[10] **viXra:1702.0330 [pdf]**
*submitted on 2017-02-27 12:42:03*

**Authors:** Edgar Valdebenito

**Comments:** 30 Pages.

Newton-Julia fractals and pi formulas

**Category:** General Mathematics

[9] **viXra:1702.0324 [pdf]**
*submitted on 2017-02-26 23:40:12*

**Authors:** Felix M. Lev

**Comments:** 10 Pages. Published in Physics of Particles and Nuclei Letters

Classical mathematics (involving such notions as infinitely small/large and continuity) is usually treated as fundamental while finite mathematics is treated as inferior which is used only in special applications. We first argue that the situation is the opposite: classical mathematics is only a degenerate special case of finite one and finite mathematics is more pertinent for describing nature than standard one. Then we describe results of a quantum theory based on finite mathematics. Implications for foundation of
mathematics are discussed.

**Category:** General Mathematics

[8] **viXra:1702.0239 [pdf]**
*submitted on 2017-02-19 05:54:26*

**Authors:** Sumera Naz, Hossein Rashmanlou, M. Aslam Malik

**Comments:** 29 Pages.

Single valued neutrosophic model as an instance of a neutrosophic model provide
an additional possibility to represent imprecise, uncertainty, inconsistent and incomplete information which exist in real situations. In this paper, the concept of energy
of a graph is introduced in the context of a single valued neutrosophic environment, where for each element the truth-membership, indeterminacy-membership
and falsity-membership degree, in [0, 1], are independently assigned. Firstly, the
novel concepts of energy of a single valued neutrosophic graph (SVNG) are proposed and their properties are investigated, then Laplacian energy of a SVNG is
introduced. Between the properties of energy and Laplacian energy of a SVNG,
there is a great deal of analogy, but also some significant differences.

**Category:** General Mathematics

[7] **viXra:1702.0238 [pdf]**
*submitted on 2017-02-18 14:00:18*

**Authors:** S. Naz, M. A. Malik, H. Rashmanlou

**Comments:** 18 Pages.

Interval-valued intuitionistic fuzzy set (IVIFS) as a generalization of intuitionistic fuzzy set (IFS) increase its elasticity drastically. In this paper, some important
types of interval-valued intuitionistic fuzzy graphs (IVIFGs) such as regular, irregular, neighbourly irregular, highly irregular and strongly irregular IVIFGs are
discussed. The relation among neighbourly irregular, highly irregular and strongly
irregular IVIFGs is proved. The notion of interval-valued intuitionistic fuzzy clique
(IVIFC) is introduced. A complete characterization of the structure of the IVIFC
is presented.

**Category:** General Mathematics

[6] **viXra:1702.0237 [pdf]**
*submitted on 2017-02-18 14:33:00*

**Authors:** S. Naz, S. Ashraf, H. Rashmanlou

**Comments:** 16 Pages.

Bipolar fuzzy set theory provides a basis for bipolar cognitive modeling and multiagent decision analysis, where in some situations, the product operator may be
preferred to the min operator, from theoretical and experimental aspects. In this
paper, the definition of product bipolar fuzzy graphs (PBFGs) is modified. The
concepts of product bipolar fuzzy multigraphs (PBFMGs), product bipolar fuzzy
planar graphs (PBFPGs) and product bipolar fuzzy dual graphs (PBFDGs) are
introduced and investigated. Product bipolar fuzzy planarity value of PBFPG is
introduced. The relation between PBFPG and PBFDG is also established. Isomorphism between PBFPGs is discussed. Finally, an application of the proposed
concepts is provided.

**Category:** General Mathematics

[5] **viXra:1702.0183 [pdf]**
*submitted on 2017-02-16 07:59:31*

**Authors:** Surapati Pramanik, Partha Pratim Dey, Bibhas C. Giri

**Comments:** 25 Pages.

This paper proposes hybrid vector similarity measures under single valued refined neutrosophic sets and proves some of its basic properties. The proposed similarity measure is then applied for solving multiple attribute decision making problems. Lastly, a numerical example of medical diagnosis is given on the basis of the proposed hybrid similarity measures and the results are compared with the results of other existing methods to validate the applicability, simplicity and effectiveness of the proposed method.

**Category:** General Mathematics

[4] **viXra:1702.0180 [pdf]**
*submitted on 2017-02-15 07:33:20*

**Authors:** Edgar Valdebenito

**Comments:** 8 Pages.

This note presents some formulas related with the elliptic integrals.

**Category:** General Mathematics

[3] **viXra:1702.0140 [pdf]**
*submitted on 2017-02-11 13:12:03*

**Authors:** Surapati Pramanik, Partha Pratim Dey, Bibhas C. Giri

**Comments:** 18 Pages.

Bipolar neutrosophic sets are the extension of neutrosophic sets and are based on the idea of positive and negative preferences of information. Projection measure is a useful apparatus for modeling real life decision making problems. In the paper, we have defined projection, bidirectional projection and hybrid projection measures between bipolar neutrosophic sets and the proposed measures are then applied to multi-attribute decision making problems. The ratings of performance values of the alternatives with respect to the attributes are expressed by bipolar neutrosophic values. We calculate projection, bidirectional projection, and hybrid projection measures between each alternative and ideal alternative with bipolar neutrosophic information and then all the alternatives are ranked to identify best option. Finally, a numerical example is provided to demonstrate the applicability and effectiveness of the developed method. Comparison analysis with other existing methods is also provided.

**Category:** General Mathematics

[2] **viXra:1702.0082 [pdf]**
*submitted on 2017-02-06 11:01:59*

**Authors:** C. A. Laforet

**Comments:** 3 Pages.

It is shown that the infinite tetration of Euler’s number is equal to any complex number. It is also found that starting with any complex number except 0 and 1, we can convert the complex number into an exponential with a complex exponent. If this is done recursively for each successive exponent, we find that the complex exponent converges to a constant number, which is named the Z-Exponential (Z_e). Derivatives for the Z-Exponential function are derived as well as its relationship to the exponential and natural logarithm.

**Category:** General Mathematics

[1] **viXra:1702.0050 [pdf]**
*submitted on 2017-02-03 11:54:49*

**Authors:** Edgar Valdebenito

**Comments:** 10 Pages.

In this note we briefly examine some elementary radical identities found in Ramanujan's work.

**Category:** General Mathematics