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Using related sequences of Lucas numbers, other 3-manifolds are constructed, their geometric structures determined, and a curious relationship between the homology and the invariant trace-field examined.
      
This is done using a descending series associated to the complex structure and the Borel spectral sequences for the corresponding set of holomorphic fibrations.
      
Exact cohomology sequences with integral coefficients for torus actions
      
It is shown that the one-dimensional sampling sets correspond to Bessel sequences of complex exponentials that are not Riesz bases for $L^2[-R,R].$ A signal processing application in which such sampling sets arise naturally is described in detail.
      
A fundamental problem with the DWT, however, is the treatment of finite length data sequences.
      
We briefly indicate when and how one can generate a Weyl-Heisenberg frame for the space of K-periodic sequences, where K=LCM (N, M), by periodization of a Weyl-Heisenberg frame for ?2? with shift parameters N, M-1.
      
Sampling and interpolating sequences for multiband-limited functions and exponential bases on disconnected sets
      
We say that {λn} is aninterpolating sequence forEp if the set of all scalar sequences {f (λn)}, with f εEp, coincides with ?p.
      
Limits of sequences of operators on spaces of vector valued functions
      
Several open questions about spaces of sequences are answered and applications in the study of commutator operators on the Paley-Wiener space are shown.
      
Lower frame bounds for sequences of exponentials are obtained in a special version of Avdonin's theorem on "1/4 in the mean" [1] and in a theorem of Duffin and Schaeffer [4].
      
It is well known that for certain sequences {tn}n∈? the usual Lp norm ∥·∥p in the Paley-Wiener space PWτp is equivalent to the discrete norm ‖f‖p,{tn}:=(∑n=-∞∞|f(tn)|p)1/p for 1 ≤ p = >amp;lt; ∞ and ‖f‖∞,{tn}:=supn∈?|f(tn| for p=∞).
      
Our approach is rooted in a dominated ergodic theorem of Mart\'{\i}n--Reyes and de la Torre which assigns $T$ a canonical family of bilateral $A_{p}$ weight sequences.
      
We present spline wavelets of class Cn(R) supported by sequences of aperiodic
      
Time-Frequency Mean and Variance Sequences of Orthonormal Bases
      
We extend the results by Jones and Rosenblatt about the series of the differences of differentiation operators along lacunary sequences to BMO and to the setting of weighted Lp spaces.
      
We find necessary and certain sufficient conditions to identify minimizing sequences.
      
NEW TECHNOLOGY FOR DRUG DISCOVERY BASED UPON INSERTION OF LIGANDS INTO GENE SEQUENCES BY NUCLEAR RECEPTOR PROTEINS
      
In this paper, the cardinality of maximum trees of finite sequences inM(s1,s2,...,sn) is obtained, which generalizes some of Frankl's results on families of finite sets with prescribed cardinalities for pairwise intersections.
      
be two sequences of random variables with unknown distribution functions F(x) and G(y) respectively.
      
 

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