Effective potential for local composite operators and the problem of factorization of multi-field condensates

A new formulation of effective potential for local composite operators is given. The two-fermion condensate \(\langle \bar \Psi \Psi \rangle \) and four-fermion condensate \(\langle \bar \Psi \Psi \bar \Psi \Psi \rangle \) are calculated simultaneously in the Gross-Neveu model up to next-to-the-leading order in 1/N expansion. It is shown that factorization \(\langle \bar \Psi \Psi \bar \Psi \Psi \rangle = C_1 \langle \bar \Psi \Psi \rangle ^2 \) holds only in theN→∞ limit and the non-factorized part of \(\langle \bar \Psi \Psi \bar \Psi \Psi \rangle \) contributed by the order-1/N terms is comparable to \(C_1 \langle \bar \Psi \Psi \rangle ^2 \) when takingN=3.     

Exponential approximations in the classes of life distributions

In this paper we discuss the approximation of life distributions by exponential ones. The main results are: (1) F NBUE, where its mean is 1, we have , 0, where = 1 - ₂/2, ₂ being the second moment ofF. The inequality is sharp. (2) In the case ofFIFR, the upper bound is . (3) For the HNBUE class, the upper bound is min . Furthermore, the improved upper bound is . In addition, we show 0} |\bar G(t) - e^{ - t} | \leqslant \sqrt {\frac{\rho }{2}} $$ " align="middle" border="0"> , where (4) For the IMRL class, the upper bound is /(1+) ([1]). Here we give a simple proof.Project supported by the National Natural Science Fund of China.     

Indirect laser photoacoustic detection for trace samples on membranes

An indirect laser photoacoustic technique is described. The basic principle, the experimental set-up and the influencing factors are discussed in detail. This method was used to quantify phenylamine, arginine and methylene blue on membranes. The linear ranges of the calibration curve are up to two orders of magnitude. With 1 microliter of sample solution, the detection limits are 0.25, 1.52 and 0.14 pmol for phenylamine, arginine and methylene blue, respectively.     

Molar conductivity calculation of Li-ion battery electrolyte based on mode coupling theory

A method is proposed to calculate molar conductivity based on mode coupling theory in which the ion transference number is introduced into the theory. The molar conductivities of LiPF6, LiClO4, LiBF4, LiAsF6 in PC (propylene carbonate) are calculated based on this method. The results fit well to the literature data. This presents a potential way to calculate the conductivities of Li-ion battery electrolytes.