Palladium complexes of bis(acyclic diaminocarbene) ligands with chiral N-substituents and 8-membered chelate rings

Reaction of cis-dichloridobis(p-trifluoromethylphenylisocyanide)palladium(II) with N,N′-bis[(R)-1-phenylethyl]-1,3-diaminopropane afforded an enantiomerically pure, C₁-symmetric bis(acyclic diaminocarbene)PdCl₂ complex in 41% yield. The X-ray crystal structure of the complex revealed that three of the four carbene nitrogens are twisted out of conjugation with the carbene units, apparently as a result of steric interactions between one phenyl group and the propylene backbone of the chelate. A similar reaction with N,N′-bis[(R)-1-(1-naphthyl)ethyl]-1,3-diaminopropane did not lead to an isolable bis(carbene) complex, instead forming significant amounts of bis(ammonium) salt as a decomposition product. However, reaction of the same palladium isocyanide precursor with a mixture of all diastereomers of N,N′-bis[1-(1-naphthyl)ethyl]-1,3-diaminopropane provided an achiral, C_s-symmetric palladium bis(acyclic diaminocarbene) complex derived exclusively from the (R,S) diamine in 20% yield. An X-ray structure showed that the (R,S) stereochemistry allows the bulky naphthyl groups to adopt an orientation that avoids steric interactions with the backbone that likely lead to the instability of the homochiral analogue. The two palladium carbene complexes catalyzed the aza-Claisen rearrangement of an allylic imidate to an allylic amide in 24–34% yield, with an enantiomeric excess of 8% ee for the [(R)-1-phenylethyl]-substituted complex.     

Ultrasound assisted,VOSO4 catalyzed synthesis of 4-thiazolidinones: Antimicrobial evaluation of indazole-4-thiazolidinone derivatives

A simple and expedient multicomponent protocol was developed to synthesize 4-thiazolidinones by employing VOSO₄ as a catalyst under ultrasonic irradiation. The significant features of this protocol includes shorter reaction time, high yields, low catalyst loading, and also the catalyst can be recovered and reused up to next four cycles without significant loss in catalytic activity. All the synthesized novel indazole compounds were evaluated for their antibacterial and anti-biofilm activities. Compounds 9n, 9o and 9q showed promising activity (MIC value of 3.9?µg/mL) against K. planticola (MTCC 530). They also exhibited significant bactericidal activity against K. planticola (MTCC 530) (MBC value of 15.6?µg/mL). Additionally, 9n, 9o and 9q inhibited biofilm formation (IC₅₀ values ranging between 20.28–20.79?μg/mL) in this organism.     

A Characterization of L-orthogonal Polynomials from?Three Term Recurrence Relations

We consider the sequence of polynomials {Q _n } satisfying the L-orthogonality ?[z ^?n+m Q _n (z)]=0, 0??m??n?1, with respect to a linear functional ? for which the moments ?[t ⁿ ]=?? _n are all complex. Under certain restriction on the moment functional these polynomials also satisfy a three term recurrence relation. We consider three special classes of such moment functionals and characterize them in terms of the coefficients of the associated three term recurrence relations. Relations between the polynomials {Q _n } associated with two of these special classes of moment functionals are also given. Examples are provided to justify this characterization.     

Maximal Lyapunov exponent and rotation numbers for two coupled oscillators driven by real noise

Asymptotic expansions for the exponential growth rate, known as the Lyapunov exponent, and rotation numbers for two coupled oscillators driven by real noise are constructed. Such systems arise naturally in the investigation of the stability of steady-state motions of nonlinear dynamical systems and in parametrically excited linear mechanical systems. Almost-sure stability or instability of dynamical systems depends on the sign of the maximal Lyapunov exponent. Stability conditions are obtained under various assumptions on the infinitesimal generator associated with real noise provided that the natural frequencies are noncommensurable. The results presented here for the case of the infinitesimal generator having a simple zero eigenvalue agree with recent results obtained by stochastic averaging, where approximate ItÔ equations in amplitudes and phases are obtained in the sense of weak convergence.Dedicated to Thomas K. Caughey on the occasion of his 65th birthday.     

On the denominator values and barycentric weights of rational interpolants

We improve upon the method of Zhu and Zhu [A method for directly finding the denominator values of rational interpolants, J. Comput. Appl. Math. 148 (2002) 341–348] for finding the denominator values of rational interpolants, reducing considerably the number of arithmetical operations required for their computation. In a second stage, we determine the points (if existent) which can be discarded from the rational interpolation problem. Furthermore, when the interpolant has a linear denominator, we obtain a formula for the barycentric weights which is simpler than the one found by Berrut and Mittelmann [Matrices for the direct determination of the barycentric weights of rational interpolation, J. Comput. Appl. Math. 78 (1997) 355–370]. Subsequently, we give a necessary and sufficient condition for the rational interpolant to have a pole.     

Normal form for generalized Hopf bifurcation with non-semisimple 1 ∶ 1 resonance

The primary result of this research is the derivation of an explicit formula for the Poincaré-Birkhoff normal form of the generalized Hopf bifurcation with non-semisimple 1:1 resonance. The classical nonuniqueness of the normal form is resolved by the choice of complementary space which yields a unique equivariant normal form. The 4 leading complex constants in the normal form are calculated in terms of the original coefficients of both the quadratic and cubic nonlinearities by two different algorithms. In addition, the universal unfolding of the degenerate linear operator is explicitly determined. The dominant normal forms are then obtained by rescaling the variables. Finally, the methods of averaging and normal forms are compared. It is shown that the dominant terms of the equivariant normal form are, indeed, the same as those of the averaged equations with a particular choice for the constant of integration.Partially supported by NSF through grant MSS 90-57437, AFOSR through grant 91-0041 and NSERC of Canada.     

Another quadrature rule of highest algebraic degree of precision

Summary. We consider certain quadrature rules of highest algebraic degree of precision that involve strong Stieltjes distributions (i.e., strong distributions on the positive real axis). The behavior of the parameters of these quadrature rules, when the distributions are strong -inversive Stieltjes distributions, is given. A quadrature rule whose parameters have explicit expressions for their determination is presented. An application of this quadrature rule for the evaluation of a certain type of integrals is also given. Received April 17, 1991 / Revised version received July 16, 1993     

Stability of noisy nonlinear auto-parametric systems

The purpose of this work is to examine the stationary motion and stability properties of stationary motion of two degree-of-freedom noisy auto-parametric systems We shall use analytical techniques to extend the existing results to examine such multi-dimensional nonlinear systems with noise, and in particular additive white noise. We obtain an approximation for the top Lyapunov exponent, the exponential growth rate, of the response of the so-called single-mode stationary motion. We show analytically that the top Lyapunov exponent is positive, and for small values of noise intensity ɛ and dissipation ɛ² the exponent grows in proportion with ɛ^2/3.