The convergent syntheses of pyrazinyl and quinoxalinyl phenylmethanones from 2-lithio pyrazines and quinoxalines

Pyrazines and quinoxalines bearing 2-substituents that direct ortho metalation reacted with lithium 2,2,6,6-tetramethylpiperidide to produce 2-substituted-3-lithiopyrazines and quinoxalines. These lithio reagents reacted with N-methoxy-N-methylbenzamide to give good to moderate yields of 3-substituted pyrazinyl or quinoxalinylphenylmethanones. The 3-methylthio substituents of some ketone products were oxidized to methylsulfonyl groups that were susceptible to nucleophilic displacement.     

The crystal structure of a Di(tetramethylammonium)-bis[R,R-tartrato(2-)]-cis-dioxomolybdate(VI), (NMe4)2[MoO2(C4H4O6)2] · EtOH · 1.5 H2O,with comments on tartrate coordination

Summary In the salt (NMe₄[MoO₂(H₂tart)₂] · EtOH · 1.5 H₂O (H₄tart = R,R-(+)-tartaric acid) the tartrato-ligands are linked to molybdenum through a carboxyl oxygen and the vicinal deprotonated hydroxyl oxygen atom, with carboxyl oxygentrans to terminal oxygen of the MoO₂ cis-dioxo core. The configuration about Mo is A. The C-C-C-C torsion angles of the ligands are almost 180°. This enables inter-ligand H-bonding from the uncoordinated hydroxyl groups. The five skeletal atoms from the uncoordinated section of a ligand are nearly co-planar. The probable strong preference fortrans coordination of carboxyl must limit the range of dissolved molybdenum(VI)-tartrate species.     

Effect of crown-ether surfactants on flame atomic absorption and flame emission signals of some monovalent cations

Two surface-active and one surface-inactive 18-crown-6 derivatives were synthesized and evaluated for their abilities to enhance flame atomic absorption and flame emission signals of monovalent cations. Enhancement of potassium signals were noted for the surface-active compounds but not for the surface-inactive compound. The critical micelle concentration was determined and compared to the degree of enhancement. Surfactant-induced signal enhancements are not due to the slight or moderate decrease in the size of the aerosol first produced in the nebulizing chamber. Additional mechanistic considerations are discussed.     

SPECTRAL PERTURBATIONS OF THE AEQUOREA GREEN-FLUORESCENT PROTEIN

Abstract— In the jellyfish Aequorea, the green-fluorescent protein (GFP) functions as the in vivo bio-luminescence emitter via energy transfer from the photoprotein aequorin. Accumulated evidence has indicated that the Aequorea GFP is a relatively inflexible protein. Present evidence, however, indicates that the chromophore environment is readily accessible to a variety of external perturbants. Native Aequorea GFP has an absorbance maximum at 395 nm and a shoulder at 470 nm. In low ionic strength buffer at neutral pH and room temperature the 395/470 nm absorbance ratio is about 2.0. We show that this ratio is highly variable depending upon temperature, ionic strength, protein concentration, and pH. A maximum ratio of 6.5 (at a protein concentration of 18.6 mg/m/) and minimum of 0.42 (at a pH of 12.2) have been measured. In the latter case, the resulting absorption and excitation spectra resemble those of Renilla GFP in spectral shape (but not wavelength maximum). In all cases as the perturbant is varied the resulting spectra pass through a sharp isosbestic point, suggesting a relatively simple two-state mechanism. These spectral perturbations are fully reversible. On the basis of these results, we suggest that the chromophore binding site is conformationally flexible. pH-Dependent changes in the near-UV and visible circular dichroism spectra plus spectrophotometric titration of tyrosine residues lend additional support to this hypothesis.     

Admission control for a multi-server queue with abandonment

In a M/M/N+M queue, when there are many customers waiting, it may be preferable to reject a new arrival rather than risk that arrival later abandoning without receiving service. On the other hand, rejecting new arrivals increases the percentage of time servers are idle, which also may not be desirable. We address these trade-offs by considering an admission control problem for a M/M/N+M queue when there are costs associated with customer abandonment, server idleness, and turning away customers. First, we formulate the relevant Markov decision process (MDP), show that the optimal policy is of threshold form, and provide a simple and efficient iterative algorithm that does not presuppose a bounded state space to compute the minimum infinite horizon expected average cost and associated threshold level. Under certain conditions we can guarantee that the algorithm provides an exact optimal solution when it stops; otherwise, the algorithm stops when a provided bound on the optimality gap is reached. Next, we solve the approximating diffusion control problem (DCP) that arises in the Halfin–Whitt many-server limit regime. This allows us to establish that the parameter space has a sharp division. Specifically, there is an optimal solution with a finite threshold level when the cost of an abandonment exceeds the cost of rejecting a customer; otherwise, there is an optimal solution that exercises no control. This analysis also yields a convenient analytic expression for the infinite horizon expected average cost as a function of the threshold level. Finally, we propose a policy for the original system that is based on the DCP solution, and show that this policy is asymptotically optimal. Our extensive numerical study shows that the control that arises from solving the DCP achieves a very similar cost to the control that arises from solving the MDP, even when the number of servers is small.     

Mixing automorphisms of compact groups and a theorem of Schlickewei

Summary We prove that every mixing ^d by automorphisms of a compact, connected, abelian group is mixing of all orders.Oblatum 5-II-1992The second author gratefully acknowledges support from NSF grant DMS-91-03056 at the Ohio State University     

Rank-one completions of partial matrices and completely rank-nonincreasing linear functionals

We obtain necessary and sufficient conditions for the existence and the uniqueness of rank-one completions of a partial matrix, and we verify a conjecture of Hadwin and Larson concerning the nature of completely rank-nonincreasing linear functionals defined on pattern subspaces.

     

Heavy-traffic limits for many-server queues with service interruptions

We establish many-server heavy-traffic limits for G/M/n+M queueing models, allowing customer abandonment (the +M), subject to exogenous regenerative service interruptions. With unscaled service interruption times, we obtain a FWLLN for the queue-length process, where the limit is an ordinary differential equation in a two-state random environment. With asymptotically negligible service interruptions, we obtain a FCLT for the queue-length process, where the limit is characterized as the pathwise unique solution to a stochastic integral equation with jumps. When the arrivals are renewal and the interruption cycle time is exponential, the limit is a Markov process, being a jump-diffusion process in the QED regime and an O–U process driven by a Levy process in the ED regime (and for infinite-server queues). A stochastic-decomposition property of the steady-state distribution of the limit process in the ED regime (and for infinite-server queues) is obtained.     

Polyharmonic and Related Kernels on Manifolds: Interpolation and Approximation

This article is devoted to developing a theory for effective kernel interpolation and approximation in a general setting. For a wide class of compact, connected C ^∞ Riemannian manifolds, including the important cases of spheres and SO(3), and using techniques involving differential geometry and Lie groups, we establish that the kernels obtained as fundamental solutions of certain partial differential operators generate Lagrange functions that are uniformly bounded and decay away from their center at an algebraic rate, and in certain cases, an exponential rate. An immediate corollary is that the corresponding Lebesgue constants for interpolation as well as for L ₂ minimization are uniformly bounded with a constant whose only dependence on the set of data sites is reflected in the mesh ratio, which measures the uniformity of the data. The kernels considered here include the restricted surface splines on spheres, as well as surface splines for SO(3), both of which have elementary closed-form representations that are computationally implementable. In addition to obtaining bounded Lebesgue constants in this setting, we also establish a “zeros lemma” for domains on compact Riemannian manifolds—one that holds in as much generality as the corresponding Euclidean zeros lemma (on Lipschitz domains satisfying interior cone conditions) with constants that clearly demonstrate the influence of the geometry of the boundary (via cone parameters) as well as that of the Riemannian metric.     

A priori bounds for approximations of Markov programs

This note determines a priori bounds for B. L. Fox's [J. Math. Anal. Appl., 34 (1971), 665–670] scheme of approximating discounted Markov programs, thus refining bounds recently obtained by D. J. White (Notes in Descision Theory No. 43, University of Manchester, 1977). The approximation scheme focuses careful attention on only a subset of the state space and uses a fixed function to characterize future returns outside the designated subset. The a priori bounds are useful to design the specific approximation, that is, to select the appropriate subset on which the approximation is based.