Nonlinear cross Gramians and gradient systems

We study the notion of cross Gramians for non-linear gradient systems, using the characterization in terms of prolongation and gradient extension associated to the system. The cross Gramian is given for the variational system associated to the original nonlinear gradient system. We obtain linearization results that precisely correspond to the notion of a cross Gramian for symmetric linear systems. Furthermore, first steps towards relations with the singular value functions of the nonlinear Hankel operator are studied and yield promising results.

Transductive Learning with String Kernels for Cross-Domain Text Classification

For many text classification tasks, there is a major problem posed by the lack of labeled data in a target domain. Although classifiers for a target domain can be trained on labeled text data from a related source domain, the accuracy of such classifiers is usually lower in the cross-domain setting. Recently, string kernels have obtained state-of-the-art results in various text classification tasks such as native language identification or automatic essay scoring. Moreover, classifiers based on string kernels have been found to be robust to the distribution gap between different domains. In this paper, we formally describe an algorithm composed of two simple yet effective transductive learning approaches to further improve the results of string kernels in cross-domain settings. By adapting string kernels to the test set without using the ground-truth test labels, we report significantly better accuracy rates in cross-domain English polarity classification.Comment: Accepted at ICONIP 2018. arXiv admin note: substantial text overlap with arXiv:1808.0840

Effect of carbon nanotube doping on critical current density of MgB2 superconductor

The effect of doping MgB2 with carbon nanotubes on transition temperature, lattice parameters, critical current density and flux pinning was studied for MgB2-xCx with x = 0, 0.05, 0.1, 0.2 and 0.3. The carbon substitution for B was found to enhance Jc in magnetic fields but depress Tc. The depression of Tc, which is caused by the carbon substitution for B, increases with increasing doping level, sintering temperature and duration. By controlling the extent of the substitution and addition of carbon nanotubes we can achieve the optimal improvement on critical current density and flux pinning in magnetic fields while maintaining the minimum reduction in Tc. Under these conditions, Jc was enhanced by two orders of magnitude at 8T and 5K and 7T and 10K. Jc was more than 10,000A/cm2 at 20K and 4T and 5K and 8.5T, respectively

Weighted Low-Regularity Solutions of the KP-I Initial Value Problem

In this paper we establish local well-posedness of the KP-I problem, with initial data small in the intersection of the natural energy space with the space of functions which are square integrable when multiplied by the weight y. The result is proved by the contraction mapping principle. A similar (but slightly weaker) result was the main Theorem in the paper " Low regularity solutions for the Kadomstev-Petviashvili I equation " by Colliander, Kenig and Staffilani (GAFA 13 (2003),737-794 and math.AP/0204244). Ionescu found a counterexample (included in the present paper) to the main estimate used in the GAFA paper, which renders incorrect the proof there. The present paper thus provides a correct proof of a strengthened version of the main result in the GAFA paper

A Model of Heat Conduction

We define a deterministic ``scattering'' model for heat conduction which is continuous in space, and which has a Boltzmann type flavor, obtained by a closure based on memory loss between collisions. We prove that this model has, for stochastic driving forces at the boundary, close to Maxwellians, a unique non-equilibrium steady state

On the particle paths and the stagnation points in small-amplitude deep-water waves

In order to obtain quite precise information about the shape of the particle paths below small-amplitude gravity waves travelling on irrotational deep water, analytic solutions of the nonlinear differential equation system describing the particle motion are provided. All these solutions are not closed curves. Some particle trajectories are peakon-like, others can be expressed with the aid of the Jacobi elliptic functions or with the aid of the hyperelliptic functions. Remarks on the stagnation points of the small-amplitude irrotational deep-water waves are also made.Comment: to appear in J. Math. Fluid Mech. arXiv admin note: text overlap with arXiv:1106.382

Variational derivation of two-component Camassa-Holm shallow water system

By a variational approach in the Lagrangian formalism, we derive the nonlinear integrable two-component Camassa-Holm system (1). We show that the two-component Camassa-Holm system (1) with the plus sign arises as an approximation to the Euler equations of hydrodynamics for propagation of irrotational shallow water waves over a flat bed. The Lagrangian used in the variational derivation is not a metric.Comment: to appear in Appl. Ana

Smooth cutoff formulation of hierarchical reference theory for a scalar phi4 field theory

The phi4 scalar field theory in three dimensions, prototype for the study of phase transitions, is investigated by means of the hierarchical reference theory (HRT) in its smooth cutoff formulation. The critical behavior is described by scaling laws and critical exponents which compare favorably with the known values of the Ising universality class. The inverse susceptibility vanishes identically inside the coexistence curve, providing a first principle implementation of the Maxwell construction, and shows the expected discontinuity across the phase boundary, at variance with the usual sharp cutoff implementation of HRT. The correct description of first and second order phase transitions within a microscopic, nonperturbative approach is thus achieved in the smooth cutoff HRT.Comment: 8 pages, 4 figure