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81.
A bowtie is a closed trail whose graph consists of two 3-cycles with exactly one vertex in common. A 2-fold bowtie system of order n is an edge-disjoint decomposition of 2K n into bowties. A 2-fold bowtie system is said to be 2-perfect provided that every pair of distinct vertices is joined by two paths of length 2. It is said to be extra provided these two paths always have distinct midpoints. The extra property guarantees that the two paths x, a, y and x, b, y between every pair of vertices form a 4-cycle (x, a, y, b), and that the collection of all such 4-cycles is a four-fold 4-cycle system. We show that the spectrum for extra 2-perfect 2-fold bowtie systems is precisely the set of all n ?? 0 or 1 (mod 3), ${n\,\geqslant\,6}$ . Additionally, with an obvious definition, we show that the spectrum for extra 2-perfect 2-fold maximum packings of 2K n with bowties is precisely the set of all n ?? 2 (mod 3), ${n\,\geqslant\,8}$ . 相似文献
82.
Periodica Mathematica Hungarica - We consider a regular infinite hyperbolic iterated function satisfying a property which guarantees that the associated Frobenius-Perron operator ? is almost... 相似文献
83.
We explore the class of elliptic functions whose critical points all contained in the Julia set are non-recurrent and whose
ω-limit sets form compact subsets of the complex plane. In particular, this class comprises hyperbolic, subhyperbolic and
parabolic elliptic maps. Leth be the Hausdorff dimension of the Julia set of such an elliptic functionf. We construct an atomlessh-conformal measurem and show that theh-dimensional Hausdorff measure of the Julia set off vanishes unless the Julia set is equal to the entire complex plane ℂ. Theh-dimensional packing measure is positive and is finite if and only if there are no rationally indifferent periodic points.
Furthermore, we prove the existence of a (unique up to a multiplicative constant) σ-finitef-invariant measure μ equivalent tom. The measure μ is shown to be ergodic and conservative, and we identify the set of points whose open neighborhoods all have
infinite measure μ. In particular, we show that ∞ is not among them.
The research of the first author was supported in part by the Foundation for Polish Science, the Polish KBN Grant No 2 PO3A
034 25 and TUW Grant no 503G 112000442200. She also wishes to thank the University of North Texas where this research was
conducted.
The research of the second author was supported in part by the NSF Grant DMS 0100078. Both authors were supported in part
by the NSF/PAN grant INT-0306004. 相似文献
84.
Spherical monodispersed magnesium fluoride has been obtained using the microwave-assisted precipitation technique from magnesium nitrate and ammonium fluoride solutions. Studies aimed at optimizing synthesis conditions from the point of view of preparing spherical MgF2 particles of possibly high monodispersity were performed. Spherical MgF2 particles of 0.25-0.36 μm in diameter have been obtained with relative standard deviation from the average value ranging from 7 to 15%. It has been established that a certain optimal range of Mg(NO3)2 and NH4F concentrations exists that enables a highly monodispersed MgF2 to be prepared. The range is narrow (0.01-0.03 mol dm−3) for both precursors. Spherical MgF2 particles have been characterized by SEM, XRD, DTG/DTA and FTIR techniques. 相似文献
85.
Photochromism of [SiW11O39Ni(X)]6- as a tetraheptylammonium salt in various solvents under broadband UV light is observed in the presence of alcohols. The reaction proceeds faster with benzyl alcohol than with ethanol. Benzaldehyde is identified as the oxidized product of benzyl alcohol. Photochemistry is a reliable means to produce stable reduced transition metal substituted heteropoly tungstates in nonpolar media, where they hold promise as multielectron reduction catalysts. Preliminary reactivity toward CO2 reduction is demonstrated. 相似文献
86.
We investigate the finer fractal structure of the set of pointsescaping to infinity under iteration of an arbitrary exponentialmap. Providing exact formulas, we show how sensitively the Hausdorffdimension depends on the rate of growth of canonical DevaneyKrychcodes. 相似文献
87.
88.
Bieniek Mariusz Burkschat Marco Rychlik Tomasz 《Methodology and Computing in Applied Probability》2020,22(1):173-189
Methodology and Computing in Applied Probability - In the failure dependent proportional hazard model, it is assumed that identical components work jointly in a system. At the moments of... 相似文献
89.
Mariusz Urbański 《Monatshefte für Mathematik》2010,159(1-2):133-162
We show that the Hausdorff dimension of Julia sets in any analytic family of semihyperbolic generalized polynomial-like mappings (GPL) depends in a real-analytic manner on the parameter. For the proof we introduce abstract weakly regular analytic families of conformal graph directed Markov systems. We show that the Hausdorff dimension of limit sets in such families is real-analytic, and we associate to each analytic family of semihyperbolic GPLs a weakly regular analytic family of conformal graph directed Markov systems with the Hausdorff dimension of the limit sets equal to the Hausdorff dimension of the Julia sets of the corresponding semihyperbolic GPLs. 相似文献
90.
We study finitely generated expanding semigroups of rational maps with overlaps on the Riemann sphere. We show that if a d-parameter family of such semigroups satisfies the transversality condition, then for almost every parameter value the Hausdorff dimension of the Julia set is the minimum of 2 and the zero of the pressure function. Moreover, the Hausdorff dimension of the exceptional set of parameters is estimated. We also show that if the zero of the pressure function is greater than 2, then typically the 2-dimensional Lebesgue measure of the Julia set is positive. Some sufficient conditions for a family to satisfy the transversality conditions are given. We give non-trivial examples of families of semigroups of non-linear polynomials with the transversality condition for which the Hausdorff dimension of the Julia set is typically equal to the zero of the pressure function and is less than 2. We also show that a family of small perturbations of the Sierpinski gasket system satisfies that for a typical parameter value, the Hausdorff dimension of the Julia set (limit set) is equal to the zero of the pressure function, which is equal to the similarity dimension. Combining the arguments on the transversality condition, thermodynamical formalisms and potential theory, we show that for each a∈C with |a|≠0,1, the family of small perturbations of the semigroup generated by {z2,az2} satisfies that for a typical parameter value, the 2-dimensional Lebesgue measure of the Julia set is positive. 相似文献