Three-dimensional correlated-fermion phase separation from analysis of the geometric mean of the individual susceptibilities

A quasi-Gaussian approximation scheme is formulated to study the strongly correlated imbalanced Fermions thermodynamics, where the mean-field theory is not applicable. The non-Gaussian correlation effects are understood to be captured by the statistical geometric mean of the individual susceptibilities. In the three-dimensional unitary fermions ground state, a universal nonlinear scaling transformation relates the physical chemical potentials with the individual Fermi kinetic energies. For the partial polarization phase separation to full polarization, the calculated critical polarization ratio is δ _C = [1−(1−ξ)^6/5]/[1+(1−ξ)^6/5] ≐ 0.34. ξ = 4/9 gives the ratio of the symmetric ground state energy density to that of the ideal fermion gas. Supported by the National Natural Science Foundation of China (Grant Nos. 10875050 and 10675052), the Fund of Central China Normal University, and the Foundation of Ministry of Education of China (Grant No. IRT0624)     

Recursive method for opacity expansion at finite temperature

Using a reaction operator approach, we derive the multiple-scattering induced gluon number distribution function to all orders in powers of opacity at finite temperature. The detailed balance effect is analyzed by taking into account both gluon emission and absorption in a thermal medium. We also calculate virtual corrections and show that the infrared divergence cancels out in the gluon distribution function at finite temperature.     

冷蒸气原子吸收光谱法测定铜精矿中的汞

本文研究了一种用冷蒸气原子吸收光谱测定铜精矿中汞的方法。铜精矿用逆王水或硫酸-高锰酸钾(固)消化后用测汞仪测定其中的汞含量。测定结果的相对标准偏差小于5%;回收率在92-107%之间。     

The Fourier slice theorem for ultrasonic reflectivity tomography and the correction to the effect caused by curvature of integral lines

For ultrasonic reflective tomographic imaging of differenttransmitter-receiver mode,we demonstrate that the Fourier slice theorem canbe used when the distance between the transducer and origin becomes muchlarger than the object to be reconstructed.Iterative reconstruction formulabased on the Fourier slice theorem is proposed for the case in which theparaxial approximation holds.The effect caused by the curvature of integrallines may be eliminated iteratively and better reconstructed images can be ex-pected.     

A Rapid Parallel Synthesis of 2-Dialkylamino-4(3H)-quinazolines

Many 4(3H)-quinazolinones possess biological and pharmaceutical activities. For example, some of them exhibited good antiinflammatory and noncompetitive AMPA receptor antagonistical activities1-3, whereas others exhibited good anticancer and antiviral activities4-6. Among them, 2-amino-4(3H)-quinazolinones were found to show significant fungicidal activities or used as potential potassium channel openers7-9. Recently, combinatorial synthesis of libraries containing small organic molecules …     

高能电子-正电子碰撞中产生喷注的标度

对高能电子-正电子对撞产生实验上可以直接观察的可视喷注的标度进行了仔细研究.根据在s=17—30Gev的电子-正电子对撞实验中最先观察到三喷注这一历史事实,论证了可视喷注的相对横动量kt.在5—10GeV/c的范围.并通过一个具体例子说明,只有k_t在这一范围时才能正确地判定事件中的喷注数.仔细比较了由不同k_t得到的喷注内部的动力学起伏,发现只有k_t在5—10GeV/c范围时,喷注内部系统才有最好的反常标度性.从而得到,可视喷注的标度是k_t～5—10GeV/c.讨论了这一标度和微扰QCD的标度1—2GeV之间的关系.     

A NOTE ON SINGULAR VALUE DECOMPOSITION FOR RADON TRANSFORM IN R~n

The singular value decomposition is derived when the Radon transform is restricted to functions which are square integrable on the unit ball in Rn with respect to the weight Wλ(x). It fulfilles mainly by means of the projection-slice theorem.The range of the Radon transform is spanned by products of Gegenbauer polynomials and spherical harmonics. The inverse transform of the those basis functions are given. This immediately leads to an inversion formula by series expansion and range characterizations.     

ON THE SINGULAR VARIATIONAL PROBLEMS

The authors deal with the singular variational problem S(a,b,λ0):=infu∈E,u(≡／)0 ∫RN(||X|-a(△)u|m ∫|x|-(a 1)m|u|m)dx/(∫RN||X|-bU|P dx)m/p as well as (S)=(S)(a,b,λ1,λ2):=u,ν,E∈,u(u,ν)(≡／)(1,1) ∫RN J(u,ν)dx/(∫RN|x|-bp|u|α|ν|βdx)m/p, whereJ(u, v) = ||x|- au|m λ1|x|- (a 1)m|u|m ||x|- av|m λ2|x|- (a 1)m|v|m,N ≥ m 1 ＞ 2, 0 ≤ a ＜ N-m/m, a ≤ b ＜ a 1 and p = p(a,b) = α β =Nm/N-m m(b-a), α, β≥ 1, E = D1,mα(RN). The aim of this paper is to show the existence of minimizer for S(a, b, A0) and S(a, b, λ1, λ2).     

Large deviations viewpoints for a heavy-tailed β-mixing sequence

Let (Xn;n≥1) be a stationary sequence of non-negative random variables with heavy tails. Under mixing conditions, we study logarithmic asymptotics for the distributions of the partial sums sn=X1 X2 … Xn. We obtain the crude estimates P(Sn>nx)≈n-αx 1 for appropriate values of x, where a is a specific parameter. The related conjecture proposed by Gantert is investigated. As a by-product, the so-called supremum large deviations principle is also studied.     

Studies on the Physical Properties of Alkanes Using Edge-adjacency Information Topological Index

Edge-adjacency index and information topological index for 82 molecules of alkanes nave been constructed and calculated. The topological indices were used to correlate with seven physical properties of the alkanes. Some empirical equations were obtained through regression. The regression and calculation results show a good agreement of the topological indices and the properties.