Relevant bibliographies by topics / Diffusions on manifolds with singularities

Academic literature on the topic 'Diffusions on manifolds with singularities'

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Published: 14 March 2023

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Journal articles on the topic "Diffusions on manifolds with singularities"

1

Antonelli, P. L., and T. J. Zastawniak. "Diffusions on Finsler manifolds." Reports on Mathematical Physics 33, no. 1-2 (August 1993): 303–15. http://dx.doi.org/10.1016/0034-4877(93)90065-m.

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Natanzon, S. M. "Singularities and noncommutative Frobenius manifolds." Proceedings of the Steklov Institute of Mathematics 259, no. 1 (December 2007): 137–48. http://dx.doi.org/10.1134/s0081543807040104.

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Liu, Zhong-Dong, Zhongmin Shen, and Dagang Yang. "Riemannian Manifolds with Conical Singularities." Rocky Mountain Journal of Mathematics 28, no. 2 (June 1998): 625–41. http://dx.doi.org/10.1216/rmjm/1181071789.

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Schrohe, Elmar. "Complex powers on noncompact manifolds and manifolds with singularities." Mathematische Annalen 281, no. 3 (August 1988): 393–409. http://dx.doi.org/10.1007/bf01457152.

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Chiu, Hung-Lin. "SINGULARITIES AND SOME INVARIANTS OF SINGULARITIES IN CONTACT 3-MANIFOLDS." Taiwanese Journal of Mathematics 10, no. 5 (September 2006): 1391–408. http://dx.doi.org/10.11650/twjm/1500557309.

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Lyons, Russell. "Diffusions and Random Shadows in Negatively Curved Manifolds." Journal of Functional Analysis 138, no. 2 (June 1996): 426–48. http://dx.doi.org/10.1006/jfan.1996.0071.

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Smith, P. D., and Deane Yang. "Removing point singularities of Riemannian manifolds." Transactions of the American Mathematical Society 333, no. 1 (January 1, 1992): 203–19. http://dx.doi.org/10.1090/s0002-9947-1992-1052910-2.

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Ma, L., and B. W. Schulze. "Operators on manifolds with conical singularities." Journal of Pseudo-Differential Operators and Applications 1, no. 1 (March 10, 2010): 55–74. http://dx.doi.org/10.1007/s11868-010-0002-5.

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Plamenevskii, B. A., and V. N. Senichkin. "Pseudodifferential operators on manifolds with singularities." Functional Analysis and Its Applications 33, no. 2 (April 1999): 154–56. http://dx.doi.org/10.1007/bf02465199.

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Stoica, Ovidiu Cristinel. "The geometry of warped product singularities." International Journal of Geometric Methods in Modern Physics 14, no. 02 (January 18, 2017): 1750024. http://dx.doi.org/10.1142/s0219887817500244.

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In this article, the degenerate warped products of singular semi-Riemannian manifolds are studied. They were used recently by the author to handle singularities occurring in General Relativity, in black holes and at the big-bang. One main result presented here is that a degenerate warped product of semi-regular semi-Riemannian manifolds with the warping function satisfying a certain condition is a semi-regular semi-Riemannian manifold. The connection and the Riemann curvature of the warped product are expressed in terms of those of the factor manifolds. Examples of singular semi-Riemannian manifolds which are semi-regular are constructed as warped products. Applications include cosmological models and black holes solutions with semi-regular singularities. Such singularities are compatible with a certain reformulation of the Einstein equation, which in addition holds at semi-regular singularities too.
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Dissertations / Theses on the topic "Diffusions on manifolds with singularities"

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Lunt, John Burnham. "Measurable perturbations of diffusions on manifolds." Thesis, University of Edinburgh, 1992. http://hdl.handle.net/1842/12486.

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Nazaikinskii, Vladimir, Anton Savin, Bert-Wolfgang Schulze, and Boris Sternin. "Differential operators on manifolds with singularities : analysis and topology : Chapter 5: Manifolds with isolated singularities." Universität Potsdam, 2003. http://opus.kobv.de/ubp/volltexte/2008/2665/.

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Contents: Chapter 5: Manifolds with Isolated Singularities 5.1. Differential Operators and the Geometry of Singularities 5.1.1. How do isolated singularities arise? Examples 5.1.2. Definition and methods for the description of manifolds with isolated singularities 5.1.3. Bundles. The cotangent bundle 5.2. Asymptotics of Solutions, Function Spaces,Conormal Symbols 5.2.1. Conical singularities 5.2.2. Cuspidal singularities 5.3. A Universal Representation of Degenerate Operators and the Finiteness Theorem 5.3.1. The cylindrical representation 5.3.2. Continuity and compactness 5.3.3. Ellipticity and the finiteness theorem 5.4. Calculus of ΨDO 5.4.1. General ΨDO 5.4.2. The subalgebra of stabilizing ΨDO 5.4.3. Ellipticity and the finiteness theorem
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Ma, L., and Bert-Wolfgang Schulze. "Operators on manifolds with conical singularities." Universität Potsdam, 2009. http://opus.kobv.de/ubp/volltexte/2009/3660/.

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We construct elliptic elements in the algebra of (classical pseudo-differential) operators on a manifold M with conical singularities. The ellipticity of any such operator A refers to a pair of principal symbols (σ0, σ1) where σ0 is the standard (degenerate) homogeneous principal symbol, and σ1 is the so-called conormal symbol, depending on the complex Mellin covariable z. The conormal symbol, responsible for the conical singularity, is operator-valued and acts in Sobolev spaces on the base X of the cone. The σ1-ellipticity is a bijectivity condition for all z of real part (n + 1)/2 − γ, n = dimX, for some weight γ. In general, we have to rule out a discrete set of exceptional weights that depends on A. We show that for every operator A which is elliptic with respect to σ0, and for any real weight γ there is a smoothing Mellin operator F in the cone algebra such that A + F is elliptic including σ1. Moreover, we apply the results to ellipticity and index of (operator-valued) edge symbols from the calculus on manifolds with edges.
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Nazaikinskii, Vladimir, Anton Savin, Bert-Wolfgang Schulze, and Boris Sternin. "Differential operators on manifolds with singularities : analysis and topology : Chapter 7: The index problem on manifolds with singularities." Universität Potsdam, 2004. http://opus.kobv.de/ubp/volltexte/2008/2670/.

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Contents: Chapter 7: The Index Problemon Manifolds with Singularities Preface 7.1. The Simplest Index Formulas 7.1.1. General properties of the index 7.1.2. The index of invariant operators on the cylinder 7.1.3. Relative index formulas 7.1.4. The index of general operators on the cylinder 7.1.5. The index of operators of the form 1 + G with a Green operator G 7.1.6. The index of operators of the form 1 + G on manifolds with edges 7.1.7. The index on bundles with smooth base and fiber having conical points 7.2. The Index Problem for Manifolds with Isolated Singularities 7.2.1. Statement of the index splitting problem 7.2.2. The obstruction to the index splitting 7.2.3. Computation of the obstruction in topological terms 7.2.4. Examples. Operators with symmetries 7.3. The Index Problem for Manifolds with Edges 7.3.1. The index excision property 7.3.2. The obstruction to the index splitting 7.4. Bibliographical Remarks
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Spathopoulos, Michael P. "Filtering and stochastic control for diffusions on manifolds." Thesis, Imperial College London, 1987. http://hdl.handle.net/10044/1/46638.

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Schulze, Bert-Wolfgang. "Pseudo-differential calculus on manifolds with geometric singularities." Universität Potsdam, 2006. http://opus.kobv.de/ubp/volltexte/2009/3020/.

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Differential and pseudo-differential operators on a manifold with (regular) geometric singularities can be studied within a calculus, inspired by the concept of classical pseudo-differential operators on a C1 manifold. In the singular case the operators form an algebra with a principal symbolic hierarchy σ = (σj)0≤j≤k, with k being the order of the singularity and σk operator-valued for k ≥ 1. The symbols determine ellipticity and the nature of parametrices. It is typical in this theory that, similarly as in boundary value problems (which are special edge problems, where the edge is just the boundary), there are trace, potential and Green operators, associated with the various strata of the configuration. The operators, obtained from the symbols by various quantisations, act in weighted distribution spaces with multiple weights. We outline some essential elements of this calculus, give examples and also comment on new challenges and interesting problems of the recent development.
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Mooers, Edith. "The heat kernel for manifolds with conic singularities." Thesis, Massachusetts Institute of Technology, 1996. http://hdl.handle.net/1721.1/38406.

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Schulze, Bert-Wolfgang, and Nikolai Tarkhanov. "The Riemann-Roch theorem for manifolds with conical singularities." Universität Potsdam, 1997. http://opus.kobv.de/ubp/volltexte/2008/2505/.

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Nazaikinskii, Vladimir, Bert-Wolfgang Schulze, Boris Sternin, and Victor Shatalov. "Quantization of symplectic transformations on manifolds with conical singularities." Universität Potsdam, 1997. http://opus.kobv.de/ubp/volltexte/2008/2508/.

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The structure of symplectic (canonical) transformations on manifolds with conical singularities is established. The operators associated with these transformations are defined in the weight spaces and their properties investigated.
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Abed, Jamil. "An iterative approach to operators on manifolds with singularities." Phd thesis, Universität Potsdam, 2010. http://opus.kobv.de/ubp/volltexte/2010/4475/.

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We establish elements of a new approach to ellipticity and parametrices within operator algebras on manifolds with higher singularities, only based on some general axiomatic requirements on parameter-dependent operators in suitable scales of spaes. The idea is to model an iterative process with new generations of parameter-dependent operator theories, together with new scales of spaces that satisfy analogous requirements as the original ones, now on a corresponding higher level. The "full" calculus involves two separate theories, one near the tip of the corner and another one at the conical exit to infinity. However, concerning the conical exit to infinity, we establish here a new concrete calculus of edge-degenerate operators which can be iterated to higher singularities.
Wir führen einen neuen Zugang ein zu Elliptizität und Parametrices in Operatorenalgebren auf Mannigfaltigkeiten mit höheren Singularitäten, nur basierend auf allgemeinen axiomatischen Voraussetzungen über parameter-abhängige Operatoren in geeigneten Skalen von Räumen. Die Idee besteht darin, ein iteratives Verfahren zu modellieren mit neuen Generationen von parameter-abhängigen Operatortheorien, zusammen mit neuen Skalen von Räumen, die analoge Voraussetzungen erfüllen wie die ursprünglichen Objekte, jetzt auf dem entsprechenden höheren Niveau. Der „volle“ Kalkül besteht aus zwei separaten Theorien, eine nahe der Spitze der Ecke und eine andere am konischen Ausgang nach Unendlich. Allerdings, bezüglich des konischen Ausgangs nach Unendlich, bauen wir hier einen neuen konkreten Kalkül von kanten-entarteten Operatoren auf, der für höhere Singularitäten iteriert werden kann.
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Books on the topic "Diffusions on manifolds with singularities"

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Hertling, Klaus. Frobenius Manifolds: Quantum Cohomology and Singularities. Wiesbaden: Vieweg+Teubner Verlag, 2004.

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Schulze, Bert-Wolfgang. Pseudo-differential operators on manifolds with singularities. Amsterdam: North-Holland, 1991.

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Frobenius manifolds and moduli spaces for singularities. Cambridge: Cambridge University Press, 2002.

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Schulze, Bert-Wolfgang, and Hans Triebel, eds. Symposium “Analysis on Manifolds with Singularities”, Breitenbrunn 1990. Wiesbaden: Vieweg+Teubner Verlag, 1992. http://dx.doi.org/10.1007/978-3-663-11577-9.

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Symposium "Analysis on Manifolds with Singularities," (1990 Breitenbrunn, Saxony, Germany). Symposium "Analysis on Manifolds with Singularities": Breitenbrunn, 1990. Stuttgart: Teubner, 1992.

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Unfolding CR singularities. Providence, R.I: American Mathematical Society, 2009.

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Bert-Wolfgang, Schulze, ed. Crack theory and edge singularities. Boston: Kluwer Academic Publishers, 2003.

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8

Katok, Anatole, Jean-Marie Strelcyn, François Ledrappier, and Feliks Przytycki. Invariant Manifolds, Entropy and Billiards; Smooth Maps with Singularities. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0099031.

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Jean-Marie, Strelcyn, ed. Invariant manifolds, entropy, and billiards: Smooth maps with singularities. Berlin: Springer-Verlag, 1986.

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Manifolds with singularities and the Adams-Novikov spectral sequence. Cambridge [England]: Cambridge University Press, 1992.

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Book chapters on the topic "Diffusions on manifolds with singularities"

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Pham, Frédéric. "Differentiable manifolds." In Singularities of integrals, 7–28. London: Springer London, 2011. http://dx.doi.org/10.1007/978-0-85729-603-0_1.

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Antonelli, P. L., and T. J. Zastawniak. "Diffusions on Finsler Manifolds." In The Theory of Finslerian Laplacians and Applications, 47–62. Dordrecht: Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-011-5282-2_4.

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Dong, Rui-Tao. "A BMO Bound for Eigenfunctions on Riemannian Manifolds." In Degenerate Diffusions, 71–76. New York, NY: Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4612-0885-3_4.

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Huang, Weiming, and Joseph Lipman. "Differential Invariants of Embeddings of Manifolds in Complex Spaces." In Singularities, 61–92. Basel: Birkhäuser Basel, 1998. http://dx.doi.org/10.1007/978-3-0348-8770-0_4.

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Malliavin, P. "Diffusions Et Geometrie Differentielle Globale." In Differential Operators on Manifolds, 207–79. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11114-3_4.

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Pham, Frédéric. "Homology and cohomology of manifolds." In Singularities of integrals, 29–53. London: Springer London, 2011. http://dx.doi.org/10.1007/978-0-85729-603-0_2.

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Stevens, Jan. "7. Deformations of compact manifolds." In Deformations of Singularities, 55–61. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-540-36464-1_8.

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Viehweg, Eckart. "Allowing Certain Singularities." In Quasi-projective Moduli for Polarized Manifolds, 239–76. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-79745-3_9.

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de Gregorio, Ignacio, and David Mond. "F-manifolds from Composed Functions." In Real and Complex Singularities, 187–99. Basel: Birkhäuser Basel, 2006. http://dx.doi.org/10.1007/978-3-7643-7776-2_13.

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Elworthy, David. "Geometric aspects of diffusions on manifolds." In Lecture Notes in Mathematics, 277–425. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0086183.

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Conference papers on the topic "Diffusions on manifolds with singularities"

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NEUMANN, WALTER D. "GRAPH 3-MANIFOLDS, SPLICE DIAGRAMS, SINGULARITIES." In Proceedings of the 2005 Marseille Singularity School and Conference. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812707499_0034.

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Staneva, Valentina, and Laurent Younes. "Learning Shape Trends: Parameter Estimation in Diffusions on Shape Manifolds." In 2017 IEEE Conference on Computer Vision and Pattern Recognition Workshops (CVPRW). IEEE, 2017. http://dx.doi.org/10.1109/cvprw.2017.101.

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Leon, J.-C., L. De Floriani, and F. Hetroy. "Classification of non-manifold singularities from transformations of 2-manifolds." In 2009 IEEE International Conference on Shape Modeling and Applications (SMI). IEEE, 2009. http://dx.doi.org/10.1109/smi.2009.5170146.

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Wu, Wen-tsun. "On generalized Chern classes and Chern numbers of irreducible complex algebraic varieties with arbitrary singularities." In Geometry and Topology of Manifolds. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2007. http://dx.doi.org/10.4064/bc76-0-12.

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Mu¨ller, Andreas. "How Likely is the Variety of Singularities of a Serial Manipulator a Smooth Manifold?" In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-28084.

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It is commonly assumed that the singularities of serial manpulators constitute generically smooth manifolds. This assumption has not been proved yet, nor is there an established notion of of genericity. In this paper two different notions of generic properties of forward kinematic mappings are discussed. Serial manipulators are classified according to the type of end-effector motion and feasible manipulator geometries. A sufficient condition for that generically singularities form locally smooth manifolds is presented. This condition admits to separately treat the individual classes. As an example it is shown that the singularities of 3-DOF manipulators form generically smooth manifolds.
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Saji, Kentaro. "Singularities of non-degenerate n-ruled (n+1)-manifolds in Euclidean space." In Geometric Singularity Theory. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2004. http://dx.doi.org/10.4064/bc65-0-14.

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Mu¨ller, Andreas. "On the Concept of Mobility Used in Robotics." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87524.

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This paper summarizes the concept of mobility used for holonomic and non-holonomic mechanisms. The mobility of mechanisms is considered from a geometric viewpoint starting with the variety generated by the constraint mapping as configuration space. While the local (finite) mobility is determined by the dimension of the configuration space, the differential mobility may be different. This is so for singular configurations, but also at regular configurations of underconstrained mechanisms. Overconstrained mechanisms are identified as those comprising manifolds of regular configurations that are critical points of the constraint mapping. The considerations include non-holonomic mechanisms. For such mechanisms the configuration space is the integral manifold of the kinematic constraints. Different types of singularities are discussed for non-holonomic mechanisms.
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