One of the important problems in group theory is characterization of a group by a given property, that is, to prove there exist only one group with a given property. Let  be a finite group. We denote by  the largest order of elements of . In this paper, we prove that some Suzuki groups are characterizable by order and the largest order of elements. In fact, we prove that if  is a group with  an...

Given a rectangle A and a set S of n points in A, the maximum empty rectangle problem is that of finding a largest-area rectangle which is contained in A. has its sides parallel to Ihose ofA. and does Dot contain any of the points in S. This Dote describes an efficient algorithm for solving this problem.

We derive an algorithm for estimating the largest p ≥ 1 values aij or |aij | for an m×n matrix A, along with their locations in the matrix. The matrix is accessed using only matrix– vector or matrix–matrix products. For p = 1 the algorithm estimates the norm ‖A‖M := maxi,j |aij | or maxi,j aij . The algorithm is based on a power method for mixed subordinate matrix norms and iterates on n × t ma...

Saving a patients live in an emergency state especially if he is far from medical institutions, is considered to be the primary concern of the physician. With a mobile physician, patients health state may vary to be in a critical situation that requires immediate medical intervention. Having chosen the medical institution as destination, the doctor must react immediately and reach his patient a...

Given a rectangle A and a set S of n points in A, we consider the problem, called the maximum empty rectangle problem, of finding a maximum area rectangle that is fully contained in A and does not contain any point of S in its interior. An O(n’) time algorithm is presented. Furthermore, it is shown that if the points of S are drawn randomly and independently from A, the problem can be solved in...

In this paper we investigate the top-k-selection problem, i.e. determine the largest, second largest, ..., and the k-th largest elements, in the dynamic data model. In this model the order of elements evolves dynamically over time. In each time step the algorithm can only probe the changes of data by comparing a pair of elements. Previously only two special cases were studied [2]: finding the l...