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Journal articles on the topic 'Geometric analysis'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Gong, Wenjuan, Bin Zhang, Chaoqi Wang, et al. "A Literature Review: Geometric Methods and Their Applications in Human-Related Analysis." Sensors 19, no. 12 (2019): 2809. http://dx.doi.org/10.3390/s19122809.

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Geometric features, such as the topological and manifold properties, are utilized to extract geometric properties. Geometric methods that exploit the applications of geometrics, e.g., geometric features, are widely used in computer graphics and computer vision problems. This review presents a literature review on geometric concepts, geometric methods, and their applications in human-related analysis, e.g., human shape analysis, human pose analysis, and human action analysis. This review proposes to categorize geometric methods based on the scope of the geometric properties that are extracted:

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2

Pinus, A. G. "Geometric and conditional geometric equivalences of algebras." Algebra and Logic 51, no. 6 (2013): 507–10. http://dx.doi.org/10.1007/s10469-013-9210-4.

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3

Ali, Akbar, M. Matejić, Igor Ž. Milovanović, Emina I. Milovanović, Stefan D. Stankov, and Zahid Raza. "On arithmetic-geometric and geometric-arithmetic indices of graphs." Journal of Mathematical Inequalities, no. 4 (2023): 1565–79. http://dx.doi.org/10.7153/jmi-2023-17-103.

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4

Mostajeran, Cyrus, Christian Grussler, and Rodolphe Sepulchre. "Geometric Matrix Midranges." SIAM Journal on Matrix Analysis and Applications 41, no. 3 (2020): 1347–68. http://dx.doi.org/10.1137/19m1273475.

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5

J. Washington, Andres. "Fingerprint Geometric Analysis." International Journal of Criminal and Forensic Science 1, no. 1 (2017): 08–10. http://dx.doi.org/10.25141/2576-3563-2017-1.0008.

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6

Artstein-Avidan, Shiri, Hermann König, and Alexander Koldobsky. "Asymptotic Geometric Analysis." Oberwolfach Reports 13, no. 1 (2016): 507–65. http://dx.doi.org/10.4171/owr/2016/11.

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7

Blasius, Joerg. "Geometric Data Analysis." Bulletin of Sociological Methodology/Bulletin de Méthodologie Sociologique 68, no. 1 (2000): 54–55. http://dx.doi.org/10.1177/075910630006800123.

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8

Hong, Seok-In. "Geometric circuit analysis." Physics Education 58, no. 6 (2023): 065021. http://dx.doi.org/10.1088/1361-6552/acf108.

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Abstract The Smith rectangle symbolises the resistor and its width, height, aspect ratio, and area represent the current through, the voltage across, the resistance of, and the power dissipated in the resistor, respectively. In this article, the mosaic of rectangles (MOR) is introduced as a geometric approach to connected planar resistive network circuits with an ideal voltage source. In the MOR, the geometric Kirchhoff’s current and voltage laws are expressed as width and height conservations, respectively and are automatically satisfied. Four basic circuits are considered as applications of

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9

Yau, Shing-Tung. "A survey of geometric structure in geometric analysis." Surveys in Differential Geometry 16, no. 1 (2011): 325–48. http://dx.doi.org/10.4310/sdg.2011.v16.n1.a7.

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10

Moakher, Maher. "A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices." SIAM Journal on Matrix Analysis and Applications 26, no. 3 (2005): 735–47. http://dx.doi.org/10.1137/s0895479803436937.

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11

Brüning, Jochen, Rafe Mazzeo, and Paolo Piazza. "Analysis and Geometric Singularities." Oberwolfach Reports 9, no. 2 (2012): 1487–562. http://dx.doi.org/10.4171/owr/2012/25.

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12

Yau, Shing-Tung. "Perspectives on geometric analysis." Surveys in Differential Geometry 10, no. 1 (2005): 275–379. http://dx.doi.org/10.4310/sdg.2005.v10.n1.a8.

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13

Yau, Shing-Tung. "Topics on geometric analysis." Surveys in Differential Geometry 17, no. 1 (2012): 459–73. http://dx.doi.org/10.4310/sdg.2012.v17.n1.a11.

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14

Martínez-Morales, José L. "Geometric data fitting." Abstract and Applied Analysis 2004, no. 10 (2004): 831–80. http://dx.doi.org/10.1155/s1085337504401043.

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15

Lim, Yongdo. "Convex geometric means." Journal of Mathematical Analysis and Applications 404, no. 1 (2013): 115–28. http://dx.doi.org/10.1016/j.jmaa.2013.03.006.

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16

Lim, Yongdo. "Riemannian Distances between Geometric Means." SIAM Journal on Matrix Analysis and Applications 34, no. 3 (2013): 932–45. http://dx.doi.org/10.1137/12090006x.

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17

Andruchow, E., E. Chiumiento, and G. Larotonda. "Geometric significance of Toeplitz kernels." Journal of Functional Analysis 275, no. 2 (2018): 329–55. http://dx.doi.org/10.1016/j.jfa.2018.02.015.

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18

Gonçalves, J. Basto. "Geometric conditions for local controllability." Journal of Differential Equations 89, no. 2 (1991): 388–95. http://dx.doi.org/10.1016/0022-0396(91)90126-t.

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19

Liu, Jian. "A geometric inequality with applications." Journal of Mathematical Inequalities, no. 3 (2016): 641–48. http://dx.doi.org/10.7153/jmi-10-51.

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20

Bellettini, G., and M. Novaga. "Minimal Barriers for Geometric Evolutions." Journal of Differential Equations 139, no. 1 (1997): 76–103. http://dx.doi.org/10.1006/jdeq.1997.3288.

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21

Sun, Churen. "On approximatingD-induced polar sets of geometric and extended geometric cones." Journal of Interdisciplinary Mathematics 11, no. 3 (2008): 301–30. http://dx.doi.org/10.1080/09720502.2008.10700561.

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22

Mageed, Ismail A. "The Info-Geometric Analysis of Wind Speed Dynamics and How Energy is Influentially Impacted by Information Geometry (IG)." Journal of Data Analytics and Engineering Decision Making 1, no. 1 (2024): 01–07. https://doi.org/10.33140/jdaedm.01.01.02.

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The use of mathematical models to forecast environmental conditions is covered in this paper. These models work well for larger-scale events, but they become more complicated when it comes to wave processes or local weather. This issue has been tackled using a variety of strategies, such as neural networks and statistical and mathematical models. This method is innovative because it makes use of statistical manifolds, which offer a more precise means of estimating cost functions and distances. To create various models that can be utilised for environmental modelling and forecasting, this work

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23

Yin, Zhou-Ping, Han Ding, Han-Xiong Li, and You-Lun Xiong. "Geometric mouldability analysis by geometric reasoning and fuzzy decision making." Computer-Aided Design 36, no. 1 (2004): 37–50. http://dx.doi.org/10.1016/s0010-4485(03)00067-8.

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24

Kong, De-Xing, and Jinhua Wang. "Einstein's hyperbolic geometric flow." Journal of Hyperbolic Differential Equations 11, no. 02 (2014): 249–67. http://dx.doi.org/10.1142/s0219891614500076.

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We investigate the Einstein's hyperbolic geometric flow, which provides a natural tool to deform the shape of a manifold and to understand the wave character of metrics, the wave phenomenon of the curvature for evolutionary manifolds. For an initial manifold equipped with an Einstein metric and assumed to be a totally umbilical submanifold in the induced space-time, we prove that, along the Einstein's hyperbolic geometric flow, the metric is Einstein if and only if the corresponding manifold is a totally umbilical hypersurface in the induced space-time. For an initial manifold which is equippe

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25

Soffer, A. "Geometric Characterization of Solitons." Communications in Partial Differential Equations 33, no. 11 (2008): 1953–74. http://dx.doi.org/10.1080/03605300802501764.

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26

Mallios, A. "On Geometric Topological Algebras." Journal of Mathematical Analysis and Applications 172, no. 2 (1993): 301–22. http://dx.doi.org/10.1006/jmaa.1993.1026.

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27

Bătineţu-Giurgiu, D. M., and Neculai Stanciu. "Some geometric inequalities of Radon – Mitrinović." Journal of Mathematical Inequalities, no. 1 (2013): 25–32. http://dx.doi.org/10.7153/jmi-07-03.

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28

Sababheh, Mohammad, Shigeru Furuichi, Zahra Heydarbeygi, and Hamid Reza Moradi. "On the arithmetic-geometric mean inequality." Journal of Mathematical Inequalities, no. 3 (2021): 1255–66. http://dx.doi.org/10.7153/jmi-2021-15-84.

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29

Morris, Jr., Walter D., and Jim Lawrence. "Geometric Properties of Hidden Minkowski Matrices." SIAM Journal on Matrix Analysis and Applications 10, no. 2 (1989): 229–32. http://dx.doi.org/10.1137/0610017.

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30

Robinson, Michael. "Imaging geometric graphs using internal measurements." Journal of Differential Equations 260, no. 1 (2016): 872–96. http://dx.doi.org/10.1016/j.jde.2015.09.014.

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31

Kadets, Vladimir, Ginés López-Pérez, and Miguel Martín. "Some geometric properties of Read's space." Journal of Functional Analysis 274, no. 3 (2018): 889–99. http://dx.doi.org/10.1016/j.jfa.2017.06.010.

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32

Fu, Xiaohui. "An operator α-geometric mean inequality". Journal of Mathematical Inequalities, № 3 (2015): 947–50. http://dx.doi.org/10.7153/jmi-09-77.

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33

an Yang, Junj, та Xiaohui Fu. "Squaring operator α-geometric mean inequality". Journal of Mathematical Inequalities, № 2 (2016): 571–75. http://dx.doi.org/10.7153/jmi-10-45.

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34

Joly, J. L., G. Metivier, and J. Rauch. "Resonant One Dimensional Nonlinear Geometric Optics." Journal of Functional Analysis 114, no. 1 (1993): 106–231. http://dx.doi.org/10.1006/jfan.1993.1065.

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35

Shvydkoy, R. V. "Geometric Aspects of the Daugavet Property." Journal of Functional Analysis 176, no. 2 (2000): 198–212. http://dx.doi.org/10.1006/jfan.2000.3626.

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36

Alterman, Deborah, and Jeffrey Rauch. "Nonlinear Geometric Optics for Short Pulses." Journal of Differential Equations 178, no. 2 (2002): 437–65. http://dx.doi.org/10.1006/jdeq.2001.4016.

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37

Polking, John, and Steven G. Krantz. "Complex Analysis: The Geometric Viewpoint." American Mathematical Monthly 101, no. 1 (1994): 91. http://dx.doi.org/10.2307/2325141.

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38

Berndtsson, Bo, John Erik Fornaess, and Nikolay Shcherbina. "Geometric Methods of Complex Analysis." Oberwolfach Reports 18, no. 2 (2022): 1291–345. http://dx.doi.org/10.4171/owr/2021/25.

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39

Singer, Brian D. "Risk Analysis: A Geometric Approach." AIMR Conference Proceedings 1999, no. 3 (1999): 73–79. http://dx.doi.org/10.2469/cp.v1999.n3.10.

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40

Berndtsson, Bo, John Erik Fornæss, and Nikolay Shcherbina. "Geometric Methods of Complex Analysis." Oberwolfach Reports 12, no. 1 (2015): 235–83. http://dx.doi.org/10.4171/owr/2015/4.

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41

Andersson, Mats, Bo Berndtsson, John Erik Fornæss, and Nikolay Shcherbina. "Geometric Methods of Complex Analysis." Oberwolfach Reports 15, no. 3 (2019): 2253–302. http://dx.doi.org/10.4171/owr/2018/37.

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42

Vereshchaha, V., A. Naidysh, A. Pavlenko, and I. Chyzhykov. "ANALYSIS OF COMPOSITE GEOMETRIC MODELING." Modern problems of modeling 22 (June 16, 2021): 22–31. http://dx.doi.org/10.33842/22195203/2021/22/22/31.

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43

Colding, T. H., and W. P. Minicozzi. "An excursion into geometric analysis." Surveys in Differential Geometry 9, no. 1 (2004): 83–146. http://dx.doi.org/10.4310/sdg.2004.v9.n1.a4.

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44

Ting, Chen, and Sun Wenchang. "Geometric inequalities in harmonic analysis." SCIENTIA SINICA Mathematica 48, no. 10 (2018): 1219. http://dx.doi.org/10.1360/n012018-00081.

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45

Osinga, Hinke M., and Krasimira T. Tsaneva-Atanasova. "Geometric analysis of transient bursts." Chaos: An Interdisciplinary Journal of Nonlinear Science 23, no. 4 (2013): 046107. http://dx.doi.org/10.1063/1.4826655.

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46

Jiang, Xianhua, Zhi-Quan Luo, and Tryphon T. Georgiou. "Geometric Methods for Spectral Analysis." IEEE Transactions on Signal Processing 60, no. 3 (2012): 1064–74. http://dx.doi.org/10.1109/tsp.2011.2178601.

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47

KARA, LEVENT BURAK, and THOMAS F. STAHOVICH. "Causal reasoning using geometric analysis." Artificial Intelligence for Engineering Design, Analysis and Manufacturing 16, no. 5 (2002): 363–84. http://dx.doi.org/10.1017/s0890060402165036.

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We describe an approach that uses causal and geometric reasoning to construct explanations for the purposes of the geometric features on the parts of a mechanical device. To identify the purpose of a feature, the device is simulated with and without the feature. The simulations are then translated into a “causal-process” representation, which allows qualitatively important differences to be identified. These differences reveal the behaviors caused and prevented by the feature and thus provide useful cues about the feature's purpose. A clear understanding of the feature's purpose, however, requ

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48

Li, Xiang, Weiji Li, and Chang’an Liu. "Geometric analysis of collaborative optimization." Structural and Multidisciplinary Optimization 35, no. 4 (2007): 301–13. http://dx.doi.org/10.1007/s00158-007-0127-1.

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49

Struve, Rolf. "Cyclic order: a geometric analysis." Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 61, no. 4 (2020): 649–69. http://dx.doi.org/10.1007/s13366-020-00490-y.

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50

Segev, Reuven. "Geometric analysis of hyper-stresses." International Journal of Engineering Science 120 (November 2017): 100–118. http://dx.doi.org/10.1016/j.ijengsci.2017.07.001.

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