A Meldrum's Acid Catalyzed Synthesis of Bis(indolyl)methanes in Water under Ultrasonic Condition

A highly effective Meldrum's acid catalyzed synthesis of bis(indol‐3‐yl)methanes has been developed. This reaction provides the corresponding bis(indol‐3‐yl)methanes in high yields after short reaction time in the presence of 2 mol % catalyst in water under ultrasonic condition.     

Highly Enantioselective Synthesis of 1,2,3‐Substituted Cyclopropanes by Using α‐Iodo‐ and α‐Chloromethylzinc Carbenoids

Herein, we report the enantio‐ and diastereoselective formation of trans‐iodo‐ and trans‐chlorocyclopropanes from α‐iodo‐ and α‐chlorozinc carbenoids by using a dioxaborolane‐derived chiral ligand. The synthetically useful iodocyclopropane building blocks were derivatized by an electrophilic trapping of the corresponding cyclopropyl lithium species or a Negishi coupling to give access to a variety of enantioenriched 1,2,3‐substituted cyclopropanes. The synthetic utility of this method was demonstrated by the formal synthesis of an HIV‐1 protease inhibitor. In addition, the related stereoselective bromocyclopropanation was also investigated. New insights about the relative electrophilicity of haloiodomethylzinc carbenoids are also presented.     

Design and Synthesis of 3‐Aryl‐5‐Alicylic‐[1,2,4]‐oxadiazoles as Novel Platelet Aggregation Inhibitors

A series of 4‐[2‐(alicyclic‐[1,2,4]oxadiazol‐3‐yl)phenoxy]‐butyric acids were synthesized from N‐hydroxy‐2‐isopropoxy benzamidine in 4 steps with good yields. These [1,2,4]oxadiazoles are novel platelet aggregation inhibitors preventing human platelet aggregation induced by thromboxane derivative U44,619 and adenosine diphosphate. A structure‐activity‐relationship study revealed that the potency for these 5‐oxadiazoles increases with the increase in the ring size of the alicylic rings. Derivative 8f may be useful as a template for the design of more potent anti‐platelet agents.     

On the Convolution of the Generalized Finite Legendre Transform

The translation operator and the convolution for the finite Legendre transformation are investigated in the space ??(?1,1) of testing-functions and its dual through an approach that emphasizes the close similarity existing between this transform and the infinite Mehler - Fock transformation. The theory developed is used in solving some distributional boundary-value problems.     

Structural Determinants of Opioid Activity in the Orvinols and Related Structures. Ethers of 7,8‐Cyclopenta‐Fused Analogs of Buprenorphine

A series of ethers of 7,8‐cyclopenta‐fused analogs of the orvinols related to buprenorphine were prepared and evaluated in opioid‐binding and functional assays. Comparison of the ethyl ethers 4b and 5b with the parent alcohols 4a and 5a , respectively, in both the (5′R) (=5′β) and (5′S) (=5′α) series, shows that the 20‐OH group in the orvinols (corresponding to 5′‐OH of 4 and 5 ) is not crucial for opioid activity, although in the [³⁵S]GTPγS assay, the 5′β‐ethyl ether 4b had 80‐fold greater κ‐agonist potency than its epimer 5b . Increasing the size of the 5′β‐OR group has a major effect on μ‐agonist efficacy and potency, a more modest effect on δ‐efficacy, and no effect on κ‐activity. These data show that μ‐ and δ‐agonist efficacy is favoured by lipophilic binding in the area occupied by the ^tBu in the lowest‐energy conformation of buprenorphine, and that κ‐agonist binding may involve interaction with an H‐bond‐donor group in that region.     

On the condition numbers associated with the polar factorization of a matrix

We are interested in the calculation of explicit formulae for the condition numbers of the two factors of the polar decomposition of a full rank real or complex m × n matrix A, where m ≥ n. We use a unified presentation that enables us to compute such condition numbers in the Frobenius norm, in cases where A is a square or a rectangular matrix subjected to real or complex perturbations. We denote by σ₁ (respectively σ _n) the largest (respectively smallest) singular value of A, and by K(A) = σ₁/σ _n the generalized condition number of A. Our main results are that the absolute condition number of the Hermitian polar factor is √2(1 + K(A)²)^1/2/(1 + K(A)) and that the absolute condition number of the unitary factor of a rectangular matrix is 1/σ _n. Copyright © 2000 John Wiley & Sons, Ltd.     

Synthesis and Solution Behavior Studies of a Bifunctional Fluorenyl Dioxotetraamine and Its Copper(II) Complex

The fluorenyl dioxotetraamine L⁴ was designed and prepared. The solution behavior of L⁴ and its interaction with the Cu^II ion were studied by pH potentiometric, fluorimetric and spectrophotometric titration. In the dioxane/water solution, it was found that the molecule L⁴ showed an “off‐on” or “on‐off” fluorescent response in the absence or presence of the Cu^II ion with the increase of the pH value. Moreover, influenced by the Cu^II ion, the fluorescence of the dioxotetraamine L⁴ can be almost quenched when the pH value was slightly higher than 4.0, which is rarely reported and useful to detect the Cu^II ion under acidic condition.     

Homogeneous quaternionic Kähler structures of linear type

A classification of homogeneous quaternionic Kähler structures by real tensors is given and related to Fino's representation theoretic decomposition. A relationship between the modules whose dimension grows linearly and quaternionic hyperbolic space is found. To cite this article: M. Castrillón López et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).