One of recent achievements in the field of nonlinear H∞ optimal control theories for Euler-Lagrange systems is the analytic solution to the Hamilton-JacobiIsaccs (HJI) equation associated to the so-called nonlinear H∞ inverse-optimal control [1]. In this paper, we address the problem of nonlinear H∞ optimal control design for an Euler-Lagrange system, rather than the inverse-optimal problem. By...

We give conditions on Gromov-Hausdorff convergent inverse systems of metric measure graphs which imply that the measured Gromov-Hausdorff limit (equivalently, the inverse limit) is a PI space i.e., it satisfies a doubling condition and a Poincaré inequality in the sense of Heinonen-Koskela [HK96]. The Poincaré inequality is actually of type (1, 1). We also give a systematic construction of exam...

In this paper we present refinements and improvement of the Young inequality in the context of linear bounded operators.

In the present paper, by Haagerup theorem, we show that if A ∈ Mn is a non scalar strictly positive matrix and 0 < ν < 1 be a real number such that ν 6= 12 , then there exists X ∈ Mn such that ‖AνXA1−ν‖ > ‖νAX + (1− ν)XA‖.

We give conditions on Gromov-Hausdorff convergent inverse systems of metric measure graphs which imply that the measured Gromov-Hausdorff limit (equivalently, the inverse limit) is a PI space i.e., it satisfies a doubling condition and a Poincaré inequality in the sense of Heinonen-Koskela [HK96]. The Poincaré inequality is actually of type (1, 1). We also give a systematic construction of exam...

Using a sharp version of the reverse Young inequality, and a Rényi entropy comparison result due to Fradelizi, Madiman, and Wang, the authors are able to derive a Rényi entropy power inequality for log-concave random vectors when Rényi parameters belong to (0, 1). Furthermore, the estimates are shown to be somewhat sharp.

In this talk we deal with a more precise estimates for the matrix versions of Young, Heinz, and Hölder inequalities. First we give an improvement of the matrix Heinz inequality for the case of the Hilbert-Schmidt norm. Then, we refine matrix Young-type inequalities for the case of Hilbert-Schmidt norm, which hold under certain assumptions on positive semidefinite matrices appearing therein. Fin...

In this paper we explore the link between wealth inequality and stability in a two-sector neoclassical growth model with heterogeneous agents. The stability of the steady state depends on the various parameters of the model and in particular on individual preferences. We show that when consumers have identical preferences and the inverse of absolute risk aversion (or risk tolerance) is a strict...

Prior empirical studies have demonstrated an association between income inequality and general health endpoints such as mortality and self-rated health, and findings have been taken as support for the hypothesis that inequality is detrimental to individual health. Unhealthy weight statuses may function as an intermediary link between inequality and more general heath endpoints. Using individual...