Integral representation formula for generalized normal derivations

For generalized normal derivations, acting on the space of all bounded Hilbert space operators, the following integral representation formulas hold:

 

and

 

whenever is a Hilbert-Schmidt class operator and is a Lipschitz class function on Applying this formula, we extend the Fuglede-Putnam theorem concerning commutativity modulo Hilbert-Schmidt class, as well as trace inequalities for covariance matrices of Muir and Wong. Some new monotone matrix functions and norm inequalities are also derived.

     

The non-integer cyclovoltammetric electron-exchange numbers of reversible redox reactions of adsorbates

Allowing for the interfacial potential distribution it can be shown that the apparent faradaic electron number, n_app, of ad-layers of chemically modified electrodes and the surface redox valency, n, relating to the slope of the peak potential/pH response [Huck (2002) J Solid State Electrochem 6:534] are at least identical, having the same thermodynamic origin. n_app is calculated from the cyclovoltammetric (CV) peak areas above the interpolated base line. At for proton-coupled surface redox reactions, the influence of the potential drop of the diffuse double layer disappears because the capacitor of the corresponding equivalent circuit becomes shortened by proton transfer, whereby the otherwise non-integer n_app or n values now approach the integer electron numbers, n, of the Nernst equation.

An open volume, high isolation, radio frequency surface coil system for pulsed magnetic resonance

We present an open volume, high isolation, RF system suitable for pulsed NMR and EPR spectrometers with reduced dead time. It comprises a set of three RF surface coils disposed with mutually parallel RF fields and a double-channel receiver (RX). Theoretical and experimental results obtained with a prototype operating at about 100 MHz are reported. Each surface RF coil (diameter 5.5 cm) was tuned to f₀ = 100.00 ± 0.01 MHz when isolated. Because of the mutual coupling and the geometry of the RF coils, only two resonances at f₁ = 97.94 MHz and f₂ = 101.85 MHz were observed. We show they are associated with two different RF field spatial distributions. In continuous mode (CW) operation the isolation between the TX coil and one of the RX coils (single-channel) was about −10 dB. By setting the double-channel RF assembly in subtraction mode the isolation values at f₁ or f₂ could be optimised to about −75 dB. Following a TX RF pulse (5 μs duration) an exponential decay with time constant of about 600 ns was observed. The isolation with single-channel RX coil was about −11 dB and it increased to about −47 dB with the double-channel RX in subtraction mode. Similar results were obtained with the RF pulse frequency selected to f₂ and also with shorter (500 ns) RF pulses. The above geometrical parameters and operating frequency of the RF assembly were selected as a model for potential applications in solid state NMR and in free radical EPR spectroscopy and imaging.     

Random coil phosphorus chemical shift of deoxyribonucleic acids

Random coil phosphorus chemical shift has been studied using 16 17-nucleotide DNA sequences. Due to the presence of residual base stacking in these sequences, the temperature and sequence effects were investigated at 50 and 55 degrees C. The phosphorus chemical shifts of random coil DNA sequences have been found to be independent of temperature. Sequence effect analysis shows that the phosphorus chemical shift of a nucleotide in a random coil DNA sequence depends on both its 5'- and 3'-nearest neighbors. A trimer model has been used to establish the random coil 31P chemical shift prediction protocol which shows an accuracy of 0.02 ppm.     

Double covering of curves

Let be a smooth projective algebraic curve of genus and an integer with . For all integers we prove the existence of a double covering with a smooth curve of genus and the existence of a degree morphism that does not factor through . By the Castelnuovo-Severi inequality, the result is sharp (except perhaps the bound ).

     

Comparison Theorems for Four Dimensional Regular Matrices

A four dimensional summability matrix is stronger than convergence in the Pringsheim sense if it sums a divergent double sequence. Presented in this paper are sufficient conditions on a four dimensional matrix transformation which ensure that the summability matrix is stronger than convergence in the Pringsheim sense. Also other sufficient conditions will be presented to ensure the failure of inclusion between two summability matrices.AMS Subject Classification (2000): Primary 40B05.     

Antigen retrieval on formaldehyde-fixed paraffin sections: its potential drawbacks and optimization for double immunostaining

It is well known that the major artifact induced by formaldehyde fixation is the masking of tissue antigens due to cross-linking of protein amino acid residues. Recently many antigen retrieval techniques have been devised to unmask the hidden antigen epitopes and recover immunoreactivity. In this study, some practical problems of two common unmasking techniques, i.e. heat-induced epitope retrieval and enzyme digestion have been reviewed in immunostaining of proliferating cell nuclear antigen (PCNA) on formaldehyde-fixed paraffin-embedded sections. As the heating conditions became more severe, false-positive staining and/or nonspecific background staining occurred. Based on the principle of protein inactivation/denaturation and the possible mechanisms of antigen retrieval, it has been suggested that the antigen retrieval itself can also denature proteins in tissues, just as many other protein inactivation processes. Thus, the total magnitude of protein conformational change caused by the overall unmasking procedure is in practice crucial. To prove this hypothesis and to overcome such undesirable drawbacks after antigen retrieval, a new combination technique of a mild heating condition (microwaved at 80°C for 15–20 min) and pepsin digestion was devised. This technique led to a strong specific immunoreactivity of PCNA, without any undesirable false positive or background staining. The procedure was also adapted for double immunostaining of PCNA together with -actin, bromodeoxyuridine, keratin, type IV collagen and vimentin.     

双程掺镱光纤放大器的增益特征及优化

比较了掺钕光纤和掺镱光纤对1064 nm光放大的特点.基于速率方程和传输方程,数值分析了在915 nm泵浦下双程掺镱光纤放大器的增益特征，并且和传统的单程放大进行了比较.分析了信号光和泵浦光，以及粒子数沿着光纤方向的分布特点.最后对双程掺镱光纤放大器进行了优化.     

基于傅立叶变换的射频场分布测量方法

提出了一种基于傅立叶变换的射频场分布测量方法，该方法可以方便地测量出射频场的分布，其测量结果与样品的均匀度无关并且可以分别观测某个像素点处的层内射频场非均匀性或某个小区域内的射频场非均匀性.     

Fractional diffusion models of option prices in markets with jumps

Most of the recent literature dealing with the modeling of financial assets assumes that the underlying dynamics of equity prices follow a jump process or a Lévy process. This is done to incorporate rare or extreme events not captured by Gaussian models. Of those financial models proposed, the most interesting include the CGMY, KoBoL and FMLS. All of these capture some of the most important characteristics of the dynamics of stock prices. In this article we show that for these particular Lévy processes, the prices of financial derivatives, such as European-style options, satisfy a fractional partial differential equation (FPDE). As an application, we use numerical techniques to price exotic options, in particular barrier options, by solving the corresponding FPDEs derived.