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81.
S. R. Nasyrov 《Mathematical Notes》2007,82(5-6):798-802
We consider functions f that are univalent in a plane angular domain of angle απ, 0 < α ≤ 2. It is proved that there exists a natural number k depending only on α such that the kth derivatives f (k) of these functions cannot be univalent in this angle. We find the least of the possible values of for k. As a consequence, we obtain an answer to the question posed by Kir’yatskii: if f is univalent in the half-plane, then its fourth derivative cannot be univalent in this half-plane. 相似文献
82.
The Gaussian property of the Brownian bridge is characterized as an application of Ramachandran's theorem in terms of the independence of the random variables that appear in the Karhunen-Loéve expansion of the process. A reference about the construction of the Brownian bridge by means of functional transformations is also included. 相似文献
83.
Several sophisticated methods to solution of symmetry specified enumeration problems are available in the modern literature.
In this paper we propose a simple technique that allows one to manually compute the exact numbers of fixed-symmetry derivatives
for a given structure either with inclusion or ignoring the substitution patterns. The basic idea of the method suggested
consists in the derivation of Pólya-like cycle indices for the automorphism groups of specially constructed orbit partition
graphs; the expansion of these indices and subsequent simple calculations result in the desired numbers of substituted derivatives
with achiral substituents. Limitations of the new technique (and a method suggested earlier) depend on the relevance of the
orbit partitions for particular subgroups of the point symmetry group. For illustration purposes, the results obtained for
the prismane (D
3h
) and adamantane (T
d
) structures are discussed. In the former case the numbers of substituted derivatives can be found for all subgroups of the
D
3h
group, whereas in the latter case these numbers can be determined for eight out of eleven subgroups of the T
d
point symmetry group.
This work is based on the text of the lecture presented by the authors at the 5th All-Russia Conference on Molecular Modeling
(Moscow, April 2007). The paper deals with the methodology and detailed treatment of applied aspects related to solution of
enumeration problems for substituted derivatives with prescribed symmetry groups. Unlike the known methods of symmetry specified
enumeration, the technique suggested is simple enough and may be regarded as generalization of the Pólya methodology, which
is widely used by chemists.
Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 227–245, February, 2008. 相似文献
84.
Periodica Mathematica Hungarica - Let X 1,X 2,... be a sequence of independent and identically distributed random variables, and put % MATHTYPE!MTEF!2!1!+-%... 相似文献
85.
A general and controlled bidirectional growth strategy enable a very rapid and efficient construction of oligo(phenyleneethynylene)s possessing functional groups such as methylthio and thioacetate groups at both ends. The strategy employs only one reaction type with good to moderate yields to grow the conjugated chains. The synthesis is efficient and can give 23 benzene rings and 22 carbon-carbon triple bonds in the conjugated chains. The compounds are fully characterized by 1H and 13C NMR and UV/vis and fluorescence spectroscopy. 相似文献
86.
We consider a discretized volume V consisting of finite, congruent and attached copies of a tile t. We find a group L
V
the orbit of which, when applied to t, is just V. We show the connection between the structural matrixQ in the formal solution of a boundary value problem formulated for volume V and the so called auxiliary matrix of the graph Γ
v
associated with V. We show boundary value problems to be isomorphic if the graphs associated with the volumes are isomorphic, or, if the covering
groups are Sunada pairs. 相似文献
87.
Scattering of surface plasmon polaritons (SPP’s) by small ellipsoid particles placed near a dielectric–metal interface is theoretically considered. Using the Green’s function formalism and the dipole approximation, we consider the differential and total scattering cross-sections associated with the SPP-to-SPP scattering as well as with the SPP scattering into waves propagating away from the interface, analyzing the influence of system parameters. As an example, scattering cross-sections of differently shaped gold spheroid particles placed near an air–gold interface are evaluated at the light wavelength of 800 nm. It is shown that the differential and total cross-sections depend strongly upon the particle-to-surface distance, the ratio between the major and minor axes and their orientation with respect to both the interface and the direction of SPP incidence. Implications of the obtained results to the design of SPP micro-optical components are also discussed. 相似文献
88.
The electronic structures of ABi2Ta2O9 (A=Ca, Sr, and Ba) were calculated by using first-principles under optimized structure. As the size of A-site cation decreases from that of Ba2+ to Ca2+, the band-gap between O 2p and Ta 5d increases from 2.0 to 2.9 eV, which responses to the stronger orbital hybridizations between Ta 5d and O 2p orbits favoring improvement of the ferroelectric property, decrease in leakage current, and increase in both spontaneous polarization and Curie temperature by the structural distortion. In contrast to CaBi2Ta2O9 and SrBi2Ta2O9, the hybridization between Ba 5p orbits and O 2p orbits in BaBi2Ta2O9 has better structural stability. 相似文献
89.
本文讨论了在区域提纯过程中,研究液态金属流的表面张力时提出的一个带有非负参数Q的两点边值问题.利用上、下解方法和Schauder不动点定理,证明了当0Q851时,该问题至少有一个解,对已有结果0Q<1进行了重要的改进. 相似文献
90.