Non-existence of reflectionless measures for the s-Riesz transform when 0 < s < 1

RIESZ s - EQUILIBRIUM MEASURES ON d - RECTIFIABLE SETS

Let A be a compact set in Rp of Hausdorff dimension d. For s ∈ (0, d), the Riesz s-equilibrium measure μs is the unique Borel probability measure with support in A that minimizes Is(μ) := " 1 |x − y|s dμ(y)dμ(x) over all such probability measures. If A is strongly (Hd , d)-rectifiable, then μs converges in the weak-star topology to normalized d-dimensional Hausdorff measure restricted to A as s...

Quranic way of presenting proofs for God`s existence

Regardless of the view of those philosophers like Plantinga who see no need in any proof for the existence of God, scholars have presented four views on Quranic way of proving the existence of God including demonstration, awakening, implication and clear demonstration. Describing and criticizing the views in detail, the author has viewed differently. God has regarded the level of the addressee`...

Evolutionary Biology Journal of I S S N 1 0 1 0 -0 6 1 X

Cover photo: A vigilant yellow-bellied marmot (Marmota flaviventris) at the Rocky Mountain Biological Laboratory, Colorado, USA. Blumstein et al. (pp. 879–887) report that the time allocated to anti-predator vigilance in marmots is heritable and is weakly correlated with locomotor performance. Interestingly, faster marmots allocate more time to vigilance while slower marmots allocate less time....

1 5 Se p 20 08 Hyperfine induced 1 s 2 s 1 S 0 → 1 s 2 1 S 0 M 1 transition of He - like ions

Hyperfine induced 1s2s S0 → 1s 2 S0 M1 transition probabilities of He-like ions have been calculated from relativistic configuration interaction wavefunctions including the frequency independent Breit interaction and QED effects. Present results for Eu and Gd are in good agreement with previous calculations [Phys. Rev. A 63, 054105 (2001)]. Electronic data are given in terms of a general scalin...

B 0 s → D − s a + 1 decay channel in the B 0 s - mixing studies