text:
This GitHub repo makes Project Buendia builds available at https://projectbuendia.github.io/builds/.

In particular, it hosts the Debian package repository that can be used to install the Project Buendia
packages at https://projectbuendia.github.io/builds/packages.  (Note that it's hosted on GitHub Pages,
so you won't be able to rely upon directory listings to browse the repository.)

To add this repository to your Debian-based distribution, use something like:

```sh
echo "deb [trusted=yes] https://projectbuendia.github.io/builds/packages unstable main java" \
    > /etc/apt/sources.list.d/buendia-base.list
```

## How new builds are added

Every time [our CircleCI build](https://circleci.com/gh/projectbuendia/buendia) runs on the
`dev` branch, the packages produced by the build are committed and pushed to this GitHub repo.
The contents of this repo are published in [our Debian package repository](https://projectbuendia.github.io/builds/packages) with GitHub pages,
so the new packages will become available to existing servers for upgrade immediately.

## Some performance caveats to be aware of

Note that there's a real chance that our CI run times will blow out significantly as a result of
cloning this repo, which is full of binary files. If / when this happens, a good solution is to:

- Clone the repo locally
- Delete the `packages` folder
- Push the repo
- Kick off a new build

Admittedly, this isn't a sustainable solution. If you have any other ideas, especially around how to only take a small number of previous builds, please take a look at
https://github.com/projectbuendia/buendia/blob/dev/.circleci/config.yml and send a pull request :)

redpajama_set_name: RedPajamaGithub


text:
HAMPSHIRE RUGBY
News Competitions Teams Info Clubs Safeguarding Contact
U18 Girls & U20s match reports 9 Nov
U18G Kent 34-10 Hampshire
After a slow start and having let Kent score two easy tries in the first half the girls raised their game and played exciting rugby. With no substitutes facing a Kent team that had a team with a full set of subs, Hampshire girls brought the fight to them.
Hampshire won the second half collisions and with a pack turning over Kent at every opportunity especially as Kent kept bringing on fresh legs the girls dug deep and continued to turn them over in the Lineouts, repeatedly taking the ball against the head in the scrums and with the backs now gaining confidence were doing switches and loops in attack.
The second half was a try a piece with 7 minutes to go and the girls on their own 10m line showed how good they were by not dropping their heads and repeatedly attacked the Kent line resulting in Kent giving away multiple penalties and Hants getting over the try line in the last play of the game but unfortunately couldn't ground the ball.
The final score was 34-10 which doesn't reflect how well the girls played.
All 15 girls had a great game and I couldn't name individuals as it was an outstanding team performance.
You only find out the potential of a team when their backs are against the wall and they were brilliant especially to find the reserves to raise their game in the last quarter.
U20 Dorset & Wilts 10 - 37 Hampshire
It is pleasing to report that we started our campaign in the national shield competition with a bonus point away win.
The score would almost certainly have been even higher if we had not suffered a red card just before half time, as our hooker was sent off on receipt of a second yellow card.
After the loss of a player, our team dug deep and it should be noted that we won the second half 17-0. The highlight was when a penalty try was awarded after our seven man pack demolished the D&W eight in a series of scrums close to their line.
Nine of our players were selected for the 'shadow' team.
The next match against Surrey is expected to be a much greater challenge as they won the competition last year.
HRFU SHOP
FOR HRFU EMAIL ALERTS
An easyWeb site produced by Media 3

redpajama_set_name: RedPajamaCommonCrawl


This function attempts to read a boolean (native type) from a file and return it. The amount of bytes read should be one.
Returns a boolean if it was successfully read from the file, nil otherwise.
This snippet demonstrates a variable file format that stores player properties depending on whether they are required.
-- Write basic details about the player instance.
-- Next write down special details given by the game.
-- Save things like player position, dimension and interior.
-- Save the time this snapshot was taken.
-- Function to restore details from a snapshot file stream.
-- Restore the basic information.
-- Set them, if read correctly.
-- Get the time the snapshot was taken at.
-- Return the save details so the runtime can react accordingly.
-- Command to save a complete snapshot of the player.
-- Command to save a quick savestate.
-- Command to load a savestate from disk.
This page was last modified on 30 January 2014, at 23:52.


text:
Orlando Bloom Changed By Son's Birth
TeamCLEO • January 3, 2017
Orlando Bloom admits watching his son Flynn – who he has with ex-wife Miranda Kerr – being born had a "profound effect" on him.
The 39 year old actor has five year old Flynn with ex-wife Miranda Kerr and seeing the 33 year old beauty go through a long labour with the youngster gave him even more respect and admiration for mothers.
He said: "No single moment has had such a profound effect on my life as when I held my son after his mother had endured 27 hours of labour.
"That should teach any man the meaning of respect for mothers the world over."
Yea this is his second season…he's 2
A photo posted by orlandobloom (@orlandobloom) on Apr 9, 2016 at 12:11pm PDT
The British actor – who is dating singer Katy Perry – divides his time between the UK and US and admits he can only spend short stints in one place before he craves a return to his other home.
He told Empire magazine: "I live between the US and the UK. Too long in one and I crave the other.
"I've called Shanghai home for the last two months, I'm here filming."
Outside of his work, Orlando's biggest "passion" is trying to "master the art of living", something he knows he can never fully achieve.
He said: "[My passion is] mastering the art of living, which I will never do, so that learning curve keeps me thoroughly occupied."
But the Lord of the Rings star worries about the impact of "stupidity, fear and greed" on the world.
Asked what he thinks is most destructive to the soul, he said: "Well, Albert Einstein, one of the wizards of our time, said, 'stupidity, fear and greed'.
"There's a lot of that around, particularly if you turn on the news.
"The antidotes are courage, wisdom and compassion – which are coincidentally the qualities of most Hobbits. The rest of us elves and humans have to work harder to manifest them."
*Sourced by Bang Showbiz
< How To Kick Social Anxiety Out Of The Picture In 2017
Check Out This Cliff-Hanging House >
It Was A Wild Night At Karlie Kloss And Joshua Kushner's Wedding Party
Katy Perry And Taylor Swift Want To Be A Symbol Of Forgiveness
Anna Camp Files For Divorce From Skylar Astin
Adele Announces Split From Husband Simon Konecki
divorce, flynn, Katy Perry, miranda kerr, orlando bloom, son


On behalf of Butler Law posted in estate planning on Thursday, September 27, 2018.
Estate planning for Myrtle Beach residents is constantly evolving. Estate planning does not just involve wills and trusts, but also can encompass guardianship designations, power of attorney, pet trusts, and digital asset planning. Digital assets are important assets that often are forgotten in estate planning. Including them allows a family to manage assets easier after a person's death and makes sure they are not lost or forgotten.


text:
Stanford350
Angel, Shlomo350
Blei, Alejandro M350
Civco, Daniel L.350
Parent, Jason[remove]350
Lincoln Institute of Land Policy350
Cities and towns--Growth[remove]350
Imagery and Base Maps350
Metropolitan areas[remove]350
Society350
Urbanization350
Land use232
Accra (Ghana)3
Addis Ababa (Ethiopia)3
Ahvāz (Iran)3
Akashi-shi (Japan)3
Alexandria (Egypt)3
Anqing Shi (China)3
Ansan-si (Kyŏnggi-do, Korea)3
Astrakhanʹ (Russia)3
Raster350
GeoTIFF350
You searched for: Author Parent, Jason Remove constraint Author: Parent, Jason Subject Metropolitan areas Remove constraint Subject: Metropolitan areas Subject Cities and towns--Growth Remove constraint Subject: Cities and towns--Growth
1. Urban Footprint, Accra, Ghana, 2000
2000. Angel, Shlomo, Parent, Jason, Civco, Daniel L., and Blei, Alejandro M. This raster layer contains the total area occupied by the built-up area of Accra, Ghana and its urbanized open space in 2000. Categories of urban l... Lincoln Institute of Land Policy.
2. Urban Footprint, Addis Ababa, Ethiopia, 2000
2000. Angel, Shlomo, Parent, Jason, Civco, Daniel L., and Blei, Alejandro M. This raster layer contains the total area occupied by the built-up area of Addis Ababa, Ethiopia and its urbanized open space in 2000. Categories o... Lincoln Institute of Land Policy.
3. Urban Footprint, Ahvaz, Iran, 2000
2000. Angel, Shlomo, Parent, Jason, Civco, Daniel L., and Blei, Alejandro M. This raster layer contains the total area occupied by the built-up area of Ahvāz, Iran and its urbanized open space in 2000. Categories of urban la... Lincoln Institute of Land Policy.
4. Urban Footprint, Akashi, Japan, 2000
2000. Angel, Shlomo, Parent, Jason, Civco, Daniel L., and Blei, Alejandro M. This raster layer contains the total area occupied by the built-up area of Akashi-shi, Japan and its urbanized open space in 2000. Categories of ur... Lincoln Institute of Land Policy.
5. Urban Footprint, Alexandria, Egypt, 2000
2000. Angel, Shlomo, Parent, Jason, Civco, Daniel L., and Blei, Alejandro M. This raster layer contains the total area occupied by the built-up area of Alexandria, Egypt and its urbanized open space in 2000. Categories of ur... Lincoln Institute of Land Policy.
6. Urban Footprint, Anqing, China, 2000
2000. Angel, Shlomo, Parent, Jason, Civco, Daniel L., and Blei, Alejandro M. This raster layer contains the total area occupied by the built-up area of Anqing Shi, China and its urbanized open space in 2000. Categories of ur... Lincoln Institute of Land Policy.
7. Urban Footprint, Ansan, Korea, 2000
2000. Angel, Shlomo, Parent, Jason, Civco, Daniel L., and Blei, Alejandro M. This raster layer contains the total area occupied by the built-up area of Ansan-si, Kyŏnggi-do, Korea and its urbanized open space in 2000. Catego... Lincoln Institute of Land Policy.
8. Urban Footprint, Astrakhan, Russia, 2000
2000. Angel, Shlomo, Parent, Jason, Civco, Daniel L., and Blei, Alejandro M. This raster layer contains the total area occupied by the built-up area of Astrakhanʹ, Russia and its urbanized open space in 2000. Categories of u... Lincoln Institute of Land Policy.
9. Urban Footprint, Aswan, Egypt, 2000
2000. Angel, Shlomo, Parent, Jason, Civco, Daniel L., and Blei, Alejandro M. This raster layer contains the total area occupied by the built-up area of Aswān, Egypt and its urbanized open space in 2000. Categories of urban l... Lincoln Institute of Land Policy.
10. Urban Footprint, Bacolod, Philippines, 2000
2000. Angel, Shlomo, Parent, Jason, Civco, Daniel L., and Blei, Alejandro M. This raster layer contains the total area occupied by the built-up area of Bacolod, Philippines and its urbanized open space in 2000. Categories of... Lincoln Institute of Land Policy.
11. Urban Footprint, Baku, Azerbaijan, 2000
2000. Angel, Shlomo, Parent, Jason, Civco, Daniel L., and Blei, Alejandro M. This raster layer contains the total area occupied by the built-up area of Baku, Azerbaijan and its urbanized open space in 2000. Categories of urb... Lincoln Institute of Land Policy.
12. Urban Footprint, Bamako, Mali, 2000
2000. Angel, Shlomo, Parent, Jason, Civco, Daniel L., and Blei, Alejandro M. This raster layer contains the total area occupied by the built-up area of Bamako, Mali and its urbanized open space in 2000. Categories of urban l... Lincoln Institute of Land Policy.
13. Urban Footprint, Bandung, Indonesia, 2000
2000. Angel, Shlomo, Parent, Jason, Civco, Daniel L., and Blei, Alejandro M. This raster layer contains the total area occupied by the built-up area of Bandung, Indonesia and its urbanized open space in 2000. Categories of u... Lincoln Institute of Land Policy.
14. Urban Footprint, Bangkok, Thailand, 2000
2000. Angel, Shlomo, Parent, Jason, Civco, Daniel L., and Blei, Alejandro M. This raster layer contains the total area occupied by the built-up area of Bangkok, Thailand and its urbanized open space in 2000. Categories of ur... Lincoln Institute of Land Policy.
15. Urban Footprint, Banjul, Gambia, 2000
2000. Angel, Shlomo, Parent, Jason, Civco, Daniel L., and Blei, Alejandro M. This raster layer contains the total area occupied by the built-up area of Banjul, Gambia and its urbanized open space in 2000. Categories of urban... Lincoln Institute of Land Policy.
16. Urban Footprint, Beijing, China, 2000
2000. Angel, Shlomo, Parent, Jason, Civco, Daniel L., and Blei, Alejandro M. This raster layer contains the total area occupied by the built-up area of Beijing, China and its urbanized open space in 2000. Categories of urban... Lincoln Institute of Land Policy.
17. Urban Footprint, Budapest, Hungary, 2000
2000. Angel, Shlomo, Parent, Jason, Civco, Daniel L., and Blei, Alejandro M. This raster layer contains the total area occupied by the built-up area of Budapest, Hungary and its urbanized open space in 2000. Categories of ur... Lincoln Institute of Land Policy.
18. Urban Footprint, Buenos Aires, Argentina, 2000
2000. Angel, Shlomo, Parent, Jason, Civco, Daniel L., and Blei, Alejandro M. This raster layer contains the total area occupied by the built-up area of Buenos Aires, Argentina and its urbanized open space in 2000. Categories... Lincoln Institute of Land Policy.
19. Urban Footprint, Cairo, Egypt, 2000
2000. Angel, Shlomo, Parent, Jason, Civco, Daniel L., and Blei, Alejandro M. This raster layer contains the total area occupied by the built-up area of Cairo, Egypt and its urbanized open space in 2000. Categories of urban l... Lincoln Institute of Land Policy.
20. Urban Footprint, Caracas, Venezuela, 2000
2000. Angel, Shlomo, Parent, Jason, Civco, Daniel L., and Blei, Alejandro M. This raster layer contains the total area occupied by the built-up area of Caracas, Venezuela and its urbanized open space in 2000. Categories of u... Lincoln Institute of Land Policy.


Francis Sydney Muschamp was elected a member of the Royal Society of British Artists (RBA) in 1893. Enid – Then breaking his Command of Silence …, exhibited at the Royal Academy in 1895, brings to life a scene from the romantic legend of King Arthur, retold in Tennyson's Idylls of the King. Enid is a humble maiden who desperately loves her husband, Geraint, one of Arthur's bravest knights. Geraint doubts his wife's loyalty and forbids her to speak on his journey to fame and fortune. Here we see Enid reluctantly breaking her husband's command of silence to warn him of an evil plot by her former suitor.


text:
At heart, Brandyn River Gallagher (they/them) is first and foremost a writer. The blood pumped by this writer's heart is that of a community empowerer, DEIB consultant, facilitator, healthcare nerd, life coach, mediator, and teacher.
Brandyn is a devoted servant leader committed to the equitable redistribution of happiness. Their voice addressing exclusions in clinical studies for transmasculine people improved research methods and design internationally. They've served communities by providing Diversity, Equity, and Inclusion training, subject matter expertise, and independent consulting on culturally responsive care in health and social services settings since 2015. They're passionate about building people up to achieve their fullest potential, bridging divides across the chasms of structural inequity, and healing collective wounds.
For two years, Brandyn served as a moderator of the WHO-recognized PrEP Facts: Rethinking HIV Prevention and Sex. They then formed the Trans MSM: Rethinking Sexuality and Health educational support group in 2015 and continue to facilitate candid, evidence-based discussions there. Brandyn loves engaging with researchers heart-to-heart in addressing the importance of trans-inclusion in medical science.
What's Brandyn's favorite job? Reminding you how awesome you already are, and helping you thrive.
In 2021, Brandyn built upon this love with an Executive Leadership Certificate in Diversity and Inclusion from Cornell University. DEIB services and coaching are available with direct professional experience in healthcare research, trucking, domestic violence, law enforcement, and serving minoritized communities. How would you put Brandyn's talents to use?
Where does Brandyn come from?
Brandyn is a Southerner rooted in the foothills of the Ozarks, a small mountain region which overlaps the States of Arkansas and Missouri. They come from eight generations of mostly poor, working, and farmer-class English descendants who, in the mid 1600's, brought their genetic material to this red land rightfully inhabited by Native American tribes. They grew up singing on the back porch and playing Mountain Dulcimer, piano, saxophone, and guitar. The Baptist Hymnal — the one for white people that don't get too exciting — is where they first learned to sight-read music.
After ten years away from the South, Brandyn has returned home, to reside on land not bound by Treaty obligation with any Native American tribe. The Osage, Caddo, and some Cherokee people lived here before white people colonized the land. The neighboring Quapaw were relocated by Treaty obligation in 1833. The Quapaw Tribe honored and upheld their Treaty agreement with the U.S. The Caddo were forcibly removed in 1834, as Arkansas prepared to establish white-dominated statehood. Approximately 16,000 Cherokee human people were forcibly removed from their homes at gunpoint by order of United States President Andrew Jackson in 1838, and passed through Brandyn's neighborhood en route to the modern-day Cherokee Nation reservation in Oklahoma. These tribal nations are alive and well today. Among them are Brandyn's friends, colleagues, and mentors. Brandyn holds a responsibility to collective healing and uplifting Native American neighbors as a sacred duty.
The views expressed on this site are Brandyn's alone and do not reflect the position of any agency or project with which they are affiliated.


The BYREDO bath and body collection features an assortment of offerings infused with the brand's signature scents. Founder Ben Gorham draws inspiration from a diverse range of interests and takes you on an enriching journey through his array of products. Nourishing hand creams and body lotions, scented bath oils, hair perfumes, and shower gels are produced with precise ingredients to envelop you in complete luxury and care. Shop Neiman Marcus' selection of BYREDO Mojave ghost, blanche, and much more.


text:
After bitter race, Obama, Romney have 'friendly lunch'
Nov 30, 2012 12:34 PM PHT
Obama and Romney promise talk about America's challenges in a private lunch meeting at the White House
MANILA, Philippines – There was no talk of "Romnesia" or the controversial 47%.
Away from the vitriol of presidential campaigns and the prying eyes of the press, US President Barack Obama and his former Republican challenger Mitt Romney got together in what aides call a "very friendly lunch."
Romney and Obama chatted for about 90 minutes in a dining room in the White House on Thursday, November 29, reported Time.
On the menu was white turkey chili and Southwestern grilled chicken salad while on the agenda was America's leadership in the world.
"Gov Romney congratulated the President for the success of his campaign and wished him well over the coming 4 years," the White House said in a statement.
"They pledged to stay in touch, particularly if opportunities to work together on shared interests arise."
The White House has said that Obama had no specific agenda in mind for the meeting but wanted to discuss Romney's ideas for making government more efficient.
"Each man wanted to have a private conversation," said White House Spokesman Jay Carney. "They didn't want to turn it into a press event."
Romney adviser Eric Fehrnstrom said, "They spoke about some of the big challenges facing America, and it gave Gov Romney the opportunity to personally congratulate President Obama for the success of his campaign."
'Not enough following in GOP'
The meeting was largely seen as a symbolic close to the presidential race, and a fulfillment of Obama's promise on election night to sit down with Romney.
Time reported that it was the two leaders' "most extensive private meeting," following a few brief exchanges before the polls and interactions limited to debates during the campaign.
Yet the meeting was not expected to produce any meaningful results, according to The Huffington Post.
"[Republican officials] said that while Romney was the face of the GOP for much of the year, he did not command enough following among the party's passionate voters or chattering class to maintain a leadership role going forward."
Romney has maintained a low profile following his loss. Reports said he has largely been in seclusion in his Southern California home and made no public appearances.
In contrast, Romney's running mate Rep Paul Ryan of Wisconsin is still a player on Capitol Hill amid fiscal cliff negotiations.
Romney met with Ryan before his lunch with Obama. – Rappler.com


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

The quantum-mechanical few-body problem is of particular interest for the physics community.
On the one hand, it determines the features of interacting nuclei, atoms, or molecules as bodies living on very different length scales. On the other hand, in certain regimes these systems display a universal behavior that is independent of the details of the interaction between the particles, but governed by the particle masses, overall symmetries, as well as the dimensionality of space.
The complexity and beauty of this problem has motivated numerous researchers to explore these systems using theoretical, numerical, and experimental approaches.

An outstanding example for the above mentioned type of universality is the Efimov effect~\cite{Efimov_PLB_1970,Efimov_NPA_1973}, describing the emergence of an infinite sequence of universal states of three bosonic particles with $s$-wave resonant pair interactions in three dimensions. Moreover, lower dimensional systems, such as three fermionic particles confined to two dimensions, display surprising universal phenomena like the so-called ``super Efimov effect''~\cite{Nishida_PRL_2013,Moroz_PRA_2014,Gridnev_JPA_2014,Volosniev_JPB_2014}.
Recently, some of the authors have demonstrated that in one dimension, universality in a mass-imbalanced three-body system is not only present in the discrete spectrum~\cite{Happ2019threebody}, but universal three-body bound states also occur in the continuum as induced by excited two-body resonances~\cite{Happ2021submitted}.

In order to provide an adequate model of these systems, novel analytical and numerical tools are required. With an increasing number of particles or dimensions, accurate predictions of the properties of the quantum system become very challenging. For instance, in Ref.~\cite{Happ2019threebody} three-body energies and the corresponding wave functions of the bound states are computed by representing the Hamiltonian as a sparse matrix, and using a Krylov subspace method to determine its lowest eigenvalues and the corresponding eigenvectors. However, with an increasing number of grid points in each dimension, the matrices and vectors grow rapidly: The three-body problem in $d$ space dimensions yields a $2d$-dimensional linear eigenvalue problem after removing the center-of-mass degree of freedom. When discretized with $n$ grid points in each direction, a single vector that represents the three-body wave function has the size $n^{2d}$. Moreover, the pseudo-spectral discretization used in~\cite{Happ2019threebody} leads to $\mathcal{O}\left(n^{2d-1}\right)$ dense blocks in the sparse matrix representation of the Hamiltonian, each of size $n\times n$. Thus, such an approach is severely limited by the `curse of dimensionality'.

In this article, we present a novel numerical approach to analyze the three-body problem. In particular, we exploit the tensor product structure of the problem to avoid storing redundant blocks in the matrix. In this way we achieve very high computational efficiency. Moreover, in order to accelerate the convergence compared to the previously used Krylov method, we use the Jacobi-Davidson iteration scheme and introduce a preconditioner for the one dimensional (1D) three-body system.
We then show how the approach can be extended to 2D, as a first step towards simulating quantum systems in 2D and 3D, or with a larger number of particles involved.

Our article is structured as follows. In Section~\ref{sec:few-body_systems} we introduce quantum-mechanical few-body systems in low dimensions and present the corresponding eigenvalue equations determining the energies and stationary wave functions. In Section~\ref{sec:tensor_form} we describe the discretization scheme and how it naturally enables a tensor formulation of the Hamiltonian operator. The Jacobi-Davidson iteration scheme is revisited in Section~\ref{sec:eigensolver}, and the implementation of the discretized operators in 1D and 2D are discussed in terms of hardware efficiency. For the 1D case, we devise a novel preconditioning technique to accelerate the convergence of the Jacobi-Davidson method.
We apply it to determine the few lowest eigenpairs by solving the corresponding eigenvalue problem. Numerical results are then presented in Section~\ref{sec:results}. They show the superior performance and convergence properties of our method. Finally, in Section~\ref{sec:conclusion} we provide concluding remarks and indicate directions of future research.

\section{Few-body systems}
\label{sec:few-body_systems}

First, we consider a system composed of two interacting particles, a heavy one of mass $M$ and a light one of mass $m$. In dimensionless units, the relative motion of these quantum particles is then governed by the stationary Schr\"odinger equation
\begin{equation}
\left[-\frac{1}{2}\Delta_{\vec{\xi}}-v_0f\left(\xi\right)\right]\psi^{(2)}(\vec{\xi})=\mathcal{E}^{(2)}\psi^{(2)}(\vec{\xi})
\label{eq:Schroedinger_equation_two_body}
\end{equation}
for the wave function $\psi^{(2)}(\vec{\xi})$ and two-particle energy $\mathcal{E}^{(2)}$, where $\Delta_{\vec{\xi}}$ denotes the Laplace operator with respect to the relative coordinate $\vec{\xi}$. Here, we have assumed that the interaction of the two particles is described by an attractive potential $-v_0 f(\xi)$ of the magnitude $v_0>0$ and the shape $f(\xi)$ as a function of the relative distance $\xi\equiv \left|\vec{\xi}\ \right|$.

Next, we turn to the mass-imbalanced three-body system displayed in Fig.~\ref{fig:3body_scheme} and confined to (a) one or (b) two spatial dimensions. This system is governed by the dimensionless form of the stationary Schr\"odinger equation
\begin{equation}
\left[-\frac{\alpha_x}{2}\Delta_{\vec{x}}-\frac{\alpha_y}{2}\Delta_{\vec{y}}+V(\vec{x},\vec{y})\right]\psi=\mathcal{E}\psi
\label{eq:Schroedinger_equation_three_body}
\end{equation}
for the three-particle wave function $\psi=\psi\left(\vec{x},\vec{y}\right)$ corresponding to the three-particle energy $\mathcal{E}$, as introduced in more detail in Refs.~\cite{Happ2019threebody,Happ2021submitted} for the one-dimensional case. Here $\Delta_{\vec{x}}$ and $\Delta_{\vec{y}}$ denote the Laplace operator with respect to the coordinate vectors $\vec{x}$ and $\vec{y}$, respectively. The positive coefficients $\alpha_x= 2/(1+\alpha)$ and $\alpha_y=(1+2\alpha)/(2+2\alpha)$ are determined by the mass ratio $\alpha\equiv M/m$ of the heavy and light particle.

\begin{figure}[h]
\begin{center}
       \includegraphics[width=0.4\textwidth]{Figure1A_1D_scheme.pdf}
        \hspace*{1cm}
         \includegraphics[width=0.4\textwidth]{Figure1B_2D_scheme.pdf}
\end{center}
    \caption{Three-body system consisting of two heavy particles of mass $M$ and a light one of mass $m$  confined to (a) one or (b) two spatial dimensions. We only allow for interactions between heavy and light particles, as indicated by the gray ellipses, and describe the system in terms of the Jacobi coordinates $\vec{x}$ and $\vec{y}$, where $C$ denotes the center-of-mass of the two heavy particles.
    \label{fig:3body_scheme}
    }
\end{figure}

For the case of non-interacting heavy particles, the interaction term in Eq.~\eqref{eq:Schroedinger_equation_three_body} is described by the potential
\begin{equation}
V(\vec{x},\vec{y})=-v_0 f\left(\left|\vec{x}+\frac{1}{2}\vec{y}\right|\right)-v_0 f\left(\left|\vec{x}-\frac{1}{2}\vec{y}\right|\right),
\label{eq:definition_potential}
\end{equation}
where $-v_0 f(\xi)$ models the interaction potential between the light particle and each heavy one. Here $\left|\vec{x}\pm \vec{y}/2\right|$ is the respective relative distance in (a) one or (b) two spatial dimensions.

Our procedure to solve the three-body problem governed by Eq.~\eqref{eq:Schroedinger_equation_three_body} is as follows. First, we choose a particular binding energy  $\mathcal{E}_0^{(2)}$ for the two-body system of the heavy and light particle. Then we determine the depth $v_0$ of the potential $-v_0 f(\xi)$ such that the two-body Schr\"odinger equation \eqref{eq:Schroedinger_equation_two_body} has the ground state solution with  energy $\mathcal{E}^{(2)}=\mathcal{E}^{(2)}_0$.  Next, we solve the three-body Schr\"odinger equation \eqref{eq:Schroedinger_equation_three_body} for this particular potential depth $v_0$ and select solutions with an energy smaller than the two-body threshold given by $\mathcal{E}^{(2)}_0$. In this way, we determine the wave functions $\psi\left(\vec{x},\vec{y}\right)$ and corresponding energies $\mathcal{E}$ of three-body bound states associated with this particular two-body interaction.

For the demonstration of our approach, we consider in the present article an attractive  potential of Gaussian shape with
\begin{equation}
f(\xi)=\exp\left(-\xi^2\right).
\label{eq:Gaussian_shaped_potential}
\end{equation}
However, we emphasize that our approach is also valid for potentials that feature  a different shape as a function of the relative coordinate $\vec{\xi}$.

\section{Discretization and tensor formulation}
\label{sec:tensor_form}

In this section, we briefly describe the discretization of the three-body Schr\"odinger equation by pseudo-spectral methods and, in particular, the Lagrange-mesh method \cite{BAYE2015Lagrange-mesh}.   In contrast to finite difference or finite element methods, pseudo-spectral methods lead to dense matrices for one-dimensional problems.  As a consequence, we obtain a faster convergence rate with respect to the number of grid points which is geometric on a finite domain and usually subgeometric on an infinite domain~\cite{boyd2000chebyshev}.

Since the three-body Hamiltonian is multi-dimensional, we aim to exploit its tensor structure when implementing the matrix-vector multiplication in an iterative eigenvalue solver. This drastically reduces the memory requirement for the operator when solving higher-dimensional eigenvalue problems.

\subsection{Discretization}

In the following, we apply a pseudo-spectral method to build a matrix representation of the Schr\"odinger equation \eqref{eq:Schroedinger_equation_three_body} of the three-body problem.
For this purpose, we consider Chebyshev polynomials as basis functions on a finite domain in each dimension. The corresponding grid points are then associated with the roots of the Chebyshev polynomials. Due to the structure of the three-body problem, we project these grid points to the infinite real domain via an algebraic map \cite{boyd2000chebyshev,boydMap}.

After discretization, the Schr\"odinger equation  \eqref{eq:Schroedinger_equation_three_body} takes the form
\begin{equation}
H \vec{\psi}=\mathcal{E}\vec{\psi},
\label{eq:matrix_evp}
\end{equation}
which is a linear eigenvalue problem for the matrix $H$ with eigenvalue $\mathcal{E}$ and eigenvector $\vec{\psi}$.

For the one-dimensional three-body problem, the eigenvector
\begin{equation}
    \vec{\psi}^{(\mathrm{1D})}\equiv \{\psi_{0,0}, \psi_{0,1},\ldots,\psi_{0, N_{y_1}-1},
    \psi_{1,0},\ldots,\psi_{N_{x_1}-1, N_{y_1}-1} \}^T
\end{equation}
corresponds to the wave function $\psi(\vec{x},\vec{y})=\psi^{(\mathrm{1D})}(x_1,y_1)$ in Eq.~\eqref{eq:Schroedinger_equation_three_body} evaluated at the grid points  $\left(x_1^{(i)},y_1^{(j)}\right)$, yielding the entries $\psi_{i,j}=\psi^{(\mathrm{1D})}(x_1^{(i)},y_1^{(j)})$ with $i=0,1,\ldots, N_{x_1}-1$ and $j=0,1,\ldots,N_{y_1}-1$. Here $N_{x_1}$ and $N_{y_1}$ denote the number of grid points in the respective direction.

Moreover, the matrix $H$ in Eq.~\eqref{eq:matrix_evp} takes the form
\begin{equation}
H^{(\mathrm{1D})}=- \frac{\alpha_x}{2} \left(D_{x_1 x_1}\otimes \mathbb{I}_{y_1}\right) - \frac{\alpha_y}{2}\left(\mathbb{I}_{x_1} \otimes D_{y_1y_1}\right) +v_0(F_+ + F_-).
\label{eq:discretized_Schroedinger_equation_1D}
\end{equation}
Here $D_{x_1 x_1}$ and $D_{y_1 y_1}$ are dense (generally non-symmetric) matrices with sizes $N_{x_1}\times N_{x_1}$ and $N_{y_1}\times N_{y_1}$ corresponding to the partial second derivatives $\partial^2/\partial x_1^2$ and $\partial^2/\partial y_1^2$ from the Laplace operators $\Delta_{\vec{x}}$ and $\Delta_{\vec{y}}$ in Eq.~\eqref{eq:Schroedinger_equation_three_body}, respectively. Moreover, $\mathbb{I}_{x_1}$ and $\mathbb{I}_{y_1} $ denote the identity matrices of corresponding size.
In addition, the diagonal matrices $F_\pm$ result from evaluating the functions $f\left(\left|\vec{x}\pm\vec{y}/2\right|\right)$ determining the potential $V(\vec{x},\vec{y})$, Eq.~\eqref{eq:definition_potential}, at the grid points $x_1^{(i)}$ and $y_1^{(j)}$. More details on the discretization procedure and the exact form of the matrices in Eq.~\eqref{eq:discretized_Schroedinger_equation_1D} have been presented in Appendix~B of Ref.~ \cite{Happ2019threebody}.

Similarly, for the three-body problem in two dimension we perform a discretization of the wave function $\psi\left(\vec{x},\vec{y}\right)=\psi^{(\mathrm{2D})}(x_1,x_2,y_1,y_2)$ with respect to the grid points $(x_1^{(i)},x_2^{(j)},y_1^{(k)},y_2^{(l)})$. The matrix $H$ in Eq.~\eqref{eq:matrix_evp} then reads
\begin{equation}
\label{eq:Ham2D}
H^{(\mathrm{2D})}=-\frac{\alpha_x}{2}\left[\left(\boldsymbol{D}_{x_1x_1}+\boldsymbol{D}_{x_2x_2}\right)\otimes \mathbb{I}_y\right]-\frac{\alpha_y}{2}\left[\mathbb{I}_x\otimes (\boldsymbol{D}_{y_1y_1}+\boldsymbol{D}_{y_2y_2}) \right]+v_0\left(\boldsymbol{F}_+ + \boldsymbol{F}_-\right),
\end{equation}
where $\boldsymbol{D}_{x_1x_1}=(D_{x_1x_1} \otimes \mathbb{I}_{x_2})$, $\boldsymbol{D}_{x_2x_2}=(\mathbb{I}_{x_1} \otimes D_{x_2x_2})$, $\mathbb{I}_x=\mathbb{I}_{x_1}\otimes\mathbb{I}_{x_2}$, etc. Also here the diagonal matrices $\boldsymbol{F}_\pm$ result from evaluating the function $f\left(\left|\vec{x}\pm \vec{y}/2\right|\right)$ in Eq.~\eqref{eq:definition_potential} at the grid points.

\subsection{Operator application for the 1D case\label{sec:op1D}}

When using an iterative method for solving the linear eigenvalue problem given by
the discretized Schr\"odinger equation \eqref{eq:matrix_evp}, only the effect of the linear operator on a given vector has to be implemented.
Our 1D Hamiltonian $H^{(\mathrm{1D})}$, Eq.~\eqref{eq:discretized_Schroedinger_equation_1D}, can be abstractly written in the form
\begin{align}
\label{eq:tensor_form}
T_{V,a_1,a_2} = & a_1\left(C_1\otimes\mathbb{I}_2\right)+a_2\left(\mathbb{I}_1\otimes C_2\right)+V
\end{align}
 with, in this case, $C_1=D_{x_1 x_1}$ and $C_2=D_{y_1 y_1}$, and a sparse (in our case diagonal) matrix $V=v_0(F_+ + F_-)$.
Note that we do not assume any structure for the potential operator $V$, in particular, it does not have to be of tensor structure $\mathbb{I}_1\otimes A + B \otimes \mathbb{I}_2$ with matrices $A$, $B$.
The application of the operator $T_{V,a_1,a_2}$, Eq.~\eqref{eq:tensor_form}, to a vector $w$ can be implemented efficiently by using dense matrix-matrix products.
Let $C_1\in\mathbb{R}^{N_1\times N_1}$, $C_2\in\mathbb{R}^{N_2\times N_2}$, $w\in\mathbb{R}^{N_1N_2}$. Let $W=\mathrm{reshape}(w,N_2,N_1)$ denote the interpretation of $w$ as an $N_2\times N_1$ matrix. Then
\begin{align}
\label{eq:tensor_op1D}
T_{V,a_1,a_2}\cdot w = \mathrm{reshape}\left(a_2 C_2 \cdot W + a_1 W \cdot C_1^T, N_1 N_2, 1\right) + V\cdot w,
\end{align}
where the $\mathrm{reshape}$ operation is used to interpret the resulting $N_2 \times N_1$-matrix as a vector of length $N_1N_2$.
Note that $\mathrm{reshape}$ does not incur any data movement, it is just a re-interpretation of a vector as a matrix stored in column-major ordering, and vice versa.

Assuming that $N_{x_1}=N_{y_1}=n$, the storage requirement of the Hamiltonian operator in 1D is now only $\mathcal{O}(n^2)$ as compared to $\mathcal{O}(n^3)$ when storing it in a sparse matrix format.
The performance of the $\mathcal{O}(n^3)$ arithmetic operations is limited by the floating point units of the hardware (compute bound).
In general, an operation is compute bound if the arithmetic intensity $I_c$, defined as the ratio of required floating point operations (flops) and bytes of memory transferred, is larger than the machine balance $I_M$, defined as the ratio of the peak floating point performance and the memory bandwidth of the hardware.
For our matrix-matrix products, $I_c=\mathcal{O}(n)\ \mathrm{byte}/\mathrm{flops}$, which is above the machine balance $I_M$ on typical CPUs.
For example, the Intel(R) Xeon(R) Gold 6152 CPU used for our 2D simulations in Section~\ref{sec:results2D} achieves a memory bandwidth (pure load) of 60 GB/s and can perform about 1\,500 Gflop/s when running at its base frequency of 2.1 GHz, yielding  $I_M\approx 25\ \mathrm{flops}/\mathrm{byte}$.
Applying the operator $V$ to $w$ is a memory-bound operation in general, because it requires only two flops per matrix entry loaded. Consequently, its cost is $\mathcal{O}(n^2)$ memory transfers.

If $H^{\mathrm{(1D)}}$ is represented as a sparse matrix, then loading and applying the operator $T_{V,a_1,a_2}$, Eq.~\eqref{eq:tensor_op1D}, would cost $\mathcal{O}(n^3)$ memory transfers and still $\mathcal{O}(n^3)$ flops.
The operation is then memory bound as $I_c=\mathcal{O}(1)$.
So the high values of $I_M$ in modern HPC hardware like CPUs and GPUs can lead to a speed-up of about a factor 100 when going from the sparse matrix representation to the tensor operations that we propose in this article. As an example, for the processor mentioned above and $I_c=1$, we would achieve a performance 200 times below the peak floating point performance for double precision data.

\subsection{Operator application for the 2D case}

For the 2D problem, both the operator $H^{(\mathrm{2D})}$, Eq.~\eqref{eq:Ham2D}, and its components
$\boldsymbol{D}_{xx}=\boldsymbol{D}_{x_1x_1}+\boldsymbol{D}_{x_2x_2}, \boldsymbol{D}_{yy}=\boldsymbol{D}_{y_1y_1}+\boldsymbol{D}_{y_2y_2}$ are of the form Eq.~\eqref{eq:tensor_form} with particular choices of $a_1$, $a_2$, and $V$.
Thus, we can now apply Eq.~\eqref{eq:tensor_op1D} in a nested way. Let
$W=\mathrm{reshape}(w,N_{y_1}N_{y_2},N_{x_1}N_{x_2})$ and $N=N_{x_1}N_{x_2}N_{y_1}N_{y_2}$. Then we arrive at
\begin{align}
\label{eq:tensor_op2D}
H^\mathrm{(2D)}\cdot w = \mathrm{reshape}\left(-\frac{\alpha_y}{2}\boldsymbol{D}_{yy} \cdot W - \frac{\alpha_x}{2}W \cdot \boldsymbol{D}_{xx}^T, N,1\right) + V\cdot w.
\end{align}

If we assume that $N_{x_1}=N_{x_2}=N_{y_1}=N_{y_2}=n$, then loading the operator still requires $\mathcal{O}(n^2)$ memory transfers. However, the vector $w$ now actually represents 4D tensors and has a storage requirement of $\mathcal{O}(n^4)$. Hence, the total amount of memory transferred is $\mathcal{O}(n^4)$.
For each of the $n^2$ columns of $W$, $\mathcal{O}(n^3)$ flops are performed, amounting to $\mathcal{O}(n^5)$ in total.
The computational intensity is therefore still $\mathcal{O}(n)$, so the operation is compute bound as before.
In practice, we implement the term $W \boldsymbol{D}_{xx}^T$ as $(\boldsymbol{D}_{xx} W^T)^T$, so that $n^4$ vector elements have to be read and written twice in each operator application due to the transpose operations.
This overhead can be avoided by using an optimized implementation of a tensor contraction, such as GETT~\cite{paolo2018gett}.

\section{Jacobi-Davidson and preconditioning}\label{sec:eigensolver}

In this section we briefly introduce the Jacobi-Davidson QR (JDQR) method~\cite{jacdav}. Compared to the Arnoldi-type iteration
(Krylov-Schur) implemented in Matlab's \texttt{eigs} command, JDQR offers some flexibility when solving the so-called correction equation. We use this
flexibility to improve the convergence dramatically by introducing a preconditioned iteration for the correction equation, exploiting again the tensor
structure of the matrices.

\subsection{The Jacobi-Davidson QR Method}

We use a Matlab implementation of the JDQR method \cite{jacdav} that is
suitable for computing a few exterior eigenvalues of a non-Hermitian matrix.
The algorithm computes a partial QR decomposition of a matrix $A$ by applying a Newton process to the system of equations
\begin{align}\label{eq:jdqr}
  \begin{cases}AQ - QR &= 0,\\
              -\frac{1}{2}Q^TQ + \frac{1}{2}\mathbb{I} &= 0.
  \end{cases}
\end{align}

The Newton updates are used to extend the search space spanned
by $Q$ and the standard Ritz pairs are used for approximating eigenpairs of the matrix $A$. Whenever the basis spanning the search space reaches a maximum size $m_{max}$, it is compressed into $m_{min}$ vectors by (implicitly) applying a truncated Singular Value Decomposition (SVD) to retain only the most relevant directions.

The Newton process requires solving the correction equation
\begin{align}\label{eq:jdcor}
  (\mathbb{I}-\tilde Q \tilde Q^T)(A-\theta\mathbb{I})(\mathbb{I}-\tilde Q\tilde Q^T) \Delta q  &= -(A q - q \theta)
\end{align}
for the new basis vector $\Delta q$ in every outer iteration $i$. Here $\tilde Q$ contains the approximation
$q\approx Q_i$ for the current eigenvector, and any previously converged (`locked') eigenvectors,
$\theta\approx R_{ii}$ denotes the current approximate eigenvalue.

The deflation operator $\mathbb{I}-\tilde Q \tilde Q^T$ improves the conditioning of the shifted matrix $A-\theta\mathbb{I}$.
We will employ a Generalized Minimal Residual (GMRES) method  for solving Eq.~\eqref{eq:jdcor} with additional acceleration by preconditioning, as discussed in the next section. Further details on how the preconditioner is combined with the projections can be found in \cite{Thies2020phist}.

\subsection{Preconditioning\label{sec:precon}}

In order to improve the convergence of the GMRES correction solver, we introduce a
shifted version of the Hamiltonian that ignores the potential $V$. We neglect $V$ in the
preconditioner so that we can exploit the tensor product structure of the differential
operator even if $V$ does not have tensor structure, as discussed above.

In the 1D case, for small values of the potential depth $v_0$, the matrix $H^{\mathrm{(1D)}}$, Eq.~\eqref{eq:discretized_Schroedinger_equation_1D}, can be approximated by an operator of the form $T_{0,1,1}$ presented in Eq.~\eqref{eq:tensor_op1D}, where $C_{1}=-\frac{\alpha_{y}}{2}D_{y_1 y_1}, C_2=-\frac{\alpha_x}{2}D_{x_1 x_1}$.
For some scalar $\sigma$, linear systems with $T_{0,1,1}-\sigma\mathbb{I}$ and some right-hand side $b$, respectively $B=\mathrm{reshape}(b,N_{y_1},N_{x_1})$, can be solved for
$w$ with the help of the Sylvester equation
\begin{align}
\left(C_1-\sigma_1\mathbb{I}_1\right) W + W \left(C_2-\sigma_2\mathbb{I}_2\right)^T = B
\label{eq:sylvester_equation}
\end{align}
where $\sigma=\sigma_1+\sigma_2$. For our system, the shift  \mbox{$\sigma_{1,2}=-\alpha_{y,x}\mathcal{E}_0^{(2)}/|\alpha_x+\alpha_y|$} is a good choice. In this case the preconditioner approximates the shift-invert operator near the value $-\mathcal{E}^{(2)}_0$ of the two-body binding energy, which is close to the desired eigenvalues.

Bartels and Steward~\cite{barstew} have introduced a direct method for solving the  Sylvester equation~\eqref{eq:sylvester_equation}.
It requires a Schur decomposition of the shifted matrices $C_{1,2}-\sigma_{1,2}\mathbb{I}$, and subsequently a
combination of two dense matrix-matrix products and a special forward/backward substitution
with the Schur factors. Since the matrices involved remain the same throughout the JDQR process, the Schur factorization has to be performed only
once. Applying our preconditioner again has a computational cost of $\mathcal{O}(n^3)$ and requires $\mathcal{O}(n^2)$ data transfers, so that the performance characteristics of the overall algorithm are unchanged.

Unfortunately, we cannot straightforwardly extend our preconditioner, which is a direct solver for a shifted operator, to the 2D case. Indeed, the Schur decomposition of the operators $\boldsymbol{D}_{xx}$ and  $\boldsymbol{D}_{yy}$ cannot be simply represented  as a sum of
Kronecker product terms. Instead one could use an iterative procedure to approximate the effect of the shift-invert operator in 2D, but we do not investigate such techniques here.
Numerical results for the 2D case without preconditioning are shown in Section~\ref{sec:results2D}.

\section{Numerical and performance results}\label{sec:results}
In this section, we present the results for our numerical study of the quantum mechanical three-body problem in one and two spatial dimensions.
We investigate the convergence of the three-body energies as a function of the number of grid points.
Moreover, we compare the performance of three iterative eigenvalue solvers: Krylov-Schur and Jacobi-Davidson QR with respectively without preconditioning.

\subsection{Results for the three-body problem in 1D}
\label{sec:Results_1D}
In order to compute the bound states of the three-body problem in 1D, we solve the discretized Schr\"odinger equation \eqref{eq:matrix_evp}.
To increase the accuracy at a given grid resolution, we apply the parity selection rule to the problem, in order to reduce the problem size for a given accuracy by a factor of $2^2$. This technique exploits the symmetry properties of the basis functions used for discretization by following the procedure outlined in Ref.~\cite{Trefethen}. In practice, this means that bosonic and fermionic bound states  have to be computed separately. These particular states
are characterized by even respectively odd wave functions with regard to the transformation $\vec{y}\to-\vec{y}$ corresponding to the exchange of the two heavy particles shown in Fig.~\ref{fig:3body_scheme}.

First, we determine the potential depth $v_0$ such that it corresponds to a particular two-body binding energy $\mathcal{E}_0^{(2)}$.
For this purpose, we choose a particular value of the two-body binding energy $\mathcal{E}^{(2)}=\mathcal{E}_0^{(2)}$ in the discretized version of the Schr\"odinger equation~\eqref{eq:Schroedinger_equation_two_body} in 1D and solve the generalized eigenvalue problem for the lowest eigenvalue $v_0$.
For the two-body binding energies $\mathcal{E}_0^{(2)}=10^{-1},10^{-2},$ and $10^{-3}$, the lowest potential depths $v_0$ are listed in Table~\ref{tab:2b_binding_energies}. These parameters are then used for solving the discretized three-body problem in 1D, Eq. \eqref{eq:matrix_evp}, with the Hamiltonian matrix given by Eq.~\eqref{eq:discretized_Schroedinger_equation_1D}. For bosonic and fermionic heavy particles with a mass ratio $\alpha=M/m=20$ between heavy and light particle, we include the resulting ratios $\mathcal{E}/\mathcal{E}_0^{(2)}$ of three-body and two-body binding energy in Table~\ref{tab:2b_binding_energies}. Our results coincide with the ones presented in Ref.~\cite{Happ2019threebody} and as $\mathcal{E}_0^{(2)}\to 0$ they approach the universal values shown in Table~1 of Ref.~\cite{Happ2021submitted}.

\begin{table}[h]
\caption{\label{tab:2b_binding_energies}
Computed ratio $\mathcal{E}/\mathcal{E}_0^{(2)}$ of three-body and two-body binding energy in one dimension for the case of two heavy bosons or fermions as obtained by solving the discretized Schr\"odinger equation~\eqref{eq:matrix_evp}. The calculations are performed for a mass ratio $\alpha=20$ of heavy and light particles, interacting via a Gaussian shaped potential $f(\xi)$, Eq.~\eqref{eq:Gaussian_shaped_potential}. Here the potential depth $v_0$ has been chosen such that it corresponds to a particular two-body binding energy  $\mathcal{E}_0^{(2)}$.}
\centering
{
\begin{tabular}{cccc}
\toprule
   $\mathcal{E}_0^{(2)}$    & $v_0$  in 1D  & eigenvalues: bosonic & fermionic     \\
\midrule
 $10^{-1}$        &  0.344595351    & -2.47603458  & -1.82589653\\
                  &                 & -1.41279329  & -1.18259157\\
                  &                 & -1.06093864  & -1.02845702\\
                  \midrule
 $10^{-2}$        &  0.088873721    & -2.66187629  & -1.68983501\\
                  &                 & -1.33267928  & -1.13394640\\
                  &                 & -1.03860624  & -1.00258200\\
                  \midrule
 $10^{-3}$        &  0.026134366    & -2.71516265  & -1.65622442\\
                  &                 & -1.32865305  & -1.12520220\\
                  &                 & -1.03745282  & -1.00045248\\
\bottomrule
\end{tabular}
}
\end{table}

In order to test the convergence of our results, we use a sequence of grid sizes $N_{x_1}$ and always choose $N_{y_1} = N_{x_1}/2$.
The results in Fig.~\ref{fig:spectral} confirm the excellent convergence properties of the discretization:
The relative spatial discretization error, estimated by the relative difference of the computed eigenvalues on successive grids, quickly reaches the tolerance of $10^{-12}$ set in the solver for the computation of each eigenpair.

\begin{figure}[h]
    \begin{center}
       \includegraphics[width=0.8\textwidth]{Figure2_spectral}
    \end{center}
    \caption{Relative spectral discretization error $|\mathcal{E}(N_{x_1} \times N_{y_1})-\mathcal{E}(2N_{x_1}\times 2N_{y_1})|/|\mathcal{E}(N_{x_1}\times N_{y_1})|$ for the three bosonic eigenvalues. The tolerance in the eigenvalue solver has been set to $10^{-12}$.
    \label{fig:spectral}
    }
\end{figure}

 Next, we compare the convergence behavior and running time of three methods, namely the Krylov-Schur (KS) and JDQR method, without (no-prec) and with (prec) preconditioning as described in Section~\ref{sec:precon}. In each case we exploit the tensor structure of the problem when applying the linear operator.

For different two-body binding energies $\mathcal{E}_0^{(2)}$, we present in Table \ref{tab:summarizedresults1D} a comparison of the number of iterations and matrix-vector multiplications (MVM) necessary for computing the three lowest 1D three-body bound energies shown in Table \ref{tab:2b_binding_energies} with the KS and no-prec/prec-JDQR methods. All the solvers have been set to the same tolerance $\mathrm{tol} = 10^{-12}$. The results shown here are for the bosonic heavy particles, but the behavior is very similar for fermionic ones.

Compared to KS, the no-prec-JDQR substantially reduces the number of matrix-vector multiplications, each of which in fact is an operator application of the discretized Hamiltonian, as described in Section~\ref{sec:op1D}.
This is explained by the superior convergence rate of the inexact Newton process within JDQR over the Krylov subspace iteration.
The prec-JDQR achieves an even more drastic reduction of the number of iterations and MVMs.
This is due to the fact that the correction equation can now be solved to sufficient accuracy in order to achieve locally quadratic convergence of the Newton process.
In addition to the MVM, this method requires a similar number of preconditioner applications, which have a similar cost as discussed in Section~\ref{sec:precon}. As a consequence of the fast convergence, the running time required to find the eigenvalues is significantly reduced, as shown in Fig.~\ref{fig:runnungtime}. In this work a Matlab implementation of our methods was used and the Matlab-command \texttt{eigs} implemented the KS method.

\begin{figure}[h]
    \begin{center}
       \includegraphics[width=0.8\textwidth]{Figure3_runningtime}
    \end{center}
    \caption{Comparison of running time for computing the three bosonic bound states for the case of $\mathcal{E}_0^{(2)} = 10^{-2}$ with the KS, no-prec-JDQR, and prec-JDQR methods.
    \label{fig:runnungtime}
    }
\end{figure}

\input{combined_table_iterations}

\subsection{Preliminary results for the three-body problem in 2D\label{sec:results2D}}

The aim of this section is not to provide conclusive results for the three-body problem in 2D. Instead, we highlight the viability of our approach to study this system.
We have developed a multi-threaded C++ implementation of the model and techniques described to evaluate the feasibility of simulations in 2D.
The dense linear algebra operations are provided by Intel MKL (version 2020.4.304) and the JDQR method by phist~\cite{Thies2020phist}, version 1.9.6.
The backend used within phist is the Trilinos library Tpetra~\cite{trilinos}, version 13.0.1.

Our discretization scheme uses $N_{x_1}=N_{x_2}=N_x$ points in the $x_1$ and $x_2$-directions, and $N_{y_1}=N_{y_2}=N_y$ points in the $y_1$ and $y_2$-direction, leading to a total problem size of $N=N_x^2N_y^2$, where we choose again $N_y=N_x/2$.
The numerical simulations are run on an Intel Xeon server with 20 cores and 128 GB of RAM. For the $(128\times 64)^2$ grid, computing ten digits of the lowest eigenvalue took about one hour at $\mathcal{E}_0^{(2)}=10^{-2}$.

We consider the mass ratio $\alpha=1$ and the two-body binding energy $\mathcal{E}^{(2)}_0=10^{-1}$, respectively $10^{-2}$, for which we have calculated the corresponding value $v_0$ for the Gaussian interaction potential as shown in Table~\ref{tab:2b_binding_energies_2D}.
For this situation, we expect only one bound state as $\mathcal{E}_0^{(2)}\to 0$, with an energy of approximately $2.39\ \mathcal{E}_0^{(2)}$~\cite{Brodsky2006} or $2.36\ \mathcal{E}_0^{(2)}$~\cite{ Pricoupenko2010}.
Our numerical results are summarized in Table~\ref{tab:2b_binding_energies_2D}.
The computed values of the three-body binding energy, relative to $\mathcal{E}_0^{(2)}$, indicate convergence for the value $\mathcal{E}_0^{(2)}=10^{-1}$ to at least eight digits.
For the smaller value $\mathcal{E}_0^{(2)}=10^{-2}$, the lowest eigenvalue is approaching the expected universal limit value of approximately $-2.4$.
Decreasing $\mathcal{E}_0^{(2)}$ to get closer to this value in turn requires a larger computational domain and thus more grid points in order to accommodate the bound states.
\begin{table}[h]
\caption{\label{tab:2b_binding_energies_2D}Preliminary results for the lowest eigenvalue $\mathcal{E}/\mathcal{E}_0^{(2)}$ of the three-body problem in 2D with mass ratio $\alpha=1$ for successively refined grids.}
\centering
\begin{tabular}{crrrrrr}
\toprule
  $\mathcal{E}_0^{(2)}$    & $v_0$ in 2D & $(32\times 16)^2$ & $(64\times 32)^2$ & $(128\times 64)^2$ & $(144 \times 72)^2$ & $(160 \times 80)^2$\\
\midrule
 $10^{-1}$ &  0.947343916     & -1.9012589  & -2.1984679  & -2.1999578  & -2.1999578 & -2.1999578 \\
 $10^{-2}$ &  0.482727283     &     -       & -1.9337722  & -2.2878081  & -2.3021863 & -2.3081557 \\
\bottomrule
\end{tabular}
\end{table}

We consider two improvements of our current implementation to enable such simulations:
First, it may be possible to exploit the parity rule (as in the 1D case) to reduce the problem size for a given accuracy by a factor of $2^4$. The details have to be clarified, though.
Second, hybrid shared/distributed memory parallelization should allow us to increase the grid size by a factor four in each direction (problem size by a factor 256) on a cluster with a few hundred nodes.
In order to go to very small binding energies (large grid sizes), an alternative may be to enforce a low-rank structure on the occurring vectors in order to reduce the memory requirement for vectors in a similar way that we have used to reduce the memory requirement for the operator in this paper.

\section{Conclusion and outlook}
\label{sec:conclusion}

In this article, we have considered a quantum system of two heavy particles interacting with a light one in both 1D and 2D. Pseudo-spectral methods and (rational) Chebyshev polynomials have been applied to create a fast converging discretization scheme for the Hamiltonian. Moreover, we have presented a novel method to exploit the tensor structure of the discretized Hamiltonian in iterative eigensolvers. The improved hardware efficiency of our tensor-based implementation is expected to deliver a speed-up of about a factor 100 when compared to the sparse matrix representation used in previous studies of the three-body problem.

Based on the direct solution of a Sylvester equation, we have developed an effective preconditioning strategy for the 1D problem. This preconditioner is then applied to accelerate a Jacobi-Davidson QR iterative eigensolver.
Our numerical simulations confirm the convergence rate of the discretization and demonstrate an improvement of orders of magnitude in the time-to-solution for the preconditioned Jacobi-Davidson method over previously used Krylov methods. Combined with the additional factor of 100 resulting from the increased hardware efficiency of our implementation, this will allow studying the three-body problem more thoroughly then before.

To enable extensive numerical simulations of the 2D problem in the future, we will follow the paths identified above, namely exploiting symmetry, hybrid parallelization and low-rank approximation. As an outlook, the three-body problem in 1D and 2D can also be investigated with a focus on the computation of bound and resonant states embedded in the continuous spectrum. The methods developed in the present article will strongly support this endeavor.

\bibliographystyle{unsrt}

redpajama_set_name: RedPajamaArXiv


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The "Cinghiale" (Italian for Wild Boar) Vineyard is named for the frequent inhabitants of the property, and was purchased in 2005. It is located in the recently approved AVA, Ft Ross-Seaview AVA. Overlooking the Pacific Ocean, it consists of 359 acres at the top of King's Ridge in the Sonoma Coast appellation, and is planted with 43 acres of Pinot Noir, Syrah, Chardonnay, and Sauvignon Blanc. In an effort to highlight the award-winning terroir, it features a variety of Pinot Noir and Chardonnay clones with lineages hailing from the top vineyards in Burgundy and top-rated clones from its neighbors in California.
Read more about the Ft Ross-Seaview AVA here.
This full bodied Pinot Noir pairs well with pork, lamb and poultry. But don't be afraid to serve with game meats like wild boar or bison. Pair also with fish, heavier pasta dishes and grilled vegetarian items. Medium-hard cheeses such as Gouda, Gruyere, and Cheddars are also excellent pairings.


Below are 17 drills (& some games) designed to practise individual penalty killing skills. How these drills are used is up to the imagination of the coach. They can be done as individual drills before or after practise or they can be done is stations.
It is important that the coach stress the fundamentals of killing penalties. Stop players often to correct them and give them feedback. Your penalty killing can be the difference in winning and losing!
Come join Coach Enio Sacilotto, Assistant Coach, Victoria Royals, President, International Hockey Camps this summer for his specialized summer camps Victoria, BC, Nanaimo, BC, North Delta, BC, Coquitlam, BC and Burnaby Winter Club. Coach Enio has over 35 years of coaching experience including 20 years coaching professional elite senior leagues in Europe. Call Coach Enio at 604 255 4747 or email at enio@coachenio.com and visit website for free articles and drills.


Lavender Pics Lavender Flowers Free Pictures On Pixabay Uploaded by pixane on Wednesday, February 21st, 2018 in category Images.
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text:
Regional Powers Getting Active in Afghan Solution
Cambodia Compares Thai Government to Nazis, Calls for Action To Stop War
Challenges Facing China's Great Water-Transfer Project
Don't Accept a Bribe Until You've Checked the Envelope
From Volume 37, Issue 32 of EIR Online, Published Aug. 20, 2010
Asia News Digest
Aug. 10 (EIRNS)—Iran, India, and Russia have begun parleying on how to stabilize Afghanistan once the U.S. and NATO call it quits in the war in that country. These three, along with some others in the region, are trying to work out a regional plan for post-war Afghanistan.
Indian Foreign Secretary Nirupama Rao held talks with Russian First Deputy Foreign Minister Andrei Denisov in Moscow on Aug. 4, sources told Indo-Asian news Service (IANS). The Russian side reportedly briefed Rao about President Dmitri Medvedev's plan to hold a trilateral summit later this month with Pakistani President Asif Ali Zardari and Afghan leader Hamid Karzai.
"Both India and Russia are inching closer to a regional approach and have shared interests in preventing a Taliban takeover after the U.S. troops leave," Arun Mohanty, an expert on India-Russia relations, told IANS.
Meanwhile, U.S. Sen. John Kerry (D-Mass.) chairman of the Senate Foreign Relations Committee, in an interview with Fareed Zakaria, posted on the Real Clear Politics website on Aug. 1, said he is against deployment of more troops, and he believes "the answer is a political resolution and that political resolution has to come about by engaging to a greater degree with India, with Pakistan itself. But I think we should also engage China, Russia, and I would say to you that the possibility could exist even of Iran playing a role in helping to change the equation on the ground." He insisted that he would talk to Iran, since "they don't like the Taliban. They don't like narcotics being transited. There are reasons that they would want a stable government there."
Iran too has stepped up diplomatic efforts. Deputy Foreign Minister Mohammad Ali Fathollahi, who was in India Aug. 5-7, had talks at the Indian Foreign Office and claimed that New Delhi and Tehran "enjoy a close viewpoint on Afghanistan." But Iran does not share India's concern that Pakistan's army and the ISI intelligence services might foist themselves on Afghanistan once the international security forces by 2014. Unlike New Delhi, Tehran wants the forces to leave Afghanistan as soon as possible. Fathollahi said Tehran was also deepening "trilateral dialogue" with Afghanistan's partners and was pursuing talks with Tajikistan, Pakistan and India.
Aug. 14 (EIRNS)—The Cambodian government today warned that the government in Thailand is preparing to launch a war on Cambodia, and compared Thailand's methods to those of the Nazis. The Cambodian Council of Ministers' statement accuses Thai Prime Minister Abhisit Vijjajiva of attempting to "intoxicate" the population to win their support "to take the Cambodian territory by force." It points to Abhisit's statements at a Yellow Shirt rally of his supporters (which Abhisit attended even though the rally was illegal under his emergency rule!), where he called for abdicating the long-standing agreement between Thailand and Cambodia that acknowledges Cambodian sovereignty over a contested area on the border, and said that military means will be used when deemed necessary. The Cambodian statement ridicules Abhisit's claim that he was misquoted, asking why he had not corrected the entire Thai press corps for reporting exactly those words.
Further, it points to the Thai use of a map which has long been rejected by international tribunals as "the same methods as the Nazis under Hitler and the Fascists under Mussolini had perpetrated during World War II when they wanted to invade and occupy foreign lands."
Aug. 8 (EIRNS)—China's "Move South Water North" project, the greatest such project being constructed in the world, is facing the challenges of building infrastructure on this scale in a densely populated and economically underdeveloped nation. China being China, however, and despite a recent spurt of nasty criticism in the western press, this work, planned over the past 50 years, is making real progress. The same western critics are still violently attacking the Three Gorges Dam, which is helping control some of the worst floods in China in many decades.
Preparatory work for the South-North project included climate studies by the Chinese Academy of Sciences, which showed that northern China was a much greener region 5,000 years ago. The goal of the project is to reverse millennia of expanding desertification in that region.
The Move South Water North project is being built to bring water from China's biggest river system, the Yangtze and its tributaries, to the much more arid northern plain, one of three large population areas, and China's wheat belt. Lack of water is hindering development in this region, not only in agriculture, but also the development of cities and industry.
China, which has a population five times the size of the United States in a similar-sized territory, is planning to become more than 50% urbanized within the coming 10 years, which will mean that some 200-300 million more people will be moving to China's cities. This will greatly increase water consumption overall.
The easternmost route of the project has been under construction since 2002. It is one of what will be three planned, 1,000-km man-made rivers, including dams, locks, and tunnels to move the water. When the first two man-made rivers are completed by 2014, they will carry 8 trillion gallons of water a year. The easternmost river follows the same route of China's ancient Grand Canal, including a huge tunnel under the Yellow River in Shandong province, to take water to the area of Beijing and Tianjin.
Second is the serious issue of water pollution. On July 6, China Daily reported that the poor quality of the water along the eastern route is causing real problems. Much lower energy and industrial efficiency are big issues for developing nations such as China, exacerbated by the huge scale of population size and density—issues which can only be resolved by rapid development of nuclear energy and other advanced technologies.
The national director of the South-North water project, Zhang Jiyao, announced that "there is still a long way to go before local authorities transform the eastern route into a clean-water corridor," meeting the minimal requirement of Grade 3, drinkable, treated water. Thousands of highly polluting small plants have been shut down along the route, and hundreds of pollution-control facilities, including water treatment plants, man made wetlands, and upgraded urban and rural sewage systems, have been built or are under construction. But water quality met the Grade 3 standard only in two-thirds of the existing truck canals, demonstrating the need for rapid advance of technology in China and the rest of the world.
Aug. 14 (EIRNS)—In May of this year, Indonesian President Susilo Bambang Yudhoyono signed a letter of intent with the Norwegian government to suspend any new development in the country's natural forests and peat lands for two years. "With the agreement, Indonesia will receive $1 billion in grants in phases from Norway to reduce emissions," according to the Jakarta Post at the time.
The official Indonesian press agency Antara reported yesterday that the bribe money will be slightly delayed.
After a meeting with Norwegian Ambassador Elvind S. Homme on Aug. 12, Indonesian Economic Coordinating Minister Hatta Rajasa reported, "The first-phase withdrawal was supposed to be $200 million [in 2011], but it was finally agreed at $30 million [to be realized in 2014], and we will make gradual withdrawals up to $1 billion."
So the grant becomes a loan; $200 million becomes $30 million, and 2011 becomes 2014. Remember, get your money up front when you sell your country out to the Greenies.


Lentil Pasta With Roasted Vegetables is vegan, gluten free and diary free.
Lentil Pasta With Roasted Vegetables & Jalapeno Cream has amazing flavor and is also, filling and nutritious. I have recently been introduced to lentil pasta, and was pleased to find out that the lentil pasta has 13 grams of protein which is great for a vegetarian or vegan diet. The roasted vegetables have vitamins and minerals, the jalapeno cream brings the kick, and the whole dish is dressed up with toasted pistachios and sweet cranberries. This recipe is perfect for dinner, lunch and is great for left-overs. Vegan, gluten free and dairy free.
Lentil Pasta With Roasted Vegetables and Jalapeno Creme. Vegan, gluten free, dairy free.
4 cups of frozen harvest vegetables my vegetables have sweet potatoes, parsnips, red onion, orange and yellow carrots.
Drizzle olive oil and maple syrup .
Bake at 400 degrees for 30 minutes, turning at 15 minutes.
Add drained pasta to bowl. Mix roasted vegetables in.
Top with toasted pistacios and dried cranberries.


Bus 568 is a Scania K320UB 4x2 (Euro VI) based at Tuggeranong Depot.
Bus 568 was delivered to Woden Depot on 1 May 2015.
In 2016 its DL2 bike rack was replaced with a VeloPorter 2.
In (apx) February 2019, it was fitted with a DL2 (black handle) model bike rack.
This page was last modified on 6 March 2019, at 12:05.


Take to the trails with confidence in the Moncler RENALD Military green shoe.
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text:
using Microsoft.Extensions.DependencyInjection;
using OrchardCore.BackgroundTasks;
using OrchardCore.Modules;
using OrchardCore.Workflows.Helpers;

namespace OrchardCore.Workflows.Timers
{
    [Feature("OrchardCore.Workflows.Timers")]
    public class Startup : StartupBase
    {
        public override void ConfigureServices(IServiceCollection services)
        {
            services.AddActivity<TimerEvent, TimerEventDisplay>();
            services.AddSingleton<IBackgroundTask, TimerBackgroundTask>();
        }
    }
}


text:
import tinyreq from 'tinyreq';

export async function scrapeByUrl(url, parser) {
  return new Promise((resolve, reject) => {
    tinyreq(url, (error, body) => {
      if (error) reject(error);
      resolve(parser(body))
    });
  })
}


text:
A simple messaging processor for AMQP

[![npm package](https://img.shields.io/npm/v/peleg.svg?style=flat-square)](https://www.npmjs.org/package/peleg)
[![build status](https://img.shields.io/travis/gabrielmoreira/peleg/master.svg?style=flat-square)](https://travis-ci.org/gabrielmoreira/peleg)
[![dependency status](https://img.shields.io/david/gabrielmoreira/peleg.svg?style=flat-square)](https://david-dm.org/gabrielmoreira/peleg)

Installation
------------

```sh
npm install peleg --save
```

How to use
--------------------

```js
var peleg = require('peleg'),
   Promise = require('bluebird');

peleg.connect().then(function() {
   peleg.queue("notification:send").publish({message: "Hello World!"});

   peleg.queue("notification:send").process(function(data) {
      console.log("Received", data.message);
      return Promise.resolve();
   })
});

```

Samples
-------

[Basic sample](examples/peleg.basic.js)

[Multiple queue bindings](examples/peleg.binding.js)

[Advanced sample](examples/peleg.advanced.js)

Roadmap
-------

- [ ] Support two connections: Publish connection, and process connection.

- [ ] Peleg RPC:
```javascript
peleg.call('calculator.add', 1, 2).then(function(sum) { console.log(sum); });
peleg.service('calculator.add').process(function(data) { return data[0] + data[1]});
```


text:
Website Designed and Maintained by Artisan Media Studio
Website Hosted by 3rd Alternative, Inc.
© 2019 3rd Alternative, Inc., All Rights Reserved
© 2019 Roy Davies, Inc., All Rights Reserved
"1964" The Tribute is not endorsed by or affiliated with Apple Corps, Ltd.
'64 Store
DO YOU WANT TO PLAY THEM?
In October of 2016 I get this email from a good friend of mine from Liverpool, Kenny Heague…'Hey Mark! Is this still your email?'
I immediately emailed back, 'KENNY!!! Yes, this is still me! Long time no see. How's things with you?'
He writes back, 'Wait till you see the pics I'm sending you, tonight!'
We met Kenny in the late 80s when we were touring in Canada. He was working for the sound company on the tour and we hit it off straight away, as they say.
A few years passed and we caught up with him again but this time he was working in Indianapolis, Indiana as the assistant to Jim Irsay, the owner of the Indianapolis Colts.
As many people know, Jim is a huge music fan and gear head. He has acquired some of the most impressive and significant celebrity owned instruments in rock history, including but not limited to:
Ringo Starr's 1963 Ludwig Black Oyster Downbeat drum kit,
The Beatles bass drum head from their first Ed Sullivan show performance,
John Lennon's 1964 red Rickenbacker 1996 guitar.
1963 orange Gretsch 6120 guitar.
Vox prototype guitar.
George Harrison's 1964 GIbson SG guitar.
George Harrison's Harptone acoustic 12-string guitar.
So, the next email I get from my scouse friend, Kenny, has him sitting on Ringo's drum set with a huge smile on his face, and the caption was: 'Not bad for a kid from Liverpool to finally be sitting behind Ringo's Drums!!!'
Of course, I'm blown away and fired back: 'LUCY…you got some 'splainin' to do!!!' In the following phone calls I found out about all the instruments in Irsay's collection and Kenny said he could set up a tour for us the next time we were in Indy.
On February 17th, 2017 we had a sold out show at The Palladium on the north side of Indianapolis. True to his word, Kenny set us up with Chris McKinney, who is in charge of the Irsay guitar collection
and we toured the facility on the afternoon of our performance.
Mark Benson with John Lennon's 1964 red Rickenbacker 1996 guitar.
Chris is as big a fan of vintage guitars as anyone and was thrilled to show us the Beatles instruments in the collection. The room is beautifully done with display cases for the guitars and a small riser for the drum set with an Ed sullivan backdrop that has a video screen right in the middle playing Beatles live clips.
We were all a bit gobsmacked just looking at these instruments that we'd seen thousands of times in videos, and then Chris says…
Unbelievable day!
Huge Thanks to Chris McKinney for being so gracious, and to my pal, Kenny Heague…'Thunderbirds are go, mate!!!'
Mark Benson
"Seeing and playing Ringo's 1st drum set was a dream come true. Being asked to tune them was unbelievable! I just happened to have a drum key in my pocket that day. Hmmmm...... Fate!!!"
Bobby Potter
"Jim Irsays's collection of Beatles instruments...
...I was literally speechless! So generous of him!"
Tom Work
"It was just unbelievable! To see and play such iconic, history making instruments was an unexpected, once in a lifetime treat."
Mac Ruffing


text:
RIDE stop yields cocaine, methamphetamine and charges for two in North Grenville
Zandbergen photo, Nation Valley News
NORTH GRENVILLE — A RIDE program conducted last week by the Grenville OPP in Bishop Mills resulted in two arrests and seizure of drugs. On January 20th, shortly after 6:15 p.m., officers pulled over a vehicle on County Road 18. While speaking to the driver, officers smelled freshly smoked cannabis and decided to search the vehicle, where they found drug paraphernalia, a quantity of cocaine, methamphetamine and, cannabis.
The detachment reports that Jeffrey Jessome, 41, from Cardinal and Brooke Fawcett-Renaud, 26, from Edwardsburgh were both charged with:
Possession of a schedule one substance for the purpose of trafficking-cocaine
Possession of a schedule one substance for the purpose of trafficking – methamphetamine
Jessome received the additional charge of failure to comply with undertaking, while Fawcett-Renaud received the additional charge of operation while impaired – alcohol and drugs, according to the Grenville OPP.
Minor injuries after snowmobile collision
AUGUSTA — On January 23rd at around 1:30 p.m., Grenville OPP officers responded to a snowmobile collision on a trail two kilometres west of Maple Hill Road in Augusta Township. The 46-year-old driver from Oxford Station, was transported to the hospital with minor injuries.


text:
Q: Set Windows system time from command line similar to Linux rdate command I need to set the time on a Windows 2008 server via an internet clock server from a command line, and ensure that Windows 2008 doesn't do it by itself.
I will use this for a .cmd file which looks like this:
:start
RunApp
SetSystemTimeViaInternet
goto start

The purpose is to ensure, that the server has the correct time, but that the time doesn't change while the app is running.
I tried to look at w32tm and "net time", but none of those seem to work. Any ideas?

A: Install and configure NTP to synchronize to your external server(s). I suppose NTP is already in Windows 2008.
NTP corrects the time in very little steps, so you won't notice it and you will have always the right time.
Or what do you really mean with "the time doesn't change while the app is running" ? Do you want to stop the system clock? This is probably not possible ...

redpajama_set_name: RedPajamaStackExchange


I have used Soholaunch to build my new website: dingoswildgreetingcards.com and everything seems to be working except the search bar.
The traffic stats function also freezes and I cannot look at by day, by hour etc.
I have used webmaster to establish meta tags and (pardon my ignorance - I am a techno dummy) I don't know how to do that with the search bar. Do I have to create a data table to which it refers?
I've tried using simple words like card and greeting and good etc. but I keep getting the no results message and get taken to the whole list of 43 products.
Please help and let me know what I can do to improve the site.


text:
Q: Can spark ignore unreadable files? I have a file structure in the following form
s3://<bucket>/year=2018/month=11/day=26/hour=10/department=x/part-xxxxx.gz.parquet
My AWS Credentials do NOT have access to all the department= values, only a few.
I'm trying to perform
df = spark.read.parquet("s3://<bucket>/year=2018/")

And that fails with
java.io.IOException: Could not read footer: java.io.IOException: Could not read footer for file FileStatus{path=s3://<bucket>/year=2018/month=11/day=26/hour=10/department=yyyyyy/part-xxxxx.gz.parquet; isDirectory=false; length=104448; replication=0; blocksize=0; modification_time=0; access_time=0; owner=; group=; permission=rw-rw-rw-; isSymlink=false}

It fails obviously because I can only access department=x and not department=yyyy, my question is : is there a way to just silently ignore those?
My current workaround is to construct only valid paths like this:
   tmpl = 's3://<bucket>/year=2018/month=11/day=26/hour={hour}/department=x/'
   df = spark.read.parquet(*list(tmpl.format(hour=hour) for hour in range(1,24)))

which is very cumbersome because

*

*some paths may not exists (missing data for some hours, etc).

*spark.read.parquet does not take a list or a generator as input, so I'm forced to use the splat/unpack operator to convert everything to individual arguments. Not sure if that works ok with thousands of paths.

Is there a better way to load this data without a changing the file structure (which I do not control)?

A:
It fails obviously because I can only access department=x and not
  department=yyyy, my question is : is there a way to just silently
  ignore those?

as per file status object you have read write access ( permission=rw-rw-rw-) to the file you mentioned in the log. It might be other issue with file path.

java.io.IOException: Could not read footer: java.io.IOException: Could
  not read footer for file
  FileStatus{path=s3:///year=2018/month=11/day=26/hour=10/department=yyyyyy/part-xxxxx.gz.parquet; isDirectory=false; length=104448; replication=0; blocksize=0;
  modification_time=0; access_time=0; owner=; group=;
  permission=rw-rw-rw-; isSymlink=false}

From the above error you are passing fileStatus object in string format which is not correct.
you have to pass fileStat.getPath.toString i.e. in your case path=s3:///year=2018/month=11/day=26/hour=10/department=yyyyyy/part-xxxxx.gz.parquet;
df = spark.read.parquet(...) will work.
if you want to pass folder of parquet files you can pass.
or you want filter certain files below example code scala snippet you can use
/**
    * getAllFilePath.
    *
    * @param filePath Path
    * @param fs       FileSystem
    * @return list of absolute file path present in given path
    * @throws FileNotFoundException
    * @throws IOException
    */
  @throws[FileNotFoundException]
  @throws[IOException]
  def getAllFilePath(filePath: Path, fs: FileSystem): ListBuffer[String] = {
    val fileList = new ListBuffer[String]
    val fileStatus = fs.listStatus(filePath)
    for (fileStat <- fileStatus) {
      logInfo(s"file path Name : ${fileStat.getPath.toString} length is  ${fileStat.getLen}")
      if (fileStat.isDirectory) fileList ++= (getAllFilePath(fileStat.getPath, fs))
      else if (fileStat.getLen > 0 && !fileStat.getPath.toString.isEmpty) {
        logInfo("fileStat.getPath.toString" + fileStat.getPath.toString)
        fileList.foreach(println)
        fileList += fileStat.getPath.toString
      } else if (fileStat.getLen == 0) {
        logInfo(" length zero files \n " + fileStat)

        // fs.rename(fileStat.getPath, new Path(fileStat.getPath+"1"))
      }
    }
    fileList
  }

like this example
    val fs = FileSystem.get(new URI(inputPath), spark.sparkContext.hadoopConfiguration)
 yourFiles = getAllFilePath(new Path(inputPath), fs)

val df = spark.read.parquet(yourFiles:_*)


text:
WALSH: Explaining Progressive Gender Theory To Right Wi...
Rep. Meadows: New Info Suggests Fusion GPS Anti-Trump R...
Chelsea Clinton Received $300k As An IAC Board Member &...
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Sex Trafficking Ringleader 'Lured Young Women Through Fake Charity Website'
Posted by Katabella Roberts | Dec 11, 2019 | Epoch Times | 0 |
https://www.theepochtimes.com/sex-trafficking-ringleader-lured-young-women-through-fake-charity-website_3171041.html
A Florida man and his two female accomplices are facing federal charges for their alleged involvement with a sex trafficking organization, the U.S. Department of Justice said.
William D. Foster, 48, of Delray Beach, Ashleigh Holloway, 36, of Fort Lauderdale, and Hanah Chan, 30, of Delray Beach, were charged in an indictment on Dec. 9 for allegedly luring women and girls through a fake website then forcing them into prostitution.
Foster faces three counts of sex trafficking by force, along with charges of conspiracy to sex traffic minors, sex trafficking of a minor and transportation of an individual for prostitution.
Holloway and Chan were charged with one count of sex trafficking by fraud and coercion, and Chan was also charged with one count of transportation of an individual for prostitution.
According to court documents, Foster was the alleged ringleader of the sex trafficking organization and is believed to have used a fake website, www.fosterscareinc.com, to facilitate the alleged trafficking by force, fraud or coercion.
Law enforcement seized the website on Nov 21, which masqueraded as a nonprofit charity to help women escape the sex trade, The Palm Beach Post reports.
The website, which is no longer open to public access, claimed to offer free help to victims of sex trafficking in the form of housing, therapy, medical treatment, job training, and police assistance, the publication says.
Court documents allege that Fosters' victims were all moved to different states to be trafficked and provided with false identities.
Foster had between five and fifteen females living and working for him at any given time. They also worked at exotic dance venues in Miami-Dade, Broward, and Palm Beach Counties and engaged in commercial sex at Foster's request, the documents state.
The victims were not allowed to keep any of the money they made from the exotic dancing and prostitution and were forced instead to give money to Foster, who promised to invest their earnings.
One of the victim's said they were recruited into Foster's sex trafficking organization in or around Aug. 2007 as a minor, and commercially sex trafficked by Foster both as a minor, and then as an adult, from Nov. 2007 to May 2010.
Another of Foster's victims was allegedly recruited into his organization and was commercially sex trafficked from May 2004 to Aug. 2011.
The court documents allege that he also regularly engaged in sex with the victims when they were still minors, and there were a number of domestic violence incidences reported by the victims who lived with him.
Foster allegedly preyed on girls who were in group homes, homeless shelters, or strip clubs, and lured them in with the promise of wealth before forcing them to diet and sell their bodies. He even paid for them to have cosmetic surgery, including breast augmentation and nose jobs, according to The Palm Beach Post.
Court documents state that officials were notified of Fosters' activities when a third victim contacted law enforcement in 2019 because she was being pressured to engage in commercial sex by Foster and his organization after being flown from Fort Lauderdale, Florida, to Detroit, Michigan.
Foster was detained on Nov 19 and remains in custody pending trial. Holloway and Chan are scheduled to have their pre-trial detention hearings on Dec. 13, 2019, and to be arraigned on Dec. 19, 2019.
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text:
Q: Normal regular sequence in noncommutative algebras Does anyone know anything about the normal regular sequences in the quantum plane?
Here are the definitions:
Normal regular sequence: Let $R$ be a ring (not necessarily commutative). A sequence $x_1, \ldots, x_n$ is a normal regular sequence in $R$ if
1) $x_1$ is a normal, regular element in $R$, and
2) $x_i$ is normal, regular element in $R/(x_1, \ldots, x_{i-1})$ for all $2 \leq i \leq n$.
Quantum plane: A $k$-algebra generated by $x, y$ subject to the relation $yx = qxy$, denoted by $k_q[x, y]$, that is,
$$k_q[x, y] = \frac{k\langle x, y\rangle}{(yx - qxy)}. $$
Here $q\in k$ is a primitive root of 1.
The length of any regular sequence in $k_q[x, y]$ is no more than 2, and I know there is some result about such normal regular sequence when $x_1, x_2$ are homogeneous elements. But anything else?
Thanks,

A: This should probably be a comment, since it is too basic an observation. Suppose that the elements $f,g\in k_q[x,y]$ are both normal in $k_q[x,y]$ (this, at least a priori is more restrictive than you want). Then, as in the answer of J.Gaddis here, there exist $a,b,c,d$ such that all monomials $x^iy^j$ appearing in $f$ have $i\equiv a\pmod{\ell}$ and $j\equiv b\pmod{\ell}$, and all monomials $x^iy^j$ appearing in $g$ have $i\equiv c\pmod{\ell}$ and $j\equiv d\pmod{\ell}$. Therefore, $gf=q^{ad-bc}fg$. This suggests that the usual Koszul complex criterion would be modifiable for this case: define
 $$
B=k\langle X,Y\mid X^2=Y^2=YX+q^{ad-bc}XY=0\rangle,
 $$
and define a structure of a chain complex on $k_q[x,y]\otimes B$ as
 $$
d(h(x,y))=0, d(h(x,y)X)=h(x,y)f(x,y), d(h(x,y)Y)=h(x,y)g(x,y),
 $$
and
 $$
d(h(x,y)YX)=h(x,y)g(x,y)X-q^{ad-bc}h(x,y)f(x,y)Y.
 $$
In this case, it seems to be fairly straightforward to prove that this complex is acyclic in positive homological degrees (we of course put the homological degrees of $X$ and $Y$ to be equal to $1$; homology in degree zero is $k_q[x,y]/(f,g)$) if and only if $f$ and $g$ form a regular sequence. Maybe that helps.

A: Let $g \in k_q[x,y]$ be normal with $q$ a primitive $\ell$th root of unity, $q \neq 1$. Then $g = \sum c_i y^{m_i} x^{n_i}$ where $c_i \in k^\times$ for all $i$ and $m_i \cong m_j\mod \ell$, $n_i \cong n_j\mod \ell$ for all $i,j$.
It's not hard to see that such elements are normal. Checking that these are all the normal elements requires a bit of computation, and it helps to know that $Aut(k_q[x,y])=(k^\times)^2$  unless $\ell=2$, in which case there is an additional automorphism switching the generators.
I'm not sure what this means in terms of finding a regularizing sequence, but of course your second element must now be in $k_q[x,y]/gk_q[x,y]$.


The pink and brown kits were out in numbers this morning at King George's Fields, as the 2018-19 season began. This year marks the 30th anniversary of the founding of the Corinthian-Casuals F.C. - Youth Section, as after 106 years as a nomadic club, we found a home in Tolworth in 1988 and put down roots. Since then thousands of players have proudly worn the pink and brown and represented this famous club!
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