Every mechanical part is fabricated with variations in size and shape in the real world. Thus, tolerances are assigned to specify the tolerance zone corresponding to the allowable range of variation in the design shape within which the entire shape element must lie after the manufacturing process. Geometric tolerances constrain the size and the thickness of an individual shape element or its relative position and orientation with respect to the related datums. The eVect of the tolerances given to the datums should be propagated to the orientation and the location tolerances in the proper order of precedence. This paper proposes a mathematical foundation for representing the propagation of geometric tolerances while considering the order of precedence of the datums. The eVect caused by the tolerances of the datum can also be mathematically handled while considering the datum order of precedence.

This study was performed to evaluate the effects of thyroid-stimulating hormone (TSH) on phosphatidylinositol-4-phosphate 5-kinase type IIgamma (PIPKIIgamma) gene expression in the thyrocytes of FRTL-5 cells. Although PIPKIIgamma mRNA was expressed constantly in the absence of added TSH, its expression increased remarkably in the presence of 10(-9) M TSH. This increase started within 6 h of the addition of TSH, and reached a maximum at 8 h. The mRNA expression properties of PIPKIIgamma in the cells were identified using inhibitors. Actinomycin D blocked PIPKIIgamma transcription strongly, while cycloheximide did not. In an experiment using 5,6-dichlo-1-beta-d -ribofuranosylbenzimidaxole, the half-life of PIPKIIgamma mRNA was approximately 6 h in the presence or absence of TSH, and it was not affected by the stability of the PIPKIIgamma mRNA. The effects of TSH on PIPKIIgamma gene expression were specific, and other growth factors examined (transferrin, insulin and hydrocortisone) did not alter its expression. It is possible that the mechanism of PIPKIIgamma gene expression is involved in the permissive effect of the TSH-cAMP cascade proper. Our results indicate, for the first time, that the expression of PIPKIIgamma is regulated transcriptionally by TSH in thyrocytes.