Construction of a surface pencil with a common special surface curve
Onur
Kaya
Manisa Celal Bayar University
author
Mehmet
Önder
Independent Researcher
author
text
article
2017
eng
In this study, we introduce a new type of surface curves called $D$-type curve. This curve is defined by the property that the unit Darboux vector $\vec{W}_{0} $ of a surface curve $\vec{r}(s)$ and unit surface normal $\vec{n} $ along the curve $\vec{r}(s)$ satisfy the condition $\left\langle \vec{n} ,\vec{W}_{0} \right\rangle =\text{constant}$. We point out that a $D$-type curve is a geodesic curve or an asymptotic curve in some special cases. Then, by using the Frenet vectors and parametric representation of a surface pencil as a linear combination of the Frenet vectors, we investigate necessary and sufficient condition for a curve to be a $D$-type curve on a surface pencil. Moreover, we introduce some corollaries by considering the $D$-type curve as a helix, a Salkowski curve or a planar curve. Finally, we give some examples for the obtained results.
Journal of Mahani Mathematical Research Center
Shahid Bahonar University of Kerman
2251-7952
6
v.
2
no.
2017
57
72
http://jmmrc.uk.ac.ir/article_1866_f228056f4057aee18d10d5b8fc41f15a.pdf
dx.doi.org/10.22103/jmmrc.2017.10079.1038
Remotality and proximinality in normed linear spaces
H.
Mazaheri
Yazd University
author
M. A.
Dehghan
Valiasr Rafsanjan University, Rafsanjan, Iran
author
S. M.
Mousavi Shams Abad
Valiasr Rafsanjan University, Rafsanjan, Iran
author
text
article
2017
eng
In this paper, we consider the concepts farthest points and nearest points in normed linear spaces, We obtain a necessary and coecient conditions for proximinal, Chebyshev, remotal and uniquely remotal subsets in normed linear spaces. Also, we consider -remotality, -proximinality, coproximinality and co-remotality.
Journal of Mahani Mathematical Research Center
Shahid Bahonar University of Kerman
2251-7952
6
v.
2
no.
2017
73
80
http://jmmrc.uk.ac.ir/article_1898_bc2ee96dad02ab26135403cd9472d474.pdf
dx.doi.org/10.22103/jmmrc.2018.10065.1037
A New Modification of Legendre-Gauss Collocation Method for Solving a Class of Fractional Optimal Control Problems
samaneh
soradi zeid
University street
author
mostafa
yousefi
NIOPDC
author
text
article
2017
eng
In this paper, the optimal conditions for fractional optimal control problems (FOCPs) were derived in which the fractional differential operators defined in terms of Caputo sense and reduces this problem to a system of fractional differential equations (FDEs) that is called twopoint boundary value (TPBV) problem. An approximate solution of this problem is constructed by using the Legendre-Gauss collocation method such that the exact boundary conditions are satisfied. Several example are given and the optimal errors are obtained for the sake of comparison. The obtained results are shown that the technique introduced here is accurate and easily applied to solve the FOCPs.
Journal of Mahani Mathematical Research Center
Shahid Bahonar University of Kerman
2251-7952
6
v.
2
no.
2017
81
94
http://jmmrc.uk.ac.ir/article_1916_714bac6f78732589040bfeb70d03dd92.pdf
dx.doi.org/10.22103/jmmrc.2018.9861.1033