On Convergence of Quasi ρ-preserving Locally Related Quasi-nonexpansive Mappings

The concept of quasi-nonexpansive mappings was initiated in Diaz and Metcalf (Bull. Amer. Math. Soc. 73 (1967), 516–519), further it was generalized by Petryshyn and Williamson (Journal of Mathematical Analysis and Applications 43, no. 2 (1973): 459-497). Further investigating the above work, in this article a Banach space with a relation ρ has been considered, the notion of ρ-preserving and quasi ρ-preserving locally related quasi-nonexpansive mappings has been introduced. It has been shown that every ρ-preserving mapping is a quasi ρ-preserving and every nonexpansive mapping is locally related quasi-nonexpansive but converse may not hold. The necessary and sufficient conditions for the convergence of Picard, Mann and Ishikawa iterations of ρ-preserving, quasi ρ-preserving locally related quasi-nonexpansive mappings are presented.     

纯奇点范畴中的Buchweitz定理

我们定义纯奇点范畴D_(psg)~b(R)为有界纯导出范畴D_(pur)~b(R)与纯投射模构成的有界同伦范畴K~b(■)的Verdier商,得到了纯奇点范畴D_(psg)~b(R)三角等价于相对纯投射模的Gorenstein范畴的稳定范畴■的一个充分必要条件.同时,还给出三角等价D_(psg)~b(R)≌D_(psg)~b(S)的充分条件,这里R和S都是环.     

Bounded sets structure of CpX and quasi‐(DF)‐spaces

For wide classes of locally convex spaces, in particular, for the space $C_p(X)$ of continuous real‐valued functions on a Tychonoff space X equipped with the pointwise topology, we characterize the existence of a fundamental bounded resolution (i.e., an increasing family of bounded sets indexed by the irrationals which swallows the bounded sets). These facts together with some results from Grothendieck's theory of $(DF)$‐spaces have led us to introduce quasi‐ $(DF)$‐spaces, a class of locally convex spaces containing $(DF)$‐spaces that preserves subspaces, countable direct sums and countable products. Regular $(LM)$‐spaces as well as their strong duals are quasi‐ $(DF)$‐spaces. Hence the space of distributions $D^{\prime }(\mathrm{\Omega })$ provides a concrete example of a quasi‐ $(DF)$‐space not being a $(DF)$‐space. We show that $C_p(X)$ has a fundamental bounded resolution if and only if $C_p(X)$ is a quasi‐ $(DF)$‐space if and only if the strong dual of $C_p(X)$ is a quasi‐ $(DF)$‐space if and only if X is countable. If X is metrizable, then $C_k(X)$ is a quasi‐ $(DF)$‐space if and only if X is a σ‐compact Polish space.     

Clique-cutsets beyond chordal graphs

Truemper configurations (thetas, pyramids, prisms, and wheels) have played an important role in the study of complex hereditary graph classes (eg, the class of perfect graphs and the class of even-hole-free graphs), appearing both as excluded configurations, and as configurations around which graphs can be decomposed. In this paper, we study the structure of graphs that contain (as induced subgraphs) no Truemper configurations other than (possibly) universal wheels and twin wheels. We also study several subclasses of this class. We use our structural results to analyze the complexity of the recognition, maximum weight clique, maximum weight stable set, and optimal vertex coloring problems for these classes. Furthermore, we obtain polynomial -bounding functions for these classes.     

Thermally Stable and Organo-soluble Polyamides Containing Triazine Rings and Ether Linkages in the Main Chain: Synthesis and Characterization

In order to synthesize new polyamide(PA) 5 and copolyamides(Co PA) 7a-7d, a new-type of dicarboxylic acid containing triazine ring was successfully synthesized from 2,4-dichloro-6-methoxy-s-triazine 1 and 4-aminobenzoic acid. New polyamide 5 containing triazine moiety was prepared from 4,4'-(6-methoxy-1,3,5-triazine-2,4-diyl)bis(azanediyl)dibenzoic acid 3 and 4,4′-diaminodiphenylether by direct polycondensation reaction. Then new series thermally stable copolyamides 7a-7d with high solubility in common organic solvents were synthesized from the direct polycondensation reaction of diacid 3 as a first monomer, aliphatic-aromatic diacids 6a-6d as second diacids and 4,4′-diaminodiphenylether. All of the above polymers were fully characterized by 1H-NMR and FTIR spectroscopy, elemental analysis(CHN), inherent viscosity, solubility tests, gel permeation chromatography(GPC), differential scanning calorimetry(DSC) and thermogravimetric analysis(TGA). The resulted Co PAs 7a-7d have shown good inherent viscosities, solubility and thermal properties.     

Strong Convergence Theorems for Mixed Typ e Asymptotically Nonexpansive Mappings

The purpose of this paper is to study a new two-step iterative scheme with mean errors of mixed type for two asymptotically nonexpansive self-mappings and two asymptotically nonexpansive nonself-mappin...     

Novel cardo polyamides with high solubility,thermally stability,and flame retardancy

Abstract

A new monomeric building block was prepared via three consecutive reactions. 4-(4-Nitrobenzyl)pyridine was catalytically reduced to 4-(4-aminobenzyl)pyridine by converting the nitro to amino group. In second step, the later compound was reacted with 3,5-dinitrobenzoyl chloride to obtain a dinitro compound which finally was converted to a new diamine by reduction of nitro groups. Polycondensation reactions of the diamine with diacidchlorides led to preparation of novel cardo polyamides with high thermal stability and flame retardancy, as well as improved solubility. The structure-property relations were studied by varying the diacidchlorides to investigate the effect of symmetry and aromaticity on the polymers.     

Ultrathin Mn Doped Ni-MOF Nanosheet Array for Highly Capacitive and Stable Asymmetric Supercapacitor

In this study, we demonstrate that an Mn-doped ultrathin Ni-MOF nanosheet array on nickel foam (Mn_0.1-Ni-MOF/NF) serves as a highly capacitive and stable supercapacitor positive electrode. The Mn_0.1-Ni-MOF/NF shows an areal capacity of 6.48 C cm⁻² (specific capacity C: 1178 C g⁻¹) at 2 mA cm⁻² in 6.0 m KOH, outperforming most reported MOF-based materials. More importantly, it possesses excellent cycle stability to maintain 80.6 % capacity after 5000 cycles. An asymmetric supercapacitor device utilizing Mn_0.1-Ni-MOF/NF as the positive electrode and activated carbon as the negative electrode attains a high energy density of 39.6 Wh kg⁻¹ at 143.8 Wkg⁻¹ power density with a capacitance retention of 83.6 % after 5000 cycles.     

Stable isotope dilution assay for the accurate determination of tricaine in fish samples by HPLC–MS–MS

Tricaine methanesulfonate is one of most commonly used anesthetics in fish during blood sampling, artificial propagation and long‐distance transportation. In this study, an accurate method for the quantitative determination of tricaine in fish samples by a stable isotope dilution assay coupled with high‐performance liquid chromatography–triple quadrupole mass spectrometry was developed. Tricaine‐D₅ was synthesized and used as an isotopically labeled internal standard for the determination of tricaine. The analytical performance of the method was validated for tricaine determination in marine fish and freshwater fish. The determination of tricaine was linear in the range of 2.0–200.0 μg L^?1. The limit of detection and limit of quantitation for fish muscle tissues were 1.0 and 4.0 μg kg^?1, respectively. Good recoveries were obtained in the range of 92.08–97.50%. The inter‐ and intra‐assay relative standard deviations (RSD values) were investigated, and the values were 0.39–3.01 and 0.85–2.77%, respectively. The values of CCα and CCβ were 10.21–10.43 and 10.42–10.87 μg kg^?1, respectively. The clearance of MS‐222 from grass carp was further studied using our method. The results demonstrate that MS‐222 could be well absorbed and rapidly eliminated after bath administration.     

Laws of Large Numbers for Cesàro alpha-integrable Random Variables under Dependence Condition AANA or AQSI

Both residual Cesàro alpha-integrability (RCI( α)) and strongly residual Cesàro alpha-integrability (SRCI(α)) are two special kinds of extensions to uniform integrability, and both asymp-totically almost negative association (AANA) and asymptotically quadrant sub-independence (AQSI) are two special kinds of dependence structures. By relating the RCI(α) property as well as the SRCI(α) property with dependence condition AANA or AQSI, we formulate some tail-integrability conditions under which for appropriate α the RCI(α) property yields L1-convergence results and the SRCI(α) property yields strong laws of large numbers, which is the continuation of the corresponding literature.