Pyridopyrimidines. X. Synthesis of 3‐Substituted 2‐Thioxo‐5,7‐dimethylpyrido[2,3‐d] pyrimidin‐4(3H)‐ones and their S‐Alkylation Under Phase Transfer Conditions

2‐Thioxo‐5,7‐dimethylpyrido[2,3‐d]pyrimidin‐4(3H)‐ones 3 were synthesized by the cyclocondensation of 2‐amino‐3‐carbethoxy‐4,6‐dimethylpyridine 1 with methyl‐N‐aryldithiocarbamates 2 and compared with the condensation between 1 and aryl isothiocyanates 4. When a comparative study of N vs S alkylation of ambident 2‐thioxo‐5,7‐dimethylpyrido[2,3‐d]pyrimidin‐4(3H)‐ones 3 was carried out under liquid‐liquid and solid‐liquid phase transfer conditions using various alkylating agents 5 , the S‐alkylated products 6 were obtained exclusively and selectively.     

Synthetic analgesics: preparation of racemic 6,7-benzomorphans

A simple preparation of 2-carbomethoxy-2-azabicyclo[3.3.1]nonan-6-one ($\text{7}$ and its conversion to the racemic benzomorphans: $\text{9}$, $\text{10}$, $\text{14}$ are described.     

A classification of orbits admitting a unique invariant measure

We consider the space of countable structures with fixed underlying set in a given countable language. We show that the number of ergodic probability measures on this space that are $S_{\infty }$-invariant and concentrated on a single isomorphism class must be zero, or one, or continuum. Further, such an isomorphism class admits a unique $S_{\infty }$-invariant probability measure precisely when the structure is highly homogeneous; by a result of Peter J. Cameron, these are the structures that are interdefinable with one of the five reducts of the rational linear order $(\mathbb{Q},<)$.     

Pure adaptive search in monte carlo optimization

Pure adaptive search constructs a sequence of points uniformly distributed within a corresponding sequence of nested regions of the feasible space. At any stage, the next point in the sequence is chosen uniformly distributed over the region of feasible space containing all points that are equal or superior in value to the previous points in the sequence. We show that for convex programs the number of iterations required to achieve a given accuracy of solution increases at most linearly in the dimension of the problem. This compares to exponential growth in iterations required for pure random search.     

On unbounded subnormal operators

A minimal normal extension of unbounded subnormal operators is established and characterized and spectral inclusion theorem is proved. An inverse Cayley transform is constructed to obtain a closed unbounded subnormal operator from a bounded one. Two classes of unbounded subnormals viz analytic Toeplitz operators and Bergman operators are exhibited.     

Algorithms for adaptive stochastic control for a class of linear systems

This paper is concerned with the control of linear, discrete-time, stochastic systems with unknown control gain parameters. Two suboptimal adaptive control schemes are derived: One is based on underestimating future control and the other is based on overestimating future control. Both schemes require little on-line computation and incorporate in their control laws some information on estimation errors. The performance of these laws is studied by Monte Carlo simulations on a computer. Two single-input, third-order systems are considered, one stable and the other unstable, and the performance of the two adaptive control schemes is compared with that of the scheme based on enforced certainty equivalence and the scheme where the control gain parameters are known.     

A two scale method for modulated vibration modes of large,nearly repetitive,structuresUne méthode asymptotique à deux échelles pour les modes de vibrations modulés des longues structures presque répétitives

Nearly repetitive structures can present at least two kinds of vibration modes: localized modes and modulated ones. In this Note, the multiple scale method is applied to characterize a packet of modulated modes. In this respect, only small size problems are to be solved: periodic problems posed on a few basic cells and amplitude equations, which define a sort of homogenized model for this type of modes. It is established that the influence of the non-repetitive part of the structure is accounted by a boundary condition. To cite this article: E.M. Daya et al., C. R. Mecanique 331 (2003).     

Small-angle x-ray investigation of a densely packed micelle system in agave hybrid

Small-angle x-ray scattering methods were applied to calculate macromolecular parameters like specific inner surface (O/V), length of coherence (l_c), and the percentage of air present in agave hybrid, treating it as a densely packed colloidal system belonging to a general micelle system. The parameters were equal to O/V = 8.50 × 10^?6 Å^?1, l_c = 150 Å, and the percentage of air = 0.03. The Kratky camera with latest design was used for the experimental measurement. Because the sample agave ybrid is a natural fiber and a highly oriented system that is celluosic in character, the theories of Kratky and Porod have been used to evaluate these parameters.     

Donor properties of some flexidentate hydroxyimino-β-diketones in their rhodium(III) complexes

Summary A series of rhodium(III) complexes of certain hydroxyimino--diketones were synthesised and their structures assigned on the basis of elemental analyses and i.r. and¹H n.m.r. spectral studies, The complexes exhibit coordination through carbonyl oxygen and nitrogen of the hydroxy-imino groups in the ligands.¹H and¹³C n.m.r. studies show that the ligands exist in the isonitroso form in CDCl₃.