Testing Monotonicity

at arguments of its choice, the test always accepts a monotone f, and rejects f with high probability if it is ε-far from being monotone (i.e., every monotone function differs from f on more than an ε fraction of the domain). The complexity of the test is O(n/ε). The analysis of our algorithm relates two natural combinatorial quantities that can be measured with respect to a Boolean function; one being global to the function and the other being local to it. A key ingredient is the use of a switching (or sorting) operator on functions. Received March 29, 1999     

Oka's conjecture on irreducible plane sextics

We partially prove and partially disprove Oka's conjecture onthe fundamental group/Alexander polynomial of an irreducibleplane sextic. Among other results, we enumerate all irreduciblesextics with simple singularities admitting dihedral coveringsand find examples of Alexander equivalent Zariski pairs of irreduciblesextics.     

Can density functional theory (DFT) be used as an aid to a deeper understanding of tandem mass spectrometric fragmentation pathways?

Prediction of tandem mass spectrometric (MS/MS) fragmentation for non‐peptidic molecules based on structure is of immense interest to the mass spectrometrist. If a reliable approach to MS/MS prediction could be achieved its impact within the pharmaceutical industry could be immense. Many publications have stressed that the fragmentation of a molecular ion or protonated molecule is a complex process that depends on many parameters, making prediction difficult. Commercial prediction software relies on a collection of general heuristic rules of fragmentation, which involve cleaving every bond in the structure to produce a list of ‘expected’ masses which can be compared with the experimental data. These approaches do not take into account the thermodynamic or molecular orbital effects that impact on the molecule at the point of protonation which could influence the potential sites of bond cleavage based on the structural motif. A series of compounds have been studied by examining the experimentally derived high‐resolution MS/MS data and comparing it with the in silico modelling of the neutral and protonated structures. The effect that protonation at specific sites can have on the bond lengths has also been determined. We have calculated the thermodynamically most stable protonated species and have observed how that information can help predict the cleavage site for that ion. The data have shown that this use of in silico techniques could be a possible way to predict MS/MS spectra. Copyright © 2009 John Wiley & Sons, Ltd.     

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Style goods pricing with demand learning

For many industries (e.g., apparel retailing) managing demand through price adjustments is often the only tool left to companies once the replenishment decisions are made. A significant amount of uncertainty about the magnitude and price sensitivity of demand can be resolved using the early sales information. In this study, a Bayesian model is developed to summarize sales information and pricing history in an efficient way. This model is incorporated into a periodic pricing model to optimize revenues for a given stock of items over a finite horizon. A computational study is carried out in order to find out the circumstances under which learning is most beneficial. The model is extended to allow for replenishments within the season, in order to understand global sourcing decisions made by apparel retailers. Some of the findings are empirically validated using data from U.S. apparel industry.     

Characterization of Kovar-to-Kovar laser welded joints and its mechanical strength

For the packaging of a pump laser in butterfly package, the most crucial assembly step is the fiber-to-laser diode coupling and attachment. The use of laser welding as the joining method offers several advantages if compared with the adhesive joints: strong joining strength, short process time and less contamination. This paper reports on laser welding process characteristics; weld strength and its fracture mode. The penetration depth and melt area of laser spot welds were found to be complicated functions of laser pulse energy, intensity, and beam diameter. Effects of pulse width, input power and size of the focal spot on the rate of energy input to the workpieces and consequently, the weld strength were reported. The weld strength was found to be dependent on the overlapping area between the two joining materials. Surface roughness, R_a, has influence on the fraction of energy absorbed, A, and therefore, affecting the penetration depth. Thermal analysis was carried out on the laser-welded joints and its heat-affected zone (HAZ) induced by various power densities was examined. These data are important in order to optimize and utilize the laser welding process as an effective manufacturing tool for fabrication of reliable pump laser.