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# Surfaces - Science topic

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A straight line intersects a circle in two, one, or no real points. In the last case, they have two complex conjugate intersecting points. We present their construction by tracing the circle with all lines. To visualize these points, the real plane is extended with the imaginary dimensions to four-dimensional real space. The surface generated by al...
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Two major types of quotation theories can be distinguished according as they regard marks of quotation as necessary (type-1) or not necessary (type-2) for quotation. I argue that, taken at face value, the empirical evidence disqualifies type-1 theories. I then show that, even if we accept that surface appearances are deceptive-'unmarked' quotations...
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In this paper, Hopf bifurcation and center problem are investigated for a class of more generalized Lorenz systems, which are Z2 symmetric and quadratic three-dimensional systems. Firstly, the singular point quantities of one equilibrium are calculated carefully, and the two symmetric fourth-order weak foci are found. Secondly, the corresponding in...
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In this study, a systematic refinement method was developed for non-uniform Catmull-Clark subdivision surfaces to improve the quality of the surface at extraordinary points (EPs). The developed method modifies the eigenpolyhedron by designing the angles between two adjacent edges that contain an EP. Refinement rules are then formulated with the hel...
Research
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https://www.mdpi.com/journal/land/special_issues/Spatiotemporal_LST. We are pleased to announce the submission deadline of your Special Issue has been updated to 25 November 2022.
Conference Paper
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The proposed intelligent reflective surface (IRS) is presented to compensate for the path loss and enhance the coverage of 5G networks at mm-wave band. A (π) shaped element with variable-sized dipoles, distributed in a certain way to maintain a phase length curve over 340° in the range of 23- 27 GHz, is addressed in this work. The proposed structur...
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We derive sufficient conditions for a dynamical systems to have a set of irregular points with full topological entropy. Such conditions are verified for nonuniformly hyperbolic systems such as positive entropy surface diffeomorphisms and rational functions on the Riemann sphere.
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We prove a criterion for Benjamini-Schramm convergence of periodic orbits of Lie groups. This general observation is then applied to homogeneous spaces and the space of translation surfaces.
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Diagonal curve is one of the most important shape measurements of tensor-product Bézier surfaces. An approach to construct Bézier surfaces with energy-minimizing diagonal curves from four input boundary curves is presented in this paper. Firstly, the expression for the diagonal energy is formulated. Secondly, the necessary and sufficient conditions...
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In the late 1990s, B. Y. Chen introduced the notion of special slant surfaces in Kähler surfaces and classified non-minimal proper special slant surfaces with constant mean curvature in 2-dimensional complex space forms. In this paper, we completely classify proper special slant surfaces with non-constant mean curvature in 2-dimensional complex spa...
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The cover image is based on the Special Issue Paper On the convergence of solving a nonlinear Volterra‐type integral equation for surface divergence based on surface thermal information by Tianyi Li et al., https://doi.org/10.1002/mma.8190. Image Credit: Tianyi Li.
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In this paper, we prove some refined estimate in the neck region when a sequence of harmonic maps from surfaces blow up. The new estimate puts more restrictions to the bubble and the weak limit map than the touching required by the classical no-neck theorem. As an application, we prove an inequality about the nullity and index when blow-up occurs.
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Persson’s theory of contact is extensively used in the study of the purely normal interaction between a nominally flat rough surface and a rigid flat. In the literature, Persson’s theory was successfully applied to the elastoplastic contact problem with a scale-independent hardness H. However, it yields a closed-form solution, P(p,ξ)\documentclass[...
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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...
Article
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In this paper, we study the global F-splitting of varieties admitting an int-amplified endomoprhism. We prove that surfaces admitting an int-amplified endomorphism are of dense globally F-split type and, in particular, of Calabi–Yau type.
Preprint
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In this article we consider PMC surfaces in complex space forms, and study the interaction between the notions of PMC, totally real and biconservative. We first consider PMC surfaces in non-flat complex space forms and prove that they are biconservative if and only if totally real. Then, we find a Simons type formula for a well-chosen vector field...
Book
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Blast Resistance Concrete Part 18 of 20 52. Tables of Stress 53.Tables of Structure 54.Tables of Surfaces Guidelines for Postgraduates and Researchers https://www.amazon.com/dp/B0B9HRZ8KP This book is a part of full version book on Blast Resistance Concrete. This book was created with help from #softwaretheses This software was created by mysel...
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In this paper we discuss the existence of prescribed mean curvature (PMC) graphs with fixed graphical boundaries in the product manifold $N\times\R$. We define a Nc-f domain in which closure does not contain certain domains with the mean curvature of the boundary of its domain equal to $f$. We show the existence of corresponding PMC graphs over bou...
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Let $X$ be a (smooth) compact complex surface. We show that the torsion subgroup of the biholomorphic automorphisms group $\operatorname{Aut}(X)$ is virtually nilpotent. Moreover, we study the Tits alternative of $\operatorname{Aut}(X)$ and virtual derived length of virtually solvable subgroups of $\operatorname{Aut}(X)$.
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An extension of the deformation models of Kérisel and Kastner to prevent distortion and collapse of underground galleries in karst or to explain breakdown processes, roof or wall collapse or land subsidence by the surface projection of the permanent stress of cave galleries is discussed
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In most natural, clinical and industrial settings, microorganisms preferentially exist in biofilms, structured communities that associate with biotic and abiotic surfaces [...]
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The Gauss map g of a surface $$\Sigma$$ in $${\mathbb {R}}^4$$ takes its values in the Grassmannian of oriented 2-planes of $${\mathbb {R}}^4$$: $$G^+(2,4)$$. We give geometric criteria of stability for minimal surfaces in $${\mathbb {R}}^4$$ in terms of g. We show in particular that if the area of the Gauss map $$|g(\Sigma ) |$$ of a minimal s...
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We study tautological vector bundles over the Hilbert scheme of points on surfaces. For each K-trivial surface, we write down a simple criterion ensuring that the tautological bundles are big and nef, and illustrate it by examples. In the K3 case, we extend recent constructions and results of Bini, Boissi\`ere and Flamini from the Hilbert scheme of...
Article
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This article presents the development of a model of a spherical robot that rolls to move and has a single point of support with the surface. The model was developed in the CoppeliaSim simulator, which is a versatile tool for implementing this kind of experience. The model was tested under several scenarios and control goals (i.e., position control,...
Article
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Rayleigh-Bénard-Marangoni instability in a bilayer system of self-rewetting fluid overlying a porous medium is investigated. The upper surface of the fluid layer is assumed non-deformable and a constant temperature gradient is imposed. Unlike in previous works, self-rewetting fluid is considered in this paper, whose surface tension is a quadratic f...
Article
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We estimate spectral gaps for the Hodge norm on quadratic differentials. To each tangent direction at any point (X, q) in the principal stratum of quadratic differentials, we associate a Hodge norm, and control the logarithmic derivative of vectors perpendicular to the principal directions in terms of the q-areas of the components corresponding to...
Conference Paper
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Atacama Desert as an analogue volcanic surface to Mars
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We study automorphism groups of fibered surfaces for finite cyclic covering fibrations of an elliptic surface. We estimate the order of a finite subgroup of automorphism groups in terms of the genus of the fiber, the genus of the base curve, the covering degree and the square of the relative canonical divisor.
Article
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The efficiency, temperature distribution, and temperature at the tip of straight rectangular, growing and decaying moving exponential fins are investigated in this article. The influence of internal heat generation, surface and surrounding temperatures, convection-conduction, Peclet number and radiation-conduction is studied numerically on the effi...
Preprint
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In [25], Moffatt introduced the concept of helicity in an inviscid fluid and examined the helicity preservation of smooth solution to barotropic compressible flow. In this paper, it is shown that the weak solutions of the above system in Onsager type spaces $\dot{B}^{1/3}_{p,c(\mathbb{N})}$ guarantee the conservation of the helicity. The parallel r...
Article
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Internal gear is an important transmission component. However, it is restricted by its ring−shaped structure, which hinders the finishing process of the tooth surfaces after the heat treatment. Honing is the most commonly used finishing technique for external gear, but it is inconvenient for internal gear. In this paper, a new type of cone−shape ho...
Preprint
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We report the discovery of a cold stream near the southern Galactic pole (dubbed as SGP-S) detected in $Gaia$ Early Data Release 3. The stream is at a heliocentric distance of $\sim$ 9.5 kpc and spans nearly 58$^\circ$ by 0.6$^\circ$ on sky. The colour-magnitude diagram of SGP-S indicates an old and metal-poor (age $\sim$ 12 Gyr, [M/H] $\sim$ -2.0...
Preprint
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We prove uniform convergence of metrics $g_k$ on a closed surface with bounded integral curvature (measure) in the sense of A.D. Alexandrov, under the assumption that the curvature measures $\mathbb{K}_{g_k}=\mu^1_k-\mu^2_k$, where $\mu^1_k,\mu^2_k$ are nonnegative Radon measures that converge weakly to measures $\mu^1,\mu^2$ respectively, and $\mu... Preprint Full-text available In this note, we study the nearly fibered knots recently introduced by Baldwin and Sivek, i.e., knots whose knot homology has top rank two. We give a topological description of the Seifert surface complement of a nearly fibered knot by showing it must fall into one of the three basic models. Conference Paper Full-text available Article Full-text available Thermal structures at the sea surface are known to affect the overlying atmospheric dynamics over various spatio‐temporal scales, from hourly and sub‐kilometric to annual and O(1,000 km). The relevant mechanisms at play are generally identified by means of correlation coefficients (in space or time) or by linear regression analysis using appropriat... Article Full-text available incremental sheet forming technique. The bead-stiffened panels were made of Alclad 2024-T3 aluminium alloy sheets commonly used in aircraft structures. The influence of forming parameters and tool strategy on surface quality and the possibility of obtaining stiffening ribs with the required profile and depth was tested through experimental research... Preprint Full-text available We prove that if$\Sigma$is a closed surface of genus at least 3 and$G$is a split real semisimple Lie group of rank at least$3$acting faithfully by isometries on a symmetric space$N$, then there exists a Hitchin representation$\rho:\pi_1(\Sigma)\to G$and a$\rho$-equivariant unstable minimal map from the universal cover of$\Sigma$to$N$.... Presentation Full-text available An automatic robot that will disinfect surfaces using UV-C rays and sanitizing spray. It can be used in the disinfection of large areas, it meets the need for mass sterilization effectively, with minimal cost. Preprint Full-text available We prove a conjecture of Ian Agol: all isometric realizations of a polyhedral surface with boundary sweep out an isotropic subset in the Kapovich-Millson moduli space of polygons isomorphic to the boundary. For a generic polyhedral disk we show that boundaries of its isometric realizations make up a Lagrangian subset. As an application of this resu... Preprint Full-text available Let$C_{n,g}$be the number of rooted cubic maps with$2n$vertices on the orientable surface of genus$g$. We show that the sequence$(C_{n,g}:g\ge 0)$is asymptotically normal with mean and variance asymptotic to$(1/2)(n-\ln n)$and$(1/4)\ln n$, respectively. We derive an asymptotic expression for$C_{n,g}$when$(n-2g)/\ln n$lies in any close... Preprint Full-text available We obtain the bifurcation of some special curves on generic 1-parameter families of surfaces in the Minkowski 3-space. The curves treated here are the locus of points where the induced pseudo metric is degenerate, the discriminant of the lines principal curvature, the parabolic curve and the locus of points where the mean curvature vanishes. Preprint Full-text available We develop the theory of d-holomorphic connections on d-holomorphic vector bundles over a Klein surface by constructing the analogous Atiyah exact sequence for d-holomorphic bundles. We also give a criterion for the existence of d-holomorphic connection in d-holomorphic bundle over a Klein surface in the spirit of the Atiyah-Weil criterion for holo... Article Full-text available We establish the second variation of sub-Riemannian surface measure for minimal non-horizontal submanifolds of a sub-Riemannian stratified Lie group. We obtain some applications for codimension one. Furthermore, we present a new proof of the fact that the hyperbolic paraboloid is stable in the Heisenberg group. Preprint Full-text available This paper presents a new approach to computation of geometric continuity for parametric bi-cubic patches, based on a simple mathematical reformulation which leads to simple additional conditions to be applied in the patching computation. The paper presents an Hermite formulation of a bicubic parametric patch, but reformulations can be made also fo... Preprint Full-text available In this paper, we introduce a new look at Finsler surfaces. Landsberg surfaces are Finsler surfaces that are solutions of a system of non-linear partial differential equations. Considering the unicorn's Landsberg problem, we reduce this system to a single non-linear PDE which we call the Landsberg's PDE. By making use of the new look of Finsler sur... Preprint Full-text available 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... Preprint Full-text available In this study, we have examined the focal surfaces of the Hasimoto surfaces and we have obtained new characterizations by comparing the Hasimoto surfaces and their focal surfaces. Especially some important results have been found regarding the parameter curves defined on these surfaces. First, the evolution of a moving space curve has been given. A... Preprint Full-text available In this paper, we investigate the deformation of generalized circle packings on ideally triangulated surfaces with boundary, which is the$(-1,-1,-1)\$ type generalized circle packing metric introduced by Guo-Luo \cite{GL2}. To find hyperbolic metrics on surfaces with totally geodesic boundaries of prescribed lengths, we introduce combinatorial Ricc...
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In this paper, we construct a surface family with a common geodesic, asymptotic curve and line of curvature of a time-like curve using the modified orthogonal frame. We present the surface as a linear combination of the modified frame and investigate the necessary and sufficient conditions to be iso-geodesic, iso-asymptotic, and line of curvature o...
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Drops impacting extremely undercooled surfaces solidify and generally adhere to them. We report the fascinating rebound of drops on dry ice in the absence of surface pinning even when they are partially solidified, and demarcate its boundary from no-bounce and fragmentation. Experiments and scaling models reveal that the extent of solidification wi...
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We prove that for any closed, connected, oriented 3-manifold M, there exists an infinite family of 2-fold branched covers of M that are hyperbolic 3-manifolds and surface bundles over the circle with arbitrarily large volume.
Article
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In the third installment in this series, applications of locally I-optimal designs for unconstrained and constrained 5-, 6-, and 7-component mixtures are discussed. Locally I-optimal designs, which minimize the average prediction variance, are extremely useful when the objective is to develop a high-quality response surface approximation. A simple...
Article
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The use of streamwise grooves for intensification of streaks created by heating in shear layers has been investigated. Three ranges of groove wave numbers were of interest: wave numbers near the critical wave number of the Rayleigh-Bénard (RB) instability, wave numbers characterizing drag-reducing grooves, and the optimal wave numbers. It is shown...
Thesis
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Surfacing the Perspective of Autistic Girls Aged Between Thirteen and Eighteen Within a Complex Social Discourse on Autism: A Qualitative Inquiry