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1.
2.
Alessio Porta 《Tetrahedron》2007,63(19):3989-3994
A highly enantioselective synthesis of the (8S,12S)-enantiomer of preclavulone A and its methyl ester is described featuring the Julia protocol for installing the (Z)-double bond in the lower chain. This procedure is suitable for the preparation of labeled preclavulone analogues for biosynthetic studies on marine clavulones. 相似文献
3.
Let f and g be two permutable transcendental holomorphic maps in the plane. We shall discuss the dynamical properties of f, g and f o g and prove, among other things, that if either f has no wandering domains or f is of bounded type, then the Julia sets of f and f(g) coincide.
Dedicated to Professor Sheng GONG on the occasion of his 75th birthday 相似文献
4.
For one-dimensional expanding mapsT with an invariant measure we consider, in a parameter space, the envelope
n
of the real lines associated to any couple of points of the orbit, connected byn iterations ofT. If the map hass inverses and is piecewise linear, then the sets
n
are just the union ofs
n
points and converge to the invariant Cantor set ofT. A correspondence between all the sets and their measures is established and allows one to associate the atomic measure on 1 to the completly continuous measure on the Cantor set. If the map is nonlinear, hyperbolic, and hass inverses, the sets
n
are homeomorphic to the Cantor set; they converge to the Cantor set ofT and their measures converge to the measure of the Cantor set whenn. The correspondence between the sets
n
allows one to define converging approximation schemes for the map an its measure: one replaces each of thes
n
disjoint sets with a point in a convenient neighborhood and a probability equal to its measure and transforms it back to the original set 1. All the approximations with linear Cantor systems previously proposed are recovered, the converging proprties being straightforward in the present scheme. Moreover, extensions to higher dimensionality and to nondisconnected repellers arte possible and are briefly examined. 相似文献
5.
For real a correspondence is made between the Julia setB
forz(z–)2, in the hyperbolic case, and the set of-chains±(±(±..., with the aid of Cremer's theorem. It is shown how a number of features ofB can be understood in terms of-chains. The structure ofB
is determined by certain equivalence classes of-chains, fixed by orders of visitation of certain real cycles; and the bifurcation history of a given cycle can be conveniently computed via the combinatorics of-chains. The functional equations obeyed by attractive cycles are investigated, and their relation to-chains is given. The first cascade of period-doubling bifurcations is described from the point of view of the associated Julia sets and-chains. Certain Julia sets associated with the Feigenbaum function and some theorems of Lanford are discussed.Supported by NSF grant No. MCS-8104862.Supported by NSF grant No. MCS-8203325. 相似文献
6.
Herbarumin Ⅲ的立体选择性全合成 总被引:1,自引:1,他引:0
以正丁醛和1,5-戊二醇为起始原料, 以不对称烯丙基化、改良的Julia成烯反应和Yamaguchi内酯化为关键步骤, 通过13步反应, 立体选择性地合成了具有植物毒性的天然十元内酯化合物Herbarumin Ⅲ(3)及其差向异构体22. 相似文献
7.
This paper firstly introduces the control methods to fractals and give the definition of synchronization of Julia sets between two different systems. Especially, the gradient control method is taken on the classic Julia sets of complex quadratic polynomial Zn+1 = zn^2+ c, which realizes its Julia sets control and synchronization. The simulations illustrate the effectiveness of the method. 相似文献
8.
9.
For a sequence (cn) of complex numbers, the quadratic polynomials fcn:= z2 + Cn and the sequence (Fn) of iterates Fn: = fcn ο ⋯ ο fc1 are considered. The Fatou set F(Cn) is defined as the set of all
such that (Fn) is normal in some neighbourhood of z, while the complement J(Cn) of F(cn) (in
) is called the Julia set. The aim of this paper is to study the stability of the Julia set J(Cn) in the case where (cn) is bounded. A problem put forward by Brück is solved. 相似文献
10.
Let be a polynomial whose Julia set is locally connected. Then a non-preperiodic non-precritical vertex of must have the limit set which coincides with the limit set of an appropriately chosen recurrent critical point of . In particular, if all critical points of are non-recurrent then all vertices of are preperiodic or precritical.