An article entitled: `A Note on Modeling Multiple Choice Requirements for Simple Mixed Integer Programming Solversa was published by Ogryczak (Comput. Oper. Res. 23 (1996) 199). In this article, Ogryczak proposed a reformulation technique called special ordered inequalities (SOI) to model the non-convex programming problems with special ordered sets (SOS) of variables. The SOI technique appears...

Let $G$ be a finite group. The prime graph of $G$ is a graph $Gamma(G)$ with vertex set $pi(G)$, the set of all prime divisors of $|G|$, and two distinct vertices $p$ and $q$ are adjacent by an edge if $G$ has an element of order $pq$. In this paper we prove that if $Gamma(G)=Gamma(G_2(5))$, then $G$ has a normal subgroup $N$ such that $pi(N)subseteq{2,3,5}$ and $G/Nequiv G_2(5)$.

Among the noncompact matrix Lie groups, the special Euclidean group and the unipotent matrix group play important roles in both theoretic and applied studies. The Riemannian means of a finite set of the given points on the two matrix groups are investigated, respectively. Based on the left invariant metric on the matrix Lie groups, the geodesic between any two points is gotten. And the sum of t...

It is known that if the support of a function $f \in L^{1}(\mathbb{R}^{n})$ and its Fourier transform have finite measure then $f=0$ almost everywhere. We study generalizations this property for semisimple Lie groups.

In this article we investigate the autotopism group of the so-called cyclic semifield planes. We show that the group generated by the homology groups of the nuclei is already the full group of autotopisms that are linear with respect to the nuclei. The full autotopism group is also computed with the exception of one special subcase.

This paper examines abstract regular polytopes whose automorphism group is the projective special linear group PSLp4,Fqq. For q odd we show that polytopes of rank 4 exist by explicitly constructing PSLp4,Fqq as a string C-group of that rank. On the other hand, we show that no abstract regular polytope exists whose group of automorphisms is PSLp4,F2k q.