Publications

Dr. Eleftherios Gkioulekas  faculty web page
 E. Gkioulekas and J. Solomon: "WalshFourier analysis of protein sequence property profiles", Technical Report CCB9503, Beckman Institute, California Institute of Technology. (1995) doi:10.13140/RG.2.1.1059.5368
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 E. Gkioulekas: "Proposal for a reinforcement model of learning that incorporates beliefs and signaling", unpublished senior thesis, California Institute of Technology.(1996) 29pp (Advisor: Colin Camerer)
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 E. Gkioulekas and KK Tung: "On the double cascades of energy and enstrophy in two dimensional turbulence. Part 1. Theoretical formulation", Discrete and Continuous Dynamical Systems  Series B 5 (2005), 79102.
[pdf][online]
 E. Gkioulekas and KK Tung: "On the double cascades of energy and enstrophy in two dimensional turbulence. Part 2. Approach to the KLB limit and interpretation of experimental evidence", Discrete and Continuous Dynamical Systems  Series B 5 (2005), 103124.
[pdf][online]
 E. Gkioulekas and KK Tung: "On the double cascades of energy and enstrophy in QG turbulence", The 15th Conference on Atmospheric and Oceanic Fluid Dynamics of the American Meteorological Society, Cambridge Massachussets, (2005) Extended abstract P2.18
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 E. Gkioulekas: "A theoretical study of the cascades of 3D, 2D, and QG turbulence", ProQuest LLC , University of WashingtonPh.D. thesis (Advisor: KaKit Tung), (2006) 154 pp. ISBN: 9780542769467
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 E. Gkioulekas and KK Tung: "Recent developments in understanding twodimensional turbulence and the NastromGage spectrum", Journal of Low Temperature Physics 145 (2006), 2557
[pdf][arxiv][online]
 E. Gkioulekas and KK Tung: "Is the subdominant part of the energy spectrum due to downscale energy cascade hidden in quasigeostrophic turbulence?", Discrete and Continuous Dynamical Systems  Series B 7 (2007), 293314
[pdf][arxiv][online]
 E. Gkioulekas and KK Tung: "A new proof on net upscale energy cascade in 2D and QG turbulence", Journal of Fluid Mechanics 576 (2007), 173189 .
[pdf][arxiv][online]
 E. Gkioulekas: "On the elimination of the sweeping interactions from theories of hydrodynamic turbulence.", Physica D 226 (2007), 151172
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 E. Gkioulekas: "Review of `LargeEddy simulations of turbulence' by M. Lesieur, O. Metais, and P. Comte", SIAM Review 49 (2007), 340342
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 E. Gkioulekas: "Winterberg's conjectured breaking of the superluminal quantum correlations over large distances", International Journal of Theoretical Physics 47 (2008), 11951205
[pdf][arxiv][online]
 E. Gkioulekas: "Locality and stability of the cascades of twodimensional turbulence", Physical Review E 78 (2008), 066302, 23 pp.
[pdf][arxiv][online]
 E. Gkioulekas: "Lecture Notes on Mathematics for Electrical Engineers", Online Lecture Notes on Mathematics, Edinburg, University of Texas Pan American (2009), 302 pp.
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 E. Gkioulekas: "Lecture Notes on College Algebra", Online Lecture Notes on Mathematics, Edinburg, University of Texas Pan American (2009), 298 pp.
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 E. Gkioulekas: "Lecture Notes on Introduction to Mathematics Proof", Online Lecture Notes on Mathematics, Edinburg, University of Texas Pan American (2009), 197 pp.
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 E. Gkioulekas: "Lecture Notes on Calculus 1", Online Lecture Notes on Mathematics, Edinburg, University of Texas Pan American (2009), 364 pp.
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 E. Gkioulekas: "Lecture Notes on Precalculus", Online Lecture Notes on Mathematics, Edinburg, University of Texas Pan American (2010), 190 pp.
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 E. Gkioulekas: "Lecture Notes on Mathematical Modeling", Online Lecture Notes on Mathematics, Edinburg, University of Texas Pan American (2010), 206 pp.
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 E. Gkioulekas: "Dissipation scales and anomalous sinks in steady twodimensional turbulence", Physical Review E 82 (2010), 046304, 21 pp.
[pdf][arxiv][online]
 E. Gkioulekas: "Lecture Notes on Calculus 3", Online Lecture Notes on Mathematics, Edinburg, University of Texas Pan American (2011), 298 pp.
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 E. Gkioulekas: "The effect of asymmetric largescale dissipation on energy and potential enstrophy injection in twolayer quasigeostrophic turbulence", Journal of Fluid Mechanics 694 (2012), 493523
[pdf][arxiv][online]
 E. Gkioulekas: "Review of `Turbulence and Shell Models' by Peter D. Ditlevsen", SIAM Review 54 (2012), 396399
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 E. Gkioulekas: "Lecture Notes on Linear Algebra", Online Lecture Notes on Mathematics, Edinburg, University of Texas Pan American (2012), 232 pp.
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 E. Gkioulekas: "On equivalent characterizations of convexity of functions", International Journal of Mathematical Education in Science and Technology, 44 (2013), 410417
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 E. Gkioulekas: "Zerobounded limits as a special case of the squeeze theorem for singlevariable and multivariable limits", International Journal of Mathematical Education in Science and Technology 44 (2013), 595609
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 E. Gkioulekas: "Review of `Turbulence, coherent structures, dynamical systems and symmetry', by P. Holmes, J.L. Lumley, G. Berkooz, and C.W. Rowley", SIAM Review 55 (2013), 579581.
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 E. Gkioulekas: "Lecture Notes on Calculus 2", Online Lecture Notes on Mathematics, Edinburg, University of Texas Pan American (2013), 316 pp.
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 E. Gkioulekas: "Generalized local test for local extrema in singlevariable functions", International Journal of Mathematical Education in Science and Technology 45 (2014), 118131
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 E. Gkioulekas: "Lecture Notes on Differential Equations", Online Lecture Notes on Mathematics, Edinburg, University of Texas Pan American (2014), 257 pp.
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 E. Gkioulekas: "Energy and potential enstrophy flux constraints in quasigeostrophic models", Physica D 284 (2014), 2741
[pdf][arxiv][online]
 E. Gkioulekas: "Review of ``Mathematics of twodimensional turbulence'' by S.Kuksin and A. Shirikyan", SIAM Review 56 (2014), 561565
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 E. Gkioulekas: "Lecture Notes on Discrete Structures", Online Lecture Notes on Mathematics, Edinburg, University of Texas Rio Grande Valley (2015), 235 pp.
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 E. Gkioulekas: "Multilocality and fusion rules on the generalized structure functions in twodimensional and threedimensional NavierStokes turbulence", Physical Review E 94 (2016), 033105, 25 pp.
[pdf][arxiv][online]
 E. Gkioulekas: "On the denesting of nested square roots", International Journal of Mathematical Education in Science and Technology 48 (2017), 942953
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 E. Gkioulekas: "Using restrictions to accept or reject solutions of radical equations", International Journal of Mathematical Education in Science and Technology 49 (2018), 12781292
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 E. Gkioulekas: "In support of Dr. Abigail Thompson, academic freedom, and viewpoint diversity", Letter to the Editor, In: "Responses to A Word from Abigail Thompson" (online only), Notices of the American Mathematical Society 67 (1) (2020), 24
[pdf][online]
 E. Gkioulekas: "The role of the asymmetric Ekman dissipation term on the energetics of the twolayer quasigeostrophic model", Physica D 403 (2020), 132372, 17 pp.
[pdf][arxiv][online]
 E. Gkioulekas: "Lecture Notes on Real Analysis 1", Online Lecture Notes on Mathematics, Edinburg, University of Texas Rio Grande Valley (2020), 296 pp.
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 E. Gkioulekas: "Solving parametric radical equations with depth 2 rigorously using the restriction set method", International Journal of Mathematical Education in Science and Technology 51 (2020), 12551277
[pdf][arxiv][online]
