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The dimension of almost spherical sections of convex bodies
 Acta Math
, 1977
"... The wellknown theorem of Dvoretzky [1] states that convex bodies of high dimension have low dimensional sections which are almost spherical. More precisely, the theorem states that for every integer k and every e> 0 there is an integer n(k, e) such that any Banach space X with dimension> n(k, ..."
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Cited by 100 (5 self)
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The wellknown theorem of Dvoretzky [1] states that convex bodies of high dimension have low dimensional sections which are almost spherical. More precisely, the theorem states that for every integer k and every e> 0 there is an integer n(k, e) such that any Banach space X with dimension> n
For Most Large Underdetermined Systems of Linear Equations the Minimal ℓ1norm Solution is also the Sparsest Solution
 Comm. Pure Appl. Math
, 2004
"... We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so that ..."
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Cited by 568 (10 self)
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. In contrast, heuristic attempts to sparsely solve such systems – greedy algorithms and thresholding – perform poorly in this challenging setting. The techniques include the use of random proportional embeddings and almostspherical sections in Banach space theory, and deviation bounds for the eigenvalues
For most large underdetermined systems of equations, the minimal l1norm nearsolution approximates the sparsest nearsolution
 Comm. Pure Appl. Math
, 2004
"... We consider inexact linear equations y ≈ Φα where y is a given vector in R n, Φ is a given n by m matrix, and we wish to find an α0,ɛ which is sparse and gives an approximate solution, obeying �y − Φα0,ɛ�2 ≤ ɛ. In general this requires combinatorial optimization and so is considered intractable. On ..."
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Cited by 122 (1 self)
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arguments. The techniques include the use of almostspherical sections in Banach space theory and concentration of measure for eigenvalues of random matrices.
DEVELOPMENTS AROUND POSITIVE SECTIONAL CURVATURE
, 902
"... Abstract. This is not in any way meant to be a complete survey on positive curvature. Rather it is a short essay on the fascinating changes in the landscape surrounding positive curvature. In particular, details and many results and references are not included, and things are not presented in chrono ..."
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Cited by 10 (1 self)
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in chronological order. Spaces of positive curvature have always enjoyed a particular role in Riemannian geometry. Classically, this class of spaces form a natural and vast extension of spherical geometry, and in the last few decades their importance for the study of general manifolds with a lower curvature bound
Desired section: Sensory and nutritive qualities of food
"... Short title: Extended shelf life of horse mackerel in slurry ice Horse mackerel shelflife in slurry ice Slurry ice, a biphasic system consisting of small spherical ice crystals surrounded by seawater, was evaluated in parallel to flake ice for the storage of horse mackerel (Trachurus trachurus). S ..."
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Short title: Extended shelf life of horse mackerel in slurry ice Horse mackerel shelflife in slurry ice Slurry ice, a biphasic system consisting of small spherical ice crystals surrounded by seawater, was evaluated in parallel to flake ice for the storage of horse mackerel (Trachurus trachurus
Corneal Asphericity and Apical Curvature in Children: A Crosssectional and Longitudinal Evaluation
, 2005
"... PURPOSE. The contour of the human cornea is closely modeled by a conic section, which is fully described by asphericity (Q) and apical radius of curvature (r o ). The relationship between corneal shape and other ocular dimensions in children, including anterior and vitreous chamber depths, axial le ..."
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PURPOSE. The contour of the human cornea is closely modeled by a conic section, which is fully described by asphericity (Q) and apical radius of curvature (r o ). The relationship between corneal shape and other ocular dimensions in children, including anterior and vitreous chamber depths, axial
Undergraduate Students
"... Margaret O’Meara Summary We present a universal coupled mode theory treatment of freespace scattering of waves from resonant objects. The range of applicability of the presented approach is fairly broad: it can be used for almost any linear wave system, as long as the resonant scatterer either has ..."
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3D spherical or 2D cylindrical symmetry, or else is sufficiently smaller than the resonant wavelength of the incident wave. The presented framework, while being intuitive and analytically simple, can nevertheless provide quantitatively very accurate modeling of: scattering cross sections, absorption
MITOCHONDRIAL MORPHOLOGY IN THE SPERMATOZOA OF THE MEXICAN AXOLOTL,
"... Thinsection and freezefracture electron microscopy of immature and mature spermatozoa of the Mexican axolotl, Ambystoma mexicanum, revealed numerous small spherical mitochondria with diameters ranging from 015 to 022 fim. Both the spherical form and the small size of these mitochondria were conf ..."
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Thinsection and freezefracture electron microscopy of immature and mature spermatozoa of the Mexican axolotl, Ambystoma mexicanum, revealed numerous small spherical mitochondria with diameters ranging from 015 to 022 fim. Both the spherical form and the small size of these mitochondria were
Collapsing threemanifolds under a lower curvature bound
 J. Differential Geom
"... Abstract The purpose of this paper is to completely characterize the topology of threedimensional Riemannian manifolds with a uniform lower bound of sectional curvature which converges to a metric space of lower dimension. Introduction We study the topology of threedimensional Riemannian manifolds ..."
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Cited by 30 (3 self)
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Abstract The purpose of this paper is to completely characterize the topology of threedimensional Riemannian manifolds with a uniform lower bound of sectional curvature which converges to a metric space of lower dimension. Introduction We study the topology of threedimensional Riemannian
NIKE HERCULES MISSILE
"... The warhead section would be mated to the rear body section, and then the forward body section mounted to the warhead section. Circuitry tests (GoNoGo) where performed, when it passed, the missile was moved to the LA (Launch Area) for final configuration. T45 The T45 is a 625 lbs. BlastFragmentati ..."
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and arming device (armed by the force of acceleration), then igniting the two M38 Explosive Harnesses that directly ignited the warhead booster charge which in turn detonates the warhead chargeThe blast pattern is almost spherical with a conical dead zone at the rear. W31 With the W31 boosted fission
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