‎In the present study‎, ‎we consider a regular curve in Galilean‎ ‎$4$-space $mathbb{G}_{4}$ whose position vector is written as a‎ ‎linear combination of its Frenet vectors‎. ‎We characterize such‎ ‎curves in terms of their curvature functions‎. ‎Further‎, ‎we obtain‎ ‎some results of rectifying‎, ‎constant ratio‎, ‎$T$-constant and‎ ‎$N$-constant curves in $mathbb{G}_{4}$‎.

‎in this work‎, ‎first the differential equation characterizing position vector‎ ‎of spacelike curve is obtained in lorentzian plane $mathbb{l}^{2}.$ then the‎ ‎special curves mentioned above are studied in lorentzian plane $mathbb{l}%‎‎^{2}.$ finally some characterizations of these special curves are given in‎ ‎$mathbb{l}^{2}.$‎

seismic ground motion is profoundly affected by geometrical and mechanical properties of soil deposits overlaying bedrock. local seismic ground response of saturated soil deposits was studied in literature by applying the effects of soil stress state and index properties on the strain-dependent normalized shear modulus reduction, g/g0, and damping ratio, d, curves in an equivalent linear analys...

An explicit method to compute algebraic equations of curves constant width and Zindler generated by a family middle hedgehogs is given thanks property Chebyshev polynomials. This extends the methodology used Rabinowitz Martinez-Maure in particular generate full equations, both curves, defined trigonometric polynomials as support functions.