We explore the geometric notion of prolongations in the setting of computational algebra, extending results of Landsberg and Manivel which relate prolongations to equations for secant varieties. We also develop methods for computing prolongations which are combinatorial in nature. As an application, we use prolongations to derive a new family of secant equations for the binary symmetric model i...

By unicorns, I am referring to those mythical single-horned horse-like creatures for which there are only rumoured sightings by a privileged few. A similar situation exists in Finsler differential geometry. There, one has the hierarchy Euclidean ⊂ Minkowskian & Riemannian ⊂ Berwald ⊂ Landsberg among five families of metrics, in which the first two inclusions are known to be proper by virtue of ...

Malignant melanoma is a highly aggressive skin cancer that can be difficult to manage once metastasis has occurred. Tumor necrosis factor-alpha(TNFα) is a cytokine that influences the tumor microenvironment, activates tumor inflammation, and induces cell death(Balkwill, 2009). TNFα induces the signal-transduction pathways associated with cell survival through NF-κB or caspase 8. Melanoma cells ...

In this paper we consider the product of two complex Cartan manifolds, the outcome being a class of product complex Cartan spaces. Then, we study the relationships between the geometric objects of a product complex Cartan space and its components, (e.g. Chern-Cartan complex nonlinear connection, Cartan tensors). By means of these, we establish the necessary and sufficient conditions under which...

Venous blood is necessary for the estimation of the erythrocyte sedimentation rate (E.S.R.) by the methods of Westergren (1921) and Wintrobe and Landsberg (1935), but venepuncture may occasionally prove difficult or impossible, owing to such factors as inadequate veins, obesity, and flexion deformities. A search was therefore undertaken for a reliable method of estimating the E.S.R. using capil...