This paper describes new analysis techniques for noise-vibration of automobiles. In the field, mode superposition technique plays an important role, because all the useful and advanced methodologies such as sensitivity analysis and substructure synthesis are derived from mode superposition technique. The authors have proposed a new mode superposition technique that is superior to all the traditional ones. This new method makes it possible to truncate both higher and lower frequency eigenmodes and it can also be used in analyzing systems that include rigid modes. Even more by choosing a parameter, our new method can be reduced to the conventional mode superposition techniques. The mode superposition technique traditionally applied to structural systems is not applicable to a problem involving fluid-structure coupling because the matrix used is asymmetric. To overcome this problem, the authors also have extended the mode superposition techniques for coupled systems using right and left eigenvectors. Based on this extended mode superposition technique, we succeeded for the first time in obtaining expressions for the sensitivity coefficients of a coupled system. It has been shown that the use of a new mode superposition technique greatly improves the convergence of a modal sensitivity analysis, and makes it possible to calculate the sensitivity with better efficiency than Fox-Kapoor's modal method and Wang's modified modal method and also with better efficiency than Nelson's method. Even more the modal sensitivity derived from the new mode superposition technique can be reduced to those conventional mode superposition techniques. With these new techniques, the possibility of being able to analyse vehicle interior noise in high frequency range has been gotten though it was hitherto very difficult.

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The methods of computational continuum mechanics such as the finite element method and the boundary element method are essentially numerical techniques for partial differential equations, whose solutions are highly reliable when the continuum assumption is valid. On the other hand, the physical models developed in computational discontinuum mechanics are effective in the simulations of highly nonlinear and discontinuous behaviors, however, they are not always reliable as numerical techniques for differential equations. The present paper is concerned with the cooperative and concurrent use of the finite element method and the methods of computational discontinuum mechanics in some solid mechanics problems. The adaptively shifted integration technique for the plastic collapse analysis of framed structures is described as an example in computational structural mechanics. The computational damage mechanics approach with the aid of a mesoscopic simulation for the analysis of brittle microcracking solids is presented in computational material science.

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Mathematical aspects of quantum field theory are reviewed. The topics included are: canonical quantization of classical fields, functional integral method, Schwinger's functional derivative equation, methods and results of constructive quantum field theory, Lamb shift in quantum electrodynamics, supersymmetric quantum field theory and related aspects.

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