Related papers: Geometric constants for quantifying the difference…
The present article studies variational principles for the formulation of static and dynamic problems involving Kirchhoff rods in a fully nonlinear setting. These results, some of them new, others scattered in the literature, are presented…
We study the concepts of orthogonality and smoothness in normed linear spaces, induced by the derivatives of the norm function. We obtain analytic characterizations of the said orthogonality relations in terms of support functionals in the…
In this article, we compute Von Neumann-Jordan constant, James constant, and Dunkl-Williams constant for small Morrey spaces. Our approach can also be seen as an alternative way in computing the three constants for the (classical) Morrey…
The interplay between quantum geometry and electron correlation has emerged as a compelling paradigm in quantum many-body physics. Recent studies have highlighted the diagnostic utility of quantum geometry in identifying magnetic…
Gaussian distributions are plentiful in applications dealing in uncertainty quantification and diffusivity. They furthermore stand as important special cases for frameworks providing geometries for probability measures, as the resulting…
In this paper we introduce the concept of the rectangular metric like spaces, along with its topology and we prove some fixed point theorems under different contraction principles. We introduce the concept of modified metric-like space as…
We describe recent work on positive descriptions of the structure constants of the cohomology of homogeneous spaces such as the Grassmannian, by degenerations and related methods. We give various extensions of these rules, some new and…
We prove metric rigidity for complete manifolds supporting solutions of certain second order differential systems, thus extending classical works on a characterization of space-forms. In the route, we also discover new characterizations of…
Motivated by the questions in the theory of Fredholm stability in Banach space and Kato's strictly singular operators we answer several natural questions concerning ``orthogonality'' in normed spaces and the properties of metric…
Detecting symmetry is crucial for effective object grasping for several reasons. Recognizing symmetrical features or axes within an object helps in developing efficient grasp strategies, as grasping along these axes typically results in a…
Topological phases are generally characterized by topological invariants denoted by integer numbers. However, different topological systems often require different topological invariants to measure, such as geometric phases, topological…
Bisectors are equidistant hypersurfaces between two points and are basic objects in a metric geometry. They play an important part in understanding the action of subgroups of isometries on a metric space. In many metric geometries…
A discussion is given of the uncertainty principle in view of the introduction of a Gravitational Planck Constant. The need for such a gravitational constant is shown first. A reduced electromagnetic Planck constant and the analogous…
Given an orbifold, we construct an orthogonal spectrum representing its stable global homotopy type. Orthogonal spectra now represent orbifold cohomology theories which automatically satisfy certain properties as additivity and the…
Motivated by research on contraction analysis and incremental stability/stabilizability the study of 'differential properties' has attracted increasing attention lately. Previously lifts of functions and vector fields to the tangent bundle…
A notion of orthogonality in multisymplectic geometry has been developed by Cantrijn, Ibort and de Le\'on and used by many authors. In this paper, we review this concept and propose a new type of orthogonality in multisymplectic geometry;…
The second Poincar\'e kinematical group serves as one of new ones in addition to the known possible kinematics. The geometries with the second Poincar\'e symmetry is presented and their properties are analyzed. On the geometries, the new…
In this paper, for a finite group, we discuss a method for calculating equivariant homology with constant coefficients. We apply it to completely calculate the geometric fixed points of the equivariant spectrum representing equivariant…
We combine the pointed Gromov-Hausdorff metric [Ron10] with the locally $C^0$ distance to obtain the pointed $C^0$-Gromov-Hausdorff distance between maps of possibly different non-compact pointed metric spaces. The latter is then combined…
Though the sharp Heisenberg Uncertainty Principle has been extensively studied in the entire Euclidean spaces, the counterpart on the half spaces or more general orthants has been missing in the literature. We investigate the sharp…