A class Ψ of strictly concave and twice continuously differentiable functions ψ : R → R with particular properties is used for constraint transformation in the framework of a Nonlinear Rescaling (NR) method with “dynamic” scaling parameter updates. We show that the NR method is equivalent to the Interior Quadratic Prox method for the dual problem in a rescaled dual space. The equivalence is use...

The cubic spline interpolation method, the Runge–Kutta method, and the Newton–Raphson method are extended to dual versions (developed in the context of dual numbers). This extension allows the calculation of the derivatives of complicated compositions of functions which are not necessarily defined by a closed form expression. The code for the algorithms has been written in Fortran and some exam...

In this paper we nd solution of linear interval equation in dual form based on the generalizedprocedure of interval extension which is called interval extended zero method.Moreover, proposed method has signicant advantage, is that it substantially decreasesthe excess width eect.

We construct new binary optimal self-dual codes of length 50. We develop a construction method for binary self-dual codes with a fixed-point-free automorphism of order 2. Using this method, we find new binary optimal self-dual codes of length 52. From these codes, we obtain Lee-optimal self-dual codes over the ring F2 + uF2 of lengths 25 and 26.

in this paper, we study spacelike dual biharmonic curves. we characterize spacelike dual biharmonic curves in terms of their curvature and torsion in the lorentzian dual heisenberg group . we give necessary and sufficient conditions for spacelike dual biharmonic curves in the lorentzian dual heisenberg group . therefore, we prove that all spacelike dual biharmonic curves are spacelike dual heli...

In this paper, the fuzzy dual matrix system as AX + B = CX + D in which A, B, C, D, X are LR fuzzy matrices is studied. At first we solve 1-cut system in order to find the core of LR fuzzy solution; then to obtain the spreads of the LR fuzzy solution, we discuss in several cases. The spreads are obtained by using multiplication, quasi norm and minimization problem with a special objective funct...

Compared to binary self-dual codes, few methods are known to construct ternary self-dual codes. In this paper, a construction method for ternary self-dual codes is presented. Using this method, a number of new extremal ternary self-dual codes are obtained from weighing matrices. In addition, a classification is given for extremal ternary self-dual codes of length 40 constructed from Hadamard ma...