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.

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.

Background and Aim: Considering the importance of the design of framework in the stress distribution and probability of creating initial cracks in connectors region, proper design of framework is considered as a requirement. For this purpose, in order to examine the stress distribution in two designs of straight and curved framework, comparison was made using FEM method.Materials and Methods: Research using a descriptive method of FEM was performed. A laboratory prototype was produced and was scanned in a digital form, using CMM equipment by the laboratory and a super spot from the geometry of the part was created. The super spot was transformed to a 3D solid model by utilizing Catia software. The above model was divided into a high number small elements, using Meshing method, by Abaqus software to analyze the finite elements. Afterwards, by Boundary Condition definition, the part was ready to be analyzed. The mechanical properties of Zirconia was entered into the software in the form of a table. Reviewing stress distribution in the bridge specially with the stress on connectors region was performed. Three vertical loading models for each part were applied in central and distal Fosa and analyzed separately.Results: In this study, the findings were described in the form of Von mises stress in Mpa scale. The stress in the curved model was more than the Straight model. As a result, the stress distribution is more desirable.Conclusion: According to the results of this study, the straight model showed a more desirable stress distribution compared with the curved model. However, it should be noted that these results were obtained in F.E. environment.