2017
6
2
0
0
Construction of a surface pencil with a common special surface curve
2
2
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 $leftlangle vec{n} ,vec{W}_{0} rightrangle =text{constant}$. 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.
1

57
72


Onur
Kaya
Manisa Celal Bayar University
Manisa Celal Bayar University
Iran
onur.kaya@cbu.edu.tr


Mehmet
Önder
Independent Researcher
Independent Researcher
Iran
mehmetonder197999@gmail.com
Surface pencil
$D$type curve
Parametric representation
Marchingscale function
Surface curve
Remotality and proximinality in normed linear spaces
2
2
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 coremotality.
1

73
80


H.
Mazaheri
Yazd University
Yazd University
Iran
hmazaheri@yazd.ac.ir


M. A.
Dehghan
Valiasr Rafsanjan University, Rafsanjan, Iran
Valiasr Rafsanjan University, Rafsanjan, Iran
Iran
dehghan@vru.ac.ir


S. M.
Mousavi Shams Abad
Valiasr Rafsanjan University, Rafsanjan, Iran
Valiasr Rafsanjan University, Rafsanjan, Iran
Iran
p92356002@post.vru.ac.ir
Farthest points
Nearest points. Uniquely remotal sets
Remotal sets
Proximinal sets
A New Modification of LegendreGauss Collocation Method for Solving a Class of Fractional Optimal Control Problems
2
2
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 LegendreGauss 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.
1

81
94


samaneh
soradi zeid
University street
University street
Iran
s_soradi@yahoo.com


mostafa
yousefi
NIOPDC
NIOPDC
Iran
mostafayousefi12@gmail.com
Fractional optimal control problem
Fractional differential equation
LegendreGauss collocation method