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91.
Tunable properties of light propagation in photonic crystal fibers filled with liquid crystals, called photonic liquid crystal
fibers (PLCFs) are presented. The propagation properties of PLCFs strongly depend on contrast between refractive indices of
the solid core (pure silica glass) and liquid crystals (LCs) filing the holes of the fiber. Due to relatively strong thermo-optical
effect, we can change the refractive index of the LC by changing its temperature. Numerical analysis of light propagation
in PLCF, based on two simulation methods, such as finite difference (FD) and multipole method (MM) is presented. The numerical
results obtained are in good agreement with our earlier experimental results presented elsewhere [1]. 相似文献
92.
B. Bojarski 《Proceedings of the Steklov Institute of Mathematics》2006,255(1):65-81
We prove that a function f is in the Sobolev class W
loc
m,p
(ℝ
n
) or W
m,p
(Q) for some cube Q ⊂ ℝ
n
if and only if the formal (m − 1)-Taylor remainder R
m−1
f(x,y) of f satisfies the pointwise inequality |R
m−1
f(x,y)| ≤ |x − y|
m
[a(x) + a(y)] for some a ε L
p
(Q) outside a set N ⊂ Q of null Lebesgue measure. This is analogous to H. Whitney’s Taylor remainder condition characterizing the traces of smooth
functions on closed subsets of ℝ
n
.
Dedicated to S.M. Nikol’skiĭ on the occasion of his 100th birthday
The main results and ideas of this paper were presented in the plenary lecture of the author at the International Conference
and Workshop Function Spaces, Approximation Theory and Nonlinear Analysis dedicated to the centennial of Sergei Mikhailovich Nikol’skii, Moscow, May 24–28, 2005. 相似文献
93.
Investigated materials were produced from polyethylene
of low density (PE-LD) and a filler: carbon black or chalk. A part of the
samples was kept in ambient temperature over several months in order to study
the effect of material ageing. The qualitative conclusions were drawn based
on a precise analysis of shape of DSC curves and the basic investigations
of PE morphologies known from literature. The influence of the thermal history
and the filler contents on the amount and kind of crystal phase was established.
Additionally, the effect of the measurement technique, in our case it was
positron annihilation lifetime spectroscopy (PALS), on the morphological feature
changes was found. The paper serves selected examples of problems solved by
DSC. However, from the other hand, the authors discuss critically the opportunity
given by this method. 相似文献
94.
We study the corrections to the Clausius-Mossotti formula for the dielectric constant of a disordered system of polarizable spherical particles. Previously we have derived an exact cluster expansion for the correction terms. Here we study the three-body correction in detail. We derive an explicit expression for the integrand of the three-body cluster integral for a system of polarizable point dipoles. 相似文献
95.
Piotr Ko?cielniak 《Topology and its Applications》2007,154(9):1951-1955
Let M be a compact manifold with dimM?2. We prove that some iteration of the generic homeomorphism on M is semiconjugated to the shift map and has infinite topological entropy (Theorem 1.1). 相似文献
96.
Antoni Leon Dawidowicz Najemedin Haribash Anna Poskrobko 《Mathematical Methods in the Applied Sciences》2007,30(7):779-787
The problem of the existence of the invariant measure is important considering its connections with chaotic behaviour. In the papers (Zesz. Nauk. Uniw. Jagiellońskiego, Pr. Mat. 1982; 23 :117–123; Ann. Pol. Math. 1983; XLI :129–137; J. Differential Equations 2004; 196 :448–465) the existence of invariant and ergodic measures according to the dynamical system generated by the Lasota equation was proved, i.e. the equation describing the dynamics and becoming different of the population of cells. In this paper, the existence of such measure for the quasi‐linear Lasota equation is proved. This measure is the carriage of the measure described by Dawidowicz (Zesz. Nauk. Uniw. Jagiellońskiego, Pr. Mat. 1982; 23 :117–123). Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
97.
J.J. Kolodziej B. Such M. Goryl F. Krok P. Piatkowski M. Szymonski 《Applied Surface Science》2006,252(21):7614-7623
Surfaces of several AIIIBV compound semiconductors (InSb, GaAs, InP, InAs) of the (0 0 1) orientation have been studied with noncontact atomic force microscopy (NC-AFM). Obtained atomically resolved patterns have been compared with structural models available in the literature. It is shown that NC-AFM is an efficient tool for imaging complex surface structures in real space. It is also demonstrated that the recent structural models of III-V compound surfaces provide a sound base for interpretation of majority of features present in recorded patterns. However, there are also many new findings revealed by the NC-AFM method that is still new experimental technique in the context of surface structure determination. 相似文献
98.
《Physics letters. A》2006,355(1):27-31
Chaotic maps can mimic random behavior in a quite impressive way. In particular, those possessing a generating partition can produce any symbolic sequence by properly choosing the initial state. We study in this Letter the ability of chaotic maps to generate order patterns and come to the conclusion that their performance in this respect falls short of expectations. This result reveals some basic limitation of a deterministic dynamic as compared to a random one. This being the case, we propose a non-statistical test based on ‘forbidden’ order patterns to discriminate chaotic from truly random time series with, in principle, arbitrarily high probability. Some relations with discrete chaos and chaotic cryptography are also discussed. 相似文献
99.
《Nonlinear Analysis: Real World Applications》2007,8(1):288-294
The existence of an energy minimizer relative to a class of rearrangements of a given function is proved. The minimizers are stationary and stable solutions of the two-dimensional barotropic vorticity equation, governing the evolution of geophysical flow over a surface of variable height. The theorem proved implies the existence of a family of stable anticyclonic vortices with cyclonic potential vorticity over a seamount, and a corresponding family of cyclonic vortices with anticyclonic potential vorticity over a localized depression. The seamount is described by a characteristic function (corresponding to a flat top) with arbitrary shape. 相似文献
100.
Jan P. Boroński 《Topology and its Applications》2007,154(18):3156-3166
A set (or a collection of sets) contained in the Euclidean space Rm is symmetric if it is invariant under the antipodal map. Given a symmetric unicoherent polyhedron X (like an n-dimensional cube or a sphere) and an odd real function f defined on vertices of a certain symmetric triangulation of X, we algorithmically construct a connected symmetric separator of X by choosing a subcollection of the triangulation. Each element of the subcollection contains the vertices v and u such that f(v)f(u)?0. 相似文献