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141.
ABSTRACTHigh sensitivity of liquid crystals to the electric field makes them highly demanded and widely used in different applications. Despite the large number of the electro-optical research on the low-molar-mass liquid crystals electro-optics of the liquid crystalline (LC) polymers is much less studied. Herein, the comparative electro-optical behaviour of two nematic comb-shaped polyacrylates with phenylbenzoate mesogenic side groups was studied in detail. These two polyacrylates have completely the same structure of polymer backbone and spacer length but different in the direction of the ester group in the phenylbenzoate fragments. It was found that this difference predetermines their completely opposite electro-optical properties.The influence of the electric field of different strength and frequency on the orientation of the mesogenic groups of these polymers is studied. It is shown that application of the electric field at temperatures above the glass transition temperature (~25°C) induces reorientation of the mesogenic groups along or perpendicular to the electric field direction depending in its turn on the ester group direction. For one of the polyacrylates an unusual textural transition is found; during cooling of the polymer sample under applied field at definite temperature a sharp change in the mesogen’s orientation from homeotropic to planar one is found. This electro-optical phenomenon is observed for the first time and probably associated with sharp change in sign of anisotropy of dielectric permittivity from positive (at high temperatures) to negative one (at lower temperatures). Kinetics of the electro-optical switching at different temperatures, influence of the molar masses of the polymer and frequency of the applied AC field on electro-optical behaviour of the polymers are studied. The possibility of the fixation of the electroinduced homeotropic alignment of the mesogenic groups by photopolymerisation of the diacrylate dissolved in the polymer is demonstrated. 相似文献
142.
We show that, if the subgroup growth of a finitely generated (abstract or profinite) groupG is super-exponential, then every finite group occurs as a quotient of a finite index subgroup ofG. The proof involves techniques from finite permutation groups, and depends on the Classification of Finite Simple Groups.The first author was partially supported by the Hungarian National Foundation for Scientific Research, Grant No. T7441. The second author was partially supported by the Israeli National Science Foundation. 相似文献
143.
Jesse Ira Deutsch 《Journal of Number Theory》2004,104(2):263-278
While various techniques have been used to demonstrate the classical four squares theorem for the rational integers, the method of modular forms of two variables has been the standard way of dealing with sums of squares problems for integers in quadratic fields. The case of representations by sums of four squares in was resolved by Götzky, while those of and were resolved by Cohn. These efforts utilized modular forms. In previous work, the author was able to demonstrate Götzky's theorem by means of the geometry of numbers. Here Cohn's theorem on representation by the sum of four squares for is proven by a combination of geometry of numbers and quaternionic techniques. 相似文献
144.
Akihiko Inoue 《Journal of multivariate analysis》2004,89(1):135-147
Let be a fractional ARIMA(p,d,q) process with partial autocorrelation function α(·). In this paper, we prove that if d∈(−1/2,0) then |α(n)|∼|d|/n as n→∞. This extends the previous result for the case 0<d<1/2. 相似文献
145.
We analyze the role and influence of a tradition of research linked to the concept of
primary matter
in nineteenth-century studies on the nature of the elements.The suggestion of William Prout
(1785-1850) in 1816 that the atomic weights of pure chemical elements are whole numbers and
multiples of the atomic weight of hydrogen, taken as unity, was met with serious confutations,which
in turn prompted several attempts to save Prouts hypothesis.We discuss these attempts in detail
and the objections raised against them, for instance by Dmitry Ivanovich Mendeleev (1834-1907).
We pay particular attention to the use of spectroscopy as a method for proving the existence of
elementary forms of matter inside atoms. Leaders in this field of research were two English scientists,
the astrophysicist Norman Lockyer (1836-1920) and the chemist William Crookes (1832-
1919). Both of their approaches involved the idea of primary matter. However, while Crookess
approach proved to be incorrect, Lockyers ideas survived for several years and supported the discovery
of the electron by J.J.Thomson (1856-1940). 相似文献
146.
We consider expansions with respect to the multi-dimensional Hermite functions which are eigenfunctions of the harmonic oscillator L=−Δ+|x|2. For the heat-diffusion and Poisson semigroups corresponding to a self-adjoint extension of L we investigate their boundary behaviour and mapping properties. All this is done for functions from Lp(w), 1?p<∞, w∈Ap. Then Riesz transforms and conjugate Poisson integrals are considered. The Riesz transforms occur to be Calderón-Zygmund operators hence their mapping properties follow by using results from a general theory. 相似文献
147.
The conformal class of a Hermitian metric g on a compact almost complex manifold (M2m, J) consists entirely of metrics that are Hermitian with respect to J. For each one of these metrics, we may define a J-twisted
version of the Ricci curvature, the J-Ricci curvature, and its corresponding trace, the J-scalar curvature sJ. We ask if the conformal class of g carries a metric with constant sJ, an almost Hermitian version of the usual Yamabe problem posed for the scalar curvature s. We answer our question in the
affirmative. In fact, we show that (2m−1)sJ−s=2(2m−1)W(ω, ω), where W is the Weyl tensor and ω is the fundamental form of g. Using techniques developed for the solution
of the problem for s, we construct an almost Hermitian Yamabe functional and its corresponding conformal invariant. This invariant
is bounded from above by a constant that only depends on the dimension of M, and when it is strictly less than the universal
bound, the problem has a solution that minimizes the almost complex Yamabe functional. By the relation above, we see that
when W (ω, ω) is negative at least one point, or identically zero, our problem has a solution that minimizes the almost Hermitian
Yamabe functional, and the universal bound is reached only in the case of the standard 6-sphere
equipped with a suitable almost complex structure. When W(ω, ω) is non-negative and not identically zero, we prove that the
conformal invariant is strictly less than the universal bound, thus solving the problem for this type of manifolds as well.
We discuss some applications. 相似文献
148.
Ralph Chill 《Journal of Functional Analysis》2003,201(2):572-601
We prove a general version of the ?ojasiewicz-Simon inequality, and we show how to apply the abstract result to study energy functionals E of the form
149.
Daniel Markiewicz 《Journal of Functional Analysis》2003,200(1):237-280
Given a W∗-continuous semigroup φ of unital, normal, completely positive maps of B(H), we introduce its continuous tensor product system . If α is a minimal dilation E0-semigroup of φ with Arveson product system F, then is canonically isomorphic to F. We apply this construction to a class of semigroups of arising from a modified Weyl-Moyal quantization of convolution semigroups of Borel probability measures on . This class includes the heat flow on the CCR algebra studied recently by Arveson. We prove that the minimal dilations of all such semigroups are completely spatial, and additionally, we prove that the minimal dilation of the heat flow is cocyle conjugate to the CAR/CCR flow of index two. 相似文献
150.
Matthew Boylan 《Journal of Number Theory》2003,98(2):377-389
Let F(z)=∑n=1∞a(n)qn denote the unique weight 16 normalized cuspidal eigenform on . In the early 1970s, Serre and Swinnerton-Dyer conjectured that