The gravitational anomaly of a polyhedral target of uniform density is amenable to analytical solution and has received wide attention. We analyze a number of apparently dissimilar solutions for consistency and comment on their suitability for numeric computation. Consistency is determined by evaluating a method over a special contour for which all methods must agree. Numerical performance is assessed through operation counts and algorithm classification into vertex, line, or surface type, each type having a known accuracy bound for a given floating‐point precision. We verify performance predictions through model calculations. In particular, we demonstrate the effectiveness of revised vertex and line algorithms and of a new analytical surface method. Our scheme of analysis and classification has general application. It provides criteria by which existing and novel solutions may be examined for consistency and numerical performance.

Zeolite Beta crystals in nanometer size (about 44 nm) were hydrothermally synthesized and its catalytic activities with and without Pt impregnation were studied for 1-hexene isomerization in presence of different carrier gases, namely, hydrogen, nitrogen and carbon dioxide and also in the absence of carrier gas at reaction temperatures of 473-573 K and 0.1 MPa. General observation for all the cases was that with reaction temperature, hexene conversion increased, however, total isomer selectivity dropped. With temperature skeletal isomerization increased at the cost of double bond shift isomerization. Observed product distribution has been explained on the basis of zeolite structure and crystal size. Catalyst performed better in nitrogen than in hydrogen or carbon dioxide as carrier gas. Nevertheless, catalyst life was shorter with nitrogen as carrier gas than that with hydrogen.