Preprints de Matemàtiques - Mathematics Preprint Series

URI permanent per a aquesta col·leccióhttps://hdl.handle.net/2445/151238

La sèrie Preprints de Matemàtiques, Mathematics Preprint Series, és una col·lecció de publicacions realitzades pel Personal Docent i Investigador de la Facultat de Matemàtiques i de l'Institut de Matemàtiques de la Universitat de Barcelona (IMUB), en col·laboració amb investigadors convidats per l'IMUB.

La col·lecció, impulsada pel professor Eduard Casas Alvero, abasta de l'any 1986 fins el 2009 i correspon a la versió d'articles científics sense revisió entre parells, alguns dels quals van ser publicats en una revista acadèmica i científica.

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Mostrant 1 - 20 de 36

Product logic and the deduction theorem
(Universitat de Barcelona, 1997) Adillón, Román; Verdú, B. (Buenaventura)
In this paper we prove the following negative result: Product Logic [9] does not have the Deduction Theorem, that is, there is no binary defined connective in the language of Product Logic such that the Deduction Theorem is satisfied with respect to it. We prove this theorem mainly by using algebraic methods: we prove that Product Logic is algebraizable, that the variety of Product Algebras is its equivalent quasivariety semantics and that this variety has no equationally definable principal congruences.
On the contributions of Helena Rasiowa to mathematical logic
(Universitat de Barcelona, 1996) Font, Josep M.
Let me begin with sorne personal reminiscences. For me, writing a paper on the contributions of HELENA RASIOWA (1917-1994) to Mathematical Logic might be the result of several unexpected coincidences1 . My relationship with RASIOWA is academic rather than personal. Her book An algebraic approach to non-classical logics [41] is one the main sources that might be found guilty of my professional dedication to research in Algebraic Logic, if sorne
Hilbert polynomials over artinian local rings
(Universitat de Barcelona, 1996) Blancafort, Cristina; Nollet, Scott, 1962-
This paper characterizes Hilbert functions and Hilbert polynomials of standard algebras over an Artinian ring R0.
On the depth of the fiber cone of filtrations
(Universitat de Barcelona, 1996) Cortadellas Benítez, Teresa; Zarzuela, Santiago
Stochastic Volterra equations in the plane: smoothness of the law
(Universitat de Barcelona, 1997) Rovira Escofet, Carles; Sanz-Solé, Marta
We give sufficient conditions ensuring the smoothness of the density for the law of the solution of Volterra equations in the plane. One of the motivations for the study of such class of equations is provided by non-linear hyperbolic stochastic partial differential equations appearing in the construction of some path-valued processes on manifolds. The proof is based on Malliavin Calculus.
Global efficency
(Universitat de Barcelona, 1996) Corcuera Valverde, José Manuel; Oller i Sala, Josep Maria
In this paper the global behaviour of an estimator is studied in framework of Intrinsic Analysis, (7). Two indices of performance of an estimator in a bounded region are analyzed: the average of the intrinsic risk (the loss function is the squared Rao distance) and the maximum risk. The Riemannian volume, provided by the Fisher metric on the manifold associated with the parametric model, allows us to take an average of the intrinsic risk. Cramér-Rao type integral inequalities for the integrated mean squared Rao distance of estimators are derived using variational methods, extending the work of éencov, [3]. Additionally, lower bounds for the maximum risk are also derived, by using integral expressions.
Intrinsic analysis of the statistical estimation
(Universitat de Barcelona, 1996) Oller i Sala, Josep Maria; Corcuera Valverde, José Manuel
The parametric statistical models with suitable regularity conditions have a natural Riemannian manifold structure, given by the information metric. Since the parameters are merely labels for the probability measures, an inferential statement should be formulated through intrinsic objects, invariant under reparametrizations. In this context the estimators will be random objects valued on the manifold corresponding to the statistical model. In spite of these considerations, classical measures of an estimator's performance, like the bias and the mean square error, are clearly dependent on the statistical model parametrizations. In this paper the authors work with extended notions of mean value and moments of random objects which take values on a Hausdorff and connected manifold, equipped with an affine connection. In particular, the Riemannian manifold case is considered. This extension is applied to the bias and the mean square error study in statistical point estimation theory. Under this approach an intrinsic version of the Cramer-Rao lower bound is obtained: a lower bound, which depends on the intrinsic bias and the curvature of the statistical model, for the mean square of the Rao distance, the invariant measure analogous to the mean square error. Further, the behavior of the mean square of the Rao distance of an estimator when conditioning with respect to a sufficient statistic is considered, obtaining intrinsic versions of the Rao-Blackwell and Lehmann-Scheffe theorems. Asymptotic properties complete the study.
Higuer bott Chern forms and Beilinson's regulator
(Universitat de Barcelona, 1996) Burgos Gil, José I.; Wang, Steve
In this paper, we prove a Gauss-Bonnet theorem for the higher algebraic K-theory of smooth complex algebraic varieties. To each exact n-cube of hermitian vector bundles, we associate a higher Bott-Chen form, generalizing the Bott-Chern forms associated to exact sequences. These forms allow us to define characteristic classes from K-theory to absolute Hodge cohomology. Then we prove that these characteristic classes agree with Beilinson's regulator map.
A characterization of monotone and regular divergences
(Universitat de Barcelona, 1996) Corcuera Valverde, José Manuel; Giummolè, F
In this paper we characterize the local structure of monotone and regular divergences, which include f-divergences as a particular case, by giving their Taylor expansion up to fourth order. We extend a previous result obtained by Čencov, using the invariant properties of Amari's α-connections.
Wedge cancellation of certain mapping cones
(Universitat de Barcelona, 1990) Llerena, Irene
A distance based approach to discriminant analysis and its properties
(Universitat de Barcelona, 1991) Cuadras, C. M. (Carlos María)
A general distance based method for allocating an observation to one of several known populations, on the ha.sis of both continuous and discrete explanatory variables, is proposed and studied. This method depends on a given statistical distance between observations, and leads to sorne classic discriminant rules by taking suitable distances. The error rates can be easily computed and, unlike other distance classification rules, the prior probabilities can be taken into account.
Composition of large deviation principles and applicatons
(Universitat de Barcelona, 1990) Millet, Annie; Sanz-Solé, Marta; Nualart, David, 1951-
The purpose of this note is to present a general result on the composition of large deviation principies (Theorem 1.2) and to apply this theorem to obtain large deviations estimates for solutions of anticipating stochastic differential equations. This problem was suggested to us by G. Benarous and we would like to thank him for his stimulating remaks...
Small perturbartions in a hyperbolic stochastic partial differential equation
(Universitat de Barcelona, 1996) Márquez, David (Márquez Carreras); Sanz-Solé, Marta
Interpolation theorems of some weighted quasi-Banach spaces
(Universitat de Barcelona, 1990) Hernández, Eugenio; Soria, Javier, 1962-
We give severa) results concerning weighted Hardy's inequalities for the case q < 1, and using some techniques based upon a reiteration theorem, we study the weighted version of severa! int.erpolation theorems for quasi-Banach spaces.
Anticipating stochastic Volterra equations
(Universitat de Barcelona, 1996) Alòs, Elisa; Nualart, David, 1951-
A four-valued modal logic arising from Monteiro's last algebras
(Universitat de Barcelona, 1989) Font, Josep M.; Rius Font, Miquel
We study the class of abstract logics projectively generated by the class of tetravalent modal algebras. They are modal logics and they turn out to be four-valued in the sense that they can be characterized using the natural logic on the four-element tetravalent modal algebra which generates this variety together with sorne special class of homomorphisms. We also characterize them by their abstract properties and prove a completeness theorem.
Stochastic differential equations with boundary conditions
(Universitat de Barcelona, 1990) Nualart, David, 1951-; Pardoux, Etienne
On Rao distance asymptotic distribution
(Universitat de Barcelona, 1989) Burbea, Jacob; Oller i Sala, Josep Maria
This paper is concerned with the study of the asymptotic properties of Rao distance maximum-likelihood estimation obtained from two independent samples of two statistical populations, under certain regularity conditions. These results allow the construction, by meaos of the Rao distance, of a statistical test to compare different populations, which may be regarded as an alternative to the standard likelihood ratio test. Furthermore, a geometrical model is supplied which can be used to obtain graphical outputs through numerical taxonomy methods or multidimensional scaling techniques. Finally, sorne of the previously-mentioned methods are illustrated by meaos of a specific example based on the univariate normal distribution.
Integrator properties of the Skorohod integral
(Universitat de Barcelona, 1990) Jolis Giménez, Maria; Sanz-Solé, Marta
Generalization of browder's fixed point theorem and its applications
(Universitat de Barcelona, 1989) Marchi, Ezio; Martínez Legaz, Juan Enrique
From an infinite dimensional version of a generalization, dueto Peleg, of the Knaster-Kuratowski-Mazurkiewicz's theorem, we obtain a generalization of Browder's fixed point theorem, for multi-valued mappings from the product of a finite family of non-empty compact convex sets ( each in a Hausdorff topological vector space) into each of its factors. By applying this thorem, we deduce sorne Ky Fan type inequalities, from one of which a generalization of the Ky Fan's intersection theorem on sets with convex sections is obtained.

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