This is a write-up of some lectures I gave in the Fall of 2021 at the Fields Institute in Toronto, as part of the Thematic Programme on Trends in Pure and Applied Model Theory. The goal of the module was to give a quick introduction to the model theo...
This article presents a path-following control law for autonomous orbital maintenance of small body missions. The control law is robust, stable, and capable of controlling only the orbital geometry, allowing the spacecraft to operate with idle-thrust...
In this paper we discuss non-commutative and non-associative geometries that emerge in the context of non-geometric closed string backgrounds. T-duality and doubled field theory plays an important role in formulating the corresponding effective actio...
Lock-in Thermography (LIT) is a type of Infrared Thermography (IRT) that can be used as a useful non-destructive testing (NDT) technique for the detection of subsurface anomalies in objects. Currently, LIT fails to estimate the thickness at a point o...
We evaluate different Neural Radiance Fields (NeRFs) techniques for the 3D reconstruction of plants in varied environments, from indoor settings to outdoor fields. Traditional methods usually fail to capture the complex geometric details of plants, w...
We report a detailed theoretical investigation into the influence of anisotropy on the magnetic and thermodynamic properties of an octanuclear nickel phosphonate cage with butterfly-shaped molecular geometry, namely $\mathrm{Ni}_8(μ_3-\mathrm{OH})_4...
Direct detection of gravitational waves and binary black hole mergers have proven to be remarkable investigations of general relativity. In order to have a definitive answer as to whether the black hole spacetime under test is the Kerr or non-Kerr, o...
The so-called generalized Ellis-Bronnikov wormhole is a modification of the standard Ellis-Bronnikov solution, in which a parameter $m>2$ is introduced-recovering the original Ellis-Bronnikov geometry when $m=2$. In this work, we investigate the prop...
We give the 3-dimensional Sklyanin algebras $S$ that are module-finite over their center $Z$ the structure of a Poisson $Z$-order (in the sense of Brown-Gordon). We show that the induced Poisson bracket on $Z$ is non-vanishing and is induced by an ex...
In differential geometry, the Laplace–Beltrami operator is a generalization of the Laplace operator to functions defined on submanifolds in Euclidean space
VC-dimension and $\varepsilon$-nets are key concepts in Statistical Learning Theory. Intuitively, VC-dimension is a measure of the size of a class of sets. The famous $\varepsilon$-net theorem, a fundamental result in Discrete Geometry, asserts that...
Third-harmonic generation (THG) is a key nonlinear optical process for ultrafast imaging, terahertz (THz) signal generation, and symmetry-sensitive probes, often dominating in centrosymmetric materials where lower-order responses vanish. Yet, the rol...
Points: 301 | Comments: 57 | Author: sohkamyung
There are many examples for point sets in finite geometry, which behave "almost regularly" in some (well-defined) sense, for instance they have "almost regular" line-intersection numbers. In this paper we investigate point sets of a desarguesian affi...
Euclidean geometry, the intersection of a line and a line can be the empty set, a single point, or a line (if they coincide). Distinguishing these cases
We report an ultrafast optical tuning of the reflectivity of AlGaAs/InAlGaAs multiple quantum well photonic crystal waveguides using a reflection geometry, pump-probe technique....
We propose a natural definition of the weighted $σ_k$-curvature for a manifold with density; i.e.\ a triple $(M^n,g,e^{-φ}\mathrm{dvol})$. This definition is intended to capture the key properties of the $σ_k$-curvatures in conformal geometry with...
The geometry of canal hypersurfaces of an n-dimensional conformal space C^n is studied. Such hypersurfaces are envelopes of r-parameter families of hyperspheres, 1 \leq r \leq n-2. In the present paper the conditions that characterize canal hypersu...
The models of endofullerenes C60 and C82 with silver atom or diatomic silver are calculated with ab initio SCF Hartree-Fock methods including the full geometry optimization. Ag@C60 is a bound system with positive binding energy while Ag2@C60 is not...
Generalized matrix-fractional (GMF) functions are a class of matrix support functions introduced by Burke and Hoheisel as a tool for unifying a range of seemingly divergent matrix optimization problems associated with inverse problems, regularization...
Math planet is a free, accessible platform for learning mathematics. We offer high school math courses in Pre-algebra, Algebra 1, Algebra 2 and Geometry.
We introduce a novel regularization for localizing an elastic-energy-driven deformation to only those regions being manipulated by the user. Our local deformation features a natural region of influence, which is automatically adaptive to the geometry...
We construct a $2\times 2$ matrix algebra as representation of functions on discrete group $Z_2$ and develop the gauge theory on discrete group proposed by Starz in the matrix algebra. Accordingly, we show that the non-commutative geometry model bu...
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In those lecture notes, we review some applications of heat semigroups methods in Riemannian and sub-Riemannian geometry. The notes contain parts of courses taught at Purdue University, Institut Henri Poincaré, Levico Summer School and Tata Institut...
Representations of nonnegative polynomials as sums of squares are central to real algebraic geometry and the subject of active research. The sum-of-squares representations of a given polynomial are parametrized by the convex body of positive semidefi...
We study the Beurling Nyman (BN) family $f_θ(x) = \{θ/x\} - θ\{1/x\}$ in $L^2((0,1])$ through a multiscale ladder parameterisation $θ_{j,k} = 2^{-j}3^{-k}$ and the associated Gram matrix structure indexed by ladder distance. Using Mellin analysis...
A classical result in Lorentzian geometry states that a strongly causal spacetime is globally hyperbolic if and only if the Lorentzian distance is finite valued for every metric choice in the conformal class. It is proven here that a non-total impr...
possible kissing number for n-dimensional spheres in (n + 1)-dimensional Euclidean space? More unsolved problems in mathematics In geometry, the kissing number
We investigate how the Aretakis instability affects non-dilatonic extremal black $p$-branes by focusing on their near-horizon geometry. Crucially, the strength of the instability, \textit{i.e.} the number of transverse derivatives needed to see non-d...
Reconstructing realistic animal fur geometry from images is a challenging task due to the fine-scale details, self-occlusion, and view-dependent appearance of fur. In contrast to human hairstyle reconstruction, there are also no datasets that can be...
A fundamental challenge in robot perception is the coupling of the sensor pose and robot pose. This has led to research in active vision where robot pose is changed to reorient the sensor to areas of interest for perception. Further, egomotion such a...
Barbilian spaces are metric spaces with a metric induced by a special procedure of metrization which is inspired by the study of the models of non-Euclidean geometry. In the present material we discuss the history of Barbilian spaces and the evolut...
Below are the problems that I formulated at Open Problems Session of {\it Workshop on Group Actions on Rational Varieties}, McGill University and University of Montreal, Canada, March 2002. To appear in: "Affine Algebraic Geometry" conference Proce...
Apr 3, 2022 · So you can have continuous functions defined over rationals; but the rationals are not a continuum. Why not? The notion of a continuum has its roots in geometry, and -- in the barest …
We discuss coincidences of pairs (f_1, f_2) of maps between manifolds. We recall briefly the definition of four types of Nielsen numbers which arise naturally from the geometry of generic coincidences. They are lower bounds for the minimum numbers MC...
Official Implementation of paper "MonST3R: A Simple Approach for Estimating Geometry in the Presence of Motion" (⭐ 1337)
We prove that a K-contact Lie group of dimension five or greater is the central extension of a symplectic Lie group by complexifying the Lie algebra and applying a result from complex contact geometry, namely, that, if the adjoint action of the compl...
The dephasing time of spin-orbit qubits is limited by the coupling with electrical and charge noise. However, there may exist "dephasing sweet spots" where the qubit decouples (to first order) from the noise so that the dephasing time reaches a maxim...
We study certain real Lie-group orbits in the compact duals of Mumford-Tate domains, verifying a prediction made in [Green, Griffiths, Kerr; Mumford-Tate domains: their geometry and arithmetic] and determining which orbits contain a limit point of so...