66 research outputs found
N-[2-Chloro-6-(4-chloro-6-methoxypyrimidin-2-ylsulfanyl)benzyl]-3,4-dimethylaniline
In the title molecule, C20H19Cl2N3OS, the dihedral angle between the two benzene rings is 79.3 (7)°. The 4-chloro-6-methoxypyrimidine group is rotationally disordered over two sites by approximately 180°, the ratio of the refined occupancies being 0.6772 (15):0.3228 (15). Both disorder components of disorder are involved in intramolecular N—H⋯N hydrogen bonds
The Growth of Business Firms: Theoretical Framework and Empirical Evidence
We introduce a model of proportional growth to explain the distribution of
business firm growth rates. The model predicts that the distribution is
exponential in the central part and depicts an asymptotic power-law behavior in
the tails with an exponent 3. Because of data limitations, previous studies in
this field have been focusing exclusively on the Laplace shape of the body of
the distribution. In this article, we test the model at different levels of
aggregation in the economy, from products to firms to countries, and we find
that the model's predictions agree with empirical growth distributions and
size-variance relationships.Comment: 22 pages, 5 Postscript figures, uses revtex4. to be published in
Proc. Natl. Acad. Sci. (2005
A Generalized Preferential Attachment Model for Business Firms Growth Rates: I. Empirical Evidence
We introduce a model of proportional growth to explain the distribution
of business firm growth rates. The model predicts that is Laplace
in the central part and depicts an asymptotic power-law behavior in the tails
with an exponent . Because of data limitations, previous studies in
this field have been focusing exclusively on the Laplace shape of the body of
the distribution. We test the model at different levels of aggregation in the
economy, from products, to firms, to countries, and we find that the its
predictions are in good agreement with empirical evidence on both growth
distributions and size-variance relationships.Comment: 8 pages, 4 figure
A Generalized Preferential Attachment Model for Complex Systems
Complex systems can be characterized by classes of equivalency of their
elements defined according to system specific rules. We propose a generalized
preferential attachment model to describe the class size distribution. The
model postulates preferential growth of the existing classes and the steady
influx of new classes. We investigate how the distribution depends on the
initial conditions and changes from a pure exponential form for zero influx of
new classes to a power law with an exponential cutoff form when the influx of
new classes is substantial. We apply the model to study the growth dynamics of
pharmaceutical industry.Comment: submitted to PR
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 φ = 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 ζ = 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.firm growth, size distribution, Gibrat law, Zipf law
A Generalized Preferential Attachment Model for Business Firms Growth Rates: I. Empirical Evidence
We introduce a model of proportional growth to explain the distribution P(g) of business firm growth rates. The model predicts that P(g) is Laplace in the central part and depicts an asymptotic power-law behavior in the tails with an exponent ζ = 3. Because of data limitations, previous studies in this field have been focusing exclusively on the Laplace shape of the body of the distribution. We test the model at different levels of aggregation in the economy, from products, to firms, to countries, and we find that the its predictions are in good agreement with empirical evidence on both growth distributions and size-variance relationships.Gibrat Law; Firm Growth; Size Distribution
Preferential attachment and growth dynamics in complex systems
Complex systems can be characterized by classes of equivalency of their elements defined according to system specific rules. We propose a generalized preferential attachment model to describe the class size distribution. The model postulates preferential growth of the existing classes and the steady influx of new classes. According to the model, the distribution changes from a pure exponential form for zero influx of new classes to a power law with an exponential cut-off form when the influx of new classes is substantial. Predictions of the model are tested through the analysis of a unique industrial database, which covers both elementary units (products) and classes (markets, firms) in a given industry (pharmaceuticals), covering the entire size distribution. The model’s predictions are in good agreement with the data. The paper sheds light on the emergence of the exponent τ ≈ 2 observed as a universal feature of many biological, social and economic problems.Firm Growth; Pareto Distribution; Pharmaceutical Industry
1,1-Bis(4-fluorophenyl)-3,4-dihydro-1H-1,3-oxazino[3,4-a]indole
The title compound, C23H17F2NO, which crystallizes with two independent molecules in the asymmetric unit, was prepared by the cyclization of 4-[2-bis(4-fluorophenyl)methyleneamino]but-3-yn-1-ol at room temperature. The molecules display a tripod conformation. The two fluorophenyl rings make dihedral angles of 79.26 (2) and 85.87 (1)° [86.53 (1) and 83.67 (2)° in the second molecule] with the indole ring, and the dihedral angles between the fluorophenyl rings are 67.74 (2) and 66.33 (2)°, respectively. Furthermore, the indole rings are located on the edge of the respective oxazine half-chair ring systems. Nonconventional C—H⋯π contacts between indole and fluorophenyl rings are observed
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 . We also find that the average
sales of products scales with the firm sales as a power law with exponent
. And that the average number products of a firm scales
with the firm sales as a power law with exponent . We
compare these findings with the predictions of models proposed till date on
growth of business firms
Preferential attachment and growth dynamics in complex systems
Complex systems can be characterized by classes of equivalency of their elements defined according to system specific rules. We propose a generalized preferential attachment model to describe the class size distribution. The model postulates preferential growth of the existing classes and the steady influx of new classes. According to the model, the distribution changes from a pure exponential form for zero influx of new classes to a power law with an exponential cut-off form when the influx of new classes is substantial. Predictions of the model are tested through the analysis of a unique industrial database, which covers both elementary units (products) and classes (markets, firms) in a given industry (pharmaceuticals), covering the entire size distribution. The model’s predictions are in good agreement with the data. The paper sheds light on the emergence of the exponent τ ≈ 2 observed as a universal feature of many biological, social and economic problems
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