Related papers: On the geometry of flat minima
A two-dimensional water wave system is examined consisting of two discrete incompressible fluid domains separated by a free common interface. In a geophysical context this is a model of an internal wave, formed at a pycnocline or…
We explicitly construct parameter transformations between gradient flows in metric spaces, called curves of maximal slope, having different exponents when the associated function satisfies a suitable convexity condition. These…
Optimization problems, generalized equations, and the multitude of other variational problems invariably lead to the analysis of sets and set-valued mappings as well as their approximations. We review the central concept of set-convergence…
A Riemannian metric is termed a Hessian metric if in some coordinate system it can be locally represented as the Hessian quadratic form of some locally defined smooth potential function. Under very mild extra technical conditions, we first…
The first aim of this paper is to examine some important properties of soft metric spaces. Second is to introduce soft continuous mappings and investigate properties of soft continuous mappings. Third is to prove some fixed point theorems…
General relativity can be formally derived as a flat spacetime theory, but the consistency of the resulting curved metric's light cone with the flat metric's null cone has not been adequately considered. If the two are inconsistent, then…
We consider two or more simple symmetric walks on some graphs, e.g. the real line, the plane or the two dimensional comb lattice, and investigate the properties of the distance among the walkers.
We define a class of two dimensional surfaces conformally related to minimal surfaces in flat three dimensional geometries. By the utility of the metrics of such surfaces we give a construction of the metrics of $2 N$ dimensional Ricci flat…
The variational principle for linear stability of three-dimensional, inhomogenious, compressible, moving magnetized plasma is suggested. The principle is ``softer'' (easier to be satisfied) than all previously known variational stability…
The theory of measurement is employed to elucidate the physical basis of general relativity. For measurements involving phenomena with intrinsic length or time scales, such scales must in general be negligible compared to the (translational…
We prove several inequalities estimating the distance between volumes of two bodies in terms of the maximal or minimal difference between areas of sections or projections of these bodies. We also provide extensions in which volume is…
We show that the recently introduced L1TV functional can be used to explicitly compute the flat norm for co-dimension one boundaries. While this observation alone is very useful, other important implications for image analysis and shape…
We establish several inequalities for manifolds with positive scalar curvature and, more generally, for the scalar curvature bounded from below, in the spirit of the classical bound on the distances between conjugates points in surfaces…
Alternative novel measures of the distance between any two partitions of a n-set are proposed and compared, together with a main existing one, namely 'partition-distance' D(.,.). The comparison achieves by checking their restriction to…
We examine the distribution and popularity of different parameters (such as the number of descents, runs, valleys, peaks, right-to-left minima, and more) on the sets of increasing and flattened permutations. For each parameter, we provide…
Flow-based models typically define a latent space with dimensionality identical to the observational space. In many problems, however, the data does not populate the full ambient data space that they natively reside in, rather inhabiting a…
Appearance of physical properties of objects is a basic for their detection in a media. Fugacity is a physical property of objects. Definition of estimations fugacity for different objects can be executed on model which principle of…
The fluctuations are termed mesoscopic, when their typical size is essentially larger then the average distance between the nearest neighbors, while being much smaller than the overall system size. Since the features of mesoscopic…
Divided into three parts, the first marks out enormous geometric issues with the notion of quasi-freenss of an algebra and seeks to replace this notion of formal smoothness with an approximation by means of a minimal unital commutative…
A model describing cell membranes as optimal shapes with regard to the $L^2$-deficit of their mean curvature to a given constant called spontaneous curvature is considered. It is shown that the corresponding energy functional is lower…