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Articles Title
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Abstract
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1
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Editorial Notes
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2
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Primordial Gravity's Breath
Christian Corda
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In a
recent paper the Laser Interferometer Gravitational-wave Observatory (LIGO)
Scientific Collaboration (LSC) obtained an upper limit on the stochastic
gravitational-wave background (SGWB) of cosmological origin by using the
data from a two-year science run of the LIGO. Such an upper limit rules out
some models of early Universe evolution, like the ones with relatively
large equation-of-state parameter and the cosmic (super) string models with
relatively small string tension arising from some String Theory's models.
This was also an upper limit for the SGWB which is proposed by the
Pre-Big-Bang Theory. Another upper bound on the SGWB which is proposed by
the Standard Inflationary Model is well known and often updated by using
the Wilkinson Microwave Anisotropy Probe (WMAP) data. By using a conformal
treatment, which represents a variation of early works, we release a
formula that directly connects the average amplitude of the SGWB with the Inflaton field in the Standard Inflationary Scenario of
General Relativity and an external Inflaton
field. Then, by joining this formula with the equation for the characteristic
amplitude h_{c} for the SGWB, the upper bounds on the SGWB from the WMAP
and LSC data will be translated in lower bounds on the Inflaton
field. The results show that the value of the Inflaton
field that arises from the WMAP bound on the SGWB is totally consistent
with the famous slow roll condition on Inflation. On the other hand, the value
of the Inflaton field that arises from the LSC
bound on the SGWB could be not consistent with such a condition. In any
case, the analysis in this paper shows that the detection of the SGWB will
permit a direct measure of the value of the Inflaton
field by giving an extraordinary precious and
precise information about the early Universe's dynamics. In other words,
the detection of the SGWB will permit to auscultate
the primordial gravity's breath.
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3
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A
Possible Mechanism for the Origin of Inertia in De Sitter-Fantappié-Arcidiacono
Projective Relativity
Leonardo Chiatti
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Fantappié-Arcidiacono
projective relativity, also known as ``de Sitter relativity'', provides a
formulation of mechanics according to which it is possible to identify an
inertial frame of reference by means of kinematic methods. This article presents
the hypothesis that inertial frames of reference originated during the
so-called ``archaic era'' of the Universe. A simple mechanism is proposed
for this process. Such a process could leave behind cosmic fluid
granulation, which could manifest itself in the present Universe as a
clustering of dark matter in galaxies.
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4
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The
Purely Geometric Part of ``Dark Matter''-A Fresh Playground for ``String
Theory''
Hagen Kleinert
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We
argue that part of ``dark matter'' is not made of matter, but of the
singular world-surfaces in the solutions of Einstein's vacuum field equation
G_\mu\nu=0., i.e., the homogenous Einstein
equation. Their Einstein-Hilbert action overns
also their quantum fluctuations. It coincides with the action of closed bosonic ``strings'' in four spacetime
dimensions, which appear here in a new physical context. Thus, part of dark
matter is of a purely geometric nature, and its quantum physics is governed
by the same string theory, whose massless spin-particles
interact like the quanta of Einstein's theory.
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5
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Landau-Ginzburg Chern-Simons model
with Ue(1)X Ug(1)
Gauge Symmetry and Internal Pseudo-Photons
P. Castelo Ferreira
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In this article it is studied, at variational level, a mathematical setup given by the
Landau-Ginzburg Chern-Simons
model for anyons in 2+1-dimensions within the
framework of dimensional reduced $U_e(1)\times U_g(1)$ extended
electromagnetism with both vector gauge fields (photons) and pseudo-vector gauge
fields (pseudo-photons) such that both magnetic and electric vortexes
coexist in the planar system. This model exhibits explicit planar $P$ and
$T$ discrete symmetries being the Hall conductivity consistently a tensor
and the Dirac quantization on the electric and magnetic coupling constants
is equivalent to the quantization of magnetic flux. It is also discussed a
thickening to 4-dimensions of the model with explicit 4-dimensional $P$
violation which allows either for electric and magnetic charge separation,
either for the Meissner effect. Although
mathematically consistent, the electromagnetic field content for this model
does not coincide with the standard Hall effect being present
an extra orthogonal electric and longitudinal magnetic fields.
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6
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A New
Procedure to Understanding Formulas of Generalized Quantum Mean Values for
a Composite A+B
F.A. R.
Navarro
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Herein
is presented a research concerning to the calculation of quantum mean
values, for a composite
A+B, by using different formulas to expressions in
Boltzmann-Gibbs-Shannon's statistics. It is analyzed why matrix formulas
with matrices E_A and E_B, in Hilbert subspaces, produce identical results
to full Hilbert space formulas. In accord to former investigations, those
matrices are the true density matrices, inside third version of nonextensive statistical mechanics. Those
investigations were obtained by calculating the thermodynamical
parameters of magnetization and internal energy for magnetic materials.
This publication shows that it is not necessary postulate the mean value
formulas in Hilbert subspaces, but they can be formally derived from full
Hilbert space, taking into consideration the very statistical independence
concept.
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7
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The
Regular Charge-Monopole Theory and Strong Interactions
E. Comay
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The
paper describes the structure of a regular charge-monopole theory and of
its application to hadronic systems. It is shown
that this theory explains many hadronic effects
whereas QCD fails to explain most of them. Predictions of results of new
kinds of experiments are put forward. The success or the failure of these
predictions can be used for testing the validity of each of these hadronic theories.
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8
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Symmetry
and Integrability of a Reduced, 3-Dimensional
Self-Dual Gauge Field Model
C. J. Papachristou
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text: Acrobat PDF
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A
3-dimensional reduction of the self-dual Yang-Mills (SDYM) equation, named
SDYM3, is examined from the point of view of its symmetry and integrability characteristics. By using a
non-auto-B\"{a}cklund
transformation, this equation is connected to its potential form (PSDYM3) and
a certain isomorphism between the Lie algebras of symmetries of the two systems
is shown to exist. This isomorphism allows us to study the infinite-dimensional
Lie algebraic structure of the ``potential symmetries'' of SDYM3 by
examining the symmetry structure of PSDYM3 (which is an easier task). By
using techniques described in a recent paper, the recursion operators for
both SDYM3 and PSDYM3 are derived. Moreover, a Lax pair and an infinite set
of nonlocal conservation laws for SDYM3 are found, reflecting the fact that
SDYM3 is a totally integrable system. This system
may physically represent gravitational fields or chiral
fields.
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9
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The Fine Structure Constant and Interpretations of
Quantum Mechanics
Ke Xiao
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The
fine structure constant give a simple derivation of the localized wavefunction, Schrödinger equation, double-slit{\small{} and the uncertainty principle in Quantum Mechanics.
The }wave-particle duality link to the space-time
property of matter by Planck constant. The double-slit formula is |\psi_{X}|^{2}=2|\mathrm{sinc}(a'kX)|^{2}[1+\cos(akX-\omega\delta
T^{'}+\underline{\varphi})], where the cross-linked
angle for double-slit, T_{1}^{'}=T_{c}\cos\left(\theta_{2}\right)
and vice versa.
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10
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Reduction of Uncertainty Relationship For Spin
Operator
M.
A. A. Sbaih, Moeen Kh. Srour, and M. S. Hamada
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We
show in this paper that schrodinger-Robertson Uncertainty
relationship for S_{x}, S_{y} , S_{z} and for
\hat{x} and \hat{p} operator can reduced to well known Heisenberg
Uncertainty relationship under suitable transformation.
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11
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Radiation Reaction and Renormalization for a
Photon-Like Charged Particle
Yurij Yaremko
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A renormalization scheme which relies on
energy-momentum and angular momentum balance equations is applied to the derivation
of effective equation of motion for a massless
point-like charge. Unlike the massive case, the rates of radiated
energy-momentum and angular momentum tend to infinity whenever the source
is accelerated. The external electromagnetic fields which do not change the
velocity of the particle admit only its presence within the interaction
area. The effective equation of motion is the equation on eigenvalues and eigenvectors of the electromagnetic tensor.
The massless charges move along base line determined
by the eigenvectors when the effective equation of motion possesses uniform
solutions. It is interesting that the same solution arises in Rylov's model of magnetosphere of a rapidly rotating
neutron star (pulsar).
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12
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Challenge to Find Quasicrystals
with Seven-Fold Symmetry
Hagen
Kleinert
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We propose that exerimentalists
should look for materials exhibiting sevenfold quasicrystalline symmetry, and show a picture of
the expected density distribution.
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13
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Bi-parameter Semigroups of
linear operators
S.
Hejazian, H. Mahdavian Rad, M. Mirzavaziri, and H. Mohammadian
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text: Acrobat PDF
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Let \mathcal{X}
be a Banach space. We define the concept of a
bi-parameter semigroup on \mathcal{X}
and its first and
second generators. We
also study bi-parameter semigroups on Banach algebras. A relation between uniformly continuous bi-parameter semigroups and \sigma-derivations is also established. It is
proved that if \{\alpha_{t,s}\}_{t,s\geqslant0} is a
uniformly continuous bi-parameter semigroup on a Banach algebra $\mathcal X$,
whose first and second generators are $d$ and \sigma, respectively, and
if d is also a \sigma-derivation
then d^{n}(ab)=(d+\sigma)^{n}(a)\star(d+\sigma)^{n}(b)
and \alpha_{t,0}(ab)=\alpha_{t,1}(a)\star\alpha_{t,1}(b)
for all a, b\in \mathcal X.
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14
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Involute Curves
Of Timelike Biharmonic Reeb Curves (LCS)3 - Manifolds
Talat Körpinar, Essin Turhan, and Vedat Asil
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In this paper, we study involute
timelike biharmonic Reeb curves in (\textit{LCS})_{3}-manifold.
We characterize curvatures of timelike biharmonic Reeb curves in (\textit{LCS})_{3}-manifold. We obtain parametric
equation involute curves\ of the timelike biharmonic Reeb curves
in
(\textit{LCS})$_{3}$-manifold.
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15
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Analytical Solutions of the Klein-Gordon Equation
for Rosen-Morse Potential via Asymptotic
Iteration Method
S.
Debnath and B. Biswas
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text: Acrobat PDF
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Analytical
solutions of the Klein-Gordon equation for the Rosen-Morse potential [1]
with equal scalar and vector potentials are studied in this paper. To
obtain the exactly normalized bound state wave function and energy
expressions we have used the asymptotic iteration method (AIM) [2-3]. Our
results are in excellent agreement with other works.
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16
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Finite Time Existence of Solutions of\ Navier--Stokes Equations
Igor
Hrnèiae
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This
paper shows, using both physical and mathematical arguments,
that all solutions of Navier--Stokes
equations do blow up in some co-ordinate systems in finite time. The reason
of solutions blowing up in finite time is viscosity force being allowed to
act in the direction of fluid motion, thus generating energy. Viscosity
force should act in the direction opposite to motion of fluid.
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17
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Covariant Analytic Mechanics with Differential Forms
and Its Application to Gravity
Yasuhito Kaminaga
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We discuss fundamentals of the covariant
analytic mechanics with differential forms. We apply it to typical field
theories, such as a scalar field, the electromagnetic field, and a non-abelian gauge field, as well as the Newtonian mechanics
of a harmonic oscillator. A significant feature of the covariant analytic
mechanics is that the canonical equations, in addition to the
Euler-Lagrange equation, are not only manifestly Lorentz covariant but also
gauge covariant. In the latter half of the paper, we apply the covariant
analytic mechanics to Einstein's general theory of relativity, and show
that the gravitational field can be successfully treated within the
framework of it. We obtain the canonical equations of gravity with manifest
diffeomorphism covariance.
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18
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Implications of an Aether
non Dragged by the Motion of Celestial Bodies on Optical Laws
Joseph
Levy
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text: Acrobat PDF
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The
conventional optical laws take for granted that the one-way phase velocity
of light in a refractive medium at rest in the Earth frame is C/n. But \textit{if one assumes the existence of a fundamental
reference frame and of an aether non-entrained by
the motion of celestial bodies}, then Hoek's
experiment shows that this velocity must be equal to C/n-V/n^2 in the
direction of the Earth absolute motion, and $C/n+V/n^2$
in the opposite direction, where $V$ is the absolute speed of the Earth
frame. It is important to draw the consequences of this data and to check
whether it complies with well established laws of physics. Such~an anisotropy~implies~that,~according to non-entrained aether
theory (NEAT), the~ratio of the speed of light in
vacuo to the speed of light in refractive media (i,e, the optical index)~must~vary
as a function of the orientation of the light signal. This is~indeed~what~the calculation shows. Therefore, if NEAT
is exact, except for some orientations, $n$ is not the optical index in refractive
media moving relative to the fundamental frame. However,~as we shall see, NEAT does not preclude the
fact that the Snell-Descartes' law~\textit{sini=nsinr} applies to a high
degree of accuracy whatever the orientation of the light signal. Thus, even
if it exists, the anisotropy remains unapparent. It is worth noting that,
while resorting to assumptions quite different from special relativity,
non-entrained aether theory accounts for well established
experimental results. Moreover, as will be checked, a thorough analysis of Fizeau's experiment in light of Hoek's
studies establishes the need for an aether drift,
providing a strong argument in support of aether theory.
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19
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LRS
Bianchi Type-II Cosmological Models with Anisotropic Dark Energy
K. S. Adhav
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The
exact solutions of the Einstein field equations for Locally Rotationally
Symmetric (LRS) Bianchi type-II metric under the assumption on the
anisotropy of the fluid(dark energy) are obtained
for exponential and power-law volumetric expansions. The isotropy of the
fluid, space and expansion are examined.
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20
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A
New Class of Magnetized Inhomogeneous Cosmological Models of Perfect Fluid
Distribution with Variable Magnetic Permeability in Lyra
Geometry
Rama S.
Singh
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A
new class of exact solutions of Einstein's modified field equations in
inhomogeneous space-time for perfect fluid distribution with variable magnetic
permeability and time dependent gauge function \beta within the framework
of Lyra geometry is investigated. The source of
the magnetic field is due to an electric current produced along the z-axis.
Only F_{12} is a non-vanishing component of the
electromagnetic field tensor. It has been found that the displacement
vector \beta(t) behaves like the cosmological
constant \Lambda in the normal gauge treatment and the solutions are
consistent with the recent observations of Type Ia
supernovae. The displacement vector \beta(t)
affects entropy. Physical and geometric aspects of the models are also
discussed.
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21
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Thermodynamical Model of the Universe
Naseer Iqbal,
M. S. Khan, Tabasum Masood,
and Ibrahim Selim
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We
inquire in to the physics of a self gravitating medium in quasi-static
equilibrium, using the phenomenological approach of thermodynamics.
Gravitational galaxy clustering is statistical and its origin is dynamical
one. Hence the aspects of clustering must be understood in order to arrive
at a proper appreciation of the subject of the formation and evolution of
the large scale structure of the universe. Long range gravitational forces modify
the thermodynamic functions and equations of state. The thermodynamical
model is discussed at many levels. First we discuss the importance of
thermodynamics as applicable to the gravitational clustering problem and
extend our remarks to study various thermodynamic functions like free
energy, entropy, pressure, internal energy and others. The various results
that we discuss have interested implications for the study of large scale
structure in the universe. They support the view that an easy and simple
approach can be made an alternative study while discussing the central
issues of cosmology ''large scale structure of universe''.
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22
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Counting
States in Spacetime
Lawrence
B. Crowell
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text: Acrobat PDF
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The
recent derivation of an exact integer partition function (IPF) is related
to a generating function for strings which compose the states of a black
hole. Quantum gravity states have
representations as modular functions for exception algebras. The SLOCC group for the accounting of
these states is a quotient group on the Jordan matrix algebra. Quantum gravity is then described by a set
of symmetries which act as quantum Golay
codes. The emulation of quantum
gravity in $n$-partite entanglements is then a technology for quantum
computing and encryption.
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23
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The
Role of Electromagnetic Field in the Stiff and Anti-stiff L.R.S Bianchi Type
II Universe
Hassan Amirhashchi
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In
this letter the role of electromagnetic field in the L.R.S Bianchi type II
universe has been investigated. To get solution, the expansion $(\theta)$ in the model is assumed to be proportional to the
shear $(\sigma)$. It is shown that when the matter phase changes from stiff
to anti-stiff fluid the universe expansion converts from decelerating to accelerating.
In case of anti-stiff fluid it is found that the electromagnetic field
caused the universe to be accelerating under certain conditions. The
physical and geometrical behavior of these models are
discussed.
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