In macro-econometrics more attention needs to be paid to the relationships among deterministic trends of different variables, or co-trending, especially when economic growth is of concern. The number of relationships, i.e., the co-trending rank, plays an important role in evaluating the veracity of propositions, particularly relating to the Japanese economic growth in view of the structural changes involved within it. This book demonstrates how to determine the co-trending rank from a given set of time series data for different variables. At the same time, the method determines how many of the co-trending relations also represent cointegrations. This enables us to perform statistical inference on the parameters of relations among the deterministic trends. Co-trending is an important contribution to the fields of econometric methods, macroeconomics, and time series analyses.

Human biomechanics is an important research field in achieving safety, health, comfort, and a high quality of life in a world where the older generation soon will outnumber the younger generation. Recently there have been significant developments in this new field ofresearch, addressing such issues as injury prevention in various types of accidents, the causes of human bodily dysfunction, function recovery through medical care and training, and func tional reinforcement by sports. These issues are studied on the basis of the biomechanics of the cells, tissues, organs, and systems of the human body. To achieve the aim of providing support for better lives from the aspect of mechanical engineering, the Human Life Support Biomechanics Endowed Chair at the Graduate School of Engineering at Nagoya University was established more than 3 years ago with a donation from the Toyota Motor Corporation. Since that time, we have been conducting intensive research in the field as well as trying to publicize our work in Japan. The results of our research have been presented at conferences both at home and abroad. We have also en deavored to underscore the importance of the field by organizing symposiums with carefully designed programs.

In recent years, there has been a major expansion of high pressure research providing unique information about systems of interest to a wide range of scientific disciplines. Since nuclear magnetic resonance has been applied to a wide spec trum of problems in chemistry, physics and biochemistry, it is not surprising to find that high pressure NMR techniques have also had many applications in these fields of science. Clearly, the high information content of NMR experiments combined with high pressure provides a powerful tool in modern chem istry. It is the aim of this monograph, in the series on NMR Basic Principles and Progress, to illustrate the wide range of prob lems which can be successfully studied by high pressure NMR. Indeed, the various contributions in this volume discuss studies of interest to physics, chemical physics, biochemistry, and chemical reaction kinetics. In many different ways, this monograph demonstrates the power of modern experimental and theoretical techniques to investigate very complex systems. The first contribution, by D. Brinkman, deals with NMR and NQR studies of superionic conductors and high-Tc supercon ductors at high pressure. Pressure effects on phase transitions, detection of new phases, and pressure effects on diffusion and spin-lattice relaxation, represent a few of the topics discussed in this contribution of particular interest to solid state physics."