Exact Lagrangian submanifolds in simply-connected cotangent bundles

We consider exact Lagrangian submanifolds in cotangent bundles. Under certain additional restrictions (triviality of the fundamental group of the cotangent bundle, and of the Maslov class and second Stiefel-Whitney class of the Lagrangian submanifold) we prove such submanifolds are Floer-cohomologically indistinguishable from the zero-section. This implies strong restrictions on their topology. An essentially equivalent result was recently proved independently by Nadler, using a different approach.Comment: 28 pages, 3 figures. Version 2 -- derivation and discussion of the spectral sequence considerably expanded. Other minor change

A doubly-refined enumeration of alternating sign matrices and descending plane partitions

It was shown recently by the authors that, for any n, there is equality between the distributions of certain triplets of statistics on nxn alternating sign matrices (ASMs) and descending plane partitions (DPPs) with each part at most n. The statistics for an ASM A are the number of generalized inversions in A, the number of -1's in A and the number of 0's to the left of the 1 in the first row of A, and the respective statistics for a DPP D are the number of nonspecial parts in D, the number of special parts in D and the number of n's in D. Here, the result is generalized to include a fourth statistic for each type of object, where this is the number of 0's to the right of the 1 in the last row of an ASM, and the number of (n-1)'s plus the number of rows of length n-1 in a DPP. This generalization is proved using the known equality of the three-statistic generating functions, together with relations which express each four-statistic generating function in terms of its three-statistic counterpart. These relations are obtained by applying the Desnanot-Jacobi identity to determinantal expressions for the generating functions, where the determinants arise from standard methods involving the six-vertex model with domain-wall boundary conditions for ASMs, and nonintersecting lattice paths for DPPs.Comment: 28 pages; v2: published versio

Amplitude of the Electrical Potential Oscillations in the Salt-Water Oscillator

The amplitude of the electrical potential oscillations of the salt water oscillator depends on the character of an electrical double layer formed in the glass capillary or at the interface between the dilute and concentrated salt solutions. When a stationary mercury electrode was used, a new type of periodic behavior, compound oscillation, was observed

Enhancement of Thermoelectric Performance of n-Type PbSe by Cr Doping with Optimized Carrier Concentration

Ti, V, Cr, Nb, and Mo are found to be effective at increasing the Seebeck coefficient and power factor of n-type PbSe at temperatures below 600 K. It is found that the higher Seebeck coefficients and power factors are due to higher Hall mobility ≈1000 cm[superscript 2] V[superscript −]1s[superscript −1] at lower carrier concentration. A larger average ZT value (relevant for applications) can be obtained by an optimization of carrier concentration to ≈10[superscript 18]–10[superscript 19] cm[superscript −3]. Even though the highest room temperature power factor ≈3.3 × 10[superscript −3] W m[superscript −1] K[superscript −2] is found in 1 at% Mo-doped PbSe, the highest ZT is achieved in Cr-doped PbSe. Combined with the lower thermal conductivity, ZT is improved to ≈0.4 at room temperature and peak ZTs of ≈1.0 are observed at ≈573 K for Pb[subscript 0.9925]Cr[subscript 0.0075]Se and ≈673 K for Pb[subscript 0.995]Cr[subscript 0.005]Se. The calculated device efficiency of Pb[subscript 0.995]Cr[subscript 0.005]Se is as high as ≈12.5% with cold side 300 K and hot side 873 K, higher than those of all the n-type PbSe materials reported in the literature.United States. Dept. of Energy. Office of Science (Solid-State Solar-Thermal Energy Conversion Center Award DE-SC0001299