中国科学院数学与系统科学研究院期刊网

15 May 1996, Volume 39 Issue 3
    

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  • Acta Mathematica Sinica, Chinese Series. 1996, 39(3): . https://doi.org/10.12386/A1996sxxb0057
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    This paper deals with a class of boundary value problems of ordinary differential equations of second order which have singular right hand term. We will show that there are no solutions when the singularity of f(t,x) with respect to t is greater than a certain value, and solutions exist while the singularity is less than the value. The singularity with respect to u at u = 0 is not restricted.
  • Acta Mathematica Sinica, Chinese Series. 1996, 39(3): . https://doi.org/10.12386/A1996sxxb0058
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    Using the equivariant Ljusternik-Schnirelmann theory, we prove that there are at least 2·(N-2)·N-3 geometrically distinct noncollision orbits with prescribed energy for a class of planar N-body-type problems.
  • Acta Mathematica Sinica, Chinese Series. 1996, 39(3): . https://doi.org/10.12386/A1996sxxb0053
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    Let be an integer number, for each integer 0 < α< n with (n, a) = 1, it is clear that there exists one and only one αwith 0 < α< n such that αα= 1(modn). The main purpose of this paper is to study the distribution behaviour of |a-a| (where αand αbelong to an arithmetical progression), and give an interesting asymptotic formula.
  • Acta Mathematica Sinica, Chinese Series. 1996, 39(3): . https://doi.org/10.12386/A1996sxxb0054
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    In this paper,the essential commutant of analytic Toeplitz algebra F(H∞) on Hardy space H2 on the unit sphere Sn of Cn is determined. An operator commutes essentially with all analytic Toeplitz operators if and only if it is a compact perturbation of a Toeplitz operator with symbol in Ac It follows that the image in the Calkin algebra of the algebra F(Ac) generated by Toeplitz operators with symbol in Ac is a maximal abelian algebra, which leads to a maximal expansion of Coburn's exact sequence. From this fact, we prove that the essential spectrum of Toeplitz operators with symbol in Ac are connected, which extends the recent results of C-S.We obtain also that the essential commutant and center of Toeplitz algebra F(L∞)are the algebra generated by Toeplitz operators with symbol in QC by the main theorem in this paper,These results lead to a characterization of automorphisms of the algebra F(H∞) + κ.
  • Acta Mathematica Sinica, Chinese Series. 1996, 39(3): . https://doi.org/10.12386/A1996sxxb0055
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    We consider Lienard equation X" + f(x)x' + g(x) =e(t) and obtain that if and for any periodic function or almost periodic function e(t) it has a periodic solution or almost periodic solution. For Lienard equation X" +f(x)x' + ex = e(t), we obtain that if and for any periodic function or almost periodic function e(t) it has a periodic solution or an almost periodic solution.
  • Acta Mathematica Sinica, Chinese Series. 1996, 39(3): . https://doi.org/10.12386/A1996sxxb0056
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    Let ri > 0(for each i) be an integer, and be the disjoint union of many real, complex, or quaterulonic projective (2ri + 1)-spaces according as or = R, C, H respectively.In this paper we show that smooth involutions(M, T)with fixed point set are not cobordat zero if and only if the total Stiefel Whitney class of all spheres whose dimensions larger than ac (m.α=1, 2, 4 respectively, when α= R, C, H) is nontrivial.
  • Acta Mathematica Sinica, Chinese Series. 1996, 39(3): . https://doi.org/10.12386/A1996sxxb0051
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    Li Anmin and Zhao Guosong proposed the following problems in [1]: Find the best pinching constant with respect to the length of curvature tensor for Riemannian manifold with parallel Ricci curvature tensor and determine the Riemannian manifolds with this constant. In this article, we obtain the best pinching constant for non-Einstein manifolds and determine the manifolds with this constallt. When,this answers the above problems.
  • Acta Mathematica Sinica, Chinese Series. 1996, 39(3): . https://doi.org/10.12386/A1996sxxb0052
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    This paper is the continuation of [1], consider the degenerate multi-point boundary Value problems of ordinary differential equations with strong singularities, obtain the existence theorem for C(i1-1)-bounded solution.
  • Acta Mathematica Sinica, Chinese Series. 1996, 39(3): . https://doi.org/10.12386/A1996sxxb0050
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    In this paper, we estalbish the real Nullstellensatz in infinite-dimensional spaces, and characterize those ordered fields for which the indnite-dimensional real Nullstellensatz holds via the Zariski topology of affine spaces and the ordering structure of fields respectively. Moreover,it is illustrated by an example that there edests really some ordered field satisfying α-dimensional real Nullstellensatz for an arbitrary cardinal α.
  • Acta Mathematica Sinica, Chinese Series. 1996, 39(3): . https://doi.org/10.12386/A1996sxxb0046
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    Let A be a multivalued increasing process valued in a separable reflexive Banach space. In this paper we study stochastic integrals of nonnegative bounded measurable processes with respect to A and measure generated by A on product measurable space. It is proved that every integrable multivalued increasing process edests unique dual optional (predictable)projection.
  • Acta Mathematica Sinica, Chinese Series. 1996, 39(3): . https://doi.org/10.12386/A1996sxxb0041
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    In this papert we provide a new way to analytically describe all of the J-selfadjoint edensions of J-symmetric ordinary differential operators associated with any J-symmetric differential expression γ by means of the solutions of the equation r(y) =λoy, instead of the solutions of the equation γ+γ(y) = -y as done in [4], under the assumption that the regularity field Π(TO),of the minimal operator To generated by T, is nonempty. Some interesting notes on the main theorem are given. Complete descriptions of J-seifadjoint domains of second order J-symmetric differential expressions with limit-circle are obtained.
  • Acta Mathematica Sinica, Chinese Series. 1996, 39(3): . https://doi.org/10.12386/A1996sxxb0044
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    For continuous surjection f of compact metric space with infinite elements,we study the relationships between f have the pseudo-orbit-tracing property and f is chaotic in the sense of Ruelle-Takens,topological mixing and have property P.
  • Acta Mathematica Sinica, Chinese Series. 1996, 39(3): . https://doi.org/10.12386/A1996sxxb0045
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    Let n be a positive integer with n > 2. Let D be a positive integer with square free,and let Ik, hk denote the ideal class group and the class number of the imaginary quadratic field K=respectively.In this paper we prove that the number of integral points (x, y) on the hyperelliptic curve f(x, y) =-Dx2-4yn+1 is no more than max (8, 2164p81gx(p)) for any odd prime factor p of n, where gK(p) is the number of ideal classes in Ik with order p.
  • Acta Mathematica Sinica, Chinese Series. 1996, 39(3): . https://doi.org/10.12386/A1996sxxb0042
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    A decomposition of pairwise matrices over an arbitrary skew field F with same numbers of rows or colunms is presented. New necessaryand sufficiellt conditions for the consistency of the matrix equations (i) AXB+CYD = E and (ii) [A1XB1, A2XB2] = [E1, E2] over F are derived and their general solutions are also given by using the decomposition theorem.
  • Acta Mathematica Sinica, Chinese Series. 1996, 39(3): . https://doi.org/10.12386/A1996sxxb0043
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    In this paper, we study the relationship between the positive expansiveness of a kind of self-maps on a circle and the expansiveness of their inverse limits, and obtain that, for every surjective continuous map f,the inverse limit of f is expansive if and only if f is topologically conjugate to an expanding map.
  • Acta Mathematica Sinica, Chinese Series. 1996, 39(3): . https://doi.org/10.12386/A1996sxxb0047
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    The set of all real n-by--n matrices whose symmetric part is positive semidefinite is denoted by PSDn. In this paper, we give the canonical form of a matrix in PSDn under congruence and a necessary and sufficient condition for two matrices in PSDn to be congruent.Moreover we give an inequality concerning the determinant of a matrix in PSDn and those of its symmetric and skew symmetric parts.
  • Acta Mathematica Sinica, Chinese Series. 1996, 39(3): . https://doi.org/10.12386/A1996sxxb0048
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    Let be an odd number, integer, Sn and rn be the unique real roots ofthe equations xn-2xn-1 -1=0 and Xn+2-3Xn- X2-1=0 on(0,+∞) respectively,tno= rn,tni = sn ().Assume f and g be the N take of expanding self-map (increasedecrease-increase type)and anti-N type of expanding self-map(decrease-increase-decrease take)on closed interval I respectively. In this paper, it is proved that f(or g) has a periodic point of period 2m n if f (or g) has an expanding constant(or). Besides,it shows that there exists a N type of (or anti-N type of)expanding self-map which has an expanding constant λ but no periodic point of period 2m·n on [0, 1]if .
  • Acta Mathematica Sinica, Chinese Series. 1996, 39(3): . https://doi.org/10.12386/A1996sxxb0049
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    In the present paper we study the dynamical properties of continuous maps on the Warsaw circle and show that for such a map a theorem similar to the Sarkovskii Theorem for interval maps holds, the closure of the set of periodic points coincides with the closure of the set of recurrent points, the depth of the center is not greater than 4, and the topological entropy is zero if and only if the periods of periodic points are the powers of 2.