REPRESENTATION OF THE PAIRED INTERACTION POTENTIAL IN THE FORM OF MULTIDIMENSIONAL RATIONAL SERIES IN JACOBI VARIABLES FOR MANY-BODY PROBLEMS

Scalar power functions of the form x1 + + xN -v Î are in some cases found in physical problems and applications, especially in many-body problems with paired interactions. There are known decompositions for two vectors in three-dimensional space. In this paper, we consider analogous decompositions with any number of N arbitrary M-dimensional vectors in Euclidean space as a product of a multidimensional rational series with respect to spatial variables and hyperspheric functions on the unit sphere SM-1. Such an advantage of expansion arises in three-body problems when solving the Faddeev equation, where it is known that the main problem is the approximate choice of approximation of interaction potentials, in which the t-matrix scattering elements acquired a separable form.

Noncommutative rational Pólya series

A (noncommutative) Pólya series over a field K is a formal power series whose nonzero coefficients are contained in a finitely generated subgroup of $$K^\times $$ K × . We show that rational Pólya series are unambiguous rational series, proving a 40 year old conjecture of Reutenauer. The proof combines methods from noncommutative algebra, automata theory, and number theory (specifically, unit equations). As a corollary, a rational series is a Pólya series if and only if it is Hadamard sub-invertible. Phrased differently, we show that every weighted finite automaton taking values in a finitely generated subgroup of a field (and zero) is equivalent to an unambiguous weighted finite automaton.

A Sensitivity-Based Approach for Reliability Analysis of Randomly Excited Structures With Interval Axial Stiffness

Reliability assessment of linear discretized structures with interval parameters subjected to stationary Gaussian multicorrelated random excitation is addressed. The interval reliability function for the extreme value stress process is evaluated under the Poisson assumption of independent up-crossing of a critical threshold. Within the interval framework, the range of stress-related quantities may be significantly overestimated as a consequence of the so-called dependency phenomenon, which arises due to the inability of the classical interval analysis to treat multiple occurrences of the same interval variables as dependent ones. To limit undesirable conservatism in the context of interval reliability analysis, a novel sensitivity-based procedure relying on a combination of the interval rational series expansion and the improved interval analysis via extra unitary interval is proposed. This procedure allows us to detect suitable combinations of the endpoints of the uncertain parameters which yield accurate estimates of the lower bound and upper bound of the interval reliability function for the extreme value stress process. Furthermore, sensitivity analysis enables to identify the most influential parameters on structural reliability. A numerical application is presented to demonstrate the accuracy and efficiency of the proposed method as well as its usefulness in view of decision-making in engineering practice.

The Generalized Rank of Trace Languages

Given a partially commutative alphabet and a set of words [Formula: see text], the rank of [Formula: see text] expresses the amount of shuffling required to produce a word belonging to [Formula: see text] from two words whose concatenation belongs to the closure of [Formula: see text] with respect to the partial commutation. In this paper, the notion of rank is generalized from concatenations of two words to an arbitrary fixed number of words. In this way, an infinite sequence of non-negative integers and infinity is assigned to every set of words. It is proved that in the case of alphabets defining free commutative monoids, as well as in the more general case of direct products of free monoids, sequences of ranks of regular sets are exactly non-decreasing sequences that are eventually constant. On the other hand, by uncovering a relationship between rank sequences of regular sets and rational series over the min-plus semiring, it is shown that already for alphabets defining free products of free commutative monoids, rank sequences need not be eventually periodic.

La universidad italiana después de la segunda guerra mundial: las propuestas de reconstrucción de Fuci

Drawing from the extensive resources available in press and historical archives, this work focuses on the role exerted by the Italian Catholic University Federation (FUCI) after World War II, with special reference to the decisions regarding University policy and reform of higher education issues made by the Catholic student body. FUCI arose as a completely new entity within the Italian Catholic Movement after the fall of fascism, and its political and cultural foundations were independent of the popularism of the 1920s. With respect to the past, the position of Catholic associations seemed to be reinforced and are therefore worthy of consideration. In particular the analysis centres on the trajectory and guidelines presented at the Congress of Studies promoted by FUCI on the problems of the University, entitled La situazione universitaria italiana (The Italian University Situation). This meeting took place at Salerno from 2nd to 5th September 1948, and gave the FUCI youngsters the opportunity to draw up a sensible and rational series of proposals for relaunching and reconstructing the Italian University System.

Spectral Method for Fatigue Damage Assessment of Structures with Uncertain Parameters

This study presents a spectral method for fatigue damage evaluation of linear structures with uncertain-but-bounded parameters subjected to the stationary multi-correlated Gaussian random excitation. The first step of the proposed method is to model uncertain parameters by introducing interval theory. Within the framework of interval analysis, the approximate expressions of the bounds of spectral moments of generic response are obtained by the improved interval analysis via the Extra Unitary Interval and Interval Rational Series Expansion. Based on the cumulative damage theory and the Tovo-Benasciutti method, the lower and upper bounds of expected fatigue damage rate are accurately evaluated by properly combining the bounds of the spectral parameters of the power density spectral function of stress of critical points. Finally, a numerical example concerning a truss under random excitation is used to illustrate the accuracy and efficiency of the proposed method by comparing with the vertex method.