In this paper we introduce a type of fractional-order polynomials based on the classical Chebyshev polynomials of the second kind (FCSs). Also we construct the operational matrix of fractional derivative of order $ gamma $ in the Caputo for FCSs and show that this matrix with the Tau method are utilized to reduce the solution of some fractional-order differential equations.

Dihedral Golay sequences are introduced and found for lengths 7,9,15, and 19. Applications include new classes of signed group Hadamard matrices and 19 real Hadamard matrices of orders 2p, p S 4169.

in this work, we consider each normal alkane as a hypothetical mixtureof methyland methylene groups, in which the interaction potential of each pair is assumed to be the average effective pair potential. then, the lir equation of state (eos) is extended for such a hypothetical mixture. also, three basic compounds, namely, propane, n-butane and cyclohexane, are used to obtain the contribution of...

‎let $g$ be a finite $p$-group and $n$ be a normal subgroup of $g$ with‎ ‎$|n|=p^n$ and $|g/n|=p^m$‎. ‎a result of ellis (1998) shows‎ ‎that the order of the schur multiplier of such a pair $(g,n)$ of finite $p$-groups is bounded‎ ‎by $ p^{frac{1}{2}n(2m+n-1)}$ and hence it is equal to $‎ ‎p^{frac{1}{2}n(2m+n-1)-t}$ for some non-negative integer $t$‎. ‎recently‎, ‎the authors have characterized...

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. ...

A pair of regular Hermitian linear functionals (U ,V) is said to be an (M,N)-coherent pair of order m on the unit circle if their corresponding sequences of monic orthogonal polynomials {φn(z)}n>0 and {ψn(z)}n>0 satisfy M ∑ i=0 ai,nφ (m) n+m−i(z) = N ∑ j=0 bj,nψn−j(z), n > 0, where M,N,m > 0, ai,n and bj,n, for 0 6 i 6 M , 0 6 j 6 N , n > 0, are complex numbers such that aM,n 6= 0, n > M , bN,n...

A sequence is called perfect if its autocorrelation function is a delta function. In this paper, we give a new definition of autocorrelation function: generalized even and odd periodic autocorrelation, and generalized even and odd periodic cyclically conjugated autocorrelation. In particular, we study a special case of autocorrelation function called cyclically conjugated autocorrelation functi...

Recently, some table-lookup decoding algorithms (TLDAs) have been used to correct the binary Golay code. This paper proposes an efficient high-speed TLDA called message-syndrome decoding algorithm (MSDA) by using the message syndrome to correct the binary systematic Golay code. The proposed MSDA is based on the novel message-syndrome lookup table (MSLT). The MSLT merely consists of 12 candidate...

in this paper, a practical review of the adomian decomposition method, to extend the procedure to handle the strongly nonlinear problems under the mixed conditions, is given and the convergence of the algorithm is proved. for this respect, a new and simple way to generate the adomian polynomials, for a general nonlinear function, is proposed. the proposed procedure, provides an explicit formula...