Journal of Advances in Mathematics and Computer Science

Predator-prey models describe the dynamics of ecological systems in which two species, the predator and the prey, interact. The objective of this study is to formulate and analyze a predator-prey mathematical model, based on a system of delay differential equations that takes into consideration time delay in migration, with a prey migration rate that depends on the predator density and other factors like availability of its food. It is shown that the population density mainly depends on both barriers during migration and the migration rate. The rates of migration may be affected by factors such as infrastructure through natural habitat, destruction of the natural habitat through logging, natural disasters like re-outbreaks among others. In view of this, relevant agencies should employ measures which will deal with factors which slow down the rate of migration or cause barriers during migration for example reducing natural habitat land allocation to human settlement, agriculture or infrastructure.

Faced with the issue of hedging risk, small businesses entrepreneurs are investing considerable resources in risk management systems in as much as to maximize profit and stay operational, as such, the types of risk are identified and quantified within each business. This paper focused on the application of stochastic processes to prove that risk could be predetermined and hence determine which kind of small business should be insured to mitigate money spent on insurance.

In this paper, exact determinants and inverses of skew symmetric generalized Loeplitz matricesare given by constructing the special transformation matrices. And an example is provided to verify the feasibility of the formulas.

This paper is concerned with oscillation criteria for a class of third-order differential equations with neutral term by using some necessary analysis techniques, some sucient conditions for oscillation are obtained, some examples are provided to illustrate the main results.

Based on the soft formal analysis, in this article, the countability of soft topological space is studied. The soft neighborhoods basis of soft points is dened in the soft topology, and the properties of soft basis and soft neighborhoods basis are given. The countable axioms are dened in the soft topological space over the soft formal context, the examples are illustrated for the first countable axioms and the second countable axioms. The properties of the countable axioms are studied, and all the results can be implied to the soft rough topological space.