Volume 17, Issue 2

For classes of additively monotone matrices and incomplete anti-Monge matrices, we describe conditions which guarantee the attainment of the optimum of the functional of the quadratic assignment problem at a given permutation. The suggested conditions generalise and unify all special cases of the quadratic assignment problems with anti-Monge and Toeplitz matrices, including the well-known theorem on a permutation of three systems proved by G. H. Hardy, J. E. Littlewood, and G. Pólya in 1926, and all known extensions of this theorem.

The state transition graph of a simplest self-controlled 2-linear shift register over Galois ring R = GR (2 rn , 2 n ) is studied. An upper bound for the length of a cycle in this graph is obtained. In the case R = Z 2 n , states belonging to cycles of maximal length are described and the number of these states is evaluated.

We describe the class L ( R ) of all left modules over a ring R such that for any matrix D over R and any solvable system of equations F η ↓ = γ ↓ over a module from L ( R ) the system of equations A ξ ↓ = β ↓ is its D -implication if and only if T ( F , γ ↓ ) = ( AD ,β ↓ ) for some matrix T . If R is a quasi-Frobenius ring, then L ( R ) contains the subclass of all faithful R -modules. A criterion for a system of equations over a module from L ( R ) to be definite is obtained.

We consider problems on transformations of principal ideal rings incompatible with some epimorphisms of a given ring. We introduce the notion of a maximally incompatible transformation and describe all maximally incompatible transformations of the principal ideals ring A by a homomorphism A → A , where is some ideal of the ring A .

In this paper, we consider a model of a covert channel of agents interaction in the wide area network and in a closed segment of a local area network. We find the limit distribution of the statistics which underly the channel implementation. We analyse how to counteract the setting up of the covert channel with the use of random interference and prove that the channel withstands the random interference.

We present an algorithm producing a dynamic non-self-financing hedging strategy in an incomplete market corresponding to investor-relevant risk criterion. The optimisation is a two stage process that first determines admissible model parameters that correspond to the market price of the option being hedged. The second stage applies various merit functions to bootstrapped samples of model residuals to choose an optimal set of model parameters from the admissible set. Results are presented for options traded on the New York Stock Exchange.