EXISTENCE AND UNIQUENESS OF GLOBAL SOLUTION FOR CERTAIN NONLINEAR DEGENERATE PARABOLIC SYSTEMS

ＥＸＩＳＴＥＮＣＥＡＮＤＵＮＩＱＵＥＮＥＳＳＯＦＧＬＯＢＡＬＳＯＬＵＴＩＯＮＦＯＲＣＥＲＴＡＩＮＮＯＮＬＩＮＥＡＲＤＥＧＥＮＥＲＡＴＥＰＡＲＡＢＯＬＩＣ　ＳＹＳＴＥＭＳＬＵＧＵＯＦＵ（卢国富）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｐｕｔｉ...     

BOUNDARY LAYER ESTIMATION OF A SINGULAR PROBLEM WITH LIMIT EQUATION OF ORDER 2

ＢＯＵＮＤＡＲＹＬＡＹＥＲＥＳＴＩＭＡＴＩＯＮＯＦＡＳＩＮＧＵＬＡＲＰＲＯＢＬＥＭＷＩＴＨＬＩＭＩＴＥＱＵＡＴＩＯＮＯＦＯＲＤＥＲ２ＨＥＣＨＥＮＧ（何成）ＺＨＡＮＧＷＥＩＴＡＯ（张维弢）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，Ｃｈｉｎｅ...     

A BLACK－SCHOLES FORMULA FOR OPTIONPRICINGWITHDIVIDENDS

ＡＢＬＡＣＫ－ＳＣＨＯＬＥＳＦＯＲＭＵＬＡＦＯＲＯＰＴＩＯＮＰＲＩＣＩＮＧＷＩＴＨＤＩＶＩＤＥＮＤＳ＊ＸＵＷＥＮＳＨＥＮＧＡＮＤＷＵＺＨＥＮＡｂｓｔｒａｃｔ．ＷｅｏｂｔａｉｎａＢｌａｃｋ－Ｓｃｈｏｌｅｓｆｏｒｍｕｌａｆｏｒｔｈｅａｒｂｉｔｒａｇｅ－ｆ...     

离散卷积的W变换算法

离散卷积的Ｗ变换算法曾泳泓（国防科技大学）ＣＯＭＰＵＴＩＮＧＤＩＳＣＲＥＴＥＣＯＮＶＯＬＵＴＩＯＮＳＢＹＷＴＲＡＮＳＦＯＲＭ￥ＺｅｎｇＹｏｎｇ－ｈｏｎｇ（ＮａｔｉｏｎａｌＵｎｉｖｅｒｓｉｔｙＯｆＤｅｆｅｎｓｅＴｅｃｈｎｏｌｏｇｙ）Ａｂｓｔｒａｃｔ：Ｆ...     

ON THE OPTIMALITY IN GENERAL SENSE FOR ODD-BLOCK SEARCH

ＯＮＴＨＥＯＰＴＩＭＡＬＩＴＹＩＮＧＥＮＥＲＡＬＳＥＮＳＥＦＯＲＯＤＤ－ＢＬＯＣＫＳＥＡＲＣＨ￥ＣＨＥＮＭＵＦＡ（陈木法）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＢｅｉｊｉｎｇＮｏｒｍａｌＵｎｉｖｅｒｓｚｔｙ，Ｂｅｉｊｉｎｇ１００８７５，Ｃ...     

TURNING POINT PROBLEMS FOR THE THIRD ORDER DIFFERENTIAL EQUATIONS EXHIBITING RESONANCE

ＴＵＲＮＩＮＧＰＯＩＮＴＰＲＯＢＬＥＭＳＦＯＲＴＨＥＴＨＩＲＤＯＲＤＥＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＥＸＨＩＢＩＴＩＮＧＲＥＳＯＮＡＮＣＥＸＩＡＯＣＨＥＮＧＹＯＵ（肖成猷）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＥａｓｔＣｈｉ...     

FREE BOUNDARY PROBLEM ARISING FROM EVAPORATION FROM POROUS MEDIUM

ＦＲＥＥＢＯＵＮＤＡＲＹＰＲＯＢＬＥＭＡＲＩＳＩＮＧＦＲＯＭＥＶＡＰＯＲＡＴＩＯＮＦＲＯＭＰＯＲＯＵＳＭＥＤＩＵＭＹＡＮＧＬＩＰＩＮＧ（杨力平）（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＴｓｉｎｇｈｕａＵｎｉｖｅｒｓｉｔｙ，Ｂｅ...     

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

ＡＤＭＩＳＳＩＢＩＬＩＴＹＯＦＬＩＮＥＡＲＥＳＴＩＭＡＴＥＯＦＲＥＧＲＥＳＳＩＯＮＣＯＥＦＦＩＣＩＥＮＴＳＩＮＧＲＯＷＴＨＣＵＲＶＥＭＯＤＥＬＵＮＤＥＲＭＡＴＲＩＸＬＯＳＳＷＡＮＧＸＵＥＲＥＮ（王学仁）（ＤｅｐａｒｔｍｅｎｔｏｆＳｔａｔｉｓｔｉｃｓ，...     

GLOBAL BEHAVIOUR OF THE SOLUTIONS OF A CLASS OF THREE－DIMENSIONSAL COMPETITIVE SYSTEM

ＧＬＯＢＡＬＢＥＨＡＶＩＯＵＲＯＦＴＨＥＳＯＬＵＴＩＯＮＳＯＦＡＣＬＡＳＳＯＦＴＨＲＥＥ－ＤＩＭＥＮＳＩＯＮＳＡＬＣＯＭＰＥＴＩＴＩＶＥＳＹＳＴＥＭＣｈｅｎｇＣｈｕｎＣｈｏｒＬｉｔｗｉｎ（ＨｏｎｇＫｏｎｇＩｎｓｔｉｔｕｔｅＯｆＥｄｕｃａｔｉｏｎ）Ａｂ...     

ON CERTAIN BOUNDARY VALUE PROBLEMS FOR NONLINEAR INTEGRODIFFERENTIAL EQUATIONS

ＯＮＣＥＲＴＡＩＮＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳＦＯＲＮＯＮＬＩＮＥＡＲＩＮＴＥＧＲＯＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＤ．Ｇ．Ｐａｃｈｐａｔｔｅ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓａｎｄＳｔａｔｉｓｉｃｓＭａｒａｔｈ...     

THE FUNCTION {\tf d}$_{{\boldkey k}}$({\tf n}) AT CONSECUTIVE INTEGERS

Let $d_{k}(n)$ denote the $k$-fold iterated divisor function $(k\geq 2)$. It is proved that for sufficiently large $x$, $d_{k}(n)=d_{k}(n+1)$ holds for $\gg x(\log\log x)^{-3}$ integers $n\leq x$.     

DENSENESS OF RADIAL-BASIS FUNCTIONS IN L^2（R^n） AND ITS APPLICATIONS IN NEURAL NETWORKS

The authors discuss problems of approximation to functions in L2(Rn) and operators fromL2(Rn1) to L2(Rn2) by Radial-Basis Functions. The results obtained solve the problem ofcapability of RBF neural networks, a basic problem in neural networks.     

{\tf S}$^{\bold 1}${\td X}{\tf S}$^{\bold 1}$-INDEX THEORY ON PRODUCT SPACE

A new index is constructed by use of the canonical representation of $S^1\times S^1$ group over a product space. This index satisfies the general properties of the usual index but does not satifsy the dimension property. As an application, two abstract critical point theorems are given.     

DISTRIBUTION OF THE（0，∞）ACCUMULATIVE LINES OF MEROMORPHIC FUNCTIONS

Suppose that f(z)is a meromorphic function of order λ（0<λ<+∞）and of lower order μ in the plane.Let ρ be a positive number such that μ≤ρ≤λ.(1)If f^(l)(z)(0≤l<+∞）has p(1≤p<+∞）finite nonzero deficient valnes αi(i=1,…，p)with deficiencies δ（αi,f^(l)),then f(z)has a (0,∞）accumulative line of order ≥ρin any angular domain whose vertex is at the origin and whose magnitude is larger than max(π/ρ，2π-4/ρ ∑i=1^p arcsin √δ（αi,f^(l))/2).(2)If f(z) has only p(0<p<+∞）（0,∞）,accumulative lines of order≥ρ：arg z=θk(0≤θ1<θ2<…<θp<2π，θp+1=θ1+2π）,then λ≤π/ω，where ω=min I≤k≤p(θk+1-θk),provided that f^(l)(z)(0≤l<+∞）has a finite nonzero deficient value.     

LIMIT CYCLES AND BIFURCATION CURVES FOR THE QUADRATIC DIFFERENTIAL SYSTEM （III）m=0 HAVING THREE ANTI-SADDLES （I）

For the quadratic system: x=-y δx lx2 ny2, y=x(1 ax-y) under conditions -10 the author draws in the (a, ()) parameter plane the global bifurcationdiagram of trajectories around O(0,0). Notice that when na2 l < 0 the system has one saddleN(0,1/n) and three anti-saddles.     

GLOBAL TOPOLOGICAL PROPERTIES OF HOMOGENEOUS VECTOR FIELDS IN {\tf R}$^{^{\hbox{\normal 3}}}$

In this paper, the authors prove that the flows of homogeneous vector field $Q(x)$ at infinity are topologically equivalent to the flows of the tangent vector field $Q_T(u)$ $(u\in S^2)$ on the sphere $S^2$, and show the theorems for the global topological classification of $Q(x)$. They derive the necessary and sufficient conditions for the global asymptotic stability and the boundedness of vector field $Q(x),$ and obtain the criterion for the global topological equivalence of two homogeneous vector fields.     

Linear Fractional Transformation Methods in $ {\shadC}^n $

We consider the generalization of linear fractional transformations of the plane to $ {\shadC}^n $ . Analogs of the one-variable theory are developed including fixed point sets and points of symmetry. The domains in $ {\shadC}^n $ that are images of the ball under these transformations are found. Finally, we see some examples where classical fixed point results follow from this theory in a natural way.     

Cn中单位球上$mu$-Bloch函数的等价刻画

设$\mu$是$[0,1)$上的正规函数, 给出了${\bf C}^{\it n}$中单位球$B$上$\mu$-Bloch空间$\beta_{\mu}$中函数的几种刻画. 证明了下列条件是等价的: (1) $f\in \beta_{\mu}$; \ (2) $f\in H(B)$且函数$\mu(|z|)(1-|z|^{2})^{\gamma-1}R^{\alpha,\gamma}f(z)$ 在$B$上有界; (3) $f\in H(B)$ 且函数${\mu(|z|)(1-|z|^{2})^{M_{1}-1}\frac{\partial^{M_{1}} f}{\partial z^{m}}(z)}$ 在$B$上有界, 其中$|m|=M_{1}$; (4) $f\in H(B)$ 且函数${\mu(|z|)(1-|z|^{2})^{M_{2}-1}R^{(M_{2})}f(z)}$ 在$B$上有界.     

共轭 A -调和张量的双权积分不等式

该文引进一类新的权函数 $-A^{\lambda_{3}}_{r}(\lambda_{1},\lambda-{2},\Omega)$ -权, 证明了共轭$\cal A$ -调和张量的局部加权积分不等式.作为局部结果的应用, 证明了在有界区域$\Omega$中共轭$\cal A$ -调和张量的整体加权积分不等式.这些结果可看成是经典结果的推广.最后, 给出了上述结果在拟正则映射理论中的应用.     

DARBOUX EQUATIONS AND ISOMETRIC EMBEDDING OF RIEMANNIAN MANIFOLDS WITH NONNEGATIVE CURVATURE IN {\tf R}$^{^{\hbox{\td 3}}}$

The present paper is concerned with the existence of golbal smooth solutions for the homogeneous Dirichlet boundary value problem of the Darboux equation and the case degenerate on the boundary is contained. As some applications the smooth isometric embeddings of positively and nonnegatively curved disks into $R^3$ are constructed.