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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.
      
Trace Inequalities, Maximal Inequalities, and Weighted Fourier Transform Estimates
      
We show that the trace of an indefinitely oscillating function on a subspace of ?d is not always indefinitely oscillating.
      
In the periodic case, the number of oscillations of the trace depends on the regularity of the function.
      
As applications, we obtain characterizations of the Besov and Triebel-Lizorkin spaces on Lipschitz curves, and the trace theorem on Γ of the Besov spaces onR2.
      
The trace representation of the dual of quaternary Goethals code G(m) is given.
      
By using the trace identity, the corresponding Hamiltonian structure is given and its Liouville integrability is proved.
      
A new discrete isospectral problem is introduced, from which the coupled discrete KdV hierarchy is deduced and is written in its Hamiltonian form by means of the trace identity.
      
Using trypsin as RRS probe, a sensitive method for the determination of trace amounts of DNA was developed.
      
An improved ion chromatographic method for determination of trace levels of perchlorate in environmental water
      
An improved ion chromatographic (IC) method was developed to determine trace levels of perchlorate in environmental water samples.
      
Bent functions in trace forms play an important role in the constructions of generalized binary Bent sequences.
      
Trace representation of some degree two Bent functions are presented in this paper.
      
Finally, a simulation application of odd leaf hyperboloid is performed before the manufacturing process; the kinematic simulation demonstrates the rationale of trace planning and the feasibility of manufacturing instruction.
      
The mixture area consists of various constituents of frictional pairs without ploughing and rolling trace.
      
Arterial compliance was measured using digital pulse wave analyzing method from the pulse trace machine (Micro medical, London), and then the stiffness index (SI) was determined.
      
In the article, we briefly trace the origins or the general ideas of the above-mentioned theories.
      
Research progress in removal of trace carbon dioxide from closed spaces
      
In this paper, the removal of trace carbon dioxide from closed spaces through membrane process and biotransformation are introduced in detail.
      
The tectonic environment discrimination by trace element reveals that these igneous complexes formed in an island-arc setting.
      
 

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