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Multi-Robot Exploration Employing Harmonic Map Transformations
Applied SciencesRobot Exploration can be used to autonomously map an area or conduct search missions in remote or hazardous environments. Using multiple robots to perform this task can improve efficiency for time-critical applications. In this work, a distributed method
Taxiarchis-Foivos Blounas +1 more
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Hyperbolic Ricci-Bourguignon-Harmonic Flow [PDF]
Mathematics Interdisciplinary Research, 2022 In this paper, we consider hyperbolic Ricci-Bourguignon flow on a compact Riemannian manifold M coupled with the harmonic map flow between M and a fixed manifold N. At the first, we prove the unique short-time existence to solution of this system.
Shahrood Azami
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On harmonic entire mappings [PDF]
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2021 In this paper, we investigate properties of harmonic entire mappings. Firstly, we give the characterizations of the order and the type for a harmonic entire mapping $f=h+\overline{g}$, respectively, and also consider the relationship between the order and the type of $f$, $h$, and $g$.
Hua Deng +3 more
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Rosette Harmonic Mappings [PDF]
Complex Analysis and Operator Theory, 2021 A harmonic mapping is a univalent harmonic function of one complex variable. We define a family of harmonic mappings on the unit disk whose images are rotationally symmetric rosettes with $n$ cusps or n nodes, where $n \ge 3$. These mappings are analogous to the $n$-cusped hypocycloid, but are modified by Gauss hypergeometric factors, both in the ...
Jane McDougall, Lauren Stierman
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A family of examples of harmonic maps into the sphere with one point singularity
Examples and Counterexamples, 2023 The radial map u(x)=x‖x‖is a well-known example of a harmonic map into the spheres with a point singularity at x=0. In our previous paper (Misawa and Nakauchi, 2022) we give two examples of harmonic maps into the standard spheres of higher dimension with
Nobumitsu Nakauchi
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Existence and Stability of α−Harmonic Maps
Journal of Mathematics, 2022 In this paper, we first study the α−energy functional, Euler-Lagrange operator, and α-stress-energy tensor. Second, it is shown that the critical points of the α−energy functional are explicitly related to harmonic maps through conformal deformation.
Seyed Mehdi Kazemi Torbaghan +2 more
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Differential Geometry of Identity Maps: A Survey
Mathematics, 2020 An identity map idM:M→M is a bijective map from a manifold M onto itself which carries each point of M return to the same point. To study the differential geometry of an identity map idM:M→M, we usually assume that the domain M and the range M admit ...
Bang-Yen Chen
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Communications in Information and Systems, 2003 We develop two different techniques to study volume mapping problem in Computer Graphics and Medical Imaging fields. The first one is to find a harmonic map from a 3 manifold to a 3D solid sphere and the second is a sphere carving algorithm which calculates the simplicial decomposition of volume adapted to surfaces.
Wang , Yalin +2 more
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Visual Informatics, 2022 We propose a novel interactive lighting editing system for lighting a single indoor RGB image based on spherical harmonic lighting. It allows users to intuitively edit illumination and relight the complicated low-light indoor scene.
Zhongyun Bao +3 more
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Univalent harmonic mappings [PDF]
Communications, Faculty Of Science, University of Ankara Series A1Mathematics and Statistics, 1996 Summary: A family of univalent harmonic functions is studied from the point of geometric function theory. This class consists of mappings of the open unit disk onto the entire complex plane except for two infinite slits along the real axis with a normalization at the origin.
Öztürk, Metin, Yamankaradeniz, Mümin
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