A note on Koornwinder's polynomials with weight function (1−x)α(1+x)β+Mδ(x+1)+Nδ(x−1)

We derive the distribution and three-term recurrence relation for the Koornwinder [2] polynomials with weight function shown above using the method developed in our paper [3]. We are able to obtain explicit expressions for the linear functional in terms of the coefficients of the three-term recurrence relation for the Jacobi polynomials and we obtain the distribution using a more direct approach.     

Mass spectrometry compatibility of two-dimensional gel protein stains

As proteomic technology evolves, protein staining sensitivity is constantly being improved, enabling researchers to better visualize the proteome of their system. The current challenge is to balance the limits of detection of protein visualization with those of the mass spectrometric methods. In this report, mass spectra generated from human serum or rat liver proteins stained with either colloidal Coomassie blue, Daiichi silver, SYPRO Orange, SYPRO Red, SYPRO Ruby, or SYPRO Tangerine are compared. It has been concluded that the newest generation of fluorescent protein stains, compared with traditional staining methods, are more compatible to matrix-assisted laser desorption/ionization (MALDI) and liquid chromatography-tandem mass spectrometry (LC-MS/MS) methods. The number of database matches obtained using each mass spectrometry method and the percent sequence coverage obtained from trypsin digested proteins stained using these six methods is provided.     

Vinylation and polymerization with trivinylaluminum. I. Vinylation of organic halides as a model for termination in cationic polymerization leading to vinyl end groups

An improved synthesis of trivinylaluminum (V₃Al) is described. The proton magnetic resonance (PMR) spectrum of V₃Al was recorded and analyzed. A new vinylation method involving the use of V₃Al as the vinylating agent has been developed, and the vinylation of organic halides by V₃Al was studied at ?30, ?50 and ?70°C. Primary alkyl chlorides, such as methyl and methylene chloride, do not react with V₃Al and were used as solvents. Secondary chlorides such as 2-chloropropane also do not react. t-Butyl chloride gives rise to t-butylethylene (70–98%), depending on reaction conditions, and the allylic chlorides, 3-chloro-1-butene, and 3-chloro-3-methyl-1-butene, yield the expected vinylated products and their isomers (～90%). Allyl and benzyl chloride do not react under the conditions tried. The reaction between V₃Al and the ditertiary dichloride 2,6-dichloro-2,6-dimethylheptane yields several isomeric C₁₃H₂₄ and C₁₁H₂₀ hydrocarbons; however, surprisingly, C₉H₁₆ does not form. The C₁₃ hydrocarbons arise by divinylation at the termini of the dichloride, while the C₁₁ hydrocarbons are formed by vinylation at one and proton elimination at the other terminus of the dichloride. The presence of unsaturated C₁₃H₂₄ and C₁₁H₂₀ isomers is most likely due to proton induced isomerization. These results are explained by a proximity effect involving vinylation at one end of the dichloride by V₃Al followed by rapid reaction of the second chlorine (mostly) by V₂AlCl generated in situ during the first vinylation in the proximity of the chloride. At the other chlorine terminus V₂AlCl causes either a second vinylation (leading to C₁₃ hydrocarbons) or a proton elimination (leading to C₁₁ hydrocarbons). The absence of C₉H₁₆ among the reaction products indicates that V₃Al exclusively effects vinylation. The RCl + V₃Al ← RV + V₂AlCl reaction may be regarded as a model for initiation followed by immediate termination in cationic olefin polymerization, a process leading to vinyl-ended polymers.     

On the Homeomorphism Groups of Cantor's Discontinuum and the Spaces of Rational and Irrational Numbers

The paper shows that the homeomorphism groups of, respectively,Cantor's discontinuum, the rationals and the irrationals haveuncountable cofinality. It is well known that the homeomorphismgroup of Cantor's discontinuum is isomorphic to the automorphismgroup Aut B of the countable, atomless boolean algebra B. Soalso Aut B has uncountable cofinality, which answers a questionposed earlier by the first author and H. D. Macpherson. Thecofinality of a group G is the cardinality of the length ofa shortest chain of proper subgroups terminating at G. 2000Mathematics Subject Classification 20B22, 20E15.     

Linear optics controlled-phase gate made simple

Linear optics quantum logic gates are the best tool to generate multiphoton entanglement. Simplifying a recent approach, we were able to implement the conditional phase gate with only one second-order interference at a polarization dependent beam splitter, thereby significantly increasing its stability. The improved quality of the gate is evaluated by analyzing its entangling capability and by performing full process tomography. The achieved results ensure that this device is well suited for implementation in various multiphoton quantum information protocols.     

Resolving pm wavelength shifts in optical sensing

The reflection or transmission properties of one and two-dimensional photonic crystals are widely used for optical sensing applications. A variety of optical sensors exist that change their optical properties upon receiving a stimulus. A compact wavelength detector capable of resolving very small changes in the spectral output of these sensors is highly desirable. A photodiode array (PDA) or position sensor device (PSD) in combination with a linear variable band-pass filter constitutes a very robust and compact device to detect those changes. The filter converts the wavelength information of the incident light into a spatial intensity distribution that is analyzed by the photodetector. We have investigated the performance of these wavelength detectors depending on the optical properties of the filter. This includes the gradient with which the transmission peak shifts across the filter surface and the spectral width of the transmission function. Also, we point out differences between the PDA and the PSD and analyze the influence of inhomogeneous illumination on the unit. PACS 42.68.Ay; 42.79.-e; 42.81.Pa     

Nonparametric Statistical Methods and the Pricing of Derivative Securities

In this review paper we summarise several nonparametric methods recently applied to the pricing of financial options. After a short introduction to martingale-based option pricing theory, we focus on two possible fields of application for nonparametric methods: the estimation of risk-neutral probabilities and the estimation of the dynamics of the underlying instruments in order to construct an internally consistent model.