PERIODIC SOLUTIONS FOR A CLASS OF DELAYED NONLINEAR DIFFERENCE EQUATIONS

With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree,some sufficient conditions are established for the global existence of positive periodic solutions of a class of delayed nonlinear difference equations.     

White‐Light Emission Strategy of a Single Organic Compound with Aggregation‐Induced Emission and Delayed Fluorescence Properties

A novel white‐light‐emitting organic molecule, which consists of carbazolyl‐ and phenothiazinyl‐substituted benzophenone (OPC) and exhibits aggregation‐induced emission‐delayed fluorescence (AIE‐DF) and mechanofluorochromic properties was synthesized. The CIE color coordinates of OPC were directly measured with a non‐doped powder, which presented white‐emission coordinates (0.33, 0.33) at 244 K to 252 K and (0.35, 0.35) at 298 K. The asymmetric donor–acceptor–donor′ (D‐A‐D′) type of OPC exhibits an accurate inherited relationship from dicarbazolyl‐substituted benzophenone (O2C, D‐A‐D) and diphenothiazinyl‐substituted benzophenone (O2P, D′‐A‐D′). By purposefully selecting the two parent molecules, that is, O2C (blue) and O2P (yellow), the white‐light emission of OPC can be achieved in a single molecule. This finding provides a feasible molecular strategy to design new AIE‐DF white‐light‐emitting organic molecules.     

Periodic solution and its stability of a delayed Beddington‐DeAngelis type predator‐prey system with discontinuous control strategy

This paper investigates the periodic solution of a delayed Beddington‐DeAngelis (BD) type predator‐prey model with discontinuous control strategy. Firstly, the regularity and visibility analysis of the delayed predator‐prey model is carried out by using the principle of differential inclusion. Secondly, the positiveness and boundeness of the solution is discussed by employing the comparison theorem. Based on the boundary conditions of the model and the Mawhin‐like coincidence theorem, it is shown that the solution of the delayed BD system is asymptotically stable in finite time. Furthermore, it is found that there exists at least one periodic solution of the nonautonomous delayed predator‐prey model by using the principle of topological degree and set value mapping. Specially, when the nonautonomous delayed BD system degenerates into an autonomous system, some criteria are obtained to guarantee the convergence behavior of the harvesting solutions for the corresponding autonomous delayed BD system. Finally, numerical examples are given to demonstrate the applicability and effectiveness of main results. It is worthy to point out that the discontinuous control strategy is superior to the continuous harvesting policies adopted in existing literature.     

Finite time stability and relative controllability of Riemann‐Liouville fractional delay differential equations

This paper firstly deals with finite time stability (FTS) of Riemann‐Liouville fractional delay differential equations via giving a series of properties of delayed matrix function of Mittag‐Leffler. We secondly study relative controllability of such type‐controlled system. With the help of the representation of solution, both Gram‐like type matrix and rank criterion are derived, which extend the corresponding results for linear systems.     

深海富钴结核微区X射线荧光光谱分析和数据挖掘

西太平洋富钴结核是近年来新发现的海底固体矿产资源,富含Mn,Fe,Co,Ni和Cu等多种关键金属元素。富钴结核是一种非均质的地球化学和矿物学集合体,粒径约6 cm的结核在生长过程中记录了数千万年的海洋沉积历史,亟需高分辨率的分析技术揭示古海洋环境信息。采用微区X射线荧光光谱仪（μ-XRF）,对C3BC1704富钴结核开展多元素面扫描,获得了原位高分辨率多元素的信号强度数据,评价了μ-XRF技术在富钴结核中的应用质量。元素信号谱峰特征和数据频谱分布结果显示,富钴结核中Mn,Fe,Ti,Co,Ca和Ni等元素信号强度敏感,数据呈现相对较好的正态分布特征,可用于定量或半定量分析;Si,Cu和Al等元素信号较弱,数据呈现左偏的正态分布特征,建议相关数据仅作参考。μ-XRF获得的数据量庞大且彼此独立,本研究将不同元素连接成彼此关联的多维矩阵,实现了数据的位置信息和特征元素之间的数学运算和筛选,了解了金属元素的分布和变化特征,揭示了富钴结核生长过程的环境变化。结果显示,Mn和Fe等元素在生长层中波动剧烈,金属元素在富钴结核中的分布极不均匀,显示出多成因类型的交替微层和7个大的生长周期旋回。C3BC1704富钴结核主体暴露在海水中,金属元素主要来自海水,化学组成指示为典型的水成成因。进一步定量分析结果显示,Mn,Cu和Ni等元素含量从内部向外围呈现同步降低的趋势,Fe,Ti和Co等元素含量则呈现同步升高的趋势,这些特征指示早期偏向于成岩富集环境,晚期则以水成富集为主。富钴结核金属元素的分布和变化特征,清晰呈现了富钴结核的生长结构,揭示了富钴结核生长过程的环境变化,有利于富钴结核的成矿模型的构建。     

盐酸溶液中氯代十六烷基吡啶在锌表面上的吸附及其缓蚀作用

盐酸溶液中氯代十六烷基吡啶在锌表面上的吸附及其缓蚀作用杨春芬，白宇新（云南大学化学系昆明６５００９１）关键词锌，氯代十六烷基吡啶，吸附，缓蚀作用在抑制金属腐蚀的方法中，缓蚀剂的应用是最受重视的一种，因为它具有用量少，不需附加设备和不改变金属制品本性等...     

Preparation and spectroscopic characterization of surface‐enriched (with active sites) polymer‐supported phase‐transfer catalysts and their efficiency in organic addition reactions: A kinetic study

We prepared two batches of surface‐enriched (with active sites) polymer‐supported phase‐transfer catalysts (SE‐PSPTC) by fixing the crosslinking monomer divinylbenzene (DVB) at 2% (first batch) and 6% (second batch) through a free‐radical suspension copolymerization method with vinylbenzyl chloride (VBC; 25%) as a functionality and with styrene (St) as a supporting monomer, followed by the quaternization of the resulting terpolymer beads with triethylamine. The enrichment of the active sites on the surfaces of the beads was accomplished by a surface‐grafting technique through the delayed addition of the functional monomer (VBC) to the partially polymerized copolymer beads of poly(St/DVB). To bring the active sites fully onto the surfaces, we prepared six different types of terpolymer beads in each batch by varying the partial polymerization time (PPT) of St/DVB—0 h [0 VBC (conventional)], 3 h (3 VBC), 6 h (6 VBC), 9 h (9 VBC), 12 h (12 VBC), and 15 h (15 VBC)—and then gradually adding the functional monomer (VBC) to the partially polymerized poly(St/DVB) system. The resulting terpolymer beads, containing different concentrations of pendant benzyl chloride (? CH₂Cl) on the surface in each batch, underwent facile quaternization [? CH₂N⁺(C₂H₅)₃Cl^?] with an increase in the PPT of St/DVB and remained constant at 12 VBC and 15 VBC. To asses the superiority of the catalysts according to the surface enrichment of the active sites, particularly between conventional (0 VBC) catalysts and other PPT‐based SE‐PSPTCs, we characterized all the catalysts by estimating the chloride‐ion concentration, by using Fourier transform infrared (FTIR), scanning electron microscopy (SEM), EDAX, and ESCA, and by carrying out the dichlorocarbene addition to olefins. The chloride‐ion concentration by the Volhard method and the peak intensity of the C? N stretching absorbance concentration, that is, the quaternary onium group in the FTIR spectra of both batches, increased with the PPT of St/DVB in both batches of catalysts. In particular, the chloride concentration of a first‐batch catalyst of a representative mesh size (?120 + 140) had a twofold enhancement between the conventional catalyst (0 VBC; 1.88 m equiv g^?1) and 9 VBC/SE‐PSPTC (3.74 m equiv g^?1), although the same amount of the functional monomer was added in both preparations. These results showed the higher enrichment of the active site on the surface of 9 VBC, and the same trend was also maintained for second‐batch catalysts, regardless of the catalyst mesh size. SEM images of both batches showed that there was a higher concentration of nodules [due to the grafting of poly(VBC)] on the surfaces of the beads of 9 VBC/SE‐PSPTC and the aforementioned PPT catalysts than on the surfaces of the conventional catalysts (0 VBCs), which exhibited smooth surfaces (because of the simultaneous addition of all three monomers). This observation confirmed the enrichment of active sites on the surfaces. In the EDAX analysis, up to a depth of 0.5–1 μm, the surface chloride concentration increased from 0 VBC to 9 VBC/SE‐PSPTC and remained constant in 12 VBC and 15 VBC, first‐batch catalysts of a representative mesh size (?120 + 140). The same trend was also observed in second‐batch catalysts, indicating the enrichment of the onium group more on the surface in 9 VBC/SE‐PSPTCs. The ESCA analysis, to a depth of about 20–30Å, proved that the concentration of covalent chloride on the surface had increased from 0 VBC (15%) to 9 VBC/SE‐PSPTCs (29%) and remained constant thereafter in first‐batch catalyst; the trend was the same for second‐batch catalysts, also confirming the strong evidence of surface enrichment of the active sites. Similarly, the rate constants of different olefin addition reactions catalyzed by both batches of catalysts also increased from 0 VBC to 9 VBC and remained constant with 12 VBC and 15 VBC catalysts. The twofold increase of the rate constants, regardless of the olefins, for conventional catalysts to 9 VBC/SE‐PSPTCs confirmed the enrichment of the active sites on the surfaces. All these experimental observations proved that 50% of the active sites were successfully brought out from inside the poly(St/DVB) networks to the exterior surfaces, although same amount of VBC was added for the preparation of all the catalyst types. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 347–364, 2003     

Regularities of triplet-triplet annihilation of aromatic hydrocarbons in aqueous micellar solutions of sodium dodecyl sulfate

Investigation of deactivation processes in triplet states of a series of aromatic hydrocarbon molecules (antracene, 1,2-benzantracene, and 3,4-benzpyrene) made it possible to reveal the presence of triplet-triplet annihilation of the molecules in aqueous micellar solutions of sodium dodecyl sulfate. It is shown that the effect of microheterogeneous solutions on the process of triplet-triplet annihilation manifests itself in an increase in the probability of excimerization upon dissociation of triplet pairs of 1,2-benzantracene and 3,4-benpyrene molecules compared to one-component solutions. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 5, pp. 626–628, September–October, 1997.     

Infinite-horizon investment consumption model with a nonterminal bankruptcy

This paper solves a general continuous-time consumption and portfolio decision problem for a single agent for whom there exists, upon bankruptcy, a possibility of recovery from his bankruptcy. The main contribution of the paper is in the modeling of the recovery process. Moreover, it is shown that the model with recovery has a one-to-one correspondence with the model with terminal bankruptcy treated in the literature.This research was supported by Grants SSHRC-410-83-9888 and NSERC-A4619 to the first author and by Grants NSF-DMS-86-01510 and AFOSR-88-0183 to the second author. Comments from E. Presman are gratefully acknowledged.