text:
Q: T-SQL - WHERE Clause to find enters where date is next week but also in current quarter I have a simple table structure containing tasks assigned to resources:
| TASK | START_DATE              | RESOURCE | CLOSED |
| T1   | 2018-10-10 00:00:00.000 | Bill     | 0      |
| T2   | 2018-11-12 00:00:00.000 | Bob      | 0      |
| T3   | 2018-11-17 00:00:00.000 | Ben      | 0      |
I have a report that is intended to show the tasks that need to be completed next week and my current filter is:
WHERE CLOSED = 0 AND ((DATEPART(wk,Tasks.Start_Date) -1) = DATEPART(wk,getutcdate()) and DATEPART(YY,Tasks.Start_Date) = DATEPART(yy,getutcdate()))
The filter works perfectly when the task has a start date that is in the next week but I also have tasks that run quarterly which are being excluded by this filter.
Is there a way to build a filter that includes all tasks for this quarter as well as the tasks for next week? For example the Task identified as T1 is still open despite having a start date in the past (2018-10-10 00:00:00.000) I still need it to show on my report.
Thanks!

A: Assuming you are using MSSQL, you can use the simplified conditions below to provide increased readability..:
WHERE CLOSED = 0
  AND Tasks.Start_Date < DATEADD(WEEK,1,GETDATE())

EDIT: If it is required to get the tasks will start in next week and started in this quarter only, since the where clause above brings all the tasks that already started and having CLOSED=0, use below:
WHERE CLOSED = 0
  AND Tasks.Start_Date < DATEADD(WEEK,1,GETDATE())
  AND YEAR(Tasks.Start_Date) = YEAR(GETDATE())
  AND DATEPART(QUARTER, Tasks.Start_Date)=DATEPART(QUARTER, GETDATE())

A: So if closed is = 0 and it is in the past?  You can do an OR statement:
WHERE CLOSED = 0
AND (
    ((DATEPART(wk,Tasks.Start_Date) -1) = DATEPART(wk,getutcdate()) and DATEPART(YY,Tasks.Start_Date) = DATEPART(yy,getutcdate()))
    OR
    Tasks.Start_Date <= GetDate()  -- if using MS SQL
)

This will return everything you already were but also where closed = 0 and the StartDate is in the past.


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Fuel starts to go bad after 30 days so do not let it sit in your machine for longer than that. After 30 days, the volatile compounds in the fuel start evaporating, and this occurs whether the gas is in your outdoor power equipment or in the gas can.
As fuel sits and grows older, it evaporates and forms brown sticky deposits that eventually turn into a hard varnish. Deposits and varnish can plug fuel lines and passages in the carburetor, preventing the engine from running properly.
Many of us use fuel stabilizers in our machines when we store them for the off-season to have an easier time starting them when the time comes. This is a good practice. When fuel stabilizers are added to fuel they separate and create a thin film on top of the fuel to keep out air and moisture. They also reduce the rate at which the fuel's volatile compounds evaporate.
Try adding fuel stabilizer to your fuel the day it is purchased. This way, the fuel will stay fresh longer.
Engines produced for use in outdoor power equipment are not designed for gasoline with more than 10% ethanol. Using higher ethanol fuel blends can lead to engine damage and performance issues. Read your John Deere Equipment Manual for information on the proper fuel to use in your machine.
Gasoline without ethanol will reduce the amount of moisture the gasoline can absorb from the atmosphere. Many areas carry ethanol-free gas. Visit https://www.pure-gas.org/ to locate ethanol-free gas stations near you.
Standard 87 octane gasoline is perfect for small engines like the ones found on lawn mowers. However, mid-grade or premium gas with an octane rating of 89 or higher can be used for engines that require the higher octane.
Again, read your owner's manual for information on the proper fuel to use in your outdoor power equipment.
Regular maintenance keeps your Lawn equipment running quietly and efficiently. If your lawn mower, snow blower, or other outdoor power equipment won't start, a damaged spark plug may be the problem. Worn or dirty spark plugs cause issues for your machine, so be on the lookout for these as well.
As a rule of thumb, you should check and/or replace the spark plug on your small engine machine every year. Also check the spark plug every season or every 25 hours of use to determine whether it should be replaced. If your John Deere equipment won't start, check and/or replace your spark plug.
Turn your machine off and allow the engine to cool to the touch. Disconnect the spark plug wire to prevent accidental starting.
Blow or clean off the area around the plug with compressed air or a brush, making sure the area is clean. This will prevent debris from getting in the combustion chamber when removing the spark plug.
Remove the spark plug with a spark plug socket and clean any deposits from the plug.
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1. Buy fresh gas. Leftover gas from summer lawnmowing won't cut it for snowblowing. Winter gas has a more volatile blend, which means quicker snowblower starts.
2. Use additive. Modern gas has a short shelflife. Old gas is actually one of the top reasons that small engines won't start. Make gas last with a fuel stabilizer—but only add the prescribed amount. Too much, and the stabilizer gums up the snowblower carburetor. Too little, and gas gums up the carburetor.
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4. Clear obstacles. Before snow starts, scout your snowblowing area for objects that could jam the auger: frozen newspapers, holiday light or extension cords, a dog cable, rocks or garden hose. If stone mulch borders an area you snowblow, mark the edges so you don't accidentally move into the gravel. In regions with heavy snowfalls, plan ahead and insert markers into soil before it freezes.
5. Adjust height. Skid shoes (also called skid plates) control how close the auger comes to snowy surfaces. Double-check these prior to cold weather. We had to make a last-minute adjustment--which required getting down on hands and knees--in a 40-degree garage. That's a cold task we don't relish repeating. If a skid shoe becomes cracked or worn, replace it.
6. Plan your attack. Think about the pattern you'll follow to move snow and where you'll put it. We tackled our first snowblowing during a windy blizzard, so quickly learned to work with the wind. The best place to blow snow is onto your lawn. Avoid blowing it too close to the house, and don't forget to clear a spot near the end of the driveway for placing garbage cans.
7. Harness the sun. Time snowblowing to take advantage of solar power. Our driveway gets morning sun, so we try to clear snow before the sun gets too high in the sky. That way, the sun melts any remaining snow and gets us to bare concrete—and safer footing—sooner.
8. Start your engine. Always start the engine outside—or just inside an open garage door. For an electric start, keep a properly rated extension cord handy. We didn't realize this for our first start. Our cords hang on a peg board—on the wall opposite from where we store and start the snowblower. With two cars in the garage, traversing from snowblower to extension cords presents an intense obstacle course. In future, I'll move a cord over near the snowblower before winter arrives.
9. Get out early. If the forecast predicts large storm totals, start blowing before snowfall finishes. This saves gas and wear on your machine, since blowing small amounts is easier. If you clear the driveway before the plows come through, take time to blow snow along the road edge heading toward your driveway to reduce what the plow will deposit.
10. Work as a team. When dealing with deep snow or a tall plow lump, I knock down snow with a shovel so my husband can easily throw it with the snowblower. I love a bent-handle snow shovel for moving snow, but that bend doesn't provide the necessary downward force for knocking down deep, cold-hardened snow. Use a shovel with a straight handle for best results.
11. Clean up after. After shutting off the engine, grab a broom to whisk snow off the blower. Use a clean-out tool or something similar to remove any snow from the chute. Knock snow off outside to avoid a wet and messy garage floor. Remove snow around the base and top of the chute so it doesn't freeze into position.
12. Buy a boot dryer. In areas with frequent heavy snowfalls, a boot dryer pays for itself in the first storm. It means you can head out, blow snow for Round 1, come inside to warm up, dry your boots and gloves, and have toasty, dry gear to put on when you head out again. It's also super handy for drying mittens and hats after friendly snowball fights!
Copyright © 2018 Iron Horse Small Engine Repair - All Rights Reserved.
We are partnered with Sears to do warranty work .


text:
MP meets Petworth Primary pupils at the Houses of Parliament
Arundel & South Downs MP Nick Herbert met students from The Petworth Primary School during their visit to the Houses of Parliament last month.
The 60 pupils from years 5 and 6 are learning about Parliament and democracy. They met their MP during a 'People's Parliament' tour and workshop. Mr Herbert spoke to them about his work as a Member of Parliament before answering their questions.
The People's Parliament workshop took place in the Discovery Space, a dedicated exhibition in the Education Centre in the Palace of Westminster. The children experienced an immersive 360-degree projection of historic events from Parliament's past.
Mr Herbert said: "It was a pleasure to welcome so many of the children from Petworth Primary School to Westminster and to hear what they had learned from their visit. I was delighted to answer some of their questions, and I hope they have enjoyed following up the visit with classroom projects."
1. Photograph – Nick Herbert with pupils from Petworth Primary School
2. To find out more about the Parliament Education Centre, opened by Professor Brian Cox in 2015, see https://www.parliament.uk/educationcentre.
News releasesMichelle Taylor May 13, 2019 Petworth, Schools, education
MP joins Snowdrop Trust charity walk in Arundel
News releasesMichelle Taylor May 13, 2019 Arundel, Charity
MP welcomes Arundel flood defence plans
News releasesMichelle Taylor May 13, 2019 Arundel, River Road

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: TagLib lacks video-metadata properties? I've been trying to set extended properties of mp4 such as Director and Publisher, but those are nowhere to be found when I browse the File.Tag suggestions that visual studio gives me. Perhaps I'm just using a bad library or something, or could someone confirm that TagLib doesn't support these?
I do however get suggestions for File.Tag properties relevant to audio files such as Album and Performers. Perhaps it's only showing audio properties for mp4? Can you switch to video/movies somehow?
I'm using the windows edition from here: http://download.banshee.fm/taglib-sharp/2.1.0.0/. just dropped the dll in my project dir and laoded it in VC#.

redpajama_set_name: RedPajamaStackExchange


Two events have marked June as a special month for us at Climate Control Middle East.
Two events have marked June as a special month for us at Climate Control Middle East. The first was DC Dialogue 2010, on June 2, which unexpectedly, drew quite a large number of people. I say unexpectedly, because we never intended to have an audience, considering that DC Dialogue has a roundtable format, and so in the strictest sense, is a series of closed-door sessions, each involving, say, 10 participants and a moderator. As it turned out, we had close to 70 people in attendance, and they participated as much as those at the table. For me, a highlight of the event was a clear evidence of an increase in mindshare for existing buildings. Even a year ago, at conferences in the UAE, the focus was steadfastly new construction – about hunting for projects that had somehow managed to proceed, despite everything, and about how smaller modular units could do the trick.
At Yas, though, substantial airtime went to EB. With more reasonable load profiles emerging, thanks to the chastening effect that the downturn has had, suddenly there was optimism that there was scope to erect smaller plant rooms in existing neighbourhoods. Footprint-related issues, it seemed, could be surmounted. Case-in point, the suggestion by Ken Currie of Mott MacDonald that the space at existing roundabouts could be used for the purpose of erecting smaller plant rooms, with the cooling towers positioned atop the chillers.
A key aspect that was not discussed in detail, though, was service corridors. Dubai's services corridors in existing neighbourhoods are highly congested. Where, then, is the scope to entrench supply and return pipelines? True, a certain portion of Sheikh Zayed Road was able to accommodate a district cooling infrastructure, but Dubai's arterial road is multilaned and nowhere as congested as Deira or Bur Dubai. It is this facility of space that has suddenly made district cooling a viable proposition for Burj Al Arab. Have I raised an issue that is worth detailed discussion? I would love to hear your thoughts.
The other event that has created quite a buzz in the newsroom is the launch of a dedicated web site for Climate Control Middle East magazine. We were so keen on a June 2 launch, to coincide with DC Dialogue, that we hurried things a bit and put it on board for you to view – climatecontrolme.com. Having said that, any web site is a work in progress, and in the coming days and months, you will see quite a ramp up, in terms of content and in the manner in which we present the words and pictures. Happy visiting!


text:
\section{Introduction}
\label{sec:int}

Experimental searches for dibaryons have been inconclusive.
In the nonstrange sector, pion-initiated reactions and pion-production
reactions were used to search for low-lying narrow $\pi NN$ resonances
below the $\Delta N$ threshold, aiming particularly at channels with
quantum numbers inaccessible to $NN$ configurations \cite{BPB02}.
Several broad $NN$ resonances are known near the $\Delta N$
and $\Delta\Delta$ thresholds and may be attributed to quasibound
states in these channels, as summarized recently \cite{CBD08}.
In the strange sector, extensive searches have been conducted
\cite{Bas97,Col97,Cra97} for the $H$ dibaryon, with strangeness
$S=-2$ and quantum numbers $(I,J^P)=(0,0^+)$, which originally was
predicted to lie below the $\Lambda\Lambda$ threshold \cite{Jaf77}.
Only few dedicated searches for $S=-1$ dibaryons have been reported,
for low-lying $L=1$ $\Lambda N$ resonances in singlet and triplet
configurations that were predicted in a quark-model study by Mulders
{\it et al.} \cite{MAD80} near the $\Sigma N$ threshold, but negative
results particularly for the singlet resonance were reported in
$K^-$-initiated experiments \cite{JHK92,CDG92}.

Here we look for low-lying $S=-1$ dibaryons associated with a `molecular'
$\pi\Lambda N$ structure, by solving three-body Faddeev equations with
pairwise phenomenological separable interactions. The $\Lambda N$ system
is known to be unbound, with $s$-wave forces in both singlet and triplet
states that are overall attractive and which yield scattering lengths of
order $-2$ fm \cite{RYa06}. The question is whether or not the pion is able
to bind an $s$-wave $\Lambda N$ pair within a $\pi\Lambda N$ bound state,
or a resonance. Since the $s$-wave $\pi N$ and $\pi\Lambda$ forces are very
weak \cite{Wei66}, we consider the $p$-wave resonances $\Delta(1232)$
$(\frac{3}{2},\frac{3}{2}^+)$ and $\Sigma(1385)$ $(1,\frac{3}{2}^+)$,
respectively, thus studying the $\pi\Lambda N$ three-body system with
$s$-wave baryons and a $p$-wave pion in a $(\frac{3}{2},2^+)$ state,
where the $\Lambda N$ subsystem is necessarily in the $^3S_1$ configuration.
For first orientation we neglect the ${^3S_1}-{^3D_1}$ channel coupling
which becomes important near and above the $\Sigma N$ threshold.

For all three partitions of this $(\frac{3}{2},2^+)$ state of the
$\pi\Lambda N$ system into an interacting pair and a spectator, the orbital
angular momenta, spins, and isospins couple to their maximal values and,
therefore, the spin and isospin recoupling coefficients are equal to one.
This three-body state is likely to represent a state with maximum possible
attraction. Furthermore, the fact that the spin and isospin recoupling
coefficients are equal to one allows for a formal reduction of the present
three-body problem to that of three spinless (and isospinless) particles.
We comment that a similar choice of $(I,J^P)=(2,2^+)$ for $\pi NN$, with
each $\pi N$ pair interacting in the $\Delta(1232)$-resonance
$(\frac{3}{2},\frac{3}{2}^+)$ channel, is impossible since a two-nucleon
$I=1,{^3S_1}$ state is forbidden by the Pauli principle.

Since we are interested in the bound-state region of the $\pi\Lambda N$
system, it is justified in first approximation to neglect the coupling
to the higher-mass systems $\bar K N N$, $\pi\Sigma N$ and $K\Xi N$.
The effect of the coupling to these higher-mass channels will be partly
taken into account by adjusting the interactions within the
$\pi\Lambda N$ system to the available experimental information on the
two-body subsystems. Less justified is the neglect of the coupling to
the lower-mass $\Sigma N$ system, with a threshold about 60 MeV below that
of $\pi\Lambda N$. This coupling renders $\pi\Lambda N$ bound states into
quasibound states through shifting and broadening the zero-width bound
states obtained when the coupling is disregarded, unless the binding energy
exceeds approximately 60 MeV and the $\pi\Lambda N$ state is genuinely bound.
In the present, exploratory calculation we ignore the coupling to $\Sigma N$.
Potential models generally yield fairly weak $\Sigma N$ interaction in the
relevant ${^1D_2}$ and ${^3D_2}$ configurations \cite{RYa06}. The quark model
of Ref.~\cite{MAD80} does not have any $(\frac{3}{2},2^+)$ $S=-1$ dibaryon
candidate in the vicinity of the $\pi\Lambda N$ threshold and below it.

The plan of this paper is as follows. In Sec.~\ref{sec:NR} we discuss the
choice of two-body interactions and the three-body Faddeev equations solved
in the nonrelativistic case, and report on the binding energies calculated
for the $(\frac{3}{2},2^+)$ $\pi\Lambda N$ system. The corresponding analysis
of, and the binding energies calculated in a relativistic version of the
three-body model are discussed in Sec.~\ref{sec:R}. The paper ends with
a brief summary and discussion in Sec.~\ref{sec:sum}, where additional
strange and charmed $\pi BB^\prime$ systems that might admit bound states
of a similar nature are listed.

\section{A nonrelativistic model}
\label{sec:NR}

\subsection{The two-body subsystems}
\label{sec:2NR}

Since both $\pi\Lambda$ and $\pi N$ subsystems are dominated by
$p$-wave resonances, we assumed a rank-one separable meson-baryon
interaction
\begin{equation}
V_i(p_i,p_i^\prime)=-g_i(p_i)g_i(p_i^\prime)~.
\label{eq1}
\end{equation}
The corresponding two-body $t$-matrix is given by
\begin{equation}
t_i(p_i,p_i^\prime;E)=-g_i(p_i)\tau_i(E)g_i(p_i^\prime)~,
\label{eq2}
\end{equation}
where $E$ is the energy in the two-body center-of-mass (c.m.) system and
\begin{equation}
\tau_i^{-1}(E)= 1+\int_0^\infty p_i^2dp_i \frac{g_i^2(p_i)}
{E-p_i^2/2\eta_i+{\rm i}\epsilon}~,
\label{eq3}
\end{equation}
with $\eta_i=m_jm_k/(m_j+m_k)$, where $\epsilon_{ijk} \neq 0$.
The form factors $g_i(p_i)$ are chosen of the form
\begin{equation}
g_i(p_i)=\sqrt{\gamma_i}p_i(1+p_i^2)e^{-p_i^2/\alpha_i^2}~,
\label{eq4}
\end{equation}
where the two parameters $\gamma_i$ and $\alpha_i$ were adjusted
to the position and width of the corresponding resonances, as given
by the Particle Data Group \cite{PDG06}. These parameters are listed
in Table I for the $\pi N$ and $\pi\Lambda$ subsystems. We also
constructed a second model of the $\pi N$ interaction of the form
\begin{equation}
g_i(p_i)=\sqrt{\gamma_i}p_i[1+(p_i/4.5)^2+(p_i/1.35)^4]e^{-p_i^2/\alpha_i^2}~,
\label{eq5}
\end{equation}
which reproduces in addition the $\pi N$ $P_{33}$ scattering volume. The
parameters of this model are also given in Table~\ref{tab:piNR}. Note that
$p_i$ in Eqs.~(\ref{eq4}) and (\ref{eq5}) assumes values in fm$^{-1}$ units.

\begin{table}
\caption{Parameters of the pion-baryon separable potentials
Eqs.~(\ref{eq4}) and (\ref{eq5}), $\alpha_i$ (in fm$^{-1}$) and $\gamma_i$
(in fm$^4$), for the nonrelativistic model.}
\label{tab:piNR}
\begin{ruledtabular}
\begin{tabular}{cccccc}
 & $\alpha_{\pi N}$ & $\gamma_{\pi N}$ & $\alpha_{\pi\Lambda}$ &
$\gamma_{\pi\Lambda}$ &  \\  \hline
Eq.~(\ref{eq4}) &  2.021352   &  0.02116  &   2.523999  &   0.00564  & \\
Eq.~(\ref{eq5}) &  1.560768  &  0.06244  &    $ - $    &   $ - $    & \\
\end{tabular}
\end{ruledtabular}
\end{table}

For the $^3S_1$ $\Lambda N$ subsystem we assume a rank-two separable
potential consisting of both attractive and repulsive terms
\begin{equation}
V_i(p_i,p_i^\prime)=-g_i^a(p_i)g_i^a(p_i^\prime)+g_i^r(p_i)g_i^r(p_i^\prime)~.
\label{eq6}
\end{equation}
The corresponding two-body $t$-matrix is given by
\begin{equation}
t_i(p_i,p_i^\prime;E)=-\sum_{\alpha=a,r}\sum_{\beta=a,r}
g_i^\alpha(p_i)\tau_i^{\alpha\beta}(E)g_i^\beta(p_i^\prime)~,
\label{eq7}
\end{equation}
where
\begin{equation}
\tau_i^{ar}(E)=\tau_i^{ra}(E)=\frac{G_i^{ar}(E)}{[1+G_i^{aa}(E)]
[1-G_i^{rr}(E)]+[G_i^{ar}(E)]^2}~,
\label{eq8}
\end{equation}
\begin{equation}
\tau_i^{aa}(E)=\frac{1-G_i^{rr}(E)}{[1+G_i^{aa}(E)]
[1-G_i^{rr}(E)]+[G_i^{ar}(E)]^2}~,
\label{eq9}
\end{equation}
\begin{equation}
\tau_i^{rr}(E)=-\frac{1+G_i^{aa}(E)}{[1+G_i^{aa}(E)]
[1-G_i^{rr}(E)]+[G_i^{ar}(E)]^2}~,
\label{eq10}
\end{equation}
\begin{equation}
G_i^{\alpha\beta}(E)=\int_0^\infty p_i^2dp_i \frac{g_i^\alpha(p_i)
g_i^\beta(p_i)}{E-p_i^2/2\eta_i+{\rm i}\epsilon}~.
\label{eq11}
\end{equation}
The form factors $g_i^\beta(p_i)$
are chosen to be of the Yamaguchi form
\begin{equation}
g_i^\beta(p_i)=\frac{\sqrt{\gamma_\beta}}{p_i^2+\alpha_\beta^2}~~~~
(\beta=a,r)~,
\label{eq12}
\end{equation}
where the parameters $\alpha_a$, $\gamma_a$, $\alpha_r$, and $\gamma_r$ are
adjusted to reproduce given values of the $\Lambda N$ $^3S_1$ scattering
length and effective range for different values of the $\Lambda$ laboratory
momentum $p_{\rm lab}^{(0)}$ at which the $^3S_1$ $\Lambda N$ phase shift
becomes negative, changing sign from attraction at low momentum to repulsion
at high momentum (as discussed in Sec.~\ref{sec:NResults}). The values of
the scattering length and effective range adopted here are $a=-1.86$~fm
and $r_0=3.13$~fm, respectively, corresponding to model ESC04d of
Ref.~\cite{RYa06}. These values are very close to those in models
NSC97e,f \cite{RSY99} which have been widely used in $\Lambda$-hypernuclear
calculations.

\subsection{The three-body system}
\label{sec:3NR}

Since all the angular momenta, spins, and isospins are coupled
to their maximal values, the recoupling coefficients of spin and
isospin are equal to one, and the Faddeev equations depend only on
the orbital angular momenta $\vec\ell,~\vec\lambda,~\vec L$, where
$\vec L=\vec\ell+\vec\lambda$, with $L=1$. The values of $\vec\ell$
and $\vec\lambda$ are $\ell=1$, $\lambda=0$ for configurations in
which the pion interacts with one of the baryons while the other
baryon is a spectator, and $\ell=0$, $\lambda=1$ for the configuration
in which the two baryons interact while the pion is a spectator.

Below we denote the $\Lambda$ hyperon as particle 1, the nucleon as
particle 2, and the pion as particle 3. Thus, the Faddeev equations for
the bound-state problem, using the separable potentials (\ref{eq1}) and
(\ref{eq6}), are
\begin{equation}
T_i(q_i)=-\tau_i(E-q_i^2/2\nu_i)\sum_{j=1}^2\int_0^\infty dq_j^\prime
H_{ij}(q_i,q_j^\prime)T_j(q_j^\prime)~~~~~(i=1,2)~,
\label{eq13}
\end{equation}
with $\nu_i=m_i(m_j+m_k)/(m_i+m_j+m_k)$, where $\epsilon_{ijk} \neq 0$,
and
\begin{equation}
H_{ij}(q_i,q_j^\prime)=(1-\delta_{ij})K_{ij}(q_i,q_j^\prime)-
\sum_{\alpha=a,r}\sum_{\beta=a,r}\int_0^\infty dq_3
K_{i3}^\alpha(q_i,q_3)\tau_3^{\alpha\beta}(E-q_3^2/2\nu_3)
K_{3j}^\beta(q_3,q_j^\prime)~.
\label{eq14}
\end{equation}
The kernels in Eq.~(\ref{eq14}) are given by
\begin{equation}
K_{12}(q_1,q_2)=\frac{1}{2}q_1q_2\int_{-1}^1 d{\cos}\theta\,
\frac{g_1(p_1)(\hat p_1\cdot\hat p_2)g_2(p_2)}
{E-p_2^2/2\eta_2-q_2^2/2\nu_2}~,
\label{eq15}
\end{equation}
\begin{equation}
K_{31}^\alpha(q_3,q_1)=\frac{1}{2}q_1q_3
\int_{-1}^1 d{\cos}\theta\,
\frac{g_3^\alpha(p_3)(\hat q_3\cdot\hat p_1)g_1(p_1)}
{E-p_1^2/2\eta_1-q_1^2/2\nu_1}~,
\label{eq16}
\end{equation}
\begin{equation}
K_{23}^\alpha(q_2,q_3)=\frac{1}{2}q_2q_3
\int_{-1}^1 d{\cos}\theta\,
\frac{g_2(p_2)(\hat p_2\cdot\hat q_3)g_3^\alpha(p_3)}
{E-p_3^2/2\eta_3-q_3^2/2\nu_3}~.
\label{eq17}
\end{equation}
From the three previous expressions one obtains the other three
that correspond to $K_{ji}(q_j,q_i)=K_{ij}(q_i,q_j)$.
One can calculate $p_i$, $p_j$, ($\hat p_1\cdot\hat p_2$),
($\hat q_3\cdot\hat p_1$), and ($\hat p_2\cdot\hat q_3$) by using
\begin{equation}
\vec p_i=-\vec q_j-a_{ij}\vec q_i~,~~~~\vec p_j=\vec q_i+a_{ji}\vec q_j~,
\label{eq18}
\end{equation}
where $(i,j)$ is a cyclic pair, ${\cos}\theta=\hat q_i\cdot\hat q_j$, and
\begin{equation}
a_{ij}=\frac{\eta_i}{m_k}~,~~~~a_{ji}=\frac{\eta_j}{m_k}~.
\label{eq19}
\end{equation}

In order to find the bound-state solutions of Eq.~(\ref{eq13}), integrals
were replaced by sums applying numerical integration quadrature. In this way
Eq.~(\ref{eq13}) becomes a set of homogeneous linear equations. This set has
solutions only if the determinant of the matrix of its coefficients (the
Fredholm determinant) vanishes at certain energies. Thus, the procedure to
find the bound-state energies of the three-body system simply consists of
searching for the zeros of the Fredholm determinant on the real energy axis.
Some limiting situations are discussed in the Appendix.

\subsection{Results}
\label{sec:NResults}

\begin{table}
\caption{Parameters of the $\Lambda N$ $^3S_1$ potentials (\ref{eq12})
$\alpha_\beta$ (in fm$^{-1}$), $\gamma_\beta$ (in fm$^{-2}$) in the
nonrelativistic model for $a=-1.86$ fm, $r_0=3.13$ fm, and the binding
energies $B_{\pi\Lambda N}$ (in MeV) of the three-body $\pi\Lambda N$
system calculated using the $\pi N$ and $\pi \Lambda$ potential parameters
listed in Table~\ref{tab:piNR}, Eq.~(\ref{eq4}) [the $B_{\pi\Lambda N}$
values in parentheses correspond to the $\pi N$ parameters listed in
Table~\ref{tab:piNR}, Eq.~(\ref{eq5})]. The momentum $p_{\rm lab}^{(0)}$
(in MeV/c) is the laboratory $\Lambda$ momentum at which the $\Lambda N$
$^3S_1$ phase shift becomes negative.}
\label{tab:NResults}
\begin{ruledtabular}
\begin{tabular}{cccccccc}
& $\alpha_a$ & $\gamma_a$ &  $\alpha_r$  & $\gamma_r$
& $p_{\rm lab}^{(0)}$  & $B_{\pi\Lambda N}$ & \\
\hline
     &   1.437 &  0.4179  & $ - $  & $ - $  & $ - $ & 140 &  \\
     &   1.6   &  0.8118  &   4.0  &  5.54  &  1184 & 111 &  \\
     &   1.6   &  0.8053  &   6.0  &  26.0  &  1069 & 96 &  \\
     &   1.6   &  0.8064  &   8.0  &  86.0  &  1045 & 86 &  \\
     &   1.7   &  1.195   &   4.0  &  10.0  &  975  & 92 &  \\
     &   1.7   &  1.186   &   6.0  &  51.0  &  910  & 66 &  \\
     &   1.7   &  1.190   &   8.0  & 190.0  &  899  & 52 &  \\
     &   1.8   &  1.735   &   4.0  &  15.5  &  877  & 72 (67) & \\
     &   1.8   &  1.718   &   6.0  &  86.0  &  834  & 38 (37) & \\
     &   1.8   &  1.745   &   8.0  &  405.0 &  826  & 21 (23) & \\
     &   1.9   &  2.513   &   4.0  &  22.7  &  814  & 51 &  \\
     &   1.9   &  2.501   &   6.0  & 145.0  &  784  &  9 &  \\
     &   1.9   &  2.573   &   8.0  & 1150.0 &  779  & unbound & \\
     &   2.0   &  3.588   &   4.0  &   31.4 &  777  & 31 &  \\
     &   2.0   &  3.602   &   6.0  &  244.0 &  753  & unbound & \\
     &   2.1   &  5.125   &   4.0  &   42.9 &  748  & 10 &  \\
     &   2.2   &  7.311   &   4.0  &   58.0 &  728  & unbound & \\
\end{tabular}
\end{ruledtabular}
\end{table}

In the last column of Table~\ref{tab:NResults}, we list the calculated
binding energies $B_{\pi\Lambda N}$ of the $\pi\Lambda N$ system in the
$(I,J^P)=(\frac{3}{2},2^+)$ channel, for the $\pi\Lambda$ and $\pi N$
interactions recorded in Table~\ref{tab:piNR} and the various models of the
$\Lambda N$ interaction also listed in Table~\ref{tab:NResults}. Most of the
results are given for the choice Eq.~(\ref{eq4}) of the $\pi N$ form factor,
except for the $\alpha_a=1.8$~fm$^{-1}$ runs for which listed in parentheses
are also the binding energies obtained using the other choice Eq.~(\ref{eq5}).
The dependence on the type of $\pi N$ form factor is seen to be rather weak.
We also checked the sensitivity to the strength parameter
$\gamma_{\pi\Lambda}$; for example, the $\pi\Lambda N$ bound state for the
case $B_{\pi\Lambda N}=51$ MeV listed in the table disappears as soon as the
standard value $\gamma_{\pi\Lambda}=0.00564$~fm$^4$ from Table~\ref{tab:piNR}
is decreased to 0.00524~fm$^4$. The dependence on the $\Lambda N$ interaction
is shown in detail in Table~\ref{tab:NResults}. Essentially, the various
$\Lambda N$ models differ from each other by the amount of repulsion they
contain. For a given value of range parameter $\alpha_a^{-1}$ for the
attractive $\Lambda N$ component, the calculated binding energy decreases as
the repulsive component gets pushed inside and requires a larger strength.
For a given value of range parameter $\alpha_r^{-1}$ for the repulsive
component, the calculated binding energy decreases as the attractive
component gets pushed inside, or equivalently as one lowers the momentum
where the $\Lambda N$ $^3S_1$ phase shift changes sign from positive
(attraction) to negative (repulsion) values. It is seen that the bound
state persists as long as this $\Lambda$ laboratory momentum
$p_{\rm lab}^{(0)}$ is larger than about $750-800$ MeV/c. Incidentally,
this is precisely the range of momenta at which the $\Lambda N$ $^3S_1$
phase shift goes through zero in Nijmegen $YN$ potential models that
relegate the ${^3S_1}-{^3D_1}$ attraction near and above the $\Sigma N$
threshold to the $^3D_1$ channel \cite{RSY99}.

\section{A relativistic model}
\label{sec:R}

Since the binding energies calculated nonrelativistically, for some of
the cases listed in Table~\ref{tab:NResults} are a sizable fraction
of the pion mass, it appears necessary to take into account relativistic
effects. Therefore, we will reformulate our model in terms of
a relativistic on-mass-shell-spectator formalism \cite{Gro82,Gar87,SGF97}.
In this formalism one starts with the Bethe-Salpeter equation for three
particles which is set in a Faddeev form. The four-vector equations are
then reduced to three-vector equations similar to the nonrelativistic
Faddeev equations by putting all the spectator particles on the mass
shell \cite{Gar87}.

In order to reach a relativistic generalization of Eq.~(\ref{eq13})
we make two approximations. First, the negative-energy components of the
fermion propagators are neglected; and second, the spin degrees of freedom
are treated nonrelativistically by means of Racah coefficients (which are
equal to one, as pointed out above).
These two approximations are reasonable since the two fermions $\Lambda$
and $N$ are very heavy compared with the pion. Thus, as pointed out in
the Introduction, our model formally  reduces to that of three
spinless (and isospinless) particles interacting by pairwise separable
interactions.

\subsection{The two-body subsystems}
\label{sec:2R}

In order to fit the $p$-wave resonance energy and width in the $\pi\Lambda$
and $\pi N$ subsystems we considered the two-body Bethe-Salpeter equation for
the pair $jk$ with particle $j$ (here the pion) on the mass shell interacting
through a rank-one separable interaction defined by Eqs.~(\ref{eq1}) and
(\ref{eq4}). Recall that $p_i$, the magnitude of the relative three-momentum
of the pair in the c.m. system, is Lorentz invariant since it is expressible
in terms of the invariant mass of the relative momentum four-vector.
The corresponding two-body $t$-matrix in the c.m. system is given by
\begin{equation}
t_i(p_i,p_i^\prime;\omega_0)=-g_i(p_i)\tau_i(\omega_0)g_i(p_i^\prime)~,
\label{eq20}
\end{equation}
where $\omega_0$ is the invariant mass of the two-body subsystem and
\begin{equation}
\tau_i^{-1}(\omega_0)= 1+\int_0^\infty \frac{p_i^2dp_i}{2\omega_j}
\frac{g_i^2(p_i)}{(\omega_0-\omega_j)^2-\omega_k^2+{\rm i}\epsilon}~,
\label{eq21}
\end{equation}
with $\omega_j=\sqrt{m_j^2+p_i^2}$ and $\omega_k=\sqrt{m_k^2+p_i^2}$. The
parameters of these separable potentials are given in Table~\ref{tab:piR}.
We did not pursue the option of keeping the respective baryon on mass shell,
with an off-shell pion, because of the appearance of a persistent unphysical
two-body bound state for this choice.

\begin{table}
\caption{Parameters of the pion-baryon separable potential
Eq.~(\ref{eq4}), $\alpha_i$ (in fm$^{-1}$) and $\gamma_i$ (in fm$^2$),
for the relativistic model with on-mass-shell $\pi$ meson.}
\label{tab:piR}
\begin{ruledtabular}
\begin{tabular}{cccccc}
 & $\alpha_{\pi N}$ & $\gamma_{\pi N}$ & $\alpha_{\pi\Lambda}$ &
$\gamma_{\pi\Lambda}$  &  \\  \hline
Eq.~(\ref{eq4}) & 2.231357 & 0.219260 & 2.720821 & 0.083916 & \\
\end{tabular}
\end{ruledtabular}
\end{table}

For the $\Lambda N$ subsystem we again used a rank-two separable
potential defined by Eqs.~(\ref{eq6}) and (\ref{eq12}) so that the
two-body $t$-matrix is given by Eqs.~(\ref{eq7})-(\ref{eq10}) with
$E$ replaced by $\omega_0$ and $G_i^{\alpha\beta}(E)$ of Eq.~(\ref{eq11})
replaced by
\begin{equation}
G_i^{\alpha\beta}(\omega_0)= \int_0^\infty \frac{p_i^2dp_i}{2\omega_j}
\frac{g_i^\alpha(p_i)g_i^\beta(p_i)}
{(\omega_0-\omega_j)^2-\omega_k^2+{\rm i}\epsilon}~.
\label{eq22}
\end{equation}
The parameters of these separable potentials are listed below in
Sec.~\ref{sec:Results}.

\subsection{The three-body system}
\label{sec:3R}

The integral equations for the three-body problem are given by
\begin{equation}
T_i(q_i)=-\tau_i(W_0;q_i)\sum_{j=1}^2\int_0^{q^{(j)}_{\rm max}}
dq_j^\prime H_{ij}(q_i,q_j^\prime)T_j(q_j^\prime)~~~~~(i=1,2)~,
\label{eq23}
\end{equation}
where $W_0$ is the invariant mass of the three-body system.
The upper limit of integration,
\begin{equation}
q^{(j)}_{\rm max}=\frac{W_0^2-m_j^2}{2W_0}~,
\label{eq24}
\end{equation}
is the momentum at which the invariant mass of the two-body subsystem
$j$ is equal to zero so that it then recoils with the speed of light
\cite{SGF97}. The entity $\tau_i(W_0;q_i)$ corresponds to the $t$-matrix
(\ref{eq20})-(\ref{eq21}) in an arbitrary frame where the spectator
particle $i$ (which is on-mass-shell) has momentum $\vec q_i$, particle
$j$ (which has also been put on-mass-shell) has momentum $\vec q_j$
and particle $k$ (which is off the mass shell) has momentum
$-\vec q_i-\vec q_j$. It is given by
\begin{equation}
\tau_i^{-1}(W_0;q_i)= 1+\frac{1}{2}\int_{-1}^1d{\cos}\theta
\int_0^\infty\frac{q_j^2dq_j}{2\omega_j}\frac{g_i^2(p_i)}
{(W_0-\omega_i-\omega_j)^2-\omega_k^2+{\rm i}\epsilon}~,
\label{eq25}
\end{equation}
with
\begin{equation}
\omega_i=\sqrt{m_i^2+q_i^2}~,~~~~\omega_j=\sqrt{m_j^2+q_j^2}~,
\label{eq26}
\end{equation}
\begin{equation}
\omega_k=\sqrt{m_k^2+q_i^2+q_j^2+2q_iq_j{\cos}\theta}~.
\label{eq27}
\end{equation}
The magnitude of the relative three-momentum $\vec p_i$ is
a Lorentz invariant given by
\begin{equation}
p_i^2=\frac{(P_{jk}^2+m_j^2-k_k^2)^2}{4P_{jk}^2}-m_j^2~,
\label{eq28}
\end{equation}
where $P_{jk}=k_j+k_k$ is the total four-momentum of the pair $jk$
and $k_k$ is the four-momentum of particle $k$, {\it i.e.},
\begin{equation}
P_{jk}^2=(W_0-\omega_i)^2-q_i^2~,
\label{eq29}
\end{equation}
\begin{equation}
k_k^2=(W_0-\omega_i-\omega_j)^2
-q_i^2-q_j^2-2q_iq_j{\cos}\theta~.
\label{eq30}
\end{equation}
Eq.~(\ref{eq25}) reduces to Eq.~(\ref{eq21}) when $q_i=0$.
Similar expressions apply to the relativistic version of the
$\Lambda N$ $t$-matrix in an arbitrary frame
$\tau_3^{\alpha\beta}(W_0;q_3)$.

The kernel of Eq.~(\ref{eq23}) is given by Eqs.~(\ref{eq14})-(\ref{eq17}),
where the upper limit $\infty$ in the integral of Eq.~(\ref{eq14}) is
replaced by $q_{\rm max}^{(3)}$, and the following substitutions are made:
\begin{equation}
\frac{1}{E-p_j^2/2\eta_j-q_j^2/2\nu_j} ~\to~
\frac{1}{2\omega_j}\frac{1}{(W_0-\omega_i-\omega_j)^2-\omega_k^2}~,
\label{eq31}
\end{equation}
\begin{equation}
a_{ij}~ \to~ \frac{W_i^2-q_i^2+m_j^2-k_k^2+2\omega_j\sqrt{W_i^2-q_i^2}}
{2\sqrt{W_i^2-q_i^2}~(W_i+\sqrt{W_i^2-q_i^2}~)}~,
\label{eq32}
\end{equation}
\begin{equation}
a_{ji}~ \to~ \frac{W_j^2-q_j^2+m_i^2-k_k^2+2\omega_i\sqrt{W_j^2-q_j^2}}
{2\sqrt{W_j^2-q_j^2}~(W_j+\sqrt{W_j^2-q_j^2}~)}~,
\label{eq33}
\end{equation}
\begin{equation}
W_i=W_0-\omega_i~,~~~~W_j=W_0-\omega_j~.
\label{eq34}
\end{equation}
Eq.~(\ref{eq31}) is the propagator when the spectator particles $i$
and $j$ are on-mass-shell and the exchanged particle $k$ is
off-mass-shell. Eqs.~(\ref{eq32})-(\ref{eq34}) correspond to the
relativitistic kinematics with particle $k$ off the mass shell.

\subsection{Results}
\label{sec:Results}

\begin{table}
\caption{Parameters of the $\Lambda N$ $^3S_1$ potentials (\ref{eq12})
$\alpha_\beta$ (in fm$^{-1}$), $\gamma_\beta$ (in fm$^{-4}$) in the
relativistic model with on-mass-shell nucleon, for $a=-1.86$ fm,
$r_0=3.13$ fm, and the binding energies $B_{\pi\Lambda N}$ (in MeV)
of the three-body $\pi\Lambda N$ system calculated using the $\pi N$
and $\pi \Lambda$ potential parameters listed in Table~\ref{tab:piR}.
The momentum $p_{\rm lab}^{(0)}$ (in MeV/c) is the laboratory $\Lambda$
momentum at which the $\Lambda N$ $^3S_1$ phase shift becomes negative.}
\label{tab:Results}
\begin{ruledtabular}
\begin{tabular}{cccccccc}
& $\alpha_a$ & $\gamma_a$ &  $\alpha_r$  & $\gamma_r$
& $p_{\rm lab}^{(0)}$  & $B_{\pi\Lambda N}$ & \\
\hline
   &  2.0     &  318.2  &  4.0  &    2270  &  866  & 152 &  \\
   &  2.0     &  309.2  &  6.0  &   12100  &  823  & 93 &  \\
   &  2.0     &  313.0  &  8.0  &   54500  &  813  & 69 &  \\
   &  2.1     &  446.9  &  4.0  &    3080  &  823  & 121 &  \\
   &  2.1     &  434.3  &  6.0  &   18000  &  788  & 59 &  \\
   &  2.1     &  440.8  &  8.0  &  105000  &  783  & 35 &  \\
   &  2.2     &  626.6  &  4.0  &    4100  &  791  & 94 &  \\
   &  2.2     &  599.1  &  6.0  &   25800  &  768  & 31 &  \\
   &  2.2     &  632.5  &  8.0  &  350000  &  756  & unbound &  \\
   &  2.3     &  878.5  &  4.0  &    5400  &  766  & 69 &  \\
   &  2.3     &  845.8  &  6.0  &   40700  &  746  & unbound &  \\
   &  2.4     & 1217    &  4.0  &    6930  &  750  & 48 &  \\
   &  2.4     & 1189    &  6.0  &   68000  &  733  & unbound &  \\
   &  2.5     & 1728    &  4.0  &    9200  &  730  & 21 &  \\
   &  2.6     & 2354    &  4.0  &   11400  &  728  & 6 &  \\
\end{tabular}
\end{ruledtabular}
\end{table}

In the last column of Table~\ref{tab:Results}, we list the calculated
binding energies $B_{\pi\Lambda N}$ of the $\pi\Lambda N$ system in the
$(I,J^P)=(\frac{3}{2},2^+)$ channel, for the $\pi\Lambda$ and $\pi N$
interactions recorded in Table~\ref{tab:piR} and the various models of
the $\Lambda N$ interaction listed also in Table~\ref{tab:Results}.
The dependence of the calculated binding energies on the ranges of the
repulsive and attractive components of the $\Lambda N$ interaction is
similar to that found in the nonrelativistic calculations.
A bound state in the relativistic model persists as long as the $\Lambda$
laboratory momentum at which the $\Lambda N$ phase shift becomes negative,
$p_{\rm lab}^{(0)}$, is larger than about 750 MeV/c.
A comparison between Tables~\ref{tab:NResults} and \ref{tab:Results}
reveals that the relativistic model provides more attraction than the
nonrelativistic one, in agreement with the slower increase of kinetic
energy with momentum when relativistic kinematics is applied.

\section{Summary and Discussion}
\label{sec:sum}

We have used a nonrelativistic separable potential model and
a relativistic version of it, solving three-body Faddeev equations,
to search for $\pi\Lambda N$ bound states. In both models we found
that a $(I,J^P)=(\frac{3}{2},2^+)$ bound state is likely to exist,
provided the $\Lambda$ laboratory momentum $p_{\rm lab}^{(0)}$
at which the ${^3S_1}$ $\Lambda N$ phase shift becomes negative
is larger than about $750-800$ MeV/c. This agrees with the range
of momenta at which Nijmegen $YN$ potential models, where applicable
\cite{RSY99}, predict that the ${^3S_1}$ $\Lambda N$ phase shift goes
through zero. The J\"{u}lich '04 model \cite{HMe05} and the recent
chiral EFT approach \cite{PHM06} predict that $p_{\rm lab}^{(0)}>900$
MeV/c, so that the existence of a $\pi\Lambda N$ bound state in
these models appears robust. The Nijmegen and J\"{u}lich $YN$
potential models differ considerably from each other within
the $\Lambda N$ $J^P=1^+$ coupled channels also in the behavior
of the ${^3D_1}$ phase shift. The ${^3S_1}-{^3D_1}$ coupling was
neglected in the present exploratory three-body calculation,
a neglect that might be justified in applications of the
J\"{u}lich models where both the coupling and the size of the
${^3D_1}$ phase shift that builds up above the $\Sigma N$
threshold at $p_{\rm lab} \approx 630$ MeV/c are weaker than
in the Nijmegen models. However, all these $YN$ models have been
constructed to fit primarily low-energy scattering data which do not
unambiguously constrain the short-range behavior of the ${^3S_1}$
$\Lambda N$ system. The extent to which the two-body short-range
repulsion varies between `soft' to `hard' is crucial for the three-body
system's ability to bind, with the $p$-wave pion maximizing its
attraction to each one of the baryons simultaneously.

More realistic three-body calculations
will have to include $\Sigma$ hyperons, extending the $\Lambda N$
channel into ${^3S_1}-{^3D_1}$ $\Lambda N-\Sigma N$ coupled channels,
and the $\pi\Lambda$ channel into $\pi\Lambda-\pi\Sigma$ coupled
channels. Although the $I=1$ $\bar K N$ channel also couples to these
$\pi Y$ coupled channels, in first approximation the three-body
$\bar K NN$ channel is decoupled from the $\pi YN$ coupled channels for
$(I,J^P)=(\frac{3}{2},2^+)$ owing to the restrictions imposed by the
Pauli principle on the two nucleons.

To search experimentally for a possible $I=\frac{3}{2},~J^P=2^+$
$\pi\Lambda N$ dibaryon bound state or resonance, which we denote
by $\cal D$, one could try in-flight $(K^-,\pi^+)$ or $(\pi^-,K^+)$
reactions on a deuteron target:
\begin{equation}
K^- + d \to  {\cal D}^- + \pi^+~,
\label{eq35}
\end{equation}
\begin{equation}
\pi^- + d \to {\cal D}^- + K^+~.
\label{eq36}
\end{equation}
These reactions lead automatically to the required value of isospin
$I=\frac{3}{2}$ for the $\cal D$ dibaryon. The values required for
spin-parity, $J^P=2^+$, are also allowed. In terms of a coupled
$\Sigma^- n$ system, the orbital angular momentum and Pauli-spin
are approximately conserved, resulting in two possibilities:
${^3D_2}$ and ${^1D_2}$. These could be explored by choosing
an incident momentum and a meson scattering angle where the
$K^- + p \to \Sigma^- + \pi^+$ or $\pi^- + p \to \Sigma^- + K^+$
underlying reactions are largely non-spin-flip ($\to {^3D_2}$) or
have a nonnegligible spin-flip component ($\to {^1D_2}$).
These experiments would be feasible at J-PARC.

The three-body calculations reported here for the $S=-1$ $\pi \Lambda N$
system may be extended to other three-body systems of the type $\pi B_1 B_2$,
with $J^P=2^+$ and a maximum value of isospin, consisting of a $p$-wave pion
and $\frac{1}{2}^+$ baryons in a relative $s$-wave state. This precludes
identical baryons: $B_1 \neq B_2$. Candidates may be classified as follows:

\begin{itemize}
\item $S=-2,-3$ strange systems obtained by substituting the SU(3)-octet $\Xi$
hyperon for the $\Lambda$ hyperon or for the nucleon in the $\pi\Lambda N$
three-body system, leading to $\pi\Xi N$ and $\pi\Lambda\Xi$, respectively.
The new $\pi \Xi$ $p$-wave resonance here is the $\frac{3}{2}^+$ $\Xi(1530)$
belonging to the same SU(3) decuplet which contains the $\Delta(1232)$ and
the $\Sigma(1385)$ considered in the present work.
\item $C=+1$ charmed systems made out of a pion, SU(3)-octet baryon
(excluding the $\Sigma$ hyperon) and $\frac{1}{2}^+$ charmed baryon
(of the lowest mass for a given strangeness):
\begin{equation}
{\pi}N\Lambda_c(2286)~,~~~~{\pi}N\Xi_c(2470)~,~~~~{\pi}N\Omega_c(2700)~,
\end{equation}
\begin{equation}
\pi\Lambda\Lambda_c(2286)~,~~~~\pi\Lambda\Xi_c(2470)~,~~~~
\pi\Lambda\Omega_c(2700)~,
\end{equation}
\begin{equation}
\pi\Xi\Lambda_c(2286)~,~~~~\pi\Xi\Xi_c(2470)~,~~~~\pi\Xi\Omega_c(2700)~.
\end{equation}
\item $C=+2$ charmed systems made out of a pion and two $\frac{1}{2}^+$
singly charmed baryons, each of the lowest mass for a given strangeness:
\begin{equation}
\pi\Lambda_c(2286)\Xi_c(2470)~,~~~~\pi\Lambda_c(2286)\Omega_c(2700)~,~~~~
\pi\Xi_c(2470)\Omega_c(2700)~.
\end{equation}
\end{itemize}
Note the appearance of the $\frac{1}{2}^+$ $\Omega_c$ baryon, of quark
structure $ssc$. In the case of charmed baryons, the $p$-wave non-charmed
SU(3)-decuplet $\frac{3}{2}^+$ resonances are replaced by charmed
SU(3)-sextet members of the same extended SU(4) {\bf 20}-plet:
\begin{equation}
\Sigma(1385)\to\Sigma_c(2520)~,~~~~\Xi(1530)\to\Xi_c(2645)~,~~~~
\Omega(1670)\to\Omega_c(2770)~.
\end{equation}
Here we limited listing to singly-charmed baryons. The only observation
we wish to make on a future charmed bound-state study is that the
$\pi N \Lambda_c(2286)$ threshold lies {\it below} $N \Sigma_c(2455)$,
where $\Sigma_c(2455)$ is the lowest lying known $\Sigma_c$, with assumed
$J^P=\frac{1}{2}^+$. Therefore, if $\pi N \Lambda_c(2286)$ is bound, it will
decay only by weak interactions. Hopefully, the study of these, and
other charmed dibaryons will become feasible in due course.

\section*{Acknowledgments}
We thank Marek Karliner for bringing to our attention possible implications
of the present calculation to binding $\pi N \Lambda_c$.
This work was supported in part by the Israel Science Foundation grant
757/05 and by COFAA-IPN (M\'exico).

\section*{Appendix: Limiting Faddeev solutions for $\pi\Lambda N$, $\pi NN$
and $\pi\Lambda\Lambda$}

It is interesting to solve the coupled Faddeev Eqs.~(\ref{eq13}) in the
limit of vanishing baryon-baryon interaction, $\tau_3^{\alpha\beta}=0$.
Eq.~(\ref{eq14}) reduces then to $H_{ij}=(1-\delta_{ij})K_{ij}$,
for $i,j=1,2$, so that Eqs.~(\ref{eq13}) become
\begin{equation}
T_i = -\tau_i K_{ij} \ast T_j~,~~~~(i \neq j)~,
\end{equation}
where the asterisk stands for convolution. Bound states are obtained by
searching for zeros of the Fredholm determinant corresponding to the
operator $(1-\tau_1 K_{12} \tau_2 K_{21})$. Using $\pi N$ and $\pi\Lambda$
interaction parameters from Table~\ref{tab:piNR}, Eq.~(\ref{eq4}),
a robust bound state is found at $B_{\pi\Lambda N}=110$~MeV.
From Table~\ref{tab:NResults} we learn that a fully attractive
$\Lambda N$ interaction leads to a higher value of $B_{\pi\Lambda N}$,
and that the introduction of a repulsive component quickly lowers the
calculated $B_{\pi\Lambda N}$ values below that for a noninteracting
$\Lambda N$ pair.

Next, let's make the two baryons identical as far as their mass,
spin-parity $\frac{1}{2}^+$, and interaction with the pion are concerned.
Then, $\tau_1=\tau_2 \equiv \tau$ and $K_{12}=K_{21}\equiv K$. Since one
is looking for a {\it symmetric} spatial configuration for these two
$s$-wave baryons, it is the symmetric combination of the $T_i$'s that
is required:
\begin{equation}
(T_1 + T_2) = -\tau K \ast (T_1 + T_2)~,
\end{equation}
and the requirement of vanishing Fredholm determinant at bound-state energies
becomes equivalent to searching for zeros of the operator $(1+\tau K)$. The
operator $\tau$ is positive definite for the attractive meson-baryon
interactions considered in the present work, and the operator $K$ is negative
definite at energies below threshold. Thus, if the meson-baryon interaction
is sufficiently strong, the operator $(1+\tau K)$ will have a zero at
a subthreshold energy. Indeed for such a fictitious $(I,J^P)=(2,2^+)$
$\pi NN$ system excluded by the Pauli principle, and using $\pi N$
interaction parameters from Table~\ref{tab:piNR}, Eq.~(\ref{eq4}),
we get a bound state with binding energy $B_{\pi NN}=29$~MeV.

For {\it physical} $\pi NN$ and $\pi \Lambda \Lambda$ systems, with
symmetric spin-isospin configurations chosen, the Pauli exclusion principle
requires that the spatial configuration be {\it antisymmetric}, leading
to the requirement of finding zeros of the operator $(1-\tau K)$. Since
$\tau K$, for the meson-baryon interactions considered here, is negative
definite below threshold, this means that the operator $(1-\tau K)$ assumes
values higher than one below threshold, which is commonly interpreted in
terms of three-body {\it repulsion}. It is unlikely that adding secondary
interaction channels into this schematic calculation will change the
conclusion that no bound states are expected for $\pi BB$ systems with
two identical ${\frac{1}{2}}^+$ baryons.

redpajama_set_name: RedPajamaArXiv


Last minute details: the weather, useful expressions and advice for DOMOTEX 2010.
Jim, Katherine and I are excited about seeing you in a few days. We have several last minute details to share with you. Starting with airport security: plan for extra time.
Definitely be prepared for cold, wintery weather. Here is a link to the BBC weather website for Hannover so you can monitor what to expect. As you can see, it will be cold and mostly overcast.
Even if you are a Domotex travel-pro, it can't hurt to be reminded of a few German expressions. If there are others you would add to the list, let us know in the comments.
Where is the train station? Wo ist der Bahnhof?
How far is the fairground? Wie weit is the Messegelaende?
Which train goes to the fairground? Welche Bahn geht zum Messegelaende?
How do I get to the entrance? Wie komme ich zum Eingang?
How do I find the exit? Wie finde ich den Ausgang?
For other words and expressions, consider this online dictionary http://www.leo.org/ which includes an English to German search window.
As it relates to flooring, you'll notice different conventions for referring to product. This listing of flooring expressions will help you make sense of the differences.
Carpet or rugs – Tapis, moquette [French terms]. The german word for carpet is Teppich, for wall-to-wall is Teppichboden (literally carpetfloor) or Teppichfliessen (carpet tile).
Wood – Parquet (pronounced parkett, not par kay); you might also say Holzboden for woodfloor.
Again, if there are others you suggest adding to the list, do let us know in the comments.
If you haven't, you might also want to listen to this recent FloorDaily interview with Kemp Harr during which Rita Dommermuth Discusses Highlights and Weather Conditions for Domotex Germany.
"Rita Dommermuth, VP of Sales for Domotex, and Kemp Harr discuss the highlights for the world's largest global flooring expo which will be held in Hanover Germany from January 16 to 19. Listen to the interview to hear more details about the anticipated attendance, U.S. participation, Contract World, a bus tour of German retailers, and more about the weather forecast."
Donna Hyland suggests, when using a taxi, having the address of your destination written down to give to the taxi driver, although most speak English quite well. Germans are modest about their foreign language capabilities so if you ask if they speak English, they usually will say "just a little".
It is generally a good idea to always have readily available your exact hotel phone number and address. After a full few days walking the show, navigating a foreign environment and being still jet lagged, it's nice to give your brain a break and simply pull out a piece of paper - or your cell phone/PDA - with your hotel information.
If you are a member of the VIP North American Delegation, Jim recommends that you meet him on Saturday morning, the opening day of Domotex, at the VIP Lounge area if you need help or direction. He will be checking email in the evening only.
Note that Domotex entrance tickets and other information will be sent out on 1/11/10. If you haven't received yours, please contact Rita, Katherine or Jim or all three.
Finally, if you need help of any kind, please don't hesitate to ask. You will find many staff members ready to help and answer your questions at DOMOTEX.
Bon Voyage! Katherine, Art, and Rita and Jim will see you very shortly in Germany.
Hardwood Investments:- Thanks for giving Flooring Product Expressions. I just need to know about the difference between Hardwood flooring, Softwood flooring, Custom flooring and also want to know which flooring is best for home use.
If you get a chance to visit DOMOTEX, you will be able to see an array of products for home flooring such as laminates, parquet,bamboo etc. DOMOTEX will give you the opportunity to see all these products first hand and speak to the manufacturers that produce them.


told them.be prepared with ur strengths and weaknesses. and u shud have suficient proof for them too. then one guy strtd lukin at my resume and was abt to ask me abt the competitions bt he got a call on his cell and he went out. bad luck. the other guy asked me basics abt optical fibre .
i told him. then asked me to solve a k-map.
i made a mistake in the beginning and he pointed it out.
i said, "yes sir." with a smile and corrected it.
then while i ws solving it, he asked, "atak gaye kya??"
i said, "no sir. just one min."
finally i solved it and it was right.
then they asked me abt macros and inline fn. in c++.
then they asked me, "pointers aate hain kya??"
he asked me, "smat pointer, auto pointer and dangling pointers kya hote hain??"
i said, "i dunno" with a confused smile.
he asked, "kabhi sune bhi nahin??"
then the lights went off.
he siad, "kya colg bandh hone ka time ho gaya kya??"
i said, "kya pata sir??" with a sweet smile.
then one guy again went out and the other one asked me abt call by value and reference.
i told him that there are 3 types, "call by value addres and reference and they all are different.call by reference and address."
he dint allow me to explain them and said 'ok"
the other person asked him, "kuch puchna hai kya??"
so it lasted just for 10 mins.
then we were called for the MR interview. there they asked abt the bond location and medical test. u shud not have any problem with any of these.
then was the HR interview.
i sat down and he asked, "tell me sumthing that is not written in u CV. what u are as a person"
i strtd off, "i m a reserved kind of a person. i dont open up my heart to everone bt wen i choose my friends, i stay loyal to them forever." .
my weakness is that i cant boss around over 10 people. i can lead them and can encourage them to work but i cant boss over them.
he said, "but we need people who can boss around over people"
i said, "sir icant boss around over them bt i can lead them. i can work with them and can encourage them to work. i cant be rude to them"
he asked, "y u cant b rude to them??"
i said, "it's not in my genes."
then he asked me abt the family background.
then came upto my hobbies.
he said, "listening to music. everybody listens to it and it's not a hobby these days,"
i said, "it soothes me, it relaxes me and that's y i listen to it."
i said, "sonu nigam in indian and aaron lewis from staind in western music."
he asked, "staind. never heard of it"
i said, "sir, it's a rock band"
he aske,d" so wat music do u generally listen to.
he said, "who's ur fav. band???"
he said, "staind???? never heard of it.... mostly people go for nirvana, metallica"
i said, "sir, metallica is too thrash for my ears. and nirvana is like evergreen.
he asked, "lawn tennis. who's ur fav. player???"
i siad, "he's the no. 1 player. great forehand, great backhand"
"on wat court does he play"
"but he loses on clay court"
then he asked me "y do u want to go into IT, wen ur branch is ECE"
i said, "coz i m interested in programming"
"then y did u chose ECE"
"versatality is the key. i kno ECE. and i kno prog. too. and i've won a few programming competitions too"
he asked, "where did u get to learn the languages??"
i said, "c++ in 11-12. c in 1st yr. c++, java in 2nd yr."
then he asked me abt my competitions and i told him everything.
"do u have any relative in IT sector?"
"yes. one cousin in Infy and another in CGI, Bangalore"
"did they advise u to join some company"
i said," no. how can they ask me to join their company. they just told me to join some nice company"
"i am not convinced with ur answer???? y TCS???"
"no. 12 company. Ratan Tata"
"ratan tata has got nothin to do with TCS"
"yes. bt still...... TCS is TCS"
"y do u want to go 4 no. 12 company. y not top 10"
now they wanted to hear, "by 2010, TCS will be in top 10"
my answer, "every journey begins with a single step.... and somethin crap"
THIS WAS THE MOST NEGATIVE ANSWER THAT I CUD GIVE.
still he took it +vely.
"do u want to ask sumthing"
"wen will the results be out?"
"best of luck. u can leave for the day"
they had selected 97 students out of 280 in aptitude. then out of 97, 55 were called for the HR interview. then finally they selected 50 students.


Information security is concerned with protecting the information assets of an organisation. It aims to ensure the confidentiality, availability and integrity of information and good information security underpins the effectiveness and value of IT systems.
The IT faculty provides materials to help organisations understand the risks to information from new technologies and the measures they can take to manage these risks.
With an ex-National Security Agency employee set for jail time for working on classified information at home, it might be best to keep work at the office.
ICAEW and its members are readying themselves for new data protection legislation. In the first of a new series on General Data Protection Regulation, Lesley Meall looked at what the IT Faculty is doing to become ready – including member experiences of GDPR and the three phases of ICAEW's GDPR-readiness programme.
If stopping processing digital information is out of the question for your business, there is just time to take action and ensure you are GDPR compliant. Alan Calder goes into detail about personal data, lawful basis and information security surrounding the imminent new regulation.
Alan Calder assesses how Brexit is likely to affect cyber security in the UK.
Cyber criminals often seem to do a better job of communicating with a company's staff than the company itself. Vicki Gavin offers her tips to compete with and defeat the phishers.
What is the lawful basis for processing personal data and retaining it under the GDPR?
Awareness of cyber threats is one thing, but increased security from change will only come from a cultural shift, say Simon Borwick and Lushin Premji.
Dr Sam De Silva explores the scope of the General Data Protection Regulation and how it's likely to affect business in the long term.
CISSP, CASP, ISO 27001 – but which is the right qualification for your IT experts? Alan Calder leads us through the minefield of cyber security qualifications.
Security experts have been telling us for years that protecting data using passwords is insecure.


An year before Myself & My Wife went to Wagle Indsl. Estate P.O for Aadhaar Updates but nothing was done even after 4 – 5 months. Later when We came to know about this We went to CITI UNION BANK – THANE WEST Br. for Aadhaar Updates once again, paying their Charges as per the norms. Now about 5 months over We have neither received the Updated Aadhaar Card Nor anything in this matter. No proper response from the telephonic call at 1947 too. Why such callousness in such critical Issues like this ? Now We will be needing the Aadhaar Cards for Voting purpose in this Election. Kindly help Us.


Valérian and Laureline has been a popular French comic series since the 1960s and director Luc Besson (Lucy) had been a fan of Pierre Christin and illustrator Jean-Claude Mézières' work for years. The acclaimed director had not considered making a film about the adventures of the space agents until he was making his cult classic, The Fifth Element. It was during the making of this cinematic fantasy that Besson hired Mézières to do work on the film. During the production, the artist that was behind the comic book odyssey mentioned that Besson should make a film about Valérian. This collaboration took 20 years to come to fruition, but for fans of the French director and comic series the wait is over.
In the 28th century of Earth's history, the international space station has now become Alpha, a modern day conduit for interplanetary diplomacy. A utopian atmosphere that eventually morphs into a modern example of the beauty of all planets and species working together for the betterment of the community at large. With the perpetual growth, it eventually has to be moved to a new galactic address that does not detrimentally impact Earth's atmosphere. Valérian (Dane DeHaan) and Laureline (Cara Delevingne) help in maintaining the peace on Alpha and throughout the galaxy by being leading agents of a interplanetary police force.
As they travel to their latest assignment, Valérian has a vision of the planet Mul and how it came to an unfortunate demise. Unable to lose the impact of this dream on his mind, he tries to find out all he can about Mul and its ill-fated inhabitants. Upon their arrival at the acclaimed space station, he and his partner are saddled with the duty of protecting Alpha's commander, Arün Filitt (Clive Owen). Their duties include holding onto a rare life form that seems to be the key to many of the mysterious events that threaten the pristine life of Alpha. During their first diplomatic event, Filitt is kidnapped by an unknown group of aliens and the crime fighting duo must investigate the origin of these invading beings and why they would want to abduct the commander.
The visual smorgasbord provided by Christin and Mézières' graphic novels and the directorial style of Besson seem to be a combination made in cinematic heaven. This eventual collaboration merely had to wait until modern advancements in computer generation would help to bring this dream partnership together.
In the future, it may be said that Valerian and the City of a Thousand Planets is visually stunning, but something went very wrong in the delivery. Two elements that Besson managed to leave behind on this intergalactic journey were a well thought out storyline and convincing lead actors.
Great computer generation can only carry a film so far to success, at the heart of every great film there needs to be a compelling plot. There are whispers of an enthralling space odyssey contained in Valerian, but it quickly becomes a convoluted mess. The script is simple enough and most plot points keep getting reiterated through each scene. This leaves little to the imagination by defusing the dramatic tension and when it does finally conclude, all the audience can do is scratch their heads in confusion.
What provided The Fifth Element's longevity and appeal was the campiness of the characters. This means that no one seemed to be taking themselves too seriously in the film and they were enjoying the ride. This detail should be part of Besson's latest production, but the cast never seem to know when to be serious and when to give a knowing wink to the camera.
DeHaan and Delevingne have proven their acting capabilities from past performances, but there is little that they can do with this poorly written script. They are left to deliver overly long monologues that contradict previous plot points and must carry the burden of the whole film, despite having an exceptional supporting cast. It is frustrating to watch as Ethan Hawke, John Goodman and Rihanna are left to play forgettable and cringe-worthybit roles, as opposed to being lively supporting characters. The excruciating pressure on these young lead actors leaves them with little to convince the audience that they truly care for one another. Their relationship is supposed to be at the heart of the film, but like the rest of the film it only provides visual appeal and no real emotional energy.
Besson proves that he has a gift for developing a visually captivating film in Valerian. Unfortunately he failed to support the visuals with a noteworthy storyline and left his acting team figuratively floating in space with little hope for success. This Besson outing did not live up to the legacy of The Fifth Element or Lucy and makes his other CGI drive children's film, Arthur and the Invisibles, look like a masterpiece.
Utopian societies are not new to literature or the cinema, it has lead to a multitude of storylines. The name was first utilised in by Sir Thomas More in 1516, but the concept has been around since the beginning of time.
Even in Valerian and the City of a Thousand Planets, this is a concept that seems to be unlikely to occur. The facade surrounding Alpha is undergirded by a dark underworld that is far from idyllic. Yet, mankind continues to seek after this perfect society. Putting our faith in politics, education or religion, this pure existence seems to draw people into the latest cause or at least into the nearest cinema.


text:
package org.cogroo.tools.checker.rules.exception;

/**
 * Exception related to the rules mechanism.
 */
public class RulesException extends RuntimeException {

  private static final long serialVersionUID = 1L;

  public RulesException(String message) {
    super(message);
  }

  public RulesException(String message, Exception e) {
    super(message, e);
  }

}

redpajama_set_name: RedPajamaGithub