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2f056f879b4948e27e76c0adc8d3d00f501414c2 | abstract | 0 | 6 | Abstract | We report the detection in CO of the far-side counterpart of the well-known
expanding 3-Kpc Arm in the central region of the Galaxy. In a CO
longitude-velocity map at b = 0 deg the Far 3-Kpc Arm can be followed over at
least 20 deg of Galactic longitude as a faint lane at positive velocities
running parallel to the Nea... | {
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} | 10.1086/591669 | 0807.1752 | A New Spiral Arm of the Galaxy: The Far 3-Kpc Arm | [
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7d0011c6ae18f14acd8936b53f6d19181990e8ae | subsection | 1 | 6 | Body | Since its identification in 21 cm emission by , the expanding 3-Kpc Arm has remained at once one of the most obvious Galactic spiral arms and the most puzzling. Its structure in 21 cm and CO longitude-velocity diagrams and its absorption of continuum emission toward the Galactic center demonstrate beyond doubt that the... | {
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... | 10.1086/591669 | 0807.1752 | A New Spiral Arm of the Galaxy: The Far 3-Kpc Arm | [
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7c338694a99c26433dbc55a2237b371ea17382d9 | subsection | 2 | 6 | Body | It is also clear from Figure 2 that the CO linewidths of the two arms are similar, with Gaussian fits yielding values of 19.7 km s^{-1}(FWHM) for the Near Arm and 22.2 km s^{-1}for the Far. We expect that further, more refined analyses, which will allow for the expected curvature of the arms with longitude, will result... | {
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44bd4dc3272438bbd8819ebcaac9668996def113 | subsection | 3 | 6 | Body | Comparison of this map to the CO b-v map in Figure 5b shows that the Far Arm has about the same thickness in both species (see also Table 1). In the positive longitude range included in Figure 5a, it is the Near Arm that is masked in HI by both distant gas beyond the solar circle and foreground gas in the inner disk. I... | {
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} | 10.1086/591669 | 0807.1752 | A New Spiral Arm of the Galaxy: The Far 3-Kpc Arm | [
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a11363f9813ea57f65e4495b0a78a75c5376f3bb | subsection | 4 | 6 | Body | Excluding the regions of blending indicated in Figure 3, the longitude range considered here covers a 1.47-kpc length of the Near Arm and a 3.24-kpc length of the Far. Over these ranges we find that the two arms have H_2 masses per unit length that differ by only 26% (Table 1). HI masses were similarly computed from th... | {
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aa99f020f895d04e0eda7a45d450d1717948c03e | subsection | 5 | 6 | Body | The two parallel lanes obvious in Figure 1 are less apparent in 21 cm data even at high angular resolution, because at negative longitudes the Far Arm is badly blended with emission from the outer and inner disks, and at positive longitudes the Near Arm is similarly blended.Detection of the Far 3-Kpc Arm immediately su... | {
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} | 10.1086/591669 | 0807.1752 | A New Spiral Arm of the Galaxy: The Far 3-Kpc Arm | [
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9453080290589c13aa039e1a4808d5a5548b91c9 | abstract | 0 | 31 | Abstract | In this paper we address the complexity issues of two agreement problems in
oblivious robot networks namely gathering and scattering. These abstractions
are fundamental coordination problems in cooperative mobile robotics. Moreover,
their oblivious characteristics makes them appealing for self-stabilization
since they ... | {
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} | 0807.1753 | The cost of probabilistic gathering in oblivious robot networks | [
"Julien Clement",
"Xavier Defago",
"Maria Gradinariu Potop-Butucaru",
"Stephane Messika"
] | [
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fa0cb1d7a384672abc78f701fc3abef53cf0f426 | subsection | 1 | 31 | Introduction | Many applications of mobile robotics envision groups of mobile robots
self-organizing and cooperating toward the resolution of common
objectives. In many cases, the group of robots is aimed at being
deployed in adverse environments, such as space, deep sea, or after
some natural (or unnatural) disaster. It results that... | {
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4372e5431189842fcae4700f9279cf31f683e4ec | subsection | 2 | 31 | Contribution | Our contribution is twofold. First, we show that the time complexity
of probabilistic gathering in
fault-free environments can be
improved from O(n^2) to O(nln(n)) when the algorithms exploit
additional information related to the environment (eg. multiplicity
knowledge). Additionally, in crash-prone
environments we pro... | {
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} | 0807.1753 | The cost of probabilistic gathering in oblivious robot networks | [
"Julien Clement",
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e10d1a314bd3251492a8eb90f54e078408c447f4 | subsection | 3 | 31 | Structure of the paper | The paper is structured as follows. Section describes the robots network and system model.
Section formally defines the gathering and
scattering problems.
We propose the complexity analysis of existent probabilistic
scattering and gathering in Sections and in fault-free
and fault-prone environments. In Section
we anal... | {
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} | 0807.1753 | The cost of probabilistic gathering in oblivious robot networks | [
"Julien Clement",
"Xavier Defago",
"Maria Gradinariu Potop-Butucaru",
"Stephane Messika"
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30332fde5014501691a34c022d53ef0f0eccf0ff | subsection | 4 | 31 | Model | In the following we propose the model of our system. Most of the
definitions are borrowed from , . | {
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a1fe1ad0f3333e709ec7b903266fa08905852ea0 | subsection | 5 | 31 | Robot networks. | We consider a network of a finite set of
robots arbitrarily deployed in a geographical area. The robots are
devices with sensing, computational and motion capabilities. They can
observe (sense) the positions of other robots in the plane and based
on these observations they perform some local
computations. Furthermore, ... | {
"cite_spans": []
} | 0807.1753 | The cost of probabilistic gathering in oblivious robot networks | [
"Julien Clement",
"Xavier Defago",
"Maria Gradinariu Potop-Butucaru",
"Stephane Messika"
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eeb47c6651f314c4260a4b4151e40c9d6f3f61d1 | subsection | 6 | 31 | System model. | A network of robots that exhibit a discrete behavior
can be modeled with an I/O automaton . A network of robots that
exhibit a continuous behavior can be modeled with a hybrid I/O automaton .
This framework allows the modeling of systems that exhibit both a discrete
and continuous behavior and in particular the modelin... | {
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020bcdd1b8505348c34584540e80a3f07d23b767 | subsection | 7 | 31 | Schedulers. | A scheduler decides at each configuration the
set of robots allowed to perform their actions.
A scheduler is fair if, in an infinite execution, a robot is activated
infinitely often. In this paper we consider the fair version of the
following schedulers:centralized: at each configuration a single robot is
allowed to pe... | {
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} | 0807.1753 | The cost of probabilistic gathering in oblivious robot networks | [
"Julien Clement",
"Xavier Defago",
"Maria Gradinariu Potop-Butucaru",
"Stephane Messika"
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fd115835f24ed630f2fa680f6d3f0dd2258bf0b9 | subsection | 8 | 31 | Faults. | In this paper, we address the following failures:crash failures: In this class, we further distinguish two
subclasses: (1) robots physically disappear from the network, and
(2) robots stop all their activities, but remain physically present
in the network;
Byzantine failures: In this case, robots may have an
arbitrary... | {
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} | 0807.1753 | The cost of probabilistic gathering in oblivious robot networks | [
"Julien Clement",
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"Maria Gradinariu Potop-Butucaru",
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837cfd1c46417c0d83b071b6f43a5b30e2b9953b | subsection | 9 | 31 | Computational models. | The literature proposes two computational models: ATOM and CORDA. The
ATOM model was introduced by Suzuki and Yamashita . In this
model each robot performs, once activated by the scheduler, a
computation cycle composed of the following three actions:
observation, computation and motion. The particularity
of the ATOM mo... | {
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afe154e1a9d109663a11ffe31dc01cc8f8f821e7 | subsection | 10 | 31 | Gathering and Scattering | A network of robots is in a legitimate configuration with respect to
the gathering requirement if all robots in the system share the same position in
the plane.
Let denote by {\mathcal {P}}_\mathit {Gathering} this predicate.An algorithm solves the gathering problem in an oblivious system
if the following two propertie... | {
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be5e1404d7716319711d5bb0fd1a7610c3a164ac | subsection | 11 | 31 | Analysis framework | In this section we introduce some notations and definitions that will
be further used in order to analyze the convergence time of
the probabilistic gathering and scattering. A detailed description of
the notions defined below can be found in . | {
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c22bb39ceb3c590ad3f636e5118a704f9ce73bb4 | subsection | 12 | 31 | Random variables | We denote X_n a random variable. For instance, in our case it might be the number of groups of size x
after n steps of the algorithm.
We will study a discrete-time stochastic process, that is : a sequence \lbrace X_n\rbrace _{n \ge 0} of random variables.In the sequel we will use the following notations:\mathbb {P}[X_n... | {
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} | 0807.1753 | The cost of probabilistic gathering in oblivious robot networks | [
"Julien Clement",
"Xavier Defago",
"Maria Gradinariu Potop-Butucaru",
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e8c06d68421f1c1eb129cabf8ce176adadcae96e | subsection | 13 | 31 | Markov chains | Markov chains are particular classes of stochastic processes. These
stochastic processes have the following fundamental property :
the probabilistic dependence on the past is only related to the previous state.Definition 1 Let \left(X_n \right)_{n \in \mathbb {N}} be a discrete time stochastic
process with countable st... | {
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} | 0807.1753 | The cost of probabilistic gathering in oblivious robot networks | [
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6350b228543c6d0b68fe5ae84c26f02b37930d14 | subsection | 14 | 31 | Probabilistic Gathering | In this section we analyze the complexity of probabilistic gathering in fault-free
and fault-prone environments. The algorithms analyzed in this section
were proposed in . | {
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93165f8fcc5b78b4af265680404ef122b18e2126 | subsection | 15 | 31 | Gathering in fault-free environments | In this section we prove that additional information on the environment drastically improves
the time convergence of gathering. Using multiplicity knowledge, for example, we obtain a tight bound of O(nln(n)) which improves
the best known bound of O(n^2).
In we proposed a probabilistic algorithm that
solves the fault-fr... | {
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bb5d1cb328d6445becc8abc5e1d2fc85b944684a | subsection | 16 | 31 | Gathering in fault-free environments | Interestingly, the multiplicity knowledge (used so far in order to
break the symmetry of the system) can also be used in order to
fasten gathering.Functions:\mathit {observe\_neighbors}:: returns the set of robots within thevision range of robot p (the set of p's neighbors);\mathit {maximal\_multiplicity}:: returns the... | {
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} | 0807.1753 | The cost of probabilistic gathering in oblivious robot networks | [
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3259860f96a56e98a4cc9e09404d6377b21cc481 | subsection | 17 | 31 | Gathering in fault-free environments | Therefore, if we note \alpha _n=[\frac{n}{2}]+1
T_1^{\alpha _n }=\displaystyle \sum _{k=1}^{\alpha _n-1}
\frac{\alpha _n}{\alpha _n-k}=
\displaystyle \alpha _n \sum _{k=1}^{\alpha _n-1}\frac{1}{k} \le \alpha _n ln(\alpha _n)
Gathering in Fault-prone environments
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50c72a00297a703e06fc5dcdb03918d27a8eab9c | subsection | 18 | 31 | Gathering in fault-free environments | Therefore,
the convergence time of Algorithm REF is \alpha _nln(\alpha _n)+2f.
Note 2 Note that the above results hold even if the crashed robots are still physically present in the system but
stop the execution of any action.
Byzantine-tolerant gathering
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448ebf1f39dd7df342d8f0dc9a6bcfd28d110834 | subsection | 19 | 31 | Gathering in fault-free environments | \mathbb {P}\left[ \ \text{reach} \ \mathcal {L} \ \text{in} \ \frac{N}{2}+1 \ \text{steps} \right] > \displaystyle \left(\frac{1}{N}\right)^{(\frac{N}{2}+1)}= \varepsilon
So
\mathbb {P}\left[ \lnot (\text{reach} \ \mathcal {L} \ \text{in} \ (\frac{N}{2}+1) \ \text{steps}) \right] \le (1-\varepsilon )
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\f... | {
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33a8f643aebdb72cb92b99948c7c535001df3b0e | subsection | 20 | 31 | Gathering in fault-free environments | The Voronoi diagram of {\mathcal {P}} is a subdivision of the plane into
n cells, one
for each point in {\mathcal {P}}. The cells have the property that a
point q belongs to the Voronoi cell of point
p_i iff for any other point p_j \in {\mathcal {P}},
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ef6039ef844735a1f71fe38440ed817d4a344e91 | subsection | 21 | 31 | Gathering in fault-free environments | Furthermore
\displaystyle \frac{1}{1-\alpha ^{j}} \mathop {\sim }_{j \rightarrow \infty } 1+\alpha ^j. Thus the partial sums are equivalent :
T_1^n \mathop {\sim }_{n \rightarrow \infty } \sum _{j=0}^{n-1} 1+\alpha ^j
Since \sum _{j=0}^{n-1} (1+\alpha ^j) = n + \sum _{j=0}^{n-1} \alpha ^j
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e2ac4c0979445c488686600f05cc6e9bea490125 | subsection | 22 | 31 | Gathering in fault-free environments | Proof:
The idea of the proof is similar to the one presented in Section .
Consider a random variable Y_t with values in \lbrace 0..n\rbrace .
Y_t=k iff there is a set {\cal M} of k non faulty robots
in which each robot shares its position with another robot.
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Y_k reaches 0. Note t... | {
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277a14faf9c662b48bafec826ba7110b3ff07851 | subsection | 23 | 31 | Gathering in fault-free environments | Finally, we proposed a discussion related to the best strategy to design
gathering. This work opens several research directions.
For example the flip/flop scattering/gathering
seems to be a promising direction to reduce the complexity of gathering.
Another interesting direction is the complexity of byzantine-tolerant g... | {
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39965dccfb6e110a5093229b8199120c047aed1e | subsection | 24 | 31 | Probabilistic scattering | In this section we address another agreement problem : the
scattering. The unique existing probabilistic solution for scattering was proposed
in (see Algorithm REF ).
Analyzing the complexity of Algorithm REF in both fault-free and fault-prone environments
we prove that scattering is much easier to
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e0353ef1fc6e940293f1fb1fdd23683d49e515a1 | subsection | 25 | 31 | Scattering in Fault-free environments | Petit et al. proved that deterministic scattering is impossible
in ATOM model without additional assumptions and proposed a
probabilistic solution based on the use of Voronoi
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a2eec4cc7beeaaf2144a37ef401a39deb25c18c3 | subsection | 26 | 31 | Scattering in Fault-free environments | If we sum from 0 to n-1 we get :
T_1^n=\sum _{k=0}^{n-1}\frac{1}{1-\alpha ^{n-(k-1)}}=\sum _{j=0}^{n-1}\frac{1}{1-\alpha ^{j}}
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ff119211ad61e4a5cc1670eeb22e236c58895fba | subsection | 27 | 31 | Scattering in Fault-free environments | With positive probability, p \ge \frac{3}{4}(\frac{1}{4})^{m-1} this robot will
change its position to a new position in its Voronoi cell and hence
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3a81a801c75ae09996eb31f5b5451899e613f414 | subsection | 28 | 31 | Scattering in Fault-free environments | Moreover, using Markov chains tools and
multiplicity knowledge we proved that the convergence time of
gathering can be reduced from O(n^2) (the best known tight
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f4d5a769ffc54cdc981dff5a086c6c48c836a7f7 | subsection | 29 | 31 | How to gather oblivious robots? | In Section we analyzed a possible strategy to gather robots that converges in O(nln(n))
in fault-free environments and in O(nln(n)+2f) in crash-proned systems.
In Section we computed the complexity of a scattering strategy
that is one of optimal (i.e. O(n) in fault-free environments and O(n-f) in fault-prone environmen... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1021,
"openalex_id": "",
"raw": "Yoann Dieudonné and Franck Petit. Robots and demons (the code of the origins). In FUN, pages 108–119, 2007.",
"source_ref_id": "c1c6e42c94173c507db1cee2eb08fc170a65ec69",
"start": 699
... | 0807.1753 | The cost of probabilistic gathering in oblivious robot networks | [
"Julien Clement",
"Xavier Defago",
"Maria Gradinariu Potop-Butucaru",
"Stephane Messika"
] | [
"cs.DC",
"cs.CC"
] | 2,008 | en | Computer Science | [
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1c0f377b7c90e63249844fbbad76ff44f376b4e3 | subsection | 30 | 31 | Conclusions and Discussions | The contribution of this paper is twofold. First, we proposed a
detailed complexity analysis of the existent probabilistic
agreement algorithms (gathering and scattering) in both fault-free and
fault-prone environments. Moreover, using Markov chains tools and
multiplicity knowledge we proved that the convergence time o... | {
"cite_spans": []
} | 0807.1753 | The cost of probabilistic gathering in oblivious robot networks | [
"Julien Clement",
"Xavier Defago",
"Maria Gradinariu Potop-Butucaru",
"Stephane Messika"
] | [
"cs.DC",
"cs.CC"
] | 2,008 | en | Computer Science | [
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0fd1129805071a1ade3af70c4f95ddd6351d7489 | abstract | 0 | 48 | Abstract | The original Dirac Equation is modified in the simplest imaginable and most
trivial manner to include a universal 4-Vector Cosmological Field term in the
space and time dimensions. This cosmological field leads to a modified Dirac
Equation capable of explaining why the Universe appears to be made up chiefly
of matter. ... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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11fd19a9a5197df5697d9e975ee2701011d628f9 | subsection | 1 | 48 | Introduction | Each electronically charged elementary particle has a counterpart with the opposite electronic charge which is known as its antiparticle (antiparticles are also referred to as antimatter) and just like normal particles, antiparticles do combine, forming atoms of antimatter which some call antiatoms – albeit, unlike ato... | {
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} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
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] | 2,008 | en | Physics | [
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a61d7bfbfa9ee6febb17acbc9fc2740d33ef54ce | subsection | 2 | 48 | Introduction | For example, in the Standard Model of Particle Physics, the Cabibbo-Kobayashi-Maskawa matrix (Cabibbo 1963; Kobayashi & Maskawa 1973) is employed and a complex phase factor is artificially injected into this matrix to bring about \textrm {CP}-violation inorder to explain the observed \rm {CP}-violation in the Kaon syst... | {
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} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
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259305a6b14d5fdd995580d8358c3cefdf7d5d86 | subsection | 3 | 48 | The Dirac Equation and its Symmetries | Without being to assuming, let us, for instructive purposes browse through the thesis leading to the Dirac Equation. Suppose we have a particle of rest-mass m_{0} and momentum p and energy E, Albert Einstein, from his 1905 Special Theory of Relativity (STR) – derived the basic equation:E^{2}=p^{2}c^{2}+m_{0}^{2}c^{4}.T... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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4090b74912dc8202c029391170412ba8a89a046f | subsection | 4 | 48 | The Dirac Equation and its Symmetries | The equation he found was:\left[i\hbar \gamma ^{\mu }\partial _{\mu }-m_{0}c\right]\psi =0,where:\begin{array}{c c}
\gamma ^{0}=
\left(\begin{array}{c c}
\textbf {I} & {0}\\
{0} & -\textbf {I} \\
\end{array}\right)
,\,\,\,\,
\gamma ^{i}=
\left(\begin{array}{c c}
\textbf {0} & {\sigma }^{i}\\
-{\sigma }^{i} & \textbf {0... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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2704716ef28960d1375554bace4044bfacfa7a4e | subsection | 5 | 48 | The Dirac Equation and its Symmetries | Obeys \rm {CPT}-symmetry. This is symmetry under all the operations \rm {C}, \rm {P} and \rm {T}.
Obeys Lorentz invariance. This is symmetry under the change of the inertial frame of reference.We shall not demonstrate these symmetries but direct the reader to Nyambuya (2008a,b) or any good book of Quantum Mechanics (Q... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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087b06b615daed18212020e91b28eee4b73da474 | subsection | 6 | 48 | The Dirac Equation and its Symmetries | After discovering his [Einstein] now famous Law of Gravitation (initially with \Lambda =0), namely:R_{\mu \nu }-\frac{1}{2}Rg_{\mu \nu }=\kappa T_{\mu \nu }+\Lambda g_{\mu \nu },where: R_{\mu \nu }, is the Riemann curvature tensor and R is the contracted Riemann curvature tensor and:T_{\mu \nu }=\varrho v_{\mu }v_{\nu ... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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a8c6b4b8587c37175803b763db5ef7a3ce335618 | subsection | 7 | 48 | Connection Between Electronic Charge & Rest-mass | As already pointed out, if as in the Dirac formulation, where the particle with positive energy \mathcal {E}_{+} is considered to be the particle; and the one with negative energy \mathcal {E}_{-} is considered to be the antiparticle – then, according to the present ideas, it would mean that antiparticles and particles... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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aa08e41e1caf7682aa07f933435cbc86fb3c227b | subsection | 8 | 48 | Connection Between Electronic Charge & Rest-mass | We thus direct the reader to this reading Nyambuya (2008b) for the full argument on this.Taking as given that, m_{0}c=\epsilon Q, it means we can write equation (REF ) as:\mathcal {E}=\pm \Lambda _{0} \hbar c\pm \sqrt{p^{2}c^{2}+\epsilon ^{2}Q^{2}c^{2}}.It is clear from this equation that under this relationship – m_{0... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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aa5516c286f8b548028e6a10cc28da15a4f80365 | subsection | 9 | 48 | Partial Cosmological Dirac Equation | There exists two avenues on which to arrive at equation (REF ). We prefare the form (REF ) than (REF ) because (REF ) makes it clear where the electronic charge (Q) of the particle fits in explicitly hence it will be easy to investigate its symmetries under the intercharge of the particle's electronic charge. Thus from... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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d92beae76b9c79b8315bff995340f683432fa19a | subsection | 10 | 48 | Case I | Given the Dirac Equation, the transformation:\frac{\partial }{\partial t}\longrightarrow \frac{\partial }{\partial t} \pm i\Lambda _{0} c,leads us to the modified Dirac Equation, namely:i\hbar \gamma ^{\mu }\partial _{\mu }\psi \pm \Lambda _{0} \hbar \gamma ^{0}\psi =\epsilon Q\psi .Let us call this the Partial Cosmolo... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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68cb57f3037bc183b929a059402881c9436c08c9 | subsection | 11 | 48 | C-Symmetry | To show invariance under charge conjugation (or lack thereof), we proceed as usual – by bringing the particle under the influence of an external electromagnetic magnetic field A_{\mu }^{ex} (which is a real function and this is the usual four vector electromagnetic potential) which leads to the transformation: \partial... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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996eeaa925a6c030cef4d4b5884c3ebe2ae78b73 | subsection | 12 | 48 | C-Symmetry | Further, we multiply both sides of this equation by \gamma ^{2}, and we are lead to: +i\hbar \gamma ^{2}\gamma ^{\mu *}\rm {D}_{\mu }\psi ^{*}-\Lambda _{0} \hbar \gamma ^{2}\gamma ^{0*}\psi ^{*}=-\epsilon Q\gamma ^{2}\psi ^{*}, and using the fact that: \gamma ^{2}\gamma ^{\mu }=-\gamma ^{\mu }\gamma ^{2} for \,\mu \ne ... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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a92b38ed65828e52ddb2f8be2753df79a34719d8 | subsection | 13 | 48 | T-Symmetry | To show invariance (or lack thereof) under time reversal, we proceed as usual – by making the transformation: t\longmapsto -t (\Longrightarrow \partial _{0}\longmapsto -\partial _{0}) into (REF ) resulting in this equation reducing to: -i\hbar \gamma ^{0}\partial _{0}\psi +i\hbar \gamma ^{k}\partial _{k}\psi +\Lambda _... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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933796abb7a40344c018c54c75005cdc7ebe05ca | subsection | 14 | 48 | P-Symmetry | To show invariance under space reversal (or lack thereof) , we proceed as usual – by making the transformation: x^{k}\longmapsto -x^{k} (\Longrightarrow \partial _{k}\longmapsto -\partial _{k}) into (REF ) resulting in this equation reducing to: i\hbar \gamma ^{0}\partial _{0}\psi -i\hbar \gamma ^{k}\partial _{k}\psi +... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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409e40613f7935334b92f7021c0643ec4269cee0 | subsection | 15 | 48 | CT-Symmetry | To show invariance under charge conjugation and time reversal (or lack thereof), we proceed by making the transformation: \partial _{\mu } \longrightarrow \textrm {D}_{\mu } (for the introduction of the external electromagnetic field), Q\longmapsto -Q & \gamma ^{\mu }\longmapsto -\gamma ^{\mu } (for the reversal of the... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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fb7bfa5a9ef1dd14dcb7ebdc0ac0aaf4a9d6cd1f | subsection | 16 | 48 | CT-Symmetry | Multiplying this throughout by -1, one is lead to: i\hbar \gamma ^{0}\partial _{0}\psi _{c}+\hbar \gamma ^{0}A_{0}^{ex}\psi _{c}+i\hbar \gamma ^{k}\rm {D}_{k}\psi _{c}+\Lambda _{0} \hbar \gamma ^{0}\psi _{c}=\epsilon Q\psi _{c}. Now, for this equation to be the same as equation (REF ), we would need the second term on ... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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36beb7dee925711bb29b52765b832e1012095c51 | subsection | 17 | 48 | CP-Symmetry | To show invariance under charge conjugation and space reversal (or lack thereof), we proceed by making the transformation: \partial _{\mu } \longrightarrow \textrm {D}_{\mu } (for the introduction of the electromagnetic field), Q\longmapsto -Q & \gamma ^{\mu }\longmapsto -\gamma ^{\mu } (for the reversal of the electro... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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42b47344354708d9116f888d99a286a0ce5231a5 | subsection | 18 | 48 | PT-Symmetry | To show invariance under a combined space and time reversal (or lack thereof), we proceed by making the transformation: x^{\mu }\longmapsto -x^{\mu } (\Longrightarrow \partial _{\mu }\longmapsto -\partial _{\mu } and this is for the reversal of the spacetime coordinates) into (REF ), we are lead to: -i\hbar \gamma ^{\m... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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90737eafadf50580f881e22083cbea1c609d72f8 | subsection | 19 | 48 | CPT-Symmetry | To show invariance under a combined charge, space and time reversal (or lack thereof), we proceed by making the transformation: \partial _{\mu } \longrightarrow \textrm {D}_{\mu } (for the introduction of the external electromagnetic field), Q\longmapsto -Q & \gamma ^{\mu }\longmapsto -\gamma ^{\mu } (for the reversal ... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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e7e2b7eeecb54c5bbb323b59f4892c8d50bd06c9 | subsection | 20 | 48 | Lorentz Invariance | To prove Lorentz invariance for (REF ) (which we shall write as: [i\hbar \gamma ^{\mu }\partial _{\mu }-\Lambda _{0} \hbar \gamma ^{0}-\epsilon Q]\psi =0), two conditions must be satisfied:1. Given any two inertial observers \textrm {O} and \textrm {O}^\prime anywhere in spacetime, if in the frame \textrm {O} we have [... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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f660df32e047f774087d4244f0028c8b75cd881d | subsection | 21 | 48 | Lorentz Invariance | The inverse is:\psi (x) = S^{-1}(\Gamma )\psi ^\prime (x^\prime ) = S^{-1}(\Gamma )\psi ^\prime (\Gamma x)or we could write:\psi (x)=S(\Gamma ^{-1})\psi ^\prime (\Gamma x)\Longrightarrow S(\Gamma ^{-1}) = S^{-1}(\Gamma )We can now write: [i\hbar \gamma ^{\mu }\partial _{\mu }-\Lambda _{0} \hbar \gamma ^{0}-\epsilon Q]\... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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296df387ef35fcb47337f603b52c333c43723752 | subsection | 22 | 48 | Lorentz Invariance | Given this, and also that: \partial _{\mu }=(\partial x^{\mu \prime }/\partial x^{\mu })\partial _{\mu \prime }, and putting all this into (REF ), we are lead to:\left[i\hbar \left(\frac{\partial x^{\mu \prime }}{\partial x^{\mu }}\right) S(\Gamma )\gamma ^{\mu } S^{-1}(\Gamma )\partial _\mu ^\prime -\Lambda _{0}^\prim... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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19a92ba308f71871abb6d18ef7dc115113a04856 | subsection | 23 | 48 | Hamiltonian | Now that we have investigated the symmetries of equation (REF ), the question is “Does this equation qualify – in principle, to describe physical phenomena?” The answer is yes and first and forest; despite it's violation of \rm {CPT}-symmetry, it is Lorentz invariant and second; because its Hamiltonian, namely:\mathcal... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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ac7ca8327715eddb1c27a324421f2118cf3a1bf1 | subsection | 24 | 48 | Case II | Proceeding to the second case, we make the following transformation:\frac{\partial }{\partial t}\longrightarrow \frac{\partial }{\partial t} \pm \Lambda _{0} c,and this leads us to:i\hbar \gamma ^{\mu }\partial _{\mu }\psi \pm i\Lambda _{0}\hbar \gamma ^{0}\psi =\epsilon Q\psi .As one can verify for themself, this equa... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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66775d5d137667c82bccf14e00408c3788434f88 | subsection | 25 | 48 | The Arrow of Time | Now having gone through the symmetries of equation (REF ) and having chosen this equation and rejected equation (REF ), we come to the question of the arrow of time and the results obtained here extend to the equation that we will derive in the next section. We note here – that, we have two Universes, one described by ... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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f22e703a9360254bf07677dd337b7b3ed7fea31f | subsection | 26 | 48 | The Arrow of Time | Let these two Universes be \mathcal {U}^{+} and \mathcal {U}^{-} where \mathcal {U}^{+} is the Universe in which time moves forward (\Lambda _{0}<0) and likewise, \mathcal {U}^{-} is the Universe in which time moves backwards (\Lambda _{0}>0). This result is independent of the the fact that we have here considered a fr... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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cc9e8456f7801f342716526389e85ed721d195d9 | subsection | 27 | 48 | Full Cosmological Dirac Equation | Given the unquenchable thirst to generalise Laws of Nature, it is most natural to wonder: “Why should the cosmological field be confined just to the time dimension alone?” Why not the space dimension as-well? To introduce a cosmological field into a particular dimension, one simply needs to add this to the partial deri... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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845092cc91398e9b7f0993983867bd4dad89ff33 | subsection | 28 | 48 | Full Cosmological Dirac Equation | Explicitly these solutions are given:\begin{array}{c c l l l}
\mathcal {E}_{1}& = &+\Lambda _{0} \hbar c+\sqrt{[( p_{1}+\Lambda _{1}\hbar )\cdot (p^{1}+\Lambda ^{1}\hbar )+( p_{2}+\Lambda _{2}\hbar )\cdot (p^{2}+\Lambda ^{2}\hbar )+( p_{3}+\Lambda _{3}\hbar )\cdot (p^{3}+\Lambda ^{3}\hbar )]c^{2}+\epsilon ^{2}Q^{2}c^{2... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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a7024b09ef3957a90b7c97930674148b5ffec7c3 | subsection | 29 | 48 | Full Cosmological Dirac Equation | \ge \mathcal {E}_{16}\ge \mathcal {E}_{17} and this is for the setting: p_{1}\le p_{2}\le p_{3}. The order of which p is greater than the other does not really matter because one can always rearrange these p's in an assending order as has been done here and then proceed to calculate the energies as above. That said, it... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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0dd497ee302c1c6b07619b816872b693b914d35d | subsection | 30 | 48 | CPT-violation & a New Spacetime Model | Now we come to the problem of \rm {CPT}-violation. The Schwinger-Lüder-Pauli theorem, which is a corner stone of QFT, states that any local Lorentz invariant field theory must obey \rm {CPT}-symmetry. \rm {CPT}-symmetry is thus considered a perfect Symmetry of Nature, so much such that any theory that violates it, is n... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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6e245a95a9c2bfdc0543ec0f3d3fee4d948ccb27 | subsection | 31 | 48 | CPT-violation & a New Spacetime Model | We shall give the justification for the limits in §REF .We propose that this function be a 4-vector differentiable none-smooth dynamic random function that takes any numerical value within the set limits as defined in (REF ). By differentiable none-smooth we mean it is not continuous at any-point but is differentiable ... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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511471c4eee0bb181ef772ed25c205a5e8a05ef9 | subsection | 32 | 48 | CPT-violation & a New Spacetime Model | The fact that Laws of Nature are \rm {T}-symmetric on the QST implies: \delta _{0}(x_{k};t)=\delta _{0}(x_{k};-t), and this means the past is preserved by \delta _{0} and is not preserved by \delta _{k}. In another way, knowing the present value of \delta _{0}(x_{k};t), means not only can one tell is past value but als... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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a95f2021771cde17a71e8c99cbc72278e8efc8f0 | subsection | 33 | 48 | Upper Space and Time Limits | In this part of the reading, we establish lower space and time limits on spacetime. To achieve this, we use the simple and well accepted Law of Nature that the speed of light, c, is an upper absolute speed limit for all material bodies and energy in the Universe. Considering the case of motion in one dimension say alon... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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6106d505d835b805b22dd8b5d3edd163b0a2fa8e | subsection | 34 | 48 | Upper Space and Time Limits | From the above thesis, what this means is that spacetime must have space and time limits if it is to have a universal and absolute maximum speed; that is, for any two points x_{2}, and x_{1}, and any two-points on the time-axis t_{2}, and t_{1}, the following must hold: x_{2}-x_{1}\ge \ell _{p}, and t_{2}-t_{1}\ge t_{p... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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9b37af70d711281dd4d7a36d8c65920fd205a4d7 | subsection | 35 | 48 | Spacetime Fluctuations/Uncertainty | An important point to take note of is that, for a point x_{k} on the CST, we are 100\% sure where to locate this point, we simple go directly to the point x_{k} and find it there – this is not true for the QST because \delta _{k}(t) is random and dynamic function – no one and absolutely no one knows what its value at a... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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6fd1017c5fd4648d7d3de2dcac404d8a8c03352f | subsection | 36 | 48 | Energy-Momentum Fluctuations/Uncertainty | Taking the time derivative of the coordinates of the QST, we have: \dot{X}_{\mu }(x)=\dot{x}_{\mu }+\ell _{p}\dot{\delta }_{\mu }(x), and this implies: \mathcal {P}_{\mu }=p_{\mu }+m\ell _{p}\dot{\delta }_{\mu }(x) where m is the mass of the particle whose momentum is \mathcal {P}_{\mu }; and comparing this with: \math... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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6fc03a0136c055e1db1953afe48ffc5d11cac941 | subsection | 37 | 48 | C-Violation: Possible Reason for Matter-Antimatter Asymmetry | In the Dirac Theory, antiparticles are negative energy particles which travel back in time and these have the opposite electronic charge of their particle counterpart. In this theory [Dirac], the Dirac Equation is symmetric under electronic charge conjugation. What this means is that the same law, or more clearly, the ... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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8875ad7ded73bec356481e6876f59ae500ae3bb4 | subsection | 38 | 48 | C-Violation: Possible Reason for Matter-Antimatter Asymmetry | For the case \Lambda _{0}>0, this entire 3\rm {D}-space will be filled at each and every-point with the cosmological field \Lambda _{0}>0, and likewise for the case \Lambda _{0}<0, this entire 3\rm {D}-space will be filled at each and every-point with the cosmological field \Lambda _{0}<0.]The “picture” of the structur... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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dc2adfd395bdcc84c6a03ef836c05667892113cb | subsection | 39 | 48 | Darkmatter and Darkenergy | The subject of Darkmatter and Darkenergy is a hot topic of intense theoretical and experimental research (see e.g. Sofua 1997; Sofua et al. 1997; Sofua et al. 1997). We find that our search – for a solution to the problem of why the Universe appears to be composed of matter with no significant quantities of antimatter,... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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b41bcf183d66445d753fa0257e21d0cac715ef6b | subsection | 40 | 48 | Darkmatter and Darkenergy | We know from the STR that a particle with imaginary momentum will have to travel at speeds greater than the speed of light. These particles, that travel faster than the speed of light are known as Tachyons and are at present nothing but hypothetical particles born out of a deep theoretical curiocity; they [Tachyons] ha... | {
"cite_spans": []
} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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b34b80345fe4608241b35dda31cf08acb581e794 | subsection | 41 | 48 | A New Model of the Vacuum | In 1930, two years after he proposed his relativistic wave equation, Dirac had to face head-on the inevitable fate of the Dirac Electron foretold by his theory. The intrinsic and inherent spacetime symmetries embodied in the usual mundane CST on which the STR is built that extend to Dirac's Theory, meant negative energ... | {
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} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
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4814ba2cfa14cf3364e86aeee2f5a4432376227c | subsection | 42 | 48 | A New Model of the Vacuum | Actually, the vacuum of QED is different from that of Dirac but retains some features of the Dirac vacuum.The vacuum of QED contains what is known as the zero-point energy, which is a finite intrinsic minimum none-zero energy contained in the vacuum. This energy continuously transforms some of its energy into mass caus... | {
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} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
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c35aacb9845392183b8937877c660ec545c10b1b | subsection | 43 | 48 | A New Model of the Vacuum | Thus the transition: \mathcal {E}_{j}\longrightarrow \mathcal {E}_{vac}:j=1,2, ..., 8, is impossible hence thus, particles will be forbidden by the light-speed barrier from entering the negative energy states!A second and much stronger reason is that, if say by shear chance, the Electron manages to get this infinite en... | {
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} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
] | [
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f7ff4683b836b63b08f0d4e2581c9fafb9347702 | subsection | 44 | 48 | T-Symmetry | The fact that the Full Cosmological Dirac Equation (REF ) is \rm {T}-symmetric, means that we can flip the positive and negative energy solutions about the vacuum energy: \mathcal {E}_{vac}=\Lambda _{0}\hbar c, that is to say, the energy solutions: \mathcal {E}_{1}, \mathcal {E}_{2}, \mathcal {E}_{3} ...., \mathcal {E}... | {
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} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
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ad0786591f03e25a8cf657dc648217ae1954e157 | subsection | 45 | 48 | Discussion and Conclusions | If the reader has gone through this reading up-until the present point, I sincerely believe they [the reader] will agree with me if I say that the intent of this reading – to address the matter/antimatter asymmetry has been dwarfed, or pretty much appears much less significant when compared to what we have actually dis... | {
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353d0d10881a0fcbe7d06109b87f810f4d817a99 | subsection | 46 | 48 | Discussion and Conclusions | The QST clearly defies the sacrosanct \rm {CPT} theorem of Lüder, Bell and Pauli, that every Lorentz invariant theory must observe \rm {CPT}-symmetry. Clearly and without any doubt, the derived Cosmological Dirac equation is Lorentz invariant yet it violates this sacrosanct \rm {CPT} theorem. Not only is this equation ... | {
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} | 0807.1754 | On a New 4-Vector Cosmological Field Theory | [
"G. G. Nyambuya"
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74caabdadc8b18c7cb98faa93a64e0fd25aeca68 | subsection | 47 | 48 | Discussion and Conclusions | This is just my opinion and obviously this may change as more understanding of reality and nature comes to light.In closing, allow me to say that, writing this reading and my other readings Nyambuya (2007,\, 2008a,b) has been such pain because in all these readings, I find myself having to introduce new ideas, terms an... | {
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e0d4526fddeeec89475b8b7c5eef3f6f780f0a7e | abstract | 0 | 13 | Abstract | The propagation of field disturbances is examined in the context of the
effective Yang-Mills Lagrangian, which is intended to be applied to QCD
systems. It is shown that birefringence phenomena can occur in such systems
provided some restrictive conditions, as causality, are fulfilled. Possible
applications to phenomen... | {
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} | 10.1103/PhysRevD.78.034004 | 0807.1755 | Propagation of field disturbances in the Yang-Mills theory | [
"V. A. De Lorenci",
"S. Y. Li"
] | [
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] | 2,008 | en | Physics | [
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9b520946c8a0222550b81d4234785765eac35351 | subsection | 1 | 13 | Introduction | Small disturbances on nonlinear fields propagate with velocity depending
on the polarization states. In general there will be two polarization
modes, leading to the existence of two waves propagating with different velocities. This
phenomenon is known in the literature as birefringence. In the Maxwell theory
(i.e., Abe... | {
"cite_spans": [
{
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"doi": "",
"end": 407,
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"raw": "See, e.g., L. Landau and E. Lifchitz, Electrodynamics of Continuous Media, (Ed. Elsevier, 1984).",
"source_ref_id": "5724a5ef06b376353161ddb555252fa9f390a321",
"start": 288
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... | 10.1103/PhysRevD.78.034004 | 0807.1755 | Propagation of field disturbances in the Yang-Mills theory | [
"V. A. De Lorenci",
"S. Y. Li"
] | [
"hep-ph"
] | 2,008 | en | Physics | [
-0.04523320496082306,
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5a8db882987d4e7b710304b0fa7b67f284c522d6 | subsection | 2 | 13 | Introduction | Sections IV and V are dedicated to the
possible applications to phenomenology
and the effective geometry issue, respectively.
Finally, some final remarks are presented in the
conclusion section.The present investigation is considered under the regime of the eikonal approximation,
as addressed in . Latin indices run in ... | {
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"doi": "",
"end": 298,
"openalex_id": "",
"raw": "V. A. De Lorenci, R. Klippert, M. Novello and J. M. Salim, Phys. Lett. B 482, 134 (2000).",
"source_ref_id": "8fe4aabbbcd0adb59706c76a2ecad713c8058d9f",
"start": 194
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} | 10.1103/PhysRevD.78.034004 | 0807.1755 | Propagation of field disturbances in the Yang-Mills theory | [
"V. A. De Lorenci",
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] | [
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1742d168032033364992b2dea129790650f20c85 | subsection | 3 | 13 | Field equations for one-parameter spin-one theories | The strength tensor field F_{\mu \nu }^{(a)} and the gauge field A_{\mu }^{(a)} are
related byF_{\mu \nu }^{(a)} = \partial _{\mu }A_{\nu }^{(a)} - \partial _{\nu }A_{\mu }^{(a)}
+ C^{abc}A_{\mu }^{(b)}A_{\nu }^{(c)},where C^{abc} represent the structure constant for a compact Lie group G.
This tensor field can be conv... | {
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} | 10.1103/PhysRevD.78.034004 | 0807.1755 | Propagation of field disturbances in the Yang-Mills theory | [
"V. A. De Lorenci",
"S. Y. Li"
] | [
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] | 2,008 | en | Physics | [
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b351654fe21aa60d54d54faf44ca3dfdb6bdfae3 | subsection | 4 | 13 | The propagation of the field disturbances | In this section we analyze the propagation of waves associated with
the discontinuities of the field .
Let us consider a surface of discontinuity \Sigma defined by
{\cal Z}(x^{\mu }) = 0. Whenever \Sigma is a global surface, it divides the spacetime
in two distinct regions U^- and U^+ ({\cal Z}<0 and {\cal Z}>0, respec... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 102,
"openalex_id": "",
"raw": "J. Hadamard, in Leçons sur la propagation des ondes et les équations de l'hydrodynamique (Ed. Hermann, Paris, 1903).",
"source_ref_id": "f38bb7849f404a0904ea87f11e38980b320ff14d",
"start... | 10.1103/PhysRevD.78.034004 | 0807.1755 | Propagation of field disturbances in the Yang-Mills theory | [
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"S. Y. Li"
] | [
"hep-ph"
] | 2,008 | en | Physics | [
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13fe3e368a1b6932dea7900e9a495bc395c32d38 | subsection | 5 | 13 | The propagation of the field disturbances | The general solution for the eigenvalue equation is formally given
by det|Z^\mu {}_\beta |=0, and results in the following light cone conditions
, , :k_+^2 &=& \gamma F^{\lambda \mu }F^{\nu }{}_{\lambda }k^+_{\mu }k^+_{\nu },
\qquad \gamma \doteq \frac{4L_{FF}}{L_F}
\\
k_-^2 &=& 0,The \pm signs are related with the tw... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 389,
"openalex_id": "",
"raw": "G. Boillat, J. Math. Phys. 11, 941 (1970).",
"source_ref_id": "1bcaf5b158e34592b8c5140b1a6c28a46b30e7d1",
"start": 0
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"end": 389,... | 10.1103/PhysRevD.78.034004 | 0807.1755 | Propagation of field disturbances in the Yang-Mills theory | [
"V. A. De Lorenci",
"S. Y. Li"
] | [
"hep-ph"
] | 2,008 | en | Physics | [
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39560cb0181ecccdaaf8a296c5ca707fa0fcdb60 | subsection | 6 | 13 | The effective Lagrangian | The effective Lagrangian for QCD in terms of the parameter background field
F can be presented in the form{\cal L}_{eff} = \frac{1}{4}\frac{F}{\bar{g}(t)^2}, \qquad t\doteq \log \frac{F}{\mu ^4}where the effective coupling \bar{g}(t) is implicitly given byt = \int _{g}^{\bar{g}(t)}\!\!\! dg\; \frac{1}{\beta (g)},with \... | {
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"doi": "",
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"raw": "H. Pagels and E. Tomboulis, Nucl. Phys. B 143, 485 (1978).",
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... | 10.1103/PhysRevD.78.034004 | 0807.1755 | Propagation of field disturbances in the Yang-Mills theory | [
"V. A. De Lorenci",
"S. Y. Li"
] | [
"hep-ph"
] | 2,008 | en | Physics | [
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0.... |
7fa5008887ff23863530a4003bd0b4ebb1188056 | subsection | 7 | 13 | Application to the effective Yang-Mills Lagrangian | For the special Lagrangian presented in Eq. (REF ), the factor \gamma in
Eq. (REF ) is given by\gamma = \frac{-4}{E^2(Z^2-1)}G(\bar{g}),where we have defined the quantities:Z^2 & \doteq & \frac{H^2}{E^2}
\\
G(\bar{g}) & \doteq & \frac{\bar{g}\dot{\bar{g}} - 3\dot{\bar{g}}^2
+ \bar{g}\ddot{\bar{g}}}{\bar{g}^2-2\bar{g}\... | {
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"start": 1096
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"doi": "... | 10.1103/PhysRevD.78.034004 | 0807.1755 | Propagation of field disturbances in the Yang-Mills theory | [
"V. A. De Lorenci",
"S. Y. Li"
] | [
"hep-ph"
] | 2,008 | en | Physics | [
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509306b6fff560c646b8983562f260f10449d89e | subsection | 8 | 13 | Application to the effective Yang-Mills Lagrangian | (REF ) that\frac{1}{\bar{g}(t)} = b_0 t - 2\frac{b_1}{b_0} \log t + \cdotsIntroducing these results in the effective Lagrangian we obtain , {\cal L}_{eff} = \frac{1}{4}b_0 F \log \frac{F}{\mu ^4}.For this case the function G(\bar{g}) results to beG(\bar{g}) = -\frac{1}{2} \frac{1}{t+1}.Since t>1 at the large mean field... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 770,
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"raw": "D. J. Gross and F. Wilczek, Phys. Rev. Lett. 30, 1343 (1973).",
"source_ref_id": "9da38af0b27a039b3b0c40233b8f27fb3c966bd3",
"start": 597
}
]
} | 10.1103/PhysRevD.78.034004 | 0807.1755 | Propagation of field disturbances in the Yang-Mills theory | [
"V. A. De Lorenci",
"S. Y. Li"
] | [
"hep-ph"
] | 2,008 | en | Physics | [
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a15e5b672fb600a5b303309bdcafc2bc58fef27f | subsection | 9 | 13 | Observable for birefringence | As shown in the previous section, birefringence effects
can occur in the Yang-Mills fields. Nevertheless, due
to confinement phenomenon, a direct measurement of these effects
on gluons propagating in an external color field seems to be improbable.
However, deconfined quark-gluon matter, also known as quark-gluon plasma... | {
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"arxiv_id": "",
"doi": "",
"end": 1343,
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"raw": "see, e.g., Z. T. Liang and X. N. Wang, Phys. Rev. Lett. 94, 102301 (2005).",
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2c42f66bb078ff718374f018c9f46797cc67a2d1 | subsection | 10 | 13 | Observable for birefringence | The conventional way to measure \vec{P} of a single \Lambda is by measuring
the direction vector (denoted as \hat{p}) of the momenta of the daughter particles,
e.g., proton or pion from the \Lambda decay, at the rest frame of \Lambda .
Then the angular distribution,\frac{dN}{d cos \theta } \sim 1+ \alpha \hat{p} \cdot ... | {
"cite_spans": []
} | 10.1103/PhysRevD.78.034004 | 0807.1755 | Propagation of field disturbances in the Yang-Mills theory | [
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6fbb8887487349b19e516c8ae89d1040429bbe55 | subsection | 11 | 13 | The effective geometry issue | The effective theory approach has long been considered as a possible way to understand
confinement phenomena. One of the possible ways to investigate these phenomena consists in
the construction of analogue models in which confinement would be related with an
event horizon formation, as it occurs in the black hole phys... | {
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"raw": "P. Castorina, D. Kharzeev and H. Satz, Eur. Phys. J. C 52, 187 (2007).",
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... | 10.1103/PhysRevD.78.034004 | 0807.1755 | Propagation of field disturbances in the Yang-Mills theory | [
"V. A. De Lorenci",
"S. Y. Li"
] | [
"hep-ph"
] | 2,008 | en | Physics | [
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91eb6f6e6a8f0dc53d4188e088abdd092c96a24f | subsection | 12 | 13 | Conclusions | In this paper the propagation of field disturbances was
investigated in the context of the effective Yang-Mills
Lagrangian. The general dispersion relations for one-parameter
Lagrangians, Eqs. (REF ) and (), were derived employing the method presented in
, . It was shown that birefringence phenomena can
occur.Let us re... | {
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"raw": "V. A. De Lorenci, R. Klippert, M. Novello and J. M. Salim, Phys. Lett. B 482, 134 (2000).",
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"... | 10.1103/PhysRevD.78.034004 | 0807.1755 | Propagation of field disturbances in the Yang-Mills theory | [
"V. A. De Lorenci",
"S. Y. Li"
] | [
"hep-ph"
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6af1db0477a8ebff02cb345206710069f4983640 | abstract | 0 | 19 | Abstract | Phylogenetic trees describe the evolutionary history of a group of
present-day species from a common ancestor. These trees are typically
reconstructed from aligned DNA sequence data. In this paper we analytically
address the following question: is the amount of sequence data required to
accurately reconstruct a tree si... | {
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} | 0807.1756 | Phylogenetic information complexity: Is testing a tree easier than
finding it? | [
"Mike Steel",
"Laszlo Szekely",
"Elchanan Mossel"
] | [
"q-bio.PE",
"q-bio.QM"
] | 2,008 | en | Quantitative Biology | [
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45819b6abfec1232375e060a85345eb8518af36a | subsection | 1 | 19 | Introduction | Phylogenetic trees are widely used in evolutionary biology to describe how species have evolved from a shared ancestral species. In the last 25 years, aligned DNA sequence data and related sequences (amino acids, codons etc) have been widely used for reconstructing and analysing these trees , . Tree reconstruction meth... | {
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"raw": "Felsenstein, J., 2003. Inferring phylogenies. Sinauer Press.",
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"doi": "... | 0807.1756 | Phylogenetic information complexity: Is testing a tree easier than
finding it? | [
"Mike Steel",
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] | [
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