[4] **viXra:1306.0138 [pdf]**
*submitted on 2013-06-18 00:03:59*

**Authors:** Antonio Leon

**Comments:** 4 Pages.

In the year 1874 Cantor proved the set of rational numbers is denumerable. An immediate consequence of this result is the impossibility of non-countable partitions of the real line, also proved by Cantor in 1885. Inspired by Cantor 1874 and 1885 proofs, the following argument defines a partition of an interval of positive rational numbers whose successive parts are defined a la Cantor by means of the successive elements of an w-ordered sequence of positive rational numbers that contains all positive rational numbers. It is then proved each part of the partition contains positive rational numbers that are not members of the defining sequence.

**Category:** General Mathematics

[3] **viXra:1306.0032 [pdf]**
*submitted on 2013-06-06 10:22:14*

**Authors:** Arun S. Muktibodh

**Comments:** 7 Pages.

Shyam Sunder Gupta [3] has dened Smarandache consecutive and reversed
Smarandache sequences of triangular numbers. Delm F.M.Torres and Viorica Teca [1] have
further investigated these sequences and dened mirror and symmetric Smarandache sequences
of triangular numbers making use of Maple system. Working on the same lines we have de-
ned and investigated consecutive, reversed, mirror and symmetric Smarandache sequences
of pentagonal numbers of dimension 2 using the Maple system .

**Category:** General Mathematics

[2] **viXra:1306.0029 [pdf]**
*replaced on 2014-03-22 02:47:34*

**Authors:** A.S.Muktibodh, Y.M. Wagh

**Comments:** 4 Pages.

In this paper we have constructed two chains of semifields. All semifieids in the chains are Smarandache semifields.

**Category:** General Mathematics

[1] **viXra:1306.0009 [pdf]**
*submitted on 2013-06-03 11:24:12*

**Authors:** Jatin Patni

**Comments:** 4 Pages.

This paper introduces a sequence of real number that models a very frequently occurring natural pattern which is observed by everyone. The pattern it tries to model is the angle subtended on the eye of the observer standing at a distance from a long line of equally spaced objects. There are some interesting properties that are captured by this series. It finds a connection with modelling certain aspects of human psychology and can create interesting study areas like stock market price prediction, resource allocations, efficient search algorithms, time versus effort modelling etc.

**Category:** General Mathematics