eng
Shahid Bahonar University of Kerman
Journal of Mahani Mathematical Research Center
2251-7952
2645-4505
2017-05-01
6
2
57
72
10.22103/jmmrc.2017.10079.1038
1866
Construction of a surface pencil with a common special surface curve
Onur Kaya
onur.kaya@cbu.edu.tr
1
Mehmet Önder
mehmetonder197999@gmail.com
2
Manisa Celal Bayar University
Independent Researcher
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.
http://jmmrc.uk.ac.ir/article_1866_f228056f4057aee18d10d5b8fc41f15a.pdf
Surface pencil
$D$-type curve
Parametric representation
Marching-scale function
Surface curve
eng
Shahid Bahonar University of Kerman
Journal of Mahani Mathematical Research Center
2251-7952
2645-4505
2017-05-01
6
2
73
80
10.22103/jmmrc.2018.10065.1037
1898
Remotality and proximinality in normed linear spaces
H. Mazaheri
hmazaheri@yazd.ac.ir
1
M. A. Dehghan
dehghan@vru.ac.ir
2
S. M. Mousavi Shams Abad
p92356002@post.vru.ac.ir
3
Yazd University
Valiasr Rafsanjan University, Rafsanjan, Iran
Valiasr Rafsanjan University, Rafsanjan, Iran
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.
http://jmmrc.uk.ac.ir/article_1898_bc2ee96dad02ab26135403cd9472d474.pdf
Farthest points
Nearest points. Uniquely remotal sets
Remotal sets
Proximinal sets
eng
Shahid Bahonar University of Kerman
Journal of Mahani Mathematical Research Center
2251-7952
2645-4505
2017-05-01
6
2
81
94
10.22103/jmmrc.2018.9861.1033
1916
A New Modification of Legendre-Gauss Collocation Method for Solving a Class of Fractional Optimal Control Problems
samaneh soradi zeid
s_soradi@yahoo.com
1
mostafa yousefi
mostafayousefi12@gmail.com
2
University street
NIOPDC
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.
http://jmmrc.uk.ac.ir/article_1916_714bac6f78732589040bfeb70d03dd92.pdf
Fractional optimal control problem
Fractional differential equation
Legendre-Gauss collocation method