The relationship between the flexural rigidity of standard warp knitted fabrics and fabric and yam parameters, such as wale and course spacing, underlap length of the front and back guide bars, yam bending rigidity, etc., is discussed. In this study, a mechanical model for the bending behaviour of the warp knitted fabrics is also presented. In theoretical analysis, the knitted fabric loop structure is assumed to consist of a series of straight and skew yam simulating legs and underlaps. The estimation of fabric bending rigidity is based on summing up the bending rigidity of the straight and skew yams that found by energy method with taking into account of rigid region lying in the direction of bending. The estimated values from this model are compared with experimental results obtained on a developed automatic cyclic pure bending tester.Comparison with experimental and theoretical data shows reasonable agreement between predicted and measured flexural rigidity of warp knitted fabrics.

The Randers metrics are popular metrics similar to the Riemannian metrics, frequently used in physical and geometric studies. The weak Einstein-Finsler metrics are a natural generalization of the Einstein-Finsler metrics. Our proof shows that if $(M,F)$ is a simply-connected and compact Randers manifold and $F$ is a weak Einstein-Douglas metric, then every special projective vector field is Killing on $(M,F)$. Furthermore, we demonstrate that if a connected and compact manifold $M$ of dimension $n \geq 3$ admits a weak Einstein-Randers metric with Zermelo navigation data $(h,W)$, then either the $S$-curvature of $(M,F)$ vanishes, or $(M,h)$ is isometric to a Euclidean sphere ${\mathbb{S}^n}(\sqrt{k})$, with a radius of $1/\sqrt{k}$, for some positive integer $k$.

We provide an extension of Obata's theorem to Finsler geometry and establish some rigidity results based on a second-order differential equation. Mainly, we prove that every complete simply connected Finsler manifold of positive constant flag curvature is isometrically homeomorphic to a Euclidean sphere endowed with a certain Finsler metric and vice versa. Based on these results, we present a classification of Finsler manifolds which admit a transnormal function. Specifically, we show that if a complete Finsler manifold admits a transnormal function with exactly two critical points, then it is homeomorphic to a sphere.

Pseudotumor cerebri syndrome (PTCS) is an uncommon disease in children. On-time diagnosis and treatment can prevent irreversible visual loss. Although headache is the most common complaint of children with this syndrome, the present case report reported a child with neck rigidity and torticollis, declined by the reduction of intracranial pressure. Despite the importance of torticollis and neck rigidity presented in various significant neurological disorders in need of thorough investigations, in the case of unexplained symptoms of those disorders, it is recommended to consider fundoscopic examinations for PTCS to prevent its vital complications.