Related papers: Weak Linear Mappings -- A Survey
A weak $f$-structure on a smooth manifold, introduced by the author and R. Wolak (2022), generalizes K. Yano's (1961) $f$-structure. This generalization allows us to revisit classical theory and discover new applications related to Killing…
After surveying some known properties of compact convex sets in the plane, we give a two rigorous proofs of the general feeling that supporting lines can be slide-turned slowly and continuously. Targeting a wide readership, our treatment is…
Let (X,dX) and (Y,dY) be semimetric spaces with distance sets D(X) and, respectively, D(Y). A mapping F : X \to Y is a weak similarity if it is surjective and there exists a strictly increasing f : D(Y) \to D(X) such that dX = f \circ dY…
A number of topics involving metrics and measures are discussed, including some of the special structure associated with ultrametrics.
A behavior of one class of mappings with finite distortion at a neighborhood of the origin is investigated. There is proved a lower estimate of distortion of a distance under mappings mentioned above.
This text is a survey of derived algebraic geometry. It covers a variety of general notions and results from the subject with a view on the recent developments at the interface with deformation quantization.
We consider the problem of joint estimation of structured inverse covariance matrices. We perform the estimation using groups of measurements with different covariances of the same unknown structure. Assuming the inverse covariances to span…
In this paper we investigate a problem of approximation of continuous mappings by smooth mappings with nonnegative Jacobian.
A survey on recent developments in (algebraic) integral geometry is given. The main focus lies on algebraic structures on the space of translation invariant valuations and applications in integral geometry.
Results on $8$-dimensional topological planes are scattered in the literature. It is the aim of the present paper to give a survey of these geometries, in particular of information obtained after the appearance of the treatise Compact…
Multidimensional Projection is a fundamental tool for high-dimensional data analytics and visualization. With very few exceptions, projection techniques are designed to map data from a high-dimensional space to a visual space so as to…
We survey a variety of results about partially isometric matrices. We focus primarily on results that are distinctly finite-dimensional. For example, we cover a recent solution to the similarity problem for partial isometries. We also…
Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to…
The aim of this paper is to introduce the concept of Delta-Compact spaces along with some basic properties of it. Here, we try to establish the behavior of Delta-Compact spaces under the continuous mapping. Finally, we define another…
In this paper we collect the main properties of free curves in the complex projective plane and a lot of conjectures and open problems, both old and new. In the quest to understand the mystery of free curves, many tools were developed and…
The weakly contractive metric type fixed point result in Berinde [Nonlinear Anal. Forum, 9 (2004), 45-53] is "almost" covered by the related altering metric one due to Khan et al [Bull. Austral. Math. Soc., 30 (1984), 1-9]. Further…
Weakly orthomodular and dually weakly orthomodular lattices were introduced by the authors in a recent paper. Similarly as for orthomodular lattices we try to introduce an implication in these lattices which can be easily axiomatized and…
The aim of this work is to study the geometry underlying mechanics and its application to describe autonomous and nonautonomous conservative dynamical systems of different types; as well as dissipative dynamical systems. We use different…
Motivated by persistent homology and topological data analysis, we consider formal sums on a metric space with a distinguished subset. These formal sums, which we call persistence diagrams, have a canonical 1-parameter family of metrics…
This survey presents some historical background and recent developments in the area of selections for set-valued mappings along with several open questions. It was written with the hope that the presented material may pique an interest in…