123986885
On Heights of Algebraic Subspaces and Diophantine Approximations
The basic problem of diophantine approximations could be formulated as follows. Assume a Cartesian coordinate system in euclidean E2 to be given. Let L be a line through the origin 0. Find a line L' through 0 and defined over the rationals Q (defined by a linear equation with rational coefficients) which is "as close as possible" to L. As a measure of their closeness, introduce /r(L, L') = sin Ap, where p is the angle between L and L', 0 0, there will be infinitely many such lines L' satisfying J(L, L') 0 and a line L through 0 which is not defined over the rationals, there are infinitely many rational lines L' through 0 satisfying !(L, L') < (5-1/2 + 8) H(L)-2 This statement would become false if 5-1/2 were replaced by a smaller constant. The problem of simultaneous approximation amounts to the problem of finding a line L' of euclidean En through the origin 0 and defined over the rationals which is "close" to a given line through 0. The problem of linear forms amounts to finding a rational hyperplane H of euclidean En through 0 and "close" to a given line through 0. This suggests the following problem. Let K be a fixed real algebraic number field of finite degree over the rationals Q. Let 0 < d < n, 0 < e < n, and A a d-dimensional subspace of euclidean En. Find a subspace B of En of dimension e and defined over K, such that B is close to A. One can also
121422615
Flächenapproximation beim Jacobialgorithmus
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.
121164029
Über höhere kritische Determinanten von Sternkörpern
120328164
Irregularities of distribution. IV
129296972
Irregularities of distribution. V
1555430
On a general class of one-factor models for the term structure of interest rates

Abstract.We propose a general one-factor model for the term structure of interest rates which based upon a model for the short rate. The dynamics of the short rate is described by an appropriate function of a time-changed Wiener process. The model allows for perfect fitting of given term structure of interest rates and volatilities, as well as for mean reversion. Moreover, every type of distribution of the short rate can be achieved, in particular, the distribution can be concentrated on an interval. The model includes several popular models such as the generalized Vasicek (or Hull-White) model, the Black-Derman-Toy, Black-Karasinski model, and others. There is a unified numerical approach to the general model based on a simple lattice approximation which, in particular, can be chosen as a binomial or 
$N$-nomial lattice with branching probabilities 
$1/N$.

121309269
Stochastic Integration for Some Rough Non‐adapted Processes
For the Wiener process W on the unit interval and 0 ⩽ θ ⩽ 1/4 consider the non-adapted process ut =sgn(Wt−θ)sgn(W1−WT+θ), θ⩽t⩽1−θ. By giving explicit descriptions of their expansions in terms of generalized Hermite polynomials we show that they possess Skorohod integral processes. In the more interesting case θ = 0, a component due to the interaction of forwards and backwards Wiener process seems to dominate the non-interaction part, whereas for θ > 0 interaction drops geometrically with respect to non-interaction. We translate these purely analytic properties into more familiar terms of samples of stochastic processes. Firstly, we construct simple approximations of the integral process which are of the type of Riemann sums. We then show that their quadratic variations are the same as for the Wiener process on [θ, 1 − θ]. Finally, using the fact that W remains a semimartingale if its filtration is enlarged by W1, we compare the resulting Ito integral process to the Skorohod integral process of u in case θ = 0. We show that they differ by a local time. Consequently the Skorohod integral process of u is a semimartingale.
120957526
On Stochastic Differential Equations with Reflecting Barriers