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设￡为定义在D内的一族亚纯函数,a1,a2,a3为三个互相判别的有穷复数,如果对于任意的f∈F,f∈S={a1,a2,a3}f(k)∈S,且f-a1(a1≠0,否则取a2或a3)的零点重级至少是k 1,那么f在D内正规. 相似文献
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Multi-layer self-organizing polynomial neural networks and their development with the use of genetic algorithms 总被引：1，自引：0，他引：1
Sung-Kwun Oh 《Journal of The Franklin Institute》2006,343(2):125-136
In this paper, we introduce a new architecture of genetic algorithms (GA)-based self-organizing polynomial neural networks (SOPNN) and discuss a comprehensive design methodology. Let us recall that the design of the “conventional” PNNs uses an extended group method of data handling (GMDH) and exploits polynomials (such as linear, quadratic, and modified quadratic functions) as well as considers a fixed number of input nodes (as being selected in advance by a network designer) at polynomial neurons (or nodes) located in each layer. The proposed GA-based SOPNN gives rise to a structurally optimized structure and comes with a substantial level of flexibility in comparison to the one we encounter in conventional PNNs. The design procedure applied in the construction of each layer of a PNN deals with its structural optimization involving the selection of preferred nodes (or PNs) with specific local characteristics (such as the number of input variables, the order of the polynomial, and a collection of the specific subset of input variables) and addresses specific aspects of parametric optimization. An aggregate performance index with a weighting factor is proposed in order to achieve a sound balance between approximation and generalization (predictive) abilities of the network. To evaluate the performance of the GA-based SOPNN, the model is experimented with using chaotic time series data. A comparative analysis reveals that the proposed GA-based SOPNN exhibits higher accuracy and superb predictive capability in comparison to some previous models available in the literature. 相似文献
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蔡惠京 《广东广播电视大学学报》2008,17(4):97-100
本文研究具有超越整函数系数的二阶线性微分方程f″＋A（z）f=^0的解的零点分布。证明当A（%）的增长级为（2,1．p）时,方程的每一个非平凡解的增长级都为（3,1．p）,而且总存在一个非平凡解f（z）的零点收敛级等于其增长级（3,1;p）。进一步给出了方程存在无零点解的条件,证明当P非为整数时,方程的两个线性无关解中至多只有一个无零点。最后,证明了该方程总存在两个线性无关解f1（z）和f2（z）,使得f1（z）×f2（z）的零点收敛级等于其增长级（3,1;P）。 相似文献
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本文回答Shapiro了提出的关于Narayana矩阵和Fibonacci矩阵的行的极限分布的公开问题,并给出了简单证明. 相似文献
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吴全荣 《福建师大福清分校学报》2008,(2):71-74
本文研究实系数三、四次函数的性质：零点、极值点、拐点的个数;奇偶性;对称中心坐标、对称轴方程,并将其拓广到一般实系数高次多项式函数。 相似文献
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介值定理在中学数学中的应用 总被引：1，自引：0，他引：1
章主要讨论介值定理在中学数学中的应用。在中学数学中介值定理主要应用在下列三类问题：(1)方程根的分布；(2)解不等式；(3)反函数的存在性与定义。 相似文献
7.
ZHAO Li-li 《浙江大学学报(A卷英文版)》2007,8(6):957-962
In this paper, we consider some polynomial (α,β)-metrics, and discuss the sufficient and necessary conditions for a Finsler metric in the form F=α a1β a2β2/α a4β4/α3 to be projectively flat, where ai (i=1,2,4) are constants with a1≠0, α is a Riemannian metric and β is a 1-form. By analyzing the geodesic coefficients and the divisibility of certain polynomials, we obtain that there are only five projectively flat cases for metrics of this type. This gives a classification for such kind of Finsler metrics. 相似文献
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Salem A.K. Al-Assadi 《Journal of The Franklin Institute》2007,344(2):107-127
A new results concerning the definitions of disturbance zeros via the concept of minimal order system inverses is presented in this paper. These definitions are then used to develop a new computation algorithm for locating the positions of the ‘disturbance blocking zeros’ in linear multivariable systems. Assignment of disturbance blocking zeros at desired locations in the complex plane plays an important role in rejection of all measurable or un-measurable disturbances, which may affect at the outputs in steady state. Numerical examples are given to illustrate the main results of this paper. 相似文献
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求多项式的最大公因式常用分解因式和辗转相除法,分解因式对次数较高的多项式有一定难度,而辗转相除法又比较繁琐,根据矩阵的性质提出了一种求两个及两个以上多项式的最大公因式的方法——数值矩阵法。 相似文献