A theoretical approach for Pareto-Zipf law

We suggest an analytical approach for the Pareto-Zipf law, where we assume random multiplicative noise and fragmentation processes for the growth of the number of citizens of each city and the number of the cities, respectively.


A new model for competition between many languages
Tuncay, Çağlar (World Scientific Pub Co Pte Lt, 2007-07-01)
Time evolution of number of cities, population of cities, world population, and size distribution of present languages are studied in terms of a new model, where population of each city increases by a random rate and decreases by a random division. World population and size distribution of languages come out in good agreement with the available empirical data.
Exact solutions of the modified Kratzer potential plus ring-shaped potential in the d-dimensional Schrodinger equation by the Nikiforov-Uvarov method
IKHDAİR, SAMEER; Sever, Ramazan (World Scientific Pub Co Pte Lt, 2008-02-01)
We present analytically the exact energy bound-states solutions of the Schrodinger equation in D dimensions for a recently proposed modified Kratzer plus ring-shaped potential by means of the Nikiforov-Uvarov method. We obtain an explicit solution of the wave functions in terms of hyper-geometric functions (Laguerre polynomials). The results obtained in this work are more general and true for any dimension which can be reduced to the well-known three-dimensional forms given by other works.
An alternative simple solution of the sextic anharmonic oscillator and perturbed coulomb problems
IKHDAİR, SAMEER; Sever, Ramazan (World Scientific Pub Co Pte Lt, 2007-10-01)
Utilizing an appropriate ansatz to the wave function, we reproduce the exact bound-state solutions of the radial Schrodinger equation to various exactly solvable sextic an-harmonic oscillator and confining perturbed Coulomb models in D-dimensions. We show that the perturbed Coulomb problem with eigenvalue E can be transformed to a sextic anharmonic oscillator problem with eigenvalue P. We also check the explicit relevance of these two related problems in higher-space dimensions. It is shown that exact solut...
Mohammad, Rezek; Katırcıoğlu, Şenay (World Scientific Pub Co Pte Lt, 2013-10-01)
The first-principles calculations based on Density Functional Theory (DFT) within generalized gradient approximation (GGA) of Engel-Vosko-Perdew-Wang and modified exact exchange potential of Becke-Johnson have been introduced for the structural and electronic properties of the ScxAl1-xN alloys, respectively. The present lattice constants calculated for the ScAlN alloys and the end compounds (AlN and ScN) are found to be in very good agreement with the available experimental and theoretical ones. The stable ...
Energetics and stability of discrete charge distribution on the surface of a sphere
Oymak, H; Erkoç, Şakir (World Scientific Pub Co Pte Lt, 2001-02-01)
We have investigated the minimum-energy distribution of N, 3 ≤ N ≤ 97, equal point charges confined to the surface of a sphere. Charges interact with each other via the Coulomb potential of the form 1/r. Minimum-energy distributions have been determined by minimizing the tangential forces on each charge. Further numerical evidence shows that in the minimum-energy state of N charges on the sphere, it is not possible to place a charge at the geometrical center. Besides, it has been found that the most and rel...
Citation Formats
Ç. Tuncay, “A theoretical approach for Pareto-Zipf law,” INTERNATIONAL JOURNAL OF MODERN PHYSICS C, pp. 1175–1181, 2008, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/41781.