Backbone curves,Neimark-Sacker boundaries and appearance of quasi-periodicity in nonlinear oscillators: application to 1:2 internal resonance and frequency combs in MEMS

Meccanica - Quasi-periodic solutions can arise in assemblies of nonlinear oscillators as a consequence of Neimark-Sacker bifurcations. In this work, the appearance of Neimark-Sacker bifurcations is...     

Choosing joint distributions so that the variance of the sum is small

The paper considers how to choose the joint distribution of several random variables each with a given marginal distribution so that their sum has a variance as small as possible. A theorem is given that allows the solution of this and of related problems for normal random variables. Several specific applications are given. Additional results are provided for radially symmetric joint distributions of three random variables when the sum is identically zero.     

New 3π‐2Spiro Ladder‐Type Phenylene Materials: Synthesis,Physicochemical Properties and Applications in OLEDs

New routes to ladder‐type phenylene materials 1 and 2 are described. The oligomers 1 and 2 , which possess a “3π‐2spiro” architecture, have been synthesized by using extended diketone derivatives 3 and 10 as key intermediates. The physicochemical properties of the new blue‐light emitter 2 were studied in detail and compared with those of the less‐extended 1 . Owing to the recent development of fluorenone derivatives and their corresponding more conjugated analogues as potential electron‐transport materials in organic light‐emitting diodes (OLEDs) and as n‐type materials for photovoltaic applications, we also report herein the thermal, optical and electrochemical behavior of the key intermediates, diketones 3 and 10 . Finally, the application of dispiro 2 as a new light‐emitting material in OLEDs is reported.     

Norbornanes. Part 21. Bridging strain in norbornyl and oxanorbornyl cations

Further evidence is presented that the 2-norbornyl cation is stabilized primarily by C(2)–C(6) bridging, and that C(2)–C(7) bridging leads to prohibitive strain. Thus, a comparison of the heats of hydrogenation of nortricyclene 17 and bicyclo[3. 2. 0. 0.^2,7]heptane 18 indicates that the strain energy of the latter is ca. 21.5 kcal/mol higher that that of 17 . Furthermore, 6-exo-2-oxabicyclo[2. 2. 1]heptyl sulfonates 8 ionize with strong O(2) participation to the bridged oxonium ion 12. In contrast, 2-endo-7-oxabicyclo[2.2.1]heptyl sulfonates 11 ionize without O(7) participation to form the unbridged carbenium ion 15 .     

Inductivity and charge dispersal in quinuclidinium and bicyclo[2.2.2]octyl-1-cations

The pK_a of 2-, 3- and 4-substituted quinuclidinium perchlorates and the solvolysis rates of the corresponding bicyclo[2.2.2]octyl-l-p-nitrobenzenesulfonates reveal the dispersal of charge in ammonium ions and carbocations.     

Synthese und Basizität 4-heterosubstituierter. Chinuclidine Chinuclidinreihe, 13. Mitteilung

The preparation of several 4-heterosubstituted quinuclidines and the pK_a values of their hydroperchlorates in water are reported.     

Ergodicity for a weakly damped stochastic non-linear Schrödinger equation

We study a damped stochastic non-linear Schr?dinger (NLS) equation driven by an additive noise. It is white in time and smooth in space. Using a coupling method, we establish convergence of the Markov transition semi-group toward a unique invariant probability measure. This kind of method was originally developed to prove exponential mixing for strongly dissipative equations such as the Navier-Stokes equations. We consider here a weakly dissipative equation, the damped nonlinear Schr?dinger equation in the one-dimensional cubic case. We prove that the mixing property holds and that the rate of convergence to equilibrium is at least polynomial of any power.     

A Reexamination of Inductive Substituent Constants Derived from pKa Values of 4-Substituted Quinuclidines. Polar effects. Part VIII

pK_a Values of 42 quinuclidinium perchlorates I have been measured in 0.1 M aqueous KCl-solution. In a few cases small corrections of earlier thermodynamic pK_a values are indicated. These measurements, in conjunction with recent X-ray structure determinations, confirm the reliability of the inductive substituent constants σ_I^q derived from them.