K-Ar Dating of Fault Gouges from the Red River Fault Zone of Vietnam

Constraining the timing of fault zone formation is fundamentally important in terms of geotectonics to understand structural evolution and brittle fault processes.This paper presents the first authigenic illite K-Ar age data from fault gouge samples collected from the Red River Shear Zone at Lao Cai province,Vietnam.The fault gouge samples were separated into three grain-size fractions（〈0.1 μm,0.1-0.4 μm and 0.4-1.0 μm）.The results show that the K-Ar age values decrease from coarser to finer grain fractions（24.1 to 19.2 Ma）,suggesting enrichment in finer fraction of morerecently grown authigenic illites.The timing of the fault movement are the lower intercept ages at 0%detrital illite（19.2 ± 0.92 Ma and 19.4 ± 0.49 Ma）.In combination with previous geochronological data,this result indicates that the metamorphism of the Day Nui Con Voi（DNCV） metamorphic complex took place before ca.26.8 Ma.At about 26.8 Ma-25 Ma,the fault strongly acted to cause the rapid exhumation of the rocks along the Red River-Ailoa Shan Fault Zone（RR-ASFZ）.During brittle deformation,the DNCV slowly uplifted,implying weak movement of the fault.This brittle deformation might have lasted for ca.5 Ma.

ASYMPTOTIC BEHAVIOR OF LINEAR ADVANCED DIFFERENTIAL EQUATIONS

In this article, we consider a general class of linear advanced differential equa- tions, and obtain explicitly sufficient conditions of convergence and exponential convergence to zero. A necessary condition is provided as well.

DENSITY ESTIMATES FOR SOLUTIONS OF STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS

In this article, we investigate the density of the solution to a class of stochastic functional differential equations by means of Malliavin calculus. Our aim is to provide upper and lower Gaussian estimates for the density.

ITÔDIFFERENTIAL REPRESENTATION OF SINGULAR STOCHASTIC VOLTERRA INTEGRAL EQUATIONS

In this paper we obtain an Itôdifferential representation for a class of singular stochastic Volterra integral equations.As an application,we investigate the rate of convergence in the small time central limit theorem for the solution.

Comparative Study of Light Manipulation in Three-Level Systems Via Spontaneously Generated Coherence and Relative Phase of Laser Fields

We present a comparative study of the control of group velocity in three-level atomic systems including Λ-, Ladder-, and V-types via spontaneously generated coherence(SGC) and relative phase of laser fields.In the steady regime, expressions of group index are derived as an analytical function of controllable parameters related to SGC and relative phase.It is shown that the group velocity can be further slowed down or speeded up under SGC in which modifications of group velocity due to the SGC in Λ-and V-systems are stronger than that in Ladder-system.In particular, when interference strength of SGC p increases from 0.7 to 1.0, the light propagation is switched from superluminal to subluminal modes(for Λ-and Ladder-systems) or from subluminal to superluminal modes(for Vsystem).In the presence of relative phase, the group velocity changes between subluminal and superluminal modes with a period of 2π.In resonant region, the largest positive value of group index reaches at the relative phase φ=π while the largest negative value of group index reaches at φ= 0 and 2π for the Λ-and Ladder-systems, otherwise, for the V-system the largest positive group index occurs at φ= 0 and 2π, and the largest negative group index occurs at φ=π.