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We consider a generalization of the three spectral inverse problem, that is, for given spectrum of the Dirichlet-Dirichlet problem (the Sturm-Liouville problem with Dirichlet conditions at both ends) on the whole interval $[0,a]$, parts of spectra of the Dirichlet-Neumann and Dirichlet-Dirichlet problems on $[0,a/2]$ and parts of spectra of the Dirichlet-Newman and Dirichlet-Dirichlet problems on $[a/2,a]$, we find the potential of the Sturm-Liouville equation., Comment: Published in Methods of Functional Analysis and Topology (MFAT), available at http://mfat.imath.kiev.ua/article/?id=842

Trabajo presentado en el 11th Intl Symposium on Scientific Bases for the Preparation of Heterogeneous Catalysts, celebrado en Louvain-la-Neuve (Bélgica) del 6 al 10 de julio de 2014., Silica is one of the most used supports in heterogeneous oxidation catalysts due to its chemical inertness for such reactions. Its low interaction with the supported active phases usually results in their low dispersion. As a way to overcome this problem, big research efforts have been done to obtain high specific surface area silicas, such as mesoporous MCM-41, SBA-15 or hexagonal mesoporous silica (HMS). This work is dedicated to preparation of new structure supports of HMS. These new structures were formed due to three simultaneously occurring phenomena: hierarchical organization, biomorphism and self-assembling. Reports in the literature [1-3] are dedicated to one of these three phenomena; however, we did not find any description of simultaneous observation of two or three of them in one system. The closest analogous materials with similar biomorphic structures were reported for mixture of SiO2 and BaCO3 [4]. In this case Ba carbonate played a role of a template; while in our work we do not apply any templating substance. Moreover, in [4] biomorphic structures with sizes ≥ 300 µm were formed; while in the present work size of biomorphic SiO2 structures is at least three orders of magnitude smaller (~ 80 nm). These unusual structures of (pure and modified) SiO2 were used as supports for preparation of gold catalysts of CO and 1-octanol oxidation., The authors acknowledge funding for this research by CONACYT Project No 79062 (Mexico), PAPIITUNAM Project IN100908 (Mexico), Russian Government Program «Science» of Tomsk Polytechnic University 3.2702.2011; Target Federal Program project 14.B37.21.0058 (Russia); CSIC project 201180E104 (Spain), MICINN project ENE2009-14522-C05 (Spain) and E. Flores, R.Velez, Sh. Sandoval, I.Gradilla, J. Mendoza, J. Diaz, J. Peralta, M. Sainz for technical assistance.

Trabajo presentado en el IX Simposio Internacional: Investigación Química en la Frontera, celebrado en Tijuana (México) del 20 al 22 de noviembre de 2013., The selective oxidation of alcohol is considered as one of the most challenging reactions in organic synthesis for conversion of products of biomass processi ng. The long chain alkanols (Cs+) has merited much less attention than that of more reactive benzylic or C1-C4 aliphatic alcohols. Supported gold nanoparticles attract great attention due to unique catalytic activity at low temperature. Hexagonal mesoporous silica (HMS) is material characterized by large specific surface areas and pore sizes about 5 nm. A high hydrophobicity of HMS is a particularly advantageous property for gold-catalyzed aerobic oxidations because these reactions prod uce water and are usually performed in aqueous or alcoholic solutions. In this work, we investigate HMS, pure and mod ified with metal oxides (Ce, Fe), as supports of gold catalysts for the aerobic oxidation of 1-octanol under green process conditions. The support was mod ified with Fe and Ce in two ways: by introducing the promoters during the HMS synthesis or by post-synthesis impregnation. Their activity for liquid-phase oxidation of 1-octanol was tested. Octanal was the main product on every catalyst under the conditions tested (80ºC, oxygen flow at atmospheric pressure, solvent base-free heptane); the ester also formed but no acid was detected. The best activity was found on catalysts with post-synthesis impregnated supports, where additional phases of the corresponding oxides are detected by XRD. IR studies of CO adsorption on the catalysts revealed that is due to the different nature of the gold species, which are smaller (or positively charged) and deposited on the modifier oxide phase.