Long-Time Dynamics of Variable Coefficient mKdV Solitary Waves

We study the Korteweg-de Vries-type equation dt u=-dx(dx^2 u+f(u)-B(t,x)u), where B is a small and bounded, slowly varying function and f is a nonlinearity. Many variable coefficient KdV-type equations can be rescaled into this equation. We study the long time behaviour of solutions with initial conditions close to a stable, B=0 solitary wave. We prove that for long time intervals, such solutions have the form of the solitary wave, whose centre and scale evolve according to a certain dynamical law involving the function B(t,x), plus an H^1-small fluctuation.Comment: 19 page

Preliminary catalog of pictures taken on the lunar surface during the Apollo 16 mission

A catalog of all pictures taken from the lunar module or the lunar surface during the Apollo 16 lunar stay is presented. The tabulations are arranged for the following specific uses: (1) given the number of a particular frame, find its location in the sequence of lunar surface activity, the station from which it was taken and the subject matter of the picture; (2) given a particular location or activity within the sequence of lunar surface activity, find the pictures taken at that time and their subject matter; and (3) given a sample number from the voice transcript listed, find the designation assigned to the same sample by the lunar receiving laboratory

Quantum Inverse Square Interaction

Hamiltonians with inverse square interaction potential occur in the study of a variety of physical systems and exhibit a rich mathematical structure. In this talk we briefly mention some of the applications of such Hamiltonians and then analyze the case of the N-body rational Calogero model as an example. This model has recently been shown to admit novel solutions, whose properties are discussed.Comment: Talk presented at the conference "Space-time and Fundamental Interactions: Quantum Aspects" in honour of Prof. A.P.Balachandran's 65th birthday, Vietri sul Mare, Italy, 26 - 31 May, 2003, Latex file, 9 pages. Some references added in the replaced versio

Existence of the Stark-Wannier quantum resonances

In this paper we prove the existence of the Stark-Wannier quantum resonances for one-dimensional Schrodinger operators with smooth periodic potential and small external homogeneous electric field. Such a result extends the existence result previously obtained in the case of periodic potentials with a finite number of open gaps.Comment: 30 pages, 1 figur

Skylab/EREP application to ecological, geological, and oceanographic investigations of Delaware Bay

Skylab/EREP S190A and S190B film products were optically enhanced and visually interpreted to extract data suitable for; (1) mapping coastal land use; (2) inventorying wetlands vegetation; (3) monitoring tidal conditions; (4) observing suspended sediment patterns; (5) charting surface currents; (6) locating coastal fronts and water mass boundaries; (7) monitoring industrial and municipal waste dumps in the ocean; (8) determining the size and flow direction of river, bay and man-made discharge plumes; and (9) observing ship traffic. Film products were visually analyzed to identify and map ten land-use and vegetation categories at a scale of 1:125,000. Digital tapes from the multispectral scanner were used to prepare thematic maps of land use. Classification accuracies obtained by comparison of derived thematic maps of land-use with USGS-CARETS land-use maps in southern Delaware ranged from 44 percent to 100 percent

Reed-Muller codes for random erasures and errors

This paper studies the parameters for which Reed-Muller (RM) codes over $GF(2)$ can correct random erasures and random errors with high probability, and in particular when can they achieve capacity for these two classical channels. Necessarily, the paper also studies properties of evaluations of multi-variate $GF(2)$ polynomials on random sets of inputs. For erasures, we prove that RM codes achieve capacity both for very high rate and very low rate regimes. For errors, we prove that RM codes achieve capacity for very low rate regimes, and for very high rates, we show that they can uniquely decode at about square root of the number of errors at capacity. The proofs of these four results are based on different techniques, which we find interesting in their own right. In particular, we study the following questions about $E(m,r)$, the matrix whose rows are truth tables of all monomials of degree $\leq r$ in $m$ variables. What is the most (resp. least) number of random columns in $E(m,r)$ that define a submatrix having full column rank (resp. full row rank) with high probability? We obtain tight bounds for very small (resp. very large) degrees $r$, which we use to show that RM codes achieve capacity for erasures in these regimes. Our decoding from random errors follows from the following novel reduction. For every linear code $C$ of sufficiently high rate we construct a new code $C'$, also of very high rate, such that for every subset $S$ of coordinates, if $C$ can recover from erasures in $S$, then $C'$ can recover from errors in $S$. Specializing this to RM codes and using our results for erasures imply our result on unique decoding of RM codes at high rate. Finally, two of our capacity achieving results require tight bounds on the weight distribution of RM codes. We obtain such bounds extending the recent \cite{KLP} bounds from constant degree to linear degree polynomials

Skylab/EREP application to ecological, geological, and oceanographic investigations of Delaware Bay

The author has identified the following significant results. Skylab/EREP S190A and S190B film products were optically enhanced and visually interpreted to extract data suitable for mapping coastal land use; inventorying wetlands vegetation; monitoring tidal conditions; observing suspended sediment patterns; charting surface currents; locating coastal fronts and water mass boundaries; monitoring industrial and municipal waste dumps in the ocean; and determining the size and flow direction of river, bay, and man-made discharge plumes. Film products were visually analyzed to identify and map ten land use and vegetation categories at a scale of 1:125,000. Thematic maps were compared with CARETS land use maps, resulting in classification accuracies of 50 to 98%. Digital tapes from S192 were used to prepare thematic land use maps. The resolutions of the S190A, S190B, and S192 systems were 20-40m, 10-20m, and 70-100m, respectively

Superconductivity in domains with corners

We study the two-dimensional Ginzburg-Landau functional in a domain with corners for exterior magnetic field strengths near the critical field where the transition from the superconducting to the normal state occurs. We discuss and clarify the definition of this field and obtain a complete asymptotic expansion for it in the large $\kappa$ regime. Furthermore, we discuss nucleation of superconductivity at the boundary

Essential spectra and exponential estimates of eigenfunctions of lattice operators of quantum mechanics

This paper is devoted to estimates of the exponential decay of eigenfunctions of difference operators on the lattice Z^n which are discrete analogs of the Schr\"{o}dinger, Dirac and square-root Klein-Gordon operators. Our investigation of the essential spectra and the exponential decay of eigenfunctions of the discrete spectra is based on the calculus of so-called pseudodifference operators (i.e., pseudodifferential operators on the group Z^n) with analytic symbols and on the limit operators method. We obtain a description of the location of the essential spectra and estimates of the eigenfunctions of the discrete spectra of the main lattice operators of quantum mechanics, namely: matrix Schr\"{o}dinger operators on Z^n, Dirac operators on Z^3, and square root Klein-Gordon operators on Z^n

Net Returns for Grain Sorghum and Corn under Alternative Irrigation Systems in Western Kansas

This study evaluates seven irrigation systems for use in production of grain sorghum and corn. These systems are medium pressure center-pivot (MPCP), low pressure center-pivot (LPCP), low drift nozzle center-pivot (LDN) , low energy precision application center-pivot (LEPA), furrow flood (FF) , surge flood (SF), and subsurface drip (SD). After-tax net present value estimates from investing in and using each system over a 10-year period to produce grain sorghum and corn are compared. The surge flood system, has the highest net returns under typical conditions for irrigation of both grain sorghum and corn. The furrow flood system generates the next highest net returns for both crops, followed by the subsurface drip system. The medium pressure center-pivot system is the least profitable for both crops. Of the center-pivot systems, the low pressure system has the highest net return, but is followed very closely by the low drift nozzle system. The results of the sensitivity analysis indicate that the net return estimates and ranking of the subsurface drip system are very sensitive to the yield response to irrigation. Lower than average crop prices also have a substantial impact on the ranking of this system. The original investment cost is also an important determinant of its net return.Crop Production/Industries,