中国科学院数学与系统科学研究院期刊网

15 February 2000, Volume 43 Issue 2
    

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  • On Generic Minimal Submanifolds of a Quaternionic Projective Space
    Cheng Qin QU(1),Wei Dong SONG(
    Acta Mathematica Sinica, Chinese Series. 2000, 43(2): 193-200. https://doi.org/10.12386/A2000sxxb0026
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    The purpose of the present paper is to study generic minimal submanifold of quaternionic projective space, an integral formula is obtained, and we obtain the sectional curvature's pinching theorem of the compact minimal submanifold.
  • Criteria of Univalence for Holomorphic Mapping on Unit Ball of Cn II
    Hong Bin CHEN,Jun Lin QIN,Hong
    Acta Mathematica Sinica, Chinese Series. 2000, 43(2): 201-204. https://doi.org/10.12386/A2000sxxb0027
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    In this paper, a general univalency criteria for holomorphic on unit ball of Cn is obtained by means subordination chains and many concrete univalancy criteria are given as special cases of the main theorem. Some of them are generalize the well known results of Ahlfors Becher and Krzyz, and others are new.
  • The Lattices of Regular Operators on Banach Lattices
    Zi Li CHEN
    Acta Mathematica Sinica, Chinese Series. 2000, 43(2): 205-212. https://doi.org/10.12386/A2000sxxb0028
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    In this paper we first present some conditions on Banach lattice E such that the space Lr(E,F) is a Riesz space even if Banach lattice F is not Dedekind a-complete, then we deduce some characterizations on Banach lattice F such that each continuous operator from a Lp-space into F is regular. Some related results are also provided.
  • On Distributive Complete Lattices for Which the Scott Topology Has a Basis of Open Filters
    Lin XIE,Yu Qing SONG
    Acta Mathematica Sinica, Chinese Series. 2000, 43(2): 213-220. https://doi.org/10.12386/A2000sxxb0029
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    In this paper, AS property is introduced, and a problem in [1] is discussed. First, the paper shows that the Scott topology on a distributive complete lattice L has a basis of open filters if and only if L is a KS. frame for some ordinal number a, i.e., KS frame. By the result, one can judge whether the Scott topology and the Scott open filter topology on a distributive complete lattice are coincide. Then some KS frames are constructed in the paper, which are not continuous.
  • The Behavior of Functions Related to the Digit-Sequence
    Xiu Yuan YU
    Acta Mathematica Sinica, Chinese Series. 2000, 43(2): 221-224. https://doi.org/10.12386/A2000sxxb0030
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    For positive integer n = a 10kn + + a0, we say that a, a0 are the digits of n, and denote s(n) = a + + a0 ), sm(n) = (a) m + + (a))m. We call 1m2m3m4m5m6m7m8m9m 1m0m1m1m1m2m1m3m1m4m the m-order sequence of digits, and define the function fm (x) = 1m + 2mx1 + + 9mx8 + 1mx9 + 0x10 + 1mx11 + 1mx12+ . Two theorems on fm(x) are given.
  • Dimensions of Subsets of a Class of Cantor-type Sets
    Wen Xia LI,Dong Mei XIAO
    Acta Mathematica Sinica, Chinese Series. 2000, 43(2): 225-232. https://doi.org/10.12386/A2000sxxb0031
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    Let E be a Cantor-type set on real line and let Ea = E+a = { } for . Let Go = { ; dimH(E E) = dimB(Ea E) = pdimH E}, 0 < p < 1, where E - E = {x - y: x,y E}. The fractal dimensions of Ea E and Gp are determined under some conditions.
  • Nonexistence of Positive Solution of a Class of Nonlinear Delay Partial Difference Equation
    Xin Ping GUAN(1),Jun YANG(2),S
    Acta Mathematica Sinica, Chinese Series. 2000, 43(2): 233-238. https://doi.org/10.12386/A2000sxxb0032
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    This paper is concerned with nonexistence of positive solution of a class of nonlinear delay partial difference equation. Sufficient conditions are obtained for the nonexistence of positive solutions of this equation.
  • Cartan Embeddings of Compact Riemannian 4-Symmetric Spaces
    Quan Qin JIN
    Acta Mathematica Sinica, Chinese Series. 2000, 43(2): 239-244. https://doi.org/10.12386/A2000sxxb0033
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    In this paper, we first give the concept of a Cartan embedding of a homogeneous space, then using the theory of automorphisms of Lie groups and Lie algebras, we determine the compact Riemannian 4-symmetric spaces whose Cartan embedings are minimal.
  • A Class of Planar n-polynomial System with at Least [3/8n~2] Family Limit Cycles
    Jing Xin BAI
    Acta Mathematica Sinica, Chinese Series. 2000, 43(2): 245-252. https://doi.org/10.12386/A2000sxxb0034
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    In this paper, we give the following results: (1) A class of planar n-polynomial system with at least [n2] weak focus of order 1. (2) A class of planar n-polynomial system with at least [n2] family limit cycles.
  • Construction of Pluriharmonic Maps into Complex Grassmann Manifolds
    Xiao Li CHAO(1),Yi Bing SHEN(2
    Acta Mathematica Sinica, Chinese Series. 2000, 43(2): 253-261. https://doi.org/10.12386/A2000sxxb0035
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    In this paper, some construction theorems of pluriharmonic maps into complex Grassmann manifolds are obtained. These generalize the results of Mo Xiaohuan, Burstall F. E., Wood J. C. and Udagawa S.
  • Growth of Meromorphic Functions Relate to Differential Polynomial
    Wen Chang Wang(1),Yong Xing GU
    Acta Mathematica Sinica, Chinese Series. 2000, 43(2): 261-268. https://doi.org/10.12386/A2000sxxb0036
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    In this paper, we discus the growth of meromorphic functions with a deficient value, and prove that. Suppose that f(z) is a transcendental meromorphic function of lower order with a deficient value, let =fnP[f] + P(f), where, P[f] and Q[f] are differential polynomials of f(z), and all of the orders of the coefficients of Q[f] and P[f] are less than , furthermore, the weight of P(f) is at most n - 3. If there exist finite number of rays satisfy with a positive number , for any small positive number , then max1 where, is the order of f(z).
  • Non-stationary MDP Average Model - The Existence of Persistently Optimal (G, B)-Generated Policies
    Xian Ping GUO
    Acta Mathematica Sinica, Chinese Series. 2000, 43(2): 269-274. https://doi.org/10.12386/A2000sxxb0037
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    In this paper, we consider the non-stationary MDP average model with countable state space and arb.iotrary action space : Using the (f, B)-generated policies of Feinberg E. A. for reference. We put forward the (G, B)-generated policies which are the generalization of Markov policies and (f, B)-generated policies of Feinberg E. A.. By probability and analysics method, we prove the existence of persistently optimal (G, B)-generated policies. under weaker ergodict conditions.
  • s-Multiplier Convergence and Theorems of the Orlicz-Pettis-Type
    Song Long WEN(1),Cheng Ri CUI(
    Acta Mathematica Sinica, Chinese Series. 2000, 43(2): 275-282. https://doi.org/10.12386/A2000sxxb0038
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    In this paper, we give the strongest admissible polar topology F(Us) for which it has the same s-multiplier convergent sequence as weak topology in the locally convex space. Also we obtain the sufficient condition and necessary condition for Thus, we prove that c0 (or lp, 0 < p < )- multiplier convergence is invariants with respect to all admissible polar topology.
  • Grtzsck Ring and Ramanujan's Modular Equations
    Song Liang QIU
    Acta Mathematica Sinica, Chinese Series. 2000, 43(2): 283-290. https://doi.org/10.12386/A2000sxxb0039
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    The author establishes the connection between the modulusμ(γ) of the plane Grtzsch ring and its generalizationμa(γ), which appears in Ramanujan's generalized modular equation, and extends several well-known results forμ(γ) toμa(γ), thus providing a method for the study of the modular equations.
  • Analytic Characterization for Mazimal Accretiveness of Singular Differential Operators
    Guang Sheng WEI,Zong Ben XU
    Acta Mathematica Sinica, Chinese Series. 2000, 43(2): 291-300. https://doi.org/10.12386/A2000sxxb0040
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    Let l(y) = be a symmetric differential expression defined on interval [a). In L2 , we give the complete characterization for all maximal accretive operators associated with l(y) via explicit boundary conditions, and we obtain the complete analytic description for all nonnegative self-adjoint extensions of the minimal operator generated by l(y).
  • On the Uniqueness of Solutions of Initial Problems for a Class of Semilinear Singular Heat Equations
    Su Wen JIAN(1),Feng Zao YANG(2
    Acta Mathematica Sinica, Chinese Series. 2000, 43(2): 301-308. https://doi.org/10.12386/A2000sxxb0041
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    Let u(x, t), u(t, x) be two nonnegative classical solution in ST = (0, T)× Rn for the following initial problem where f(x) is a continuous, bounded and nonnegative real function. Then we have the following results: (1) If f(x) is not identically equal to zero, then u(t, x) = u(t, x) in ST; (2) Ifγ> 1, then u(t,x) = u(t,x) in ST, (3) If 0 <γ< 1, f(x) 0 then the solution for (1.1), (1.2) is not unique, and the whole set of all nontrivial solutions is u(t, s) = where is a parameter, Sign = max {γ, 0}.
  • Regularity of n Dimensional Mbius Transformations
    Xian Tao WANG,Yue Ping JIANG
    Acta Mathematica Sinica, Chinese Series. 2000, 43(2): 309-316. https://doi.org/10.12386/A2000sxxb0042
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    In this paper, by using the Clifford matrix representation of higher dimensional Mobius transformations, we discuss the regularity of n dimensional Mobius transformations. We prove that each three dimensional parabolic Mobius transformation is regular. Also we obtain a necessary and sufficient condition for three dimensional nonparabolic Mobius transformations to be regular. In the end, we construct an example to show that the above necessary and sufficient condition does not hold in SL(2, n ) when n = 2k, k 2.
  • The Periodic Coexistence of Ecosystems with Three Species
    Ying Dong LIU,Zheng Yuan LI
    Acta Mathematica Sinica, Chinese Series. 2000, 43(2): 317-328. https://doi.org/10.12386/A2000sxxb0043
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    In this paper by using degree theory and upper-lower solution method conditions for ensuring the periodic coexistence of ecosystems with three species are given.
  • On the Problem of Continuous Selections for Upper Semicontinuous Maps
    Shu Wen XIANG
    Acta Mathematica Sinica, Chinese Series. 2000, 43(2): 329-336. https://doi.org/10.12386/A2000sxxb0044
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    The purpose of this paper is to give a further study on the existence of continuous selections for upper semicontinuous multivalued maps. First we show that a statement in Aubin J. P.[1] about continuous selections is not correct by a counter example. Next we obtain some results with uniform approximation about selectionable properties of upper semicontinuous maps.
  • Right Clifford Semigroups as Left Quotient Semigroups
    Yuan Ping ZHANG
    Acta Mathematica Sinica, Chinese Series. 2000, 43(2): 337-342. https://doi.org/10.12386/A2000sxxb0045
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    The right Clifford semigroups as left quotient semigroups are investigated in this paper. The left orders in right Clifford semigroups have been characterized by means of so-called suitable pairs. The results have extended the scope of the study of quotient semigroups.
  • Essential Spectrum of p-Hyponormal Operators and Quasisimilarity
    Ying Bin RUAN,Zi Kun YAN
    Acta Mathematica Sinica, Chinese Series. 2000, 43(2): 343-348. https://doi.org/10.12386/A2000sxxb0046
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    In this paper, we prove that for every p-hyponormal operator A, there corresponds a hyponormal operator A such that A and A have the same closed range points and same essential spectrum and same spectrum. This is then used to derive that if A is a p - hyponormal operator, B is any bounded linear operator and there exists a dense range operator X such that XB = AX, then (A) (B). We also prove that if A is a p-hyponormal operator and R(A) is closed or KerA = KerA , B is any bounded linear operator, B and A are quasisimilar, then (A) (B).
  • Linearized Oscillations for First Order Delay Differential Equations in a Critical State
    Xian Hua TANG(1),Jian She YU(2
    Acta Mathematica Sinica, Chinese Series. 2000, 43(2): 349-358. https://doi.org/10.12386/A2000sxxb0047
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    We establish an equivalent theorem of oscillation of the following first order nonlinear delay differential equation x'(t) and a related second order ordinary differential equation in a critical state. And then we obtain some sufficient conditions which guarantee the first order nonlinear nonautonomous differential equation and the corresponding linear equation have the same oscillatory behavior. A open problem proposed by Zhang is solved.
  • Littlewood-Paley's g-Function on Herz-type Spaces
    Zong Guang LIU,Si Lei WANG
    Acta Mathematica Sinica, Chinese Series. 2000, 43(2): 359-366. https://doi.org/10.12386/A2000sxxb0048
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    In this papers the boundedness properties are considered for a large class of sublinear operators, including Littlewood-Paley's g-function, from Herz spaces Kq to weak Herz space WK (Rn) , When the boundedness for g-function from Herz-type Hardy space HKq(Rn) to Herz space K(Rn) or weak Herz space WK (Rn) are also established.
  • On the Simultaneous Approximation of Functions and Their Derivatives by the Bernstein-Durrmeyer Operators
    Shun Sheng GUO(1),Xi Wu LIU(2)
    Acta Mathematica Sinica, Chinese Series. 2000, 43(2): 367-374. https://doi.org/10.12386/A2000sxxb0049
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    Using the pointwise modulus of continuity, we discussed the simultaneous approximation for Bernstein-Durrmeyer operators. The results include the results on functions of bounded variation and continuous functions.
  • The Solvability of Operator Equation AX - XA = C with Unbounded Operator A
    Gen Qi XU,De Xing FENG
    Acta Mathematica Sinica, Chinese Series. 2000, 43(2): 375-384. https://doi.org/10.12386/A2000sxxb0050
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    The solvability of the operator equation AX - XA = C with unbounded operator A is studied in Banach space E. Based on integrated bisemigroup and using the Posed weak solution concept in this paper, concerning the jumped initial value problem in the space C(E), it is shown that if the operator A reduced by an operator A in C(E) is the generator of a weak integrated bisemigroup, then the operator eqution mentioned above is solvable for any C satisfying certain constraint conditions.
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