Covariant Affine Integral Quantization(s)

Covariant affine integral quantization of the half-plane is studied and applied to the motion of a particle on the half-line. We examine the consequences of different quantizer operators built from weight functions on the half-plane. To illustrate the procedure, we examine two particular choices of the weight function, yielding thermal density operators and affine inversion respectively. The former gives rise to a temperature-dependent probability distribution on the half-plane whereas the later yields the usual canonical quantization and a quasi-probability distribution (affine Wigner function) which is real, marginal in both momentum p and position q.Comment: 36 pages, 10 figure

POVM Quantization

We present a general formalism for giving a measure space paired with a separable Hilbert space a quantum version based on normalized positive operator-valued measure. The latter are built from families of density operators labelled by points of the measure space. We specially focus on various probabilistic aspects of these constructions. Simple or more elaborate examples illustrate the procedure: circle, 2-sphere, plane, half-plane. Links with POVM quantum measurement and quantum statistical inference are sketched

Hierarchy of Conservation Laws of Diffusion--Convection Equations

We introduce notions of equivalence of conservation laws with respect to Lie symmetry groups for fixed systems of differential equations and with respect to equivalence groups or sets of admissible transformations for classes of such systems. We also revise the notion of linear dependence of conservation laws and define the notion of local dependence of potentials. To construct conservation laws, we develop and apply the most direct method which is effective to use in the case of two independent variables. Admitting possibility of dependence of conserved vectors on a number of potentials, we generalize the iteration procedure proposed by Bluman and Doran-Wu for finding nonlocal (potential) conservation laws. As an example, we completely classify potential conservation laws (including arbitrary order local ones) of diffusion--convection equations with respect to the equivalence group and construct an exhaustive list of locally inequivalent potential systems corresponding to these equations.Comment: 24 page

Calcifying epithelial odontogenic tumour-case series from five Nigerian Teaching Hospital

Background: Calcifying epithelial odontogenic tumour (CEOT) also known as Pindborg’s tumour is a relatively rare odontogenic neoplasm of epithelial derivationthat constitutes about 0.4-3% of all intraosseous odontogenic tumours.Objectives: To document all cases of CEOT encountered in five tertiary centres in Nigeria and their clinical, radiologic and histologic characteristics.Design: A retrospective study.Setting: Tertiary Dental Facilities in Lagos, Ibadan, Ife, Port Harcourt and Zaria (all in Nigeria) were involved in the study.Subjects: All odontogenic tumours (OTs) in the period from 1970 -2014. Case file records and biopsy reports were retrieved from the records of the five Teaching Hospitals, to obtain age, gender, location, size, clinical symptoms, pathological reports and radiographic description.Results: Out of a total of 1369 OTs, 20 (1.5%) cases of CEOT were reported. CEOT had a male to female ratio of 1.9:1, with mandible: maxilla ratio of 1.5:1 and the most common location being the premolar /molar region in the mandible. Nine (45%) cases appeared radiolucent while 11(55%) cases had mixed radio density. The mean diameter for mixed radio-dense lesions (4.83±2.99) was higher than that for radiolucent lesions (2.75±1.17) and the difference was statistically significant (p=0.049).Conclusion: CEOT is a rare tumour representing 1.5% of OTs. CEOT presents with some subtle geographic differences in its demography, however, further studies are required to investigate if these differences are coincidental or genetically  determined

Euskarazko artikuluaren sintaxiaz

This work tries to identify th specific semantic contribution and syntactic position of the article in Basque. The analysis centers on absolutive marked Determiner Phrases.Lan honetan euskal artikuluaren balio espezifikoa aztertzen da, determinatzaile sintagmak betetzen duen lekuan, duen funtzioan eta aurkezten duen hitz hurrenkeran oinarrituz, eta analisia, beti ere, absolutiboz markaturik agertzen diren sintagmetara mugatuaz