Abstract The dual-frame formalism leads to an approach extend numerical relativity simulations in generalized harmonic gauge (GHG) all the way null infinity. A major setback is that without care, even simple choices of initial data give rise logarithmically divergent terms would result irregular variables and equations on compactified domain, which turn prevent accurate approximation. It has be...

We construct dual formulation of linearised gravity in first order tetrad formalism in arbitrary dimensions within the path integral framework following the standard duality algorithm making use of the global shift symmetry of the tetrad field. The dual partition function is in terms of the (mixed symmetric) tensor field Φ[ν1ν2···νd−3]ν in frame-like formulation. We obtain in d-dimensions the d...

essence of the frame theory: When one encounters a new situation (or makes a substantial change tn one's view of a problem), one selects from memory a structure called a frame. This is a remembered framework to be adapted to fit reality by changing details as necessary. A frame is a data-structure for representing a stereotyped situation like being in a certain kind of living room or going to a...

In a novel dual bed reactor Fischer-Tropsch synthesis was studied by using two diffrent cobalt catalysts. An alkali-promoted cobalt catalyst was used in the first bed of a fixed-bed reactor followed by a Rutenuim promoted cobalt catalyst in the second bed. The activity, product selectivity and accelerated deactivation of the system were assessed and compared with a conventional single bed r...

By sampling the window of a Gabor frame for L(R) belonging to Feichtinger’s algebra, S0(R), one obtains a Gabor frame for l(Z). In this article we present a survey of results by R. Orr and A.J.E.M. Janssen and extend their ideas to cover interrelations among Gabor frames for the four spaces L(R), l(Z), L([0, L]) and C. Some new results about general dual windows with respect to sampling and per...

In this study, we introduce a primal-dual prediction-correction algorithm framework for convex optimization problems with known saddle-point structure. Our unified frame adds the proximal term with a positive definite weighting matrix. Moreover, different proximal parameters in the frame can derive some existing well-known algorithms and yield a class of new primal-dual schemes. We prove the co...

We say that a Hausdorff locale is compactly generated if it is the colimit of the diagram of its compact sublocales connected by inclusions. We show that this is the case if and only if the natural map of its frame of opens into the second Lawson dual is an isomorphism. More generally, for any Hausdorff locale, the second dual of the frame of opens gives the frame of opens of the colimit. In or...

Frame theory is closely intertwined with signal processing by providing a canon of methodologies for the analysis of signals using (redundant) linear measurements. The dual frame associated with a frame then provides a means for reconstruction by a least squares approach. The novel paradigm of sparsity entered this area lately in various ways. Of those, in this survey paper, we will focus on th...

We study singly-generated wavelet systems on R that are naturally associated with rank-one wavelet systems on the Heisenberg group N . We prove a necessary condition on the generator in order that any such system be a Parseval frame. Given a suitable subset I of the dual of N , we give an explicit construction for Parseval frame wavelets that are associated with I . We say that g ∈ L(I×R) is Ga...

BACKGROUND In Australia telephone surveys have been the method of choice for ongoing jurisdictional population health surveys. Although it was estimated in 2011 that nearly 20% of the Australian population were mobile-only phone users, the inclusion of mobile phone numbers into these existing landline population health surveys has not occurred. This paper describes the methods used for the incl...