We define the differential operator ∂ ∂z on infinitely differentiable functions (also called smooth or C∞ functions) on some open set in C by ∂ ∂z = 1 2 ( ∂ ∂x + i ∂ ∂y ). A quick calculation shows that ∂ ∂z obeys the product rule. Recall that a function f is holomorphic if and only if ∂ ∂z (f) = 0. A function is biholomorphic, or an analytic isomorphism, if it is holomorphic and has holomorphi...

This study consists of four sections. In the first section, objective and background are given. Second section is devoted to basic definitions theorems related 3-dimensional Euclidean spaces. Bertrand-B curve definition given subject was mentioned. third chapter common isoasymptotic surface families were examine, so we obtain necessary sufficient condition for a (with Bishop 2-frame) such that ...

We investigate a DNA model that takes into account stacking interactions with neighbors up to three bases away. The model is a generalization of the well-known Peyrard-Bishop (PB) model and is motivated by studies that suggest that nearest-neighbor models for base-pair interaction in a DNA chain might not be enough to capture the mechanism and dynamics of DNA base-pair opening. We study station...

OBJECTIVES To determine the ability of Bishop score and sonographic cervical length to predict time to spontaneous onset of labor and time to delivery in prolonged pregnancy. METHODS Ninety-seven women underwent transvaginal ultrasound examination and palpation of the cervix at 291-296 days' gestation according to ultrasound fetometry at 12-20 weeks' gestation. Sonographic cervical length and...