Trace formula of the integro-differential operator on a quantum graph

In this paper we study the eigenvalue problem for integro-differential operators on a lasso graph.The trace formula of the operator is established by applying the residual technique in complex analysis.

Inverse resonance problems with the discontinuous conditions

In this paper,we consider the inverse resonance problems for the discontinuous and non-selfadjoint Sturm-Liouville problem.We prove the uniqueness theorem and provide a reconstructive algorithm for the potential by using the Cauchy data and Weyl function.

Inverse nodal problem for the Sturm-Liouville operator with a weight

In this work,we consider the inverse nodal problem for the Sturm-Liouville problem with a weight and the jump condition at the middle point.It is shown that the dense nodes of the eigenfunctions can uniquely determine the potential on the whole interval and some parameters.

Reconstruction of the Sturm-Liouville operator with discontinuities from a particular set of eigenvalues

Sturm-Liouville operators on a finite interval with discontinuities are considered. We give a uniqueness theorem for determining the potential and the parameters in boundary and under discontinuous conditions from a particular set of eigenvalues, and provide corresponding reconstruction algorithm, which can be applicable to McLaughlin-Rundell＇s uniqueness theorem （see J. Math. Phys. 28, 1987）.

黄土隧道仰拱填充层致裂原因及处治措施研究

为了避免仰拱填充层裂缝对隧道寿命及行车安全产生的不良影响,依托位于甘肃省的某隧道,通过现场调查、数值模拟及现场监测方式,分析了4种不同浸水工况下仰拱填充层变形及开裂规律,探究了隧道仰拱填充层致裂原因,给出了仰拱填充层裂缝的处治措施。结果表明:隧道仰拱部位浸水导致仰拱填充层开裂,开裂位置大致位于浸水区域与未浸水区域的分界上,裂缝沿着隧道开挖方向平行于隧道中线分布,随着横向浸水区域的增大,仰拱填充层裂缝逐渐出现由表面向仰拱底部扩展的趋势;随着隧道横向浸水区域的增加,浸水区域土体强度降低,导致仰拱填充层出现较大沉降,未浸水区域土体强度较高,对隧道仰拱结构有一定支撑作用,使得隧道两侧仰拱填充层出现差异性沉降,在仰拱填充层顶部产生一定的负弯矩,在负弯矩的作用下,仰拱填充层表面出现了较大拉应力,当拉应力大于混凝土极限抗拉强度后,材料发生破坏,导致仰拱填充层表面开裂;当横向软化区域为12 m时,仰拱填充层竖向位移数值计算结果与现场监测数据最大值差约10.95%,仰拱填充层开裂位置与现场裂缝位置大致相同,可确定该隧道横向浸水区域为12 m;采用钢管桩加固以及疏通排水管后,仰拱填充层变形减至8.63 mm,由此可见,采用钢管桩及排水措施对仰拱填充层处治效果较好。