A Generalized Preferential Attachment Model for Business Firms Growth Rates: II. Mathematical Treatment

We present a preferential attachment growth model to obtain the distribution $P(K)$ of number of units $K$ in the classes which may represent business firms or other socio-economic entities. We found that $P(K)$ is described in its central part by a power law with an exponent $\phi=2+b/(1-b)$ which depends on the probability of entry of new classes, $b$. In a particular problem of city population this distribution is equivalent to the well known Zipf law. In the absence of the new classes entry, the distribution $P(K)$ is exponential. Using analytical form of $P(K)$ and assuming proportional growth for units, we derive $P(g)$, the distribution of business firm growth rates. The model predicts that $P(g)$ has a Laplacian cusp in the central part and asymptotic power-law tails with an exponent $\zeta=3$. We test the analytical expressions derived using heuristic arguments by simulations. The model might also explain the size-variance relationship of the firm growth rates.Comment: 19 pages 6 figures Applications of Physics in Financial Analysis, APFA

Phantom Mimicry on the Normal Branch of a DGP-inspired Braneworld Scenario with Curvature Effect

It has been shown recently that phantom-like effect can be realized on the normal branch of the DGP setup without introduction of any phantom matter neither in the bulk nor on the brane and therefore without violation of the null energy condition. It has been shown also that inclusion of the Gauss-Bonnet term in the bulk action modifies this picture via curvature effects. Here, based on the Lue-Starkman conjecture on the dynamical screening of the brane cosmological constant in the DGP setup, we extend this proposal to a general DGP-inspired $f(R,\phi)$ model that stringy effects in the ultra-violet sector of the theory are taken into account by inclusion of the Gauss-Bonnet term in the bulk action. We study cosmological dynamics of this setup, especially its phantom-like behavior and possible crossing of the phantom divide line especially with a non-minimally coupled quintessence field on the brane. In this setup, scalar field and curvature quintessence are treated in a unified framework.Comment: 25 Figures, To appear in MPL

Optical fiber sensors for coal mine shaft integrity and equipment condition monitoring

Shaft is an important structure of mine. Deep mining increases mine pressure, induces shaft deformation and affects mine normal lifting. How to improve the inspection efficiency, reduce the maintenance cost and ensure the normal operation of the shaft is an important problem facing the mine. The paper introduces the optical fiber sensing technology to monitor the equipment status of the main shaft, puts forward the implementation scheme of the optical fiber monitoring of shaft deformation, and sets up a shaft equipment condition monitoring system based on the optical fiber sensing technology. It can realize equipment displacement monitoring, strain monitoring and vibration signal monitoring in the process of shaft operation. Comprehensive on-line monitoring of shaft running state can be realized, which opens up a new method for shaft deformation monitoring technology. Fiber optic sensing monitoring technology is of great significance to the safe operation of shaft

Statistical Properties of Business Firms Structure and Growth

We analyze a database comprising quarterly sales of 55624 pharmaceutical products commercialized by 3939 pharmaceutical firms in the period 1992--2001. We study the probability density function (PDF) of growth in firms and product sales and find that the width of the PDF of growth decays with the sales as a power law with exponent $\beta = 0.20 \pm 0.01$. We also find that the average sales of products scales with the firm sales as a power law with exponent $\alpha = 0.57 \pm 0.02$. And that the average number products of a firm scales with the firm sales as a power law with exponent $\gamma = 0.42 \pm 0.02$. We compare these findings with the predictions of models proposed till date on growth of business firms