Catalytic coupling of arene C-h bonds and alkynes for the synthesis of coumarins: substrate scope and application to the development of neuroimaging agents

C-H bond functionalization offers strategically novel approaches to complex organic compounds. However, many C-H functionalization reactions suffer from poor compatibility with Lewis basic functional groups, especially amines, which are often essential for biological activity. This study describes a systematic examination of the substrate scope of catalytic hydroarylation in the context of complex amino coumarin synthesis. The choice of substrates was guided by the design and development of the next generation of fluorescent false neurotransmitters (FFNs), neuroimaging probes we recently introduced for optical imaging of neurotransmission in the brain. Comparison of two mild protocols using catalytic PtCl(4) or Au(PPh(3))Cl/AgSbF(6)revealed that each method has a broad and mutually complementary substrate scope. The relatively less active platinum system out-performed the gold catalyst with indole substrates lacking substitution at the C-3 position and provided higher regioselectivity in the case of carbazole-based substrates. On the other hand, the more active gold catalyst demonstrated excellent functional group tolerance, and the ability to catalyze the formation of strained, helical products. The development of these two protocols offers enhanced substrate scope and provides versatile synthetic tools required for the structure-activity examination of FFN neuroimaging probes as well as for the synthesis of complex coumarins in general.     

Bilinear Fourier Restriction Theorems

We provide a general scheme for proving L ^p estimates for certain bilinear Fourier restrictions outside the local L ² setting. As an application, we show how such estimates follow for the lacunary polygon. In contrast with prior approaches, our argument avoids any use of the Rubio de Francia Littlewood?CPaley inequality.     

One-phase supported titanium-based catalyst for polymerization of ethylene. IV. Effect of alkyl group at organoaluminium compound on catalyst performance

The effect of a basic layer (SiO₂—R₃Al intermediate) in the one-phase silica supported titanium-based catalyst was investigated using the simple model catalyst systems obtained by reacting the activated silica gel consecutively with R₃Al and TiCl₄. Mode of the interaction of SiO₂ with R₃Al—resulting in the formation of the basic layer—was observed via analysis of the concentration of the unreacted OH groups on the silica surface employing IR spectroscopy and via analysis of the concentration of aluminium in solvent using AA spectroscopy. It was found that nature of the alkyl group in R₃Al modified the structure of the basic layer, thus influencing the catalyst performance including the concentration of both the sum of Ti²⁺ and Ti³⁺ and the ESR-active Ti (III) centers. The sum of Ti²⁺ and Ti³⁺ ranged from 45 to 52 mol % and the amount of the ESR-active Ti (III) species ranged from 6 to 17 mol % of the all titanium content. A significant effect of alkyl group at organoaluminium compound on the molecular weight distribution of the resulting polymer was observed. © 1996 John Wiley & Sons, Inc.     

Iboga Inspired N-Indolylethyl-Substituted Isoquinuclidines as a Bioactive Scaffold: Chemoenzymatic Synthesis and Characterization as GDNF Releasers and Antitrypanosoma Agents

The first stage of the drug discovery process involves the identification of small compounds with biological activity. Iboga alkaloids are monoterpene indole alkaloids (MIAs) containing a fused isoquinuclidine-tetrahydroazepine ring. Both the natural products and the iboga-inspired synthetic analogs have shown a wide variety of biological activities. Herein, we describe the chemoenzymatic preparation of a small library of novel N-indolylethyl-substituted isoquinuclidines as iboga-inspired compounds, using toluene as a starting material and an imine Diels–Alder reaction as the key step in the synthesis. The new iboga series was investigated for its potential to promote the release of glial cell line-derived neurotrophic factor (GDNF) by C6 glioma cells, and to inhibit the growth of infective trypanosomes. GDNF is a neurotrophic factor widely recognized by its crucial role in development, survival, maintenance, and protection of dopaminergic neuronal circuitries affected in several neurological and psychiatric pathologies. Four compounds of the series showed promising activity as GDNF releasers, and a leading structure (compound 11) was identified for further studies. The same four compounds impaired the growth of bloodstream Trypanosoma brucei brucei (EC₅₀ 1–8 μM) and two of them (compounds 6 and 14) showed a good selectivity index.     

Weak convergence to the fractional Brownian sheet in Besov spaces

In this paper we study the problem of the approximation in law of the fractional Brownian sheet in the topology of the anisotropic Besov spaces. We prove the convergence in law of two families of processes to the fractional Brownian sheet: the first family is constructed from a Poisson procces in the plane and the second family is defined by the partial sums of two sequences of real independent fractional brownian motions.     

A necessary and sufficient condition for the existence of an exponential attractor

We give a necessary and sufficient condition for the existence of an exponential attractor. The condition is formulated in the context of metric spaces. It also captures the quantitative properties of the attractor, i.e., the dimension and the rate of attraction. As an application, we show that the evolution operator for the wave equation with nonlinear damping has an exponential attractor.     

Likelihood ratio tests for goodness-of-fit of a nonlinear regression model

We propose likelihood and restricted likelihood ratio tests for goodness-of-fit of nonlinear regression. The first-order Taylor approximation around the MLE of the regression parameters is used to approximate the null hypothesis and the alternative is modeled nonparametrically using penalized splines. The exact finite sample distribution of the test statistics is obtained for the linear model approximation and can be easily simulated. We recommend using the restricted likelihood instead of the likelihood ratio test because restricted maximum-likelihood estimates are not as severely biased as the maximum-likelihood estimates in the penalized splines framework.     

Sums of continuous and differentiable functions in dynamical systems

We investigate stability of Martin boundaries for positive solutions of elliptic partial differential equations. We define a perturbation which isG _L ^D -semismall at infinity, show that Martin boundaries are stable under this perturbation, and give sufficient conditions for it. This work was carried out partially while the author was visiting the Department of Mathematics, Technion — Israel Institute of Technology. He wishes to thank the Israel Association for the Promotion of International Scientific Relations, the Japan Society of Promotion of Science, and the Technion.     

On the four block problem,II: The singular system

In this paper we study the singular values of a four block operator which naturally appears in control engineering. This extends our previous results from [7]. As before, we will show that this question is reducible to a skew Toeplitz operator problem of the kind studied in [1].