Variable Coefficient Third Order KdV Type of Equations

We show that the integrable subclassess of a class of third order non-autonomous equations are identical with the integrable subclassess of the autonomous ones.Comment: Latex file , 15 page

Realization of Resistorless Lossless Positive and Negative Grounded Inductor Simulators Using Single ZC-CCCITA

This paper is in continuation with the very recent work of Prasad et al. [14], wherein new realizations of grounded and floating positive inductor simulator using current differencing transconductance amplifier (CDTA) are reported. The focus of the paper is to provide alternate realizations of lossless, both positive and negative inductor simulators (PIS and NIS) in grounded form using z-copy current-controlled current inverting transconductance amplifier (ZC-CCCITA), which can be considered as a derivative of CDTA, wherein the current differencing unit (CDU) is reduced to a current-controlled current inverting unit. We demonstrate that only a single ZC-CCCITA and one grounded capacitor are sufficient to realize grounded lossless PIS or NIS. The proposed circuits are resistorless whose parameters can be controlled through the bias currents. The workability of the proposed PIS is validated by SPICE simulations on three RLC prototypes

Boundary Value Problems For Integrable Equations Compatible With The Symmetry Algebra

Boundary value problems for integrable nonlinear partial differential equations are considered from the symmetry point of view. Families of boundary conditions compatible with the Harry-Dym, KdV and MKdV equations and the Volterra chain are discussed. We also discuss the uniqueness of some of these boundary conditions.Comment: 25 pages , Latex , no figure

Developing the Quantitative Histopathology Image Ontology : A case study using the hot spot detection problem

Interoperability across data sets is a key challenge for quantitative histopathological imaging. There is a need for an ontology that can support effective merging of pathological image data with associated clinical and demographic data. To foster organized, cross-disciplinary, information-driven collaborations in the pathological imaging field, we propose to develop an ontology to represent imaging data and methods used in pathological imaging and analysis, and call it Quantitative Histopathological Imaging Ontology – QHIO. We apply QHIO to breast cancer hot-spot detection with the goal of enhancing reliability of detection by promoting the sharing of data between image analysts

Godel-type Metrics in Various Dimensions II: Inclusion of a Dilaton Field

This is the continuation of an earlier work where Godel-type metrics were defined and used for producing new solutions in various dimensions. Here a simplifying technical assumption is relaxed which, among other things, basically amounts to introducing a dilaton field to the models considered. It is explicitly shown that the conformally transformed Godel-type metrics can be used in solving a rather general class of Einstein-Maxwell-dilaton-3-form field theories in D >= 6 dimensions. All field equations can be reduced to a simple "Maxwell equation" in the relevant (D-1)-dimensional Riemannian background due to a neat construction that relates the matter fields. These tools are then used in obtaining exact solutions to the bosonic parts of various supergravity theories. It is shown that there is a wide range of suitable backgrounds that can be used in producing solutions. For the specific case of (D-1)-dimensional trivially flat Riemannian backgrounds, the D-dimensional generalizations of the well known Majumdar-Papapetrou metrics of general relativity arise naturally.Comment: REVTeX4, 17 pp., no figures, a few clarifying remarks added and grammatical errors correcte

Integrable nonlinear equations on a circle

The concept of integrable boundary value problems for soliton equations on $\mathbb{R}$ and $\mathbb{R}_+$ is extended to bounded regions enclosed by smooth curves. Classes of integrable boundary conditions on a circle for the Toda lattice and its reductions are found.Comment: 23 page

Hydrodynamic type integrable equations on a segment and a half-line

The concept of integrable boundary conditions is applied to hydrodynamic type systems. Examples of such boundary conditions for dispersionless Toda systems are obtained. The close relation of integrable boundary conditions with integrable reductions of multi-field systems is observed. The problem of consistency of boundary conditions with the Hamiltonian formulation is discussed. Examples of Hamiltonian integrable hydrodynamic type systems on a segment and a semi-line are presented

Universal optical amplification without nonlinearity

We propose and experimentally realize a new scheme for universal phase-insensitive optical amplification. The presented scheme relies only on linear optics and homodyne detection, thus circumventing the need for nonlinear interaction between a pump field and the signal field. The amplifier demonstrates near optimal quantum noise limited performance for a wide range of amplification factors.Comment: 5 pages, 4 figure