Necessary conditions and non-existence results for autonomous nonconvex variational problems

Classical one-dimensional, autonomous Lagrange problems are considered. In absence of any smoothness, convexity or coercivity condition on the energy density, we prove a DuBois-Reymond type necessary condition, expressed as a differential inclusion involving the subdifferential of convex analysis. As a consequence, a non-existence result is obtained.     

Estimates of covering numbers of convex sets with slowly decaying orthogonal subsets

Covering numbers of precompact symmetric convex subsets of Hilbert spaces are investigated. Lower bounds are derived for sets containing orthogonal subsets with norms of their elements converging to zero sufficiently slowly. When these sets are convex hulls of sets with power-type covering numbers, the bounds are tight. The arguments exploit properties of generalized Hadamard matrices. The results are illustrated by examples from machine learning, neurocomputing, and nonlinear approximation.     

R.F. (280 MHz) EPR imaging of extended samples: Apparatus and preliminary results

This paper presents the preliminary results obtained using an Electron Paramagnetic Resonance imaging apparatus operating at 280 MHz. The acquisition technique and the procedure used to obtain the spin density spatial localization are presented and specimen images of extended samples are given. The accuracy of the images and the spatial resolution are also discussed.     

An unusual syn conformation of 5‐formyluracil stabilized by supramolecular interactions

The asymmetric unit of the amino–oxo tautomer of 5‐formyluracil (systematic name: 2,4‐dioxo‐1,2,3,4‐tetrahydropyrimidine‐5‐carbaldehyde), C₅H₄N₂O₃, comprises one planar amino–oxo tautomer, as every atom in the structure lies on a crystallographic mirror plane. At variance with all the previously reported small‐molecule crystal structures containing the 5‐formyluracil residue, the formyl substituent in the title compound exhibits an unusual syn conformation. The molecules are linked into planar sheets parallel to the bc plane by a combination of six N—H...O and C—H...O hydrogen bonds. Four of the hydrogen bonds are utilized to stabilize the formyl group in the syn conformation.     

Determination of doxorubicin in human plasma by excitation-emission matrix fluorescence and multi-way analysis

Direct determination of doxorubicin (DXR), a cytotoxic anthracycline antibiotic, in human plasma was accomplished based on excitation-emission matrix (EEM) fluorescence measurements and multi-way chemometric methods based on parallel factor analysis (PARAFAC) and N-PLS. Several different procedures, such as residual analysis, core consistency diagnostic (CONCORDIA) and split-half analysis were employed to determine the correct number of factors in PARAFAC. These procedures converged to a choice of two factors, attributed to DXR and to the sum of two fluorescence species present in the plasma. Sample PARAFAC loadings were employed to build a regression model against concentration, resulting in a RMSECV of 0.060 μg ml⁻¹. N-PLS using two factors produced a RMSECV of 0.045 μg ml⁻¹. Figures of merit (FOM), such as sensitivity (SEN), selectivity (SEL) and limit of detection (L_D) were determined for both PARAFAC and N-PLS.     

Is styrene planar in liquid phases?

The proton NMR spectra of two (13)C-labeled isotopomers of styrene dissolved in two liquid crystalline solvents have been obtained and analyzed to yield four sets each of 24 dipolar couplings. These couplings were then used to investigate the structure of the ring and the ene fragments of the molecule, and the position of the maximum, phi(0), in the ring-ene bond rotational probability distribution. To do this, the effect on the dipolar couplings of small-amplitude vibrational motion was taken into account using vibrational wave functions calculated by molecular orbital and density functional methods. It is concluded that the NMR data are consistent with the ring fragment, averaged over the ring-ene rotation, planar, while the ene fragment is not. The value of phi(0) is found to be 18.0 degrees +/-0.2 degrees for the two solutions, compared with a value of 27 degrees calculated by the molecular method MP2/6-31G(*).     

An artificial ionophore based on a polyhydroxylated steroid dimer

The Na+ transporting properties of the first member of a new class of artificial ionophores, based on a C2-symmetric polyhydroxylated steroid dimer, are described.     

Altered mechanisms of reactions of phosphate esters bridging a dinuclear metal center

Kinetic isotope effects in the nucleophile and leaving group were obtained for the reaction of p-nitrophenyl phosphate monoester coordinated to a dinuclear Co(III) complex. The metal complex of the p-nitrophenyl phosphate monoester was found to hydrolyze by a single-step concerted mechanism, with significant nucleophilic participation in the transition state. By contrast, the hydrolysis of uncomplexed p-nitrophenyl phosphate occurs by a very loose transition state with little bond formation to the nucleophile. Previously, the metal complex of the diester methyl-p-nitrophenyl phosphate was found to hydrolyze via a two-step addition-elimination mechanism, in contrast to the concerted hydrolysis mechanism followed by uncomplexed diesters with the p-nitrophenolate leaving group. These results show that coordination to a metal complex can significantly alter the mechanism of phosphoryl transfer.     

Monodromic unbounded polycycles

The artiche extends and proves a Conjecture of R. Conti. Let be a plane polynomial vector field, its Poincaré compactification, the central projection of the sphere S² on the plane T tangent at the north pole. If is a monodromic polycycle (cyclic separatrix) of, intersecting but not coinciding with the equator S¹, is said a monodromic unbounded polycycle (m.u.p.). Conti's Conjecture can be so rephrased: If is a m.u.p. and deg, then has at most n–1 connected components. The proof is in two steps: Theorem 3.1 and Theorem 4.1. The main technique utilized is that of iterated directional blow-ups (-process) of the singular points at infinity of (i.e. the singularities of on S¹).     

The reactions of some halogenated pyridines with methoxide and methanethiolate ions in dimethylformamide

The reactions of 2,6- and 2,5-dibromopyridines and of 2,3- and 3,5-dichloropyridines with sodium isopropanethiolate and methanethiolate afforded the products of mono- or of bis-substitution depending on the experimental conditions. The same pyridines reacted with sodium methoxide to give good yields of the mono-substituted products; bis-substitution occurred easily only in the case of the 2,6-dibromo- and of the 3,5-dichloropyridine. The syntheses of some methoxy thiomethoxypyridine, starting from the halogeno methoxypyridines or from the halogeno thiomethoxypyhdines are also described. The bis-(alkylthio)pyridines can be fragmented by sodium in HMPA to give the bis(mercapto)pyridines.