The exactness of the projective limit functor on the category of quotients of Frechet spaces

We give conditions under which the functor projective limit is exact on the category of quotients of Fréchet spaces of L.Waelbroeck [18].     

Finding more perfect matchings in leapfrog fullerenes

We use some recent results on the existence of long cycles in leapfrog fullerenes to establish new exponential lower bounds on the number of perfect matchings in such graphs. The new bounds are expressed in terms of Fibonacci numbers.     

Elliptic Solutions of Dynamical Lucas Sequences

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.     

Quantification of the push-pull character of azo dyes and a basis for their evaluation as potential nonlinear optical materials

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, d_NN, the ¹⁵N NMR chemical shift differences, Δδ_15N, 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 d_NN 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.     

包含$l^{\beta}(0<\beta<1)$渐近等距翻版的有界线性算子空间

Assume X is a normed space,every x ＊ ∈ S（X＊） can reach its norm at some point in B（X）,and Y is a β-normed space.If there is a quotient space of Y which is asymptotically isometric to l β,then L（X,Y） contains an asymptotically isometric copy of l β.Some sufficient conditions are given under which L（X,Y） fails to have the fixed point property for nonexpansive mappings on closed bounded β-convex subsets of L（X,Y）.     

On Kaufmanʼs theorem

Kaufman?s theorem (Kaufman, 1978 [9]) on representing closed linear operators as quotients of bounded operators is given a new constructive proof, and is extended to operators between two Hilbert spaces. Two different definitions of operator quotients existing in the literature are compared.     

关于nZ的理想及商环

给出了nZ的全部理想、极大理想和素理想,并研究了nZ的商环的构造以及为域的条件,解决了Z<,n>的子域的存在和个数问题.     

Some Alternating Double Binomial Sums

We consider some new alternating double binomial sums. By using the Lagrange inversion formula, we obtain explicit expressions of the desired results which are related to a third-order linear recursive sequence. Furthermore, their recursive relation and generating functions are obtained.     

A sensitive, rapid ferricyanide-mediated toxicity bioassay developed using Escherichia coli

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.