Revistas académicas de la Universidad Católica del Norte
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A weakened version of Davis-Choi-Jensen’s inequality for normalised positive linear maps
No full textIn this paper we show that the celebrated Davis-Choi-Jensen’s inequality for normalised positive linear maps can be extended in a weakened form for convex functions. A reverse inequality and applications for important instances of convex (concave) functions are also given
Spectral properties of horocycle flows for compact surfaces of constant negative curvature
No full textWe consider flows, called Wu flows, whose orbits are the unstable manifolds of a codimension one Anosov flow. Under some regularity assumptions, we give a short proof of the strong mixing property of Wuflows and we show that Wu flows have purely absolutely continuous spectrum in the orthocomplement of the constant functions. As an application, we obtain that time changes of the classical horocycle flows for compact surfaces of constant negative curvature have purely absolutely continuous spectrum in the orthocomplement of the constant functions for time changes in a regularity class slightly less than C2. This generalises recent results on time changes ofhorocycle flows
About an existence theorem of the Henstock-Fourier transform
No full textWe show that if f is lying on the intersection of the space of Henstock-Kurzweil integrable functions and the space of the bounded variation functions in the neighborhood of ± ∞, then its Fourier Transform exists in all R. This result is more general than the classical result which enunciates that if f is Lebesgue integrable, then the Fourier Transform of f exists in all R, because we also have proved that there are functions which belong to the intersection of the space of the Henstock-Kurzweil integrable functions and the space of the bounded variation functions which are not Lebesgue integrable
The modes of posterior distributions for mixed linear models
No full textMixed linear models, also known as two-level hierarchical models, are commonly used in many applications. In this paper, we consider the marginal distribution that arises within a Bayesian framework, when the components of variance are integrated out of the joint posterior distribution. We provide analytical tools for describing the surface of the distribution of interest. The main theorem and its proof show how to determine the number of local maxima, and their approximate location and relative size. This information can be used by practitioners to assess the performance of Laplace-type integral approximations, to compute possibly disconnected highest posterior density regions, and to custom-design numerical algorithms
Occupation times sequences and martingales of simple random walks on the real line
No full textGiven a simple random walk on the real line, we consider the sequences of occupation times on states and associate to them martingales defined by the moments of first order of this random walk. We deduce by this way recurrent relations for the expectations of the occupation times in states before a given time, and then remarkable identities for the expectations of the absolute values of the random walk
The natural vector bundle of the set of multivariate density functions
No full textWe find a description of the set of multivariate density functions with given marginals and introduce an associated vector bundle. The interest for the probability theory is restricted to the nonnegative elements in the sets of the derived vector bundle. The fiber is the space of all correlation measures among a multivariate density function and its unidimensional marginals.
Inertial relativity - a functional analysis review
No full textThe theory of special relativity (TSR) exhibits an unquestionable success, at the expense of an unresolved axiomatic conflict with functional analysis and operator theory, as this paper demonstrates. These mathematical disciplines —amongst the newest developments in the field— could not possibly be incorporated into the original formulation of the TSR because they were in an incipient state at the turn of the 20th century when the TSR was being formulated, maturing only decades later
Sequential S?-compactness in L-topological spaces
No full textIn this paper, a new notion of sequential compactness is introduced in L-topological spaces, which is called sequentially S?-compactness. If L = [0, 1], sequential ultra-compactness, sequential N-compactness and sequential strong compactness imply sequential S?-compactness, and sequential S?-compactness implies sequential F-compactness. The intersection of a sequentially S?-compact L-set and a closed L-set is sequentially S?-compact. The continuous image of an sequentially S?- compact L-set is sequentially S?-compact. A weakly induced L-space (X, T ) is sequentially S?-compact if and only if (X, [T ]) is sequential compact. The countable product of sequential S?-compact L-sets is sequentially S?-compact
Generalizations of the Orlicz - Pettis theorem
No full textThe Orlicz-Pettis Theorem for locally convex spaces asserts that a series in the space which is subseries convergent in the weak topology is actually subseries convergent in the original topology of the space. A subseries convergent series can be viewed as a multiplier convergent series where the terms of the series are multiplied by elements of the scalar sequence space m0 of sequences with finite range. In this paper we show that the conclusion of the Orlicz-Pettis Theorem holds (and can be strengthened) if the multiplier space m0 is replaced by a sequence space with the signed weak gliding hump property
An extension of the poincaré compactification and a geometric interpretation
No full textOur purpose in this paper is to understand the geometry of the Poincaré compactification and to apply this technique to prove that there exists a Poincaré compactification of vector fields defined by rational functions and of vector field that are the quotient of some power of polynomial. We will give also a global expressions for the Poincaré vector field associated. Furthermore, we summarize these results proving that there exist a Poincaré vector field for any vector field whose rate of growth at infinity of each component is not bigger than a polynomial growth