A review of power laws in real life phenomena

Power law distributions, also known as heavy tail distributions, model distinct real life phenomena in the areas of biology, demography, computer science, economics, information theory, language, and astronomy, amongst others. In this paper, it is presented a review of the literature having in mind applications and possible explanations for the use of power laws in real phenomena. We also unravel some controversies around power laws.

A straightforward method to obtain the cohesive laws of bonded joints under mode I loading

A simple procedure to measure the cohesive laws of bonded joints under mode I loading using the double cantilever beam test is proposed. The method only requires recording the applied load–displacement data and measuring the crack opening displacement at its tip in the course of the experimental test. The strain energy release rate is obtained by a procedure involving the Timoshenko beam theory, the specimen’s compliance and the crack equivalent concept. Following the proposed approach the influence of the fracture process zone is taken into account which is fundamental for an accurate estimation of the failure process details. The cohesive law is obtained by differentiation of the strain energy release rate as a function of the crack opening displacement. The model was validated numerically considering three representative cohesive laws. Numerical simulations using finite element analysis including cohesive zone modeling were performed. The good agreement between the inputted and resulting laws for all the cases considered validates the model. An experimental confirmation was also performed by comparing the numerical and experimental load–displacement curves. The numerical load–displacement curves were obtained by adjusting typical cohesive laws to the ones measured experimentally following the proposed approach and using finite element analysis including cohesive zone modeling. Once again, good agreement was obtained in the comparisons thus demonstrating the good performance of the proposed methodology.

Double power laws, fractals and self-similarity

Power law (PL) distributions have been largely reported in the modeling of distinct real phenomena and have been associated with fractal structures and self-similar systems. In this paper, we analyze real data that follows a PL and a double PL behavior and verify the relation between the PL coefficient and the capacity dimension of known fractals. It is to be proved a method that translates PLs coefficients into capacity dimension of fractals of any real data.

Double power laws, fractals and self-similarity

Power law (PL) distributions have been largely reported in the modeling of distinct real phenomena and have been associated with fractal structures and self-similar systems. In this paper, we analyze real data that follows a PL and a double PL behavior and verify the relation between the PL coefficient and the capacity dimension of known fractals. It is to be proved a method that translates PLs coefficients into capacity dimension of fractals of any real data.

Leniency programs, antitrust enforcement and multimarket contact : three essays in industrial organization

The Layout of My Thesis This thesis contains three chapters in Industrial Organization that build on the work outlined above. The first two chapters combine leniency programs with multimarket contact and provide a thorough analysis of the potential effects of Amnesty Plus and Penalty Plus. The third chapter puts the whole discussion on leniency programs into perspective by examining other enforcement tools available to an antitrust authority. The main argument in that last chapter is that a specific instrument can only be as effective as the policy in which it is embedded. It is therefore important for an antitrust authority to know how it best accompanies the introduction or modification of a policy instrument that helps deterrence. INTRODUCTION Chapter 1 examines the efféct of Amnesty Plus and Penalty Plus on the incentives of firms to report cartel activities. The main question is whether the inclusion of these policies in a leniency program undermine the effectiveness of the latter by discouraging the firms to apply for amnesty. The model is static and focus on the ex post incentives of firms to desist from collusion. The results suggest that, because Amnesty Plus and Penalty Plus encourage the reporting of a second cartel after a first detection, a firm, anticipating this, may be reluctant to seek leniency and to report in the first place. However, the effect may also go in the opposite direction, and Amnesty Plus and Penalty Plus may encourage the simultaneous reporting of two cartels. Chapter 2 takes this idea further to the stage of cartel formation. This chapter provides a complete characterization of the potential anticompetitive and procompetitive effects of Amnesty Plus in a infinitely repeated game framework when the firms use their multimarket contact to harshen punishment. I suggest a clear-cut policy rule that prevents potential adverse effects and thereby show that, if policy makers follow this rule, a leniency program with Amnesty Plus performs better than one without. Chapter 3 characterizes the socially optimal enforcement effort of an antitrust authority and shows how this effort changes with the introduction or modification of specific policy instruments. The intuition is that the policy instrument may increase the marginal benefit of conducting investigations. If this effect is strong enough, a more rigorous detection policy becomes socially desirable.

Mr. Giles' speech, delivered in the Senate of the United States, on Thursday, 24th November, 1808, on the resolution of Mr. Hillhouse, to repeal the embargo laws. --

Caption title.

By-laws of the municipal council of the United Counties of Lincoln and Welland, 1852

By-laws included are numbers 31-34 and deal with school issues, raising funds for the municipality, payment of fees, and remuneration to the sheriff of the municipality.

By Laws of the Corporation of the Town of Welland, 1878 [fragment]

The fragment appears to be part of a larger group of bylaws for the Town of Welland, 1878. The fragment includes bylaws Cap. I and Cap. II. Cap. I is a bylaw appointing auditors for the town for the year 1878. Due to paper loss only a portion of the title of the Cap. II bylaw is extent but appears to be a bylaw appointing a Hey…….trustee for the town. Welland was incorporated in 1858 as a town and became a city in 1917.

Mr. Giles' speech, delivered in the Senate of the United States, on Thursday, 24th November, 1808, on the resolution of Mr. Hillhouse, to repeal the embargo laws

Printed by Pool and Palfray

Ontario Game and Fishery Laws 1916

A paperback booklet of the Ontario Game and Fishery Laws 1916. The booklet is 91 pages in length and includes an index. See the full text in the Brock University Special Collections and Archives.

By-Laws No. 1 through 11

The by-laws are signed by George Barnes and include the first two which state the name of the company is the Ontario Grape Growing and Wine Manufacturing Company and the second by-law states that the place of business is at Barnesdale, St. Catharines, Ontario.

Constitution and By-Laws of the Citizens' Hose Company

Constitution and By-laws of the Citizens’ Hose Company is a 12 page 14 cm. x 9 ½ cm. booklet. The booklet is slightly discoloured and has had some water damage. This does not affect the text, Aug. 1, 1871.