A duality relation for busy cycles inGI/G/1 queues

Using a generalization of the classical ballot theorem, Niu and Cooper [7] established a duality relation between the joint distribution of several variables associated with the busy cycle inM/G/1 (with a modified first service) and the corresponding joint distribution of several related variables in its dualGI/M/1. In this note, we generalize this duality relation toGI/G/1 queues with modified first services; this clarifies the original result, and shows that the generalized ballot theorem is superfluous for the duality relation.     

Design of the cold atom PHARAO space clock and initial test results

In this paper we describe the cold atom clock PHARAO, designed for microgravity operation. All elements of the PHARAO engineering model have been manufactured and delivered to CNES, the French space agency. We present the clock design, its main characteristics, and initial science operation. PHARAO is one of the main components of the Atomic Clock Ensemble in Space payload that is scheduled to fly on board the International Space Station in 2010. PACS 07.87.+v; 06.30.Ft; 95.55.Sh; 32.80.Pj     

A Partial Differential Inequality in Geological Models

Sedimentation and erosion processes in sedimentary basins can be modeled by a parabolic equation with a limiter on the fluxes and a constraint on the time variation.This limiter happens to satisfy a stationary scalar hyperbolic inequality,within a constraint,for which the authors prove the existence and the uniqueness of the solution.Actually,this solution is shown to be the maximal element of a convenient convex set of functions.The existence proof is obtained thanks to the use of a numerical scheme.     

Some remarks on Newton–Sabatier methods

It is shown how Newton–Sabatier methods (arising in inverse scattering at fixed energy) can be related to spectral measures and typically when they correspond to regular potentials. A number of spectral formulae for various transmutation kernels are also given in terms of general Kontorovi?–Lebedev theory and connections to generating functions, generalized orthogonal polynomials, etc. are indicated.     

Microstructure array on Si and SiOx generated by micro-contact printing, wet chemical etching and reactive ion etching

A method, combining micro-contact printing (μCP), wet chemical etching and reactive ion etching (RIE), is reported to fabricate microstructures on Si and SiOx. Positive and negative structures were generated based on different stamps used for μCP. The reproducibility of the obtained microstructures shows the methodology reported herein could be useful in Micro-Electro-Mechanical Systems (MEMS), optical and biological sensing applications.     

Colliding stacks: A large deviations analysis

We analyze the performance of a prototypical scheme for shared storage allocation: two initially empty stacks evolving in a contiguous block of memory of size m. We treat the case in which the stacks are more likely to shrink than grow, but with the probabilities of insertion and deletion allowed to depend arbitrarily on stack height as a fraction of m. New results are obtained on the m → ∞ asymptotics of the stack collision time, and of the final stack heights. The results of Wentzell and Freidlin on the large deviations of Markov chains are used, and the relation of their formalism to the Hamiltonian formulation of classical mechanics is emphasized. Certain results on higher-order asymptotics follow from WKB expansions.     

Continuous-Wave Operation of a 460-GHz Second Harmonic Gyrotron Oscillator

We report the regulated continuous-wave (CW) operation of a second harmonic gyrotron oscillator at output power levels of over 8 W (12.4 kV and 135 mA beam voltage and current) in the TE(0,6,1) mode near 460 GHz. The gyrotron also operates in the second harmonic TE(2,6,1) mode at 456 GHz and in the TE(2,3,1) fundamental mode at 233 GHz. CW operation was demonstrated for a one-hour period in the TE(0,6,1) mode with better than 1% power stability, where the power was regulated using feedback control. Nonlinear simulations of the gyrotron operation agree with the experimentally measured output power and radio-frequency (RF) efficiency when cavity ohmic losses are included in the analysis. The output radiation pattern was measured using a pyroelectric camera and is highly Gaussian, with an ellipticity of 4%. The 460-GHz gyrotron will serve as a millimeter-wave source for sensitivity-enhanced nuclear magnetic resonance (dynamic nuclear polarization) experiments at a magnetic field of 16.4 T.