Novel Copolymers of Vinyl Acetate and Alkyl Ring‐Substituted 2‐Phenyl‐1,1‐dicyanoethylenes

Electrophilic trisubstituted ethylene monomers, alkyl ring‐substituted 2‐phenyl‐1,1‐dicyanoethylenes, RC₆H₄CH?C(CN)₂ (where R is 2‐methyl, 3‐methyl,4‐methyl, 4‐ethyl, 4‐isopropyl, 4‐butyl, and 4‐t‐butyl), were synthesized by piperidine catalyzed Knoevenagel condensation of ring‐substituted benzaldehydes and malononitrile, and characterized by CHN elemental analysis, IR, ¹H‐ and ¹³C‐NMR. Novel copolymers of the ethylenes and vinyl acetate were prepared at equimolar monomer feed composition by solution copolymerization in the presence of a radical initiator (ABCN) at 70°C. The composition of the copolymers was calculated from nitrogen analysis, and the structures were analyzed by IR, ¹H and ¹³C‐NMR, GPC, DSC, and TGA. High T_g of the copolymers, in comparison with that of polyvinyl acetate, indicates a substantial decrease in chain mobility of the copolymer due to the high dipolar character of the trisubstituted ethylene monomer unit. The gravimetric analysis indicated that the copolymers decompose in the 190–700°C range.     

Overtone spectroscopy of some benzaldehyde derivatives

Overtone spectrum of o, m and p-nitrobenzaldehydes and p-chlorobenzaldehyde has been studied in 2000–12000 cm⁻¹ region. Vibrational frequencies and anharmonicity constants for aryl as well as alkyl CH stretch vibrations have been determined. We have also determined the internuclear distances for the aryl CH bond in the different molecules. The small variation observed in these distances is an indication of the substitution effect. It is observed that in the case of p-disubstituted benzens, the shift in aryl CH bond is proportional to sum of the Hammet σ of the substituents. However in the case of o-disubstituted benzenes it is only 80% of the para-substituted shift.     

Stabilization of Unstable Limit Cycles in Systems with Limited Controllability: Expanding the Basin of Convergence of OGY-Type Controllers

The underlying geometric structure of the standard OGY control scheme is analyzed. Some of the main mechanisms that under certain conditions lead to failure of the control algorithm are revealed. The limited controllability available in a system is investigated and it is shown that it may lead to serious problems that will significantly enlarge the state space region of failure of the standard OGY controller. A minimal distance algorithm is analyzed and shown to be, for some problems, more advantageous than the standard OGY technique. Nevertheless, for a broad category of problems, the minimal distance scheme is also shown to fail. As a solution for these problems, two new techniques are proposed: the penalized minimal distance and the multi-step OGY-type scheme. The standard OGY and minimal distance algorithms are particular cases of the new techniques proposed. Finally, we give a necessary condition that estimates the region of controllability under the multi-step OGY-type control. We demonstrate a significantly improved basin of convergence for the new multi-step OGY-type algorithm.