Relevant bibliographies by topics / Mathematical relativity

Academic literature on the topic 'Mathematical relativity'

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Published: 4 June 2021
Last updated: 29 January 2023

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Journal articles on the topic "Mathematical relativity"

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Cederbaum, Carla, Mihalis Dafermos, James Isenberg, and Hans Ringström. "Mathematical General Relativity." Oberwolfach Reports 15, no. 3 (August 26, 2019): 2157–251. http://dx.doi.org/10.4171/owr/2018/36.

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Dafermos, Mihalis, James Isenberg, and Hans Ringström. "Mathematical Aspects of General Relativity." Oberwolfach Reports 9, no. 3 (2012): 2269–333. http://dx.doi.org/10.4171/owr/2012/37.

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Dafermos, Mihalis, James Isenberg, and Hans Ringström. "Mathematical Aspects of General Relativity." Oberwolfach Reports 12, no. 3 (2015): 1867–935. http://dx.doi.org/10.4171/owr/2015/33.

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Chruściel, Piotr T., Gregory J. Galloway, and Daniel Pollack. "Mathematical general relativity: A sampler." Bulletin of the American Mathematical Society 47, no. 4 (2010): 567. http://dx.doi.org/10.1090/s0273-0979-2010-01304-5.

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Cederbaum, Carla, Mihalis Dafermos, James A. Isenberg, and Hans Ringström. "Mathematical Aspects of General Relativity." Oberwolfach Reports 18, no. 3 (November 25, 2022): 2157–267. http://dx.doi.org/10.4171/owr/2021/40.

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Hall, Graham. "Some remarks on mathematical general relativity theory." Filomat 29, no. 10 (2015): 2403–10. http://dx.doi.org/10.2298/fil1510403h.

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This paper gives a brief survey of the development of general relativity theory starting from Newtonian theory and Euclidean geometry and proceeding through to special relativity and finally to general relativity and relativistic cosmology.
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Pommaret, Jean-Francois. "The Mathematical Foundations of General Relativity Revisited." Journal of Modern Physics 04, no. 08 (2013): 223–39. http://dx.doi.org/10.4236/jmp.2013.48a022.

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Pereboom, Derk. "Mathematical expressibility, perceptual relativity, and secondary qualities." Studies in History and Philosophy of Science Part A 22, no. 1 (March 1991): 63–88. http://dx.doi.org/10.1016/0039-3681(91)90015-k.

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Andersson, Lars. "On the relation between mathematical and numerical relativity." Classical and Quantum Gravity 23, no. 16 (July 27, 2006): S307—S317. http://dx.doi.org/10.1088/0264-9381/23/16/s02.

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Gadre, Nitin Ramchandra. "Mathematical model II. Basic particle and special relativity." AIP Advances 1, no. 1 (March 2011): 012106. http://dx.doi.org/10.1063/1.3559461.

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Dissertations / Theses on the topic "Mathematical relativity"

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Norgren, Ofelia. "Mathematical Special Relativity." Thesis, Uppsala universitet, Matematiska institutionen, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-435242.

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Abdelfattah, Derhham. "General Relativity and penrose process." Master's thesis, University of Cape Town, 2016. http://hdl.handle.net/11427/28961.

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Sakovich, Anna. "A study of asymptotically hyperbolic manifolds in mathematical relativity." Doctoral thesis, KTH, Matematik (Avd.), 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-102874.

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This thesis consists of ve papers where certain problems arising in mathematical relativity are studied in the context of asymptotically hyperbolic manifolds. In Paper A we deal with constant mean curvature solutions of the Einstein-scalar field constraint equations on asymptotically hyperbolic manifolds. Conditions on the scalar field and its potential are given which lead to existence and non-existence results. In Paper B we construct non-constant mean curvature solutions of the constraint equations on asymptotically hyperbolic manifolds. Our approach consists in decreasing a certain exponent appearing in the equations, constructing solutions of these sub-critical equations and then letting the exponent tend to its true value. We prove that if a certain limit equation admits no non-trivial solution, then the set of solutions of the constraint equations is non empty and compact. W ealso give conditions ensuring that the limit equation admits no nontrivial solution. This is a joint work with Romain Gicquaud. In this Paper C we obtain Penrose type inequalities for asymptotically hyperbolic graphs. In certain cases we prove that equality is attained only by the anti-de Sitter Schwarzschild metric. This is a joint work with Mattias Dahl and Romain Gicquaud. In Paper D we construct a solution to the Jang equation on an asymptotically hyperbolic manifold with a certain asymptotic behaviour at infinity. In Paper E we study asymptotically hyperbolic manifolds which are also conformally hyperbolic outside a ball of fixed radius, and for which the positive mass theorem holds. For such manifolds we show that when the mass tends to zero the metric converges uniformly tot he hyperbolic metric. This is a joint work with Mattias Dahl and Romain Gicquaud.

QC 20120928

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Sbierski, Jan. "On the initial value problem in general relativity and wave propagation in black-hole spacetimes." Thesis, University of Cambridge, 2014. https://www.repository.cam.ac.uk/handle/1810/248837.

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The first part of this thesis is concerned with the question of global uniqueness of solutions to the initial value problem in general relativity. In 1969, Choquet-Bruhat and Geroch proved, that in the class of globally hyperbolic Cauchy developments, there is a unique maximal Cauchy development. The original proof, however, has the peculiar feature that it appeals to Zorn’s lemma in order to guarantee the existence of this maximal development; in particular, the proof is not constructive. In the first part of this thesis we give a proof of the above mentioned theorem that avoids the use of Zorn’s lemma. The second part of this thesis investigates the behaviour of so-called Gaussian beam solutions of the wave equation - highly oscillatory and localised solutions which travel, for some time, along null geodesics. The main result of this part of the thesis is a characterisation of the temporal behaviour of the energy of such Gaussian beams in terms of the underlying null geodesic. We conclude by giving applications of this result to black hole spacetimes. Recalling that the wave equation can be considered a “poor man’s” linearisation of the Einstein equations, these applications are of interest for a better understanding of the black hole stability conjecture, which states that the exterior of our explicit black hole solutions is stable to small perturbations, while the interior is expected to be unstable. The last part of the thesis is concerned with the wave equation in the interior of a black hole. In particular, we show that under certain conditions on the black hole parameters, waves that are compactly supported on the event horizon, have finite energy near the Cauchy horizon. This result is again motivated by the investigation of the conjectured instability of the interior of our explicit black hole solutions.
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Luo, Xianghui 1983. "Symmetries of Cauchy Horizons and Global Stability of Cosmological Models." Thesis, University of Oregon, 2011. http://hdl.handle.net/1794/11543.

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ix, 111 p.
This dissertation contains the results obtained from a study of two subjects in mathematical general relativity. The first part of this dissertation is about the existence of Killing symmetries in spacetimes containing a compact Cauchy horizon. We prove the existence of a nontrivial Killing symmetry in a large class of analytic cosmological spacetimes with a compact Cauchy horizon for any spacetime dimension. In doing so, we also remove the restrictive analyticity condition and obtain a generalization to the smooth case. The second part of the dissertation presents our results on the global stability problem for a class of cosmological models. We investigate the power law inflating cosmological models in the presence of electromagnetic fields. A stability result for such cosmological spacetimes is proved. This dissertation includes unpublished co-authored material.
Committee in charge: James Brau, Chair; James Isenberg, Advisor; Paul Csonka, Member; John Toner, Member; Peng Lu, Outside Member
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Reid, James Andrew. "Conformal holonomy and theoretical gravitational physics." Thesis, University of Aberdeen, 2014. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=215305.

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Conformal holonomy theory is the holonomy theory of the tractor connection on a conformal manifold. In this thesis, we present the first application of conformal holonomy theory to theoretical physics and determine the conformal holonomy groups/algebras of physically relevant spaces. After recalling some necessary background on conformal structures, tractor bundles and conformal holonomy theory in chapter 1, we begin in chapter 2 by discussing the role of conformal holonomy in the gauge-theoretic MacDowell-Mansouri formulation of general relativity. We show that the gauge algebra of this formulation is uniquely determined by the conformal structure of spacetime itself, in both Lorentzian and Riemannian metric signatures, through the conformal holonomy algebra. We then show that one may construct a MacDowell-Mansouri action functional for scale-invariant gravity, and we discuss a geometric interpretation for the scalar field therein. In chapter 3 we study a class of spacetimes relevant to Maldacena's AdS5=CFT4 correspondence in quantum gravity. It is well known that a Lie group coincidence lies at the heart of this correspondence: the proper isometry group of the bulk precisely matches the conformal group of the boundary. It has previously been proposed that the AdS5=CFT4 correspondence be extended to so-called Poincar e-Einstein spacetimes, which need not be as symmetric as anti-de Sitter space. We show that the conformal holonomy groups of the boundary and bulk furnish such a Lie group coincidence for 5-dimensional Poincar e-Einstein spacetimes in general. We completely characterise this boundary-bulk conformal holonomy matching for the Riemannian theory and present partial results for the Lorentzian theory. In chapter 4 we use the tools developed in the preceding chapters to further the classiification of the conformal holonomy groups of conformally Einstein spaces. Specifically, we determine the conformal holonomy groups of generic neutral signature conformally Einstein 4-manifolds subject to a condition on the conformal holonomy representation. Lastly, in chapter 5, we investigate the conformal holonomy reduction of the Fefferman conformal structures of residual twistor CR manifolds. A sufficient condition for reducible conformal holonomy is that the (Fefferman conformal structure of a) residual twistor CR manifold admit a parallel tractor. We show that this occurs if and only if the residual twistor CR manifold admits a Sasakian structure.
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Muir, Stuart. "A relativisitic, 3-dimensional smoothed particle hydrodynamics (SPH) algorithm and its applications." Monash University, School of Mathematical Sciences, 2003. http://arrow.monash.edu.au/hdl/1959.1/9513.

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Fama, Christopher J., and -. "Non-smooth differential geometry of pseudo-Riemannian manifolds: Boundary and geodesic structure of gravitational wave space-times in mathematical relativity." The Australian National University. School of Mathematical Sciences, 1998. http://thesis.anu.edu.au./public/adt-ANU20010907.161849.

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[No abstract supplied with this thesis - The first page (of three) of the Introduction follows] ¶ This thesis is largely concerned with the changing representations of 'boundary' or 'ideal' points of a pseudo-Riemannian manifold -- and our primary interest is in the space-times of general relativity. In particular, we are interested in the following question: What assumptions about the 'nature' of 'portions' of a certain 'ideal boundary' construction (essentially the 'abstract boundary' of Scott and Szekeres (1994)) allow us to define precisely the topological type of these 'portions', i.e., to show that different representations of this ideal boundary, corresponding to different embeddings of the manifold into others, have corresponding 'portions' that are homeomorphic? ¶ Certain topological properties of these 'portions' are preserved, even allowing for quite unpleasant properties of the metric (Fama and Scott 1995). These results are given in Appendix D, since they are not used elsewhere and, as well as representing the main portion of work undertaken under the supervision of Scott, which deserves recognition, may serve as an interesting example of the relative ease with which certain simple results about the abstract boundary can be obtained. ¶ An answer to a more precisely formulated version of this question appears very diffcult in general. However, we can give a rather complete answer in certain cases, where we dictate certain 'generalised regularity' requirements for our embeddings, but make no demands on the precise functional form of our metrics apart from these. For example, we get a complete answer to our question for abstract boundary sets which do not 'wiggle about' too much -- i.e., they satisfy a certain Lipschitz condition -- and through which the metric can be extended in a manner which is not required to be differentiable (C[superscript1]), but is continuous and non--degenerate. We allow similar freedoms on the interior of the manifold, thereby bringing gravitational wave space-times within our sphere of discussion. In fact, in the course of developing these results in progressively greater generality, we get, almost 'free', certain abilities to begin looking at geodesic structure on quite general pseudo-Riemannian manifolds. ¶ It is possible to delineate most of this work cleanly into two major parts. Firstly, there are results which use classical geometric constructs and can be given for the original abstract boundary construction, which requires differentiability of both manifolds and metrics, and which we summarise below. The second -- and significantly longer -- part involves extensions of those constructs and results to more general metrics.
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Muench, Uwe. "Studies in the physical foundations of gravitational theories /." free to MU campus, to others for purchase, 2002. http://wwwlib.umi.com/cr/mo/fullcit?p3060127.

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Schlue, Volker. "Linear waves on higher dimensional Schwarzschild black holes and Schwarzschild de Sitter spacetimes." Thesis, University of Cambridge, 2012. https://www.repository.cam.ac.uk/handle/1810/243640.

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I study linear waves on higher dimensional Schwarzschild black holes and Schwarzschild de Sitter spacetimes. In the first part of this thesis two decay results are proven for general finite energy solutions to the linear wave equation on higher dimensional Schwarzschild black holes. I establish uniform energy decay and improved interior first order energy decay in all dimensions with rates in accordance with the 3 + 1-dimensional case. The method of proof departs from earlier work on this problem. I apply and extend the new physical space approach to decay of Dafermos and Rodnianski. An integrated local energy decay estimate for the wave equation on higher dimensional Schwarzschild black holes is proven. In the second part of this thesis the global study of solutions to the linear wave equation on expanding de Sitter and Schwarzschild de Sitter spacetimes is initiated. I show that finite energy solutions to the initial value problem are globally bounded and have a limit on the future boundary that can be viewed as a function on the standard cylinder. Both problems are related to the Cauchy problem in General Relativity.
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Books on the topic "Mathematical relativity"

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Natário, José. An Introduction to Mathematical Relativity. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-65683-6.

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Boskoff, Wladimir-Georges, and Salvatore Capozziello. A Mathematical Journey to Relativity. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-47894-0.

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Mathematical problems of general relativity theory. Zu rich: European Mathematical Society, 2008.

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Das, Anadijiban. Special theory of relativity: A mathematical exposition. Berlin: Springer, 1993.

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Introductory special relativity. London: Taylor & Francis, 1991.

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Conference on Mathematical Relativity. (1988 Canberra, A.C.T.). Conference on Mathematical Relativity: Canberra, July 1988. [Canberra]: Centre for Mathematical Analysis, Australian National University, 1989.

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García-Parrado, Alfonso, Filipe C. Mena, Filipe Moura, and Estelita Vaz, eds. Progress in Mathematical Relativity, Gravitation and Cosmology. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-642-40157-2.

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Frauendiener, Jörg, Domenico Giulini, and Volker Perlick, eds. Analytical and Numerical Approaches to Mathematical Relativity. Berlin/Heidelberg: Springer-Verlag, 2006. http://dx.doi.org/10.1007/11550259.

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Frauendiener, Jörg, Domenico J. W. Giulini, and Volker Perlick, eds. Analytical and Numerical Approaches to Mathematical Relativity. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/b11550259.

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Esposito, Giampiero. Complex general relativity. Dordrecht: Kluwer Academic Publishers, 1995.

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Book chapters on the topic "Mathematical relativity"

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Mould, Richard A. "Mathematical Tools." In Basic Relativity, 91–112. New York, NY: Springer New York, 1994. http://dx.doi.org/10.1007/978-1-4612-4326-7_4.

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Tsamparlis, Michael. "Mathematical Part." In Special Relativity, 1–53. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-03837-2_1.

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Tsamparlis, Michael. "Mathematical Part." In Special Relativity, 1–55. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-27347-7_1.

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Krantz, Steven G., and Harold R. Parks. "Special Relativity." In A Mathematical Odyssey, 163–81. Boston, MA: Springer US, 2014. http://dx.doi.org/10.1007/978-1-4614-8939-9_7.

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Boskoff, Wladimir-Georges, and Salvatore Capozziello. "Special Relativity." In A Mathematical Journey to Relativity, 217–55. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-47894-0_8.

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Rau, René T., Daniel Weiskopf, and Hanns Ruder. "Special Relativity in Virtual Reality." In Mathematical Visualization, 269–79. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-662-03567-2_20.

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Günther, Helmut, and Volker Müller. "Mathematical Formalism of Special Relativity." In The Special Theory of Relativity, 149–233. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-7783-9_9.

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Asanov, G. S. "Primary Mathematical Definitions." In Finsler Geometry, Relativity and Gauge Theories, 19–46. Dordrecht: Springer Netherlands, 1985. http://dx.doi.org/10.1007/978-94-009-5329-1_2.

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Natário, José. "Mass in General Relativity." In An Introduction to Mathematical Relativity, 119–52. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-65683-6_6.

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Balakrishnan, V. "A Bit of Electromagnetism and Special Relativity." In Mathematical Physics, 137–62. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-39680-0_9.

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Conference papers on the topic "Mathematical relativity"

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CHRUŚCIEL, PIOTR T. "RECENT RESULTS IN MATHEMATICAL RELATIVITY." In Proceedings of the 17th International Conference. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701688_0005.

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Vaz, E. G. L. R. "Mathematical Properties of the Elasticity Difference Tensor." In A CENTURY OF RELATIVITY PHYSICS: ERE 2005; XXVIII Spanish Relativity Meeting. AIP, 2006. http://dx.doi.org/10.1063/1.2218255.

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CHRISTODOULOU, DEMETRIOS. "THE FORMATION OF BLACK HOLES IN GENERAL RELATIVITY." In XVIth International Congress on Mathematical Physics. WORLD SCIENTIFIC, 2010. http://dx.doi.org/10.1142/9789814304634_0002.

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Alcubierre, Miguel. "Brief Introduction to Numerical Relativity." In GRAVITATION AND COSMOLOGY: 2nd Mexican Meeting on Mathematical and Experimental Physics. AIP, 2005. http://dx.doi.org/10.1063/1.1900520.

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RINGSTRÖM, HANS. "On a wave map equation arising in general relativity." In XIVth International Congress on Mathematical Physics. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812704016_0031.

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KLAINERMAN, SERGIU. "RECENT RESULTS IN MATHEMATICAL GR." In Proceedings of the MG13 Meeting on General Relativity. WORLD SCIENTIFIC, 2015. http://dx.doi.org/10.1142/9789814623995_0006.

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BRANDES, JÜRGEN. "General Relativity Theory — Well Proven and Also Incomplete?" In Proceedings of the 8th Symposium Honoring Mathematical Physicist Jean-Pierre Vigier. WORLD SCIENTIFIC, 2013. http://dx.doi.org/10.1142/9789814504782_0013.

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Kremer, Gilberto M., Leonardo Dagdug, A. García-Perciante, A. Sandoval-Villalbazo, and L. S. García-Colín. "Relativistic Fluids in Special and General Relativity." In IV MEXICAN MEETING ON MATHEMATICAL AND EXPERIMENTAL PHYSICS: RELATIVISTIC FLUIDS AND BIOLOGICAL PHYSICS. AIP, 2010. http://dx.doi.org/10.1063/1.3533205.

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Horn, Martin Erik. "Translating cosmological special relativity into geometric algebra." In 9TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2012. AIP, 2012. http://dx.doi.org/10.1063/1.4765533.

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GIESE, ALBRECHT. "Relativity Based on Physical Processes Rather Than Space-Time." In Proceedings of the 8th Symposium Honoring Mathematical Physicist Jean-Pierre Vigier. WORLD SCIENTIFIC, 2013. http://dx.doi.org/10.1142/9789814504782_0015.

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Reports on the topic "Mathematical relativity"

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Saptsin, V., Володимир Миколайович Соловйов, and I. Stratychuk. Quantum econophysics – problems and new conceptions. КНУТД, 2012. http://dx.doi.org/10.31812/0564/1185.

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This article is dedicated to the econophysical analysis of conceptual fundamentals and mathematical apparatus of classical physics, relativity theory, non-relativistic and relativistic quantum mechanics. The historical and methodological aspects as well as the modern state of the problem of the socio-economic modeling are considered.
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Saptsin, Vladimir, and Володимир Миколайович Соловйов. Relativistic quantum econophysics – new paradigms in complex systems modelling. [б.в.], July 2009. http://dx.doi.org/10.31812/0564/1134.

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This work deals with the new, relativistic direction in quantum econophysics, within the bounds of which a change of the classical paradigms in mathematical modelling of socio-economic system is offered. Classical physics proceeds from the hypothesis that immediate values of all the physical quantities, characterizing system’s state, exist and can be accurately measured in principle. Non-relativistic quantum mechanics does not reject the existence of the immediate values of the classical physical quantities, nevertheless not each of them can be simultaneously measured (the uncertainty principle). Relativistic quantum mechanics rejects the existence of the immediate values of any physical quantity in principle, and consequently the notion of the system state, including the notion of the wave function, which becomes rigorously nondefinable. The task of this work consists in econophysical analysis of the conceptual fundamentals and mathematical apparatus of the classical physics, relativity theory, non-relativistic and relativistic quantum mechanics, subject to the historical, psychological and philosophical aspects and modern state of the socio-economic modeling problem. We have shown that actually and, virtually, a long time ago, new paradigms of modeling were accepted in the quantum theory, within the bounds of which the notion of the physical quantity operator becomes the primary fundamental conception(operator is a mathematical image of the procedure, the action), description of the system dynamics becomes discrete and approximate in its essence, prediction of the future, even in the rough, is actually impossible when setting aside the aftereffect i.e. the memory. In consideration of the analysis conducted in the work we suggest new paradigms of the economical-mathematical modeling.
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Clausen, Jay, Christopher Felt, Michael Musty, Vuong Truong, Susan Frankenstein, Anna Wagner, Rosa Affleck, Steven Peckham, and Christopher Williams. Modernizing environmental signature physics for target detection—Phase 3. Engineer Research and Development Center (U.S.), March 2022. http://dx.doi.org/10.21079/11681/43442.

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The present effort (Phase 3) builds on our previously published prior efforts (Phases 1 and 2), which examined methods of determining the probability of detection and false alarm rates using thermal infrared for buried object detection. Environmental phenomenological effects are often represented in weather forecasts in a relatively coarse, hourly resolution, which introduces concerns such as exclusion or misrepresentation of ephemera or lags in timing when using this data as an input for the Army’s Tactical Assault Kit software system. Additionally, the direct application of observed temperature data with weather model data may not be the best approach because metadata associated with the observations are not included. As a result, there is a need to explore mathematical methods such as Bayesian statistics to incorporate observations into models. To better address this concern, the initial analysis in Phase 2 data is expanded in this report to include (1) multivariate analyses for detecting objects in soil, (2) a moving box analysis of object visibility with alternative methods for converting FLIR radiance values to thermal temperature values, (3) a calibrated thermal model of soil temperature using thermal IR imagery, and (4) a simple classifier method for automating buried object detection.
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Heinz, Kevin, Itamar Glazer, Moshe Coll, Amanda Chau, and Andrew Chow. Use of multiple biological control agents for control of western flower thrips. United States Department of Agriculture, 2004. http://dx.doi.org/10.32747/2004.7613875.bard.

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The western flower thrips (WFT), Frankliniella occidentalis (Pergande), is a serious widespread pest of vegetable and ornamental crops worldwide. Chemical control for Frankliniella occidentalis (Pergande) (Thysanoptera: Thripidae) on floriculture or vegetable crops can be difficult because this pest has developed resistance to many insecticides and also tends to hide within flowers, buds, and apical meristems. Predatory bugs, predatory mites, and entomopathogenic nematodes are commercially available in both the US and Israel for control of WFT. Predatory bugs, such as Orius species, can suppress high WFT densities but have limited ability to attack thrips within confined plant parts. Predatory mites can reach more confined habitats than predatory bugs, but kill primarily first-instar larvae of thrips. Entomopathogenic nematodes can directly kill or sterilize most thrips stages, but have limited mobility and are vulnerable to desiccation in certain parts of the crop canopy. However, simultaneous use of two or more agents may provide both effective and cost efficient control of WFT through complimentary predation and/or parasitism. The general goal of our project was to evaluate whether suppression of WFT could be enhanced by inundative or inoculative releases of Orius predators with either predatory mites or entomopathogenic nematodes. Whether pest suppression is best when single or multiple biological control agents are used, is an issue of importance to the practice of biological control. For our investigations in Texas, we used Orius insidiosus(Say), the predatory mite, Amblyseius degeneransBerlese, and the predatory mite, Amblyseius swirskii(Athias-Henriot). In Israel, the research focused on Orius laevigatus (Fieber) and the entomopathogenic nematode, Steinernema felpiae. Our specific objectives were to: (1) quantify the spatial distribution and population growth of WFT and WFT natural enemies on greenhouse roses (Texas) and peppers (Israel), (2) assess interspecific interactions among WFT natural enemies, (3) measure WFT population suppression resulting from single or multiple species releases. Revisions to our project after the first year were: (1) use of A. swirskiiin place of A. degeneransfor the majority of our predatory mite and Orius studies, (2) use of S. felpiaein place of Thripinema nicklewoodi for all of the nematode and Orius studies. We utilized laboratory experiments, greenhouse studies, field trials and mathematical modeling to achieve our objectives. In greenhouse trials, we found that concurrent releases of A.degeneranswith O. insidiosusdid not improve control of F. occidentalis on cut roses over releases of only O. insidiosus. Suppression of WFT by augmentative releases A. swirskiialone was superior to augmentative releases of O. insidiosusalone and similar to concurrent releases of both predator species on cut roses. In laboratory studies, we discovered that O. insidiosusis a generalist predator that ‘switches’ to the most abundant prey and will kill significant numbers of A. swirskiior A. degeneransif WFTbecome relatively less abundant. Our findings indicate that intraguild interactions between Orius and Amblyseius species could hinder suppression of thrips populations and combinations of these natural enemies may not enhance biological control on certain crops. Intraguild interactions between S. felpiaeand O. laevigatus were found to be more complex than those between O. insidiosusand predatory mites. In laboratory studies, we found that S. felpiaecould infect and kill either adult or immature O. laevigatus. Although adult O. laevigatus tended to avoid areas infested by S. felpiaein Petri dish arenas, they did not show preference between healthy WFT and WFT infected with S. felpiaein choice tests. In field cage trials, suppression of WFT on sweet-pepper was similar in treatments with only O. laevigatus or both O. laevigatus and S. felpiae. Distribution and numbers of O. laevigatus on pepper plants also did not differ between cages with or without S. felpiae. Low survivorship of S. felpiaeafter foliar applications to sweet-pepper may explain, in part, the absence of effects in the field trials. Finally, we were interested in how differential predation on different developmental stages of WFT (Orius feeding on WFT nymphs inhabiting foliage and flowers, nematodes that attack prepupae and pupae in the soil) affects community dynamics. To better understand these interactions, we constructed a model based on Lotka-Volterra predator-prey theory and our simulations showed that differential predation, where predators tend to concentrate on one WFT stage contribute to system stability and permanence while predators that tend to mix different WFT stages reduce system stability and permanence.
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