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On s-Quasinormal and c-Normal Subgroups of a Finite Group

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Acta Mathematica Sinica,English Series 2008年第4期24卷 647-654页

作者： Shi rong LI Department of Mathematics Guangxi University Nanning Guangxi 530004 P. R. China

Let F be a saturated formation containing the class of supersolvable groups and let G be a finite group. The following theorems are shown：（1） G ∈ F if and only if there is a normal subgroup H such that G/H ∈ F and every maximal subgroup of all Sylow subgroups of H is either c-normal or s-quasinormally embedded in G; （2） G ∈F if and only if there is a soluble normal subgroup H such that G/H∈F and every maximal subgroup of all Sylow subgroups of F（H）, the Fitting subgroup of H, is either e-normally or s-quasinormally embedded in G.

关键词： s-quasinormally embedded subgroup c-normal subgroup p-nilpotent group saturated formation

Real-Time Thermal Schwinger-Dyson Equation for Quark Self-energy in Landau Gauge

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Communications in Theoretical Physics 2005年第5X期44卷 873-878页

作者： ZHOU Bang-rong College of Physical Sciences Graduate School of the Chinese Academy of Sciences Beijing 100049 China

By means of a formal expression of Cornwall-Jackiw-Tomboulis effective potential for quark propagator at finite temperatures and finite quark chemical potentials, we derive the real-time thermal Schwinger-Dyson equation for quark propagator in Landau gauge. Denote the inverse quark propagator by A（p^2）ψ - B（p^2）, we argue that, when temperature T is lower than the given infrared momentum cutoff pc, A（p^2） = 1 is a feasible approximation and can be assumed in discussions of chiral symmetry phase transition problem in QCD.

关键词： real-time thermal QCD Schwinger-Dyson equation quark propagator Landau gauge

Regularity of the Density for the Total Weighted Occupation Measure of Super-Brownain Motion

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Acta Mathematica Sinica,English Series 2011年第8期27卷 1557-1572页

作者： rong Li LIU Department of Mathematics Nanjing University Nanjing 210093 P. R. China

Let （Xt） be a super-Brownian motion in a bounded domain D in R^d. The random measure Y^D（.） = ∫o^∞ Xt（.）dt is called the total weighted occupation time of （Xt）. We consider the regularity properties for the densities of a class of yD. When d = 1, the densities have continuous modifications. When d ≥ 2, the densities are locally unbounded on any open subset of D with positive y D （dx）-measure.

关键词： Superprocesses Poisson point processes regularity total weighted occupation time

On the Dynamics of the Singularly Perturbed Rational Maps

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Acta Mathematica Sinica,English Series 2010年第2期26卷 265-276页

作者： Lian rong DING Institute of Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 P. R. China

In this paper, we study the dynamics of the family of rational maps fλ,（z） = zn - λ/zm, n ≥2, m ≥ 1,λ ∈ C. We construct an example of buried Sierpinski curve Julia set in this family. We also give an estimate ... 详细信息

关键词： Julia set Sierpinski curve bifurcation locus

Chiral Phase Transition at Finite Isospin Density in Linear Sigma Model

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Communications in Theoretical Physics 2005年第3期43卷 487-492页

作者： SHUSong LIJia-rong InstituteofParticlePhysics Central-ChinaNormalUniversityWuhan430079China

Using the linear sigma model, we have introduced the pion isospin chemical potential. The chiral phase transition is studied at finite temperatures and finite isospin densities. We have studied the μ - T phase diagram for the chiral phase transition and found the transition cannot happen below a certain low temperature because of the BoseEinstein condensation in this system. Above that temperature, the chiral phase transition is studied by the isotherms of pressure versus density. We indicate that the transition, in the chiral limit, is a first-order transition from a low-density phase to a high-density phase like a gas-liquid phase transition.

关键词： finite temperature field theory nuclear matter chiral symmetries

The slip rate and strong earthquake recur-rence interval on the Qianning-Kangding segment of the Xianshuihe fault zone

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Acta Seismologica Sinica(English Edition) 2001年第3期14卷 263-273页

作者： ZHOU rong-jun 1. Seismological Bureau of Sichuan Province 610041 Chengdu China

The geometry of the Qianning-Kangding segment of the Xianshuihe fault zone is quite complex, and it is composed of four secondary-faults, i.e., the Yalahe fault, Selaha-Kangding fault, Zeduotang fault and Moxi fault. On this segment, three strong earthquakes with M greater than or equal 7.0 occurred in 1725, 1786 and 1955, respectively. Based on a study of fault landform and geochronology (14C and Thermoluminesense), this paper documents the average horizontal slip rates during the late-Quaternary on all the secondary-faults of the Qianning-Kangding segment as follows: Yalahe fault: (2.0±0.2) mm/a; Selaha-Kangding fault: (5.5±0.6) mm/a; Zeduotang fault: (3.6±0.3) mm/a; Moxi fault: (9.9±0.6) mm/a. The results from the investigation of surface ruptures of historical earthquakes, coseismic-slip and paleo-earthquakes show that the strong-earthquake recurrence intervals are thousands of years on the Yalahe fault, and 230 to 350 years on the Selaha-Kangding and Zeduotang faults. In the next one hundred years, the recurrence of a strong-earthquake on these faults appears impossible. However, the strong-earthquake recurrence interval on the Moxi fault is about 300 years. Up to now, it has been 214 years since the last earthquake (magnitude 7 3/4) occurred in 1786, therefore, this fault is now approaching the condition favorable for the next strong earthquake recurrence.

关键词： slip rate recurrence interval fault landform paleo-earthquake seismic potential P315.72+5

The Existence of Weak Solutions to the 2D Euler Equations with Initial Vorticity in BMO

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Acta Mathematica Sinica,English Series 2007年第10期23卷 1881-1888页

作者： Xiang rong ZHU Department of Mathematics Zhejiang University Hangzhou 310027 P. R. China

We shall prove that there exists a weak solution to the 2D Euler equations with initial vorticity in BMO and initial velocity in L^∞.

关键词： Euler equation weak solution BMO

Explicit Proof of Equivalence of Two—Point Functions in the Two Formalisms of Thermal Field Theory

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Communications in Theoretical Physics 2002年第1期37卷 49-54页

作者： ZHOUBang－rong DepartmentofPhysics GraduateSchoolTheChineseAcademyofSciencesBeijing100039China

We give an explicit proof of equivalence of the two-point function to one-loop order in the two formalisms of thermal theory based on the expressions in the real-time formalism and indicate that the key point of completing the proof is to separate carefully the imaginary part of the zero-temperature loop integral from relevant expressions and this fact will certainly be very useful for examination of the equivalent problem of two formalisms of thermal field theory in other theories, including the one of the propagators for scalar bound states in an NJL model.

关键词： two-point function thermal field theory equivalence of the imaginary-time and real-time formalisms imaginary part of zero-temperature loop

On Two Theorems of Finite Solvable Groups

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Acta Mathematica Sinica,English Series 2005年第4期21卷 797-802页

作者： Shi rong LI Department of Mathematics Guangxi University Nanning 530004 P. R. China

For a finite group G, let T（G） denote a set of primes such that a prime p belongs to T（G） if and only if p is a divisor of the index of some maximal subgroup of G. It is proved that if G satisfies any one of the following conditions：（1） G has a p-complement for each p∈T（G）; （2）│T（G）│= 2：（3） the normalizer of a Sylow p-subgroup of G has prime power index for each odd prime p∈T（G）; then G either is solvable or G/Sol（G）≌PSL（2, 7） where Sol（G） is the largest solvable normal subgroup of G.

关键词： Finite solvable group The index of a maximal subgroup Simple group