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THIS report gives a general solution of the problem of the calculation of the Glauert loading of wings with discontinuities of incidence. The three existing variations of the original theory, the Glauert solution, the Gates' least squares solution, and the Lotz' solution, are not entirely satisfactory and may involve a considerable amount of labour. The present solution divides the Fourier series representing the circulation into two parts: (a) a standard solution representing the discontinuities, which includes the slowly convergent part of the solution, and which is expressible as a precise infinite series dependent only upon the position of discontinuities along the span, and (b) a secondary solution due to plan form, aspect ratio, slope of section lift curve, and so on, which is the quickly convergent part of the solution and usually requires a terminated scries of only from four to six terms. Once the standard solution has been computed, the remaining work is little more than for the standard Glauert solution for a flat wing.

The purpose of this paper is to find two iterative methods to solve the general coupled matrix equations over the generalized centro‐symmetric and central antisymmetric matrices.

By extending the idea of conjugate gradient (CG) method, the authors present two iterative methods to solve the general coupled matrix equations over the generalized centro‐symmetric and central antisymmetric matrices.

When the general coupled matrix equations are consistent over the generalized centro‐symmetric and central anti‐symmetric matrices, the generalized centro‐symmetric and central anti‐symmetric solutions can be obtained within nite iterative steps. Also the least Frobenius norm generalized centrosymmetric and central anti‐symmetric solutions can be derived by choosing a special kind of initial matrices. Furthermore, the optimal approximation generalized centrosymmetric and central anti‐symmetric solutions to given generalized centro‐symmetric and central anti‐symmetric matrices can be obtained by finding the least Frobenius norm generalized centro‐symmetric and central anti‐symmetric solutions of new matrix equations. The authors employ some numerical examples to support the theoretical results of this paper. Finally, the application of the presented methods is highlighted for solving the projected generalized continuous‐time algebraic Lyapunov equations (GCALE).

By the algorithms, the solvability of the general coupled matrix equations over generalized centro‐symmetric and central anti‐symmetric matrices can be determined automatically. The convergence results of the iterative algorithms are also proposed. Several examples and an application are given to show the efficiency of the presented methods.

Food sector supply chains have significant negative environmental impacts, including the expansion of global food commodity production, which is driving tropical deforestation – a major climate and biodiversity problem. Innovative supply chain monitoring services promise to address such impacts. Legislation also designates “forest-risk commodities”, demanding supply chain due diligence of their provenance. But such data alone does not produce change. This study investigates how theory in performance measurement and management (PMM) can combine with sustainable supply chain management (SSCM) and decision theory (DT) via case study research that addresses paradoxes of simplicity and complexity.

Given existing relevant theory but the nascent nature of the topic, theory elaboration via abductive case study research is conducted. Data collection involves interviews and participatory design workshops with supply chain actors across two supply chains (coffee and soy), exploring the potential opportunities and challenges of new deforestation monitoring services for food supply chains.

Two archetypal food supply chain structures (short food supply chains with high transparency and direct links between farmer and consumer and complex food supply chains with highly disaggregated and opaque links) provide a dichotomy akin to the known/unknown, structured/unstructured contexts in DT, enabling novel theoretical elaboration of the performance alignment matrix model in PMM, resulting in implications for practice and a future research agenda.

The novel conceptual synthesis of PMM, SSCM and DT highlights the importance of context specificity in developing PMM tools for SSCM and the challenge of achieving the general solutions needed to ensure that PMM, paradoxically, is both flexible to client needs and capable of replicable application to deliver economies of scale. To advance understanding of these paradoxes to develop network-level PMM systems to address deforestation impacts of food supply chains and respond to legislation, a future research agenda is presented.

In the context of systems and cybernetics theory, we present a new general stochastic method of search and optimization of solutions of problems that we have named Prototyped Genetic Search. Our new method is based mainly on prototype and learning concepts, although it uses concepts of population and evolution just as Evolutionary Algorithms. Moreover, and in order to show the interest of this method and to demonstrate its real potential, we have chosen to apply it on the Job‐Shop Scheduling Problem in the context of the flexible production. This paper is also the opportunity for us to present an other new kind of genetic algorithms, resulting from the integration of the recursivity in the basis functioning of genetic algorithms, and that we have named Recursive Genetic Algorithm.

The different types of estimators of rational expectations models are surveyed. A key feature is that the model′s solution has to be taken into account when it is estimated. The two ways of doing this, the substitution and errors‐in‐variables methods, give rise to different estimators. In the former case, a generalised least‐squares or maximum‐likelihood type estimator generally gives consistent and efficient estimates. In the latter case, a generalised instrumental variable (GIV) type estimator is needed. Because the substitution method involves more complicated restrictions and because it resolves the solution indeterminacy in a more arbitary fashion, when there are forward‐looking expectations, the errors‐in‐variables solution with the GIV estimator is the recommended combination.

The purpose of this paper is to describe a proposed framework for traceability purpose. Hence, the framework provides a formal and structured way of viewing a traceability solution. This structure lays the required bases for a traceability system before starting development and deployment.

The paper examines several traceability publications, including systems and literature review. The study covers the traceability implementation phase. Therefore, this research approaches the traceability issue from three perspectives (description, engineering and executive one). The separation between aspects is essential when describing and comparing traceability systems. This distinction is also helpful when recommending solution improvements.

The framework identifies six traceability bases: aims, functions, specifications, data classification, processes and procedures. These can establish a basis for a general purpose tool that can enable users to develop an efficient traceability solution. Thus, the first ontology expresses the framework domain and ensures optimal use of it. The second one represents the bases that can serve as a knowledge base to manage the product data.

The suggested framework tackles the implementation of traceability. Therefore, the design emphasizes the importance of technological concerns. Some studied cases could require more research angles (i.e. economic and legislative). Thus, framework enrichment is essential for further improvements.

The framework helps users to develop a general, interoperable and scalable traceability solution. These are important to promote the generalization of traceability systems.

The framework fulfills a requirement for establishing general traceability foundations. Therefore, the guide independently operates of the product or the industry specificity. Moreover, the bases aim to bridge the gap between solution engineering and traceability requirements.

The purpose of this paper is to find the efficient iterative methods for solving the general matrix equation A1X+ XA2+A3XH+XHA4=B (including Lyapunov and Sylvester matrix equations as special cases) with the unknown complex (reflexive) matrix X.

By applying the principle of hierarchical identification and the Hermitian/skew‐Hermitian splitting of the coefficient matrix quadruplet A1; A2; A3; A4 the authors propose a shift‐splitting hierarchical identification (SSHI) method to solve the general linear matrix equation A1X+XA2+A3XH+XHA4=B. Also, the proposed algorithm is extended for finding the reflexive solution to this matrix equation.

The authors propose two iterative methods for finding the solution and reflexive solution of the general linear matrix equation, respectively. The proposed algorithms have a simple, neat and elegant structure. The convergence analysis of the methods is also discussed. Some numerical results are given which illustrate the power and effectiveness of the proposed algorithms.

So far, several methods have been presented and used for solving the matrix equations by using vec operator and Kronecker product, generalized inverse, generalized singular value decomposition (GSVD) and canonical correlation decomposition (CCD) of matrices. In several cases, it is difficult to find the solutions by using matrix decomposition and generalized inverse. Also vec operator and Kronecker product enlarge the size of the matrix greatly therefore the computations are very expensive in the process of finding solutions. To overcome these complications and drawbacks, by using the hierarchical identification principle and the Hermitian=skew‐Hermitian splitting of the coefficient matrix quadruplet (A1; A2; A3; A4), the authors propose SSHI methods for solving the general matrix equation.

This paper aims to propose a semi-analytical benchmarking framework for enthalpy-based methods used in problems involving phase change with latent heat. The benchmark is based on a class of semi-analytical solutions of spatially symmetric Stefan problems in an arbitrary spatial dimension. Via a public repository this study provides a finite element numerical code based on the FEniCS computational platform, which can be used to test and compare any method of choice with the (semi-)analytical solutions. As a particular demonstration, this paper uses the benchmark to test several standard temperature-based implementations of the enthalpy method and assesses their accuracy and stability with respect to the discretization parameters.

The class of spatially symmetric semi-analytical self-similar solutions to the Stefan problem is found for an arbitrary spatial dimension, connecting some of the known results in a unified manner, while providing the solutions’ existence and uniqueness. For two chosen standard semi-implicit temperature-based enthalpy methods, the numerical error assessment of the implementations is carried out in the finite element formulation of the problem. This paper compares the numerical approximations to the semi-analytical solutions and analyzes the influence of discretization parameters, as well as their interdependence. This study also compares accuracy of these methods with other traditional approach based on time-explicit treatment of the effective heat capacity with and without iterative correction.

This study shows that the quantitative comparison between the semi-analytical and numerical solutions of the symmetric Stefan problems can serve as a robust tool for identifying the optimal values of discretization parameters, both in terms of accuracy and stability. Moreover, this study concludes that, from the performance point of view, both of the semi-implicit implementations studied are equivalent, for optimal choice of discretization parameters, they outperform the effective heat capacity method with iterative correction in terms of accuracy, but, by contrast, they lose stability for subcritical thickness of the mushy region.

The proposed benchmark provides a versatile, accessible test bed for computational methods approximating multidimensional phase change problems. The supplemented numerical code can be directly used to test any method of choice against the semi-analytical solutions.

While the solutions of the symmetric Stefan problems for individual spatial dimensions can be found scattered across the literature, the unifying perspective on their derivation presented here has, to the best of the authors’ knowledge, been missing. The unified formulation in a general dimension can be used for the systematic construction of well-posed, reliable and genuinely multidimensional benchmark experiments.