The graph of an odd function has the general appearance of fig 4. 1b . 一个奇函数的图形一般如图41（b）所示。
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The graph of an odd function has the general appearance of fig 4 . 1b 一个奇函数的图形一般如图4 1 （ b ）所示。
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Chapter two is the preparation knowledge of this paper , which firstly covers the current definition of the said - ball curves as well as their properties , and secondly finds for the first time the matrix representation of such curves one degree lower based on the degree elevation formula of the said - ball curves , and finally offers the general formulae of derivatives of arbitrary orders at endpoints by differentiation 第二章介绍了本文的预备知识。作者首先介绍了said - ball奇函数的定义及其基本性质并通过said - ball曲线的升阶公式得到了said - ball曲线的降一阶的矩阵表示，通过对端点求导，得到了端点任意阶导数的一般表示式。
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Hi the aspect of symmetry analyzing to the hopfield model neural network with hebbian learning , we study on the dynamical behavior of the state space under the action of isometric transformation group g = z2 ? n , and prove the invariant property of the energy orientation ? / / " ) of the state space under the action of g . we find that the symmetry relationship of the network is sx - sw = sh when the active function of the neuron is odd , where sx is the symmetry of the patterns set x under hebbian learning rule , sh is the symmetry of the network and sw is the symmetry of the weight matrix w of the network ) s _ n为手段，研究了网络状态空间在群g作用下各点的运动情况，证明了群g作用下的不变性。证明了当神经元的激活函数f为奇函数时， hebb法则下存储样本集x的对称性s _ x 、网络对称性s _ h以及连接矩阵对称性s _ w三者之间满足s _ x = s _ w = s _ h的关系；同时，我们还证明了：网络稳定态集vf同一s _ h轨道中的两个稳定态的动力学行为(能量和吸引域大小)相同；两个等距网络h和h 1 = g ? h ， ( ? ) g (
