On fixed point and almost fixed point problems of lower semicontinuous type multivalued mappings

In the present paper, some new almost fixed point theorems and fixed point theorems for lower semicontinuous type multivalued mappings are obtained in metrizable <em>H</em>-spaces.     

On Super-KMS functionals and entire cyclic cohomology

We formulate the super-KMS condition suggested by Connes and Kastler, in the context of entire cyclic cohomology of quantum algebras. We show that the Chern character of Jaffe, Lesniewski, and Osterwalder — associated by Kastler to a super-KMS functional — satisfies the entire growth condition. Hence, a super-KMS functional defines a cocycle for the entire cyclic cohomology of quantum algebras.Supported in part by the National Science Foundation.     

Fields as Kolmogzrov flows

It is widely recognized that for highly unstable dynamical systems there exists a fundamental limitation on predictability and determinism. An important class of such highly unstable systems is the class of K-flow, which is further characterized by the existence of time-asymmetric objects in the form of K-partition. Our recent approach to the problem of irreversibility has shown that when the implications of the limitation on determinism arising from strong form of instability and those of the existence of K-partition are consistently taken into account, one is naturally led from the physically unrealizable deterministic evolution of phase points to an entropy-increasing stochastic Markovian evolution. Furthermore, this transition is not the result of extraneously imposed coarse graining and/or approximation schemes, but can be brought about by an invertible transformation whose existence and construction are determined by the nature of the instability of the dynamical system itself. After a brief review of this theory which also contains some relatively new remarks, we prove that classical Klein-Gordon field (both massive and massless) possess the structure of K-flow. This seems to provide the first examples of relativistic systems that are K-flows. Some of the implications of this result are briefly discussed. From a mathematical point of view, this seems to be a first step toward an ergodic theory of partial differential equations. In the process, we also provide an independant group-theoretic proof of the existence of incoming and outgoing subspaces of the scattering theory of Lax and Phillips for the wave equation.     

Synthesis and Characterization of Tetraosmium Carbonyl Complexes Containing a Bridging CO2 Ligand

Treatment of (thd)H (thd=2,2,6,6-tetramethyl-3,5-heptandionate) with excess Os<sub>3</sub>(CO)<sub>12</sub> in an autoclave at 180°C gives the formation of a brown metal chain complex [Os<sub>2</sub>(CO)<sub>5</sub>(thd)<sub>2</sub>]<sub>2</sub> (<b>1</b>) and a yellow CO<sub>2</sub> cluster complex [Os<sub>4</sub>(<i><img src="/content/l37r212v9kk208g5/xxlarge956.gif" alt="mgr" align="MIDDLE" BORDER="0"></i>-H)(<i><img src="/content/l37r212v9kk208g5/xxlarge956.gif" alt="mgr" align="MIDDLE" BORDER="0"></i>-CO<sub>2</sub>)(thd)(CO)<sub>13</sub>] (<b>2</b>) in low yields. Complex <b>2</b> was fully identified by a combination of spectroscopic methods and X-ray diffraction study, showing a unique CO<sub>2</sub> ligand bridging a triosmium metal fragment, Os<sub>3</sub>(<i><img src="/content/l37r212v9kk208g5/xxlarge956.gif" alt="mgr" align="MIDDLE" BORDER="0"></i>-H)(CO)<sub>10</sub> and a monometallic osmium fragment, Os(CO)<sub>3</sub>(thd). Upon treatment of <b>1</b> with Me<sub>3</sub>NO at an elevated temperature, oxidation of the CO ligand occurred at the position trans to the unique CO<sub>2</sub> ligand on the Os(CO)<sub>3</sub>(thd) fragment, giving the formation of a second CO<sub>2</sub> cluster [Os<sub>4</sub>(<i><img src="/content/l37r212v9kk208g5/xxlarge956.gif" alt="mgr" align="MIDDLE" BORDER="0"></i>-H)(<i><img src="/content/l37r212v9kk208g5/xxlarge956.gif" alt="mgr" align="MIDDLE" BORDER="0"></i>-CO<sub>2</sub>)(thd)(CO)<sub>12</sub>(NCMe)] (<b>3</b>), which is stabilized by a weakly coordinated acetonitrile molecule.     

Phosphorescence lifetime of naphthalene and phenanthrene in aggregated aromatic molecule-β-cyclodextrin-precipitant complexes

Aggregated aromatic molecule-<img src="/content/n172l724h5304v21/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-cyclodextrin-precipitant complexes exhibit long-lived phosphorescence at room temperature in water after the chemical binding of oxygen. The temperature dependences of the phosphorescence lifetimes of naphthalene-h<sub>8</sub>, naphthalene-de, and phenanthrene in the aggregates were measured. For example, the phosphorescence lifetimes of naphthalene-d<sub>8</sub> aggregated with <img src="/content/n172l724h5304v21/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-cyclodextrin and cyclohexane are equal to 25.1, 17.6, and 6.8 s at 77, 276, and 347 K, respectively, and that of phenanthrene aggregated with isooctane and <img src="/content/n172l724h5304v21/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-cyclodextrin are 3.24, 3.06, and 1.26 s at 268, 274, and 335 K, respectively. The temperature dependences of the phosphorescence lifetimes at room temperature are determined by the rate constants of the radiative and nonradiative transitions from the triplet state of an aromatic molecule.Translated from<i>Izvestiya Akademii Nauk. Seriya Khimicheskaya</i>, No. 9, pp. 2225–2228, September, 1996.     

On-column injection onto capillary columns. Part 2: Study of sampling conditions; practical recommendations

During one year continuous use of on-column injection, the typical advantages described in our first report have fully been confirmed. In addition the analysis of large sample volumes has proved promising. Only minor modifications have been applied to the on-column injector device. Broad evidence has been gathered showing that full separation efficiency of the capillary columns after on-column injection is attained only when cold trapping or the solvent effect, as band shortening mechanisms, are working- While, under the conditions of on-column injection, cold trapping is less efficient than with other injection techniques, the opposite holds true for the solvent effect. Compared with splitless injection, the danger of excessive solvent condensation on the column is increased. A working rule is presented for establishing the optimal chromatographic conditions for handling large sample volumes while ensuring full separation efficiency yet avoiding harm to the column.     

Reaction paths of some open-shell reactive intermediates

The intermolecular interaction energy for reacting systems in singlet, triplet and doublet states was partitioned by the perturbation expansion method into the chemically meaningful five interaction terms: the Coulomb, exchange-repulsion, induction, dispersion, and charge-transfer energies. In the local ZDO approximation, these energy terms were evaluated for the dimerization of methylenes (<sup>1,3</sup>CH<sub>2</sub>), the additions of carbenes (<sup>1,3</sup>CH<sub>2</sub> and<sup>1,3</sup>CF<sub>2</sub>) as well as amino radicals (<sup>2</sup>NH<sub>2</sub> and<sup>2</sup>NF<sub>2</sub>) toward ethylene, and the hydrogen abstractions by methylenes (<sup>1,3</sup>CH<sub>2</sub>), nitrene (<sup>3</sup>NH), and hydroxyl radical (<sup>2</sup>OH) from methane. It has been found that the reaction path is much influenced by the spinmultiplicity, and that the charge-transfer and exchange-repulsion terms play a dominant role in determining the course of reactions.     

Molecular Structure of 1,3,5-Tris (Trimethylstannyl) Benzene: An Electron Diffraction Study

The molecular structure of 1,3,5-<i>tris</i> (trimethylstannyl) benzene has been determined by gas-phase electron diffraction. The C — C bond length is in good agreement with that in benzene. In agreement with the somewhat electron-releasing character of the substituents, the endocyclic bond angles at the substituents are somewhat smaller than 120°. The mean value of Sn — C bond lengths is greater than that in tetraphenyltin and tetramethyltin. The SnMe<sub>3</sub> groups appear freely rotating around the C<sub>aryl</sub> — Sn bonds. The following bond lengths (<i>r</i> <sub>g</sub>) and bond angles were determined: (Sn — C)<sub>mean</sub> 2.150 ± 0.007 Å, C — C 1.399 ± 0.005 Å, (C — H)<sub>mean</sub> 1.105 ± 0.006 Å, < C — C(Sn) — C 117.7 ± 1.7º, < C<sub>aryl</sub> — Sn — C<sub>methyl</sub> 106.7 ± 0.7º < Sn — C — H 111.5 ± 0.9º.     

Thermostability of landscape phage probes

Immunoassays have traditionally relied on antibodies as diagnostic probes. Their use outside of a laboratory, however, may be problematic because antibodies are often unstable in severe environmental conditions. Environmental monitoring requires thermostable probes, such as landscape phage, that carry thousands of foreign peptides on their surfaces, are superior to antibodies, and can operate in non-controlled conditions. While parent wild-type phage are known to be extremely stable in various media at high temperatures, no work has been done to demonstrate the stability of landscape phage probes. We examined the thermostability of a landscape phage probe and a monoclonal antibody specific for <img src="/content/p2w93882l7520834/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-galactosidase in parallel in an enzyme-linked immunosorbent assay (ELISA) format. They were both stable for greater than six months at room temperature, but at higher temperatures the antibody degraded more rapidly than the phage probe. Phage retained detectable binding ability for more than six weeks at 63 °C, and three days at 76 °C. The activation energy of phage degradation was determined to be 1.34×10<sup>5</sup> J/mol. These results confirm that phage probes are highly thermostable and can function even after exposure to high temperatures during shipping, storage and operation.     

Electroreduction of Pd(II) Complexes with α-Alanine on a Palladium Electrode

The kinetics of electroreduction of Pd(II) complexes with <img src="/content/l765605h27720278/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">-alanine, Pd(ala)<sub>2</sub>, is studied on a rotating Pd disk electrode in solutions of pH 8–13 containing large excess of <img src="/content/l765605h27720278/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">-alanine and various supporting electrolytes (NaF, Na<sub>2</sub>SO<sub>4</sub>, NaClO<sub>4</sub>). On a Pd electrode, complexes Pd(ala)<sub>2</sub> undergo reduction at potentials much more negative than on an Hg electrode. This is attributed to the chemisorption of water on the Pd electrode, which hampers adsorption of Pd(ala)<sub>2</sub> that take part in the slow electrochemical stage. As with the Hg electrode, perchlorate ions hinder the Pd(ala)<sub>2</sub> reduction on a Pd electrode. Studying adsorption of Pd(ala)<sub>2</sub> on a Pd electrode is hampered by parallel processes of hydrogen adsorption and absorption.