Augmented non-quadratic penalty algorithms

Auslender, Cominetti and Haddou have studied, in the convex case, a new family of penalty/barrier functions. In this paper, we analyze the asymptotic behavior of augmented penalty algorithms using those penalty functions under the usual second order sufficient optimality conditions, and present order of convergence results (superlinear convergence with order of convergence 4/3). Those results are related to the analysis of pure penalty algorithms, as well as augmented penalty using a quadratic penalty function. Limited numerical examples are presented to appreciate the practical impact of this local asymptotic analysis.This research was partially supported by NSERC grant OGP0005491     

Bicomplex Quantum Mechanics: I. The Generalized Schrödinger Equation

We introduce the set of bicomplex numbers which is a commutative ring with zero divisors defined by where We present the conjugates and the moduli associated with the bicomplex numbers. Then we study the bicomplex Schr?dinger equation and found the continuity equations. The discrete symmetries of the system of equations describing the bicomplex Schr?dinger equation are obtained. Finally, we study the bicomplex Born formulas under the discrete symmetries. We obtain the standard Born’s formula for the class of bicomplex wave functions having a null hyperbolic angle.     

A Markov partition that reflects the geometry of a hyperbolic toral automorphism

We show how to construct a Markov partition that reflects the geometrical action of a hyperbolic automorphism of the -torus. The transition matrix is the transpose of the matrix induced by the automorphism in -dimensional homology, provided this is non-negative. (Here denotes the expanding dimension.) That condition is satisfied, at least for some power of the original automorphism, under a certain non-degeneracy condition on the Galois group of the characteristic polynomial. The rectangles are constructed by an iterated function system, and they resemble the product of the projection of a -dimensional face of the unit cube onto the unstable subspace and the projection of minus the orthogonal -dimensional face onto the stable subspace.

     

Miller–Urey Revisited: When Lightning Strikes the Earth

A discharge is arced to different solutions containing the simple molecular species water, methanol, and ammonia. We show that the impact of the discharge at the discharge-solution interface produces a range of organic molecules, including amino acids and polymers containing carboxylate, amine, imine, and cyano groups. The classic Miller-Urey experiment, of which there are hundreds of variations, changing parameters such as gas composition, pressures, and voltage have been tested, involves the production of simple amino acids and other species in the gas phase in an arc discharge. This works emphasis is the production of various chemical species at a discharge-liquid interface. The analysis of the product is conducted by IR, UV–VIS, LC–MS and MALDI–MS. As a laboratory exercise or a demonstration, this simple derivation of the Miller-Urey experiment can be used in a variety of teaching settings, from high school through advanced undergraduate research classes to demonstrate the basic hypothesis of how life on Earth may have started.     

Convenient One-Pot Synthesis of dℓ-Pyrocin

Abstract

Treatment of readily available monomethyl maleic acid (1) with three equivalents of methyl magnesium iodide followed by an excess of 2-methyl-1-propenyl magnesium bromide and a catalytic amount of CuBr produces d?-pyrocin (3) in a high yield.     

Microwave-assisted,one-pot reaction of 7-azaindoles and aldehydes: a facile route to novel di-7-azaindolylmethanes

A novel and highly efficient synthetic method leveraging microwave-assisted organic synthesis (MAOS) to yield di-7-azaindolylmethanes (DAIMs) is reported. Under MAOS conditions, reaction of 7-azaindole with aldehydes resulted predominantly in DAIMs, as opposed to the expected 7-azaindole addition products that form at ambient temperature. Based upon studies of different indoles and azaindoles with various aromatic and aliphatic aldehydes, we herein propose a mechanism where rapid and efficient microwave heating promotes nucleophilicity of 7-azaindoles toward the corresponding alkylidene–azaindolene intermediate to form the DAIM. This sequence provides a versatile approach to efficiently synthesize novel DAIMs that may be useful pharmaceuticals.     

Reducing visitor noise levels at Muir Woods National Monument using experimental management

Noise impacts resources and visitor experience in many protected natural areas, and visitors can be the dominant source of noise. This experimental study tested the efficacy and acceptability of signs asking visitors to be quiet at Muir Woods National Monument, California. Signs declaring a "quiet zone" (at the park's Cathedral Grove) or a "quiet day" (throughout the park) were posted on a randomized schedule that included control days (no signs). Visitor surveys were conducted to measure the cognitive and behavioral responses of visitors to the signs and test the acceptability of these management practices to visitors. Visitors were highly supportive of these management practices and reported that they consciously limited the amount of noise they produced. Sound level measurements showed substantial decreases on days when signs were posted.     

Shape Selectivity by Guest‐Driven Restructuring of a Porous Material

A flexible metal‐organic framework selectively sorbs para‐ (pX) over meta‐xylene (mX) by synergic restructuring around pX coupled with generation of unused void space upon mX loading. The nature of the structural change suggests more generally that flexible structures which are initially mismatched in terms of fit and capacity to the preferred guest are strong candidates for effective molecular separations.