This paper addresses the Mountain Pass Theorem for locally Lipschitz functions on finite-dimensional vector spaces in terms of tangencies. Namely, let $f \colon \mathbb R^n \to \mathbb R$ be a locally Lipschitz function with a mountain pass geometry....
specific portion of a metal casting mould. Normally the metal in the mould cools at a certain rate relative to thickness of the casting. When the geometry of
We analyze the fluctuations of Nielsen-Olesen vortices arising in the six-dimensional Abelian-Higgs model. The regular geometry generated by the defect breaks spontaneously six-dimensional Poincaré symmetry leading to a warped space-time with fini...
Starting from our work on Harder-Narasimhan filtrations of finite flat group schemes over a $p$-adic field, we developp a theory of Harder-Narasimhan filtrations for $p$-divisible groups. We apply this to the study of the geometry of period morphisms...
A recent paper proposes a static ellipsoidal space-time metric that reduces to Schwarzschild. After examining the corrected line element using Maple's Differential geometry package, we find that the Einstein tendor and Ricci scalar are non-zero, and...
The concept of illumination bodies studied in convex geometry is used to amend the halfspace depth for multivariate data. The proposed notion of illumination enables finer resolution of the sample points, naturally breaks ties in the associated depth...
In three articles published in CNJ in 2012 and 2016 , we discussed some links between mathematical sciences, coin minting and numismatics. This article is a continuation of this cycle. It tells the story of selected important developments in the hist...
This paper proves a linear algebra result that has to do with the geometry of "widgets". For us a widget is a collection of n pairs of points in a vector space. (The pairs represent the different possible spin states of a particle.) We investigate li...
The problem of computing the exact stretch factor (i.e., the tight bound on the worst case stretch factor) of a Delaunay triangulation is one of the longstanding open problems in computational geometry. Over the years, a series of upper and lower bou...
The geometry of a floating bridge on a drumhead soundboard produces string stretching that is first order in the amplitude of the bridge motion. This stretching modulates the string tension and consequently modulates string frequencies at acoustic fr...
Gupta et al. [1, 2] describe a very beautiful application of algebraic geometry to lattice structures composed of quadric of revolution (quador) implicit surfaces. However, the shapes created have concave edges where the stubs meet, and such edges ca...
a geometry class with filleted edges for THREE.js (⭐ 67)
Direct numerical simulations are presented for a porous media model consisting of two immiscible fluids, an invading and defending phase, in a two-dimensional micro-geometry filled with randomly sized and randomly distributed cylinders. First, interf...
The goal of the current paper is to characterize $*$-$k$-Ricci-Yamabe soliton within the framework on Kenmotsu manifolds. Here, we have shown the nature of the soliton and find the scalar curvature when the manifold admitting $*$-$k$-Ricci-Yamabe sol...
Our paper presents the design of a unique annular ring-shaped planar monopole antenna with octal geometry intended for a broad spectrum of frequency applications. Utilizing FR4 epoxy for the substrate and copper material for the top patch, the antenn...
We develop a systematic approach to calculating the electrostatic force between point charges in an arbitrary geometry with arbitrary boundary conditions. When the boundary is present, the simple expression for the force acting on a charge as ``the...
Learning to generate textures for a novel 3D mesh given a collection of 3D meshes and real-world 2D images is an important problem with applications in various domains such as 3D simulation, augmented and virtual reality, gaming, architecture, and de...
It is shown that the tessellation of a compact, negatively curved surface induced by a typical long geodesic segment, when properly scaled, looks locally like a Poisson line process. This implies that the global statistics of the tessellation -- for...
The geometry of dual-polarization four-dimensional constellations is optimized in the optical fiber channel using a recent nonlinear interference model. A 0.27 bit/4D rate gain and 13% reach increase are attained compared to polarization-multiplexed...
This paper looks at effects, due to the boundary, on inference in logistic regression. It shows that first -- and, indeed, higher -- order asymptotic results are not uniform across the model. Near the boundary, effects such as high skewness, discrete...