• Journal of the Korean Mathematical Society
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• v.44 no.3
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• pp.733-745
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• 2007

We prove the $L^p(1 boundedness of the parabolic Marcinkiewicz integral with the kernel function $\Omega{\in}L(log^+L)^{1/2}(S^{n-1})$. The result is an improvement and extension of some known results.

• Bulletin of the Korean Chemical Society
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• v.34 no.6
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• pp.1656-1662
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• 2013

The ternary phase $EuZn_xIn_{4-x}$ has been identified as the main product of reactions of Eu, Zn, and In by using the In-flux method and characterized by both powder and single-crystal X-ray diffraction. The structure belongs to the common $BaAl_4$-type (tetragonal space group I4/mmm, Pearson code tI10) with lattice parameters of a = 4.5610(9) ${\AA}$, c = 12.049(3) ${\AA}$ for composition $EuZn_{1.10(12)}In_{2.90}$ and a = 4.5463(3) ${\AA}$, c = 12.028(2) ${\AA}$ for composition $EuZn_{1.18(2)}In_{2.82}$, respectively. In this structure, the Eu atoms are situated at the center of 18-vertex Fedorov polyhedra made of Zn and In atoms, where the 4d site is preferentially occupied by In and the 4e site is occupied by randomly mixed Zn and In atoms. Theoretical investigations using tight-binding linear muffintin orbital (TB-LMTO) method provide rationale for the observed site preferences and suggest potentially wider homogeneity range than the experimentally established for $EuZn_xIn_{4-x}$ ($x{\approx}1.1$).