in this paper, we study spacelike dual biharmonic curves. we characterize spacelike dual biharmonic curves in terms of their curvature and torsion in the lorentzian dual heisenberg group . we give necessary and sufficient conditions for spacelike dual biharmonic curves in the lorentzian dual heisenberg group . therefore, we prove that all spacelike dual biharmonic curves are spacelike dual heli...

We consider frames arising from the action of a unitary representation of a discrete countable abelian group. We show that the range of the analysis operator can be determined by computing which characters appear in the representation. This allows one to compare the ranges of two such frames, which is useful for determining similarity and also for multiplexing schemes. Our results then partiall...

In the study of Weyl-Heisenberg frames the assumption of having a finite frame upper bound appears recurrently. In this note it is shown that it actually depends critically on the timefrequency lattice used. Indeed, for any irrational > 0 we can construct a smooth g 2 L2(R) such that for any two rationals a > 0 and b > 0 the collection (gna;mb)n;m2Zof time-frequency translates of g has a finite...

In [arXiv:0706.4180], a certain natural phenomenon of self-observing consciousness was shown to be incompatible with the standard axioms of quantum theory. In order to consider a possibility of removing this inconsistency, which arises due to the separation between an observing party and a state vector being observed stated in the quantum theory axioms, we provide a conjecture where ‘being’ is ...

Born proposed a unification of special relativity and quantum mechanics that placed position, time, energy and momentum on equal footing through a reciprocity principle and extended the usual position-time and energy-momentum line elements to this space by combining them through a new fundamental constant. Requiring also invariance of the symplectic metric yields as the invariance group, the in...

Coherent wavelets form a unified basis of the multichannel perfect reconstruction analysis-synthesis filter bank of high resolution radar imaging and clinical magnetic resonance imaging (MRI). The filter bank construction is performed by the Kepplerian temporospatial phase detection strategy which allows for the stroboscopic and synchronous cross sectional quadrature filtering of phase historie...

We study Weyl-Heisenberg (=Gabor) expansions for either L2(IR ) or a subspace of it. These are expansions in terms of the spanning set X = (EM φ : k ∈ K, l ∈ L,φ ∈ Φ), where K and L are some discrete lattices in IR, Φ ⊂ L2(IR ) is finite, E is the translation operator, and M is the modulation operator. Such sets X are known as WH systems. The analysis of the “basis” properties of WH systems (e....

We study Weyl-Heisenberg (=Gabor) expansions for either L 2 (IR d) or a subspace of it. These are expansions in terms of the spanning set where K and L are some discrete lattices in IR d , L 2 (IR d) is nite, E is the translation operator, and M is the modulation operator. Such sets X are known as WH systems. The analysis of the \basis" properties of WH systems (e.g. being a frame or a Riesz ba...

We study Weyl-Heisenberg (=Gabor) expansions for either L 2 (IR d) or a subspace of it. These are expansions in terms of the spanning set where K and L are some discrete lattices in IR d , L 2 (IR d) is nite, E is the translation operator, and M is the modulation operator. Such sets X are known as WH systems. The analysis of the \basis" properties of WH systems (e.g. being a frame or a Riesz ba...