Condensed heterocyclic lactams. I. Study on the cyclization methods resulting in 4-aryl-3,4-dihydroquinolin-2(1H)-ones

Cyclization reactions with polyphosphoric acid of 3-aryl-3-hydroxypropionanilides carrying a p-nitro- 7a or p-amino substituent 10 on the C-3 phenyl group were investigated. In the case of p-nitro substitution the preferred reaction is, instead of cyclization, the elimination of water to give the corresponding cinnamic acid derivative. On the other hand, reaction of the p-amino-substituted analogue gave the new compound 4-(4-aminophenyl)-3,4-dihydroquinolin-2(1H)-one ( 2b ) in a good yield. The intermediate product of the cyclization was isolated and its structure established.     

Subgroup 4 (Ti,Zr, Hf) derivatives of Cobalt Carbonyls

Bimetallic and trimetallic compounds containing unsupported bonds of subgroup 4 metals (M = Ti, Zr, Hf) and Co were prepared by hydride elimination (A) from RM derivatives (R¹ = PhCH₂; RN; R² = Me, Et)) and by salt elimination (B) from RMX (X = Cl, Br; R.¹ = PhCH₂, RN and R³O; R³= i-Pr, n-Bu)) by reaction with HCo(CO)₄ and Na[Co(CO)₄], respectively. Compounds RMCo(CO)₄ with R¹ = PhCH₂, RM[Co(CO)₄]₂ R.¹ = PhCH₂, were prepared both by methods A and B, while (R³O)₄-n Ti[Co(Co)₄]n (n = 1, 2) compounds were obtained by reaction B. Several tertiary phosphine and phosphite derivatives of the former two types were obtained by substitution of a carbonyl group by PR ligand or by A type reaction of HCo(CO)³(PR with RM compounds.     

(E/Z)‐Isomerization of 3′‐Epilutein

3′‐Epilutein (=(all‐E,3R,3′S,6′R)‐4′,5′‐didehydro‐5′,6′‐dihydro‐β,β‐carotene‐3,3′‐diol; 1 ), isolated from the flowers of Caltha palustris, was submitted to both thermal isomerization and I₂‐catalyzed photoisomerization. The structures of the main products (9Z)‐ 1 , (9′Z)‐ 1 , (13Z)‐ 1 , (13′Z)‐ 1 , (15Z)‐ 1 , and (9Z,9′Z)‐ 1 were determined based on UV/VIS, CD, ¹H‐NMR, and MS data.     

Photo-induced disproportionation of iodomalonic acid

The stoichiometry, equilibrium, and kinetics of the photo-induced disproportionation of iodomalonic acid to I^?, I₂, and tartronic acid have been studied by means of spectrophotometry and iodide selective electrode at 20.0 ± 0.2°C, pH 2.0–4.0. At pH > 2.9, only I^? and HOCH(COOH)₂ are detected as major products and the reaction reaches 100% conversion. At pH < 2.9, I₂ and malonic acid are also formed and the reaction stops at a conversion rate less than 100%. Both UV (band with a peak at 360 nm) and visible light (480 nm) have been found to be effective. Two primary photochemical processes are identified: While both reactions are sensitive to UV light, only (M2) can be affected by visible light. (M1) and (M2) are considered to initiate a chain reaction sequence in which I^· radicals oxidize iodomalonic acid. Dual effects of reaction products on the reaction rate have been observed: while iodine increases the efficiency of visible light and accelerates the reaction, malonic acid inhibits the photo-decomposition by mediating the recombination of I^· radicals to I₂. © 1995 John Wiley & Sons, Inc.     

Convergence of Noncommutative Triangular Arrays of Probability Measures on a Lie Group

A measure-theoretic approach to the central limit problem for noncommutative infinitesimal arrays of random variables taking values in a Lie group G is given. Starting with an array of probability measures on G and instance 0st one forms the finite convolution products . The authors establish sufficient conditions in terms of Lévy-Hunt characteristics for the sequence to converge towards a convolution hemigroup (generalized semigroup) of measures on G which turns out to be of bounded variation. In particular, conditions are stated that force the limiting hemigroup to be a diffusion hemigroup. The method applied in the proofs is based on properly chosen spaces of difierentiable functions and on the solution of weak backward evolution equations on G.     

Random field forward interest rate models,market price of risk and their statistics

In this paper we consider discrete time forward interest rate models. In our approach, unlike in the classical Heath–Jarrow–Morton framework, the forward rate curves are driven by a random field. Hence we get a general interest rate structure. Our aim is to give an overview of our results in such a model on the following questions: no-arbitrage conditions, maximum likelihood estimation of the volatility, as well as the joint estimation of the parameters and the asymptotic behaviour of the estimators, relationship with continuous models. Finally we give discussion on the practical problems of the estimation and we show several numerical results on the statistics of such models. This research has been supported by the Hungarian Scientific Research Fund under Grants No. OTKA–F046061/2004 and OTKA–T048544/2005.     

Asymptotic Inference for Unit Roots in Spatial Triangular Autoregression

A spatial autoregressive process with two parameters is investigated both in the stable and in the unstable case. It is shown that the limiting distribution of the least squares estimator of these parameters is normal and the rate of convergence is n ^3/2 if one of the key parameters equals zero and n otherwise.     

Advanced operator splitting-based semi-implicit spectral method to solve the binary phase-field crystal equations with variable coefficients

We present an efficient method to solve numerically the equations of dissipative dynamics of the binary phase-field crystal model proposed by Elder et al. [K.R. Elder, M. Katakowski, M. Haataja, M. Grant, Phys. Rev. B 75 (2007) 064107] characterized by variable coefficients. Using the operator splitting method, the problem has been decomposed into sub-problems that can be solved more efficiently. A combination of non-trivial splitting with spectral semi-implicit solution leads to sets of algebraic equations of diagonal matrix form. Extensive testing of the method has been carried out to find the optimum balance among errors associated with time integration, spatial discretization, and splitting. We show that our method speeds up the computations by orders of magnitude relative to the conventional explicit finite difference scheme, while the costs of the pointwise implicit solution per timestep remains low. Also we show that due to its numerical dissipation, finite differencing can not compete with spectral differencing in terms of accuracy. In addition, we demonstrate that our method can efficiently be parallelized for distributed memory systems, where an excellent scalability with the number of CPUs is observed.     

Bounds on Maximal Families of Sets Not Containing Three Sets with A ∩ B ⊂ C, A ⊄ B

Lower and upper estimates are given on the size of a family of subsets of an n-element set containing no three distinct sets satisfying A ∩ B ⊂ C, A ⊄ B. This is a sharpening of an earlier result where the same question was solved under the condition that there are no three distinct sets such that A ∩ B ⊂ C. The second author was supported by the Hungarian National Foundation for Scientific Research grant numbers NK062321, AT048826, the Bulgarian National Science Fund under Grant IO-03/2005 and the projects of the European Community: INTAS 04-77-7171, FIST–MTKD-CT-2004-003006.     

Archimax copulas and invariance under transformations

Copulas which are invariant under transformations by means of increasing bijections on the unit interval are investigated, and the relationship to maximum attractors and Archimax copulas is discussed. To cite this article: E.P. Klement et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005).