In this paper, we study the special tube surfaces generated by rectifying curves with respect to Darboux frame in terms of geodesic curvature, normal curvature and torsion Galilean 3-space. During establish some definite results geodesics on specific help Clairaut’s theorem detail compute Gaussian mean frame. After that, considering conditions curvatures surface, give theorems for $v$-parameter...

The present paper deals with some characterizations of rectifying and osculating curves on a smooth surface respect to the reference frame {T?,N?,T?×N?}. We have computed components position vectors along T?,N?,T?×N? then investigated their invariancy under isometry surfaces, it is shown that they are invariant iff either normal curvature curve or vector in direction tangent curve.

In this work, we give parallel transport frame of a curve and we introduce the relations between the frame and Frenet frame of the curve in 4-dimensional Euclidean space. The relation which is well known in Euclidean 3-space is generalized for the …rst time in 4-dimensional Euclidean space. Then we obtain the condition for spherical curves using the parallel transport frame of them. The conditi...

In this work, the rectifying isotropic curves are investigated in three-dimensional complex space C3. The conclusion that an curve is a if and only its pseudo curvature linear function of arc-length achieved. Meanwhile, expressed by Bessel functions explicitly. Last but not least, centrodes explored detail.

In this paper, we study the geometry of rectifying curves in 3-dimensional hyperbolic space $\mathbb H^{3}(-r)$. Further obtain distance function terms arc length when curve lying upper half plane. Then find and also give general equations curvature torsion helices $\mathbb{H}^3(-r)$.

The strength-interval curve plays a major role in understanding how cardiac tissue responds to an electrical stimulus. This complex behavior has been studied previously using the bidomain formulation incorporating the Beeler-Reuter and Luo-Rudy dynamic ionic current models. The complexity of these models renders the interpretation and extrapolation of simulation results problematic. Here we uti...

Intracellular pH was recorded in immature starfish oocytes using pH-sensitive microelectrodes, and inwardly rectifying potassium currents were measured under voltage clamp. When the intracellular pH was lowered using acetate-buffered artificial sea water from the normal value of 7.09 to 5.9, inward rectification was completely blocked. The relationship between inward rectification and internal ...

We consider patches that contain any given 3D polynomial curve as a pregeodesic (i.e. geodesic up to reparametrization). A curve is a pregeodesic if and only if its rectifying plane coincides with the tangent plane to the surface, we use this fact to construct ruled cubic patches through pregeodesics and bicubic patches through pairs of pregeodesics. We also discuss the G1 connection of (1, k) ...

In this work, we firstly introduce notions of principal directed curves and donor which are associated a Frenet curve in the dual Lorentzian space D 3 1 D13 . We give some relations between curvature torsion curve. show that general helix is plane obtain equation by using position vector Then circle $\mathbb{D}^{2}$ or hyperbola $\mathbb{D}_{1}^{2}$ slant $\mathbb{D}_{1}^{3}$ helix, respectivel...