[8] **viXra:1906.0485 [pdf]**
*submitted on 2019-06-25 08:38:38*

**Authors:** Edgar Valdebenito

**Comments:** 2 Pages.

We give a formula for Pi.

**Category:** Algebra

[7] **viXra:1906.0475 [pdf]**
*submitted on 2019-06-26 01:58:32*

**Authors:** Han Xiao

**Comments:** 19 Pages.

Traditionally, an infinitesimal is regarded as a variable that runs toward 0. Since a differential is a kind of infinitesimal, a differential is essentially a variable running toward 0 too. As a result, differentials are form invariant but not meaning invariant. This paper proposes a Number Field of Ordered Infinitesimals and Infinities (OII Number Field) which can be seen as a kind of extension of real number field. The terminus of a variable running toward 0 is no longer 0, but a point in the OII Number Field, with an Order and a Weight. In this way, the process of running is recorded in the destination, making infinitesimals a kind of number which can be compared and operated easily. On this basis, the differential of a variable is invariant not only in form, but also in meaning. As a differential becomes a variable on another number axis parallel to the real number axis in OII Number Field, a differential can generate differential too, thus giving rise to high order differentials which are also invariant both in form and in meaning.

**Category:** Algebra

[6] **viXra:1906.0447 [pdf]**
*replaced on 2019-06-25 14:27:50*

**Authors:** Ajda Foˇsner, Mehsin Jabel Atteya

**Comments:** 22 Pages.

The main purpose of this paper is to study and investigate certain results concerning the (σ,τ)-generalized derivation D associated with the (σ,τ)-derivation d of semiprime and prime rings R, where σ and τ act as two automorphism mappings of R. We focus on the composition of (σ,τ)-generalized derivations of the Leibniz’s formula, where we introduce the general formula to compute the composition of the (σ,τ)-generalized derivation D of R.

**Category:** Algebra

[5] **viXra:1906.0343 [pdf]**
*submitted on 2019-06-18 09:09:35*

**Authors:** Henry Wong

**Comments:** 1 Page.

An addendum to group theory.

**Category:** Algebra

[4] **viXra:1906.0304 [pdf]**
*replaced on 2019-08-17 10:29:26*

**Authors:** Anamitra Palit

**Comments:** 2 Pages.

The short writing seeks to demonstrate certain lapses in the theory of the linear vector spaces.

**Category:** Algebra

[3] **viXra:1906.0145 [pdf]**
*submitted on 2019-06-09 22:32:11*

**Authors:** Henry Wong

**Comments:** 2 Pages.

An addendum to group theory.

**Category:** Algebra

[2] **viXra:1906.0120 [pdf]**
*submitted on 2019-06-07 08:34:30*

**Authors:** Edgar Valdebenito

**Comments:** 3 Pages.

We give some roots of the equation: 8*x*x*(cos(x))*(cos(x))-(4-2*sqrt(2))*x*x-1=0.

**Category:** Algebra

[1] **viXra:1906.0002 [pdf]**
*submitted on 2019-06-01 04:49:44*

**Authors:** Henry Wong

**Comments:** 1 Page.

An addendum to group theory.

**Category:** Algebra