On the intensity of linear elastic high order singularities ahead of cracks and re-entrant corners

The paper deals with high order elastic singular terms at cracks and re-entrant corners (sharp V-notches), which are commonly omitted in linear elastic analyses by the argument that the strain energy and displacements in the near-tip region should be bounded. The present analysis proves that these terms are fully included in the elastic part of complete elastic–plastic stress and strain solutions.The intensities of high order singular terms are found to be linked to the linear elastic stress intensity factor and the extension of the plastic zone along the crack bisector line. The smaller the plastic radius, the smaller the intensities of high order singular terms are.A physical justification of the existence of high order singular terms is provided on the basis of the strain energy density distribution detected along the crack bisector line. Finally, the influence of the V-notch opening angle is made explicit, discussing also the relationship between the singularity orders and the solution of a Williams’ type sinusoidal eigen-equation.     

Rational Krylov methods for fractional diffusion problems on graphs

BIT Numerical Mathematics - In this paper we propose a method to compute the solution to the fractional diffusion equation on directed networks, which can be expressed in terms of the graph...     

Euler equations for Blake and Zisserman functional

We derive many necessary conditions for minimizers of a functional depending on free discontinuities, free gradient discontinuities and second derivatives, which is related to image segmentation.     

Reciprocal and variational theorems for nonlocal theory of viscoelastic materials

Summary We study some variational and reciprocal problems for viscoelastic materials with nonlocal constitutive equations and in particular with dissipative boundary conditions.

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Riassunto Si determinano alcuni teoremi variazionali e di reciprocitá per materiali viscoelastici con una dipendenza anche spaziale e con condizioni al contorno dissippative.

     

A multiplicity result for a class of nonlinear boundary value problems of the ambrosetti-prodi type

Summary In this paper we prove the existence of at least two solutions for a nonlinear elliptic boundary value problem of the Ambrosetti-Prodi type in the case when there exist two suitable supersolutions. This result follows from an abstract theorem of existence of multiple solutions which is a variant of a result due to Ambrosetti and Hess, [5].

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Riassunto In questo lavoro si prova che per un problema al contorno del tipo Ambrosetti-Prodi esistono almeno due soluzioni se esistono due opportune soprasoluzioni. Tale risultato discende da un teorema astratto di esistenza di soluzioni multiple che é una variante di un risultato di Ambrosetti ed Hess, [5].

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Paper written under the auspices of G.N.A.F.A., C.N.R., Italy.     

The unsatisfiability threshold revisited

The problem of determining the unsatisfiability threshold for random 3-SAT formulas consists in determining the clause to variable ratio that marks the experimentally observed abrupt change from almost surely satisfiable formulas to almost surely unsatisfiable. Up to now, there have been rigorously established increasingly better lower and upper bounds to the actual threshold value. In this paper, we consider the problem of bounding the threshold value from above using methods that, we believe, are of interest on their own right. More specifically, we show how the method of local maximum satisfying truth assignments can be combined with results for the occupancy problem in schemes of random allocation of balls into bins in order to achieve an upper bound for the unsatisfiability threshold less than 4.571. In order to obtain this value, we establish a bound on the q-binomial coefficients (a generalization of the binomial coefficients). No such bound was previously known, despite the extensive literature on q-binomial coefficients. Finally, to prove our result we had to establish certain relations among the conditional probabilities of an event in various probabilistic models for random formulas. It turned out that these relations were considerably harder to prove than the corresponding ones for unconditional probabilities, which were previously known.     

Restrictions and expansions of holomorphic representations

We compute tensor products of representations of the holomorphic discrete series of a Lie group G, or restrictions to some subgroup G′. A detailed study is done for the case of the conformal group O(4, 2).     

Principio di entropia e restrizioni termodinamiche per fluidi con memoria

Riassunto In questo lavoro si affrontano i problemi relativi alle restrizioni termodinamiche, imposte dal principio di entropia nella formulazione di Müller [1], per fluidi con memoria, mediante il metodo dei moltiplicatori di Lagrange.

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Summary In this work Author deals with the problems pertinent to the thermodynamic restrictions, which are due to principle of entropy in the formulation of Müller [1], for fluids with a memory, through the Lagrange multipliers.

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Lavoro eseguito nell'ambito del G.N.F.M. del C.N.R.     

Extending homeomorphisms from punctured surfaces to handlebodies

Let Hg be a genus g handlebody and MCG2n(Tg) be the group of the isotopy classes of orientation preserving homeomorphisms of Tg=∂Hg, fixing a given set of 2n points. In this paper we find a finite set of generators for , the subgroup of MCG2n(Tg) consisting of the isotopy classes of homeomorphisms of Tg admitting an extension to the handlebody and keeping fixed the union of n disjoint properly embedded trivial arcs. This result generalizes a previous one obtained by the authors for n=1. The subgroup turns out to be important for the study of knots and links in closed 3-manifolds via (g,n)-decompositions. In fact, the links represented by the isotopy classes belonging to the same left cosets of in MCG2n(Tg) are equivalent.