无界域上1-集弱压缩算子的新不动点结果

本文证明Banach空间中无界域上一类弱序列连续和1-集弱压缩算子的若干新不动点定理.我们引入原点处弱半闭算子,得到该算子的若干不动点定理.进而将著名的Leray-Schauder不动点定理、Altman定理、Roth定理和Petryshyn定理推广到弱序列连续算子和1-集弱压缩算子以及原点处弱半闭算子的情形.本文的主要结果依赖于非紧性弱原子测度的有关条件.     

Rota–Baxter Hom-Lie–Admissible Algebras

We study Hom-type analogs of Rota–Baxter and dendriform algebras, called Rota–Baxter G-Hom–associative algebras and Hom-dendriform algebras. Several construction results are proved. Free algebras for these objects are explicitly constructed. Various functors between these categories, as well as an adjunction between the categories of Rota–Baxter Hom-associative algebras and of Hom-(tri)dendriform algebras, are constructed.     

Fixed points, eigenvalues and surjectivity for (ws)-compact operators on unbounded convex sets

The paper studies the existence of fixed points for some nonlinear (ws)-compact, weakly condensing and strictly quasibounded operators defined on an unbounded closed convex subset of a Banach space. Applications of the newly developed fixed point theorems are also discussed for proving the existence of positive eigenvalues and surjectivity of quasibounded operators in similar situations. The main condition in our results is formulated in terms of axiomatic measures of weak noncompactness.     

Functionally rigid bistable [2]rotaxanes

Two-station [2]rotaxanes in the shape of a degenerate naphthalene (NP) shuttle and a nondegenerate monopyrrolotetrathiafulvalene (MPTTF)/NP redox-controllable switch have been synthesized and characterized in solution. Their dumbbell-shaped components are composed of polyether chains interrupted along their lengths by (i) two pi-electron-rich stations-two NP moieties or a MPTTF unit and a NP moiety-with (ii) a rigid arylethynyl or butadiynyl spacer situated between the two stations and terminated by (iii) flexibly tethered hydrophobic stoppers at each end of the dumbbells. This modification was investigated as a means to simplify both molecular structure and switching function previously observed in related bistable [2]rotaxanes with flexible spacers between their stations and incorporating a cyclobis(paraquat-p-phenylene) (CBPQT4+) ring. The nondegenerate MPTTF-NP switch was isolated as near isomer-free bistable [2]rotaxane. Utilization of MPTTF removes the cis/trans isomerization that characterizes the tetrathiafulvalene (TTF) parent core structure. Furthermore, only one translational isomer is observed (> 95 < 5), surprisingly across a wide temperature range (198-323 K), meaning that the CBPQT4+ ring component resides, to all intents and purposes, predominantly on the MPTTF unit in the ground state. As a consequence of these two effects, the assignment of NMR and UV-vis data is more simplified as compared to previous donor-acceptor bistable [2]rotaxanes. This development has not only allowed for much better control over the position of the ring component in the ground state but also for control over the location of the CBPQT4+ ring during solution-state switching experiments, triggered either chemically (1H NMR) or electrochemically (cyclic voltammetry). In this instance, the use of the rigid spacer defines an unambiguous distance of 1.5 nm over which the ring moves between the MPTTF and NP units. The degenerate NP/NP [2]rotaxane was used to investigate the shuttling barrier by dynamic 1H NMR spectroscopy for the movement of the CBPQT4+ ring across the new rigid spacer. It is evident from these measurements that the rigid spacer poses a much lower barrier to the 1.0 nm movement of the CBPQT4+ ring from one station to another as compared with previous systems-a finding that is thought to be a result of the combination of fewer favorable interactions between the spacer and the CBPQT4+ ring and a relatively unimpeded path between the two NP stations. This example augers well for exploiting rigidity during the development of well-defined bistable [2]rotaxanes, which are unencumbered by the excesses of structural conformations that have characterized the first generations of molecular switches based on the donor-acceptor recognition motif.     

Polarized naphthalimide CH donors enhance Cl- binding within an aryl-triazole receptor

The dipolar character of 1,8-naphthalimide together with polarization of the C(4)-H and C(5)-H donors has been utilized in receptor 1 to effectively bind chloride alongside triazole and phenylene units. The Cl(-) binding strength of 1 shows that the naphthalimide provides greater anion stabilization than an unactivated phenylene, and DFT calculations show that its collinear donor array can be a "urea-like" analog for CH···anion interactions.     

Nanometer-sized reactor--a porphyrin-based model system for anion species

Although many cagelike molecules can create a catalytic environment for promoting chemical reactions, the construction of receptors that can host anionic species and sensitize their reaction is novel. Here we report the photochemically induced dimerization of the anion radicals of TCNQ (7,7,8,8-tetracyano-para-quinodimethane) in organic solvent under aerobic conditions when they are encapsulated inside a cationic photoactive receptor. There is clear evidence for a rate increase of over two orders of magnitude, photosensitization of the host, and demonstrated turnover of the catalyst.     

Aromatic and aliphatic CH hydrogen bonds fight for chloride while competing alongside ion pairing within triazolophanes

Triazolophanes are used as the venue to compete an aliphatic propylene CH hydrogen‐bond donor against an aromatic phenylene one. Longer aliphatic C? H ??? Cl^? hydrogen bonds were calculated from the location of the chloride within the propylene‐based triazolophane. The gas‐phase energetics of chloride binding (ΔG_bind, ΔH_bind, ΔS_bind) and the configurational entropy (ΔS_config) were computed by taking all low‐energy conformations into account. Comparison between the phenylene‐ and propylene‐based triazolophanes shows the computed gas‐phase free energy of binding decreased from ΔG_bind=?194 to ?182 kJ mol^?1, respectively, with a modest enthalpy–entropy compensation. These differences were investigated experimentally. An ¹H NMR spectroscopy study on the structure of the propylene triazolophane’s 1:1 chloride complex is consistent with a weaker propylene CH hydrogen bond. To quantify the affinity differences between the two triazolophanes in dichloromethane, it was critical to obtain an accurate binding model. Four equilibria were identified. In addition to 1:1 complexation and 2:1 sandwich formation, ion pairing of the tetrabutylammonium chloride salt (TBA⁺ ? Cl^?) and cation pairing of TBA⁺ with the 1:1 triazolophane–chloride complex were observed and quantified. Each complex was independently verified by ESI‐MS or diffusion NMR spectroscopy. With ion pairing deconvoluted from the chloride–receptor binding, equilibrium constants were determined by using ¹H NMR (500 μM ) and UV/Vis (50 μM ) spectroscopy titrations. The stabilities of the 1:1 complexes for the phenylene and propylene triazolophanes did not differ within experimental error, ΔG=(?38±2) and (?39±1) kJ mol^?1, respectively, as verified by an NMR spectroscopy competition experiment. Thus, the aliphatic CH donor only revealed its weaker character when competing with aromatic CH donors within the propylene‐based triazolophane.