We consider the scattering and lens rigidity of compact surfaces with boundary that have a trapped geodesic. In particular we show that the flat cylinder and the flat Möbius strip are determined by their lens data. We also see by example that the flat Möbius strip is not determined by it’s scattering data. We then consider the case of negatively curved cylinders with convex boundary and show th...

We study the local geometry of the space of horizontal curves with endpoints freely varying in two given submanifolds P and Q of a manifold M endowed with a distribution D ⊂ TM. We give a different proof, that holds in a more general context, of a result by Bismut [2, Theorem 1.17] stating that the normal extremizers that are not abnormal are critical points of the sub-Riemannian action functio...

The Jacobin doubly periodic wave solution, the Weierstrass elliptic function solution, the bell-type solitary wave solution, the kink-type solitary wave solution, the algebraic solitary wave solution, and the triangular solution of a generalized Korteweg-de Vries-modified Korteweg-de Vries equation (GKdV-mKdV) with higher-order nonlinear terms are obtained by a generalized subsidiary ordinary d...

Agriculture workers have increased rates of airway and skeletal disease. Inhalant exposure to agricultural organic dust extract (ODE) induces bone deterioration in mice; yet, mechanisms underlying lung-bone crosstalk remain unclear. Because Toll-like receptor 2 (TLR2) and TLR4 are important in mediating the airway consequences of ODE, this study investigated their role in regulating bone respon...

stylistic is a branch of modern linguistic which surveys and analyzes the literary styles and technical methods. formalism school is one of important modern approaches in stylistics. russian formalisms believe that only the style (frame) can determine the meaning and the concept of the context. mahmoud darvish – palestinian poet – is one of the poets who worked in modernism style. he could pres...

in the modern era, under the  influence of the western literary criticism has been highly spoken  about organic  unity in arabic ode but many  researchers and critics is established incomplete concept of organic unity in their minds and think it means the ode become confined  to an personal experience or a feeling and while they study it in the poetry they are amaze between logical unity and th...

We consider model selection and estimation in a context where there are competing ordinary differential equation (ODE) models, and all the models are special cases of a "full" model. We propose a computationally inexpensive approach that employs statistical estimation of the full model, followed by a combination of a least squares approximation (LSA) and the adaptive Lasso. We show the resultin...