Implicit Solutions of PDE's

Further investigations of implicit solutions to non-linear partial differential equations are pursued. Of particular interest are the equations which are Lorentz invariant. The question of which differential equations of second order for a single unknown $\phi$ are solved by the imposition of an inhomogeneous quadratic relationship among the independent variables, whose coefficients are functions of $\phi$ is discussed, and it is shown that if the discriminant of the quadratic vanishes, then an implicit solution of the so-called Universal Field Equation is obtained. The relation to the general solution is discussed.Comment: 11 pages LaTeX2

Using the AHP to determine the correlation of product issues to profit

Analyzes the correlation between product issues and product profit using the analytic hierarchy process (AHP). Estimation on the effect of profit on product issues by AHP; failure of the AHP to determine the correlation factors; development of procedure for determining correlation factors

Integrable Top Equations associated with Projective Geometry over Z_2

We give a series of integrable top equations associated with the projective geometry over Z_2 as a (2^n-1)-dimensional generalisation of the 3D Euler top equations. The general solution of the (2^n-1)D top is shown to be given by an integration over a Riemann surface with genus (2^{n-1}-1)^2.Comment: 8 pages, Late

The Reversed q-Exponential Functional Relation

After obtaining some useful identities, we prove an additional functional relation for $q$ exponentials with reversed order of multiplication, as well as the well known direct one in a completely rigorous manner.Comment: 6 pages, LaTeX, no figure

A universal solution

The phenomenon of an implicit function which solves a large set of second order partial differential equations obtainable from a variational principle is explicated by the introduction of a class of universal solutions to the equations derivable from an arbitrary Lagrangian which is homogeneous of weight one in the field derivatives. This result is extended to many fields. The imposition of Lorentz invariance makes such Lagrangians unique, and equivalent to the Companion Lagrangians introduced in [baker].Comment: arxiv version is already officia

Entrepreneurship, Self-Employment and Business Data: An Introduction to Several Large, Nationally-Representative Datasets

Only a few large, nationally-representative datasets include information on both the owner and the business. We briefly describe several of the most respected and up-to-date sources of data on entrepreneurs, the self-employed, and small businesses. More information including estimates of recent trends in business ownership and performance (e.g. survival rates, sales, employment, payroll, profits and industry) from these datasets is contained in Fairlie and Robb (2008).small businesses, business owners, self-employment, entrepreneurship, data

Gender Differences in Business Performance: Evidence from the Characteristics of Business Owners Survey

Using confidential microdata from the U.S. Census Bureau, we investigate the performance of female-owned businesses making comparisons to male-owned businesses. Using regression estimates and a decomposition technique, we explore the role that human capital, especially through prior work experience, and financial capital play in contributing to why female-owned businesses have lower survival rates, profits, employment and sales. We find that female-owned businesses are less successful than male-owned businesses because they have less startup capital, and business human capital acquired through prior work experience in a similar business and prior work experience in family business. We also find some evidence that female-owned businesses work fewer hours and may have different preferences for the goals of their business.female entrepreneurship, business outcomes

Determinants of Business Success: An Examination of Asian-Owned Businesses in the United States

Using confidential microdata from the U.S. Census Bureau, we investigate the performance of Asian-owned businesses. Using regression estimates and a special nonlinear decomposition technique, we explore the role that class resources, such as financial capital and human capital, play in contributing to the relative success of Asian businesses. We find that Asian-owned businesses are more successful than white-owned businesses for two main reasons – Asian owners have high levels of human capital and their businesses have substantial startup capital. Using detailed information on both the owner and the firm, we estimate the explanatory power of several additional factors. This research was partially funded by the Russell Sage Foundation and Kauffman Foundation. The research in this paper was conducted while the authors were Special Sworn Status researchers of the U.S. Census Bureau at the Center for Economic Studies and California Research Data Center at U.C. Berkeley. This paper has been screened to insure that no confidential data are revealed. The data can be obtained at a Census Research Data Center or at the Center for Economic Studies (CES) only after approval by the CES and IRS. See www.ces.census.gov for details on the application and approval process. The views expressed here are solely the responsibility of the authors and should not be interpreted as reflecting the views of the Russell Sage Foundation, the Kauffman Foundation, the U.S. Census Bureau, or the Board of Governors of the Federal Reserve System.Asian, entrepreneurship, business outcomes

Patterns of Financing: A Comparison Between White- and African-American Young Firms

Based on Kauffman Firm Survey data, examines differences in start-up and follow-on capital injections into and capital use by firms with African-American and white owners. Explores how access to capital affects the racial gap in new business formation