In recent years, there has seen much interest and increased research activities in Ricci solitons. Ricci solitons are natural generalizations of Einstein metrics. They are also special solutions to Hamilton’s Ricci flow and play important roles in the singularity study of the Ricci flow. In this paper, we survey some of the recent progress on Ricci solitons. The concept of Ricci solitons was in...

Classical variational data assimilation methods address the problem of optimally combining model predictions with observations in the presence of zero-mean Gaussian random errors. However, in many natural systems, uncertainty in model structure and/or model parameters often results in systematic errors or biases. Prior knowledge about such systematic model error for parametric removal is not al...

In this paper, we study the class of of C3-like Finsler metrics which contains the class of semi-C-reducible Finsler metric. We find a condition on C3-like metrics under which the notions of Landsberg curvature and mean Landsberg curvature are equivalent.

BACKGROUND Videofluoroscopic swallow study (VFSS) is the gold standard for diagnosis of dysphagia in veterinary medicine but lacks standardized protocols that emulate physiologic feeding practices. Age impacts swallow function in humans but has not been evaluated by VFSS in dogs. HYPOTHESIS/OBJECTIVES To develop a protocol with custom kennels designed to allow free-feeding of 3 optimized form...

There are two natural metrics defined on an arbitrary convex cone: Thompson’s part metric and Hilbert’s projective metric. For both, we establish an inequality giving information about how far the metric is from being non-positively curved.

in this paper the general relatively isotropic l -curvature finsler metrics are studied. it isshown that on constant relatively landsberg spaces, the concepts of weakly landsbergian, landsbergianand generalized landsbergian metrics are equivalent. some necessary conditions for a relativelyisotropic l -curvature finsler metric to be a riemannian metric are also found.

various human pressures are affecting the aquatic biocoenosis in running waters of iran - similar to many other areas of the world. overall 190 sites, 88 at salmonid (44 reference/impacted respectively) and 102 at cyprinid (50 reference/52 impacted) streams of the southern caspian sea basin were investigated in terms of human pressures present and the related impact on fish assemblages. in tota...

We give a new construction of Ricci-flat self-dual metrics which is a natural extension of the Gibbons–Hawking ansatz. We also give characterisations of both these constructions, and explain how they come from harmonic morphisms.