Response mechanism for widened pavement structure subjected to ground differential settlement

By the use of a large-scale ground differential settlement simulator, a full-size model test is performed to study the strain response and the deformation behavior of both the wearing course of asphalt cement and the base course of cement-stabilized gravel. Moreover, with the differential settlement at the bottom of the pavement structure as the constraint condition, a plane finite element model is established, which is used to study the stress variation of different pavement layers in response to the differential settlement of varying magnitudes. It shows that, under the effects of the ground differential settlement, the wearing course is subjected to the tensile stress while the base course to the compressive stress and the maximum additional tensile stress and compressive stress occur in the area of 1 m from the splicing joint between the new and the old subgrade. Plastic deformation develops in both layers when the ground differential settlement reaches 14 cm. When the differential settlement at the bottom of the pavement goes up to 1 cm, the maximum additional stress in the surface of the base course will reach 0. 28 MPa, which surpasses 0.276 MPa that is specified in the current specifications as the maximum splitting tensile strength for cement-stabilized base material.

Periodic Solutions to a Kind of Second Order Neutral Functional Differential Equation in the Critical Case

In this paper, the authors consider the existence of periodic solutions for a kind of second neutral functional differential equation as follows：（x（t） - cx（t -τ）＂ = g（t, x（t - μ（t））） ＋ e（t）,in the critical case ｜c｜ = 1. By employing Mawhin＇s continuation theorem and some analysis techniques, some new results are obtained.

Rational maps as Schwarzian primitives

We examine when a meromorphic quadratic differential φ with prescribed poles is the Schwarzian derivative of a rational map. We give a necessary and sufficient condition: In the Laurent series of φ around each pole c, the most singular term should take the form(1- d2)/(2(z- c)2), where d is an integer, and then a certain determinant in the next d coefficients should vanish. This condition can be optimized by neglecting some information on one of the poles(i.e., by only requiring it to be a double pole). The case d = 2 was treated by Eremenko(2012). We show that a geometric interpretation of our condition is that the complex projective structure induced by φ outside the poles has a trivial holonomy group. This statement was suggested to us by Thurston in a private communication. Our work is related to the problem of finding a rational map f with a prescribed set of critical points, since the critical points of f are precisely the poles of its Schwarzian derivative.Finally, we study the pole-dependency of these Schwarzian derivatives. We show that, in the cubic case with simple critical points, an analytic dependency fails precisely when the poles are displaced at the vertices of a regular ideal tetrahedron of the hyperbolic 3-ball.