A time-continuous simple symmetric branching random walk on a one-dimensional integer lattice in an inhomogeneous random environment is considered. The branching environment is defined by one multiplication center of particles with nonrandom multiplication intensity anad by a field of identically distributed random variables symmetrically located with respect to the multiplication center, which specify the intensities of particle deaths. It is assumed that the number of sources is finite and that there is only one particle on the lattice at the initial moment of time. The goal of the work is to estimate the probabilities of exponential growth in the average number of particles at each point of the lattice.
Let ℕ be the set of natural numbers and ℤ_+=ℕ∪{0} be the set of integers. For any m,n∈ℕ, r∈ℤ_+, 0
This paper studies the number of one-generated associative finite-dimensional algebras with an identity over a finite field. A method for calculating the number of commutative matrix subalgebras generated by nonderogatory matrices over a field of low cardinality is proposed.
We consider a continuous-time random walk on a multidimensional integer lattice ℤ^d,d⩾ 1 , on which absorption of particles is possible at a finite number of selected points. It is assumed that at the initial time instance, one particle is located at each point of the lattice. The limit behavior of the particle numbers at every point is investigated under the assumption of a finite variance of the random walk jumps underlying the process.
The paper considers the order relations between the senior Lyapunov and the upper special and central indicators of a linear system defined in a discrete way. Examples of unbounded systems are given for which these indicators satisfy inequalities that differ from the known inequalities for bounded systems.
