中立型脉冲微分方程正解的存在性

本文利用Banach压缩映射原理，讨论了中立型时滞脉冲微分方程正解的存在性。     

Partially isometric dilations of noncommuting -tuples of operators

Given a row contraction of operators on a Hilbert space and a family of projections on the space that stabilizes the operators, we show there is a unique minimal joint dilation to a row contraction of partial isometries that satisfy natural relations. For a fixed row contraction the set of all dilations forms a partially ordered set with a largest and smallest element. A key technical device in our analysis is a connection with directed graphs. We use a Wold decomposition for partial isometries to describe the models for these dilations, and we discuss how the basic properties of a dilation depend on the row contraction.

     

求解一类变形变分不等式的投影收缩算法及其性质

对一类变形的变分不等式：求，使得提出了一类投影收缩算法，并得到了该算法的收敛性及相关性质．     

On structure of small contractions of odd dimensional projective varieties

Let X be a smooth projective variety of dimension 2k-1 (k≥3) over the complex number field. Assume that fR: X→Y is a small contraction such that every irreducible component Ei of the exceptional locus of fR is a smooth subvariety of dimension k. It is shown that each Ei is isomorphic to the k-dimensional projective space Pk, the k-dimensional hyperquadric surface Qk in Pk 1, or a linear Pk-1-bundle over a smooth curve.     

The alicyclic ring contraction of perfluoro-1-phenyltetralin in reaction with antimony pentafluoride

Perfluoro-1-phenyltetralin (1) heated with antimony pentafluoride at 130 °C, then treated with water, gave a mixture of perfluorinated 3-methyl-2-phenylindenone (3), 3-methyl-2-phenylindene (4), 3-hydroxy-1-methyl-3-phenylindan (5), 1-methyl-3-phenylindan (6), 9-methyl-1,2,3,4,5,6,7,8-octahydroanthracene (7), and 1,9-dimethyl-5,6,7,8-tetrahydro-β-naphthindan (8). When heated with SbF₅ in the presence of HF, then treated with water, compound 1 is transformed to a mixture of products 3-6. The reaction at 170 and 200 °C forms compounds 3-6 together with perfluoro-2-(cyclohexen-1-yl)-3-methylindene (10).     

A novel heterocyclization of 1-acetylenyl-9,10-anthraquinones

I-Acetylenyl-9,10-anthraquinones react with an excess of NH₂NH₂ at 80–115°C to give a mixture of substituted 7H-dibenzo[de,h]quinolin-7-ones and anthra[9,1-cd]-1,2-diazepin-8-ones. The latter compounds undergo reductive contraction of the sevenmembered ring to give the corresponding 7H-dibenzo[de,h]quinolin-7-ones. Bulky substituents in position 2 of the initial acetylenylanthraquinones prevent the formation of the sevenmembered heterocycle. A scheme of the cyclocondensation was proposed. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 2027–2030, October, 1998.     

A MORPHOLOGICAL STUDY OF POLY（DIVINYLBENZENE-co-ACRYLIC ACID） IN CROSSLINKING PRECIPITATION POLYMERIZATION

Divinylbenzene-80 （DVB-80） and polar monomer acrylic acid （AA） having hydrogen bonding at a total monomer loading of 5 vol% were precipitated-copolymerized in a variety of organic solvents with 2,2＇-azobis（isobutyronitrile） （AIBN） as initiator. The experiments were investigated from a two-dimensional matrix, i.e., the actual crosslinking degree of DVB varying from 0 to 80% and the solvent composition varying from 0 to 100% of toluene mixture with acetonitrile, when the mixture of acetonitrile and toluene was used as the reaction solvent. Under various reaction conditions, six distinct morphologies including soluble polymers, swellable microgels, coagulum, irregular microparticles, and nano-/micrometer microspheres were formed and the structures of these polymer architectures were described. A morphological map was utilized to discuss the effects of both crosslinking degree of DVB and composition of solvent on the transitions between morphology domains. The results demonstrated that the microspheres are formed by an internal contraction due to the marginal solvency of the continuous phase and the crosslinking of the polymer network through the covalent bonding from DVB as well as the interchain hydrogen-bonding between the carboxylic acid units.     

Untersuchungen von Reaktionsmechanismen durch Isotopenmarkierung,IX Zum Ringverengungsmechanismus von 1,4-Benzthiazin-2,3-4H-dion

By¹⁴C-labeling it is shown that the ring contraction reaction of 1,4-benzothiazin-2,3-4H-dione (1), leading via benzthiazol-2-carbonic acid (2) finally to benzthiazole (3), proceeds via hydrolytic opening of the thiolactone-bond in1, irrespectively of H⁺ or OH^– catalysis.

     

Dynamic stability of a class of fractional-order nonlinear systems via fixed point theory

In this paper, the problem of the uniform stability for a class of fuzzy fractional-order genetic regulatory networks with random discrete delays, distributed delays, and parameter uncertainties is studied. Although there is a portion of literature on using fixed point theorems to study the stability of fractional neural networks, most of them required the fractional order to be in $\left(\frac{1}{2},1\right)$. However, the case of the fractional-order belonging to $(0,\frac{1}{2})$ has not been discussed. To solve it, this work proposes a novel idea of using fixed point theory to study the stability of fuzzy (0,1) order neural networks, the problem of the uniqueness of the solution of the considered genetic regulatory networks is resolved, and a novel sufficient condition to guarantee the uniform stability of above genetic regulatory networks is also derived. Eventually, an example is given to demonstrate that the obtained result is effective.