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The dynamics of coupling between spectrum and resolvent under ε‐perturbations of operator and matrix spectra are studied both theoretically and numerically. The phenomenon of non‐trivial pseudospectra encountered in these dynamics is treated by relating information in the complex plane to the behaviour of operators and matrices. On a number of numerical results we show how an intrinsic blend of theory with symbolic and numerical computations can be used effectively for the analysis of spectral problems arising from engineering applications.

In this paper, we give a complete description of efficient formulae for the numerical integration of fast oscillating functions of two variables. The focus is on the case encountered frequently in many engineering applications where an accurate value of the Lipschitz constant is not available. Using spline approximations, we demonstrate the main idea of our approach on the example of piecewise bilinear interpolation, and propose optimal‐by‐order (with a constant not exceeding two) cubature formulae that are applicable for a wide range of oscillatory patterns. This property makes the formulae indispensable in many engineering applications dealing with signal processing and image recognition. Illustrative results of numerical experiments are presented.

In this paper, we consider problems of numerical integration of fast oscillatory functions of one variable, obtained by using α‐dense curves and approximating multiple integrals. Using first, periodic and regular α‐dense curves we propose a trapezoidal formula for calculating the periodic integrand obtained. Then, we consider the simple integrals as integrals with weight. We propose a method to evaluate the moments of the weight function. This allows us to build a recurrent formula for the orthogonal polynomials family and to use a Gaussian rule to estimate the simple integral. Finally, we adapt the Filon's method, consisting in evaluating the Fourier coefficients of a function, to the oscillatory integrand obtained by using reducing transformations.

The purpose of this paper is to investigate the stress distribution in shape memory alloy (SMA) composite due to phase transformations in the fiber in view of the applied boundary conditions on the matrix.

A consistent homogenization of a SMA wire‐reinforced polymer composite volume element undergoing quasi‐static deformation was performed and SMA wire‐matrix interface behaviour was presented. For the SMA wire, a one‐dimensional phenomenological constitutive model was used. Eshelby's inclusion theory was employed for homogenization. A strain averaging approach was reviewed in which the average strain was substituted back to obtain the expressions for the effective stiffness, the inelastic strain, and the average stresses in the constituent phases. In order to study the stress distribution in SMA composite and constituent phases (fiber and matrix) as a consequence of the SMA wire‐matrix interface effect, interfacial stress model was derived. Interfacial axial and shear stress distribution is characterized for forward and reverse phase transformations. Finally, the thermomechanical behaviours were computed by applying strain energy approach incorporating the interface effects.

The results presented show that due to the difference between the shear modulus of matrix and SMA wire, and because of the strain non‐uniformity at the SMA wire‐matrix interface, shear stress is developed within the matrix under the axial loading of the representative volume element (RVE). The shear stress increases more rapidly as the SMA wire radius is increased but not with increase in the length. However, the axial stress does not increase much with increase in the SMA wire radius and length. Further, the average stress equation of the RVE at the SMA wire‐matrix interface is effectively addressed. The modeling approach is successfully validated extensively for different geometric and volumetric parameters for different loading conditions. It is evident that the interface effect of SMA wire composites is SMA stiffness dominated due to the fact that the geometric parameters do not influence much the stresses as compared to the change in SMA wire stiffness.

The approach is based on modeling the fiber matrix interface effect using homogenization scheme. Further, the strain energy approach is applied to compute the stress‐strain response. This indicates the importance of modeling the SMA wire‐matrix interface effect, and in particular, the energy exchange between the constituent phases. The results have been compared for different geometric parameters as well as volume fractions of the constituent phases under different loading conditions.

This paper explores the health rights of prisoners as defined in international law, and the mechanisms that have been used to ensure the rights of persons in detention to realise the highest attainable standard of health. It examines this right as articulated within United Nations and regional human rights treaties, non‐binding or so‐called soft law instruments from international organisations and the jurisprudence of international human rights bodies. It explores the use of economic, social and cultural rights mechanisms, and those within civil and political rights, as they engage the right to health of prisoners, and identifies the minimum legal obligations of governments in order to remain compliant with human rights norms as defined within the international case law. In addressing these issues, this article adopts a holistic approach to the definition of the highest attainable standard of health. This includes a consideration of adequate standards of general medical care, including preventative health and mental health services. It also examines the question of environmental health, and those poor conditions of detention that may exacerbate health decline, disease transmission, mental illness or death. The paper examines the approach to prison health of the United Nations human rights system and its various monitoring bodies, as well as the regional human rights systems in Europe, Africa and the Americas. Based upon this analysis, the paper draws conclusions on the current fulfilment of the right to health of prisoners on an international scale, and proposes expanded mechanisms under the UN Convention against Torture and Other Cruel, Inhuman or Degrading Treatment to monitor and promote the health rights of prisoners at the international and domestic levels.

When Stalin, in 1936, declared socialism achieved in the Soviet Union, he opened the door for the codification of the political economy of socialism beyond Marx’s political economy of capitalism. Indeed, at the same time as he executed the tyrannical policies he is known for, he led a series of private conversations with economists about a textbook on the political economy of socialism that spanned nearly 20 years. In these conversations, Stalin repeatedly argued for an open debate and against dogmatism. Most notably, he accepted the existence of the so-called law of value in socialism, which appears to subject the state to scientific authority. Reconstructing these conversations, we show that his claim to a pluralist scientific debate helped paper over his tyranny, first by diverting attention from the real issues, second by establishing his personal authority as an intellectual, and third by creating conflicts that would exclude his opponents.