31 research outputs found
Study of the boundary conditions describing the contact with a well-stirred fluid
No full textThe authors study the asymptotic behavior of a 1-D diffraction problem when the conductivity of
one of the two media in contact becomes infinite. It is established, by means of heat potentials
and Laplace transforms, that the temperature of the good conductor (well-stirred fluid) is spatially
constant and the contact conditions between the two media, involving time derivatives, are found.
The convergence of the solution of the diffraction problem to the solution of the well-stirred
problem in the L1 norm is proved and an upper bound for the difference between these two
solutions is establishe
Generalized Cauchy means
No full textGiven two means M and N, the operator MM,NMM,N assigning to a given mean μ the mean MM,N(μ)(x,y)=M(μ(x,N(x,y)),μ(N(x,y),y)) was defined in Berrone and Moro (Aequationes Math 60:1–14, 2000) in connection with Cauchy means: the Cauchy mean generated by the pair f, g of continuous and strictly monotonic functions is the unique solution μ to the fixed point equation MA(f),A(g)(μ)=μ, where A(f) and A(g) are the quasiarithmetic means respectively generated by f and g. In this article, the operator MM,NMM,N is studied under less restrictive conditions and a general fixed point theorem is derived from an explicit formula for the iterates MnM,NMM,Nn . The concept of class of generalized Cauchy means associated to a given family of mixing pairs of means is introduced and some distinguished families of pairs are presented. The question of equality in these classes of means remains a challenging open problem.Fil: Berrone, Lucio Renato. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin
The Aumann functional equation for general weighting procedures
No full textThe functional equation of composite type
M(M(x; M(x; y)); M(M(x; y); y)) = M(x; y)
arose in the course of the studies on the problem of extension and restriction of the number of arguments of a mean M performed by G. Aumann at the third decade of the past century. A solution to (1) in the analytic case was ulteriorly obtained by Aumann himself and remained as a noteworthy characterization of analytic quasiarithmetic means. An ample generalization of equation (1) which involves general weighting operators is considered in this paper. Under mild conditions on the regularity of the involved means, the general solution to this generalized equation is obtained for a particularly tractable class of weighting operators.Fil: Berrone, Lucio Renato. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Cientifico Tecnológico Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingenieria y Agrimensura. Escuela de Ingenieria Electrónica. Laboratorio de Acústica y Electroacústica; Argentin
Solution of a functional equation related to the Pythagorean Proposition
No full textLa ecuación funcional f(x + y) = f(x) + f(y) + 2f(Φ(x, y)), x, y > 0, es resuelta para pares (f, Φ) constituidos por una función estrictamente monótona y un Lagrangiano suficientemente regular Φ. Algunas preguntas formuladas en un reciente artículo de R. Ger ([5]) son respondidas.The functional equation f(x + y) = f(x) + f(y) + 2f(Φ(x, y)), x, y > 0, is solved for pairs (f, Φ) constituted by a strictly monotonic function f and a sufficiently regular Lagrangian mean Φ. Some related questions stated in a recent paper by R. Ger ([5]) are answered.Fil: Berrone, Lucio Renato. Universidad Nacional de Rosario; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin
P-means and the solution of a functional equation involving Cauchy differences
No full textSolutions to the functional equation
f(x+y)−f(x)−f(y)=2f(Φ(x,y)),x,y>0,
are sought for the admissible pairs (f,Φ)(f,Φ) constituted by a strictly monotonic function f and a strictly increasing in both variables mean ΦΦ . A related class of means, P-means, is introduced, studied and then employed in solving (1) under additional hypotheses on ΦΦ . For instance, Ger has proved that the unique P-mean which is also quasiarithmetic is the geometric mean G(x,y)=xy−−√G(x,y)=xy . An elementary proof to this result is given in this paper. Moreover, as a consequence of a fundamental result on the uniqueness of representation of P-means it is proved that the geometric mean G is the unique homogeneous P-mean.Fil: Berrone, Lucio Renato. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingenieria y Agrimensura. Escuela de Ingenieria Electrónica. Laboratorio de Acústica y Electroacústica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Cientifico Tecnológico Rosario; Argentin
Weighting by Iteration: The Case of Ryll-Nardzewski’s Iterations
No full textAczél’s and Ryll-Nardzewski’s dyadic iterations are iterative procedures which associate to a given mean M a family of means { Md: d∈ Dyad ([ 0 , 1 ]) } parameterized by Dyad ([ 0 , 1 ]) , the dyadic fractions of the interval [0, 1]. Aczél’s iterations exhibit a nice characteristic: when M is a strict continuous mean and x < y, the set { Md(x, y) : d∈ Dyad ([ 0 , 1 ]) } is dense in [x, y]. This fact is in the basis of the construction of an algorithm of weighting for an ample class of means. In pursuit of a similar algorithm using Ryll-Nardzewski’s instead of Aczél’s iterations, a series of obstacles is found, which motivates the detailed study of these last conducted along this paper. Among other result of interest, several conditions on the mean M are identified which make viable a weighting algorithm based on these iterations.Fil: Berrone, Lucio Renato. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura. Escuela de Ingeniería Electrónica. Laboratorio de Acústica y Electroacústica; Argentin
M-affine functions composing Sturm–Liouville families
No full textGiven an n-variable mean M defined on a real interval I, an M-affine function is a solution to the functional equation [Equation not available: see fulltext.]When M is a quasilinear mean, the set of continuous M-affine functions is a Sturm–Liouville family on every compact interval [a, b] ⊆ I; i.e., for every α, β∈ [a, b] , there exists an M-affine function f such that f(a) = α and f(b) = β. The validity of the converse statement is explored in this paper and several consequences are derived from this study. New characterizations of quasilinear means and the solution to Eq. (1) under suitable conditions are among the more important ones.Fil: Berrone, Lucio Renato. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; ArgentinaFil: Sbergamo, Gerardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentin
On the number of finite topological spaces
No full textIn this paper we deal with the problem of enumerating the finite topological spaces, studying the enumeration of a restrictive class of them. By employing simple techniques, we obtain a recursive lower bound for the number of topological spaces on a set of n elements. Besides we prove some collateral results, among which we can bring a new proof (Cor. 1.5) of the fact that p(n) – the number of partitions of the integer n – is the number of non-isomorphic Boolean algebras on a set of n elements.</span
Lifting a circular membrane by unitary forces
No full textLet Ω be a convex membrane. We lift certain parts Γ of its boundary by means of unitary forces while the remaining parts are maintained at level 0. Call u[Γ] the position that the such lifted membrane assumes. When the parts Γ are varying on ∂Ω so that their total lenght C is preserved, it has been conjectured that the functional Γ ||u(Γ)||p attain its maximum value for a certain conected arc of lenght C. In this paper we present a proof of this conjecture for the case in which Ω is a circle and p = 1
