On the computation of the rank of block bidiagonal Toeplitz matrices

In the present paper we study the computation of the rank of a block bidiagonal Toeplitz (BBT) sequence of matrices. We propose matrix-based, numerical and symbolical, updating and direct methods, computing the rank of BBT matrices and comparing them with classical procedures. The methods deploy the special form of the BBT sequence, significantly reducing the required flops and leading to fast and efficient algorithms. The numerical implementation of the algorithms computes the numerical rank in contrast with the symbolical implementation, which guarantees the computation of the exact rank of the matrix. The combination of numerical and symbolical operations suggests a new approach in software mathematical computations denoted as hybrid computations.     

Energy Transfer from the Aminophthalate Dianion to Fluorescein

Energy transfer from the excited aminophthalate dianion species to fluorescein at pH 8.32 (Tris-HCl buffer) was studied. The excited aminophthalate dianion species was obtained either by excitation with UV radiation (330 nm), with fluorescence emission, or by the well-known chemical reaction luminol-hydrogen peroxide in an alkaline medium, with chemiluminescent emission, both with _max at 425 nm. The influence of Co²⁺ and Mg²⁺ on fluorescence and chemiluminescence (CL) was studied. It was found that at low concentrations (10^–7–10^–9 M), these ions do not modify the fluorescein fluorescence, however, the CL is strong affected. The effect of the concentration of these elements, which exert an influence on CL even at a high dilution (nanomolar concentration), was determined. In the case of Co²⁺ the prooxidant character is stronger than in the case of Mg²⁺, and therefore the CL enhancer effect is higher. Compared to the system without catalyst, their presence ensures stronger, prolonged, and stable light emission. The emission spectra, in the presence of fluorescein, show two bands with maxima at 425 and 520 nm, the second one being specific to fluorescein emission. The intensity of aminophthalate dianion luminescence is lower and the duration shorter in the presence of fluorescein. The influence of Co²⁺ and Mg²⁺ catalyst and fluorescein concentration on the energy transfer process was studied. The efficiency of the energy transfer process for these two situations (fluorescence and CL) was compared. An attempt was made to replace hydrogen peroxide with superoxide anion (solubilized by means of crown ether) and its effect upon the energy transfer process was observed.     

Third-Order Phase Transition: Random Matrices and Screened Coulomb Gas with Hard Walls

Journal of Statistical Physics - Consider the free energy of a d-dimensional gas in canonical equilibrium under pairwise repulsive interaction and global confinement, in presence of a volume...     

Spectroscopic study on nystatin conformational modifications generated by its interaction with the solvent

Conformational transformations of the tetraenic nystatin chromophore under the influence of solvents and UV irradiation have been studied by absorption, fluorescence and wide-line NMR spectroscopy.     

Synthesis of new 3,5-diarylisoxazolidines by cycloaddition of oxaziridines and alkenes

This article reports a novel process of cycloaddition of C-aryloxaziridines with a variety of alkenes to afford stable, five-membered heterocycles 13–24. The steric hindrance of the tert-butyl group on the nitrogen atom of the oxaziridine is responsible for the high stereoselectivity of the cycloaddition reaction.     

Guerbet condensation of methanol with n-propanol to isobutyl alcohol over heterogeneous copper chromite/Mg–Al mixed oxides catalysts

The synthesis of isobutyl alcohol (ⁱBuOH) from methanol (MeOH) and n-propanol (PrOH) through the Guerbet condensation has been studied at 200 °C and under inert atmosphere (3.0 MPa of N₂), using a two-component heterogeneous catalytic system based on pre-activated copper chromite and Mg–Al mixed oxides deriving from hydrotalcite-type (HT) precursors with different Mg/Al ratios. All the investigated catalysts displayed a significant activity, with an almost complete selectivity to ⁱBuOH. Unlike the copper chromite/soluble sodium methoxide system, the catalysts were tolerant of the co-produced water and did not display any appreciable deactivation during the course of the reaction. The catalyst productivity was found to increase by reducing the Mg/Al ratio in the heterogeneous base, according to the increase of the fraction of medium–strong and strong basic sites which favour the aldol condensation between the aldehydes derived from MeOH and PrOH.     

Ziegler-Natta catalytic systems

A calorimetric investigation on the reactions of TiCl₄ with phthalates in 1,1,2,2-tetrachloroethane (TCE) is presented in order to better understand the complex interactions present in Ziegler-Natta catalytic systems. The Lewis bases diethyl isophthalate (L1), diethyl terephthalate (L2) and the ortho-isomer diethylphthalate (L3), have been chosen to study how the substituent positions could influence the energy and the stoichiometry of the complexation reactions. FTIR spectroscopy was used to obtain information on the coordination mode of the ligands and diffusion measurements by NMR was carried out to verify the presence of oligo-or polymeric species. Experimental results were compared with theoretical calculations based on Density Functional Theory (DFT).     

On the Asymptotic Behavior of Dilution Parameters for Gaussian and Hole–Gaussian Log-Conductivity Covariance Functions

Using a Lagrangian approach, the authors have previously shown that the kinetics of concentration variance and dilution of passive solutes in heterogeneous aquifers depend on the ratio between two- and one-particle covariances. Extending this approach, it is here demonstrated that, for point injections, the two-particle covariance coincides with the variance of the centroid location. Then, based on an Eulerian formulation, analytical first-order approximations are obtained for the two-particle covariance, for two types of log-conductivity covariance. For Gaussian covariance functions, whereas the transverse moments are asymptotically constant, the longitudinal moment tends to increase logarithmically over time. For hole–Gaussian covariances, both transverse and longitudinal moments tend to constant values. In both cases, the longitudinal two-particle correlation, which plays a crucial role in determining the dynamics of the concentration fluctuations, is controlled by the magnitude of the local dispersivity. The theoretical predictions are compared to the data collected at the Cape Cod site in terms of time derivative of the longitudinal two-particle moment, for Gaussian log-conductivity covariance and resorting to maximum likelihood estimates. Generally, good agreement is there, between experimental data and analytical expressions.     

Influence of Film Structure and Precursor Composition on Rhodamine B Retention in Dye-Dopped Ormosils

The interplay between the chemical structure of the precursors, internal organization in the end materials and dye retention was investigated for composites (ormosils) doped with rhodamine B. Besides formulations with triethoxysilanes (RTES) only, we synthesized as well organic–inorganic hybrids with addition of titanium isopropoxide (TIP) and maleic anhydride (MA). The organic (R) functionality of RTES was changed from methyl (MeTES), to phenyl (PTES) and octyl (OTES). Atomic force microscopy and electron microscopy, coupled with thermogravimetric analysis prove that hydrophobicity increase stimulates the transition of film structure: from well-defined, compact particles (for MeTES), to a mixture of porous particles and non-granular material (for MeTES/PTES), with extreme results observed for octyl-based composites. For this latter, the apparent homogeneity comes from cluster-like organization, where the primary entities are pseudo—granules produced by hydrophobic interactions of oligomeric siloxanes. Controlling the composition and gelation procedure resulted in doped composites with good optical transparency and rhodamine B fluorescence emission bands at around 580 nm. Dye transport inside the inorganic structure is not facilitated when: (a) the particles have a compact (nonporous) inner structure and (b) the recipe does not contain the TIP/MA combination. For silica-based films, the dye is located in the macropores (between the granules) of the material and could be easy removed by washing with acetone. On the contrary, using TIP/MA changes not only the internal composition of the granular-like material (by creating a microporous titania-rich outer-shell of the particles) but also the affinity of the Rh-B to permeate and reside inside these new structures.     

Magnetic anisotropy and molecular assembling in d complex cation–f complex anion type coordination compounds

The system [Fe(bpca)₂][Er(NO₃)₄(H₂O)₂] (1) (Hbpca = bis(2-pyridil-carbonyl) amine) is a complex cation–complex anion type coordination compound consisting of distinct d and f units, interlinked by hydrogen bonds. Particularly, the association of f-type complex anions in dimers is remarked and discussed. The energy decomposition analyses based on DFT calculations offered supplementary insight into the coordination effects at the lanthanide ions and the hydrogen bond driven supramolecular association of the complex units. Special ab initio procedures and subsequent modeling afforded the computation of anisotropic magnetization tensors of the [Er(NO₃)₄(H₂O)₂]^? f-type units. The computed results are in line with the experimental data for compound 1.