[7] **viXra:0902.0007 [pdf]**
*replaced on 2013-02-12 01:04:20*

**Authors:** Teimuraz Bregadze

**Comments:** 8 Pages.

Spherical wave vs. plane wave approximation to the nature of the electromagnetic waves in regard to the Doppler shift and aberration is considered. The first approach is free from the blueshift – redshift transition paradox innate for the second one. For spherical electromagnetic waves, in contrast with the plane ones, we have to assume that not only the magnitude, but also the direction of the light velocity is the same in any inertial frame, which leads to the accepted expression for time dilation. The rest frame of the source of electromagnetic waves is unique among all inertial frames (in it the angles of emission and reception coincide, and there is no shift in wavelength in all directions). The spherical approximation to electromagnetic waves preserves this uniqueness without violating the principle of relativity of the uniform motion, while the planar approximation ignores the source completely. Both approximations give the same expression of the Lorentz–FitzGerald contraction. Both spherical and planar approaches give the same Doppler shift in the directions of the relative motion of the frames, but in the directions with perpendicular components there may be significant differences. A geometrical picture of the transformation of wavefronts of spherical electromagnetic waves, which differs from the one according to the Lorentz transformation, is suggested.

**Category:** Relativity and Cosmology

[6] **viXra:0902.0006 [pdf]**
*submitted on 14 Feb 2009*

**Authors:** Jaiyeola Temitope Gbolahan

**Comments:** recovered from sciprint.org

A Study Of New Concepts In Smarandache Quasigroups And Loops

**Category:** Algebra

[5] **viXra:0902.0005 [pdf]**
*submitted on 14 Feb 2009*

**Authors:** Akito Takahashi

**Comments:** recovered from sciprint.org

This paper gives the follow-up study on the basics for our previous papers, Study on
4D/Tetrahedral Symmetric Condensate Condensation Motion by Non-Linear Langevin Equation,
Symposium 998-Low Energy Nuclear Reactions Source Book, ACS, published on August 2008
from Oxford University Press.
Pertaining to the quantum mechanics, the basics of new approach using the stochastic
differential equation (Langevin equation) is written for quantifying dynamic motion of
known molecules as D_{2}^{+}, D_{2} and D_{3}^{+}
as well as D-atom state. The role of the Platonic
symmetry in these known molecules are discussed for deducing simple one-dimensional
(R_{dd} dependent; here R_{dd} is distance between nearest d-d pair) Langevin equation and
making quantum-mechanical ensemble averaging to obtain equation for expectation value.
The methodology is applied for more complicated D-clusters as 4D/TSC and 6D/OSC which
would keep the Platonic symmetry, by introducing the force fluctuation deviating from
the ideal Platonic symmetry. Time-dependent TSC and OSC trapping potentials which take
balance to getting back to the Platonic symmetry from the distorted states were defined
and used for numerical solution of Langevin equation. Finally, time-dependent fusion
rate formula for simultaneous 4D interaction was obtained based on the Fermi's golden
rule and one-pion exchange potential of strong interaction. The 4D fusion is regarded to
cause radiation-less excess heat and ^{4}He ash in metal-deuterium systems under dynamic conditions

**Category:** Condensed Matter

[4] **viXra:0902.0004 [pdf]**
*submitted on 14 Feb 2009*

**Authors:** Akito Takahashi, Norio Yabuuchi

**Comments:** recovered from sciprint.org

Tetrahedral symmetric condensate (TSC) with 4 deuterons and 4 electrons has been proposed as
a seed of clean 4D fusion with 4He product in condensed matter. To solve molecular dynamics
motion of 4D/TSC condensation, a nonlinear Langevin equation was formulated with a Coulombic
main condensation force term under Platonic symmetry, 6 balancing forces by quantum mechanical
electron clouds of dde*(2,2) EQPET molecules on 6 faces of TSC cube and a random quantum
mechanical fluctuation term f(t) for d-d distance. Gaussian wave functions for d-d pairs and
their ground state energies were first obtained by variational method, for D2 and EQPET molecules.
Then same sigma-value was used for time-dependent Gaussian wave functions of d-d pairs of TSC
system to calculate the ensemble-averaged <f(t)> for changes of Coulomb energy and force of
distorted TSC system deviated from the ideal double Platonic symmetry. Molecular dynamics
calculation with TSC Langevin equation by the Verlet time-step method was then done. We
obtained mean relative final-stage d-d kinetic energy 13.68 keV with -130.4 keV deep trapping
TSC potential at Rdd-minimum = 25 fm and time-to-TSC-minimum =1.4007 fs. Mean kinetic energy
of electron of a "d-e-d-e" EQPET molecule of TSC system was estimated as 57.6 keV at Rdd =25
fm. These time-dependent trapping potential for d-d pair of TSC can be approximated by HMEQPET
potentials with the empirical relation of m=4.36x10^{4}/R_{dd}, (Rdd in fm unit), continuously as a
change of condensation time or Rdd(t). Barrier factors for fusion reactions as a function of
Rdd(t) and 4D fusion rate per TSC generation were calculated using these HMEQPET potentials
and Fermi's golden rule. We found that 4D/TSC got to the TSC-minimum state with 10 fm-20 fm
radius in 1.4007 fs and 4D fusion rate was 100 % per 4D/TSC generation-condensation. Thus we
concluded that 4He production rate by 4D/TSC was equal to two times of 4D/TSC generation rate
in condensed matter (e.g., PdDx).

**Category:** Condensed Matter

[3] **viXra:0902.0003 [pdf]**
*submitted on 14 Feb 2009*

**Authors:** Akito Takahashi

**Comments:** recovered from sciprint.org

This paper gives further discussions and explanations on the timedependent
quantum-mechanical behaviors of electron-clouds in 4D/TSC
condensation motion by Langevin equation, in comparison with steady
ground state electron orbits and their de Broglie wave lengths for D-atom
and D_{2} molecule.

**Category:** Condensed Matter

[2] **viXra:0902.0002 [pdf]**
*submitted on 13 Feb 2009*

**Authors:** Fu Yuhua, Fu Anjie, Zhao Ge

**Comments:** recovered from sciprint.org

According to the viewpoints of "one divides into two", "one divides into three" (e.g. Neutrosophy)
and "one divides into many", at present there exist six kinds of matter in the universe altogether
(one divides into six). If there exists the ordinary matter (called matter for short), there must
exist its opposite. However there may exist more than one kind of its opposite, today the known
opposites of matter may be the antimatter and dark matter; Other three kinds of matter are the neutral
ones: the first neutral matter between matter and antimatter (Prof. Smarandache named it unmatter),
the second neutral matter between matter and dark matter, and the third neutral matter between
antimatter and dark matter. Similarly, if there exists the original "law of universal gravitation"
(positive law of universal gravitation), there must exist its opposites (negative laws of universal
gravitation), and the neutral ones (neutral laws of universal gravitation). According to this
analysis, it is impossible to find the unified and ultimate gravitational theory.

**Category:** Relativity and Cosmology

[1] **viXra:0902.0001 [pdf]**
*submitted on 6 Feb 2009*

**Authors:** José Francisco García Juliá

**Comments:** recovered from sciprint.org

The gravitational redshift might explain any case of light redshift.

**Category:** Relativity and Cosmology