Book review

Communicated by Professor Zimmermann     

Biradical and zwitterionic cyclizations of oxy-substituted enyne-allenes

[see reaction]. Oxyanion substitution of enyne-allenes causes both Myers-Saito and Schmittel cyclizations to switch their product formation preferences from diradicals to polar, closed-shell singlets. The oxyanion stabilization is larger for the Schmittel products than the Myers-Saito products because the latter must sacrifice aromaticity to maximize interaction. The changing character of the different reaction paths is reflected in their activation energies.     

The critical behavior of random digraphs

We study the critical behavior of the random digraph D(n,p) for np = 1 + ε, where ε = ε(n) = o(1). We show that if ε³n →—∞, then a.a.s. D(n,p) consists of components which are either isolated vertices or directed cycles, each of size O_p(|ε|^?1). On the other hand, if ε³n →∞, then a.a.s. the structure of D(n,p) is dominated by the unique complex component of size (4 + o(1))ε²n, whereas all other components are of size O_p(ε^?1). © 2009 Wiley Periodicals, Inc. Random Struct. Alg., 2009     

Constrained retarded nonlinear optimal control problems in Banach state space

Necessary conditions are proved for the optimal control of solutions of ordinary and retarded differential equations in a Banach state space, with mixed and pure state restrictions. The treatment includes the possibility of point targets. A generalization of earlier results for finite-dimensional or Hilbert state spaces is obtained.     

Experimental and theoretical characterization of the 3,5-didehydrobenzoate anion: a negatively charged meta-benzyne

A negatively charged analogue of meta-benzyne, 3,5-didehydrobenzoate, was synthesized in a Fourier transform ion cyclotron resonance mass spectrometer, and its reactivity was compared to that of the same ion generated previously in a flowing afterglow apparatus and to its positively charged cousin, N-(3,5-didehydrophenyl)-3-fluoropyridinium. 3,5-Didehydrobenzoate was found to react as a nucleophile with electrophilic reagents. In contrast, N-(3,5-didehydrophenyl)-3-fluoropyridinium does not react with the same electrophilic reagents but reacts instead with nucleophilic reagents. Neither ion is able to abstract hydrogen atoms from typical hydrogen atom donors. The absence of any radical reactivity for these meta-benzynes is consistent with predictions that radical reactions of singlet biradicals should be hindered as compared to their monoradical counterparts. High-level calculations predict that the carboxylate moiety does not significantly perturb the singlet-triplet splitting of 3,5-didehydrobenzoate relative to the parent meta-benzyne.     

Conditions implying the vanishing of the Hamiltonian at infinity in optimal control problems

In an infinite horizon optimal control problem the Hamiltonian vanishes at infinity when the differential equation is autonomous and the integrand in the criterion satisfies some weak integrability conditions. A generalization of Michel’s result (in Econometrica 50:975–985, 1982) is obtained.     

Existence of open loop Nash equilibria in certain types of nonlinear differential games

This paper yields sufficient conditions for existence of open loop Nash equilibria in certain types of nonlinear differential games satisfying certain monotonicity and/or convexity conditions.     

Maximum Principle for Stochastic Control in Continuous Time with Hard End Constraints

A maximum principle is proved for certain problems of continuous–time stochastic control with hard end constraints (end constraints satisfied a.s.). In the problems, the dynamics (the state differential equation) changes at certain stochastic points in time.     

On the normality of giant components

We consider a general family of random graph processes, which begin with an empty graph, and where at every step an edge is added at random according to some rule. We show that when certain general conditions are satisfied, the order of the giant component tends to a normal distribution. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 43, 452–485, 2013