Crystallographic Structure and in Silico Molecular Docking Analysis of 2-Cyclohexylidene-Hydrazine-Carbothiomide

Crystallography Reports - The structure of 2-cyclohexylidene-hydrazine-carbothiomide (CHCT) was determined by X-ray crystallography. It crystallizes in P1 space group of triclinic crystal system...     

Inequalities for weighted sums of Mertens functions

Archiv der Mathematik - In this article we derive some polynomial inequalities for Mertens functions.     

Uniformly locally univalent harmonic mappings associated with the pre-Schwarzian norm

In this paper, we consider the class of uniformly locally univalent harmonic mappings in the unit disk and build a relationship between its pre-Schwarzian norm and uniformly hyperbolic radius. Also, we establish eight ways of characterizing uniformly locally univalent sense-preserving harmonic mappings. We also present some sharp distortions and growth estimates and investigate their connections with Hardy spaces. Finally, we study subordination principles of norm estimates.     

Characterization and the pre-Schwarzian norm estimate for concave univalent functions

Let Co(α) denote the class of concave univalent functions in the unit disk \mathbbD{\mathbb{D}}. Each function f ? Co(a){f\in Co(\alpha)} maps the unit disk \mathbbD{\mathbb{D}} onto the complement of an unbounded convex set. In this paper we find the exact disk of variability for the functional (1-|z|²)( f^￠￠(z)/f^￠(z)), f ? Co(a){(1-|z|^2)\left ( f^{\prime\prime}(z)/f^{\prime}(z)\right), f\in Co(\alpha)}. In particular, this gives sharp upper and lower estimates for the pre-Schwarzian norm of concave univalent functions. Next we obtain the set of variability of the functional (1-|z|²)(f^￠￠(z)/f^￠(z)), f ? Co(a){(1-|z|^2)\left(f^{\prime\prime}(z)/f^{\prime}(z)\right), f\in Co(\alpha)} whenever f′′(0) is fixed. We also give a characterization for concave functions in terms of Hadamard convolution. In addition to sharp coefficient inequalities, we prove that functions in Co(α) belong to the H ^p space for p < 1/α.     

Radii of covering disks for locally univalent harmonic mappings

Monatshefte für Mathematik - For a univalent smooth mapping f of the unit disk $${\mathbb D}$$ of complex plane onto the manifold $$f({\mathbb D})$$ , let $$d_f(z_0)$$ be the radius of the...     

Bounds for the product of modified Bessel functions

In this note our aim is to present some monotonicity properties of the product of modified Bessel functions of the first and second kind. Certain bounds for the product of modified Bessel functions of the first and second kind are also obtained. These bounds improve and extend known bounds for the product of modified Bessel functions of the first and second kind of order zero. A new Turán type inequality is also given for the product of modified Bessel functions, and some open problems are stated, which may be of interest for further research.     

N-H…O,C-H… O hydrogen-bonded supramolecular frameworks in 4-fluoroanilinium and dicyclohexylaminium picrate salts

The asymmetric unit of compound (I), 4-fluoroanilinium picrate, C₆H₇NF⁺.C₆H₂N₃O₇^? contain one 4-fluoroanilinium cation and one picrate anion whereas in compound (II), dicyclohexylaminium picrate, C₁₂H₂₂N⁺.C₆H₂N₃O₇^? the asymmetric unit contains two sets of dicyclohexylaminium cation and picrate anion due to conformational difference between the molecules. In (I), all three nitro groups of the picrate anion are positionally disordered over two sites refined to major and minor components. The molecular ions of (I), interlinked through N–H???O and C–H???O hydrogen bonds forming two-dimensional supramolecular sheet along (-1 0 1) plane. Whereas in (II), the symmetry-independent molecules labeled as A and B molecule form independent one-dimensional supramolecular tape extending along (1 1 0) and (1 0 0) direction. The supramolecular tapes are interlinked through C–H???O interaction to form three-dimensional network in the crystalline solid in (II).