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# Geometry - Science topic

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Publications related to Geometry (10,000)

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The impact of taper ratio, dihedral angle and wing tip shape on the aerodynamics of a Very Light Aircraft's wing has been investigated by performing URANS simulations at Reynolds number of 5×10 6 for pre-and post-stall conditions. SD 7062 airfoil is selected for the cross-section of the wing geometries investigated. The mean aerodynamic coefficient...

The proposition of a method to verify the punching resistance for very large supports based on the EN 1992-1-1 standard is described in this paper. The present standard guidelines for the calculation of the punching resistance for large supports are also summarised. The proposed direct method is compared with other standard methods using an example...

Graph neural networks are attractive for learning properties of atomic structures thanks to their intuitive graph encoding of atoms and bonds. However, conventional encoding does not include angular information, which is critical for describing atomic arrangements in disordered systems. In this work, we extend the recently proposed ALIGNN (Atomisti...

In this paper, we initiate the study of the global stability of nonlinear wave equations with initial data that are not required to be localized around a single point. More precisely, we allow small initial data localized around any finite collection of points which can be arbitrarily far from one another. Existing techniques do not directly apply...

We show that the geometry-of-numbers method used by A. Bounemoura to obtain filling times for linear flow on the torus satisfying Diophantine conditions may be extended to the case of linear flow with truncated Diophantine conditions, and we use these methods to recover the optimal estimate first obtained by M. Berti, L. Biasco, and P. Bolle in 200...

The disjointness problem—where Alice and Bob are given two subsets of {1,⋯,n}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{1, \dots, n\}$$\end{document} and they ha...

The JRR-3M reactor is a water-cooled plate-type reactor for research. A macro benchmark based on the JRR-3M reactor is established with the Monte-Carlo code RMC and deterministic direct transport code SHARK with accurate and explicit geometry modeling. A series of cases from 2D lattice to 3D whole-core are adopted for the verification of SHARK. In...

Point cloud upsampling is to densify a sparse point set acquired from 3D sensors, providing a denser representation for the underlying surface. Existing methods divide the input points into small patches and upsample each patch separately, however, ignoring the global spatial consistency between patches. In this paper, we present a novel method PC2...

It is well-known that there are 19 classes of geometries for 4-dimensional manifolds in the sense of Thurston. We could ask that to what extent the geometric information is revealed by the profinite completion of the fundamental group of a closed smooth geometric 4-manifold. In this paper, we show that if two geometric manifolds, neither of whose g...

We propose an analytic torsion for the Rumin complex associated with generic rank two distributions on closed 5-manifolds. This torsion behaves as expected with respect to Poincaré duality and finite coverings. We establish anomaly formulas, expressing the dependence on the sub-Riemannian metric and the 2-plane bundle in terms of integrals over loc...

In the present work, we study the Hausdorff dimension of the limit set of Schottky groups on the boundary of the complex hyperbolic group via the Eigenvalue algorithm as in [17]. The visual geometry on HC2¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepacka...

We study length-minimizing closed generalized Euclidean billiard trajectories in convex bodies in R^n and investigate their relation to the inclusion minimal affine sections that contain these trajectories. We show that when passing to these sections, the length-minimizing closed billiard trajectories are still billiard trajectories, but their leng...

The effect of welding and rotational speeds are investigated in friction stir lap welding of 3 mm sheets of 7020-T6 Aluminium. The distorsions of the interface between sheets are observed and analyzed on the Advancing and Retreating sides depending on the process parameters used for the study. The process parameters were varied in a range from 800...

We give a normal form for pseudo-Einstein contact forms and apply it to construct intrinsic CR normal coordinates parametrized by the structure group of CR geometry. The proof is based on the construction of parabolic normal coordinates by Jerison and Lee.

In this paper we prove a formula relating the equivariant Euler characteristic of K-theoretic stable envelopes to an object known as the index vertex for the cotangent bundle of the full flag variety. Our formula demonstrates that the index vertex is the power series expansion of a rational function. This result is a consequence of the 3d mirror se...

A miniaturized multiband broadband quasi‐self‐complementary antenna (QSCA) is presented, which mainly consists of a third‐step radiation patch on the right and a third‐step wide slot on the left. With the help of an L‐shaped metal ground patch, a coplanar waveguide (CPW)‐like matching technique is used to improve the impedance matching of the anten...

In this article, we study the geometry of compact quasi-Einstein manifolds with boundary. We establish sharp boundary estimates for compact quasi-Einstein manifolds with boundary that improve some previous results. Moreover, we obtain a characterization theorem for such manifolds in terms of the surface gravity of the boundary components, which lea...

The ability to detect small targets in sea clutter is still an ongoing challenge, even for modern radar systems. Over the past decade, the development of new radar waveforms and signal processing algorithms has been assisted by an increasingly good understanding of the characteristics of sea clutter. Nevertheless, many challenges remain in the deve...

For a given field F of characteristic different from 2 and a,b,d∈F∗ we construct an invariant inv for an element D∈2Br(F(a,b,d)/F). This invariant takes value in the quotient group H3(F,μ2)/D∪NFd,ab/FFd,ab∗.Let k be a field, let k(a,b,d)/k be a triquadratic field extension. We apply the invariant inv and a few deep results from algebraic geometry a...

We consider the M-neighbor approximation in the problem of one-qubit pure state transfer along the N-node zigzag and alternating spin chains governed by the XXZ-Hamiltonian with the dipoledipole interaction. We show that always M > 1, i.e., the nearest neighbor approximation is not applicable to such interaction. Moreover, only all-node interaction...

In the present paper, we study the outer automorphism groups of the absolute Galois groups of mixed-characteristic local fields from the point of view of anabelian geometry. Let us recall that it is well-known that the natural homomorphism from the automorphism group of a mixed-characteristic local field to the outer automorphism group of the absol...

The sealing surfaces subjected to the hydrostatic load from the sealed fluid can deform to such an extent that leakage occurs when the sealed fluid pressure is sufficiently high, and this critical pressure that the seal can sustain without leakage is a fundamental aspect of the seal design. This paper presents a new numerical method based on the bi...

Students’ issues dealing with reflection tasks, especially with inclined mirror lines, are widely known. Previous research conducted with primary school students mainly focussed on task difficulty and students’ outcomes, especially their errors of reflection. Little is known about which not obviously sustainable understanding of reflection leads to...

In this paper we establish a higher integrability result up to the boundary of weak solutions to doubly nonlinear parabolic systems. We show that the spatial gradient of a weak solution with vanishing lateral boundary values is integrable to a larger power than the natural power p, where the statement holds for parameters in the subquadratic case m...

We study the Laplacian flow and coflow on contact Calabi–Yau 7-manifolds. We show that the natural initial condition leads to an ancient solution of the Laplacian flow with a finite time Type I singularity which is not a soliton, whereas it produces an immortal (though neither eternal nor self-similar) solution of the Laplacian coflow which has an...

Um dos fatores geradores de queda de blocos mais importantes é a presença de água nas
descontinuidades. Por esse motivo, é muito comum o uso de drenos horizontais profundos para aliviar as poropressões. Assim esse trabalho visava criar um programa que pudesse calcular o fluxo de água e a carga hidráulica no maciço rochoso fraturado que auxiliasse n...

Geometrinin aktif konularına ilgi duyan araştırmacılar için 24-26 Ağustos tarihlerinde Ege Üniversitesi Fen Fakültesi Matematik Bölümünde Yaz Okulu Düzenlenecektir. Toplam 21 saat anlatılacak derslerde Diferansiyel Geometrinin temel konularından, uygulamalarına ve proje eğitimine kadar pek çok konu anlatılacaktır. İletişim: egeyazokulu@gmail.com....

We develop analytic techniques to construct the leading dissipative terms in a derivative expansion of holograhpic fluids. Our basic ingredient is the Crnkovic-Witten symplectic current of classical gravity which we use to extract the dissipative transport coefficients of holographic fluids, assuming knowledge of the thermodynamics and the near hor...

In this paper, a dual-band implantable rectenna is proposed for recharging and operating biomedical implantable devices at 0.915 and 2.45 GHz. The rectenna system consists of a compact dual-band antenna based on a meandered-resonator as well as efficient dual-band rectifier circuit. Both components (antenna and rectifier) are integrated inside a ca...

We study the geometry of some proper 4-colorings of the vertices of sphere triangulations with degree sequence 6,...,6,2,2,2. Such triangulations are the simplest examples which have non-negative combinatorial curvature. The examples we construct, which are roughly extremal in some sense, are based on a novel geometric interpretation of continued f...

In this paper, we try to understand what considerations and possible sources of inspiration Desargues used to formulate his concepts of involution and transversal, and to state the related theorems that are at the basis of his Brouillon project. To this end, we trace some clues which are found scattered throughout his works, we connect them togethe...

The generalization of Birkhoff's theorem to higher dimensions in Lovelock gravity allows for black hole solutions with horizon geometries of non-constant curvature. We investigate thermodynamic aspects of these `exotic' black hole solutions, with a particular emphasis on their phase transitions. We consider an extended phase space where the cosmolo...

"La Silla Criolla Argentina (Parte 2). Cuando la teoría del Arte se convierte en un paradigma teórico para explicar la tipología del diseño artesanal de la silla proto-racionalista de estilo campo en la República Argentina".
El objetivo de este trabajo, consiste en explicar la tipología del diseño de la silla “estilo campo” (rural), de la República...

Monolithic arrays of silicon p-n junctions are commonly used to deliver spatial information on impinging radiation, with the advantages of low-noise and fast signal generation. Additionally, array geometries also allow for a segmentation of a large area into individual channels that can be read out in parallel, so that a high-event rate can be mana...

Topological defects have long been known to encode symmetries and dualities between physical systems. In the context of string theory, defects have been intensively studied at the level of the worldsheet. Although marked by a number of pioneering milestones, the target space picture of defects is much less understood. In this paper, we show, at the...

This paper introduces an interactive form finding technique to design and explore continuous Shellular Funicular Structures in the context of Polyhedral Graphic Statics (PGS). Shellular funicular forms are two-manifold shell-based geometries dividing the space into two interwoven sub-spaces, each of which can be represented by a 3D graph named laby...

A series of experiments for steady state rotation of water in vessels of various geometries is presented. The experiments focus on the geometrical characteristics of the rotating liquids and the change in their surface topology, from that akin to a sphere to that of a torus (i.e., from genus 0 to 1), for sufficiently large angular speeds. Cylindric...

In this study, an enhancement to the Multiquadric Radial Basis Function (MQ-RBF) method is presented for solving Elasticity Boundary Value Problems (E-BVPs). MQ-RBF is utilized to reproduce the system of governing partial differential equations and boundary conditions. Also the inefficacies of some existing methods in determining the Optimal Shape...

This article presents the design of a novel miniaturized 2.5D frequency selective surface (FSS) for radiofrequency and microwave shielding applications is proposed. The proposed FSS is configured to offer multiple band‐stop characteristics with a wide frequency ratio. The unit cell is developed using traces that run on the top and bottom layers of...

Recently, based on elementary geometry, Gutman proposed several Sombor-index-like invariants (i.e., $SO$, $SO_{1}$, $SO_{2}$, $SO_{3}$, $SO_{4}$, $SO_{5}$, $SO_{6}$). The Sombor index was defined as $SO(G)=\sum\limits_{uv\in E(G)}\sqrt{d_{u}^{2}+d_{v}^{2}}$, the first Sombor index was defined as $SO_{1}(G)= \frac{1}{2}\sum\limits_{uv\in E(G)}|d_{u}...

La manufactura aditiva (AM) es una tecnología que ha revolucionado los procesos de fabricación en los últimos 20 años. Para el caso de materiales poliméricos ya es una tecnología madura, mientras que en el caso de su aplicación a materiales metálicos es aún un área de fuerte desarrollo. En este sentido, técnicas como Selective Laser Melting (SLM) o...

Variational autoencoders (VAEs) are susceptible to adversarial attacks. An adversary can find a small perturbation in the input sample to change its latent encoding non-smoothly, thereby compromising the reconstruction. A known reason for such vulnerability is the latent space distortions arising from a mismatch between approximated latent posterio...

The steady, laminar, incompressible, axisymmetric stenotic blood flow is investigated with a non-polynomial solution assumption. The wall geometry of the stenosis is constructed as a fixed cosine curve. The rheology of blood is modeled as a generalized power-law fluid. The variations of the coefficients constructing both axial and radial velocity p...

In this work, we propose a new perspective on the quasi-local studies of the circular orbits in spacetime. Unlike the definition of the photon surface given by studying the geometry of the surface, we give a quasi-local definition of the pole-dipole particle surface in general static spherical symmetric spacetime based on the condition of the circu...

In this paper, the S32101 duplex stainless steel welded joints were produced by a K-TIG welding system. The weld geometry parameters under different welding speeds were analyzed by combining the morphological characteristics of the keyhole. The microstructure and impact toughness of the base metal and weld metal zone under different welding speeds...

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 linear relations among such collections. A corollary of our theorem was conjectured in arXiv:2208.0247...

A destructive rockfall event occurred in northern Taiwan, wherein the falling blocks severely damaged the retaining structures of a mountain road. To elucidate the trajectory of rockfalls, a series of investigations was conducted to produce high-precision topographical models. In addition, the discontinuity distribution of the source area, geometri...

We study the Steiner Tree problem on unit disk graphs. Given a n vertex unit disk graph G, a subset R⊆V(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R\subseteq V(G...

This chapter is a review of numerical modelling of rifting with emphasis on how conceptual and numerical models of continental extension have developed over time and key factors that influence model outcomes and rift geometry.

We study the electronic transport through a finite-size slit in a barrier in a two-dimensional sample in the hydrodynamic regime. We assume a negligible disorder-induced Ohmic resistance, so that dissipation is purely viscosity-induced. We find that the only solution to the Stokes equation in this geometry, which yields a finite dissipation at fini...

Este material didático foi utilizado durante algumas das aulas do curso "Geometria Olímpica com GeoGebra" para professores de Matemática do Ensino Fundamental e Médio de todo o Brasil. O texto conta com 39 figuras que facilitam acompanhar a resolução. Todas têm como complemento links para os gráficos interativos no site do GeoGebra e, vários, a res...

We study a duality transformation from the gauge-invariant subspace of a $\mathbb{Z}_N$ lattice gauge theory on a two-leg ladder geometry to an $N$-clock model on a single chain. The main feature of this mapping is the emergence of a longitudinal field in the clock model, whose value depends on the superselection sector of the gauge model, implying...

Valve leaflets and chordae structurally normal characterize functional mitral regurgitation (FMR), which in heart failure (HF) setting results from an imbalance between closing and tethering forces secondary to alterations in the left ventricle (LV) and left atrium geometry. In this context, FMR impacts the quality of life and increases mortality....

In the design of a large deployable mesh reflector, high surface accuracy is one of ultimate goals since it directly determines overall performance of the reflector. Therefore, evaluation of surface accuracy is needed in many cases of design and analysis of large deployable mesh reflectors. The surface accuracy is usually specified as root-mean-squ...

The NxN system of linear equations, Ax = b, represents N intersecting hyperplanes, whose intersection is the solution to the system of equations. The solution is often obtained iteratively by minimizing an appropriate quadratic form using well known optimization techniques. These methods do not consider the geometrical nature of the intersecting hy...

We prove $\mathcal{H}^{\alpha_1}\times\mathcal{H}^{\alpha_2}\to L^q_tL^r_x$ null form estimates for solutions to homogeneous wave equations with $(q,r)$ on the endline of the condition concerning geometry of the cone, except the critical index. This extends the previous endpoint result of Tao, Math. Z. 238, no. 2, 215-268, (2001) in symmetric norms...

We study the Newman--Unti (NU) group from the viewpoint of infinite-dimensional geometry. The NU group is a topological group in a natural coarse topology, but it does not become a manifold and hence a Lie group in this topology. To obtain a manifold structure we consider a finer Whitney-type topology. This turns the unit component of the NU group...

The evolution of 3D visual content calls for innovative methods for modelling shapes based on their intended usage, function and role in a complex scenario. Even if different attempts have been done in this direction, shape modelling still mainly focuses on geometry. However, 3D models have a structure, given by the arrangement of salient parts, an...

Graphene can be turned into a semimetal with broken time-reversal symmetry by adding a valley-dependent pseudo-scalar potential that shifts the Dirac point energies in opposite directions, as in the modified Haldane model. We consider a bilayer obtained by stacking two time-reversed copies of the modified Haldane model, where conduction and valence...

Static vacuum near horizon geometries are solutions $(M,g,X)$ of a certain quasi-Einstein equation on a closed manifold $M$, where $g$ is a Riemannian metric and $X$ is a closed 1-form. It is known that when the cosmological constant vanishes, there is rigidity: $X$ vanishes and consequently $g$ is Ricci flat. We study this form of rigidity for all...

Contact geometry is well known to play an important and manifold role in the geometric approach to the study of partial differential systems. In this talk we showcase a novel application of three-dimensional contact geometry, where it helps answering a longstanding question of just how exceptional are partial differential systems in four independen...

Let $K$ be an imaginary quadratic number field and let $L(s,\xi_{\ell})$ denote the Hecke $L$-function to an angular character $\xi_{\ell}$ with frequency $\ell$. We detect values of $\log |L(\tfrac12,\xi_{\ell})|$ with size at least $(\sqrt{2} + o_K(1))(\log X / \log \log X)^{1/2}$ along each dyadic range $X \leqslant \ell \leqslant 2X$. This resu...

We present high resolution rotational Raman spectra and derived geometry parameters for benzene. Rotational Raman spectra with sub-5 MHz resolution were obtained via high-resolution mass-correlated rotational alignment spectroscopy. Isotopologue spectra for C 6 H 6 , 13 CC 5 H 6 , C 6 D 6 , and 13 CC 5 D 6 were distinguished through their correlate...

This paper gives a new, simplified presentation of the classical pure braid group. The generators are given by the squares of the longest elements over connected subgraphs, and we prove that the only relations are either commutators or certain palindromic length 5 box relations. This presentation is motivated by twist functors in algebraic geometry...

The study aimed to identify the level of mathematical knowledge of mathematics teachers for the first four grades in Nablus governorate, and its relationship to gender variables, years of experience, academic qualification and specialization. To achieve this, the researcher used the analytical descriptive method through applying the mathematical kn...

Due to the limited space in the tunnel environment, multiple-input multiple-output (MIMO) systems with double-port fed leaky coaxial cables (LCXs) can not only reduce the number of LCXs, but also improve the channel capacity. Based on the geometry based on single bonce (GBSB) and electromagnetic field radiation theory of LCX, a MIMO channel model w...

Leibniz proposed the "Most Determined Path Principle" in seventeenth century. According to it, "ease" of travel is the end purpose of motion. Using this principle and his calculus method he demonstrated Snell"s Laws of reflection and refraction. This method shows that light follows extremal (local minimum or maximum) time path in going from one poi...