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

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

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

A note on spin chain/string duality

Recently a significant progress in matching the anomalous dimensions of certain class of operators in N=4 SYM theory and rotating strings was made. The correspondence was established mainly using Bethe ansatz technique applied to the spin s Heisenberg model. In a recent paper Kruczenski (hep-th/0311203) suggested to solve the Heisenberg model by using of sigme model approach. In this paper we generalize the solutions obtained by Kruczenski and comment on the dual string theory. It turns out that our solutions are related to the so called Neumann-Rosochatius integrable system. We comment on the spin chain solutions and on the string/gauge theory correspondence.Comment: v.2 One reference added, typos corrected, 21 page

Incidence of epulides in the dog: A retrospective histopathological study

The retrospective histopathological study of 468 samples of tumour material obtained from dogs, referred to the Faculty of Veterinary Medicine, Trakia University, Stara Zagora during the period 1991-2000 showed that 29 specimens (6.19%) were epulides. According to their histogenesis, the lesions were classified in two primary groups: reactive lesions – 37.94% and peripheral odontogenic tumours – 62.06%. Epulides were most commonly encountered in males (68.96%) compared to females (31.04%). The average age of affected dogs was 4 years for both genders. In 18 cases (62.06%), the lesions were mandibular whereas in 11 (37.94%) – maxillar. The highest predilection to epulides was observed in German Shepherds – 27.58%

Towards Crowdsourced Online Dispute Resolution

Using crowdsourcing for solving disputes is a subject that has not been discussed in many scientific publications. However, since Crowdsourced Online Dispute Resolution (CODR) provides a cheap, fast, and democratic dispute resolution, it has a potential that needs to be explored scientifically. How should eBay solve otherwise 60 millions disputes per year? Building a CODR platform with the convenience and attractiveness of other collective intelligence systems, such as Wikipedia, YouTube, and Google, may cause many variants of traditional forms of dispute resolution fading away. In order to shed more light on CODR, the present contribution defines this new type of dispute resolution, describes the present state of play, and builds a theoretical framework by investigating CODR building blocks. Although the paper provides only the start of a profound discussion, it shows introductory explorations of the key theoretical issues involved in CODR

Spiky strings and single trace operators in gauge theories

We consider single trace operators of the form O_{m_1 ... m_n} = tr D_+^{m_1} F ... D_+^{m_n} F which are common to all gauge theories. We argue that, when all m_i are equal and large, they have a dual description as strings with cusps, or spikes, one for each field F. In the case of N=4 SYM, we compute the energy as a function of angular momentum by finding the corresponding solutions in AdS_5 and compare with a 1-loop calculation of the anomalous dimension. As in the case of two spikes (twist two operators), there is agreement in the functional form but not in the coupling constant dependence. After that, we analyze the system in more detail and find an effective classical mechanics describing the motion of the spikes. In the appropriate limit, it is the same (up to the coupling constant dependence) as the coherent state description of linear combinations of the operators O_{m_1 ... m_n} such that all m_i are equal on average. This agreement provides a map between the operators in the boundary and the position of the spikes in the bulk. We further suggest that moving the spikes in other directions should describe operators with derivatives other than D_+ indicating that these ideas are quite generic and should help in unraveling the string description of the large-N limit of gauge theories.Comment: 23 pages, 5 figures. v2: References and comments adde