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91.
92.
The continuity of Gaussian processes is an extensively studied topic and it culminates in Talagrand’s notion of majorizing measures that gives complicated necessary and sufficient conditions. In this note we study the Hölder continuity of Gaussian processes. It turns out that necessary and sufficient conditions can be stated in a simple form that is a variant of the celebrated Kolmogorov–Čentsov condition. 相似文献
93.
We prove a generalization of the Kibble–Slepian formula (for Hermite polynomials) and its unitary analogue involving the 2D Hermite polynomials recently proved in [16]. We derive integral representations for the 2D Hermite polynomials which are of independent interest. Several new generating functions for 2D q-Hermite polynomials will also be given. 相似文献
94.
George Pitsevich Elena Shalamberidze Alex Malevich Valdas Sablinskas Vytautas Balevicius Lars G. M. Pettersson 《Molecular physics》2017,115(20):2605-2613
The frequencies and intensities of vibration–rotational transitions of water molecules in an argon matrix were calculated for temperatures of 6 and 30 K. The rigid asymmetric top approximation was used with available literature values of the effective rotational constants in the ground and excited vibrational states. The calculations were carried out by taking into account the existence of a non-equilibrium population distribution between the rotational levels of ortho- and para-water isomers. It was assumed that the temperature relaxation of the population of rotational levels is independent of the ortho- and para-isomers. Comparison of the results of the theoretical calculations with experimental literature data shows good agreement for the majority of the rotational structure lines for symmetric and antisymmetric stretching vibrations both in the frequency values and in the values of the relative intensities. 相似文献
95.
Eight new homologous series of 4-alkyl-N-(4-alkloxysalicylidene)anilines were synthesized. The phase transitions of these homologues were determined using differential scanning calorimetry and polarizing optical microscopy. The homologues began to exhibit liquid crystalline phases as the terminal alkyl or alkoxyl chains were lengthened. In addition, some members of these homologues series exhibited photochromism in the solid state. 相似文献
96.
Treatment of 4‐arylthio‐3‐hydroxy‐2‐pyrones with acetylenedicarboxylates gave 4‐arylthio‐3‐hydroxyphthalates by the base‐catalyzed Diels–Alder reaction via a decarboxylation in good yields. 相似文献
97.
Alya A. Dawood Martin C. Grossel Robert M. Richardson Bakir A. Timimi Neil J. Wells 《Liquid crystals》2017,44(1):106-126
ABSTRACTOne of the current challenges in liquid crystal science is to understand the molecular factors leading to the formation of the intriguing twist-bend nematic phase (NTB) and determine its properties. During our earlier hunt for the NTB phase created on cooling directly from the isotropic phase and not the nematic phase, we had prepared 30 symmetric liquid crystal dimers. These had odd spacers and methylene links to the two mesogenic groups; desirable but clearly not essential features for the formation of the NTB. Here, we report the phases that the dimers exhibit and their transition temperatures as functions of both the lengths of the spacer and the terminal chains. In addition we describe the transitional entropies, their optical textures, the X-ray scattering patterns and the 2H NMR spectra employed in characterising the phases. All of which may lead to important properties of the twist-bend nematic phase. 相似文献
98.
《Indagationes Mathematicae》2017,28(1):91-107
Primitive constant length substitutions generate minimal symbolic dynamical systems. In this article we present an algorithm which can produce the list of injective substitutions of the same length that generate topologically conjugate systems. We show that each conjugacy class contains infinitely many substitutions which are not injective. As examples, the Toeplitz conjugacy class contains three injective substitutions (two on two symbols and one on three symbols), and the length two Thue–Morse conjugacy class contains twelve substitutions, among which are two on six symbols. Together, they constitute a list of all primitive substitutions of length two with infinite minimal systems which are factors of the Thue–Morse system. 相似文献
99.
We prove the existence of stationary turbulent flows with arbitrary positive vortex circulation on non-simply connected domains. Our construction yields solutions for all real values of the inverse temperature with the exception of a quantized set, for which blow-up phenomena may occur. Our results complete the analysis initiated in Ricciardi and Zecca (2016). 相似文献
100.
Hsiu‐Fu Hsu Corresponding author Shih‐Jay Chien Hsiu‐Hui Chen Chien‐Hsing Chen Li‐Ya Huang Chung‐Hao Kuo 《Liquid crystals》2013,40(6):683-689
Liquid crystalline α,α′‐bis(4‐alkoxyphenylethynyl)oligothiophenes (bi‐ and ter‐thiophene) have been synthesized and their mesogenic behaviour and optical properties investigated. They all exhibited a nematic mesophase, and compounds with long alkoxy chains also showed lamellar phases. Increasing the number of thiophene units increased both the transition temperatures and the mesophase ranges. As for their optical properties, incorporating more thiophene units results in red‐shifted absorption and emission spectra, slightly enhanced quantum efficiency, and a larger Stoke's shift. Most importantly, in terms of the absorption and emission maxima, the incorporation of one 4‐alkoxyphenylethynyl moiety was found to be equivalent to adding one thiophene ring. 相似文献