Operator expansion: definition and molecular integral applications

Es defineix l'expansió general d'operadors com una combinació lineal de projectors i s'exposa la seva aplicació generalitzada al càlcul d'integrals moleculars. Com a exemple numèric, es fa l'aplicació al càlcul d'integrals de repulsió electrònica entre quatre funcions de tipus s centrades en punts diferents, i es mostren tant resultats del càlcul com la definició d'escalat respecte a un valor de referència, que facilitarà el procés d'optimització de l'expansió per uns paràmetres arbitraris. Es donen resultats ajustats al valor exacte

Exploration of geological variability and possible processes through the use of compositional data analysis: an example using scottish metamorphosed

Developments in the statistical analysis of compositional data over the last twodecades have made possible a much deeper exploration of the nature of variability,and the possible processes associated with compositional data sets from manydisciplines. In this paper we concentrate on geochemical data sets. First we explainhow hypotheses of compositional variability may be formulated within the naturalsample space, the unit simplex, including useful hypotheses of subcompositionaldiscrimination and specific perturbational change. Then we develop through standardmethodology, such as generalised likelihood ratio tests, statistical tools to allow thesystematic investigation of a complete lattice of such hypotheses. Some of these tests are simple adaptations of existing multivariate tests but others require specialconstruction. We comment on the use of graphical methods in compositional dataanalysis and on the ordination of specimens. The recent development of the conceptof compositional processes is then explained together with the necessary tools for astaying- in-the-simplex approach, namely compositional singular value decompositions. All these statistical techniques are illustrated for a substantial compositional data set, consisting of 209 major-oxide and rare-element compositions of metamorphosed limestones from the Northeast and Central Highlands of Scotland.Finally we point out a number of unresolved problems in the statistical analysis ofcompositional processes

Problemàtica ambiental associada a la implantació de polígons industrials en municipis petits, el cas de Vilamalla i el Far d’Empordà

Aquest treball pretén identificar, predir i valorar les problemàtiques associades a la implantació i desenvolupament dels polígons industrials LOGIS Empordà (El Far d’Empordà), Empordà Internacional i CM3 (Vilamalla) utilitzant diversos indicadors (aigües, residus industrials, mobilitat, contaminació atmosfèrica). Posteriorment es fa una proposta per tal de millorar aquests aspectes ambientals

Polítiques de joventut estatals a Europa : una perspectiva comparada

Recerca en política comparada a Europa, concretament sobre les polítiques estatals de joventut. L’objectiu és identificar característiques singulars, idees força i pràctiques concretes, d’aquest camp de les polítiques, en alguns països europeus escollits per un seguit de factors i veure si això serveix per formular amb solvència una (o unes) classificació dels països europeus en funció del seu tipus de polítiques de joventut. En última instància també es tracta de veure si el model català de fer polítiques de joventut, és compartit per altres països i per tant homologable o és eminentment singular i únic

I ara què? que hi ha en polítiques de joventut després del Plans de Joventut?

Fa més de 10 anys del primer Pla Nacional de Joventut de Catalunya, del pas de les polítiques de suport a l’associacionisme a les polítiques integrals, i amb aquestes la prolífica etapa dels Plans de Joventut i de l’expansió real de les polítiques de joventut al territori català. És a dia d’avui, en un moment de grans esdeveniments en aquest camp, en que es proposa un anàlisi sobre la futura evolució de les polítiques de joventut, basat en l’estudi i la interpretació de la informació existent i les aportacions de 9 persones vinculades al món de les polítiques de joventut

KAM theory for conformally symplectic systems

We present a KAM theory for some dissipative systems (geometrically, these are conformally symplectic systems, i.e. systems that transform a symplectic form into a multiple of itself). For systems with n degrees of freedom depending on n parameters we show that it is possible to find solutions with n-dimensional (Diophantine) frequencies by adjusting the parameters. We do not assume that the system is close to integrable, but we use an a-posteriori format. Our unknowns are a parameterization of the solution and a parameter. We show that if there is a sufficiently approximate solution of the invariance equation, which also satisfies some explicit non–degeneracy conditions, then there is a true solution nearby. We present results both in Sobolev norms and in analytic norms. The a–posteriori format has several consequences: A) smooth dependence on the parameters, including the singular limit of zero dissipation; B) estimates on the measure of parameters covered by quasi–periodic solutions; C) convergence of perturbative expansions in analytic systems; D) bootstrap of regularity (i.e., that all tori which are smooth enough are analytic if the map is analytic); E) a numerically efficient criterion for the break–down of the quasi–periodic solutions. The proof is based on an iterative quadratically convergent method and on suitable estimates on the (analytical and Sobolev) norms of the approximate solution. The iterative step takes advantage of some geometric identities, which give a very useful coordinate system in the neighborhood of invariant (or approximately invariant) tori. This system of coordinates has several other uses: A) it shows that for dissipative conformally symplectic systems the quasi–periodic solutions are attractors, B) it leads to efficient algorithms, which have been implemented elsewhere. Details of the proof are given mainly for maps, but we also explain the slight modifications needed for flows and we devote the appendix to present explicit algorithms for flows.

Speed of reaction-diffusion fronts in spatially heterogeneous media

The front speed problem for nonuniform reaction rate and diffusion coefficient is studied by using singular perturbation analysis, the geometric approach of Hamilton-Jacobi dynamics, and the local speed approach. Exact and perturbed expressions for the front speed are obtained in the limit of large times. For linear and fractal heterogeneities, the analytic results have been compared with numerical results exhibiting a good agreement. Finally we reach a general expression for the speed of the front in the case of smooth and weak heterogeneities

Algunas consideraciones en el debate sobre ámbitos emergentes en la educación social

En esta comunicación se propone reflexionar sobre el peso que ha tenido el debate de los ámbitos en el proceso de construcción de la identidad profesional en la educación social y cómo, a su vez, esta forma de plantear la construcción de la identidad está condicionando su desarrollo posterior, con el riesgo de perder mucho de lo que se ha avanzado. El origen histórico de la profesión y la singular forma como ésta se ha construido ha centrado el debate de la identidad profesional en la definición de los ámbitos de intervención, de manera que el profesional se ha venido identificando más por lo que hace en determinados lugares que por lo que esencialmente debería ser, al margen del lugar donde desarrolla su actividad. En segundo lugar, también ha contribuido a poner el énfasis de la identidad en el espacio de intervención el hecho de proceder de una cultura profesional actuadora, más centrada en la acción que en la reflexión.

A variational approach for calculating Franck-Condon factors including mode-mode anharmonic coupling

We have implemented our new procedure for computing Franck-Condon factors utilizing vibrational configuration interaction based on a vibrational self-consistent field reference. Both Duschinsky rotations and anharmonic three-mode coupling are taken into account. Simulations of the first ionization band of Cl O2 and C4 H4 O (furan) using up to quadruple excitations in treating anharmonicity are reported and analyzed. A developer version of the MIDASCPP code was employed to obtain the required anharmonic vibrational integrals and transition frequencies

Arnau de Montrodon y la catedral de San Carlomagno. Sobre la imagen y el culto al emperador carolingio en Gerona

In 1345, the unique worship of Saint Charlemagne was institutionalized in the cathedral of Gerona. The roots (and for many, the reasons) of this celebration are found in the existence of an old local legend, the well-known testimonies to which go back to the eleventh century. Nevertheless, a lengthy analysis of the facts that marked the life of the cathedral during the long permanence Amau de Montrodon had there—first in quality of canon (1297-1335) and later as bishop (1333-1348)- make it possible for us to verify that the promotion of the cult to San Charlemagne falls within a complex program of ideological and symbolic exaltation of the See of Girona that was designed by this notable and restlessly active ecclesiastic

Anàlisi d'errades: la concordança de nombre en alemanys aprenents de castellà

Aquest treball analitza els errors de concordança de nombre (singular,plural en subjectes alemanys, d’entre 18 i 20 anys, que tenen com a llengua materna (L1) l’alemany i/o el turc o polonès i es caracteritzen per haver rebut una formació prèvia d’altres llengües estrangeres (L2, L3, L4) com ara l’anglès i/o el francès.

The Standard Biplot

Biplots are graphical displays of data matrices based on the decomposition of a matrix as the product of two matrices. Elements of these two matrices are used as coordinates for the rows and columns of the data matrix, with an interpretation of the joint presentation that relies on the properties of the scalar product. Because the decomposition is not unique, there are several alternative ways to scale the row and column points of the biplot, which can cause confusion amongst users, especially when software packages are not united in their approach to this issue. We propose a new scaling of the solution, called the standard biplot, which applies equally well to a wide variety of analyses such as correspondence analysis, principal component analysis, log-ratio analysis and the graphical results of a discriminant analysis/MANOVA, in fact to any method based on the singular-value decomposition. The standard biplot also handles data matrices with widely different levels of inherent variance. Two concepts taken from correspondence analysis are important to this idea: the weighting of row and column points, and the contributions made by the points to the solution. In the standard biplot one set of points, usually the rows of the data matrix, optimally represent the positions of the cases or sample units, which are weighted and usually standardized in some way unless the matrix contains values that are comparable in their raw form. The other set of points, usually the columns, is represented in accordance with their contributions to the low-dimensional solution. As for any biplot, the projections of the row points onto vectors defined by the column points approximate the centred and (optionally) standardized data. The method is illustrated with several examples to demonstrate how the standard biplot copes in different situations to give a joint map which needs only one common scale on the principal axes, thus avoiding the problem of enlarging or contracting the scale of one set of points to make the biplot readable. The proposal also solves the problem in correspondence analysis of low-frequency categories that are located on the periphery of the map, giving the false impression that they are important.

Ratio maps and correspondence analysis

We compare two methods for visualising contingency tables and developa method called the ratio map which combines the good properties of both.The first is a biplot based on the logratio approach to compositional dataanalysis. This approach is founded on the principle of subcompositionalcoherence, which assures that results are invariant to considering subsetsof the composition. The second approach, correspondence analysis, isbased on the chi-square approach to contingency table analysis. Acornerstone of correspondence analysis is the principle of distributionalequivalence, which assures invariance in the results when rows or columnswith identical conditional proportions are merged. Both methods may bedescribed as singular value decompositions of appropriately transformedmatrices. Correspondence analysis includes a weighting of the rows andcolumns proportional to the margins of the table. If this idea of row andcolumn weights is introduced into the logratio biplot, we obtain a methodwhich obeys both principles of subcompositional coherence and distributionalequivalence.

Spanning tests in return and stochastic discount factor mean-variance frontiers: A unifying approach

We propose new spanning tests that assess if the initial and additional assets share theeconomically meaningful cost and mean representing portfolios. We prove their asymptoticequivalence to existing tests under local alternatives. We also show that unlike two-step oriterated procedures, single-step methods such as continuously updated GMM yield numericallyidentical overidentifyng restrictions tests, so there is arguably a single spanning test.To prove these results, we extend optimal GMM inference to deal with singularities in thelong run second moment matrix of the influence functions. Finally, we test for spanningusing size and book-to-market sorted US stock portfolios.

Power transformations in correspondence analysis

Power transformations of positive data tables, prior to applying the correspondence analysis algorithm, are shown to open up a family of methods with direct connections to the analysis of log-ratios. Two variations of this idea are illustrated. The first approach is simply to power the original data and perform a correspondence analysis this method is shown to converge to unweighted log-ratio analysis as the power parameter tends to zero. The second approach is to apply the power transformation to thecontingency ratios, that is the values in the table relative to expected values based on the marginals this method converges to weighted log-ratio analysis, or the spectral map. Two applications are described: first, a matrix of population genetic data which is inherently two-dimensional, and second, a larger cross-tabulation with higher dimensionality, from a linguistic analysis of several books.