唐张阶《黄赋》本事考

张阶《黄赋》,见存于《文苑英华》卷一一四、《历代赋汇》卷二三、《全唐文》卷四○五。有关张阶其人,《全唐文》卷四○五仅以“阶,天宝时人”简言之。清徐松《登科记考》卷八将其列为“开元二十三年进士”,另据天宝七载(748)张阶撰《唐故河南府洛阳县尉顿丘李公墓志铭并序》。

唐代士人张阶的《无声乐赋》探究

唐代士人张阶的《无声乐赋》出自清代董诰等人编写的《全唐文》,目前学界鲜有人关注。《全唐文》中对张阶的介绍只有一句话:"阶,天宝时人。"(1)虽然短短五个字难以充分描述张阶的个人特点,但"天宝时人"这一年号信息却透漏出这位唐代士人所生活的年代正经历着唐王朝最为动荡的历史时期。天宝十四年(755)对于唐王朝来说是个不寻常的一年,掌管平卢、范阳、河东三镇的节度使安禄山联合将领史思明以诛杀宰相杨国忠为名发动叛乱,史称"安史之乱"。

Second Order Parallel Tensors on Quasi-constant Curvature Manifolds

The author establishes in this paper the following results: (1) In a quasiconstant curvature manifold M a parallel tensor of type is constant multiple of the metric tensor. (2) On a quasi_constant curvature manifold there is no nonzero parallel 2_form. Unless the Ricci principal curvature corresponding to the generator of M is equal to zero.

Crack fluid identification of shale reservoir based on stress-dependent anisotropy

Shale reservoirs are typically very tight, and crack are only a small part of the reservoir. The directional arrangement of cracks leads to the anisotropic characteristics of shale, and the type of fluid filled in cracks affects the shale reservoir evaluation and late development. Many rock physics theories and methods typically use second-and fourthorder crack density tensors to characterize the elastic anisotropy induced by cracks as well as the normal-to-tangential crack compliance ratio to distinguish between dry and saturated cracks. This study def ines an anisotropic crack f luid indicator for vertical transversely isotropy(VTI) media with vertical symmetry axis which is the integration of the normal-to-tangential crack compliance ratio in three directions. A new dimensionless fourth-order tensor, including crack f luid type, azimuth distribution, and geometric shape, is constructed by substituting the normal and tangential compliance into the fourth-order crack density tensor, which can also be used to identify the type of crack fluid in the VTI media. Using the Callovo–Oxfordian shale experimental data, the variation of the elastic properties of dry and saturated shale samples with axial stress is analyzed. The results demonstrate that the anisotropic crack f luid indicator of water-bearing shale samples is less than that of the dry shale samples and that the dimensionless fourth-order tensor of water-bearing shale samples is nearly one order of magnitude greater than that of the dry shale samples. Therefore, the anisotropic crack f luid indicator and dimensionless fourth-order tensor can ref lect the crack f luid type in shale samples and can be used for shale reservoir prediction and f luid identif ication.

A Remark on the Generalized Roper-Suffridge Extension Operator for Almost Stalike Mappings of Order α

Suppose f is an almost starlike function of order α on the unit disk D. In this paper, we will prove that Фn,β2,γ2,…βn,γn（f）（z）=（f（z1）,（f（z1）/z1）^β2（f＇（z1））^γ2 z2,…,（f（z1）/z1）^βn（f＇（z1））^γnzn）1 preserves almost starlikeness of order α on Ωn,p2,…,pn={z=（z1,z2,…,zn）＇∈Cn：∑^n j=1｜zj｜^pj〈1},where 0〈p1≤2,pj≥1,j=2,…,n,are real numbers.

Exact Boundary Observability for a Kind of Second-Order Quasilinear Hyperbolic Systems

Based on the theory of semi-global classical solutions to quasilinear hyperbolic systems, the local exact boundary observability for a kind of second-order quasilinear hyperbolic systems is obtained by a constructive method.

Tensor Fields on Self-Dual Warped AdS_3 Background

Considering rank s fields obey first order equation of motion, we study the dynamics of such fields in a 3-dimensionaJ self-duaJ space-like warped AdS3 black hole background. We obtain a Klein-Gordon-like equation for tensor fields. By using gauge constraint and traceless condition, we will find the exact solutions of the equations of motion. Then, we will Compute the quasi-normal modes by imposing appropriate boundary conditions at horizon and infinity.

Relaxation oscillations induced by an order gap between exciting frequency and natural frequency

The main purpose of the paper is to display the relaxation oscillations, known as the bursting phenomena, for the coupled oscillators with periodic excitation with an order gap between the exciting frequency and the natural frequency. For the case when the exciting frequency is much smaller than the natural frequency, different types of bursting oscillations such as fold/fold, Hopf/Hopf bursting oscillations can be observed. By regarding the whole exciting term as a slow-varying parameter on the fact that the exciting term changes on a much smaller time scale, bifurcations sets of the generalized autonomous system is derived, which divide the parameter space into several regions associated with different types of dynamical behaviors. Two cases with typical bifurcation patterns are focused on as examples to explore the dynamical evolution with the variation of the amplitude of the external excitation. Bursting oscillations which alternate between quiescent states (QSs) and repetitive spiking states (SPs) can be obtained, the mechanism of which is presented by introducing the transformed phase portraits overlapping with the bifurcation diagrams of the generalized autonomous system. It is found that not only the forms of QSs and SPs, but also the bifurcations at the transition points between QSs and SPs, may influence the structures of bursting attractors. Furthermore, the amplitudes and the frequencies related to SPs may depend on the bifurcation patterns from the quiescent sates.