On generalized Erd?s spaces

During the last years both Erd?s space and complete Erd?s space were topologically characterized by Dijkstra and van Mill. Applications include results about Erd?s type spaces in ?p-spaces as well as results about Polishable ideals on ω. We present an unifying theorem in terms of sets with a reflexive relation that among other things contains these apparently dissimilar results as special cases.     

Rhodium(I)/cationic 2,2′-bipyridyl-catalyzed [2+2+2] cycloaddition of α,ω-diynes with alkynes in water under air

A simply performed procedure for the [Rh(cod)Cl]₂/cationic 2,2′-bipyridyl system-catalyzed [2+2+2] cycloaddition of α,ω-diynes with terminal and internal alkynes was achieved in water under air at 60 °C. The reaction proceeded smoothly with 1 equiv α,ω-diynes and 3 equiv alkynes in the presence of 20 mol % KOH for 1 h or 9 h, resulting in the formation of tri- and tetra-substituted benzene derivatives in moderate to high yields. After separation of the organic products by extraction, the residual aqueous solution could be reused for further reactions until complete degradation of its catalytic activity.     

基于集群的高频合成孔径声纳并行处理方法

大测绘带下的高频合成孔径声纳需要解决的主要问题是海量数据的实时处理。该问题对数据处理的计算平台、成像处理和架构提出了很高的要求。本文利用非均匀离散快速傅里叶变换改进了成像算法,使之能够适应采用了多子阵技术的合成孔径声纳;提出了高频合成孔径声纳信号并行处理方法,在集群上实施了该方法,并进行了湖试试验。实时成像结果表明,改进的并行处理方法可以满足分辨率为距离向4cm、方位向5 cm,测绘带宽为200m的高频合成孔径声纳实时成像要求,具有较高的稳定性。     

A Cahn-Hilliard model in a domain with non-permeable walls

We consider in this article a Cahn-Hilliard model in a bounded domain with non-permeable walls, characterized by dynamic-type boundary conditions. Dynamic boundary conditions for the Cahn-Hilliard system have recently been proposed by physicists in order to account for the interactions with the walls in confined systems and are obtained by writing that the total bulk mass is conserved and that there is a relaxation dynamics on the boundary. However, in the case of non-permeable walls, one should also expect some mass on the boundary. It thus seems more realistic to assume that the total mass, in the bulk and on the boundary, is conserved, which leads to boundary conditions of a different type. For the resulting mathematical model, we prove the existence and uniqueness of weak solutions and study their asymptotic behavior as time goes to infinity.     

A monotone version of the Sokolov property and monotone retractability in function spaces

We introduce the monotone Sokolov property and show that it is dual to monotone retractability in the sense that X   is monotonically retractable if and only if _Cp(X)$C_p(X)$ is monotonically Sokolov. Besides, a space X   is monotonically Sokolov if and only if _Cp(X)$C_p(X)$ is monotonically retractable. Monotone retractability and monotone Sokolov property are shown to be preserved by R$\mathbb{R}$-quotient images and _Fσ$F_{\sigma }$-subspaces. Furthermore, every monotonically retractable space is Sokolov so it is collectionwise normal and has countable extent. We also establish that if X   and _Cp(X)$C_p(X)$ are Lindelöf Σ-spaces then they are both monotonically retractable and have the monotone Sokolov property. An example is given of a space X   such that _Cp(X)$C_p(X)$ has the Lindelöf Σ-property but neither X   nor _Cp(X)$C_p(X)$ is monotonically retractable. We also establish that every Lindelöf Σ-space with a unique non-isolated point is monotonically retractable. On the other hand, each Lindelöf space with a unique non-isolated point is monotonically Sokolov.     

Thermodynamics of fusion and sublimation for a homologous series of eleven alkane-α,ω-diols HO-(CH2)n-OH: Structure-related odd–even effect

Temperatures and enthalpies of fusion and solid-to-solid transition of a homologous series of linear alkane-α,ω-diols, HO-(CH₂)_n-OH where n = (6 to 16), were measured by differential scanning calorimetry (d.s.c.). The enthalpies and temperatures of fusion displayed a marked odd–even effect as a function of the number of methylene groups in the alkyl chains, with even terms showing higher values than odd terms. Thermodynamic parameters of fusion were compared with those of isoelectronic linear alkanes and earlier measured alkane-α,ω-diamines, alkane-α,ω-diamides and alkane-α,ω-dinitriles. Results were discussed with reference to the effects of chain length on crystal structures and packing patterns raised on hydrogen bonding and hydrophobic interaction interplay. The enthalpies of sublimation at T = 298.15 K were obtained from the enthalpies of fusion and the literature enthalpies of vaporisation, both adjusted to 298.15 K. A smoother odd–even pattern was observed for the enthalpies of sublimation.     

Intramolecular Cyclization of 1-(ω-Phenylalkyl)-2-(nitromethylene)pyrrolidines in Triflic Acid

1-(ω-Phenylalkyl)-2-(nitromethylene)pyrrolidines in triflic acid undergo a C,O-diprotonation, followed by loss of water, to form conjugated iminium–hydroxynitrilium dications, which react with the tethered phenyl ring by electrophilic aromatic substitution to afford tricyclic iminium compounds as triflate salts. The scope and mechanism of this reaction are discussed.     

On ω-Linked Overrings

Let R (C) T be an extension of commutative rings. T is called ω-linked over R if T as an R-module is a ω-module. In the case of R (C) T (C) Q0(R), T is called a ω-linked overring of R. As a generalization of Wang-McCsland-Park-Chang Theorem, we show that if R is a reduced ring, then R is a ω-Noetherian ring with ω-dim(R) ≤1 if and only if each ω-linked overring T of R is a ω-Noetherian ring with ω-dim(T) ≤ 1. In particular, R is a ω-Noetherian ring with ω-dim(R) = 0 if and only if R is an Artinian ring.     

Thermodynamics of the interaction between hydroxypropyl-α-cyclodextrin and alkanols in aqueous solutions

The interactions of hydroxypropyl-α-cyclodextrin (HP-α-CD) with 1-alkanols and with some α,ω-alkanediols have been studied by calorimetric titration at 298.15 K. This technique enables the determination of the enthalpy and association constant for the complex formation, from which Gibbs energy and entropy can be derived. The results are compared to those reported for the complex formation between the native α-cyclodextrin (α-CD) and 1-alkanols or α,ω-alkanediols in the literature. Thermodynamic parameters corresponding to the transfer process of the alkanol from the native to the modified α-CD are also calculated. The results clearly show that the hydrophobic interactions are important in this process, but there are other effects like the size of the alkanol that are also of some importance.