text:
\section{Introduction}
Quantum mechanics and general relativity are the two most successful theories explaining the phenomena at two most fundamental length scales of the universe. While quantum mechanics explains the intricacies of the atomic length scale, general relativity \cite{Einstein15,Einstein16} sheds light on the large-scale structure of the universe. In order to understand the fundamental mysteries of the universe, we need a quantum theory of gravity, explaining the analytical structure of the gravitational interaction at the quantum length scale. Theories like loop quantum gravity\cite{ROVELLI,CARLIP}, string theory\cite{ACV,KOPAPR}, and noncommutative geometry\cite{GLO} have provided a convincing theoretical framework explaining the Planck-scale nature of gravity but none of them have compelling experimental evidence to support their claim of providing an exact description of the quantum nature of gravity.  Although all of them prescribe the existence of an observer-independent minimal length which can be incorporated by the modification of the standard Heisenberg uncertainty principle (HUP), also known as the generalized uncertainty principle (GUP). The first few attempts to improvise an integral relation between minimal length scale and gravity was shown in \cite{BRON1,BRON2}, followed by \cite{MEAD}. We also get a strong evidence of the existence of this fundamental length scale from the various gedanken experiments in quantum gravity phenomenology as well.  This GUP framework has been used to investigate several areas of theoretical physics, like black hole physics and its thermodynamics\cite{MAGGIORE,SCARDIGLI,ADLERSAN,ADLERCHENSAN,RABIN,SG1,SCARDIGLI2,
SG2,Ong,EPJC,BMajumder}, various quantum systems like particle in a box, simple harmonic oscillator\cite{DAS1,DAS2}, optomechanical systems\cite{IVASP,IVASP2,KSP}, and gravitational wave bar detectors\cite{SG3,SG4}. There have been several recent studies involving the path integral formalism of a non-relativistic particle moving in an arbitrary potential in the generalized uncertainty principle framework\cite{SG3,DAS3,SGSB}. The simplest form the modified HUP can be written in the following form\cite{Kempf}
\begin{equation}\label{1.01}
\Delta q_i\Delta p_i\geq \frac{\hbar}{2}\left[1+\gamma\left(\Delta p^2+\left<p\right>^2\right)+2\gamma\left(\Delta p_i^2+\left<p_i\right>^2\right)\right];~i=1,2,3
\end{equation}
where $p^2=\sum_{k=1}^3p_kp_k$ and $q_k, p_k$ are the phase space position and its conjugate momenta.
In eq.(\ref{1.01}) the GUP parameter $\gamma$ in terms of the dimensionless parameter $\gamma_0$ can be recast as follows
\begin{equation}\label{1.02}
\gamma=\frac{\gamma_0}{m_p^2 c^2}
\end{equation}
where $m_p$ is the Planck mass and $c$ is the speed of light. It is quite natural to realize that the order of magnitude of the GUP parameter will play a significant role in providing an understanding of the GUP effects. There have been several studies to find a bound on the GUP parameter itself\cite{SG4,SCARDIGLI2, DAS1, BM, FENG, BBGK, SCARDIGLI3,GRD,RCSG,OTM}.

\noindent In the 1969, the first proposition to detect gravitational waves was made by J. Weber\cite{Detect1} which was followed by a subsequent paper in 1982 by Ferrari \textit{et} \textit{al.}\cite{Detect2}. Bar detectors currently have a sensitivity $\frac{\Delta L}{L}\sim 10^{-19}$\cite{Detect3}, where $\Delta L$ is fractional variation of the length $L$ ($\sim1$ meter) of the bar detector. A historical perspective of these resonant detectors is given in \cite{Aguiar}. The detection of gravitational waves by the LIGO\cite{LIGO,LIGO2} and Virgo\cite{VIRGO} detectors have unveiled a new realm of quantum gravity phenomenology. There have been several recent investigations regarding the traces of quantum gravitational effects in these gravitational wave detectors. A lot of investigation has been done to check if any signature of this fundamental Planck length, whether it is noncommutativity\cite{SGA1,SGA2,SGA3,SGA4,SGA5,SGA6} or GUP\cite{LIGO3,SG4}, is visible in GW bar detectors. We would like to point out that till date there has not been a successful detection of gravitational waves in resonant bar detectors. However, there is a good hope that the sensitivity of the detectors would increase in future enabling detection of these waves. The AURIGA (\textit{Antenna Ultracriogenica Risonante per l'Indagine Gravitazionale Astronomica}) detector at INFN, Italy is probably the only functional bar detector. These bar detectors are sensitive to frequencies of the order of $1$kHz along with a strain sensitivity of the order $10^{-19}$\cite{Piz}. In case of astrophysical events, collapsing and bouncing cores of supernova can be a source to huge intensities of gravitational waves having frequencies in the vicinity of $1-3$kHz. The value of the strain sensitivity can be calculated using Thorne's formula\cite{Thorne}. The strain sensitivity ($h$), according to this formula, is given by
\begin{equation}\label{0.01}
h=2.7\times 10^{-20}\left[\frac{\Delta E_{GW}}{M_sc^2}\right]^{\frac{1}{2}}\left[\frac{1kHz}{f}\right]^{\frac{1}{2}}\left[\frac{10Mpc}{d}\right]
\end{equation}
where $\Delta E_{GW}$ is the energy converted to gravitational waves, $f$ is the characteristic frequency of the burst, $M_s$ is the solar mass and $d$ is the distance of the burst source from earth. A possible value of fraction of energy converted to gravitational waves for supernova events is around $7\times10^{-4}$. Now for $h\sim 3\times 10^{-19}$ and $f\sim 0.9 kHz$, the distance $d$ has the value around $25kpc$. The occurrence of such a supernova event of the required magnitude at this distance from the earth would definitely result in the detection of gravitational waves by the bar detectors. An effort to increase the sensitivity of these detectors to $h\sim10^{-20}$ is presently being carried out, and achieving this sensitivity would increase the distance of the supernova event from the earth to $250kpc$, which is more likely to occur. The main motivation to work with a gravitational wave bar detector is that it is a very resourceful and economic alternative to the LIGO/VIRGO detectors.

\noindent In this work we investigate the path integral formalism of a resonant gravitational wave bar detector interacting with the gravitational wave emitted from a distant source in the GUP framework. The incoming gravitational waves interact with the elastic matter in the resonant bar detector causing tiny vibrations called phonons. Physically we can describe these detectors as a quantum mechanical \textit{gravitational wave-harmonic oscillator} (GW-HO) system because we call these vibrations; the quantum mechanical forced harmonic oscillator. To calculate the perturbative solution to the system we use the gravitational wave and generalized uncertainty modifications as perturbations. Our study presents a path integral approach to look at such a system and is the first work using path integral. The advantage of working with path integrals is that the effective action describing the system can be easily read off from the structure of the configuration space path integral\cite{SGPRL}.
\section{The gravitational wave resonant detector interaction model}
\noindent To begin the discussion, we need to write down the Hamiltonian for the resonant bar detector in the presence of a gravitational wave in the generalized uncertainty principle framework. The modified commutation relation following from eq.(\ref{1.01}) takes the following from\cite{Kempf}
\begin{equation}\label{1.03}
[\hat{q}_i,\hat{p}_j]=i\hbar\left[\delta_{ij}+\gamma\delta_{ij}\hat{p}^2+2\gamma\hat{p}_i\hat{p}_j\right]
\end{equation}
where $i,j=1,2,3$. The modified position and momentum operators $\hat{q}_i$ and $\hat{p}_i$ in terms of the usual variables $\hat{q}_{0i}$ and $\hat{p}_{0i}$ read
\begin{equation}\label{1.04}
\hat{q}_i=\hat{q}_{0i}~,~\hat{p}_i=\hat{p}_{0i}\left(1+\gamma \hat{p}_0^2\right)~.
\end{equation}
Here $\hat{p}_0^2=\sum_{k=1}^3\hat{p}_{0k}\hat{p}_{0k}$ and $[\hat{q}_{0i},\hat{p}_{0j}]=i\hbar\delta_{ij}$.
In order to write the Hamiltonian of the system we start by analyzing the background metric as a superposition of a small perturbation on the flat background metric. The background metric is taken as follows
\begin{equation}\label{1.05}
g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu}
\end{equation}
where $\eta_{\mu\nu}=\text{diag}\{1,-1,-1,-1\}$ and $|h_{\mu\nu}|\ll 1$.   We now consider a two dimensional harmonic oscillator with mass $m$ and intrinsic frequency $\varpi$. The geodesic deviation equation for the aforementioned system in the proper detector frame is given as follows\cite{Maggiore}
\begin{equation}\label{1.06}
\begin{split}
m\ddot{q}^k&=-mR^k_{~0l0}q^l-m\varpi^2q^k\\
\implies \ddot{q}^k&=\frac{d\Gamma^k_{~0l}}{dt}q^l-\varpi^2q^k~;~k=1,2
\end{split}
\end{equation}
where $R^k_{~0l0}$ in terms of the background perturbation is given by
\begin{equation}\label{1.07}
R^k_{~0l0}=-\frac{d\Gamma^k_{~0l}}{dt}=-\frac{\ddot{h}_{kl}}{2}~.
\end{equation}
Note that here we are using the transverse traceless gauge to get rid of the unphysical degrees of freedom. The Lagrangian from which eq.(\ref{1.07}) can be obtained reads
\begin{equation}\label{1.08}
L=\frac{1}{2}m\dot{q}_k^2-m\Gamma^{k}_{~0l}\dot{q}_kq^l-\frac{1}{2}m\varpi^2q_k^2~.
\end{equation}
The Hamiltonian corresponding to the Lagrangian in eq.(\ref{1.08}) reads
\begin{equation}\label{1.09}
H=\frac{1}{2m}\left(p_k+m\Gamma^k_{~0l}q^l\right)^2+\frac{1}{2}m\varpi^2q_l^2~.
\end{equation}
To write the Hamiltonian in eq.(\ref{1.09}) in quantum mechanical description we just elevate $q$ and $p$ to the operator prescription. Therefore, the Hamiltonian in terms of the position and momentum operators can be expressed as follows

\begin{equation}\label{1.10}
\hat{H}=\frac{1}{2m}\left(\hat{p}_k+m\Gamma^k_{~0l}\hat{q}^l\right)^2+\frac{1}{2}m\varpi^2\hat{q}_l^2~.
\end{equation}
Using the representation of the position and momentum operators in eq.(\ref{1.04}), the Hamiltonian (\ref{1.10}) {of the GW-HO system in presence of GUP } can be written as follows
\begin{equation}\label{1.11}
\hat{H}=\left(\frac{\hat{p}_{0k}^2}{2m}+\frac{1}{2}m\varpi^2\hat{q}_{0k}^2\right)+\frac{\gamma}{m}\hat{p}_{0k}^2\hat{p}_0^2+\frac{1}{2}\Gamma^{k}_{~0l}\left(\hat{p}_{0k}\hat{q}^{0l}+\hat{q}^{0l}\hat{p}_{0k}\right)+\frac{\gamma}{2}\Gamma^{k}_{~0l}\left(\hat{p}_{0k}\hat{p}_0^2\hat{q}^{0l}+\hat{q}^{0l}\hat{p}_{0k}\hat{p}_0^2\right)~.
\end{equation}
Now a typical bar is a cylinder of length $L \equiv 3 m$ and radius $R \equiv 30 cm$\cite{Maggiore}. Hence in a first approximation, we can treat the GW detector in presence of GUP as a one dimensional HO. The Hamiltonian in eq.(\ref{1.11}) can be recast in one dimension as follows
\begin{equation}\label{1.12}
\hat{H}=\frac{p^2}{2m}+\frac{1}{2}m\varpi^2q^2+\gamma\frac{p^4}{m}+\frac{1}{2}\Gamma^1_{~01}(pq+qp)+\frac{\gamma}{2}\Gamma^1_{~01}(p^3q+qp^3)
\end{equation}
where for notational simplicity we have used $\hat{p}_{01}=p$ and $\hat{q}_{01}=q$. In the next section we will proceed to construct the path integral formalism of the GW-HO system in presence of the GUP and calculate the propagation kernel for that system.
\section{Path integral and the propagation kernel}
In this section we will use the Hamiltonian in eq.(\ref{1.12}) to calculate the propagation kernel via the path integral approach. We consider the initial and the final state of the Hamiltonian in eq.(\ref{1.12}) at initial time $t_i$ and final time $t_f$ as $\left|q_i,t_i\right>$ and $\left|q_f,t_f\right>$ respectively. The general form of the propagation kernel can be written as follows
\begin{equation}\label{1.13}
\begin{split}
\left<q_f,t_f|q_i,t_i\right>&=\lim\limits_{N\rightarrow\infty}\int_{-\infty}^{+\infty}dq_{N-1}\ldots dq_1\left<q_f,t_f|q_{N-1},t_{N-1}\right>\left<q_{N-1},t_{N-1}|q_{N-2},t_{N-2}\right>\ldots\left<q_1,t_1|q_{i},t_{i}\right>\\
&=\lim\limits_{N\rightarrow\infty}\int_{-\infty}^{+\infty}\prod\limits_{\alpha=1}^{N-1}dq_\alpha\left<q_f\right|e^{-\frac{i\hat{H}(t_f-t_{N-1})}{\hbar}}\left|q_{N-1}\right>\ldots\left<q_1\right|e^{-\frac{i\hat{H}(t_1-t_i)}{\hbar}}\left|q_i\right>\\
&=\lim\limits_{N\rightarrow\infty}\int_{-\infty}^{+\infty}\prod\limits_{\alpha=1}^{N-1}dq_\alpha\prod\limits_{\beta=0}^{N-1}\left<q_{\beta+1}\right|e^{-\frac{i\hat{H}(t_{\beta+1}-t_\beta)}{\hbar}}\left|q_\beta\right>
\end{split}
\end{equation}
where $t_f=t_N$, $t_i=t_0$ and $t_{N}-t_{N-1}=\Delta t$. Now we will introduce the complete set of momentum eigenstates $\left(\int_{-\infty}^{+\infty}dp\left|p\right>\left<p\right|=1\right)$ in the following way
\begin{equation}\label{1.14}
\begin{split}
\left<q_f,t_f|q_i,t_i\right>=&\lim\limits_{N\rightarrow\infty}\int\prod\limits_{\alpha=1}^{N-1}dq_\alpha\prod\limits_{\beta=0}^{N-1}\int ~dp_\beta\left<q_{\beta+1}|p_\beta\right>\left<p_\beta|q_\beta\right>\exp\left(-\frac{iH(q_\beta,p_\beta)(t_{\beta+1}-t_\beta)}{\hbar}\right)\\
=&\lim\limits_{N\rightarrow\infty}\int_{-\infty}^{+\infty}\prod\limits_{\alpha=1}^{N-1}dq_\alpha\prod\limits_{\beta=0}^{N-1}\int_{-\infty}^{+\infty} \frac{dp_\beta}{2\pi\hbar}\exp\biggr[\frac{i\Delta t}{\hbar}\sum\limits_{\beta=0}^{N-1}\biggr[\frac{p_\beta(q_{\beta+1}-q_\beta)}{\Delta t}-\biggr(\frac{p_\beta^2}{2m}+\frac{1}{2}m\varpi^2q_\beta^2+\frac{\gamma p_\beta^4}{m}\\&+\frac{p_\beta q_\beta(h_{\beta+1}-h_\beta)}{2\Delta t}+\frac{\gamma p_\beta^3q_\beta({h}_{\beta+1}-h_\beta)}{2\Delta t}\biggr)\biggr]\biggr]
\end{split}
\end{equation}
where we have used $h_{11}=h$~. The final form of eq.(\ref{1.14}) in the $\Delta t\rightarrow0$ limit can be recast as follows
\begin{equation}\label{1.15}
\left<q_f,t_f|q_i,t_i\right>=\int\mathcal{D}q\mathcal{D}p\exp\left(\frac{i}{\hbar}\mathcal{S}\right)
\end{equation}
where $\mathcal{S}$ is the phase space action. The phase space action is given as follows
\begin{equation}\label{1.16}
\mathcal{S}=\int_{t_i}^{t_f} dt\left[p\dot{q}-\left(\frac{p^2}{2m}+\frac{\dot{h}_{11}}{2}pq+\frac{1}{2}m\varpi^2q^2+\frac{\gamma p^4}{m}+\frac{\gamma\dot{h}_{11}}{2}p^3q\right)\right]~.
\end{equation}
To obtain the configuration space Lagrangian we will simplify eq.(\ref{1.14}) as follows
\begin{equation}\label{1.17}
\begin{split}
\left<q_f,t_f|q_i,t_i\right>&\cong\lim\limits_{N\rightarrow\infty}\int_{-\infty}^{+\infty}\prod\limits_{\alpha=1}^{N-1}dq_\alpha\prod\limits_{\beta=0}^{N-1}\int_{-\infty}^{+\infty} \frac{dp_\beta}{2\pi\hbar}\left[1-\frac{i\gamma\Delta t}{m\hbar}\left(p_\beta^4+\frac{h_{\beta+1}-h_\beta}{2\Delta t}p_\beta^3q_\beta\right)+\mathcal{O}(\gamma^2)\right]
\end{split}
\end{equation}
\begin{equation*}
\begin{split}
\times\exp\left[\frac{i\Delta t m}{2\hbar}\left[\left(\frac{q_{\beta+1}-q_\beta}{\Delta t}-\frac{h_{\beta+1}-h_\beta}{4\Delta t}q_\beta\right)^2-\varpi^2q_\beta^2\right]\right]\exp\left[-\frac{i\Delta t}{2m\hbar}\left[p_\beta-\left(\frac{m(q_{\beta+1}-q_\beta)}{\Delta t}-\frac{m(h_{\beta+1}-h_\beta)q_\beta}{4\Delta t}\right)\right]^2\right]~.
\end{split}
\end{equation*}
To do the momentum integral for each $\beta$ value, we shall do the following coordinate transformation
\begin{equation}\label{1.18}
\bar{p}_\beta=p_\beta-\left(\frac{m(q_{\beta+1}-q_\beta)}{\Delta t}-\frac{m(h_{\beta+1}-h_\beta)q_\beta}{4\Delta t}\right)~.
\end{equation}
Using eq.(\ref{1.18}) in eq.(\ref{1.17}), the propagation kernel upto $\sim \gamma,h$  can be recast as
\begin{equation}\label{1.19}
\begin{split}
\left<q_f,t_f|q_i,t_i\right>\cong&\lim\limits_{N\rightarrow\infty}\int_{-\infty}^{+\infty}\prod\limits_{\alpha=1}^{N-1}dq_\alpha\prod\limits_{\beta=0}^{N-1}\int_{-\infty}^{+\infty} \frac{d\bar{p}_\beta}{2\pi\hbar}\left[1-\frac{i\gamma\Delta t}{m\hbar}\biggr[\biggr(\bar{p}_\beta+\left(\frac{m(q_{\beta+1}-q_\beta)}{\Delta t}-\frac{m(h_{\beta+1}-h_\beta)q_\beta}{4\Delta t}\right)
\right)^4+\\&\frac{h_{\beta+1}-h_\beta}{2\Delta t}\left(\bar{p}_\beta+\left(\frac{m(q_{\beta+1}-q_\beta)}{\Delta t}-\frac{m(h_{\beta+1}-h_\beta)q_\beta}{4\Delta t}\right)\right)^3q_\beta\biggr]+\mathcal{O}(\gamma^2)\biggr]\exp\left[-\frac{i\Delta t}{2m\hbar}{\bar{p}_\beta}^2\right]\\&\times\exp\left[\frac{i\Delta t m}{2\hbar}\left[\left(\frac{q_{\beta+1}-q_\beta}{\Delta t}-\frac{h_{\beta+1}-h_\beta}{4}q_\beta\right)^2-\varpi^2q_\beta^2\right]\right]~.
\end{split}
\end{equation}
The momentum integral in eq.(\ref{1.19}) can be obtained as follows
\begin{equation}\label{1.20}
\begin{split}
\left<q_{\beta+1},t_{\beta+1}|q_\beta,t_\beta\right>\cong&\sqrt{\frac{m}{2\pi i\hbar\Delta t}}\biggr\{1-6\gamma m^2\left(\frac{q_{\beta+1}-q_\beta}{\Delta t}-\frac{h_{\beta+1}-h_\beta}{4\Delta t}q_\beta\right)^2-\frac{3\gamma m^2(h_{\beta+1}-h-\beta)}{2\Delta t}\biggr(\frac{q_{\beta+1}-q_\beta}{\Delta t}\\&-\frac{(h_{\beta+1}-h_\beta)}{4\Delta t}q_\beta\biggr)q_\beta+\frac{3i\gamma m\hbar}{\Delta t}\biggr\}~\exp\biggr[\frac{im\Delta t}{2\hbar}\biggr[\biggr(\frac{q_{\beta+1}-q_\beta}{\Delta t}-\frac{(h_{\beta+1}-h_\beta)q_\beta}{4}\biggr)^2-2\gamma m^2\\&\times\biggr[\biggr(\frac{q_{\beta+1}-q_\beta}{\Delta t}-\frac{(h_{\beta+1}-h_\beta)q_\beta}{4}\biggr)^4+\frac{(h_{\beta+1}-h_\beta)q_\beta}{2}\biggr(\frac{q_{\beta+1}-q_\beta}{\Delta t}-\frac{(h_{\beta+1}-h_\beta)q_\beta}{4}\biggr)^3\biggr]-\varpi^2q_\beta^2\biggr]\biggr]~.
\end{split}
\end{equation}
Using eq.(\ref{1.20}) in eq.(\ref{1.19}), we obtain the form of the propagation kernel upto some constant factor as follows
\begin{equation}\label{1.21}
\begin{split}
\left<q_f,t_f|q_i,t_i\right>&=\int_{-\infty}^{+\infty}\prod\limits_{\alpha=1}^ {N-1}dq_\alpha\exp\biggr[\sum\limits_{\beta=0}^{N-1}\frac{im\Delta t}{2\hbar}\biggr\{\biggr(\frac{q_{\beta+1}-q_\beta}{\Delta t}-\frac{(h_{\beta+1}-h_\beta)q_\beta}{4}\biggr)^2-2\gamma m^2\biggr(\biggr(\frac{q_{\beta+1}-q_\beta}{\Delta t}\\&-\frac{(h_{\beta+1}-h_\beta)q_\beta}{4}\biggr)^4+\frac{(h_{\beta+1}-h_\beta)q_\beta}{2}\biggr(\frac{q_{\beta+1}-q_\beta}{\Delta t}-\frac{(h_{\beta+1}-h_\beta)q_\beta}{4}\biggr)^3\biggr)-\varpi^2q_\beta^2\biggr\}\biggr]~.
\end{split}
\end{equation}
Imposing the $\Delta t\rightarrow 0$ limit in eq.(\ref{1.21}), the final form of the propagation kernel has the usual configuration space path integral structure as follows
\begin{equation}\label{1.22}
\left<q_f,t_f|q_i,t_i\right>=\mathcal{N}(T,\gamma,\dot{h})\int\mathcal{D}qe^{\frac{i}{\hbar}S}~.
\end{equation}
In the above equation the configuration space structure of the action $S$ is given as follows
\begin{equation}\label{1.23}
\begin{split}
S=&\int_{t_i}^{t_f}dt\left(\frac{m}{2}\left(\dot{q}-\frac{\dot{h}q}{4}\right)^2-\frac{1}{2}m\varpi^2q^2-\gamma m^3\left(\dot{q}-\frac{\dot{h}q}{4}\right)^4-\frac{\gamma m^3\dot{h}q}{2}\left(\dot{q}-\frac{\dot{h}q}{4}\right)^3\right)\\
\cong&\int_{t_i}^{t_f}dt\left(\frac{m}{2}\dot{q}^2-\frac{1}{2}m\varpi^2q^2-\frac{m\dot{h}\dot{q}q}{4}-\gamma m^3\dot{q}^4+\frac{1}{2}m^3\gamma\dot{h}\dot{q}^3q\right)~.
\end{split}
\end{equation}
In the last line of the above eq.(\ref{1.23}), we have kept terms upto $\mathcal{O}(h,\gamma)$.
The Lagrangian can be easily read off from eq.(\ref{1.23}) as follows
\begin{equation}\label{1.24}
L=\frac{m}{2}\dot{q}^2-\frac{1}{2}m\varpi^2q^2-\frac{m\dot{h}\dot{q}q}{4}-\gamma m^3\dot{q}^4+\frac{1}{2}\gamma m^3\dot{h}\dot{q}^3q~.
\end{equation}
The equation of motion following from the Lagrangian reads
\begin{equation}\label{1.25}
\ddot{q}-\frac{\ddot{h}q}{4}+\varpi^2 q-12m^2\gamma\ddot{q}\dot{q}^2+3\gamma m^2\dot{h}\ddot{q}\dot{q}q+\frac{3}{2}\gamma m^2\ddot{h}\dot{q}^2q+\gamma m^2\dot{h}\dot{q}^3=0~.
\end{equation}
In the next section we calculate the classical solution for the above equation of motion.
\section{Obtaining the classical solution for a periodic circularly polarized gravitational wave}
To obtain the classical solution we shall consider a circularly polarized gravitational wave in the transverse traceless gauge.  Now for a periodic circularly polarized gravitational wave the perturbation term $h$ containing the polarization information reads
\begin{equation}\label{1.26}
h_{kl}(t)=2f_0\left(\varepsilon_\times(t)\sigma^1_{kl}+\varepsilon_+(t)\sigma^3_{kl}\right)~;~k,l=1,2
\end{equation}
where $2f_0$ is the amplitude of the gravitational wave (here $f_0$ is very small), $\sigma^1$ and $\sigma^3$ are the Pauli spin matrices. In eq.(\ref{1.26}) $(\varepsilon_+(t),\varepsilon_\times(t))$ are the two possible polarization states of the gravitational wave satisfying the condition $\varepsilon_+(t)^2+\varepsilon_\times(t)^2=1$. In this particular scenario the chosen functional forms of the polarization states can be written as follows
\begin{equation}\label{1.27}
\varepsilon_+(t)=\cos(\Omega t)~,~\varepsilon_\times(t)=\sin(\Omega t)
\end{equation}
with $\Omega$ being the frequency of the gravitational wave. In our case, we will consider that the only non zero polarization state is $\varepsilon_+(t)=\cos(\Omega t)$. Therefore, in one dimension the perturbation term can be written as $h=2f_0\cos(\Omega t)$. The equation of motion in eq.(\ref{1.25}) upto $\mathcal{O}(f_0,\gamma)$ takes the form as follows
\begin{equation}\label{1.27a}
\ddot{q}+\omega^2q-12m^2\gamma\ddot{q}\dot{q}^2=0
\end{equation}
where $\omega^2=\varpi^2-\frac{\ddot{h}}{4}$. For the equation of motion in eq.(\ref{1.27a}), we consider a solution upto $\mathcal{O}(f_0,\gamma)$ as
\begin{equation}\label{1.28}
q(t)=q_0(t)+f_0 q_{f_0}(t)+\gamma q_\gamma(t)~.
\end{equation}
For the form $q(t)$ in the above equation, we obtain the solution of eq.(\ref{1.25}) as a linear combination as $q_0(t), q_{f_0}(t) \text{ and }q_\gamma(t)$. The analytical forms of $q_0(t), q_{f_0}(t) \text{ and }q_\gamma(t)$ are given as follows
\begin{align}
q_0(t)=&\mathcal{A}_1\cos(\varpi t)+\mathcal{A}_2\sin(\varpi t)~,\label{1.29}\\
q_{f_0}(t)=&\mathcal{A}_3\cos(\varpi t)+\mathcal{A}_4\sin(\varpi t)-\frac{\Omega}{2(4\varpi^2-\Omega^2)}[\Omega\cos(\Omega t)\left\{\mathcal{A}_1\cos(\varpi t)+\mathcal{A}_2\sin(\varpi t)\right\}\nonumber\\&-2\varpi\sin(\Omega t)\left\{\mathcal{A}_2\cos(\varpi t)-\mathcal{A}_1\sin(\varpi t)\right\}]~,\label{1.30}\\
q_\gamma(t)=&\mathcal{A}_5\cos(\varpi t)+\mathcal{A}_6\sin(\varpi t)-\frac{3m^2\varpi^2}{2}[t\varpi \mathcal{A}_1(\mathcal{A}_1^2+\mathcal{A}_2^2)\sin(\varpi t)-t\varpi \mathcal{A}_2(\mathcal{A}_1^2+\mathcal{A}_2^2)\cos(\varpi t)\nonumber\\&+\frac{\mathcal{A}_1}{4}(\mathcal{A}_1^2-3\mathcal{A}_2^2)\cos(3\varpi t)-\frac{\mathcal{A}_2}{4}(\mathcal{A}_2^2-3\mathcal{A}_1^2)\sin(3\varpi t)]\label{1.31}
\end{align}
where $\mathcal{A}_1,\mathcal{A}_2,\mathcal{A}_3,\mathcal{A}_4,\mathcal{A}_5\text{ and }\mathcal{A}_6$ are arbitrary constants which we will calculate for the $q_{cl}(t)$. To obtain the form of the above constants we will apply the following set of the initial conditions
\begin{equation}\label{1.32}
\begin{split}
q(t)=\biggr\{\begin{matrix}
&q_0&\text{for}&t=0\\
&q_f&\text{for}&t=T
\end{matrix}~.
\end{split}
\end{equation}
Using the initial conditions in eq.(\ref{1.32}), the constants can be obtained as follows
\begin{align}
\mathcal{A}_1&=q_0~,~\mathcal{A}_2=\frac{q_f-q_0\cos(\varpi T)}{\sin(\varpi T)}~,\label{1.33}\\
\mathcal{A}_3&=\frac{\mathcal{A}_1\Omega^2}{2(4\varpi^2-\Omega^2)}~,\label{1.34}\\
\mathcal{A}_4&=\frac{\Omega\left\{\cos(\varpi T)\left[\Omega\mathcal{A}_1\cos(\Omega T)-2\varpi\mathcal{A}_2\sin(\Omega T)\right]+\sin(\varpi T)\left[\Omega\mathcal{A}_2\cos(\Omega T)+2\varpi \mathcal{A}_1\sin(\omega T)\right]\right\}}{2(4\varpi^2-\Omega^2)\sin(\varpi T)}-\mathcal{A}_3\cot(\varpi T)~,\label{1.35}\\
\mathcal{A}_5&=\frac{3}{8}m^2\varpi^2\mathcal{A}_1\left(\mathcal{A}_1^2-3\mathcal{A}_2^2\right)~,\label{1.36}\\
\mathcal{A}_6&=\frac{3m^2\varpi^2\left[\varpi T\left(\mathcal{A}_1\sin(\varpi T)-\mathcal{A}_2\cos(\varpi T)\right)(\mathcal{A}_1^2+\mathcal{A}_2^2)+ \frac{\mathcal{A}_1(\mathcal{A}_1^2-3\mathcal{A}_2^2)\cos(3\varpi T)}{4}-\frac{\mathcal{A}_2(\mathcal{A}_2^2-3\mathcal{A}_1^2)\sin(3\varpi T)}{4}\right]}{2\sin(\varpi T)}-\mathcal{A}_5\cot(\varpi T).\label{1.37}
\end{align}
Using eq.(\ref{1.28}) along with eq.(s)(\ref{1.33}-\ref{1.37}) in eq.(\ref{1.23}) (with $h$ being replaced by $2f_0\cos(\Omega t)$), we obtain the form of the classical action upto $\mathcal{O}(\gamma,f)$ as follows

\begin{equation}\label{1.39}
S_\mathcal{C}=S_{\mathcal{C}}^{(0)}+S_{\mathcal{C}}^{(\gamma)}+S_{\mathcal{C}}^{(f_0)}
\end{equation}
where $S_{\mathcal{C}}^{(0)},~S_{\mathcal{C}}^{(\gamma)}$, and $S_{\mathcal{C}}^{(f_0)}$ are given by the following equations
\begin{align}
S_{\mathcal{C}}^{(0)}&=\frac{m\varpi}{2\sin(\varpi T)}\left((q_0^2+q_f^2)\cos(\varpi T)-2q_0q_f\right)~,\label{1.40}\\
S_{\mathcal{C}}^{(\gamma)}&=-\frac{\gamma m^3\varpi^3}{32\sin^4(\varpi T)}\biggr[12\varpi T \left(q_f^4+4q_f^2q_0^2+q_0^4\right)-48q_0q_f\varpi T\cos(\varpi T)(q_f^2+q_0^2)+24 q_0^2q_f^2\varpi T \cos(2\varpi T)\nonumber\\&-44q_0q_f\sin(\varpi T)(q_0^2+q_f^2)+4\sin(2\varpi T)\left(2q_0^4+15q_0^2q_f^2+2q_f^4\right)-12q_0q_f\sin(3\varpi T)(q_0^2+q_f^2)+\sin(4\varpi T)(q_0^4+q_f^4)\biggr],\label{1.41}
\end{align}
\begin{align}\label{1.41a}
S_{\mathcal{C}}^{(f_0)}&=-\frac{f_0m\varpi\Omega}{2\sin(\varpi T)(4\varpi^2-\Omega^2)}\biggr[\frac{\varpi\sin(\Omega T)}{\sin(\varpi T)}\left(q_0^2-2q_0q_f\cos(\varpi T)+q_f^2\cos(2\varpi T)\right)+2q_0q_f\Omega\cos^2\left(\frac{\Omega T}{2}\right)\nonumber\\
&-\Omega\cos(\varpi T)\left(q_0^2+q_f^2\cos(\Omega T)\right)\biggr]~.
\end{align}
Therefore, we now have the final form of the propagator for the resonant bar detector interacting with a gravitational wave as follows
\begin{equation}\label{1.42}
\left<q_f,T|q_0,0\right>=\sqrt{\frac{m\varpi}{2\pi i\hbar \sin(\varpi T)}}\tilde{\mathcal{N}}(T,\gamma,f_0)e^{\frac{i}{\hbar}S_{cl}}.
\end{equation}
To obtain an overall structure of the fluctuation parameter in the above equation we consider the free particle structure involving gravitational wave (GW) interaction only. In this case, the infinitesimal propagator considering the particle GW interaction from eq.(\ref{1.14}) can be extracted as follows (in the $\varpi\rightarrow 0$ limit)
\begin{equation}\label{1.43}
\begin{split}
\left<q_1,\Delta t|q_0,0\right>=&\int_{-\infty}^{\infty}\frac{dp_0}{2\pi\hbar}\exp\biggr[\frac{i\Delta t}{\hbar}\left(p_0\frac{(q_1-q_0)}{\Delta t}-\left(\frac{p_0^2}{2m}+\frac{\gamma p_0^4}{m}+\frac{p_0q_0f_0}{\Delta t}\left(\cos(\Omega\Delta t)-1\right)\right)\right)\biggr]\\
\simeq&\sqrt{\frac{m}{2\pi i\hbar\Delta t}}e^{\frac{im}{2\hbar \Delta t}(q_1-	q_0)^2}\biggr[1+\frac{3im\gamma\hbar}{\Delta t}-6\gamma m^2\left(\frac{q_1-q_0}{\Delta t}\right)^2-\frac{i\gamma m^3(q_1-q_0)^4}{\hbar\Delta t^3}\\&-\frac{if_0q_0}{\hbar}\left(\frac{m(q_1-q_0)}{\Delta t}\right)(\cos(\Omega\Delta t)-1)\biggr]~.
\end{split}
\end{equation}
Now the total propagator can be written using the set of infinitesimal propagators as follows
\begin{equation}\label{1.44}
\begin{split}
\left<q_f,T|q_0,0\right>&\simeq\left(\frac{m}{2\pi i\hbar\Delta t}\right)^\frac{N}{2}\int dq_1dq_2\cdots dq_{N-1} e^{\frac{im}{2\hbar\Delta t}\left[(q_1-q_0)^2+(q_2-q_1)^2+\cdots+(q_f-q_{N-1})^2\right]}\biggr[1+\frac{3i\gamma m\hbar N}{\Delta t}-\frac{6\gamma m^2}{\Delta t^2}((q_1-q_0)^2\\&+(q_2-q_1)^2+\cdots+(q_f-q_{N-1})^2)-\frac{i\gamma m^3}{\hbar\Delta t^3}((q_1-q_0)^4+(q_2-q_1)^4+\cdots+(q_f-q_{N-1})^4)\\&-\frac{if_0m}{\hbar\Delta t^2}\left[q_0(q_1-q_0)(\cos(\Omega\Delta t)-1)+\cdots+q_{N-1}(q_f-q_{N-1})(\cos(N\Omega\Delta t)-\cos((N-1)\Omega\Delta t))\right]\biggr]~.
\end{split}
\end{equation}
In the absence of the gravitational wave\cite{Pramanik}, the form of the propagator in eq.(\ref{1.44}) reads
\begin{equation}\label{1.45}
\left<q_f,T|q_0,0\right>=\sqrt{\frac{m}{2\pi i\hbar T}}e^{\frac{im}{2\hbar T}(q_f-q_0)^2}\left(1+\frac{3i\gamma m\hbar}{T}-6\gamma m^2\left(\frac{q_f-q_0}{T}\right)^2-\frac{i\gamma m^3}{\hbar T^3}(q_f-q_0)^4\right)~.
\end{equation}
In presence of the gravitational wave, the propagator has the form given as
\begin{equation}\label{1.46}
\begin{split}
\left<q_f,T|q_0,0\right>&\simeq\sqrt{\frac{m}{2\pi i\hbar T}}e^{\frac{im}{2\hbar T}(q_f-q_0)^2}\biggr(1+\frac{3i\gamma m\hbar}{T}-6\gamma m^2\left(\frac{q_f-q_0}{T}\right)^2-\frac{i\gamma m^3}{\hbar T^3}(q_f-q_0)^4\\&+\frac{if_0mT}{\hbar}\left(\frac{(q_f-q_0)}{T}\right)^2[\cos(\Omega T)-1]-\frac{if_0q_f}{\hbar}\left(\frac{m(q_f-q_0)}{T}\right)[\cos(\Omega T)-1]\biggr)\\
&\simeq\sqrt{\frac{m}{2\pi i\hbar T}}\tilde{\mathcal{N}}(T,\gamma,f_0)e^{\frac{i}{\hbar}S_{cl}^{(f)}}
\end{split}
\end{equation}
where $S_{cl}^{(f)}$ is the classical action involving free particles and gravitational waves given by
\begin{equation}\label{1.47}
\begin{split}
S_{cl}^{(f)}=\frac{m}{2T}(q_f-q_0)^2-\frac{\gamma m^3}{T^3}(q_f-q_0)^4-\frac{mf_0}{2 T}(q_f-q_0)\left[(q_f\cos[\Omega T]-q_0)-(q_f-q_0)\frac{\sin[\Omega T]}{\Omega T}\right]
\end{split}
\end{equation}
and the form of the fluctuation term is given as follows
\begin{equation}\label{1.48}
\begin{split}
\tilde{\mathcal{N}}(T,\gamma,f_0)&\simeq 1+\frac{3i\gamma m\hbar}{T}-6\gamma m^2\left[\frac{q_f-q_0}{T}\right]^2+\frac{if_0mT}{\hbar}\left[\frac{q_f-q_0}{T}\right]^2[\cos(\Omega T)-1]-\frac{if_0mq_f}{\hbar}\left[\frac{q_f-q_0}{T}\right][\cos(\Omega T)-1]\\&-\frac{imf_0(q_f-q_0)}{2\hbar T}\biggr[\frac{(q_f-q_0)\sin(\Omega T)}{\Omega T}-(q_f\cos(\Omega T)-q_0)\biggr]~.
\end{split}
\end{equation}
\section{Summary}
In this work, we have constructed the path integral formalism of the propagation kernel for a resonant bar detector in the presence of a gravitational wave in the generalized uncertainty principle framework. In this framework, we have considered only quadratic order correction in the momentum. We have obtained the configuration space action for this system using the path integral formalism. With the action in hand, we have then obtained the equation of motion of the system. From the equation of motion, we observe that the overall frequency of the resonant detector shifts due to interaction with the gravitational wave. Next, we have used the form of the perturbation term for a circularly polarized gravitational wave to calculate the classical solution of the detector coordinate $q(t)$. Using this form of $q(t)$ we have finally obtained the classical action for a resonant bar detector interacting with a gravitational wave in the generalized uncertainty principle framework. We have then investigated the quantum fluctuation parameter of the bar detector in presence of a circularly polarized gravitational wave. In order to obtain the final form of the fluctuation, we have considered a free particle interacting with the gravitational wave. The final form of the fluctuation picks up correction terms due to both GUP correction and gravitational wave interaction. In this process we have neglected cross terms considering both GUP and GW interactions as it would result in a much smaller correction to the fluctuation factor than the other corrections present in the analytical form of the quantum fluctuation. It would also be important to carry out the above analysis in a linear GUP framework. However, we would like to report this in future. From the observational point of view, the importance of our work lies in the fact that resonant bar detectors have the potential of detecting gravitational waves with their present sensitivity at distances of the order of $10^2kpc$ from the earth. The propagator captures the quantum effects also. Hence, detectability of such quantum effects in resonant bar detectors is also a possibility in the near future. A knowhow of the propagator  of the detector coordinates is therefore necessary if not absolutely essential.

redpajama_set_name: RedPajamaArXiv


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Nov 8, 2022), Kizomba Core 1 Level 2(Oct 19, 2022 - Nov 9, 2022), Kizomba Fundamentals(Oct 19, 2022 - Nov 9, 2022), Kizomba Core 2 Skill Building(Oct 19, 2022 - Nov 9, 2022), Zouk Core 1 Level 3(Oct 19, 2022 - Nov 9, 2022), Zouk Core 2 Level 1(Oct 19, 2022 - Nov 9, 2022), Zouk Fundamentals(Oct 19, 2022 - Nov 9, 2022), Lead/Follow Sensual Body Movement Technique (Intermediate Prep Class)(Oct 20, 2022 - Nov 10, 2022), Head Movement Technique (Prep Class)(Nov 14, 2022 - Dec 12, 2022), Intermediate Zouk(Nov 14, 2022 - Dec 12, 2022), Bachata Fundamentals(Nov 15, 2022 - Dec 13, 2022), Bachata Core 1 Level 1(Nov 15, 2022 - Dec 13, 2022), Bachata Core 2 Skill Building(Nov 15, 2022 - Dec 13, 2022), Zouk Fundamentals(Nov 16, 2022 - Dec 14, 2022), Lead/Follow Sensual Body Movement Technique (Intermediate Prep Class)(Nov 17, 2022 - Dec 15, 2022), Head Movement Technique (Prep Class)(Jan 9, 2023 - Jan 30, 2023), Intermediate Zouk(Jan 9, 2023 - Jan 30, 2023), Bachata Fundamentals(Jan 10, 2023 - Jan 31, 2023), Bachata Core 1 Level 1(Jan 10, 2023 - Jan 31, 2023), Bachata Core 2 Level 1(Jan 10, 2023 - Jan 31, 2023), Kizomba Core 2 Skill Building(Jan 11, 2023 - Feb 1, 2023), Zouk Fundamentals(Jan 11, 2023 - Feb 1, 2023), Kizomba Intermediate, Kizomba Intermediate(Jan 11, 2023 - Feb 1, 2023), Zouk Core 1 Level 1(Jan 11, 2023 - Feb 1, 2023), Kizomba Fundamentals(Jan 11, 2023 - Feb 1, 2023), Zouk Core 2 Level 1(Jan 11, 2023 - Feb 1, 2023), Salsa on1 Fundamentals(Jan 12, 2023 - Feb 2, 2023), Lead/Follow Sensual Body Movement Technique (Intermediate Prep Class)(Jan 12, 2023 - Feb 2, 2023)
For the more serious learner that wants to follow our carefully designed curriculum as it was intended in order to produce the best results. Commit to 6 months of learning upfront and we'll shape you into the best social dancer you can be! This committment package includes all of the core 1 and core 2 classes plus any intermediate prep classes needed for your genre for one of our 4 main dance styles. If you'd like to focus on more than one dance style, you may sign up for a maximum of 2 commitment packages simultaneously.

redpajama_set_name: RedPajamaCommonCrawl


Hi, i'm having some problems with videos, sometimes i can post them, sometime i have this message "There has been an error processing your request". Sometimes i can see thme, sometimes not.
I have tried with yoyutube and dailymotion and i'm using blog mu theme from here.
Wordpress handles embeds by only allowing them from specific sites and those that meet specific protocol.
Do you have support for o-embed?
to see it in action. Before someone told me about this plugin I was trying to use embed codes from youtube and everything was a mess. This works great!
Go to add plugins and search for cool video gallery and install.
Thanks for your suggestion, but it's compatible with buddypress wall ?
can you give me a link to one that is not working and one that is?
Hello @puccino and @KimberlyL I don't recall if I was using buddypress wall before or not. The company I used to have maintain my stuff retired. All I know is that since I started using the Cool Video Gallery plugin I haven't ran into any issues that used used to.
Have you tried Dean's suggestion?
I just want to share my experience with video embedding within buddypress.
I have my own videos and I decide to host them on Amazon S3 for best performances.
I use a great service called "Easy Video Player".
You import your video in Easy video player, you customize your player and options.
When your player is ready, you copy your code directly in your activity stream.
With buddypress, I use the iframe code.
Hello @visitonweb @KimberlyL and @puccino I'm not familiar with the Amazon S3 site, is that who hosts your website? The nice thing about the Cool Video Gallery is that you can upload (or in the event your video files are Hugh you can FTP) the files to your own server. The advantage to that is you have complete control.
I've had videos on youtube, vimeo etc and used the embedded code to put into my site. Some themes don't always play nice with this setting. Also Someone (probably one of my competitors) flagged the site and my video was removed without mt knowledge. Not cool. This seemed strange to me as I found portions of one of my copyrighted videos used by someone else who got paid for basically putting together Highlight type reels and he doesn't even own a video camera! He just steals everyone Else's work and Ironically myself and 3 other videographers whose work was stolen complained to YouTube. We had to jump through hoops to prove that the original footage was ours and yet that video still remains on youtube.
All in all there appear to be several choices out there. I saved a ton of time trying all of them as I was referred to the Cool Video Gallery as the one that had the least amount of problems as suggested by a group of professional videographers.
Anyway let me know what ended up working best for you.
I'm not familiar with the Amazon S3 site, is that who hosts your website?
Amazon S3 is a CDN (Content Delivery Network) which allows the streaming/delivery of static content to your web site faster then on a good hosting platform for those with less then good hosting.
I personally tried Amazon S3 some time ago before I owned my own servers and it worked good with the cheap hosting I had then, but now with my Dual Xeon Quad Core servers my opinion is simply that it bites - Can't touch this.
Nothing but nothing compares to good hosting, yet many folks are trying to build million dollar web sites on four dollar hosting. Rather then upgrade their hosting they will go with CDN's paying them what could be accomplished by just having a good hosting platform to begin with.
I was hoping to find a recent ticket where a Member told the tale of hosting so well and in a way that I am not at a liberty to say.
@puccino if i remember correctly you are one of the few with a real dedicated server and there have been enough recommendations in this thread to include your own current testing.
I am happy to know you are well on the track to getting this issue resolved to your satisfaction.


text:
HFF Secures $10M Financing for NC Industrial Portfolio
By Mihaela Coste
CharlotteFinanceIndustrialNews More South
Arrowridge Business Park consists of four rear-load buildings totaling 194,560 square feet of space. The portfolio is currently 98 percent leased to a mix of 26 tenants.
8100 Arrowridge Blvd., Charlotte, N.C.
HFF secured $10.2 million in acquisition financing for Arrowridge Business Park, a four-building, office-warehouse portfolio located in Charlotte, N.C. The company arranged the 10-year, fixed-rate loan through a life company, working on behalf of a joint venture between Childress Klein, WHI Real Estate Partners and affiliates of Ocean Road Advisors Inc.
HFF will service the loan, proceeds of which were used for the acquisition of the 194,560-square-foot portfolio. Senior Managing Director Travis Anderson and Senior Director Cory Fowler led the debt placement team representing the borrower. Earlier this month, HFF secured a $15 million financing for a warehouse building located in South Brunswick, N.J.
Location and tenure mix
Arrowridge Business Park is situated on a 13.6-acre site at 8041, 8107, 8227 and 8301 Arrowridge Blvd., in close proximity to the intersection of interstates 77 and 485, providing convenient access to the Charlotte CBD and Charlotte Douglas International Airport. A variety of dining and lodging options are situated nearby, including a Starbucks and a Hyatt Place.
The four rear-load buildings feature 16-foot ceiling heights, a total of 37 dock-high doors, 17 drive-in ramps, wet sprinkler systems and 35 percent of the space designed for office purposes.
The portfolio is 98 percent leased to 26 tenants, including Sears Home Improvement Products, Centimark, Interior Specialists and Lennox Industries. "At 98 percent occupancy, the acquisition of Arrowridge Business Park was an outstanding opportunity for the borrower to add additional stabilized assets to their already-strong portfolio within the submarket," said Fowler in a prepared statement. "By leveraging its market knowledge and experience, the partnership can ensure that the portfolio continues to operate at a level above its competition."
Images courtesy of Childress Klein
Childress Klein
WHI Real Estate Partners LP


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Learn more about 12T2.5/420 Timing Belts and B&B Manufacturing, Inc. View product specifications, download a CAD file in your preferred format, or purchase online.
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Sandy McIver is putting out a call for Thank You Cards to help kids at Ronald McDonald House.
Head on over to Sandy's blog to find out more. This seems like a great cause if you can just make a few extra cards for sick kids at Ronald McDonald House.


text:
GroupedTableViewCellSelection
=============================

iOS grouped table view master-detail application which explains how to customize cell selection color for grouped table view cells.

redpajama_set_name: RedPajamaGithub


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text:
Upcoming ULI event asks, should Toronto bid to host EXPO 2025?
Josh Sherman May 13, 2016
Photo: Larry Koester
This past summer, Toronto hosted the Pan Am/Parapan Am Games, and now the city is mulling a bid to hold another major worldwide event, Expo 2025.
With council's debate approaching, Urban Land Institute (ULI)'s Toronto chapter is set to explore whether or not the city should throw its hat into the ring and bring the world's fair here.
To do this, the local branch of ULI, which is a worldwide non-profit urban research and education organization, is hosting a panel discussion at the Toronto Region Board of Trade (77 Adelaide Street West) on May 17th from 5:30pm to 7:30pm.
"Historically, Toronto's flirtations with hosting a major world event — something it has rarely done — has been mixed," ULI Toronto says, highlighting one of the challenges a facing a potential bid.
"Most recently it rejected the opportunity to advance an Olympic bid, and past bids have both united and divided the city," it adds.
Sevaun Palvetzian, CEO of CivicAction, a non-profit coalition of the city's civic leaders, will be moderating the discussion, and the panelists backgrounds cover a broad range of disciplines from political to economic.
Panelists include David Peterson, one-time Ontario premier and former chair of Toronto Pan/Para Pan American Games, Barbara Hall, once Toronto's mayor, Dr. Kwame McKenzie, president and CEO of the Wellesley Institute, an urban-health think tank, and Andrew Grantham, CIBC's senior economist.
The event follows previous ULI panels, including its recent Meet the Chiefs Gala, which brought together senior planners from municipalities across the GTA, and Startup City, an event looking at what brings burgeoning tech firms to some cities and not others.
To register for the event, call 1 800 321 5011. Admission is $90 for non-ULI members. For a full price scale and further details, visit the event page on ULI's website.


By water The Venetian archipelago consists of 118 islands, so canals - quite sensibly - take the place of roads. It's usually possible to take a traditional gondola to your destination, but the extensive water bus network (known as the vaporetto) offers a speedier and cheaper alternative. With 19 lines operating throughout the day, you can reach almost any location within an hour. A range of tickets are available for the service, including 12-hour, day and week passes.
On foot The 409 bridges connecting the Venetian islands mean you can often walk to your destination. You'll have to get to grips with a labyrinthine street network and take on the crowds at busy bottlenecks, but this is the best way to explore the six sestieri (districts) and discover hidden gems.
By train The rail network offers easy access to the islands from the mainland, but Venice Saint Lucia railway station at the southern end of the causeway is as far as you can go. This busy terminal is your starting point for day trips into the wider Province of Venice, but there are no local services on the islands.
By car Venice has motor vehicle access via the Ponte della Libertà bridge, which opened in 1933, but the road ends at the Piazzale Roma gateway. If you plan to hire a car, park it in the multi-storey facility on the neighbouring Tronchetto island.


Zen Car will bring 29 vehicles into circulation, edging out a larger effort that will be unveiled in Paris in the fall.
It's the green transport geek's equivalent of a Superman-Batman comic: car sharing meets electric vehicles.
Next month, a company called Zen Car will launch an EV car-sharing scheme in Brussels, with support from a regional investment society. Twenty-nine cars are going into circulation, with about fifteen charging stations around the city. It costs 40 euros to join, plus a 6-euro monthly subscription and a 7-euro hourly fee for use. The cars are 100% electric, according to the helpful "Zen Car? C'est quoi?" information page.
Zen Car isn't the only EV-for-hire service coming soon to Europe, though it may be one of the first. The Autolib' Project in Paris will unroll a somewhat larger-scale project over the course of the coming year. In late December, it was announced that the electric Bluecar had won the market for the Autolib' project, itself inspired by Paris's bike-sharing service, Velib'. With Autolib', some 3,000 cars will be available at about 100 hire points. The EV company Better Place has also experimented with EV car sharing in Denmark, where it partnered with a commuter train service to offer electric-cars-for-hire at train stations.
Could we see something similar soon in major American cities? To a certain extent, we already have. While we don't appear to have broad, all-electric, government supported car-sharing fleets (Zen Car may ultimately be funded by the Belgian government), American car-sharing companies and startups have ventured into the EV market. Though Zipcar introduced an all-electric Citroen C1 into its fleet in 2009, hybrids are more common that full-on EVs, even in forward-thinking markets like San Francisco. A few weeks ago, Zipcar said eight new plugin hybrid electric Priuses would enter its fleet, meaning Zipcar customers would actually be beta-testing the car before it comes to market.
Could Zipcar learn from Zen Car, or vice versa? Regis Leluth of Zen Car tells Fast Company in an email that he once reached out to Zipcar, but "without success," and that he has been especially impressed with Zipcar's marketing. But he'll have his own mobile advertisements on the streets soon, in the form of the cars themselves.


text:
Q: Question aboute a quote from a TV show where I've noticed two different tenses in the same sentence there is a famous quote from Game of Thrones Episode 10 season 3 where a character says "Any man who must say, "I am the king" is no true king. I'll make sure you understand that when I've won your war for you." I've noticed that there is two different tenses in the second part of the quote where we can see "I'll" which is supposed to refer to the future, and then he said "when I've won" which is supposed to refer to the past, so I'm a little bit confused, thanks in advance for your answer.

A: The second part of the second sentence uses the present perfect, which isn't exactly the past tense. The present perfect is used in the present to show a relationship to something done or completed in the past, almost always at a time close to the present.
For example, "I have done my homework" is something you would say in the present to acknowledge that, at some point shortly before the present, you completed your homework.
The first part of the second sentence is just the simple future ("I will make sure you understand...").
In this case, Tywin (the character) is saying that when he can say in the present that the war is won (by him), then he will (in the near future) be able to show the king that no true king needs to say "I am the king."

redpajama_set_name: RedPajamaStackExchange


text:
PS-116 Keamari-V () is a constituency of the Provincial Assembly of Sindh.

General elections 2013

General elections 2008

See also
 PS-115 Keamari-IV
 PS-117 Karachi West-I

References

External links
 Election commission Pakistan's official website
 Awazoday.com check result
 Official Website of Government of Sindh

Constituencies of Sindh

redpajama_set_name: RedPajamaWikipedia


What is 'atmosphere' and what is 'outer space'? The term 'atmosphere' is sometimes used interchangeably with 'air'. Moreover, it is often assumed that 'outer space' is simply the area above and beyond 'air space' (another term often used). While understandings such as these are certainly reasonable for most discussions, the effective development of international environmental law may well demand more precise definitions. This article provides an overview of key atmospheric and outer space environmental challenges that have been – and continue to be – addressed by international environmental law. It examines transboundary air pollution, ozone layer depletion, global climate change, and outer space. For each of these issue areas, the article describes a particular environmental problem (or set of environmental problems). It also reviews key elements of the international legal response (including especially significant agreements), focusing on innovative approaches taken as part of this response. In addition, the article discusses transboundary transport of industrial pollutants as well as major industrial accidents.
Ian H. Rowlands is Associate Professor in Environment and Resource Studies at the University of Waterloo, Canada. He is also Associate Dean of Research for the Faculty of Environmental Studies at the University of Waterloo.


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text:
Mrs. Angela M. Van Dekker
Angela Van Dekker of Hastings-on-Hudson, NY died peacefully on May 23, 2019 surrounded by her family at the age of 76 after a valiant battle with pancreatic cancer. Angela was born on September 23, 1942 to John and Rose DeVivo who predeceased her. She graduated Saint Agnes Seminary High School and Fordham University undergraduate in 1963, obtained a Masters in Education from Fordham in 1964. She received her MBA from Fordham in 2001 with induction into Beta Gamma Sigma, the business school honor society (receiving the Zeta Chapter Medallion award), and Alpha Mu Alpha, the national marketing honor society. She also has a Masters degree from the School of Education where she served as a Graduate Assistant. Angela married Benjamin Van Dekker on June 29, 1973. Angela was the co-founder of the "Committee for Youth, Inc." a not-for-profit corporation that provided services and activities for the youth of Hastings-on-Hudson. She co-wrote the grant for the Youth Advocates of Hastings that became a model for Westchester County Youth Services. She was the Director for the Continuing Education Program for Hastings, Dobbs Ferry and Irvington. She was trainer for the Junior League of Westchester and provided seminars for the Westchester County Office of Women on "Women in Power". Angela started her employment at Fordham University as the Student Employment Coordinator June 1st 1983. In her tenure there, she has worked in education, as a teacher, a trainer, director of Continuing Education Programs, and of Student Employment culminating in Assistant Vice President of Student Financial Services responsible for financial aid, student employment and student accounts. Angela was appointed to Congressman Gillmans' education advisory board for many years. She was nominated by Governor George Pataki and approved by the state senate and served for 12 years HESC Board of Trustees, the last two spent as vice-chair and then chair. She was active in the New York State Financial Aid Administrators Association (NYSFAAA) at the state level previously as Vice President of the association, conference program committee chair, as well as serving on several statewide committees, and in the NYC region as secretary, then chairperson and was the greater New York metropolitan area representative to the NYSFAAA Executive Council. She was a trainer and presenter for the Junior League of Westchester, the College board, the national association (NASFAA), the eastern regional association (EASFAA), NYSFAAA, CUNY the Higher Education Services Corporation (HESC) and annually for the National College Fair in NYC, as well as local high schools and other projects. She served on the advisory boards of ELM (Electronic Loan Management) Resources; two software companies APPWORKS and Overture and several lenders Citibank, AFC (Academic Finance Corporation) and Education Finance Partners (formerly served on Chase, Fleet and Key Education Resources boards). She served on the 22nd Congressional Education Advisory Committee from 1989- 2002 when the congressman retired. She was awarded Alpha sigma nu - Jesuit honor society Fordham's Sursum Corda Award March 2016, CBA Leadership award Multiple Certificates of Appreciation from NYSFAAA professional association. Angela lived a full and rewarding life retiring as Associate Vice President of Student Financial Services of Fordham University after 36 years. She is survived by her devoted husband Benjamin Van Dekker, loving children Angela (Robert) Outhouse, John (Jessica) Van Dekker and Carl Van Dekker. She was adored by her grandchildren Melissa (Ron) Dinsmore, Danielle & Michael Moray; Jackson, Violet & Elyse Van Dekker; great grandchildren Charlotte and Grayson, many cousins, coworkers and friends. Her family was her life. Visitation is Tuesday May 28th, 2019, 4-9 pm at Edwards-Dowdle Funeral Home, 64 Ashford Avenue, Dobbs Ferry, NY. Mass of Christian Burial at Fordham University Church, Wednesday, May 29, 2019, 10:00 a.m. In lieu of flowers, donations may be made to the Angela Van Dekker Endowed Financial Aid Fund Scholarship which Fordham University graciously honored her with upon her retirement.
Angela Van Dekker of Hastings-on-Hudson, NY died peacefully on May 23, 2019 surrounded by her family at the age of 76 after a valiant battle with pancreatic cancer. Angela was born on September 23, 1942 to John and Rose DeVivo who predeceased... View Obituary & Service Information
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I don't know how this happened, but it has, and I can't see how or where to change it back.
Or even where the 'send later' files have gone.
OR where the 'SEND LATER' time is controlled from !
I have restarted T-Bird, and got my SEND back.
But during the 'reboot' I was asked if I wanted to send my UNSENT messages NOW or LATER.
I chose LATER, but as they were just 4 copies of the same email, I would prefer to have the option to CANCEL.
So...................had I clicked on SEND NOW, would they all have gone immediately, or would I get asked one by one ?
And would there be an option to NOT send them at all ?
I'm asking this, as I'm worried that if I click SEND NOW they will all go at once to the same person !
So I have erred on the side of 'caution' !
But would still like to know.
And what to do should it happen again !
It sounds as though Thunderbird did not have an Internet connection when it first offered that "Send Later" option. That would prevent it from sending immediately so it offered the alternative. Along with that offer, Thunderbird stores outgoing messages in a folder called Outbox in the Local Folders structure so they can be...sent later.
If that happens again, disconnect the computer from the Internet (remove any network cable from the computer or from the router or turn off the computer's wifi) before launching Thunderbird. Open the Outbox folder and delete any duplicates in that location before relaunching Thunderbird with Internet access restored.
Thanks. I'm 100% certain that is correct, as there was an Internet problem mainly owing to a thunderstorm, I think, just before this happened.
Thanks for the help and the info !
If you have the status bar displayed, there is an icon in the lower left corner that displays either two computers on top of each other (online) or the same two computers with an X (offline). Clicking on the icon (or going in the menus and selecting File–> Work offline) toggles from online to offline mode.


Zweig here captures two striking truths. First, the transition from child to adult comes not by steady gradualism but in catalytic episodes in which the membrane between the two worlds thins by means of betrayal, violence (emotional and otherwise), and critical acts of independence. Second, a shocking number of life's Big Moments would entirely resemble cheap melodrama if not for the transmuting--almost alchemical--effect these moments initiate deep in the souls of innocent parties who are snared in the drama's orbit. A compulsive read!
Meet Amber. She's immobilized in a hospital bed, unable to move or speak but capable of hearing all that goes on around her. How she got here is the one thing she doesn't know. What don't we know about Amber? Everything.
And you'll have to read to the very end to find out if she's lying.
Have you ever wondered what you will read this summer? Wonder no longer. This is the thriller of the year, it deserves to accompany you to the beach, the mountains, the airport. Put it in your travel bag and ENJOY.


Updated version of vintage Hawaiian Hibiscus mini-band print, this Hawaiian T-Shirt is now available in our popular Pro-Fit style. Hawaiian Hibiscus Heavyweight T-shirt will make a great gift for any man in your family. Wear it in summer or, because of the heavyweight fabric, you can wear it every season of the year. Hawaiian T-Shirts bring a little aloha to your life any day you wear them.
As with all our tees, this premium tee is garment dyed which pre-shrinks it and eliminates the chance of twisting, fading or additional shrinkage. This one is in the TALL-fit version so be sure to check the fit guide found on this page to confirm your size. Each of our custom t-shirts are pre-shrunk in the dye process so feel free to throw them into the dryer. After the dye process we add the unique vintage Hawaiian style print to make it just what you are looking for.


Between St Raphael and St Maxime, Holiday villa home: "Le Clapotis, St Aygulf" to rent with secured swimming pool in a garden of 2500M2 planted with trees and Provencal essences.
Villa in Provence with a private swimming pool at garden level and a remarkable panoramic view over the coast. Able to accommodate up to 8 people, the 100m2 villa has, amongst other things, 3 bedrooms, 2 separate WCs, a fully equipped kitchen and 2 terraces, one of which is partially covered. The 2500m2 garden is enclosed for visitors greater comfort. Situated at 200m from the sea and the regional road between Fréjus and Sainte Maxime, the villa is very good situated to visit the surroundings. The villa is also situated 20 minutes from St. Tropez by coastal shuttle and only 10 km from Saint Raphael, and is also close to the centre of the village of St Aygulf and Fréjus.
Cost to foresee: Èlec:0,15 / KW, beyond 3€/M3 of water to pay.


OL president Jean-Michel Aulas has said he will announce a decision as to the future of coach Bruno Genesio - whose contract is up at the end of the current season - in early April.
Speculation has been ongoing for much of Bruno Genesio's tenure at the helm of Olympique Lyonnais since he stepped up from his role as assistant coach when Hubert Fournier was sacked in December 2015. At the end of that season, he signed a three-year deal that comes to term this June, but Aulas has only just announced when he will decide whether to offer Genesio a new contract - and it's right after their crunch COupe de France semi-final against Rennes.
"It will be 2 April," announced the OL president, who has seen his coach engineer victory over Paris Saint-Germain - the capital club's only league defeat so far this season - as well as an away win against Manchester City and a scoreless home draw against Barcelona in the UEFA Champions League this season. "The 31st of March is a Sunday. On 1 April, we will have a directors' meeting and on 2 April, we will be able to tell you what we have decided with Bruno Genesio."
Doubts about Genesio among Lyon's supporter base came to a head recently when key fan group Les Bad Gones released a communiqué calling for Genesio's departure, but Aulas, ever the king of his domain, ruled out any external influence on his decision.
"As we will be having a meeting on this very subject next week, it's perhaps not that useful to take notice of this demand - especially as the fans have taken the step of talking directly to the media before the meeting has even been held," said Aulas, whose presidency has taken the club from the lower reaches of Domino's Ligue 2 in 1987 to a run of seven consecutive Ligue 1 Conforama titles (2002-08) and a UEFA Champions League semi-final (2009-10).
"We are talking about a club that is among the most important in Europe and it's not the fans who decide how it is to be governed. I'm surprised, as we have always been able to communicate openly with each other. Will it influence our choice? Not at all. I asked them if they wanted to have some input in to the criteria, but that's it. The club's governance is a question for the directors, who invest a lot of their money, passion and time. Decisions will be made the same way they been for the last 32 years at OL."