Acid-catalysed, '3+3' condensation of m-bispyrryl benzene derivatives with acetone afforded new non-aromatic macrocycles that can be converted to meso-alkylidenyl dibenzohexaphyrins carrying four exocyclic double bonds at meso-positions by DDQ oxidation.

Many rendering or image-analysis systems require calculation of versions of an image at lesser resolutions than the original. Because the filtering required to perform such calculations accurately cannot typically be done in real time, many systems use interpolation between images at precalculated resolutions. This discrete sampling of the scale component of multiresolution image spaces is anal...

The simplest finite difference approximations for spatial derivatives are centered, explicit, and applied to “regular” equispaced grids. Well-established generalizations include the use of implicit (compact) approximations and staggered grids. We find here that the combination of these two concepts, together with high formal order of accuracy, is very effective for approximating the first deriv...

An algorithm is presented to integrate nonlinear partial differential equations, which is particularly useful when accurate estimation of spatial derivatives is required. It is based on an analytic approximation method, referred to as distributed approximating functionals (DAF's), which can be used to estimate a function and a finite number of derivatives with a specified accuracy. As an applic...

We present a systematic approach for calculating higher-order derivatives of smooth functions on a uniform grid using Padé approximants. We illustrate our findings by deriving higher-order approximations using traditional second-order finite-difference formulas as our starting point. We employ these schemes to study the stability and dynamical properties of K(2,2) Rosenau-Hyman compactons inclu...

Information on the structural complexity of forest stands is required to inform conservation priorities that guide the sustainable management of private native vegetation for multiple objectives of landowners. Whilst research into methods for the operational mapping of vegetation structure is expanding, the research is largely exploratory, and no methods have yet seen widespread acceptance. Thi...

introduction: previous studies have shown that vitamin a and its derivatives such as retinoid and all-trans retinoic acid have a crucial role in memory, learning and synaptic plasticity. the receptors of vitamin a are seen in different parts of the brain such as hippocampus, where vitamin a has an important role in learning. in this study, the effect of intrahippocampal (ca1) injection of all –...

In this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. We utilize spectral-collocation method combining with a product integration technique in order to discretize the terms involving spatial fractional order derivatives that leads to a simple evaluation of the related terms. By using Bernstein polynomial basis, the problem is transformed in...