Lanthanide modulation of the orientation of macromolecules induced by purple membrane.

Addition of Tb3+ to purple membrane (PM) suspensions changes the orientation of the menbrane normal from parallel to perpendicular with respect to the magnetic field. Residual dipolar couplings measured in protein L in the presence of PM are scaled by a factor of -1/2. NMR line broadening and cross-correlation effects induced by the addition of PM are partially reversed by Tb3+ but not by Tm3+ that has no effect on the orientation of PM. This is interpreted as the result of anisotropically restricted motion of protein L in the transiently PM-bound form.     

Vapor-particle partitioning of hydrocarbons in Western Mediterranean urban and marine atmospheres

An analytical procedure is described for a comprehensive determination of the composition of hydrocarbons in the atmosphere, based on: (a) aerosol filtration and subsequent adsorption of the vapor phase onto active charcoal and polyurethane foam; (b) GPC and HPLC fractionation of the extracts, and (c) analysis of the fractions by GC-MS under EI and NICI modes. Special emphasis is placed onn-alkanes, PAHs and their oxygenated derivatives.The characterization of samples collected in a coastal urban area (Barcelona city), and far away over the Western Mediterranean, at sea level and at 1100 m of altitude, revealed significant changes in the aerosol composition, mainly attributed to initial vapor-particle partitioning processes, influenced by ambient temperature variations, and to others taking place during long-range atmospheric transport, related with the different compound photoreactivities and with an unexplained source-decoupling phenomenon.     

Graphs whose every transitive orientation contains almost every relation

Given a graphG onn vertices and a total ordering ≺ ofV(G), the transitive orientation ofG associated with ≺, denotedP(G; ≺), is the partial order onV(G) defined by settingx<y inP(G; ≺) if there is a pathx=x ₁ x ₂…x _r=y inG such thatx ₁ ≺x _j for 1≦i<j≦r. We investigate graphsG such that every transitive orientation ofG contains ₂ ⁿ −o(n ²) relations. We prove that almost everyG _n,p satisfies this requirement if , but almost noG _n,p satisfies the condition if (pn log log logn)/(logn log logn) is bounded. We also show that every graphG withn vertices and at mostcn logn edges has some transitive orientation with fewer than ₂ ⁿ −δ(c)n ² relations. Partially supported by MCS Grant 8104854.     

The spectrum of a quasiperiodic Schrödinger operator

The spectrum (H) of the tight binding Fibonacci Hamiltonian (H _mn= _m,n+1+ _m+1,n + _m,n v(n),v(n)= ((n–1)), 1/ is the golden number) is shown to coincide with the dynamical spectrum, the set on which an infinite subsequence of traces of transfer matrices is bounded. The point spectrum is absent for any , and (H) is a Cantor set for 4. Combining this with Casdagli's earlier result, one finds that the spectrum is singular continuous for 16.On leave from the Central Research Institute for Physics, Budapest, Hungary     

Estimation of density functions by order statistics

The properties of the empirical density function,f _n(x) = k/n( _j ⁺ – _j-1 ⁺ ) if _j-1 ⁺ < x ⁺ where _j-1 ⁺ and _j ⁺ are sample elements and there are exactlyk – 1 sample elements between them, are studied in that practical point of view how to choose a suitablek for a good estimation. A bound is given for the expected value of the absolute value of difference between the empirical and theoretical density functions.     

Problems and results on additive properties of general sequences,V

A very special case of one of the theorems of the authors states as follows: Let 1a ₁a ₂... be an infinite sequence of integers for which all the sumsa _i +a _j , 1ij, are distinct. Then there are infinitely many integersk for which 2k can be represented in the forma _i +a _j but 2k+1 cannot be represented in this form. Several unsolved problems are stated.Dedicated to our friend Professor E. Hlawka on the occasion of his seventieth birthday     

Single-step preparation and catalytic activity of mesoporous MCM-41 and SBA-15 silicas functionalized with perfluoroalkylsulfonic acid groups analogous to Nafion

Preparation of hybrid organic-inorganic MCM-41 and SBA-15 silicas functionalized with perfluoroalkylsulfonic acid groups has been achieved in a single step by reacting the mesoporous silicas with 1,2,2-trifluoro-2-hydroxy-1-trifluoromethylethane sulfonic acid beta-sultone; the catalysts showed higher activity than commercial Nafion-silica composite for the esterification of long chain fatty acids with ethanol.