Marinids, from 7th to 9th centuries emerged in the FARTHEST Maghreb by overcoming Movahhedoon. They had built the New Fas beside the Old Fas as their state center. By Marinids’ political triumphal, Maghreb was in peace and quiet for a while and its cities were flourished among Islamic cities by building new mosques, schools, bazaars, libraries libraries, etc.Marinids state had done its cultural and scientific affairs alongside its political and military ones. Within this period the greatests scientists and schoolars semerged in west Islamic World. We can name here same great people like ibn Khaldun, ibn Khatib, al-Muqri, ibn marzooq. The Fas schools and other Maghreb cities which were built by the Marinids` rulers had become prominent schools in Islamic World. The Qaravieen school which was the base of the oldest Maghreb`s schools, became so important in this period.Many educational centers were built by rulers in different cities of the Maghreb. These centers made Maghreb culture getting scientific flourish, and those who were eager gathered there from Islamic Africa.

In this paper, we first introduce the nearest and the FARTHEST POINTs in normed spaces, then introduce nonlinear semi inner product spaces, negative dual sets and sun sets. We make statements about these concepts. Define the concept of orthogonality of the nonlinear semi inner product and describe its properties. Finally, we bring the nearest and the FARTHEST POINTs in linear spaces. we introduce the nearest and the FARTHEST POINTs in normed spaces, then introduce nonlinear semi inner product spaces, negative dual sets and sun sets. We make statements about these concepts. Define the concept of orthogonality of the nonlinear semi inner product and describe its properties. Finally, we bring the nearest and the FARTHEST POINTs in linear spaces. we bring the nearest and the FARTHEST POINTs in linear spaces. we introduce the nearest and the FARTHEST POINTs in normed spaces, then introduce nonlinear semi inner product spaces, negative dual sets and sun sets. We make statements about these concepts. Define the concept of orthogonality of the nonlinear semi inner product and describe its properties. Finally, we bring the nearest and the FARTHEST POINTs in linear spaces.

Common nearest-neighbor density estimators usually do not work well for high dimensional datasets. Moreover, they have high time complexity of )(2nO and require high memory usage especially when indexing is used. In order to overcome these limitations, we proposed a new method that calculates distances to nearest and FARTHEST neighbor nodes to create dataset subgroups. Therefore computational time complexity becomes of )log(nnO and space complexity becomes constant. After subgroup formation, assembling technique is used to derive correct clusters. In order to overcome high dimensional datasets problem, Principal Component Analysis (PCA) in the clustering method is used, which preprocesses high-dimensional data. Many experiments on synthetic data sets are carried out to demonstrate the feasibility of the proposed method. Furthermore we compared this algorithm to the similar algorithm – DBSCAN-on real-world datasets and the results showed significantly higher accuracy of the proposed method.

Through the genesis, which means deep harmony at the FARTHEST distance, the meanings of Bildung in Kant's Third Critique will increase and intensify.  Deep harmony at the FARTHEST distance means, it is possible to defend the doubling of the intensities of faculties with different functions when the hierarchy of faculties loses or messes and again harmonizes them based on the degree of their intensities.

Given a set𝑆 of 𝑛 POINTs in the plane and a constant 𝛼, (𝑛, 1, 1, a) -center problem is to find two closed disks which each covers the whole 𝑆, the diameter of the bigger one is minimized, and the distance of the two centers is at least 𝛼. Constrained (𝑛, 1, 1, a) -center problem is the (𝑛, 1, 1, 𝛼) -center problem in which the centers are forced to lie on a given line 𝐿. In this paper, we first introduce (𝑛, 1, 1, a) -center problem and its constrained version. Then, we present an 𝑂 (𝑛log𝑛) algorithm for solving the (𝑛, 1, 1, a) -center problem. Finally, we propose a linear time algorithm for its constrained version.

We extend the study of Chebyshev centers in pre-Hilbert C*-modules by considering the C*-algebra valued map defined by ½x½=<x, x>1/2. We prove that if T is a remotal subset of a pre-Hilbert C*-module M, and F Í M is star-shaped at a relative Chebyshev center c of T with respect to F, then ½x-qT (x)½2 ³ ½x-c½2+½c-qT (c)½2 (x  Î F). The uniqueness of Chebyshev center follows from this inequality. This is a generalization of a well-known result on Hilbert spaces.