An inverse problem for non-selfadjoint Sturm–Liouville operator with discontinuity conditions inside a finite interval

This paper is concerned with the inverse problem for non-selfadjoint Sturm–Liouville operator with discontinuity conditions inside a finite interval. Firstly, we give the definitions of generalized weight numbers for this operator which may have the multiple spectrum and then investigate the connections between the generalized weight numbers and other spectral characteristics. Secondly, we obtain the generalized spectral data, which consists of the generalized weight numbers and the spectrum. Then the operator is determined uniquely by the method of spectral mappings. Finally, we give an algorithm for reconstructing the potential function and the coefficients of the boundary conditions and the coefficients of the discontinuity conditions.     

The approximate solutions to source inverse problem of 1-D convection–diffusion equation by LS-SVM

This article deals with the determination of the source in 1-D convection–diffusion problem. A method which based on the least squares support vector machines is proposed. The approximate solutions consist of two parts. The first part is a known function that satisfies the initial/boundary conditions. The other part is the combination of Gauss Kernel functions with regression coefficients, which is not affected from the initial/boundary conditions. According to the principle of least squares support vector machines regression, the problem can be transformed into a quadratic programming. The method has been tested on four examples and has yielded accurate results.     

The inverse problem of Lagrangian mechanics for Meshchersky’s equation

Variable-mass systems are not included in the conventional domain of the analytical and variational methods of classical mechanics. This is due to the fact that the fundamental principles of mechanics were primarily conceived for constant-mass systems. In the present article, an analytical and variational formulation for variable-mass systems will be proposed. This will be done from the solution of the here called ‘inverse problem of Lagrangian mechanics for Meshchersky’s equation’. The first problem of this nature was posed in 1887, by Helmholtz (J. reine angew. Math. 100:137–166, 1887). Investigations on the matter are far from being exhausted. Within mechanics, it means the construction of a Lagrangian from a given equation of motion. To the authors’ best knowledge, aiming at general results, the inverse problem of Lagrangian mechanics has not been properly connected to Meshchersky’s equation yet. This is the main goal of this article. We will address the issue by assuming that mass depends on generalized coordinate, generalized velocity and on time. After the construction of a Lagrangian from Meshchersky’s equation, a general and unifying mathematical formulation will emerge in accordance. Therefore, variable-mass systems will be accommodated at the level of analytical mechanics. A variational formulation, which will be written via a principle of stationary action, and a Hamiltonian formulation will be both stated. The latter could be read as the ‘Hamiltonization’ of variable-mass systems from the solution of the inverse problem of Lagrangian mechanics. An energy-like conservation law will naturally appear from the simplification of the general theory to the case of a system with mass solely dependent on a generalized coordinate.     

An inverse thermal–mechanical analysis of the hot torsion test for calibrating the constitutive parameters

One of the key tasks for mathematical representation of a constitutive model is calibration of its parameters. An inverse computational–experimental solution with the data modelling approach was employed here to estimate the parameters of a hyperbolic sine type constitutive equation. The solution utilizes a multi-layer constitutive model. The computational component of the inverse solution includes a rigid viscoplastic finite element code based on the thermo-mechanical coupling. The hot torsion test data comprises the experimental component of the inverse solution. Determination of the primary constitutive parameters (PCPs) pertinent to a 303 Austenitic stainless steel is presented here as an example. In order to facilitate the calibration of the sub-models, a procedure to provide an initial guess vector for the secondary constitutive parameters (SCPs) is given.     

Proposing integrated Shannon’s entropy–inverse data envelopment analysis methods for resource allocation problem under a fuzzy environment

In this study, a two-phase methodology for resource allocation problems under a fuzzy environment is proposed. In the first phase, the imprecise Shannon’s entropy method and the acceptability index are suggested, for the first time in the literature, to select input and output variables to be used in the data envelopment analysis (DEA) application. In the second step, an interval inverse DEA model is executed for resource allocation in a short run. In an effort to exemplify the practicality of the proposed fuzzy model, a real case application has been conducted involving 16 cement firms listed in Borsa Istanbul. The results of the case application indicated that the proposed hybrid model is a viable procedure to handle input–output selection and resource allocation problems under fuzzy conditions. The presented methodology can also lend itself to different applications such as multi-criteria decision-making problems.     

The inverse problem of a mixed Liénard-type nonlinear oscillator equation from symmetry perspective

In this paper, we discuss the inverse problem for a mixed Liénard-type nonlinear oscillator equation \({\ddot{x}+f(x)\dot{x}^2+g(x)\dot{x}+h(x)=0}\), where \({f(x), g(x)}\) and h(x) are arbitrary functions of x. Very recently, we have reported the Lie point symmetries of this equation. By exploiting the interconnection between Jacobi last multiplier, Lie point symmetries and Prelle–Singer procedure, we construct a time-independent integral for the case exhibiting maximal symmetry from which we identify the associated conservative nonstandard Lagrangian and Hamiltonian functions. The classical dynamics of the nonlinear oscillator is also discussed, and certain special properties including isochronous oscillations are brought out.     

Trends of pharmaceutical corporations’ external innovation strategies: An inverse sigmoid curve

For decades, scholars believe major pharmaceutical corporations have been facing a decline in R&D efficiency, leading to an increasing demand for early-stage (R&D stage) external innovation. However, after outlining pharmaceutical corporations’ demands on external innovation toolkits by an inverse sigmoid curve, this research indicates an increasing focus of major players on late-stage (commercial or late-development stage) external innovation. Initial results deliver a potential strategy that transferring external innovation focus in advance for R&D excellence, and also suggests policy-makers provide further platforms for enhancing external innovation ecosystem in the pharmaceutical industry.     

An analysis for the elasto-plastic problem of the moderately thick plate using the meshless local Petrov–Galerkin method

A meshless local Petrov–Galerkin method for the analysis of the elasto-plastic problem of the moderately thick plate is presented. The discretized system equations of the moderately thick plate are obtained using a locally weighted residual method. It uses a radial basis function (RBF) coupled with a polynomial basis function as a trial function, and uses the quartic spline function as a test function of the weighted residual method. The shape functions have the Kronecker delta function properties, and no additional treatment to impose essential boundary conditions. The present method is a true meshless method as it does not need any grids, and all integrals can be easily evaluated over regularly shaped domains and their boundaries. An incremental Newton–Raphson iterative algorithm is employed to solve the nonlinear discretized system equation. Numerical results show that the present method possesses not only feasibility and validity but also rapid convergence for the elasto-plastic problem of the moderately thick plate.     

An ordered flow-shop sequencing problem with mean completion time criterion†

This paper investigates a subcategory of the classical n job m machine problem in which the processing times of different jobs are ' ordered '. An extremely simple algorithm is presented which obtains a sequence minimizing the mean completion time of all jobs. The proof of optimality is presented in the Appendix. The problem illustratos that although no efficient procedure exists to solve the classical flow-shop problem with the mean completion time criterion, it is possible to develop such a procedure for a specially structured problem.     

Metamodel-based inverse method for parameter identification: elastic–plastic damage model

This article proposed a metamodel-based inverse method for material parameter identification and applies it to elastic–plastic damage model parameter identification. An elastic–plastic damage model is presented and implemented in numerical simulation. The metamodel-based inverse method is proposed in order to overcome the disadvantage in computational cost of the inverse method. In the metamodel-based inverse method, a Kriging metamodel is constructed based on the experimental design in order to model the relationship between material parameters and the objective function values in the inverse problem, and then the optimization procedure is executed by the use of a metamodel. The applications of the presented material model and proposed parameter identification method in the standard A 2017-T4 tensile test prove that the presented elastic–plastic damage model is adequate to describe the material's mechanical behaviour and that the proposed metamodel-based inverse method not only enhances the efficiency of parameter identification but also gives reliable results.     

An integrated neural network–simulation algorithm for performance optimisation of the bi-criteria two-stage assembly flow-shop scheduling problem with stochastic activities

This paper presents an integrated computer simulation and Artificial Neural Network (ANN) algorithm for a stochastic Two-Stage Assembly Flow-Shop Scheduling Problem (TSAFSP) with setup times under a weighted sum of makespan and mean completion time (MCT) criteria, known as bi-criteria. Significantly, it should be noted that there is no mathematical model to analyse the stochastic model, therefore simulation is used to solve the problem. The simulation model enables decision makers to consider the influence of job scheduling on machines in order to examine both criteria simultaneously. Since it is not possible to evaluate all sequence combinations using the simulation model in a reasonable time, multilayered neural network meta-models have been trained and used to estimate objective function values composed of both makespan and mean completion time criteria for the stochastic TSAFSP. To the best of the authors’ knowledge, this is the first study that considers stochastic machine breakdown, processing times, setup times, makespan and mean completion time as objectives concurrently. The TSAFSP is modelled by Visual SLAM simulation software. The simulation output results are then given to the ANN as inputs to build the meta-model. This meta-model is then used to obtain the results with the optimum values. The advantage of these meta-model applications is a reduction in the number of simulation runs and consequently a reduced run time. Also, this is the first study that introduces an intelligent and flexible algorithm for handling stochastic TSAFSP.     

An ablation problem in a finite medium with time‐dependent heat flux

Abstract

The objective of this work is to develop an approximate analytical solution for the transient ablation problem in a finite medium. The medium is subjected to time‐dependent boundary heat flux, i. e., q₀=at^P , and with this refined integral technique, the complicated nonlinear problem is reduced to an initial value problem, which is then solved by the Runge‐Kutta method. Results are more accurate than with the classical heat balance integral method and also indicate that the dependence of the solution on the assumed temperature profile is much weaker than is the case with the classical integral method.     

An integrated CPU–GPU heuristic inspired on variable neighbourhood search for the single vehicle routing problem with deliveries and selective pickups

Environmental issues have become increasingly important to industry and business in recent days. This trend forces the companies to take responsibility for product recovery, and proper recycling and disposal, moving towards the design of sustainable green supply chains. This paper addresses the backward stream in transportation of products, by means of reverse logistics applied to vehicle routing. This problem, called single vehicle routing problem with deliveries and selective pickups, consists in finding a route that starts from the depot and visits all delivery customers. Some pickup customers may also be visited, since the capacity of the truck is not exceeded, and there is also a revenue associated with each pickup. We develop an algorithm inspired on the variable neighbourhood search metaheuristic that explores the power of modern graphics processing unit (GPU) to provide routes in reasonable computational time. The proposed algorithm called four-neighbourhood variable neighbourhood search (FN-VNS) includes a novel high-quality initial solution generator, a CPU–GPU integrated perturbation strategy and four different neighbourhood searches implemented purely in GPU for the local search phase. Our experimental results show that FN-VNS is able to improve the quality of the solution for 51 instances out of 68 instances taken from the literature. Finally, we obtained speedups up to 14.49 times, varying from 17.42 up to 76.84 for each local search, measured over a set of new large-size instances.     

Initial precipitation and coarsening of the γ phase in inverse Ni–Al alloys

Coalescence coarsening and Ostwald ripening as well as the kinetics of γ precipitation in the γ′ matrix of inverse Ni–Al alloys are investigated by phase field simulations. The ordering of the γ′ matrix during the initial phase transformation of inverse Ni–Al alloys is faster than clustering, and disordering of the γ precipitates is faster than dissolution. As the Al content increases from 20.2 to 20.8 at.% Al, the initial precipitation and growth of γ precipitates decelerates, and the volume fractions of γ precipitates decreases with higher Al content. The rate constants of steady-state coarsening decrease with decreasing volume fraction of γ precipitates, the particle size distributions (PSDs) are broader than the PSDs predicted by Lifshitz–Slyozov–Wagner theory at steady-state coarsening, and the PSD becomes broad with increasing volume fraction of γ precipitates. The simulated morphology and kinetics variation of the γ precipitates are similar to previous experimental results.     

An optimum spacing problem for four chips on a horizontal substrate – mixed convection

 The optimum spacing problem for four heated chips rested on a conductive substrate in a channel is solved by an operator-splitting pseudo-time-stepping finite element method, which automatically satisfies the continuity of the interfacial temperature and heat flux. It is found that the conventional equi-spaced arrangement is not an optimum option for mixed convection situation. An optimum thermal performance can be obtained when the center-to-center distances between the chips follow a geometric series. When the ratio is larger than 1.2, the maximum temperature and the maximum temperature difference can be decreased significantly compared to the ratio of 1.0. Received 6 June 2000     

A Dirichlet–Neumann cost functional approach for the Bernoulli problem

The Bernoulli problem is rephrased into a shape optimization problem. In particular, the cost function, which turns out to be a constitutive law gap functional, is borrowed from inverse problem formulations. The shape derivative of the cost functional is explicitly determined. The gradient information is combined with the level set method in a steepest descent algorithm to solve the shape optimization problem. The efficiency of this approach is illustrated by numerical results for both interior and exterior Bernoulli problems.