The fourth molar in a mandible found in a Jomon skeleton in Japan

A fourth molar in a mandible occurs very rarely, even in clinical surveys involving a large number of modern people. Having encountered a case with the fourth mandibular molar in a prehistoric skull in Japan, we would like to report on the macroscopic morphology of the case using X-rays, and to discuss the case with reference to literature concerning supernumerary teeth in the molar region.     

LEONTIEF TECHNOLOGY AND THE LOCATION OF THE FIRM IN A WEBER TRIANGLE–SPECIFIC LOCALIZATION THEOREMS*

In special cases of the Leontief technology's constant input-output coefficients, the general localization theorem that an interior location is a global optimum if every input or market vertex is not a local optimum [Kusumoto (1984)] is confirmed and strengthened. Sufficient conditions are proposed for the portion of a triangular space in which the firm will locate. Finally, it is shown that, if input substitution is permitted and its effects dominate spatial effects, the firm's total cost function will be monotone, as well as concave, hence the vertex is a global optimum if it is a local optimum.