We report on the i-dropouts detected in two exceptionally deep ACS fields (B435, V606, i775, and z850 with 10σ limits of 28.8, 29.0, 28.5, and 27.8, respectively) taken in parallel with the UDF NICMOS observations. Using an i− z > 1.4 cut, we find 30 i-dropouts over 21 arcmin down to z850,AB = 28.1, or 1.4 i-dropouts arcmin, with significant field-to-field variation (as expected from cosmic var...

We introduce the concept of the modular function for a shiftinvariant subspace that can be represented by normalized tight frame generators for the shift-invariant subspace and prove that it is independent of the selections of the frame generators for the subspace. We shall apply it to study the connections between the dimension functions of wavelet frames for any expansive integer matrix A and...

We have carried out a study of the luminosity function (henceforth LF) of galaxies in the region of the HDF-North using our very complete redshift catalog. We divide the sample into five redshift bins covering the range 0.01 < z < 1.5 and consider three primary galaxy spectral classes. We solve for the LF at four rest frame wavelengths from 0.24 to 2.2μ. We find that the LFs for quiescent galax...

— We have computed the luminosity rest frame light curves of the first 40 Gamma-ray bursts (GRBs) detected by Swift with well established redshift. We studied average properties of the light curves in the four subsamples of bursts given by z < 1, 1 < z < 2, 2 < z < ∼ 4, and z > ∼ 4. We conclude that all the last three subsamples share the same morphology and the same luminosity range. Very high...

ing frames O (X ) coming from a topological space to general frames is a genuine generalization of the concept of a space, as plenty of frames exist tha t are not of the form O (X ). A simple example is the frame Oreg(R) of regular open subsets of R, i.e. of open subsets U with the property ——U = U, where —U is the interior of the complement of U . This may be contrasted with the situation for ...

We use the deep NIR imaging of the FIRES survey to investigate trends with redshift of the properties of galaxies selected to have strong Balmer/4000 Å breaks at 2 < z < 4.5. Analagous to the J−K > 1.3 (AB) color criterion designed to select red galaxies at z > 2, we propose two color criteria, J−H > 0.9 and H−K > 0.9, to select red galaxies in two redshift bins at 2 < z < 3 and 3 < z < 4.5, re...

Results from the Hubble Deep Field (HDF) North and South show a large percentage of high-redshift galaxies whose appearance falls outside traditional classification systems. The nature of these objects is poorly understood, but sub-mm observations indicate that at least some of these systems are heavily obscured (Sanders 2000). This raises the intriguing possibility that a physically meaningful...

We consider a generator F 1⁄4 ðf1; y ;fNÞ for either a multi-frame or a super-frame generated under the action of a projective unitary representation for a discrete countable group. Examples of such frames include Gabor multi-frames, Gabor super-frames and frames for shift-invariant subspaces. We show that there exists a unique normalized tight multi-frame (resp. super-frame) generator C 1⁄4 ðc...

Frames consisting of translates of a single function play an important role in sampling theory as well as in wavelet theory and Gabor analysis. We give a necessary and sufficient condition for a subfamily of regularly spaced translates of a function φ ∈ L(R), (τnbφ)n∈Λ, Λ ⊂ Z, to form a frame (resp. Riesz basis) for its closed linear span. One consequence is that if Λ ⊂ N , then this family is ...

Abstract In certain physical cases, the angular momentum of a vector particle may naturally align with direction not exactly contained in production plane, leading to an attenuation polarization magnitude observable any experimentally defined frame. this chapter we consider two possible causes phenomenon: higher-order, non-planar processes contributing Drell--Yan, W and Z production, intrinsic ...