Enzymatic kinetic resolution of piperidine atropisomers: synthesis of a key intermediate of the farnesyl protein transferase inhibitor, SCH66336

The resolution of secondary amines via enzyme-catalyzed acylation is a relatively rare process. The kinetic resolution of a series of intermediates of SCH66336 (1), by either enzymatic acylation of the pendant piperidine (4, 5) or hydrolysis of the corresponding carbamate 3, was investigated. In the case of 4, the molecule exists as a pair of enantiomers due to atropisomerism about the exocyclic double bond. The enzymatic acylation of (+/-)-4 was optimized in terms of acylating agent, solvent, and moisture content. The use of lipase, Toyobo LIP-300, and trifluoroethyl isobutyrate as acylating agent resulted in isobutyrylation of the (+)-enantiomer, which is easily separated from the unwanted (-)-4. Hydrolysis of the isobutyramide 6c yielded the desired (+)-4 in high enantiomeric excess. (-)-4 may be recovered from the resolution step, racemized, and resubjected to enzymatic acylation to increase material throughput.     

2H NMR measurements of the molecular orientational ordering in a reentrant liquid-crystalline mixture

Deuterium NMR measurements of the molecular orientational ordering (nematic order) are reported for a reentrant binary mixture of some alkoxy-eyanobiphenyls (nOCB) to which small amounts of perdeuterated p-xylene have been added. The results indicate that the degree of orientational order is enhanced at the smectic A to reentrant nematic phase transition. This effect is shown to be in agreement with the predictions of a Landau-type theory of the reentrant phase transition where-by this phase transition is explained as the result of a coupling between the smectic and the nematic order parameters.     

Randomized LU decomposition

Randomized algorithms play a central role in low rank approximations of large matrices. In this paper, the scheme of the randomized SVD is extended to a randomized LU algorithm. Several error bounds are introduced, that are based on recent results from random matrix theory related to subgaussian matrices. The bounds also improve the existing bounds of already known randomized SVD algorithm. The algorithm is fully parallelized and thus can utilize efficiently GPUs without any CPU–GPU data transfer. Numerical examples, which illustrate the performance of the algorithm and compare it to other decomposition methods, are presented.     

Optimal on-line colorings for minimizing the number of ADMs in optical networks

We consider the problem of minimizing the number of ADMs in optical networks. All previous theoretical studies of this problem dealt with the off-line case, where all the lightpaths are given in advance. In a real-life situation, the requests (lightpaths) arrive at the network on-line, and we have to assign them wavelengths so as to minimize the switching cost. This study is thus of great importance in the theory of optical networks. We present a deterministic on-line algorithm for the problem, and show its competitive ratio to be $\frac{7}{4}$. We show that this result is best possible in general. Moreover, we show that even for the ring topology network there is no on-line algorithm with competitive ratio better than $\frac{7}{4}$. We show that on path topology the competitive ratio of the algorithm is $\frac{3}{2}$. This is optimal for in this topology. The lower bound on ring topology does not hold when the ring is of bounded size. We analyze the triangle topology and show a tight bound of $\frac{5}{3}$ for it. The analyses of the upper bounds, as well as those for the lower bounds, are all using a variety of proof techniques, which are of interest by their own, and which might prove helpful in future research on the topic.     

Phase transitions of p-type (Pb,Sn,Ge)Te-based alloys for thermoelectric applications

p-type (Pb,Sn,Ge)Te-based alloys for thermoelectric applications were prepared using Bridgman technique. Second-order, rhombohedral to cubic phase transitions are involved, as evaluated from anomalies in the temperature dependence values of Seebeck coefficient, electrical conductivity, heat flow and the elongation, in the vicinity of the phase transition temperature, T_c. The correlation between these anomalies in both the electronic and thermodynamic properties was interpreted by means of the relationship of Fermi energy to the chemical potential (or to the molar Gibbs free energy).     

On the Spectrum of Non-Selfadjoint Schrödinger Operators with Compact Resolvent

We determine the Schatten class for the compact resolvent of Dirichlet realizations, in unbounded domains, of a class of non-selfadjoint differential operators. This class consists of operators that can be obtained via analytic dilation from a Schrödinger operator with magnetic field and a complex electric potential. As an application, we prove, in a variety of examples motivated by physics, that the system of generalized eigenfunctions associated with the operator is complete, or at least the existence of an infinite discrete spectrum.     

Idiotypic network dysregulation

The pathogenesis of autoimmune disease is still an enigma. Whereas the diverse clinical manifestations of many autoimmune diseases cannot be explained by the existence of autoantibodies, idiotypic dysregulation may provide an alternative explanation. Experimental models, serum level changes of pathogenic idiotypes during exacerbation and remission, and the increased expression of pathogenic idiotypes following common infections all support this notion. In this article we review experimental models of autoimmune disease induction (systemic lupus erythematosus, antiphospholipidsyn drome, Goodpasture's syndrome, autoimmune thyroiditis, and vasculitis) by manipulation of the idiotypic network and discuss the utilization of idiotypes for the immunotherapy of autoimmune diseases and other conditions that involve the immune system (e.g., atherosclerosis).     

Semiclassical spectrum of the two-dimensional non-linear σ models

The spectrum of O(N) invariant two-dimensional non-linear σ models is analyzed for large N by the methods of Dashen, Hasslacher and Neveu. Calculations to $\text{O}\text{(}\text{1}\text{N}\text{)}$ are carried out and the spectrum is shown to consist solely of N degenerate massive mesons. This is consistent with strong coupling lattice calculations and indicates that for sufficiently large N there is no phase transition between the weak and strong coupling regions.