Unlike the basic operations in arithmetic/logical circuits (additions, multiplications, etc. that call for the respective homomorphy in the encryption), Turing machines can accomplish their basic operations much simpler and by exploiting group homomorphy only.
Given a symmetric body-bar framework, this paper exploits group representation theory to provide necessary conditions for rigidity in the form of very simply stated restrictions on the numbers of those structural components that are unshifted by the symmetry operations of the framework.
History abounds with examples of tyrants exploiting groups of people who believed they were about to be saved from the uncertainties of life.
According to both philosophers' theories, there are moral, political, and epistemological terms of the contract, and its effect has been to allow one group of persons effectively to dominate, subordinate, and exploit another group.
Subsequently, the source node and destination node exploit the group and interregion keys to perform secure multicast communications.
For estimating velocity vectors of K targets, we again exploit the group sparsity-based signal recovery method.
This is important because the overall impact of some phages may be over-estimated if they exploit a group of phylogenetically related hosts.
This allows us to exploit a group of monochromatic interactions for efficient encoding by a codebook that assigns strong interactions of the appropriate short codewords.
"We don't exploit other groups," he says, the "we" referring explicitly to white people.
Rangers' exploits in Group E have already confounded all expectations, the Ibrox side widely regarded at the outset as justified fourth seeds in a section that comprises Barcelona and the champions of France (Lyon) and Germany (Stuttgart).
