By rearranging the weakly singular boundary, integral equations developed by Han and Atluri, an SGBEM-CG, which is abbreviated as CG, is developed in this chapter. The CG, representing a single grain of a material, can include arbitrarily shaped voids, inclusions (of a different material), and microcracks. The CG has a stiffness matrix and a load vector, which have similar physical meanings to the traditional displacement FEM. The stiffness matrix is symmetric, positive-definite, and has the same number of rigid-body modes. Different CGs, each with different isotropic material properties, can be directly coupled by the assembly procedure, and are used to directly and efficiently model the microstructure of heterogeneous composite materials. Some examples are also presented, with microcracks interacting with inclusions and holes. This provides some insight of a possible future study of the micro-cracking and damage of heterogeneous material. By introducing stochastic variations of the shapes of CG, and stochastic variations of the properties of the constituent materials, the realistic statistical bounds on the overall properties of composite materials will be determined in future studies.

Group Analysis is a particular approach to group psychotherapy as developed by S. H. Foulkes. Key influences and shared ground with other approaches are noted. This brief overview focuses largely on key constituents of the setting and format of group analysis as a psychological treatment. The group analyst, referred to as the conductor, and their dual roles of group administrator and group therapist are briefly explored. Vignettes show this therapeutic approach, in both therapeutic and non-clinical settings. Some key group analytic phenomena are illuminated as is the minimally interventive, analytical approach of the conductor. We encounter ‘John’ at three key stages namely pre-group preparation, joining a new group, and a preparing to leave the group. The conductor’s responsibilities are explored, specifically their intention to help the group develop a therapeutic culture, where dependence on the group conductor is replaced by a greater connectedness to each other. The conductor’s ability to trust the group to find its way is noted while their role in helping this process is not undervalued. Communication, both conscious and unconsciously is a central concern of the group analytic approach.

New product development processes need to be compliant to regulatory requirements, and this chapter highlights the salient processes and quality systems to put into place to achieve success. Project management is made simple with specific tools provided here. Customer feedback is channeled into specific product characteristics, and the right tools are shown in this chapter. The biopharma industry has statistics showing less than 10% of starting compounds succeed in reaching market approval, and this chapter explains what causes these failures. The key issues that have repeatedly caused failure during device and diagnostic product development are also pointed out. Ethical decisions have to be made during product development as shown in this chapter. Outsourcing is a real option due to the availability of many contract research and manufacturing organizations, and judicious use of this option is discussed in this chapter. Key milestones that reduce risk and show transition from early stage to preclinical prototype stages are reviewed here. Does the popular concept of minimum viable product in software development apply in biomedicine prototyping? Other similar questions that help the reader understand pitfalls and best practices are answered here.

We present several facts about the natural transformations between vector spaces, and their representations via matrices. We introduce induced matrix norms, and the spectral decomposition of nondefective matrices

We present some of the basic definitions and properties of matrices necessary to implement the matrix formulation of quantum mechanics.

Viewing an algebraic number field as a vector space relative to a subfield, which was foreshadowed in Chapter 4, involves varying the field of "scalars" in the definition of vector space. This leads in turn to relative concepts of "basis" and "dimension" which must be taken into account in algebraic number theory. In this chapter we review linear algebra from the ground up, with an emphasis on the relative point of view. This brings some nonstandard results into the picture, such as the Dedekind product theorem and the representation of algebraic numbers by matrices.

Compositions and classification of chondritic and differentiated meteories and of interplanetary dust particles

GAL is one of the most ambitious projects to capture the role of procedure in global governance. Other concepts are briefly introduced and compared. The idea of procedural justice as akin to GAL in scope but focusing on perceptions of fairness and legitimacy rather than normativity emerges.

The main strands of international relations theory regarding institutions are briefly introduced. The work focuses on rational choice, notably Rational Institutional Design theory.

To unite the concept of procedural justice with the perspective and methods of rational institutional design, the factor of state interest is studied. It is shown how state interest can operate even within nominally private institutions and which factors determine whether and how a state is interested in introducing procedural justice.

The codebook variables creating the matrix of sensitivity of state interest - quantitative and qualitative procedural density is introduced. The mode of sample collection is explained.

This book intends to be self-contained, and this chapter provides a short recap of (almost) all the necessary mathematical background that is required to understand the rest of this book.

The usage of composite materials continues to expand rapidly. The current world-wide market value is not easy to estimate, but is certainly more than US$100 billion. Composites now constitute one of the broadest and most important classes of engineering materials – second only to steels in industrial significance and range of applications. There are several reasons for this. One is that they often offer highly attractive combinations of stiffness, strength, toughness, lightness and corrosion resistance. Another is that there is considerable scope for tailoring their structure to suit service conditions. This concept is well illustrated by biological materials such as wood, bone, teeth and hide, which are all composites with complex internal structures that have been designed (via evolutionary processes) to give mechanical properties well suited to the performance requirements. This versatility is, of course, attractive for many industrial purposes, although it also leads to complexity that needs to be well understood if they are to be used effectively. In fact, adaptation of manufactured composite structures for different engineering purposes requires input from several branches of science. In this introductory chapter, an overview is given of the types of composites that have been developed.