In this paper, quadratic and sextic B-splines are used to construct an approximating function based on the integral values instead of the function values at the knots. This process due to the type of used B-splines (fourth order or sixth order), called integro quadratic or sextic spline interpolation. After introducing the integro quartic and sextic B-spline interpolation, their convergence is ...

Let Q be a positive definite integral quadratic form in ti variables, with the additional property that the adjoint form Q' is also integral. Using the functional equation of the Epstein zeta function, we obtain a symmetric functional equation of the ¿-function of Q with a primitive character to mod q (additive or multiplicative) defined by £io(2(x))C(x)-ï. Re(s) > nl2> where the summation exte...

This paper presents analytical solutions for the forward displacement and velocity kinematics of the “321-HEXA”, a fully-parallel manipulator design with R-RR-RRR legs as in the “HEXA” design and with a “3-2-1” top platform. The forward position and velocity kinematics rely on simple geometric algorithms that find the position and velocity of the top of a tetrahedron from the knowledge of the t...

We present a general semidefinite relaxation scheme for general n-variate quartic polynomial optimization under homogeneous quadratic constraints. Unlike the existing sum-of-squares (SOS) approach which relaxes the quartic optimization problems to a sequence of (typically large) linear semidefinite programs (SDP), our relaxation scheme leads to a (possibly nonconvex) quadratic optimization prob...

The association of algebraic objects to forms has had many important applications in number theory. Gauss, over two centuries ago, studied quadratic rings and ideals associated to binary quadratic forms, and found that ideal classes of quadratic rings are exactly parametrized by equivalence classes of integral binary quadratic forms. Delone and Faddeev, in 1940, showed that cubic rings are para...