IN THE TITLE COMPOUND (COMMON NAME: iodiconazole), C(19)H(19)F(2)IN(4)O, there is an intra-molecular O-H⋯N hydrogen bond and mol-ecules are linked by weak inter-actions only, namely C-H⋯N, C-H⋯O and C-H⋯F hydrogen bonds, and π-electron ring-π-electron ring inter-actions between the triazole rings with centroid-centroid distances of 3.725 (3) Å.

In the title compound, C(11)H(10)N(3)O(4)S(+)·C(2)F(3)O(2) (-), the dihedral angle between the benzene ring and the pyridinium ring is 88.7 (4)°. In the crystal structure, a network of N-H⋯O, C-H⋯O and C-H⋯F hydrogen bonds links the constituent ions. One O atom of the nitro group is disordered over two positions, with site-occupancy factors of 0.57 (2) and 0.43 (2).

A famous result of Christol gives that a power series $$F(t)=\sum _{n\ge 0} f(n)t^n$$ with coefficients in finite field $$\mathbb {F}_q$$ characteristic p is algebraic over the rational functions t if and only there finite-state automaton accepting base-p digits n as input giving f(n) output for every $$n\ge 0$$ . An extension Christol’s theorem, complete description closure {F}_q(t)$$ , was la...

The complete mol-ecule of the title compound, C(27)H(18)F(4)N(2)O(2), is generated by crystallographic twofold symmetry, with one C atom lying on the rotation axis. The dihedral angle between fluoro-substituted phenyl ring and the adjacent benzene ring is 10.37 (5)°. In the crystal, mol-ecules are connected by N-H⋯O and C-H⋯F hydrogen bonds, resulting in supra-molecular chains propagating along...

Abstract: Systematic studies on the substituent effect in para substituted Fe(CO)4–pyridine complexes have been studied on the basis of DFT quantum-chemical calculations. The following substituents were taken into consideration: NO2, CN, CHO, F, H, CH3, and OH. Additionally, the Fe–N and Fe–C bonds were characterized on the basis of Atoms in Molecules topological analysis of electron density. I...

Let $R$ be a commutative ring and $M$ an $R$-module. A submodule $N$ of is called d-submodule $($resp., fd-submodule$)$ if $\ann_R(m)\subseteq \ann_R(m')$ $\ann_R(F)\subseteq \ann_R(m'))$ for some $m\in N$ finite subset $F\subseteq N)$ $m'\in M$ implies that N.$ Many examples, characterizations, properties these submodules are given. Moreover, we use them to characterize modules satisfying Prop...

Let G be a noncyclic group of order 4, and let K = Z, Z (2) and Z 2 be the ring of rational integers, the localization of Z at the prime 2 and the ring of 2-adic integers, respectively. We describe, up to conjugacy, all of the indecomposable subgroups in the group GL(m, K) which are isomorphic to G. The first explicit description of the Z-representations of the noncyclic group G of order 4 was ...

In title compound, C(8)H(8)F(3)NO, the meth-oxy group is inclined at 8.7 (4)° to the benzene ring plane. The crystal structure is stabilized by inter-molecular N-H⋯F, N-H⋯N and C-H⋯F hydrogen-bonding inter-actions.

Let F be a field of characteristic p > 0. Let Ω(F ) be the F vector space of n-differentials of F over F . Let K = F (g) be the function field of an irreducible polynomial g in m > 1 variables over F . We derive an explicit description of the kernel of the restriction map Ω(F ) → Ω(K). As an application in the case p = 2, we determine the kernel of the restriction map when passing from the Witt...