Yellow-green fluorescent crystals of the title compound, C19H18O3, were obtained by the reaction of hy-droxy-aceto-phenone and 4-tert-butyl-benzaldehyde with hydrogen peroxide as oxidant. The plane of the benzene ring is slightly twisted to the mean plane of the 4H-chromene-4-one moiety (r.m.s. deviation = 0.0191 Å) by 10.53 (8)°. In the crystal, mol-ecules are linked by pairs of O-H⋯O hydrogen...

In the title mol-ecule, C(8)H(8)IN(3)O(2), there is an intra-molecular O-H⋯N hydrogen bond between the hy-droxy group and the imine N atom, which generates an S(6) ring. In the crystal, the carbonyl O atom accepts two different N-H⋯O hydrogen bonds, which connect mol-ecules with two R(2) (2)(8) motifs.

In the title compound, C(16)H(14)ClFO(3), the dihedral angle between the mean planes of the two benzene rings is 71.50 (5)°. Due to an intra-molecular O-H⋯O hydrogen bond between the hy-droxy group and the carbonyl O atom of the ethyl ester group, the ethyl ester group lies within the ring plane. The crystal structure is consolidated by inter-molecular C-H⋯O and C-H⋯F inter-actions.

The title compound, C(13)H(13)F(2)N(6)O(+)·C(6)H(2)N(3)O(7) (-), is the first structurally characterized salt of the cation of fluconazole [systematic name 2-(2,4-difluorophenyl)-1,3-bis(1H-1,2,4-triazol-1-yl)propan-2-ol], a synthetic anti-fungal agent. In the crystal, the components are linked by O-H⋯O hydrogen bonding between the hy-droxy group of the fluconazolium cation and the C=O(-) group...

We consider the number of zeros of the integral $I(h) = oint_{Gamma_h} omega$ of real polynomial form $omega$ of degree not greater than $n$ over a family of vanishing cycles on curves $Gamma_h:$ $y^2+3x^2-x^6=h$, where the integral is considered as a function of the parameter $h$. We prove that the number of zeros of $I(h)$, for $0 < h < 2$, is bounded above by $2[frac{n-1}{2}]+1$.

Let $R$ be a prime ring with extended centroid $C$, $H$ a generalized derivation of $R$ and $ngeq 1$ a fixed integer. In this paper we study the situations: (1) If $(H(xy))^n =(H(x))^n(H(y))^n$ for all $x,yin R$; (2) obtain some related result in case $R$ is a noncommutative Banach algebra and $H$ is continuous or spectrally bounded.