A NEW DETECTING METHOD FOR CONDITIONS OF EXISTENCE OF HOPF BIFURCATION

ＡＮＥＷＤＥＴＥＣＴＩＮＧＭＥＴＨＯＤＦＯＲＣＯＮＤＩＴＩＯＮＳＯＦＥＸＩＳＴＥＮＣＥＯＦＨＯＰＦＢＩＦＵＲＣＡＴＩＯＮＳＨＥＮＪＩＡＱＩ（沈家骐）；ＪＩＮＧＺＨＵＪＵＮ（井竹君）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｈａｎｄｏｎｇＵｎ...     

FORCING BONDS OF A BENZENOID SYSTEM

ＦＯＲＣＩＮＧＢＯＮＤＳＯＦＡＢＥＮＺＥＮＯＩＤＳＹＳＴＥＭＺＨＡＮＧＦＵＪＩ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＸｉａｍｅｎＵｎｉｖｅｒｓｉｔｙ，Ｘｉａｍｅｎ８５００４６，Ｃｈｉｎａ）ＬＩＸＵＥＬＩＡＮＧ（ＤｅｐａｒｔｍｅｎｔｏｆＡｐ...     

EXISTENCE FOR A FREE BOUNDARY PROBLEM IN GROUND FREEZING

ＥＸＩＳＴＥＮＣＥＦＯＲＡＦＲＥＥＢＯＵＮＤＡＲＹＰＲＯＢＬＥＭＩＮＧＲＯＵＮＤＦＲＥＥＺＩＮＧＧＵＡＮＺＨＩＣＨＥＮＧＷＡＮＧＸＵＪＩＡＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＪａｎｕａｒｙ１７，１９９５．ＲｅｖｉｓｅｄＪａｎｕａｒｙ２７，１９...     

CONNECTIVITIES OF RANDOM CIRCULANT DIGRAPHS

ＣＯＮＮＥＣＴＩＶＩＴＩＥＳＯＦＲＡＮＤＯＭＣＩＲＣＵＬＡＮＴＤＩＧＲＡＰＨＳ￥ＭＥＮＧＪＩＸＩＡＮＧＡＮＤＨＵＡＮＧＱＩＯＮＧＸＩＡＮＧＡｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒｌｗｅｐｒｏｖｅｔｈａｔａｌｍｏｓｔａｌｌｃｉｒｃｕｌａｎｔｄｉｇｒａｐ...     

SUBJECTIVE RADE-OFF RATE METHOD OF MULTIOBJECTIVE DECISION-MAKING

ＳＵＢＪＥＣＴＩＶＥＲＡＤＥ－ＯＦＦＲＡＴＥＭＥＴＨＯＤＯＦＭＵＬＴＩＯＢＪＥＣＴＩＶＥＤＥＣＩＳＩＯＮ－ＭＡＫＩＮＧ￥ＷａｎｇＸｉａｎｊｉａ（王先甲）（ＷｕｈａｎＵｎｉｖｅｒｓｉｔｙｏｆＨｙｄｒａｕｌｉｃａｎｄＥｌｅｃｔｒｉｃＥｎｇｉｎｅｅｒｉｎｇ...     

ADMISSIBILITY OF LINEAR ESTIMATE OF REGRESSION COEFFICIENTS IN GROWTH CURVE MODEL UNDER MATRIX LOSS

ＡＤＭＩＳＳＩＢＩＬＩＴＹＯＦＬＩＮＥＡＲＥＳＴＩＭＡＴＥＯＦＲＥＧＲＥＳＳＩＯＮＣＯＥＦＦＩＣＩＥＮＴＳＩＮＧＲＯＷＴＨＣＵＲＶＥＭＯＤＥＬＵＮＤＥＲＭＡＴＲＩＸＬＯＳＳＷＡＮＧＸＵＥＲＥＮ（王学仁）（ＤｅｐａｒｔｍｅｎｔｏｆＳｔａｔｉｓｔｉｃｓ，...     

A SUCCESSIVE APPROXIMATION METHOD FOR SOLVING PROBABILISTIC CONSTRAINED PROGRAMS

ＡＳＵＣＣＥＳＳＩＶＥＡＰＰＲＯＸＩＭＡＴＩＯＮＭＥＴＨＯＤＦＯＲＳＯＬＶＩＮＧＰＲＯＢＡＢＩＬＩＳＴＩＣＣＯＮＳＴＲＡＩＮＥＤＰＲＯＧＲＡＭＳＷＡＮＧＪＩＮＤＥ（王金德）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮａｎｊｉｎｇＵｎｉｖｅｒｓ...     

CONNECTIVITY OF CARTESIAN PRODUCT DIGRAPHS AND FAULT-TOLERANT ROUTINGS OF GENERALIZED HYPERCUBE

ＣＯＮＮＥＣＴＩＶＩＴＹＯＦＣＡＲＴＥＳＩＡＮＰＲＯＤＵＣＴＤＩＧＲＡＰＨＳＡＮＤＦＡＵＬＴ┐ＴＯＬＥＲＡＮＴＲＯＵＴＩＮＧＳＯＦＧＥＮＥＲＡＬＩＺＥＤＨＹＰＥＲＣＵＢＥＸＵＪＵＮＭＩＮＧＡｂｓｔｒａｃｔ．Ｉｎｔｈｉｓｐａｐｅｒ，ｔｈｅｐｒｏｂｌｅｍ...     

Weighted approximation of random functions

ＷＥＩＧＨＴＥＤＡＰＰＲＯＸＩＭＡＴＩＯＮＯＦＲＡＮＤＯＭＦＵＮＣＴＩＯＮＳＹＵＪＩＡＲＯＮＧＡｂｓｔｒａｃｔ：Ｌｅｔ（Ω,Ａ,Ｐ）ｂｅａｐｒｏｂａｂｉｌｉｔｙｓｐａｃｅ,Ｘ（ｔ,ω）ａｒａｎｄｏｍｆｕｎｃｔｉｏｎｃｏｎｔｉｎｕｏｕｓｉｎｐｒｏｂａｂ...     

ON TWO CONJECTURES OF THE QUADRATIC DIFFERENTIAL SYSTEMS

ＯＮＴＷＯＣＯＮＪＥＣＴＵＲＥＳＯＦＴＨＥＱＵＡＤＲＡＴＩＣＤＩＦＦＥＲＥＮＴＩＡＬＳＹＳＴＥＭＳＺＨＡＮＧＸＩＡＮＧ＊ＡｂｓｔｒａｃｔＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＳｅｐｔｅｍｂｅｒ２９，１９９５．＊ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃ...     

COMPUTING THE NEAREST BISYMMETRIC POSITIVE SEMIDEFINITE MATRIX UNDER THE SPECTRAL RESTRICTION

Let A and C denote real n × n matrices. Given real n-vectors x1, ... ,xm, m ≤ n, and a set of numbers L = {λ1,λ2,... ,λm}. We describe (I) the set (?) of all real n × n bisymmetric positive seidefinite matrices A such that Axi is the "best" approximate to λixi, i = 1,2,...,m in Frobenius norm and (II) the Y in set (?) which minimize Frobenius norm of ||C - Y||.An existence theorem of the solutions for Problem I and Problem II is given and the general expression of solutions for Problem I is derived. Some sufficient conditions under which Problem I and Problem II have an explicit solution is provided. A numerical algorithm of the solution for Problem II has been presented.     

线性流形上Hermite-广义反Hamilton矩阵反问题的最小二乘解

1.引言 令Rn×m表示所有n×m实矩阵集合,Cn×m表示所有n×m复矩阵集合,Cn=Cn×1,HCn×n表示所有n阶Hermite矩阵集合,UCn×n表示所有n阶酉矩阵集合,AHCn×n表示所有n阶反Hermite矩阵集合,R(A)表示A的列空间,N(A)表示A的零空间,A+表示A的Moore—Penrose广义逆,A*B表示A与B的Hadamard积,rank(A)表示矩阵A的秩.tr(A)表示矩阵A的迹.矩阵A,B的内积定义为(A,B)=tr(BHA),A,B∈Cn×m,由此内积诱导的范数为||A||=√(A,A)=[tr(AHA)]1/2,则此范数为Frobenius范数,并且Cn×m构成一个完备的内积空间,In表示n阶单位阵,i=√-1,记OASRn×n表示n×n阶正交反对称矩阵的全体,即     

有关广义中心三项式系数的3个超同余式

设b,c为整数,定义广义中心三项式系数Tn(b,c)=[xn](x2+bx+c)n=「n/2」∑k=0(n2k)(2kk)bn-2kck(n∈N={0,1,…}),这里[xn]P(x)表示多项式P(x)中xn项的系数.特别地,中心Delannoy多项式Dn(x)=Tn(2x+1,x2+x)(n ∈ N),中心三项式系数...     

具有阻尼项的非线性波动方程的初值问题

本文研究具有阻尼项的非线性波动方程的初值问题ｕｔｔ－２ｂｕｘｘｔ＋ａｕｘｘｘｘ＝β（ｕｘ＾ｎ）ｘ,;ｕ（ｘ,０）＝ψ（ｘ）,ｕｔ（ｘ,０）＝ψ（ｘ）,其中ｂ〉０,β≠０为任意实数,ｎ≥２为整 当ａ≠ｂ＾２,ψ∈Ｌ１（Ｒ）∩Ｈ＾２（Ｒ）,ψ∈Ｋ１（Ｒ）∩Ｌ３（Ｒ）时,上述问题存在唯一的整体光滑解。     

恰含d个非零对角元的本原矩阵的广义最大密度指数集

设Ａ是一个具有周期ｐ的ｎ×ｎ不可约布尔矩阵,文［１］定义了矩阵的广义最大密度指数ｈＡ（ｋ）令ＤＩＳｎ,ｄ（ｋ）＝｛ｈＡ（ｋ）｜ Ａ ＰＭｎ（ｄ）｝,其中ＰＭｎ（ｄ）是所有恰含ｄ个非零对角元的ｎ×ｎ本原矩阵的集合．本文证明了另外,我们定义矩阵Ａ的范数,用Ａ表示,为Ａ中１的个数,并且刻划了具有最小范数的极矩阵．     

Location of best simultaneous approximations

Amir and Ziegler have proved that a real normed space E of dimension ≥ 3 is an inner product space if and only if, for any x,y ε E and any two dimensional subspace M of E, the expression max(‖x — w‖,‖y — w‖) attains its minimum in some point w of each segment [u,v], with u and v, respectively, best approximations to x and y from M. We extend this result to expressions π(‖x — w‖,‖y — w‖), where π denotes a monotonic norm in R²     

Thue inequalities with a small number of primitive solutions

Several upper bounds are known for the numbers of primitive solutions (x; y) of the Thue equation (1) j F(x; y) j = m and the more general Thue inequality (3) 0 < j F(x; y) j m. A usual way to derive such an upper bound is to make a distinction between "small" and "large" solutions, according as max( j x j ; j y j ) is smaller or larger than an appropriate explicit constant Y depending on F and m; see e.g. [1], [11], [6] and [2]. As an improvement and generalization of some earlier results we give in Section 1 an upper bound of the form cn for the number of primitive solutions (x; y) of (3) with max( j x j ; j y j )Y0 , wherec 25 is a constant and n denotes the degree of the binary form F involved (cf. Theorem 1). It is important for applications that our lower bound Y0 for the large solutions is much smaller than those in [1], [11], [6] and [4], and is already close to the best possible in terms of m. ByusingTheorem1 we establish in Section 2 similar upper bounds for the total number of primitive solutions of (3), provided that the height or discriminant of F is suficiently large with respect to m (cf. Theorem 2 and its corollaries). These results assert in a quantitative form that, in a certain sense, almost all inequalities of the form (3) have only few primitive solutions. Theorem 2 and its consequences are considerable improvements of the results obtained in this direction in [3], [6], [13] and [4]. The proofs of Theorems 1 and 2 are given in Section 3. In the proofs we use among other things appropriate modifications and refenements of some arguments of [1] and [6].     

矩阵方程AX=B的双反对称最佳逼近解

本文主要讨论下而两个问题并得到相关结果:问题Ⅰ:给定A ∈ R~(k×n),B ∈ R~(k×n),求X ∈ BASR~(n×n),使得AX=B.问题Ⅱ:给定X* ∈R~(n×n),求X使得‖X-X~*‖=minX∈S_E‖X-X~*‖,其中S_E是问题Ⅰ的解集合,‖·‖是Frobenius范数.通过对上述问题的讨论给出了问题Ⅰ解存在的充分必要条件和其解的一般表达式同时给出了问题Ⅱ的解,算法,和数值例子.     

The Jackson Inequality for the Best L2-Approximation of Functions on [0, 1] with the Weight x

Let L^2（[0, 1], x） be the space of the real valued, measurable, square summable functions on [0, 1] with weight x, and let n be the subspace of L2（[0, 1], x） defined by a linear combination of Jo（μkX）, where Jo is the Bessel function of order 0 and {μk} is the strictly increasing sequence of all positive zeros of Jo. For f ∈ L^2（[0, 1], x）, let E（f, n） be the error of the best L2（[0, 1], x）, i.e., approximation of f by elements of n. The shift operator off at point x ∈[0, 1] with step t ∈[0, 1] is defined by T（t）f（x）=1/π∫0^π f（√x^2 ＋t^2-2xtcosO）dθ The differences （I- T（t））^r/2f = ∑j=0^∞（-1）^j（j^r/2）T^j（t）f of order r ∈ （0, ∞） and the L^2（[0, 1],x）- modulus of continuity ωr（f,τ） = sup{｜｜（I- T（t））^r/2f｜｜：0≤ t ≤τ] of order r are defined in the standard way, where T^0（t） = I is the identity operator. In this paper, we establish the sharp Jackson inequality between E（f, n） and ωr（f, τ） for some cases of r and τ. More precisely, we will find the smallest constant n（τ, r） which depends only on n, r, and % such that the inequality E（f, n）≤ n（τ, r）ωr（f, τ） is valid.     

Banach空间中非线性奇异两点边值问题的多重正解

本文研究Banach空间E中非线性奇异边值问题-x'=f(t,x), t∈(0,1), a₁x(0)-a₂x'(0)=θ, b₁x(0)-b₂x'(1)=θ.其中θ是E中的零元素, f({t,x})在端点t=0和t=1处具有奇性. 利用不动点定理获得了该问题至少有两个正解的结果.