[9] **viXra:1809.0249 [pdf]**
*submitted on 2018-09-11 06:07:48*

**Authors:** Vu B Ho

**Comments:** 33 Pages.

In this work, by summarising our recent works on the differential geometric and topological structures of quantum particles and spacetime manifold, we discuss the possibility to classify quantum particles according to their intrinsic geometric structures associated with differentiable manifolds that are solutions to wave equations of two and three dimensions. We show that fermions of half-integer spin can be identified with differentiable manifolds which are solutions to a general two-dimensional wave equation, in particular, a two-dimensional wave equation that can be derived from Dirac equation. On the other hand, bosons of integer spin can be identified with differentiable manifolds which are solutions to a general three-dimensional wave equation, in particular, a three-dimensional wave equation that can be derived from Maxwell field equations of electromagnetism. We also discuss the possibility that being restricted to three-dimensional spatial dimensions we may not be able to observe the whole geometric structure of a quantum particle but rather only the cross-section of the manifold that represents the quantum particle and the space in which we are confined. Even though not in the same context, such view of physical existence may comply with the Copenhagen interpretation of quantum mechanics which states that the properties of a physical system are not definite but can only be determined by observations.

**Category:** Mathematical Physics

[8] **viXra:1809.0244 [pdf]**
*submitted on 2018-09-11 11:49:24*

**Authors:** Timoteo Briet Blanes

**Comments:** 51 Pages.

CFD STUDY OF PIKES PEAK RACE CAR 2017.

**Category:** Mathematical Physics

[7] **viXra:1809.0232 [pdf]**
*submitted on 2018-09-12 01:58:30*

**Authors:** Antonio Puccini

**Comments:** 8 Pages.

The Electron Capture(EC) is a peculiar phenomenon that unstable atoms can use to become more stable. During EC, an electron(e) in an atom's inner shell is drawn into the nucleus where it combines with a proton(P), forming a neutron(N) and a neutrino():
P + e N + (1).
Electrons are usually captured from the inner K layer, leaving 'holes' process or Auger’s es. Such a capture may also leave the nucleus in an excited state, causing it to release γ rays.
This emission of highly energetic electro-magnetic radiation(EMR), generally originates the production of pairs of light particles:
γ e + e+(2),
or:γ + ῡ(3),
where ῡ is an anti-neutrino.
Yet, if this phenomenon of materialization of the EMR that accompanies the EC, manifesting in the production of lepton pairs(described in this case by the Eq.3), was represented in the equation describing the EC, we could better justify that appeared ex abrupto in Eq.(1).
Therefore, taking into account also the EMR(γ) emitted at the time of the EC, and inserting it in
Eq.(1) on the side of the captured e, we have:
P + e + γ P + e + ῡe.+ e N + e(4),
that is:P + e + ῡe.+ e ↔ N + e(5).
However, as the e mass is considered 2eV, Eq,(1) and (5) show a conspicuous mass gap problem, since according to Pauli and Fermi the proposed to compensate for the mass gap of the N decay must have the same mass of e. Unless one wishes to hypothesize the existence of the neutral electron(e°). In this case, Eq.(5) should be rewritten as follows:
P + e + ē° + e° ↔ N + e°(6).

**Category:** Mathematical Physics

[6] **viXra:1809.0192 [pdf]**
*submitted on 2018-09-11 02:27:48*

**Authors:** Timoteo Briet Blanes

**Comments:** 41 Pages.

Vehicles running at high speed are greatly influenced by their aerodynamic profile. Racing car teams strive to tune the setup seeking higher levels of downforce aerodynamic load. Wind tunnel tests or track data for specific vehicle positions are useful but incomplete and very expensive. Transient loads on the vehicle come from very different sources and, to date, there is no established methodology to take them into consideration. Computer simulation seems to be a good starting point to study the effect of transient aerodynamic loads in the design and optimization of the tuning of the suspension of a racing car.
This paper studies the effect of transient aerodynamic loads on the downforce of a vehicle. Heave vibrations on an aileron are analyzed on a simulation model. The data obtained in this simulation model are validated both in a steady and a transient state for different frequencies (1-800Hz). These results lead to the obtainment of a transfer function for the downforce on the aileron in question. Finally, a new quarter car model including aerodynamic effects from these studies is presented and some results on the influence of heave transient aerodynamics loads on a racing car are obtained.

**Category:** Mathematical Physics

[5] **viXra:1809.0191 [pdf]**
*submitted on 2018-09-11 02:30:13*

**Authors:** Timoteo Briet Blanes

**Comments:** 57 Pages.

The performance of an F1 race car is greatly influenced by its aerodynamics. Race teams try to improve the vehicle performance by aiming for more levels of downforce. A huge amount of time is spent in wind tunnel and track testing. Typical wind tunnel testing is carried out in steady aerodynamic conditions and with car static configurations. However, the ride heights of a car are continuously changing in a race track because of many factors.
These are, for example, the roughness and undulations of the track, braking, accelerations, direction changes, aerodynamic load variations due to varying air speed and others. These factors may induce movements on suspensions components (sprung and unsprung masses) at different frequencies and may cause aerodynamic fluctuations that vary tires grip. When the frequency of the movement of a race car is high enough the steady aerodynamic condition and the car static configurations are not fulfilled. Then, transient effects appear and the dynamics of the system changes:
heave, pitch and roll transient movements of the sprung mass affect both downforce and center of pressure position. The suspension system have to cope with them, but in order for the suspension to be effective, unsteady aerodynamics must be considered.
The main objective is to model the effects of unsteady aerodynamics and know really the car dynamic, with the aim of optimizing the suspension performance, improving tire grip and finally reducing lap times.

**Category:** Mathematical Physics

[4] **viXra:1809.0088 [pdf]**
*submitted on 2018-09-04 13:57:14*

**Authors:** Biruk Alemayehu Petros

**Comments:** 3 Pages. millenium prize problem counter example.

Abstract
Due to the existence of huge number of different information on Navier_Stokes equation on internet, introduction and method used to come to the following solution is less important than the solution its self. As a result the paper shows the periodic solution for Navier_Stokes equations. All conditions for physically reasonable solution as posted by clay mathematics institute is fulfilled. The following solution is counter example for existence of smooth unique periodic solution.

**Category:** Mathematical Physics

[3] **viXra:1809.0069 [pdf]**
*submitted on 2018-09-05 07:50:31*

**Authors:** Spiros Konstantogiannis

**Comments:** 16 Pages.

We present a method of constructing complex PT-symmetric sextic oscillators using quotient polynomials and we apply it to derive complex oscillators from real quotient polynomials.

**Category:** Mathematical Physics

[2] **viXra:1809.0061 [pdf]**
*submitted on 2018-09-03 13:36:10*

**Authors:** Andrey Gomes Martins, R.V. Lobato, G.A. Carvalho, A.P.N. Cronemberger

**Comments:** 5 Pages.

We formulate and solve the problem of boundary values in non-relativistic quantum mechanics in non-commutative boundary spaces-times. The formalism developed can be useful to the formulation of the boundary value problem in in
Noncommutative Quantum Mechanics

**Category:** Mathematical Physics

[1] **viXra:1809.0052 [pdf]**
*submitted on 2018-09-04 01:22:36*

**Authors:** Jack Bidnik

**Comments:** Pages.

Abstract
© US 2015
Gravitational Periodicity from Special Relativity by Jack Bidnik
This is my derivation of the sinusoidal variation of planetary orbits by means of relativistic relative momentum of two masses. It may be considered Chapter 3 of my paper Gravitational Forces Revisited (GFR), http://vixra.org/abs/1707.0128
where I derived a force, Fm, which I analogized to Newton's force of gravity by the equation
Fm = Gs Mm /r^2, where Gs is a velocity dependent variable.
Here I derive the same force, but I use a separate method to show that it is the force of gravity. This chapter can be seen as a completely independent, stand alone, method of deriving gravity from Special Relativity, and that Fm is both a necessary and a sufficient condition for the gravitational force.

**Category:** Mathematical Physics