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More Obituaries for Claudia Commo
Claudia Commo
Claudia Commo, LVN, age 68, died Monday, July 22, 2013, in the care of her loving colleagues and friends at Houston Hospice. She was born in Philadelphia, Pa on July 10, 1945, to her parents Kathryn G. and Claude W. Commo. She is survived by her niece, Cynthia Ann Ridling, of Griffin, Georgia.
Ms. Commo's lifelong passion was her nursing career which she pursued with great love and unflagging compassion for 41 years. She graduated from St. Luke's Hospital School of Vocational Nursing in September, 1972. She worked fulltime as an LVN in a wide variety of settings including St. Luke's Hospital Cardiac Intensive Care, Community School of Vocational Nursing at Eastway General Hospital, Bering-Omega Community Services/Omega House and Houston Hospice. The last 25 years of her career were spent in very challenging, non-profit home and inpatient/residential hospice settings caring for those who were dying; thus she earned widespread respect and admiration in her profession and the communities she served. She was known as a trailblazer in the early days of both HIV and residential hospice care and was frequently called upon to provide teaching and training to nursing and medical students as well as to many volunteer and professional caregivers. Her great skill, her fierce advocacy for the comfort and well-being of her patients and their friends and families, and her always-at-the-ready, quick wit were her trademarks.
Claudia's personal interests and hobbies included reading, gardening and her pets. She always cherished long-term animal companions, her beloved Chihuahua, Gizmo, and, more recently her cat, Clem, and she frequently offered temporary shelter to stray or injured animals in her neighborhood or to pets of friends who could no longer care for them. She also provided years of dedicated service on the Board of Directors of two homeowners' associations in the areas where she resided.
A Memorial Service will be held Sunday, August 4, 2013, at 4:00 p.m. at St. Mark's United Methodist Church, 600 Pecore, Houston, TX, 77009. In lieu of flowers, please consider remembering Claudia with a donation to Houston Hospice, Bering-Omega Community Services, SPCA/Houston or the .
Published in Houston Chronicle on July 28, 2013
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Aeroport Henri Coandă T1 este o haltă situată pe Aeroportul Internațional Henri Coandă București, la 19 km nord-est de Gara de Nord. Trenurile sunt programate să plece la fiecare 40 minute și durează 25 de minute pentru a ajunge la Gara de Nord. Stația a fost deschisă la 13 septembrie 2020, împreună cu stația Pationar PO, cu câteva luni înainte de campionatul de fotbal Euro 2020.

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\section{Introduction}

The relativistic quantum dynamics of scalar and spin-$\frac{1}{2}$ particles on curved background space-time geometries as well as G\"{o}del, and G\"{o}del-type metrics have been investigated by various authors (see \cite{aa1} and references therein). The Klein-Gordon and Dirac equations in a G\"{o}del-type space-times with positive, zero and negative curvatures were first studied in \cite{aa2}. The close relationship between the quantum dynamics of the scalar particle in the background of general relativity with the G\"{o}del solutions and the Landau levels in flat, spherical and hyperbolic spaces were investigated in \cite{aa3}. Later, the same problem was studied by solving the Klein-Gordon equation in the Som-Raychaudhuri space-time in \cite{aa4}. The authors in \cite{aa5} solved the Klein-Gordon equation in a family of G\"{o}del-type solutions with the cosmic string and analyzed the similarity of the energy eigenvalue with the Landau levels in flat, spherical and hyperbolic spaces. Quantum influence of topological defects in a G\"{o}del-type space-times in flat, spherical and hyperbolic cases, were investigated in \cite{aa6}. The relativistic quantum dynamics of a Dirac particle with topological defects in a G\"{o}del-type space-times with torsion have been investigated in \cite{aa7}. The relativistic quantum dynamics of an electrically charged particle described by the Klein-Gordon oscillator subject to a Coulomb-type potential was investigated in \cite{cc5}. Weyl fermions in a family of G\"{o}del-type geometries with topological defects were investigated in \cite{aa8}. The relativistic quantum dynamics of a scalar particle in 4D curved space-time with the cosmic string was investigated in \cite{EPJP}. The relativistic quantum dynamics of scalar and spin-$\frac{1}{2}$ particles subject to various kind of potentials have been investigated in several areas of physics ({\it e. g.}, \cite{aa9,aa10,aa11,aa12,aa13,aa14,aa15,aa16,aa17,aa18,aa19,aa20,aa21,aa22,aa23}). Linear confinement of quantum particle by introducing a linear scalar potential into the relativistic system by modifying the mass term has great importance for models of confinement of quarks \cite{Chric}. It is worth mentioning that the linear scalar potential has attracted a great interest in atomic and molecular physics \cite{aa25,aa26,aa27,aa28,aa29,aa30}, and in the relativistic quantum mechanics \cite{EPJC,EPJC2,d12,d16,d15,aa31,aa32, aa33,aa35,aa36,aa37,aa38,aa40,aa47,aa48,aa49, aa50,aa51}.

Interactions of the Dirac oscillator with the gravitational fields produced by topological defects were investigated in \cite{cc1}. The influence of Aharonov-Casher effect on the Dirac oscillator in three different scenarios of general relativity: the Minkowski space-time, the cosmic string and the cosmic dislocation space-time were studied in \cite{cc2}. The influence of non-inertial effects on the Dirac oscillator in the cosmic string space-time was investigated in \cite{cc3}. The Dirac equation in a class of topologically trivial flat G\"{o}del-type space-time was investigated in \cite{EPJC3}. Dirac fermions in the Som-Raychaudhuri space-time with a linear scalar and vector potentials were investigated in \cite{d12}. A new model for study the confinement of spin-half particles in a two-dimensional quantum ring systems described by the Dirac equation with a new coupling were studied in \cite{cc4}. The Dirac oscillator in the context of Doubly General Relativity was investigated in \cite{cc6}. Effects of gravitational fields produced by topological defects on the Dirac field and oscillator in a spinning cosmic string was examined in \cite{cc7}. The dynamics of 2D Dirac oscillator in the space-time of a magnetic cosmic string were investigated in \cite{cc8}. The generalized Dirac oscillator in the cosmic string space-time replacing the momentum $p_{\mu}$ with its alternative $p_{\mu}+m\,\omega\,\beta\,f_{\mu} (x_{\mu})$ was studied in \cite{cc9}. In particular, the quantum dynamics was considered for the function $f_{\mu} (x_{\mu})$ to be taken as Cornell-type, exponential-type and singular potentials form. The generalized Dirac oscillator was introduced in (2+1)-dimensional the world \cite{cc10}. The Dirac oscillator under the influence of non-inertial effects in a rotating frame in the cosmic string space-time were investigated in \cite{cc11}. The Dirac oscillator has also been analyzed in various physical systems, such as in the presence of external fields \cite{cc12}, and in the presence of a magnetic quantum flux \cite{cc13,cc14,cc15,cc16}. Investigation of magnetization and persistent current of mass-less Dirac fermions confined in a quantum dot in a graphene layer with topological defects were done in \cite{cc17}. Non-inertial effects on the Dirac oscillator in the background space-time generated by a cosmic string have been investigated \cite{cc18,cc19,cc20}. The (1+2)-dimensional Dirac oscillator in the presence of a homogeneous magnetic field in an Aharonov-Casher system were investigated in \cite{cc21}. The relativistic quantum dynamics of spin-half particle by solving the Dirac equation in (1+2)-dimensional G\"{u}rses space-time was investigated in \cite{cc22}.

The Klein-Gordon oscillator \cite{bb1,bb2} was inspired by the Dirac oscillator \cite{bb3} applied to half-integer spin particles. The spectral distribution of energy levels and eigenfunction describing the state of a particle by solving the Klein-Gordon equation in one-dimensional version of the Minkowski space-time were studied in \cite{bb4}. The Klein-Gordon oscillator in the cosmic string space-time in the presence of external fields were studied in \cite{bb5}. The Klein-Gordon oscillator in the presence of a Coulomb-type potential was investigated by two ways : (i) by modifying the mass term $m \rightarrow m+S(r)$ \cite{bb6} and (ii) via the minimal coupling \cite{aa50} besides a linear scalar potential. The relativistic quantum effects on the Klein-Gordon oscillator with linear scalar and Coulomb-type potentials were investigated in \cite{aa49}. The Klein-Gordon oscillator has also been investigated in various physical system, such as in the background space-time generated by the cosmic string \cite{bb8}, in the background of a G\"{o}del-type space-time under the influence of gravitational fields produced by topological defects \cite{bb9}, in the background of the Som-Raychaudhuri space-time with a disclination parameter \cite{aa5}, Aharonov-Bohm effect for bound states on a scalar particle in a space-time with a spacelike dislocation \cite{bb48}, in non-commutative (NC) phase space \cite{bb10}, in (1+2)-dimensional G\"{u}rses space-time background \cite{ff4}, and in (1+2)-dimensional G\"{u}rses space-time background subject to Coulomb-type potential \cite{ff5}.

Our intention now is to extend the above studies not only to two-,three-, and four-dimensions but to consider this dynamics in general background space-time produced by topological defects using the Kaluza-Klein theory \cite{bb12,bb13,bb11}. This new proposal establishes that the electromagnetism can be introduced through an extra (compactified) dimension in the space-time where, the spatial dimension becomes five-dimensional. These sources of gravitational fields play an important role in condensed matter physics systems \cite{bb17,bb18,bb19,bb20}. Besides, the topological defects like the cosmic strings \cite{bb21}, domain walls \cite{bb22}, and global mono-pole \cite{bb23} provides a tiny relation between the effects in cosmology and gravitation. In condensed matter physics systems where, topological defects analogue to the cosmic strings appear in phase transitions in liquid crystals \cite{bb24,bb25}. In addition, the Kaluza-Klein theory has found wide applications in string theory \cite{bb26}, in the presence of torsion \cite{bb31,bb32}, fermions \cite{bb33,bb34,bb35}, and in the studies of Lorentz symmetry violation (LSV) in  \cite{bb36,bb37,bb38}. Based on these generalizations of topological defects space-time within the Kaluza-Klein theory, analogue effects to the Aharonov-Bohm effect for bound states were investigated in \cite{aa6,bb28,bb39,bb40, bb50}. The Klein-Gordon oscillator on curved background within the Kaluza-Klein theory were investigated in \cite{aa6}. Some other physical systems in the Kaluza-Klein theory were studied in \cite{bb14,bb15, bb16,bb27,bb29}

The relativistic quantum dynamics of scalar particle of mass $m$ is described by the Klein-Gordon equation :
\begin{equation}
\frac{1}{\sqrt{-g}}\,\partial_{\mu} (\sqrt{-g}\,g^{\mu\nu}\,\partial_{\nu}\,\Psi)=m^2\,\Psi,
\label{1}
\end{equation}
with $g$ is the determinant of metric tensor with $g^{\mu\nu}$ its inverse. If one introduces a scalar potential into the Klein-Gordon equation by modifying the mass term: $m \rightarrow m + S (r)$ \cite{WG} where, $S (r)$ is the scalar potential. The KG-equation becomes
\begin{equation}
\frac{1}{\sqrt{-g}}\,\partial_{\mu} (\sqrt{-g}\,g^{\mu\nu}\,\partial_{\nu}\,\Psi)=(m + S(r))^2\,\Psi.
\label{2}
\end{equation}
To couple the Klein-Gordon field with the oscillator \cite{bb1,bb2}, the following change in the momentum operator is considered \cite{dd2} :
\begin{equation}
p_{\mu}\rightarrow p_{\mu}+i\,m\,\omega\,X_{\mu},
\label{3}
\end{equation}
where $\omega$ is the frequency of oscillatory particle and the vector $X_{\mu}=(0, r, 0, 0, 0)=r\,\hat{r}$ where, $r$ being the distance of the particle from the string. To generalize the Klein-Gordon oscillator we have replaced $\vec{r}$ by the function $f(r)$ into $X_{\mu}$ as:
\begin{equation}
X_{\mu}=(0, f(r), 0, 0, 0)=f(r)\,\hat{r}.
\label{4}
\end{equation}
Therefore, we have the following generalized Klein-Gordon oscillator equation:
\begin{equation}
\frac{1}{\sqrt{-g}}\,(\partial_{\mu}+m\,\omega\,X_{\mu})\sqrt{-g}\,g^{\mu\nu}\,(\partial_{\nu}-m\,\omega\,X_{\nu})\,\Psi=(m+ S(r))^2\,\Psi.
\label{5}
\end{equation}

This paper comprises as follow : in {\it section 2}, we study the generalized Klein-Gordon oscillator in the cosmic string space-time in the Kaluza-Klein theory subject to a linear scalar potential; in {\it section 3}, the generalized Klein-Gordon oscillator in the background of a magnetic cosmic string in the Kaluza-Klein theory subject to a linear scalar potential, and finally the conclusion in {\it section 4}.

\section{Generalized Klein-Gordon oscillator in the cosmic string space-time with a linear scalar potential in the Kaluza-Klein theory}

The purpose of this section is to study the Klein-Gordon equation in the background space-time generated by the cosmic string within the Kaluza-Klein theory subject to a linear scalar potential. Linear scalar potential is introduced into the relativistic system by modifying the mass term discussed earlier and this kind of potential has great importance in different branch of physics mentioned in the introduction.

The first study of topological defects in the Kaluza-Klein theory was carried out in \cite{bb14} where, a series of cylindrically symmetric solutions of Einstein and Einstein-Gauss-Bonet equations, were investigated. Various solutions of the cosmic string form in five-dimensions, such as: neutral cosmic string, cosmic dislocation, superconducting cosmic, multi-cosmic string space-time were studied there. The metric corresponding to this geometry can be written as,
\begin{equation}
ds^2=-dt^2+dr^2+\alpha^2\,r^2\,d\phi^2+dz^2+dx^2,
\label{6}
\end{equation}
where $t$ is the time coordinate, $x$ is the coordinate associated with the fifth additional dimensions and $(r, \phi, z)$ are cylindrical coordinates. These coordinates assumed the ranges $-\infty < (t, z) < \infty$, $0 \leq r < \infty$, $0 \leq \phi \leq 2\,\pi$, and $0 < x < 2\,\pi\,a$ where, $a$ is the radius of the compact dimension $x$. The $\alpha$ parameter characterizing the cosmic string and in terms of linear mass density $\mu$ is $\alpha=1-4\,\mu$ \cite{bb21}, where $G=1=c=\hbar$. Cosmology and gravitation imposes limits of $\alpha$ parameter which is restricted to $\alpha < 1$ \cite{bb21}. Moreover, in condensed matter physics systems, this restriction is free and the opposite case $\alpha > 1$, the known negative disclination \cite{bb29} can occur in several systems as those described by \cite{bb25}.

By considering the line element (\ref{6}) into the Eq. (\ref{5}), we obtain the following differential equation:
\begin{eqnarray}
&&[-\partial_{t}^2+\partial_{z}^2+\partial_{x}^2+\partial_{r}^2+\frac{1}{r}\,\partial_{r}+\frac{1}{\alpha^2\,r^2}\,\partial_{\phi}^2-m\,\omega\,(f'(r)+\frac{f (r)}{r})-m^2\,\omega^2\,f^{2} (r)\nonumber\\
&&-(m+ S(r))^2]\,\Psi=0.
\label{7}
\end{eqnarray}
The above equation is independent of $t, \phi ,z, x$, so we choose the following ansatz for the function $\Psi$
\begin{equation}
\Psi (t, r, \phi, z, x)=e^{i\,(-E\,t+l\,\phi+k\,z+q\,x)}\,\psi(r),
\label{8}
\end{equation}
where $E$ is the total energy, $l=0,\pm\,1,\pm\,2...\in {\bf Z}$ are the eigenvalue of the $z$-component of the angular momentum operator, and $k, q$ are constants.

Substituting the above ansatz into the Eq. (\ref{7}), we get the following radial wave-equation for $\psi (r)$ :
\begin{eqnarray}
&&\psi''(r)+\frac{1}{r}\,\psi'(r)+[E^2-k^2-q^2-\frac{l^2}{\alpha^2\,r^2}-m\,\omega\,(f'(r)+\frac{f (r)}{r})\nonumber\\
&&-m^2\,\omega^2\,f^{2}(r)-(m+S(r))^2]\,\psi(r)=0.
\label{9}
\end{eqnarray}

In this work, we consider a special kind of potential which has many applications including the linear confinement of quarks which we discussed in the introduction is given by
\begin{equation}
S(r)=k_{L}\,r.
\label{10}
\end{equation}
where $k_{L}$ is the linear confining parameter.

We choose the function $f(r)$ as Cornell-type potential form given by \cite{cc9,bb41}
\begin{equation}
f(r)=a\,r+\frac{b}{r}\quad,\quad a, b>0.
\label{function}
\end{equation}

Substituting the function Eq. (\ref{function}) into the Eq. (\ref{9}) and using the potential (\ref{10}), we obtain the following equation :
\begin{equation}
\psi''(r)+\frac{1}{r}\,\psi'(r)+[\lambda-\tilde{\omega}^2\,r^2-\frac{\xi^2_{s}}{r^2}-2\,m\,k_{L}\,r]\,\psi(r)=0,
\label{11}
\end{equation}
where
\begin{eqnarray}
&&\lambda=E^2-k^2-q^2-m^2-2\,m\,\omega\,a-2\,m^2\,\omega^2\,a\,b,\nonumber\\
&&\tilde{\omega}=\sqrt{m^2\,\omega^2\,a^2+k^{2}_{L}},\nonumber\\
&&\xi_{s}=\sqrt{\frac{l^2}{\alpha^2}+m^2\,\omega^2\,b^2}.
\label{12}
\end{eqnarray}
Transforming $\rho=\sqrt{\tilde{\omega}}\,r$ into the Eq. (\ref{11}), we obtain
\begin{equation}
\psi''(\rho)+\frac{1}{\rho}\,\psi'(\rho)+[\lambda_0-\rho^2-\frac{\xi^2_{s}}{\rho^2}-\theta\,\rho]\,\psi(\rho)=0,
\label{13}
\end{equation}
where
\begin{equation}
\lambda_0=\frac{\lambda}{\tilde{\omega}}\quad,\quad \theta=\frac{2\,m\,k_{L}}{\tilde{\omega}^{\frac{3}{2}}}.
\label{aa}
\end{equation}

Now, we use the appropriate boundary conditions to investigate the bound states solution in this problem. It is require that the regularity of wave-function at the origin and the normalizability at infinity. Then we proceed with
the analysis of the asymptotic behaviour of the radial eigenfunction at origin and in the infinite. These conditions are necessary since the wave-function must be well-behaved in these limit, and thus, bound states of the energy
eigenvalue for the confinement can be obtained. With these conditions, we obtain the convergence of the wave-function at the origin ($\rho \rightarrow 0$) and at infinity ($\rho \rightarrow \infty$). Let us impose the requirement that $\psi (\rho) \rightarrow 0$ both at $\rho \rightarrow 0$ and $\rho \rightarrow \infty$. Suppose the possible solution to the Eq. (\ref{13}) is
\begin{equation}
\psi (\rho)=\rho^{|\xi_{s}|}\,e^{-\frac{1}{2}\,(\theta+\rho)\,\rho}\,H (\rho),
\label{14}
\end{equation}
where $H (\rho)$ is an unknown function. Substituting the solution Eq. (\ref{14}) into the Eq. (\ref{13}), we obtain
\begin{equation}
H''(\rho)+[\frac{\gamma}{\rho}-\theta-2\,\rho]\,H'(\rho)+[-\frac{Q}{\rho}+\Theta]\,H (\rho)=0,
\label{17}
\end{equation}
where
\begin{eqnarray}
&&\gamma=1+2\,\xi_s,\nonumber\\
&&\Theta=\lambda_0+\frac{\theta^2}{4}-2\,(1+\xi_s),\nonumber\\
&&Q=\frac{\theta}{2}\,(1+2\,\xi_s).
\label{18}
\end{eqnarray}
Equation (\ref{17}) is the biconfluent Heun differential equation \cite{aa30,aa49,aa50,bb41,bb42,ff2,ff3} with $H (\rho)$ is the Heun polynomials function.

The above Eq. (\ref{17}) can be solved by the power series method \cite{bb43}
\begin{equation}
H (\rho)=\sum^{\infty}_{i=0} c_{i}\,\rho^{i}.
\label{19}
\end{equation}
Substituting Eq. (\ref{19}) into the Eq. (\ref{17}), we get the following recurrernce relation for the coefficients:
\begin{equation}
c_{n+2}=\frac{1}{(n+2)(n+1+\gamma)}\,[\{Q+\theta\,(n+1) \}\,c_{n+1}-(\Theta-2\,n)\,c_{n}].
\label{20}
\end{equation}
And the various coefficients are
\begin{equation}
c_1=\frac{Q}{\gamma}\,c_0,\quad c_2=\frac{1}{2\,(1+\gamma)}\,[(Q+\theta)\,c_{1}-\Theta\,c_{0}].
\label{21}
\end{equation}
The bound states solution to the Eq. (\ref{17}) can be obtained because there is no divergence of the wave-function both at $\rho \rightarrow 0$ and $\rho \rightarrow \infty$. As we have written the function $H (\rho)$ as a power series expansion around the origin in Eq. (\ref{19}). Thereby, the bound states solution can be achieved by imposing that the power series expansion becomes a polynomial of degree $n$. Through the recurrence relation Eq. (\ref{20}), we can see that the power series expansion becomes a polynomial of degree $n$ by imposing two conditions \cite{aa30,aa50,ff2,ff3,bb41,bb44,bb45,bb46,bb47}:
\begin{equation}
\Theta=2\,n.
\label{22}
\end{equation}
And
\begin{equation}
c_{n+1}=0,\quad (n=1,2,3,4,......).
\label{23}
\end{equation}
Using the condition $\Theta=2\,n$, we get the following eigenvalue $E_{n,l}$:
\begin{eqnarray}
&&\lambda_0+\frac{\theta^2}{4}-2\,(1+\xi_s)=2\,n\nonumber\\\Rightarrow
&&E^{2}_{n,l}=k^2+q^2+m^2+2\,m\,\omega\,a+2\,m^2\,\omega^2\,a\,b\nonumber\\
&&+2\,\tilde{\omega}\,(n+1+\sqrt{\frac{l^2}{\alpha^2}+m^2\,\omega^2\,b^2})-\frac{m^2\,k^{2}_{L}}{\tilde{\omega}^2}.
\label{24}
\end{eqnarray}
Equation (\ref{24}) is the bound states energy eigenvalue of a scalar particle associated with $n^{th}$ radial modes.

The corresponding wave-function is given by
\begin{equation}
\psi_{n,l} (\rho)=\rho^{|\xi_s|}\,e^{-\frac{1}{2}\,[\frac{2\,m\,k_{L}}{\tilde{\omega}^{\frac{3}{2}}}+\rho]\,\rho}\,H (\rho).
\label{25}
\end{equation}

Now, we impose the additional condition $c_{n+1}=0$ to find the individual energy levels and corresponding wave function one by one as done in \cite{aa30,aa50,bb44,bb45}. As example, for $n=1$, we have $c_2=0$ which implies
\begin{eqnarray}
&&c_1=\frac{2}{Q+\theta}\,c_0 \Rightarrow \frac{Q}{\gamma}=\frac{2}{Q+\theta}\nonumber\\\Rightarrow
&&\tilde{\omega}_{1,l}=[m^2\,k^2_{L 1}\,(\frac{3}{2}+\sqrt{\frac{l^2}{\alpha^2}+m^2\,\omega^2\,b^2})]^{\frac{1}{3}},
\label{26}
\end{eqnarray}
where we have adjusted the parameter $k_{L}$ such that the first degree polynomial solution for $n=1$ can be obtained \cite{bb41}. Therefore, the ground state energy eigenvalue for $n=1$ is given by
\begin{eqnarray}
&&E^{2}_{1,l}=k^2+q^2+m^2+2\,m\,\omega\,a+2\,m^2\,\omega^2\,a\,b\nonumber\\
&&+2\,\tilde{\omega}_{1,l}\,(n+1+\sqrt{\frac{l^2}{\alpha^2}+m^2\,\omega^2\,b^2})-\frac{m^2\,k^{2}_{L 1}}{\tilde{\omega}^2_{1,l}},
\label{27}
\end{eqnarray}
where $\tilde{\omega}_{1,l}$ is given by Eq. (\ref{26}). The corresponding wave-function is given by
\begin{equation}
\psi_{1,l} (\rho)=\rho^{\sqrt{\frac{l^2}{\alpha^2}+m^2\,\omega^2\,b^2}}\,e^{-\frac{1}{2}\,(2\,c_1+\rho)\,\rho}\,(c_0+c_1\,\rho),
\label{28}
\end{equation}
where
\begin{equation}
c_1=\frac{1}{\sqrt{\frac{3}{2}+\sqrt{\frac{l^2}{\alpha^2}+m^2\,\omega^2\,b^2}}}.
\label{29}
\end{equation}

We discuss below few case of the above relativistic energy eigenvalue Eq. (\ref{24}) of the relativistic system.

\vspace{0.2cm}
{\bf Case 1} : If one choose $b \rightarrow 0$, $a \rightarrow 1$, that is, the Klein-Gordon oscillator subject to a linear scalar potential in the cosmic string space-time in the Kaluza-Klein theory.
\vspace{0.2cm}

The energy eigenvalue Eq. (\ref{24}) becomes
\begin{equation}
E^{2}_{n,l}=k^2+q^2+m^2+2\,m\,\omega+2\,\tilde{\omega}_{n,l}\,(n+1+\frac{|l|}{\alpha})-\frac{m^2\,k^{2}_{L}}{\tilde{\omega}^2_{n,l}}.
\label{30}
\end{equation}
Equation (\ref{30}) is the energy eigenvalue of the Klein-Gordon oscillator field in the cosmic string background within the Kaluza-Klein theory subject to a linear scalar potential. Note that for $k=0=q$, the energy eigenvalue Eq. (\ref{30}) reduces to the result obtained in \cite{aa49}. Thus the relativistic energy eigenvalue Eq. (\ref{30}) is the generalised result in five-dimensions in comparison to those obtained in (1+2)-dimensional case in  \cite{aa49}.

Therefore, the bound state energy eigenvalue for $n=1$ is given by
\begin{equation}
E^{2}_{1,l}=k^2+q^2+m^2+2\,m\,\omega+2\,\tilde{\omega}_{1,l}\,(n+1+\frac{|l|}{\alpha})-\frac{m^2\,k^{2}_{L 1}}{\tilde{\omega}^2_{1,l}}.
\label{31}
\end{equation}
And the corresponding wave function is
\begin{equation}
\psi_{1,l} (\rho)=\rho^{\frac{|l|}{\alpha}}\,e^{-\frac{1}{2}\,(2\,c_1+\rho)\,\rho}\,(c_0+c_1\,\rho),
\label{32}
\end{equation}
where
\begin{eqnarray}
&&c_1=\frac{1}{\sqrt{\frac{3}{2}+\frac{|l|}{\alpha}}},\nonumber\\
&&\tilde{\omega}_{1,l}=[m^2\,k^2_{L 1}\,(\frac{3}{2}+\frac{|l|}{\alpha})]^{\frac{1}{3}}.
\label{33}
\end{eqnarray}

\vspace{0.2cm}
{\bf Case 2} : If one choose $k_{L} \rightarrow 0$, that is, without any scalar potential in the relativistic system.
\vspace{0.2cm}

From Eq. (\ref{11}), we obtain the following equation
\begin{equation}
\psi''(r)+\frac{1}{r}\,\psi'(r)+[\lambda-m^2\,\omega^2\,a^2\,r^2-\frac{\xi^2_{s}}{r^2}]\,\psi(r)=0,
\label{34}
\end{equation}
Introducing a new variable $s=m\,\omega\,a\,r^2$ into the above equation, we obtain \cite{bb49}
\begin{equation}
\psi''(s)+\frac{1}{s}\,\psi' (s)+\frac{1}{s^2}\,(-\xi_1\,s^2+\xi_2\,s-\xi_3)\,\psi (s)=0,
\label{35}
\end{equation}
where
\begin{equation}
\xi_1=\frac{1}{4}\quad,\quad \xi_2=\frac{\lambda}{4\,m\,\omega\,a}\quad,\quad \xi_3=\frac{\xi^2_{s}}{4}.
\label{36}
\end{equation}
Compairing the above Eq. (\ref{35}) with (\ref{A.1}) in appendix A, we get
\begin{eqnarray}
&&\alpha_1=1,\quad \alpha_2=0,\quad \alpha_3=0,\quad \alpha_4=0,\quad \alpha_5=0,\nonumber\\
&&\alpha_6=\xi_1,\quad \alpha_7=-\xi_2,\quad \alpha_8=\xi_3,\quad \alpha_9=\xi_1,\nonumber\\
&&\alpha_{10}=1+2\,\sqrt{\xi_3},\quad \alpha_{11}=2\,\sqrt{\xi_1},\quad \alpha_{12}=\sqrt{\xi_3},\quad \alpha_{13}=-\sqrt{\xi_1}.
\label{37}
\end{eqnarray}
The energy eigenvalue using (\ref{36})--(\ref{37}) into the Eq.(\ref{A.8}) in appendix A is given by
\begin{eqnarray}
&&(2\,n+1)\,\sqrt{\xi_1}-\xi_2+2\,\sqrt{\xi_1\,\xi_3}=0\nonumber\\\Rightarrow
E^{2}_{n,l}&=&k^2+q^2+m^2+2\,m^2\,\omega^2\,a\,b\nonumber\\
&+&2\,m\,\omega\,a\,(2\,n+2+\sqrt{\frac{l^2}{\alpha^2}+m^2\,\omega^2\,b^2}),
\label{38}
\end{eqnarray}
where $n=0,1,2,3,....$.

If one choose $b \rightarrow 0$, $a \rightarrow 1$, that is, the Klein-Gordon oscillator in the cosmic string without potential in the Kaluza-Klein theory. Then, the energy eigenvalue (\ref{38}) becomes
\begin{equation}
E^{2}_{n,l}=k^2+q^2+m^2+4\,m\,\omega\,(n+1+\frac{|l|}{2\,\alpha})
\label{39}
\end{equation}
which is similar to the result obtained in \cite{aa6} (see Eq. (12) in \cite{aa6}). We can see that the Eq. (\ref{38}) is the extended energy eigenvalue of the generalized Klein-Gordon oscillator in the cosmic string space-time without potential in the Kaluza-Klein theory.

\vspace{0.2cm}
{\bf Case 3} : If one choose $b \rightarrow 0$, $a \rightarrow 0$, the Klein-Gordon particle subject to linear scalar potential in a cosmic string background in a Kaluza-Klein theory.
\vspace{0.2cm}

In that case, the Eq. (\ref{11}) becomes
\begin{equation}
\psi''(r)+\frac{1}{r}\,\psi'(r)+[E^2-m^2-k^2-q^2-k^2_{L}\,r^2-\frac{l^2}{\alpha^2\,r^2}]\,\psi(r)=0.
\label{40}
\end{equation}
Transforming $s=K_{L}\,r^2$ into the above equation, we obtain the following differential equation \cite{bb49}
\begin{equation}
\psi''(s)+\frac{1}{s}\,\psi'(s)+\frac{1}{s^2}\,[\frac{E^2-m^2-k^2-q^2}{4\,k_{L}}\,s-\frac{1}{4}\,s^2-\frac{l^2}{4\,\alpha^2}]\,\psi(s)=0.
\label{41}
\end{equation}
As done earlier, we obtain the following energy eigenvalue of the system
\begin{equation}
E_{n,l}=\pm\,\sqrt{k^2+q^2+m^2+2\,k_{L}\,(2\,n+1+\frac{|l|}{\alpha})}.
\label{42}
\end{equation}
Equation (\ref{42}) is the relativistic energy eigenvalue of a scalar particle in the cosmic string space-time in the Kaluza-Klein theory with a linear scalar potential.

\section{Generalized Klein-Gordon oscillator in the magnetic cosmic string space-time with a linear scalar potential in the Kaluza-Klein theory}

In this section, we investigate analogue effect to the Aharonov-Bohm effect for bound states \cite{aa6,bb28,bb48,bb39, bb40,bb50} solution of a scalar particle. By using the Kaluza-Klein theory, we introduce a magnetic flux through the line element of the cosmic string and thus write the generalized Klein-Gordon oscillator equation in five-dimensional space-time subject to a linear scalar potential. This kind of potential has great reserach interested and used for the confinement of quark models and in other branches of physics discussed earlier.

Let us consider the quantum dynamics of a scalar particle moving in the magnetic cosmic string background. In the Kaluza-Klein theory \cite{bb29}, the corresponding metric with the magnetic quantum flux $\Phi$ passing along the symmetry axis of the string assumes the following form
\begin{equation}
ds^2=-dt^2+dr^2+\alpha^2\,r^2\,d\phi^2+dz^2+(dx+\frac{\Phi}{2\,\pi}\,d\phi)^2
\label{43}
\end{equation}
with cylindrical coordinates are used. The quantum dynamics is described by the Eq. (\ref{2}) with the following change in the inverse matrix tensor $g^{\mu\nu}$,
\begin{equation}
g^{\mu\nu}=\left (\begin{array}{lllll}
-1 & 0 & \quad 0 & 0 & \quad 0 \\
\quad 0 & 1 & \quad 0 & 0 & \quad 0 \\
\quad 0 & 0 & \quad \frac{1}{\alpha^2\,r^2} & 0 & -\frac{\Phi}{2\,\pi\,\alpha^2\,r^2} \\
\quad 0 & 0 & \quad 0 & 1 & \quad 0 \\
\quad 0 & 0 & -\frac{\Phi}{2\,\pi\,\alpha^2\,r^2} & 0 & 1+\frac{\Phi^2}{4\,\pi^2\,\alpha^2\,r^2}
\end{array} \right).
\label{44}
\end{equation}
By considering the line element (\ref{43}) into the Eq. (\ref{5}), we obtain the following differential equation :
\begin{eqnarray}
&&[-\partial_{t}^2+\partial_{r}^2+\frac{1}{r}\,\partial_{r}+\frac{1}{\alpha^2\,r^2}\,(\partial_{\phi}-\frac{\Phi}{2\,\pi}\,\partial_{x})^2+\partial_{z}^2+\partial_{x}^2-m\,\omega\,(f' (r)+\frac{f(r)}{r})\nonumber\\
&&-m^2\,\omega^2\,f^{2}(r)-(m + S(r))^2]\,\Psi (r)=0.
\label{45}
\end{eqnarray}
Since the space-time is independent of $t, \phi, z, x$, substituting the ansatz Eq. (\ref{8}) into the Eq. (\ref{45}), we get the following equation :
\begin{eqnarray}
&&\psi ''(r)+\frac{1}{r}\,\psi'(r)+[E^2-k^2-q^2-\frac{l^2_{eff}}{r^2}-m\,\omega\,(f'(r)+\frac{f(r)}{r})\nonumber\\
&-&m^2\,\omega^2\,f^{2}(r)-(m+S (r))^2]\,\psi (r)=0,
\label{46}
\end{eqnarray}
where
\begin{equation}
l_{eff}=\frac{1}{\alpha}\,(l-\frac{q\,\Phi}{2\,\pi})
\label{47}
\end{equation}
is called the effective angular quantum number which depends on the cosmic string parameter as well as the magnetic quantum flux.

Substituting the function Eq. (\ref{function}) into the Eq. (\ref{46}) and using the scalar potential Eq. (\ref{10}), we obtain the following equation:
\begin{equation}
\psi''(r)+\frac{1}{r}\,\psi'(r)+[\lambda-\tilde{\omega}^2\,r^2-\frac{\chi^2_{eff}}{r^2}-2\,m\,k_{L}\,r]\,\psi(r)=0,
\label{48}
\end{equation}
where
\begin{eqnarray}
&&\lambda=E^2-k^2-q^2-m^2-2\,m\,\omega\,a-2\,m^2\,\omega^2\,a\,b,\nonumber\\
&& \tilde{\omega}=\sqrt{m^2\,\omega^2\,a^2+k^{2}_{L}},\nonumber\\
&&\chi_{eff}=\sqrt{l^2_{eff}+m^2\,\omega^2\,b^2}.
\label{49}
\end{eqnarray}
Transforming $\rho=\sqrt{\tilde{\omega}}\,r$ into the Eq. (\ref{48}), we get
\begin{equation}
\psi''(\rho)+\frac{1}{\rho}\,\psi'(\rho)+[\lambda_0-\rho^2-\frac{\chi^2_{eff}}{\rho^2}-\theta\,\rho]\,\psi (\rho)=0,
\label{50}
\end{equation}
where $\lambda_0, \theta$ are in Eq. (\ref{aa}).

As similar to the technique done earlier, suppose the solution to the Eq. (\ref{50}) is
\begin{equation}
\psi (\rho)=\rho^{\chi_{eff}}\,e^{-\frac{1}{2}\,(\theta+\rho)\,\rho}\,H (\rho).
\label{51}
\end{equation}
Substituting Eq. (\ref{51}) into the Eq. (\ref{50}), we get the biconfluent Heun's differential equation \cite{aa30,aa49,aa50,bb41,bb42,ff2,ff3} form:
\begin{equation}
H''(\rho)+[\frac{\bar \gamma}{\rho}-\theta-2\,\rho]\,H'(\rho)+[-\frac{\bar Q}{r}+{\bar \Theta}]\,H (\rho)=0,
\label{52}
\end{equation}
where
\begin{eqnarray}
&&{\bar \gamma}=(1+2\,\chi_{eff}),\nonumber\\
&&{\bar \Theta}=\lambda_0+\frac{\theta^2}{4}-2\,(1+\chi_{eff}),\nonumber\\
&&{\bar Q}=\frac{\theta}{2}\,(1+2\,\chi_{eff}).
\label{53}
\end{eqnarray}

Substituting Eq. (\ref{19}) into the Eq. (\ref{52}), we get the following recurrernce relation for the coefficients:
\begin{equation}
c_{n+2}=\frac{1}{(n+2)(n+1+\gamma)}\,[\{{\bar Q}+\theta\,(n+1) \}\,c_{n+1}-({\bar \Theta}-2\,n)\,c_{n}].
\label{54}
\end{equation}
And the various coefficients are
\begin{equation}
c_1=\frac{\bar Q}{\bar \gamma}\,c_0,\quad c_2=\frac{1}{2\,(1+\gamma)}\,[({\bar Q}+\theta)\,c_{1}-{\bar \Theta}\,c_{0}].
\label{55}
\end{equation}
A polynomial form of degree $n$ for the function $H (r)$ is achieved when we impose requirement that the series solution terminates. For this, we must have \cite{aa30,aa50,ff2,ff3,bb41,bb44,bb45,bb46,bb47}
\begin{equation}
{\bar \Theta}=2\,n.
\label{56}
\end{equation}
And
\begin{equation}
c_{n+1}=0,\quad (n=1,2,3,4,....).
\label{57}
\end{equation}
Using the condition ${\bar \Theta}=2\,n$, we obtain the following energy eigenvalue $E_{n,l}$:
\begin{eqnarray}
E^{2}_{n,l}&=&k^2+q^2+m^2+2\,m\,\omega\,a+2\,m^2\,\omega^2\,a\,b-\frac{m^2\,k^{2}_{L}}{\tilde{\omega}^2}\nonumber\\
&+&2\,\tilde{\omega}\,(n+1+\sqrt{\frac{1}{\alpha^2}\,(l-\frac{q\,\Phi}{2\,\pi})^2+m^2\,\omega^2\,b^2}).
\label{58}
\end{eqnarray}
Equation (\ref{58}) is the energy eigenvalue associated with $n^{th}$ radial modes for the generalized Klein-Gordon oscillator in the magnetic cosmic string with a linear scalar potential in the Kaluza-Klein theory. We can see in comparision to the case without magnetic flux as obtained earlier by Eq. (\ref{24}), the angular quantum number $l$ is shifted, $l \rightarrow l_{eff}=\frac{1}{\alpha}\,(l-\frac{q\,\Phi}{2\,\pi})$, an effective angular quantum number. We see that the relativistic energy eigenvalue Eq. (\ref{58}) depends on the Aharonov-Bohm geometric quantum phase \cite{bb50}. Thus, we have that $E_{n,{\bar l}} (\Phi+\Phi_0)=E_{n,{\bar l}\pm \tau} (\Phi)$ where, $\Phi_0=\mp\,\frac{2\,\pi\,\alpha}{q}\,\tau$ with $\tau=1,2,3,...$ and ${\bar l}=\frac{l}{\alpha}$. This dependence of the relativistic energy eigenvalue on the geometric quantum phase gives rise to the analogoue effects to the Aharonov-Bohm effect for bound states \cite{bb28,bb48,bb39,bb40,bb50}.

The corresponding wave-function is given by
\begin{equation}
\psi_{n,l} (\rho)=\rho^{\sqrt{\frac{(l-\frac{q\,\Phi}{2\,\pi})^2}{\alpha^2}+m^2\,\omega^2\,b^2}}\,e^{-\frac{1}{2}\,(\theta+\rho)\,\rho}\,H (\rho).
\label{59}
\end{equation}

Now, we impose the additional condition $c_{n+1}=0$ in the above eigenvalue problem to obtain the individual energy levels and corresponding wave-function one by one as done in \cite{aa30,aa50,bb44,bb45}. As example, for $n=1$, we have $c_2=0$ which implies
\begin{eqnarray}
&&c_1=\frac{2}{{\bar Q}+{\bar \beta}}\,c_0 \Rightarrow \frac{{\bar Q}}{{\bar \gamma}}=\frac{2}{{\bar Q}+{\bar \beta}}\nonumber\\\Rightarrow
&&B^2_{2}=\frac{1}{1+A_2} \Rightarrow \tilde{\omega}_{1,l}=[m^2\,k^2_{L 1}\,(\frac{3}{2}+\sqrt{\frac{(l-\frac{q\,\Phi}{2\,\pi})^2}{\alpha^2}+m^2\,\omega^2\,b^2})]^{\frac{1}{3}}.
\label{60}
\end{eqnarray}
Therefore, the ground state energy level for $n=1$ is given by
\begin{eqnarray}
&&E^{2}_{1,l}=k^2+q^2+m^2+2\,m\,\omega\,a+2\,m^2\,\omega^2\,a\,b\nonumber\\
&&+2\,\tilde{\omega}_{1,l}\,(n+1+\sqrt{\frac{(l-\frac{q\,\Phi}{2\,\pi})^2}{\alpha^2}+m^2\,\omega^2\,b^2})-\frac{m^2\,k^{2}_{L 1}}{\tilde{\omega}^2_{1,l}},
\label{61}
\end{eqnarray}
where $\tilde{\omega}_{1,l}$ is given by Eq. (\ref{60}). The corresponding wave-function is
\begin{equation}
\psi_{1,l} (\rho)=\rho^{\sqrt{\frac{(l-\frac{q\,\Phi}{2\,\pi})^2}{\alpha^2}+m^2\,\omega^2\,b^2}}\,e^{-\frac{1}{2}\,(2\,c_1+\rho)\,\rho}\,(c_0+c_1\,\rho),
\label{62}
\end{equation}
where
\begin{equation}
c_1=\frac{1}{\sqrt{\frac{3}{2}+\sqrt{\frac{(l-\frac{q\,\Phi}{2\,\pi})^2}{\alpha^2}+m^2\,\omega^2\,b^2}}}.
\label{63}
\end{equation}

Below we discuss few cases of the above energy eigenvalue of the relativistic system considered in this section.

\vspace{0.2cm}
{\bf Case 1} : If one choose $b \rightarrow 0$, $a \rightarrow 1$.
\vspace{0.2cm}

In that case, the energy eigenvalue Eq. (\ref{58}) becomes
\begin{equation}
E^{2}_{n,l}=k^2+q^2+m^2+2\,m\,\omega+2\,\tilde{\omega}_{n,l}\,(n+1+\frac{|l-\frac{q\,\Phi}{2\,\pi}|}{\alpha})-\frac{m^2\,k^{2}_{L}}{\tilde{\omega}^2_{n,l}}.
\label{64}
\end{equation}
Equation (\ref{64}) is the energy eigenvalue associated with $n^{th}$ radial modes for the Klein-Gordon oscillator in the magnetic cosmic string background with a linear scalar potential in the Kaluza-Klein theory.

The bound state energy level for $n=1$ is given by
\begin{eqnarray}
&&E^{2}_{1,l}=k^2+q^2+m^2+2\,m\,\omega\,a\nonumber\\
&&+2\,\tilde{\omega}_{1,l}\,(n+1+\frac{|l-\frac{q\,\Phi}{2\,\pi}|}{\alpha})-\frac{m^2\,k^{2}_{L 1}}{\tilde{\omega}^2_{1,l}}.
\label{65}
\end{eqnarray}
And the corresponding wave-function is
\begin{equation}
\psi_{1,l} (\rho)=\rho^{\frac{|l-\frac{q\,\Phi}{2\,\pi}|}{\alpha}}\,e^{-\frac{1}{2}\,(2\,c_1+\rho)\,\rho}\,(c_0+c_1\,\rho),
\label{66}
\end{equation}
where
\begin{eqnarray}
&&c_1=\frac{1}{\sqrt{\frac{3}{2}+\frac{|l-\frac{q\,\Phi}{2\,\pi}|}{\alpha}}},\nonumber\\
&&\tilde{\omega}_{1,l}=[m^2\,k^2_{L 1}\,(\frac{3}{2}+\frac{|l-\frac{q\,\Phi}{2\,\pi}|}{\alpha})]^{\frac{1}{3}}.
\label{67}
\end{eqnarray}

\vspace{0.1cm}
{\bf Case 2} : If one choose $k_{L} \rightarrow 0$, that is, without any linear scalar potential into the considered system.
\vspace{0.1cm}

In that case, from Eq. (\ref{48}) we have the following equation
\begin{equation}
\psi''(r)+\frac{1}{r}\,\psi'(r)+[\lambda-m^2\,\omega^2\,a^2\,r^2-\frac{\chi^2_{eff}}{r^2}]\,\psi(r)=0
\label{68}
\end{equation}
which can be transformed to the following equation \cite{bb49}
\begin{equation}
\psi''(s)+\frac{1}{s}\,\psi' (s)+\frac{1}{s^2}\,(-\xi_1\,s^2+\xi_2\,s-\xi_3)\,\psi (s)=0,
\label{69}
\end{equation}
where
\begin{equation}
\xi_1=\frac{1}{4}\quad,\quad \xi_2=\frac{\lambda}{4\,m\,\omega\,a}\quad,\quad \xi_3=\frac{\chi^2_{eff}}{4}.
\label{70}
\end{equation}

The energy eigenvalue is given by
\begin{eqnarray}
E^{2}_{n,l}&=&k^2+2\,m^2\,\omega^2\,a\,b+q^2+m^2\nonumber\\
&+&2\,m\,\omega\,a\,(2\,n+2+\sqrt{\frac{(l-\frac{q\,\Phi}{2\,\pi})^2}{\alpha^2}+m^2\,\omega^2\,b^2}),
\label{71}
\end{eqnarray}
where $n=0,1,2,3,...$. Equation (\ref{71}) is the energy eigenvalue associated with $n^{th}$ radial modes for the generalized Klein-Gordon oscillator in the magnetic cosmic string without potential in the Kaluza-Klein theory.

If one choose $b \rightarrow 0$, $a \rightarrow 1$, that is, the Klein-Gordon oscillator in the magnetic cosmic string background in the Kaluza-Klein theory, the energy eigenvalue Eq. (\ref{71}) becomes
\begin{equation}
E^{2}_{n,l}=k^2+q^2+m^2+4\,m\,\omega\,(n+1+\frac{|l-\frac{q\,\Phi}{2\,\pi}|}{2\,\alpha})
\label{72}
\end{equation}
which is similar to the result obtained in \cite{aa6} (see Eq. (25) in \cite{aa6}). Thus the Eq. (\ref{71}) is the extended energy eigenvalue of the generalized Klein-Gordon oscillator in the magnetic cosmic string background without potential in the Kaluza-Klein theory.

\vspace{0.2cm}
{\bf Case 3} : If one choose $b \rightarrow 0$, $a \rightarrow 0$, the Klein-Gordon particle subject to a linear scalar potential into the relativistic system.
\vspace{0.2cm}

In that case, the Eq. (\ref{61}) becomes
\begin{equation}
\psi''(r)+\frac{1}{r}\,\psi'(r)+[E^2-m^2-k^2-q^2-k^2_{L}\,r^2-\frac{l^2_{eff}}{r^2}]\,\psi(r)=0.
\label{73}
\end{equation}
Transforming $s=k_{L}\,r^2$ into the above equation, we obtain \cite{bb49}
\begin{equation}
\psi''(s)+\frac{1}{s}\,\psi'(s)+\frac{1}{s^2}\,[\frac{E^2-m^2-k^2-q^2}{4\,k_{L}}\,s-\frac{1}{4}\,s^2-\frac{l^2_{eff}}{4}]\,\psi(s)=0.
\label{74}
\end{equation}
The energy eigenvalue of the system is
\begin{equation}
E^{2}_{n,l}=k^2+q^2+m^2+2\,k_{L}\,(2\,n+1+\frac{|l-\frac{q\,\Phi}{2\,\pi}|}{\alpha}),
\label{75}
\end{equation}
where $n=0,1,2,3,....$. Equation (\ref{75}) is the energy eigenvalue of a scalar field in the magnetic cosmic string background in the Kaluza-Klein theory with a linear scalar potential.

In all the above cases, we can see that there is an effective angular quantum number, $l \rightarrow l_{eff}=\frac{1}{\alpha}\,(l-\frac{q\,\Phi}{2\,\pi})$. Therefore, the above relativistic energy eigenvalue depends on the geometric quantum phase \cite{bb50}. Thus, we have that $E_{n,{\bar l}} (\Phi+\Phi_0)=E_{n,{\bar l} \pm \tau} (\Phi)$ where, $\Phi_0=\mp\,\frac{2\,\pi\,\alpha}{q}\,\tau$ with $\tau=1,2,3,....$ and ${\bar l}=\frac{l}{\alpha}$. This dependence of the relativistic energy eigenvalue on the geometric quantum phase gives rise to the analogoue effect to the Aharonov-Bohm effect for bound states \cite{aa6,bb28,bb48,bb39,bb40,bb50}.

Formula (\ref{47}) suggests that, when the particle circles the string, the wave-function changes according to
\begin{equation}
\Psi\rightarrow \Psi'=e^{2\,i\,\pi\,l_{eff}}\,\Psi=e^{i\,\frac{2\,\pi}{\alpha}\,(l-\frac{q\,\Phi}{2\,\pi})}\,\Psi.
\label{76}
\end{equation}
An immediate consequence of Eq. (\ref{47}) is that the angular momentum operator may be redefined as
\begin{equation}
\hat{l}_{eff}=-\frac{i}{\alpha}\,(\partial_{\phi}-i\,\frac{q\,\Phi}{2\,\pi}),
\label{77}
\end{equation}
where the additional term, $-\frac{q\,\Phi}{2\,\pi\,\alpha}$, takes into account the Aharonov-Bohm magnetic quantum flux $\Phi$.

\vspace{0.5cm}
\section{Conclusions}

In Ref. \cite{aa6}, authors studied the relativistic scalar particle in the cosmic string, magnetic cosmic string and cosmic dispiration background in the Kaluza-Klein theory. They solved the Klein-Gordon oscillator without any potential and obtained the relativistic energy eigenvalue and eigenfunction. In Ref. \cite{aa49}, the relativistic quantum dynamics of a scalar particle in (1+2)-dimensional space-time with topological defects subject to a linear scalar potential were studied. They solved the Klein-Gordon oscillator in the considered framework and obtained the relativistic energy eigenvalue and wave-function.

In this work, we have investigated the relativistic quantum dynamics of a scalar particle interacting with gravitational field produced by topological defects via the generalized Klein-Gordon oscillator in the cosmic string and magnetic cosmic string space-time within the Kaluza-Klein theory subject to a linear scalar potential. We have determined the manner in which the non-trivial topology due to topological defects and the magnetic quantum flux modifies the energy spectrum and wave-function of the relativistic system. We have studied the quantum dynamics of a scalar particle interacting with an external field sources, by using the five-dimensional version of the General Relativity. The quantum dynamics in the usual as well as magnetic cosmic string cases allow us to obtain the energy eigenvalue and wave-functions depending on the external parameters characterizing the background space-time, a result known by gravitational analogue of the well studied Aharonov-Bohm effect.

In {\it section 2}, we have studied the relativistic quantum dynamics of a scalar particle in the background of cosmic string space-time in the Kaluza-Klein theory with a linear scalar potential. In this study, we have considered the Cornell-type potential form function $f(r)=a\,r+\frac{b}{r}$ \cite{cc9,bb41} and a linear scalar potential $S(r)=k_{L}\,r$ where, $k_{L}$ is the linear confining parameter. Then, we have solved the generalized Klein-Gordon oscillator subject to this potential in the cosmic string background space-time in the Kaluza-Klein theory. We have obtained the bound states energy eigenvalue Eq. (\ref{24}) and corresponding wave-function Eq. (\ref{25}). By imposing the additional recurrence condition $c_{n+1}=0$ in the eiegnvalue problem, for example, $n=1$, we have evaluated the ground state energy level  Eq. (\ref{27}) and corresponding wave-function Eqs. (\ref{28})-(\ref{29}), respectively. We have seen that gravitational field produced by topological defects and the scalar potential modifies the energy spectrum. Furthermore, we have discussed three cases {\it 1-3} and seen that the energy eigenvalue in very special case reduces to the result obtained in \cite{aa49} (for case {\bf 1}) and in \cite{aa6} (for case {\bf 2}).

In {\it section 3}, we have studied the relativistic quantum dynamics of a scalar particle in the magnetic cosmic string within the Kaluza-Klein theory with a linear scalar potential. We have chosen the same function $f(r)=a\,r+\frac{b}{r}$ considered earlier and the linear scalar potential $S(r)=k_{L}\,r$ into the relativistic system. We have derived the radial wave-equation of the generalized Klein-Gordon oscillator by choosing this function $f(r)$ subject to this potential in the magnetic cosmic string in the Kaluza-Klein theory. We have obtained the bound states energy eigenvalue Eq. (\ref{58}) and corresponding wave-function Eq. (\ref{59}). By imposing the additional condition $c_{n+1}=0$, for example $n=1$, we have obtained the ground state energy level and eigenfunction. In addition, we have discussed few cases {\it 1-3} and obtained the relativistic energy eigenvalue. We have seen in case {\bf 2} that the energy eigenvalue reduces to the result obtained in \cite{aa6} in very special case. In this section, we have seen that the relativistic energy eigenvalue obtained here depends on the geometric quantum phase \cite{bb50}. Thus, we have that $E_{n,{\bar l}} (\Phi+\Phi_0)=E_{n,{\bar l} \pm \tau} (\Phi)$ where, $\Phi_0=\mp\,\frac{2\,\pi\,\alpha}{q}\,\tau$ with $\tau=1,2,3,...$ and ${\bar l}=\frac{l}{\alpha}$. This dependence of the relativistic energy eigenvalue on the geometric quantum phase $\Phi$ gives rise to the analogoue effect to the Aharonov-Bohm effect for bound states \cite{bb28,bb48,bb39,bb40,bb50}. Besides, even though there is no direct intractions between the particle and external fields, influence on the energy eigenvalue is due to the internal magnetic quantum flux $\Phi$ yielding an effective angular quantum number $l \rightarrow l_{eff}=\frac{1}{\alpha}\,(l-\frac{q\,\Phi}{2\,\pi})$. For $\alpha \rightarrow 1$, the change in angular quantum number $\bigtriangleup\,l=l-l_{eff}$ is directly proportional to the magnetic quantum flux $\Phi$. So we have shown some results which are in addition to the previous results obtained in \cite{aa6,aa49} present many interesting effects. This is the fundamental subject in physics and the connection between these theories (gravitation and quantum mechanics) are not well understood.

\section*{Appendix A : Brief review of the Nikiforov-Uvarov (NU) method}

\setcounter{equation}{0}
\renewcommand{\theequation}{A.\arabic{equation}}

The Nikiforov-Uvarov method is helpful in order to find eigenvalues and eigenfunctions of the Schr\"{o}dinger like equation, as well as other second-order differential equations of physical interest. According to this method, the eigenfunctions of a second-order differential equation \cite{bb49}
\begin{equation}
\frac{d^2 \psi (s)}{ds^2}+\frac{(\alpha_1-\alpha_2\,s)}{s\,(1-\alpha_3\,s)}\,\frac{d \psi (s)}{ds}+\frac{(-\xi_1\,s^2+\xi_2\,s-\xi_3)}{s^2\,(1-\alpha_3\,s)^2}\,\psi (s)=0.
\label{A.1}
\end{equation}
are given by
\begin{equation}
\psi (s)=s^{\alpha_{12}}\,(1-\alpha_3\,s)^{-\alpha_{12}-\frac{\alpha_{13}}{\alpha_3}}\,P^{(\alpha_{10}-1,\frac{\alpha_{11}}{\alpha_3}-\alpha_{10}-1)}_{n}\,(1-2\,\alpha_3\,s).
\label{A.2}
\end{equation}
And that the energy eigenvalues equation
\begin{eqnarray}
&&\alpha_2\,n-(2\,n+1)\,\alpha_5+(2\,n+1)\,(\sqrt{\alpha_9}+\alpha_3\,\sqrt{\alpha_8})+n\,(n-1)\,\alpha_3+\alpha_7\nonumber\\
&&+2\,\alpha_3\,\alpha_8+2\,\sqrt{\alpha_8\,\alpha_9}=0.
\label{A.3}
\end{eqnarray}
The parameters $\alpha_4,\ldots,\alpha_{13}$ are obatined from the six parameters $\alpha_1,\ldots,\alpha_3$ and $\xi_1,\ldots,\xi_3$ as follows:
\begin{eqnarray}
&&\alpha_4=\frac{1}{2}\,(1-\alpha_1)\quad,\quad \alpha_5=\frac{1}{2}\,(\alpha_2-2\,\alpha_3),\nonumber\\
&&\alpha_6=\alpha^2_{5}+\xi_1\quad,\quad \alpha_7=2\,\alpha_4\,\alpha_{5}-\xi_2,\nonumber\\
&&\alpha_8=\alpha^2_{4}+\xi_3\quad,\quad \alpha_9=\alpha_6+\alpha_3\,\alpha_7+\alpha^{2}_3\,\alpha_8,\nonumber\\
&&\alpha_{10}=\alpha_1+2\,\alpha_4+2\,\sqrt{\alpha_8}\quad,\quad \alpha_{11}=\alpha_2-2\,\alpha_5+2\,(\sqrt{\alpha_9}+\alpha_3\,\sqrt{\alpha_8}),\nonumber\\
&&\alpha_{12}=\alpha_4+\sqrt{\alpha_8}\quad,\quad \alpha_{13}=\alpha_5-(\sqrt{\alpha_9}+\alpha_3\,\sqrt{\alpha_8}).
\label{A.4}
\end{eqnarray}

A special case where $\alpha_3=0$, as in our case, we find
\begin{equation}
\lim_{\alpha_3\rightarrow 0} P^{(\alpha_{10}-1,\frac{\alpha_{11}}{\alpha_3}-\alpha_{10}-1)}_{n}\,(1-2\,\alpha_3\,s)=L^{\alpha_{10}-1}_{n} (\alpha_{11}\,s),
\label{A.5}
\end{equation}
and
\begin{equation}
\lim_{\alpha_3\rightarrow 0} (1-\alpha_3\,s)^{-\alpha_{12}-\frac{\alpha_{13}}{\alpha_3}}=e^{\alpha_{13}\,s}.
\label{A.6}
\end{equation}
Therefore the wave-function from (\ref{A.2}) becomes
\begin{equation}
\psi (s)=s^{\alpha_{12}}\,e^{\alpha_{13}\,s}\,L^{\alpha_{10}-1}_{n} (\alpha_{11}\,s),
\label{A.7}
\end{equation}
where $L^{(\alpha)}_{n} (x)$ denotes the generalized Laguerre polynomial.

The energy eigenvalues equation reduces to
\begin{equation}
n\,\alpha_2-(2\,n+1)\,\alpha_5+(2\,n+1)\,\sqrt{\alpha_9}+\alpha_7+2\,\sqrt{\alpha_8\,\alpha_9}=0.
\label{A.8}
\end{equation}
Noted that the simple Laguerre polynomial is the special case $\alpha=0$ of the generalized Laguerre polynomila:
\begin{equation}
L^{(0)}_{n} (x)=L_{n} (x).
\label{A.9}
\end{equation}

\section*{Acknowledgement}

Author acknowledged the anonymous kind referee(s) for their valuable comments and suggestions which have improved the present paper.

\section*{Data Availability}

There is no data associated with this paper or no data have been used to prepare this.

redpajama_set_name: RedPajamaArXiv


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The Walking Dead: Season 3 Premieres December 20; First Look at The Game Awards
Ryan Meitzler
November 22, 2016 12:22 PM EST
NewsXbox OneXbox 360PS4PS3PC
A good amount of time has passed since players saw Clementine with Telltale's The Walking Dead series, though the wait is nearly over as the studio has announced the release date for the upcoming third season of the episodic series.
In a press release, Telltale Games has announced that the first episode for The Walking Dead: The Telltale Series – A New Frontier (Season 3 of the episodic series) will release on December 20th, 2016 for PS4, Xbox One, PS3, Xbox 360, PC, iOS, and Android.
Along with the digital release of the first episode in late December, Telltale also detailed that a retail version of A New Frontier will be available on February 7th, 2017 for PS4 and Xbox One, with the "Season Pass Disc" including the first episode and a code to redeem for the remaining four episodes as they are released. Currently, the game can be pre-ordered on PS4 and purchasers there will also receive bonus copies of The Walking Dead: Season 2 and The Walking Dead: Michonne for free – PC users on Steam can pre-order the title and receive a 10% discount.
An extended first look at the premiere episode will be showcased at The Game Awards 2016, live on stage, during the show's broadcast on December 1st, 2016. A full description of what the third season of The Walking Dead will entail can be found below:
"When family is all you have left… how far will you go to protect it? Four years after society was ripped apart by undead hands, pockets of civilization emerge from the chaos. But at what cost? Can the living be trusted on this new frontier? As Javier, a young man determined to find the family taken from him, you meet a young girl who has experienced her own unimaginable loss. Her name is Clementine, and your fates are bound together in a story where every choice you make could be your last."
The Walking Dead: The Telltale Series – A New Frontier will debut on PS4, Xbox One, PS3, Xbox 360, PC, iOS, and Android on December 20th, 2016.
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Read Community Guidelines
The Walking Dead: The Telltale Series Gets Recapped in An 8-Bit Style Video Showing Clementine's Journey
Watch as Clementine grows from a young girl to a hardened survivor in this 8-bit style recap video of Telltale's The Walking Dead series.
The Walking Dead: A New Frontier: Episodes 1 & 2 Review — New Beginnings
The Walking Dead: A New Frontier – Episode 3 Launches March 28, 2017
The Walking Dead: A New Frontier – Episode 3 Debuts in March; Retail Release Coming Feb 28
Win a Steam Copy of The Walking Dead: The Telltale Series – A New Frontier to Celebrate the Holidays
Telltale Games Details New Story Generator Feature in The Walking Dead: The Telltale Series – A New Frontier
The Walking Dead: Season Three Not Releasing on PS3/Xbox 360; Telltale Offers Solutions for Importing Saves
The Walking Dead: The Telltale Series – A New Frontier Looks Excellent in Debut Gameplay Trailer; Will Release With First Two Episodes
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redpajama_set_name: RedPajamaCommonCrawl


The latest in our Big Question series asks: Who was United's best-ever crosser?
Everyone loves a good cross into the box, especially when it results in a goal. Whether it's a low, driven ball in behind the defence or a pin-point clip onto the head of the on-rushing forward, accurate crossing is a great skill. Usually associated with wingers, good crosses can also come from overlapping full-backs or even a striker who strays out wide or who takes the occasional corner.
What we want to know is who you think has been the club's best-ever crosser of a football. Let @OUFCOfficial know, along with your memories of great crosses, using the hashtag #OUFCBigQ, and the best responses will be printed in our Emirates FA Cup fourth round programme against Blackburn Rovers.


Marlborough Rotary at Trunk or Treat!
On October 21st, the Marlborough Rotary Club participated in the first annual "Trunk or Treat" event, sponsored by the Marlborough Junior Woman's Club (MJWC) and the One Hines Women's Network. The event was held at The Campus in Marlborough, a business complex located off of Rt. 20, just west of Rt. 495.
Trunk or Treat provided safe, free, family-friendly trick-or-treating, craft activities, food trucks, pumpkin carving contests, costume contests, music and more. There was a photo booth, and free pumpkins and decorating kits were given out so that families could continue the fun at home.
A DJ provided music and led games. Activities took place around the lot including face painting, a photo booth and pumpkin tic-tac-toe. Free pumpkins and decorating kits were distributed. Event sponsors and vendor fees covered costs, and raised funds for the MJWC's ongoing charitable work.
This fun day gave Marlborough Rotary the opportunity to participate in and support a new community event, and to gain exposure to young parents who might be potential Rotarians. Members braved the cold and wind to make a happy experience for the estimated 200 Disney characters and super heroes who attended the event. As an unexpected added bonus, the club won the children's favorite vehicle award!


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"Pill Papa"
Pablo Picasso was a pill. Remember Arianna Huffington's biography, Picasso: Creator and Destroyer? He consumed women as quickly as he moved through artistic styles. There seem to be two currents of thought about this shape-shifting: 1) that it represents a wildly energetic creativity that cannot be contained in just one mode, and 2) it represents a fickle sort of personality, an inability to commit.
I, for one, wouldn't wish to restrict anyone's expressive attempts. Stravinsky, in music, has also been labeled as another of these style-changers, often insultingly. However, both Picasso and Stravinsky are generally considered (whether one appreciates their particular art products or not) as the two giants of twentieth century art.
I'm trying to think through out loud, so to speak, how we mythologize, even romanticize dysfunction when attached to a great creator. How the "suffering" artist is worth more than the joyous one. How a giant ego is an accompaniment to the often difficult journey to realize what one sees (or hears) within. Really, if we removed every picture or piece of music created by an asshole, the catalog would be horribly slim, wouldn't it?
And can the work really be separated from the creator? This requires holding multiple ideas at the same time, rejecting none of them. The work is definitely an outgrowth of a deep-seated need to create, coming from the innermost part of a person. However, through what I call mutation (technique[s]) it begins to take on its own independent life and energy. Most symphonies are nowhere near as messed-up as their composers, music being a positive-energy act.
There's no such thing as a "depressed" symphony, because that portion of the sentiment has been incorporated and transformed. I will say, though, that in our time, the valuation of absolutely everyone's creative "vomit" (pardon the gross word) and the equalization of everyone's opinion, has led to a rather self-indulgent climate for creation. No longer does this transformation even have to take place, and we get spewing, which can be quite depressing.
Perhaps spewing is what one might call an "adolescent" stage on the way to a deeper synthesis. I myself have written confessional poetry that with examination turns out to be more therapeutic for me perhaps than uplifting to the reader. I always strive, however, to use interesting imagery, and other tools of the poet's craft. The important thing is to do, make it as good as possible, and then send it out. You can't control the response.
I was taught to question everything, absolutely everything, and never to relent. No received ideas if possible.
Creator and destroyer. Perhaps to create one thing, is to have destroyed something else. Not: create art/destroy a happy home. But: create a new thing/destroy the space where there was previously nothing. Sondheim says in Sunday in the Park with George: "Look I made a hat, where there never was a hat."
So: back to Pablo. He was often "pitted" against Matisse (though the two men actually respected each other and were even quite friendly). Matisse was seen as the colorful, happy one; versus PP's (early) poverty and torment and his choice of dismal subjects.
Never mind that Matisse himself had more than his share of personal suffering, particularly toward the end of a long life. Readers who can (and who can also bear the crowds and the timed ticket entry) should hasten to MoMA in New York to view the famous "cutouts" of Matisse, his last works, often executed by assistants, but always with his sure guiding hand. Distillation of a life's work.
Ravel said: "I have always found that joy is a far more fertile ground for creativity than suffering." Because Ravel and Matisse are both French (and PP Spanish), can we draw any conclusion from that? Best not to, but observe intently.
Today, I ramble. Why? Because I can.


In the last month or so, many of my friends and colleagues have had family members graduate from high school or college, and even some of my colleagues have graduated with advanced degrees. Graduation is an accomplishment and a milestone event, but does not mean automatic success.
And never looked back with regret….
This is to be a success.
Shared thinking is faster than solo thinking. In this fast paced industry, it's easier to learn together, and from each other, than alone. Members of the workforce are now focusing on attributes of community value rather than higher pay in their job searches.
Shared thinking is more innovative than solo thinking. Innovation comes from collaboration. By combining your thoughts with others, you can come up with more ideas than you could on your own.
Shared thinking brings more maturity than solo thinking. You can gain a broader sense of knowledge by asking questions and listening to the expertise of others.
Shared thinking is stronger than solo thinking. Synergy is stronger together than as one. The author gives an analogy of two horses pulling a wagon, and how they can pull more together than either of them could individually.
Shared thinking returns greater value than solo thinking. Compounding actions of shared thinking will produce a higher return.
One person cannot be successful without the help of others. That is what is so great about AHRA. We have the help of others through the forum, Annual Meeting, Spring Conference, the Fall Virtual Conference, textbooks, vendors, and many other resources. It's a perfect example of shared thinking. AHRA is a great resource to help us be the best that we can be, strive for our goals, and shape our destiny in the imaging profession. As we approach this year's Annual Meeting, if you have not registered, I encourage you to do so. If you have registered, I look forward to seeing you there. You do not want to miss it!
In addition, I wish my congratulations, best wishes and much success to all of the recent graduates. I especially want to wish my congratulations to our own AHRA president, Ernie Cerdena, who has just received his PhD and is now officially President Dr. Ernie Cerdena.
Maxwell J. How Successful People Think: Change Your Thinking, Change Your Life. New York: Center Street, 2009.
Wanda Coker, BHS, CRA, FAHRA is the radiology director at Shriners Hospital for Children in Greenville, SC. She can be reached at wcoker@shrinenet.org.
Are You Marketing With Your Eyes Closed?
Thanks for sharing these thoughts Wanda! We all have the oppertunity to be that successful person and this organization surely does help us down that path!
SO TRUE! Thank you for so eloquently putting success into perspective for us. Well said!


Mile High Eye Institute examines and treats 'red eyes' of all different varieties. It's important to note that not all eye infections result from bacteria and consequently, antibiotic eye drops or over-the-counter remedies may not be the solution to your eye problem.
It is important to contact your doctor immediately if you notice any eye pain, redness, decreased vision, discharge from the eye, or excessive tearing. If you are a contact lens wearer and experience any of these symptoms, it is critical to remove your contact lenses immediately until you see your doctor.
Culture: We can identify the etiology of your red eye and prescribe eye drops that specifically target the exact cause of your condition which results in a quicker and optimal recovery.
Network: MHEI works closely with world class doctors in all areas of healthcare in the Denver metro area to ensure that all of our patients who have an eye infection related to a systemic issue are managed thoroughly and appropriately.
Access: MHEI has working relationships with compounding and specialized pharmacies all over the world. No matter how rare or severe the eye infection, we have access to a medication that will treat you. From California to England, we have access to the most advanced medications in the world.
Expertise: The doctors at MHEI have the training and experience required to treat the most severe and rare eye infections known.
Technology: In some cases, an eye infection or red eye can lead to scarring and permanent vision loss. MHEI has technology at its disposal, such as the amniotic membrane transplant, to eliminate or minimize corneal scarring, therefore restoring and sustaining good vision and ocular function.


Changing bulbs can bring real and noticeable improvements, but in small amounts. We succeeded in developing HID conversions for classic cars many years ago and were granted a Stage 1 Patent. We have continued to improve these conversions to the point where they are as different from the poor quality equipment generally available as an E-Type is from a Trabant. They are designed to work on both positive earth and negative earth cars, and with a dynamo or an alternator. They generate no radio interference and create no huge spike of demand on starting. Our latest version (G4) even has no warm-up period - they are instant. This means that they are suitable not only for H4 equipped cars, but also for both dipped and high beams on quad lamp cars. This is a world first and has taken a great deal of patient development from our little team. They are fully guaranteed for 2 years and we give a money-back guarantee. They have been proven in the rigours of the Classic Le Mans 24 hour endurance race and also at endurance racing at The Nurburgring and are used by many of the foremost restorers worldwide. They will not make a rusty headlamp shiny again or restore the focus of badly eroded lenses ( we can supply replacements for these) but they will give you a 300% increase in light output compared to a standard bulb as well as a 40% reduction in the electrical load. That is hard to beat.
We sell our lighting to customers in 33 countries and you are advised to check regulations in the region in which you intend to use any lighting upgrades.
These vary widely in quality, and there are limits to what can be achieved with the traditional halogen bulb format, using a slim quartz glass cylinder, a filament,and various gases. Some high wattage bulbs can damage sensitive vehicle electrics, burn out switches and drain batteries on older cars - so try to ensure that you act on recommendation and get a money-back guarantee before you buy.We now have a range of LED headlamp upgrade bulbs for cars from 1930 onwards ( 12v only).
These bulbs were first developed by General Electric in the USA when they were researching to find ways to overcome the perceived problems with HID Xenon conversions. The bulbs use a larger quartz glass envelope than halogen bulbs, and this is coated with highly reflective materials on the inside. Halogen bulbs waste 90% of their energy as heat, which escapes through the glass. HOD bulbs reflect this energy back onto the filament, which because of it's special alloy and the carefully tailored mix of gases, can achieve much higher temperatures and therefore give off approximately 50% - 80% more light, and achieve other advantages. The bulbs get no hotter on the outside than halogen, use no more energy than halogen, but do emit considerably more light. They also project the light extremely well, in the same way that a high-power hose can throw water further, so they can illuminate the road further ahead. This is helped by extremely good colour rendering, which has been a problem on HID. In other words, things look more like they do in daylight than they do with either halogen or HID. They can also be whiter than halogen, or yellow, for a "period" look on classic cars. The high-tech materials used to achieve this also give the bulbs a life cycle which is typically 50% more than conventional halogen bulbs. They also are a straightforward swap for standard bulbs, as they have no ballasts and cause no warning lights to come on and generate no fault codes. The usual caveats apply - rogue traders will buy poor quality units and sell them cheaply. Good quality ones will be dearer, but will work well, will come with a proper guarantee and you will only need to do the job once.
These are making great progress, and have at last becom a viable alternative to halogen or HOD for headlamp bulbs, and are especially good in foglights ( which are short range lights), interior lights, number plate lights, and now, for sidelights, tail lights and indicator lights. We have many new models for this year ( 2012) and they will include non-polarity bulbs for all positions ( they will work either way around), error-free bulbs for tail lights, stop/tail lights and indicators that do not require you to fit external resistor kits as everything is built-in. You will be able to enjoy the advantages of LED technology for the very first time in car indicators without needing a soldering iron! They give that characteristic "instant" on/off, last many times longer, run cool, and use a tiny amount of energy, and they won't flash at a different speed than your standard bulbs. Our new interior light bulbs have been designed here in the UK by people who know that polarity sensitivity can be annoying and that many cars have interior lights which just will not allow the fitting of the current generation of LED bulbs without modifications to the lamp body, because they are too bulky. Our new W5W LED bulbs are twice as powerful, thanks to the use of the amazing Cree chips, but no bulkier than the standard bulb, and allow, for the first time, the quick and easy upgrading of interior lights on all of the cars that use these bulbs in a bayoneted bulbholder.
In the unlikely event that you are not completely satisfied with your investment, we will refund the complete cost of the product you purchased, as long as you have not damaged the equipment.
We cannot arrange fitting but will be happy to liaise with your local specialist if you prefer. We closed our fitting centre in Birmingham in 2011 after 38 years, so we are well equipped to answer any fitting queries.
We can upgrade the lighting on most cars, motor cycles and commercial vehicles. Spotlights and foglights can also be upgraded in most cases. We can also produce LED custom length lights to suit commercial vehicle, boat, motor-homes, caravans etc. Just call us. You may be surprised at how much is available.


Photonics Buyers' Guide / Urology Laser Systems / Convergent Laser Technologies, Sub. of Xintec Corp.
Manufacturer of multispecialty 100-W 1470-nm diode lasers and 30-W holmium lasers, flexible fiber optic delivery systems and accessories for urology and other applications. Direct sale and OEM.
When you click "Send Request", we will send the contact details you supply to Convergent Laser Technologies so they may respond to your inquiry directly.


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Jay Stone 91 results
Jay Stone has been a fixture in Canadian media for decades, and one of the most beloved movie critics in the country. He worked at the Ottawa Citizen and Postmedia News service until he retired.
(Along with one honourable mention and one movie that every one else loved conspicuous by its absence) By Jay Stone Here are my favourite movies of 2019, in alphabetical order: Honeyland: An amazing documentary, filmed in Macedonia, about a female beekeeper who lives with her ailing mother in rocky isolation, and harvests honey in a way compatible with her deep understanding of the life of bees. This hard-scrabble harmony is disrupted by a family of raucous nomads who move next door. The result is a galvanizing drama about society, greed, culture and, well, bees. Gloria Bell: Sebastián Lelio's remake of his own 2013 Spanish-language movie Gloria stars Julianne Moore as a divorcee who assuages her loneliness at dance clubs, and John Turturro as the constricted man who falls for her. The final scene, with the magnificent Moore dancing to the titular disco hit, is one of the great cinematic shouts of joy of the year. Jojo Rabbit: New ...
Adam Sandler stars as a hyperkinetic gambler in this New York City drama about gambling that perfectly captures the anxiety of the city
This documentary examines how a Canadian literary icon went from being a much-heralded writer to becoming the prophet of dystopia in a post-Trump world
Movie review: Honeyland is a parable of capitalism
Documentary about a beekeeper in Macedonia takes an intimate look at what happens when neighbours move in and see the profits that can be made
Tiff 2019 finds its controversy in Jojo Rabbit
A young boy in Nazi Germany turns for moral guidance to a fantasy figure of Adolf Hitler in this satire that has sharply divided critics By Jay Stone TORONTO — Film festivals need movies that people can argue about, and the Toronto film festival has been blessed with a good one: Jojo Rabbit, a comedy set in Nazi Germany. Some people, including half of the representatives of Ex-Press.com, argue that it's juvenile, and in bad taste, and — worst of all — not funny. Others, including the other half of Ex-Press.com staff, think it's bold, original and filled with laughs. And we're not the only ones. The aggregate site Rotten Tomatoes gives it a favourable rating in the 70s, but the opinions are wildly divergent, from raves ("a triumph. A film of sophisticated brilliance and humour:" Jason Gorber, HighDef Digest) to pans ("conventional, lazy and incredibly irresponsible filmmaking:" Jordan Ruimy, World of Reel.) Personally, I ...
The movies of TIFF 2019, but not all of them
You don't always get to see a whole movie at a film festival, but sometimes what you do see is enough, Jay Stone discovers By Jay Stone TORONTO — Another thing that happens at film festivals is that you don't see a whole movie because maybe you had to leave to get to another theatre for an even more important film, or because it's late and you have to get some sleep or you'll pass out, or because it's late and you do pass out right there in the cinema and the nice lady next to you has to poke you in the ribs because it turns out you were snoring. You can actually follow a movie this way — often you hear enough dialogue that you dream it — unless it's a foreign film, in which case you jerk yourself awake and you're not sure where you are and it takes a few seconds for your eyes to focus enough to read the subtitles. This is part of the reason that professional film criticism is a young person's game, or at least an awake person's ...
All the mothers of TIFF 2019
There are many problems for mothers in this year's Toronto film festival movies, but Jay Stone finds that his real-life mother is still going strong By Jay Stone TORONTO — The other night I played hooky from the Toronto film festival to have dinner with my mother, who lives in north Toronto. She's 97, but she's in terrific shape. She works out every day at the gym, and, as she tells it, the people at the retirement home are less amazed by the fact that she can still get down to stretch on the Pilates ball than they are by the fact that she can get back up. This gives me a tremendous genetic advantage in life: Robert Benchley once wrote that one of the keys to a long life is to keep one's parents alive, at gunpoint if necessary. It also gives me a huge edge over a lot of people in movies at the festival, many of which feature plots revolving around mothers who have just died, although they continue to haunt their offspring with varying dramatic ...
Beautiful day in the Oscarhood: Academy Award hopes of TIFF
The Toronto film festival features several movies that could be in the discussion for this year's top movie awards, Jay Stone writes By Jay Stone TORONTO — The Toronto film festival is known as a launching pad for Oscar movies. Here are a few of the early contenders. A Beautiful Day in the Neighborhood: The re-evaluation of Fred Rogers — from figure of fun in a thousand parodies of his children's program to American hero in a famous Esquire magazine article to secular sainthood in the documentary Won't You Be My Neighbor? — continues in this movie that's actually based on that Esquire article. Tom Junod, an investigative journalist, was assigned in 1998 to do a short profile of Rogers (Tom Hanks) and emerged with a 10,000-word cover story that painted him as an unexpected wise man, a life coach whose simple wisdom could heal fractures of the heart. It was as if Being There had come to life as a puppet show for children. In this ...
TIFF 2019: When the theme is the theme
Movies: #TIFF19 Jay Stone discovers that you can go from dance to geriatric sex at the Toronto film festival, with barely time for a refreshing doughnut By Jay Stone TORONTO — One of the secrets of formerly professional film criticism (I can now reveal) is to find a common theme around which you can elucidate your theories of the creative imagination. The good news is, if a common theme doesn't occur to you, you can always make one up because who cares really? So it was the other day that I saw a 3-D movie about dance and a black-and-white drama about geriatric sex, then attended a lunch party that was so jammed with loud freeloaders that I could barely get to the dessert table for a second doughnut. What do these things have in common?, I asked my daughter, who got me into the party because she knows a guy who knows a guy. "Three things you don't like," she ventured, which is a pretty good guess. But it's a daughter guess. I actually liked the party, especially ...
The dark recesses of TIFF19 and some great expectations
Movies: #TIFF19 Smelling something familiar in the air? It's the gentle fragrance of auteurism, leavened with the sharp odour of Oscar bait. In other words, it's the dawn of TIFF19. Jay Stone places his bets on Tom Hanks, Nicole Kidman and Ed Norton's directorial debut as a detective with Tourette's. By Jay Stone SOMEWHERE ON THE WAY TO TORONTO — And here we go again, heading to the Toronto International Film Festival with a suitcase packed with black clothes and a head filled with dark hopes. Will our feet hold up? Can we stay awake through those evening screenings? Will we ever eat dinner before midnight? Did someone remember to pack the Lipitor? Also: Will the movies be wonderful? Some of them always are, but you never know: the hot buzz titles can land with a clunk, while the unknown thing you walk into because you have nothing else to do or the title grabs you — I always remember the unheralded documentary Carmen Miranda: Bananas Is My Business as the ...


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ZeroPaid's Dormant State Leaves Sites Future Uncertain
Drew Wilson | June 9, 2017
The famed filesharing news website is now entering week 4 of its downtime. With no further signs of life, it's hard to say if the site is ever coming back.
We've been monitoring the website for signs of life for over a month now. It's almost hard to believe, but last week, we noted that the site has been more or less down for three weeks running now.
Earlier that week, we noticed that it is possible to access the homepage. While it is possible to access the https version of the homepage, but the page is largely broken. Still, we remained vigilant, monitoring for any further signs of life.
Now, we have entered week four of this downtime. At this point, it brings into serious question whether or not the site is ever going to make a return. At this point in time, the downed webpages will lose page ranking (if they still have any at all at this point). That potentially translates into a loss of potential traffic to the page in and of itself.
In addition, it's going to get harder and harder for more hardcore fans of the site to keep watching and waiting to see if the site will ever make a return. Some may continue to hold out hope, but others will eventually move on.
Compounding the problem is the fact that the home page currently contains no ads. While that may sound like a good thing on the surface, no money is likely flowing into the site at all. With a lack of cash, it does increase the challenge of bringing the site back in the first place.
At this point, it is hard to say if the site is ever going to make a comeback at this stage. Administration is active, but actively doing things outside of ZeroPaid. All this does make it difficult to really gauge what potential plans are for the site.
For me, the biggest surprise is that the admins decided to not make the domain name redirect to a specialized welcome page for one of the other projects administration has on the go. If the site is to be shut down, at the very least, all that potential traffic would have proven to be a great benefit to another website project.
Another possibility is that the site is to go dormant for an extended period of time, then have it re-branded at a later time and relaunch the site. At that point, who knows when the site will come back and who knows if a re-launch like that would even work. The longer the site remains dormant, the taller the order that would be.
What we do know is that a single fully functional page is all that is left of the site. Beyond that, the site is showing no signs of life otherwise. So while we can't say the site is dead completely, we also can't say the site is alive either.
Categories: File-Sharing Tags: downtime, filesharing, p2p, website, ZeroPaid | Comments
ZeroPaid Situation Deteriorates Further As Home Page Goes Offline
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Raheem Sterling and Joe Gomez: Robbie Fowler says rows happen all the time | Football News | Sky Sports
Former Liverpool forward Robbie Fowler says everyone should move on following the training ground row between England team-mates Raheem Sterling and Joe Gomez
Liverpool legend Robbie Fowler says training ground rows happen all the time after the very public altercation between Raheem Sterling and Joe Gomez in the England camp.
Manager Gareth Southgate will not select Sterling for Thursday's European Qualifier against Montenegro at Wembley after the Manchester City star was involved in an argument with Gomez at the national team's St George's Park training base.
It was a continuation of hostility which was sparked during Liverpool's 3-1 win over City at Anfield on Sunday with Southgate likening the row to a family disagreement and insisting the group are united.
Sterling and Gomez trained together on Wednesday, two days after their altercation at St George's Park
"It's probably not ideal in terms of getting the right camaraderie in the camp but the player has obviously apologised and both are happy with what's happened and been said since.
"The manager has made his statement – I probably don't agree with it to be honest as if it was a World Cup semi-final a player wouldn't be getting dropped.
"But I can't sit here and have a go at Gareth Southgate – he's dealt with it in the way he sees fit and players are players. We should draw a line under it now and move on."
'Training ground spat didn't help my Liverpool career'
Fowler had a much-publicised spat with Liverpool assistant manager Phil Thompson back in 2001
England's recent incident also sparked memories of Fowler's own training ground confrontation back in 2001 with Liverpool assistant manager Phil Thompson.
The forward was subsequently dropped for the Charity Shield game against Manchester United and although Fowler believes it didn't end his Anfield career, it certainly didn't help.
"When I wasn't playing I wasn't a nice person as I wanted to play all the time," Fowler admits. "I let my anger out in a number of ways that probably wasn't ideal.
"Was that the reason why I left Liverpool? It wasn't pivotal but it is certainly one of the reasons and I probably think I knew my days were numbered anyway.
"A lot of clubs were trying to get me out of the club at the time and Liverpool were talking to them.
Sterling trains with England at St George's Park
"So I sort of knew I wasn't in the manager's plans and if a manager deems you not as good as others it's hard to take.
"I always felt I was better than what was there and that's not me being egotistical, I would have backed my record against anyone.
"But ultimately when you finish your career you sit back and realise managers are entitled to pick any team and any players he wants.
"You've got to move on though and I've more than made up with everyone since but perhaps I should have made up with Phil [Thompson] a lot earlier and I may have got another medal."
Robbie Fowler was speaking to Sky Sports News ahead of the release of his new book, 'Robbie Fowler – My Life in Football ', which is out on November 14.
Watch England highlights for free on Sky Sports
Watch highlights of all of England's Euro 2020 qualifying games for free with Sky Sports – including England vs Montenegro on Thursday and Kosovo vs England on Sunday.
The best bits from each game will be available on SkySports.com, the Sky Sports app and the YouTube channel from 15 minutes after full-time – and you won't need a Sky Sports subscription to tune in.
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Eurostar Celebrates 5th Anniversary
Many Happy Festive Returns for Eurostar this Christmas!
Published 3rd January 2013
Eurostar celebrates the 5th anniversary of using St. Pancras in style with new services announced
International train operator Eurostar has reported a surge in bookings this Christmas. The busiest travel days were December 21 and 22 suggesting passengers are taking advantage of the way Christmas Day falls this year.
This busy time has also seen the introduction of the new direct 'Ski Train' from St. Pancras to The Swiss Alps.
Eurostar transported tens of thousands of passengers from all over the UK to France, Belgium and Switzerland for the festive period. From Friday 21 December to Thursday 3 January, Eurostar's bookings showed that more than 160,000 passengers travelling from the UK.
New Swiss Ski Train from London
The new Ski Train was due to take hundreds of passengers from St. Pancras to some of Switzerland's most popular ski resorts on Saturday 22 December for its inaugural journey. The train calls at Ashford en-route to the heart of the Swiss Alps and the Valais region serving the resorts at Verbier, Zermatt, Saas Fee and Gstaad. The service runs until 13 April 2013.
Cross platform connections are also available at Lille to a high-speed TGV Lyria service for passengers going to Aigle, Martigny, Visp and Brig stations for quick onward transfers to their ski resorts. Eurostar and TGV Lyria will allow passengers to carry skis or snowboards at no extra cost.
French Alps Overnight Ski Train resumes from London
Eurostar's annual direct ski services to the French Alps also commenced on December 21 with the first night service to the popular French ski towns of Moûtiers, Aime-La-Plagne and Bourg St Maurice running on Friday 21 December and the first day service the following day.
Nick Mercer, Commercial Director for Eurostar commented; "We're expecting this to be one of our busiest festive periods for years. Our French ski service grows in popularity year on year and with our new Swiss Alps ski service launching as well this weekend we're expecting a bumper 2012 festive period."
New Spring Service to Lyon and Provence
As the Ski trains depart, the tickets for the summer services to the south of France are already on sale. Next summer, Eurostar is launching a trial service to Lyon and Provence through May and June to complement our annual Avignon summer services.
Direct trains will reach Lyon, Avignon and Aix-en-Provence for the first time from London operating a weekly service. The new train runs from 4 May to the 29 June 2013 inclusive. On the return leg, passengers will need to disembark in Lille Europe to complete the necessary security and passport checks before re-boarding a dedicated Eurostar service to the UK.
Nick Mercer, Commercial Director for Eurostar commented, "Our direct Avignon summer services grow in popularity year on year and our customers tell us they'd like to see it extended to offer even more choice of holiday destinations. We're committed to listening to their feedback, which is why we're testing this new service to Lyon, Avignon and Aix-en-Provence, three of the most popular destinations in the South of France.
"By trialling this new service for future years, and by opening sales to our existing annual summer Avignon services earlier than usual, we are giving customers even more flexibility and choice when planning their trips to the South of France next year. Journeys with Eurostar avoid the summer scramble at the airports and we encourage passengers to book early to avoid disappointment."
High Speed 1 - Five years old as Eurostar comes of Age
Eurostar has celebrated the 18th anniversary of the start of high-speed passenger services which commenced with 'preview' services in 1994. The Secretary of State for Transport, Patrick McLoughlin MP, joined Eurostar chief executive Nicolas Petrovic on the Eurostar platforms, to mark the occasion with the cutting of a special birthday cake.
The same celebrations marked the 5th anniversary of Eurostar moving from Waterloo International to St Pancras International and the opening of HS1, the UK's first high-speed rail line, in 2007.
The Secretary of State for Transport, Patrick Loughlin MP, said; "This important milestone marks the coming of age of Eurostar and it is testament to its success that we now think nothing of hopping on a train in London and getting off in Paris or Brussels. The last five years have also given the UK its first real taste of high speed rail. From the splendour of the redesigned St Pancras to the mouth of the channel tunnel itself, HS1 shows what a difference such projects can make. That is why I am determined to press ahead with HS2 – a network that will build on the success of HS1 to deliver jobs, growth and much-needed extra rail capacity."
Nicolas Petrovic, Eurostar Chief Executive, said; "What once seemed like the stuff of science fiction is now part of our everyday lives. We're proud to have changed the way people think about travelling between the UK and the Continent.
"Everyone from business travellers and holiday makers to day trippers and second home-owners, now enjoys the speed, ease and convenience of city centre to city centre high-speed rail. We have our eyes firmly set on the future and with many exciting projects in the pipeline our customers can look forward to the next chapter in Eurostar's story."
When the first Eurostar trains left London in 1994, they carried a total of 38,000 in the first month of operation. Now, 18 years later, passenger numbers in 2012 average more than 830,000 a month. Over the course of those 18 years Eurostar has carried more than 130 million travellers more than doubling the total number of passengers travelling (by air or rail) between London and Paris, Lille and Brussels.
In 1994 journey times between London and Paris were 3h00 and Brussels 3h15. Since then, as successive sections of the high-speed line in the UK have been completed those journey times have fallen considerably. With the completion of HS1 five years ago today, the London-Paris journey time was slashed again to 2h15 and London Brussels to 2h00.
Eurostar Website