A note on the application of integrals involving cyclic products kernels

A l'estadística de processos estocàstics i camps aleatoris, una funció de moments o un cumulant d'un estimador de la funció de correlació o de la densitat espectral sovint pot contenir una integral amb un producte cíclic de nuclis. En aquest treball es defineix i s'investiga aquesta classe d'integrals i es demostra la desigualtat de Young-Hölder que permet estudiar el comportament asimptòtic de les esmentades integrals en la situació quan els nuclis depenen d'un pàràmetre. Es considera una aplicació al problema d'estimació de la funció de resposta en un sistema de Volterra.

Convergence of singular integrals with general measures

We show that L2-bounded singular integrals in metric spaces with respect to general measures and kernels converge weakly. This implies a kind of average convergence almost everywhere. For measures with zero density we prove the almost everywhere existence of principal values.

On the boundedness on inhomogeneous Lipschitz spaces of fractional integrals, singular integrals and hypersingular integrals associated to non-doubling measures on metric spaces

In this paper we prove T1 type necessary and sufficient conditions for the boundedness on inhomogeneous Lipschitz spaces of fractional integrals and singular integrals defined on a measure metric space whose measure satisfies a n-dimensional growth. We also show that hypersingular integrals are bounded on these spaces.

Rational first integrals in the Darboux theory of integrability in Cn

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Known and new results on absolute convergence of Fourier integrals

New sufficient conditions for representation of a function via the absolutely convergent Fourier integral are obtained in the paper. In the main result, Theorem 1.1, this is controlled by the behavior near infinity of both the function and its derivative. This result is extended to any dimension d &= 2.

Singular integrals on Ahlfors-David regular subsets of the Heisenberg group

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A characterization of two weight norm inequalities for maximal singular integrals

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Absolute convergence of Fourier integrals

In this survey, results on the representation of a function as an absolutely convergent Fourier integral are collected, classified and discussed. Certain applications are also given.

Indicators for the characterization of discrete Choquet integrals

Ordered weighted averaging (OWA) operators and their extensions are powerful tools used in numerous decision-making problems. This class of operator belongs to a more general family of aggregation operators, understood as discrete Choquet integrals. Aggregation operators are usually characterized by indicators. In this article four indicators usually associated with the OWA operator are extended to discrete Choquet integrals: namely, the degree of balance, the divergence, the variance indicator and Renyi entropies. All of these indicators are considered from a local and a global perspective. Linearity of indicators for linear combinations of capacities is investigated and, to illustrate the application of results, indicators of the probabilistic ordered weighted averaging -POWA- operator are derived. Finally, an example is provided to show the application to a specific context.

Global eriodicity and complete integrability of discrete dynamical systems

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Inverse Problems for multiple invariant curves

Planar polynomial vector fields which admit invariant algebraic curves, Darboux integrating factors or Darboux first integrals are of special interest. In the present paper we solve the inverse problem for invariant algebraic curves with a given multiplicity and for integrating factors, under generic assumptions regarding the (multiple) invariant algebraic curves involved. In particular we prove, in this generic scenario, that the existence of a Darboux integrating factor implies Darboux integrability. Furthermore we construct examples where the genericity assumption does not hold and indicate that the situation is different for these.

Large deviation for BSDE with subdifferential operator

In this paper we prove that the solution of a backward stochastic differential equation, which involves a subdifferential operator and associated to a family of reflecting diffusion processes, converges to the solution of a deterministic backward equation and satisfes a large deviation principle.

On the complexity of the Whitehead minimization problem

The Whitehead minimization problem consists in finding a minimum size element in the automorphic orbit of a word, a cyclic word or a finitely generated subgroup in a finite rank free group. We give the first fully polynomial algorithm to solve this problem, that is, an algorithm that is polynomial both in the length of the input word and in the rank of the free group. Earlier algorithms had an exponential dependency in the rank of the free group. It follows that the primitivity problem – to decide whether a word is an element of some basis of the free group – and the free factor problem can also be solved in polynomial time.

Avaluació dels algorismes d'encaminament per a una NoC amb topologia Mesh 2D

Aquest projecte presenta una avaluació de les diferents alternatives d'encaminament per a una NoC amb una topologia mesh 2D. Per tal d'exposar aquestes alternatives s'ha estudiat la composició d'un router implementat amb l'algorisme determinista XY i s'ha adaptat per tal que aquest suportés els algorismes parcialment adaptatius West First, North Last i Negative First. Un cop tenim els routers implementats es disposa un estudi dels diferents algorismes i com cadascun d'aquests actuen en front uns mateixos estímuls per tal de crear una comparativa entre ells que ens faciliti una elecció a priori.

The Euler characteristic of a category

The Euler characteristic of a finite category is defined and shown to be compatible with Euler characteristics of other types of object, including orbifolds. A formula is proved for the cardinality of a colimit of sets, generalizing the classical inclusion-exclusion formula. Both rest on a generalization of Rota's Möbius inversion from posets to categories.