Background: The anterior loop of mental nerve is commonly described as that part of the neurovascular bundle that transverses anterior and inferior to the mental foramen only to loop back to exit the mental foramen. The aim of the study is to evaluate the incidence and extension of anterior loop of mental nerve by using digital panoramic imaging system to avoid nerve damage during different surgical procedures in dentistry. Materials and Method: Panoramic image was taken for all 400 patients and stored in the computer. Then Horizontal and Vertical for the anterior loop extension when exist was measured and recorded in a special case sheet prepared for each subject. Results: Results indicated that out of 400 patients there were only 25 patients (6.25%) having anterior of the inferior alveolar nerve, 14 cases (56%) of them were males and 11 cases (44%) were females. The extension of the anterior loop of mental nerve was with wide range, for horizontal extension it was 1.3-6.36mm with significant difference between right and left sides, and with vertical extension was between 1.44 -5.98mm with no significant difference between the right and left sides. Conclusion: No significant difference among subjects according to sex and the pattern of visualization of the anterior loop was shown. The anterior loop was visible in 6.25% of the dental panoramic radiographs with 3.5% for males and 2.75% for females
For any group G, we define G/H (read” G mod H”) to be the set of left cosets of H in G and this set forms a group under the operation (a)(bH) = abH. The character table of rational representations study to gain the K( SL(2,81)) and K( SL(2, 729)) in this work.
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A factor group is a mathematical group obtained by aggregating similar elements of a larger group using an equivalence relation that preserves some of the group structure. In this paper, the factor groups K(SL(2,121)) and K(SL(2,169)) computed for each group from the character table of rational representations.
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The group for the multiplication of closets is the set G|N of all closets of N in G, if G is a group and N is a normal subgroup of G. The term “G by N factor group” describes this set. In the quotient group G|N, N is the identity element. In this paper, we procure K(SL(2,125)) and K(SL(2,3125)) from the character table of rational representations for each group.
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The diverse urban spaces of the streets is an important part of the city's physicist configuration and a link between architectural and civilizational communication through time starting from the historic towns down to the contemporary cities, within the proposals of the future cities. From general observations and literature review a research problem is crystallized as some directions not arbitrary rational when expansion and the growth of cities, and other measures wrong or the existence of some incorrect actions and processes related to the cities planning as a categorizing the goals and priorities in city plan.The streets were constitute a high proportion of the total area of cities, where up to over 30% in major cities. These
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