Decision and approximation complexity for identifying codes and locating-dominating sets in restricted graph classes

An identifying code is a subset of vertices of a graph with the property that each vertex is uniquely determined (identified) by its nonempty neighbourhood within the identifying code. When only vertices out of the code are asked to be identified, we get the related concept of a locating-dominating set. These notions are closely related to a number of similar and well-studied concepts such as the one of a test cover. In this paper, we study the decision problems Identifying Code and Locating-Dominating Set (which consist in deciding whether a given graph admits an identifying code or a locating-dominating set, respectively, with a given size) and their minimization variants Minimum Identifying Code and Minimum Locating-Dominating Set. These problems are known to be NP-hard, even when the input graph belongs to a number of specific graph classes such as planar bipartite graphs. Moreover, it is known that they are approximable within a logarithmic factor, but hard to approximate within any sub-logarithmic factor. We extend the latter result to the case where the input graph is bipartite, split or co-bipartite: both problems remain hard in these cases. Among other results, we also show that for bipartite graphs of bounded maximum degree (at least 3), the two problems are hard to approximate within some constant factor, a question which was open. We summarize all known results in the area, and we compare them to the ones for the related problem Dominating Set. In particular, our work exhibits important graph classes for which Dominating Set is efficiently solvable, but Identifying Code and Locating-Dominating Set are hard (whereas in all previous works, their complexity was the same). We also introduce graph classes for which the converse holds, and for which the complexities of Identifying Code and Locating-Dominating Set differ.     

A colorimetric squaraine-based probe and test paper for rapid naked eyes detection of copper ion (II)

A colorimetric probe N,N’-bis(2-methoxy-ethyl)-2,3,3-trimethyl-3H-squaraine (MOESQ) with H₂O solubility was synthesized to detect Cu²⁺. MOESQ exhibits good selectivity, high sensitivity and fast UV-Vis response toward Cu²⁺ over other competing ions in CH₃CN. The detection limit of MOESQ for Cu²⁺ in CH₃CN can reach 1.88?×?10^?7?molL^?1. By adsorbing MOESQ on the chromatography paper, a colorimetric test paper for Cu²⁺ was prepared, which could detect Cu²⁺ with the color change from blue to faint yellow even in the limit of detection concentration of 10^?6?molL^?1.     

Test films for test-determinations on the base of reagents, immobilized in gelatinous gel

Gelatinous solidified layers of the photographic film were used for the immobilization of analytical reagents for detection and determination of reductants and primary aromatic amines. It was shown, that the films with immobilized iron(III)-Dipy or iron(III)-Phen complexes as test films for reductants and films with immobilized aldehydes (vanillin, p-dimethylaminobenzaldehyde) as the test films for primary aromatic amines can be used. The improving of reagents immobilization in the presence of sodium dodecylsulfate micelles was obtained. Metrological characteristics of visual detection and photometric determination using test films were evaluated on the basis of statistical approach and investigation of detection probability distribution in the concentration range of unreliable reaction. The suggested test films for the determination of ascorbic acid, analgin (dipyrone), novocaine and streptocide in drugs were examined successfully.     

Degradation issues of polymer materials used in railway field

Polymer materials used in railway field are degraded by environmental factors such as thermal, oxidative, photolytic, hydrolytic, and mechanical. The expected service life of the polymer materials used in railway field is approximately 20 years that is relatively long period for the polymer material; therefore, respective degradation factors should be well considered. Some of the degradation conditions indicate similar mechanism. The oxidative reaction was seen in every degradation conditions under air atmosphere. The hydrolytic reaction was mainly observed in chemical and biological degradations. The degradation behavior of the polymer material was analyzed by various methods. FTIR, thermal analysis (TG, DSC), and molecular weight determination were mainly applied for its purpose. However, the degradation mechanism of practical products made of polymer material was insufficiently studied and the exchange criteria of the products depended on the visual inspection without the suitable degradation analysis not only in the railway field but also in other commercial and industrial fields. In addition, most of the methods to analyze degradation of polymer material are performed on the standard specimen forms. For the installed product, some kinds of damage are generated through the sample collection process; therefore, the damaged products have to be exchanged for brand new ones or repaired totally to be used for more period. Moreover, it is hard to suspend the railway service for the degradation analysis of polymer products. From these backgrounds, the prospect of degradation analysis related to polymer materials used in railway field was proposed.     

Experimental investigation on the yield loci of PA66

Compression, tensile and mixed compression/shear tests were performed on PA66 by using a universal material testing machine in order to identify the experimental yield loci of PA66. For the mixed compression/shear tests, instead of using a complex loading device, SCS (shear-compression specimens) were used to generate the additional shear stresses. Then, the mechanical behavior of materials under complex stress states can be obtained for further analysis. Results show that the experimental yield loci of PA66 obtained by the test method proposed in the present paper agree well with the theoretical model based on three stresses invariant, which indicates the reliability of the test method.     

基于极大似然的异方差多正态总体均值的参数Bootstrap检验

本文考虑了异方差下多正态总体均值的检验问题。传统检验方法多为近似分布检验,且受总体数目及其样本量的影响较为严重,只有在总体数目较少、样本量适中或较大时才能很好的控制第一类错误。较近提出的参数bootstrap检验有效解决了在总体数目较多时检验的任意性,但在总体样本量都较小时,检验控制第一类错误倾向保守,或总体中存在个别样本量较少时犯第一类错误概率上升。本文从极大似然的角度推导出具有修正权重的极大似然检验统计量,并与bootstrap方法有效的结合,得到新的参数bootstrap检验方法。通过Monte Carlo模拟第一类错误和检验的势与Welch检验和广义F检验进行比较,结果表明本文提出的极大似然参数bootstrap检验在总体数目较多和存在小样本量时,均能很好地控制第一类错误,同时且有较好的势,适用范围更加广泛。     

一体化小卫星综合测试系统的设计

在卫星的研制测试过程中,现有的测试设备通用性不强、开放性和灵活性不够、设备集成化程度低、自动化和智能化程度不高;通过提出一种小型化、一体化的综合测试系统的设计方法,并结合现有的资源进行了具体的项目开发,为未来的小卫星提升测试效率,降低系统成本,缩减系统规模探索出一条新路;实践表明,该方案在满足现有测试要求的情况下,在研制成本、系统体积、组建时间和无故障运行方面等均有较大改善。     

Direct limits of infinite-dimensional Lie groups compared to direct limits in related categories

Let G be a Lie group which is the union of an ascending sequence G₁⊆G₂⊆? of Lie groups (all of which may be infinite-dimensional). We study the question when in the category of Lie groups, topological groups, smooth manifolds, respectively, topological spaces. Full answers are obtained for G the group Diffc(M) of compactly supported C^∞-diffeomorphisms of a σ-compact smooth manifold M; and for test function groups of compactly supported smooth maps with values in a finite-dimensional Lie group H. We also discuss the cases where G is a direct limit of unit groups of Banach algebras, a Lie group of germs of Lie group-valued analytic maps, or a weak direct product of Lie groups.     

A visual test paper for extremely strong concentrated acidity with a new synthesized isoindole reagent

A visual test paper by taking common filter paper as solid support for extremely strong concentrated acidity has been developed in this contribution with a new synthesized isoindole compound starting from p-phenylenediamine and the coupled fluorogenic reagent of o-phthaldialdehyde-β-mercaptoethanol. It was very easy for semiquantitative detection of acidity in the range of 0.2-18 M ([H⁺]) in extreme acidic solution based on the color changes of the solution or the visual test paper prepared by immerging filter paper slides into the solution of the new synthesized reagent. Quantitative detection of concentrated strong acids could be successfully constructed through the linear relationship exists between the absorbance of the chromogenic reagent at 510 nm and the acid concentrations.     

Test for parameter change in discretely observed diffusion processes

In this paper, we consider the problem of testing for the parameter change in discretely observed diffusion processes. For a test, we perform the cusum test based on the estimator proposed by Kessler (J Stat 24:211–229, 1997). It is shown that the test statistic weakly converges to the sup of the square of a Browian bridge. Simulation results are illustrated for the Ornstein-Uhlenbeck and Cox-Ingersoll-Ross processes.