The trajectory planning, which is known as a movement from starting to end point by satisfying the constraints along the path is an essential part of robot motion planning. A common way to create trajectories is to deal with polynomials which have independent coefficients. This paper presents a trajectory formulation as well as a procedure to arrange the suitable trajectories for applications. ...

the trajectory planning, which is known as a movement from starting to end point by satisfying the constraints along the path is an essential part of robot motion planning. a common way to create trajectories is to deal with polynomials which have independent coefficients. this paper presents a trajectory formulation as well as a procedure to arrange the suitable trajectories for applications. ...

in this study test-day records of milk (kg), fat (g), and protein (g) yields, somatic cell score (scs, cells/ml) collected by animal breeding center of iran during 2007 and 2009 were used to estimate genetic parameters using random regression model. models with different order of legendre polynomials were compared using bayesian information criterion (bic).for milk, fat yield and scs genetic an...

Every finite field has many multiplicative generators. However, finding one in polynomial time is an important open problem. In fact, even finding elements of high order has not been solved satisfactorily. In this paper, we present an algorithm that for any positive integer c and prime power q, finding an element of order exp(Ω( √ qc)) in the finite field Fq(qc−1)/(q−1) in deterministic time (q...

Let N∗(m) be the minimal length of a polynomial with ±1 coefficients divisible by (x − 1)m. Byrnes noted that N∗(m) ≤ 2m for each m, and asked whether in fact N∗(m) = 2m. Boyd showed that N∗(m) = 2m for all m ≤ 5, but N∗(6) = 48. He further showed that N∗(7) = 96, and that N∗(8) is one of the 5 numbers 96, 144, 160, 176, or 192. Here we prove that N∗(8) = 144. Similarly, let m∗(N) be the maxima...