Efficiency and duality for multiobjective fractional variational problems with (ρ,b) - quasiinvexity

The necessary conditions for (normal) efficient solutions to a class of multi-objective fractional variational problems (MFP) with nonlinear equality and inequality constraints are established using a parametric approach to relate efficient solutions of a fractional problem and a non-fractional problem. Based on these normal efficiency criteria a Mond-Weir type dual is formulated and appropriate duality theorems are proved assuming (?,b) - quasi-invexity of the functions involved.

THE PRODUCTION OF 11-DEOXYCORTISOL (REICHSTEIN'S SUBSTANCE S) IN PATIENTS WITH ADRENOCORTICAL HYPERFUNCTION

SUMMARY Using an isotope dilution technique, secretion rates of both 11-deoxycortisol and cortisol were measured simultaneously in a group of control subjects and in 13 patients with adrenocortical hyperplasia or tumour. The rate of 11-deoxycortisol secretion was 3·0% of the combined cortisol and 11-deoxycortisol secretions in the control patients, and 2·5% in most cases of Cushing's syndrome due to adrenocortical hyperplasia. This implied a normal efficiency of the 11β-hydroxylase system in most of these patients. In four patients with adrenocortical tumour there was evidence of reduction of the efficiency of the 11β-hydroxylase system below the normal range.

Experimental Production of Atrophied and Partly Deficient Limbs (Phocomelias) in the Axolotl Embryo

1. The results obtained indicate the development of some types of atrophied and locally deficient limbs as related to the method applied. 2. The larvae operated after method 3 (implantation along a vertical line) show the implanted ectoderm still attached along the radial border of the operated limbs (figs. 5 and 6). The length of these limbs is half as long as normal and the distal ends show rudiments of fingers, the number of which is reduced. 3. The length of the limbs, the primordia of which were operated after method 2 (superficial implantation), was always normal, but the digits of those limbs are either deformed (case 999) or they show the implanted ectoderm replacing a digit (case 983) or they possess an abnormal number of digits or some of the digits are abnormally long (case 1009). 4. All cases developing after application of method 1 (deep implantation) showed abnormally short and atrophied limbs. The type of deformity developing after this method is the so-called phocomelias. In the phocomelias the proximal parts of the limb are essentially reduced in length and the distal parts show normal or slightly reduced lengths of the digits. 5. Phocomelias is not uncommon in the human newborn and it is considered as a deformity developing on a genetical basis. It has not yet been proved that phocomelias can be produced experimentally by non-genetical methods. We can conclude from the experimental method applied that the ectoderm implanted into the deep area of the embryonic primordium of the limb bud acts as a factor preventing the normal efficiency of developmental potencies.