Academic literature on the topic 'Splitting theorem'

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Journal articles on the topic "Splitting theorem"

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Anderson, Michael T. "splitting theorem." Duke Mathematical Journal 68, no. 1 (October 1992): 67–82. http://dx.doi.org/10.1215/s0012-7094-92-06803-7.

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Camillo, Victor. "On Zimmermann-Huisgen's Splitting Theorem." Proceedings of the American Mathematical Society 94, no. 2 (June 1985): 206. http://dx.doi.org/10.2307/2045375.

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Wu, Guoqiang. "Splitting theorem for Ricci soliton." Proceedings of the American Mathematical Society 149, no. 8 (May 18, 2021): 3575–81. http://dx.doi.org/10.1090/proc/15466.

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Let ( M , g , f ) (M, g, f) be a gradient Ricci soliton ∇ 2 f + R i c = λ g \nabla ^2 f+Ric=\lambda g with λ ∈ { 1 2 , 0 , − 1 2 } \lambda \in \{\frac {1}{2}, 0, -\frac {1}{2}\} . Suppose there is a geodesic line γ : ( − ∞ , ∞ ) → M \gamma : (-\infty , \infty )\rightarrow M satisfying lim inf t → ∞ ∫ 0 t R i c ( γ ′ ( s ) , γ ′ ( s ) ) d s + lim inf t → − ∞ ∫ t 0 R i c ( γ ′ ( s ) , γ ′ ( s ) ) d s ≥ 0 , \begin{eqnarray*} \liminf _{t\rightarrow \infty }\int _0^{t}Ric(\gamma ’(s), \gamma ’(s))ds +\liminf _{t\rightarrow -\infty }\int _{t}^{0}Ric(\gamma ’(s), \gamma ’(s))ds \geq 0, \end{eqnarray*} then ( M , g , f ) (M, g, f) splits off a line isometrically.
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Croke, Christopher B., and Bruce Kleiner. "A warped product splitting theorem." Duke Mathematical Journal 67, no. 3 (September 1992): 571–74. http://dx.doi.org/10.1215/s0012-7094-92-06723-8.

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Lempp, Steffen, and Sui Yuefei. "An extended Lachlan splitting theorem." Annals of Pure and Applied Logic 79, no. 1 (May 1996): 53–59. http://dx.doi.org/10.1016/0168-0072(95)00039-9.

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Covolo, Tiffany, Janusz Grabowski, and Norbert Poncin. "Splitting theorem for Z2n-supermanifolds." Journal of Geometry and Physics 110 (December 2016): 393–401. http://dx.doi.org/10.1016/j.geomphys.2016.09.006.

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Borzellino, Joseph E., and Shun-Hui Zhu. "The splitting theorem for orbifolds." Illinois Journal of Mathematics 38, no. 4 (December 1994): 679–91. http://dx.doi.org/10.1215/ijm/1256060999.

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Camillo, Victor. "On Zimmermann-Huisgen’s splitting theorem." Proceedings of the American Mathematical Society 94, no. 2 (February 1, 1985): 206. http://dx.doi.org/10.1090/s0002-9939-1985-0784163-6.

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Szigeti, Zoltán. "On the local splitting theorem." Electronic Notes in Discrete Mathematics 19 (June 2005): 57–61. http://dx.doi.org/10.1016/j.endm.2005.05.009.

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Li, Chong, Shujie Li, and Jiaquan Liu. "Splitting theorem, Poincaré–Hopf theorem and jumping nonlinear problems." Journal of Functional Analysis 221, no. 2 (April 2005): 439–55. http://dx.doi.org/10.1016/j.jfa.2004.09.010.

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Dissertations / Theses on the topic "Splitting theorem"

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Krishtopenko, Sergey. "Spin splitting and collective effects in InAs/AlSb quantum well heterostructures." Toulouse 3, 2011. http://thesesups.ups-tlse.fr/1459/.

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Les travaux de cette thèse, essentiellement théorique, concernent l'étude des phénomènes dépendants du spin, à un électron et à n-corps, dans les puits quantiques (PQ) de semiconducteurs (SC) à faible gap InAs/AlSb. Les résultats obtenus permettent de prévoir de nouveaux effets physiques, ils sont comparés aux résultats expérimentaux existants. L'asymétrie du champ électrique aux interfaces InAs/AlSb est étudiée expérimentalement et théoriquement, son effet sur le spectre d'énergie des sous bandes électriques est mis en évidence. La possibilité de contrôler optiquement ce champ électrique, et par là le clivage de spin par effet Rashba sous champ magnétique nul, est démontrée. La prise en compte des interactions e-e sur les niveaux de Landau des quasi-particules ainsi que sur la densité d'états au niveau de Fermi est réalisée dans ce système pour la première fois. Le calcul théorique de l'exaltation du facteur g par échange dans les puits quantiques à faible gap est développé. Le calcul permet de prédire l'évolution du facteur g "magnéto-optique" dans les hétérostructures InAs/AlSb déterminé par résonance de spin, il met en évidence la violation du théorème de Larmor dans les hétérostructures à base de SC à faible gap. L'étude théorique de la résonance cyclotron, en régime quantique, d'un gaz bidimensionnel d'électrons de haute mobilité démontre aussi la violation du théorème de Kohn dans les hétérostructures InAs/AlSb. Les résultats obtenus dans ce travail de thèse apportent des informations utiles pour le "design" et la mise au point de nouveaux dispositifs électroniques ou optoélectroniques basés sur des hétérostructures InAs/AlSb
The Thesis is devoted to the study of "single-particle" and "many-body" spin-related phenomena in narrow-gap InAs/AlSb quantum well (QW) heterostructures. The scientific significance of the results obtained consists in the discovering and prediction of new physical effects. The asymmetry of the built-in electric field in InAs/AlSb QW heterostructures has been probed both experimentally and theoretically and its effect on the electron energy spectrum splitting in electric subbands is demonstrated. A principle possibility to control by optical means the "built-in" electric field and the Rashba spin splitting in zero magnetic field is exhibited. The theoretical investigation into e-e interaction effect on quasiparticle Landau levels and density-of-states at the Fermi level is undertaken for the first time. Theory of the exchange enhancement of quasiparticle g-factor in narrow gap QW heterostructures is developed in the Thesis. Calculation results on the "magnetooptical" g-factor in InAs/AlSb heterostructure measured in electron spin resonance are the first demonstration of Larmor theorem violation in narrow gap QW heterostructures. Cyclotron resonance study in the samples with high mobility 2D electron gas in quantizing magnetic fields provides evidences of Kohn theorem violation in InAs/AlSb heterostructures. The results obtained in the Thesis can be utilized at the designing new electronic and optoelectronic units as well the spintronic devices based on InAs/AlSb heterostructures
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COLOMBO, GIULIO. "GLOBAL GRADIENT BOUNDS FOR SOLUTIONS OF PRESCRIBED MEAN CURVATURE EQUATIONS ON RIEMANNIAN MANIFOLDS." Doctoral thesis, Università degli Studi di Milano, 2021. http://hdl.handle.net/2434/813095.

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This thesis is concerned with the study of qualitative properties of solutions of the minimal surface equation and of a class of prescribed mean curvature equations on complete Riemannian manifolds. We derive global gradient bounds for non-negative solutions of such equations on manifolds satisfying a uniform Ricci lower bound and we obtain Liouville-type theorems and other rigidity results on Riemannian manifolds with non-negative Ricci curvature. The proof of the aforementioned global gradient bounds for non-negative solutions u is based on the application of the maximum principle to an elliptic differential inequality satisfied by a suitable auxiliary function z=f(u,|Du|), in the spirit of Bernstein’s method of a priori estimates for nonlinear PDEs and of Yau’s proof of global gradient bounds for harmonic functions on complete Riemannian manifolds. The particular choice of the auxiliary function z parallels the one in Korevaar’s proof of a priori gradient estimates for the prescribed mean curvature equation in Euclidean space. The rigidity results obtained in the last part of the thesis include a Liouville theorem for positive solutions of the minimal surface equation on complete Riemannian manifolds with non-negative Ricci curvature, a splitting theorem for complete parabolic manifolds of non-negative sectional curvature supporting non-constant solutions with linear growth of the minimal surface equation, and a splitting theorem for domains of complete parabolic manifolds with non-negative Ricci curvature supporting non-constant solutions of overdetermined problems involving the mean curvature operator.
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Batista, Alex de Moura. "Sobre um Sistema do tipo Schrödinger-Poisson." Universidade Federal da Paraí­ba, 2012. http://tede.biblioteca.ufpb.br:8080/handle/tede/7369.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
In this dissertation, we study the existence of two types of non-negative weak solutions for a class of problems of Schrodinger-Poisson type. This kind of problem models, for example, several physical phenomena in quantum mechanics. Initially, by minimization arguments, Splitting Lemma and the Variational Principle of Ekeland we find a weak solution that minimizes the minimum energy level associated to the variety of Nehari N. This is the so-called ground state solution. Afterwards we will find, by using the Linking Theorem, a strictly positive weak solution which is not a ground state solution: the so-called bound state solution.
Nesta dissertação, estudaremos a existência de dois tipos de soluções fracas não negativas para uma classe de problemas do tipo Schrödinger-Poisson, os quais modelam fenômenos físicos, por exemplo, em Mecânica Quântica. Inicialmente, encontraremos através de argumentos de minimização, do Lema Splitting e do Princípio Variacional de Ekeland, uma solução fraca que minimiza o nível de energia mínima associado a variedade de Nehari N. Tal solução é denominada do tipo ground state. Em seguida, encontraremos através do Teorema de Linking, uma solução fraca estritamente positiva que não é do tipo ground state. Tal solução é denominada do tipo bound state.
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吳潔貞 and Kit-ching Betty Ng. "Correlation effects in crystal field splitting." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1986. http://hub.hku.hk/bib/B31230714.

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Ng, Kit-ching Betty. "Correlation effects in crystal field splitting /." [Hong Kong : University of Hong Kong], 1986. http://sunzi.lib.hku.hk/hkuto/record.jsp?B12323342.

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Cavalcante, Marcius Petrúcio de Almeida. "Teorema de Decomposição de Cheeger-Gromoll." Universidade Federal de Alagoas, 2007. http://repositorio.ufal.br/handle/riufal/1020.

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We demonstrate the Splitting Theorem due to Cheeger and Gromoll, which ensures that a complete Riemannian n-manifold which has nonnegative Ricci curvature and a line, can be split isometrically into the Riemannian product of real with a (n-1 )- manifold.
Conselho Nacional de Desenvolvimento Científico e Tecnológico
Demonstramos o Teorema de Decomposição de Cheeger-Gromoll, o qual garante que uma variedade Riemanniana completa ndimensional, com curvatura de Ricci não-negativa, que possui uma linha, pode ser decomposta isometricamente num produto Riemanniano de uma variedade (n-1 )-dimensional com o conjunto dos reais.
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Ura, Hiroyuki. "Multiple feature-checking : a theory of grammatical function splitting." Thesis, Massachusetts Institute of Technology, 1995. http://hdl.handle.net/1721.1/11238.

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Li, Xinxin. "Some operator splitting methods for convex optimization." HKBU Institutional Repository, 2014. https://repository.hkbu.edu.hk/etd_oa/43.

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Many applications arising in various areas can be well modeled as convex optimization models with separable objective functions and linear coupling constraints. Such areas include signal processing, image processing, statistical learning, wireless networks, etc. If these well-structured convex models are treated as generic models and their separable structures are ignored in algorithmic design, then it is hard to effectively exploit the favorable properties that the objective functions possibly have. Therefore, some operator splitting methods have regained much attention from different areas for solving convex optimization models with separable structures in different contexts. In this thesis, some new operator splitting methods are proposed for convex optimiza- tion models with separable structures. We first propose combining the alternating direction method of multiplier with the logarithmic-quadratic proximal regulariza- tion for a separable monotone variational inequality with positive orthant constraints and propose a new operator splitting method. Then, we propose a proximal version of the strictly contractive Peaceman-Rachford splitting method, which was recently proposed for the convex minimization model with linear constraints and an objective function in form of the sum of two functions without coupled variables. After that, an operator splitting method suitable for parallel computation is proposed for a convex model whose objective function is the sum of three functions. For the new algorithms, we establish their convergence and estimate their convergence rates measured by the iteration complexity. We also apply the new algorithms to solve some applications arising in the image processing area; and report some preliminary numerical results. Last, we will discuss a particular video processing application and propose a series of new models for background extraction in different scenarios; to which some of the new methods are applicable. Keywords: Convex optimization, Operator splitting method, Alternating direction method of multipliers, Peaceman-Rachford splitting method, Image processing
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Dierolf, Bernhard [Verfasser], and Leonhard [Akademischer Betreuer] Frerick. "Splitting theory for PLH spaces / Bernhard Dierolf ; Betreuer: Leonhard Frerick." Trier : Universität Trier, 2014. http://d-nb.info/1197700307/34.

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Seidel, Markus. "Über die Splitting-Eigenschaft der Approximationszahlen von Matrix-Folgen: l1-Theorie." Master's thesis, Universitätsbibliothek Chemnitz, 2007. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200700129.

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In dieser Arbeit wird das asymptotische Verhalten der Approximationszahlen für Operatorfolgen aus einer speziellen Klasse von Banachalgebren untersucht. Es werden bemerkenswerte Eigenschaften der Folgen und der Approximationszahlen ihrer Operatoren gezeigt, darunter die so genannte splitting-Eigenschaft. Ein typisches Beispiel solcher Operatorfolgen stellen die Finite Sections von Toeplitzoperatoren dar, die exemplarisch behandelt werden. Dabei werden hier auch die Folgenräume l1 und l-unendlich betrachtet.
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Books on the topic "Splitting theorem"

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Lewis, L. G. Splitting theorems for certain equivariant spectra. Providence, R.I: American Mathematical Society, 2000.

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Morton, Alan Q. Splitting the atom. London: Evans, 2008.

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Agnes, Havasiy, ed. Operator splittings and their applications. Hauppauge, NY: Nova Science Publishers, 2009.

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Institute for Computer Applications in Science and Engineering., ed. Gas-kinetic theory based flux splitting method for ideal magnetohydrodynamics. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1998.

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Institute for Computer Applications in Science and Engineering., ed. Gas-kinetic theory based flux splitting method for ideal magnetohydrodynamics. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1998.

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Institute for Computer Applications in Science and Engineering., ed. Gas-kinetic theory based flux splitting method for ideal magnetohydrodynamics. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1998.

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Institute for Computer Applications in Science and Engineering., ed. Gas-kinetic theory based flux splitting method for ideal magnetohydrodynamics. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1998.

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Patrick, Le Tallec, ed. Augmented Lagrangian and operator-splitting methods in nonlinear mechanics. Philadelphia: Society for Industrial and Applied Mathematics, 1989.

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Lui, Shiu-Hong. Entropy analysis of kinetic flux vector splitting schemes for the compressible Euler equations. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1999.

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United States. National Aeronautics and Space Administration., ed. Effective control of computationally simulated wing rock in subsonic flow. [Washington, DC: National Aeronautics and Space Administration, 1997.

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Book chapters on the topic "Splitting theorem"

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Rutkowski, Leszek, Maciej Jaworski, and Piotr Duda. "Splitting Criteria Based on the McDiarmid’s Theorem." In Studies in Big Data, 51–62. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-13962-9_4.

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Beem, John K., Paul E. Ehrlich, Steen Markvorsen, and Gregory J. Galloway. "A Toponogov splitting theorem for Lorentzian manifolds." In Lecture Notes in Mathematics, 1–13. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/bfb0075081.

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Baaz, Matthias, and Alexander Leitsch. "Strong splitting rules in automated theorem proving." In Lecture Notes in Computer Science, 424–25. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/3-540-51517-8_147.

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Khanduja, Sudesh Kaur. "Splitting of Rational Primes and Dedekind’s Theorem." In UNITEXT, 71–86. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-16-9150-8_4.

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Khanduja, Sudesh Kaur. "Splitting of Rational Primes and Dedekind’s Theorem." In UNITEXT, 71–86. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-16-9150-8_4.

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Martínez-Legaz, Juan Enrique, Dominikus Noll, and Wilfredo Sosa. "Non-polyhedral Extensions of the Frank and Wolfe Theorem." In Splitting Algorithms, Modern Operator Theory, and Applications, 309–29. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-25939-6_12.

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Li, Angsheng. "The Low Splitting Theorem in the Difference Hierarchy." In New Computational Paradigms, 287–96. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11494645_35.

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Barthel, Tobias. "A Short Introduction to the Telescope and Chromatic Splitting Conjectures." In Bousfield Classes and Ohkawa's Theorem, 261–73. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-1588-0_9.

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Bréhier, Charles-Edouard, Ludovic Goudenège, and Loïc Tudela. "Central Limit Theorem for Adaptive Multilevel Splitting Estimators in an Idealized Setting." In Springer Proceedings in Mathematics & Statistics, 245–60. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-33507-0_10.

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Ohta, Shin-ichi. "Splitting Theorems." In Springer Monographs in Mathematics, 257–67. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-80650-7_17.

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Conference papers on the topic "Splitting theorem"

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Fofana, M. S. "A Unified Framework for the Study of Periodic Solutions of Nonlinear Delay Differential Equations." In ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/vib-21617.

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Abstract Periodic solutions of delay differential equations (DDEs) splitting into stable and unstable branches are examined in an infinite-dimensional space for fixed and multiple time delays. The center manifold theorem and the classical Hopf bifurcation theorem for the study of periodic solutions of ordinary differential equations (ODEs) are employed to reduce the infinite-dimensional character of the DDEs to finite-dimensional ODEs. Using integral averaging method, the vector field of the ODEs is converted and averaged into amplitude a and phase φ relations. From these relations bifurcation equations of the form ℑ(a, φ) = 0 for the solution branches are derived.
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Sun, Yazhen, Jiemin Liu, and Tianqing Yu. "Coupling Analysis of Fracture Mechanics and Damage Mechanics for Fiber-Reinforced Asphalt Concrete Pavement." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-13983.

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The initial damage and fracture zone are determined by the approach of coupling analysis of fracture mechanics and damage mechanics. An optimum fiber content of 0.2% in the asphalt concrete is proposed in comparison of the results obtained from composite theory with that obtained from the splitting tests. Crack growth with number of load cycles and fiber mass fraction of asphalt concrete pavement in which an initial surface crack of 4 cm length is included under cyclic temperature loading (-15°C) is simulated using damage mechanics theorem. By computing fatigue life, a new type of fiber-reinforced asphalt concrete pavement is developed.
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Schleimer, Saul. "Waldhausen's Theorem." In Heegaard splittings of 3--manifolds. Mathematical Sciences Publishers, 2007. http://dx.doi.org/10.2140/gtm.2007.12.299.

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Narducci, L. M., G. L. Oppo, P. Ru, J. R. Tredicce, and M. O. Scully. "Sub-natural Resonance Fluorescence Spectra." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1989. http://dx.doi.org/10.1364/oam.1989.pd12.

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This study concerns the shape of the resonance fluorescence spectrum emitted by a V-type three-level atom driven by two coherent fields which are resonant with the transitions connecting the ground state and the second and third level, respectively. We are especially interested in monitoring the spontaneous emission from the top level to the ground state. If the field connecting levels 1 and 2 is absent or small, the spontaneous emission from level 3 is characterized by the standard Mollow spectrum. If instead the 1-2 transition is saturated, the spectrum of resonance fluorescence from the top level is characterized by the following signatures: (i) the appearance of sidebands due to Rabi splitting effects, (ii) a reduction of its integrated area because of coherent population trapping1, and (iii) a significant reduction of its linewidth if the natural lifetime of level 2 is longer than level 3. The latter effect is especially interesting and rather unexpected, as the decay properties of an optical transition are being transferred to another by controlling the relative magnitudes of the driving fields. We have carried out our calculations with the help of the regression theorem and also developed a simple physical interpretation in terms of appropriate dressed states2.
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Foster, Dylan J., and Vasilis Syrgkanis. "Statistical Learning with a Nuisance Component (Extended Abstract)." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. California: International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/654.

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We provide excess risk guarantees for statistical learning in a setting where the population risk with respect to which we evaluate a target parameter depends on an unknown parameter that must be estimated from data (a "nuisance parameter"). We analyze a two-stage sample splitting meta-algorithm that takes as input two arbitrary estimation algorithms: one for the target parameter and one for the nuisance parameter. We show that if the population risk satisfies a condition called Neyman orthogonality, the impact of the nuisance estimation error on the excess risk bound achieved by the meta-algorithm is of second order. Our theorem is agnostic to the particular algorithms used for the target and nuisance and only makes an assumption on their individual performance. This enables the use of a plethora of existing results from statistical learning and machine learning literature to give new guarantees for learning with a nuisance component. Moreover, by focusing on excess risk rather than parameter estimation, we can give guarantees under weaker assumptions than in previous works and accommodate the case where the target parameter belongs to a complex nonparametric class. We characterize conditions on the metric entropy such that oracle rates---rates of the same order as if we knew the nuisance parameter---are achieved. We also analyze the rates achieved by specific estimation algorithms such as variance-penalized empirical risk minimization, neural network estimation and sparse high-dimensional linear model estimation. We highlight the applicability of our results in four settings of central importance in the literature: 1) heterogeneous treatment effect estimation, 2) offline policy optimization, 3) domain adaptation, and 4) learning with missing data.
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Sorensen, Jesper H., Cedomir Stefanovic, and Petar Popovski. "Coded splitting tree protocols." In 2013 IEEE International Symposium on Information Theory (ISIT). IEEE, 2013. http://dx.doi.org/10.1109/isit.2013.6620748.

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FICHTNER, K. H., VOLKMAR LIEBSCHER, and MASANORI OHYA. "A LIMIT THEOREM FOR CONDITIONALLY INDEPENDENT BEAM SPLITTINGS." In From Foundations to Applications. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702104_0015.

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Creutz, Michael. "Minimal doubling and point splitting." In The XXVIII International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2011. http://dx.doi.org/10.22323/1.105.0078.

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Kuppinger, Patrick, Giuseppe Durisi, and Helmut Bolcskei. "Improved sparsity thresholds through dictionary splitting." In 2009 IEEE Information Theory Workshop (ITW 2009). IEEE, 2009. http://dx.doi.org/10.1109/itw.2009.5351511.

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Tian, Chao, and Jun Chen. "Quantization splitting for symmetric K-channel multiple descriptions." In 2009 IEEE Information Theory Workshop on Networking and Information Theory (ITW). IEEE, 2009. http://dx.doi.org/10.1109/itwnit.2009.5158582.

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Reports on the topic "Splitting theorem"

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Allen, Philip B. Quantum Theory of Semiconductor Photo-Catalysis and Solar Water Splitting. Office of Scientific and Technical Information (OSTI), February 2020. http://dx.doi.org/10.2172/1602013.

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Parzen, G. The Residual Tune Splitting due to Linear Coupling – Theory and Correction. Office of Scientific and Technical Information (OSTI), June 1991. http://dx.doi.org/10.2172/1119111.

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