The leapfrog scheme is a commonly used second-order method for solving differential equations. Letting Z denote the state of the system, we compute the state at the next time step as Z (t + 1) = H (Z(t);Z(t 1); W), where t denotes a particular time step, H is the nonlinear timestepping operator, and W are parameters that are not time dependent. In this article, we show how the associativity of ...

In the title compound, C(16)H(11)FN(2)O(4)S, the mean planes of the bicyclic chromone system and of the benzene ring of the benzothia-diazine derivative make a dihedral angle of 54.28 (5)°. An intra-molecular N-H⋯O hydrogen bond occurs. In the crystal, mol-ecules are linked into layers by N-H⋯O and C-H⋯O hydrogen bonds, generating an infinite two-dimensional network.

The title adamantane derivative, C(12)H(21)NO·0.5H(2)O, was synthesized as part of an investigation into the biological activities of cage amino-alcohol compounds as potential anti-tuberculosis agents. The structure displays inter-molecular O-H⋯N, N-H⋯O, O-H⋯O hydrogen bonding and a layered packing structure with distinct hydro-philic and hydro-phobic regions. The water molecule lies on a twofo...

The title pyrimidine derivative, C7H8N4S, is essentially planar, with a maximum deviation of 0.029 (2) Å from the mean plane of the non-H atoms. In the crystal, mol-ecules are linked by an inter-molecular bifurcated N-H⋯N hydrogen bond between the cyano N atom and the two amino groups, an N-H⋯N hydrogen bond between the two amino groups and a weak C-H⋯π inter-action, forming a three-dimensional...

The title compound, C(10)H(12)ClNO(2), is a halogenated derivative of a secondary amide bearing an aromatic substituent. The C(=O)-N(H)-C(ar)-C(ar) torsion angle of -33.70 (18)° rules out the presence of resonance spanning the amide as well as the aromatic system. In the crystal, classical N-H⋯O hydrogen bonds, as well as C-H⋯O contacts connect the mol-ecules into chains propagating along the a...

In the title compound, C(8)H(5)F(3)O(2), a halogenated derivative of benzoic acid, the carboxyl group is tilted by 16.8 (3)° with respect to the plane of the aromatic ring. In the crystal, O-H⋯O hydrogen bonding gives rise to carb-oxy-lic acid dimers, which are further connected into double chains along [1,1/4,1] by C-H⋯O contacts. C-H⋯F and C-F⋯π contacts are also observed.

The asymmetric unit of the title compound, C(5)H(4)F(6)O(3), a polyfluorinated derivative of β-hy-droxy-butyric acid, comprises two mol-ecules. Intra-molecular O-H⋯O hydrogen bonds occur. In the crystal, inter-molecular O-H⋯O hydrogen bonds give rise to the formation of carb-oxy-lic acid dimers. Along with these hydrogen bonds, C-H⋯O contacts connect the mol-ecules into infinite strands along t...

Let F be a continuous function from an open subset D of a separable Banach space X into a Banach space Y. We show that if there is a dense G8 subset A of D and a Gs subset H of X whose closure has nonempty interior, such that for each a E A and each x E H the directional derivative DxF(a) of F at a in the direction x exists, then F is Giteaux differentiable on a dense G8 subset of D. If X is re...

In this paper, we study the convergence and superconvergence properties of the discontinuous Galerkin (DG) method for a linear convection-diffusion problem in one-dimensional setting. We prove that the DG solution and its derivative exhibit optimal O(h) and O(h) convergence rates in the L-norm, respectively, when p-degree piecewise polynomials with p ≥ 1 are used. We further prove that the p-de...

Nitrogen heterocyclic compounds are used in the pharmaceutical industry, in medicine and in agriculture for their biological activity. 4-Amino-3-acetylquinoline, a new synthetically prepared quinoline derivative, was the most effective compound in our primary cytotoxic screening. In this study, we evaluated cytotoxic/antiproliferative activity of quinoline using murine leukemia cell line L1210....