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1.
Normal Families and Shared Values   总被引:55,自引:0,他引:55  
For f a meromorphic function on the plane domain D and a C,let f(a) = {z D: f(z) = a}. Let F be a family of meromorphicfunctions on D, all of whose zeros are of multiplicity at leastk. If there exist b 0 and h > 0 such that for every f F,f(0) = f(k)(b) and 0 < |f(k+1)(z)| h whenever z f(0), thenF is a normal family on D. The case f(0) = Ø is a celebratedresult of Gu [5]. 1991 Mathematics Subject Classification 30D45,30D35.  相似文献
2.
Flow past a stretching plate   总被引:24,自引:0,他引:24  
Zusammenfassung Eine Platte aus plastischem Material fliesst aus einem Spalt mit einer Geschwindigkeit, die proportional zum Abstand vom Spalt ist. Eine exakte Lösung der Grenzschichtgleichungen für die von der Platte erzeugte Luftbewegung wird gegeben. Oberflächenreibung und Wärmeleitungskoeffizient werden berechnet.  相似文献
3.
Normality and shared values   总被引:19,自引:0,他引:19  
LetF be a family of meromorphic functions on the unit disc Δ and leta andb be distinct values. If for everyfF,f andf′ sharea andb on Δ, thenF is normal on Δ. The first author was supported by NNSF of China approved no. 19771038 and by the Research Institute for Mathematical Sciences, Bar-Ilan University.  相似文献
4.
On the size of balls covered by analytic transformations   总被引:5,自引:0,他引:5  
Two quantitative forms of the inverse function theorem giving estimates on the size of balls covered biholomorphically are proved for holomorphic mappings of a ball in a Banach space into the space. Also, a Bloch theorem forK-quasiconformal mappings on the open unit ball of a Banach space is given and some mapping properties ofK-quasiconformal mappings are deduced.Research supported by N. S. F. Grant GP-33117A-2.  相似文献
5.
On a Connection of Number Theory with Graph Theory   总被引:2,自引:2,他引:0  
We assign to each positive integer n a digraph whose set of vertices is H = {0, 1, ..., n – 1} and for which there is a directed edge from a H to b H if a 2 b (mod n). We establish necessary and sufficient conditions for the existence of isolated fixed points. We also examine when the digraph is semiregular. Moreover, we present simple conditions for the number of components and length of cycles. Two new necessary and sufficient conditions for the compositeness of Fermat numbers are also introduced.  相似文献
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This paper presents a systematic procedure to explicitly determinethe algebraic equations arising from the method of harmonicbalance with an arbitrary number of modes in the assumed solutions.The technique can be used for a wide variety of nonlinear oscillators(including systems of ordinary differential equations). Themethod is illustrated in the case of second-order differentialequations with nonlinear restoring force. Although numericalmethods have been employed to solve the resulting systems ofalgebraic equations, the general approach is analytic. As such,this study confirms independently (i.e. nonsimulation) the period-doublingcascade of an escape equation including the bifurcation universalscaling laws.  相似文献
9.
Geometric Realization of a Bellamy Continuum   总被引:1,自引:0,他引:1  
A geometric realization of a tree-like continuum T consistingof a Cantor set of arcs in the form of a fan together with anindecomposable chainable continuum is constructed, and it isshown that T does not have the fixed point property. This complementswork of Bellamy on the notable question of the existence ofacyclic continua without the fixed point property.  相似文献
10.
We examine the component procurement problem in a single-item, make-to-stock assembly system. The suppliers are uncapacitated and have independent but non-identically distributed stochastic delivery lead times. Assembly is instantaneous, product demand follows a Poisson process and unsatisfied demand is backordered. The objective is to minimize the sum of steady-state holding and backorder costs over a pre-specified class of replenishment policies. To keep the analysis tractable, we impose a synchronization assumption that no mixing occurs between sets of component orders. Combining existing results from queueing theory with original results concerning distributions that are closed under maximization and translation, we derive a simple approximate solution to the problem when lead time variances are identical. In simulations, our derived policy is within 2% of optimal and significantly outperforms policies that ignore either component dependence or lead time stochasticity. It is also quite robust with respect to various model assumptions, except the synchronization one.  相似文献
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