Dynamics of tournaments: the soccer case

A random walk-like model is considered to discuss statistical aspects of tournaments. The model is applied to soccer leagues with emphasis on the scores. This competitive system was computationally simulated and the results are compared with empirical data from the English, the German and the Spanish leagues and showed a good agreement with them. The present approach enabled us to characterize a diffusion where the scores are not normally distributed, having a short and asymmetric tail extending towards more positive values. We argue that this non-Gaussian behavior is related with the difference between the teams and with the asymmetry of the scores system. In addition, we compared two tournament systems: the all-play-all and the elimination tournaments.     

Hexasulfanyl analogues of cyclotriveratrylene

The synthesis of four 3,4-di(alkylsulfanyl)benzyl alcohol derivatives is described, in five steps from methyl 3,4-di(hydroxy)benzoate via a Newman–Kwart rearrangement. Incubation of these derivatives in formic acid affords 2,3,7,8,12,13-hexakis(alkylsulfanyl)-10,15-dihydro-5H-tribenzo[a,d,g]cyclononene products, which are hexa-sulfanyl analogues of the well-known supramolecular cavitand host, cyclotriveratrylene (CTV). The yield of this cyclization depends strongly on the alkylsulfanyl substituents present, in the order SMe > SEt ≈ SiPr ? SBn. A crystal structure determination of one of the cyclotrimers shows a mode of self-association that is commonly exhibited by CTV itself.     

In vivo absorption spectra of the two stable states of the Euglena photoreceptor photocycle

Euglena gracilis possesses a simple but sophisticated light detecting system, consisting of an eyespot formed by carotenoids globules and a photoreceptor. The photoreceptor of Euglena is characterized by optical bistability, with two stable states. In order to provide important and discriminating information on the series of structural changes that Euglena photoreceptive protein(s) undergoes inside the photoreceptor in response to light, we measured the in vivo absorption spectra of the two stable states A and B of photoreceptor photocycle. Data were collected using two different devices, i.e. a microspectrophotometer and a digital microscope. Our results show that the photocycle and the absorption spectra of the photoreceptor possess strong spectroscopic similarities with a rhodopsin-like protein. Moreover, the analysis of the absorption spectra of the two stable states of the photoreceptor and the absorption spectrum of the eyespot suggests an intriguing hypothesis for the orientation of microalgae toward light.     

Spectroscopic Investigation on the Acrolein Hydration

The progress with time of the UV and ¹H NMR spectra of an aqueous solution of acrolein shows that, contrary to assumptions of previous authors, hydracrylaldehyde is not the only reaction product: in addition to it and its hydrated form, spontaneous oxidation products are present.     

'HNMR Spectra of Intermediate Tetrasubstituted Cyclopropane Derivatives in the Synthesis of New Pyrethroids

The proton magnetic resonance spectra of several 1,2,3,3-tetrasubstituted cyclopropane compounds obtained as intermediates in a new pyrethroid synthesis and containing double bond and carbonyl functions, have been studied in benzene and chloroform as solvents.     

Solution of De Saint Venant flexure-torsion problem for orthotropic beam via LEM (Line Element-less Method)

In this paper the numerical technique, labelled Line Element-less Method (LEM), is employed to provide approximate solutions of the coupled flexure-torsion De Saint Venant problem for orthotropic beams having simply and multiply-connected cross-section. The analysis is accomplished with a suitable transformation of coordinates which allows to take full advantage of the theory of analytic complex functions as in the isotropic case.A boundary value problem is formulated with respect to a novel complex potential function whose real and imaginary parts are related to the shear stress components, the orthotropic ratio and the Poisson coefficients. This potential function is analytic in all the transformed domain and then expanded in the double-ended Laurent series involving harmonic polynomials.The solution is provided employing an element-free weak form procedure imposing that the squared net flux of the shear stress across the border is minimum with respect to the series coefficients.Numerical implementation of the LEM results in system of linear algebraic equations involving symmetric and positive-definite matrices. All the integrals are transferred into the boundary without requiring any discretization neither in the domain nor in the contour.The technique provides the evaluation of the shear stress field at any interior point as shown by some numerical applications worked out to illustrate the efficiency and the accuracy of the developed method to handle shear stress problems in presence of orthotropic material.