Correlations in a Mozart's music score (K-73x) with palindromic and upside-down structure

In this work, we study long-range correlations in a “Scherzo-Duetto di Mozart” score (K-73x) for two violins. This is a fascinating piece, as the second violin part is upside down on the same sheet below the first violin, and some parts are like a palindrome. Given such ingenious structure, it is expected the existence of long-range correlations in the score structure. In order to quantify long-range correlations, we considered the music score as a sequence of integer numbers, each of them corresponding to last common denominator units of note. By using detrended fluctuation analysis (DFA), correlations are quantified by means of the scaling exponent that reflects the type of correlations for a given distance between neighbors note. The following conclusions can be drawn from the analysis: (a) For about 10-25 neighbor note distances, correlations are similar to 1/f-noise. This is an interesting finding since it has been shown that pleasant sounds for humans display a behavior similar to 1/f noise. (b) As the neighbor note distance increases, the long-range correlations decays continuously. For some score sections, the music score behaves like non-correlated (i.e., purely random) noise. Summing up, the results show that the studied Mozart's score contains a certain degree of correlation for relatively small note distances, and becomes close to non-correlated behavior for long note distances. We considered also the sequence constructed by considering the distance between the simultaneously played notes of the two violins. Interestingly, for relatively small neighbor note distances, a scaling behavior similar to that found for individual violins is also displayed. In some sense, this is an expression of the specific structure (palindromes plus upside down construction) used by Mozart in the composition of this music score. Although we focused on a particular high-art music score, our results suggest that modern methods borrowed from statistical physics can be useful for the systematic study of music composition techniques.     

One‐pot Preparation,Spectroscopic and Structural Characterization of Mercury(II) Complexes of Bulky Diimines with Halides and Pseudohalides

The preparation and characterization of two novel HgCl₂ and Hg(SCN)₂ complexes with bis[N‐(2‐tert‐butylphenyl)imine]acenaphthene is here described. One‐pot reaction techniques were used, leading to high yields of 75 % and 81 %, respectively. The complexes were characterized by microanalysis, i.r. and ¹HNMR spectroscopy, and by single crystal X‐ray diffraction. The structures of the complexes present similar characteristics, the most outstanding being the formation of dimers via intermolecular interaction. Whereas the HgCl₂ complex shows a unidimensional network due to strong π–π interactions, its Hg(SCN)₂ counterpart displays a supramolecular arrangement resulting from non classical hydrogen bond formation.     

Renormalization Group Flow¶of the Two-Dimensional Hierarchical Coulomb Gas

We consider a quasilinear parabolic differential equation associated with the renormalization group transformation of the two-dimensional hierarchical Coulomb system in the limit as the size of the block L&\darr; 1. We show that the initial value problem is well defined in a suitable function space and the solution converges, as t→∞, to one of the countably infinite equilibrium solutions. The j ^th nontrivial equilibrium solution bifurcates from the trivial one at . These solutions are fully described and we provide a complete analysis of their local and global stability for all values of inverse temperature β >0. Gallavotti and Nicoló's conjecture on infinite sequence of “phases transitions” is also addressed. Our results rule out an intermediate phase between the plasma and the Kosterlitz–Thouless phases, at least in the hierarchical model we consider. Received: 29 November 1999 / Accepted: 13 January 2001     

Topological duality for Tarski algebras

In this paper we will generalize the representation theory developed for finite Tarski algebras given in [7]. We will introduce the notion of Tarski space as a generalization of the notion of dense Tarski set, and we will prove that the category of Tarski algebras with semi-homomorphisms is dually equivalent to the category of Tarski spaces with certain closed relations, called T-relations. By these results we will obtain that the algebraic category of Tarski algebras is dually equivalent to the category of Tarski spaces with certain partial functions. We will apply these results to give a topological characterization of the subalgebras. Received August 21, 2005; accepted in final form December 5, 2006.     

Radon gas activity measurements in the frame of an international comparison

In order to validate its original method for the radon gas activity standardization and to assure the international metrological traceability and equivalence, the Radionuclide Metrology Laboratory of IFIN-HH participated recently in the international comparison CCRI(II)-K2.Rn-222, organized by the International Committee for Weights and Measures—CIPM-CCRI(II)-Radionuclide Measurements. The radon gas sample received, the measurement equipment and the experimental procedures are described. Because the comparison is underway, the results are presented only as relative values to the liquid scintillator vial measurement result. The uncertainty budget of the measurements performed is provided.     

Simultaneous determination of angiotensins II and 1-7 by capillary zone electrophoresis in plasma and urine from hypertensive rats

We describe the procedure developed for the simultaneous detection and quantification of angiotensin II and angiotensin-(1-7), by capillary zone electrophoresis with UV detection by photodiode-array, at a wavelength of 200 nm, in the plasma and urine from hypertensive rats. Optimal separation was achieved with a 100 mM boric acid + 3 mM tartaric acid + 10 fM gold (III) chloride electrolyte solution at pH 9.80. The applied voltage was 30 kV and the capillary temperature was kept constant at 20 °C. The method was over the concentration range of 0.01-500 pmol/mL. All determination coefficients were higher or equal to 0.9985. Limits of detection and quantification for angiotensin II were 0.0110 pmol/mL (S/N = 3) and 0.0195 pmol/mL (S/N = 5), respectively. While for angiotensin-(1-7), the limits were 0.0112 pmol/mL (S/N = 3) and 0.0193 pmol/mL (S/N = 5), respectively. The present method offers a time-saving way to simultaneous determination of angiotensin II and angiotensin-(1-7), since it can be completed in 10 min, compared to other methodologies reported in the literature for capillary electrophoresis and liquid chromatography, which require more than 1 h for analysis of complex matrices, such as plasma and urine. The procedure is illustrated by experiments that quantify simultaneously angiotensin II and angiotensin-(1-7) in plasma and urine from hypertensive and normotensive rats, with and without antihypertensive treatment. The levels of angiotensin II and angiotensin-(1-7) detected in the experimental model, resulted in a recovery of 99.00-106.01% and a reproducibility of less than 10%. The proposed analytical method is a use full tool for the simultaneous detection of angiotensin II and angiotensin-(1-7) implicated in vascular remodeling in pathologies such as hypertension.