HTML PDF (615KB) ( 29 )   Save In this paper we develope a theory of new generalized functions by using Nonstandard Analysis which is closely relevant to that of Colombeau's new generalized functions. Related Articles | Metrics

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BOSON-FERMION ALGEBRA AND BOSON-FERMION REPRESENTATION OF LIE SUPERALGEBRA OSP (1, 2) Zeng Gaojian Acta mathematica scientia,Series B. 1992, 12 (3):  270-281.  Abstract ( 72 )   RICH HTML PDF (699KB) ( 29 )   Save We describe the establishing process for the Boson-Fermion algebra of OSP(1, 2) starting from the fundamental Wigner operators of OSP(1, 2), and study its structure feature and representation theory. We also give the Boson-Fermion representation of OSP (1, 2), which is an infinite dimensional and grade star representation. Related Articles | Metrics

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A NOTE ON THE NUMBER OF CUBIC PLANAR MAPS Liu Yanpei Acta mathematica scientia,Series B. 1992, 12 (3):  282-285.  Abstract ( 74 )   RICH HTML PDF (238KB) ( 32 )   Save This note shows that the number of rooted cubic planar maps (loops and multi-edges are allowed) with 2n-3 non-root-vertices, n ≥ 3, is ∑i=0n-1(22n-i-1!(2n-i-1)!)/(i!(n-i-2)!n!(n+1)!). Related Articles | Metrics

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SOLUTIONS OF THE BENJAMIN-ONO EQUATION IN FRACTIONAL ORDER SOBOLEV SPACES Feng Xueshang Acta mathematica scientia,Series B. 1992, 12 (3):  286-291.  Abstract ( 69 )   RICH HTML PDF (341KB) ( 30 )   Save We show for the Benjamin-Ono equation an existence uniqeness theorem in Sobolev spaces of arbitrary fractional order s ≥ 2, provided the initial data is given in the same space. Related Articles | Metrics

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POSITIVE SOLUTIONS OF NONLINEAR ELLIPTIC EQUATIONS WITH MIXED BOUNDARY CONDITIONS Xue Ruying Acta mathematica scientia,Series B. 1992, 12 (3):  292-303.  Abstract ( 64 )   RICH HTML PDF (658KB) ( 28 )   Save We consider the nonlinear elliptic equation with mixed boundary conditions (P)-△u=b(x)up+λu,u>0 for x∈Ω,u|Γ0=0,(∂u)/∂n|Γ1=0, where Ω is a smooth bounded domain in RN (N ≥ 3), whose boundary ∂Ω is made of two open sets Γ0 and Γ1,Γ0∩Γ1=ϕ, ∂Ω=Γ0∪Γ1,p=(N+2)/N-2. We prove the existence of a positive solution of (P)when b (x) and λ satisfy suitable conditions. Related Articles | Metrics

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UNIQUENESS OF SOLUTIONS OF SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR THIRD QRDER NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS Zhao Weilic Acta mathematica scientia,Series B. 1992, 12 (3):  304-307.  Abstract ( 54 )   RICH HTML PDF (248KB) ( 34 )   Save 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: εy'"=q(x,y,y',y",ε), y(i)(0,ε)=ai(ε),y(1,ε)=β(ε),y'(1,ε)=γ(ε),where i=1, 2; ai(ε), β(ε) and γ(ε) are functions defined on (0, ε0], while ε0>0 is a constant. This paper is the continuation of our works[4, 6]. Related Articles | Metrics

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ON ALMOST ISOMETRIES FROM L1 (μ) INTO L∞(v) OR Cb (△) Ding Gunanggui Acta mathematica scientia,Series B. 1992, 12 (3):  308-311.  Abstract ( 70 )   RICH HTML PDF (235KB) ( 36 )   Save Let μ,ν be measures with diem L1(μ)=dim L∞(ν)=∞ and △ be a "subinterval" of the real line. Let E=L∞(ν) or Cb(△), in this paper it turns out that the IAP for the space B(L1(μ)→E) has a negative answer. Related Articles | Metrics

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THE INTERACTIONS OF SHOCK WAVES OF NONSTRICTLY HYPERBOLIC SYSTEMS Liu Hailiang Acta mathematica scientia,Series B. 1992, 12 (3):  312-336.  Abstract ( 71 )   RICH HTML PDF (1346KB) ( 27 )   Save The interaction of shock waves is investigated for the following nonstrictly hyperbolic system: ut+(1)/2(au2+v2)x=0 vt+(uv)x=0 (1 < α < 2) The interaction of shock waves is complicated, with new types of shock waves, and new singula rities in the dependence of interaction on the relative positions of the three states separated by shock waves. Several ideas are introduced to helo organize and clarify the new phenomena. Related Articles | Metrics

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POSITIVE SOLUTIONS OF HIGHER ORDER SUBLINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS Miao Yihua Acta mathematica scientia,Series B. 1992, 12 (3):  337-345.  Abstract ( 66 )   RICH HTML PDF (515KB) ( 31 )   Save In this paper, we discuss higher order sublinear functional differential equation x(n)(t)+p(t)xv(g(t))=0 t ≥ t0 where n ≥ 2,0 < v < 1,p(t)∈C(R+,R+),g(t)∈C([t0,∞),R+),0 ≤ g(t) ≤ t (t ≥ t0) and limt→∞g(t)=∞.R+=[0,∞). Some necessary and sufficient conditions for existence of positive solution of the equation are established. Related Articles | Metrics

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STRUCTURE OF COMPUTATIVE TREE FOR COMPUTABLE FUNCTION Li Chuanxiang Acta mathematica scientia,Series B. 1992, 12 (3):  346-354.  Abstract ( 67 )   RICH HTML PDF (532KB) ( 31 )   Save In this paper, we study the computative Structure of computable function——a structure of computative tree, and, by analysis on it, got the most general algorithm and model for computation on computable functions. Related Articles | Metrics

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SOME PROBLEMS IN PARTIAL ABSTRACT DATA TYPE Li Zhongzhang, Li Chuanxiang, Wang Hanfei Acta mathematica scientia,Series B. 1992, 12 (3):  355-360.  Abstract ( 73 )   RICH HTML PDF (392KB) ( 28 )   Save In this paper, we discuss some characteristic properties of partial abstract data type (PADT) and show the diffrence between PADT and abstract data type (ADT) in specification of programming language. Finally, we clarify that PADT is necessary in programming language description. Related Articles | Metrics