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Results are given which establish a computational foundation for simplicial approximation and design centering of a convex body. A simplicial polyhedron is used to approximate the convex body and the “design center”, i.e. the point inside the body furthest in some norm from its exterior, is approximated by the point in the polyhedron furthest from its exterior. A point representation of the polyhedron is used, so that there is no necessity for computing or storing the faces of the approximation. Since in N space there can be factorially more faces than points, we are able to achieve significant efficiencies in both operation count and storage requirements, compared to previously reported methods. We give results for the 2 norm and the max norm, and demonstrate that our new method is operable in the nonconvex case, and can handle a mixed basis of faces and points as well.

Posits that methods to achieve robustness for single response are well established. For multiple response problems, however, very few methods have been developed successfully. Presents a new method of achieving robustness for multiple response problems using Taguchi’s loss model. Develops loss models for all the responses involved and identifies a design solution that minimizes the total cost loss. This formulation leads to a solution with minimal variance and also has an inherent property of optimizing the manufacturing yield of the design. Compares the proposed method with another formulation. Shows that the proposed method gave better results.

Many works have been written on numerical simulation in semiconductor device theory. In this paper we consider the following problem:

This paper aims to propose a new approach on the problem of circuit optimisation by using the generalised optimisation methodology presented earlier. This approach is focused on the application of the maximum principle of Pontryagin for searching the best structure of a control vector providing the minimum central processing unit (CPU) time.

The process of circuit optimisation is defined mathematically as a controllable dynamical system with a control vector that changes the internal structure of the equations of the optimisation procedure. In this case, a well-known maximum principle of Pontryagin is the best theoretical approach for finding of the optimum structure of control vector. A practical approach for the realisation of the maximum principle is based on the analysis of the behaviour of a Hamiltonian for various strategies of optimisation and provides the possibility to find the optimum points of switching for the control vector.

It is shown that in spite of the fact that the maximum principle is not a sufficient condition for obtaining the global minimum for the non-linear problem, the decision can be obtained in the form of local minima. These local minima provide rather a low value of the CPU time. Numerical results were obtained for both a two-dimensional case and an N-dimensional case.

The possibility of the use of the maximum principle of Pontryagin to a problem of circuit optimisation is analysed systematically for the first time. The important result is the theoretical justification of formerly discovered effect of acceleration of the process of circuit optimisation.

The purpose of this paper is to solve unsteady compressible Navier–Stokes equations without the commonly used dual-time loop. The authors would like to use an adaptive time-stepping (ATS)-based local error control instead of CFL-based time-stepping technique. Also, an all-speed flow algorithm is implemented with simple low dissipation AUSM convective scheme, which can be computed without preconditioning which in general destroys the time accuracy.

In transient flow computations, the time-step is generally determined from the CFL condition. In this paper, the authors demonstrate the usefulness of ATS based on local time-stepping previously used extensively in ordinary differential equations (ODE) integration. This method is implemented in an implicit framework to ensure the numerical domain of dependence always contains the physical domain of dependence.

In this paper, the authors limit their focus to capture the unsteady physics for three cases: Sod’s shock-tube problem, Stokes’ second problem and a circular cylinder. The use of ATS with local truncation error control enables the solver to use the maximum allowable time-step, for the prescribed tolerance of error. The algorithm is also capable of converging very rapidly to the steady state (if there is any) after the initial transient phase. The authors present here only the first-order time-stepping scheme. An algorithmic comparison is made between the proposed adaptive time-stepping method and the commonly used dual time-stepping approach that indicates the former will be more efficient.

The original method of ATS based on local error control is used extensively in ODE integration, whereas, this method is not so popular in the computational fluid dynamics (CFD) community. In this paper, the authors investigate its use in the unsteady CFD computations. The authors hope that it would provide CFD researchers with an algorithm based on an adaptive time-stepping approach for unsteady calculations.

In this paper, on the basis of a previously developed approach to circuit optimization, the main element of which is the control vector that changes the form of the basic equations, the structure of the control vector is determined, which minimizes CPU time.

The circuit optimization process is defined as a controlled dynamic system with a special control vector. This vector serves as the main tool for generalizing the problem of circuit optimization and produces a huge number of different optimization strategies. The task of finding the best optimization strategy that minimizes processor time can be formulated. There is a need to find the optimal structure of the control vector that minimizes processor time. A special function, which is a combination of the Lyapunov function of the optimization process and its time derivative, was proposed to predict the optimal structure of the control vector. The found optimal positions of the switching points of the control vector give a large gain in CPU time in comparison with the traditional approach.

The optimal positions of the switching points of the components of the control vector were calculated. They minimize processor time. Numerical results are obtained for various circuits.

The Lyapunov function, which is one of the main characteristics of any dynamic system, is used to determine the optimal structure of the control vector, which minimizes the time of the circuit optimization process.

The purpose of this paper is to define the process of analog circuit optimization on the basis of the control theory application. This approach produces many different strategies of optimization and determines the problem of searching of the best strategy in sense of minimal computer time. The determining of the best strategy of optimization and a searching of possible structure of this strategy with a minimal computer time is a principal aim of this work.

Different kinds of strategies for circuit optimization have been evaluated from the point of view of operations’ number. The generalized methodology for the optimization of analog circuit was formulated by means of the optimum control theory. The main equations for this methodology were elaborated. These equations include the special control functions that are introduced artificially. This approach generalizes the problem and generates an infinite number of different strategies of optimization. A problem of construction of the best algorithm of optimization is defined as a typical problem of the control theory. Numerical results show the possibility of application of this approach for optimization of electronic circuits and demonstrate the efficiency and perspective of the proposed methodology.

Examples show that the better optimization strategies that are appeared in limits of developed approach have a significant time gain with respect to the traditional strategy. The time gain increases when the size and the complexity of the optimized circuit are increasing. An additional acceleration effect was used to improve the properties of presented optimization process.

The obtained results show the perspectives of new approach for circuit optimization. A large set of various strategies of circuit optimization serves as a basis for searching the better strategies with a minimum computer time. The gain in processor time for the best strategy reaches till several thousands in comparison with traditional approach.

To study the magnetic shielding and the losses of non‐linear, hysteretic multilayered shields by using fast to evaluate analytical expressions.

In order to evaluate the shield in the frequency domain, the non‐linear shield is divided into a sufficient number of piecewise linear sublayers. Each sublayer has a permeability that is constant (space independent) and complex (to model hysteresis). This expression for the permeability is found from the Preisach model by a Fourier transform. Once H is known in the entire shield, analytical expressions calculate the eddy current losses and hysteresis losses in the material. The validity of the analytical expressions is verified by numerical experiments.

In the Rayleigh region, the shielding factor of perfectly linear material is better than the one of non‐linear metal sheets, but also the eddy current losses are higher. The results of the optimization show that steel is only a useful shielding material at low frequencies.

The analytical method is valid for infinitely long shields and for weak imposed fields in the Rayleigh region.

As the analytical expressions can be evaluated very fast (in comparison with slow finite elements models), many magnetic shields can be compared in parametric studies.

Analytical expressions exist for the shielding factor and the losses of linear materials. In this paper, the method is extended for non‐linear hysteretic materials. The effects of several parameters (material parameters, incident fields parameters) on the shielding and the losses are shown.

This work seeks to present the theoretical study considerations and the characteristics of a general design methodology in optimal time for electronic systems using numerical methods and optimal control theory. Through this, the design problem of a system is formulated in terms of optimal control in minimal time.

This general design methodology includes the traditional design strategy (TDS), and the modified traditional design strategy (MTDS), where the model of the system is part of the optimization procedure but an objective function of the optimization process is constructed such as includes the traditional objective function and some penalty functions that feign the model of the system. Many special control functions are introduced artificially to generalize the methodology and produce several design trajectories for the same optimization process – the first and final trajectories correspond to TDS and MTDS, respectively. The combination of these trajectories produce an infinite number of design strategies, some of these are quasi‐optimal in time and only one is optimal in time.

Qualitative and numeric results of this iterative process are generated in a personal computer in a C++ language elaborated with a visual C++ graphic user interface. An algorithm is constructed to form an optimal in time design strategy switching from a MTDS subset to a TDS subset. Results of measured times are analyzed, showing that there is a control input U, such that the objective function is minimized in a minimum time.

These ideas are proposed using method of gradient optimization and special acceleration effect.

Malaria is one of the most sinister life-threatening disease and generally transmitted by the bite of an Anopheles mosquito which was infected. These mosquitoes carry the Plasmodium parasite. Worldwide risk of malaria thread is very hard to deal, because of extreme temperature and climate changes which lead to uncontrolled changes in the mosquito population, as many deaths from malaria occur outside the healthcare system and other infections might be misdiagnosed as malaria unless a diagnostic test is done. The purpose of this study is creating a system which is early diagnosing malaria for settlements adequate healthcare units and non-immune travellers.

In this study’s system, the authors developed a new medical expert system (MES) process using the decreased rule base to detect malaria. The authors’ purpose was to successfully identify the illness by taking all symptoms of malaria into consideration in the MES (six basic signs, 64 different conditions). In the proposed MES process, in place of inspecting all the malaria-related signs, the authors used the decreased rule bases.

So as to take the lessen decreased bases, Boolean functions are used in a two-level simplification method. Using this method, decreased cases were evaluated by taking six symptoms of malaria into account instead of assessing 64 individual conditions.

The system can be used in diagnosis of asthma and chronic obstructive respiratory disease.

The system can be used in absence of adequate healthcare units. Thus, malaria can be diagnosed early.

The authors hope that the system they have developed will be useful for settlements in the absence of adequate healthcare units and non-immune travellers.