On Mathematical Models of the Classic Maya Collapse: The Class Conflict Hypothesis Reexamined

1982 ◽  
Vol 47 (3) ◽  
pp. 643-652 ◽  
Author(s):  
John W. G. Lowe

Recently, Hamblin and Pitcher (1980) have attempted to buttress the class conflict explanation of the Classic Maya collapse using a series of mathematical models. However, despite the exceptionally good agreement between these mathematical relations and the empirical data, the same cannot be said for the fit between the conceptual and mathematical models. The relations employed are very general, so much so as to often be isomorphic with very different processes. In one case at least, the same model appears to be consistent with several entirely distinct explanations of the collapse, and other mathematical readings of the monument data are by no means precluded. While these particular mathematical relationships fail to make a very strong case that the Classic Maya collapse was engendered primarily through peasant revolt and class conflict, which was very possibly Hamblin's and Pitcher's underlying aim, the attempt to cast explanations of the collapse into mathematical form points the way for the next generation of collapse models.


1980 ◽  
Vol 45 (2) ◽  
pp. 246-267 ◽  
Author(s):  
Robert L. Hamblin ◽  
Brian L. Pitcher

Several lines of archaeological evidence are presented in this paper to suggest the existence of class warfare among the Classic Maya and of issues that historically have been associated with class conflict. This evidence indicates that class warfare may have halted the rule of the monument-producing, or Classic, elites and precipitated the depopulation of the lowland area. The theory is evaluated quantitatively by testing for time-related mathematical patterns that have been found to characterize large-scale conflicts in historical societies. The information used in the evaluation involves the time series data on the duration of rule by Classic elites as inferred from the production of monuments with Long Count dates at a sample of 82 ceremonial centers. The analyses confirm that the Maya data do exhibit the temporal and geographical patterns predicted from the class conflict explanation of the Classic Maya collapse. Alternative predictions from the other theories are considered but generally not found to be supported by these data.



2005 ◽  
Vol 15 (11) ◽  
pp. 1667-1683 ◽  
Author(s):  
MIROSŁAW LACHOWICZ

In this paper two new mathematical models are proposed that correspond to a macroscopic model of tissue invasion of solid tumours, in terms of a system of reaction-diffusion-chemotaxis equations. The first model is defined at the micro-scale level of a large number of interacting individual entities, and is in terms of a linear (Markov) equation. The second model refers to the meso-scale level of description of test-entities and is given in terms of a bilinear Boltzmann-type equation. Mathematical relationships among these three possible descriptions are formulated. Explicit error estimates are given.



2017 ◽  
pp. 244-275
Author(s):  
Guy D. Middleton
Keyword(s):  


Nature ◽  
1979 ◽  
Vol 281 (5730) ◽  
pp. 407-407
Author(s):  
I. STERNS ◽  
C. LORIA ◽  
R. GARBER




Author(s):  
Manish Dak ◽  
Radha Charan Verma ◽  
Manoj Kumar Jain

Rheological characteristics of pineapple juice have been investigated and rheological parameters were evaluated using rotational viscometer at temperatures 20, 30 and 40*C at concentration 26.77, 18.99 and 14 % total solids. The experimental results followed the power law model for the best fit and the values of flow behaviour index (n) was less than unity (0.08 to 0.87) at all temperatures and concentrations indicating the shear thinning (pseudoplasticity) nature of juice. An obvious correlation between consistency coefficient in the range of 0.1 - 37.16 Pa.sn and inverse absolute temperature has been exhibited by Arrhenius model. The Power equation indicated that the consistency coefficient increased non-linearly with an increase in concentration. Mathematical models were developed for prediction of the consistency coefficient as a function of temperature and concentration. A good agreement was observed between experimental and theoretical values of the consistency coefficient predicted by models. The magnitude of activation energy was found to be in the range of 3.67 to 4.62 kJ/mol.K.



Geophysics ◽  
1993 ◽  
Vol 58 (2) ◽  
pp. 293-297
Author(s):  
Shelby C. Worley

The two‐dimensional (2-D) reflection path from a dipping plane between an offset source‐receiver combination in a constant velocity medium can be described with several parameters (coordinates, offsets, angles, and lengths). Although there are many parameters, only four independent ones are needed to locally determine the reflection geometry. Given four determining parameters, the evaluations of other ones present problems that range from trivial to formidable. The circumscribed circle about the source, receiver, and specular point turns out to have a number of remarkable properties that are useful for the solution of these problems. The radius of the circle is a useful new auxiliary parameter. Triangles constructed in the circle provide nonintuitive mathematical relationships between angles and lengths. The use of mathematical relations derived from the circle has allowed the creation of formulas to fully recover the reflection geometry in a vast majority of valid sets of four known parameters. This circle provides a powerful tool for the calculation of nondetermining parameters as well as new insight into the geometry of reflection with straight raypaths.



1997 ◽  
Vol 8 (2) ◽  
pp. 209-227 ◽  
Author(s):  
Arthur A. Demarest

AbstractThe background, research design, structure, personnel, and history of investigations of the Vanderbilt Petexbatun Archaeological Project are summarized and critiqued. The major findings of each of the dozen subprojects of this multidisciplinary investigation of Maya civilization in the southwestern Peten region of Guatemala are reviewed. Subproject results include important new evidence on Classic Maya history, warfare, ecology, nutrition, cave ritual, social organization, and trade. These are summarized with particular emphasis on the implications of the Petexbatun findings for theories of the decline of southern lowland Maya civilization at the end of the Classic period.



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