Smooth parametric surfaces and n-sided patches

The theory of 'geometric continuity' within the subject of CAGD is reviewed. In particular, we are concerned with how parametric surface patches for CAGD can be pieced together to form a smooth Ck surface. The theory is applied to the problem of filling an n-sided hole occurring within a smooth rectangular patch complex. A number of solutions to this problem are surveyed

An Analysis of U.S. Postwar Consumption and Saving: Part II -- Empirical Results

A new empirical analysis of aggregate United States consumption and saving for the period 1947-80 is presented. The model is based on the theory of exact aggregation. It recognizes explicitly that households with different characteristics may be heterogeneous in their behavior and that aggregate behavior may depend on the changing composition of households by characteristics and therefore may not be adequately portrayed by a representative consumer, but otherwise it imposes minimal assumptions on household behavior. The model integrates longitudinal and cross-sectional microeconomic data on household characteristics with the traditional aggregate time-series data. Various hypotheses on consumption, such as age independence, proportionality to wealth, and price independence, are tested , and rejected. Strong evidence of relative price effects and a systematic variation of aggregate consumption with changing age distribution of wealth in the economy is found. Especially important is the substantial estimated difference in the shares of wealth consumed between households headed by persons born prior to and those born after 1939. One important lesson from this study is that modeling the aggregate U.S. economy as a representative consumer may give rise to misleading results.

Post-War Economic Growth in the Group-of-Five Countries: A New Analysis

An inter-country aggregate production function is estimated using annual data for the post-war period drawn from the Group-of-Five (G-5) countries: France, West Germany, Japan, United Kingdom and United states. It is assumed that all countries have the same underlying production function, not in terms of the measured outputs and inputs, but in terms of efficiency equivalent units of outputs and inputs. The measured quantities of outputs and inputs of each country may be converted into efficiency-equivalent quantities of outputs and inputs by the multiplication of country and commodity-specific and time-varying augmentation factors. These augmentation factors are estimated simultaneously with the parameters of the aggregate production function. Within this framework, the traditional assumptions for the measurement of productivity--constant returns to scale, neutrality of technical progress and profit maximization--are tested and all are rejected. Additional hypotheses about the nature of technical progress are also tested. It is found that technical progress may be represented as purely capital augmenting. In particular, the rate of augmentation is estimated at between 14 and 16 percent per annum for France, West Germany and Japan, and between 8 and 10 percent per annum for the U.K. and the U.S. for the period under study. It is also found that technical progress is capital-saving rather than labor-saving and is therefore unlikely to be a cause of structural unemployment. Using the estimated production function parameters, a growth-accounting exercise is carried out and the results are compared with those obtained from the conventional approach. Technical progress is found to be the most important source of growth, accounting for more than 50 percent, followed by the growth of capital input. Together they account for more than 75 percent of the growth of real output in the Group-of-Five (G-5) countries in the period under study. An international and intertemporal comparison of the productive efficiencies is also undertaken. It is found that the United States had the highest level of overall productive efficiency for the whole period under study. However, the productive efficiencies of France, West Germany and Japan rose rapidly from less than 40 percent of the U.S. level in 1949 to two-thirds of the U.S. level in 1985. There is thus some evidence of convergence.

An Analysis of Postwar U.S. Consumption and Saving: Part I -- The Model and Aggregation

A new empirical analysis of aggregate United States consumption and saving for the period 1947-80 is presented. The model is based on the theory of exact aggregation. It recognizes explicitly that households with different characteristics may be heterogeneous in their behavior and that aggregate behavior may depend on the changing composition of households by characteristics and therefore may not be adequately portrayed by a representative consumer, but otherwise it imposes minimal assumptions on household behavior. The model integrates longitudinal and cross-sectional microeconomic data on household characteristics with the traditional aggregate time-series data. Various hypotheses on consumption, such as age independence, proportionality to wealth, and price independence, are tested and rejected. Strong evidence of relative price effects and a systematic variation of aggregate consumption with changing age distribution of wealth in the economy is found. Especially important is the substantial estimated difference in the shares of wealth consumed between households headed by persons born prior to and those born after 1939. One important lesson from this study is that modeling the aggregate U. S. economy as a representative consumer may give rise to misleading results.

Action and Energy of the Gravitational Field

We present a detailed examination of the variational principle for metric general relativity as applied to a ``quasilocal'' spacetime region \M (that is, a region that is both spatially and temporally bounded). Our analysis relies on the Hamiltonian formulation of general relativity, and thereby assumes a foliation of \M into spacelike hypersurfaces $\Sigma$. We allow for near complete generality in the choice of foliation. Using a field--theoretic generalization of Hamilton--Jacobi theory, we define the quasilocal stress-energy-momentum of the gravitational field by varying the action with respect to the metric on the boundary \partial\M. The gravitational stress-energy-momentum is defined for a two--surface $B$ spanned by a spacelike hypersurface in spacetime. We examine the behavior of the gravitational stress-energy-momentum under boosts of the spanning hypersurface. The boost relations are derived from the geometrical and invariance properties of the gravitational action and Hamiltonian. Finally, we present several new examples of quasilocal energy--momentum, including a novel discussion of quasilocal energy--momentum in the large-sphere limit towards spatial infinity.Comment: To be published in Annals of Physics. This final version includes two new sections, one giving examples of quasilocal energy and the other containing a discussion of energy at spatial infinity. References have been added to papers by Bose and Dadhich, Anco and Tun

Canonical Quasilocal Energy and Small Spheres

Consider the definition E of quasilocal energy stemming from the Hamilton-Jacobi method as applied to the canonical form of the gravitational action. We examine E in the standard "small-sphere limit," first considered by Horowitz and Schmidt in their examination of Hawking's quasilocal mass. By the term "small sphere" we mean a cut S(r), level in an affine radius r, of the lightcone belonging to a generic spacetime point. As a power series in r, we compute the energy E of the gravitational and matter fields on a spacelike hypersurface spanning S(r). Much of our analysis concerns conceptual and technical issues associated with assigning the zero-point of the energy. For the small-sphere limit, we argue that the correct zero-point is obtained via a "lightcone reference," which stems from a certain isometric embedding of S(r) into a genuine lightcone of Minkowski spacetime. Choosing this zero-point, we find agreement with Hawking's quasilocal mass expression, up to and including the first non-trivial order in the affine radius. The vacuum limit relates the quasilocal energy directly to the Bel-Robinson tensor.Comment: revtex, 22 p, uses amssymb option (can be removed

Modal analysis of high frequency acoustic signal approach for progressive failure monitoring in thin composite plates

During the past few decades, many successful research works have evidently shown remarkable capability of Acoustic Emission (AE) for early damage detection of composite materials. Modal Analysis of AE signals or Modal Acoustic Emission (MAE) offers a better theoretical background for acoustic emission analysis which is necessary to get more qualitative and quantitative result. In this paper, the application of MAE concept in a single channel AE source location detection method for failure characterization and monitoring in thin composite plates was presented. Single channel AE source location is one of the recent studies for composite early damage localization, owing to the growing interest and knowledge of modal analysis of AE wave. A tensile test was conducted for glass fiber epoxy resin specimen with small notch. A single channel of AE system was used to determine the AE source location on specimen under testing. The results revealed that AE single channel source location provides reasonable accuracy for glass fiber laminate which was tested