Global Dynamics of a Rapidly Forced Cart and Pendulum

In this paper, we study emergent behaviors elicited by applying open-loop, high-frequency oscillatory forcing to nonlinear control systems. First, we study hovering motions, which are periodic orbits associated with stable fixed points of the averaged system which are not fixed points of the forced system. We use the method of successive approximations to establish the existence of hovering motions, as well as compute analytical approximations of their locations, for the cart and pendulum on an inclined plane. Moreover, when small-amplitude dissipation is added, we show that the hovering motions are asymptotically stable. We compare the results for all of the local analysis with results of simulating Poincaré maps. Second, we perform a complete global analysis on this cart and pendulum system. Toward this end, the same iteration scheme we use to establish the existence of the hovering periodic orbits also yields the existence of periodic orbits near saddle equilibria of the averaged system. These latter periodic orbits are shown to be saddle periodic orbits, and in turn they have stable and unstable manifolds that form homoclinic tangles. A quantitative global analysis of these tangles is carried out. Three distinguished limiting cases are analyzed. Melnikov theory is applied in one case, and an extension of a recent result about exponentially small splitting of separatrices is developed and applied in another case. Finally, the influence of small damping is studied. This global analysis is useful in the design of open-loop control laws.     

Paspalinine,a tremorgenic metabolite from Claviceps paspali Stevens et Hall

The structure of paspalinine, a tremorgenic fungal metabolite, is presented.     

Synthesis of 2‐Deoxy‐2‐thiophenylglucosyl Azides through 1,2 Thio Migration of Thiophenyl Mannosides

2‐Deoxy‐2‐thio glucosyl azides bearing or not bearing an azido group at the 6‐position can be conveniently obtained through a 1,2‐thio migration from thiophenyl mannoside derivatives.     

Photon stimulated ion desorption studies from poly(sulphone) using synchrotron radiation in a single-bunch mode

Photon stimulated ion desorption (PSID) studies from poly(sulphone) (PS) have been carried out by using high-resolution time-of-flight mass spectrometry. Synchrotron radiation at the Brazilian Synchrotron Light Source (LNLS) operating in a single-bunch mode was used as excitation source. PS was excited at the sulphur 1s-edge and the desorption of small and large fragments has been observed. The results are discussed in terms of the X-ray induced electron stimulated desorption mechanism. The present results contrast with previous ones reported for poly(3-methylthiophene) (PMeT), in which the observation of S⁺ and S²⁺ was interpreted solely in terms of an Auger-stimulated ion desorption mechanism.     

K(A,B,I): II

The KABI conjecture states that double relative K-theory and cyclic homology agree, at least in characteristic zero. We show that K ₂(A, B, I) maps onto HC ₁ (A, B, I) whenever A B is a map of Q-algebras and I BIB. We also reinterpret the KABI conjecture in terms of the injectivity of the inverse limit of the map from NK(A, B, I) to the inverse limit of the truncated polynomial versions of NK(A, B, I).Supported by National Science Foundation Grant RII — 8700009.Partially supported by National Science Foundation Grants DMS — 8503018 and 8803497.     

Substituenteneinfluss bei der massenspektrometrischen Fragmentierung: Untersuchungen an N-methyl-β,β′-diphenyl-diäthylaminen. 19. Mitteilung über das massenspektrometrische Verhalten von Stickstoffverbindungen

Some different substituted N-methyl-β,β′-diphenyl-diethylamines (I) were investigated mass spectrometrically. The main fragmentations and their genesis are summarized in Scheme 2. The molecular ion generates the major fragmentions a (m/e 148) and b (m/e (147 + X)); c (m/e 105) is formed from a and d (m/e (104+X)) from b by further decomposition. The logarithms of the ratios of the relative ion intensities a/b , c/a and d/b were correlated according to the Hammett equation with different substituent constants. The following correlation coefficients (at 20ev) were found: r = 0,98 (σ⁺), r = 0,63 (σ) and r = 0,96 (σ) respectively. On the basis of the above Hammett correlations, the value of this kind of investigation for the elucidation of mass spectral fragmentation mechanisms is discussed.