We give a new proof of the L2 version of Hardy’s uncertainty principle based on calculus and on its dynamical version for the heat equation. The reasonings rely on new log-convexity properties and the derivation of optimal Gaussian decay bounds for solutions to the heat equation with Gaussian decay at a future time. We extend the result to heat equations with lower order variable coefficient.

Some basic results for Dirichlet series ψ with positive terms via log-convexity properties are pointed out. Applications for Zeta, Lambda and Eta functions are considered. The concavity of the function 1/ψ is explored and, as a main result, it is proved that the function 1/ζ is concave on (1,∞) . As a consequence of this fundamental result it is noted that Zeta at the odd positive integers is b...

We study the convexity of mutual information along the evolution of the heat equation. We prove that if the initial distribution is log-concave, then mutual information is always a convex function of time. We also prove that if the initial distribution is either bounded, or has finite fourth moment and Fisher information, then mutual information is eventually convex, i.e., convex for all large ...

In this paper we consider a class of non-Lipschitz and non-convex minimization problems which generalize the L2 − Lp minimization problem. We propose an iterative algorithm that decides the next iteration based on the local convexity/concavity/sparsity of its current position. We show that our algorithm finds an -KKT point within O(log −1) iterations. The same result is also applied to the prob...

Abstract Assuming the generalized Riemann hypothesis, we provide explicit upper bounds for moduli of $$\log {\mathcal {L}(s)}$$ log L ( s ) and $$\mathcal {L}'(s)/\mathcal {L}(s)$$ ′ </mml:ms...

We prove that a closed, geodesically convex subset C of P 2 (R) is closed with respect to weak convergence in P 2 (R). This means that if (μn) ⊂ C is such that μn ⇀ μ in duality with continuous bounded functions and supn ∫ |x|dμn <∞, then μ ∈ C as well.

We extend a result of Minsky to show that for a map of a surface to a hyperbolic 3-manifold which is not necessarily π1-injective but is 2-incompressible rel a geodesic link with a definite tube radius, the set of noncontractible simple loops with a bounded length representatives is quasi-convex in the complex of curves.

This paper presents an analysis of the problem of aggregating preference orderings under subjective uncertainty. Individual preferences, or opinions, agree on the ranking of risky prospects, but are quite general because we do not specify the perception of ambiguity or the attitude towards it. A convexity axiom for the ex-ante preference characterizes a (collective) decision rule that can be in...

fracture system in carbonate reservoirs is very complex. understanding the features of fractures such as dip, strike and the other parameters can help to distinguish the behaviour of reservoir in any exploration and production plan. image log is the best way to investigate feature planes like fracture and bedding. image log in one of drilled well #10x393 of bangestan reservoir in gachsaran oilf...

convexity theory and duality theory are important issues in math- ematical programming. within the framework of credibility theory, this paper rst introduces the concept of convex fuzzy variables and some basic criteria. furthermore, a convexity theorem for fuzzy chance constrained programming is proved by adding some convexity conditions on the objective and constraint functions. finally,...