Abstract: In this work, position vector of a time-like dual curve
according to standard frame of D31
is investigated. First, it is proven
that position vector of a time-like dual curve satisfies a dual vector
differential equation of fourth order. The general solution of this dual
vector differential equation has not yet been found. Due to this, in
terms of special solutions, position vectors of some special time-like
dual curves with respect to standard frame of D31
are presented.
Abstract: In this researcha particle swarm optimization (PSO)
algorithm is proposedfor no-wait flowshopsequence dependent
setuptime scheduling problem with weighted earliness-tardiness
penalties as the criterion (|,
|Σ
"
).The
smallestposition value (SPV) rule is applied to convert the continuous
value of position vector of particles in PSO to job permutations.A
timing algorithm is generated to find the optimal schedule and
calculate the objective function value of a given sequence in PSO
algorithm. Twodifferent neighborhood structures are applied to
improve the solution quality of PSO algorithm.The first one is based
on variable neighborhood search (VNS) and the second one is a
simple one with invariable structure. In order to compare the
performance of two neighborhood structures, random test problems
are generated and solved by both neighborhood
approaches.Computational results show that the VNS algorithmhas
better performance than the other one especially for the large sized
problems.
Abstract: In this paper, position vector of a partially null unit speed curve with respect to standard frame of Minkowski space-time is studied. First, it is proven that position vector of every partially null unit speed curve satisfies a vector differential equation of fourth order. In terms of solution of the differential equation, position vector of a partially null unit speed curve is expressed.
Abstract: The curves, of which the square of the distance
between the two points equal to zero, are called minimal or isotropic
curves [4]. In this work, first, necessary and sufficient conditions to
be a Pseudo Helix, which is a special case of such curves, are
presented. Thereafter, it is proven that an isotropic curve-s position
vector and pseudo curvature satisfy a vector differential equation of
fourth order. Additionally, In view of solution of mentioned
equation, position vector of pseudo helices is obtained.
Abstract: In this paper, first, a characterization of spherical
Pseudo null curves in Semi-Euclidean space is given. Then, to
investigate position vector of a pseudo null curve, a system of
differential equation whose solution gives the components of the
position vector of a pseudo null curve on the Frenet axis is
established by means of Frenet equations. Additionally, in view of
some special solutions of mentioned system, characterizations of
some special pseudo null curves are presented.