General transformation formulas for Fermi–Walker coordinates

General Transformation Formulas for Fermi-Walker Coordinates

We calculate the transformation and inverse transformation, in the form of Taylor expansions, from arbitrary coordinates to Fermi-Walker coordinates in tubular neighborhoods of arbitrary timelike paths for general spacetimes. Explicit formulas for coefficients and the Jacobian matrix are given.

Range Restriction for General Formulas

Deductive databases need general formulas in rule bodies, not only conjuctions of literals. This is well known since the work of Lloyd and Topor about extended logic programming. Of course, formulas must be restricted in such a way that they can be effectively evaluated in finite time, and produce only a finite number of new tuples (in each iteration of the TP -operator: the fixpoint can still ...

Combinatorial formulas for Γ - coordinates in a totally

Postnikov constructed a decomposition of a totally nonnegative Grassmannian (Grkn)≥0 into positroid cells. We provide combinatorial formulas that allow one to decide which cell a given point in (Grkn)≥0 belongs to and to determine affine coordinates of the point within this cell. This simplifies Postnikov’s description of the inverse boundary measurement map and generalizes formulas for the top...

ar X iv : 0 71 2 . 38 38 v 3 [ gr - q c ] 3 1 M ay 2 00 8 General Transformation Formulas for Fermi - Walker Coordinates

New Inversion Formulas for the Krätzel Transformation

We study in distributional sense by means of the kernel method an integral transform introduced by Krätzel. It is well known that the cited transform generalizes to the Laplace and Meijer transformation. Properties of analyticity, boundedness, and inversion theorems are established for the generalized transformation. 2000 Mathematics Subject Classification. Primary 44A15, 46F12.