Let $f,g$ be completely multiplicative functions, $\vert f(n)\vert=\vert g(n)\vert =1 (n\in\mathbb{N})$. Assume that $${1\over {\log x}}\sum_{n\le x}{\vert g([\sqrt{2}n])-Cf(n)\vert\over n}\to 0 \quad (x\to\infty).$$ Then $$f(n)=g(n)=n^{i\tau},\quad C=(\sqrt{2})^{i\tau}, \tau\in \mathbb{R}.$$

In the title compound, C(18)H(19)N(3)O(3)S, the phenyl ring and the pyrazole ring are twisted with respect to each other by an angle of 49.11 (7)°. The C-N-S-C torsion angle is -122.5 (2)°. The methyl group bonded to the N atom of the pyrazole ring has a large deviation from the mean ring plane of 0.603 (3) Å. One inter-molecular N-H⋯O and two non-classical inter-molecular C-H⋯O hydrogen bonds ...

In the title mol-ecule, C(14)H(14)ClNO, the cyclo-hexane ring adopts a chair conformation. The cyano group and the methyl group have axial and equatorial orientations, respectively. The benzene ring has an equatorial orientation. A C-H⋯π inter-action involving the benzene ring is found in the crystal structure.

Convenient and efficient synthesis of a new environmentally sensitive chlorine-substituted 2,3-naphthalimide-based fluorophore is reported. Benzotriazole carboxyl group activation of the 6-chloro-fluorophore enabled quick labeling of free and Fmoc-protected amino acids. The photophysical properties of the compounds obtained include high quantum yields in solvents of different polarity: water, m...