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.

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.     

大学物理实验的简化与深化

以复摆实验、地磁实验和衍射光栅实验为例,说明在大学物理实验中,通过提供简单的实验器材,就可以将实验内容延伸扩展,将原来内容单一的实验扩展为多层次、多目的的实验项目,实现大学物理实验的简化与深化.     

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.     

Synthesis and reconstruction of computer generated holograms by a double pass technique on a twisted nematic-based liquid crystal spatial light modulator

Achieving phase only modulation from a spatial light modulator (SLM) is useful for many optical processing tasks. In this paper, we demonstrate a simple method of decoupling phase and amplitude modulation in a twisted nematic liquid crystal (TNLC) SLM using a double pass technique. A Jones calculus model is developed which matches our experimental data.     

On singular univariate specializations of bivariate hypergeometric functions

It is tempting to evaluate F₂(x,1) and similar univariate specializations of Appell's functions by evaluating the apparent power series at x=0 straight away using the Gauss formula for ₂F₁(1). But this kind of naive evaluation can lead to errors as the ₂F₁(1) coefficients might eventually diverge; then the actual power series at x=0 might involve branching terms. This paper demonstrates these complications by concrete examples.     

Double peaks on ac magnetization in a superconducting Pb-porous glass nanocomposite

Studies of temperature dependences of ac magnetization were carried out for a superconducting lead-porous glass nanocomposite. Double peaks were found on the imaginary part of ac magnetization which were accompanied with double steps on the real part. The lower-temperature anomalies in ac magnetization differed noticeably when they were obtained upon cooling and warming. The double peaks were treated as two phase transitions in the vortex system: the liquid-solid transition which occurs close to the onset of superconductivity and solid-solid one which is triggered by superconductivity in confined lead islands.