Explicit breather solution of the nonlinear Schrödinger equation

Theoretical and Mathematical Physics - We present a one-line closed-form expression for the three-parameter breather of the nonlinear Schrödinger equation. This provides an analytic proof of...     

Cutting sequences, regular polygons, and the Veech group

We describe the cutting sequences associated to geodesic flow on regular polygons, in terms of a combinatorial process called derivation. This work is an extension of some of the ideas and results in Smillie and Ulcigrai’s recent paper, where the analysis was made for the regular octagon. It turns out that the main structural properties of the octagon generalize in a natural way.     

On the Newton-Kantorovich method inK-normed spaces

Nondifferentiable operator equations in spaces equipped with aK-norm — map taking values in the cone of an ordered Banach space — are studied. The majorant method is used to derive the convergence of a modified sequence of Newton-Kantorovich approximations.     

Markov interest rate models

A general procedure for creating Markovian interest rate models is presented. The models created by this procedure automatically fit within the HJM framework and fit the initial term structure exactly. Therefore they are arbitrage free. Because the models created by this procedure have only one state variable per factor, twoand even three-factor models can be computed efficiently, without resorting to Monte Carlo techniques. This computational efficiency makes calibration of the new models to market prices straightforward. Extended Hull- White, extended CIR, Black-Karasinski, Jamshidian's Brownian path independent models, and Flesaker and Hughston's rational log normal models are one-state variable models which fit naturally within this theoretical framework. The ‘separable’ n-factor models of Cheyette and Li, Ritchken, and Sankarasubramanian - which require n(n + 3)/2 state variables - are degenerate members of the new class of models with n(n + 3)/2 factors. The procedure is used to create a new class of one-factor models, the ‘β-η models.’ These models can match the implied volatility smiles of swaptions and caplets, and thus enable one to eliminate smile error. The β-η models are also exactly solvable in that their transition densities can be written explicitly. For these models accurate - but not exact - formulas are presented for caplet and swaption prices, and it is indicated how these closed form expressions can be used to efficiently calibrate the models to market prices.     

First‐principles calculations of Mössbauer hyperfine parameters for solids and large molecules

Electronic structure calculations based on density functional theory were performed for solids and large molecules. The solids were represented by clusters of 60–100 atoms embedded in the potential of the external crystal. Magnetic moments and Mössbauer hyperfine parameters were derived.     

Solid-State 1H-NMR Relaxation Properties of the Fruit of a Wild Relative of Eggplant at Different Proton Larmor Frequencies

¹H longitudinal relaxation time profiles (T1) at different proton Larmor frequencies were registered for a solid-state plant tissue by using fast field cycling (FFC) nuclear magnetic resonance (NMR) spectroscopy. T1 distributions were obtained and the curves deconvoluted in order to differentiate among the different T1 components. Among the components, two were assigned to hydrophobic (e.g., fatty acid) and hydrophilic (e.g., saccharide) molecular systems, whereas the others were attributed to bulk and bound water. This paper shows for the first time solid-state FFC-NMR spectroscopy applied to plant tissue and reveals that relaxometry is a very promising technique for studying plant systems.     

Linear stability analysis of the natural convection in inclined rotating parallel plates

The linear stability analysis of the natural convection in a rectangular tilted infinite cavity filled with a Boussinesq fluid subject to Coriolis force is presented. The bottom and top surfaces have fixed temperatures. Both unstable and stable thermal conditions are studied (heated from below and heated from above respectively). The rotation axis passes through the center and it is orthogonal to the hot and cold surfaces. The stability equations were solved using the Tau–Chebyshev spectral method. The critical Rayleigh number and critical wave number were obtained for several rotation rates and different orientation of convective oblique rolls in a range of inclination of the cavity from 0 to 120 degrees. The stability analysis show that rotation rate affects the basic velocity profile, onset of convection, wave number and critical orientation of convective rolls.     

Bifunctional, conjugated oligomers for orthogonal self-assembly: selectivity varies from planar substrates to nanoparticles

A diphenylacetylene containing two different end groups (isonitrile and thioacetate) was synthesized, showing that the chemistry used to install each end group is compatible with that of the others. The isonitrile group binds preferentially to platinum, and the thiol group binds preferentially to gold. However, the selectivity was different when nanoparticles were compared to planar substrates.     

Asymptotic conditional distribution of exceedance counts: fragility index with different margins

We consider a random vector X, whose components are neither necessarily independent nor identically distributed. The fragility index (FI), if it exists, is defined as the limit of the expected number of exceedances among the components of X above a high threshold, given that there is at least one exceedance. It measures the asymptotic stability of the system of components. The system is called stable if the FI is one and fragile otherwise. In this paper, we show that the asymptotic conditional distribution of exceedance counts exists, if the copula of X is in the domain of attraction of a multivariate extreme value distribution, and if the marginal distribution functions satisfy an appropriate tail condition. This enables the computation of the FI corresponding to X and of the extended FI as well as of the asymptotic distribution of the exceedance cluster length also in that case, where the components of X are not identically distributed.