Existence of Periodic Properties of Solutions of Certain Autonomous Third Order Nonlinear Differential Equations

Abstract

Introduction: Knowledge of food composition is crucial in the assessment of nutritional quality and potential contribution to recommended nutrient intakes. Fish plays a major role in ensuring food and nutritional security among the poor, vulnerable and rural fishing communities. However, in Nigeria, information on the nutrition content of some locally important fish species particularly after smoking or sun-drying is either lacking or missing. Aim: The present study was carried out to evaluate (i) the nutritional value of two locally smoked clupeids (Sardinella maderensis and Pellonula leonensis); (ii) in relation to recommended nutrient intakes in pre-school children (< 5 years) and elderly (men and women >70 years) and (iii) linkages between nutrient access and intake. Materials and Methods: Fresh samples were collected from Badagry Creek, smoked using local smoking kiln and analyzed according to AOAC standard method. Data were collected in duplicates and analyzed using t-test. Results: There were significant differences (P =.05) in the proximate composition except for crude fibre between the two fish species. The percentage cover of daily recommended intake of phosphorous and calcium from the two species were very low (1. 81-3.7%; 0.023% - 0.0912%) but low to moderate for zinc (2 % - 22.50%) in pre-school children and the elderly. Conclusion: Sequel to the results obtained in this study, the two smoked fish species showed good nutritive qualities for human health despite the low to moderate contents of calcium, zinc and phosphorus. Keywords: Badagry Creek, clupeids, nutritional quality, smoked fish, Nigeria, recommended nutrient intakes.

Stability and Ultimate Boundedness of Solutions of Certain Third Order Nonlinear Rectangular Matrix Differential Equations

“…In particular, the intuitive idea of qualitative properties of solutions of rectangular matrix differential equations is of practical importance in analyzing the layout of control systems, models of cross interactions between competing species, and spread of diseases in a community with different traits as well in image compression and processing of tasks. Also, the results obtained in this work will be comparable in generality to the results obtained in [3,12,16,22,26,27] and some results existing in the literature. A numerical instance is provided to demonstrate the importance and relevance of the results achieved as well as provide a graphical analysis to corroborate our discoveries regarding the behaviour of solutions of the rectangular matrix equation (1.1).…”

“…The investigations in Olutimo [16] are related to [27] and provided the extensions of some of the results of [27] to (1.1), where X is a rectangular matrix (i.e., X : R → R n×m ) and A, B are n × n symmetric matrices with constant values. X, H(X), and P (t, X, Ẋ, Ẍ) being continuous n × m matrices in the real domain.…”

“…X, H(X), and P (t, X, Ẋ, Ẍ) being continuous n × m matrices in the real domain. The present investigation is based on [16] where X : R → R n×m , n ̸ = m and B Ẋ = Ψ( Ẋ) in (1.1). Based on our review of the literature, no research derived from [16] was discovered.…”

“…The present investigation is based on [16] where X : R → R n×m , n ̸ = m and B Ẋ = Ψ( Ẋ) in (1.1). Based on our review of the literature, no research derived from [16] was discovered. Moreover, the results for which the unknown function X is not a square matrix were left open in [27].…”

“…To our knowledge, results in this path do not exist. In this case, we shall give augmentation of some results of [16] to certain third order matrix differential equations (1.1). In addition, matrix differential equations contribute appreciably to the study and plan of complex dynamic systems across various fields, giving valuable insights into the dynamic behaviour of interconnected elements.…”