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51.
We study two types of dynamical extensions of Lucas sequences and give elliptic solutions for them. The first type concerns a level-dependent (or discrete time-dependent) version involving commuting variables. We show that a nice solution for this system is given by elliptic numbers. The second type involves a non-commutative version of Lucas sequences which defines the non-commutative (or abstract) Fibonacci polynomials introduced by Johann Cigler. If the non-commuting variables are specialized to be elliptic-commuting variables the abstract Fibonacci polynomials become non-commutative elliptic Fibonacci polynomials. Some properties we derive for these include their explicit expansion in terms of normalized monomials and a non-commutative elliptic Euler–Cassini identity. 相似文献
52.
The push-pull characters of a large series of donor-acceptor substituted azo dyes—71 structures in all—have been quantified by the NN double bond lengths, dNN, the 15N NMR chemical shift differences, Δδ15N, of the two nitrogen atoms and the quotient, π∗/π, of the occupations of the antibonding π∗, and bonding π orbitals of this partial NN double bond. The excellent correlation of the occupation quotients with the bond lengths strongly infers that both π∗/π and dNN are excellent parameters for quantifying charge alternation in the push-pull chromophore and the molecular hyperpolarizability, β0, of these compounds. By this approach, selected compounds can be appropriately considered as viable candidates for nonlinear optical (NLO) applications. 相似文献
53.
A need for rapid toxicity techniques has seen recent research into developing new microbiological assays and characterising their toxicity responses using a range of substances. A microbiological bioassay that determines changes in ferricyanide-mediated respiration for toxicity measurement (FM-TOX) shows particular promise. The development and optimisation of an improved FM-TOX method, incorporating novel features, is described using Escherichia coli as the biocatalyst. Omission of an exogenous carbon source, used in previously described FM-TOX assays, substantially improves the assay sensitivity. In addition, the development of a two-step procedure (toxicant exposure followed by determination of microbial respiratory activity) was found to enhance the inhibition of E. coli by 3,5-dichlorophenol and four other toxicants, compared to single-step procedures. Other assay parameters, such as the ferricyanide concentration, exposure times and optical density of the biocatalyst were also optimised, sometimes based on practical aspects. Toxicity tests were carried out using the adopted technique on both organic and inorganic toxicants, with classic sigmoid-shaped dose-response curves observed, as well as some non-standard responses. IC50 data is presented for a number of common toxicants. The optimised assay provides a good foundation for further toxicity testing using E. coli, as well as the potential for expanding the technique to utilise other bacteria with complementary toxicity responses, thereby allowing use of the assay in a range of applications. 相似文献
54.
两个模糊子半群集合之间的同态 总被引:1,自引:0,他引:1
设S,T是半群,F(S)和Fs(S)分别表示S的所有模糊子集的集合和所有模糊子半群的集合。文中,讨论了F(S)(Fs(S))和F(T)(Fs(T))之间的模糊同态,建立了模糊商子半群的概念,把分明半群的基本同态定理推广到模糊子半群。 相似文献
55.
HUANG Xiaojun 《中国科学A辑(英文版)》2006,49(11):1441-1450
In this paper, we discuss some recent studies on the complex structure of an isolated normal singularity by using the information
from its link. We also give some open problems to be further pursued.
Dedicated to Professor Sheng GONG on the occasion of his 75th birthday 相似文献
56.
Ronald C. Scherer Fariborz Alipour Eileen Finnegan Chwen Geng Guo 《Journal of voice》1997,11(3):277-284
The membranous contact quotient (MCQ) is introduced as a measure of dynamic glottal competence. It is defined as the ratio of the membranous contact glottis (the anterior-posterior length of contact between the two membranous vocal folds) and the membranous vocal fold length. An elliptical approximation to the vocal fold contour during phonation was used to predict MCQ values as a function of vocal process gap (adduction), maximum glottal width, and membranous glottal length. MCQ is highly dependent on the vocal process gap and the maximum glottal width, but not on vocal fold length. Five excised larynges were used to obtain MCQ data for a wide range of vocal process gaps and maximum glottal widths. Predicted and measured MCQ values had a correlation of 0.93, with an average absolute difference of 9.6% (SD = 10.5%). The model is better at higher values of MCQ. The theory for MCQ is also expressed as a function of vocal process gap and subglottal pressure to suggest production control potential. The MCQ measure is obtainable with the use of stroboscopy and appears to be a potentially useful clinical measure. 相似文献
57.
Miroslav Hušek 《Applied Categorical Structures》2007,15(5-6):615-620
If sequential cardinals do not exist then every topological space is generated from a converging sequence by using finite
products, disjoint sums and quotients.
The author acknowledges the support of the grants MSM 0021620839 and GAČR 201/06/0933 of Czech Republic. 相似文献
58.
In this paper some decompositions of Cauchy polynomials, Ferrers-Jackson polynomials and polynomials of the form x
2n
+ y
2n
, n ∈ ℕ, are studied. These decompositions are used to generate the identities for powers of Fibonacci and Lucas numbers as well
as for powers of the so called conjugate recurrence sequences. Also, some new identities for Chebyshev polynomials of the
first kind are presented here. 相似文献
59.
60.
On ground states for the 2D Schrödinger equation with combined nonlinearities and harmonic potential
We consider the nonlinear Schrödinger equation with a harmonic potential in the presence of two combined energy-subcritical power nonlinearities. We assume that the larger power is defocusing, and the smaller power is focusing. Such a framework includes physical models, and ensures that finite energy solutions are global in time. We address the questions of the existence and the orbital stability of the set of standing waves. Given the mathematical features of the equation (external potential and inhomogeneous nonlinearity), the set of parameters for which standing waves exist in unclear. In the two-dimensional case, we adapt the method of fundamental frequency solutions, introduced by the second author in the higher-dimensional case without potential. This makes it possible to describe accurately the set of fundamental frequency standing waves and ground states, and to prove its orbital stability. 相似文献