Ultrafilter translations

We develop a method for extending results about ultrafilters into a more general setting. In this paper we shall be mainly concerned with applications to cardinality logics. For example, assumingV=L, Gödel's Axiom of Constructibility, we prove that if > then the logic with the quantifier there exist many is (,)-compact if and only if either is weakly compact or is singular of cofinality<. As a corollary, for every infinite cardinals and , there exists a (,)-compact non-(,)-compact logic if and only if either < orcf<cf or < is weakly compact.Counterexamples are given showing that the above statements may fail, ifV=L is not assumed.However, without special assumptions, analogous results are obtained for the stronger notion of [,]-compactness.     

Infinite-dimensional flag manifolds in integrable systems

In this paper, we present several instances where infinite-dimensional flag varieties and their holomorphic line bundles play a role in integrable systems. As such, we give the correspondence between flag varieties and Darboux transformations for the KP hierarchy and the nth KdV hierarchy. We construct solutions of the nth MKdV hierarchy from the space of periodic flags and we treat the geometric interpretation of the Miura transform. Finally, we show how the group extension connected with these line bundles shows up at integrable deformations of linear systems on ¹().     

Markov snakes and superprocesses

Summary We suggest the name Markov snakes for a class of path-valued Markov processes introduced recently by J.-F. Le Gall in connection with the theory of branching measure-valued processes. Le Gall applied this class to investigate path properties of superdiffusions and to approach probabilistically partial differential equations involving a nonlinear operator v–v ². We establish an isomorphism theorem which allows to translate results on continuous superprocesses into the language of Markov snakes and vice versa. By using this theorem, we get limit theorems for discrete Markov snakes.Partially supported by National Science Foundation Grant DMS-9301315 and by The US Army Research Office through the Mathematical Sciences Institute at Cornell University     

Hereditarily extended properties, quasi-random graphs and not necessarily induced subgraphs

Recently much attention has been focused on the theory of quasi-random graph and hypergraph properties. The class of quasi-random graphs is defined by certain equivalent graph properties possessed by random graphs. We shall investigate propertiesP which do not imply quasi-randomnes for sequences (G _n ) of graphs on their own, but do imply if they hold not only for the whole graphG _n but also for every sufficiently large subgraph ofG _n . Here the properties are strongly connected to countingnot necessarily induced subgraphs of a given type, while in a subsequent paper we shall investigate the properties connected with counting induced subgraphs.Dedicated to the memory of Paul ErdsResearch supported by OTKA N1909.     

Edge disjoint spanning trees in random graphs

We show that almost everyG _m-out containsm edge disjoint spanning trees.     

Sonoelectroanalysis: Anodic Stripping Voltammetric Determination of Cadmium in Whole Human Blood

The quantitative detection of cadmium in human blood is shown to be possible by anodic stripping voltammetry under conditions of insonation. An immersion horn probe is introduced into a thermostatted conventional three‐electrode cell opposite a Nafion‐coated mercury plated glassy carbon electrode. The enhanced mass transport associated with power ultrasound yields efficient preconcentration of the cadmium before it is detected using anodic differential‐pulse stripping voltammetry. Insonation further offers the crucial benefits of first surface activation and cleaning, helping to prevent electrode fouling by the organic components in blood and second fully equilibrating “free” and “bound” Cd²⁺ ions in the complex matrix. Acoustic streaming and cavitation promote the mass transport of cadmium to the surface of electrode, facilitating measurements in solutions of low cadmium concentration, where “silent” measurements fail to yield an analytical signal. The system is calibrated using standard micro additions of cadmium to give the total amount of cadmium in blood. The calibration plot, showing the dependence of the cadmium stripping peak height on cadmium concentration in 1 : 50 diluted blood samples, was linear in the range 1×10^?10 M to 4×10^?9 M Cd²⁺. The values of cadmium concentration obtained using sonoelectroanalytical methodology were compared with the results obtained by independent atomic absorption spectroscopy (AAS) measurements and good agreement was found.     

Kinetics of asparaginase II fermentation in Saccharomyces cerevisiae ure2dal80 mutant

Although the quality of nitrogen source affects fermentation product formation, it has been managed empirically, to a large extent, in industrial scale. Laboratory-scale experiments successfully use the high-cost proline as a nonrepressive source. We evaluated urea as a substitute for proline in Saccharomyces cerevisiae ure2dal80 fermentations for asparaginase II production as a model system for nitrogen-regulated external enzymes. Maximum asparaginase II levels of 265 IU/L were observed in early stationary-phase cells grown on either proline or urea, whereas in ammonium cells, the maximum enzyme level was 157 IU/L. In all cases, enzyme stability was higher in buffered cultures with an initial pH of 6.5.     

Direct synthesis of tetrahydropyrans via one-pot Babier-Prins cyclization of allylbromide with carbonyl compounds promoted by RTILs BPyX/SnX′2 or BBIMBr/SnBr2

Tetrahydropyran compounds can be directly synthesized from allylbromide and carbonyl compounds by means of one-pot Babier-Prins cyclization promoted by BPyX/SnX′₂ or BBIMBr/SnBr₂ complex (functionalized RTILs) under solvent-free conditions. 2,6-Homo-bissubstituted- and 2,6,6-trisubstituted, especially 6-(spirocycloalkyl)-, tetrahydropyran compounds can be prepared in good yields.     

A bifunctional rhodamine derivative as chemosensor for recognizing Cu~(2+) and Hg~(2+) ions via different spectra

A new simple bifunctional chemosensor 1 based on rhodamine was synthesized by hydrazide and formylformic acid,which could detect Cu~(2+) and Hg~(2+) via dif ferent detecting methods in CH3 CN-HEPES buffer solution(20 mmol/L,pH 7.4)(1:9,v/v) respectively.When sensor 1 bound with Cu~(2+),it showed a colorimetric change,while a selective enhancement in fluorescence occurred upon 1 binding with Hg~(2+),resulting from the spirolatam-ring opening process.The binding modes of 1 with Cu~(2+) and Hg~(2+) were investigated based on UV,fluorescence change,ESI-Mass and Job's Plot data.Moreover,sensor 1 could selectively detect target ion in a mixed solution of Cu~(2+) and Hg~(2+),and the two metal ions do not inte rfere with each other in the process of detecting Cu~(2+) or Hg~(2+) with 1.     

Separation of Mercury with an Ammonium Sulfate‐Ammonium Thiocyanate‐Ethyl Violet Flotation System

The separation behavior of mercury by a flotation system consisting of ammonium sulfate, ammonium thiocyanate and ethyl violet, and the conditions for the separation of Hg(II) with other common metal ions have been studied. The studies show that in aqueous solutions, Hg(II) combines with NH₄SCN and ethyl violet(EV) into dissoluble ternary ion‐association complex [Hg(SCN)4^2?]?(EV)₂. In the presence of ammonium sulfate, the precipitate is floats well on the surface of the water phase and separates from water thoroughly. It shows that Hg(II) can be separated completely from Cd(II), Fe(II), Co(II), Ni(II), Mn(II) and Al(III) by flotation at pH1.0. The flotation mechanism of Hg(II) is described in this paper.