[7] **viXra:1707.0249 [pdf]**
*submitted on 2017-07-18 12:52:38*

**Authors:** Ulrich E. Bruchholz, Horst Eckardt

**Comments:** 19 Pages.

The well known numerical method of approximating differential
quotients by quotients of differences is used in a novel context.
This method is commonly underestimated, wrongly.
The method is explained by an ordinary differential equation first.
Then it is demonstrated how this simple method
proves successful for non-linear field equations with chaotic
behaviour. Using certain discrete values of their integration constants,
a behaviour comparable with Mandelbrot sets is obtained.
Instead of solving the
differential equations directly, their convergence behaviour is analyzed.
As an example the Einstein-Maxwell equations are investigated,
where discrete
particle quantities are obtained from a continuous theory, which is possible
only by this method.
The special set of integration constants contains values identical with
particle characteristics.
Known particle values are confirmed, and unknown values can be predicted.
In this paper, supposed neutrino masses are presented.

**Category:** Geometry

[6] **viXra:1707.0242 [pdf]**
*submitted on 2017-07-17 13:20:25*

**Authors:** Edgar Valdebenito

**Comments:** 4 Pages.

In this note we briefly examine the curve: x^3+y^3=sqrt(2)*x*y

**Category:** Geometry

[5] **viXra:1707.0181 [pdf]**
*submitted on 2017-07-12 20:58:33*

**Authors:** Pan Zhang

**Comments:** 14 Pages.

Let $V$ be an asymptotically cylindrical K\"{a}hler manifold with asymptotic
cross-section $\mathfrak{D}$. Let $E_\mathfrak{D}$ be a stable Higgs bundle over $\mathfrak{D}$, and $E$ a Higgs bundle over $V$ which is asymptotic to
$E_\mathfrak{D}$. In this paper, using the continuity method of Uhlenbeck and Yau, we prove that there exists an asymptotically translation-invariant Hermitian projectively Hermitian Yang-Mills metric on $E$.

**Category:** Geometry

[4] **viXra:1707.0046 [pdf]**
*submitted on 2017-07-04 11:58:48*

**Authors:** Antoine Balan

**Comments:** 2 pages, written in french

A Laplacian operator is defined bound to a riemannian manifold with a pseudo-complex structure.

**Category:** Geometry

[3] **viXra:1707.0011 [pdf]**
*submitted on 2017-07-01 08:14:34*

**Authors:** John Atwell Moody

**Comments:** 17 Pages. written September 2014

When a meromorphic vector field is given on the projective plane, a complete holomorphic limit cycle, because it is a closed singular submanifold of projective space, is defined by algebraic equations. Also the meromorphic vector field is an algebraic object. Poincare had asked, is there just an algebraic calculation leading from the vector field to the defining equations of the solution, without the
mysterious intermediary of the dynamical system.
The answer is yes, that there is nothing more mysterious or wonderful that happens when a complete holomorphic limit cycle is formed than could have been defined using algebra.

**Category:** Geometry

[2] **viXra:1707.0010 [pdf]**
*submitted on 2017-07-01 08:17:31*

**Authors:** John Atwell Moody

**Comments:** Pages.

Contents:

Analytic primality testing 1

Lefshetz numbers of modular curves 23

Grothendieck sections and rational points of modular curves 29

Rational points of modular curves 33

Conclusion about modular forms 41

Outline geometric proof of Mordell’s conjecture 48

Example:the Fermat curves

63 The residue calculation 69

The meaning of positive and negative 81

**Category:** Geometry

[1] **viXra:1707.0009 [pdf]**
*submitted on 2017-07-01 08:21:26*

**Authors:** John Atwell Moody

**Comments:** Pages.

Contents

Projective toric varieties

Divisors

Maps

Chow ring

Fourier series and generalizations

**Category:** Geometry