前缀码与极大前缀码的一种新刻画

在语言图Γ(X*)概念的基础上,用新引入的语言竹竿l(X*)和语言竹竿集L(X*)的概念形象地刻画了前缀码与极大前缀码:A是前缀码l(X*)∈L(X*),S_l_((X*))∩A或为单点集或为Φ;A是极大前缀码l(X*)∈L(X*),i)S_(l(X*))∩A或为单点集或为Φ.ii)S_(l(X*))∩A=Φ■u∈S_(l(X*)),■a∈A,ω∈X~+使a=uw.     

On the Hamming distances of repeated-root constacyclic codes of length 4ps

Let $p$ be an odd prime, $s$, $m$ be positive integers, $\gamma ,\lambda$ be nonzero elements of the finite field ${\mathbb{F}}_{p^m}$ such that ${\gamma }^{p^s}=\lambda$. In this paper, we show that, for any positive integer $\eta$, the Hamming distances of all repeated-root $\lambda$-constacyclic codes of length $\eta p^s$ can be determined by those of certain simple-root $\gamma$-constacyclic codes of length $\eta$. Using this result, Hamming distances of all constacyclic codes of length $4p^s$ are obtained. As an application, we identify all MDS $\lambda$-constacyclic codes of length $4p^s$.     

Monofluoroalkene-Isostere as a 19F NMR Label for the Peptide Backbone: Synthesis and Evaluation in Membrane-Bound PGLa and (KIGAKI)3

Solid-state ¹⁹F NMR is a powerful method to study the interactions of biologically active peptides with membranes. So far, in labelled peptides, the ¹⁹F-reporter group has always been installed on the side chain of an amino acid. Given the fact that monofluoroalkenes are non-hydrolyzable peptide bond mimics, we have synthesized a monofluoroalkene-based dipeptide isostere, Val-Ψ[(Z)-CF=CH]-Gly, and inserted it in the sequence of two well-studied antimicrobial peptides: PGLa and (KIGAKI)₃ are representatives of an α-helix and a β-sheet. The conformations and biological activities of these labeled peptides were studied to assess the suitability of monofluoroalkenes for ¹⁹F NMR structure analysis.     

Gray codes extending quadratic matchings

Is it true that every matching in the n-dimensional hypercube can be extended to a Gray code? More than two decades have passed since Ruskey and Savage asked this question and the problem still remains open. A solution is known only in some special cases, including perfect matchings or matchings of linear size. This article shows that the answer to the Ruskey–Savage problem is affirmative for every matching of size at most . The proof is based on an inductive construction that extends balanced matchings in the completion of the hypercube by edges of into a Hamilton cycle of . On the other hand, we show that for every there is a balanced matching in of size that cannot be extended in this way.     

The dual code of any (δ+αu2)-constacyclic code over F2m[u]∕〈u4〉 of oddly even length

Let ${\mathbb{F}}_{2^m}$ be a finite field of cardinality $2^m$, $R={\mathbb{F}}_{2^m}\left[u\right]∕〈u^4〉={\mathbb{F}}_{2^m}+u{\mathbb{F}}_{2^m}+u^2{\mathbb{F}}_{2^m}+u^3{\mathbb{F}}_{2^m}$ $(u^4=0)$ which is a finite chain ring, and $n$ is an odd positive integer. For any $\delta ,\alpha \in {\mathbb{F}}_{2^m}^{\times }$, an explicit representation for the dual code of any $(\delta +\alpha u^2)$-constacyclic code over $R$ of length $2n$ is given. And some dual codes of $(1+u^2)$-constacyclic codes over $R$ of length 14 are constructed. For the case of $\delta =1$, all distinct self-dual $(1+\alpha u^2)$-constacyclic codes over $R$ of length $2n$ are determined.     

Two new compounds from Melodinus suaveolens

Two new compounds, 19-hydroxy-melodinine K (1) and melodiside (2), and 25 known compounds were isolated from leaves and twigs of Melodinus suaveolens. Their structures were elucidated based on 1- and 2-D NMR, FTIR, UV and MS spectroscopic data. 19-hydroxy-melodinine K showed cytotoxic activity against MDA-MB-231 breast, BCG-823 gastric, SW480 colon and Hela cancer cells.     

19F-detected dual-optimized inverted 1JCC 1,n-ADEQUATE

Modification of the recently reported ¹⁹F-detected 1,1-ADEQUATE experiment that incorporates dual-optimization to selectively invert a wide range of ¹J_CC correlations in a 1,n-ADEQUATE experiment is reported. Parameters for the dual-optimization segment of the pulse sequence were modified to accommodate the increased size of ¹J_CC homonuclear coupling constants of poly- and perfluorinated molecules relative to protonated molecules to allow broadband inversion of the ¹J_CC correlations. The observation and utility of isotope shifts are reported for the first time for 1,1- and 1,n-ADEQUATE correlations.