Studies on the synthesis of heterocyclic compounds. Part IX. Action of N,N-dimethylformamide dimethylacetal on some oximino-β-dicarbonyl compounds

3-Oximino-2,4-pentanedione ( 1 ) and ethyl 2-oximino-3-oxobutanoate ( 6 ) reacted with N,N-dimethylformamide dimethylacetal (DFDA) to give 1,7-bisdimethylamino-3,5-dioxo-4-methoximinohepta-1,6-diene ( 4 ) and ethyl 5-dimethylamino-2-methoximino-3-oxo-4-pentenoate ( 8 ), respectively. When compounds 4 and 8 were treated with hydrazine hydrate, they gave O-methyldipyrazol-3(5)-ylketoxime ( 5 ) and ethyl 2-methoximino-3(5)-pyrazolylethanoate ( 9 ) together with its corresponding hydrazide 10 , respectively. Upon action of DFDA on 3-oximino-2,4-pentanedione ( 1 ) at -20° an explosive crystalline product was obtained. On the other hand, the reaction of 3-acetoximino-2,4-pentanedione ( 11 ) with DFDA at -20° afforded a product which in ethanol solution, spontaneously deacetylated to give 1-dimethylamino-3,5-dioxo-4-oximinohexa-1-ene ( 13 ). The structures of all the new compounds were assigned on the basis of satisfactory analytical and spectroscopic data.     

Excess enthalpies of some aromatic aldehydes in n-hexane, n-heptane and benzene

Calorimetric measurements of molar excess enthalpies, H^E, at 298.15 K, of mixtures containing aromatic aldehydes of general formula C₆H₅(CH₂)_mCHO (with m = 0, 1 and 2) + n-hexane, n-heptane or benzene are reported, together with the values of H^E at equimolar composition compared with the corresponding values of H^E for the aromatic ketones in the same solvents. The experimental results clearly indicate that the intermolecular interactions between the carbonyl groups (CHO) are influenced by the intramolecular interactions between the carbonyl and phenyl groups, particularly for the mixtures containing benzaldehyde.     

Synthesis of Ir Catalysts Featuring Amide-functionalized NHC Ligands and Survey of their Activity on Formic Acid Dehydrogenation

2 a and 2 b , [Ir(CI)(COD)(NHC)] (COD=1,5-cyclooctadiene), have been prepared via transmetallation from NHC−Ag complexes. [Rh(CI)(COD)(NHC)] ( 4 ) was prepared analogously. [Ir({κ-C,N-(NHC-acetamide−1H)}(COD)] ( 3 c ) has been synthesized via transmetallation from the deprotonated NHC−Ag complex. [IrCp*({κ-C,N-(NHC-acetamide−1H)}] ( 5 ) (Cp*=pentamethylcyclopentadienyl), has been obtained analogously. [Ir(CI)(CO)₂(NHC)] ( 6 ) and [Ir({κ-C,N-(NHC-acetamide−1H)}(CO)₂] ( 7 ) have been prepared by carbonylation of 2 b and 3 c , respectively. The catalytic activity of these complexes has been evaluated in the dehydrogenation of formic acid, under solventless conditions, in the presence of water as a cosolvent, and in a 5 : 2 HCOOH/Et₃N mixture, with the best TOF values being obtained in the case of the latter. Stoichiometric experiments suggest COD hydrogenation as the preactivation step.     

Harnack estimates for quasi-linear degenerate parabolic differential equations

We establish the intrinsic Harnack inequality for non-negative solutions of a class of degenerate, quasilinear, parabolic equations, including equations of the p-Laplacian and porous medium type. It is shown that the classical Harnack estimate, while failing for degenerate parabolic equations, it continues to hold in a space-time geometry intrinsic to the degeneracy. The proof uses only measure-theoretical arguments, it reproduces the classical Moser theory, for non-degenerate equations, and it is novel even in that context. Hölder estimates are derived as a consequence of the Harnack inequality. The results solve a long standing problem in the theory of degenerate parabolic equations.     

Generation of analytic semigroups by degenerate elliptic operators

We consider the generation of analytic semigroups by degenerate elliptic operators satisfying a uniform H?rmander condition under homogeneous Dirichlet boundary conditions. Received January 12, 1996     

Generalized derivations as Jordan homomorphisms on lie ideals and right ideals

Let R be a prime ring, L a non-central Lie ideal of R and g a non-zero generalized derivation of R. If g acts as a Jordan homomorphism on L, then either g（x） = x for all x ∈ R, or char（R） = 2, R satisfies the standard identity s4（x1, x2, x3, x4）, L is commutative and u2 ∈ Z（R）, for any u C L. We also examine some consequences of this result related to generalized derivations which act as Jordan homomorphisms on the set [I, I], where I is a non-zero right ideal of R.     

Involutions for upper triangular matrix algebras

In this paper we describe completely the involutions of the first kind of the algebra UT_n(F) of n×n upper triangular matrices. Every such involution can be extended uniquely to an involution on the full matrix algebra. We describe the equivalence classes of involutions on the upper triangular matrices. There are two distinct classes for UT_n(F) when n is even and a single class in the odd case.Furthermore we consider the algebra UT₂(F) of the 2×2 upper triangular matrices over an infinite field F of characteristic different from 2. For every involution *, we describe the *-polynomial identities for this algebra. We exhibit bases of the corresponding ideals of identities with involution, and compute the Hilbert (or Poincaré) series and the codimension sequences of the respective relatively free algebras.Then we consider the *-polynomial identities for the algebra UT₃(F) over a field of characteristic zero. We describe a finite generating set of the ideal of *-identities for this algebra. These generators are quite a few, and their degrees are relatively large. It seems to us that the problem of describing the *-identities for the algebra UT_n(F) of the n×n upper triangular matrices may be much more complicated than in the case of ordinary polynomial identities.     

A Note on the analytic solutions of the Camassa–Holm equation

In this Note we are concerned with the well-posedness of the Camassa–Holm equation in analytic function spaces. Using the Abstract Cauchy–Kowalewski Theorem we prove that the Camassa–Holm equation admits, locally in time, a unique analytic solution. Moreover, if the initial data is real analytic, belongs to $H^s(\mathbb{R})$ with $s>3/2$, $6u_0{6}_{L^1}<\infty$ and $u_0?u_{0xx}$ does not change sign, we prove that the solution stays analytic globally in time. To cite this article: M.C. Lombardo et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Generalized Skew Derivations Cocentralizing Multilinear Polynomials

Let R be a prime ring of characteristic different from 2, Q _r be its right Martindale quotient ring and C be its extended centroid. Suppose that F, G are generalized skew derivations of R and \({f(x_1, \ldots, x_n)}\) is a non-central multilinear polynomial over C with n non-commuting variables. If F and G satisfy the following condition:

$$F(f(r_1,\ldots, r_n))f(r_1, \ldots,r_n)-f(r_1,\ldots,r_n)G(f(r_1,\ldots, r_n))\in C$$

for all \({r_1, \ldots, r_n \in R}\), then we describe all possible forms of F and G.