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Abstract We consider the Cauchy-type problem associated to time fractional partial differential equation: $$\begin{aligned} {\left\{ \begin{array}{ll} \partial _t u+\partial _t^{\beta }u-\varDelta u=g(t,x), &amp;{} t&gt;0, \ x\in {\mathbb {R}}^n \\ u(0,x)=u_0(x), \end{array}\right. } \end{aligned}$$ <mml...

We show that if a complete, doubling metric space is annulus linearly connected then its conformal dimension is greater than one, quantitatively. As a consequence, hyperbolic groups whose boundaries have no local cut points have conformal dimension greater than one; this answers a question of Bonk and Kleiner.

The Hamiltonian flow of the standard metric Hamiltonian with respect to the twisted symplectic structure on the cotangent bundle describes the motion of a charged particle on the base. We prove that under certain natural hypotheses the number of periodic orbits on low energy levels for this flow is at least the sum of Betti numbers of the base. The problem is closely related to the existence qu...

Extended Abstract. The simplest and the most common way of comparing two random variables is through their means and variances. It may happen that in some cases the median of X is larger than that of Y, while the mean of X is smaller than the mean of Y. However, this confusion will not arise if the random variables are stochastically ordered. Similarly, the same may happen if one would like to ...