Supersymmetric KdV equation: Darboux transformation and discrete systems

For the supersymmetric KdV equation, a proper Darboux transformation is presented. This Darboux transformation leads to the B\"{a}cklund transformation found early by Liu and Xie \cite{liu2}. The Darboux transformation and the related B\"{a}cklund transformation are used to construct integrable super differential-difference and difference-difference systems. The continuum limits of these discrete systems and of their Lax pairs are also considered.Comment: 13pages, submitted to Journal of Physics

Representation of perfectly reconstructed octave decomposition filter banks with set of decimators {2,4,4} via tree structure

In this letter, we prove that a filter bank with set of decimators {2,4,4} achieves perfect reconstruction if and only if it can be represented via a tree structure and each branch of the tree structure achieves perfect reconstruction

Global well-posedness for the Gross-Pitaevskii equation with an angular momentum rotational term in three dimensions

In this paper, we establish the global well-posedness of the Cauchy problem for the Gross-Pitaevskii equation with an angular momentum rotational term in which the angular velocity is equal to the isotropic trapping frequency in the space \Real^3.Comment: 11 page

Temperature-frequency scaling in amorphous niobium-silicon near the metal-insulator transition

Millimeter-wave transmission measurements have been performed in amorphous niobium-silicon alloy samples where the DC conductivity follows the critical temperature dependence $\sigma_{dc} \propto T^{1/2}$. The real part of the conductivity is obtained at eight frequencies in the range 87--1040 GHz for temperatures 2.6 K and above. In the quantum regime ($\hbar \omega > k_B T$) the real part of the high-frequency conductivity has a power-law frequency dependence $Re~\sigma(\omega) \propto \omega^{1/2}$. For temperatures 16 K and below the data exhibits temperature-frequency scaling predicted by theories of dynamics near quantum-critical points.Comment: 4 pages, 3 Postscript figures; revised version to be published in Physical Review Letters: changed several references, fixed typos, and reworded several paragraph

Parametric entry corridors for lunar/Mars aerocapture missions

Parametric atmospheric entry corridor data are presented for Earth and Mars aerocapture. Parameter ranges were dictated by the range of mission designs currently envisioned as possibilities for the Human Exploration Initiative (HEI). This data, while not providing a means for exhaustive evaluation of aerocapture performance, should prove to be a useful aid for preliminary mission design and evaluation. Entry corridors are expressed as ranges of allowable vacuum periapse altitude of the planetary approach hyperbolic orbit, with chart provided for conversion to an approximate flight path angle corridor at entry interface (125 km altitude). The corridor boundaries are defined by open-loop aerocapture trajectories which satisfy boundary constraints while utilizing the full aerodynamic control capability of the vehicle (i.e., full lift-up or full lift-down). Parameters examined were limited to those of greatest importance from an aerocapture performance standpoint, including the approach orbit hyperbolic excess velocity, the vehicle lift to drag ratio, maximum aerodynamic load factor limit, and the apoapse of the target orbit. The impact of the atmospheric density bias uncertainties are also included. The corridor data is presented in graphical format, and examples of the utilization of these graphs for mission design and evaluation are included

Representations of linear dual rate system via single SISO LTI filter, conventional sampler and block sampler

In this brief, it is proved that a linear dual-rate system can be represented via a series cascade of: 1) a conventional expander, a single-input single-output (SISO) linear time-invariant (LTI) filter and a block decimator, or 2) a block expander, an SISO LTI filter and a conventional decimator. Hence, incompatible nonuniform filter banks could achieve perfect reconstruction via LTI filters, conventional samplers and block samplers without expanding the input-output dimension of a subsystem of linear dual-rate systems or converting the nonuniform filter banks to uniform filter banks. The main advantage of the proposed representations is to avoid complicated design of the circuit layout caused by connecting subsystems with large input-output dimension or a lot of subsystems togethe

CIVIC LIFE: Evidence Base for the Triennial Review

This document forms part of the Equality and Human Rights Commission triennial review and covers equalities in civic life. It examines equality in political participation, freedom of language and freedom of worship. The primary aim is to map the various dimensions of equality and inequality in participation in civic and political life. We explore and review equalities, good relations and human rights in relation to civic life, and where possible we examine some of the driving forces behind the differences that we observe

Remote downconversion with wavelength reuse for the radio/fiber uplink connection

The authors present a novel technology for uplink transmission in radio-over-fiber distribution systems. The technique employs remote downconversion of the uplink data to intermediate frequency (IF) in the base station (BS). The local oscillator signal for the downconversion is optically generated in the central station (CS) and sent to the BS via optical fiber. The IF uplink data is then modulated onto an optical carrier, retrieved from the downlink signal, and sent to the CS, where the baseband conversion takes place. By employing this method of uplink connection, simplicity and cost efficiency of the BS is achieved