Results 1 - 10 of 1168
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[en] The equilibrium of a flexible inextensible string, or chain, in the centrifugal force field of a rotating reference frame is investigated. It is assumed that the end points are fixed on the rotation axis. The shape of the curve, the skipping rope curve or troposkien, is given by the Jacobi elliptic function sn
[en] We give an exact procedure for the evaluation of the Jacobian of a path transformation. This procedure is verified for the case of a particular function for which the Jacobian can be evaluated by another procedure
[en] The ternary commutator or ternutator, defined as the alternating sum of the product of three operators, has recently drawn much attention as an interesting structure generalizing the commutator. The ternutator satisfies cubic identities analogous to the quadratic Jacobi identity for the commutator. We present various forms of these identities and discuss the possibility of using them to define ternary algebras.
[en] We analyze the super n-bracket built from associative operator products. Since the super n-bracket with n even satisfies the so-called generalized super Jacobi identity, we deal with the n odd case and give the generalized super Bremner identity. For the infinite conserved operators in the supersymmetric Landau problem, we derive the super n-algebra which satisfies the generalized super Jacobi and Bremner identities for the n even and odd cases, respectively. Moreover the super sub-2n-algebra is also given. (paper)
[en] We study the Hankel determinant of the generalized Jacobi weight (x - t)γxα(1 - x)β for x in [0, 1] with α, β > 0, t < 0 and γ element of R. Based on the ladder operators for the corresponding monic orthogonal polynomials Pn(x), it is shown that the logarithmic derivative of the Hankel determinant is characterized by a Jimbo-Miwa-Okamoto σ-form of the Painleve VI system.
[en] The Jacobian and singularity analysis of parallel robots is necessary to analyze robot motion. The derivations of the Jacobian matrix and singularity configuration are complicated and have no geometrical earning in the velocity form of the Jacobian matrix. In this study, the screw theory is used to derive the Jacobian of parallel robots. The statics form of the Jacobian has a geometrical meaning. In addition, singularity analysis can be performed by using the geometrical values. Furthermore, this study shows that the screw theory is applicable to redundantly actuated robots as well as non redundant robots