Mathematics and Computational Sciences
Volume:3 Issue: 4, Autumn 2022

Fish stocks in the developing world are often depleted as a result of the application of excessive fishing effort on the part of the fishermen. A bioeconomic model with logistic growth, proportional harvesting and quadratic costs is proposed to study the effect of overcapacity on a marine fishery. Also incorporated into the model is an isoperimetric constraint to account for the annual total allowable catch (TAC). Pontryagin's maximum principle is employed to determine the necessary conditions for optimality of the model. Additionally, the sufficiency conditions that guarantee the existence and uniqueness of the optimality system are discussed. Furthermore, the relationship between the shadow price of fish stock, the shadow price of the total allowable catch and the marginal net revenue as it relates to the optimal fishing effort is explored. Numerical simulation with empirical data on the Ghana sardinella fishery is performed to validate the theoretical results. The findings of the study indicate that for a TAC equal to the maximum sustainable yield (MSY), the average fishing effort should not exceed $95\%$ of the MSY effort, provided that the initial stock size is exactly 55% of the carrying capacity.

In this paper, we study the existence of positive solutions for a class of multi points boundary value problems. We introduce a completely continuous operator such that, the fixed points of this operator are positive solutions of the problem. We establish some theorems to prove the existence ofsolutions for this system.

One of the most important decisions in project appraisal and enterprise economic policy under constrained and inconsistent circumstances is to select an option among several others. If all variables can be measured by a measure called money, methods such as Internal Rate of Return (IRR) and Average Internal Rate of Return (AIRR) can be used. The AIRR method is a mode developed by the IRR method. However, this method (AIRR) may occasionally result in unrealistic (huge) periodic rates. This article adopted a simple technique to address this problem. Finally, the technique is further explained by solving several numerical examples. According to the results, the proposed method led to distribution of large periodic rates over other periodic rates producing slightly unrealistic results. The results of research indicated that the proposed method causes distribution of large size periodic rates between the rates of other periods so that the new values do not go far beyond reality.

Today, the desire to use mixed-critical systems in the industry is increasing. In order to provide the processing power required by mixed-critical systems, multi-core architectures are considered a suitable option. One of the main challenges in mixed-critical systems is task scheduling, which is even more challenging in multi-core architectures. Many studies of task scheduling in mixed-critical multi-core systems have dealt with the scheduling of independent tasks. But in many real systems, tasks are dependent on each other. In this research, we will deal with the scheduling of dependent periodic tasks in mixed-critical multi-core systems in such a way that the presented schedule satisfies the system constraints. The proposed algorithm provides the best possible schedule using linear programming. The results of the experiments showed that the presented method has been able to significantly reduce the number of preemptions while maintaining the scheduling capability.

Capacity, also known as a non-additive measure, is an extension of the Lebesgue measure. In recent years, bi-capacity was presented as a generalization of capacity with several bipolar fuzzy integrals related to bi-capacity, one of them being the bipolar Shilkret integral. In this paper, we propose a new approach to calculating the bipolar Shilkret integral to be suitable for bipolar scales. Then, we give some main properties of this integral related to bi-capacity.

The variational iteration algorithm using shifted Chebyshev polynomials of the third kind was used to obtain the numerical solution of seventh order Boundary Value Problems(PVBs) in this paper. The proposed method is made by constructing the shifted Chebyshev polynomials of the third kind for the given boundary value problems and used as a basis functions for the approximation. Numerical examples where also given to show the efficiency and reliability of the proposed method. Calculations were performed using maple 18 software.