Swivel support for gas bearings Patent

Swivel support for gas bearing for position adjustment between ball and supporting cu

Expressing Forms as a sum of Pfaffians

Let A= (a_{ij}) be a symmetric non-negative integer 2k x 2k matrix. A is homogeneous if a_{ij} + a_{kl}=a_{il} + a_{kj} for any choice of the four indexes. Let A be a homogeneous matrix and let F be a general form in C[x_1, \dots x_n] with 2deg(F) = trace(A). We look for the least integer, s(A), so that F= pfaff(M_1) + \cdots + pfaff(M_{s(A)}), where the M_i's are 2k x 2k skew-symmetric matrices of forms with degree matrix A. We consider this problem for n= 4 and we prove that s(A) < k+1 for all A

The Pfaff lattice and skew-orthogonal polynomials

Consider a semi-infinite skew-symmetric moment matrix, m_{\iy} evolving according to the vector fields \pl m / \pl t_k=\Lb^k m+m \Lb^{\top k} , where \Lb is the shift matrix. Then the skew-Borel decomposition m_{\iy}:= Q^{-1} J Q^{\top -1} leads to the so-called Pfaff Lattice, which is integrable, by virtue of the AKS theorem, for a splitting involving the affine symplectic algebra. The tau-functions for the system are shown to be pfaffians and the wave vectors skew-orthogonal polynomials; we give their explicit form in terms of moments. This system plays an important role in symmetric and symplectic matrix models and in the theory of random matrices (beta=1 or 4).Comment: 21 page

The Effect of the Context on the Anisotropy of the Visual Field

The phenomenal (visual) field is not homogeneous (anisotropic). Clear examples of this are given by Bartlett’s “replication experiments” and Blum’s “firegrass model”. In 1991, Stadler, Kruse, Richter and Pfaff attempted to develop a vector field model of the visual field, and on this basis, Kruse, Luccio, Pfaff and Stadler (1996) demonstrated relevant context effects introducing different directionally oriented shapes in the field. In this paper, we propose some methodological modifications, aimed to improve the consistency of the results