Numerical methods for Fredholm integral equations on the square

In this paper we shall investigate the numerical solution of two-dimensional Fredholm integral equations by Nyström and collocation methods based on the zeros of Jacobi orthogonal polynomials. The convergence, stability and well conditioning of the method are proved in suitable weighted spaces of functions. Some numerical examples illustrate the efficiency of the methods.     

Multimodal integration of EEG, MEG and fMRI data for the solution of the neuroimage puzzle

In this paper, advanced methods for the modeling of human cortical activity from combined high-resolution electroencephalography (EEG), magnetoencephalography (MEG) and functional magnetic resonance imaging (fMRI) data are presented. These methods include a subject's multicompartment head model (scalp, skull, dura mater, cortex) constructed from magnetic resonance images, multidipole source model and regularized linear inverse source estimates of cortical current density. Determination of the priors in the resolution of the linear inverse problem was performed with the use of information from the hemodynamic responses of the cortical areas as revealed by block-designed (strength of activated voxels) fMRI. Examples of the application of these methods to the estimation of the time varying cortical current density activity in selected region of interest (ROI) are presented for movement-related high-resolution EEG data.     

Using high pressure to prepare polymorphs of the Ba2Co(1-x)Zn(x)S3 (0 ≤ x ≤ 1.0) compounds

In this work, high pressure was used as a tool to induce structural transition and prepare metastable polymorphs of ternary sulfides. Structural transformations under high pressure of compounds belonging to the Ba(2)Co(1-x)Zn(x)S(3) (0 ≤ x ≤ 1.0) series were studied using X-ray diffraction and electron microscopy. All members of the Ba(2)Co(1-x)Zn(x)S(3) series show the Ba(2)CoS(3)-type one-dimensional structure, but, after heating under pressure, the Ba(2)CoS(3) compound (x = 0) separates into BaS and the two-dimensional BaCoS(2-δ) (δ ≈ 0), while Ba(2)Co(1-x)Zn(x)S(3) compounds with x ≥ 0.25 maintain their one-dimensional features but rearrange into polymorphs showing the Ba(2)MnS(3)-type structure. All structural transformations can be linked to shortening in interchain metal-metal distances caused by the high pressure, and the role of the zinc in preventing loss of one-dimensionality is discussed.     

Toward a stable α-cycloalkyl amino acid with a photoswitchable cationic side chain

The N-alkylated indanylidenepyrroline (NAIP) Schiff base 3 is an unnatural α-amino acid precursor potentially useful for the preparation of semisynthetic peptides and proteins incorporating charged side chains whose structure can be modulated via Z/E photoisomerization. Here we report that the heteroallylic protons of 3 led to partial loss of ethanol accompanied by formation of the novel heterocyclic system 4 during attempted deprotection. We also show that the same protons catalyze the thermal isomerization of 3, making the light-driven conformational control concept ineffective for times longer than a few hours. These problems are not present in the previously unreported compound 5 where the acidic methyl group is replaced by an H atom. Therefore, 5, rather than 3, constitutes a promising prototype for the design of building blocks capable to modulate the electrostatic potential of a protein in specific locations via light irradiation.     

Observations in the synthesis of the core of the antitumor illudins via an enyne ring closing metathesis cascade

Observations concerning the synthesis of the core spirocyclic AB-ring system of illudins using an enyne ring closing metathesis (EYRCM) cascade are discussed. Substituent effects, in addition to optimization of the reaction conditions and the olefin tether for the key EYRCM reaction, are examined.     

Transmission problem in thermoelasticity with symmetry

In this paper we show the existence, uniqueness and regularityof the solutions to the thermoelastic transmission problem.Moreover, when the solutions are symmetrical we show that theenergy decays exponentially as time goes to infinity, no matterhow small is the size of the thermoelastic part.     

Enantioselective transfer hydrogenation catalyzed by iridium(I) complexes with nitrogen donor ligands

The reduction of prochiral ketones by hydrogen transfer from isopropanol is catalyzed by cationic iridium(I) complexes containing optically active Schiff bases. Optical yields of up to 33% have been obtained.     

Synthesis and demethylation of new 5,6,7,8-tetrahydro-4,9-dimethoxy-1H-benz[f]indole

The title compound 17 was prepared in good yield starting from 5,6,7,8-tetrahydro-l-naphthol ( 9 ) by an advantageous synthesis route consisting of eight steps, as indicated in Scheme 2. Demethylation by reflux heating with anhydrous aluminium chloride in dry benzene furnished 4,9-dihydroxy- and 4,9-dioxo-5,6,7,8-tetrahydro-1H-benz[f]indoles (compounds 18 and 19 , respectively). All new products were identified on the basis of spectral and analytical data.     

A reinvestigation of the structure of melanochrome

Reduction and subsequent acetylation of melanochrome, the last UV detectable intermediate in the biosynthesis of eunelanins, leads to the isolation of a crystalline derivative, leucomelanochrome A acetate, identified as 5,6,5′,6′-tetraacetoxy-2,2′-biindolyl ($\text{5}$).     

Synthesis of 4,9-dimethoxy-1H-benz[f]indole

A three-step synthesis of 4,9-dimethoxy-1H-benz[f]indole (4) starting from 1,4-dimethoxy-2-aminonaphthalene (1) is described. Compound 1 was condensed with epichlorohydrin in acidic methanolic solution and the crude reaction product, purified by column chromatography, was cyclized to compound 3 by reflux heating in bromobenzene solution in the presence of excess diethylaniline. Appropriate oxidization with periodate in alkaline solution produced the title compound 4.