In the title compound, C(16)H(11)Cl(2)F(3)N(4)OS(2), the benzene ring and the thia-zole ring make dihedral angles of 83.2 (3) and 78.3 (3)°, respectively, with the pyrazole ring. The crystal packing shows S⋯N contacts of 3.309 (2) Å.

In the title compound, C(20)H(14)FN(3), the pyrimidine ring adopts a half-chair conformation. The dihedral angle between the benzimidazole ring system and the fluoro-phenyl ring is 84.18 (10)°. In the crystal structure, mol-ecules are linked into a two-dimensional network parallel to the bc plane by N-H⋯N and C-H⋯F hydrogen bonds.

summary by Philippe Dumas] Linear recurrences and linear diierential equations with polynomial coeecients provide a nite representation of special functions or special sequences. Many algorithms are at our disposal; some give a way to automate the computation of recurrences or diierential equations; some provide solutions to recurrences or diierential equations; and some give the asymptotic beh...

For a frame $L$, consider the $f$-ring $ mathcal{F}_{mathcal P}L=Frm(mathcal{P}(mathbb R), L)$. In this paper, first we show that each minimal ideal of $ mathcal{F}_{mathcal P}L$ is a principal ideal generated by $f_a$, where $a$ is an atom of $L$. Then we show that if $L$ is an $mathcal{F}_{mathcal P}$-completely regular frame, then the socle of $ mathcal{F}_{mathcal P}L$ consists of those $f$...

Abstract Let R be a finite commutative ring. The set $${{\mathcal{F}}}(R)$$ F ( R ) of polynomial functions on is ring with pointwise operations. Its group units $${{\mathcal{F}}}(R)^\times $$ × j...

It is proved that a commutative ring is clean if and only if it is Gelfand with a totally disconnected maximal spectrum. It is shown that each indecomposable module over a commutative ring R satisfies a finite condition if and only if R P is an artinian valuation ring for each maximal prime ideal P. Commutative rings for which each indecomposable module has a local endomorphism ring are studied...

In the title compound, C(17)H(15)F(3)N(4)O(2), the dihedral angle between the trifluoro-meth-oxy-substituted benzene ring and the pyrimidinone ring is 45.1 (5)°, while that between the fused benzene ring and the pyrimidinone ring is 0.67 (1)°. Part of one of the benzene rings and its trifluoro-meth-oxy substituent are disordered over two positions of approximately equal occupancy (0.51:0.49). I...

The crystal structure of the title compound, C(15)H(11)FN(6)S, forms a three-dimensional network stabilized by π-π inter-actions between the imidazole core and the tetra-zole ring of the tetra-zolopyridine-unit; the centroid-centroid distance is 3.627 (1) Å. The crystal structure also displays bifurcated N-H⋯(N,N) hydrogen bonding and C-H⋯F inter-actions. The former involve the NH H atom of the...

z l.5 Time-consuming 13C N M R measurements o f sparingly soluble ring-substituted cyclopentadienyl metal complexes can be avoided if INEPT techniques are applied. In particular, polarization transfer based on long range 13C -'H couplings (V (13C 1H); n = 2, 3) can be used to observe 13C N M R signals o f quaternary ,3C nuclei, which are difficult to observe in normal 13C N M R spectra. The imp...