Practical guide for selection of 1H qNMR acquisition and processing parameters confirmed by automated spectra evaluation

In our recent paper, a new technique for automated spectra integration and quality control of the acquired results in qNMR was developed and validated (Monakhova & Diehl, Magn. Res. Chem. 2017, doi: 10.1002/mrc.4591 ). The present study is focused on the influence of acquisition and postacquisition parameters on the developed automated routine in particular, and on the quantitative NMR (qNMR) results in general, which has not been undertaken previously in a systematic and automated manner. Results are presented for a number of model mixtures and authentic pharmaceutical products measured on 500‐ and 600‐MHz NMR spectrometers. The influence of the most important acquisition (spectral width, transmitter [frequency] offset, number of scans, and time domain) and processing (size of real spectrum, deconvolution, Gaussian window multiplication, and line broadening) parameters for qNMR was automatically investigated. Moderate modification of the majority of the investigated parameters from default instrument settings within evaluated ranges does not significantly affect the trueness and precision of the qNMR. Lite Gaussian window multiplication resulted in accuracy improvement of the qNMR output and is recommended for routine measurements. In general, given that the acquisition and processing parameters were selected based on the presented guidelines, automated qNMR analysis can be employed for reproducible high‐precision concentration measurements in practice.     

An Alternative Way to Generalize the Pentagon

We introduce the concept of a pentagonal geometry as a generalization of the pentagon and the Desargues configuration, in the same vein that the generalized polygons share the fundamental properties of ordinary polygons. In short, a pentagonal geometry is a regular partial linear space in which for all points x, the points not collinear with the point x, form a line. We compute bounds on their parameters, give some constructions, obtain some nonexistence results for seemingly feasible parameters and suggest a cryptographic application related to identifying codes of partial linear spaces.     

基于W77E58的多路数据采集系统的设计与实现

为了对实际信号进行监测,设计了以W77E58微控制器为核心的多路数据采集系统,介绍了系统总体结构,阐明了模拟量采集的硬件和软件设计方法,给出了具体的电路图和软件程序,经实际测试表明,该系统具有采集精度高、功耗低、抗干扰能力强、通用性好的特点。     

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 $4p^s$.     

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.