Superintegrability and associated polynomial solutions: Euclidean space and the sphere in two dimensions

In this work we examine the basis functions for those classical and quantum mechanical systems in two dimensions which admit separation of variables in at least two coordinate systems. We do this for the corresponding systems defined in Euclidean space and on the two-dimensional sphere. We present all of these cases from a unified point of view. In particular, all of the special functions that arise via variable separation have their essential features expressed in terms of their zeros. The principal new results are the details of the polynomial bases for each of the nonsubgroup bases, not just the subgroup Cartesian and polar coordinate cases, and the details of the structure of the quadratic algebras. We also study the polynomial eigenfunctions in elliptic coordinates of the n-dimensional isotropic quantum oscillator

Nondegenerate three-dimensional complex Euclidean superintegrable systems and algebraic varieties

A classical (or quantum) second order superintegrable system is an integrable n-dimensional Hamiltonian system with potential that admits 2n−1 functionally independent second order constants of the motion polynomial in the momenta, the maximum possible. Such systems have remarkable properties: multi-integrability and multiseparability, an algebra of higher order symmetries whose representation theory yields spectral information about the Schrödinger operator, deep connections with special functions, and with quasiexactly solvable systems. Here, we announce a complete classification of nondegenerate (i.e., four-parameter) potentials for complex Euclidean 3-space. We characterize the possible superintegrable systems as points on an algebraic variety in ten variables subject to six quadratic polynomial constraints. The Euclidean group acts on the variety such that two points determine the same superintegrable system if and only if they lie on the same leaf of the foliation. There are exactly ten nondegenerate potentials. ©2007 American Institute of Physic

Jugoslovanska katoliška jednota (1898-1920)

Jugoslovanska Katoliška Jednota was founded in 1898 in Ely, Minnesota. The founders were members of two former local associations of the oldest Slovene aid organisation - Kranjska Slovenska Katoliška Jednota (The Slovene Catholic Unit of Camiola). The author concentrates on the internal structure of the organisation and its development as reflected through the general assemblies.Jugoslovanska katoliška jednota je nastala leta 1898, Minnesota. Ustanovili so jo člani dveh bivših krajevnih društev najstarejše slovenske bratske podporne organizacije Kranjske slovenske katoliške jednote. Avtorja je zanimala predvsem organiziranost Jednote in njen razvoj na glavnih zborovanjih

Quelques faits moins connus à propos des activités des associations locales de l\u27Union catholique carniolaise slovène (1894–1924)

Slovenski su doseljenici nakon dolaska u SAD ubrzo spoznali da u slučaju nesreće na radu ili bolesti mogu računati isključivo na sebe same i zato su počeli osnivati vlastita potporna društva. Prva slovenska bratska potporna organizacija – Kranjsko slovenska katoliška jednota (Kranjsko slovenski katolički savez) osnovan je 1894. u Jolietu (Illinois). Temelj bratskih potpornih organizacija predstavljali su odsjeci koji su djelovali širom SAD-a. Najveći broj članova Savez je okupljao u državama Illinois, Pennsylvanija, Ohio i Minnesota. Osnovna djelatnost bratskih potpornih organizacija bila je pomoć članstvu, odnosno njihovoj rodbini u slučaju smrti, a druga je djelatnost bila bolničko osiguranje. U organizaciji su njegovali i druge važne vrijednosti: slovensku kulturnu tradiciju, slovenski jezik i tijesne veze sa »starom domovinom«. Odsjek St. Francis de Sales Society No. 29 osnovan je u Jolietu (Illinois) 2. veljače 1896. On nije ni najstariji niti najveći u KSKS-u, ali je jedan od najutjecajnijih u Savezu. Članovi iz redova odsjeka zauzimali su u KSKS-u najviše položaje. Na takav su način imali odlučujući utjecaj na politiku Saveza u ključnoj fazi njegova djelovanja, kada se razvio iz male i financijski nestabilne bratske potporne organizacije u moderno osiguravajuće društvo. Savez već više od stotinu godina uspješno ispunjava svoju misiju i na području vjerskoga, nacionalnoga, političkoga i kulturnog ujedinjavanja.The first Slovenian emigrants realized soon after their arrival to the USA that in the event of work accidents or disease they depended solely on themselves. For this reason they started to found their own benefit societies, following the example of other nationalities (e.g. the Czechs, the Finns). At first these were of a local character with a limited number of members, which did not guarantee enough financial safety. In order to decrease the possibility of a financial break down, they started to found benefit societies which united members of the same ethnical group throughout the whole country. The first Slovenian fraternal benefit society called the Carniolian Slovenian Catholic Society (“Kranjsko slovenska katoliška jednota” in Slovene, abbrev. KSKJ) was founded in Joliet (Illinois) in 1894. It was founded by Slovenian Catholic priests in the USA, who often encountered the misery and helplessness of victims of accidents and their families. The society functioned according to strict Catholic principles. Its ideological orientation was expressed in the name itself, and St. Joseph was chosen as its patron saint. All the local societies were also mostly named after saints. The basic aim of the fraternal benefit society was to help the members or their families in the event of death, while the additional activity was to provide health insurance. However, the organization also cultivated other important values, such as the Slovenian cultural tradition, the Slovenian language, and close contacts with “the old country”. The basis of fraternal benefit organizations was represented by local societies, which were active throughout all of the USA. The local society of the Carniolian Slovenian Catholic Society called St. Francis de Sales Society No. 29 was founded in Joliet (Illinois) on February 2, 1896. It was already the fourth local society of the KSKJ in the town of Joliet. The reasons for the setting up of a new society came from the dissatisfaction of important members of imigrant communities with the work of the existing societies in the town. In their opinion they were not represented high enough in the hierarchy of these societies. The fact was that the highest positions in local societies, expecially on the main board, brought not only respect, but also financial benefits. Thus it is not surprising that the presidency of the society was taken over by the undertaker Anton Nemanich, one of the town\u27s wealthiest Slovenian imigrants and cofounder of the KSKJ. Nemanich\u27s rise in the KSKJ started in 1896, the same year when he was, at the third convention, elected to the position of the chief president of the KSKJ. This started a period of more than 20 years in which the members of this local society held the most important positions in the KSKJ. The duties of the members of the KSKJ included the rules of both their local society and the rules of the main organization. They had to attend the society meetings, particularly when there were elections for the members of the board, and regularly pay assessment. According to the rules, the society had to provide for a respectable funeral of their members, including escort by men in uniform and society banners. In addition to this, their members had to visit their sick colleagues. An important way of raising money for the local societies was through the organization of dances. If the members failed to fulfill their duties, they were fined. The societies often recieved invitations to various ceremonies organized by Slovene imigrants, which they gladly accepted. The regular monthly meetings of the local societies started with a Mass, while the daily meetings were opened and closed by the presiding member with a prayer. The members of the KSKJ had to go to confession and receive Holy Communion at least once a year. The society was in general closely connected with the Slovenian parish of St. Joseph. Local societies had a very important charity function. They received pleas for help by various empoverished Slovenian imigrants, not rarely by other local societies. They were very successful in attaining new members, since their monthly meetings regularly brought the inclusion of new members. St. Francis de Sales Society No. 29 was among the most successful in this activity. The society was among the winners of the competition for attracting new members more than 10 times. St. Francis de Sales Society No. 29 was neither the oldest nor the largest local society of the KSKJ, but it was one of the most influential. Its members held the highest positions in the main organization. In this way they had a significant influence on the politics of the KSKJ in the most important phase of its existence, when it developed from a small and financially unstable fraternal benefit organization into a modern insurance company. The society has over a hundred years successfully continued to carry out its uniting mission in the areas of religion, politics and culture.Les premiers immigrants slovènes découvrirent peu après leur arrivée aux États Unis qu\u27en cas d\u27accident au travail ou de maladie ne pouvaient compter que sur eux-mêmes. Ainsi, ils commencèrent à fonder, selon l\u27exemple des autres nationalités (des Cheques, des Finnois etc.) leurs propres associations de soutien. Au début, leur caractère fut local et le nombre de leurs membres limité, ce qui n\u27assurait pas une sécurité financière suffisante. Afin de minimiser la possibilité de faillite financière, ils fondèrent des organismes de soutien qui unissaient des membres de la même communauté ethnique à travers l\u27Amérique. Le premier organisme slovène de soutien fraternel, l\u27Union catholique carniolaise slovène (l\u27UCCS) fut fondée en 1894 à Joliet (Illinois). Ses fondateurs furent les prêtres catholiques slovènes qui dans leur travail rencontraient souvent la misère et l\u27impuissance des accidentés et de leurs proches. L\u27Union fonctionnait selon des principes catholiques rigoureux et les idées que les membres se faisaient du monde furent exprimées clairement dans le nom même de l\u27Union. Saint Joseph fut choisi comme patron de l\u27Union et les associations locales pour la plupart portaient aussi les noms des saints. L\u27activité fondamentale de l\u27organisme de soutien fraternel consistait en l\u27assistance aux membres ou, en cas de mort, leurs proches, mais aussi en l\u27assurance maladie. Les membres cultivaient également d\u27autres valeurs importantes: la tradition culturelle slovène, la langue slovène et des contacts étroits avec «la vieille patrie». À la base des organismes de soutien fraternel furent des associations locales, qui fonctionnaient partout aux États Unis. Le 2 février 1896 l\u27association locale de l\u27Union catholique carniolaise slovène St. Francis de Sales Society n. 29 fut fondée à Joliet (Illinois). Ce fut déjà la quatrième association locale de l\u27UCCS dans la ville de Joliet. Les raisons pour la fondation de la nouvelle association sont à chercher dans le mécontentement des membres importants de la communauté slovène au sujet des activités des associations déjà existantes. Ils n\u27y détenaient pas des positions suffisamment importantes qui leur appartenaient pourtant selon leur propre opinion. Les plus hautes fonctions dans les associations locales et avant tout au sein du conseil principal n\u27apportaient non seulement des honneurs mais aussi des profits financiers. Ainsi, il n\u27est aucunement surprenant que le président de la nouvelle association fut devenu personne d\u27autre que le propriétaire des pompes funéraires Anton Nemanich, un des immigrants slovènes les plus riches de Joliet et le co-fondateur de l\u27UCCS. L\u27ascension de Nemanich au sein de l\u27UCCS commença justement en 1896 quand il fut élu président principal de l\u27UCCS lors de sa 3ième convention tenue la même année. Par la suite s\u27étendit une période de vingt ans pendant laquelle les membres de l\u27association locale occupaient des fonctions-clefs à l\u27UCCS. Citons encore quelques devoirs des membres. Les membres de l\u27Union devaient respecter les règles de leur association locale ainsi que celles de l\u27Union. Ils devaient participer aux réunions de l\u27association, particulièrement celles ou ils élisaient les conseillers, et dûment régler leur assessment. Selon les règles l\u27association devait organiser les obsèques des membres décédés et les accompagner avec toute la dignité sur leur dernier chemin y compris avec les drapeaux et en uniformes de l\u27association. Les membres de l\u27association devaient aussi rendre visite aux collègues tombés malades. Si les membres ne remplissaient pas leurs devoirs, ils furent sanctionnés. Les assemblées mensuelles régulières des associations locales commençaient avec une messe commune, et le président commençait et clorait les réunions journalières par une prière. Les membres de l\u27UCCS devaient aller à la confession et à la communion au moins une fois dans l\u27année. Par ailleurs, l\u27association fut étroitement liée à la paroisse slovène de saint Joseph. Les fêtes représentaient une manière importante de collecte des moyens financiers des associations locales. Le siège de l\u27association recevait souvent des invitations aux célébrations diverses organisées par les immigrants slovènes et les membres y participaient avec plaisir. Les associations locales jouaient aussi un rôle caritatif important. Les immigrants slovènes appauvris adressaient à elles leurs demandes d\u27aide, et même des autres associations locales demandaient l\u27assistance assez régulièrement. Les associations n\u27eurent pas mal de succès dans le recrutement de nouveaux membres puisqu\u27il n\u27y avait pas une assemblée mensuelle où un nouveau membre ne fut pas admis. L\u27association en question fut parmi les plus prospères au sein de l\u27UCCS quant au recrutement des nouveaux membres; elle gagna la compétition plus de dix fois. St. Francis de Sales Society n. 29 ne fut ni la plus ancienne ni la plus grande association locale de l\u27UCCS mais elle fut sans doute une des plus influentes. Les membres de l\u27association occupaient les plus hauts postes dans l\u27UCCS. De cette manière, ils détenaient une influence décisive sur la politique de l\u27Union dans une période extrêmement importante de son existence quand elle évoluait d\u27un petit organisme de soutien fraternel financièrement instable en une société d\u27assurance moderne. L\u27association depuis plus de cent ans remplit sa mission aussi dans le domaine religieux, ethnique, politique et culturelle

Efficient computation of intersections for meshes of different dimmension based on Plücker coordinates

Pro konečnoprvkové metody byl vyvinut optimalizovaný algoritmus výpočtu průniku úsečky a trojúhelníku s čtyřstěnem, který je postaven na efektivním výpočtu průniku přímky s trojúhelníkem pomocí Plückerových souřadnic. Průniky jsou reprezentovány barycentrickými souřadnicemi na obou elementech. Dále byl vyvinut lineární algoritmus pro výpočet průniků sítí různých dimenzí, který procházísíť sousedních elementů do šířky.Implementace algoritmu, potřebných tříd a dalších funkcí je provedenav jazyce C++.For the finite element method was developed optimized algorithm for calculating the intersection of a line and a triangle with a tetrahedron, which is based on the efficient calculating line-triangle intersection using Plücker coordinates. Intersections are represented by barycentric coordinates of the two elements. Furthermore, linear algorithm was developed to calculate the intersections of meshes with different dimensions, which using breadth-first search for meshes withadjacent elements.The algorithm, the necessary classes and other functions are implemented in C++

Delovanje šolskih sester kongregacije Sv. Frančiška Asiškega- Kristusa Kralja v ZDA med letoma 1909 in 1915

The beginning in 1909 of the activity of sisters of Maribor's St. Francis of Assisi congregation in the USA marked a new era in education of children of Slovene and Croatian immigrants. The instruction was taken over by women-teachers. The instruction was in English with a few hours per week in the Slovene and Croatian languages, which was very important from the aspect of preservation of religious and national identity and a gradual adaptation of children to the American way of life. The archival materials of the St. Francis of Assisi congregation which I used in the study are kept in the Maribor bishopric archives.Začetki delovanja šolskih sester mariborske kongregacije Sv. Frančiška v ZDA leta 1909 pomenijo za šolanje otrok slovenskih in hrvaških izseljencev novo obdobje. Poučevanje so prevzele usposobljene učiteljice. Pouk je potekal v angleškem in nekaj ur tedensko v slovenskem oziroma hrvaškem jeziku, kar je bilo zelo pomembno za ohranjanje vere in narodne identitete, kakor tudi za privajanje otrok na ameriški način življenja. Arhivsko gradivo kongregacije Sv. Frančiška, ki sem ga uporabil, hranijo v Škofijskem arhivu v Mariboru

The Quantitative X-Ray Analysis of Bauxite. I. The System Hydrargillite-Boehmite-Goehtite-Haematite

A photographic X-Ray method for quantitative analysis of the main four- component system in bauxites is described. The required standard straigp.t lines are given. The use of the overl apping haematite- goehtite line (d = 2.69 A a nd d = 2.67 A resp.) is shown theoretically to be possible and is experimentally verified