Zeru Yimer Kebede
Background and objectives: The production and productivity of dry beans in Ethiopia is hindered by multiple challenges; among these were biotic, abiotic and socioeconomic factors. Thus, this review paper highlighted and discussed those factors that impose dry beans not to give reasonable grain yield and acceptable quality there by to identify and discuss the main challenges of common beans under the study area, and to document the information generated from the paper for future improvement of dry beans.
Material and Methods: A number of peer reviewed papers were critically viewed and reanalyzed based on the current situation of legumes production. Based on the investigation and observations made the author distinguished and prioritized the major threats of beans production for the study area.
Results: Via different sources, information generated. The author also identified and prioritized the agents that limit the production of dry beans under the area and means of managing the challenges separately or by integration them.
Conclusion: Therefore, the author recommend and suggest that to cultivate our farmlands in sustainable way we have to follow and apply the cropping patterns and systems of rotation with legumes to achieve this we must made bridge between technology generated with producers.
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Teodor Dumitru Valcan
As in two other papers regarding I-cevian and I-circumcevian triangles, respectively, in this paper we propose, using logical deductibility relations and the analogy method, to present some interesting results in Triangle Geometry, more specifically regarding iterative I-circumcevian triangles. Thus, we consider a triangle ABC and the interior bisectors of the angles of the triangle, which intersect at point I and which intersect the sides of the given triangle at points A?, B? and C?, and the circumcircle of triangle ABC at A1, B1 and C1. Then, we will call the triangle A?B?C? the I-cevian triangle attached to the triangle ABC and the point I, and we will call the triangle A1B1C1 the I-circumcevian triangle attached to the triangle ABC and the point I. In the following, for any n?N, n?2, we will denote by AnBnCn the I-circumcevian triangle attached to the An-1Bn-1Cn-1 triangle. Using common mathematical knowledge, valid in any triangle, but also the results presented in the two papers mentioned above, we can obtain a series of very interesting geometric or trigonometric identities and inequalities, some of them very difficult to prove synthetically. The work is exclusively about Mathematics Didactics and is addressed to both students and teachers eager for performance in this field of Mathematics or, in Mathematics in general.
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