中国科学院数学与系统科学研究院期刊网

15 November 1995, Volume 38 Issue 6
    

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  • Acta Mathematica Sinica, Chinese Series. 1995, 38(6): . https://doi.org/10.12386/A1995sxxb0099
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    In this paper,We defined the isoparametric maps in a complex projective spaceP_n(C) and proved the horizontal lift f in S ̄(2n+1) of the isoparametric map f in P_n(C) under theHopf principal bundle is the isoparametric map in S ̄(2n+1) Many examples of the isoparametricsubmanifolds in P_n(C) are obtained by the isotropy representations of symmetric spaces.
  • Acta Mathematica Sinica, Chinese Series. 1995, 38(6): . https://doi.org/10.12386/A1995sxxb0100
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    A monoid S is called left perfect if every strongly flat left S-act is projective. The chain conditions of left and right S-acts over a left perfect monoid are discussed in this paper. Particularly Bjork Theorem of right S-act is established.
  • Acta Mathematica Sinica, Chinese Series. 1995, 38(6): . https://doi.org/10.12386/A1995sxxb0101
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    In this paper, we proved that a minimum set of generating elements of a lattice must be the smallest set of generating elements, and it is exactly the set of all completely irreducible elements, proved t hat a necessary condi t io n under wh ich a dist ributive lat t ice possesses the smallest set of generating elements is that it satisfies the sup infinitely distributive law,we also proved that a complete Heyting algebra possesses a minimum set of generating elements if and only it is a strong algebraic lattice, proved that a complete lattice is a strong algebraic lattice if and only if it and its dual lattice are distributive lattices with the smallest set of generating elements.
  • Acta Mathematica Sinica, Chinese Series. 1995, 38(6): . https://doi.org/10.12386/A1995sxxb0102
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    A complete characterization of the range of propagation operator for the sphericalreaction-diffusion equation is provided in t his pap er.
  • Acta Mathematica Sinica, Chinese Series. 1995, 38(6): . https://doi.org/10.12386/A1995sxxb0104
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    This paper studies weak cancellation of niodules and stable range condition of regularrings.We introduce the concept of qu-regular rings and apply it to characterizing a class ofmodules satisfying weak cancellation. We characterize qu-regular rings and indicate that allregular rings satisfying comparability axiom are qu-regular.We also consider the applicationsof these results,e.g.,we characterized quasi-injectiVe modules satisfying weak cancellation;weproved that every nonsingular injective right R-module over a prime,regular and right self-inective ring R can be weakly cancelled from direct summands.
  • Acta Mathematica Sinica, Chinese Series. 1995, 38(6): . https://doi.org/10.12386/A1995sxxb0103
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    In this paper,by use of some new comparison results,the max1mal and minimal solutions, the unique solution and iterative apprOximation of solutions of the initial value problem for nonlinear integro-differential equations of mixed type in Banach spaces are investigated.The results presented here unify and extend many recent results.
  • Acta Mathematica Sinica, Chinese Series. 1995, 38(6): . https://doi.org/10.12386/A1995sxxb0108
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    In this paper,we consider reduced groups of group rings.As applications,we obtainthe following results:(1)R is a commutative semihereditary ring with torsion reduced group if and only if there exists some s > 0 such that for any finitely generated semireflexiveR-module P.(2)Let R a semilocal Dedekind domain,G be a finitely generated abellan group.Then K_0RG is a torsion group if and only if whenever G has some element of primeorder p.(3)Suppose K_0RG is a torsion group. If L is the fractional field of integral domain Rand [G∶H]<∞,then for any .
  • Acta Mathematica Sinica, Chinese Series. 1995, 38(6): . https://doi.org/10.12386/A1995sxxb0107
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    Using the method of Lyapunov function, we will discuss the stochastic stability ofthe trivial solutions of Doleans-Dade-Protter equations dX_t=σ(X_t)dM_t+b(X_t)dA_t,where(M_t)is a continuous locally square integrable martingale and (A_t) is a continuous process with finitevariation. Also we will give the criterion of stocliastic stability and a specific Lyapunov function.
  • Acta Mathematica Sinica, Chinese Series. 1995, 38(6): . https://doi.org/10.12386/A1995sxxb0106
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    This paper provides a regularity theorem for some 4n ̄(th)-order linear nonsymmetric or nonlinear differential operator that arises in considering certain types of moving behaviors of some objects, which includes two homeomorphism and extended homeomorphism classes in real (nolinear) case or contains three linear homeomorphism and extended linear homeomorphism classes in complex (linear) case. It is useful to illustrate some stabilities in both directions of certain objects(such as some flying apparatus)in their moving processes.
  • Acta Mathematica Sinica, Chinese Series. 1995, 38(6): . https://doi.org/10.12386/A1995sxxb0105
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    In this paper the main goal is to discuss decompositions of nest algebras T(N)in direct sums. Firstly we give a characterization of the commutative subspace lattice L which is with T(N)=R+alg L,where R is a special subspace of nest algebra T(N),and obtain the sufficient and necessary condition of T(N)to be decomposed into the direct sum of its diagonal and its ideals(i.e.,Jacobson radical and Larson ideal),at the same time,we characterize a closedleft ideal J_N of T(N).Finally we study the direct sums of the diagonal of T(N)and some of itshypercausal ideals.
  • Acta Mathematica Sinica, Chinese Series. 1995, 38(6): . https://doi.org/10.12386/A1995sxxb0110
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    In the paper we give solid commulative diagram of short exact sequences induced by product αβγof morphisms. There are seven 3 × 3 planes,30 lines in the commutative diagram,every line (zero object of both ends be omitted)is a short exact sequence。These short exact sequences can induce a series of identity on the rank of matrices over p-division ring.Our resuhts not only generalize some results of rank of matrices over field,also can obtain some new dependence relations and formulas.
  • Acta Mathematica Sinica, Chinese Series. 1995, 38(6): . https://doi.org/10.12386/A1995sxxb0109
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    This paper is mainly devoted to the embeddings of M-continuous lattices in Hilbert cubes. we establish the subdirect product representation theory of M-continuous lattices,whichgeneralizes and unifies the corresponding work of Raneyt Bruns,Lawson,Bandelt,Erne andothers. The classical technique of Raney and Bruns,baised on the deep investigations of maximalcomplete strict chains of suitable auxiliary relations,is skillful and the situations to which it canapply are limited.comparatively,the method used in this paper not ouly is very natural andconceptual,but also can deal with more general cases.
  • Acta Mathematica Sinica, Chinese Series. 1995, 38(6): . https://doi.org/10.12386/A1995sxxb0095
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    et E be a reflexive Banach Space,T: be maximal monotoneand satisfy f∈T_x, where Ω is an open bounded subset of E and0∈Ω∩D(T),then T has a zero point in Ω∩D(T).
  • Acta Mathematica Sinica, Chinese Series. 1995, 38(6): . https://doi.org/10.12386/A1995sxxb0096
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    In this paper,by using an abstract continuation theorem,we study the problem ofperiodic solution for t hehigher order nonli ne ar p erio dical sy stem and obt ain so me new res ult son the existence,uniqueness and stability periodic solution.
  • Acta Mathematica Sinica, Chinese Series. 1995, 38(6): . https://doi.org/10.12386/A1995sxxb0093
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    In th paper,we investigate the properties of convex maps on some Banach spaces,find the characteristic of convex maps on unit ball of a class of Banach spaces.By using theseresults,we determine all convex maps on a class of bounded domains.
  • Acta Mathematica Sinica, Chinese Series. 1995, 38(6): . https://doi.org/10.12386/A1995sxxb0094
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    In this paper,it is proved that every strong or weak solution must be monotone fora class of functional differential equations x′(t)=a(t)f(x(t),x(x(t))),the deviating argument ofwhich depends on its state. It is the first time to study in detial for the existences and asymptoticbehaviors of strong solutions for the equation x′(t)=ax(t) + bx(x(t)),a·b≠0.
  • Acta Mathematica Sinica, Chinese Series. 1995, 38(6): . https://doi.org/10.12386/A1995sxxb0097
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    In this paper,we discuss the convexity of Toeplitz operators on Bergman spaces,andprove that the Teoplitz operators with harmonic symbols and a class of continuous symbols areconvexoid operators.In addition,we give an example showing that there exist non-convexiodToeplitz operators with continuous symbols.
  • Acta Mathematica Sinica, Chinese Series. 1995, 38(6): . https://doi.org/10.12386/A1995sxxb0098
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    In this paper,a decomposition theorem for permutable orthogroups is used to discussthe structure and classification of permutable orthogroups.we proved that there are 20 classesof permutable orthogroups.We prove that there are 29 permutable bands,and every permutableband is finite with elements does not exceed 13.