Hermite Multiplier Sequences and Their Associated Operators

Introducing spatial data into multidimensional models leads to the concept of Spatial OLAP (SOLAP). Existing SOLAP models do not completely integrate the semantic component of geographic information (alphanumeric attributes and relationships) or the flexibility of spatial analysis into multidimensional analysis. In this paper, the authors propose the GeoCube model and its associated operators to overcome these limitations. GeoCube enriches the SOLAP concepts of spatial measure and spatial dimension and take into account the semantic component of geographic information. The authors define geographic measures and dimensions as geographic and/or complex objects belonging to hierarchy schemas. GeoCube’s algebra extends SOLAP operators with five new operators, i.e., Classify, Specialize, Permute, OLAP-Buffer and OLAP-Overlay. In addition to classical drill-and-slice OLAP operators, GeoCube provides two operators for navigating the hierarchy of the measures, and two spatial analysis operators that dynamically modify the structure of the geographic hypercube. Finally, to exploit the symmetrical representation of dimensions and measures, GeoCube provides an operator capable of permuting dimension and measure. In this paper, GeoCube is presented using environmental data on the pollution of the Venetian Lagoon.

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Sets of determination and kernels of certain associated operators

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091507001277 ◽

2010 ◽

Vol 53 (2) ◽

pp. 503-510

Author(s):

Arne Stray

Keyword(s):

Unit Circle ◽

Unit Disc ◽

Closed Subset ◽

Bounded Function ◽

Harmonic Extension ◽

Linear Map ◽

Associated Operators

AbstractLet m be a measure supported on a relatively closed subset X of the unit disc. If f is a bounded function on the unit circle, let fm denote the restriction to X of the harmonic extension of f to the unit disc. We characterize those m such that the pre-adjoint of the linear map f → fm has a non-trivial kernel.

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Difference and Associated Operators, with some Applications

Journal of Mathematics and Physics ◽

10.1002/sapm1948271183 ◽

1948 ◽

Vol 27 (1-4) ◽

pp. 183-192 ◽

Cited By ~ 7

Author(s):

W. G. Bickley

Keyword(s):

Associated Operators

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INTEGRABLE CONFORMAL FIELD THEORY IN FOUR DIMENSIONS AND FOURTH-RANK GEOMETRY

International Journal of Modern Physics D ◽

10.1142/s0218271893000295 ◽

1993 ◽

Vol 02 (04) ◽

pp. 413-429 ◽

Cited By ~ 7

Author(s):

VICTOR TAPIA

Keyword(s):

Field Theory ◽

Conformal Field Theory ◽

Critical Dimension ◽

Conformal Killing ◽

Infinitely Many Solutions ◽

Four Dimensions ◽

Conformal Field ◽

Killing Equation ◽

Associated Operators ◽

Line Elements

We consider the conformal properties of geometries described by higher-rank line elements. A crucial role is played by the conformal Killing equation (CKE). We introduce the concept of null-flat spaces in which the line element can be written as dsr=r!dζ1 … dζr. We then show that, for null-flat spaces, the critical dimension, for which the CKE has infinitely many solutions, is equal to the rank of the metric. Therefore, in order to construct an integrable conformal field theory in four dimensions we need to rely on fourth-rank geometry. We consider the simple model ℒ = ¼ Gμνλρ ∂μ ϕ ∂ν ϕ ∂λ ϕ ∂ρϕ and show that it is an integrable conformal model in four dimensions. Furthermore, the associated operators satisfy a Vir4 algebra.

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Extended Supersymmetric Structures in Gapped and Superconducting Graphene

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887815501145 ◽

2015 ◽

Vol 12 (10) ◽

pp. 1550114 ◽

Cited By ~ 4

Author(s):

V. K. Oikonomou

Keyword(s):

Domain Wall ◽

Quantum Field ◽

Exact Form ◽

Gapped Graphene ◽

One Dimensional ◽

Witten Index ◽

Associated Operators ◽

The Many ◽

Localized Fermions ◽

Topological Charges

In view of the many quantum field theoretical descriptions of graphene in 2 + 1 dimensions, we present another field theoretical feature of graphene, in the presence of defects. Particularly, we shall be interested in gapped graphene in the presence of a domain wall and also for superconducting graphene in the presence of a vortex. As we explicitly demonstrate, the gapped graphene electrons that are localized on the domain wall are associated with four N = 2 one-dimensional supersymmetries, with each pair combining to form an extended N = 4 supersymmetry with non-trivial topological charges. The case of superconducting graphene is more involved, with the electrons localized on the vortex being associated with n one-dimensional supersymmetries, which in turn combine to form an N = 2n extended supersymmetry with non-trivial topological charges. As we shall prove, all supersymmetries are unbroken, a feature closely related to the number of the localized fermions and also to the exact form of the associated operators. In addition, the corresponding Witten index is invariant under compact and odd perturbations.

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