Matrix orthogonal polynomials associated with perturbations of block Toeplitz matrices

Let {c _j } _j=0 ⁿ be a sequence of matrix moments associated with a matrix of measures supported on the unit circle, and let {P _j } _j=0 ⁿ be its corresponding sequence of monic matrix orthogonal polynomials. In this contribution, we consider a perturbation on the moments and find an explicit relation for the perturbed orthogonal polynomials in terms of {P _j } _j=0 ⁿ . We also obtain an expression for the corresponding second kind polynomials.     

Atomic force microscopy images of lyotropic lamellar phases

For the very first time, atomic force microscope images of lamellar phases were observed combined with a freeze fracture technique that does not involve the use of replicas. Samples are rapidly frozen, fractured, and scanned directly with atomic force microscopy, at liquid nitrogen temperature and in high vacuum. This procedure can be used to investigate micro-structured liquids. The lamellar phases in Sodium bis(2-ethylhexyl) sulfosuccinate (AOT)/water and in C12E5/water systems were used to asses this new technique. Our observations were compared with x-ray diffraction measurements and with other freeze fracture methods reported in the literature. Our results show that this technique is useful to image lyotropic lamellar phases and the estimated repeat distances for lamellar periodicity are consistent with those obtained by x-ray diffraction.     

Simplifying capillary electrophoresis-mass spectrometry operation: eliminating capillary derivatization by using self-coating background electrolytes

To simplify capillary electrophoresis-mass spectrometry (CE-MS) operation, a background electrolyte (BGE) containing a polymer additive is introduced that allows the analysis of peptides and protein mixtures in underivatized fused-silica capillaries without any pretreatment, thereby increasing throughput. The most important characteristic of these polymer additives is that they do not significantly suppress the signals of the proteins and peptides under electrospray ionization, thereby allowing them to be used as an additive to common BGEs that are used for CE-MS analysis of peptide and protein mixtures. In addition, because the fused-silica capillary inner wall is continuously coated with the polymer additive, migration irreproducibility, due to the degradation of the capillary inner wall coating, under CE-MS is minimized. High sensitivity of detection, migration reproducibility, and ease of fabrication allow CE-MS analyses that require long analysis time, such as (CE-MS/MS)n, to be performed with ease. The utility of this background electrolyte has been demonstrated for the analysis of complex protein digests and intact proteins.     

Relationship between the critical points found by the electron localization function and atoms in molecules approaches in adducts with hydrogen bonds

In this work, 11 adducts with hydrogen bonds were studied by using the B3LYP exchange-correlation functional of the Kohn-Sham approach and the M?ller-Plesset second-order perturbation theory MP2. With both approaches, the geometry of each adduct was optimized with the aug-cc-pVTZ basis set. The binding energies of the considered systems, found by the MP2 method, range from 1.2 to 8.3 kcal/mol. By using the atoms in molecules (AIM) analysis and the electron localization function (ELF) we found that the critical points positions characteristic of hydrogen bonds obtained by AIM and ELF are very similar each other. Besides, we found a linear correlation between the critical points positions found by AIM and those obtained by ELF with the B3LYP method and also with the MP2 method. The slope of such a linear relationship was close to 1 and the y-intercept close to 0.     

Flash ignition and initiation of explosives-nanotubes mixture

Optical ignition and initiation of energetic materials could thus far be only accomplished through lasers, with specific characteristics of high power, pulse length, wavelength, and a small target area that greatly inhibit their applications. Here, we report that an ignition and an initiation process, further leading to actual detonation, does occur for energetic materials in lax contact with carbon nanotubes that are prone to opto-thermal activity via a conventional flashbulb. Our results show that, for the first time, optical initiation of energetic materials is possible on a large surface area and using ordinary light intensity of several W/cm2. The implication is that energetic materials mixed with optically active nanotubes could be new ideal candidates for safety apparatus, such as the firing of bolts on space shuttle rockets and aircraft exit doors.     

(Li6Si5)2–5: The Smallest Cluster-Assembled Materials Based on Aromatic Si56− Rings

Extensive explorations of their potential energy surfaces, combined with high-level quantum chemical computations, strikingly show that the lowest energy structures of the (Li₆Si₅)_2–5 systems consist of 2–5 Si₅⁶⁻ aromatic units, surrounded by Li⁺ counterions, respectively. These viable gas-phase compounds are the pioneering reported cases of oligomers made by planar aromatic silicon rings. Based on the key evidence that these oligomers are energetically favored, and that their silicon rings aromaticity is thoroughly preserved, the Li₆Si₅ cluster is proposed as a potential assembly unit to build silicon-lithium nanostructures, thus opening new paths to design Zintl compounds at the nanoscale level.     

Conformational Preferences of trans-1,2- and cis-1,3-Cyclohexanedicarboxylic Acids in Water and Dimethyl Sulfoxide as a Function of the Ionization State As Determined from NMR Spectroscopy and Density Functional Theory Quantum Mechanical Calculations

The populations of diaxial (aa) and diequatorial (ee) conformers of trans-1,2- and cis-1,3-cyclohexanedicarboxylic acids (CDCAs; 1 and 2, respectively) and their salts were determined in water and dimethyl sulfoxide (DMSO) solutions from vicinal proton-proton NMR J couplings ((3)J(HH)). Optimized geometries and free energies for these compounds were obtained at the M06-2X/cc-pVTZ(-f)++ level. Although carboxylic acid groups in cyclohexane rings are generally believed to be far more stable (～2 kcal/mol) in equatorial than axial positions, this investigation demonstrated that an aa conformation (normally assumed to be completely insignificant for these compounds) can be favored depending on the medium and ionization state: strong ee preferences (>90%) were observed in water and DMSO for both diacids and their salts, except for the dianion of 1 in DMSO, which was found to be substantially aa (～57%). The possibility of intramolecular hydrogen bonding (H-bonding) was also investigated; the ratios of the ionization constants (K(1)/K(2)) indicated an absence of intramolecular H-bonding because K(1)/K(2) ? 10(4) (a standard criterion for non-H-bonding in dicarboxylic acids) for both 1 and 2 in water and also for 2 in DMSO. For 1, K(1)/K(2) increased drastically in DMSO (K(1)/K(2) = 4 × 10(6)), where (3)J(HH) and the ratio K(1)/K(E) = 10, K(E) being the acidity constant of the monomethyl ester of 1, indicated the formation of an intramolecular H-bond for the monoanion in this solvent. An explanation for the observation of compact dianions in solution in terms of the generalized Born equation is also provided.