121164029
Über höhere kritische Determinanten von Sternkörpern
122689116
On simultaneous approximations of two algebraic numbers by rationals
123627311
Irregularities of distribution. II
(The constant cx and other constants c2, c3,... introduced below are positive and independent of N.) It is not known whether this estimate is best possible, but it can be shown that the exponent of the logarithm in (2) cannot be replaced by numbers larger than a certain constant c2(n). (One may take c2(2) = 1 by [3, inequality (3)], and when n>2 one may take c2(n) = n by [4, Theorem 3], since the estimate given there is easily checked to be independent of the box considered.) Little could be gained by allowing translations of the boxes B(u). Namely, if u, v are any points, let B(u; v) be the box consisting of the points x + v where x £ B(u). Now suppose that both u, v have positive coordinates, and set B=B(u; v). Then at least one of the 2n boxes B' = B(w) where each coordinate w} of w is either v, or Uj + Vj, satisfies A(B')^2~n A(B). The situation is rather different if we allow rotations. If t is an orthogonal transformation of En, write B(u; v; t) for the box consisting of the points tx + v where x e B{u). The diameter of this box is |«| =(«?+■•• -r-wf)1'2.
122349525
Eine Verschärfung des Satzes von Minkowski-Hlawka
120078825
A metrical theorem in diophantine approximation
A method and apparatus is provided for measuring the content of a low-molecular weight compound in a complex medium which includes a dialyzer, conduits for conveying the complex medium through the dialyzer and conduits for supplying dialysis fluid to the dialyzer to receive by diffusion a portion of the low-molecular weight compound in the complex medium to produce a dialysate. Apparatus is also provided for conducting the dialysate produced from the dialyzer to a measuring unit, wherein the conducting apparatus includes a main flow line having an enzyme bed and a shunt flow line. A control device is provided for directing the flow of dialysate through the main flow line and the enzyme bed or the shunt flow line, so that the flow of dialysate bypasses the enzyme bed. Apparatus is also provided for comparing the dialysates in the main and shunt flow lines.
120952401
The measure of the set of admissible lattices
A0 denotes the lattice of points with integral coordinates. Theorem 4 will be used to prove Theorem 5 which is an improvement of the Minkowski-Hlawka Theorem. We also prove two existence theorems which are in a certain sense converses of the MinkowskiHlawka Theorem (Theorem 6 and Theorem 7). The author is very indebted to the referee who pointed out some errors of the originally submitted paper and made useful suggestions. The originally stated Theorem 1 was wrong.
120009511
On semimartingale diffusions and stochastic differential equations
Given a regular diffusion X on the real axis which is a semimartingale we describe the semimartingale decomposition of X. We then give necessary and sufficient conditions in terms of the scale and the speed measure for X being a solution of an Ito type stochastic differential equation driven by a Wiener process and with classical drift or a drift term involving the local time of X. A regular diffusion is also characterized as unique solution of a certain martingale problem. Finally we discuss an example related to skew Brownian motion