Bifunctional Iminophosphorane-Catalyzed Enantioselective Nitroalkane Addition to Unactivated α,β-Unsaturated Esters**

Herein we describe the enantioselective intermolecular conjugate addition of nitroalkanes to unactivated α,β-unsaturated esters, catalyzed by a bifunctional iminophosphorane (BIMP) superbase. The transformation provides the most direct access to pharmaceutically relevant enantioenriched γ-nitroesters, utilizing feedstock chemicals, with unprecedented selectivity. The methodology exhibits a broad substrate scope, including β-(fluoro)alkyl, aryl and heteroaryl substituted electrophiles, and was successfully applied on a gram scale with reduced catalyst loading, and, additionally, catalyst recovery was carried out. The formal synthesis of a range of drug molecules, and an enantioselective synthesis of (S)-rolipram were achieved. Additionally, computational studies revealed key reaction intermediates and transition state structures, and provided rationale for high enantioselectivities, in good agreement with experimental results.     

The synthesis of azadirachtin: a potent insect antifeedant

We describe in full the first synthesis of the potent insect antifeedant azadirachtin through a highly convergent approach. An O-alkylation reaction is used to unite decalin ketone and propargylic mesylate fragments, after which a Claisen rearrangement constructs the central C8-C14 bond in a stereoselective fashion. The allene which results from this sequence then enables a second critical carbon-carbon bond forming event whereby the [3.2.1] bicyclic system, present in the natural product, is generated via a 5-exo-radical cyclisation process. Finally, using knowledge gained through our early studies into the reactivity of the natural product, a series of carefully designed steps completes the synthesis of this challenging molecule.     

Twisted Frobenius Extensions of Graded Superrings

We define twisted Frobenius extensions of graded superrings. We develop equivalent definitions in terms of bimodule isomorphisms, trace maps, bilinear forms, and dual sets of generators. The motivation for our study comes from categorification, where one is often interested in the adjointness properties of induction and restriction functors. We show that A is a twisted Frobenius extension of B if and only if induction of B-modules to A-modules is twisted shifted right adjoint to restriction of A-modules to B-modules. A large (non-exhaustive) class of examples is given by the fact that any time A is a Frobenius graded superalgebra, B is a graded subalgebra that is also a Frobenius graded superalgebra, and A is projective as a left B-module, then A is a twisted Frobenius extension of B.     

The use of Raman spectroscopy to provide an estimation of the gross biochemistry associated with urological pathologies

Near-infrared Raman spectroscopy, an optical technique that is able to interrogate biological tissues, has been used to study bladder and prostate tissues, with the objective being to provide a first approximation of gross biochemical changes associated with the process of carcinogenesis. Prostate samples for this study were obtained by taking a chip at TURP, and bladder samples from a biopsy taken at TURBT and TURP, following ethical approval. Spectra were taken from purchased biochemical constituents and different pathologies within the bladder and the prostate. We were then able to determine the biochemical basis for these pathologies by utilising an ordinary least-squares fit. We have shown for the first time that we are able to utilise Raman spectroscopy in determining the biochemical basis for the different pathologies within the bladder and prostate gland. In this way we can achieve a better understanding of disease processes such as carcinogenesis. This could have major implications in the future of the diagnosis of disease within the bladder and the prostate gland.     

The Structure of Generalized Lorenz-Mie Theory for Elliptical Infinite Cylinders

Generalized Lorenz-Mie theory (GLMT) for elliptical cylinders is concisely described. Rather than insisting on technicalities which will appear elsewhere, this paper provides a guide allowing one to gain a bird view over the structure of the theory. As a by-product, the structure of the GLMT for circular cylinders is revisited.     

On the Effect of Tether Composition on cis/trans Selectivity in Intramolecular Diels–Alder Reactions

Intramolecular Diels–Alder (IMDA) transition structures (TSs) and energies have been computed at the B3LYP/6‐31+G(d) and CBS‐QB3 levels of theory for a series of 1,3,8‐nonatrienes, H₂C?CH? CH?CH? CH₂? X? Z? CH?CH₂ [? X? Z? =? CH₂? CH₂? ( 1 ); ? O? C(?O)? ( 2 ); ? CH₂? C(?O)? ( 3 ); ? O? CH₂? ( 4 ); ? NH? C(?O)? ( 5 ); ? S? C(?O)? ( 6 ); ? O? C(?S)? ( 7 ); ? NH? C(?S)? ( 8 ); ? S? C(?S)? ( 9 )]. For each system studied ( 1 – 9 ), cis‐ and trans‐TS isomers, corresponding, respectively, to endo‐ and exo‐positioning of the ? C? X? Z? tether with respect to the diene, have been located and their relative energies (E_rel^TS) employed to predict the cis/trans IMDA product ratio. Although the E_rel^TS values are modest (typically <3 kJ mol^?1), they follow a clear and systematic trend. Specifically, as the electronegativity of the tether group X is reduced (X?O→NH or S), the IMDA cis stereoselectivity diminishes. The predicted stereochemical reaction preferences are explained in terms of two opposing effects operating in the cis‐TS, namely (1) unfavorable torsional (eclipsing) strain about the C4? C5 bond, that is caused by the ? C? X? C(?Y)? group’s strong tendency to maintain local planarity; and (2) attractive electrostatic and secondary orbital interactions between the endo‐(thio)carbonyl group, C?Y, and the diene. The former interaction predominates when X is weakly electronegative (X?N, S), while the latter is dominant when X is more strongly electronegative (X?O), or a methylene group (X?CH₂) which increases tether flexibility. These predictions hold up to experimental scrutiny, with synthetic IMDA reactions of 1 , 2 , 3 , and 4 (published work) and 5 , 6 , and 8 (this work) delivering ratios close to those calculated. The reactions of thiolacrylate 5 and thioamide 8 represent the first examples of IMDA reactions with tethers of these types. Our results point to strategies for designing tethers, which lead to improved cis/trans‐selectivities in IMDAs that are normally only weakly selective. Experimental verification of the validity of this claim comes in the form of fumaramide 14 , which undergoes a more trans‐selective IMDA reaction than the corresponding ester tethered precursor 13 .     

Crystals, quiver varieties, and coboundary categories for Kac-Moody algebras

Henriques and Kamnitzer have defined a commutor for the category of crystals of a finite-dimensional complex reductive Lie algebra that gives it the structure of a coboundary category (somewhat analogous to a braided monoidal category). Kamnitzer and Tingley then gave an alternative definition of the crystal commutor, using Kashiwara's involution on Verma crystals, that generalizes to the setting of symmetrizable Kac-Moody algebras. In the current paper, we give a geometric interpretation of the crystal commutor using quiver varieties. Equipped with this interpretation we show that the commutor endows the category of crystals of a symmetrizable Kac-Moody algebra with the structure of a coboundary category, answering in the affirmative a question of Kamnitzer and Tingley.     

Towards the Development of an Evolution Equation for Flame Turbulence Interaction in Premixed Turbulent Combustion

Flame turbulence interaction is one of the leading order terms in the scalar dissipation \(\left (\widetilde {\varepsilon }_{c}\right )\) transport equation [35] and is thus an important phenomenon in premixed turbulent combustion. Swaminathan and Grout [36] and Chakraborty and Swaminathan [15, 16] have shown that the effect of strain rate on the transport of \(\widetilde {\varepsilon }_{c}\) is dominated by the interaction between the fluctuating scalar gradients and the fluctuating strain rate, denoted here by \(\overline {\rho }\widetilde {\Delta }_{c}= \overline {\rho {\alpha }\nabla c^{\prime \prime }S_{ij}^{\prime \prime }\nabla c^{\prime \prime }}\) ; this represents the flame turbulence interaction. In order to obtain an accurate representation of this phenomenon, a new evolution equation for \(\widetilde {\Delta }_{c}\) has been proposed. This equation gives a detailed insight into flame turbulence interaction and provides an alternative approach to model the important physics represented by \(\widetilde {\Delta }_{c}\) . The \(\widetilde {\Delta }_{c}\) evolution equation is derived in detail and an order of magnitude analysis is carried out to determine the leading order terms in the \(\widetilde {\Delta }_{c}\) evolution equation. The leading order terms are then studied using a Direct Numerical Simulation (DNS) of premixed turbulent flames in the corrugated flamelet regime. It is found that the behaviour of \(\widetilde {\Delta }_{c}\) is determined by the competition between the source terms (pressure gradient and the reaction rate), diffusion/dissipation processes, turbulent strain rate and the dilatation rate. Closures for the leading order terms in \(\widetilde {\Delta }_{c}\) evolution equation have been proposed and compared with the DNS data.