Well-posedness and stability results for the Gardner equation

In this article we present local well-posedness results in the classical Sobolev space H^s(R) with s > 1/4 for the Cauchy problem of the Gardner equation, overcoming the problem of the loss of the scaling property of this equation. We also cover the energy space H^1(R) where global well-posedness follows from the conservation laws of the system. Moreover, we construct solitons of the Gardner equation explicitly and prove that, under certain conditions, this family is orbitally stable in the energy space.Comment: 1 figure. Accepted for publication in Nonlin.Diff Eq.and App

William Barton Rogers and the Idea of MIT

Winner, 2009 Outstanding Book Award, History of Education SocietyWinner, 2009 Richard Slatten Prize for Excellence in Virginia Biography, Virginia Historical SocietyConceptual founder of the Massachusetts Institute of Technology, William Barton Rogers was a highly influential scientific mind and educational reformer of the nineteenth century. A. J. Angulo recounts the largely unknown story of one man's ideas and how they gave way to the creation of one of America’s premier institutions of higher learning. MIT's long tradition of teaching, research, and technological innovation for real-world applications is inexorably linked to Rogers’ educational philosophy. Emphasizing the “useful arts”—a curriculum of specialized scientific study stressing theory and practice, innovation and functionality—Rogers sought to revolutionize standard educational practices of the day. Controversial in an era typified by a generalist approach to teaching the sciences, Rogers’ model is now widely emulated by institutions throughout the world. Exploring the intersection of Rogers' educational philosophy and the rise of technical institutes in America, this biography offers a long-overdue account of the man behind MIT

Ultra Low-Power Analog Median Filters

The design and implementation of three analog median filter topologies, whose transistors operate in the deep weak-inversion region, is described. The first topology is a differential pairs array, in which drain currents are driven into two nodes in a differential fashion, while the second topology is based on a wide range OTA, which is used to maximize the dynamic range. Finally, the third topology uses three range-extended OTAs. The proposed weak-inversion filters were designed and fabricated in ON Semiconductor 0.5 micrometer technology through MOSIS. Experimental results of three-input fabricated prototypes for all three topologies are show, where power consumptions of 90nW in the first case, and 270nW in the other two cases can be noticed. A dual power supply +/-1.5 Volts were used

A possible cosmological application of some thermodynamic properties of the black body radiation in n−n-dimensional Euclidean spaces

In this work we present the generalization of some thermodynamic properties of the black body radiation (BBR) towards an $n-$dimensional Euclidean space. For this case the Planck function and the Stefan-Boltzmann law have already been given by Landsberg and de Vos and some adjustments by Menon and Agrawal. However, since then no much more has been done on this subject and we believe there are some relevant aspects yet to explore. In addition to the results previously found we calculate the thermodynamic potentials, the efficiency of the Carnot engine, the law for adiabatic processes and the heat capacity at constant volume. There is a region at which an interesting behavior of the thermodynamic potentials arise, maxima and minima appear for the $n-d$ BBR system at very high temperatures and low dimensionality, suggesting a possible application to cosmology. Finally we propose that an optimality criterion in a thermodynamic framework could have to do with the $3-d$ nature of the universe.Comment: 9 pages, 8 figure

Status of superpressure balloon technology in the United States

Superpressure mylar balloon technology in United States - applications, balloon size criteria, and possible improvement

High Gain Amplifier with Enhanced Cascoded Compensation

A two-stage CMOS operational amplifier with both, gain-boosting and indirect current feedback frequency compensation performed by means of regulated cascode amplifiers, is presented. By using quasi-floating-gate transistors (QFGT) the supply requirements, the number of capacitors and the size of the compensation capacitors respect to other Miller schemes are reduced. A prototype was fabricated using a 0.5 μm technology, resulting, for a load of 45 pF and supply voltage of 1.65 V, in open-loop-gain of 129 dB, 23 MHz of gain-bandwidth product, 60o phase margin, 675 μW power consumption and 1% settling time of 28 ns

Orbital stability of periodic waves for the nonlinear Schroedinger equation

The nonlinear Schroedinger equation has several families of quasi-periodic travelling waves, each of which can be parametrized up to symmetries by two real numbers: the period of the modulus of the wave profile, and the variation of its phase over a period (Floquet exponent). In the defocusing case, we show that these travelling waves are orbitally stable within the class of solutions having the same period and the same Floquet exponent. This generalizes a previous work where only small amplitude solutions were considered. A similar result is obtained in the focusing case, under a non-degeneracy condition which can be checked numerically. The proof relies on the general approach to orbital stability as developed by Grillakis, Shatah, and Strauss, and requires a detailed analysis of the Hamiltonian system satisfied by the wave profile.Comment: 34 pages, 7 figure