Simulation of harmonic oscillators on the lattice

This work deals with the simulation of a two-dimensional ideal lattice having simple tetragonal geometry. The harmonic character of the oscillators give rise to a system of second-order linear differential equations, which can be recast into matrix form. The explicit solutions which govern the dynamics of this system can be expressed in terms of matrix trigonometric functions. For the derivation we employ the Lagrangian formalism to determine the correct solutions, which extremize the underlying action of the system. In the numerical evaluation we develop diverse state-of-the-art algorithms which efficiently tackle equations with matrix sine and cosine functions. For this purpose, we introduce two special series related to trigonometric functions. They provide approximate solutions of the system through a suitable combination. For the final computation an algorithm based on Taylor expansion with forward and backward error analysis for computing those series had to be devised. We also implement several MATLAB programs which simulate and visualize the two-dimensional lattice and check its energy conservation.     

The Hurwitz subgroups of $$E_6(2)$$

We prove that the exceptional group \(E_6(2)\) is not a Hurwitz group. In the course of proving this, we complete the classification up to conjugacy of all Hurwitz subgroups of \(E_6(2)\), in particular, those isomorphic to \(L_2(8)\) and \(L_3(2)\).     

A new type of Hermite matrix polynomial series

Conventional Hermite polynomials emerge in a great diversity of applications in mathematical physics, engineering, and related fields. However, in physical systems with higher degrees of freedom it will be of practical interest to extend the scalar Hermite functions to their matrix analogue. This work introduces various new generating functions for Hermite matrix polynomials and examines existence and convergence of their associated series expansion by using Mehler’s formula for the general matrix case. Moreover, we derive interesting new relations for even- and odd-power summation in the generating-function expansion containing Hermite matrix polynomials. Some new results for the scalar case are also presented.     

Amyloid fibril formation and other aggregate species formed by human serum albumin association

Under in vitro solution conditions where the native state is destabilized, many proteins present an abnormal structure and metabolism associated with a strong tendency to self-aggregation into a polymeric amyloid fibril structure, suggesting that this ability is a generic feature of the polypeptide chains. Such structures play a key role in different pathogenesis of neurodegenerative diseases such as Alzheimer, Parkinson, or Creutzfeldt-Jakob. Here, we report the formation of amyloid fibrils in the plasma protein human serum albumin under different in vitro conditions monitored using a combination of spectrophotometric and microscopic techniques. Amyloid fibril formation, therefore, is also allowed in a protein with a high degree of structural complexity. We also infer from experimental data the existence of other protein aggregated species than fibrils, some of which seem to be formed by a structural rearrangement of the proper fibrils.     

The 1H NMR method for the determination of the absolute configuration of 1,2,3-prim,sec,sec-triols

The absolute configuration of 1,2,3-prim,sec,sec-triols can be assigned by comparison of the 1H NMR spectra of the tris-(R)- and the tris-(S)-MPA ester derivatives. An experimental demonstration of this correlation with 24 triols of known absolute configuration and a protocol using two parameters-Deltadelta(RS)(H3) and the difference between Deltadelta RS (H2) and Deltadelta RS (H3) = absolute value (Delta(Deltadelta RS))-for its application to the determination of the absolute configuration of other triols are presented.     

Optical mercury sensing using a benzothiazolium hemicyanine dye

[structure: see text] The selectivity and sensitivity of a benzothiazolium hemicyanine dye toward mercury(II) in aqueous solutions are described. Mercury ions coordinate to the dye forming a 1:1 complex. This interaction induces a color change in the dye at micromolar concentrations of mercury. Furthermore, the color change and quenching of the dye emission are selective for mercury when compared with other ions such as lead(II), cadmium(II), zinc(II), or iron(II).     

ABS methods for continuous and integer linear equations and optimization

ABS methods are a large class of algorithms for solving continuous and integer linear algebraic equations, and nonlinear continuous algebraic equations, with applications to optimization. Recent work by Chinese researchers led by Zunquan Xia has extended these methods also to stochastic, fuzzy and infinite systems, extensions not considered here. The work on ABS methods began almost thirty years. It involved an international collaboration of mathematicians especially from Hungary, England, China and Iran, coordinated by the university of Bergamo. The ABS method are based on the rank reducing matrix update due to Egerváry and can be considered as the most fruitful extension of such technique. They have led to unification of classes of methods for several problems. Moreover they have produced some special algorithms with better complexity than the standard methods. For the linear integer case they have provided the most general polynomial time class of algorithms so far known; such algorithms have been extended to other integer problems, as linear inequalities and LP problems, in over a dozen papers written by Iranian mathematicians led by Nezam Mahdavi-Amiri. ABS methods can be implemented generally in a stable way, techniques existing to enhance their accuracy. Extensive numerical experiments have shown that they can outperform standard methods in several problems. Here we provide a review of their main properties, for linear systems and optimization. We also give the results of numerical experiments on some linear systems. This paper is dedicated to Professor Egerváry, developer of the rank reducing matrix update, that led to ABS methods.     

Alternating local search based VNS for linear classification

We consider the linear classification method consisting of separating two sets of points in d-space by a hyperplane. We wish to determine the hyperplane which minimises the sum of distances from all misclassified points to the hyperplane. To this end two local descent methods are developed, one grid-based and one optimisation-theory based, and are embedded into a VNS metaheuristic scheme. Computational results show these approaches to be complementary, leading to a single hybrid VNS strategy which combines both approaches to exploit the strong points of each. Extensive computational tests show that the resulting method can always be expected to approach the global optimum close enough that any deviations from the global optimum are irrelevant with respect to the classification power.     

SERS detection of red organic dyes in Ag‐agar gel

Micro‐Raman spectroscopy has been widely employed in the last few years for the study of artworks, allowing for the characterization of a high class of pictorial materials. However, the detection of organic dyes by conventional Raman spectroscopy is quite difficult, due to the high fluorescence provided by these compounds. Recently, remarkable improvements have been achieved by the introduction of the surface enhanced Raman spectroscopy (SERS) technique for the analysis of organic dyes. In the present work, a new method is presented, based on the use of a SERS probe made of agar‐agar coupled with silver nanoparticles, for a non‐destructive and minimally invasive micro‐extraction of dyes from textiles. Ag‐agar gel has been tested first on textile mock‐ups dyed with alizarin, purpurin and carminic acid. SERS measurements have been performed adopting laser light excitations at 514.5 and 785 nm of a micro‐Raman setup. Highly structured SERS band intensities have been obtained. After having verified the safety of the method by colorimetric, X‐ray fluorescence and attenuated total reflectance Fourier transform infrared techniques, a real case, a pre‐Columbian piece of textile, have been investigated by Ag‐agar gel. This cutting‐edge method offers new possibilities for a sensitive and non‐destructive analysis of fluorescent materials. Copyright © 2012 John Wiley & Sons, Ltd.     

Relaxation Height in Energy Landscapes: An Application to Multiple Metastable States

The study of systems with multiple (not necessarily degenerate) metastable states presents subtle difficulties from the mathematical point of view related to the variational problem that has to be solved in these cases. We prove sufficient conditions to identify multiple metastable states. Since this analysis typically involves non-trivial technical issues, we give different conditions that can be chosen appropriately depending on the specific model under study. We show how these results can be used to attack the problem of multiple metastable states via the use of the modern approaches to metastability. We finally apply these general results to the Blume–Capel model for a particular choice of the parameters for which the model happens to have two multiple not degenerate in energy metastable states. We estimate in probability the time for the transition from the metastable states to the stable state. Moreover we identify the set of critical configurations that represent the minimal gate for the transition.