Deviations from normality in random strings

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Mellin transforms and asymptotics : digital sums

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30 years of collaboration

We highlight some of the most important cornerstones of the long standing and very fruitful collaboration of the Austrian Diophantine Number Theory research group and the Number Theory and Cryptography School of Debrecen. However, we do not plan to be complete in any sense but give some interesting data and selected results that we find particularly nice. At the end we focus on two topics in more details, namely a problem that origins from a conjecture of Rényi and Erdős (on the number of terms of the square of a polynomial) and another one that origins from a question of Zelinsky (on the unit sum number problem). This paper evolved from a plenary invited talk that the authors gaveat the Joint Austrian-Hungarian Mathematical Conference 2015, August 25-27, 2015 in Győr (Hungary)

Formal and Informal Financing Decisions of Small Businesses

This study investigates small businesses’ financing decisions. Drawing upon asymmetric information theory, institutional theory and relevant literature on cognitive financial constraints, human capital and social capital, we propose a theoretical framework in which financing determinants come from three dimensions: entrepreneurs’ individual factors, organisational (firm-level) factors and contextual (institutional) factors. We employ this model to distinguish four types of firms: (1) firms that use no external finance, (2) firms that use informal finance only, (3) firms that use formal finance only and (4) firms that use both formal and informal finance. An empirical test on Vietnamese small businesses shows that factors from all three dimensions are important in understanding small businesses’ financing decisions

The influence of social capital on opportunity emergence and exploitation: a comparison of portfolio and serial entrepreneurs

Habitual entrepreneurs are a frequent and important phenomenon in entrepreneurship and for the economy. We lack, however, a systematic understanding of the advantages or disadvantages of multiple business ownership and specifically if portfolio and serial entrepreneurs are different in detecting and exploiting opportunities. Research on habitual entrepreneurs has mainly focused on a human capital and an organizational perspective. In order to further advance our understanding of habitual entrepreneurship, we conducted a case study research focusing on the social capital of habitual entrepreneurs and on how, by investigating differences between serial and portfolio entrepreneurs, it is related to the emergence and exploitation of opportunities

Deviations from Uniformity in Random Strings

We show that almost all binary strings of length n contain all blocks of size (1-&)log, n a close to uniform number of times. From this, we derive tight bounds on the discrepancy of random infinite strings. Our results are obtained through explicit generating function expressions and contour integration estimates