Mathematical modelling of social obesity epidemic in the region of Valencia,Spain

In this article, we analyse the incidence of excess weight in 24- to 65-year-old residents in the region of Valencia, Spain, and predict its behaviour in the coming years. In addition, we present some possible strategies to prevent the spread of the obesity epidemic.

We use classical logistic regression analysis to find out that a sedentary lifestyle and unhealthy nutritional habits are the most important causes of obesity in the 24- to 65-year-old population in Valencia. We propose a new mathematical model of epidemiological type to predict the incidence of excess weight in this population in the coming years. Based on the mathematical model sensitivity analysis, some possible general strategies to reverse the increasing trend of obesity are suggested.

The obese population in the region of Valencia is increasing (11.6% in 2000 and 13.48% in 2005) and the future is worrisome. Our model predicts that 15.52% of the population in Valencia will be obese by 2011. Model sensitivity analysis suggests that obesity prevention strategies (healthy advertising campaigns) are more effective than obesity treatment strategies (physical activity) involving the obese and overweight subpopulation in controlling the increase of adulthood obesity in the region of Valencia.     

Persistence and extinction in a mathematical model of cell populations affected by radiation

A mathematical model consisting of a system of two ordinary differential equations is formulated to represent the interrelationship between healthy and radiated cells at a given cite. Three different modes of radiation are considered: constant, decaying, and periodic radiation. For the constant case, precise criteria for persistence and extinction are obtained. In the decaying case, it is shown that the radiated cells always become extinct. Finally in the periodic case, criteria are obtained for a perturbed positive periodic solution. Dedicated to the memory of Professor Miklós Farkas     

运动机械质心数学模型及其在机构质心稳定中的应用

以四连杆机械为例,其自由度是1,整个机构的质心只需一个独立参变数描述.故机构的质心对该参数的导数等于零即机构质量中心保持固定的充要条件.通过对线性方程组基础理论的巧妙利用,给出了四连杆在工作状态下质心保持稳定的几何特征.     

On the (in)stability of quasi‐static paths of smooth systems: definitions and sufficient conditions

A concept of stability of quasi‐static paths is discussed in this paper that takes into account the existence of fast (dynamic) and slow (quasi‐static) time scales in the evolution of many mechanical systems. The proposed concept is essentially a continuity property with respect to the smallness of the initial perturbations (as in Lyapunov stability) and the smallness of the quasi‐static loading rate (that plays the role of the small parameter in singular perturbation problems). A related concept of attractiveness is also proposed. Several examples illustrate the relevance of the definitions. Sufficient conditions for attractiveness or for instability of quasi‐static paths of smooth systems are proved. Copyright © 2005 John Wiley & Sons, Ltd.     

On Existence of Solutions to Differential Equations or Inclusions Remaining in a Prescribed Closed Subset of a Finite-Dimensional Space

This paper is devoted to existence of trajectories to differential equations and inclusions remaining in a given closed (or compact) set. Topological properties of the boundary of this set enables us to conclude the existence of such trajectories in many cases.     

Modelling the landing of a plane in a calculus lab

We exhibit a simple model of a plane landing that involves only basic concepts of differential calculus, so it is suitable for a first-year calculus lab. We use the computer algebra system Maxima and the interactive geometry software GeoGebra to do the computations and graphics.     

Numerical model of a pine in a wind

Steady-state nonlinear differential equations govering the stem curve of a wind-loaded pine are derived and solved numerically. Comparison is made between the results computed and the data from photographs of a pine stem during strong wind. The pine breaking is solved at the end.     

Stabilization of a class of hybrid systems arising in flexible spacecraft

We consider the problem of rigorous modelling of flexible spacecraft and their stabilization. It is shown that the dynamics of the flexible spacecraft can be described by a coupled system of ordinary differential equations and partial differential equations (hybrid system). Lyapunov's approach is used to prove the stabilizability of the system. Simple feedback controls are suggested for stabilization of flexible spacecraft.This work was supported in part by the Natural Science and Engineering Research Council of Canada under Grant No. A7109. The authors would like to thank Professor L. Meirovitch and the reviewers for some valuable suggestions.     

一个呼吸动力学模型的全局吸引性

研究了一个呼吸动力学时滞微分方程模型.x(t)=1-αx(t)xn(t-τ)1+xn(t-τ).通过利用一种映射方法得到了该系统平衡点全局吸引的充分条件.所得结论优于已有的结果.     

某常微分方程教材中的一个错例

针对东北师范大学微分方程教研室所编教材《常微分方程》中的一道例题,经过实际验算发现,原题所给向量函数并非如其所称是其所给微分方程组的基本解组;随后通过两种方法对该道例题给出正确求解．     

An analytical and numerical study of liquid dynamics in a one‐dimensional capillary under entrapped gas action

Capillary dynamics has been and is yet an important field of research, because of its very relevant role played as the core mechanism at the base of many applications. In this context, we are particularly interested in the liquid penetration inspection technique. Because of the obviously needed level of reliability involved with such a non‐destructive test, this paper is devoted to study how the presence of an entrapped gas in a close‐end capillary may affect the inspection outcome. This study is carried out through a one‐dimensional ordinary differential model that despite its simplicity is able to point out quite well the capillary dynamics under the effect of an entrapped gas. The paper is divided into two main parts; the first starts from an introductory historical review of capillary flows modelling, goes on presenting the one‐dimensional second order ordinary differential model, taking into account the presence of an entrapped gas and therefore ends by showing some numerical simulation results. The second part is devoted to the analytical study of the model by separating the initial transitory behaviour from the stationary one. Besides, these solutions are compared with the numerical ones, and finally, an expression is deduced for the threshold radius switching from a fully damped transitory to an oscillatory one. Copyright © 2013 John Wiley & Sons, Ltd.     

Well-posedness results for a class of partial differential equations with hysteresis arising in electromagnetism

We consider an evolutionary PDE motivated by models for electromagnetic processes in ferromagnetic materials. Magnetic hysteresis is represented by means of a hysteresis operator. Under suitable assumptions, an existence and uniqueness theorem is obtained, together with the Lipschitz continuous dependence on the data and some further regularity results. The discussion of the behaviour of the solution in dependence on physical parameters of the problem is also outlined.     

An exact solution of a quasilinear Fisher equation in cylindrical coordinates

Lie symmetry method is applied to analyse Fisher equation in cylindrical coordinates. Symmetry algebra is found and symmetry invariance is used to reduce the equation to a first-order ODE. The first-order ODE is further analysed to obtain exact solution of Fisher equation in explicit form.     

Group classification of a class of equations arising in financial mathematics

We provide a group classification of a class of nonlinearisable evolution partial differential equations which arise in Financial Mathematics. Sixteen different cases are identified for the general problem and another seven for a restricted version. In the cases for which the algebra is suitable we determine the solution to the problem u(0,x)=U, where U is a constant. In addition we provide a number of solutions based upon reduction using inequivalent subalgebras.     

An example of Bautin-type bifurcation in a delay differential equation

In a previous paper we gave sufficient conditions for a system of delay differential equations to present Bautin-type bifurcation. In the present work we present an example of delay equation that satisfies these conditions.