Journal articles: 'Courbes de Hilbert 3D'

1

Perrin, Daniel. "La connexité asymptotique du schéma de Hilbert des courbes gauches." ANNALI DELL UNIVERSITA DI FERRARA 49, no. 1 (January 2003): 183–95. http://dx.doi.org/10.1007/bf02844916.

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Crnojevic-Bengin, Vesna, and Djuradj Budimir. "Novel 3D Hilbert microstrip resonators." Microwave and Optical Technology Letters 46, no. 3 (2005): 195–97. http://dx.doi.org/10.1002/mop.20943.

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3

Templier, Nicolas. "Sur le rang des courbes elliptiques sur les corps de classes de Hilbert." Compositio Mathematica 147, no. 4 (February 10, 2011): 1087–104. http://dx.doi.org/10.1112/s0010437x10005051.

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AbstractLet E/ℚ be an elliptic curve and let D<0 be a sufficiently large fundamental discriminant. If $E(\overline {\BmQ })$ contains Heegner points of discriminant D, those points generate a subgroup of rank at least |D|δ, where δ>0 is an absolute constant. This result is compatible with the Birch and Swinnerton-Dyer conjecture.

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Guffroy, Sébastien. "Sur l’incomplétude de la série linéaire caractéristique d’une famille de courbes planes à nœuds et à cusps." Nagoya Mathematical Journal 171 (2003): 51–83. http://dx.doi.org/10.1017/s0027763000025514.

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AbstractSince J.Wahl ([27]), it is known that degree d plane curves having some fixed numbers of nodes and cusps as its only singularities can be represented by a scheme, let say H, which can be singular. In Wahl’s example, H is singular along a subscheme F but the induced reduced scheme Hred is smooth along F. In this work, we construct explicitly a family of plane curves with nodes and cusps which are represented by singular points of Hred.To this end, we begin to show that the Hilbert scheme of smooth and connected space curves of degree 12 and genus 15 is irreducible and generically smooth. It follows that it is singular along a hypersurface (3.10). This example is minimal in the sense that the Hilbert scheme of smooth and connected space curves is regular in codimension 1 for d < 12 (B.2). Finally we construct our plane curves from the space curves represented by points of this hypersurface (4.7).

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Martin-Deschamps, Mireille, and Daniel Perrin. "Le schéma de Hilbert des courbes gauches localement Cohen-Macaulay n'est (presque) jamais réduit." Annales scientifiques de l'École normale supérieure 29, no. 6 (1996): 757–85. http://dx.doi.org/10.24033/asens.1753.

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Aït Amrane, Samir. "Sur le schéma de Hilbert des courbes de degré d et genre de ℙk3." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 326, no. 7 (April 1998): 851–56. http://dx.doi.org/10.1016/s0764-4442(98)80049-9.

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Ginouillac, Stéphane. "Sur le nombre de composantes du schéma de Hilbert des courbes ACM de pk3." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 329, no. 10 (November 1999): 857–62. http://dx.doi.org/10.1016/s0764-4442(00)87488-1.

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Ujang, Uznir, Francois Anton, Suhaibah Azri, Alias Abdul Rahman, and Darka Mioc. "3D Hilbert Space Filling Curves in 3D City Modeling for Faster Spatial Queries." International Journal of 3-D Information Modeling 3, no. 2 (April 2014): 1–18. http://dx.doi.org/10.4018/ij3dim.2014040101.

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The advantages of three dimensional (3D) city models can be seen in various applications including photogrammetry, urban and regional planning, computer games, etc. They expand the visualization and analysis capabilities of Geographic Information Systems on cities, and they can be developed using web standards. However, these 3D city models consume much more storage compared to two dimensional (2 D) spatial data. They involve extra geometrical and topological information together with semantic data. Without a proper spatial data clustering method and its corresponding spatial data access method, retrieving portions of and especially searching these 3D city models, will not be done optimally. Even though current developments are based on an open data model allotted by the Open Geospatial Consortium (OGC) called CityGML, its XML-based structure makes it challenging to cluster the 3D urban objects. In this research, the authors propose an opponent data constellation technique of space-filling curves (3D Hilbert curves) for 3D city model data representation. Unlike previous methods, that try to project 3D or n-dimensional data down to 2D or 3D using Principal Component Analysis (PCA) or Hilbert mappings, in this research, they extend the Hilbert space-filling curve to one higher dimension for 3D city model data implementations. The query performance was tested for single object, nearest neighbor and range search queries using a CityGML dataset of 1,000 building blocks and the results are presented in this paper. The advantages of implementing space-filling curves in 3D city modeling will improve data retrieval time by means of optimized 3D adjacency, nearest neighbor information and 3D indexing. The Hilbert mapping, which maps a sub-interval of the ([0,1]) interval to the corresponding portion of the d-dimensional Hilbert's curve, preserves the Lebesgue measure and is Lipschitz continuous. Depending on the applications, several alternatives are possible in order to cluster spatial data together in the third dimension compared to its clustering in 2 D.

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JIA, Lianyin, Binbin LIANG, Mengjuan LI, Yong LIU, Yinong CHEN, and Jiaman DING. "Efficient 3D Hilbert Curve Encoding and Decoding Algorithms." Chinese Journal of Electronics 31, no. 2 (March 2022): 277–84. http://dx.doi.org/10.1049/cje.2020.00.171.

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Nguyen, Giap, Patrick Franco, Rémy Mullot, and Jean-Marc Ogier. "Proposition d’une famille de courbes remplissant l’espace de niveau de localité comparable à la courbe de Hilbert." Traitement du signal 29, no. 6 (December 28, 2012): 553–74. http://dx.doi.org/10.3166/ts.29.553-574.

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11

Rosenberg, Ori Izhak, and David Abookasis. "Application of Hilbert Analysis in Orthogonal Fourier Fringe-projection to Improve Object Shape Reconstruction -=SUP=-*-=/SUP=-." Оптика и спектроскопия 129, no. 5 (2021): 658. http://dx.doi.org/10.21883/os.2021.05.50894.1039-20.

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Three-dimensional (3D) measurement of an object is widely used in many fields including machine vision, quality control, robotics, medical diagnostics, and others. High-precision 3D surface topography is necessary for describing object shape accurately with high spatial resolution. A combined approach to improve 3D object shape recovery based on Fourier orthogonal fringe projection together with Hilbert transform is proposed and demonstrated. This new idea of combination is highly effective due to the suppressing of background intensity of the deformed fringe pattern while the zero spectrum is extracted precisely and easily. Removing the zero order component leads to increase the visualization and resolution of the measured object. Application of Hilbert processing for object shape recovery in orthogonal Fourier projection domain to improve 3D visualization has not been reported before. The processing framework of this strategy is described in detail. Validation of the proposed method is verified by experiments including visualization of objects with various shapes and sizes. A comparison between profilometry methods is also given which verify better performance in reconstruction of complex objects. 3D reconstruction of flow running at different speeds on a scattering medium with this combined approach is also demonstrated for the first time. Keywords: 3D shape measurements, orthogonal fringes, Fourier and Hilbert transform, image processing.

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12

Mickelsson, Jouko. "3D Current Algebra and Twisted K Theory." Reviews in Mathematical Physics 30, no. 07 (July 25, 2018): 1840011. http://dx.doi.org/10.1142/s0129055x18400111.

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Equivariant twisted K theory classes on compact Lie groups [Formula: see text] can be realized as families of Fredholm operators acting in a tensor product of a fermionic Fock space and a representation space of a central extension of the loop algebra [Formula: see text] using a supersymmetric Wess–Zumino–Witten model. The aim of the present paper is to extend the construction to higher loop algebras using an abelian extension of a 3D current algebra. We have only partial success: Instead of true Fredholm operators we have formal algebraic expressions in terms of the generators of the current algebra and an infinite dimensional Clifford algebra. These give rise to sesquilinear forms in a Hilbert bundle which transform in the expected way with respect to 3D gauge transformations but do not define true Hilbert space operators.

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Saniman, M. N. F., M. H. M Hashim, K. A. Mohammad, K. A. Abd Wahid, W. M. Wan Muhamad, and N. H. Noor Mohamed. "Tensile Characteristics of Low Density Infill Patterns for Mass Reduction of 3D Printed Polylactic Parts." International Journal of Automotive and Mechanical Engineering 17, no. 2 (July 3, 2020): 7927–34. http://dx.doi.org/10.15282/ijame.17.2.2020.11.0592.

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Various infill patterns are introduced in 3D printing to generate low density objects that leads to reduced cost and fabrication time through mass reduction. However, as a trade-off, the strength of the 3D printed component is uncertain. Confusions arise in determining the infill pattern with highest value of tensile strength since most studies limited only to rectilinear, honeycomb, and concentric infill patterns. As consequences, there are very little information on rarely used infill patterns such as Hilbert curve, Archimedean cord and octagram spiral. Therefore, the purpose of this research is to investigate and compare the tensile strength and strain of all infill patterns in mass reduction of 3D printed components experimentally. Following ASTM D638 type III standard, ten tensile test specimens of each infill patterns with 20% density were printed with an FFF 3D printer and were then tested. It was found that Archimedean cords infill pattern had the highest specific tensile strength of 33.23×103 MPa∙mm3/g which made it as the optimum infill pattern for the mass reduction of 3D printed parts with a high tensile strength. On the other hand, having the highest specific tensile strain of 18.21×103 %∙mm3/g, concentric infill pattern was found to be more suitable for producing lightweight parts with a higher elongation before break. Additionally, Hilbert curve infill was the worst selection for mass reduction since it had the lowest values of specific tensile strength and specific strain of 19.80×103 MPa∙mm3/g and 8.34 %∙mm3/g, respectively. Nevertheless, the trends of tensile strength and strain of all six infill patterns had been obtained, especially for rarely investigated infill patterns of Archimedean cords, octagram spiral, and Hilbert curve. Specifically, the trend from the strongest to the weakest (in % compared to solid) for specific tensile strength is rectilinear (38.57%), Archimedean chords (37.29%), concentric (36.57%), octagram spiral (34.79%), honeycomb (27.84%), and Hilbert curve (22.25%), while for specific strain is concentric (102.6%), octagram spiral (83.94%), rectilinear (78.22%), Archimedean cords (77.99%), honeycomb (54.84%), and Hilbert curve (45.14%).

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Stoica, Ovidiu Cristinel. "No-go results on emergent space and other structures." Journal of Physics: Conference Series 2533, no. 1 (June 1, 2023): 012027. http://dx.doi.org/10.1088/1742-6596/2533/1/012027.

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Abstract It is often claimed that, from the abstract quantum state vector and Hamiltonian, everything emerges uniquely (for example the 3D-space, a preferred factorization of the Hilbert space, and a preferred basis). This thesis, called Hilbert-Space Fundamentalism (HSF), is assumed for example in Carroll and Singh’s “Mad-dog Everettianism”, some proposals based on decoherence, proposals that aim to describe everything by the quantum structure alone, and proposals that spacetime emerges from a purely quantum theory of gravity. I show that whenever the 3D-space, a preferred factorization, or any other structure emerges like this, there are infinitely many solutions. This refutes Hilbert-Space Fundamentalism. Implications for various research programs aiming to show that certain structures emerge uniquely, and for various interpretations of Quantum Mechanics, are discussed.

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15

Amrane, Samir Ait. "Sur le schéma de Hilbert des courbes gauches de degré $d$ et genre $g=(d-3)(d-4)/2$." Annales de l’institut Fourier 50, no. 6 (2000): 1671–707. http://dx.doi.org/10.5802/aif.1804.

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16

Gao, Peng. "Approximate Controllability of a 3D Nonlinear Stochastic Wave Equation." Journal of Applied Mathematics 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/524860.

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We study the well-posedness of a 3D nonlinear stochastic wave equation which derives from the Maxwell system by the Galerkin method. Then we study the approximate controllability of this system by the Hilbert uniqueness method.

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17

Guizilini, Vitor, and Fabio Ramos. "Towards real-time 3D continuous occupancy mapping using Hilbert maps." International Journal of Robotics Research 37, no. 6 (May 2018): 566–84. http://dx.doi.org/10.1177/0278364918771476.

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The ability to model the surrounding space and determine which areas are occupied is of key importance in many robotic applications, ranging from grasping and manipulation to path planning and obstacle avoidance. Occupancy modeling is often hindered by several factors, such as: real-time constraints, that require quick updates and access to estimates; quality of available data, that may contain gaps and partial occlusions; and memory requirements, especially for large-scale environments. In this work we propose a novel framework that elegantly addresses all these issues, by producing an efficient non-stationary continuous occupancy function that can be efficiently queried at arbitrary resolutions. Furthermore, we introduce techniques that allow the learning of individual features for different areas of the input space, that are better able to model its contained information and promote a higher-level understanding of the observed scene. Experimental tests were conducted on both simulated and real large-scale datasets, showing how the proposed framework rivals current state-of-the-art techniques in terms of computational speed while achieving a substantial decrease (of orders of magnitude) in memory requirements and demonstrating better interpolative powers, that are able to smooth out sparse and noisy information.

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Memon, Muhammad Usman, Manos M. Tentzeris, and Sungjoon Lim. "Inkjet-printed 3D Hilbert-curve fractal antennas for VHF band." Microwave and Optical Technology Letters 59, no. 7 (May 16, 2017): 1698–704. http://dx.doi.org/10.1002/mop.30613.

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19

Lopes, L., M. Almeida, and D. Reis. "Influence of 3D microstructure for improving the thermal performance of building façades." IOP Conference Series: Earth and Environmental Science 1196, no. 1 (June 1, 2023): 012064. http://dx.doi.org/10.1088/1755-1315/1196/1/012064.

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Abstract The thermal performance of a building is highly dependent on the heat transmission through the envelope. On the other hand, additive manufacturing has been increasingly used in several industrial applications due to its possibility to produce complex structures. However, most studies of the 3d printing process focused on mechanical performance. This study aims to evaluate how the internal 3D-printed microstructure affects thermal performance. Twelve infill patterns were analysed, including Gyroid, Grid, Hilbert curve, Line, Rectilinear, Stars Triangles, 3D Honeycomb, Honeycomb, Concentric, Cubic, and Octagram spiral. Using fused deposition modelling (FDM), the samples were printed with polyethene terephthalate-glycol (PET-G) thermoplastic filaments. Thermal tests were conducted using a calibrated hotbox, following the recommendations of ASTM C1363-11:2014. The results obtained show a variation of 70% by changing the internal microstructure using fix infill density of 25%. Concentric, Gyroid and Hilbert curve achieved the best thermal insulation properties.

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Azencott, R., R. Glowinski, J. He, A. Jajoo, Y. Li, A. Martynenko, R. H. W. Hoppe, S. Benzekry, and S. H. Little. "Diffeomorphic Matching and Dynamic Deformable Surfaces in 3d Medical Imaging." Computational Methods in Applied Mathematics 10, no. 3 (2010): 235–74. http://dx.doi.org/10.2478/cmam-2010-0014.

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AbstractWe consider optimal matching of submanifolds such as curves and surfaces by a variational approach based on Hilbert spaces of diffeomorphic transformations. In an abstract setting, the optimal matching is formulated as a minimization problem involving actions of diffeomorphisms on regular Borel measures considered as supporting measures of the reference and the target submanifolds. The objective functional consists of two parts measuring the elastic energy of the dynamically deformed surfaces and the quality of the matching. To make the problem computationally accessible, we use reproducing kernel Hilbert spaces with radial kernels and weighted sums of Dirac measures which gives rise to diffeomorphic point matching and amounts to the solution of a finite dimensional minimization problem. We present a matching algorithm based on the first order necessary optimality conditions which include an initial-value problem for a dynamical system in the trajectories describing the deformation of the surfaces and a final-time problem associated with the adjoint equations. The performance of the algorithm is illustrated by numerical results for examples from medical image analysis.

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Meusburger, Catherine, and Karim Noui. "The Hilbert space of 3d gravity: quantum group symmetries and observables." Advances in Theoretical and Mathematical Physics 14, no. 6 (2010): 1651–715. http://dx.doi.org/10.4310/atmp.2010.v14.n6.a3.

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Zheng, Yikang, Yibo Wang, and Xu Chang. "3D forward modeling of upgoing and downgoing wavefields using Hilbert transform." GEOPHYSICS 83, no. 1 (January 1, 2018): F1—F8. http://dx.doi.org/10.1190/geo2016-0637.1.

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The separation of upgoing and downgoing wavefields is an important technique in the processing of vertical seismic profiling data and ocean bottom cable data. It is also used in reverse time migration (RTM) based on the two-way wave equation to suppress low-frequency, high-amplitude noises and false images. Therefore, we model upgoing and downgoing wavefields directly in the wavefield propagation. There are several methods to obtain separated wavefields. The methods using the Fourier transform require storage of the wavefields, which is not practical due to the extremely high disk-space requirements. Methods using Poynting vectors have an ambiguity problem when crossing a peak or a trough of the wavefields. To improve the accuracy and stability of the modeled upgoing and downgoing wavefields in a complicated velocity model, we evaluate an efficient forward-modeling approach purely based on the Hilbert transform in 3D acoustic wavefield simulation. This method is implemented by the Hilbert transform along the time and depth axis, instead of the Fourier transform. We explicitly derive the formulas for upgoing and downgoing wavefield propagation and attach reproducible source codes. Applications to synthetic models indicate that this method can forward propagate upgoing and downgoing wavefields effectively and improve the imaging quality in migration. This method has various potential applications, e.g., 3D seismic imaging with high computation efficiency.

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Nasu, Hirokazu. "The Hilbert Scheme of Space Curves of Degreedand Genus 3d−18." Communications in Algebra 36, no. 11 (November 6, 2008): 4163–85. http://dx.doi.org/10.1080/00927870802175089.

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Ding, Gang, Liankun Sun, Zhenkai Wan, Jialu Li, Xiaoyuan Pei, and Youhong Tang. "Recognition of Damage Modes and Hilbert–Huang Transform Analyses of 3D Braided Composites." Journal of Composites Science 2, no. 4 (November 14, 2018): 65. http://dx.doi.org/10.3390/jcs2040065.

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The identification and classification of acoustic emission (AE) based failure modes are complex due to the fact that AE waves are generally released simultaneously from all AE-emitting damage sources. To fully understand the occurrence of damage and the damage evolution law of 3D braided composites, the tensile response characteristics and failure mechanisms of such composites were revealed by experiments, followed by frequency domain analyses. The results indicated good correlation between the number of AE events and the evolution of damage in 3D braided composites. After an AE signal was decomposed by the Hilbert–Huang transform (HHT) method, it might extract and separate all damage modes included in this AE signal. Additionally, the frequency saltation in the HHT spectra implied changes in the failure mode of the 3D braided composites. This study provides an effective new method for the analysis of the tensile fracture mechanism in 3D braided composites.

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Pauly, Dirk. "A global div-curl-lemma for mixed boundary conditions in weak Lipschitz domains and a corresponding generalized A 0 * \mathrm{A}_{0}^{*} - A 1 \mathrm{A}_{1} -lemma in Hilbert spaces." Analysis 39, no. 2 (August 1, 2019): 33–58. http://dx.doi.org/10.1515/anly-2018-0027.

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Abstract We prove global and local versions of the so-called {\operatorname{div}} - {\operatorname{curl}} -lemma, a crucial result in the homogenization theory of partial differential equations, for mixed boundary conditions on bounded weak Lipschitz domains in 3D with weak Lipschitz interfaces. We will generalize our results using an abstract Hilbert space setting, which shows corresponding results to hold in arbitrary dimensions as well as for various differential operators. The crucial tools and the core of our arguments are Hilbert complexes and related compact embeddings.

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Mendonça, Diego C. M., and Olivier Piguet. "Loop Quantization of a 3D AbelianBFModel withσ-Model Matter." Advances in Mathematical Physics 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/307132.

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The main goal of this work is to explore the symmetries and develop the dynamics associated with a 3D AbelianBFmodel coupled to scalar fields submitted to a sigma model like constraint, at the classical and quantum levels. Background independence, on which the model is founded, strongly constrains its nature. We adapt to the present model the techniques of Loop Quantum Gravity in order to construct its physical Hilbert space and its observables.

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Comandini, Gianni, Valeska Ting, Mahdi Azarpeyvand, and Fabrizio Scarpa. "Experimental and Numerical Studies on the Hilbert Fractal Architecture as an Acoustic Metamaterial." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 265, no. 5 (February 1, 2023): 2358–61. http://dx.doi.org/10.3397/in_2022_0336.

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Experiments and numerical methods were used to investigate the key parameters which affect the transmission loss behaviour of Hilbert fractal acoustic metamaterials. The tests were conducted using a four-microphone impedance tube, and the numerical simulation was performed using COMSOL Multiphysics software. Fractal order and cavity slot widths on Hilbert fractal metamaterials were investigated. 3D printing manufacturing techniques were used to make polylactic acid specimens. The COMSOL model developed utilised thermo-viscous and lossless domains with boundary layer mesh in the fractal cavities. The tests and simulations' frequency range were 0.2 kHz to 3.0 kHz, with parametric gap widths ranging from 0.5 mm to 3.0 mm. There is a reasonable agreement between the numerical models and the experimental results; the second-order Hilbert fractal had the most significant effect on transmission loss, with an experimental peak of nearly 50 dB around 1600 Hz. Moreover, multiple transmission loss peaks were observed as a function of the gap width in the five Hilbert fractal orders studied. The gap width is one of the critical parameters for optimising the performance of the Hilbert fractal as an acoustic metamaterial.

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Kiran, K. Surya, Chethan Krishnan, and Avinash Raju. "3D gravity, Chern–Simons and higher spins: A mini introduction." Modern Physics Letters A 30, no. 32 (October 5, 2015): 1530023. http://dx.doi.org/10.1142/s0217732315300232.

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We give a review on (a) elements of (2+1)-dimensional gravity, (b) some aspects of its relation to Chern–Simons theory, (c) its generalization to couple higher spins, and (d) cosmic singularity resolution as an application in the context of flat space higher spin theory. A knowledge of the Einstein–Hilbert action, classical non-Abelian gauge theory and some (negotiable amount of) maturity are the only pre-requisites.

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Suzuki, Osamu, and Zhidong Zhang. "A Method of Riemann–Hilbert Problem for Zhang’s Conjecture 1 in a Ferromagnetic 3D Ising Model: Trivialization of Topological Structure." Mathematics 9, no. 7 (April 2, 2021): 776. http://dx.doi.org/10.3390/math9070776.

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A method of the Riemann–Hilbert problem is applied for Zhang’s conjecture 1 proposed in Philo. Mag. 87 (2007) 5309 for a ferromagnetic three-dimensional (3D) Ising model in the zero external field and the solution to the Zhang’s conjecture 1 is constructed by use of the monoidal transform. At first, the knot structure of the ferromagnetic 3D Ising model in the zero external field is determined and the non-local behavior of the ferromagnetic 3D Ising model can be described by the non-trivial knot structure. A representation from the knot space to the Clifford algebra of exponential type is constructed, and the partition function of the ferromagnetic 3D Ising model in the zero external field can be obtained by this representation (Theorem I). After a realization of the knots on a Riemann surface of hyperelliptic type, the monodromy representation is realized from the representation. The Riemann–Hilbert problem is formulated and the solution is obtained (Theorem II). Finally, the monoidal transformation is introduced for the solution and the trivialization of the representation is constructed (Theorem III). By this, we can obtain the desired solution to the Zhang’s conjecture 1 (Main Theorem). The present work not only proves the Zhang’s conjecture 1, but also shows that the 3D Ising model is a good platform for studying in deep the mathematical structure of a physical many-body interacting spin system and the connections between algebra, topology, and geometry.

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Zhang, Zhidong, and Osamu Suzuki. "A Method of the Riemann–Hilbert Problem for Zhang’s Conjecture 2 in a Ferromagnetic 3D Ising Model: Topological Phases." Mathematics 9, no. 22 (November 18, 2021): 2936. http://dx.doi.org/10.3390/math9222936.

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A method of the Riemann–Hilbert problem is employed for Zhang’s conjecture 2 proposed in Philo. Mag. 87 (2007) 5309 for a ferromagnetic three-dimensional (3D) Ising model in a zero external magnetic field. In this work, we first prove that the 3D Ising model in the zero external magnetic field can be mapped to either a (3 + 1)-dimensional ((3 + 1)D) Ising spin lattice or a trivialized topological structure in the (3 + 1)D or four-dimensional (4D) space (Theorem 1). Following the procedures of realizing the representation of knots on the Riemann surface and formulating the Riemann–Hilbert problem in our preceding paper [O. Suzuki and Z.D. Zhang, Mathematics 9 (2021) 776], we introduce vertex operators of knot types and a flat vector bundle for the ferromagnetic 3D Ising model (Theorems 2 and 3). By applying the monoidal transforms to trivialize the knots/links in a 4D Riemann manifold and obtain new trivial knots, we proceed to renormalize the ferromagnetic 3D Ising model in the zero external magnetic field by use of the derivation of Gauss–Bonnet–Chern formula (Theorem 4). The ferromagnetic 3D Ising model with nontrivial topological structures can be realized as a trivial model on a nontrivial topological manifold. The topological phases generalized on wavevectors are determined by the Gauss–Bonnet–Chern formula, in consideration of the mathematical structure of the 3D Ising model. Hence we prove the Zhang’s conjecture 2 (main theorem). Finally, we utilize the ferromagnetic 3D Ising model as a platform for describing a sensible interplay between the physical properties of many-body interacting systems, algebra, topology, and geometry.

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Papacharalampopoulos, Alexios, Harry Bikas, and Panagiotis Stavropoulos. "Path planning for the infill of 3D printed parts utilizing Hilbert curves." Procedia Manufacturing 21 (2018): 757–64. http://dx.doi.org/10.1016/j.promfg.2018.02.181.

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32

Wu, Yuhao, Xuefeng Cao, and Wanzhong Sun. "MI-HCS: Monotonically Increasing Hilbert Code Segments for 3D Geospatial Query Window." IEEE Access 8 (2020): 47580–95. http://dx.doi.org/10.1109/access.2020.2979250.

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Man, Xian-feng, Bai-zhan Xia, Zhen Luo, and Jian Liu. "3D Hilbert fractal acoustic metamaterials: low-frequency and multi-band sound insulation." Journal of Physics D: Applied Physics 52, no. 19 (March 7, 2019): 195302. http://dx.doi.org/10.1088/1361-6463/ab092a.

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Bisu, Claudiu, Alain Gerard, Miron Zapciu, and Olivier Cahuc. "The Milling Process Monitoring Using 3D Envelope Method." Advanced Materials Research 423 (December 2011): 77–88. http://dx.doi.org/10.4028/www.scientific.net/amr.423.77.

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This paper proposes a method to vibration analysis in order to on-line monitoring of milling process quality. Adapting envelope analysis to characterize the milling tool materials is an important contribution to the qualitative and quantitative characterization of milling capacity and a step by modeling the three-dimensional cutting process. An experimental protocol was designed and developed for the acquisition, processing and analyzing three-dimensional signal. The vibration envelope analysis is proposed to detect the cutting capacity of the tool with the optimization application of cutting parameters. The research is focused on Hilbert transform optimization to evaluate the dynamic behavior of the machine/ tool/workpiece.

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Hansen, R. O. "3D multiple-source Werner deconvolution for magnetic data." GEOPHYSICS 70, no. 5 (September 2005): L45—L51. http://dx.doi.org/10.1190/1.2073883.

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Werner deconvolution has been widely used for at least 30 years for rapid interpretation of magnetic data. Since 1993, a multiple-source generalization of the method has been known, and at least two implementations of the algorithm are in use. Recently, Werner deconvolution has been extended to three dimensions through the use of generalized Hilbert transforms. In this paper, a multiple-source extension of the 3D Werner algorithm is developed which also generalizes the 2D multiple-source algorithm. The implementation of this algorithm is tested on both 3D multiple-source synthetic data, for which good agreement with the model is obtained, and on complex data from the Albuquerque basin, which yields results corresponding well with other interpretations and with known geology.

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Arnison, M. R., C. J. Cogswell, N. I. Smith, P. W. Fekete, and K. G. Larkin. "Using the Hilbert transform for 3D visualization of differential interference contrast microscope images." Journal of Microscopy 199, no. 1 (July 2000): 79–84. http://dx.doi.org/10.1046/j.1365-2818.2000.00706.x.

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Han, Jie, Tao Zhang, Zhaoyang Qiu, and Xiaoyu Zheng. "Communication emitter individual identification via 3D-Hilbert energy spectrum-based multiscale segmentation features." International Journal of Communication Systems 32, no. 1 (October 21, 2018): e3833. http://dx.doi.org/10.1002/dac.3833.

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Eryildiz, Meltem. "The effects of infill patterns on the mechanical properties of 3D printed PLA parts fabricated by FDM." Ukrainian Journal of Mechanical Engineering and Materials Science 7, no. 1-2 (2021): 1–8. http://dx.doi.org/10.23939/ujmems2021.01-02.001.

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The purpose of this study is to analyze the effect of the infill pattern on the mechanical properties of 3D printed PLA parts. Polylactic acid (PLA) parts were fabricated by fused deposition modeling (FDM) at various infill patterns at 30% infill density. Five different infill patterns (stars, 3D honeycomb, honeycomb, gyroid, Hilbert curve) have been investigated. The results have shown that the honeycomb infill pattern exhibited the highest mechanical properties with 29.43 MPa and 2.04 mm elongation due to the improved strength of the strut junctions in this pattern. In the case of the Hilbert curve pattern, compared to the other patterns, though they have the same infill density, tensile strength was lowest because of the presence of large air gaps in the pattern that induced rapid fracture during the test. The optical microscope images of the fracture surfaces were compatible with the tensile strength results. Also considering the build time and the spent filament, it can be said that the honeycomb infill pattern is very promising. Lastly, the results showed that the tensile strength and elongation of 3D printed PLA parts increased 43.4% and 32%, respectively, under optimum infill pattern conditions. The findings of this study will help manufacturing firms and researchers to decide on the appropriate infill pattern, so that FDM parts can be fabricated with minimal production cost and good mechanical properties.

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Guizilini, Vitor, and Fabio Ramos. "Learning to reconstruct 3D structures for occupancy mapping from depth and color information." International Journal of Robotics Research 37, no. 13-14 (August 14, 2018): 1595–609. http://dx.doi.org/10.1177/0278364918783061.

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Real-world scenarios contain many structural patterns that, if appropriately extracted and modeled, can be used to reduce problems associated with sensor failure and occlusions while improving planning methods in such tasks as navigation and grasping. This paper devises a novel unsupervised procedure that models 3D structures from unorganized pointclouds as occupancy maps. Our methodology enables the learning of unique and arbitrarily complex features using a variational Bayesian convolutional auto-encoder, which compresses local information into a latent low-dimensional representation and then decodes it back in order to reconstruct the original scene, including color information when available. This reconstructive model is trained on features obtained automatically from a wide variety of scenarios, in order to improve its generalization and interpolative powers. We show that the proposed framework is able to recover partially missing structures and reason over occlusions with high accuracy while maintaining a detailed reconstruction of observed areas. To combine localized feature estimates seamlessly into a single global structure, we employ the Hilbert maps framework, recently proposed as a robust and efficient occupancy mapping technique, and introduce a new kernel for reproducing kernel Hilbert space projection that uses estimates from the reconstructive model. Experimental tests are conducted with large-scale 2D and 3D datasets, using both laser and monocular data, and a study of the impact of various accuracy–speed trade-offs is provided to assess the limits of the proposed methodology.

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Wu, Haitao, Yiping Cao, Haihua An, Yang Li, Hongmei Li, Cai Xu, and Na Yang. "High-precision 3D shape measurement of rigid moving objects based on the Hilbert transform." Applied Optics 60, no. 27 (September 15, 2021): 8390. http://dx.doi.org/10.1364/ao.435462.

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MARKOWICH, PETER A., and NORBERT J. MAUSER. "THE CLASSICAL LIMIT OF A SELF-CONSISTENT QUANTUM-VLASOV EQUATION IN 3D." Mathematical Models and Methods in Applied Sciences 03, no. 01 (February 1993): 109–24. http://dx.doi.org/10.1142/s0218202593000072.

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Under natural assumptions on the initial density matrix of a mixed quantum state (Hermitian, non-negative definite, uniformly bounded trace, Hilbert-Schmidt norm and kinetic energy) we prove that accumulation points (as the scaled Planck constant tends to zero) of solutions of a corresponding slightly regularized Wigner-Poisson system are distributional solutions of the classical Vlasov-Poisson system. The result holds for the gravitational and repulsive cases. Also, for every phase-space density in [Formula: see text] (with bounded kinetic energy) we prepare a sequence of density matrices satisfying the above assumptions, such that the given density is the limit of the Wigner transforms of these density matrices.

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Bulavskaya, A., E. Bushmina, A. Grigorieva, I. Miloichikova, and S. Stuchebrov. "X-ray study of the density distribution of FFF-printed samples with different fill patterns." Journal of Instrumentation 19, no. 06 (June 1, 2024): C06013. http://dx.doi.org/10.1088/1748-0221/19/06/c06013.

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Abstract Three-dimensional printing has a wide range of applications in science and technology. Fused filament fabrication (FFF) is a commonly used 3D printing technology, which is now being increasingly employed in radiation physics. In FFF, the internal structure of an object is primarily determined by its fill pattern and selected print modes. Therefore, this study aims to examine the interaction between X-rays and 3D-printed plastic samples with various infill patterns. The 3D-printed objects were produced using FFF with plastic and different infill patterns, including Rectilinear, Grid, Triangles, Stars, Honeycomb, Concentric, Archimedean Chords, Gyroid, and Hilbert Curve. Infill densities of 80% and 90% were utilized. Tomographic methods were applied to analyze the resulting samples. The study provides tomograms of the internal structure for each infill pattern. It was observed that Rectilinear and Grid patterns produced the most homogeneous samples. The findings of this study contribute to understanding of the propagation of X-rays through 3D-printed plastic samples with complex internal structures.

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Davis, Kristofer, and Yaoguo Li. "Efficient 3D inversion of magnetic data via octree-mesh discretization, space-filling curves, and wavelets." GEOPHYSICS 78, no. 5 (September 1, 2013): J61—J73. http://dx.doi.org/10.1190/geo2012-0192.1.

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Airborne magnetic survey data sets can contain from hundreds of thousands to millions of observations and typically cover large areas. The large number of measurements combined with a model mesh to accommodate the survey extent can render an inversion of these data intractable. Faced with this challenge, we have developed a three-step procedure to locally optimize the degree of model discretization and to compress the corresponding sensitivity matrix for the inversion of magnetic data. The mesh optimization is achieved through the use of adaptive octree discretization. The compression is achieved by first reordering the model cells using the Hilbert space filling curve and then applying the one-dimensional wavelet transform to the corresponding sensitivities. The fractal property of the Hilbert curve groups the spatially adjacent cells into algebraically adjacent positions in the reordered model mesh and thereby maximizes the number of zero or near-zero coefficients in the one-dimensional wavelet transform. Winnowing these insignificant coefficients finally leads to a highly sparse representation of the sensitivity matrix, which dramatically reduces the required memory and CPU time in the inversion. As a result, the proposed algorithm is capable of inverting huge data sets ([Formula: see text] measurements) with commensurate model sizes in a short time on a single desktop computer. As a test, we inverted an entire magnetic data set with 170,000 observations from a large uranium exploration program and achieved a reduction in computational cost exceeding 10,000 times.

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Ahmadpour, Ali, Abdolmajid Dejamkhooy, and Hossein Shayeghi. "Fault Diagnosis of HTS–SLIM Based on 3D Finite Element Method and Hilbert–Huang Transform." IEEE Access 10 (2022): 35736–49. http://dx.doi.org/10.1109/access.2022.3159693.

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Zhang, Suqi, Yue Lu, Jian Sun, Yu Gu, Xiaodan Zhang, and Zhiyong Tang. "The process intensification of CO2 absorption in Hilbert fractal reactor fabricated by a 3D printer." Energy Sources, Part A: Recovery, Utilization, and Environmental Effects 41, no. 4 (September 20, 2018): 481–92. http://dx.doi.org/10.1080/15567036.2018.1520331.

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Cremonesi, Stefano. "The Hilbert series of 3d ${\boldsymbol{\mathcal{N}}}=2$ Yang–Mills theories with vectorlike matter." Journal of Physics A: Mathematical and Theoretical 48, no. 45 (October 20, 2015): 455401. http://dx.doi.org/10.1088/1751-8113/48/45/455401.

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Mohan, Shashi Ranjan, Syed Nizamuddin Khaderi, and Suryakumar Simhambhatla. "3D Printing of Components with Tailored Properties Through Hilbert Curve Filling of a Discretized Domain." 3D Printing and Additive Manufacturing 7, no. 6 (December 1, 2020): 288–99. http://dx.doi.org/10.1089/3dp.2020.0048.

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郑, 晓美. "Three-Frequency Three-Step Phase-Shift Structured Light 3D Reconstruction Method Based on Hilbert Transform." Modeling and Simulation 12, no. 05 (2023): 4437–48. http://dx.doi.org/10.12677/mos.2023.125404.

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Tan, Guangjun, Zhi Chen, Wei Zhao, and Xiaofeng Sun. "Research on phase-locked loop technique based on three-dimensional coordinate transformation." Engineering Research Express 4, no. 1 (February 10, 2022): 015013. http://dx.doi.org/10.1088/2631-8695/ac4de5.

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Abstract The traditional phase-locked loop (PLL) technique widely used in three-phase four-wire system can only obtain one phase angle, and cannot obtain other parameters of unbalanced voltages, such as the amplitude and phase angle of each phase voltage. In order to improve the performance of PLL in unbalanced three-phase four-wire system with disturbance and reduce the order of PLL to improve the stability of the system, a PLL technique based on three-dimensional (3D) coordinate transformation was proposed in this paper. Firstly, the phase detector error of three-phase unbalanced voltage was deduced based on the 3D coordinate transformation. The error can be regarded as the expression form in Hilbert space after linearizing of it. Based on the correspondence between the orthonormal basis in Hilbert space and the unit vectors in Euclidean space, the error can be mapped to Euclidean space, and the detection control law for each voltage parameter can be designed respectively based on the principle of perpendicular decoupling. Then, the voltage parameter detection control law in Euclidean space is mapped back to Hilbert space, so the PLL technique scheme can be obtained which is beneficial to the implementation in the actual system. The control law of each unbalance indices, such as the amplitude and initial phase of each phase voltage, can be decoupled into a first-order or second-order system, so the system structure is simple, and the control parameter design is convenient. The detection of unbalance indices of the three-phase unbalanced voltages with zero-sequence component can be realized with fast and stable characteristics. The simulation and experiments of the proposed PLL technique are carried out finally under several transient conditions of grid voltages, stable within a quarter cycle at the fastest and always stable in 50 ms, so as to validate the rapidness and stability of the proposed PLL technique.

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Yim, Jong Hyuk, Su-yeon Kim, Yiseob Kim, Suyoung Cho, Jangsun Kim, and Yeong Hwan Ahn. "Rapid 3D-Imaging of Semiconductor Chips Using THz Time-of-Flight Technique." Applied Sciences 11, no. 11 (May 22, 2021): 4770. http://dx.doi.org/10.3390/app11114770.

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In this study, we developed a rapid three-dimensional (3D) time-of-flight imaging tool for inspection of packaged semiconductor chips, using terahertz (THz) time-domain spectroscopy techniques. A high-speed THz system based on the optical sampling by cavity tuning technique is incorporated with a 2-axis galvano scanner to deliver a scanning speed of more than 100 Hz/pixel with a signal-to-noise ratio larger than 20 dB. Through the use of the Hilbert transformation, we reconstruct the 3D structure of the packaged chip in a nondestructive manner. Additionally, the use of frequency-selective imaging allows us to manipulate image resolution; the higher resolution was obtained when monitored using the higher frequency component. Further, using phase information, we were able to detect and identify defects in the packaged chip, such as the delamination area and epoxy-rich regions.

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Journal articles on the topic 'Courbes de Hilbert 3D'

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