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BoseEinstein Condensation in a Gas of Sodium Atoms
, 1995
"... We have observed BoseEinstein condensation of sodium atoms. The atoms were trapped in a novel trap that employed both magnetic and optical forces. Evaporative cooling increased the phasespace density by 6 orders of magnitude within seven seconds. Condensates contained up to 5 3 10 5 atoms at dens ..."
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Cited by 282 (6 self)
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at densities exceeding 10 14 cm 23 . The striking signature of Bose condensation was the sudden appearance of a bimodal velocity distribution below the critical temperature of ϳ 2 mK. The distribution consisted of an isotropic thermal distribution and an elliptical core attributed to the expansion of a dense
Unspecified Book Proceedings Series
"... Abstract. We show that fully nonlinear elliptic PDEs (which may not have classical solutions) can be approximated with integrodifferential equations which have C 2,α solutions. For these approximated equations we prove a uniform C 1,α estimate. We also study the rate of convergence. ..."
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Abstract. We show that fully nonlinear elliptic PDEs (which may not have classical solutions) can be approximated with integrodifferential equations which have C 2,α solutions. For these approximated equations we prove a uniform C 1,α estimate. We also study the rate of convergence.
Density of rational points on elliptic K3 surfaces
 Asian J. Math
"... Let X be a smooth projective algebraic variety defined over a number field K. We will say that rational points on X are potentially dense if there exists a finite extension K ′ /K such that the set X(K ′ ) of K ′rational points is Zariski dense. What are possible strategies to propagate rational po ..."
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Cited by 43 (3 self)
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Let X be a smooth projective algebraic variety defined over a number field K. We will say that rational points on X are potentially dense if there exists a finite extension K ′ /K such that the set X(K ′ ) of K ′rational points is Zariski dense. What are possible strategies to propagate rational points on
Invariant tests for symmetry about an unspecified point based on the empirical characteristic function
 Journal of Multivariate Analysis
, 2003
"... Abstract. This paper considers a flexible class of omnibus affine invariant tests for the hypothesis that a multivariate distribution is symmetric about an unspecified point. The test statistics are weighted integrals involving the imaginary part of the empirical characteristic function of suitably ..."
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Cited by 10 (2 self)
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Abstract. This paper considers a flexible class of omnibus affine invariant tests for the hypothesis that a multivariate distribution is symmetric about an unspecified point. The test statistics are weighted integrals involving the imaginary part of the empirical characteristic function
Optimal tests for homogeneity of covariance, scale, and shape
 J. Multivariate Anal
, 2008
"... The assumption of homogeneity of covariance matrices is the fundamental prerequisite of a number of classical procedures in multivariate analysis. Despite its importance and long history, however, this problem so far has not been completely settled beyond the traditional and highly unrealistic cont ..."
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Cited by 8 (5 self)
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, while preserving the optimality features of the MLRT under multinormal assumptions, remain valid under unspecified elliptical densities with finite fourthorder moments. As a first step, the Le Cam LAN approach is used for deriving locally and asymptotically optimal testing procedures φ (n) f for any
Twodimensional KellerSegel model: Optimal critical mass and qualitative properties of the solutions
 J. DIFF. EQNS
, 2006
"... The KellerSegel system describes the collective motion of cells which are attracted by a chemical substance and are able to emit it. In its simplest form it is a conservative driftdiffusion equation for the cell density coupled to an elliptic equation for the chemoattractant concentration. It is k ..."
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Cited by 128 (15 self)
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The KellerSegel system describes the collective motion of cells which are attracted by a chemical substance and are able to emit it. In its simplest form it is a conservative driftdiffusion equation for the cell density coupled to an elliptic equation for the chemoattractant concentration
On the Origin of Density Cusps in Elliptical Galaxies
, 1998
"... We investigated the dynamical reaction of the central region of galaxies to a falling massive black hole by Nbody simulations. As the initial galaxy model, we used an isothermal King model and placed a massive black hole at around the halfmass radius of the galaxy. We found that the central core o ..."
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of the galaxy is destroyed by the heating due to the black hole and that a very weak density cusp (ρ ∝ r −α, with α ∼ 0.5) is formed around the black hole. This result is consistent with recent observations of large elliptical galaxies with Hubble Space Telescope. The velocity of the stars becomes tangentially
DENSITY OF RATIONAL POINTS ON ELLIPTIC SURFACES
"... Abstract. Suppose V is a surface over a number field k that admits two elliptic fibrations. We show that for each integer d there exists an explicitly computable closed subset Z of V , not equal to V , such that for each field extension K of k of degree at most d over the field of rational numbers, ..."
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Abstract. Suppose V is a surface over a number field k that admits two elliptic fibrations. We show that for each integer d there exists an explicitly computable closed subset Z of V , not equal to V , such that for each field extension K of k of degree at most d over the field of rational numbers
An optimal variance estimate in stochastic homogenization of discrete elliptic equations
 Ann. Probab
, 2011
"... We consider a discrete elliptic equation on the ddimensional lattice Zd with random coefficients A of the simplest type: they are identically distributed and independent from edge to edge. On scales large w.r.t. the lattice spacing (i.e., unity), the solution operator is known to behave like the so ..."
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Cited by 71 (27 self)
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We consider a discrete elliptic equation on the ddimensional lattice Zd with random coefficients A of the simplest type: they are identically distributed and independent from edge to edge. On scales large w.r.t. the lattice spacing (i.e., unity), the solution operator is known to behave like
Seismic Ray Theory
, 2001
"... Introduction T he propagation of seismic body waves in complex, laterally varying 3D layered structures is a complicated process. Analytical solutions of the elastodynamic equations for such types of media are not known. The most common approaches to the investigation of seismic wavefields in such ..."
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Cited by 131 (4 self)
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are very general; they are applicable both to isotropic and anisotropic structures, to arbitrary 3D variations of elastic parameters and density, to curved interfaces arbitrarily situated in space, to an arbitrary sourcereceiver configuration, and to very general types of waves. Highfrequency asymptotic
Results 1  10
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1,517