The effect on the performance of listed family and non-family firms

Purpose: The purpose of this paper is to examine whether the ownership of public firms is related to accounting and market performance, comparing family and non-family listed firms. Design/methodology/approach: We use regression analysis, considering a sample of Portuguese family and non-family firms for the period between 1999 and 2010. Findings: Overall, the results show that family firms are older, are more indebted and have higher debt costs than non-family firms. However, they present lower levels of risk. The evidence suggests that family firms outperform non-family firms when we consider a market performance measure. The market performance of family-controlled firms is more sensitive to the crisis periods and age, compared to their counterparts. The empirical findings suggest that under economic adversity, the performance is especially compromised by the firms’ age. Research limitations/implications: A limitation of this study is the small size of the sample, which derives from the small size of the Portuguese stock market, the Euronext Lisbon. Originality/value: This paper offers some insights on the ownership of public firms and firm performance by investigating a small European economy. The study also contributes to the stream of firm performance, considering new independent variables as determinants of firm performance, such as operational risk. Finally, the study examines the interaction between ownership and performance under both steady and adverse economic conditions, giving the opportunity to analyze whether firm performance differs according to market conditions.

Numerical and combinatorial applications of generalized Appell polynomials

This thesis studies properties and applications of different generalized Appell polynomials in the framework of Clifford analysis. As an example of 3D-quasi-conformal mappings realized by generalized Appell polynomials, an analogue of the complex Joukowski transformation of order two is introduced. The consideration of a Pascal n-simplex with hypercomplex entries allows stressing the combinatorial relevance of hypercomplex Appell polynomials. The concept of totally regular variables and its relation to generalized Appell polynomials leads to the construction of new bases for the space of homogeneous holomorphic polynomials whose elements are all isomorphic to the integer powers of the complex variable. For this reason, such polynomials are called pseudo-complex powers (PCP). Different variants of them are subject of a detailed investigation. Special attention is paid to the numerical aspects of PCP. An efficient algorithm based on complex arithmetic is proposed for their implementation. In this context a brief survey on numerical methods for inverting Vandermonde matrices is presented and a modified algorithm is proposed which illustrates advantages of a special type of PCP. Finally, combinatorial applications of generalized Appell polynomials are emphasized. The explicit expression of the coefficients of a particular type of Appell polynomials and their relation to a Pascal simplex with hypercomplex entries are derived. The comparison of two types of 3D Appell polynomials leads to the detection of new trigonometric summation formulas and combinatorial identities of Riordan-Sofo type characterized by their expression in terms of central binomial coefficients.