Convexity of strata in diagonal pants graphs of surfaces

We prove a number of convexity results for strata of the diagonal pants graph of a surface, in analogy with the extrinsic geometric properties of strata in the Weil-Petersson completion. As a consequence, we exhibit convex flat subgraphs of every possible rank inside the diagonal pants graph.Comment: 14 pages, 4 figure

A glimpse into Thurston's work

We present an overview of some significant results of Thurston and their impact on mathematics. The final version of this paper will appear as Chapter 1 of the book "In the tradition of Thurston: Geometry and topology", edited by K. Ohshika and A. Papadopoulos (Springer, 2020)

Role of high tibial osteotomy in chronic injuries of posterior cruciate ligament and posterolateral corner

High tibial osteotomy (HTO) is a surgical procedure used to change the mechanical weight-bearing axis and alter the loads carried through the knee. Conventional indications for HTO are medial compartment osteoarthritis and varus malalignment of the knee causing pain and dysfunction. Traditionally, knee instability associated with varus thrust has been considered a contraindication. However, today the indications include patients with chronic ligament deficiencies and malalignment, because an HTO procedure can change not only the coronal but also the sagittal plane of the knee. The sagittal plane has generally been ignored in HTO literature, but its modification has a significant impact on biomechanics and joint stability. Indeed, decreased posterior tibial slope causes posterior tibia translation and helps the anterior cruciate ligament (ACL)-deficient knee. Vice versa, increased tibial slope causes anterior tibia translation and helps the posterior cruciate ligament (PCL)-deficient knee. A review of literature shows that soft tissue procedures alone are often unsatisfactory for chronic posterior instability if alignment is not corrected. Since limb alignment is the most important factor to consider in lower limb reconstructive surgery, diagnosis and treatment of limb malalignment should not be ignored in management of chronic ligamentous instabilities. This paper reviews the effects of chronic posterior instability and tibial slope alteration on knee and soft tissues, in addition to planning and surgical technique for chronic posterior and posterolateral instability with HTO

Convexity of strata in diagonal pants graphs of surfaces

We prove a number of convexity results for strata of the diagonal pants graph of a surface, in analogy with the extrinsic geometric properties of strata in the Weil-Petersson completion. As a consequence, we exhibit convex flat subgraphs of every possible rank inside the diagonal pants graph

Convexity of strata in diagonal pants graphs of surfaces

We prove a number of convexity results for strata of the diagonal pants graph of a surface, in analogy with the extrinsic geometric properties of strata in the Weil-Petersson completion. As a consequence, we exhibit convex flat subgraphs of every possible rank inside the diagonal pants graph

Selective transfer of cations between two electrolytes using the intercalation properties of Chevrel phases

International audienceA device based on an electrochemical transfer junction (constituted by MxMo6S8 or MxMo6Se8) placed between two tanks allows the transfer of cations by application of current density controlled between electrodes placed in tanks. The transfer protocol was tested on different mixed electrolytes containing cations directly engaged in the batteries industry (M2+ = Co2+, Ni2+, Cd2+, Zn2+, Mn2+, Cu2+). Good performances of the process are provided until 1.6 mA cm−2. The electrolysis through an electrochemical transfer junction made of Chevrel phases represents a suitable method for the selective extraction of cations with appreciable selectivity rates with an appropriate choice of the host lattice (sulfide or selenide). Remarkable separations between Co/Ni, Zn/Mn with Mo6S8 and Cd/Zn, Cd/Ni, Cd/Co and Zn/Ni, with Mo6Se8 were observed