Products of two involutions with prescribed eigenvalues and some applications

Let F be a field. In [Djokovic, Product of two involutions, Arch. Math. 18 (1967) 582-584] it was proved that a matrix A∈F^n×n can be written as A=BC, for some involutions B,C∈F^n×n, if and only if A is similar to A^-1. In this paper we describe the possible eigenvalues of the matrices B and C.As a consequence, in case charF≠2, we describe the possible similarity classes of (P₁₁⊕P₂₂)P^-1, when the nonsingular matrix P=[P_ij]∈F^n×n, i,j∈{1,2} and P₁₁∈F^s×s, varies.When F is an algebraically closed field and charF≠2, we also describe the possible similarity classes of [A_ij]∈F^n×n, i,j∈{1,2}, when A₁₁ and A₂₂ are square zero matrices and A₁₂ and A₂₁ vary.     

Geometric phases in graphitic cones

In this Letter we use a geometric approach to study geometric phases in graphitic cones. The spinor that describes the low energy states near the Fermi energy acquires a phase when transported around the apex of the cone, as found by a holonomy transformation. This topological result can be viewed as an analogue of the Aharonov-Bohm effect. The topological analysis is extended to a system with n cones, whose resulting configuration is described by an effective defect.     

Optimization of photo-polymerized sol–gel monolithic stationary phases prepared in polyacrylate-coated fused-silica capillaries for capillary electrochromatography

The preparation of photo-polymerized sol–gel monolithic stationary phases (MSP) within 100 μm internal diameter polyacrylate-coated fused-silica capillaries for use in capillary electrochromatography (CEC) was optimized. Eight mixtures containing different amounts of methacryloxypropyltrimethoxysilane (MPTMS) as the polymeric precursor, hydrochloric acid solution as the catalyst, toluene as the porogen and bis(2,4,6-trimethylbenzoyl)-phenylphosphine oxide (Irgacure 819) as the photo-initiator were irradiated at 370 nm inside the capillaries in order to complete the MSP polymerization, according to a fractional factorial experimental design 2_IV^4-1. All the preparation procedure, from capillary pretreatment until the MSP is ready to use in CEC, were made in less than four hours in mild conditions. A high pressurization injection device (HPID) useful for micro-volume syringes was built in order to achieve practical, controlled and precise injections of sols, solvents and electrolytes in the capillaries. The eight MSP were equally washed, conditioned and submitted to CEC procedures via short-end injection, which showed higher efficiency and peak height taking shorter analysis time. Electrochromatographic behaviors of the MSP were corroborated with morphological characterizations by scanning electron microscopy. The optimum condition, which allowed the separation of standard mixture containing thiourea (marker compound), naphthalene, acenaphthene, fluorene, phenanthrene and anthracene in twelve minutes without external pressure assistance, showed efficiencies up to 51,460 N/m, relative standard deviation from 0.05 to 3.3% for migration/retention time and from 0.14 to 1.6% for relative area (considering thiourea as an internal standard) and also showed no statistical evidence that three MSP prepared at the same condition are different within 95% confidence interval.     

Bioinspired Bioadhesive Polymers: Dopa‐Modified Poly(acrylic acid) Derivatives

The one‐step synthesis and characterization of novel bioinspired bioadhesive polymers that contain Dopa, implicated in the extremely adhesive byssal fibers of certain gastropods, is reported. The novel polymers consist of combinations of either of two polyanhydride backbones and one of three amino acids, phenylalanine, tyrosine, or Dopa, grafted as side chains. Dopa‐grafted hydrophobic backbone polymers exhibit as much as 2.5× the fracture strength and 2.8× the tensile work of bioadhesion of a commercially available poly(acrylic acid) derivative as tested on live, excised, rat intestinal tissue.

     

Holonomic quantum computation based on the scalar Aharonov–Bohm effect for neutral particles and linear topological defects

We discuss holonomic quantum computation based on the scalar Aharonov–Bohm effect for a neutral particle. We show that the interaction between the magnetic dipole moment and external fields yields a non-abelian quantum phase allowing us to make any arbitrary rotation on a one-qubit. Moreover, we show that the interaction between the magnetic dipole moment and a magnetic field in the presence of a topological defect yields an analogue effect of the scalar Aharonov–Bohm effect for a neutral particle, and a new way of building one-qubit quantum gates.     

Spectral variation under congruence

In this paper we study the possible spectra among matrices congruent to a given A?M_n (C). It is important to distinguish singular A from nonsingular and, among non-singular matrices, to distinguish where 0 lies relative to the field of values of A.     

Determination of Lead in Coal Using Direct Solid Sampling and High-Resolution Continuum Source Graphite Furnace Atomic Absorption Spectrometry

A method has been developed for the determination of Pb in coal using direct solid sampling (SS) and high-resolution continuum source graphite furnace atomic absorption spectrometry (HR-CS GF AAS). The certified coal reference materials used in this study were ground in an agate mortar to particle size ≤50 μm. Mass aliquots between 0.1 and 1 mg were weighed onto pyrolytic graphite platforms, and inserted directly into the graphite tube. For pyrolysis temperatures lower than 600 °C, a continuous background due to radiation scattering at solid particles preceded the atomic signal, as the coal matrix could not be sufficiently eliminated under these conditions. An optimized pyrolysis temperature of 700 °C was adopted for Pb without the use of a modifier. The optimum atomization temperature was found to be 1700 °C. Under these conditions, interference-free determination could be performed with calibration against aqueous standards in 0.5% v/v HNO₃. A total of six certified reference coal samples were analyzed, and the results obtained were all in good agreement with certified and informed values, respectively, according to a Student t-test at a 95% confidence level. A detection limit of 0.008 μg g⁻¹ for Pb was obtained at the 217.000 nm resonance line, a value comparable to those obtained by other sensitive, but much more sophisticated techniques, showing that the absence of dilution in the SS-HR-CS GF AAS method allows at least equivalent detection performance.     

Cation environment in polyether complexes based on poly(tetramethylene glycol) doped with zinc and cobalt chlorides

X‐ray absorption spectroscopy [extended X‐ray absorption fine structure (EXAFS) and X‐ray absorption near‐edge structure (XANES)], differential scanning calorimetry, and Raman spectroscopy measurements were performed for a series of liquid polyether/salt systems prepared with poly(tetramethylene glycol) (PTMG) and the copolymer poly(tetramethylene glycol‐co‐ethylene glycol) as matrices and zinc and cobalt chlorides as dopants in the concentration range of n = 30–90, where n is the molar ratio of oxygen to metal cation. According to EXAFS, XANES, and Raman results, even in diluted solutions, these complexes exist mostly as undissociated ZnCl₂ and CoCl₂ species, presenting a weak cation–polymer interaction. EXAFS results indicate that for polymer/ZnCl₂ systems, the nearest metal neighbors are only chlorine atoms. However, for polymer/CoCl₂ samples, oxygen is also observed coordinating the metal. Raman spectra do not support any feature related specifically to the cation–polymer interaction. Nevertheless, for both salts the symmetric stretching vibrations are located in frequencies characteristic of salt in solution, which means that the polymer solvating action is effective. Differential scanning calorimetry data show an increase in the glass‐transition temperature for all polymer/salt systems in relation to the pure polymer samples, a consequence of the increase in the macromolecular chain stiffening produced by the presence of the salt. This result corroborates the existence of polymer–salt interactions. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2572–2580, 2001     

Holonomy transformation in the FRW metric

In this work we investigate loop variables in Friedman-Robertson-Walker spacetime. We analyze the parallel transport of vectors and spinors along several paths in this spacetime in order to classify its global properties. Band holonomy invariance is analysed in this background.     

Dynamical system where proving chaos is equivalent to proving Fermat's conjecture

We prove that we can explicitly construct the expression for a low-dimensional Hamiltonian system where proving the existence of a Smale horseshoe is equivalent to proving that Fermat's Conjecture is true. We then show that some sets of similar intractable problems are dense (in the usual topology) in the space of all dynamical systems over a finite-dimensional real manifold.