We endow the set of real numbers with a family of fuzzy quasi-metrics, in the sense of George and Veeramani, which are compatible with the Sorgenfrey topology. Although these fuzzy quasi-metrics are not deduced explicitly from a quasi-metric, they possess interesting properties related to completeness. For instance, we prove that they are balanced and complete in the sense of Doitchinov and tha...

We describe a non-Arrhenius mechanism for slowing down of dynamics that is inherent to the high dimensionality of the phase space. We show that such a mechanism is at work both in a family of mean-field spin-glass models without any domain structure and in the case of ferromagnetic domain growth. The marginality of spin-glass dynamics, as well as the existence of a ‘quasi equilibrium regime’ ca...

In a recent paper [5], we introduced a classes of derived equivalences called almost ν-stable derived equivalences. The most important property is that an almost ν-stable derived equivalence always induces a stable equivalence of Morita type, which generalizes a well-known result of Rickard: derived-equivalent self-injective algebras are stably equivalent of Morita type. In this paper, we shall...

We introduce and characterize the class of multivariate quasi-copulas with quadratic sections in one variable. We also present and analyze examples to illustrate our results.

We study the relationship between multivariate quasi-copulas and measures that they may or may not induce on [0, 1]n . We first study the mass distribution of the pointwise best possible lower bound for the set of n-quasi-copulas for n ≥ 3. As a consequence, we show that not every n-quasi-copula induces a signed measure on [0, 1]n . © 2010 Elsevier B.V. All rights reserved.

Let us consider the differential equation ẋ = (A+ εQ(t, ε))x, |ε| ≤ ε0, where A is an elliptic constant matrix and Q depends on time in a quasi-periodic (and analytic) way. It is also assumed that the eigenvalues of A and the basic frequencies of Q satisfy a diophantine condition. Then it is proved that this system can be reduced to ẏ = (A∗(ε) + εR∗(t, ε))y, |ε| ≤ ε0, where R∗ is exponentially ...