Transformations of differentiable functions
Transformations which preserve convexity.
Translation of nonstandard definitions to standard ones
Transport equations with partially velocities
We prove the uniqueness of weak solutions for the Cauchy problem for a class of transport equations whose velocities are partially with bounded variation. Our result deals with the initial value problem where is the vector fieldwith a boundedness condition on the divergence of each vector field . This model was studied in the paper [LL] with a regularity assumption replacing our hypothesis. This settles partly a question raised in the paper [Am]. We examine the details of the argument of...
Trend to equilibrium and particle approximation for a weakly selfconsistent Vlasov-Fokker-Planck equation
We consider a Vlasov-Fokker-Planck equation governing the evolution of the density of interacting and diffusive matter in the space of positions and velocities. We use a probabilistic interpretation to obtain convergence towards equilibrium in Wasserstein distance with an explicit exponential rate. We also prove a propagation of chaos property for an associated particle system, and give rates on the approximation of the solution by the particle system. Finally, a transportation inequality...
Trends to equilibrium in total variation distance
This paper presents different approaches, based on functional inequalities, to study the speed of convergence in total variation distance of ergodic diffusion processes with initial law satisfying a given integrability condition. To this end, we give a general upper bound “à la Pinsker” enabling us to study our problem firstly via usual functional inequalities (Poincaré inequality, weak Poincaré,…) and truncation procedure, and secondly through the introduction of new functional inequalities ....
Triangular maps with the chain recurrent points periodic.
Triangular norm-based addition preserving linearity of T-sums of linear fuzzy intervals.
The addition of fuzzy intervals based on a triangular norm T is studied. It is shown that the addition based on a t-norm T weaker than the Lukasiewicz t-norm TL acts on linear fuzzy intervals just as the TL-based addition. Some examples are given.
Trichotomy, stability, and oscillation of a fuzzy difference equation.
Turán-type inequalities for some -special functions.
Turán-type inequalities for some special functions.
Turbulent maps and their ω-limit sets
One-dimensional turbulent maps can be characterized via their ω-limit sets [1]. We give a direct proof of this characterization and get stronger results, which allows us to obtain some other results on ω-limit sets, which previously were difficult to prove.
Two classes of Darboux-like, Baire one functions of two variables
Among the many characterizations of the class of Baire one, Darboux real-valued functions of one real variable, the 1907 characterization of Young and the 1997 characterization of Agronsky, Ceder, and Pearson are particularly intriguing in that they yield interesting classes of functions when interpreted in the two-variable setting. We examine the relationship between these two subclasses of the real-valued Baire one defined on the unit square.
Two constructions of the real numbers via alternating series.
Two convergence theorems for Henstock-Kurzweil integrals and their applications to multiple trigonometric series
We establish two new norm convergence theorems for Henstock-Kurzweil integrals. In particular, we provide a unified approach for extending several results of R. P. Boas and P. Heywood from one-dimensional to multidimensional trigonometric series.
Two inequalities for means.
Two inequalities for series and sums
In this paper we refine an inequality for infinite series due to Astala, Gehring and Hayman, and sharpen and extend a Holder-type inequality due to Daykin and Eliezer.
Two inequalities of simpson type for quasi-convex functions and applications.
Two kinds of chaos and relations between them.
Two large subsets of a functional space.