In this paper, we introduce the adapted frame of framed curves and give relations between Frenet type curve in four-dimensional Euclidean space. Moreover, define normal We obtain some characterizations terms their curvature functions. Furthermore, necessary sufficient condition for a to be curve.

where the constant c = c(L, p) > 0 does not depend of n and Pn, and μn(L, h, p) → ∞, as n → ∞, depending on geometrical properties of the curve L and the weight function h in neighborhoods of {zj}mj=1. The classical results of (2)-type can be found in [5], [8]. The estimation of (2)-type was investigated by [6], [7, pp.122-133], [4], [1]-[3] and others. In this work, we investigate the conditio...

Selective fusion of the thoracolumbar/lumbar (TL/L) curve is an effective method for the treatment of Lenke type 5C curves. Several studies have demonstrated that spontaneous correction of the thoracic curve does indeed occur. However, how this correction occurs after isolated posterior segmental instrumentation of the structural lumbar curve has not been well described. The aim of this study w...

The rating curve is the relationship between the water stage and the associated discharge in a givensection of a channel. In steady flow, this relationship usually has exponential type, whereas inunsteady it flow has a looped shape. Since direct developing of actual looped rating curve by usinghydrometric methods is merely possible, steady-state rating curve is commonly used as a downstreamboun...

In this work, the notion of a slant helix is extended to the space E. First, we introduce the type-2 harmonic curvatures of a regular curve. Thereafter, by using this, we present some necessary and sufficient conditions for a curve to be a slant helix in Euclidean n-space. We also express some integral characterizations of such curves in terms of the curvature functions. Finally, we give some c...