Fast carbon dioxide fixation by 2,6-pyridinedicarboxamidato-nickel(II)-hydroxide complexes: influence of changes in reactive site environment on reaction rates

The planar complexes [Ni(II)(pyN(2)(R2))(OH)](-), containing a terminal hydroxo group, are readily prepared from N,N'-(2,6-C(6)H(3)R(2))-2,6-pyridinedicarboxamidate(2-) tridentate pincer ligands (R(4)N)(OH), and Ni(OTf)(2). These complexes react cleanly and completely with carbon dioxide in DMF solution in a process of CO(2) fixation with formation of the bicarbonate product complexes [Ni(II)(pyN(2)(R2))(HCO(3))](-) having η(1)-OCO(2)H ligation. Fixation reactions follow second-order kinetics (rate = k(2)'[Ni(II)-OH][CO(2)]) with negative activation entropies (-17 to -28 eu). Reactions were monitored by growth and decay of metal-to-ligand charge-transfer (MLCT) bands at 350-450 nm. The rate order R = Me > macro > Et > Pr(i) > Bu(i) > Ph at 298 K (macro = macrocylic pincer ligand) reflects increasing steric hindrance at the reactive site. The inherent highly reactive nature of these complexes follows from k(2)' ≈ 10(6) M(-1) s(-1) for the R = Me system that is attenuated by only 100-fold in the R = Ph complex. A reaction mechanism is proposed based on computation of the enthalpic reaction profile for the R = Pr(i) system by DFT methods. The R = Et, Pr(i), and Bu(i) systems display biphasic kinetics in which the initial fast process is followed by a slower first order process currently of uncertain origin.     

Confluence of fuchsian second-order differential equations

Ordinary linear homogeneous second-order differential equations with polynomial coefficients including one in front of the second derivative are studied. Fundamental definitions for these equations: of s-rank of the singularity (different from Poincaré rank), of s-multisymbol of the equation, and of s-homotopic transformations are proposed. The generalization of Fuchs' theorem for confluent Fuchsian equations is proved. The tree structure of types of equations is shown, and the generalized confluence theorem is proved.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 104, No. 2, pp. 233–247, August, 1995.     

Derriswurzel Rotenon

Ohne Zusammenfassung     

The source of trimuon events in neutrino scattering

A comprehensive study indicates that equally likely sources for trimuon events neutrino scattering are (a) charged heavy lepton production (with decay to three muons) and (b) simultaneous production of a neutral lepton (with decay to two muons) and a heavy quark (with decay to one muon). The sequential decay of a heavy quark to two muons is less likely. An intriguing model yielding simultaneous M⁰ and b quark production is proposed.     

On a problem of Katona on minimal separating systems

Let S be an n-element set. In this paper, we determine the smallest number f(n) for which there exists a family of subsets of S{A₁,A₂,…,A_f(n)} with the following property: Given any two elements x, y ∈ S (x ≠ y), there exist k, l such that A_k ∩ A_l= ?, and x ∈ A_k, y ∈ A_l. In particular it is shown that f(n)= 3 log₃n when n is a power of 3.     

Stability analysis of impulsive control systems

This paper studies impulsive control systems. Several stability criteria are established by employing the method of Lyapunov functions. These criteria may be used for impulsive feedback control design. As an application, impulsive control of the Lorenz chaotic system is discussed. Numerical experiments are carried out for the control of the Lorenz system. It is shown that small and frequent impulses need to be used in order to stabilize the Lorenz system.     

A class of optimal state-delay control problems

We consider a general nonlinear time-delay system with state-delays as control variables. The problem of determining optimal values for the state-delays to minimize overall system cost is a non-standard optimal control problem–called an optimal state-delay control problem–that cannot be solved using existing optimal control techniques. We show that this optimal control problem can be formulated as a nonlinear programming problem in which the cost function is an implicit function of the decision variables. We then develop an efficient numerical method for determining the cost function’s gradient. This method, which involves integrating an auxiliary impulsive system backwards in time, can be combined with any standard gradient-based optimization method to solve the optimal state-delay control problem effectively. We conclude the paper by discussing applications of our approach to parameter identification and delayed feedback control.