Approximation to M/D/1 for ATM CAC, buffer dimensioning and cellloss performance

The authors derive a new, accurate, closed form approximation for the M/D/I queue. This can be arranged to yield expressions for the cell loss probability, the admissible load and the buffer length. These expressions have a direct application to cell scale queueing in ATM networks     

Bayesian network management

We formulate some general network (and risk) management problems in a Bayesian context, and point out some of the essential features. We argue and demonstrate that, when one is interested in rare events, the Bayesian and frequentist approaches can lead to very different strategies: the former typically leads to strategies which are more conservative. We also present an asymptotic formula for the predictive probability of ruin (for a random walk with positive drift) for large initial capital and large number of past observations. This is a preliminary investigation which raises many interesting questions for future research. This revised version was published online in June 2006 with corrections to the Cover Date.     

Nevanlinna-Pick interpolation for non-commutative analytic Toeplitz algebras

The non-commutative analytic Toeplitz algebra is the WOT-closed algebra generated by the left regular representation of the free semigroup onn generators. We obtain a distance formula to an arbitrary WOT-closed right ideal and thereby show that the quotient is completely isometrically isomorphic to the compression of the algebra to the orthogonal complement of the range of the ideal. This is used to obtain Nevanlinna-Pick type interpolation theoremsFirst author partially supported by an NSERC grant and a Killam Research Fellowship.Second author partially supported by an NSF grant.     

Three-dimensional optical measurement of instantaneous pressure

Local perturbations in material density induced in a material by a compressional wave give rise to local perturbations in refractive index. Accurate, high-resolution, three-dimensional, optical measurements of an instantaneous refractive index perturbation in a homogeneous, optically transparent medium may be obtained from measurements of scattered optical intensity alone. The method of generalized projections allows incorporation of optical intensity measurements into an iterative algorithm for computing the phase of the interrogating optical pulse as the solution of a fixed point equation. The complex optical field amplitude, computed in this manner, is unique up to a constant unit magnitude complex coefficient. The three-dimensional refractive index distribution may be computed via the Fourier slice reconstruction algorithm from the optical phase data under the assumption of weak optical scattering. The refractive index perturbation is related to local instantaneous pressure under a linear, small-displacement model for the mechanical wave. A numerical simulation of the measurement experiment, phase recovery, and reconstruction process for a plane piston ultrasound transducer with a semicircular aperture and center frequency of 1.5 MHz is described and corresponds very well with experiment. Experimental data obtained using an 810-nm laser source are used to reconstruct the three-dimensional pressure field from two elements of a 2.5-MHz linear array. Comparison with a measurement obtained via a 500-microm needle hydrophone shows excellent agreement.     

Rate constants for the gas-phase reaction of OH radicals with a series of ketones at 299 ± 2 K

Relative rate constants for the reaction of OH radicals with a series of ketones have been determined at 299 ± 2 K, using methyl nitrite photolysis in air as a source of hydroxyl radicals. Using a rate constant for the reaction of OH radicals with cyclohexane of 7.57 × 10^?12 cm³ molecule^?1 s^?1, the rate constants obtained are (× 10¹² cm³ molecule^?1 s^?1): 2-pentanone, 4.74 ± 0.14; 3-pentanone, 1.85 ± 0.34; 2-hexanone, 9.16 ± 0.61; 3-hexanone, 6.96 ± 0.29; 2,4-dimethyl-3-pentanone, 5.43 ± 0.41; 4-methyl-2-pentanone, 14.5 ± 0.7; and 2,6-dimethyl-4-heptanone, 27.7 ± 1.5. These rate constants indicate that while the carbonyl group decreases the reactivity of C? H bonds in the α position toward reaction with the OH radical, it enhances the reactivity in the β position.     

Magnetic field induced cross relaxation between two different spin transitions of triplet coumarin

At certain magnetic fields, when the energy separations between the τ_x — τ_y spin levels and between the τ_y — τ_z levels of triplet coumarin become equal, intensity changes are observed in the phosphorescence of coumarin doped in a single crystal of durence cooled to 1.6 K that can be attributed to cross relaxation (CR) between the τ_x — τ_y spin levels of one triplet coumarin molecule and the τ_y — τ_z spin levels of another triplet coumarin. Rate equations that describe the time behavior of the populations of the spin levels which are involved in the CR process are described and numerically solved. CR behavior is found to be strongly dependent on the total coumarin triplet concentration.     

Distortion and orientation for triplet coronene in different n-heptane shpol'skii sites using polarized microwave midp technique

Using phosphorescence microwave double resonance techniques, the type of distortion and the orientation of the magnetic axes are determined for triplet coronene molecules in different Shpol'skii sites in n-heptane single crystals at 1.6 K. Coronene triplet molecules in different sites are found to differ one from another not only in orientation but also in the degree and the sense (quinoidal versus antiquinoidal) of the distortion of the hexagonal coronene structure.     

The Optimal Choice of the Smoothing Constant in an Inventory Control System

In controlling stock it is necessary to make some estimate of future demand for each stock item. Exponential smoothing is a convenient and automatic means of making such an estimate and the optimal choice of the smoothing constant alpha will depend upon the order of smoothing employed, the relative magnitudes of the random and systematic variations in demand which may occur, the replenishment lead time and also the manner in which the rule used for generating replenishment orders is formulated. The dependence both of optimal alpha and of the necessary safety stock upon these factors has been investigated by means of a model which is believed to be of wide application in industry, and a method has been developed for setting up decision rules for both single and multi-stage systems.     

A modified approach to 2-(N-aryl)-1,3-oxazoles: application to the synthesis of the IMPDH inhibitor BMS-337197 and analogues

[structure: see text] A modified approach to the synthesis of 2-(N-aryl)-1,3-oxazoles, employing an optimized iminophosphorane/heterocumulene-mediated methodology, and its application to the synthesis of BMS-337197, a potent inhibitor of IMPDH, are described.