In this paper a particular case of z-ideals, called strongly z-ideal, is defined by introducing zero sets in pointfree topology. We study strongly z-ideals, their relation with z-ideals and the role of spatiality in this relation. For strongly z-ideals, we analyze prime ideals using the concept of zero sets. Moreover, it is proven that the intersection of all zero sets of a prime ideal of C(L),...

‎For any archimedean$f$-ring $A$ with unit in whichbreak$awedge‎ ‎(1-a)leq 0$ for all $ain A$‎, ‎the following are shown to be‎ ‎equivalent‎: ‎ ‎1‎. ‎$A$ is isomorphic to the $l$-ring ${mathfrak Z}L$ of all‎ ‎integer-valued continuous functions on some frame $L$‎. 2‎. ‎$A$ is a homomorphic image of the $l$-ring $C_{Bbb Z}(X)$‎ ‎of all integer-valued continuous functions‎, ‎in the usual se...

The desCribed architecture is based on a fusion of scan-line rendering and the conventional z-buffer algorithm. The frame buffers of several z-buffer engines are modified to scan out z-values as well as color values. Multiplexing devices combine the z/color streams from each pair of frame-buffers. These z/color streams are then combined by further multiplexers, creating a binary tree that funne...

Under certain assumptions we show that a wavelet frame {τ(Aj , bj,k)ψ}j,k∈Z := {|detAj |−1/2ψ(A−1 j (x− bj,k))}j,k∈Z in L2(Rd) remains a frame when the dilation matrices Aj and the translation parameters bj,k are perturbed. As a special case of our result, we obtain that if {τ(Aj , ABn)ψ}j∈Z,n∈Zd is a frame for an expansive matrix A and an invertible matrix B, then {τ(Aj , ABλn)ψ}j∈Z,n∈Zd is a ...

We determine the importance of redshift-dependent systematic effects in the determination of stellar masses from broad band spectral energy distributions (SEDs), using high quality kinematic and photometric data of early-type galaxies at z ∼ 1 and z ∼ 0. We find that photometric masses of z ∼ 1 galaxies can be systematically different, by up to a factor of 2, from photometric masses of z ∼ 0 ga...

We give lower frame bounds for finite subfamilies of a frame of exponentials {ek}k∈Z in L2(−π, π). We also present a method for approximation of the inverse frame operator corresponding to {ek}k∈Z, where knowledge of the frame bounds for finite subfamilies is crucial.

The paper considers the basis and frame properties of the system of weighted exponentials E(g,Z\F ) = {eg(x)}n∈Z\F in L(T), where g ∈ L2(T)\{0} and F ⊂ Z. It is shown that many of the frame properties of E(g,Z\F ) are affected by the cardinalities of F and the behavior of the zeros of g.

AWeyl-Heisenberg frame {EmbTnag}m,n∈Z = {eg(·−na)}m,n∈Z for L2(R) allows every function f ∈ L2(R) to be written as an infinite linear combination of translated and modulated versions of the fixed function g ∈ L2(R). In the present paper we find sufficient conditions for {EmbTnag}m,n∈Z to be a frame for span{EmbTnag}m,n∈Z , which, in general, might just be a subspace of L2(R) . Even our conditio...