During his political career, Helmut Kohl used his own life story to promote a normalization of German nationalism and to overcome the stigma of the Nazi period. In the context of the cold war and the ...memory of the fascist past, he was able to exploit the combination of his religious, generational, regional, and educational (he has a PhD in History) experiences by connecting nationalist ideas to particular biographical narratives. Kohl presented himself as the embodiment of "normality": a de-radicalized German nationalism which was intended to eclipse any anti-Western and post-national peculiarities. This book takes a biographical approach to the study of nationalism by examining its manifestation in Helmut Kohl and the way he historicized Germany's past.
This paper deals with the hidden structure of prime numbers. Previous numerical studies have already indicated a fractal-like behavior of prime-indexed primes. The construction of binary images ...enables us to generalize this result. In fact, two-integer sequences can easily be converted into a two-color image. In particular, the resulting method shows that both the coprimality condition and Ramanujan primes resemble the Minkowski island and Cantor set, respectively. Furthermore, the comparison between prime-indexed primes and Ramanujan primes is introduced and discussed. Thus the Cantor set covers a relevant role in the fractal-like description of prime numbers. The results confirm the feasibility of the method based on binary images. The link between fractal sets and chaotic dynamical systems may allow the characterization of the Hénon map only in terms of prime numbers.
Consider a left J-module I. The present study introduces the conception of rad-Quasi- Prime submodule, that serves as a dual popularization of both Quasi-Prime submodules and primary submodules. An ...apposite submodule A of an J-module named as rad- Quasi Prime if for all and with implies that either or . Numerous facts and characterizations that concerning are acquired.
Let q be an odd prime and B={bj}j=1l be a finite set of nonzero integers that does not contain a perfect qth power. We show that B has a qth power modulo every prime p≠q and not dividing ∏b∈Bb if and ...only if B corresponds to a linear hyperplane covering of Fqk. Here, k is the number of distinct prime factors of the q-free part of elements of B. Consequently: (i) a set B⊂Z∖{0} with cardinality less than q+1 cannot have a qth power modulo almost every prime unless it contains a perfect qth power and (ii) For every set B={bj}j=1l⊂Z∖{0} and for every (cj)j=1l∈(Fq∖{0})l the set B contains a qth power modulo every prime p≠q and not dividing ∏j=1l if and only if the set {bjcj}j=1l does so.
In this paper double, quadruple and octuple primes are discussed. Computational and theoretical properties as well as examples of quadruple and octuple primes are presented, where the octuple primes ...in most cases have primes between the defining quadruples although the existence of a pure quadruple prime has also been demonstrated computationally. The possibility of sixtentuple primes is also briefly discussed.
In this industrial era the innovation of industrial machines had a significant impact on industrial evaluation which minimize manpower, time consumption for product making, material wastage. Heavy ...usage of machines leads to the occurrence of some faults in it. Such damaged parts of each machine have been identified to overhaul which is defined as a set called neutro-prime set under its topological structure. Some related properties of such space have been proved and some are disproved with counterexamples. Also, the idea of interior and closure dealt with this space with few basic properties. This article provides a decision-making process to identify the best fit of those damages under a neutrosophic environment and the priority is given to the heavily damaged machine. We also use step by step algorithm and formulae to compute machine values. Our objective is to demonstrate that our proposed algorithm can calculate key measurements for fault diagnostic in machines as well as to provide fair and reliable forecasted outcomes. Keywords: Neutro-prime sets; neutro-prime topological spaces; neutro-prime interior; neutro-prime closure; neutro-prime absolute complement; decision making.
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