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Journal articles on the topic 'Structure Geometry'

Author: Grafiati

Published: 5 June 2025

Last updated: 1 August 2025

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1

Song, Xiao Zhuang, Ming Liang Lu, and Tao Qin. "Projective Geometry on the Structure of Geometric Composition Analysis Application." Applied Mechanics and Materials 166-169 (May 2012): 127–30. http://dx.doi.org/10.4028/www.scientific.net/amm.166-169.127.

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The analysis rule of geometry composition analysis in building structure must rely on geometry theory, while the traditional Euclidean geometry theory can not solve some building structures problems of the geometry components. This problem can be solved in the use of projective geometry theory. In this paper we introduce the proof of projective geometry in the geometry composition analysis and we discuss the application of this theory.

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Kumar, Nanda Kishor. "Symmetry in the context of the Almost Contact 3-Structure and Almost Quaternion Structure." Pragnya Sarathi प्रज्ञा-सारथि 23, no. 1 (2025): 141–46. https://doi.org/10.3126/ps.v23i1.77528.

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The aim of this paper is to explores the characteristics, relationships, and applications of nearly contact 3-structure and nearly quaternion structure in current mathematical study, as well as their foundations. The Interplay between almost contact 3-structure and almost quaternion structure and significance and future direction have also been described. The study of symmetry in Almost Contact 3-Structures and Almost Quaternion Structures provides deep insights into differential geometry and mathematical physics. These structures serve as a bridge between classical Riemannian geometry and mod

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Sun, Haoxuan, and Taoyang Wang. "A Stereo Disparity Map Refinement Method Without Training Based on Monocular Segmentation and Surface Normal." Remote Sensing 17, no. 9 (2025): 1587. https://doi.org/10.3390/rs17091587.

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Stereo disparity estimation is an essential component in computer vision and photogrammetry with many applications. However, there is a lack of real-world large datasets and large-scale models in the domain. Inspired by recent advances in the foundation model for image segmentation, we explore the RANSAC disparity refinement based on zero-shot monocular surface normal prediction and SAM segmentation masks, which combine stereo matching models and advanced monocular large-scale vision models. The disparity refinement problem is formulated as follows: extracting geometric structures based on SAM

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4

WANAS, M. I., and SAMAH A. AMMAR. "SPACETIME STRUCTURE AND ELECTROMAGNETISM." Modern Physics Letters A 25, no. 20 (2010): 1705–21. http://dx.doi.org/10.1142/s0217732310032883.

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Two Lagrangian functions are used to construct geometric field theories. One of these Lagrangians depends on the curvature of space, while the other depends on curvature and torsion. It is shown that the theory constructed from the first Lagrangian gives rise to pure gravity, while the theory constructed using the second Lagrangian gives rise to both gravity and electromagnetism. The two theories are constructed in a version of absolute parallelism geometry in which both curvature and torsion are, simultaneously, nonvanishing. One single geometric object, W-tensor, reflecting the properties of

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YOUSSEF, NABIL L., AMR M. SID-AHMED, and EBTSAM H. TAHA. "ON FINSLERIZED ABSOLUTE PARALLELISM SPACES." International Journal of Geometric Methods in Modern Physics 10, no. 07 (2013): 1350029. http://dx.doi.org/10.1142/s0219887813500291.

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The aim of this paper is to construct and investigate a Finsler structure within the framework of a Generalized Absolute Parallelism (GAP)-space. The Finsler structure is obtained from the vector fields forming the parallelization of the GAP-space. The resulting space, which we refer to as a Finslerized absolute parallelism (parallelizable) space, combines within its geometric structure the simplicity of GAP-geometry and the richness of Finsler geometry, hence is potentially more suitable for applications and especially for describing physical phenomena. A study of the geometry of the two stru

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Beldean, Calin, Ioan Vuşcan, Kalman Kacso, and Nicolae Panc. "The Geometry Equations for Multiple Kinematic Structures Using Direct Geometry." Applied Mechanics and Materials 808 (November 2015): 292–97. http://dx.doi.org/10.4028/www.scientific.net/amm.808.292.

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In this paper are presented two kinematic structures able to move/rotate along/around tree axis each simultaneous. These two structures are restricted on a common fix bed and have the possibility perform a translational motion first and then to rotate along or around each axis. The equation used to describe the position and orientation of the first structure in relation to the second are then presented. Furthermore a reduction of the general case is made to prove the general mathematical model on a structure similar to a five axis turning and milling machine.

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Petrović, Milica, Isidora Ilić, Svetislav Mijatović, and Nenad Šekularac. "The Geometry of Timber Lamella Vaults: Prototype Analysis." Buildings 12, no. 10 (2022): 1653. http://dx.doi.org/10.3390/buildings12101653.

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This paper presents timber lamella structures applied to the circular cylinder surface when all lamellae axes intersect at the nodes. To achieve the uniformity of all elements in this structure, the geometry of the structure must be carefully designed. The main methods for the research are graphical and numerical methods for geometric design and a prototype construction for a specific geometric pattern. The methods are discussed for their ease of replication, as well as the possibility of reinterpretation on other surfaces, while the prototype design and construction give insight into the proc

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8

MARTIN, MIRCEA. "ALGEBRA ENVIRONMENTS I." Revue Roumaine Mathematiques Pures Appliquees LXIX, no. 1 (2024): 17–60. http://dx.doi.org/10.59277/rrmpa.2024.17.60.

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Algebra environments capture properties of non–commutative conditional expectations in a general algebraic setting. Their study relies on algebraic geometry, topology, and differential geometry techniques. The structure algebraic and Banach manifolds of algebra environments and their Zariski and smooth tangent vector bundles are particular objects of interest. A description of derivations on algebra environments compatible with geometric structures is an additional issue. Grassmann and flag manifolds of unital involutive algebras and spaces of projective compact group representations in C∗–alg

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Кириллов, Александр Николаевич, Андрей Анатольевич Крижановский, Alexander Kirillov, and Andrew Krizhanovsky. "Synset geometry structure model." Proceedings of the Karelian Research Centre of the Russian Academy of Sciences, no. 08 (September 1, 2016): 45. http://dx.doi.org/10.17076/mat394.

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10

Dong, Yan, and Mei Li. "The Geometrical Feature Recognition Method of Part Drawing." Advanced Materials Research 415-417 (December 2011): 523–26. http://dx.doi.org/10.4028/www.scientific.net/amr.415-417.523.

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This paper put forward a geometry feature recognition method of part drawing based on graph matching. Describe the constraints structure of geometric feature in geometric elements and those constraint relationships. Match sub-graph in contour closure graphics and those combination. Using linear symbol notation of chemical compounds in chemical database for reference, encode to constraint structure of geometry graphics, establish recognition mechanism of geometric characteristics by structure codes. Taking the fine-tune screw and fork parts for example, this method has been proved to be effecti

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11

N. Jagadesh Babu, B.Rajesh kumar. "Enhancing Performance through Geometry and Structure Optimization in Thermoelectric Systems." Communications on Applied Nonlinear Analysis 32, no. 9s (2025): 2575–88. https://doi.org/10.52783/cana.v32.4561.

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This study aims to create and simulate a highly advantageous device is the thermoelectric generator for the waste heat recovery by optimizing its geometric configuration for high efficiency. Each thermoelectric module operates based on the Seebeck effect. Electrons move from the hot junction to the cold junction through thermoelectric materials due to variations in electron density. This movement generates an electric field, linked to the temperature difference via the Seebeck effect caused by hole and electron motion. The potential difference V is proportional to the α temperature difference

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12

Volenec, Vladimir, and Ružica Kolar-Šuper. "On the Noteworthy Properties of Tangentials in Cubic Structures." Axioms 13, no. 2 (2024): 122. http://dx.doi.org/10.3390/axioms13020122.

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The cubic structure, a captivating geometric structure, finds applications across various areas of geometry through different models. In this paper, we explore the significant characteristics of tangentials in cubic structures of ranks 0, 1, and 2. Specifically, in the cubic structure of rank 2, we derive the Hessian configuration (123,164) of points and lines. Finally, we introduce and investigate the de Vries configuration of points and lines in a cubic structure.

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Sun, B. W., L. T. Jiang, H. Pan, and H. Zhu. "Realization on Fractal Interpolation of Non-Rule Geometry." Key Engineering Materials 392-394 (October 2008): 523–25. http://dx.doi.org/10.4028/www.scientific.net/kem.392-394.523.

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The traditional geometric modeling is generally described by means of Euclidean geometry, and objects for the geometric modeling are usually artificial work-pieces with smooth and regular contour. However in real world, there are so many irregular geometric objects(such as cavernous body, geological body, rough surface body and so on) with extremely complicated structure that the constructing method based on Euclidean geometry equation has been already helpless, while the process constructing method based on fractal geometry can. Taking rough surface body as examples, in order to explore a met

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Macioszczyk, Jan, Karol Malecha, Andrzej Stafiniak, and Leszek J. Golonka. "Impact of processing parameters on the LTCC channels geometry." Materials Science-Poland 33, no. 4 (2015): 816–25. http://dx.doi.org/10.1515/msp-2015-0104.

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AbstractA great advantage of Low Temperature Co-fired Ceramics (LTCC) yields the possibility of channel and air cavity fabrication. Such empty spaces have numerous applications, for example, in microfluidics, microwave techniques and integrated packaging. However, improper geometry of these structures can degrade the performance of the final device. The processing parameters recommended by the LTCC tape supplier are relevant for the production of multilayer circuits but not surface embedded channels and/or cavities. Thus, it is important to examine which factors of the fabrication process are

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15

Jovic, Biljana, Milos Tripkovic, and Aleksandar Cucakovic. "Geometric correlation of cultural landscape patterns and Prunus domestica L. species leaf." Bulletin of the Faculty of Forestry, no. 104 (2011): 29–40. http://dx.doi.org/10.2298/gsf1104029j.

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This paper provides the basics for more detailed research on the structures of bionic forms of different plant species and their application in the domain of landscape planning. The aim of this type of research is to expand knowledge of landscape planning with a deeper understanding of different geometric relations present in the existing natural forms. The correlation between structures in nature and structures that are present in contemporary landscape architecture could be established by the congruence with the geometric models from landscape. This paper is focused solely on the geometry of

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16

Gorelov, Yu V., and T. N. Tkacheva. "Approaches to determining the geometry coefficient of network organizational structures." Herald of the Ural State University of Railway Transport, no. 3 (2022): 61–66. http://dx.doi.org/10.20291/2079-0392-2022-3-61-66.

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The article analyzes the methods of determining the geometry coefficient in network organizational structures and offers its own ways of calculating it. The geometry coefficient is presented as an integral indicator which consolidates the coefficients of filling orbits, connectivity and criticality of connections. The orbit filling coefficient characterizes the organizational network through the reserve production capacities realized by the enterprises of the organizational network in the free market. The connectivity coefficient characterizes excess mileage, transport load, fuel consumption a

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17

Leparov, M. "About Geometry, One More Time." Geometry & Graphics 10, no. 1 (2022): 3–13. http://dx.doi.org/10.12737/2308-4898-2022-10-1-3-13.

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This paper has been devoted to an analysis of geometry from an engineering point of view. Has been based 23 statements about geometry contribution to physics, mathematics, engineering, as well as to other sciences. Geometry propagation in all types of objects and processes (such as material, energetic and information/signal ones), as well as in everything and everywhere (all-encompassing geometry) has been shown. Special attention is paid to geometry importance, emphasizing its crucial role at each stage of any technical object design (which predetermines geometry as the basis of design), as w

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18

Matamba, T. Tshikuna. "Almost Paracontact 3-Submersions." JOURNAL OF ADVANCES IN MATHEMATICS 17 (December 10, 2019): 390–400. http://dx.doi.org/10.24297/jam.v17i0.8507.

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In this paper, we discuss some geometric properties of Riemannian submersions whose total space is an almost paracontact manifold with 3-structure. The study is focused on the transference of structures, the geometry of the fibres and sectional curvature tensor.

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19

Giunashvili, Z. "Geometry of Poisson Structures." gmj 2, no. 4 (1995): 347–59. http://dx.doi.org/10.1515/gmj.1995.347.

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Abstract The purpose of this paper is to consider certain mechanisms of the emergence of Poisson structures on a manifold. We shall also establish some properties of the bivector field that defines a Poisson structure and investigate geometrical structures on the manifold induced by such fields. Further, we shall touch upon the dualism between bivector fields and differential 2-forms.

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20

Xin, Yijing. "Constructivism of Ballet Movement Used in Fashion Design." Arts Studies and Criticism 5, no. 4 (2024): 201. http://dx.doi.org/10.32629/asc.v5i4.2675.

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In this century, both ballerinas and fashion designers have developed ideals and ideas with form, geometry space and creativity. Fashion designers prefer to combine dance aesthetics with details.This paper take the geometric structure design of constructivism as the core, apply these special structures to the fashion design. The unique structures and fabric modification technique are used in clothing, and express different and special visual effects in several ways. By exploring the relationship between people, free, space and geometry in ballet, and extending the design concept of constructiv

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21

Burger, William F. "Geometry." Arithmetic Teacher 32, no. 6 (1985): 52–56. http://dx.doi.org/10.5951/at.32.6.0052.

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The elementary school mathemalics curriculum contains no substitute for the study of informal concepts in geometry. in geometry, children organize and structure their spatial experiences. Also, geometry provides a vehicle for developing mathematical reasoning abilities about visual concepts, for example, through the study of planar shapes. In this article, I shall focus on how reasoning can be developed through the study of two-dimensional shapes, their properties, and the relationships among them. Additional topics, such as tessellations with shapes, motions and symmetry, congruence, similari

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22

Vitrac, Bernard, and Guillaume Dye. "Le Contre les géomètres de Sextus Empiricus: sources, cible, structure." Phronesis 54, no. 2 (2009): 155–203. http://dx.doi.org/10.1163/156852809x403621.

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AbstractIn this paper, we examine Sextus Empiricus' treatise Against the geometers. We first set this treatise in the overall context of the sceptic's polemics against the liberal arts. After a discussion of Sextus' attitude to the quadrivium, we discuss the structure, the sources and the target of the Against the geometers. It appears that Euclid is not Sextus' source, and neither he, nor the professional geometers, seem to be Sextus' main targets. Of course, Sextus never really makes clear his precise target, but his attacks are rather directed against geometry as a means of modelling the ph

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Muñoz Velázquez, Vicente. "The Hodge conjecture: The complications of understanding the shape of geometric spaces." Mètode Revista de difusió de la investigació, no. 8 (June 5, 2018): 51. http://dx.doi.org/10.7203/metode.0.8253.

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The Hodge conjecture is one of the seven millennium problems, and is framed within differential geometry and algebraic geometry. It was proposed by William Hodge in 1950 and is currently a stimulus for the development of several theories based on geometry, analysis, and mathematical physics. It proposes a natural condition for the existence of complex submanifolds within a complex manifold. Manifolds are the spaces in which geometric objects can be considered. In complex manifolds, the structure of the space is based on complex numbers, instead of the most intuitive structure of geometry, base

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24

Weber, Melanie. "Exploiting Data Geometry in Machine Learning." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 20 (2024): 22681. http://dx.doi.org/10.1609/aaai.v38i20.30297.

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A key challenge in Machine Learning (ML) is the identification of geometric structure in high-dimensional data. Most algorithms assume that data lives in a high-dimensional vector space; however, many applications involve non-Euclidean data, such as graphs, strings and matrices, or data whose structure is determined by symmetries in the underlying system. Here, we discuss methods for identifying geometric structure in data and how leveraging data geometry can give rise to efficient ML algorithms with provable guarantees.

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Rojas, Osvaldo, Mauro GarcÃa, and Javier GonzÃ¡lez. "On the Intuitive Geometry." INTERNATIONAL JOURNAL OF RESEARCH IN EDUCATION METHODOLOGY 7, no. 3 (2016): 1208–12. http://dx.doi.org/10.24297/ijrem.v7i3.3835.

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In this paper the origin of the concepts of geometry and the way and the reason for systematization is analyzed. A first approach to the analysis of the processes involved in the development of geometry determines its target and leads us to clarify what is meant by a mathematical object and, further, what is meant by geometric object, and leads into the structure essential geometry.

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Shen, Han Xin, Wen Zhang Zhu, and Ai Yu Li. "Structure of Chromium Atomic Chains." Advanced Materials Research 415-417 (December 2011): 553–56. http://dx.doi.org/10.4028/www.scientific.net/amr.415-417.553.

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The geometric and electronic structures of Cr chains are studied by the first-principles of density-functional method. The present calculation results show that chromium can form planar chains in linear, zigzag, dimer, and ladder form one-dimensional structures. The most stable geometry chain among the studied structures is the ladder-form chain with five nearest neighbors. The dimer structure is found to be more stable than the zigzag one. Further more, the relative structural stability, the electronic energy bands, the density of states is discussed based on the ab initio calculations.

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27

Park, Sungsoo, and Hyeoncheol Kim. "FaceVAE: Generation of a 3D Geometric Object Using Variational Autoencoders." Electronics 10, no. 22 (2021): 2792. http://dx.doi.org/10.3390/electronics10222792.

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Deep learning for 3D data has become a popular research theme in many fields. However, most of the research on 3D data is based on voxels, 2D images, and point clouds. At actual industrial sites, face-based geometry data are being used, but their direct application to industrial sites remains limited due to a lack of existing research. In this study, to overcome these limitations, we present a face-based variational autoencoder (FVAE) model that generates 3D geometry data using a variational autoencoder (VAE) model directly from face-based geometric data. Our model improves the existing node a

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28

Chen, Kuan Yu, Yi Ting Kong, and Shyi Long Lee. "Theoretical Studies of Au₃^+/0/- Clusters Using Density Funtional Theory." Key Engineering Materials 862 (September 2020): 94–98. http://dx.doi.org/10.4028/www.scientific.net/kem.862.94.

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In this study, the PW91PW91 method with LANL2DZ level was carried out to settle the dispute about the most stable structure of Au3+/0/-. Molecular orbital analyses and Walsh diagram were adopted to rationalize our computational result about the ground state geometry of Au3+/0/-. Our results show that the most stable geometry of Au3 is bent structure (C2v) with bond angle 146.0°. The less stable structure is equilateral triangle structure (D3h) with relative energies of 1.74 eV. The D3h structure possesses multiplicity 4 while the C2v structure 2. In addition, the most stable geometry of Au3+ a

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Weibel, E. R. "Fractal geometry: a design principle for living organisms." American Journal of Physiology-Lung Cellular and Molecular Physiology 261, no. 6 (1991): L361—L369. http://dx.doi.org/10.1152/ajplung.1991.261.6.l361.

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Fractal geometry allows structures to be quantitatively characterized in geometric terms even if their form is not even or regular, because fractal geometry deals with the geometry of hierarchies and random processes. The hypothesis is explored that fractal geometry serves as a design principle in biological organisms. The internal membrane surface of cells, or the inner lung surface, are difficult to describe in terms of classical geometry, but they are found to show properties describable by fractal geometry, at least sectionwise and within certain bounds set by deterministic design properti

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Elbasraoui, Abdelkrim, and Abdellah Sebbar. "Equivariant Forms: Structure and Geometry." Canadian Mathematical Bulletin 56, no. 3 (2013): 520–33. http://dx.doi.org/10.4153/cmb-2011-195-2.

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Abstract.In this paper we study the notion of equivariant forms introduced in the authors' previous works. In particular, we completely classify all the equivariant forms for a subgroup of SL2(ℤ) by means of the cross-ratio, weight 2 modular forms, quasimodular forms, as well as differential forms of a Riemann surface and sections of a canonical line bundle.

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Krumhansl, Carol L. "The geometry of musical structure." Computers in Entertainment 3, no. 4 (2005): 1–14. http://dx.doi.org/10.1145/1095534.1095542.

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Alfinito, E., R. Manka, and G. Vitiello. "Vacuum structure for expanding geometry." Classical and Quantum Gravity 17, no. 1 (1999): 93–111. http://dx.doi.org/10.1088/0264-9381/17/1/307.

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Preisinger, Clemens. "Linking Structure and Parametric Geometry." Architectural Design 83, no. 2 (2013): 110–13. http://dx.doi.org/10.1002/ad.1564.

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Kökçam, Zeynep Gülcan, Murat Şahin, and Ayça Gülten. "Benchmarking Tree-Inspired-Fractal Branching Dendriform Structures From BC to L-System Based Contemporary Structures." Turkish Journal of Science and Technology 20, no. 1 (2024): 193–207. https://doi.org/10.55525/tjst.1555517.

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Nature has its own complex geometry, which couldn’t be explained using traditional methods until the advent of Fractal Geometry. Nowadays, we can observe and represent almost every geometry using quantitative tools. In this study, the compatibility of geometric compositions, referencing Euclidean geometry from hand-drawing environments to digital drawing and computational Computer-aided design (CAD) tools in the architectural products of complex parametric designs, was observed. Historical structures such as Maison Carrée, The Sakyamuni Pagoda of Fogong Temple, Saint Chapelle, Gloucester Cathe

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Mohammadi, Hanieh, and Nima Valibeig. "THE ANALYSIS OF ELEMENTS GEOMETRY POSITION IN THE IRANIAN GARDEN STRUCTURE." JOURNAL OF ARCHITECTURE AND URBANISM 42, no. 2 (2018): 112–19. http://dx.doi.org/10.3846/jau.2018.6138.

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Iranian garden has been known as a specific architecture in the whole world. Among all its special features, the geometrical structure of Iranian garden has always attracted the attention of architects and researchers. Nowadays, despite numerous studies on the Iranian gardens, the lack of geometrical studies and the extension of some old concepts have led to recognize the Iranian gardens based on a unique pattern in terms of geometry. This pattern has been known as an archetype and typifies the Iranian Garden Geometry as a quarter pattern. That it could not be a true hypothesis, because the im

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Sal'kov, N. "A Systematic Approach to the Study of Descriptive Geometry." Geometry & Graphics 10, no. 1 (2022): 14–23. http://dx.doi.org/10.12737/2308-4898-2022-10-1-14-23.

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The issues of inconsistency of some terms used in descriptive geometry with the rules of GOST R 2.105-2019 ESCD "General Requirements for Text Documents", as well as related to the projection of surfaces, are considered. The structure of descriptive geometry’s textbooks is considered, according to which all textbooks of this discipline have been built up until recently. This structure forms a sequence in the study of descriptive geometry in almost all higher education institutes. Criticism of this structure, which has been using for teaching since time immemorial without significant changes wh

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Liu, Su. "Analysis of the Car Model and Ackermann’s Steering Geometry." Highlights in Science, Engineering and Technology 37 (March 18, 2023): 1–13. http://dx.doi.org/10.54097/hset.v37i.6033.

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In order to solve the problem of the inside and outside wheels that trace out circles of different radii in a turn, Ackermann's steering geometry was developed. It is a geometric design of the connecting linkage arrangement in the steering of a vehicle to address the steering problems. However, because other factors also influence the design of steering structures, the majority of cars do not have a steering structure that is 100% Ackermann geometry or 100% Anti-Ackermann geometry. The dominant explanation for it has primarily relied on complicated calculations considering the whole structure

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Saddek, Ahmed Abdalfatah, Tzu-Kang Lin, Wen-Kuei Chang, Chia-Han Chen, and Kuo-Chun Chang. "Metamaterials of Auxetic Geometry for Seismic Energy Absorption." Materials 16, no. 15 (2023): 5499. http://dx.doi.org/10.3390/ma16155499.

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The propagation of earthquake energy occurs primarily through elastic waves. If the seismic force input to a structure can be directly reduced from the source, then the structure can be protected from seismic wave energy. Seismic metamaterials, regarded as periodic structures with properties different from conventional materials, use wave propagation characteristics and bandgaps to dissipate seismic wave energy. When the seismic wave is located in the bandgap, the transmission of seismic wave energy is effectively reduced, which protects the structure from the damage caused by seismic disturba

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FERNÁNDEZ, V. V., A. M. MOYA, and W. A. RODRIGUES. "GEOMETRIC AND EXTENSOR ALGEBRAS AND THE DIFFERENTIAL GEOMETRY OF ARBITRARY MANIFOLDS." International Journal of Geometric Methods in Modern Physics 04, no. 07 (2007): 1117–58. http://dx.doi.org/10.1142/s0219887807002478.

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We give in this paper which is the third in a series of four a theory of covariant derivatives of representatives of multivector and extensor fields on an arbitrary open set U ⊂ M, based on the geometric and extensor calculus on an arbitrary smooth manifold M. This is done by introducing the notion of a connection extensor field γ defining a parallelism structure on U ⊂ M, which represents in a well-defined way the action on U of the restriction there of some given connection ∇ defined on M. Also we give a novel and intrinsic presentation (i.e. one that does not depend on a chosen orthonormal

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Cantrijn, F., A. Ibort, and M. De León. "On the geometry of multisymplectic manifolds." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 66, no. 3 (1999): 303–30. http://dx.doi.org/10.1017/s1446788700036636.

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AbstractA multisymplectic structure on a manifold is defined by a closed differential form with zero characteristic distribution. Starting from the linear case, some of the basic properties of multisymplectic structures are described. Various examples of multisymplectic manifolds are considered, and special attention is paid to the canonical multisymplectic structure living on a bundle of exterior k-forms on a manifold. For a class of multisymplectic manifolds admitting a ‘Lagrangian’ fibration, a general structure theorem is given which, in particular, leads to a classification of these manif

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Shen, Han Xin, Wen Zhang Zhu, and Ai Yu Li. "Spatial Configurations of Molybdenum Atomic Chains." Advanced Materials Research 366 (October 2011): 447–50. http://dx.doi.org/10.4028/www.scientific.net/amr.366.447.

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The geometric and electronic structures of Molybdenum chains are studied by the first-principles of density-functional method. The present calculations reveal that Molybdenum can form planner chains in zigzag, dimer, and ladder structures. The most stable geometry is the Dimer structure chain. The ladder structure is found to be more stable than the zigzag one. Furthermore, the relative structural stability, the electronic energy bands, the density of states are discussed based on the ab initio calculations.

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42

Bracken, Paul. "Geometric aspects of quantization and relationship to integrability." Physica Scripta 98, no. 12 (2023): 125202. http://dx.doi.org/10.1088/1402-4896/ad052a.

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Abstract It is the case that quantum mechanics has a deep geometric structure and can be presented accordingly. Quantum mechanics is to a certain degree foreshadowed by the geometry inherent in the geometric structure of classical mechanics. The purpose here is to present some new results and proofs which impact the mathematical structure of quantum mechanics. The relationship between integrability and quantum physics is investigated in terms of geometric ideas and structures. Two physical examples are drawn from these mathematical ideas which directly relate to physics. An introduction as to

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Biswas, Indranil, та Sorin Dumitrescu. "Fujiki class 𝒞 and holomorphic geometric structures". International Journal of Mathematics 31, № 05 (2020): 2050039. http://dx.doi.org/10.1142/s0129167x20500391.

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For compact complex manifolds with vanishing first Chern class that are compact torus principal bundles over Kähler manifolds, we prove that all holomorphic geometric structures on them, of affine type, are locally homogeneous. For a compact simply connected complex manifold in Fujiki class [Formula: see text], whose dimension is strictly larger than the algebraic dimension, we prove that it does not admit any holomorphic rigid geometric structure, and also it does not admit any holomorphic Cartan geometry of algebraic type. We prove that compact complex simply connected manifolds in Fujiki cl

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Eberhart, Mark. "From topology to geometry." Canadian Journal of Chemistry 74, no. 6 (1996): 1229–35. http://dx.doi.org/10.1139/v96-138.

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A systematic study of the charge density topologies corresponding to a number of transition metal aluminides with the B2 structure indicates that unstable crystal structures are sometimes associated with uncharacteristic topologies. This observation invites the speculation that the "distance" to a topological instability might relate to a metals phase behavior. Following this speculation, a metric is imposed on the topological theory of Bader, producing a geometrical theory, where it is now possible to assign a distance from a calculated charge density topology to a topological instability. Fo

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PITEA, ARIANA. "A GEOMETRIC STUDY OF SOME EQUATIONS OF MATHEMATICAL PHYSICS." International Journal of Geometric Methods in Modern Physics 09, no. 04 (2012): 1250030. http://dx.doi.org/10.1142/s0219887812500302.

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We introduce geometric structures (connections, pseudo-Riemannian metrics) adapted to some fundamental problems of Differential Geometry, and find geometrical characteristics associated to equations of Mathematical Physics. Also, we introduce a geometric study of some boundary problems. Throughout this work, as main tool we employed an adequate Riemannian Hessian structure, suggested in [Int. J. Geom. Meth. Mod. Phys.7(7) (2010) 1104–1113].

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Hu, Kejian, and Xiaoguang Wu. "A Bridge Structure 3D Representation for Deep Neural Network and Its Application in Frequency Estimation." Advances in Civil Engineering 2022 (March 22, 2022): 1–13. http://dx.doi.org/10.1155/2022/1999013.

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Currently, most predictions related to bridge geometry use shallow neural networks, which limit the network’s ability to fit since the input form limits the depth of the neural network. Therefore, this study proposed a new 3D representation of bridge structures. Based on the geometric parameters of the bridge structure, three 4D tensors were formed. This form of representation not only retained all geometric information but also expressed the spatial relationship of the structure. Then, this study constructed the corresponding 3D convolutional neural network and used it to estimate the frequen

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Cushman, Richard, and Jędrzej Śniatycki. "Intrinsic Geometric Structure of Subcartesian Spaces." Axioms 13, no. 1 (2023): 9. http://dx.doi.org/10.3390/axioms13010009.

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Every subset S of a Cartesian space Rd, endowed with differential structure C∞(S) generated by restrictions to S of functions in C∞(Rd), has a canonical partition M(S) by manifolds, which are orbits of the family X(S) of all derivations of C∞(S) that generate local one-parameter groups of local diffeomorphisms of S. This partition satisfies the frontier condition, Whitney’s conditions A and B. If M(S) is locally finite, then it satisfies all definitions of stratification of S. This result extends to Hausdorff locally Euclidean differential spaces. The partition M(S) of a subcartesian space S b

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Wildman, Raymond A., and George A. Gazonas. "Gravitational and magnetic anomaly inversion using a tree-based geometry representation." GEOPHYSICS 74, no. 3 (2009): I23—I35. http://dx.doi.org/10.1190/1.3110042.

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Gravitational and magnetic anomaly inversion of homogeneous 2D and 3D structures is treated using a geometric parameterization that can represent multiple, arbitrary polygons or polyhedra and a local-optimization scheme based on a hill-climbing method. This geometry representation uses a tree data structure, which defines a set of Boolean operations performed on convex polygons. A variable-length list of points, whose convex hull defines a convex polygon operand, resides in each leaf node of the tree. The overall optimization algorithm proceeds in two steps. Step one optimizes geometric transf

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Burrowes, Kelly S., Peter J. Hunter, and Merryn H. Tawhai. "Anatomically based finite element models of the human pulmonary arterial and venous trees including supernumerary vessels." Journal of Applied Physiology 99, no. 2 (2005): 731–38. http://dx.doi.org/10.1152/japplphysiol.01033.2004.

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Studies of the origin of pulmonary blood flow heterogeneity have highlighted the significant role of vessel branching structure on flow distribution. To enable more detailed investigation of structure-function relationships in the pulmonary circulation, an anatomically based finite element model of the arterial and venous networks has been developed to more accurately reflect the geometry found in vivo. Geometric models of the arterial and venous tree structures are created using a combination of multidetector row X-ray computed tomography imaging to define around 2,500 vessels from each tree,

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Al-Qashbari, Adel Mohammed Ali, and Fahmi Ahmed Mothana Al-ssallal. "HIGHER-ORDER CARTAN DERIVATIVES AND CURVATURE TENSOR DECOMPOSITION IN FINSLER SPACES: INSIGHTS INTO MATHEMATICAL AND PHYSICAL APPLICATIONS." Electronic Journal of University of Aden for Basic and Applied Sciences 6, no. 2 (2025): 141–51. https://doi.org/10.47372/ejua-ba.2025.2.449.

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This paper delves into the intricate structure of curvature tensors within the realm of Finsler geometry. By harnessing the power of higher-order Cartan derivatives, we introduce a novel decomposition scheme for curvature tensors. This innovative approach not only provides deeper insights into the geometric properties of Finsler spaces but also establishes a foundational framework for further investigations. Our findings reveal that the proposed decomposition is instrumental in unraveling the connections between curvature, torsion, and the underlying metric structure. Moreover, we demonstrate

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