A NOTE ON SLq(2) COVARIANCE AND QUANTUM EUCLIDEAN PLANE

2007 ◽  
Vol 22 (14) ◽  
pp. 1031-1037 ◽  
Author(s):  
Z. BENTALHA ◽  
M. TAHIRI
Keyword(s):  
Euclidean Space ◽  
Quantum Group ◽  
Bilinear Form ◽  
Algebraic Structure ◽  
Euclidean Distance ◽  
Euclidean Plane ◽  
Three Dimensional ◽  
Central Element ◽  
The Other ◽  
Euclidean Metric

A quantum analogue of SL(2) covariance is given. The method consists of defining a bilinear form on SL q(2) co-module, then we ask the defined form to be invariant under SL q(2) co-actions. We showed that the required invariance leads to the standard algebraic structure of SL q(2) ideal. On the other hand, the geometry of the three-dimensional quantum Euclidean space has been evoked by computing the quantum Euclidean metric, the quantum Euclidean "distance" (the central element) and the relation of orthogonality of SO q(3) quantum group.

On Pedal Quadrics in Non-Euclidean Hyperspace

1925 ◽  
Vol 22 (5) ◽  
pp. 751-758
Author(s):  
J. P. Gabbatt
Keyword(s):  
Orthogonal Projection ◽  
Euclidean Plane ◽  
Dimensional Space ◽  
Three Dimensional ◽  
The Other ◽  
Elementary Geometry ◽  
Orthogonal Projections ◽  
Point Pair ◽  
Straight Line ◽  
Three Dimensional Space

1. The following are well-known theorems of elementary geometry: Given any euclidean plane triangle, A0 A1 A2, and any pair of points, X, Y, isogonally conjugate q. A0 A1 A2; then the orthogonal projections of X, Y on the sides of A0 A1 A2 lie on a circle, the pedal circle of the point-pair. If either of the points X,- Y describe a (straight) line, m, then the other describes a conic circumscribing A0 A1 A2, and the pedal circle remains orthogonal to a fixed circle, J; thus the pedal circles in question are members of an ∞2 linear system of circles of which the circle J and the line at infinity constitute the Jacobian. In particular, if the line m meet Aj Ak at Lt (i, j, k = 0, 1, 2), then the circles on Ai Li as diameter, which are the pedal circles of the point-pairs Ai, Li, are coaxial; the remaining circles of the coaxial system being the director circles of the conics, inscribed in the triangle A0 A1 A2, which touch the line m. If Mi denote the orthogonal projection on m of Ai, and Ni the orthogonal projection on Aj Ak of Mi, then the three lines Mi Ni meet at a point (Neuberg's theorem), viz. the centre of the circle J. Analogues for three-dimensional space of most of these theorems are also known ‖.

THE FISHER–RAO METRIC FOR LINES IN A CONVEX IMAGE

2007 ◽  
Vol 21 (06) ◽  
pp. 977-994 ◽  
Author(s):  
STEPHEN J. MAYBANK
Keyword(s):  
Euclidean Space ◽  
Parameter Space ◽  
Three Dimensional ◽  
Experimental Results ◽  
Dimensional Euclidean Space ◽  
Two Dimensional ◽  
Euclidean Metric ◽  
Sample Points

The Fisher–Rao metric on the parameter space for the set of lines in a two-dimensional convex image is approximated under the assumption that the errors in the measurements are small. The volume of the parameter space under the approximating metric is proportional to the area of the image under the Euclidean metric. In the case of a rectangular image, expressions for the approximating metric are obtained and an algorithm is given for sampling the parameter space. The sample points are used in an algorithm for detecting lines in a rectangular image. Experimental results are reported. In the case of a disc shaped image the parameter space for lines embeds isometrically, under the approximating metric, into three-dimensional Euclidean space.

Three-Dimensional Reconstruction of Two Forms of the Chaperonin GRO EL

1990 ◽  
Vol 48 (1) ◽  
pp. 258-259
Author(s):  
J.L. Carrascosa ◽  
G. Abella ◽  
S. Marco ◽  
M. Muyal ◽  
J.M. Carazo
Keyword(s):  
Three Dimensional ◽  
The Other ◽  
Two Dimensional ◽  
Series Method ◽  
Three Dimensional Reconstruction ◽  
Structural Components ◽  
E Coli ◽  
Dimensional Reconstruction ◽  
Morphogenetic Factors ◽  
Tilt Series

Chaperonins are a class of proteins characterized by their role as morphogenetic factors. They trantsiently interact with the structural components of certain biological aggregates (viruses, enzymes etc), promoting their correct folding, assembly and, eventually transport. The groEL factor from E. coli is a conspicuous member of the chaperonins, as it promotes the assembly and morphogenesis of bacterial oligomers and/viral structures.We have studied groEL-like factors from two different bacteria:E. coli and B.subtilis. These factors share common morphological features , showing two different views: one is 6-fold, while the other shows 7 morphological units. There is also a correlation between the presence of a dominant 6-fold view and the fact of both bacteria been grown at low temperature (32°C), while the 7-fold is the main view at higher temperatures (42°C). As the two-dimensional projections of groEL were difficult to interprete, we studied their three-dimensional reconstruction by the random conical tilt series method from negatively stained particles.

An Efficient Multiple Description Coding for Multi-View Video Based on the Correlation of Spatial Polyphase Transformed Subsequences

2019 ◽  
Vol 63 (5) ◽  
pp. 50401-1-50401-7 ◽  
Author(s):  
Jing Chen ◽  
Jie Liao ◽  
Huanqiang Zeng ◽  
Canhui Cai ◽  
Kai-Kuang Ma
Keyword(s):  
Video Transmission ◽  
Video Sequence ◽  
Three Dimensional ◽  
The Other ◽  
Multiple Description Coding ◽  
Multiple Description ◽  
Prediction Mode ◽  
Gradient Based ◽  
Directional Interpolation ◽  
Description Coding

Abstract For a robust three-dimensional video transmission through error prone channels, an efficient multiple description coding for multi-view video based on the correlation of spatial polyphase transformed subsequences (CSPT_MDC_MVC) is proposed in this article. The input multi-view video sequence is first separated into four subsequences by spatial polyphase transform and then grouped into two descriptions. With the correlation of macroblocks in corresponding subsequence positions, these subsequences should not be coded in completely the same way. In each description, one subsequence is directly coded by the Joint Multi-view Video Coding (JMVC) encoder and the other subsequence is classified into four sets. According to the classification, the indirectly coding subsequence selectively employed the prediction mode and the prediction vector of the counter directly coding subsequence, which reduces the bitrate consumption and the coding complexity of multiple description coding for multi-view video. On the decoder side, the gradient-based directional interpolation is employed to improve the side reconstructed quality. The effectiveness and robustness of the proposed algorithm is verified by experiments in the JMVC coding platform.

scholarly journals On the Kirchhoff-Love Hypothesis (Revised and Vindicated)

2021 ◽  
Author(s):  
Olivier Ozenda ◽  
Epifanio G. Virga
Keyword(s):  
Free Energy ◽  
Dimension Reduction ◽  
Three Dimensional ◽  
Energy Functional ◽  
The Other ◽  
Variational Model ◽  
Two Dimensional ◽  
Elastic Plates ◽  
Kinematic Constraint ◽  
Free Energy Functional

AbstractThe Kirchhoff-Love hypothesis expresses a kinematic constraint that is assumed to be valid for the deformations of a three-dimensional body when one of its dimensions is much smaller than the other two, as is the case for plates. This hypothesis has a long history checkered with the vicissitudes of life: even its paternity has been questioned, and recent rigorous dimension-reduction tools (based on standard $\varGamma $ Γ -convergence) have proven to be incompatible with it. We find that an appropriately revised version of the Kirchhoff-Love hypothesis is a valuable means to derive a two-dimensional variational model for elastic plates from a three-dimensional nonlinear free-energy functional. The bending energies thus obtained for a number of materials also show to contain measures of stretching of the plate’s mid surface (alongside the expected measures of bending). The incompatibility with standard $\varGamma $ Γ -convergence also appears to be removed in the cases where contact with that method and ours can be made.

scholarly journals Ground Reaction Forces of Dressage Horses Performing the Piaffe

Animals ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 436 ◽  
Author(s):  
Hilary Mary Clayton ◽  
Sarah Jane Hobbs
Keyword(s):  
Coefficient Of Variation ◽  
Three Dimensional ◽  
Individual Variability ◽  
The Other ◽  
Ground Reaction Forces ◽  
High Coefficient ◽  
Reaction Forces

The piaffe is an artificial, diagonally coordinated movement performed in the highest levels of dressage competition. The ground reaction forces (GRFs) of horses performing the piaffe do not appear to have been reported. Therefore, the objective of this study was to describe three-dimensional GRFs in ridden dressage horses performing the piaffe. In-ground force plates were used to capture fore and hindlimb GRF data from seven well-trained dressage horses. Peak vertical GRF was significantly higher in forelimbs than in the hindlimbs (7.39 ± 0.99 N/kg vs. 6.41 ± 0.64 N/kg; p < 0.001) with vertical impulse showing a trend toward higher forelimb values. Peak longitudinal forces were small with no difference in the magnitude of braking or propulsive forces between fore and hindlimbs. Peak transverse forces were similar in magnitude to longitudinal forces and were mostly directed medially in the hindlimbs. Both the intra- and inter-individual variability of longitudinal and transverse GRFs were high (coefficient of variation 25–68%). Compared with the other diagonal gaits of dressage horses, the vertical GRF somewhat shifted toward the hindlimbs. The high step-to-step variability of the horizontal GRF components is thought to reflect the challenge of balancing on one diagonal pair of limbs with no forward momentum.

scholarly journals Heritage Artefacts in the COVID-19 Era: The Aura and Authenticity of 3D Models

2021 ◽  
Vol 7 (1) ◽  
pp. 519-539
Author(s):  
Thiago Minete Cardozo ◽  
Costas Papadopoulos
Keyword(s):  
User Experience ◽  
Three Dimensional ◽  
3D Models ◽  
Essential Elements ◽  
The Other ◽  
Social Distancing ◽  
The Public ◽  
Affective Experiences ◽  
The One ◽  
Digital Engagement

Abstract Museums have been increasingly investing in their digital presence. This became more pressing during the COVID-19 pandemic since heritage institutions had, on the one hand, to temporarily close their doors to visitors while, on the other, find ways to communicate their collections to the public. Virtual tours, revamped websites, and 3D models of cultural artefacts were only a few of the means that museums devised to create alternative ways of digital engagement and counteract the physical and social distancing measures. Although 3D models and collections provide novel ways to interact, visualise, and comprehend the materiality and sensoriality of physical objects, their mediation in digital forms misses essential elements that contribute to (virtual) visitor/user experience. This article explores three-dimensional digitisations of museum artefacts, particularly problematising their aura and authenticity in comparison to their physical counterparts. Building on several studies that have problematised these two concepts, this article establishes an exploratory framework aimed at evaluating the experience of aura and authenticity in 3D digitisations. This exploration allowed us to conclude that even though some aspects of aura and authenticity are intrinsically related to the physicality and materiality of the original, 3D models can still manifest aura and authenticity, as long as a series of parameters, including multimodal contextualisation, interactivity, and affective experiences are facilitated.

scholarly journals MorphOT: transport-based interpolation between EM maps with UCSF ChimeraX

2020 ◽  
Author(s):  
Arthur Ecoffet ◽  
Frédéric Poitevin ◽  
Khanh Dao Duc
Keyword(s):  
Optimal Transport ◽  
Three Dimensional ◽  
Linear Interpolation ◽  
The Other ◽  
Supplementary Information ◽  
Conformational Heterogeneity ◽  
Supplementary Data ◽  
Image Dataset ◽  
Standard Linear ◽  
Unique Potential

Abstract Motivation Cryogenic electron microscopy (cryo-EM) offers the unique potential to capture conformational heterogeneity, by solving multiple three-dimensional classes that co-exist within a single cryo-EM image dataset. To investigate the extent and implications of such heterogeneity, we propose to use an optimal-transport-based metric to interpolate barycenters between EM maps and produce morphing trajectories. Results While standard linear interpolation mostly fails to produce realistic transitions, our method yields continuous trajectories that displace densities to morph one map into the other, instead of blending them. Availability and implementation Our method is implemented as a plug-in for ChimeraX called MorphOT, which allows the use of both CPU or GPU resources. The code is publicly available on GitHub (https://github.com/kdd-ubc/MorphOT.git), with documentation containing tutorial and datasets. Supplementary information Supplementary data are available at Bioinformatics online.

Sight distance red zones on combined horizontal and sag vertical curves

1998 ◽  
Vol 25 (4) ◽  
pp. 621-630 ◽  
Author(s):  
Yasser Hassan ◽  
Said M Easa
Keyword(s):  
Quantitative Analysis ◽  
Three Dimensional ◽  
The Other ◽  
Two Dimensional ◽  
Horizontal Curve ◽  
Sight Distance ◽  
Stopping Sight Distance ◽  
Three Dimensional Models ◽  
Highway Alignment ◽  
Current Standards

Coordination of highway horizontal and vertical alignments is based on subjective guidelines in current standards. This paper presents a quantitative analysis of coordinating horizontal and sag vertical curves that are designed using two-dimensional standards. The locations where a horizontal curve should not be positioned relative to a sag vertical curve (called red zones) are identified. In the red zone, the available sight distance (computed using three-dimensional models) is less than the required sight distance. Two types of red zones, based on stopping sight distance (SSD) and preview sight distance (PVSD), are examined. The SSD red zone corresponds to the locations where an overlap between a horizontal curve and a sag vertical curve should be avoided because the three-dimensional sight distance will be less than the required SSD. The PVSD red zone corresponds to the locations where a horizontal curve should not start because drivers will not be able to perceive it and safely react to it. The SSD red zones exist for practical highway alignment parameters, and therefore designers should check the alignments for potential SSD red zones. The range of SSD red zones was found to depend on the different alignment parameters, especially the superelevation rate. On the other hand, the results showed that the PVSD red zones exist only for large values of the required PVSD, and therefore this type of red zones is not critical. This paper should be of particular interest to the highway designers and professionals concerned with highway safety.Key words: sight distance, red zone, combined alignment.

A new three-dimensional anionic cadmium(II) dicyanamide network

2014 ◽  
Vol 70 (11) ◽  
pp. 1054-1056 ◽  
Author(s):  
Qiang Li ◽  
Hui-Ting Wang
Keyword(s):  
Crystal Structure ◽  
Aqueous Solution ◽  
Unit Cell Volume ◽  
Three Dimensional ◽  
Building Blocks ◽  
The Other ◽  
Dimensional Structure ◽  
Cadmium Nitrate ◽  
Nitrate Tetrahydrate ◽  
Anionic Framework

A new cadmium dicyanamide complex, poly[tetramethylphosphonium [μ-chlorido-di-μ-dicyanamido-κ4N1:N5-cadmium(II)]], [(CH3)4P][Cd(NCNCN)2Cl], was synthesized by the reaction of tetramethylphosphonium chloride, cadmium nitrate tetrahydrate and sodium dicyanamide in aqueous solution. In the crystal structure, each CdIIatom is octahedrally coordinated by four terminal N atoms from four anionic dicyanamide (dca) ligands and by two chloride ligands. The dicyanamide ligands play two different roles in the building up of the structure; one role results in the formation of [Cd(dca)Cl]2building blocks, while the other links the building blocks into a three-dimensional structure. The anionic framework exhibits a solvent-accessible void of 673.8 Å3, amounting to 47.44% of the total unit-cell volume. The cavities in the network are occupied by pairs of tetramethylphosphonium cations.

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