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On some functional equations in rings
Maja Fošner, Joso Vukman, 2011, izvirni znanstveni članek

Opis: In this article we prove the following result. Let ▫$n ge 1$▫ be some fixed integer, and let ▫$R$▫ be a prime ring with ▫$2n le char(R) ne 2$▫. Suppose there exists an additive mapping ▫$T: R to R$▫ satisfying the relation ▫$T(x^{2n+1}) = sum_{i=1}^{2n+1}(-1)^{i+1} x^{i-1} T(x)x^{2n+1-i}$▫ for all ▫$x in R$▫. In this case, ▫$T$▫ is of the form ▫$4T(x) = qx + xq$▫ for all ▫$x in R$▫, where ▫$q$▫ is some fixed element from the symmetric Martindale ring of quotients. This result makes it possible to solve some functional equations in prime rings with involution which are related to bicircular projections.
Ključne besede: bicircular projection, derivation, functional identity, Jordan tripple derivation, prime ring, ring with involution, semiprime ring
Objavljeno: 07.06.2012; Ogledov: 755; Prenosov: 68
URL Povezava na celotno besedilo

Self-concept of students in inclusive settings
Majda Schmidt, Branka Čagran, 2008, izvirni znanstveni članek

Opis: The present evaluation case study investigates the self-concept of the students from 7th grade in regular primary school. The study results indicate that, in comparison to their hearing peers, integrated students with a hearingimpairment have a lower academic and social self-concept, as well as a general self-concept but a higher physical self-concept. There are differences among students with a hearing impairment in both the individual dimension and general self-concept. There are no statistically significant differences between the class with integrated students, on the one hand, and the class without them, on the other; however, there is a noticeable advantage for the students from the class with integrated learners over the other class serving as control group in all three individual dimensions as well as in general self-concept.
Ključne besede: education, primary education, integration, inclusion, children with special needs, self-concept, awareness, evaluation, identity
Objavljeno: 07.06.2012; Ogledov: 1592; Prenosov: 43
URL Povezava na celotno besedilo

A characterization of the centroid of a prime ring
Dominik Benkovič, Daniel Eremita, Joso Vukman, 2008, izvirni znanstveni članek

Opis: We characterize certain maps by their action on a fixed polynomial in noncommuting variables on algebras satisfying certain d -freeness condition. Consequently, a characterization of the centroid of a prime ring is obtained.
Ključne besede: mathematics, algebra, operator algebra, prime rings, semiprime rings, derivation, functional identity, centroid
Objavljeno: 07.06.2012; Ogledov: 975; Prenosov: 64
URL Povezava na celotno besedilo

Functional identities and d-free sets
Matej Brešar, 2005, objavljeni povzetek znanstvenega prispevka na konferenci

Ključne besede: mathematics, algebra, generalized functional identity, derivation
Objavljeno: 07.06.2012; Ogledov: 771; Prenosov: 23
URL Povezava na celotno besedilo

Robert Odreitz, 2013, diplomsko delo

Opis: Diplomska naloga obravnava vodenje identitet v računalniškem oblaku. Prikazani so osnovni mehanizmi v Microsoft Forefront Identity Manager 2010 (FIM). Izveden je poskus namestitve FIM v Amazon AWS. Pokazalo se je, da s trenutnim znanjem in razpoložljivimi informacijami ni možno namestiti delujoče rešitve FIM v AWS. Predlagan je osnutek specifikacije zahtevanih lastnosti vmesnika, ki bo omogočal povezavo dveh sistemov upravljanja identitet v oblačnem okolju.
Ključne besede: • računalništvo v oblaku, • sistem upravljanja identitet, • federacija identitet, • Forefront Identity Manager 2010.
Objavljeno: 17.09.2013; Ogledov: 1178; Prenosov: 59
.pdf Celotno besedilo (7,56 MB)

Aloisius Paulin, 2015, doktorska disertacija

Opis: The present doctoral thesis develops a pioneering system for the self-management of jural eligibilities by means of ICTs as the basis for a novel form of government of juropolitical societies. By means of this system we aim to contribute towards a form of government that would not require a dedicated civil service for the creation, storage, change, and deletion of jural eligibilities in the context of the res publica. In the thesis we explore the concept of jural relations as the atomic links of governmental systems, the composition of the jural relations as such, as well as the role of the jural subjectivity as a crucial component for creating complex systems of jural relations that serve as the underlying structures of juropolitical systems. We then walk through the history of the civil service – the bureaucratic machine, as Banfield called it, to understand its role and implications on the course of civilization, up till present time, where we discuss the impacts of ICTs on the development of the bureaucratic machine as such. We argue that the changes which ICTs so far brought to the government sector through what is known as e-government, e-democracy, and e-governance respectively, are based on unsustainable artefacts and hence there are strong reasons for them to be considered more of a burden to future generations, rather than a source of relief. Based on the implications of the so explored context we describe a model for an information system that would enable self-managed creation and determination of jural eligibilities, and thus self-managed government of juropolitical societies as such. We call this model Sustainable Non-Bureaucratic Government (SNBG). SNBG bases on a network of electronic registries, which store jural facts, from which eligibilities can be derived through a dedicated mechanism, which we call constellation-based reasoning (CBR). CBR bases on a purposely developed fine-grained data access control mechanism, which does not rely on predefined accessor roles, but dynamically enables / disables access to data based on the context of the request and the context of the data stored in the accessed registry. As such, CBR is purposely designed to support changing the rules of access to the stored data by means of collaborative decision making, as such is required in the political legislative context, whereby the rules that regulate such decision making, are again governed by the very same system, which ensures full flexibility of the SNBG system to fluidly undergo at design-time unpredictable transitions that would happen through time. This feature amongst others then, assures the system’s sustainability. We describe the architecture and the stakeholders of SNBG, as well as auxiliary constructs for planning and communicating regulations which make-up the CBR rules. We define the functional characteristics that instances of the electronic registries must satisfy in order to assure sustainability and to be applicable in the juropolitical context in accordance with core jural principles (and in order to avoid the mistakes as conducted in the course of development of e-government artefacts). Then, we describe the instantiation of a prototype SNBG system, i.e. the instantiation of a respective electronic registry that provides CBR-based access to the underlying data stored in a relational database. We evaluate this prototype instantiation based on three demo applications, which prove its technical feasibility in different scenarios. Finally, we evaluate the SNBG model in four different real-world scenarios to argue for its feasibility in crucial governance situations.
Ključne besede: unsustainability of e-government, self-management of jural relations, computability of jural eligibilities, non-bureaucratic government, collaborative decision making, liquid democracy, fine-grained data access control, fair non-repudiation, digital identity
Objavljeno: 04.06.2015; Ogledov: 992; Prenosov: 24
.pdf Celotno besedilo (11,06 MB)

Ines Kožuh, 2015, doktorska disertacija

Opis: Social networking site use among the d/Deaf and hard of hearing has triggered a growing interest in examining the impact of online activities on their experiences. Despite extensive research on the use of social networking sites among hearing users, only a few studies have focused on use among the d/Deaf and hard of hearing. There is an evident lack of comprehensive research on d/Deaf and hard of hearing users’ experiences with social networking sites in which both the effects of the users’ characteristics on their identification with other users and their tendency to connect with members of online communities are examined. In our study, we developed a theoretical model for examining D/HH users’ experiences with social networking sites. The model investigates the relationships and effects among the aspects (identity, community building and connections between communities) and factors (hearing loss, educational background, communication situation and use of technology) relating to the experiences of d/Deaf and hard of hearing with social networking sites. The primary purpose of the model was to define how the aspects are associated with each other and how the factors influence the aspects. In line with the model, an online questionnaire in sign and written language was developed. A study was conducted in Germany, Slovenia, Austria and Switzerland, where the questionnaire was completed by 199 German, 43 Slovene, 21 Austrian and 20 Swiss d/Deaf and hard of hearing users of social networking sites. Due to sample size the main emphasis was on the results gained from the study conducted in Germany. It was shown that online Deaf identity is negatively related to online hearing identity, but positively related to community building and connections among communities. While community building is positively related to connections between communities, online hearing identity is neither related to community building nor connections between communities. Additionally, hearing status was found to have a significant effect on online Deaf and online hearing identity. Frequency of use of social networking sites has no significant effect on any aspect, while frequency of posting videos is the only activity having a significant effect on community building. Frequency of communication with the deaf in sign language on social networking sites has a positive effect on online Deaf identity and community building; frequency of communication with the deaf and hard of hearing in written language has a further positive effect on community building. Results of examining the effects of different countries on the aspects showed that Slovene users were more engaged in community building and connecting with members of other communities than German users. These findings imply a high potential for using social networking sites in the education process. Accordingly, we developed recommendations for teachers, and designers and developers of educational processes in order to assure efficient communication support for the d/Deaf and hard of hearing. These recommendations might be most beneficial in distance education in terms of globalization, since social networking sites provide opportunities for inclusion of students from abroad. Similarly, social networking sites provide wider opportunities for work between mentors and mentees, since questions can be posed and answers can be given directly on social networking sites.
Ključne besede: Deaf and hard of hearing, social networking sites, online identity, online community, community building, connections between communities
Objavljeno: 24.04.2015; Ogledov: 1132; Prenosov: 132
.pdf Celotno besedilo (19,96 MB)

Diophantine Steiner triples
Bojan Hvala, 2010

Opis: V članku opišemo vse trojice ▫$(R, r, d)$▫, ▫$R > r+d$▫, naravnih števil, za katere ima konfiguracija dveh krogov z radiji ▫$R$▫ in ▫$r$▫ ter razdaljo ▫$d$▫ med središči sklenjeno Steinerjevo verigo. To pomeni, da obstaja cilkično zaporedje ▫$n$▫ krogov, ki se dotikajo začetnih dveh krogov in se dotikajo sosednjih krogov v cikličnem zaporedju. Izkaže se, da je v primeru naravnih vrednosti ▫$R$▫, ▫$r$▫ in ▫$d$▫ dolžina ▫$n$▫ Steinerjeve verige lahko le 3, 4 ali 6.
Ključne besede: matematika, diofantske Steinerjeve trojice, Steinerjev porizem, Steinerjeva formula, diofantske enačbe, mathematics, dDiophantine Steiner triples, Steiner porism, Steiner identity, diophantine equations
Objavljeno: 10.07.2015; Ogledov: 442; Prenosov: 58
URL Povezava na celotno besedilo

Trace-positive polynomials, sums of hermitian squares and the tracial moment problem
Sabine Burgdorf, 2011, doktorska disertacija

Opis: A polynomial ▫$f$▫ in non-commuting variables is trace-positive if the trace of ▫$f(underline{A})$▫ is positive for all tuples ▫$underline{A}$▫ of symmetric matrices of the same size. The investigation of trace-positive polynomials and of the question of when they can be written as a sum of hermitian squares and commutators of polynomials are motivated by their connection to two famous conjectures: The BMV conjecture from statistical quantum mechanics and the embedding conjecture of Alain Connes concerning von Neumann algebras. First, results on the question of when a trace-positive polynomial in two non-commuting variables can be written as a sum of hermitian squares and commutators are presented. For instance, any bivariate trace-positive polynomial of degree at most four has such a representation, whereas this is false in general if the degree is at least six. This is in perfect analogy to Hilbert's results from the commutative context. Further, a partial answer to the Lieb-Seiringer formulation of the BMV conjecture is given by presenting some concrete representations of the polynomials ▫$S_{m,4}(X^2; Y^2)$▫ as a sum of hermitian squares and commutators. The second part of this work deals with the tracial moment problem. That is, how can one describe sequences of real numbers that are given by tracial moments of a probability measure on symmetric matrices of a fixed size. The truncated tracial moment problem, where one considers only finite sequences, as well as the tracial analog of the ▫$K$▫-moment problem are also investigated. Several results from the classical moment problem in Functional Analysis can be transferred to this context. For instance, a tracial analog of Haviland's theorem holds: A traciallinear functional ▫$L$▫ is given by the tracial moments of a positive Borel measure on symmetric matrices of a fixed size s if and only if ▫$L$▫ takes only positive values on all polynomials which are trace-positive on all tuples of symmetric ▫$s times s$▫-matrices. This result uses tracial versions of the results of Fialkow and Nie on positive extensions of truncated sequences. Further, tracial analogs of results of Stochel and of Bayer and Teichmann are given. Defining a tracial Hankel matrix in analogy to the Hankel matrix in the classical moment problem, the results of Curto and Fialkow concerning sequences with Hankel matrices of finite rank or Hankel matrices of finite size which admit a flat extension also hold true in the tracial context. Finally, a relaxation for trace-minimization of polynomials using sums of hermitian squares and commutators is proposed. While this relaxation is not always exact, the tracial analogs of the results of Curto and Fialkow give a sufficient condition for the exactness of this relaxation.
Ključne besede: matematika, algebra, polinomi s pozitivno sledjo, prosta algebra, nekomutativni polinom, centralna enostavna algebra, reducirana sled, polinomska identiteta, kvadratna forma, prosta pozitivnost, vsota hermitskih kvadratov, problem momentov, mathematics, algebra, free algebra, noncommutative polynomial, central simple algebra, (reduced) trace, polynomial identity, central polynomial, quadratic form, free positivity, sum of hermitian squares, (truncated) moment problem
Objavljeno: 10.07.2015; Ogledov: 715; Prenosov: 70
URL Povezava na celotno besedilo
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