LINE REGULAR FUZZY SEMIGRAPHS

           تقدم هذه الورقة نوعين من درجات الحافة (الدرجة الخطية والدرجة قريب الخطية) ودرجات الحافة الكلية (الدرجة الكلية الخطية ودرجة قريب الخطية الكلية) للحافة في شبه البيان ضبابي، حيث يُعرّف الخط الضبابي بأنه (V, σ, μ, η ) مُعرَّفة على شبه البيان G * حيث σ : V → [0, 1], μ : VxV → [0, 1] و η : X → [0, 1]  تفي بالشروط التي تناسب جميع الرؤوس  u، v في مجموعة الرأس، μ(u, v) ≤ σ(u) ᴧ σ(v) و η(e) = μ(u1, u2) ᴧ μ(u2, u3) ᴧ … ᴧ μ(un-1, un) ≤ σ(u1) ᴧ σ(un) اذا كانت e = (u1, u2, …, un), n ≥ 2 هي حافة في نصف الرسم البياني G *، حيث يتم تعريف النصف البياني كزوج من المجموعات (V, X) حيث تكون مجموعة الرأس V مجموعة غير فارغة ومجموعة الحافة X عبارة عن مجموعة من n - tuples لمختلف n ≥ 2، من العناصر المميزة لـ V مع الخصائص التي، أي عنصرين في حافة المجموعة X لها رأس مشترك واحد تقريبًا ولأي حافتين (ɑ1, ɑ2,…, ɑn )  و (b1, b2,…, bm) في مجموعة الحافة  X متساوية إذا، وفقط إذا، n = m  وأيًا منهما أحد الشروط ɑj = bjأو ɑj = bn-j + 1 تتحقق ل  r لـ j  حيث تقع قيمة j بين 1 و n.  بالإضافة إلى انتظام الحواف (الخط المنتظم والخط القريب المنتظم) وإجمالي انتظام الحواف (الخط الكلي المنتظم والإجمالي القريب من الخط المنتظم) لدرجات الحافة المقابلة ودرجات الحافة الكلية التي تمت دراستها، تم فحص خصائصها وتم الحصول على نتائج قليلة تربط انتظام الرأس وانتظام الحافة لشبه البيان الضبابي.            This paper introduce two types of edge degrees (line degree and near line degree) and total edge degrees (total line degree and total near line degree) of an edge in a fuzzy semigraph, where a fuzzy semigraph is defined as (V, σ, μ, η) defined on a semigraph G* in which σ : V → [0, 1], μ : VxV → [0, 1] and η : X → [0, 1] satisfy the conditions that for all the vertices u, v in the vertex set,  μ(u, v) ≤ σ(u) ᴧ σ(v) and  η(e) = μ(u1, u2) ᴧ μ(u2, u3) ᴧ … ᴧ μ(un-1, un) ≤ σ(u1) ᴧ σ(un), if e = (u1, u2, …, un), n ≥ 2 is an edge in the semigraph G*, in which a semigraph is defined as a pair of sets (V, X) in which the vertex set V is a non - empty set and edge set X is a set of n – tuples for various n ≥ 2, of distinct elements of V with the properties that, any two elements in the edge set X has at most one vertex in common and for any two edges (ɑ1, ɑ2,…, ɑn ) and (b1, b2,…, bm)  in the edge set X are equal if, and only if, n = m and either one of the conditions ɑj = bj  or ɑj = bn-j+1 occur for j where the value of j lies between 1 and n. In addition to that edge regularities (line regular and near line regular) and total edge regularities (total line regular and total near line regular) of the corresponding edge degrees and total edge degrees are studied, their properties are examined and a few results connecting vertex regularity and edge regularity of a fuzzy semigraph are obtained. 2020 Mathematics Subject Classification: 05C72, 05C07

Comparative Evaluation of Shear Bond Strength and Microleakage of Biodentine and Resin modified Glass Ionomer Cement using Two Adhesive Systems in Premolars Restored with Composites: An Invitro Study

BACKGROUND AND OBJECTIVES: It is important to have good marginal seal and better bond strength for the longevity of restorative material, thereby reducing the marginal leakage which is the precursor of secondary caries, staining of restoration, tooth discoloration, marginal deterioration, postoperative sensitivity and pulpal pathology. Several factors contribute to the high incidence of recurrent caries in the gingival area. These include improper restorative technique by the clinician, plaque accumulation due to patient difficulty in cleaning and lack of patient compliance with proper oral hygiene. It is therefore critical to achieve a seal on the gingival margin of class II sandwich restorations. The objective is to evaluate and compare the shear bond strength and microleakage in premolars using Biodentine – tricalcium silicate–based bioactive restorative material and resin modified glass ionomer cement with Adper single bond (etch and rinse adhesive system) and Universal bond – 3M (1 step self etch adhesive system) adhesive systems. MATERIALS AND METHODOLOGY: 80 premolars extracted for orthodontic purpose were collected. The samples were divided into two groups namely, Group A (Biodentin group) and Group B (resin modified glass ionomer cement group respectively. Each group is then further subdivided into subgroup1 (Adper single bond) and subgroup 2 (Universal Bond). The occlusal surfaces of the tooth were ground flat and PVC molds were stabilized over flat dentin surface. It is then filled according to the groups ascertained which is then restored with composite resin. Shear bond strength were evaluated with Universal Testing Machine (INSTRON) using a steel knife edge (1mm thickness) at a cross head speed of 0.5 mm/ minute. Standardized class II cavities were prepared in premolars and restored with tricalcium silicate-based restorative material (Biodentine) and resin modified glass ionomer cement and was applied with adhesives, according to groups ascertained. After the application of adhesives, composite resin material is restored, using open sandwich technique. The samples were then subjected to 1000 thermocycles followed by methylene blue dye penetration. The extent of microleakage was examined using stereomicroscope at 40X magnification. RESULTS: The result showed that the shear bond strength of Biodentine with Adper single bond was better with the mean value of 12.4 and there was a statistical significance when compared to other groups and RMGIC with Adper single bond shows less microleakage with the mean value of 2.7 when compared to other groups but there was no statistical significance. CONCLUSION: Biodentine with Adper single bond shows better shearbond strength which is followed by RMGIC with Universal bond (self etch system) and RMGIC with Adper single bond and then Biodentine with Universal bond. RMGIC with Adper single bond shows less microleakage when compared to RMGIC with Universal bond which is then followed by Biodentine with Adper single bond and then the Biodentine with Universal bond

Randomized Clinical Trial of High-Dose Rifampicin With or Without Levofloxacin Versus Standard of Care for Pediatric Tuberculous Meningitis: The TBM-KIDS Trial

Background. Pediatric tuberculous meningitis (TBM) commonly causes death or disability. In adults, high-dose rifampicin may reduce mortality. The role of fluoroquinolones remains unclear. There have been no antimicrobial treatment trials for pediatric TBM. Methods. TBM-KIDS was a phase 2 open-label randomized trial among children with TBM in India and Malawi. Participants received isoniazid and pyrazinamide plus: (i) high-dose rifampicin (30 mg/kg) and ethambutol (R30HZE, arm 1); (ii) high-dose rifampicin and levofloxacin (R30HZL, arm 2); or (iii) standard-dose rifampicin and ethambutol (R15HZE, arm 3) for 8 weeks, followed by 10 months of standard treatment. Functional and neurocognitive outcomes were measured longitudinally using Modified Rankin Scale (MRS) and Mullen Scales of Early Learning (MSEL). Results. Of 2487 children prescreened, 79 were screened and 37 enrolled. Median age was 72 months; 49%, 43%, and 8% had stage I, II, and III disease, respectively. Grade 3 or higher adverse events occurred in 58%, 55%, and 36% of children in arms 1, 2, and 3, with 1 death (arm 1) and 6 early treatment discontinuations (4 in arm 1, 1 each in arms 2 and 3). By week 8, all children recovered to MRS score of 0 or 1. Average MSEL scores were significantly better in arm 1 than arm 3 in fine motor, receptive language, and expressive language domains (P < .01). Conclusions. In a pediatric TBM trial, functional outcomes were excellent overall. The trend toward higher frequency of adverse events but better neurocognitive outcomes in children receiving high-dose rifampicin requires confirmation in a larger trial. Clinical Trials Registration. NCT02958709

LINE REGULAR FUZZY SEMIGRAPHS

           This paper introduce two types of edge degrees (line degree and near line degree) and total edge degrees (total line degree and total near line degree) of an edge in a fuzzy semigraph, where a fuzzy semigraph is defined as (V, σ, μ, η) defined on a semigraph G* in which σ : V → [0, 1], μ : VxV → [0, 1] and η : X → [0, 1] satisfy the conditions that for all the vertices u, v in the vertex set,  μ(u, v) ≤ σ(u) ᴧ σ(v) and  η(e) = μ(u1, u2) ᴧ μ(u2, u3) ᴧ … ᴧ μ(un-1, un) ≤ σ(u1) ᴧ σ(un), if e = (u1, u2, …, un), n ≥ 2 is an edge in the semigraph G*, in which a semigraph is defined as a pair of sets (V, X) in which the vertex set V is a non - empty set and edge set X is a set of n – tuples for various n ≥ 2, of distinct elements of V with the properties that, any two elements in the edge set X has at most one vertex in common and for any two edges (ɑ1, ɑ2,…, ɑn ) and (b1, b2,…, bm)  in the edge set X are equal if, and only if, n = m and either one of the conditions ɑj = bj  or ɑj = bn-j+1 occur for j where the value of j lies between 1 and n. In addition to that edge regularities (line regular and near line regular) and total edge regularities (total line regular and total near line regular) of the corresponding edge degrees and total edge degrees are studied, their properties are examined and a few results connecting vertex regularity and edge regularity of a fuzzy semigraph are obtained. 2020 Mathematics Subject Classification: 05C72, 05C07.</jats:p

Comparative Evaluation of Microleakage of Three Different Restorative Materials (Cention N, Zirconomer Improved and Glass Hybrid Restorative System) in Class V Cavity Restoration Using Stereomicroscope: In vitro Study

Aim and Objective: Microleakage is the most important factor responsible for the destruction of restoration margins. The aim of this study was to compare and evaluate the microleakage of three different restorative materials namely glass hybrid restorative system, zirconomer improved and Cention N under stereomicroscope.&#x0D; Materials and Methods: In this in-vitro experimental study, 45 Class V cavities were prepared on the buccal surface of maxillary premolars. The prepared cavities were divided into three groups for restoration with Cention N(group I), Zirconomer Improved(group II), Equiaforte (group III). All the samples were thermocycled for 500 cycles between 5-55°C initially and then immersed in 0.5% methylene blue for 24 hours before sectioning. All the sectioned samples were observed for microleakage under a stereomicroscope.&#x0D; Results: Data was analyzed using one way ANOVA test for comparison between three groups and the result revealed statistically significant difference between the groups(p&lt;0.05). Post hoc Tukey test was used for intergroup comparison and it was observed that both Cention and Equiaforte are inferior to Zirconomer improved in terms of microleakage (p&lt;0.05).&#x0D; Conclusion: Zirconomer improved exhibited lower microleakage when compared to Cention N and Equiaforte cements.</jats:p