排序方式: 共有37条查询结果,搜索用时 0 毫秒
1.
Jenkinson Oliver; Gonzalez Luis Felipe; Urbanski Mariusz 《Proceedings London Mathematical Society》2003,86(3):755-778
For any non-empty subset I of the natural numbers, let I denotethose numbers in the unit interval whose continued fractiondigits all lie in I. Define the corresponding transfer operator
for , where Re (rß) = I is the abscissa of convergence of the series . When acting on a certain Hilbert space HI, rß, weshow that the operator LI, rß is conjugate to an integraloperator KI, rß. If furthermore rß is real,then KI, rß is selfadjoint, so that LI, rß: HI, rß HI, rß has purely real spectrum.It is proved that LI, rß also has purely real spectrumwhen acting on various Hilbert or Banach spaces of holomorphicfunctions, on the nuclear space C [0, 1], and on the Fréchetspace C [0, 1]. The analytic properties of the map rß LI, rßare investigated. For certain alphabets I of an arithmetic nature(for example, I = primes, I = squares, I an arithmetic progression,I the set of sums of two squares it is shown that rß LI, rß admits an analytic continuation beyond thehalf-plane Re rß > I. 2000 Mathematics SubjectClassification 37D35, 37D20, 30B70. 相似文献
2.
We describe the fractal structure of expanding meromorphic maps of the form , where H and Q are rational functions whose most transparent examples are among the functions of the form with . In particular we show that depending upon whether the Hausdorff dimension of the Julia set is greater or less than 1, the
finite non-zero geometric measure is provided by the Hausdorff or packing measure. In order to describe this fractal structure
we introduce and explore in detail Walters expanding conformal maps and jump-like conformal maps.
Received: 3 May 2001 / Published online: 5 September 2002 相似文献
3.
In this paper, we give sufficient conditions for the existence of (pseudo) weakly conformal and conformal families of measures for fibred systems. We describe a general construction principle for these families, modelled on the one developed by Denker and Urbanski for conformal measures. For those systems that are fibrewise local homeomorphisms, the constructed families are (pseudo) conformal. If a system is, moreover, weakly topologically exact along fibres, then each measure in the associated family is supported on the whole fibre where it is naturally defined. 相似文献
4.
From a study of the 1H NMR spectra of a number of 3,7-disubstituted derivatives of 1,3,5,7-tetraazabicycio - [3.3.1] - nonane it is concluded that these molecules exist in either chair-chair or flattened chair-chair conformations. The derivatives containing COCH3 and NO substitutents have room temperature spectra consistent with restricted rotation about their NC and NN bonds respectively. High temperature spectra reveal an activation energy, for the rotational barrier of the NC bond in the diacetyl derivative, of 23±2K.Cal/mol. 相似文献
5.
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
6.
7.
8.
9.
Volker Mayer Mariusz Urbanski 《Proceedings of the American Mathematical Society》2003,131(12):3695-3702
We consider infinite conformal iterated function systems in the phase space with . Let be the limit set of such a system. Under a mild technical assumption, which is always satisfied if the system is finite, we prove that either the Hausdorff dimension of exceeds the topological dimension of the closure of or else the closure of is a proper compact subset of either a geometric sphere or an affine subspace of dimension . A similar dichotomy holds for conformal expanding repellers.
10.
P. W. Wachulak M. C. Marconi A. Isoyan L. Urbanski A. Bartnik H. Fiedorowicz R. A. Bartels 《Opto-Electronics Review》2012,20(1):1-14
Imaging systems with nanometer resolution are instrumental to the development of the fast evolving field of nanoscience and
nanotechnology. Decreasing the wavelength of illumination is a direct way to improve the spatial resolution in photon-based
imaging systems and motivated a strong interest in short wavelength imaging techniques in the extreme ultraviolet (EUV) region.
In this review paper, various EUV imaging techniques, such as 2D and 3D holography, EUV microscopy using Fresnel zone plates,
EUV reconstruction of computer generated hologram (CGH) and generalized Talbot self-imaging will be presented utilizing both
coherent and incoherent compact laboratory EUV sources. Some of the results lead to the imaging with spatial resolution reaching
50 nm in a very short exposure time. These techniques can be used in a variety of applications from actinic mask inspection
in the EUV lithography, biological imaging to mask-less lithographic processes in nanofabrication. 相似文献