Time evolution of spin state of radical ion pair in microwave field: An analytical solution

The paper reports an exact solution for the problem of spin evolution of radical ion pair in static magnetic and resonant microwave field taking into account Zeeman and hyperfine interactions and spin relaxation. The values of parameters that provide one of the four possible types of solution are analysed. It is demonstrated that in the absence of spin relaxation, besides the zero field invariant an invariant at large amplitudes of the resonant microwave field can be found. The two invariants open the possibility for simple calculation of microwave pulses to control quantum state of the radical pair. The effect of relaxation on the invariants is analysed and it is shown that changes in the high field invariant are induced by phase relaxation.Comment: 18 pages, 7 figure

Simulation of Coherent Diffraction Radiation Generation by Pico-Second Electron Bunches in an Open Resonator

In this report we present new approach for calculation of processes of diffraction radiation generation, storage and decay in an open resonator based on generalized surface current method. The radiation characteristics calculated using the developed approach were compared with those calculated using Gaussian-Laguerre modes method. The comparison shows reasonable coincidence of the results that allows to use developed method for investigation of more complicated resonators

Cluster analysis and classification of process data by use of principal curves

Thesis (M.Ing.) -- University of Stellenbosch, 1999.ENGLISH SUMMARY: In this thesis a new method of clustering as wen as a new method of classification is proposed. Cluster analysis is a statistical method used to search for natural groups in an unstructured multivariate data set. Clusters are obtained in such. a way that the observations belonging to the same group are more alike than observations across groups. For instance, long data records are found in mineral processing plants, where the data can be reduced to clusters according to different ore types. Most of the existing clustering methods do not give reliable results when applied to engineering data, since these methods were mainly developed in the domains of psychology and biology. Classification analysis can be regarded as the natural continuation of cluster analysis. In order to classify objects, two types of observations are needed. The first are those observations whose group memberships are known a priori, which can be acquired through cluster analysis. The second kind of observations are those whose group memberships are unidentified. By means of classification these observations are allocated to one of the existing groups. Both of the proposed techniques are based on the use of a smooth one-dimensional curve, passing through the middle of the data set. To formalise such an idea, principal curves were developed by Hastie and Stuetzle (1989). A principal curve summarises the data in a non-linear fashion. For clustering, the principal curve of the entire unstructured data set is extracted. This one-dimensional representation of the data set is then used to search for different clusters. For classification, a principal curve is fitted to every known group in the data set. The observations to be assigned to one of the known groups are allocated to the group closest to the new point. Clustering with principal curves grouped engineering data better than most of the well-known clustering algorithms. Some shortcomings of this method were also established. Classification with principal curves gave similar, optimal results as compared to some existing classification methods. This classification method can be applied to data of any distribution, unlike statistical classification techniques.AFRIKAANSE OPSOMMING: In hierdie tesis word 'n nuwe metode elk vir trosanalise en klassifikasie analise voorgestel. Trosanalise is 'n statistiese tegniek waarrnee natuurlike groepe in 'n ongestruktureerde meerveranderlike datastel gevind word. Groepe word op so 'n wyse verkry dat die waamemings in dieselfde groep meer eenders is as waarnemings tussen groepe. Byvoorbeeld, in mineraalaanlegte is lang datarekords algemeen, wat deur middel van trosanalise gereduseer kan word na verskillende groepe, ooreenkomstig verskillende ertstipes. Die meerderheid bestaande groeperingsmetodes lewer nie betroubare resultate in hul toepassing op ingenieursdata nie, aangesien hierdie tegnieke meestal hul oorsprong in die sielkundige en biologiese velde het. Klassifikasie analise kan gesien word as die natuurlike opvolging van trosanalise. Om objekte te klassifiseer, word gebruik gemaak van twee soorte waarnemings. Die eerste tipe is daardie waamemings met a priori bekende groepsidentiteite, wat deur trosanalise gevind kan word. Die tweede soort is die waarnemings met onbekende groepsidentiteite. Elkeen van hierdie waarnemings kan deur middel van klassifikasie toegewys word aan een van die bestaande groepe. Beide hierdie voorgestelde tegnieke is gebaseer op die gebruik van 'n gladde, eendimensionele kromme wat deur die middel van die datastel beweeg. Om hierdie idee te formaliseer, is hoojkrommes ontwikkel deur Hastie en Stuetzle (1989). 'n Hoofkromme gee 'n nie-lineere opsomming van die data. Vir groeperingsdoeleindes word 'n hoofkromme uit die algehele ongestruktureerde datastel onttrek. Met klassifikasie word'n hootkurwe aan elke bekende groep in die datastel gepas. Die waameming wat aan een van die bestaande groepe toegewys moet word, word in die groep naaste aan die betrokke punt geplaas. Groepering met behulp van hoofkrommes, het met ingenieursdata beter resultate gelewer as meeste van die bestaande tegnieke. Deur middel van praktiese voorbeelde is sekere tekortkominge van hierdie groeperingsmetode vasgestel. Klassifikasie met behulp van hoofkrornmes lewer soortgelyke, optimale resultate as die van bekende vergelykende tegnieke. Die voorgestelde klassifikasie tegniek kan toegepas word op datastelle van enige verde ling, in teenstelling met die statistiese klassifikasietegnieke.Maste

Tamga Signs on a Silver Vessel from Yustyd (South Altai)

The author for the first time reproduces and interprets the tamga-like and other signs on the silver vessel, found by V.D. Kubarev in 1976 in the early medieval memorial enclosure in the valley of the river Yustyd in the South Altai. In all 12 signs were carved on the vessel, half of them make two groups. One of them includes the tamgas of the Ashina dynasty Turks-togyu in the form of a goat figure, the other is the Karluk tamgas shaped as an acute angle. Other tamgas probably belonged to Tiele tribes. The sign, carved on the base of the Yustyd vessel, resembles a runic letter (nč), the most likely interpretation of it is the name of the vessel’s owner – Ench. The tamgas of Karluks and Ashina Türk dynasty on the silver mug from Yustyd could be a symbol of the contracting an alliance and/or a system of suzerainty-vassalage of these two the large Turkic-speaking nomadic groups between each other in the period of the Second Turkic Khaganate. Based on the historical events known from written sources, the author dates back to 682–710 both the Yustyd complex and the tamgas, carved on the vessel