Bose-Einstein condensates in standing waves: the cubic nonlinear Schrödinger equation with a periodic potential

We present a new family of stationary solutions to the cubic nonlinear Schr?dinger equation with an elliptic function potential. In the limit of a sinusoidal potential our solutions model a quasi-one-dimensional dilute gas Bose-Einstein condensate trapped in a standing light wave. Provided that the ratio of the height of the variations of the condensate to its dc offset is small enough, both trivial phase and nontrivial phase solutions are shown to be stable. Recent developments allow for experimental investigation of these predictions.     

Measurement of the neutron radius of 208Pb through parity violation in electron scattering

We report the first measurement of the parity-violating asymmetry A(PV) in the elastic scattering of polarized electrons from 208Pb. A(PV) is sensitive to the radius of the neutron distribution (R(n)). The result A(PV)=0.656±0.060(stat)±0.014(syst) ppm corresponds to a difference between the radii of the neutron and proton distributions R(n)-R(p)=0.33(-0.18)(+0.16) fm and provides the first electroweak observation of the neutron skin which is expected in a heavy, neutron-rich nucleus.     

Classification tree models for the prediction of blood-brain barrier passage of drugs

The use of classification trees for modeling and predicting the passage of molecules through the blood-brain barrier was evaluated. The models were built and evaluated using a data set of 147 molecules extracted from the literature. In the first step, single classification trees were built and evaluated for their predictive abilities. In the second step, attempts were made to improve the predictive abilities using a set of 150 classification trees in a boosting approach. Two boosting algorithms, discrete and real adaptive boosting, were used and compared. High-predictive classification trees were obtained for the data set used, and the models could be improved with boosting. In the context of this research, discrete adaptive boosting gives slightly better results than real adaptive boosting.     

Sol鈥揼el (combustion) synthesis and characterization of different alkaline earth metal (Ca, Sr, Ba) stannates

In this study, monophasic strontium and barium stannate (SrSnO₃, Sr₂SnO₄, BaSnO₃, Ba₂SnO₄) powders were synthesized by means of environmentally friendly aqueous sol–gel technique under neutral conditions. However, it was established that the successful sol–gel synthesis of appropriate calcium stannates (CaSnO₃ and Ca₂SnO₄) can be performed only at acidic sol–gel processing conditions. Moreover, the influence of nature of alkaline earth metal source on the phase purity of different metal stannates was evaluated. The thermal behaviour of Ca–Sn–O, Sr–Sn–O and Ba–Sn–O precursor gels was investigated by TG-DSC measurements. The phase purity, crystallization peculiarities and microstructural evolution of the sol–gel derived alkaline earth metal stannate powders were studied by XRD and SEM measurements.     

Synthesis and characterization of imidized poly(styrene‐maleic anhydride) nanoparticles in stable aqueous dispersion

Organic nanoparticles are synthesized by partial imidization of high‐molecular weight styrene(maleic‐anhydride) with 26 to 34 mol% maleic anhydride, in aqueous environment and presence of ammonium hydroxide. The nanoparticle dispersions have a maximum solid content of 35 wt% and good stability that critically depends on the ratio of imidized and ammonolyzed maleic anhydride moieties. The deprotonated residual maleic anhydride moieties provide dispersion stability at pH > 4, while protonation at pH < 4 causes nanoparticle sedimentation. After presentation of the synthesis conditions, the imidization reaction is characterized by FT‐IR and Raman spectroscopy, followed by thermal analysis (TGA, DSC), and morphological characterization (DLS, SEM, TEM, AFM). The reaction conditions were optimized by physical characterization of various dispersions, and finally nanoparticles could be obtained with a maximum degree of imidization of 77% in dispersed conditions, or 90 to 95% after drying that are favorable for coating applications. Copyright © 2010 John Wiley & Sons, Ltd.     

Interface Problems for Dispersive Equations

The interface problem for the linear Schrödinger equations in one‐dimensional piecewise homogeneous domains is examined by providing an explicit solution in each domain. The location of the interfaces is known and the continuity of the wave function and a jump in their derivative at the interface are the only conditions imposed. The problem of two semi‐infinite domains and that of two finite‐sized domains are examined in detail. The problem and the method considered here extend that of an earlier paper by Deconinck et al. (2014) [1]. The dispersive nature of the problem presents additional difficulties that are addressed here.     

Universal Approach Towards r‐Hirudin Derivatives with High Anti‐Thrombin Activity Based on Chemical Differentiation of Primary Amino Groups

Chemical modification of recombinant hirudin (r‐hirudin) is necessary whenever surface‐confinement to a biomaterial or biotinylation for subsequent conjugation with carriers is intended. Here, we report a modification strategy that permits chemical discrimination between r‐hirudin's amino groups and preserves its thrombin inhibitor activity. By reaction with Msc‐ONSu, protective groups were successively introduced in r‐hirudin yielding four derivatives (Msc)_x‐hirudin (1 ≤ x ≤ 4) and pure fractions were isolated by ion exchange chromatography. Structure–function relationships were studied for all derivatives and revealed a decrease in activity of more than 90% as compared to unprotected r‐hirudin. MALDI‐TOF MS was used to determine the locations of the Msc groups. Furthermore, evidence was provided that r‐hirudin's N‐terminal amino group is highly important for its anti‐thrombin activity. Selective modification of the lysine residues which maintained the free N‐terminal amino group preserved the anti‐thrombin activity of r‐hirudin even after biotinylation and subsequent linkage to streptavidin or confinement to a polymer surface.     

Dynamics and Stability of Bose-Einstein Condensates: The Nonlinear Schrödinger Equation with Periodic Potential

Summary. The cubic nonlinear Schr?dinger equation with a lattice potential is used to model a periodic dilute-gas Bose-Einstein condensate. Both two- and three-dimensional condensates are considered, for atomic species with either repulsive or attractive interactions. A family of exact solutions and corresponding potential is presented in terms of elliptic functions. The dynamical stability of these exact solutions is examined using both analytical and numerical methods. For condensates with repulsive atomic interactions, all stable, trivial-phase solutions are off-set from the zero level. For condensates with attractive atomic interactions, no stable solutions are found, in contrast to the one-dimensional case [8].     

Factor orbit equivalence of compact group extensions and classification of finite extensions of ergodic automorphisms

In §§1–5, we classifyn-point extensions of ergodic automorphisms up to factor orbit-equivalence (which is the natural analogue of factor isomorphism). This classification is in terms of conjugacy classes of subgroups of the symmetric group onn points, and parallels D. Rudolph’s classification ofn-point extensions of Bernoulli shifts up to factor isomorphism. In §6, we give another proof of A. Fieldsteel’s theorem on factor orbit-equivalence of compact group extensions.