Abstract: A catalyst includes molybdenum, palladium, and an iron oxide, for producing at least one of an aldehyde and an alcohol from a carboxylic acid via hydrogenation. The catalyst preferably contains 0.1 to 40 parts by weight of molybdenum and 1 to 50 parts by weight of palladium per 100 parts by weight of the iron oxide. The catalyst is preferably obtained by preparing a dispersion or solution containing a molybdenum component, a palladium component, and an iron component, drying the dispersion or solution to give a solid, and firing the solid.

Abstract: The x-y coordinates are determined of a multiplicity of points set at very small intervals of a fixed value on a contour line, the coordinates of a selected number of points on either side of one (central point) of the aforementioned multiplicity of points are averaged, the two points corresponding to the two sets of averaged coordinates are connected by a straight line, a perpendicular line is drawn to this straight line from the aforementioned central point, and the distance from the central point to the foot of the perpendicular line on the straight line is calculated. This distance varies with the change in the shape of the contour line. By finding this distance with respect to each of the points on the contour line and displaying the distances found, there can be obtained a figure indicative of features of the shape of the contour image.