[7] **viXra:1712.0636 [pdf]**
*replaced on 2018-07-28 17:16:01*

**Authors:** Waldemar Zieliński

**Comments:** Pages.

Let A, B denote arithmetic progressions with initial terms equal to 0. The union of A, B is sequence U, containing all elements of A, B without repetitions. We will derive the formula for the n-th element of the union U(A,B)=(u_n) in the form: u_n=f(n,a,b).
The continuations of this paper are available in:
http://vixra.org/author/waldemar_zielinski

**Category:** General Mathematics

[6] **viXra:1712.0486 [pdf]**
*submitted on 2017-12-17 06:23:16*

**Authors:** Martin Nicholson

**Comments:** 9 Pages.

Several infinite products are studied along with their finite counterparts. For certain values of the parameters these infinite products reduce to modular forms. The finite product formulas give an elementary proof of a particular modular transformation.

**Category:** General Mathematics

[5] **viXra:1712.0392 [pdf]**
*submitted on 2017-12-11 16:58:18*

**Authors:** Gergő Cosmin Tudor Jr.

**Comments:** 14 Pages.

ABSTARCT:
Following recent development in http://vixra.org/abs/1712.0372 , we propose
scientific paper of three parts.
1. We proove strengh of freindship letter proof method
2. Proof of F. Smarandache mathematial skill via S. Wolfram method
3. Th

**Category:** General Mathematics

[4] **viXra:1712.0131 [pdf]**
*submitted on 2017-12-06 01:33:15*

**Authors:** Kohji Suzuki

**Comments:** 9 Pages.

Attempting to abstract exterior derivative and Hodge star operator, we discuss two number systems sketchily.

**Category:** General Mathematics

[3] **viXra:1712.0123 [pdf]**
*replaced on 2018-10-09 08:01:02*

**Authors:** Timothy W. Jones

**Comments:** 8 Pages. This draft adds screen captures.

Code is given for complete, exact solutions of quadratic polynomials using the TI-83 family of calculators.

**Category:** General Mathematics

[2] **viXra:1712.0121 [pdf]**
*submitted on 2017-12-04 08:35:04*

**Authors:** Liu Ran

**Comments:** 3 Pages.

芝诺悖论的前提假设，抽象模型不一致导致的混乱。

**Category:** General Mathematics

[1] **viXra:1712.0111 [pdf]**
*submitted on 2017-12-04 21:59:05*

**Authors:** D Williams

**Comments:** 8 Pages.

Some examples are given of very counterintuitive results from betting on a tossed fair coin. Various betting schemes are examined and a preliminary partial classification scheme produced. A call is made for more research with a list of things that are needed.

**Category:** General Mathematics