119634267
On Thue's equation
and more precisely for the number of primitive solutions to (1.1), that is, solutions in coprime integers x, y. The first important results on the number of solutions of Thue's equation were obtained by C.L. Siegel, in the case r = 3 and in the binomial case F ( x , y ) = a x r b y r. In view of his results and comments, we should attribute to Siegel the problem to decide whether the number of primitive solutions to (1.1), for irreducible F of degree r > 3, could be bounded by a function depending only on r and h, but otherwise independent of F. In 1983, Siegel's question was answered in the affirmative by J.-H. Evertse [2]. As a special case of his results (he also treats equations in number fields), Evertse obtains the bound
129296972
Irregularities of distribution. V
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.
120616848
Stetige Funktionen auf dem Torus.
121229043
Some results in probabilistic geometry
120328164
Irregularities of distribution. IV
121073876
Existence of solutions of certain nonconvex optimal control problems governed by nonlinear integral equations
Optimal control problems with nonlinear equations usually do not have a solution, i.e. an optimal control. Nevertheless, if the cost functional is uniformly concave with respect to the state, the solution may exist. Using the Balder's technique based on a Youngmeasure relaxation, Bauer's external principle and investigation of extreme Young measures; the existence is demonstrated here for optimal control processes described by nonlinear integral equations
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 
$1/N$.

120957526
On Stochastic Differential Equations with Reflecting Barriers