Differentiation of chiral phosphorus enantiomers by P and H NMR spectroscopy using amino acid derivatives as chemical solvating agents

The ability of commercially available amino acid derivatives, especially Fmoc-Trp(Boc)-OH, to differentiate enantiomers of chiral phosphonates, phosphinates, phosphates, phosphine oxides, and phosphonamidates is demonstrated with (31)P, (13)C, and (1)H NMR spectroscopy. The chiral differentiation provided a rapid and convenient method for measuring the enantiomeric purity of these phosphorus compounds.     

Construction of solutions with exactly k blow-up points for the Schrödinger equation with critical nonlinearity

We consider the nonlinear Schrödinger equation: (1) $${{i\partial u} \mathord{\left/ {\vphantom {{i\partial u} {\partial t}}} \right. \kern-\nulldelimiterspace} {\partial t}} = - \Delta u - \left| u \right|^{{4 \mathord{\left/ {\vphantom {4 N}} \right. \kern-\nulldelimiterspace} N}} uandu\left( {0,.} \right) = \varphi \left( . \right),$$ whereu:[0,T)×? ^N →?. For any given pointsx ₁,x ₂,...,x _k in ? ^N , we construct a solution of Eq. (1),u(t), which blows up in a finite timeT at exactlyx ₁,x ₂,...,x _k . In addition, we describe the precise behavior of the solutionu(t) whent→T, at the blow-up points {x ₁,x ₂,...,x _k } and in ? ^N ?{x ₁,x ₂,...,x _k }.     

Inner multipliers of de Branges's spaces

For a given functionb in the unit ball ofH and an arbitraryH functionm, the question of whenm is a multiplier of the de Branges space (that is, when is invariant under multiplication bym) is examined. Some necessary and sufficient conditions thatm be a multiplier of are found and it is shown that there are no nonconstant inner multipliers of whenb is a nonconstant extreme point of the unit ball ofH . A new proof is given of the known fact that is invariant under multiplication byz whenb is not an extreme point of the unit ball ofH . Finally, we give a new proof of the known fact that an inner functionm is a multiplier of forb(z)=(1+z)/2 if and only ifm belongs to the range of .Some of the work in this paper originally appeared in the author's doctoral disseratation written at the University of California at Berkeley under the supervision of Donald Sarason.     

Linear equations depending differentiably on a parameter

We investigate operator functionsT(x) inBanach spaces, depending differentiably (meaning of classC orC ) on a parameterx and enjoying a certain regularity property. Iff is a given differentiable function such that the equationT(x)e=f(x) is solvable for eachx then the existence of a functione is proved which belongs to the same differentiability class asf andT, solving the equationT(x)e(x)f(x) identically inx. As an application we extend a result ofJ. Leiterer [9] and give a comprehensive answer to a question posed byJ.L. Taylor in [15] concerning the exactness of certain cochain complexes.     

Nanoscale organization of the pathogen receptor DC-SIGN mapped by single-molecule high-resolution fluorescence microscopy.

DC-SIGN, a C-type lectin exclusively expressed on dendritic cells (DCs), plays an important role in pathogen recognition by binding with high affinity to a large variety of microorganisms. Recent experimental evidence points to a direct relation between the function of DC-SIGN as a viral receptor and its spatial arrangement on the plasma membrane. We have investigated the nanoscale organization of fluorescently labeled DC-SIGN on intact isolated DCs by means of near-field scanning optical microscopy (NSOM) combined with single-molecule detection. Fluorescence spots of different intensity and size have been directly visualized by optical means with a spatial resolution of less than 100 nm. Intensity- and size-distribution histograms of the DC-SIGN fluorescent spots confirm that approximately 80 % of the receptors are organized in nanosized domains randomly distributed on the cell membrane. Intensity-size correlation analysis revealed remarkable heterogeneity in the molecular packing density of the domains. Furthermore, we have mapped the intermolecular organization within a dense cluster by means of sequential NSOM imaging combined with discrete single-molecule photobleaching. In this way we have determined the spatial coordinates of 13 different individual dyes, with a localization accuracy of 6 nm. Our experimental observations are all consistent with an arrangement of DC-SIGN designed to maximize its chances of binding to a wide range of microorganisms. Our data also illustrate the potential of NSOM as an ultrasensitive, high-resolution technique to probe nanometer-scale organization of molecules on the cell membrane.     

Thermodynamic properties of transition metals in aqueous solution. 2. The enthalpies of mixing of aqueous solutions of CoCl2, CuCl2, and MnCl2 with NaCl at varying ionic strength at 25°C

Enthalpies of mixing (_m H) aqueous solutions of CoCl₂, CuCl₂, and MnCl₂ with NaCl solutions were measured at constant ionic strengths of 0.5, 1.0, and 3.0 molal at 25°C. The excess enthalpy equations of Pitzer were then fit to the resulting _m H data. The resulting parameters are the temperature derivatives of the activity coefficient mixing parameters in the Pitzer system. The heat of mixing data for CoCl₂ and CuCl₂ were in agreement with earlier isomolal results by other workers.