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Monthly prescribing behaviour is assessed over a 3‐year period, 1 April 1992 to 31 March 1995. Total monthly number of items prescribed and overall net ingredient cost are analysed for 263 general practices, serving the 1 million residents of Birmingham, UK. Patients aged over 65 years play an important role in elevated prescribing activity. Practice composition varies considerably between training and non‐training practices, and between fundholding and non‐fundholding practices. Accounting for these differences, fundholders expend less and prescribe fewer items than their non‐fundholding counterparts. This is observed against a steady increase in prescribing activity over the study period. There are, however, marked downward shifts in both the number of items prescribed and overall monthly expenditure occurring with every new wave of fundholding. The magnitude of these changes raises doubts about the efficacy of the transition to fundholding and the impact of such large changes upon patient care.

The purpose of this paper is to present a new method based on the homotopy analysis method (HAM) with the aim of fast searching and calculating multiple solutions of nonlinear boundary value problems (NBVPs).

A major problem with the previously modified HAM, namely, predictor homotopy analysis method, which is used to predict multiplicity of solutions of NBVPs, is a time-consuming computation of high-order HAM-approximate solutions due to a symbolic variable namely “prescribed parameter”. The proposed new technique which is based on traditional shooting method, and the HAM cuts the dependency on the prescribed parameter.

To demonstrate the computational efficiency, the mentioned method is implemented on three important nonlinear exactly solvable differential equations, namely, the nonlinear MHD Jeffery–Hamel flow problem, the nonlinear boundary value problem arising in heat transfer and the strongly nonlinear Bratu problem.

The more high-order approximate solutions are computable, multiple solutions are easily searched and discovered and the more accurate solutions can be obtained depending on how nonhomogeneous boundary conditions are transcribed to the homogeneous boundary conditions.

The purpose of this paper is to present a new approximate analytical procedure to obtain dual solutions of nonlinear differential equations arising in mixed convection flow in a semi-infinite domain. This method, which is based on Padé-approximation and homotopy–Padé technique, is applied to a model of magnetohydrodynamic Falkner–Skan flow as well. These examples indicate that the method can be successfully applied to solve nonlinear differential equations arising in science and engineering.

Homotopy–Padé method.

The main focus of the paper is on the prediction of the multiplicity of the solutions, however we have calculated multiple (dual) solutions of the model problem namely, mixed convection heat transfer in a porous medium.

The authors conjecture here that the combination of traditional–Pade and Hankel–Pade generates a useful procedure to predict multiple solutions and to calculate prescribed parameter with acceptable accuracy as well. Validation of this conjecture for other further examples is a challenging research opportunity.

Dual solutions of nonlinear differential equations arising in mixed convection flow in a semi-infinite domain.

In this study, the authors are using two modified methods.

This paper aims to describe the development and application of a manpower planning system for the Slovenian armed forces using a system approach, system dynamics (SD) and numerical optimization.

The model of the hierarchical manpower system was developed by SD methodology and formulated in discrete time space. The problem of tracking the goal trajectories in the eight topmost ranks at the prescribed boundaries was solved by application of the quadratic performance index and finite automata (FA) which was used for classification of acceptable strategies. Genetic algorithms (GA) as well as pattern search were compared at the numeric optimization.

Employing SD and a system approach increases the understanding of the system control. The definition of an optimum strategy, which would consider only target values for ranks within prescribed parameter boundaries, could provide an undesired oscillatory solution. Inclusion of rules by FA to determine acceptable strategies based on the time response of a strategy provided acceptable, nonoscillatory solutions. GA and pattern search were considered where pattern search was shown to be significantly more suitable for the task of control strategy determination.

The developed system and methodology was applied by the Slovenian Armed Forces in the process of restructuring.

The developed approach permits a moderate transition to the new desired structure. Restructuring without a clear understanding of the system structure and dynamics might result in undesired social impacts such as strikes and riots.

Provision of the systemic view of the hierarchical manpower system and application of FA to determine the proper control of a complex system.

Visco‐elastic fluid flow and heat transfer in a porous medium over a non‐isothermal stretching sheet have been investigated. The flow is influenced by linearly stretching the sheet in the presence of suction, blowing and impermeability of the wall. Thermal conductivity is considered to vary linearly with temperature. The intricate non‐linear problem has been solved numerically by shooting technique with fourth order Runge‐Kutta algorithm after using perturbation method. The zeroth order solutions are obtained analytically in the form of Kummer’s function. An analysis has been carried out for two different cases, namely prescribed surface temperature (PST) and prescribed heat flux (PHF) to get the effect of porosity and visco‐elasticity at various physical situations. The important finding is that the effect of visco‐elasticity and porosity is to increase the wall temperature in case of blowing and to decrease in both the cases of suction and when the stretching sheet is impermeable.

The purpose of this paper is to investigate the effects of surface texture with roughness orientation considered on tribological properties under a mixed lubrication state numerically and experimentally.

Based on the average Reynolds equation and asperity contact model, the impacts of surface texture parameters and roughness orientation on lubrication properties have been calculated using finite difference method. Tin–bronze samples with various prescribed surface texture geometric parameters and roughness orientation were fabricated by laser surface texturing technique, and the tribology performance of the textured surface was studied experimentally.

The effects of surface geometric parameters and roughness orientation parameters have been discerned. The experimental observations are in good agreement with the numerical prediction, which suggests that the numerical scheme adopted in this work is suitable in capturing the surface texture and roughness effect under mixed lubrication state.

By meticulously controlling the surface roughness and surface texture geometric characteristics based on the laser surface texturing process, samples with prescribed surface texture parameters and roughness orientation consistent with that in theoretical studies were fabricated and the theoretical model and results were verified experimentally.

The purpose of this paper is to propose a pre-defined performance robust control method for pre-assembly configuration establishment of in-space assembly missions, and collision avoidance is considered during the configuration establishment process.

First, six-degrees-of-freedom error kinematic and dynamic models of relative translational and rotational motion between transportation systems are developed. Second, the prescribed transient-state performance bounds of tracking errors are designed. In addition, based on the backstepping, combining the pre-defined performance control method with a robust control method, a pre-defined performance robust controller is designed.

By designing prescribed transient-state performance bounds of tracking errors to guarantee that there is no overshoot, collision-avoidance can be achieved. Combining the pre-defined performance control method with a robust control method, robustness to disturbance is guaranteed.

This paper proposed a pre-defined performance robust control method. Simulation results demonstrate that the proposed controller can achieve a pre-assembly configuration establishment with collision avoidance in the existence of external disturbances.

The purpose of this paper is to introduce a new arc-length control method for physically non-linear problems based on the rates of the internal and the dissipated energy.

In this paper, the authors derive from the second law of thermodynamics the arc-length method based on the rate of the dissipated energy and from the time derivative of the energy density the arc-length method based on the rate of the internal energy.

The method requires only two parameters and can automatically trace equilibrium paths which display multiple snap-through and/or snap-back phenomena.

A fully energy-based control procedure is developed, which facilitates switching between dissipative and non-dissipative arc-length control equations in a natural way. The method is applied to a plate with an eccentric hole using the phase field model for brittle fracture and to a perforated beam using interface elements with decohesion.

The purpose of this paper is to present the computational model of the neonate’s brain cooling process. The main aim of the analysis is to tune the developed computational model, make it convergent and representing the hypothermia therapy reasonably. To find the appropriate model parameters the trial of an inverse analysis, based on the standard least-square method, is performed. Having partially validated model the number of numerical simulations are carried out to compare their results with measurements made during real therapy.

The geometrical model of the newborn’s body is built using MRI and CT scans utilizing Mimics software and the Design Modeler while Ansys Fluent with its User Defined Function capability was used to implement the whole model and to carry out simulations. To model the bioheat transfer the Pennes bioheat equation is applied. In the mathematical model blood perfusion rate, metabolic heat generation rate as well as the arterial blood temperature are dependent on the tissue temperature. In order to determine the proper values of model parameters of bioheat transport in neonate’s body the attempt to inverse analysis is also performed.

The performed inverse analysis resulted in the values of model parameters (metabolic heat sources, blood perfusions etc.). Tuned model was then applied to simulate brain cooling process with reasonable accuracy. Obtained model parameters were also compared to the data obtained from neonatologists.

The presented numerical model still requires tests and simulations. The results from the inverse analysis based on the real measurements can be very valuable.

The determination of the proper parameters of the bioheat transfer in the neonatal body can finally be used to control the numerical simulations of the brain cooling process. The simulation of the re-warming process after hypothermic therapy can be improved considerably.

The performance of the numerical simulations of the brain cooling process in the proper way can finally helps protect newborns’ health and life.

In the paper 3-D real geometrical model of the newborn’s body includes head, torso and limbs and different types of tissues are distinguished in the model. The considered bioheat transfer problem is also fully 3-D. This model is then utilised together with inverse analysis in order to determine the model parameters for the newborn’s body.

This paper aims to focus on the assessment of the ability of computer models with imperfect functional forms and uncertain input parameters to represent reality.

In this assessment, both the agreement between a model’s predictions and available experiments and the robustness of this agreement to uncertainty have been evaluated. The concept of satisfying boundaries to represent input parameter sets that yield model predictions with acceptable fidelity to observed experiments has been introduced.

Satisfying boundaries provide several useful indicators for model assessment, and when calculated for varying fidelity thresholds and input parameter uncertainties, reveal the trade-off between the robustness to uncertainty in model parameters, the threshold for satisfactory fidelity and the probability of satisfying the given fidelity threshold. Using a controlled case-study example, important modeling decisions such as acceptable level of uncertainty, fidelity requirements and resource allocation for additional experiments are shown.

Traditional methods of model assessment are solely based on fidelity to experiments, leading to a single parameter set that is considered fidelity-optimal, which essentially represents the values which yield the optimal compensation between various sources of errors and uncertainties. Rather than maximizing fidelity, this study advocates for basing model assessment on the model’s ability to satisfy a required fidelity (or error tolerance). Evaluating the trade-off between error tolerance, parameter uncertainty and probability of satisfying this predefined error threshold provides us with a powerful tool for model assessment and resource allocation.