Super-\L ukasiewicz logics expanded by Δ\Delta

Baaz's operator $\Delta$ was introduced (by Baaz) in order to extend G\"odel logics, after that this operator was used to expand fuzzy logics by H\'ajek in his celebrated book. These logics were called $\Delta$-fuzzy logics. On the other hand, possibility operators were studied in the setting of \L ukasiewicz-Moisil algebras; curiously, one of these operators coincide with the Baaz's one. In this paper, we study the $\Delta$ operator in the context of ($n$-valued) Super-\L ukasiewicz logics. An algebraic study of these logics is presented and the cardinality of Lindembaun-Tarski algebra with a finite number of variables is given. Finally, as a by-product, we present an alternative axiomatization of H\'ajek's \L ukasiwicz logic expanded with $\Delta$

Tense distributive lattices: algebra, logic and topology

Tense logic was introduced by Arthur Prior in the late 1950s as a result of his interest in the relationship between tense and modality. Prior's idea was to add four primitive modal-like unary connectives to the base language today widely known as Prior's tense operators. Since then, Prior's operators have been considered in many contexts by different authors, in particular, in the context of algebraic logic. Here, we consider the category tdlat of bounded distributive lattices equipped with Prior's tense operators. We establish categorical dualities for tdlat in terms of certain categories of Kripke frames and Priestley spaces, respectively. As an application, we characterize the congruence lattice of any tense distributive lattice as well as the subdirectly irreducible members of this category. Finally, we define the logic that preserves degrees of truth with respect to tdlat-algebras and precise the relation between particular sub-classes of tdlat and know tense logics found in the literature

Some Results on Diagonal-free Two-dimensional Cylindric Allgebras

Formulas for computing the number of Df2-algebra structures that can be defined over Bn, where Bn is the Boolean algebra with n atoms, as well as the fine spectrum of Df2 are obtained. Properties of the lattice of all subvarieties of Df2, (Df 2), are exhibited. In particular, the poset Sifin(Df2) is described

Bone necrosis as a complication of sodium hypochlorite extrusion. A case report

Sodium hypochlorite is the most used irrigant in endodontics, although its toxic effect on tissue is known. Sodium hypochlorite extrusion to periapical tissue can cause complications of varying severity, from oedemas and haemorrhagic lesions to life-thre

Analysis of marginal bone loss and implant stability quotient by resonance frequency analysis in different osteointegrated implant systems. Randomized prospective clinical trial

The aim of the present prospective clinical study is to compare the stability of the implant-bone interface by the ISQ quotient and marginal bone loss (MBL) rate during one year of follow-up in four system implants with the same surface and different design. Prospective randomized clinical trial of 21 patients in which four implant systems with the same surface and different design were placed. Patients were treated by the same operator following a similar surgical protocol with submerged technique. The second surgery to perform the prosthesis was performed at 3 months. All patients went to their review at 6 months and a year. A periapical radiograph for crestal bone analysis and an Implant stability quotient by resonance frequency analysis (ISQ) analysis were taken at baseline and the reviews. No statistically significant differences were found in the Implant stability quotient by resonance frequency analysis and Marginal Bone Loss in the four types of implants. The ISQ increased from the moment of insertion of the implant until the revision to the year, showing an increase of the stability implant, being this increasing less between the 6 months and the year. Differences in the design of the four implants tested in this study did not show statistically significant differences in any of the variables studied, so the implant design does not influence implant stability and marginal bone loss in the first year after placement

Evolution of oral cancer treatment in an andalusian population sample : rehabilitation with prosthetic obturation and removable partial prosthesis

Radical surgical resection as a treatment modality for oral cancer often leads to an extensive deficit in both the maxillary and mandibular levels, where the use of a palatal obturator prosthesis (POP) or removable partial denture (RPP). The aim of this study was to evaluate the treatment with POP and RPP in patients treated for oral cancer in the Unit of Prosthetic Rehabilitation of the University Hospital Virgen del Rocío in a period of 20 years. Retrospective descriptive study during the years 1991 and 2011 analyzing oral cancer type, characteristics, treatment and follow-up. The sample consisted of patients whose tumor had previously been removed and who had been referred to the Oncological Rehabilitation Unit of the Oral and Maxillofacial Surgery Unit of the ?Virgen del Rocío? University Hospital for rehabilitation. The inclusion criteria were patients whose underlying pathology was any type of neoplasia, which after its treatment had been referred to the aforementioned Oncological Prosthetic Rehabilitation unit. Of the 45 patients included in our study, 15 patients were rehabilitated with palatal obturator (33.3%) and 5 patients with removable partial denture (11.1%). The mean age of the sample of patients with POP was 57.3 ± 9.23, while the mean age of the sample of patients with RPP was 58 ± 13.5. The most common underlying pathology in patients with POP was squamous cell carcinoma (60%), whereas in patients with RPP it was 100%. The most frequent location found among POP patients was the upper jaw, while in the PRP patients there was no predominant location. The univariate and multivariate logistic regressions did not show any statistically significant association between the independent variables age, sex, smoking habit and alcoholic habit with the dependent variable type of rehabilitating prosthesis. Based on our data, we can conclude that RPP is used in few cases of oncological rehabilitation. The POP has a greater use, as long as the defect in the bones of the facial middle third is limited

Production of bone mineral material and BMP-2 in osteoblasts cultured on double acid-etched titanium

Background: The study of osteoblasts and their osteogenic functions is essential in order to understand them and their applications in implantology. In this sense, this study try to study BMP-2 production and bone matrix deposition, in addition to other biological variables, in osteoblasts cultured on a rough double acid-etched titanium surface (Osseotite®, Biomet 3i, Palm Beach Garden, Florida, USA) in comparison to a smooth titanium surface (machined) and a control Petri dish. Material and Methods: An in vitro prospective study. NHOst human osteoblasts from the femur were cultured on three different surfaces: Control group: 25-mm methacrylate dish (n = 6); Machined group: titanium discs with machined surface (n = 6) and Experimental group: titanium discs with a double acid-etched nitric and hydrofluoric Osseotite® acid surface (n = 6). A quantification of the mitochondrial membrane potential, and studies of apoptosis, mobility and adhesion, bone productivity (BMP-2) and cellular bone synthesis were carried out after culturing the three groups for forty-eight hours. Results: A statistically significant difference was observed in the production of BMP-2 between the experimental group and the other two groups (22.33% ± 11.06 vs. 13.10% ± 5.51 in the machined group and 3.88% ± 3.43 in the control group). Differences in cellular bone synthesis were also observed between the groups (28.34% ± 14.4% in the experimental group vs. 20.03% ± 6.79 in the machined group and 19.34% ± 15.93% in the control group). Conclusions: In comparison with machined surfaces, Osseotite® surfaces favor BMP-2 production and bone synthesis as a result of the osteoblasts in contact with it. Key words:BMP-2, Cytoskeleton, cell culture, bone matrix, apoptosis, cell viability

Detection of NOTCH1 mutations in paraffin samples in patients with potentially malignant lesions

On certain occasions, oral cancer is preceded by potentially malignant lesions. The degree of dysplasia in Guinea pigs attempts to determine the risk of developing a malignant lesion. The search for genetic mutations, biomarkers, as a more truthful and r

Some Results on Diagonal-free Two-dimensional Cylindric Allgebras

Formulas for computing the number of \bb {Df}_2-algebra structures that can be defined over \bbb B_n, where \bbb B_n is the Boolean algebra with n atoms, as well as the fine spectrum of \bb {Df}_2 are obtained. Properties of the lattice of all subvarieties of \bb {Df}_2, \Lamda(\bb {Df}_2), are exhibited. In particular, the poset Si_{fi n} (\bb {Df}_2) is described