On the existence of fractal strings whose set of dimensions of fractality is not perfect

In this paper we give an example of a nonlattice self-similar fractal string such that the set of real parts of their complex dimensions has an isolated point. This proves that, in general, the set of dimensions of fractality of a fractal string is not a perfect set.

Solubility, Density, Refractive Index, and Viscosity for the Polyhydric Alcohol + CsBr + H2O Ternary Systems at Different Temperatures

The solubility, density, refractive index, and viscosity data for the ethylene glycol + CsBr + H2O, 1,2-propanediol + CsBr + H2O, and glycerin + CsBr + H2O ternary systems have been determined at (288.15, 298.15, and 308.15) K. In all cases, the solubility of CsBr in aqueous solutions was decreased significantly due to the presence of polyhydric alcohol. The liquid–solid equilibrium experimental data were correlated using the NRTL (nonrandom two-liquid) activity coefficient model, considering nondissociation of the dissolved salt in the liquid phase, and new interaction parameters were estimated. The mean deviations between calculated and experimental compositions were low, showing the good descriptive quality and applicability of the NRTL model. The refractive indices, densities, and viscosities for the unsaturated solutions of the three ternary systems have also been measured at three temperatures. Values for all of the properties were correlated with the salt concentrations and proportions of polyhydric alcohol in the solutions.

A note on the real projection of the zeros of partial sums of Riemann zeta function

This paper proves that the real projection of each simple zero of any partial sum of the Riemann zeta function ζn(s):=∑nk=11ks,n>2 , is an accumulation point of the set {Res : ζ n (s) = 0}.

El edificio urbano como gesto cívico. A propósito de la obra de Francisco Candel

La relación dialéctica entre la casa y la ciudad es el tema de este breve discurso, partiendo del modelo clásico, que Alberti formula y describe, y pasando a través de los sucesivos modelos, romántico burgués, moderno y posmoderno, para llegar a definir el sentido, en el entorno actual, de la casa entre medianeras que la limitan jurídica y físicamente. La posibilidad de observar el canon moderno, sin renunciar a una convincente inserción del modelo en la ciudad de ascendencia burguesa, se argumenta por medio de dos ejemplos tomados del mismo arquitecto, Francisco Candel Jiménez, en el ensanche de una ciudad de provincias, Albacete, tratando de demostrar que se puede ser rigurosamente moderno en el lenguaje y, a la vez, obediente a los límites urbanos establecidos. En el primer caso, un edificio de tres plantas para vivienda y estudio de arquitectura en entreplanta, la modestia del entorno no impide que el edificio inscrito en él sea a la vez altamente singular sin sustraerse a las reglas del planeamiento oficial. En el segundo, edificio de viviendas en cinco alturas más ático, y “atendiendo a su carácter urbano y a la actualidad de soluciones técnicas y constructivas”, despliega una amplia ceremonia de cortesía, que, por medio de los recursos propios de una avanzada high-tech, juega con los ritmos de su doble límite, doméstico y urbano, y hace que su modernidad radical eleve la dignidad del vecindario urbano que lo acompaña, sin alzar la voz, pero transmitiendo una lección de arquitectura que hace ciudad.

On a conjecture of Lapidus and van Frankenhuysen

In this paper it is shown that a conjecture of Lapidus and van Frankenhuysen of 2003 on the existence of a vertical line such that the density of the complex dimensions of nonlattice fractal strings with M scaling ratios off this line vanishes in the limit as M→∞, fails on the class of nonlattice self-similar fractal strings.

New glimpses on convex infinite optimization duality

Given a convex optimization problem (P) in a locally convex topological vector space X with an arbitrary number of constraints, we consider three possible dual problems of (P), namely, the usual Lagrangian dual (D), the perturbational dual (Q), and the surrogate dual (Δ), the last one recently introduced in a previous paper of the authors (Goberna et al., J Convex Anal 21(4), 2014). As shown by simple examples, these dual problems may be all different. This paper provides conditions ensuring that inf(P)=max(D), inf(P)=max(Q), and inf(P)=max(Δ) (dual equality and existence of dual optimal solutions) in terms of the so-called closedness regarding to a set. Sufficient conditions guaranteeing min(P)=sup(Q) (dual equality and existence of primal optimal solutions) are also provided, for the nominal problems and also for their perturbational relatives. The particular cases of convex semi-infinite optimization problems (in which either the number of constraints or the dimension of X, but not both, is finite) and linear infinite optimization problems are analyzed. Finally, some applications to the feasibility of convex inequality systems are described.