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This work approaches the fields of homogenization and of materials design for the linear and nonlinear mechanical properties with prescribed properties-profile. The set of achievable properties is bounded by the zeroth-order bounds (which are material specific), the first-order bounds (containing volume fractions of the phases) and the second-order Hashin-Shtrikman bounds with eigenfields in terms of tensorial texture coefficients for arbitrarily anisotropic textured materials.

Theoretische Schranken --- Materialdesign --- Materials design --- Homogenisierung --- Theoretical bounds --- Homogenization --- Polycrystals --- Polykristalle --- Mehrphasige Materialien --- Multiphase materials

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When measuring inequality of opportunity, researchers usually opt to eliminate within-type variation. Provided that in practice it is impossible to observe all circumstances, this implies that the researcher estimates a lower bound of the true level of inequality of opportunity. By using data drawn from 27 Demographic Household Surveys (circa 2008), it is found that lower bound estimates can have substantial measurement error, and that measurement error can vary considerably across countries. As a consequence, lower bound estimates of inequality of opportunity can demand too little redistribution to equalize inequalities due to circumstances and can make the "traditional" cross-country comparisons misleading.

Education --- Equity and development --- Gender --- Gender & law --- Inequality --- Inequality of opportunity --- Lower bounds --- Measurement error --- Poverty reduction --- Science and technology development --- Science education --- Scientific research & science parks

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The paper proposes a modification of Baulch's parity bounds model to measure the market integration of food markets in developing countries. Instead of extrapolating a single observation of transaction costs, it estimates transaction costs. Predicted transaction costs compare well with survey data of traders. Probabilities of market regimes, computed on the basis of predicted transaction costs, fluctuate significantly and do not support fixed regime probabilities over time. The probability of market integration with trade decreases consistently during food shortages, increasing either the probability of no trade or loss-making trade or the probability of profitable but unexploited trade opportunities. The data support a negative trend in market integration with trade.

Debt Markets --- Economic Theory & Research --- Finance and Financial Sector Development --- Food & Beverage Industry --- Macroeconomics and Economic Growth --- Market integration --- Markets and Market Access --- Parity bounds model --- Trade --- Transaction costs --- Transport Economics Policy & Planning --- Africa --- Malawi

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The paper proposes a modification of Baulch's parity bounds model to measure the market integration of food markets in developing countries. Instead of extrapolating a single observation of transaction costs, it estimates transaction costs. Predicted transaction costs compare well with survey data of traders. Probabilities of market regimes, computed on the basis of predicted transaction costs, fluctuate significantly and do not support fixed regime probabilities over time. The probability of market integration with trade decreases consistently during food shortages, increasing either the probability of no trade or loss-making trade or the probability of profitable but unexploited trade opportunities. The data support a negative trend in market integration with trade.

Debt Markets --- Economic Theory & Research --- Finance and Financial Sector Development --- Food & Beverage Industry --- Macroeconomics and Economic Growth --- Market integration --- Markets and Market Access --- Parity bounds model --- Trade --- Transaction costs --- Transport Economics Policy & Planning --- Africa --- Malawi

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Numerical linear algebra is a very important topic in mathematics and has important recent applications in deep learning, machine learning, image processing, applied statistics, artificial intelligence and other interesting modern applications in many fields. The purpose of this Special Issue in Mathematics is to present the latest contributions and recent developments in numerical linear algebra and applications in different real domains. We invite authors to submit original and new papers and high-quality reviews related to the following topics: applied linear algebra, linear and nonlinear systems of equations, large matrix equations, numerical tensor problems with applications, ill-posed problems and image processing, linear algebra and applied statistics, model reduction in dynamic systems, and other related subjects. The submitted papers will be reviewed in line with the traditional submission process. This Special Issue will be dedicated to the inspired mathematician Constantin Petridi, who has devoted his life to mathematics.

Information technology industries --- inverse scattering --- reciprocity gap functional --- chiral media --- mixed boundary conditions --- non-linear matrix equations --- perturbation bounds --- Lyapunov majorants --- fixed-point principle --- nonsymmetric differential matrix Riccati equation --- cosine product --- Golub–Kahan algorithm --- Krylov subspaces --- PCA --- SVD --- tensors --- quadratic form --- estimates --- upper bounds --- networks --- perron vector --- power method --- lanczos method --- pseudospectra --- eigenvalues --- matrix polynomial --- perturbation --- Perron root --- large-scale matrices --- approximation algorithm --- high-dimensional --- minimum norm solution --- regularisation --- Tikhonov --- ℓp-ℓq --- variable selection