Shahid Bahonar University of Kerman
Journal of Mahani Mathematical Research Center
2251-7952
6
2
2017
05
01
Construction of a surface pencil with a common special surface curve
57
72
EN
Onur
Kaya
Manisa Celal Bayar University
onur.kaya@cbu.edu.tr
Mehmet
Önder
Independent Researcher
mehmetonder197999@gmail.com
10.22103/jmmrc.2017.10079.1038
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.
Surface pencil,$D$-type curve,Parametric representation,Marching-scale function,Surface curve
http://jmmrc.uk.ac.ir/article_1866.html
http://jmmrc.uk.ac.ir/article_1866_f228056f4057aee18d10d5b8fc41f15a.pdf
Shahid Bahonar University of Kerman
Journal of Mahani Mathematical Research Center
2251-7952
6
2
2017
05
01
Remotality and proximinality in normed linear spaces
73
80
EN
H.
Mazaheri
Yazd University
hmazaheri@yazd.ac.ir
M. A.
Dehghan
Valiasr Rafsanjan University, Rafsanjan, Iran
dehghan@vru.ac.ir
S. M.
Mousavi Shams Abad
Valiasr Rafsanjan University, Rafsanjan, Iran
p92356002@post.vru.ac.ir
10.22103/jmmrc.2018.10065.1037
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.
Farthest points,Nearest points. Uniquely remotal sets,Remotal sets,Proximinal sets
http://jmmrc.uk.ac.ir/article_1898.html
http://jmmrc.uk.ac.ir/article_1898_bc2ee96dad02ab26135403cd9472d474.pdf
Shahid Bahonar University of Kerman
Journal of Mahani Mathematical Research Center
2251-7952
6
2
2017
05
01
A New Modification of Legendre-Gauss Collocation Method for Solving a Class of Fractional Optimal Control Problems
81
94
EN
samaneh
soradi zeid
University street
s_soradi@yahoo.com
mostafa
yousefi
NIOPDC
mostafayousefi12@gmail.com
10.22103/jmmrc.2018.9861.1033
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.
Fractional optimal control problem,Fractional differential equation,Legendre-Gauss collocation method
http://jmmrc.uk.ac.ir/article_1916.html
http://jmmrc.uk.ac.ir/article_1916_714bac6f78732589040bfeb70d03dd92.pdf