A simple, accurate depth check guage

Easily made, pen-light battery operated production check gauge has probe-activated switch with fail-safe features to insure proper operation. Parts can be reliably and quickly checked. Gauge is equipped with tolerance band adjustment and can use interchangeable probes for different applications. Accompanying tester permits frequent check of calibration

Optimal Focusing for Monochromatic Scalar and Electromagnetic Waves

For monochromatic solutions of D'Alembert's wave equation and Maxwell's equations, we obtain sharp bounds on the sup norm as a function of the far field energy. The extremizer in the scalar case is radial. In the case of Maxwell's equation, the electric field maximizing the value at the origin follows longitude lines on the sphere at infinity. In dimension $d=3$ the highest electric field for Maxwell's equation is smaller by a factor 2/3 than the highest corresponding scalar waves. The highest electric field densities on the balls $B_R(0)$ occur as $R\to 0$. The density dips to half max at $R$ approximately equal to one third the wavelength. The extremizing fields are identical to those that attain the maximum field intensity at the origin.Comment: 30 pages, 7 figure

Bureaucracy, Infrastructure, and Economic Growth: Evidence from U.S. Cities During the Progressive Era

Recent work in the sociology of economic development has emphasized the establishment of a professional bureaucracy in place of political appointees as an important component of the institutional environment in which private enterprise can flourish. I hypothesize that establishment of such a bureaucracy will lengthen the period that public decision makers are willing to wait to realize the benefits of expenditures, leading to allocation of a greater proportion of government resources to long-gestation period projects such as infrastructure. This hypothesis can be tested using data generated by a `natural experiment' in the early part of this century, when a wave of municipal reform transformed the governments of many U.S. cities. Controlling for city and time effects, adoption of Civil Service is found to increase the share of total municipal expenditure allocated to road and sewer investment. Other estimates imply that this increased share raises the growth rate of city manufacturing employment by one-half percent per year.

Development Through Synergistic Reform

Several studies suggest that production of high-quality output is a precondition for firms in less developed countries to participate in the export market. Institutional deficiencies that raise the costs of entry into high-quality production therefore limit the positive impact that trade liberalization can have on income or growth. Institutional reform that reduces the costs of entry into high-quality production and trade reform therefore have synergistic effects on income and, possibly, growth. In contrast, institutional reform that reduces the costs of entry into low-quality production (e.g., reforms targeted at small businesses) interferes with the impact of trade reform. The model that yields these results is also used to analyze impacts of foreign direct investment and of subsidies to entrepreneurship in the presence of unemployment.

Trade and Search: Social Capital, Sogo Shosha, and Spillovers

A network/search view of international trade in differentiated products is proposed. It is shown that this view can explain the importance of ethnic and extended family ties in trade, the success of diversified trading intermediaries such as Japan's sogo shosha, and the ubiquity of government export promotion policies such as subsidized trade missions.

Productivity Gains From Geographic Concentration of human Capital: Evidence From the Cities

Based on recent theoretical developments I argue that the average level of human capital is a local public good. Cities with higher average levels of human capital should therefore have higher wages and higher land rents. After conditioning on the characteristics of individual workers and dwellings, this prediction is supported by data for Standard Metropolitan Statistical Areas (SMSAs) in the United States, where the SMSA average levels of formal education and work experience are used as proxies for the average level of human capital. I evaluate the alternative explanations of omitted SMSA variables and self-selection. I conclude by computing an estimate of the effect of an additional year of average education on total factor productivity.

Does History Matter Only When it Matters Little? The Case of City-Indu try Location

When will an industry subject to agglomeration economies move from an old, high-cost site to a new, low-cost site? It is argued that history, in the form of sunk costs resulting from the operation of many firms at a site, creates a first-mover disadvantage that can prevent relocation. It is demonstrated that developers of industrial parks can partly overcome this inertia through discriminatory pricing of land over time, and empirical evidence is provided that they actually engage in such behavior. It is also shown that other aspects of developer land-sale strategy can be a source of information on the nature of interfirm externalities.

Adaptive Filtering for Large Space Structures: A Closed-Form Solution

In a previous paper Schaechter proposes using an extended Kalman filter to estimate adaptively the (slowly varying) frequencies and damping ratios of a large space structure. The time varying gains for estimating the frequencies and damping ratios can be determined in closed form so it is not necessary to integrate the matrix Riccati equations. After certain approximations, the time varying adaptive gain can be written as the product of a constant matrix times a matrix derived from the components of the estimated state vector. This is an important savings of computer resources and allows the adaptive filter to be implemented with approximately the same effort as the nonadaptive filter. The success of this new approach for adaptive filtering was demonstrated using synthetic data from a two mode system

Flow Equations for Uplifting Half-Flat to Spin(7) Manifolds

In this short supplement to [1], we discuss the uplift of half-flat six-folds to Spin(7) eight-folds by fibration of the former over a product of two intervals. We show that the same can be done in two ways - one, such that the required Spin(7) eight-fold is a double G_2 seven-fold fibration over an interval, the G_2 seven-fold itself being the half-flat six-fold fibered over the other interval, and second, by simply considering the fibration of the half-flat six-fold over a product of two intervals. The flow equations one gets are an obvious generalization of the Hitchin's flow equations (to obtain seven-folds of G_2 holonomy from half-flat six-folds [2]). We explicitly show the uplift of the Iwasawa using both methods, thereby proposing the form of the new Spin(7) metrics. We give a plausibility argument ruling out the uplift of the Iwasawa manifold to a Spin(7) eight fold at the "edge", using the second method. For $Spin(7)$ eight-folds of the type $X_7\times S^1$, $X_7$ being a seven-fold of SU(3) structure, we motivate the possibility of including elliptic functions into the "shape deformation" functions of seven-folds of SU(3) structure of [1] via some connections between elliptic functions, the Heisenberg group, theta functions, the already known $D7$-brane metric [3] and hyper-K\"{a}hler metrics obtained in twistor spaces by deformations of Atiyah-Hitchin manifolds by a Legendre transform in [4].Comment: 12 pages, LaTeX; v3: (JMP) journal version which includes clarifying remarks related to connection between Spin(7)-folds and SU(3)structur

Entrepreneurship in International Trade

Motivated by evidence on the importance of incomplete information and networks in international trade, we investigate the supply of 'network intermediation.' We hypothesize that the agents who become international trade intermediaries first accumulate networks of foreign contacts while working as employees in production or sales, then become entrepreneurs who sell access to and use of the networks they accumulated. We report supportive results regarding this hypothesis from a pilot survey of international trade intermediaries. We then build a simple general-equilibrium model of this type of entrepreneurship, and use it for comparative statics and welfare analysis. One welfare conclusion is that intermediaries may have inadequate incentives to maintain or expand their networks, suggesting a rationale for the policies followed by some countries to encourage large-scale trading companies that imitate the Japanese sogo shosha.