Stochastic variational inequalities with jumps

This work is devoted to the study of a stochastic variational inequality with a Wiener–Poisson driving term. Existence and uniqueness are proven for Lipschitz coefficients and under general conditions for the unbounded term. One of the main tools used in order to obtain the existence result is a penalization method involving Moreau–Yosida regularization.     

On the Possible Automorphism Groups of a Steiner Quintuple System of Order 21

A Steiner system is called a Steiner quintuple systems of order v. The smallest order for which the existence, or otherwise, of a Steiner quintuple system is unknown is 21. In this article, we prove that, if an S(4, 5, 21) exists, the order of its full automorphism group is 1, 2, 3, 4, 5, 6, 7, or 10.     

Sabitov polynomials for volumes of polyhedra in four dimensions

In 1996 I.Kh. Sabitov proved that the volume of a simplicial polyhedron in a 3-dimensional Euclidean space is a root of certain monic polynomial with coefficients depending on the combinatorial type and on edge lengths of the polyhedron only. Moreover, the coefficients of this polynomial are polynomials in edge lengths of the polyhedron. This result implies that the volume of a simplicial polyhedron with fixed combinatorial type and edge lengths can take only finitely many values. In particular, this yields that the volume of a flexible polyhedron in a 3-dimensional Euclidean space is constant. Until now it has been unknown whether these results can be obtained in dimensions greater than 3. In this paper we prove that all these results hold for polyhedra in a 4-dimensional Euclidean space.     

On some free boundary problems of the prey–predator model

In this paper we investigate some free boundary problems for the Lotka–Volterra type prey–predator model in one space dimension. The main objective is to understand the asymptotic behavior of the two species (prey and predator) spreading via a free boundary. We prove a spreading–vanishing dichotomy, namely the two species either successfully spread to the entire space as time t goes to infinity and survive in the new environment, or they fail to establish and die out in the long run. The long time behavior of solution and criteria for spreading and vanishing are also obtained. Finally, when spreading successfully, we provide an estimate to show that the spreading speed (if exists) cannot be faster than the minimal speed of traveling wavefront solutions for the prey–predator model on the whole real line without a free boundary.     

The diameter of the acyclic Birkhoff polytope

In this work we give an interpretation of vertices and edges of the acyclic Birkhoff polytope, T_n=Ω_n(T), where T is a tree with n vertices, in terms of graph theory. We generalize a recent result relatively to the diameter of the graph G(T_n).     

Projective remoteness planes

A new axiomatization involving incidence and remoteness of planes with nondivision coordinate rings is introduced and a coordinatization theorem is obtained. A geometric process of splitting points and lines to obtain another plane with the same coordinates is described. It is also shown that a group of Steinberg type is parametrized by a nonassociative ring. The notion of elementary basis sets for an associative ring is introduced and constructions of projective and affine planes are given. A plane with reflections determining a system of rotations is shown to have commutative, associative coordinates.     

On the existence of semifields of prime power order admitting free automorphism groups

The purpose of this paper is to prove the existence of semifields of order q ⁴ for any odd prime power q = p^r, q > 3, admitting a free automorphism group isomorphic to Z ₂ × Z ₂.     

Harmonische Involutionen und Kreisspiegelungen in Möbiusebenen

An involutory automorphism of an inversive plane whose set of fixed points consists of exactly two points resp. of a circle is called a harmonic involution resp. an inversion. In this paper we study inversive planes with sufficiently many such involutions. Herrn Walter Benz zum 75. Geburtstag gewidmet