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Relevant bibliographies by topics / Geometric measure and integration theory

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Academic literature on the topic 'Geometric measure and integration theory'

Author: Grafiati

Published: 4 June 2021

Last updated: 4 February 2022

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Journal articles on the topic "Geometric measure and integration theory"

1

Langer, Carlotta, and Nihat Ay. "Complexity as Causal Information Integration." Entropy 22, no. 10 (2020): 1107. http://dx.doi.org/10.3390/e22101107.

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Complexity measures in the context of the Integrated Information Theory of consciousness try to quantify the strength of the causal connections between different neurons. This is done by minimizing the KL-divergence between a full system and one without causal cross-connections. Various measures have been proposed and compared in this setting. We will discuss a class of information geometric measures that aim at assessing the intrinsic causal cross-influences in a system. One promising candidate of these measures, denoted by ΦCIS, is based on conditional independence statements and does satisf

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BLOCH, ANTHONY M., and ARIEH ISERLES. "COMMUTATORS OF SKEW-SYMMETRIC MATRICES." International Journal of Bifurcation and Chaos 15, no. 03 (2005): 793–801. http://dx.doi.org/10.1142/s0218127405012417.

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In this paper we develop a theory for analysing the "radius" of the Lie algebra of a matrix Lie group, which is a measure of the size of its commutators. Complete details are given for the Lie algebra 𝔰𝔬(n) of skew symmetric matrices where we prove [Formula: see text], X, Y ∈ 𝔰𝔬(n), for the Frobenius norm. We indicate how these ideas might be extended to other matrix Lie algebras. We discuss why these ideas are of interest in applications such as geometric integration and optimal control.

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Bonotto, E. M., M. Federson, and P. Muldowney. "The Black–Scholes Equation with Impulses at Random Times Via Generalized Riemann Integral." Proceedings of the Singapore National Academy of Science 15, no. 01 (2021): 45–59. http://dx.doi.org/10.1142/s2591722621400068.

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The classical pricing theory requires that the simple sets of outcomes are extended, using the Kolmogorov Extension Theorem, to a sigma-algebra of measurable sets in an infinite-dimensional sample space whose elements are continuous paths; the process involved are represented by appropriate stochastic differential equations (using Itô calculus); a suitable measure for the sample space can be found by means of the Girsanov and Radon–Nikodym Theorems; the derivative asset valuation is determined by means of an expression using Lebesgue integration. It is known that if we replace Lebesgue’s by th

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Fang, Huiqing, and Zhaohui Qi. "A Hybrid Interpolation Method for Geometric Nonlinear Spatial Beam Elements with Explicit Nodal Force." Mathematical Problems in Engineering 2016 (2016): 1–16. http://dx.doi.org/10.1155/2016/8980676.

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Based on geometrically exact beam theory, a hybrid interpolation is proposed for geometric nonlinear spatial Euler-Bernoulli beam elements. First, the Hermitian interpolation of the beam centerline was used for calculating nodal curvatures for two ends. Then, internal curvatures of the beam were interpolated with a second interpolation. At this point, C1 continuity was satisfied and nodal strain measures could be consistently derived from nodal displacement and rotation parameters. The explicit expression of nodal force without integration, as a function of global parameters, was founded by us

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Dong, Hou, and Gong. "Algorithm for Neutrosophic Soft Sets in Stochastic Multi-Criteria Group Decision Making Based on Prospect Theory." Symmetry 11, no. 9 (2019): 1085. http://dx.doi.org/10.3390/sym11091085.

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To address issues involving inconsistencies, this paper proposes a stochastic multi-criteria group decision making algorithm based on neutrosophic soft sets, which includes a pair of asymmetric functions: Truth-membership and false-membership, and an indeterminacy-membership function. For integrating an inherent stochastic, the algorithm expresses the weights of decision makers and parameter subjective weights by neutrosophic numbers instead of determinate values. Additionally, the algorithm is guided by the prospect theory, which incorporates psychological expectations of decision makers into

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Ozawa, Misaki, Walter Kob, Atsushi Ikeda, and Kunimasa Miyazaki. "Equilibrium phase diagram of a randomly pinned glass-former." Proceedings of the National Academy of Sciences 112, no. 22 (2015): 6914–19. http://dx.doi.org/10.1073/pnas.1500730112.

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We use computer simulations to study the thermodynamic properties of a glass-former in which a fraction c of the particles has been permanently frozen. By thermodynamic integration, we determine the Kauzmann, or ideal glass transition, temperature TK(c) at which the configurational entropy vanishes. This is done without resorting to any kind of extrapolation, i.e., TK(c) is indeed an equilibrium property of the system. We also measure the distribution function of the overlap, i.e., the order parameter that signals the glass state. We find that the transition line obtained from the overlap coin

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Fesenko, Ivan. "Analysis on arithmetic schemes. II." Journal of K-theory 5, no. 3 (2010): 437–557. http://dx.doi.org/10.1017/is010004028jkt103.

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AbstractWe construct adelic objects for rank two integral structures on arithmetic surfaces and develop measure and integration theory, as well as elements of harmonic analysis. Using the topological Milnor K2-delic and K1×K1-delic objects associated to an arithmetic surface, an adelic zeta integral is defined. Its unramified version is closely related to the square of the zeta function of the surface. For a proper regular model of an elliptic curve over a global field, a two-dimensional version of the theory of Tate and Iwasawa is derived. Using adelic analytic duality and a two-dimensional t

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GUENDELMAN, E. I. "GAUGE CONDENSATES AND GAUGE DYNAMICS, THE COSMOLOGICAL AND STRONG CP PROBLEMS." International Journal of Modern Physics A 14, no. 22 (1999): 3497–530. http://dx.doi.org/10.1142/s0217751x99001627.

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Some evidence for gauge field condensation in gauge theories is reviewed. The gravitational effects of gauge field condensates, in particular those associated with four-index field strengths are analyzed, paying special attention to their effect on the cosmological constant problem (CCP) and on the matching of different phases of the theory. Gauge fields composed of elementary scalars and their role in the CCP are studied. In particular such gauge fields can define a composite measure of integration which is a total derivative leading to the invariance under changes in the Lagrangian density L

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Kirchheim, B. "Seminar on geometric measure theory." Acta Applicandae Mathematicae 23, no. 1 (1991): 95–101. http://dx.doi.org/10.1007/bf00046922.

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Toro, Tatiana. "Geometric Measure Theory–Recent Applications." Notices of the American Mathematical Society 66, no. 04 (2019): 1. http://dx.doi.org/10.1090/noti1853.

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Dissertations / Theses on the topic "Geometric measure and integration theory"

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Short, K. M. "Geometric approach to path integration in string theory." Thesis, Imperial College London, 1988. http://hdl.handle.net/10044/1/47256.

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Odell, Anders. "Quantum transport and geometric integration for molecular systems." Doctoral thesis, KTH, Tillämpad materialfysik, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-26780.

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Molecular electronics is envisioned as a possible next step in device miniaturization. It is usually taken to mean the design and manufacturing of electronic devices and applications where organic molecules work as the fundamental functioning unit. It involves the measurement and manipulation of electronic response and transport in molecules attached to conducting leads. Organic molecules have the advantages over conventional solid state electronics of inherent small sizes, endless chemical diversity and ambient temperature low cost manufacturing. In this thesis we investigate the switching an

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Morgan, Frank. "Compactness." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/96708.

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In my opinion, compactness is the most important concept in mathematics. We 'll track it from the one-dimensional real line in calculus to infinite dimensional spaces of functions and surfaces and see what it can do.

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Donzella, Michael A. "The Geometry of Rectifiable and Unrectifiable Sets." Kent State University / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=kent1404332888.

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Kissel, Kris. "Generalizations of a result of Lewis and Vogel /." Thesis, Connect to this title online; UW restricted, 2007. http://hdl.handle.net/1773/5741.

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Reichl, Paul 1973. "Flow past a cylinder close to a free surface." Monash University, Dept. of Mechanical Engineering, 2001. http://arrow.monash.edu.au/hdl/1959.1/9212.

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Wells-Day, Benjamin Michael. "Structure of singular sets local to cylindrical singularities for stationary harmonic maps and mean curvature flows." Thesis, University of Cambridge, 2019. https://www.repository.cam.ac.uk/handle/1810/290409.

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In this paper we prove structure results for the singular sets of stationary harmonic maps and mean curvature flows local to particular singularities. The original work is contained in Chapter 5 and Chapter 8. Chapters 1-5 are concerned with energy minimising maps and stationary harmonic maps. Chapters 6-8 are concerned with mean curvature flows and Brakke flows. In the case of stationary harmonic maps we consider a singularity at which the spine dimension is maximal, and such that the weak tangent map is homotopically non-trivial, and has minimal density amongst singularities of maximal spine

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Carnovale, Marc. "Arithmetic Structures in Small Subsets of Euclidean Space." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1555657038785892.

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Graham, David(David Warwick) 1976. "Forced Brakke flows." Monash University, School of Mathematical Sciences, 2003. http://arrow.monash.edu.au/hdl/1959.1/7774.

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Graham, David (David Warwick) 1976. "Forced Brakke flows." Monash University, School of Mathematical Sciences, 2003. http://arrow.monash.edu.au/hdl/1959.1/5712.

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Books on the topic "Geometric measure and integration theory"

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1949-, Parks Harold R., ed. Geometric integration theory. Birkhäuser, 2008.

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1963-, Giannopoulos Apostolos, and Milman Vitali D. 1939-, eds. Asymptotic geometric analysis. American Mathematical Society, 2015.

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Federer, Herbert. Geometric measure theory. Springer, 1996.

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Federer, Herbert. Geometric Measure Theory. Edited by B. Eckmann and B. L. van der Waerden. Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-62010-2.

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Whitney, Hassler. Geometric integration theory. Dover Publications, 2005.

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Krantz, Steven, and Harold Parks. Geometric Integration Theory. Birkhäuser Boston, 2008. http://dx.doi.org/10.1007/978-0-8176-4679-0.

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Measure theory and integration. American Mathematical Society, 2006.

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8

Measure theory and integration. 2nd ed. Marcel Dekker, 2004.

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9

Measure and integration theory. W. de Gruyter, 2001.

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10

Measure theory and integration. Wiley, 1987.

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Book chapters on the topic "Geometric measure and integration theory"

1

Federer, Herbert. "Homological integration theory." In Geometric Measure Theory. Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-62010-2_5.

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Doob, J. L. "Integration." In Measure Theory. Springer New York, 1994. http://dx.doi.org/10.1007/978-1-4612-0877-8_7.

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Federer, Herbert. "General measure theory." In Geometric Measure Theory. Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-62010-2_3.

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Federer, Herbert. "Grassmann algebra." In Geometric Measure Theory. Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-62010-2_2.

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Federer, Herbert. "Rectifiability." In Geometric Measure Theory. Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-62010-2_4.

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Federer, Herbert. "Applications to the calculus of variations." In Geometric Measure Theory. Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-62010-2_6.

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"Invariant Measures and the Construction of Haar Measure." In Geometric Integration Theory. Birkhäuser Boston, 2008. http://dx.doi.org/10.1007/978-0-8176-4679-0_3.

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"Carathéodory’s Construction and Lower-Dimensional Measures." In Geometric Integration Theory. Birkhäuser Boston, 2008. http://dx.doi.org/10.1007/978-0-8176-4679-0_2.

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Morgan, Frank. "Geometric Measure Theory." In Geometric Measure Theory. Elsevier, 2000. http://dx.doi.org/10.1016/b978-012506851-2/50001-7.

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Morgan, Frank. "Geometric Measure Theory." In Geometric Measure Theory. Elsevier, 2016. http://dx.doi.org/10.1016/b978-0-12-804489-6.50001-x.

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Conference papers on the topic "Geometric measure and integration theory"

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Toro, Tatiana. "Potential Analysis Meets Geometric Measure Theory." In Proceedings of the International Congress of Mathematicians 2010 (ICM 2010). Published by Hindustan Book Agency (HBA), India. WSPC Distribute for All Markets Except in India, 2011. http://dx.doi.org/10.1142/9789814324359_0107.

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Rodriguez Hertz, Federico. "Measure Theory and Geometric Topology in Dynamics." In Proceedings of the International Congress of Mathematicians 2010 (ICM 2010). Published by Hindustan Book Agency (HBA), India. WSPC Distribute for All Markets Except in India, 2011. http://dx.doi.org/10.1142/9789814324359_0120.

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Bär, Sebastian, and Michael Groß. "Higher order accurate geometric integration in endochronic theory." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4992483.

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Edalat, Abbas. "A computable approach to measure and integration theory." In 22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007). IEEE, 2007. http://dx.doi.org/10.1109/lics.2007.5.

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Goldluecke, Bastian, and Daniel Cremers. "An approach to vectorial total variation based on geometric measure theory." In 2010 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2010. http://dx.doi.org/10.1109/cvpr.2010.5540194.

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Shcherbakov, Dmitry, and Matthias Ehrhardt. "Geometric Numerical Integration Structure-Preserving Algorithms for QCD Simulations." In XXIX International Symposium on Lattice Field Theory. Sissa Medialab, 2012. http://dx.doi.org/10.22323/1.139.0327.

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Mollenhoff, Thomas, and Daniel Cremers. "Lifting Vectorial Variational Problems: A Natural Formulation Based on Geometric Measure Theory and Discrete Exterior Calculus." In 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2019. http://dx.doi.org/10.1109/cvpr.2019.01137.

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Zhu, Jun, and Rui Fen Zhou. "Research on Transient Mechanics Behavior of Pumping Rod in Pumping System." In ASME 2008 27th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2008. http://dx.doi.org/10.1115/omae2008-57049.

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More than 75% pumping rod well accounted is artificial lifting production well. With the development of the oilfield, eccentric wearing of rod is becoming the main problem. Numerous factors influencing eccentric wearing of rod heighten the difficulties in the prediction and comprehensive analysis. In the past, it is emphasized on the avoiding and curing measures application, and short of system analysis in respect of flectional reason, flectional conformation and influencing factors. In order to reduce eccentric wearing of rod and show the flectional conformation, the transient mechanics behav

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Palese, Joseph W., Sergio DiVentura, Ken Hill, and Peter Maurice. "Optimizing Tamper Efficiency Through the Integration of Inertial Based Track Geometry Measurement." In 2017 Joint Rail Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/jrc2017-2255.

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Maintaining track geometry is key to the safe and efficient operations of a railroad. Failure to properly maintain geometry can lead to costly track structure failures or even more costly derailments. Currently, there exists a number of different methods for measuring track geometry and then if required, maintaining the track to return track geometry to specified levels of acceptance. Because of this need to have proper track geometry, tampers are one of the most common pieces of maintenance equipment in a railroad operation’s fleet. It is therefore paramount from both a cost and track time pe

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Bahabadi, Hossein Gohari, and Ahmad Barari. "Geometric Complexity Estimation of Continuous Surfaces for Fitting Processes." In ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/detc2019-98456.

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Abstract The advances in manufacturing methods such as Additive manufacturing provide more flexibility in fabrication of complex geometries. Meanwhile, design tools such as aesthetic design and topology optimization algorithms have been implemented in industrial applications mostly due to the provided flexibility to manufacture freeform surfaces. Computational time and efficiency of the developed algorithms for design, manufacturing and inspection are heavily dependent on the geometric complexity of surfaces. In this paper a measure to estimate the geometric complexity is introduced based on t

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