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Relevant bibliographies by topics / Geometric analysis / Journal articles

Journal articles on the topic 'Geometric analysis'

To see the other types of publications on this topic, follow the link: Geometric analysis.

Author: Grafiati

Published: 4 June 2021

Last updated: 1 August 2024

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1

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

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2

Gong, Wenjuan, Bin Zhang, Chaoqi Wang, Hanbing Yue, Chuantao Li, Linjie Xing, Yu Qiao, Weishan Zhang, and Faming Gong. "A Literature Review: Geometric Methods and Their Applications in Human-Related Analysis." Sensors 19, no. 12 (June 23, 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: object-oriented geometric methods, feature-oriented geometric methods, and routine-based geometric methods. Considering the broad applications of deep learning methods, this review also studies geometric deep learning, which has recently become a popular topic of research. Validation datasets are collected, and method performances are collected and compared. Finally, research trends and possible research topics are discussed.

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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 (January 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 (October 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 (October 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 geometric circuit analysis. Resistors in series and in parallel are analysed using the MOR, and the effect of changing one resistor is visualised by superposing the initial and new MORs. The effect of loading an unloaded voltage divider with a parallel resistor is also visualised. The Wheatstone bridge is explored as an example of rather complicated resistive networks and the consistency of the assumed current directions, the shape of the MOR, and the geometric Kirchhoff’s laws is discussed. The geometric and game-like circuit analysis would be beneficial to high school and university students as well as their teachers.

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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 (January 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 (August 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 (January 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 (July 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 (February 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 (September 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 (June 2008): 301–30. http://dx.doi.org/10.1080/09720502.2008.10700561.

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22

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 (January 2004): 37–50. http://dx.doi.org/10.1016/s0010-4485(03)00067-8.

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23

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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24

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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25

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

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26

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

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27

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

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28

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

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29

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

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30

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

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31

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

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32

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

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33

Kong, De-Xing, and Jinhua Wang. "Einstein's hyperbolic geometric flow." Journal of Hyperbolic Differential Equations 11, no. 02 (June 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 equipped with an Einstein metric, assumed to be a totally umbilical submanifold with constant mean curvature in the induced space-time, we prove that, along the Einstein's hyperbolic geometric flow, the metric remains an Einstein metric, and the corresponding manifold is a totally umbilical hypersurface in the induced space-time. Moreover, the global existence and blowup phenomenon of the constructed metric is also investigated here.

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34

Soffer, A. "Geometric Characterization of Solitons." Communications in Partial Differential Equations 33, no. 11 (October 29, 2008): 1953–74. http://dx.doi.org/10.1080/03605300802501764.

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35

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

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36

Karthi, R. R., B. Tamilarasu, and S. Mukesh K. M. Naveen Kumar. "Geometric Modeling, Design and Analysis of Custom-Engineered Milling Cutters." International Journal of Trend in Scientific Research and Development Volume-2, Issue-3 (April 30, 2018): 543–50. http://dx.doi.org/10.31142/ijtsrd10986.

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37

Polking, John, and Steven G. Krantz. "Complex Analysis: The Geometric Viewpoint." American Mathematical Monthly 101, no. 1 (January 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 (August 24, 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 (August 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 (August 26, 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 (October 1, 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 (December 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 (March 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 (November 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, requires a detailed analysis of the causal connections between the caused and prevented behaviors. This presents a significant challenge because one has to understand how a behavior that normally takes place affects (or is affected by) another behavior that is normally absent. This article describes techniques for identifying such elusive relationships. These techniques employ a set of rules that can determine if one behavior enables or disables another that is spatially and temporally far away. They do so by geometrically examining the traces of the causal processes in the device's configuration space. Using the results of this analysis, our program can automatically generate text output describing how the feature performs its function.

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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 (May 3, 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 (February 21, 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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