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...

A bstract We perform a consistent reduction of 6d matter-coupled F(4) supergravity on compact Riemann surface $$ {\Sigma}_{\mathfrak{g}} ? g genus \mathfrak{g} , at the level bosonic action. The result is an \mathcal{N} N = 2 gauged coupled to two vecto...

In this paper, we introduce $(mathcal{C},mathcal{C}')$-controlled continuous $g$-Bessel families and their multipliers in Hilbert spaces and investigate some of their properties. We show that under some conditions sum of two $(mathcal{C},mathcal{C}')$-controlled continuous $g$-frames is a $(mathcal{C},mathcal{C}')$-controlled continuous $g$-frame. Also, we investigate when a $(mathcal{C},mathca...

in the present study, the effects of two arbuscular mycorrhizal fungi, glomus mosseae andglomus intraradices, alone and in combination, on the growth parameters, chlorophyll and the root-rot disease of pea (pisum sativum) caused by fusarium solani f.sp. pisi were evaluated under greenhouse conditions. eight different treatments in four replications were designed in randomized blocks. compared w...

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...

Given an arbitrary sequence of elements ξ = { n } ∈ N $\xi =\lbrace \xi _n\rbrace _{n\in \mathbb {N}}$ a Hilbert space ( H , ⟨ · ⟩ ) $(\mathcal {H},\langle \cdot ,\cdot \rangle )$ the operator T $T_\xi$ is defined as associated to sesquilinear form Ω f g ∑ $\Omega _\xi (f,g)=\sum {N}} \langle _n\rangle _n g\rangle$ for h : | 2 < ∞ $f,g\in \lbrace h\in \mathcal {H}: \sum {N}}|\langle |^2<\infty ...

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...

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...