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  • Articles  (139)
  • Oxford University Press  (139)
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  • Mathematics  (139)
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  • Articles  (139)
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  • Oxford University Press  (139)
  • American Meteorological Society
  • Blackwell Publishing Ltd
  • Copernicus
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  • 2020-2022
  • 2010-2014  (95)
  • 1990-1994
  • 1985-1989
  • 1960-1964  (44)
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  • Mathematics  (139)
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  • 1
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    ON FEFFERMAN-STEIN INEQUALITY FOR RUBIO DE FRANCIA OPERATORS (2012)
    Oxford University Press
    Details
    Publication Date: 2012-02-14
    Description: Given a Calderón–Zygmund singular integral operator, it is an open question whether the Fefferman inequality holds true with u as an arbitrary weight. This inequality is known as the Muckenhoupt–Wheeden conjecture. In this paper we prove that, for a wider class of operators called Rubio de Francia operators, if || u || ≤1, then where the function is slightly bigger than the identity. Applications of this inequality in the setting of rearrangement invariant spaces are given.
    Print ISSN: 0033-5606
    Electronic ISSN: 1464-3847
    Topics: Mathematics
    Published by Oxford University Press
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  • 2
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    TRUNCATED SIMPLICIAL RESOLUTIONS AND SPACES OF RATIONAL MAPS (2012)
    Oxford University Press
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    Publication Date: 2012-02-14
    Description: We show that whenever m ≤ n , the space of all continuous rational maps from CP m to CP n has the same homology as the space of all continuous maps between these spaces in dimensions smaller than d (2 n – 2 m + 1) – 1. This improves the result of the paper ‘Spaces of rational maps and the Stone–Weierstrass theorem’ ( Topology 45 (2006), 281–293).
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    Electronic ISSN: 1464-3847
    Topics: Mathematics
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  • 3
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    EXACT COVERING SYSTEMS IN QUADRATIC NUMBER FIELDS (2012)
    Oxford University Press
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    Publication Date: 2012-02-14
    Description: A theorem of Davenport, Mirsky, Newman and Rado shows that there does not exist an exact covering system with distinct moduli. Motivated by this, we raise the question whether or not this is true for covering systems in algebraic number fields. We provide an affirmative answer for certain quadratic fields.
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    Topics: Mathematics
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  • 4
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    CAUSTICS OF SURFACES IN THE MINKOWSKI 3-SPACE (2012)
    Oxford University Press
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    Publication Date: 2012-02-14
    Description: The caustic of a smooth surface in the Euclidean 3-space is the envelope of the normal rays to the surface. It is also the locus of the centres of curvature (the focal points) of the surface. This is why it is also referred to as the focal set of the surface. It has Lagrangian singularities and its generic models are given in [V. I. Arnol’d, S. M. Gusein-Zade and A. N. Varchenko, Singularities of Differentiable Maps , Vol. I, Birkhäuser, Boston, 1986]. The aim of this paper is to define the caustic C ( M ) of a smooth surface M embedded in the Minkowski 3-space and to study its geometry. We denote by the locus of degeneracy (LD) the locus of points on M where the metric is degenerate. If M is a closed surface then its LD is not empty. At a point on the LD the ‘normal’ line to M is lightlike and is tangent to M . Also, the focal set of M is not defined at points on the LD. We define the caustic of M as the bifurcation set of the family of distance-squared functions on M . Then C ( M ) coincides with the focal set of M \ LD and provides an extension of the focal set to the LD. We study the local behaviour of the metric on C ( M ).
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    Topics: Mathematics
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  • 5
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    LOCAL AND ASYMPTOTIC REGULARITY RESULTS FOR QUASICONVEX AND QUASIMONOTONE PROBLEMS (2012)
    Oxford University Press
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    Publication Date: 2012-05-15
    Description: Considering vectorial integrals in the multidimensional calculus of variations and quasilinear elliptic systems of partial differential equations, we prove gradient regularity of minimizers and weak solutions, respectively. In contrast to the classical theory, we impose our assumptions on the structure functions only locally (i.e. near a single point) or asymptotically (i.e. near infinity). In particular, we point out relations between the local and the asymptotic point of view, and we discuss notions of quasiconvexity at infinity and quasimonotonicity at infinity, which arise in this context.
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    Topics: Mathematics
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  • 6
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    THE ALIQUOT CONSTANT (2012)
    Oxford University Press
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    Publication Date: 2012-05-15
    Description: The average value of log s ( n )/ n taken over the first N even integers is shown to converge to a constant when N tends to infinity; moreover, the value of this constant is approximated and proved to be less than 0. Here, s ( n ) sums the divisors of n less than n . Thus, the geometric mean of s ( n )/ n , the growth factor of the function s , in the long run tends to be less than 1. This could be interpreted as probabilistic evidence that aliquot sequences tend to remain bounded.
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    Topics: Mathematics
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  • 7
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    WEIGHTED METRICS ON TANGENT SPHERE BUNDLES (2012)
    Oxford University Press
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    Publication Date: 2012-05-15
    Description: Natural metric structures on the tangent bundle and tangent sphere bundles S r M of a Riemannian manifold M with radius function r enclose many important unsolved problems. Admitting metric connections on M with torsion, we deduce the equations of induced metric connections on those bundles. Then the equations of reducibility of TM to the almost Hermitian category. Our purpose is the study of the natural contact structure on S r M and the G 2 -twistor space of any oriented Riemannian 4-manifold.
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    Topics: Mathematics
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  • 8
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    A NOTE ON FRAGMENTABILITY AND WEAK-G{delta} SETS (2012)
    Oxford University Press
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    Publication Date: 2012-05-15
    Description: In terms of fragmentability, we describe a new class of Banach spaces which may be c 0 -saturated but do not contain weak- G open bounded subsets. In particular, none of these spaces is isomorphic to a separable polyhedral space.
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    Topics: Mathematics
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  • 9
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    THE HEISENBERG GROUP AND CONFORMAL FIELD THEORY (2012)
    Oxford University Press
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    Publication Date: 2012-05-15
    Description: A mathematical construction of the conformal field theory (CFT) associated to a compact torus, also called the ‘non-linear Sigma-model’ or ‘lattice-CFT’, is given. Underlying this approach to CFT is a unitary modular functor, the construction of which follows from a ‘quantization commutes with reduction’-type of theorem for unitary quantizations of the moduli spaces of holomorphic torus-bundles and actions of loop groups. This theorem in turn is a consequence of general constructions in the category of affine symplectic manifolds and their associated generalized Heisenberg groups.
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    Topics: Mathematics
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  • 10
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    POLYGONAL WORDS IN FREE GROUPS (2012)
    Oxford University Press
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    Publication Date: 2012-05-15
    Description: A longstanding question of Gromov asks whether every one-ended word-hyperbolic group contains a subgroup isomorphic to the fundamental group of a closed hyperbolic surface. An infinite family of word-hyperbolic groups can be obtained by taking doubles of free groups amalgamated along words that are not proper powers. We define the set of polygonal words in a free group of finite rank, and prove that polygonality of the amalgamating word guarantees that the associated square complex virtually contains a 1 -injective closed surface. We provide many concrete examples of classes of polygonal words. For instance, in the case when the rank is 2, we establish polygonality of words without an isolated generator, and also of almost all simple height-1 words, including the Baumslag–Solitar relator a p ( a q ) b for pq != 0.
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    Topics: Mathematics
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