1,004 research outputs found
Moduli of smoothness and growth properties of Fourier transforms: two-sided estimates
We prove two-sided inequalities between the integral moduli of smoothness of
a function on and the weighted tail-type integrals
of its Fourier transform/series.
Sharpness of obtained results in particular is given by the equivalence
results for functions satisfying certain regular conditions. Applications
include a quantitative form of the Riemann-Lebesgue lemma as well as several
other questions in approximation theory and the theory of function spaces.Comment: 22 page
Quantum discord in spin-cluster materials
The total quantum correlation (discord) in Heisenberg dimers is expressed via
the spin-spin correlation function, internal energy, specific heat or magnetic
susceptibility. This allows one to indirectly measure the discord through
neutron scattering, as well as calorimetric or magnetometric experiments. Using
the available experimental data, we found the discord for a number of binuclear
Heisenberg substances with both antiferro- and ferromagnetic interactions. For
the dimerized antiferromagnet copper nitrate Cu(NO_3)_2*2.5H_2O, the three
independent experimental methods named above lead to a discord of approximately
0.2-0.3 bit/dimer at a temperature of 4 K. We also determined the temperature
behavior of discord for hydrated and anhydrous copper acetates, as well as for
the ferromagnetic binuclear copper acetate complex [Cu_2L(OAc)]*6H_2O, where L
is a ligand.Comment: 7 pages, 6 figure
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