Landesman–Lazer resonance problems and saddle point methods

We show how saddle point techniques can be used to obtain new results for general resonance problems of the type considered by Landesman and Lazer.     

Connection machine simulation of ultrasonic wave propagation in materials III: The three-dimensional case

A formalism for the simulation by parallel processing of the propagation of ultrasonic pulses of arbitrary shape (i.e. not restricted to continuous waves) in complex media is presented. Recursive relationships yielding the time evolution of the displacement field are derived for both homogeneous and heterogeneous materials. In the latter case, formulas for cross-points at the intersection of up to eight different materials are obtained. A few examples of numerical results obtained with the proposed method are shown to demonstrate its applicability and efficiency. The problem of visualization of the results is also briefly discussed.     

MgBr2 · OEt2: A Lewis Acid Catalyst for the O- and N-Boc Protection of Phenols and Amines

MgBr₂ · OEt₂ efficiently catalyzes the O- and N-tert-butoxycarbonylation of functionalized phenols and amines. The presented procedure is operationally simple and done under solvent-free conditions.     

Mechanisms of electrochemical nitrogen gas reduction to ammonia under ambient conditions: a focused review

Journal of Solid State Electrochemistry - Electrocatalytic nitrogen reduction reaction (E-NRR) to ammonia is becoming a major topic of interest in the field of large-scale energy storage from...     

Computational and experimental investigation of the fields generated by a 1-3 piezocomposite transducer

Large-scale three-dimensional numerical simulations using the finite-difference time domain technique are used to compute the continuous wave fields associated with a composite transducer. The interior of the transducer is made of a periodic array of square rods. This lattice causes elastic wave Bragg diffraction similar to electrons in a periodic lattice. A low frequency mode shape is assumed for the rods. This prescribed motion includes longitudinal and transverse components. It is shown that the transverse motion in the rod gives rise to shear waves causing standing waves (lateral resonances) in the polymer regions. This is also confirmed by experimental results presented here and other independent analytical and experimental work. The full-scale numerical simulation is performed on a large parallel supercomputer and permits modeling of not only the composite transducer but the radiated pressure from near to far field. In addition, cover plates and edge effects are included, unlike analytical treatments. Although only mechanical effects are included, the wave propagation approach captures many essential features.     

Sufficient conditions for duality in homogeneous programming

A symmetric duality theory for programming problems with homogeneous objective functions was published in 1961 by Eisenberg and has been used by a number of authors since in establishing duality theorems for specific problems. In this paper, we study a generalization of Eisenberg's problem from the viewpoint of Rockafellar's very general perturbation theory of duality. The extension of Eisenberg's sufficient conditions appears as a special case of a much more general criterion for the existence of optimal vectors and lack of a duality gap. We give examples where Eisenberg's sufficient condition is not satisfied, yet optimal vectors exist, and primal and dual problems have the same value.     

Magnetic response of disordered metallic rings: large contribution of far levels

We calculate the orbital linear magnetic response of disordered metallic rings to an Aharonov-Bohm flux using the BCS model for attractive electron-electron interaction. The contribution of all levels including those up to a high energy cutoff results in a much larger value than previously obtained using the local interaction model. The possible relevance of our results to the resolution of the discrepancy between the experimental and theoretical values for the ensemble-averaged persistent currents in these systems is discussed.