[8] **viXra:1701.0617 [pdf]**
*replaced on 2017-05-18 05:57:40*

**Authors:** Ilya Chernykh

**Comments:** 11 Pages. Now in English

We propose an extension of real numbers which reveals a surprising algebraic role of Bernoulli numbers, Hurwitz Zeta function, Euler-Mascheroni constant as well as generalized summations of divergent series and integrals. We extend elementary functions to the proposed numerical system and analyze some symmetries of the special elements. This reveals intriguing closed-form relations between trigonometric and inverse trigonometric functions. Besides this we show that the proposed system can be naturally used as a cardinality measure for fine comparison between infinite countable sets in metric space which respects the intuitive notion of the set's size.

**Category:** Functions and Analysis

[7] **viXra:1701.0511 [pdf]**
*submitted on 2017-01-15 16:19:44*

**Authors:** Stephen C. Pearson.

**Comments:** 42 Pages.

This particular submission contains a copy [PART 5/6] of the author's original paper and is therefore a continuation of his previous submission, namely - "An Introduction to Functions of a Quaternion Hypercomplex Variable - PART 4/6", which has been published under the 'VIXRA' Mathematics subheading:- 'Functions and Analysis'.

**Category:** Functions and Analysis

[6] **viXra:1701.0510 [pdf]**
*submitted on 2017-01-15 17:01:34*

**Authors:** Stephen C. Pearson.

**Comments:** 24 Pages.

This particular submission contains a copy [PART 6/6] of the author's original paper and is therefore a continuation of his previous submission, namely - "An Introduction to Functions of a Quaternion Hypercomplex Variable - PART 5/6", which has been published under the 'VIXRA' Mathematics subheading:- 'Functions and Analysis'.

**Category:** Functions and Analysis

[5] **viXra:1701.0505 [pdf]**
*submitted on 2017-01-15 14:34:25*

**Authors:** Stephen C. Pearson.

**Comments:** 42 Pages.

This particular submission contains a copy [PART 3/6] of the author's original paper and is therefore a continuation of his previous submission, namely - "An Introduction to Functions of a Quaternion Hypercomplex Variable - PART 2/6", which has been published under the 'VIXRA' Mathematics subheading:- 'Functions and Analysis'.

**Category:** Functions and Analysis

[4] **viXra:1701.0504 [pdf]**
*submitted on 2017-01-15 15:44:13*

**Authors:** Stephen C. Pearson.

**Comments:** 42 Pages.

This particular submission contains a copy [PART 4/6] of the author's original paper and is therefore a continuation of his previous submission, namely - "An Introduction to Functions of a Quaternion Hypercomplex Variable - PART 3/6", which has been published under the 'VIXRA' Mathematics subheading:- 'Functions and Analysis'.

**Category:** Functions and Analysis

[3] **viXra:1701.0502 [pdf]**
*submitted on 2017-01-15 11:15:18*

**Authors:** Stephen C. Pearson.

**Comments:** 42 Pages.

This particular submission contains (inter alia) a copy [PART 1/6] of the author's original paper, which was completed on 31st March 1984 and thus comprises a total of 161 handwritten foolscap pages. Subsequently, its purpose is to enunciate various definitions and theorems, which pertain to the following topics, i.e. (a) the algebra of quaternion hypercomplex numbers; (b) functions of a single quaternion hypercomplex variable; (c) the concepts of limit and continuity applied to such functions; (d) the elementary principles of differentiation and integration applied to quaternion hypercomplex functions. Many of the concepts presented therein are analogous to well established notions from real and complex variable analysis with any divergent results being due to the non-commutativity of quaternion products.

**Category:** Functions and Analysis

[2] **viXra:1701.0501 [pdf]**
*submitted on 2017-01-15 12:58:04*

**Authors:** Stephen C. Pearson.

**Comments:** 42 Pages.

This particular submission contains a copy [PART 2/6] of the author's original paper and is therefore a continuation of his previous submission, namely - "An Introduction to Functions of a Quaternion Hypercomplex Variable - PART 1/6", which has been published under the 'VIXRA' Mathematics subheading:- 'Functions and Analysis'.

**Category:** Functions and Analysis

[1] **viXra:1701.0324 [pdf]**
*submitted on 2017-01-08 04:19:38*

**Authors:** Adam Chmaj

**Comments:** 6 Pages. Original 2014 version of the result is posted here. Some minor corrections are left to the reader.

The existence of traveling waves for the fractional Burgers equation is established, using an operator splitting trick. This solves a 1998 open problem.

**Category:** Functions and Analysis