1,721,630 research outputs found
On the Hausdorff Convergence of Functions of One Real Variable
No full textLet X be a bounded subset of the real line and let Y be a metric space. In the function space C(X, Y), we give an intrinsic characterization of the functions f for which the neighborhood system in the Hausdorff topology coincides with the neighborhood system in the uniform convergence topology. (C) 2001 Elsevier Science B.V. All rights reserved
On a theorem about orderability
No full textThe purpose of this note is proving that a locally connected space with
a continuous selection is orderable
Interface pinning and slow ordering kinetics on infinitely ramified fractal structures
No full textWe investigate the time-dependent Ginzburg-Landau (TDGL) equation for a nonconserved order parameter on an infinitely ramified (deterministic) fractal lattice employing two alternative methods: the auxiliary field approach and a numerical method of integration of the equations of evolution. In the first case the domain size evolves with time as L(t)similar to t(l/dw), where d(w) is the anomalous random-walk exponent associated with the fractal and differs from the normal value 2, which characterizes all Euclidean lattices. Such a power-law growth is identical to the one observed in the study of the spherical model on the same lattice, but fails to describe the asymptotic behavior of the numerical solutions of the TDGL equation for a scalar order parameter. In fact, the simulations pet-formed on a two dimensional Sierpinski carpet indicate that, after an initial stage dominated by a curvature reduction mechanism in the manner of Allen and Cahn [Acta. Metall. 27, 1085 (1979)], the system enters in a regime where the domain walls between competing phases rue pinned by lattice defects. The lack of translational invariance determines a rough free-energy landscape, the existence of many metastable minima, and the suppression of the marginally stable modes, which in translationally invariant systems lead to power-law growth and self-similar patterns. On fractal structures, as the temperature vanishes the evolution is frozen since only thermally activated processes can sustain the growth of pinned domain
Soft Matter and Density Functional Theory Project presented by Prof. Rene van Roiji Nederlands
No full textIl progetto e' stato approvat
Hausdorff topology and uniform convergence topology in spaces of continuous functions
No full textThe local and global coincidence of the Hausdorff topology and the uniform
convergence topology on the hyperspace consisting of closed graphs of
multivalued (or continuous) functions is related to the existence of continuous
functions which fail to be uniformly continuous. The problem of the coincidence of these topologies on C(X,Y) is investigated for
some classes of spaces: topological groups, zero-dimensional metric spaces,
omega_mu-metric spaces
On the compactness of minimal spectrum
Get PDFLet A be a commutative ring with 1. Denote by Spec(A) the set of all prime ideals of A equipped with the hull-kernel topology, by Min(A) the subspace consisting of minimal prime ideals.
We give a new characterization of the compactness of Min(A), which seems to give more light to the topological situation; this characterization, among other things, allows us to show that the
class of (weakly) Baer rings coincides with the class of rings such that:
1) their minimal spectrum is compact, and
2) every prime ideal contains a unique minimal prime ideal.
We always deal with rings without non-zero nilpotents; but of course all purely topological results are independent of this hypothesis
A complete omega(mu)-metric space is not necessarily supercomplete
No full textUnder the diamond axiom, there exists a complete omega_mu-metric space which is not supercomplete. If omega_mu is not a weakly inaccessible cardinal, we provide an example in ZFC
Tracer diffusion of hard-sphere binary mixtures under nano-confinement
Get PDFThe physics of diffusion phenomena in nano- and microchannels has attracted a lot of attention in recent years, due to its close connection with many technological, medical, and industrial appli- cations. In the present paper, we employ a kinetic approach to investigate how the confinement in nanostructured geometries affects the diffusive properties of fluid mixtures and leads to the appearance of properties different from those of bulk systems. In particular, we derive an expression for the friction tensor in the case of a bulk fluid mixture confined to a narrow slit having undulated walls. The boundary roughness leads to a new mechanism for transverse diffusion and can even lead to an effective diffusion along the channel larger than the one corresponding to a planar channel of equivalent section. Finally, we discuss a reduction of the previous equation to a one dimensional effective diffusion equation in which an entropic term encapsulates the geometrical information on the channel shape
A continuity result in calculus
No full textWe answer to a question of D.Repovs and P.V.Semenov about an application of the theory of selections in elementary real analysis in Abstr. Amer. Math. Soc. by proving that the ccondition of local compactness may be removed
Critical Adsorption and Finite-geometry Effects
No full textThe nature of adsorption of fluids confined in pores in the proximity of the bulk critical point is investigated by means of Landau phenomenological models and non local free energy functionals.
We also discuss the possibility of observing experimentally the critical exponents for the adsorption in the case of finite-geometry systems
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