Predicting trabecular bone microdamage initiation and accumulation using a non-linear perfect damage model

Studies evaluating the mechanical behavior of the trabecular microstructure play an important role in our understanding of pathologies such as osteoporosis, and in increasing our understanding of bone fracture and bone adaptation. Understanding of such behavior in bone is important for predicting and providing early treatment of fractures. The objective of this study is to present a numerical model for studying the initiation and accumulation of trabecular bone microdamage in both the pre- and post-yield regions. A sub-region of human vertebral trabecular bone was analyzed using a uniformly loaded anatomically accurate microstructural three-dimensional finite element model. The evolution of trabecular bone microdamage was governed using a non-linear, modulus reduction, perfect damage approach derived from a generalized plasticity stress-strain law. The model introduced in this paper establishes a history of microdamage evolution in both the pre- and post-yield regions

Net spaces and boundedness of integral operators

In this paper we introduce new functional spaces which we call the net spaces. Using their properties, the necessary and sufficient conditions for the integral operators to be of strong or weak-type are obtained. The estimates of the norm of the convolution operator in weighted Lebesgue spaces are presented.

Convolution inequalities in Lorentz spaces

In this paper we study boundedness of the convolution operator in different Lorentz spaces. In particular, we obtain the limit case of the Young-O'Neil inequality in the classical Lorentz spaces. We also investigate the convolution operator in the weighted Lorentz spaces. Finally, norm inequalities for the potential operator are presented.

Is the consumption-income ratio stationary? Evidence from linear and nonlinear panel unit root tests for OECD and non-OECD countries

This paper applies recently developed heterogeneous nonlinear and linear panel unit root tests that account for cross-sectional dependence to 24 OECD and 33 non-OECD countries’ consumption-income ratios over the period 1951–2003. We apply a recently developed methodology that facilitates the use of panel tests to identify which individual cross-sectional units are stationary and which are nonstationary. This extends evidence provided in the recent literature to consider both linear and nonlinear adjustment in panel unit root tests, to address the issue of cross-sectional dependence, and to substantially expand both time-series and cross sectional dimensions of the data analysed. We find that the majority (65%) of the series are nonstationary with slightly fewer OECD countries’ (61%) series exhibiting a unit root than non-OECD countries (68%).

A theoretical and practical study on linear reforms of dual taxes

We extend the linear reforms introduced by Pf¨ahler (1984) to the case of dual taxes. We study the relative effect that linear dual tax cuts have on the inequality of income distribution -a symmetrical study can be made for dual linear tax hikes-. We also introduce measures of the degree of progressivity for dual taxes and show that they can be connected to the Lorenz dominance criterion. Additionally, we study the tax liability elasticity of each of the reforms proposed. Finally, by means of a microsimulation model and a considerably large data set of taxpayers drawn from 2004 Spanish Income Tax Return population, 1) we compare different yield-equivalent tax cuts applied to the Spanish dual income tax and 2) we investigate how much income redistribution the dual tax reform (Act ‘35/2006’) introduced with respect to the previous tax.

Mather invariants in groups of piecewise-linear homeomorphisms

We describe the relation between two characterizations of conjugacy in groups of piecewise-linear homeomorphisms, discovered by Brin and Squier in [2] and Kassabov and Matucci in [5]. Thanks to the interplay between the techniques, we produce a simplified point of view of conjugacy that allows ua to easily recover centralizers and lends itself to generalization.

The simultaneous conjugacy problem in groups of piecewise linear functions

Guba and Sapir asked, in their joint paper [8], if the simultaneous conjugacy problem was solvable in Diagram Groups or, at least, for Thompson's group F. We give an elementary proof for the solution of the latter question. This relies purely on the description of F as the group of piecewise linear orientation-preserving homeomorphisms of the unit. The techniques we develop allow us also to solve the ordinary conjugacy problem as well, and we can compute roots and centralizers. Moreover, these techniques can be generalized to solve the same questions in larger groups of piecewise-linear homeomorphisms.

A public key encryption based on third order linear sequences

Based on third order linear sequences, an improvement version of the Diffie-Hellman distribution key scheme and the ElGamal public key cryptosystem scheme are proposed, together with an implementation and computational cost. The security relies on the difficulty of factoring an RSA integer and on the difficulty of computing the discrete logarithm.

Conjugacy of piecewise linear Lorenz map that expand on average

For piecewise linear Lorenz map that expand on average, we show that it admits a dichotomy: it is either periodic renormalizable or prime. As a result, such a map is conjugate to a ß-transformation.

Quasiconformal maps, analytic capacity, and non linear potentials

"Vegeu el resum a l'inici del document del fitxer adjunt."

Near-linear dynamics in KdV with periodic boundary conditions

Near linear evolution in Korteweg de Vries (KdV) equation with periodic boundary conditions is established under the assumption of high frequency initial data. This result is obtained by the method of normal form reduction.

The non-linear Dirichlet problem in Hadamard manifolds

We prove existence theorems for the Dirichlet problem for hypersurfaces of constant special Lagrangian curvature in Hadamard manifolds. The first results are obtained using the continuity method and approximation and then refined using two iterations of the Perron method. The a-priori estimates used in the continuity method are valid in any ambient manifold.

Geometry and physics of knots

KNOTS are usually categorized in terms of topological properties that are invariant under changes in a knot's spatial configuration(1-4). Here we approach knot identification from a different angle, by considering the properties of particular geometrical forms which we define as 'ideal'. For a knot with a given topology and assembled from a tube of uniform diameter, the ideal form is the geometrical configuration having the highest ratio of volume to surface area. Practically, this is equivalent to determining the shortest piece of tube that can be closed to form the knot. Because the notion of an ideal form is independent of absolute spatial scale, the length-to-diameter ratio of a tube providing an ideal representation is constant, irrespective of the tube's actual dimensions. We report the results of computer simulations which show that these ideal representations of knots have surprisingly simple geometrical properties. In particular, there is a simple linear relationship between the length-to-diameter ratio and the crossing number-the number of intersections in a two-dimensional projection of the knot averaged over all directions. We have also found that the average shape of knotted polymeric chains in thermal equilibrium is closely related to the ideal representation of the corresponding knot type. Our observations provide a link between ideal geometrical objects and the behaviour of seemingly disordered systems, and allow the prediction of properties of knotted polymers such as their electrophoretic mobility(5).

Homotopy Batalin-Vilkovisky algebras

This paper provides an explicit cofibrant resolution of the operad encoding Batalin-Vilkovisky algebras. Thus it defines the notion of homotopy Batalin-Vilkovisky algebras with the required homotopy properties. To define this resolution we extend the theory of Koszul duality to operads and properads that are defined by quadratic and linear relations. The operad encoding Batalin-Vilkovisky algebras is shown to be Koszul in this sense. This allows us to prove a Poincaré-Birkhoff-Witt Theorem for such an operad and to give an explicit small quasi-free resolution for it. This particular resolution enables us to describe the deformation theory and homotopy theory of BV-algebras and of homotopy BV-algebras. We show that any topological conformal field theory carries a homotopy BV-algebra structure which lifts the BV-algebra structure on homology. The same result is proved for the singular chain complex of the double loop space of a topological space endowed with an action of the circle. We also prove the cyclic Deligne conjecture with this cofibrant resolution of the operad BV. We develop the general obstruction theory for algebras over the Koszul resolution of a properad and apply it to extend a conjecture of Lian-Zuckerman, showing that certain vertex algebras have an explicit homotopy BV-algebra structure.

Norm convolution inequalities in Lebesgue spaces

We obtain upper and lower estimates of the (p; q) norm of the con-volution operator. The upper estimate sharpens the Young-type inequalities due to O'Neil and Stepanov.