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Unstable Solutions to Nonlinear Vector Differential Equations of Sixth Order with Delay
Get PDFThis paper investigates the instability of the zero solution of a certain vector differential equation of the sixth order with delay. Using the Lyapunov- Krasovskiĭ functional approach, we obtain a new result on the topic and give an example for the related illustration
Control approach to an ill-posed variational inequality
No full textWe are concerned with the proof of a generalized solution to an ill-posed variational inequality. This is determined as a solution to an appropriate minimization problem involving a nonconvex functional, treated by an optimal control technique. © EDP Sciences, 2014
Constant versus periodic fishing: Age structured optimal control approach
No full textThe paper investigates an age-structured infinite-horizon optimal control model of harvesting a biological resource, interpreted as fish. Time and age are considered as continuum variables. The main result shows that in case of selective fishing, where only fish of prescribed sizes is harvested, it may be advantageous in the log run to implement a periodic fishing effort, rather than constant (the latter suggested by single-fish models that disregard the age-heterogeneity). Thus taking into account the age-structure of the fish may qualitatively change the theoretically optimal fishing mode. This result is obtained by developing a technique for reliable numerical verification of second order necessary optimality conditions for the considered problem. This technique could be useful for other optimal control problems of periodic age-structured systems. © EDP Sciences, 2014
Optimal vaccination, treatment, and preventive campaigns in regard to the SIR epidemic model
No full textThe Susceptible-Infected-Recovered (SIR) model for the spread of an infectious disease in a population of constant size is considered. In order to control the spread of infection, we propose the model with four bounded controls which describe vaccination of newborns, vaccination of the susceptible, treatment of infected, and indirect strategies aimed at a reduction of the incidence rate (e. g. quarantine). The optimal control problem of minimizing the total number of the infected individuals on a given time interval is stated and solved. The optimal solutions are obtained with the use of the Pontryagin Maximum Principle and investigated analytically. Numerical results are presented to illustrate the optimal solutions. © EDP Sciences, 2014
Mr. Prairie View A&M Scholarship Pageant April 2, 2014
Get PDFhttps://digitalcommons.pvamu.edu/prairie-view-pageant/1049/thumbnail.jp
String Fluid Cosmological Model with Magnetic Field in Bimetric Theory of Gravitation
Get PDFIn this paper, LRS Bianchi type I string fluid cosmological model with magnetic field in bimetric theory of gravitation is investigated by assuming barotropic equation of state for pressure and density and assuming the bulk viscosity to be inversely proportional to the scalar expansion. The source of energy momentum tensor is a bulk viscous fluid containing one dimensional string with electromagnetic field. The physical and geometrical properties of the model are discussed. The bulk viscosity affected the whole properties of the model
Private Out-Domination Number of Generalized de Bruijn Digraphs
Get PDFDominating sets are widely applied in the design and efficient use of computer networks. They can be used to decide the placement of limited resources, so that every node has access to the resource through neighbouring node. The most efficient solution is one that avoids duplication of access to the resources. This more restricted version of minimum dominating set is called an private dominating set. A vertex v in a digraph D is called a private out-neighbor of the vertex u in S (subset of V(D)) if u is the only element in the intersection of in-neighborhood set of v and S. A subset S of the vertex set V (D) of a digraph D is called a private out-dominating set of D if every vertex of V − S is a private out-neighbor of some vertex of S. The minimum cardinality of a private out-dominating set is called the private out-domination number. In this paper, we investigate the private out-domination number of generalized de Bruijn digraphs. We estabilsh the bounds of private out-domination number. Finally, we present exact values and sharp upperbounds of private out-domination number of some classes of generalized de Bruijn digraphs
Effect of Toxic Metal on Root and Shoot Biomass of a Plant A Mathematical Model
Get PDFIn this paper, a mathematical model is proposed to study the impact of toxic metals on plant growth dynamics due to transfer of the toxic metal in plant tissues. In the model, it is assumed that the plant uptakes the metal from the soil through the roots and then it is transfered in the plant tissues and cells by transport mechanisms. It is observed experimently that when toxic (heavy) metals combines with the nutrient they form a complex compound due to which nutrient loses its inherent properties and the natural charaterstics of the nutrient are damaged. It is noticed that due to the presence of toxic (heavy) metal in the plant tissues and loss of inherent properties of nutrient due to reaction with the toxic metal, the growth rate of the plant decreases. In order to understand the impact on plant growth dynamics, we have studied two models: One model for a plant growth with no toxic effect and the other model for plant growth with toxic effect. From the analysis of the models the criteria for plant growth with and without toxic effects are derived. The numerical simulation to support the analytical results is done using MathLab