A Whiteheadian-type description of Euclidean spaces, spheres, tori and Tychonoff cubes

In the beginning of the 20th century, A. N. Whitehead and T. de Laguna proposed a new theory of space, known as {\em region-based theory of space}. They did not present their ideas in a detailed mathematical form. In 1997, P. Roeper has shown that the locally compact Hausdorff spaces correspond bijectively (up to homeomorphism and isomorphism) to some algebraical objects which represent correctly Whitehead's ideas of {\em region} and {\em contact relation}, generalizing in this way a previous analogous result of de Vries concerning compact Hausdorff spaces (note that even a duality for the category of compact Hausdorff spaces and continuous maps was constructed by de Vries). Recently, a duality for the category of locally compact Hausdorff spaces and continuous maps, based on Roeper's results, was obtained by G. Dimov (it extends de Vries' duality mentioned above). In this paper, using the dualities obtained by de Vries and Dimov, we construct directly (i.e. without the help of the corresponding topological spaces) the dual objects of Euclidean spaces, spheres, tori and Tychonoff cubes; these algebraical objects completely characterize the mentioned topological spaces. Thus, a mathematical realization of the original philosophical ideas of Whitehead and de Laguna about Euclidean spaces is obtained.Comment: 29 page

Spatial analyses and growth of trees in selected bottomland hardwood stands

Sustainable management and conservation of the extensive bottomland hardwood forest resource in the southeastern U.S. requires a good understanding of basic structural and competitive relationships within these forests. To gain an insight into these relationships, plot information from stands in Arkansas, Louisiana, and Mississippi were analyzed. The effects of individual tree attributes, distance-dependant, and distance-independent competition measures on 5-yr radial growth of red oak crop trees were examined. Selected species included cherrybark oak (Quercus pagoda Raf.), water oak (Q. nigra L.), and Nuttall oak (Q. nuttallii Palmer). Spatial continuity of tree variables was explored through geostatistical analysis. Finally, spatial distribution patterns of all species, the intraspecific pattern of cherrybark oak, water oak, and sweetgum (Liquidambar styraciflua L.), and the interspecific pattern of their pairs was examined with point pattern analysis. In the analysis of 5-yr radial growth, the crown class score (from Meadows et al. 2001) accounted for a large portion of tree diameter growth. However, average plot-level characteristics failed to account for a significant proportion of the variability in tree growth. The basal area of trees taller than the crop trees and located within 2.5 mean crown radii had the highest negative correlation with crop tree 5-yr radial growth. Red oaks were likely exerting the greatest competition. Crop tree radial growth was also positively associated with the basal area of other red oaks taller than the crop tree and located between 3 and 4 mean crown radii from the crop tree (the indirect neighbors). Geostatistical analysis demonstrated that spatial continuity of unsuppressed tree attributes extended to a distance equal to 4 times the mean crown radius, suggesting that when resources are nonlimiting, multiple trees may be able to coexist and grow well in close proximity. Spatial point pattern analysis indicated that when species were combined, they were frequently aggregated and sometimes overdispersed. Plots with larger trees were more likely to exhibit overdispersion suggesting a shift to this pattern as trees grow. Interspecific and intraspecific pattern analyses suggested that strong interspecific competition resulted in species segregation, while weaker intraspecific competition led to aggregations of conspecifics

Generalized pulsating strings

In this paper we consider new solutions for pulsating strings. For this purpose we use tha idea of the generalized ansatz for folded and circular strings in hep-th/0311004. We find the solutions to the resulting Neumann-Rosochatius integrable system and the corrections to the energy. To do that we use the approach developed by Minahan in hep-th/0209047 and find that the corrections are quite different from those obtained in that paper and hep-th/0310188. We conclude with comments on our solutions and obtained corrections to the energy, expanded to the leading order in lambda.Comment: v.2 references added, citations corrected, 18 page

On the pulsating strings in Sasaki-Einstein spaces

We study the class of pulsating strings in AdS_5 x Y^{p,q} and AdS_5 x L^{p,q,r}. Using a generalized ansatz for pulsating string configurations, we find new solutions for this class in terms of Heun functions, and derive the particular case of AdS_5 x T^{1,1}, which was analyzed in arXiv:1006.1539 [hep-th]. Unfortunately, Heun functions are still little studied, and we are not able to quantize the theory quasi-classically and obtain the first corrections to the energy. The latter, due to AdS/CFT correspondence, is supposed to give the anomalous dimensions of operators of the gauge theory dual N=1 superconformal field theory.Comment: 9 pages, talk given at the 2nd Int. Conference AMiTaNS, 21-26 June 2010, Sozopol, Bulgaria, organized by EAC (Euro-American Consortium) for Promoting AMiTaNS, to appear in the Proceedings of 2nd Int. Conference AMiTaN

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