2-Indolyl ketone synthesis

The preparation of 2-indolyl alkyl ketones by reductive cleavage of a β-keto sulfone or by the reaction of 1-chloro-2-propanone (chloroacetone) with a 2-aminobenzoic acid derivative is described. The β-keto sulfone intermediates are prepared by condensation of the carbanion of dimethyl sulfone and indole-2-carboxylic acid esters. Lack of reactivity of several 2-aminobenzoic acids in the 1-chloro-2-propanone process is related to the presence of electron-withdrawing substituents in the aromatic ring.     

Riemannian submersions and the regular interval theorem of Morse theory

A generalized version of the regular interval theorem of Morse theory is proven using techniques from the theory of Riemannian submersions and conformal deformations. This approach provides an interesting link between Riemannian submersions (for real valued functions) and Morse theory.Let % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWexLMBb50ujb% qegi0BVTgib5gDPfxDHbacfaGae8NKbmiaaa!3E95!\[f\]: (M,) R be a smooth real valued function on a non-compact complete connected Riemannian manifold (M,g) such that df is bounded in norm away from zero. By pointwise conformally deforming g to pg, p = d% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWexLMBb50ujb% qegi0BVTgib5gDPfxDHbacfaGae8NKbmiaaa!3E95!\[f\]², we show that (M,pg) is a complete Riemannian manifold, and that % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWexLMBb50ujb% qegi0BVTgib5gDPfxDHbacfaGae8NKbmiaaa!3E95!\[f\]: (M,pg) R is a surjective Riemannian submersion and a globally trivial fiber bundle over R. In particular, all of the level hypersurfaces of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWexLMBb50ujb% qegi0BVTgib5gDPfxDHbacfaGae8NKbmiaaa!3E95!\[f\] are diffeomorphic, and M is globally diffeomorphic to the product bundle R × % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWexLMBb50ujb% qegi0BVTgib5gDPfxDHbacfaGae8NKbmiaaa!3E95!\[f\] ^–1(0) by a diffeomorphism F ⁰: R × % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWexLMBb50ujb% qegi0BVTgib5gDPfxDHbacfaGae8NKbmiaaa!3E95!\[f\]^–1(0) M that straightens out the level hypersurfaces of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWexLMBb50ujb% qegi0BVTgib5gDPfxDHbacfaGae8NKbmiaaa!3E95!\[f\].Moreover, we show that (F ⁰)^*(pg) is a parameterized Riemannian product manifold on R×% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWexLMBb50ujb% qegi0BVTgib5gDPfxDHbacfaGae8NKbmiaaa!3E95!\[f\]^–1(0), i.e., a product manifold with a metric that varies on the fibers {t} × % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWexLMBb50ujb% qegi0BVTgib5gDPfxDHbacfaGae8NKbmiaaa!3E95!\[f\]^–1(0). Also, F ⁰: (R × % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWexLMBb50ujb% qegi0BVTgib5gDPfxDHbacfaGae8NKbmiaaa!3E95!\[f\]^–1(0),(F ⁰)^*(pg)) (M,g) is a conformal diffeomorphism between the Reimannian manifolds (R × % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWexLMBb50ujb% qegi0BVTgib5gDPfxDHbacfaGae8NKbmiaaa!3E95!\[f\]^–1(0), (F ⁰)^*(pg)) and (M,g),so that (M,g) is conformally equivalent to a parameterized Riemannian product manifold. The conformal diffeomorphism F ⁰ is an isometry between the Riemannian product manifold (R × % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWexLMBb50ujb% qegi0BVTgib5gDPfxDHbacfaGae8NKbmiaaa!3E95!\[f\]^–1(0), 1 + g ₀) (where g ₀) is the metric induced by g on % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWexLMBb50ujb% qegi0BVTgib5gDPfxDHbacfaGae8NKbmiaaa!3E95!\[f\]^–1(0) and (M,g) if and only if d% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWexLMBb50ujb% qegi0BVTgib5gDPfxDHbacfaGae8NKbmiaaa!3E95!\[f\] = 1 and Hess % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWexLMBb50ujb% qegi0BVTgib5gDPfxDHbacfaGae8NKbmiaaa!3E95!\[f\] = 0.     

Quantum conformal superspace

For a compact connected orientablen-manifoldM, n 3, we study the structure ofclassical superspace ,quantum superspace ,classical conformal superspace , andquantum conformal superspace . The study of the structure of these spaces is motivated by questions involving reduction of the usual canonical Hamiltonian formulation of general relativity to a non-degenerate Hamiltonian formulation, and to questions involving the quantization of the gravitational field. We show that if the degree of symmetry ofM is zero, thenS,S ₀,C, andC ₀ areilh orbifolds. The case of most importance for general relativity is dimensionn=3. In this case, assuming that the extended Poincaré conjecture is true, we show that quantum superspaceS ₀ and quantum conformal superspaceC ₀ are in factilh-manifolds. If, moreover,M is a Haken manifold, then quantum superspace and quantum conformal superspace arecontractible ilh-manifolds. In this case, there are no Gribov ambiguities for the configuration spacesS ₀ andC ₀. Our results are applicable to questions involving the problem of thereduction of Einstein's vacuum equations and to problems involving quantization of the gravitational field. For the problem of reduction, one searches for a way to reduce the canonical Hamiltonian formulation together with its constraint equations to an unconstrained Hamiltonian system on a reduced phase space. For the problem of quantum gravity, the spaceC ₀ will play a natural role in any quantization procedure based on the use of conformal methods and the reduced Hamiltonian formulation.     

Crystal and Molecular Structure of an Iodo-derivative of the Cyclic Undecapeptide Cyclosporin A

The crystal structure of an iodo-derivative of cyclosporin A has been determined in order to elucidate the constitution of this cyclic undecapeptide. Crystals of iodocyclosporin A are monoclinic, a = 10.475(5), b = 19.60(1), c = 21.04(1) Å, β 99.35(2)°, space group P2₁ (C, No. 4). The structure was solved by the heavy atom method and refined by block-diagonal least-squares analysis to a final R-factor of 0.135 with hydrogen atoms in calculated positions. The cyclic peptide has a conformation which is partly β-pleated sheet and partly open loop. The structure analysis demonstrates for the first time the reality of a new type of dipeptide hydrogen-bonding, predicted by Pullman from MO calculations and leading to a conformation described by him as C.     

Vinylogous urethanes in alkaloid synthesis: formal syntheses of Elaeocarpus alkaloids

The substituted dehydroindolizidine $\text{8}$ has been prepared from the exocyclic vinylogous urethane $\text{7}$ via an acylative ring closure. The specific formation of the enolate required for further elaboration to Elaeocarpus alkaloid precursors has been achieved by making use of the vinylogous amide $\text{12}$.     

Novel fragmentation reaction of 2-alkyl- and 2,4-dialkyl-3-iodo-1-oxocyclohexan-2,4-carbolactones

2-Alkyl- and 2,4-dialkyl-3-iodo-1-oxocyclohexan-2,4-carbolactones undergo lithium hydroxide- and lithium alkoxide-induced fragmentation reactions to provide butenolides, gamma-hydroxycyclohexenones, and/or gamma-butyrolactones. In general, product distribution is governed by two factors: (1) the nature of nucleophiles and (2) the steric bulkiness of the substituents at C-2 and C-4 of the cyclohexanones. Lithium hydroxide-induced fragmentation provides butenolides and gamma-hydroxycyclohexenones. In contrast, lithium alkoxide-promoted fragmentation results in predominantly 5-substituted gamma-butyrolactones along with a small amount of butenolides in limited cases. Fragmentation products induced by lithium hydroxide are largely influenced by the steric bulkiness of the substituents at C-2 and C-4 of the cyclohexanone ring. The bulky substituents render the exclusive formation of butenolides.     

Adsorption of a phospholipid-hydroperoxide glutathione peroxidase into phospholipid monolayers at the air-water interface

The interfacial behavior differences of two glutathione peroxidase isoforms have been investigated. The first isoform is the phospholipid-hydroperoxide glutathione peroxidase (EC 1.11.1.12) (GPx-4) isolated from rat testes and the second one is the cytosolic glutathione peroxidase (EC 1.11.1.9) (GPx-1) from bovine erythrocytes. Injected in the subphase buffer of a Langmuir trough, GPx-4 was able to adsorb quickly at the air-water interface whereas the GPx-1 was not. Then, the protein interaction with phospholipid monolayers was explored. Indeed, a monolayer of phospholipids containing a different number of polyunsaturated fatty acyl chains was prepared at the air-water interface. Under each kind of monolayer, the protein solution was injected and its adsorption was visualized by the measurement of successive pressure-area isotherms. We have, then, determined the molecular area increase due to the protein adsorption. It was found that the GPx-4 is adsorbed in each kind of monolayer tested whereas no molecular area increase was detected with the GPx-1. This indicates that the GPx-4 has a higher affinity for the interface, recovered or not by lipids, than the GPx-1. Moreover, the GPx-4 presents a different affinity for the phospholipid monolayers depending on the number of polyunsaturated fatty acyl chains.