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We investigated maximal Prym varieties on  nite  elds by attaining their upper bounds on the number of rational points. This concept gave us a motivation for de ning a generalized de ni-tion of maximal curves i. e., maximal morphisms. By MAGMA, we give some non-trivial examples of maximal morphisms that results in non-trivial examples of maximal Prym varieties.

An optimal labeling of a graph with $n$ vertices and $m$ edges is an injective assignment of the first $n$ nonnegative integers to the vertices‎, ‎that induces‎, ‎for each edge‎, ‎a weight given by the sum of the labels of its end-vertices with the property that the set of all induced weights consists of the first $m$ positive integers‎. ‎We explore the connection of this labeling with other well-known functions such as super edge-magic and $\alpha$-labelings‎. ‎A graph with $n$ vertices is maximal when the number of edges is $2n-3$; all the results included in this work are about maximal graphs‎. ‎We determine the number of optimally labeled graphs using the adjacency matrix‎. ‎Several techniques to construct maximal graphs that admit an optimal labeling are introduced as well as a family of outerplanar graphs that can be labeled in this form.

Objective: Anesthetic techniques like the Akinosi technique were introduced to surmount the problems of the conventional inferior alveolar nerve block (IANB) technique. This study aimed to compare the local anesthetic efficacy of IANB via the conventional and Akinosi techniques in patients presenting to the Maxillofacial Surgery Department of School of Dentistry, Shahid Beheshti University.Methods: This clinical trial was conducted on 80 candidates for bilateral extraction of mandibular molars. For each patient, local anesthesia was induced by IANB injection, which was done by the conventional technique in one side and by the Akinosi technique in the other side of the mouth. The allocation of technique to side was randomized. Time to anesthesia for the long buccal, lingual and inferior alveolar nerves (IAN), degree of pain during injection and tooth extraction and incidence of positive aspiration in the two techniques were evaluated and analyzed using Wilcoxon Signed Rank and Chi square tests.Results: The mean time to anesthesia for the IAN was 2.82 minutes in the conventional and 3.05 minutes for the Akinosi technique. These values were 1.47 and 1.55 minutes, respectively for the lingual nerve and 1.43 and 1.56 minutes, respectively for the long buccal nerve. Four patients in the Akinosi technique and 12 patients in the conventional technique had positive aspiration. During anesthetic injection with the Akinosi technique, 72.5% were pain free, 18.8% experienced mild, 5% experienced moderate and 3.8% experienced severe pain. These values in the conventional technique were 51.3%, 27.5%, 11.3% and 10%, respectively.Conclusion: Considering the lack of a significant difference between the success rate of conventional and Akinosi IANB techniques, Akinosi technique seems to be a suitable alternative to the conventional technique since it is less painful and has lower risk of positive aspiration.

In this note we describe some recent advances in the area of maximal function inequalities. We also study the behaviour of the centered Hardy- Littlewood maximal operator associated to certain families of doubling, radial decreasing measures, and acting on radial functions. In fact, we precisely determine when the weak type (1, 1) bounds are uniform in the dimension.

Let (X,T) be a minimal transformation group and let j  be a homomorphism of (X,T). We will find a maximal factor of (X,T)  with respect toj. That is, we will find a minimal transformation group (Y,T), an auto Orphism y: ((Y,T)® (Y,T), and a homomorphism p: (X,T) ®(Y,T), such that the following diagram commutes X®X ¯p     ¯p Yy®Y ….