New biorthogonal potential--density basis functions

We use the weighted integral form of spherical Bessel functions, and introduce a new analytical set of complete and biorthogonal potential--density basis functions. The potential and density functions of the new set have finite central values and they fall off, respectively, similar to $r^{-(1+l)}$ and $r^{-(4+l)}$ at large radii where $l$ is the latitudinal quantum number of spherical harmonics. The lowest order term associated with $l=0$ is the perfect sphere of de Zeeuw. Our basis functions are intrinsically suitable for the modeling of three dimensional, soft-centred stellar systems and they complement the basis sets of Clutton-Brock, Hernquist & Ostriker and Zhao. We test the performance of our functions by expanding the density and potential profiles of some spherical and oblate galaxy models.Comment: 8 pages, 6 figures, Accepted for publication in Monthly Notices of the Royal Astronomical Societ

Evaluation of factors affecting the association between thickening of sinus mucosa and the presence of periapical lesions using cone beam CT

sener, elif/0000-0003-1402-9392WOS: 000553220800001PubMed: 32627204Aim To evaluate the effect of various parameters of periapical lesion(s) on the amount and type of mucosal thickening using cone beam CT images. Methodology CBCT scans of 1000 patients were evaluated retrospectively for the presence of apical lesions in maxillary posterior teeth associated with sinus mucosal thickening. the number of cases with pathological mucosal thickening was recorded and classified according to the amount and type of mucosal thickening. the parameters evaluated as the cause of mucosal thickening were the type and number of posterior teeth, number of root(s), diameter of the periapical lesion and distance between maxillary sinus and lesion. Descriptive statistics and multiple logistic regression was used for data analyses. Spearman's correlation coefficient was used for pair-wise comparisons. Intrarater reliability was tested by Cohen's kappa. Results Mucosal thickening associated with periapical lesions was determined in 48% of 202 cases. the most frequently detected extent of mucosal thickening was type 3 (42%), whereas flat type thickening (59%) was the most frequent type. the tooth most frequently associated with mucosal thickening was the maxillary first molar (44%). Parameters significantly affecting the extent of mucosal thickening were gender, number of roots, number of teeth with periapical lesions and diameter of periapical lesions (P < 0.05). the single parameter with an association with the type of mucosal thickening was the number of roots with an apical lesion (P < 0.05). Conclusion Mucosal thickening associated with periapical lesions was observed in almost 50% of all mucosal thickening cases. Therefore, collaboration amongst endodontists and otolaryngologists is mandatory to provide successful treatment and prevent recurrence of maxillary sinusitis