Isospectral theory of Euler equations

Isospectral problem of both 2D and 3D Euler equations of inviscid fluids, is investigated. Connections with the Clay problem are described. Spectral theorem of the Lax pair is studied.     

Optimal estimation of linear operators from inaccurate data: A second look

This paper intends to re-examine some results and proofs given in a previous publication on optimal estimation under uncertainty. In a rather general setting we showed that regularization of an element of a linear space relative to a quadratic criterion and inaccurate linear observations is an optimal method for recovering a linear operator of that element. For this to be the case, the regularization parameter must be chosen with care.     

The completely positive and doubly nonnegative completion problems

We prove the following. Let G be an undirected graph. Every partially specified symmetric matrix, the graph of whose specified entries is G and each of whose fully specified submatrices is completely positive (equal to BB^T for some entrywise nonnegative matrix B), may be completed to a completely positive matrix if and only if G is a block-clique graph (a chordal graph in which distinct maximal cliques overlap in at most one vertex). The same result holds for matrices that are doubly nonnegative (entrywise nonnegative and positive semidefinite).     

Synthesis and cationic photopolymerization of new fluorinated,polyfunctional propenyl ether oligomers

New fluorinated, polyfunctional propenyl ether functionalized resins were synthesized, and their behavior in cationic photopolymerization was investigated. The photopolymerization proceeded efficiently with a high double‐bond conversion (>90%), giving rise to UV‐cured coatings characterized by low glass‐transition temperatures (?33 °C ≤ glass‐transition temperature ≤ ?15 °C) and hydrophobic surface properties. A fluorinated additive was also employed as a reactive additive in the cationic photopolymerization of trimethylolpropane tripropenyl ether, increasing the double‐bond conversion, polymer network flexibility, thermal stability, and surface hydrophobicity. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 6943–6951, 2006     

Partial molal heat capacities of aqueous tetraalkylammonium bromides as functions of temperature

Enthalpies of solution have been measured from 5 to 85°C for aqueous tetraethyl- and tetrapropylammonium bromides, and the integral heat method is employed to evaluate for these electrolytes over a wide temperature range. Data taken from the literature have been used to evaluate for aqueous Bu₄NBr over a similar temperature range. These data, along with similar data for Me₄NBr, previously reported, have been used to evaluate absolute ionic heat capacities. While the absolute values agree only qualitatively with two other methods of division, the temperature dependences of the three methods essentially agree up to 65°C. Heat capacities due to structural effects on the solvent, obtained by subtracting the inherent heat capacities of the ions, are extraordinarily positive for all four tetraalkylammonium ions and have negative temperature coefficients, indicating that all four ions, including the tetramethylammonium ion, are structure-making ions.     

Deuterium exchange of 4-pyrimidones and 4-pyrimidthiones

The hydrogen-deuterium exchange of H-2 in 4-pyrimidone, a number of 1- and 3-alkyl-4-pyrimidones and several of their thione analogs in deuterium oxide at moderate temperatures is reported. This reaction is apparently not susceptible to acid or base catalysis. Cations of the 4-pyrimidones were found not to exchange H-2 at all in acid media. Catalytic amounts of bases do not alter the exchange rates whereas more concentrated alkali decompose the pyrimidone. However, 1,4(3,4)-dihydro-1,3-dimethyl-4-oxopyrimidinium iodide (and its 6-methyl analog) exchange H-2 quite rapidly in neutral deuterium oxide, almost instantly when triethylamine is added as a catalyst, and very slowly in dilute solutions of deuterium chloride in deuterium oxide. Mechanisms are proposed to account for these phenomena.     

Comparison of fluorimetric methods of assay for 7 H-Benz(de)anthracen-7-one in airborne particulates and air pollution source effluents

Summary Various modifications of a thin-layer chromatography fluorimetric method for the determination of 7 H-benz(de)anthracen-7-one (BO) and phenalen-1-one (PO) in complex mixtures have been compared. The best modifications consisted of one-dimensional thin-layer chromatography followed by elution, evaporation, solution in trifluoroacetic acid, followed by either spectrophotofluorimetric or fluorimetric assay. In some cases a quenching agent was necessary to quench the fluorescence of the interferences. Urban atmospheres and air pollution source effluents can be analyzed by these micromethods. These methods with slight modification could be applied to the determination of the aza heterocyclic and the other ring-carbonyl compounds found in urban atmospheres and air pollution source effluents.

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Zusammenfassung Verschiedene Modifikationen einer dünnschichtchromatographischen, fluorimetrischen Methode zur Bestimmung von 7 H-Benz(de)-anthracen-7-on (BO) und Phenalen-1-on (PO) in komplexen Gemischen wurden verglichen. Am besten bewährte sich eindimensionale Dünnschichtchromatographie, nachfolgende Elution, Abdampfen, Aufnehmen in Trifluoressigsäure und schließlich Bestimmung durch Spektralfluoreszenz-oder Fluoreszenzmessung. In manchen Fällen war es nötig, die Fluoreszenz störender Substanzen mit einem geeigneten Reagens zu löschen. Stadtatmosphäre oder Quellen der Luftverunreinigung können mit diesen Mikromethoden analysiert werden. Sie eignen sich nach geringfügiger Modifikation auch zur Bestimmung von azaheterocyklischen und anderen Ring-Carbonylverbindungen in der Atmosphäre.

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Résumé On a comparé entre elles différentes modifications d'une méthode de fluorimétrie avec chromatographie en couche mince pour le dosage de la benzo-7 H anthracène-one-7 (BO) et de la phénalène-one-1 (PO) en mélanges complexes. Les modifications les meilleures ont consisté en une Chromatographie en couche mince unidimensionnelle suivie d'élution, évaporation, mise en solution dans l'acide trifluoroacétique, opérations suivies d'une recherche spectrophotofluorimétrique ou fluorimétrique. Dans certains cas, un agent d'extinction s'est montré nécessaire pour éteindre la fluorescence due aux interférences. On peut analyser par ces microméthodes les atmosphères urbaines et les écoulements sources de pollution de l'air. Ces méthodes ont pu être appliquées après légère modification au dosage des composés aza hétérocycliques et autres composés carbonyles cycliques trouvés dans les atmosphères urbaines et dans les écoulements sources de pollution de l'air.

     

On the nature and origin of complexity in discrete,homogeneous, locally-interacting systems

The observed complexity of nature is often attributed to an intrinsic propensity of matter to self-organize under certain (e.g., dissipative) conditions. In order better to understand and test this vague thesis, we define complexity as logical depth, a notion based on algorithmic information and computational time complexity. Informally, logical depth is the number of steps in the deductive or causal path connecting a thing with its plausible origin. We then assess the effects of dissipation, noise, and spatial and other symmetries of the initial conditions and equations of motion on the asymptotic complexity-generating abilities of statistical-mechanical model systems. We concentrate on discrete, spatially-homogeneous, locally-interacting systems such as kinetic Ising models and cellular automata.