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The first aim of this study is to define soft sequential compact metric spaces and to investigate some important theorems on soft sequential compact metric space. Second is to introduce net and totally bounded soft metric space and study…
We propose a novel measure of statistical depth, the metric spatial depth, for data residing in an arbitrary metric space. The measure assigns high (low) values for points located near (far away from) the bulk of the data distribution,…
It turns out that one can read off facts about schemes up to universal homeomorphism from their Galois categories. Here we propose a first modest slate of entries in a dictionary between the geometric features of a perfectly reduced scheme…
We study the local Lipschitz one subsets of a finite dimensional space, that is, sets for which there exists a continuous function whose local Lipschitz derivative is the characteristic function of said set. We give a characterization of a…
This paper is devoted to the study of a newly introduced tool, projectional coderivatives and the corresponding calculus rules in finite dimensions. We show that when the restricted set has some nice properties, more specifically, is a…
We study a cut-off function lemma in projective spaces. We believe that this is well-known. We provide the details of the computation for later uses.
We construct the differential geometry of smooth manifolds equipped with an algebraic curvature map acting as an area measure. Area metric geometry provides a spacetime structure suitable for the discussion of gauge theories and strings,…
A high-order quadrature scheme is constructed for the evaluation of Laplace single and double layer potentials and their normal derivatives on smooth surfaces in three dimensions. The construction begins with a harmonic approximation of the…
Based on the Gale-Ryser theorem for the existence of suitable $(0,1)$-matrices for different partitions of a natural number, we revisit the classical result of G. G. Lorentz regarding the characterization of a plane measurable set, in terms…
We generalize the classical de Rham decomposition theorem for Riemannian manifolds to the setting of geodesic metric spaces of finite dimension.
We explore the Lipschitz stability of solutions to the Hunter-Saxton equation with respect to the initial data. In particular, we study the stability of $ \alpha $-dissipative solutions constructed using a generalised method of…
We study a new bi-Lipschitz invariant \lambda(M) of a metric space M; its finiteness means that Lipschitz functions on an arbitrary subset of M can be linearly extended to functions on M whose Lipschitz constants are enlarged by a factor…
The Lipschitz geometry of segments of the infinite Hamming cube is studied. Tight estimates on the distortion necessary to embed the segments into spaces of continuous functions on countable compact metric spaces are given. As an…
This work provides a unified formalism for studying difference and (Hasse-) differential algebraic geometry, by introducing a theory of "iterative Hasse rings and schemes". As an application, Hasse jet spaces are constructed generally,…
The notion of geometric version of an infinitely divisible law is introduced. Concepts parallel to attraction and partial attraction are developed and studied in the setup of geometric summing of random variables.
This paper analyzes the Lipschitz behavior of the feasible set in two parametric settings, associated with linear and convex systems in R^n. To start with, we deal with the parameter space of linear (finite/semi-infinite) systems identified…
Closed subschemes in projective space with a fixed Hilbert polynomial are parametrized by a Hilbert scheme. We classify the smooth ones. We identify numerical conditions on a polynomial that completely determine when the Hilbert scheme is…
This paper attempts to study the continuity of the Hurwitz metric in arbitrary proper subdomains of the complex plane and to introduce a new invariant metric bi-Lipschitz equivalent to the Hurwitz metric in hyperbolic domains. The lower…
We develop techniques to split the principal parts on the projective line over an arbitrary ring and apply these techniques to give a complete classification of the principal parts on the projective line over any field of characteristic…
We obtain a uniform stability of recovering entire functions of a special form from their zeros. To this form, one can reduce the characteristic determinants of strongly regular differential operators and pencils of the first and the second…