On the Prolate Spheroidal Wave Functions and Hardy’s Uncertainty Principle

We prove a weak version of Hardy’s uncertainty principle using properties of the prolate spheroidal wave functions. We describe the eigenvalues of the sum of a time limiting operator and a band limiting operator acting on \(L^2(\mathbb {R})\) . A weak version of Hardy’s uncertainty principle follows from the asymptotic behavior of the largest eigenvalue as the time limit and the band limit approach infinity. An asymptotic formula for this eigenvalue is obtained from its well-known counterpart for the prolate integral operator.     

Minimizing the number of machines for minimum length schedules

In this paper, we present a new objective function for scheduling on parallel machines: minimizing the number of machines for schedules of minimum length. We study its complexity and we prove the NP-completeness of this problem, even if there is no precedences or for unitary execution times. We propose several polynomial algorithms for various particular cases.     

Synthesis of novel fluorinated 4-aminoquinoline derivatives

New 4-aminoquinolines having a -CF₂CH-(heteroaryl)-OH moiety are obtained in moderate yields from the electrochemical catalyzed reaction of the corresponding 4-amino-3-chlorodifluoroacetyl-2-methoxyquinoline in the presence of heteroaryl aldehydes. A one-pot intramolecular zinc mediated aromatic nucleophilic substitution also gave access to novel difluorinated 5-aminodihydropyrano[2,3-b]quinolin-4-ones.     

A Boundary Problem Concerning Inner Functions

Results in Mathematics -