A semi-analytic approach for the nonlinear dynamic response of circular plates

This paper presents a new semi-analytic perturbation differential quadrature method for geometrically nonlinear vibration analysis of circular plates. The nonlinear governing equations are converted into a linear differential equation system by using Linstedt–Poincaré perturbation method. The solutions of nonlinear dynamic response and the nonlinear free vibration are then sought through the use of differential quadrature approximation in space domain and analytical series expansion in time domain. The present method is validated against analytical results using elliptic function in several examples for both clamped and simply supported circular plates, showing that it has excellent accuracy and convergence. Compared with numerical methods involving iterative time integration, the present method does not suffer from error accumulation and is able to give very accurate results over a long time interval.     

Multivalued nonlinear equations on the half line: A fixed point approach

New fixed point theorems of the authors are used to establish the existence of one (or more) C[0, ∞) solutions to the nonlinear integral inclusion y(t)∈ ∫₀^∞ K(t, s) F(s, y(s))ds fort ∈ [0,∞).     

Modelling condition monitoring intervals: A hybrid of simulation and analytical approaches

This paper reports on a study of modelling condition monitoring intervals. The model is formulated based upon two important concepts. One is the failure delay time concept, which is used to divide the failure process of the item into two periods, namely a normal working period followed by a failure delay time period from a defect being first identified to the actual failure. The other is the conditional residual time concept, which assumes that the residual time also depends on the history condition information obtained. Stochastic filtering theory is used to predict the residual time distribution given all monitored information obtained to date over the failure delay time period. The solution procedure is carried out in two stages. We first propose a static model that is used to determine a fixed condition monitoring interval over the item life. Once the monitored information indicates a possible abnormality of the item concerned, that is the start of the failure delay time, a dynamic approach is employed to determine the next monitoring time at the current monitoring point given that the item is not scheduled for a preventive replacement before that time. This implies that the dynamic model overrides the static model over the failure delay time since more frequent monitoring might be needed to keep the item in close attention before an appropriate replacement is made prior to failure. Two key problems are addressed in the paper. The first is which criterion function we should use in determining the monitoring check interval, and the second is the optimization process for both models, which can be solved neither analytically nor numerically since they depend on two unknown quantities, namely, the available condition information and a decision of the time to replace the item over the failure delay time. For the first problem, we propose five appealingly good criterion functions, and test them using simulations to see which one performs best. The second problem was solved using a hybrid of simulation and analytical solution procedures. We finally present a numerical example to demonstrate the modelling methodology.     

A degree theoretic approach for multiple solutions of constant sign for nonlinear elliptic equations

We consider nonlinear elliptic equations driven by the p-Laplacian differential operator. Using degree theoretic arguments based on the degree map for operators of type (S)₊ , we prove theorems on the existence of multiple nontrivial solutions of constant sign.     

Modelling taxation and redistribution: A discrete active particle kinetic approach

In this paper a general framework is proposed, suitable for the modelling of the taxation and redistribution process in a closed society. This framework arises within a discrete kinetic approach for active particle systems, and is expressed by a system of nonlinear ordinary differential equations. It is intended to describe the evolution of the wealth distribution over the population, based on the interactions of single individuals. The framework is then employed towards the construction of a toy model, which is analytically and computationally investigated.     

Modelling and assessing ERP project risks: A Petri Net approach

Risk management of Enterprise Resource Planning (ERP) projects is largely recognized as a very complex task both by academics and practitioners. Strict interconnections among risk factors often occur so that indirect effects on the overall project performance are very likely. Unfortunately, the implications of interdependency are usually underestimated by project managers and decision makers since they are difficult to include in any risk assessment logic. This work shows how Colored Petri Nets (CPNs) can be used to model risk factors in ERP projects in order to deal with the problem of interdependence in risk assessment. The technique is presented through an application to a real case study. Findings highlight the importance of interdependence and the indirect links for an effective ranking of risks. Furthermore, results emphasize the valuable support of CPNs in risk factor modelling since they allow both a more structured and systematic risk analysis and a more accurate planning for effective risk treatment actions.     

Existence of multiple and sign-changing solutions for a second-order nonlinear functional difference equation with periodic coefficients

In the present paper, we apply the method of invariant sets of descending flow to establish a series of criteria to ensure that a second-order nonlinear functional difference equation with periodic boundary conditions possesses at least one trivial solution and three nontrivial solutions. These nontrivial solutions consist of sign-changing solutions, positive solutions and negative solutions. Moreover, as an application of our theoretical results, an example is elaborated. Our results generalize and improve some existing ones.     

A computational approach for understanding immune response to multiple epitopes based on optimal control formulation

The immune system does not response in equal probability to every epitope of an invader. We investigate the immune system’s decision making process using optimal control principles. Mathematically, this formulation requires the solution of a two-point boundary-value problem, which is a challenging task especially when the control variables are bounded. In this work, we develop a computational approach based on the shooting technique for bounded optimal control problems. We then utilize the computational approach to carry out extensive numerical studies on a simple immune response model of two competing controls. Numerical solutions demonstrate that the results of optimal control depend on the objective function, the limitations on control inputs, as well as the amounts of peptides. Moreover, the state space of peptides can be divided into different regions according the properties of the solutions. The developed algorithm not only provides a useful tool for understanding decision making strategies of the immune system but can also be utilized to solve other complex optimal control problems.     

Attractors and transients for a perturbed periodic KdV equation: A nonlinear spectral analysis

Summary In this paper we rigorously show the existence and smoothness inε of traveling wave solutions to a periodic Korteweg-deVries equation with a Kuramoto-Sivashinsky-type perturbation for sufficiently small values of the perturbation parameterε. The shape and the spectral transforms of these traveling waves are calculated perturbatively to first order. A linear stability theory using squared eigenfunction bases related to the spectral theory of the KdV equation is proposed and carried out numerically. Finally, the inverse spectral transform is used to study the transient and asymptotic stages of the dynamics of the solutions.     

Specification and estimation of multiple output technologies: A primal approach

This paper addresses specification and estimation of multiple-outputs and multiple-inputs production technology in the presence of technical inefficiency. The primary focus is on the primal formulations. Several competing specifications such as production function, input (output) distance function, input requirement function are considered. We show that all these specifications come from the same transformation function and are algebraically identical. We also show that: (i) unless the transformation function is separable (i.e., outputs are separable from inputs), the input (output) ratios in the input (output) distance function can not be treated as exogenous (uncorrelated with technical inefficiency) resulting inconsistent estimates of the input (output) distance function parameters. (ii) Even if input (output) ratios are exogenous, estimation of the input (output) distance function will result in inconsistent parameter estimates if outputs (inputs) are endogenous. We address endogeneity and instrumental variable issues in details in the context of flexible (translog) functional forms. Estimation of several specifications using both single and system approaches are discussed using Norwegian dairy farming data.     

Newton's method for the nonlinear complementarity problem: A B-differentiable equation approach

This paper describes a damped-Newton method for solving the nonlinear complementarity problem when it is formulated as a system of B-differentiable equations through the use of the Minty-map. This general Newton algorithm contains a one-dimensional line search and possesses a global convergence property under certain conditions; modifications and heuristic implementations of the algorithm for the case when these conditions do not hold are also discussed. The numerical experiments show that, in general, this new scheme is more efficient and robust than the traditional Josephy-Newton algorithm.     

Optimizing the packing of cylinders into a rectangular container: A nonlinear approach

The container loading problem has important industrial and commercial applications. An increase in the number of items in a container leads to a decrease in cost. For this reason the related optimization problem is of economic importance. In this work, a procedure based on a nonlinear decision problem to solve the cylinder packing problem with identical diameters is presented. This formulation is based on the fact that the centers of the cylinders have to be inside the rectangular box defined by the base of the container (a radius far from the frontier) and far from each other at least one diameter. With this basic premise the procedure tries to find the maximum number of cylinder centers that satisfy these restrictions. The continuous nature of the problem is one of the reasons that motivated this study. A comparative study with other methods of the literature is presented and better results are achieved.     

A nonlinear superposition principle and multibump solutions of periodic Schrödinger equations

In an abstract setting we prove a nonlinear superposition principle for zeros of equivariant vector fields that are asymptotically additive in a well-defined sense. This result is used to obtain multibump solutions for two basic types of periodic stationary Schrödinger equations with superlinear nonlinearity. The nonlinear term may be of convolution type. If the superquadratic term in the energy functional is convex, our results also apply in certain cases if 0 is in a gap of the spectrum of the Schrödinger operator.     

Modelling and optimization of average travel time for a metro line by simulation and response surface methodology

This research presents a modelling and solution approach based on discrete-event simulation and response surface methodology for dealing with average passenger travel time optimization problem inherent to the metro planning process. The objective is to find the headways optimizing passenger average travel time with a satisfactory rate of carriage fullness. Due to some physical constraints, traffic safety and legal requirements, vehicle speeds cannot be raised any further to decrease travel time. But travel time can be optimized by arranging headways (i.e. the time period between the departure times of two consecutive transportation vehicles) in a timetable. In the presented approach, simulation metamodels that best fit the data collected from the simulated experiments are constructed to describe the relationship between the responses (average travel time and rate of carriage fullness) and input factors (headways). Then, the Derringer–Suich multi-response optimization procedure is used to determine the optimal settings of the input factors that produce the minimum value of the average travel time by providing a proper rate of carriage fullness. This methodology is applied for a real metro line, and good quality solutions are obtained with reduced number of experiments that needed to provide sufficient information for statistically acceptable results.     

A quasilinear method in the theory of small eigenfunctions for nonlinear periodic boundary-value problems

Small eigenfunctions of a nonlinear periodic boundary-value problem are studied for the case of double degeneration of the eigenvalue of the linearized problem; the quasilinear representation is used.