A search on the Nikiforov-Uvarov formalism

An alternative treatment is proposed for the calculations carried out within the frame of Nikiforov-Uvarov method, which removes a drawback in the original theory and by pass some difficulties in solving the Schrodinger equation. The present procedure is illustrated with the example of orthogonal polynomials. The relativistic extension of the formalism is discussed.Comment: 10 page

Pituitary macroadenomas (>3cm) in young adulthood: Pathologic and proliferative characteristics

Background There are scarce data regarding the significance of the tumor size, hormonal activity and size of the pituitary tumor of the young; therefore, the study was designed to define the relation of the hormonal status of the large pituitary adenomas. Objective We compared those features with tumors of the elderly (>40) with the young patients, and analyzed the clinicopathologic and proliferative features of pituitary macroadenomas in young adulthood (≤40). Methods 20-year archives of pituitary tumors in our clinics were reviewed and macroadenomas with diameter ≥3cm were included in the study. We identified 46 pituitary adenomas and immunohistochemically stained them with pituitary hormones, p53 and Ki-67. Twenty-four cases were ≤40-year with an age range of 11–40 years (mean 28.0). Twenty-two cases were >40 with an age range of 44–78 years (mean 58.8). Results In the young patient group, 15 (62.5%) were functional adenomas (6 prolactinomas, six growth hormone [GH], one adrenocorticotrophic hormone [ACTH] adenoma, two multihormonal [GH+ACTH]) and nine (37.5%) were either gonadotrophic or null cell adenomas. In the elderly group, five (22.7%) were functional adenomas (two adrenocorticotrophic hormone [ACTH] adenoma, one prolactinoma, one growth hormone [GH], one multihormonal [GH+ACTH]) and 17 (77.3%) were either gonadotrophic or null cell adenomas. Ki-67 proliferation index in adenomas of the young was approximately two-folds higher than the elderly (2.7% vs. 1.2%). Conclusion In both groups, rare p53 positivity was identified. In conclusion, pituitary macroadenomas of the young show hormonal expression frequently with relatively high Ki-67 proliferation indices

Polynomial Solution of Non-Central Potentials

We show that the exact energy eigenvalues and eigenfunctions of the Schrodinger equation for charged particles moving in certain class of non-central potentials can be easily calculated analytically in a simple and elegant manner by using Nikiforov and Uvarov (NU) method. We discuss the generalized Coulomb and harmonic oscillator systems. We study the Hartmann Coulomb and the ring-shaped and compound Coulomb plus Aharanov-Bohm potentials as special cases. The results are in exact agreement with other methods.Comment: 18 page