The intramolecular Morita-Baylis-Hillman-type alkylation reaction

From the initial development of a homologous Morita-Baylis-Hillman reaction utilizing epoxides as electrophiles, the method was expanded to enable the exclusively organocatalyzed intramolecular allylation of enones and to develop the intramolecular MBH-type alkylation of activated alkenes. We successfully utilized both enones and unsaturated thioesters as the activated alkene component. This work, carried out using stoichiometric amounts of the trialkylphosphine, gave an array of functionalized five- and six-membered carbocycles in high yields. With the cycloalkylation of enones and thioesters, conditions that allowed the use of substoichometric amounts of the phosphine catalyst were developed. As a result both five- and six-membered rings can be formed efficiently with little to no loss in yield upon comparison to yields obtained when stoichiometric amounts of trialkylphosphines were employed. We isolated, for the first time, an MBH-type intermediate exhibiting unprecedented trans geometry of the phosphonium salt and acyl group.     

Self-assembly approach toward chiral bimetallic catalysts: bis-urea-functionalized (salen)cobalt complexes for the hydrolytic kinetic resolution of epoxides

A series of novel bis-urea-functionalized (salen)Co complexes has been developed. The complexes were designed to form self-assembled structures in solution through intermolecular urea-urea hydrogen-bonding interactions. These bis-urea (salen)Co catalysts resulted in rate acceleration (up to 13 times) in the hydrolytic kinetic resolution (HKR) of rac-epichlorohydrin in THF by facilitating cooperative activation, compared to the monomeric catalyst. In addition, one of the bis-urea (salen)Co(III) catalyst efficiently resolves various terminal epoxides even under solvent-free conditions by requiring much shorter reaction time at low catalyst loading (0.03-0.05 mol %). A series of kinetic/mechanistic studies demonstrated that the self-association of two (salen)Co units through urea-urea hydrogen bonds was responsible for the observed rate acceleration. The self-assembly study with the bis-urea (salen)Co by FTIR spectroscopy and with the corresponding (salen)Ni complex by (1)H NMR spectroscopy showed that intermolecular hydrogen-bonding interactions exist between the bis-urea scaffolds in THF. This result demonstrates that self-assembly approach by using non-covalent interactions can be an alternative and useful strategy toward the efficient HKR catalysis.     

Q-admissibility of certain nonsolvable groups

A finite groupG is calledQ-admissible if there exists a finite dimensional central division algebra overQ, containing a maximal subfield which is a Galois extension ofQ with Galois group isomorphic toG. It is proved thatS ₅ ⁻ , one of the two nontrivial central extensions ofS ₅ byZ/2Z, isQ-admissible. As a consequence of that result and previous results of Sonn and Stern, every finite Sylow-metacyclic group, havingA ₅ as a composition factor, isQ-admissible. This paper is part of a M.Sc. thesis written at the Technion — Israel Institute of Technology, under the supervision of Professor J. Sonn, whom the author wishes to thank for his valuable guidance.     

The Markovian Two-echelon Repairable Item Provisioning Problem

A repairable-item provisioning system with two levels of repair is presented. Under the assumption that the machine time-to-failure and the repair times are exponentially distributed, a new algorithm is developed to compute the long-run average number of machines operating. Using the new algorithm we determine the optimal number of machines and repair channels at the two repair centres to minimize cost and meet a service-level constraint. The algorithm, which is based on Little's result in queueing theory and the theory of regenerative processes, is extremely efficient in terms of computer storage and execution time.     

Why Does Pivalaldehyde (Trimethylacetaldehyde) Unexpectedly Seem More Basic Than 1‐Adamantanecarbaldehyde in the Gas Phase? FT‐ICR and High‐Level Ab Initio Studies

Fourier transform ion cyclotron resonance spectroscopy (FT ICR) techniques, including collision-induced dissociation (CID) methodology, were applied to the study of the gas-phase protonation of pivalaldehyde (1) and 1-adamantanecarbaldehyde (2). A new synthetic method for 2 was developed. The experiments, together with a thorough computational study involving ab initio and density functional theory (DFT) calculations of high level, conclusively show that upon monoprotonation in the gas phase, compound 1 yields monoprotonated methyl isopropyl ketone 3. The mechanism of this gas-phase acid-catalyzed isomerization is different from that reported by Olah and Suryah Prakash for the reaction in solution. In the latter case, isomerization takes place through the diprotonation of 1.     

On Word Equations Originated from Discrete Dynamical Systems Related to Antisymmetric Cubic Maps with Some Applications

In this article, we solve some word equations originated from discrete dynamical systems related to antisymmetric cubic map. These equations emerge when we work with primitive and greatest words. In particular, we characterize all the cases for which <β₁β₁>=<β₂β₂> where β₁ and β₂ are the greatest words in <<β₁>> and <<β₂>> of M(n).