Relevant bibliographies by topics / Abstract boundary

Academic literature on the topic 'Abstract boundary'

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Published: 4 June 2021
Last updated: 28 January 2023

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Journal articles on the topic "Abstract boundary"

1

Knox, Robert W. O'B. "Kaolinite influx within Paleocene/Eocene boundary strata of western Europe (Extended abstract)." Newsletters on Stratigraphy 36, no. 1 (January 15, 1998): 49–53. http://dx.doi.org/10.1127/nos/36/1998/49.

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Gür, H. "Relativistic Electromagnetic Boundary Conditions - Abstract." Journal of Electromagnetic Waves and Applications 13, no. 9 (January 1999): 1207–8. http://dx.doi.org/10.1163/156939399x01483.

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Palencia, C., and I. Alonso Mallo. "Abstract initial boundary value problems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 124, no. 5 (1994): 879–908. http://dx.doi.org/10.1017/s0308210500022393.

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We consider abstract initial boundary value problems in a spirit similar to that of the classical theory of linear semigroups. We assume that the solution u at time t is given by u(t) = S(t) ξ + V(t)g, where ξ and g are respectively the initial and boundary data and S(t) and V(t) are linear operators. We take as a departing point the functional equations satisfied by the propagators S and V. We discuss conditions under which a pair (S, V) describes the solution of an abstract differential initial boundary value problem. Several examples are provided of parabolic and hyperbolic problems that can be accommodated within the abstract theory. We study the backward Euler's method for the time integration of the problems considered.
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Prüss, Jan. "Maximal regularity for abstract parabolic problems with inhomogeneous boundary data in $L_p$-spaces." Mathematica Bohemica 127, no. 2 (2002): 311–27. http://dx.doi.org/10.21136/mb.2002.134160.

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Whale, Ben E., Michael J. S. L. Ashley, and Susan M. Scott. "Generalizations of the abstract boundary singularity theorem." Classical and Quantum Gravity 32, no. 13 (May 28, 2015): 135001. http://dx.doi.org/10.1088/0264-9381/32/13/135001.

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Ashley, Michael J. S. L. "The Stability of Abstract Boundary Essential Singularities." General Relativity and Gravitation 34, no. 10 (October 2002): 1625–35. http://dx.doi.org/10.1023/a:1020168106488.

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Shakhmurov, Veli. "Abstract elliptic equations with integral boundary conditons." Chinese Annals of Mathematics, Series B 37, no. 4 (June 29, 2016): 625–42. http://dx.doi.org/10.1007/s11401-016-0948-6.

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Mugnolo, Delio. "Abstract wave equations with acoustic boundary conditions." Mathematische Nachrichten 279, no. 3 (February 2006): 299–318. http://dx.doi.org/10.1002/mana.200310362.

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Hillion, P. "IMPEDANCE BOUNDARY CONDITIONS ON A CHIRAL FILM - Abstract." Journal of Electromagnetic Waves and Applications 18, no. 3 (January 2004): 373–74. http://dx.doi.org/10.1163/156939304323085766.

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Lampart, Jonas, and Julian Schmidt. "On Nelson-Type Hamiltonians and Abstract Boundary Conditions." Communications in Mathematical Physics 367, no. 2 (February 23, 2019): 629–63. http://dx.doi.org/10.1007/s00220-019-03294-x.

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Dissertations / Theses on the topic "Abstract boundary"

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Mugnolo, Delio. "Second order abstract initial-boundary value problems." [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=971647674.

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Ashley, Michael John Siew Leung, and ashley@gravity psu edu. "Singularity theorems and the abstract boundary construction." The Australian National University. Faculty of Science, 2002. http://thesis.anu.edu.au./public/adt-ANU20050209.165310.

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The abstract boundary construction of Scott and Szekeres has proven a practical classification scheme for boundary points of pseudo-Riemannian manifolds. It has also proved its utility in problems associated with the re-embedding of exact solutions containing directional singularities in space-time. Moreover it provides a model for singularities in space-time - essential singularities. However the literature has been devoid of abstract boundary results which have results of direct physical applicability.¶ This thesis presents several theorems on the existence of essential singularities in space-time and on how the abstract boundary allows definition of optimal em- beddings for depicting space-time. Firstly, a review of other boundary constructions for space-time is made with particular emphasis on the deficiencies they possess for describing singularities. The abstract boundary construction is then pedagogically defined and an overview of previous research provided.¶ We prove that strongly causal, maximally extended space-times possess essential singularities if and only if they possess incomplete causal geodesics. This result creates a link between the Hawking-Penrose incompleteness theorems and the existence of essential singularities. Using this result again together with the work of Beem on the stability of geodesic incompleteness it is possible to prove the stability of existence for essential singularities.¶ Invariant topological contact properties of abstract boundary points are presented for the first time and used to define partial cross sections, which are an generalization of the notion of embedding for boundary points. Partial cross sections are then used to define a model for an optimal embedding of space-time.¶ Finally we end with a presentation of the current research into the relationship between curvature singularities and the abstract boundary. This work proposes that the abstract boundary may provide the correct framework to prove curvature singularity theorems for General Relativity. This exciting development would culminate over 30 years of research into the physical conditions required for curvature singularities in space-time.
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Ganchev, Alexander Hristov. "Boundary value and Wiener-Hopf problems for abstract kinetic equations with nonregular collision operators." Diss., Virginia Polytechnic Institute and State University, 1986. http://hdl.handle.net/10919/50020.

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We study the linear abstract kinetic equation T𝜑(x)′=-A𝜑(x) in the half space {x≥0} with partial range boundary conditions. The function ψ takes values in a Hilbert space H, T is a self adjoint injective operator on H and A is an accretive operator. The first step in the analysis of this boundary value problem is to show that T⁻¹A generates a holomorphic bisemigroup. We prove two theorems about perturbation of bisemigroups that are interesting in their own right. The second step is to obtain a special decomposition of H which is equivalent to a Wiener-Hopf factorization. The accretivity of A is crucial in this step. When A is of the form "identity plus a compact operator", we work in the original Hilbert space. For unbounded A’s we consider weak solutions in a larger space HT, which has a natural Krein space structure. Using the Krein space geometry considerably simplifies the analysis of the question of unique solvability.
Ph. D.
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Hýl, Petr. "Slovinské národní divadlo v Lublani." Master's thesis, Vysoké učení technické v Brně. Fakulta architektury, 2009. http://www.nusl.cz/ntk/nusl-215582.

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Ashley, Michael. "Singularity theorems and the abstract boundary construction." Phd thesis, 2002. http://hdl.handle.net/1885/46055.

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The abstract boundary construction of Scott and Szekeres has proven a practical classification scheme for boundary points of pseudo-Riemannian manifolds. It has also proved its utility in problems associated with the re-embedding of exact solutions containing directional singularities in space-time. Moreover it provides a model for singularities in space-time - essential singularities. However the literature has been devoid of abstract boundary results which have results of direct physical applicability.¶ This thesis presents several theorems on the existence of essential singularities in space-time and on how the abstract boundary allows definition of optimal em- beddings for depicting space-time. Firstly, a review of other boundary constructions for space-time is made with particular emphasis on the deficiencies they possess for describing singularities. The abstract boundary construction is then pedagogically defined and an overview of previous research provided.¶ We prove that strongly causal, maximally extended space-times possess essential singularities if and only if they possess incomplete causal geodesics. This result creates a link between the Hawking-Penrose incompleteness theorems and the existence of essential singularities. Using this result again together with the work of Beem on the stability of geodesic incompleteness it is possible to prove the stability of existence for essential singularities.¶ Invariant topological contact properties of abstract boundary points are presented for the first time and used to define partial cross sections, which are an generalization of the notion of embedding for boundary points. Partial cross sections are then used to define a model for an optimal embedding of space-time.¶ Finally we end with a presentation of the current research into the relationship between curvature singularities and the abstract boundary. This work proposes that the abstract boundary may provide the correct framework to prove curvature singularity theorems for General Relativity. This exciting development would culminate over 30 years of research into the physical conditions required for curvature singularities in space-time.
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6

Mugnolo, Delio [Verfasser]. "Second order abstract initial-boundary value problems / vorgelegt von Delio Mugnolo." 2004. http://d-nb.info/971647674/34.

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Whale, Ben Edward. "Foundations of and Applications for the Abstract Boundary Construction for Space-Time." Phd thesis, 2010. http://hdl.handle.net/1885/49393.

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The original content of this thesis is comprised of three parts. First, we investigate the foundations of the Abstract Boundary. We start by presenting a one-to-one correspondence between the set of envelopments and a subset of the set of distances on our manifold. This correspondence allows us to define the Abstract Boundary in terms of mathematical structures defined on the manifold, rather than having to use structures additional to the manifold. We take the ideas used in the correspondence and generalise the Abstract Boundary to be applicable to any first countable topological space. Then, using the correspondence and the generalisation we give two alternative constructions for the Abstract Boundary. These new methods of construction allow us to bring many new tools to the analysis of the Abstract Boundary and thus enrich the subject and provide new avenues for research. Second, we discuss how the limiting behaviour of curves relates to the Abstract Boundary. We restrict our attention to the manifold itself and give a classification of the behaviour of curves via the number of limit points they possess. As an application of the classification we weaken the causality assumption of the Abstract Boundary singularity theorem. As an illustration of the problems that curves in a certain class of the classification can cause we give a definition of causality for Abstract Boundary points. In the process of doing so we generalise the distinguishing and strong causality conditions for the boundaries of envelopments and the Abstract Boundary itself. Third, we investigate the link between the Penrose-Hawking singularity theorems and the Krolak strong curvature condition. We review the singularity theorems and analyse their proofs to determine what can be said about the predicted incomplete geodesics. We see that the conclusions that can be made and the criteria for the Krolak strong curvature condition do not mesh easily. For this reason we present two necessary and sufficient conditions for a geodesic to satisfy the Krolak strong curvature condition, that provide a link between the conclusions and the Krolak condition. The result is that we need to investigate the limiting behaviour of jacobi fields along conjugate point free geodesics. Hence we provide a preliminary result showing that maximal extension of the metric places real constraints on the behaviour of parallelly propagated frames. This material provides some interesting results, and opens the door to a number of new problems.
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Barry, Richard Alexander. "Topological properties of the abstract boundary construction for general relativity and their application to space-time extensions." Phd thesis, 2014. http://hdl.handle.net/1885/155941.

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The abstract boundary construction of Scott and Szekeres provides a 'boundary' for any n-dimensional, paracompact, connected, Hausdorff, smooth space-time manifold. For a space-time, singularities and points at infinity may then be defined as objects within this boundary. The abstract boundary of a manifold is typically very large. Even so, one does not necessarily have to consider every abstract boundary point in order to provide detailed comments on the structure of the abstract boundary. Towards this end, this thesis develops a number of results concerning the topological contact properties of elements of the abstract boundary. For the first time two topologies, referred to as the attached point topology and the strongly attached point topology, are defined for a manifold together with its abstract boundary. We consider properties of these topologies related to the topological separation of abstract boundary points. In particular, it is demonstrated that the attached point topology is Hausdorff but the strongly attached point topology is not. Even so, it is observed that the strongly attached point topology loses Hausdorff separability in a way that provides further insight into the structure of the abstract boundary. We next consider how regular abstract boundary points of different space-time extensions are related to each other. We conjecture that if two regular abstract boundary points are in contact with each other, then, under certain physically reasonable conditions, such as strong causality holding, they must be equivalent. This has major implications when considering how to best present the geometrical features of a space-time within an embedding. In particular, this result says that the structure of the boundary through which space-time extensions are performed does not depend on the extension. Great progress is made in proving this result. It is rigorously shown that a significant amount of topological information is preserved around the boundary between different envelopments. In order to prove this result a number of reasonable restrictions were placed on the manifold. By considering special cases it is possible to weaken some of these restrictions. A form of the result is proven for isolated abstract boundary points using weakened assumptions. In the final component of the thesis we apply results developed in the previous sections to collections of abstract boundary points called partial cross sections. Partial cross sections allow one to simplify the appearance of the abstract boundary. In particular, they can be used to formulate optimal embeddings which, in essence, are a formal definition for an embedding of a manifold which clearly displays the important geometric features of that manifold. Refined definitions of partial cross sections and optimal embeddings are presented which incorporate the insights gained regarding the contact properties of abstract boundary points. In particular, optimal presentations are defined for the first time. These objects generalise the notion of an optimal embedding of a space-time to include those space-times which require more then one embedding in order to reveal its geometric structure.
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(8774624), Guojun Han. "AURORAMAP: A BOUNDARY-HOMOGRAPHIC VISUALIZATION FOR MAPPING MULTIVARIATE 2D SPATIAL DISTRIBUTIONS." Thesis, 2020.

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Visualizing multidimensional spatial data is an essential visual analysis strategy, it helps us interpret and communicate how different variables correlate to geographical information. In this study, we proposed an abstract contextual visualization that encodes data on the boundaries of spatial distributions and developed a new algorithm, AuroraMap. AuroraMap projects the spatial data to the boundaries of the distributions and color-encodes the densities continuously. We further conducted the user experiments, and the results show users can detect the relative locations and scopes of the clusters. Furthermore, users can quantitatively determine the peak value of each cluster’s density. The method provides three contributions: (1) freeing up and saving the graphical visualization space; (2) assisting the users to quantitatively estimate the clusters inside distributions; (3) facilitating the visual comparisons for multiple and multivariate spatial distributions. In the end, we demonstrated two applications with real-world religious infrastructural data by AuroraMap to visualize geospatial data within complex boundaries and compare multiple variables in one graph.

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Rieger, Christian. "Sampling Inequalities and Applications." Doctoral thesis, 2008. http://hdl.handle.net/11858/00-1735-0000-0006-B3B9-0.

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Books on the topic "Abstract boundary"

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Mee, C. V. M. van der and Protopopescu Vladimir, eds. Boundary value problems in abstract kinetic theory. Basel: Birkhäuser Verlag, 1987.

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Greenberg, William, Cornelis van der Mee, and Vladimir Protopopescu. Boundary Value Problems in Abstract Kinetic Theory. Basel: Birkhäuser Basel, 1987. http://dx.doi.org/10.1007/978-3-0348-5478-8.

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Pan-Lithoprobe, Workshop (2nd 2000 Banff Canada). Where crust meets mantle : lithoprobe perspectives on the continental crust-mantle boundary--, or, --The Moho, 90 years old : abstract volume. [S.l: s.n., 2000.

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Workshop on Boundary Layer Models in Short Range Weather Forecasting (1986 De Bilt, Utrecht, Netherlands). Report of the Workshop on Boundary Layer Models in Short Range Weather Forecasting, including the abstract of all the presentations during the workshop (De Bilt, The Netherlands, 10-12 March, 1986). De Bilt: Koninklijk Nederlands Meteorologisch Instituut, 1986.

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Canadian Meteorological and Oceanographic Society. Congress. Programme with abstracts. [Newfoundland]: Memorial University of Newfoundland, 1987.

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Akademii͡a︡ nauk SSSR. Sibirskoe otdelenie., ed. The Fourth International Conference on Boundary and Interior Layers: Computational and asymptotic methods : abstracts. Novosibirsk: USSR Academy of Sciences, Siberian Branch, 1986.

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Moore, Graham. Wet end chemistry strategies: A literature review. 2nd ed. Leatherhead, Surrey: Pira International, 1998.

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Moore, Graham. Wet end chemistry strategies: A literature review. Leatherhead, Surrey: Pira International, 1992.

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International Symposium for the Advancement of Boundary Layer Remote Sensing (13th 2006 Garmisch-Partenkirchen, Germany). International Symposium for the Advancement of Boundary Layer Remote Sensing: Garmisch-Partenkirchen, Germany, July 18-July 20, 2006 : extended abstracts. Edited by Emeis Stefan and Forschungszentrum Karlsruhe. Karlsruhe, [Germany]: Forschungszentrum Karlsruhe, 2006.

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Austria) RECCCE Workshop (2009 Bad Gams. Rapid environmental/climate changes and catastrophic events in late Cretaceous and Early Pleogene: RECCCE Workshop : IGCP 555 European Group Meeting : abstracts and excursion guide, April 25th-28th, 2009, Gams, Austria. Edited by Wagreich Michael, IGCP 555 (Project). European Group Meeting, Fonds zur Förderung der Wissenschaftlichen Forschung (Austria), and Geologische Bundesanstalt (Austria : 1945- ). Wien: Geological Survey of Austria, 2009.

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Book chapters on the topic "Abstract boundary"

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Agarwal, Ravi P., and Patricia J. Y. Wong. "Boundary Value Problems in Abstract Spaces." In Advanced Topics in Difference Equations, 464–70. Dordrecht: Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-015-8899-7_37.

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Kovalevsky, Vladimir. "Boundary Presentation Using Abstract Cell Complexes." In Image Processing with Cellular Topology, 7–16. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-5772-6_2.

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Krabs, W. "On abstract boundary control problems for vibrations." In Modelling and Optimization of Distributed Parameter Systems Applications to engineering, 139–48. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-0-387-34922-0_13.

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Greenberg, William, Cornelis van der Mee, and Vladimir Protopopescu. "Elements of Linear Kinetic Theory." In Boundary Value Problems in Abstract Kinetic Theory, 1–22. Basel: Birkhäuser Basel, 1987. http://dx.doi.org/10.1007/978-3-0348-5478-8_1.

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Greenberg, William, Cornelis van der Mee, and Vladimir Protopopescu. "Indefinite Sturm-Liouville Problems." In Boundary Value Problems in Abstract Kinetic Theory, 331–64. Basel: Birkhäuser Basel, 1987. http://dx.doi.org/10.1007/978-3-0348-5478-8_10.

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Greenberg, William, Cornelis van der Mee, and Vladimir Protopopescu. "Time Dependent Kinetic Equations: Method of Characteristics." In Boundary Value Problems in Abstract Kinetic Theory, 365–403. Basel: Birkhäuser Basel, 1987. http://dx.doi.org/10.1007/978-3-0348-5478-8_11.

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Greenberg, William, Cornelis van der Mee, and Vladimir Protopopescu. "Time Dependent Kinetic Equations: Semigroup Approach." In Boundary Value Problems in Abstract Kinetic Theory, 404–39. Basel: Birkhäuser Basel, 1987. http://dx.doi.org/10.1007/978-3-0348-5478-8_12.

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Greenberg, William, Cornelis van der Mee, and Vladimir Protopopescu. "Applications of the Initial Value Problem." In Boundary Value Problems in Abstract Kinetic Theory, 440–79. Basel: Birkhäuser Basel, 1987. http://dx.doi.org/10.1007/978-3-0348-5478-8_13.

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Greenberg, William, Cornelis van der Mee, and Vladimir Protopopescu. "Strictly Dissipative Kinetic Models." In Boundary Value Problems in Abstract Kinetic Theory, 23–54. Basel: Birkhäuser Basel, 1987. http://dx.doi.org/10.1007/978-3-0348-5478-8_2.

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Greenberg, William, Cornelis van der Mee, and Vladimir Protopopescu. "Conservative Kinetic Models." In Boundary Value Problems in Abstract Kinetic Theory, 55–84. Basel: Birkhäuser Basel, 1987. http://dx.doi.org/10.1007/978-3-0348-5478-8_3.

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Conference papers on the topic "Abstract boundary"

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Piasecki, Tomasz. "Steady compressible Oseen flow with slip boundary conditions." In Nonlocal and Abstract Parabolic Equations and their Applications. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2009. http://dx.doi.org/10.4064/bc86-0-16.

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Inger, George. "Boundary Layer/Shock Interaction with Wall Slip Extended Abstract." In 16th AIAA/DLR/DGLR International Space Planes and Hypersonic Systems and Technologies Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2009. http://dx.doi.org/10.2514/6.2009-7200.

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Gusev, M. I. "Computing the reachable set boundary for an abstract control problem." In APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 10th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’18. Author(s), 2018. http://dx.doi.org/10.1063/1.5064893.

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Gear, C. W., E. Chiavazzo, and I. G. Kevrekidis. "Manifolds defined by points: Parameterizing and boundary detection (extended abstract)." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2015 (ICNAAM 2015). Author(s), 2016. http://dx.doi.org/10.1063/1.4951749.

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Tiselj, Iztok, Elena Pogrebnyak, Albert Mosyak, and Gad Hetsroni. "Abstract of "NUMERICAL STUDY OF THERMAL STREAK SPACING IN TURBULENT BOUNDARY LAYER WITH CONSTANT HEAT-FLUX BOUNDARY CONDITION"." In Thermal Sciences 2000. Proceedings of the International Thermal Science Seminar Bled. Connecticut: Begellhouse, 2000. http://dx.doi.org/10.1615/ichmt.2000.thersieprocvol2.320.

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Hansen, Scott W., and A. Ozkan Ozer. "Exact boundary controllability of an abstract Mead-Marcus sandwich beam model." In 2010 49th IEEE Conference on Decision and Control (CDC). IEEE, 2010. http://dx.doi.org/10.1109/cdc.2010.5717319.

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Demir, Huseyin. "Abstract of "THERMAL CONVECTION OF VISCOELASTIC FLUID WITH BIOT BOUNDARY CONDUCTION"." In Thermal Sciences 2000. Proceedings of the International Thermal Science Seminar Bled. Connecticut: Begellhouse, 2000. http://dx.doi.org/10.1615/ichmt.2000.thersieprocvol2.900.

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Garcke, Harald, Kazuo Ito, and Yoshihito Kohsaka. "Stability analysis of phase boundary motion by surface diffusion with triple junction." In Nonlocal and Abstract Parabolic Equations and their Applications. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2009. http://dx.doi.org/10.4064/bc86-0-5.

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Sai Sundara Krishnan, G., and N. Vijaya. "Algorithm on tracing the boundary of medical images using abstract cellular complex." In 2012 International Conference on Machine Vision and Image Processing (MVIP). IEEE, 2012. http://dx.doi.org/10.1109/mvip.2012.6428780.

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Iftime, O. V., and T. C. Ionescu. "On an approximation with prescribed zeros of SISO abstract boundary control systems." In 2013 European Control Conference (ECC). IEEE, 2013. http://dx.doi.org/10.23919/ecc.2013.6669440.

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