Single and Multi-Dimensional Optimal Auctions - A Network Approach

This paper highlights connections between the discrete and continuous approaches to optimal auction design with single and multi-dimensional types. We provide an interpretaion of an optimal auction design problem in terms of a linear program that is an instance of a parametric shortest path problem on a lattice. We also solve some cases explicitly in the discrete framework.Auctions, Networks, Linear Programming

Variability of magnetic field spectra in the Earth's magnetotail

We investigate the variability of magnetic fluctuation spectra below 1 Hz in the Earth's plasma sheet using specially selected long observation intervals by Geotail spacecraft. The spectra can be generally described by a negative power law with two kinks. The range between kinks ~0.02–0.2 Hz has the most stable power law index ~2.4–2.6. Indices at the lower and the higher frequencies are more variable and generally increase with power of fluctuations. In the sub-second range fluctuations are strongly localized and indices are closer to 3. At the lower-frequency end indices are about 1.5. The lower kink is usually well defined on average spectra and its frequency tends to increase with activity. Combination of spectrum index α and fractal dimension δ is expected to follow the Berry relation α+2δ=5, but actually is ~5.5

Stoichiography: New Ways Determining Chemical Composition and Real Structure of Materials

The principles of stoichiography and novel reference-free methods of molecular and phase analysis for complex unknown mixtures are considered. The stoichiography can be inferred from stoichiometry of mass transfer of unsteady homo- and heterophase processes and joins both operations: separation of mixture by means of chromatography, electromigration, dissolution or others and determination of stoichiometry of a substance flow with time. The stoichiography allows a chemical compound to be determined by its primary property, namely, by stoichiometry of elemental composition. Stoichiograms provided a basis for such type of information. They are time variances of molar ratio for mass transfer rates of chemical elements from multielement substances. Invariancy to concentration and temperature of solvents, hydrodynamic regime is a fundamental property of the stoichiograms in the case of individual compounds. Therefore the  stoichiograms are kept constant and are equal to formula stoichiometric coefficients of the individual compound. Theory and methodology of new stoichographic methods, differential dissolution and ion-chromato-stoichiography are presented. New equipment, stoichiograph, and a new procedure of differential dissolution, stoichiographic titration, are discussed here in details. Applications of differential dissolution to analyze multielement and polyphase crystalline and amorphous samples are given. ***The author devotes this paper to memory of his teacher, Professor O. A. Songina, an outstanding scientist, who began to develop fundamental ideas concerning chemical and electrochemical methods of the phase analysis. The essence of this paper was reported on International Conference of Analytical Chemistry, which was organized on the occasion of the 100th Birthday of Professor O. A. Songina on May 22-25th, 2001, in Almaty, Kazakhstan