ORIGINAL_ARTICLE
Construction of a surface pencil with a common special surface curve
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.
http://jmmrc.uk.ac.ir/article_1866_f228056f4057aee18d10d5b8fc41f15a.pdf
2017-05-01T11:23:20
2018-10-21T11:23:20
57
72
10.22103/jmmrc.2017.10079.1038
Surface pencil
$D$-type curve
Parametric representation
Marching-scale function
Surface curve
Onur
Kaya
onur.kaya@cbu.edu.tr
true
1
Manisa Celal Bayar University
Manisa Celal Bayar University
Manisa Celal Bayar University
LEAD_AUTHOR
Mehmet
Önder
mehmetonder197999@gmail.com
true
2
Independent Researcher
Independent Researcher
Independent Researcher
AUTHOR
ORIGINAL_ARTICLE
Remotality and proximinality in normed linear spaces
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
2017-05-01T11:23:20
2018-10-21T11:23:20
73
80
10.22103/jmmrc.2018.10065.1037
Farthest points
Nearest points. Uniquely remotal sets
Remotal sets
Proximinal sets
H.
Mazaheri
hmazaheri@yazd.ac.ir
true
1
Yazd University
Yazd University
Yazd University
LEAD_AUTHOR
M. A.
Dehghan
dehghan@vru.ac.ir
true
2
Valiasr Rafsanjan University, Rafsanjan, Iran
Valiasr Rafsanjan University, Rafsanjan, Iran
Valiasr Rafsanjan University, Rafsanjan, Iran
AUTHOR
S. M.
Mousavi Shams Abad
p92356002@post.vru.ac.ir
true
3
Valiasr Rafsanjan University, Rafsanjan, Iran
Valiasr Rafsanjan University, Rafsanjan, Iran
Valiasr Rafsanjan University, Rafsanjan, Iran
AUTHOR
ORIGINAL_ARTICLE
A New Modification of Legendre-Gauss Collocation Method for Solving a Class of Fractional Optimal Control Problems
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
2017-05-01T11:23:20
2018-10-21T11:23:20
81
94
10.22103/jmmrc.2018.9861.1033
Fractional optimal control problem
Fractional differential equation
Legendre-Gauss collocation method
samaneh
soradi zeid
s_soradi@yahoo.com
true
1
University street
University street
University street
LEAD_AUTHOR
mostafa
yousefi
mostafayousefi12@gmail.com
true
2
NIOPDC
NIOPDC
NIOPDC
AUTHOR