Phase retrieval has become a very active area of research. We will classify when phase retrieval by Parseval frames passes to the Naimark complement and when phase retrieval by projections passes to the orthogonal complements. We introduce a new concept we call norm retrieval and show that this is what is necessary for passing phase retrieval to complements. This leads to a detailed study of no...

and Applied Analysis 3 Proposition 1.3 see 4, 10 . A closed subspace X of L2 n is a reducing subspace if and only if X { f ∈ L2 n : supp ( f̂ ) ⊆ S } 1.5 for some measurable set S ⊆ n with ãS S. So, to be specific, one denotes a reducing subspace by L2 S ∨ instead of X. In particular, L2 n is a reducing subspace of L2 n . Definition 1.4 see 5–7 . Let B n be a subgroup of the integral affine grou...

In the present paper the authors introduce the exponential integral transform and the complementary error transform, then it is shown that the third iterate of the Laplace transform is the exponential integral transform and a modified third iterate of the Laplace transform is the complementary error transform. Some identities involving these new transforms, the Laplace transform and the Stieltj...

We present the first results for recovering word-word dependencies from a probabilistic parser for Portuguese trained on and evaluated against human annotated syntactic analyses. We use the Floresta Sintá(c)tica with the Bikel multi-lingual parsing engine and evaluate performance on both PARSEVAL and unlabeled dependencies. We explore several configurations, both in terms of parameterizing the ...

Hilbert space frame theory has applications to various areas of pure mathematics, applied mathematics, and engineering. However, the question of how applying an invertible operator to a frame changes its properties has not yet been satisfactorily answered, and only partial results are known to date. In this paper, we will provide a comprehensive study of those questions, and, in particular, pro...

We examine relations between popular variational methods in image processing and classical operator splitting methods in convex analysis. We focus on a gradient descent reprojection algorithm for image denoising and the recently proposed Split Bregman and alternating Split Bregman methods. By identifying the latter with the so-called DouglasRachford splitting algorithm we can guarantee its conv...

In this chapter we survey several recent results on the existence of frames with prescribed norms and frame operator. These results are equivalent to Schur-Horn type theorems which describe possible diagonals of positive self-adjoint operators with specified spectral properties. The first infinite dimensional result of this type is due to Kadison who characterized diagonals of orthogonal projec...

Abstract In this article, we present the Laguerre wavelet exact Parseval frame method (LWPM) for two-dimensional flow of a rotating micropolar fluid in porous channel with huge mass transfer. This is governed by highly nonlinear coupled partial differential equations (PDEs) are reduced to ordinary (ODEs) using Berman's similarity transformation before being solved numerically method. We also co...

This paper compares three evaluation metrics for a CCG parser trained and tested on a CCG version of the Penn Treebank. The standard Parseval metrics can be applied to the output of this parser; however, these metrics are problematic for CCG, and a comparison with scores given for standard Penn Treebank parsers is uninformative. As an alternative, we consider two evaluations based on headdepend...

The definition of combinatory categorial grammar (CCG) in the literature varies quite a bit from author to author. However, the differences between the definitions are important in terms of the language classes of each CCG. We prove that a wide range of CCGs are strongly context-free, including the CCG of CCGbank and of the parser of Clark and Curran (2007). In light of these new results, we tr...