[11] **viXra:1804.0336 [pdf]**
*submitted on 2018-04-24 00:07:05*

**Authors:** Walter Gress

**Comments:** 2 Pages.

The behavior of vectors whence taken upon limits to infinity.

**Category:** General Mathematics

[10] **viXra:1804.0288 [pdf]**
*submitted on 2018-04-21 00:44:20*

**Authors:** Kishan Sharma

**Comments:** 7 Pages.

In the present paper, the author derived the results based on
q-Laplace transform of the K-Function introduced by Sharma[7]. Some
special cases of interest are also discussed.

**Category:** General Mathematics

[9] **viXra:1804.0287 [pdf]**
*submitted on 2018-04-21 00:47:59*

**Authors:** N.Vithya, P.Thangavelu

**Comments:** 8 Pages.

In this paper the notion of b#D-sets is introduced. Some weak separation axioms namely
b#
−Dk, b#
−R0, b#-R1 and b#-S0 are introduced and studied. Some lower separation axioms
are characterized by using these separation axioms.

**Category:** General Mathematics

[8] **viXra:1804.0225 [pdf]**
*submitted on 2018-04-16 07:54:40*

**Authors:** Edgar Valdebenito

**Comments:** 4 Pages.

This note presents continued radicals and trigonometric formulas for the argument 2npi/13, n=1,2,3,4,5,6.

**Category:** General Mathematics

[7] **viXra:1804.0195 [pdf]**
*submitted on 2018-04-14 11:41:48*

**Authors:** Claude Michael Cassano

**Comments:** 10 Pages.

This linear algebra technique provides a useful method of obtaining exact solutions to homogeneous linear ordinary differential equations. The Bessel half integer solutions, being long well known, have been used here to verify with confidence the above linear independence technique for solving ordinary differential equations. The Bessel second order LHODE has been used, here, as an example application of this vector space transformation technique. Clearly, it may be used on other non-general elementary second order LHODE, such as the Legendre, Laguerre, Hermite and other second order LHODE's. Using the two linearly independent solutions of a second order linear homogeneous ordinary differential equations insures that the two functions are linearly independent. However, any two linearly independent functions may be used, and the two resulting differential equations need not be the same, as was the case for the Bessel's above. In fact, clearly, the technique may also be used for higher order LHODE's, since there are N linearly independent solutions of an N-th order LHODE there would be an equal number of transformation equations.

**Category:** General Mathematics

[6] **viXra:1804.0173 [pdf]**
*submitted on 2018-04-12 14:33:36*

**Authors:** Yeray Cachón Santana

**Comments:** 11 Pages.

As far as I know, there is no a study on fractals on non euclidean metrics.This paper proposes a first approach method about generating fractals on a non-euclidean metric. The idea is to extend the calculus of fractals on non-euclidean metrics. Using the Riemann metric, there will be defined a non-euclidean modulo of a complex number in order to check the divergence of the series generated by the Mandelbrot set. It also shown that the
fractals are not invariant versus rotations. The study will be extended to the quaternions, where is shown that the study of fractals might not be extended to quaternions with a general metric because of the high divergence of the series (a condition in order to generate a fractal is selecting bounded operators). Finally, a Java program will be found as example to show those kind of fractals, where any metric can be defined, so it will be helpful to study those properties.

**Category:** General Mathematics

[5] **viXra:1804.0171 [pdf]**
*submitted on 2018-04-12 14:59:06*

**Authors:** Allen C. Conti

**Comments:** 1 Page. (c) Allen C. Conti 2015-2018

Possible solution to the Fermat Conjecture regarding other exponents satisfying the Pythagorus relationship. Solution uses algebraic substitution, logical deduction and modulus verification.

**Category:** General Mathematics

[4] **viXra:1804.0073 [pdf]**
*submitted on 2018-04-04 08:06:18*

**Authors:** Christophe Chalons

**Comments:** 8 Pages.

Papier décrivant des procédés usant abusivement du mot science et qui met en garde

**Category:** General Mathematics

[3] **viXra:1804.0066 [pdf]**
*submitted on 2018-04-04 15:53:11*

**Authors:** Franco Sabino Stoianoff Lindstron

**Comments:** 3 Pages.

This paper shows, for the first time, that the explicit and exact solution to the Troesch nonlinear twopoint
boundary value problem may be computed in a direct and straightforward fashion from the
general solution obtained by a generalized Sundman transformation for the related differential
equation, which appeared to be a special case of a more general equation. As a result, various initial
and boundary value problems may be solved explicitly and exactly.

**Category:** General Mathematics

[2] **viXra:1804.0015 [pdf]**
*submitted on 2018-04-02 07:53:08*

**Authors:** Edgar Valdebenito

**Comments:** 3 Pages.

This note presents some formulas of pi in terms of sum of arctangents.

**Category:** General Mathematics

[1] **viXra:1804.0001 [pdf]**
*replaced on 2018-04-16 19:32:29*

**Authors:** Koji KOBAYASHI

**Comments:** 15 Pages.

This paper describes about relation between circuit complexity and accept inputs structure in Hamming space by using almost all monotone circuit that emulate deterministic Turing machine(DTM).
Circuit family that emulate DTM are almost all monotone circuit family except some NOT-gate which connect input variables (like negation normal form (NNF)). Therefore, we can analyze DTM limitation by using this NNF Circuit family. NNF circuit family cannot compute sandwich structure effectively (Sandwich structure is two accept inputs that sandwich reject inputs in Hamming space). So NNF circuit have to use unique AND-gate to identify each different vector of sandwich structure. That is, we can measure problem complexity by counting different vectors.
Some dicision problem have characteristic in sandwich structure. Different vectors of Negate HornSAT prob- lem are at most constant length because we can delete constant part of each negative literal in Horn clauses by using definite clauses. Therefore, number of these different vector is at most polynomial size. The other hand, we can design problem with coding theory. For the example, we design new problem by using linear coding which expand vector space.

**Category:** General Mathematics