scholarly journals Quaternionic Serret-Frenet Frames for Fuzzy Split Quaternion Numbers

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Cansel Yormaz ◽  
Simge Simsek ◽  
Serife Naz Elmas
Keyword(s):  
Natural Extension ◽  
Frenet Frame ◽  
Real Numbers ◽  
Split Quaternion ◽  
Geometric Properties ◽  
Split Quaternions ◽  
Fuzzy Real Numbers

We build the concept of fuzzy split quaternion numbers of a natural extension of fuzzy real numbers in this study. Then, we give some differential geometric properties of this fuzzy quaternion. Moreover, we construct the Frenet frame for fuzzy split quaternions. We investigate Serret-Frenet derivation formulas by using fuzzy quaternion numbers.

scholarly journals Nörlund and Riesz mean of sequences of fuzzy real numbers

2010 ◽  
Vol 23 (5) ◽  
pp. 651-655 ◽  
Author(s):  
Binod Chandra Tripathy ◽  
Achyutananda Baruah
Keyword(s):  
Real Numbers ◽  
Riesz Mean ◽  
Fuzzy Real Numbers

scholarly journals ON I-ACCELERATION CONVERGENCE OF SEQUENCES OF FUZZY REAL NUMBERS

2012 ◽  
Vol 17 (4) ◽  
pp. 549-577 ◽  
Author(s):  
Amar Jyoti Dutta ◽  
Binod Chandra Tripathy
Keyword(s):  
Decomposition Theorem ◽  
Real Numbers ◽  
Different Types ◽  
Fuzzy Real Numbers ◽  
Convergence Of Sequences

In this article we introduce the notion of ideal acceleration convergence of sequences of fuzzy real numbers. We have proved a decomposition theorem for ideal acceleration convergence of sequences as well as for subsequence transformations and studied different types of acceleration convergence of fuzzy real valued sequence.

scholarly journals Some Double Sequence Spaces of Fuzzy Real Numbers of Paranormed Type

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Bipul Sarma
Keyword(s):  
Double Sequence ◽  
Sequence Spaces ◽  
Real Numbers ◽  
Double Sequence Spaces ◽  
Fuzzy Real Numbers ◽  
Sequence Algebra ◽  
Inclusion Results

We study different properties of convergent, null, and bounded double sequence spaces of fuzzy real numbers like completeness, solidness, sequence algebra, symmetricity, convergence-free, and so forth. We prove some inclusion results too.

scholarly journals Canonical Set Theory for Classic Mathematics: A Linear Order on Finite Groups and Structures, with A Natural Extension To Infinite Structures

2021 ◽  
Author(s):  
Juan Pablo Ramírez
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Linear Order ◽  
Natural Extension ◽  
Natural Numbers ◽  
Real Numbers ◽  
Tree Structures ◽  
Mathematical Objects ◽  
Finite Group Theory ◽  
Block Form

We provide an axiomatic base for the set of natural numbers, that has been proposed as a canonical construction, and use this definition of $\mathbb N$ to find several results on finite group theory. Every finite group $G$, is well represented with a natural number $N_G$; if $N_G=N_H$ then $H,G$ are in the same isomorphism class. We have a linear order on all finite groups, that is well behaved with respect to cardinality. In fact, if $H,G$ are two finite groups such that $|H|=m<n=|G|$, then $H<\mathbb Z_n\leq G$. Internally, there is also a canonical order for the elements of any finite group $G$, and we find equivalent objects. This allows us to find the automorphisms of $G$. The Cayley table of $G$ takes canonical block form, and a minimal set of independent equations that define the group is obtained. Examples are given, using all groups with less than ten elements, to illustrate the procedure for finding all groups of $n$ elements, and we order them externally and internally. The canonical block form of the symmetry group $\Delta_4$ is given and we find its automorphisms. These results are extended to the infinite case. A real number is an infinite set of natural numbers. A real function is a set of real numbers, and a sequence of real functions $f_1,f_2,\ldots$ is well represented by a set of real numbers, also. We make brief mention on the calculus of real numbers. In general, we are able to represent mathematical objects using the smallest possible data-type. In the last section, mathematical objects of all types are well assigned to tree structures. We conclude with comments on type theory and future work on computational and physical aspects of these representations.

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