A Note on (i,j)-πgβ Closed Sets in Intuitionistic Fuzzy Bitopological Spaces
S. Jothimani,
T. Jenitha Premalatha
Issue:
Volume 2, Issue 2, March 2017
Pages:
14-19
Received:
22 April 2017
Accepted:
4 May 2017
Published:
27 June 2017
Abstract: In this paper we introduce the concept of (i,j)–πgβ-closed set in intuitionistic fuzzy bitopological spaces as a generalization of πgβ-closed set in fuzzy bitopological space and study their related notions in bitopological spaces. Next, we introduce (i,j)–πgβ- open sets in intuitionistic fuzzy bitopological spaces, and investigate some of their basic properties. Using these concepts, the characterizations for the intuitionistic fuzzy pairwise (i,j)–πgβ continuous mappings are obtained. The relationships between intuitionistic fuzzy pairwise (i,j)–πgβ continuous mappings are discussed. Finally, we prove the irresoluteness in (i,j)–πgβ intuitionistic fuzzy bitopological spaces.
Abstract: In this paper we introduce the concept of (i,j)–πgβ-closed set in intuitionistic fuzzy bitopological spaces as a generalization of πgβ-closed set in fuzzy bitopological space and study their related notions in bitopological spaces. Next, we introduce (i,j)–πgβ- open sets in intuitionistic fuzzy bitopological spaces, and investigate some of their ba...
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Calculation of the Riemann Zeta-function on a Relativistic Computer
Issue:
Volume 2, Issue 2, March 2017
Pages:
20-26
Received:
10 May 2017
Accepted:
20 May 2017
Published:
6 July 2017
Abstract: The problem of calculating the sum of a divergent series for the Riemann ζ-function of a complex argument is considered in the paper, using the effects of the general theory of relativity. The parameters of the reference frame metric in which the calculation is performed are determined and solutions of the relativistic equations of motion of the material point realizing the calculation are found. The work lies at the junction of the direction known as "Beyond Turing", considering the application of the so-called "relativistic supercomputers" for solving non-computable problems and a direction devoted to the study of non-trivial zeros of the Riemann ζ-function. The formulation of the Riemann hypothesis concerning the distribution of nontrivial zeros of the ζ-function from the point of view of their computability on a relativistic computer is given. In view of the importance of the latter issue for studying the distribution of prime numbers, the results of the work may be of interest to specialists in the field of information security.
Abstract: The problem of calculating the sum of a divergent series for the Riemann ζ-function of a complex argument is considered in the paper, using the effects of the general theory of relativity. The parameters of the reference frame metric in which the calculation is performed are determined and solutions of the relativistic equations of motion of the ma...
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