Massima estensione della soluzione di Schwarzschild e diagrammi di Penrose

Il punto di partenza dell'elaborato riguarda il modo in cui si giunge, a partire dalla relatività ristretta, a quella generale. Quest'ultima viene poi identificata come una teoria della gravitazione in cui si ottengono le equazioni di campo. Da qui si discute la soluzione delle equazioni di Einstein trovata da Schwarzschild evidenziandone i limiti. Si procede alla estensione di questa soluzione introducendo dapprima le coordinate di Eddington-Finkelstein e poi l'estensione massima data da Kruskal. Infine viene mostrato come è possibile compattificare l'infinito spaziotempo in una regione finita senza alterare la struttura causale. Questo viene fatto tramite delle trasformazioni particolari: le trasformazioni conformi. I diagrammi spaziotemporali che si ottengono dopo la compattificazione conforme sono conosciuti come i digrammi di Penrose e qui si vede come ottenere quelli dello spaziotempo di Minkowski e quelli dello spaziotempo della soluzione di Schwarzschild.

New perspectives on forbidden symmetries, quasicrystals, and Penrose tilings

Quasicrystals are solids with quasiperiodic atomic structures and symmetries forbidden to ordinary periodic crystals—e.g., 5-fold symmetry axes. A powerful model for understanding their structure and properties has been the two-dimensional Penrose tiling. Recently discovered properties of Penrose tilings suggest a simple picture of the structure of quasicrystals and shed new light on why they form. The results show that quasicrystals can be constructed from a single repeating cluster of atoms and that the rigid matching rules of Penrose tilings can be replaced by more physically plausible cluster energetics. The new concepts make the conditions for forming quasicrystals appear to be closely related to the conditions for forming periodic crystals.

An endogenous rate of time preference, the Penrose effect, and dynamic optimality of environmental quality.

In the present paper, the endogenous theory of time preference is extended to analyze those processes of capital accumulation and changes in environmental quality that are dynamically optimum with respect to the intertemporal preference ordering of the representative individual of the society in question. The analysis is carried out within the conceptual framework of the dynamic analysis of environmental quality, as has been developed by a number of economists for specific cases of the fisheries and forestry commons. The duality principles on intertemporal preference ordering and capital accumulation are extended to the situation where processes of capital accumulation are subject to the Penrose effect, which exhibit the marginal decrease in the effect of investment in private and social overhead capital upon the rate at which capital is accumulated. The dynamically optimum time-path of economic activities is characterized by the proportionality of two systems of imputed, or efficient, prices, one associated with the given intertemporal ordering and another associated with processes of accumulation of private and social overhead capital. It is particularly shown that the dynamically optimality of the processes of capital accumulation involving both private and social overhead capital is characterized by the conditions that are identical with those involving private capital, with the role of social overhead capital only indirectly exhibited.

Senators from Pennsylvania. Memorial addresses delivered in the Senate and House of Representatives of the United States in memory of Philander C. Knox, Boies Penrose, William E. Crow, late senators from Pennsylvania. Sixty-seventh Congress. Proceedings in the Senate, January 28, 1923. Proceedings in the House, February 18, 1923.

Running title: Memorial addresses.

Penrose's annual.

Publication suspended 1917-1919.

Considerations on miracles; containing the substance of an article in the British Critic, on Mr. Penrose's Treatise on the evidence of the scripture miracles with additions.

Mode of access: Internet.

The Penrose annual

Publication suspended, 1917-1919; 1941-1948

Operationalizing the resource based view for nascent and young firms : developing scales for resource advantages and disadvantages

Principal Topic: It is well known that most new ventures suffer from a significant lack of resources, which increases the risk of failure (Shepherd, Douglas and Shanley, 2000) and makes it difficult to attract stakeholders and financing for the venture (Bhide & Stevenson, 1999). The Resource-Based View (RBV) (Barney, 1991; Wernerfelt, 1984) is a dominant theoretical base increasingly drawn on within Strategic Management. While theoretical contributions applying RBV in the domain of entrepreneurship can arguably be traced back to Penrose (1959), there has been renewed attention recently (e.g. Alvarez & Busenitz, 2001; Alvarez & Barney, 2004). This said, empirical work is in its infancy. In part, this may be due to a lack of well developed measuring instruments for testing ideas derived from RBV. The purpose of this study is to develop a measurement scales that can serve to assist such empirical investigations. In so doing we will try to overcome three deficiencies in current empirical measures used for the application of RBV to the entrepreneurship arena. First, measures for resource characteristics and configurations associated with typical competitive advantages found in entrepreneurial firms need to be developed. These include such things as alertness and industry knowledge (Kirzner, 1973), flexibility (Ebben & Johnson, 2005), strong networks (Lee et al., 2001) and within knowledge intensive contexts, unique technical expertise (Wiklund and Shepard, 2003). Second, the RBV has the important limitations of being relatively static and modelled on large, established firms. In that context, traditional RBV focuses on competitive advantages. However, newly established firms often face disadvantages, especially those associated with the liabilities of newness (Aldrich & Auster, 1986). It is therefore important in entrepreneurial contexts to expand to an investigation of responses to competitive disadvantage through an RBV lens. Conversely, recent research has suggested that resource constraints actually have a positive effect on firm growth and performance under some circumstances (e.g., George, 2005; Katila & Shane, 2005; Mishina et al., 2004; Mosakowski, 2002; cf. also Baker & Nelson, 2005). Third, current empirical applications of RBV measured levels or amounts of particular resources available to a firm. They infer that these resources deliver firms competitive advantage by establishing a relationship between these resource levels and performance (e.g. via regression on profitability). However, there is the opportunity to directly measure the characteristics of resource configurations that deliver competitive advantage, such as Barney´s well known VRIO (Valuable, Rare, Inimitable and Organized) framework (Barney, 1997). Key Propositions and Methods: The aim of our study is to develop and test scales for measuring resource advantages (and disadvantages) and inimitability for entrepreneurial firms. The study proceeds in three stages. The first stage developed our initial scales based on earlier literature. Where possible, we adapt scales based on previous work. The first block of the scales related to the level of resource advantages and disadvantages. Respondents were asked the degree to which each resource category represented an advantage or disadvantage relative to other businesses in their industry on a 5 point response scale: Major Disadvantage, Slight Disadvantage, No Advantage or Disadvantage, Slight Advantage and Major Advantage. Items were developed as follows. Network capabilities (3 items) were adapted from (Madsen, Alsos, Borch, Ljunggren & Brastad, 2006). Knowledge resources marketing expertise / customer service (3 items) and technical expertise (3 items) were adapted from Wiklund and Shepard (2003). flexibility (2 items), costs (4 items) were adapted from JIBS B97. New scales were developed for industry knowledge / alertness (3 items) and product / service advantages. The second block asked the respondent to nominate the most important resource advantage (and disadvantage) of the firm. For the advantage, they were then asked four questions to determine how easy it would be for other firms to imitate and/or substitute this resource on a 5 point likert scale. For the disadvantage, they were asked corresponding questions related to overcoming this disadvantage. The second stage involved two pre-tests of the instrument to refine the scales. The first was an on-line convenience sample of 38 respondents. The second pre-test was a telephone interview with a random sample of 31 Nascent firms and 47 Young firms (< 3 years in operation) generated using a PSED method of randomly calling households (Gartner et al. 2004). Several items were dropped or reworded based on the pre-tests. The third stage (currently in progress) is part of Wave 1 of CAUSEE (Nascent Firms) and FEDP (Young Firms), a PSED type study being conducted in Australia. The scales will be tested and analysed with a random sample of approximately 700 Nascent and Young firms respectively. In addition, a judgement sample of approximately 100 high potential businesses in each category will be included. Findings and Implications: The paper will report the results of the main study (stage 3 – currently data collection is in progress) will allow comparison of the level of resource advantage / disadvantage across various sub-groups of the population. Of particular interest will be a comparison of the high potential firms with the random sample. Based on the smaller pre-tests (N=38 and N=78) the factor structure of the items confirmed the distinctiveness of the constructs. The reliabilities are within an acceptable range: Cronbach alpha ranged from 0.701 to 0.927. The study will provide an opportunity for researchers to better operationalize RBV theory in studies within the domain of entrepreneurship. This is a fundamental requirement for the ability to test hypotheses derived from RBV in systematic, large scale research studies.

The growth-profitability relationship : strategic orientations as moderator

Principal Topic: In this study we investigate how strategic orientation moderates the impact of growth on profitability for a sample of Danish high growth (Gazelle) firms. ---------- Firm growth has been an essential part of both management research and entrepreneurship research for decades (e.g. Penrose 1959, Birch 1987, Storey 1994). From a societal point of view, firm growth has been perceived as economic generator and job creator. In entrepreneurship research, growth has been an important part of the field (Davidsson, Delmar and Wiklund 2006), and many have used growth as a measure of success. In strategic management, growth has been seen as an approach to achieve competitive advantages and a way of becoming increasing profitable (e.g. Russo and Fouts 1997, Cho and Pucic 2005). However, although firm growth used to be perceived as a natural pathway to profitability recently more skepticism has emerged due to both new theoretical development and new empirical insights. Empirically, studies show inconsistent and inconclusive empirical evidence regarding the impact of growth on profitability. Our review reveals that some studies find a substantial positive relationship, some find a weak positive relationship, some find no relationship and further some find a negative relationship. Overall, two dominant yet divergent theoretical positions can be identified. The first position, mainly focusing on the environmental fit, argues that firms are likely to become more profitable if they enter a market quickly and on a larger scale due to first mover advantages and economic of scale. The second position, mainly focusing the internal fit, argues that growth may lead to a range of internal challenges and difficulties, including rapid change in structure, reward systems, decision making, communication and management style. The inconsistent empirical results together with two divergent theoretical positions call for further investigations into the circumstances by which growth generate profitability and into the circumstances by which growth do not generate profitability. In this project, we investigate how strategic orientations influence the impact of growth on profitability by asking the following research question: How is the impact of growth on profitability moderated by strategic orientation? Based on a literature review of how growth impacts profitability in areas such as entrepreneurship, strategic management and strategic entrepreneurship we develop three hypotheses regarding the growth-profitability relationship and strategic orientation as a potential moderator. ---------- Methodology/Key Propositions: The three hypotheses are tested on data collected in 2008. All firms in Denmark, including all listed and non-listed (VAT-registered) firms who experienced a 100 % growth and had a positive sales or gross profit over a four years period (2004-2007) were surveyed. In total 2,475 fulfilled the requirements. Among those 1,107 firms returned usable questionnaires satisfactory giving us a response rate on 45 %. The financial data together with data on number of employees were obtained from D&B (previously Dun & Bradstreet). The remaining data were obtained through the survey. Hierarchical regression models with ROA (return on assets) as the dependent variable were used to test the hypotheses. In the first model control variables including region, industry, firm age, CEO age, CEO gender, CEO education and number of employees were entered. In the second model, growth measured as growth in employees was entered. Then strategic orientation (differentiation, cost leadership, focus differentiation and focus cost leadership) and then interaction effects of strategic orientation and growth were entered in the model. ---------- Results and Implications: The results show a positive impact of firm growth on profitability and further that this impact is moderated by strategic orientation. Specifically, it was found that growth has a larger impact on profitability when firms do not pursue a focus strategy including both focus differentiation and focus cost leadership. Our preliminary interpretation of the results suggests that the value of growth depends on the circumstances and more specifically 'how much is left to fight for'. It seems like those firms who target towards a narrow segment are less likely to gain value of growth. The remaining market shares to fight for to these firms are not large enough to compensate for the cost of growing. Based on our findings, it therefore seems like growth has a more positive relationship with profitability for those who approach a broad market segment. Furthermore we argue that firms pursuing af Focus strategy will have more specialized assets that decreases the possibilities of further profitable expansion. For firms, CEOs, board of directors etc., the study shows that high growth is not necessarily something worth aiming for. It is a trade-off between the cost of growing and the value of growing. For many firms, there might be better ways of generating profitability in the long run. It depends on the strategic orientation of the firm. For advisors and consultants, the conditional value of growth implies that in-depth knowledge on their clients' situation is necessary before any advice can be given. And finally, for policy makers, it means they have to be careful when initiating new policies to promote firm growth. They need to take into consideration firm strategy and industry conditions.

Micro-family-owned business : transitory survival mechanism or long term wealth creator?

Principal Topic: Entrepreneurship is key to employment, innovation and growth (Acs & Mueller, 2008), and as such, has been the subject of tremendous research in both the economic and management literatures since Solow (1957), Schumpeter (1934, 1943), and Penrose (1959). The presence of entrepreneurs in the economy is a key factor in the success or failure of countries to grow (Audretsch and Thurik, 2001; Dejardin, 2001). Further studies focus on the conditions of existence of entrepreneurship, influential factors invoked are historical, cultural, social, institutional, or purely economic (North, 1997; Thurik 1996 & 1999). Of particular interest, beyond the reasons behind the existence of entrepreneurship, are entrepreneurial survival and good ''performance'' factors. Using cross-country firm data analysis, La Porta & Schleifer (2008) confirm that informal micro-businesses provide on average half of all economic activity in developing countries. They find that these are utterly unproductive compared to formal firms, and conclude that the informal sector serves as a social security net ''keep[ing] millions of people alive, but disappearing over time'' (abstract). Robison (1986), Hill (1996, 1997) posit that the Indonesian government under Suharto always pointed to the lack of indigenous entrepreneurship , thereby motivating the nationalisation of all industries. Furthermore, the same literature also points to the fact that small businesses were mostly left out of development programmes because they were supposed less productive and having less productivity potential than larger ones. Vial (2008) challenges this view and shows that small firms represent about 70% of firms, 12% of total output, but contribute to 25% of total factor productivity growth on average over the period 1975-94 in the industrial sector (Table 10, p.316). ---------- Methodology/Key Propositions: A review of the empirical literature points at several under-researched questions. Firstly, we assess whether there is, evidence of small family-business entrepreneurship in Indonesia. Secondly, we examine and present the characteristics of these enterprises, along with the size of the sector, and its dynamics. Thirdly, we study whether these enterprises underperform compared to the larger scale industrial sector, as it is suggested in the literature. We reconsider performance measurements for micro-family owned businesses. We suggest that, beside productivity measures, performance could be appraised by both the survival probability of the firm, and by the amount of household assets formation. We compare micro-family-owned and larger industrial firms' survival probabilities after the 1997 crisis, their capital productivity, then compare household assets of families involved in business with those who do not. Finally, we examine human and social capital as moderators of enterprises' performance. In particular, we assess whether a higher level of education and community participation have an effect on the likelihood of running a family business, and whether it has an impact on households' assets level. We use the IFLS database compiled and published by RAND Corporation. The data is a rich community, households, and individuals panel dataset in four waves: 1993, 1997, 2000, 2007. We now focus on the waves 1997 and 2000 in order to investigate entrepreneurship behaviours in turbulent times, i.e. the 1997 Asian crisis. We use aggregate individual data, and focus on households data in order to study micro-family-owned businesses. IFLS data covers roughly 7,600 households in 1997 and over 10,000 households in 2000, with about 95% of 1997 households re-interviewed in 2000. Households were interviewed in 13 of the 27 provinces as defined before 2001. Those 13 provinces were targeted because accounting for 83% of the population. A full description of the data is provided in Frankenberg and Thomas (2000), and Strauss et alii (2004). We deflate all monetary values in Rupiah with the World Development Indicators Consumer Price Index base 100 in 2000. ---------- Results and Implications: We find that in Indonesia, entrepreneurship is widespread and two thirds of households hold one or several family businesses. In rural areas, in 2000, 75% of households run one or several businesses. The proportion of households holding both a farm and a non farm business is higher in rural areas, underlining the reliance of rural households on self-employment, especially after the crisis. Those businesses come in various sizes from very small to larger ones. The median business production value represents less than the annual national minimum wage. Figures show that at least 75% of farm businesses produce less than the annual minimum wage, with non farm businesses being more numerous to produce the minimum wage. However, this is only one part of the story, as production is not the only ''output'' or effect of the business. We show that the survival rate of those businesses ranks between 70 and 82% after the 1997 crisis, which contrasts with the 67% survival rate for the formal industrial sector (Ter Wengel & Rodriguez, 2006). Micro Family Owned Businesses might be relatively small in terms of production, they also provide stability in times of crisis. For those businesses that provide business assets figures, we show that capital productivity is fairly high, with rates that are ten times higher for non farm businesses. Results show that households running a business have larger family assets, and households are better off in urban areas. We run a panel logit model in order to test the effect of human and social capital on the existence of businesses among households. We find that non farm businesses are more likely to appear in households with higher human and social capital situated in urban areas. Farm businesses are more likely to appear in lower human capital and rural contexts, while still being supported by community participation. The estimation of our panel data model confirm that households are more likely to have higher family assets if situated in urban area, the higher the education level, the larger the assets, and running a business increase the likelihood of having larger assets. This is especially true for non farm businesses that have a clearly larger and more significant effect on assets than farm businesses. Finally, social capital in the form of community participation also has a positive effect on assets. Those results confirm the existence of a strong entrepreneurship culture among Indonesian households. Investigating survival rates also shows that those businesses are quite stable, even in the face of a violent crisis such as the 1997 one, and as a result, can provide a safety net. Finally, considering household assets - the returns of business to the household, rather than profit or productivity - the returns of business to itself, shows that households running a business are better off. While we demonstrate that uman and social capital are key to business existence, survival and performance, those results open avenues for further research regarding the factors that could hamper growth of those businesses in terms of output and employment.

Organic and acquisitive growth : re-examining, testing and extending Penrose’s growth theory

The Theory of the Growth of The Firm by Edith Penrose, first published in 1959, is a seminal contribution to the field of management. Penrose's intention was to create a theory of firm growth which was logically consistent and empirically tractable (Buckley and Casson, 2007). Much attention, however, has been focused on her unintended contribution to the resource-based view (henceforth RBV) (e.g. Kor and Mahoney, 2004; Lockett and Thompson, 2004) rather than her firm growth theory. We feel that this is unfortunate because despite a rapidly growing body of empirical work, conceptual advancement in growth studies has been limited (Davidsson and Wiklund, 2000; Davidsson et ai., 2006; Delmar, 1997; Storey, 1994). The growth literature frequently references Penrose's work, but little explicit testing of her ideas has been undertaken. This is surprising given that Penrose's work remains the most comprehensive theory of growth to date. One explanation is that she did not formality present her arguments, favouring verbal exposition over formalized models (Lockett, 2005; Lockett and Thompson, 2004). However, the central propositions and conclusions of her theory can be operationalized and empirically tested.

Entrepreneurial growth : the role of international knowledge acquisition as moderated by firm age

In line with repeated recent calls for research on specific forms of growth rather than on an undifferentiated notion of “total growth,” our study contributes to the understanding of entrepreneurial growth. By this we mean growth through expansion into new geographic markets and/or via the introduction of new products or services. Building on Penrose's theory of the growth of the firm and on the research streams she has in part inspired, we investigate the impact of knowledge acquisition from international markets on entrepreneurial growth both at home and abroad. We further suggest that the effects of international knowledge acquisition on entrepreneurial growth will vary with firm age. Utilizing longitudinal data on 138 small and medium-sized enterprises (SMEs), we find that the acquisition of knowledge from international markets fuels growth through market development, and that this effect is stronger for international expansion than domestic expansion. Our results also show that firm age negatively moderates the relationship between international knowledge acquisition and entrepreneurial growth via the introduction of new products or services. Specifically, international knowledge acquisition has a positive effect on growth via new products/services development in young firms, but a negative effect in mature firms. We assume this reflects changes over time in how international knowledge is managed.

Generalised quaternion methods in conformal geometry

A new approach to Penrose's twistor algebra is given. It is based on the use of a generalised quaternion algebra for the translation of statements in projective five-space into equivalent statements in twistor (conformal spinor) space. The formalism leads toSO(4, 2)-covariant formulations of the Pauli-Kofink and Fierz relations among Dirac bilinears, and generalisations of these relations.