The equivariant K-theory of toric varieties

This paper contains two results concerning the equivariant K-theory of toric varieties. The first is a formula for the equivariant K-groups of an arbitrary affine toric variety, generalizing the known formula for smooth ones. In fact, this result is established in a more general context, involving the K-theory of graded projective modules. The second result is a new proof of a theorem due to Vezzosi and Vistoli concerning the equivariant K-theory of smooth (not necessarily affine) toric varieties.Comment: 12 page

Quantum Loop Subalgebra and Eigenvectors of the Superintegrable Chiral Potts Transfer Matrices

It has been shown in earlier works that for Q=0 and L a multiple of N, the ground state sector eigenspace of the superintegrable tau_2(t_q) model is highly degenerate and is generated by a quantum loop algebra L(sl_2). Furthermore, this loop algebra can be decomposed into r=(N-1)L/N simple sl_2 algebras. For Q not equal 0, we shall show here that the corresponding eigenspace of tau_2(t_q) is still highly degenerate, but splits into two spaces, each containing 2^{r-1} independent eigenvectors. The generators for the sl_2 subalgebras, and also for the quantum loop subalgebra, are given generalizing those in the Q=0 case. However, the Serre relations for the generators of the loop subalgebra are only proven for some states, tested on small systems and conjectured otherwise. Assuming their validity we construct the eigenvectors of the Q not equal 0 ground state sectors for the transfer matrix of the superintegrable chiral Potts model.Comment: LaTeX 2E document, using iopart.cls with iopams packages. 28 pages, uses eufb10 and eurm10 fonts. Typeset twice! Version 2: Details added, improvements and minor corrections made, erratum to paper 2 included. Version 3: Small paragraph added in introductio

Correlation functions for the three state superintegrable chiral Potts spin chain of finite lengths

We compute the correlation functions of the three state superintegrable chiral Potts spin chain for chains of length 3,4,5. From these results we present conjectures for the form of the nearest neighbor correlation function.Comment: 10 pages; references update

Geoid undulations and gravity anomalies over the Aral Sea, the Black Sea and the Caspian Sea from a combined GEOS-3/SEASAT/GEOSAT altimeter data set

Satellite-based altimetric data taken by GOES-3, SEASAT, and GEOSAT over the Aral Sea, the Black Sea, and the Caspian Sea are analyzed and a least squares collocation technique is used to predict the geoid undulations on a 0.25x0.25 deg. grid and to transform these geoid undulations to free air gravity anomalies. Rapp's 180x180 geopotential model is used as the reference surface for the collocation procedure. The result of geoid to gravity transformation is, however, sensitive to the information content of the reference geopotential model used. For example, considerable detailed surface gravity data were incorporated into the reference model over the Black Sea, resulting in a reference model with significant information content at short wavelengths. Thus, estimation of short wavelength gravity anomalies from gridded geoid heights is generally reliable over regions such as the Black Sea, using the conventional collocation technique with local empirical covariance functions. Over regions such as the Caspian Sea, where detailed surface data are generally not incorporated into the reference model, unconventional techniques are needed to obtain reliable gravity anomalies. Based on the predicted gravity anomalies over these inland seas, speculative tectonic structures are identified and geophysical processes are inferred

User's guide: Programs for processing altimeter data over inland seas

The programs described were developed to process GEODYN-formatted satellite altimeter data, and to apply the processed results to predict geoid undulations and gravity anomalies of inland sea areas. These programs are written in standard FORTRAN 77 and are designed to run on the NSESCC IBM 3081(MVS) computer. Because of the experimental nature of these programs they are tailored to the geographical area analyzed. The attached program listings are customized for processing the altimeter data over the Black Sea. Users interested in the Caspian Sea data are expected to modify each program, although the required modifications are generally minor. Program control parameters are defined in the programs via PARAMETER statements and/or DATA statements. Other auxiliary parameters, such as labels, are hard-wired into the programs. Large data files are read in or written out through different input or output units. The program listings of these programs are accompanied by sample IBM job control language (JCL) images. Familiarity with IBM JCL and the TEMPLATE graphic package is assumed

Analysis of altimetry over inland seas

Satellite-based altimetric data taken by GEOS-3 and SEASAT over the Black Sea and Caspian Sea are analyzed and a least squares collocation technique is used to predict the geoid undulation on a .25-degree by .25-degree grid and to transform these geoid undulations to free air gravity anomalies. This project entailed processing satellite altimeter data over inland seas for recovery of area mean gravity information. Gravity information in this area of the world is not readily available, so the possibility of obtaining it from the processing of altimeter observations is attractive. The principal objective was to complete and extend analyses done in a previous study, verify those results, and document the results and techniques. A secondary objective was to improve the algorithms and results, if possible. The approach used involved editing geoid height data to remove overland data; evaluating geoid height differences at crossover points; removing orbit errors from geoid heights using crossover differences; gridding geoid height data at .25-degree by .25-degree intervals; and estimating the gravity anomalies from gridded geoid heights using the collocation technique

Analysis of altimetry over the Aral Sea

Satellite based altimetric data taken by GEOS-3, SEASAT, and GEOSAT over the Aral Sea are analyzed and a least squares collocation technique is used to predict the geoid undulations on a 0.25 by 0.25 degree grid and to transform these geoid undulations to free air gravity anomalies. Rapp's 180 by 180 geopotential model is taken as the empirical model. The collocation procedure is performed with a set of local residual empirical covariance functions. For comparison, Rapp's global covariance functions and Jordan's self-consistent theoretical covariance functions based on Jordan's formulation and on locally derived parameters are also used to grid geoid undulations and to predict gravity anomalies. The sensitivity of the collocation results to the choice of covariance functions is discussed

Coherence properties of infrared thermal emission from heated metallic nanowires

Coherence properties of the infrared thermal radiation from individual heated nanowires are investigated as function of nanowire dimensions. Interfering the thermally induced radiation from a heated nanowire with its image in a nearby moveable mirror, well-defined fringes are observed. From the fringe visibility, the coherence length of the thermal emission radiation from the narrowest nanowires was estimated to be at least 20 um which is much larger than expected from a classical blackbody radiator. A significant increase in coherence and emission efficiency is observed for smaller nanowires.Comment: 4 pages,figures include

Identities in the Superintegrable Chiral Potts Model

We present proofs for a number of identities that are needed to study the superintegrable chiral Potts model in the $Q\ne0$ sector.Comment: LaTeX 2E document, using iopart.cls with iopams packages. 11 pages, uses eufb10 and eurm10 fonts. Typeset twice! vs2: Two equations added. vs3: Introduction adde