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Article electronically published on May 21, 1999 ON THE MODULAR CURVES YE(7)
"... Abstract. Let E denote an elliptic curve over Q and YE(7) the modular curve classifying the elliptic curves E ′ over Q such that the representations of Gal(Q/Q) in the 7torsion points of E and of E ′ are symplectically isomorphic. In case E is given by a Weierstraß equation such that the c4 invaria ..."
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Abstract. Let E denote an elliptic curve over Q and YE(7) the modular curve classifying the elliptic curves E ′ over Q such that the representations of Gal(Q/Q) in the 7torsion points of E and of E ′ are symplectically isomorphic. In case E is given by a Weierstraß equation such that the c4
November 1997THE DISSIPATION RATE TRANSPORT EQUATION AND SUBGRIDSCALE MODELS IN ROTATING TURBULENCE ∗ ROBERT RUBINSTEIN † AND YE ZHOU ‡
"... Abstract. The dissipation rate transport equation remains the most uncertain part of turbulence modeling. The difficulties are increased when external agencies like rotation prevent straightforward dimensional analysis from determining the correct form of the modelled equation. In this work, the dis ..."
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Abstract. The dissipation rate transport equation remains the most uncertain part of turbulence modeling. The difficulties are increased when external agencies like rotation prevent straightforward dimensional analysis from determining the correct form of the modelled equation. In this work
Consider the numbers: A = \ll • 11 + 2V5 + y/E;
, 1985
"... Although one feels that these numbers couldn f t be equal, Shanks [2] assures us that they are. Indeed, Follin (as reported by Spohn [3]) points out that one may take 5, 11, and 116 as indetevrninates subject only to the identity 5 = ll 2 116 (1) (which certainly is true for the usual interpretatio ..."
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= 5 (3) to obtain a and b as 11 + VTL6 and 11 /116. At this point, it is clear that our quantities A and B are the two different ways of associating 1 /ll? + A using (2) to express the first sum that one takes in each case. Q.E.D. 62 [Feb. INCREDIBLE IDENTITIES REVISITED Equation (2) has led
Visual Comput (2007) DOI 10.1007/s003710070191y ORIGINAL ARTICLE Ye Zhao Lattice Boltzmann based PDE solver
, 2007
"... A variety of applications require solving partial differential equations (PDEs) to model, manipulate and visualize images, surfaces and volumes, such as Laplace equation in image denoising and surface fairing [8], Poisson equation ..."
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A variety of applications require solving partial differential equations (PDEs) to model, manipulate and visualize images, surfaces and volumes, such as Laplace equation in image denoising and surface fairing [8], Poisson equation
SPLINE APPROXIMATION OF THIN SHELL DYNAMICS
, 1996
"... A splinebased method for approximating thin shell dynamics is presented here. While the method is developed in the context of the DonnellMushtari thin shell equations, it can be easily extended to the ByrneFlüggeLur'ye equations or other models for shells of revolution as warranted by appli ..."
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Cited by 8 (6 self)
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A splinebased method for approximating thin shell dynamics is presented here. While the method is developed in the context of the DonnellMushtari thin shell equations, it can be easily extended to the ByrneFlüggeLur'ye equations or other models for shells of revolution as warranted
On Polynomials Solutions of Quadratic Diophantine Equations
, 2011
"... Let be a polynomial in :P P t \ 0,1.X In this paper, we consider the number of polynomial solutions of Diophantine equation 2: 4 2 4 4 = 0E X P P Y P X P P Y2 2 2 . We also obtain some formulas and recurrence relations on the polynomial solution ,n nX Y.E = 1ax by 2 2bxy ..."
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Let be a polynomial in :P P t \ 0,1.X In this paper, we consider the number of polynomial solutions of Diophantine equation 2: 4 2 4 4 = 0E X P P Y P X P P Y2 2 2 . We also obtain some formulas and recurrence relations on the polynomial solution ,n nX Y.E = 1ax by 2 2
Spline Approximation of Thin Shell Dynamics  Numerical Examples
, 1996
"... A splinebased method for approximating thin shell dynamics is presented here. While the method is developed in the context of the DonnellMushtari thin shell equations, it can be easily extended to the ByrneFluggeLur'ye equations or other models for shells of revolution as warranted by appli ..."
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Cited by 2 (1 self)
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A splinebased method for approximating thin shell dynamics is presented here. While the method is developed in the context of the DonnellMushtari thin shell equations, it can be easily extended to the ByrneFluggeLur'ye equations or other models for shells of revolution as warranted
1 The evolution equation
, 2003
"... We introduce an evolution equation which deforms metrics on 3manifolds with sectional curvature of one sign. Given a closed 3manifold with an initial metric with negative sectional curvature, we conjecture that this flow will exist for all time and converge to a hyperbolic metric after a normaliza ..."
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We introduce an evolution equation which deforms metrics on 3manifolds with sectional curvature of one sign. Given a closed 3manifold with an initial metric with negative sectional curvature, we conjecture that this flow will exist for all time and converge to a hyperbolic metric after a
Deformations of Axially Symmetric Initial Data and the Angular MomentumMass Inequality Ye Sle Cha to The Graduate School in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy Deformations of Axially Symmetric Initial Data and
"... in Mathematics Stony Brook University 2013 In this dissertation, we study geometric inequalities for black holes, mainly the angular momentummass inequality and the angular momentummasscharge inequality. Firstly, we show how to reduce the general formulation of the angular momentummass inequali ..."
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mass inequality, for (nonmaximal) axially symmetric initial data of the Einstein equations, to the known maximal case. This procedure is based on a certain deformation of the initial data which preserves the relevant geometry, while achieving the maximal condition. More importantly, we compute the scalar iii
Ephemeris Protection Level Equations and Monitor Algorithms for GBAS
 Proceedings of ION GPS 2001. Salt Lake City, UT
"... One troublesome failure mode for Ground Based Augmentation Systems (GBAS) is the possibility of large discrepancies between satellite locations in space and the locations derived by the ephemeris data that they broadcast. For the Global Positioning System (GPS), nominal ephemeris errors are typicall ..."
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Cited by 6 (6 self)
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applications. These equations define position error bounds as functions of the approximate aircraft location with respect to each satellite and the GBAS ground station as well as the magnitude of the satellite orbit error detectable by the ground station. This Minimum Detectable Error (MDE) determines
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