There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

According to W. Edwards Deming, American companies require nothing less than a transformation of management style and of governmental relations with industry. In Out of the Crisis, originally published in 1982, Deming offers a theory of management based on his famous 14 Points for Management. Management's failure to plan for the future, he claims, brings about loss of market, which brings about loss of jobs. Management must be judged not only by the quarterly dividend, but by innovative plans to stay in business, protect investment, ensure future dividends, and provide more jobs through improved product and service. In simple, direct language, he explains the principles of management transformation and how to apply them.

Out of the Crisis

The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

Series Preface * Preface to the Third Edition * 1 Linear Systems * 2 Nonlinear Systems: Local Theory * 3 Nonlinear Systems: Global Theory * 4 Nonlinear Systems: Bifurcation Theory * References * Index

/pdf/differential-equations-and-dynamical-systems-3chsjx2k45.pdf

Differential Equations and Dynamical Systems

Modelling the Impact of Drug Abuse on a Nation’s Education Sector

Cancer and hepatitis are global infectious diseases claiming millions of lives every year. In this study, we develop and analyse a cancer and hepatitis co-infection model to examine the relationship between the two diseases. In addition, we derive and analyse the reproduction numbers of each and both diseases. We explore the sensitivity of the reproduction numbers of both diseases to parameters, and performed the numerical simulations of the model. Our analyses show that the cancer-hepatitis model has disease-free equilibrium whenever the reproduction number is less than unity, and has a unique endemic equilibrium if the reproduction number is greater than one. Also our analyses highlight the impact of hepatitis on cancer and vise versa. Furthermore, our numerical solutions indicate that the carrying capacity and progression rate from susceptible to hepatitis and cancer play crucial roles in determining the population dynamics of both diseases. Although, our results highlight the impact of hepatitis on cancer, an increase in the proportion of cells migrating from susceptible to hepatitis will have more impact on the hepatitis-infected than cancer-infected cells. Our results also suggest that more cells are recovered under a reduced carrying capacity.

A cancer and hepatitis co-infection model

In this paper, we propose and analyse a mathematical model to study the dynamics of a fishery resource system in an aquatic environment that consists of two zones: water hyacinth zone and water hyacinth free zone, fishing was allowed in both zones. The developed model describes the quantitative relationship of water hyacinth and fish biomass densities. The conditions for the validity of the model were established. The biological equilibria of the model was determined, and proved to be not locally stable. Small increments on the parameters of the model associated with water hyacinth shifted the equilibria of the model significantly, moreover in each shift of an equilibrium point, the fish subpopulation in water hyacinth zone decreased more rapidly than the fish subpopulation in water hyacinth free zone. Optimal harvesting policy in the two zones was discussed using Pontryagin's maximum principle where by mathematical equations governing the optimal fish biomass densities and optimal harvestings at any time t were determined. The model best fits the Lake Victoria fishery which has greatly hampered by water hyacinth infestation. The study provides a mathematical proof that infestation of water hyacinth have negative effects on fish stocks and fish production. MSC: 65P99 92B05 37N25

http://www.ijaamm.com/uploads/2/1/4/8/21481830/v2n1p5.pdf

A model of a fishery resource in the presence of water hyacinth, the case of lake Victoria

We consider a system of coupled partial differential equations describing transient fluid flow and heat transfer with variable flow properties Classical Lie point symmetry analysis of this system 

https://journals.sagepub.com/doi/pdf/10.1155/2013/983962

Computational Modelling and Similarity Reduction of Equations for Transient Fluid Flow and Heat Transfer with Variable Properties.

Catalytic converter in an automobile’s exhaust system is made up of a finely divided platinum–iridium catalyst (i.e. forming a porous matrix) and provides a platform for exothermic chemical reaction where unburned hydrocarbons completely combust. In this paper, the steady-state solutions of a strongly exothermic reaction of a viscous combustible fluid (fuel) in a catalytic converter-modelled as a cylindrical pipe filled with a saturated porous medium under Arrhenius kinetics, neglecting reactant consumption, are presented. The Brinkman flow model is employed. Having known the velocity distribution, the nonlinear energy equation is solved using a perturbation technique together with a special type of Hermite– Padé approximants and the important properties of the temperature field including bifurcations and thermal criticality are discussed.

Oluwole Daniel Makinde

Papers

Modelling the Impact of Drug Abuse on a Nation’s Education Sector

A cancer and hepatitis co-infection model

A model of a fishery resource in the presence of water hyacinth, the case of lake Victoria

Computational Modelling and Similarity Reduction of Equations for Transient Fluid Flow and Heat Transfer with Variable Properties.

Modelling the Thermal Operation in a Catalytic Converter of an Automobile's Exhaust