Transformation of Space and Representation Theories



Linear Canonical Domains and Degrees of Freedom of Signals and Systems
Öktem, Sevinç Figen (2016-01-01)
We discuss the relationships between linear canonical transform (LCT) domains, fractional Fourier transform (FRT) domains, and the space-frequency plane. In particular, we show that LCT domains correspond to scaled fractional Fourier domains and thus to scaled oblique axes in the space-frequency plane. This allows LCT domains to be labeled and monotonically ordered by the corresponding fractional order parameter and provides a more transparent view of the evolution of light through an optical system modeled...
Linear Canonical Transforms, Degrees of Freedom, and Sampling in Optical Signals and Systems
ÖZAKTAŞ, MEMDUH HALDUN; Öktem, Sevinç Figen (2014-04-23)
We study the degrees of freedom of optical systems and signals based on space-frequency (phase-space) analysis. At the heart of this study is the relationship of the linear canonical transform domains to the space-frequency plane. Based on this relationship, we discuss how to explicitly quantify the degrees of freedom of first-order optical systems with multiple apertures, and give conditions for lossless transfer. Moreover, we focus on the degrees of freedom of signals in relation to the space-frequency su...
Nonlinear analysis of shells of revolution
Odeh, Ghassan M. H.; Akkaş, Nuri; Polat, Uğur; Department of Civil Engineering (1998)
Continuous dimensionality characterization of image structures
Felsberg, Michael; Kalkan, Sinan; Kruger, Norbert (Elsevier BV, 2009-05-04)
Intrinsic dimensionality is a concept introduced by statistics and later used in image processing to measure the dimensionality of a data set. In this paper, we introduce a continuous representation of the intrinsic dimension of an image patch in terms of its local spectrum or, equivalently, its gradient field. By making use of a cone structure and barycentric co-ordinates, we can associate three confidences to the three different ideal cases of intrinsic dimensions corresponding to homogeneous image patche...
Interpretation of searches for supersymmetry with simplified models
Chatrchyan, S.; et. al. (American Physical Society (APS), 2013-09-01)
The results of searches for supersymmetry by the CMS experiment are interpreted in the framework of simplified models. The results are based on data corresponding to an integrated luminosity of 4.73 to 4.98 fb(-1). The data were collected at the LHC in proton-proton collisions at a center-of-mass energy of 7 TeV. This paper describes the method of interpretation and provides upper limits on the product of the production cross section and branching fraction as a function of new particle masses for a number o...
Citation Formats
A. Savaş Sargın, “Transformation of Space and Representation Theories,” 2017, Accessed: 00, 2021. [Online]. Available: