text:
About Essay Contests
Enlisted Prize
NPS Foundation
The Proceedings Podcast
U.S. Naval Institute Blog
American Sea Power Project
Contact Proceedings
Vol. 24/4/88
Back to Proceedings Home
P Article
The Mine Defense of Santiago Harbor
Lieutenant E. E. Capehart, U. S. Navy
The entrance to the harbor of Santiago, where ships of any considerable draft can navigate, is scarcely more than one hundred and twenty-five yards wide, in its narrowest places, and ...
Pyro-Collodion Smokeless Powder - Part II
Professor D. Mendeléef
(Translated from the Russian by Lieutenant John B. Bernadou, U.S. N.)The "combustion" of a powder is the union of the carbon and hydrogen of the mixture or compound with the ...
Diseases of Electrical Installations in the Navy: Their Causes and Remedies
Lieutenant B. T. Walling, U. S. N.
(From lectures delivered before the U. S. Naval War College—Concluded from No. 86.)Fig. 31 is a correction to Fig. 17 which inadvertence in transmission is made to represent a C ...
The Secondary Battery
Lieut. F. K. Hill, U. S. Navy
During the late war with Spain the writer was on the Iowa and had command of the secondary battery on the upper deck—sixteen 6-pounders and two 4-inch R.F.So much has ...
Naval Reserves and Naval Volunteers
Lieutenant R. C. Smith, U. S. Navy
To naval readers it is not necessary to expatiate on the experiences of Naval Reserves in the late war. The fleet was largely increased and it was necessary to man ...
Views of Admiral Cervera Regarding the Spanish Navy in the Late War
Richardson Clover, Chief Intelligence Officer
INTRODUCTORY.Under the title "Vindication of the Navy," there appeared in the La Epoca, Madrid, November 5, 1898, this article, which is made up mainly of extracts from letters from Admiral ...
Comments of Rear-Admiral Plüddemann, German Navy, on the Main Features of the War with Spain
M. Plüddemann, Rear-Admiral, German Navy
INTRODUCTORY.This able analysis of the main features of the Spanish-American war by M. Plüddemann, Rear-Admiral, German navy, presents in a comprehensive form many of the technical deductions of the late ...
Russian Views of Our War.Admiral Makaroff's Views of the Lessons of Santiago.Rely on your Guns - Never Sacrifice Artillery to Armor - The Sword Always Mightier than the Shield ...
Publishing Notice
The next number of the Institute Proceedings, issued the last of March, will contain the following articles:THE ST. LOUIS AS AN ARMY TRANSPORT.By her Commanding Officer, Captain C. F. Goodrich ...
Bibliographic Notes
[American.]CASSIER'S MAGAZINE.November, 1898. Mechanical Draught for Steam Boilers. Compressed Air on Warships. The Distilling Ship Iris for the United States Fleet.December. High Explosives in Naval Warfare. Early Marine Engine Construction ...
Officers of the Institute
President.Rear-Admiral WILLIAM T. SAMPSON, U. S. Navy. Vice-President.Rear-Admiral F. V. McNAIR, U. S. Navy. Secretary and Treasurer.Lieutenant GEORGE F. COOPER, U. S. Navy. Board of Control.Lieut.-Commander RICHARD WAIN WRIGHT, U ...
Special Notice: Naval Institute Prize Essay, 1899
A prize of one hundred dollars, with a gold medal, is offered by the Naval Institute for the best essay presented on any subject pertaining to the naval profession, subject ...
The U. S. Naval Institute was established in 1873, having for its object the advancement of professional and scientific knowledge in the Navy. It now enters upon its twenty-sixth year ...
The U.S. Naval Institute is a private, self-supporting, not-for-profit professional society that publishes Proceedings as part of the open forum it maintains for the Sea Services. The Naval Institute is not an agency of the U.S. government; the opinions expressed in these pages are the personal views of the authors.
Digital Proceedings content made possible by a gift from CAPT Roger Ekman, USN (Ret.)
About the Naval Institute
Naval History Magazine
Naval Institute Foundation
Photos & Historical Prints
Naval Institute Archives
Sign up to get updates about new releases and event invitations.
Example NewsletterPrivacy Policy
Copyright © 2022 U.S. Naval Institute Privacy PolicyTerms of UseContact UsAdvertise With UsFAQContent LicenseMedia Inquiries
Powered by Unleashed Technologies


A question that I've been asked several times over the course of working towards my CCIE has been, "What is your motivation to do this?" I've even asked myself this question, but the answer hasn't been what I expected after I really analyzed it, but it has helped me gain a new awareness and insight into how powerful motivation is in driving towards goals in life.
My motivation has changed since I initially started studying over a year ago. In the beginning, I viewed it as the pinnacle of where I wanted to be in my career. I thought of the CCIE as proof that I had a certain set of knowledge, and that it would look good on my resume if I ever needed it. As I progressed in my studies, waking up at 4am M-F so that I could get 3 hours of study time in before work, along with numerous hours on the weekends, my perspective changed. I began to enjoy the journey, which was not the case in the beginning. I found joy in learning new things about technologies I only thought I knew, and the more I learned, the less I realized I knew. This was exciting rather than frustrating, which may sound unusual unless you've been in a similar point in your life.
Since I was a kid, I never felt challenged in an academic sense. To clarify, it's not that I didn't succeed in the garden variety academic world through school, it's that I never found it interesting and didn't have any appreciation for it. When I didn't find it interesting, I found learning things boring and tedious, and I did what was required to succeed in spite of not having an appreciation of the process of learning. The same thing happened with my earlier certifications, I didn't enjoy learning the tedious stuff in my CCNA and CCNP studies, but I did them because I wanted to have those certifications. Something with the CCIE, however, finally broke through and awakened the joy of learning for me. Apparently I'm a much slower learner than I viewed myself in the past.
Motivation at different stages in my life has changed dramatically. In my 20s, it was all about money. I thought that if I wanted to earn X, I needed to do A, B, and C, and then I would be happy because I'd be earning $X. I usually succeeded in this path, but I never felt fulfilled in the end. Once I hit my mid-30s, and yes, I realize I'm dating myself here, I learned that time is a much more important asset than money. Time to not only do what I enjoy, but spending time with those who I loved, and time to enhance my own abilities and grow as a person.
Finding the joy in failure, in discovering how little I know about things, has brought about new motivation in my life to continue to improve myself not only academically but as a person as well. I began to turn from the introverted person who was afraid of having conversations with people to finding a community of people who I enjoyed engaging with. Fear was once a motivator for running away from things I didn't want to do, but fear became a motivator to try new things and face things I once ran away from because I didn't want to fail.
In the end, my motivation has become simply to be someone who is always in pursuit of growth. I don't want to be content with being good enough, or thinking that I have all of the answers, because I never will. Challenge yourself to seek out new paths in life and new opportunities, because even when you fail, you will grow and learn. It's one thing that if I could go back to my early 20s and tell myself, I would.


text:
North Carolina State Laboratory of Public Health and the Office of Chief Medical Examiner
7,800 sf addition to the hospital
Approx. 7,300 sf renovation to existing hospital and clinic space
New single entrance for hospital and clinic
The CPI Group is working with Mobridge Regional Hospital to consolidate the access to the clinic and the hospital into a single new front entrance to enhance the hospital's presence in the community. The addition will include expanded physical and cardiac rehabilitation space as well as consolidated business functions for the hospital and clinic. The additional space will also allow enhancements to the existing clinic, lab and radiology spaces.
New full glass entrance with clearstory, enhanced lobby and waiting, upgraded business offices, lab and outpatient clinic.
Approximately 7,300 square feet of renovation and a 7,800 square foot addition
Partnership with the USDA Rural Development and Northeast Council of Governments
The new entrance will provide a clearly recognizable 'front door' and fresh new look for the community in the ongoing reinvestments efforts for the Medical Center and the Community.
Back To The Projects Gallery

redpajama_set_name: RedPajamaCommonCrawl


text:
package ravtrix.backpackerbuddy.interfacescom;

/**
 * Created by Ravinder on 9/17/16.
 */
public interface UserLocationInterface {
    void onReceivedLocation(double latitude, double longitude);
}

redpajama_set_name: RedPajamaGithub


text:
Gypsy Sally's
Gypsy Sally's is a live music venue in Washington DC featuring national, regional and local Americana, bluegrass, rock, folk, blues and country acts in a comfortable setting at reasonable prices. Located adjacent to the Potomac River in Georgetown, Gypsy Sally's has a capacity of 300 and offers tiered seating, concert dining and a dance floor, as well as the adjacent Vinyl Lounge where patrons can enjoy a no-cover bar, restaurant and art gallery.
PH: 202 * 333 * 7700
Disco Risqué, Radii – Tickets – Gypsy Sally's – Washington, DC – July 12th, 2019
Gypsy Sally's Presents
Disco Risqué
Advance $12/ Day of Show $12 + fees
https://www.gypsysallys.com/event/1875965/
Disco Risque - Something For Nothing - Tiny Desk Competition 2016 Disco Risqué - March 2016
Disco Risqué is a heavy funk band from central Virginia. Formed in late 2014, the band released their eponymous debut double album in November of 2015. Following that release the band went on to share the stage with up and coming greats such as Pigeons Playing Ping Pong, Tauk, and People's Blues of Richmond. Disco Risqué spent 2016 and 2017 playing shows and festivals throughout Virginia and the Atlantic Northeast, including Rooster Walk 8 and 9, Peace of Mind Festival 2016 and 2017, Threestival 2017, and a Saturday night closing set at Devil's Backbone Hoopla Festival 2017. The band is currently recording their follow-up record, set to be released this summer, which will capture and reflect the growth, energy, and heavy-dancey sound the band has garnered on the road.
Based out of the Washington D.C. Metropolitan area, Radii draws from a diverse range of music in an attempt to create an explorative experience.
We play a mix of progressive rock, funk, and alternative music -- genres that everybody can get down to. Our goal is to take the listener on an exciting musical journey, and we do this by mixing hard-hitting original songs with groovy takes on some of our favorite covers.
Ben Fisher - Vocals, Guitar
Philip Whitcomb - Guitar
Kevin Koehncke - Drums
Daniel Peckaitis - Synth bass/keys
Fernando Concepcion - Keys/synth
http://www.gypsysallys.com/
Gypsy Sally's Calendar
Vinyl Lounge Calendar
Buy Gypsy Sally's Merch
Yak Attack
Nicky C & the Consiglieri
Freekbass & The Bump Assembly (ft. Sammi Garett from Turkuaz)
The Funky Knuckles
The Wooks
On the Bus, John Kadlecik Solo Acousti'Lectric
Vinyl Lounge
Directions & Contact
All Content Property of Gypsy Sally's © 2013
Website by WLCR
Powered by TicketFly


text:
American Diploma
Canadian Diploma
Australian Diploma
British Diploma
Malaysian Diploma
French Diploma
Copy from customer
1.Fill order information on the form
2.Pay 50% of order value as deposit
3.Make electronic draft for client approval
4.Check and amend the draft
5.Pay the balance amount
6.Print out, send photos to client
7.Ship out and advise tracking number
How's The Quality of Your Carleton University Fake Diploma
Carleton University fake diploma, Carleton University degree,
Where to purchase Carleton University fake diploma, buy a Carleton University degree certificate, buy fake Canada diploma. Founded in 1942 and situated just minutes away from central government headquarters in Ottawa, Ontario, Carleton University describes itself as Canada's 'capital university'.
It was the first private, non-denominational college in Ontario, established largely as a way for young people adversely affected by the Depression to continue their formal education.
Carleton University is now a public university with an operating budget of around $390 million. It receives additional research funding of close to $60 million, and awards scholarships and bursaries worth up to $18 million.
Just south of the city centre, the university's campus sits within 100 acres of land and lies between the Rideau River and the historic Rideau Canal. It also has a five kilometre network of underground tunnels that connect all of the university's buildings.
Enrolled at Carleton University are around 28,000 students from over 100 countries.
The university offers 65 degree programmes in more than 50 academic disciplines, and is particularly renowned for its courses in journalism, public affairs, international affairs, architecture and technology.
It comprises many prominent buildings, including the 22-story Dunton Tower, the Kailash Mital theatre, which seats up to 444 people, and the Minto Centre for Advanced Studies in Engineering.
Link: Pinterest YouTube Twitter Tumblr Facebook Flickr Instagram Contact us
Copyright © 2023 www.buybestdiploma.com, Document Printing Services


Boasting beautiful box-pressed construction and bold maduro taste in every puff, the 601 Blue Label Maduro is your ticket to deep, satisfying flavor with tones of earth, coffee, almond, and more.
A blend recipe of aged Cuban-seed long-leaf tobaccos under a dazzlingly dark Nicaraguan wrapper gives way to a rich and complex medley of tasting notes punctuated by just the right touch of peppery spice. If you're looking for a full-bodied smoke with real balance and character, look no further - these immaculately rolled top-shelfers are certain to fit the bill.


text:
\section{Introduction}
The equations of motion for reduced density matrices have a coupling scheme known as
the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy \cite{Bonitz} where an $n$-body density matrix couples to
$n$-body and $n+1$-body density matrices.
To solve the equations of motion for the one-body and two-body density matrices, we need to truncate the BBGKY hierarchy
at a two-body level. The simplest truncation scheme is to approximate
a three-body density matrix with the antisymmetrized products of the one-body and two-body density matrices neglecting the correlated
part of the three-body density matrix (the three-body correlation matrix) \cite{WC,GT}.
We refer to this truncation scheme as the time-dependent density-matrix theory (TDDM).
In some cases TDDM
overestimates ground-state correlations \cite{TTS}, gives unphysical results \cite{schmitt,gherega} and causes instabilities of the obtained solutions \cite{toh12}
for strongly interacting cases. Obviously the problems originate in the
truncation scheme where the three-body correlation matrix is completely neglected. This is related to the loss of $N$-representability \cite{coleman} which is preserved only in the case of the
untruncated BBGKY hierarchy.
To remedy to such difficulties of the naive truncation scheme,
better approximations for the three-body correlation matrix
have been proposed. One is to approximate the three-body correlation matrix with the products of the
correlated part of the two-body correlation matrices based on a perturbative consideration \cite{ts2014}, which corresponds to the cumulant expansion \cite{mazz1999}:
The three-body correlation matrix may also be called the three-body cumulant.
We refer to this truncation scheme as TDDM1.
It was found in the applications of TDDM1 to the Lipkin model \cite{Lip} that TDDM1 can remedy the overestimation of ground-state correlations in TDDM.
It was also found that TDDM1 underestimates ground-state correlations in strongly interacting regions when the number of particles $N$ becomes large.
This suggests that higher-order effects which effectively reduce the contribution of the three-body correlation matrix should be taken into account.
We proposed another truncation scheme \cite{ts2017} which includes a normalization factor in the three-body correlation
matrix in TDDM1. We refer to it as TDDM2.
In this work we pursue our investigation of the cumulant approximation to the
correlated part of the three-body density matrix which enters the equation of motion for the two-body density matrix.
In particular we will continue in this sense our investigation of the two-level
Lipkin model where we will find that TDDM solves this model exactly in the
thermodynamic limit staying in the symmetry unbroken (spherical) basis.
Additionally we then also study the three-level Lipkin model \cite{li} which will turn
out to have a quite different behavior with respect to the three-body correlations.
We will find a particular approximation scheme for the cumulant expression of
the three-body correlation matrix which also solves the three-level Lipkin model almost
exactly for the ground state energy in the large $N$ limit staying in the
symmetry unbroken description. However, this scheme will not be able to
reproduce the rotational spectrum. A detailed discussion of this behavior will
be given and the particularities of the three-level Lipkin model in this respect
will be discussed.
At the end, we will try to give some general conclusions concerning the
performance of the cumulant approximation to the three-body correlation matrix in
the TDDM approach.

The paper is organized as follows. The three truncation schemes TDDM, TDDM1 and TDDM2 are explained in sect. 2. The results for the two and three-level Lipkin models are
presented in sect. 4 and sect. 4 is devoted to summary.

\section{Formulation}
We consider a system of $N$ fermions and assume that the Hamiltonian $H$ consisting of a one-body part and a two-body interaction
\begin{eqnarray}
H=\sum_{\alpha\alpha'}\langle\alpha|t|\alpha'\rangle a^\dag_\alpha a_{\alpha'}
+\frac{1}{2}\sum_{\alpha\beta\alpha'\beta'}\langle\alpha\beta|v|\alpha'\beta'\rangle
a^\dag_{\alpha}a^\dag_\beta a_{\beta'}a_{\alpha'},
\nonumber \\
\label{totalH}
\end{eqnarray}
where $a^\dag_\alpha$ and $a_\alpha$ are the creation and annihilation operators of a particle at
a single-particle state $\alpha$.
\subsection{Time-dependent density-matrix theories}
The TDDM approaches give the coupled equations of motion for the one-body density matrix (the occupation matrix) $n_{\alpha\alpha'}$
and the correlated part of the two-body density matrix $C_{\alpha\beta\alpha'\beta'}$.
These matrices are defined as
\begin{eqnarray}
n_{\alpha\alpha'}(t)&=&\langle\Phi(t)|a^\dag_{\alpha'} a_\alpha|\Phi(t)\rangle,
\\
C_{\alpha\beta\alpha'\beta'}(t)&=&\langle\Phi(t)|a^\dag_{\alpha'}a^\dag_{\beta'}
 a_{\beta}a_{\alpha}|\Phi(t)\rangle
\nonumber \\
&-&(n_{\alpha\alpha'}(t)n_{\beta\beta'}(t)-n_{\alpha\beta'}(t)n_{\beta\alpha'}(t)) ,
 \label{rho2}
\end{eqnarray}
where $|\Phi(t)\rangle$ is the time-dependent total wavefunction
$|\Phi(t)\rangle=\exp[-iHt] |\Phi(t=0)\rangle$.
We use units such that $\hbar=1$.
The equations of motion for $n_{\alpha\alpha'}$ and $C_{\alpha\beta\alpha'\beta'}$ are written as
\begin{eqnarray}
i \dot{n}_{\alpha\alpha'}&=&
\sum_{\lambda}(\epsilon_{\alpha\lambda}{n}_{\lambda\alpha'}-{n}_{\alpha\lambda}\epsilon_{\lambda\alpha'})
\nonumber \\
&+&\sum_{\lambda_1\lambda_2\lambda_3}
[\langle\alpha\lambda_1|v|\lambda_2\lambda_3\rangle C_{\lambda_2\lambda_3\alpha'\lambda_1}
\nonumber \\
&-&C_{\alpha\lambda_1\lambda_2\lambda_3}\langle\lambda_2\lambda_3|v|\alpha'\lambda_1\rangle],
\label{n1}
\end{eqnarray}
\begin{eqnarray}
i\dot{C}_{\alpha\beta\alpha'\beta'}&=&
\sum_{\lambda}(\epsilon_{\alpha\lambda}{C}_{\lambda\beta\alpha'\beta'}
+\epsilon_{\beta\lambda}{C}_{\alpha\lambda\alpha'\beta'}
\nonumber \\
&-&\epsilon_{\lambda\alpha'}{C}_{\alpha\beta\lambda\beta'}
-\epsilon_{\lambda\beta'}{C}_{\alpha\beta\alpha'\lambda})
\nonumber \\
&+&B_{\alpha\beta\alpha'\beta'}+P_{\alpha\beta\alpha'\beta'}+H_{\alpha\beta\alpha'\beta'}
\nonumber \\
&+&\sum_{\lambda_1\lambda_2\lambda_3}
[\langle\alpha\lambda_1|v|\lambda_2\lambda_3\rangle C_{\lambda_2\lambda_3\beta\alpha'\lambda_1\beta'}
\nonumber \\
&+&\langle\lambda_1\beta|v|\lambda_2\lambda_3\rangle C_{\lambda_2\lambda_3\alpha\alpha'\lambda_1\beta'}
\nonumber \\
&-&\langle\lambda_1\lambda_2|v|\alpha'\lambda_3\rangle C_{\alpha\lambda_3\beta\lambda_1\lambda_2\beta'}
\nonumber \\
&-&\langle\lambda_1\lambda_2|v|\lambda_3\beta'\rangle C_{\alpha\lambda_3\beta\lambda_1\lambda_2\alpha'}],
\label{r2}
\end{eqnarray}
where $C_{\alpha\beta\gamma\alpha'\beta'\gamma'}$ is the three-body correlation matrix
which is neglected in the original version of TDDM \cite{WC,GT}.
The energy matrix $\epsilon_{\alpha\alpha'}$ is given by
\begin{eqnarray}
\epsilon_{\alpha\alpha'}=\langle \alpha|t|\alpha'\rangle
+\sum_{\lambda_1\lambda_2}
\langle\alpha\lambda_1|v|\alpha'\lambda_2\rangle_A
n_{\lambda_2\lambda_1}
\label{hf},
\end{eqnarray}
where the subscript $A$ means that the corresponding matrix is antisymmetrized.
The matrix $B_{\alpha\beta\alpha'\beta'}$ in eq. (\ref{r2}) does not contain $C_{\alpha\beta\alpha'\beta'}$ and describes 2p--2h and 2h--2p
excitations, where ${\rm p}$ and ${\rm h}$ refer to particle and hole states, respectively.
The terms $P_{\alpha\beta\alpha'\beta'}$ and $H_{\alpha\beta\alpha'\beta'}$
contain $C_{\alpha\beta\alpha'\beta'}$ and describe
p--p (and h--h) and p--h
correlations to infinite order, respectively \cite{GT}. These matrices are given in ref. \cite{GT}
but listed again in Appendix A for completeness.
Equations (\ref{n1}) and (\ref{r2}) satisfy the conservation laws of the total energy and the
total number of particles \cite{WC,GT}.
As mentioned above,
$C_{\alpha\beta\gamma\alpha'\beta'\gamma'}$ in eq. (\ref{r2}) is neglected in TDDM \cite{WC,GT}.
In order to remedy difficulties of TDDM,
we have proposed a truncation scheme for $C_{\alpha\beta\gamma\alpha'\beta'\gamma'}$ \cite{ts2014} such that
\begin{eqnarray}
C_{\rm p_1p_2h_1p_3p_4h_2}&=&\sum_{\rm h}C_{\rm hh_1p_3p_4}C_{\rm p_1p_2h_2h},
\label{purt1}\\
C_{\rm p_1h_1h_2p_2h_3h_4}&=&\sum_{\rm p}C_{\rm h_1h_2p_2p}C_{\rm p_1ph_3h_4}.
\label{purt2}
\end{eqnarray}
These expressions were derived from perturbative consideration \cite{ts2014} using
the following CCD (Coupled-Cluster-Doubles)-like ground state wavefunction $|Z\rangle$ \cite{shavitt}
\begin{eqnarray}
|Z\rangle=e^Z|{\rm HF}\rangle
\end{eqnarray}
with
\begin{eqnarray}
Z=\frac{1}{4}\sum_{\rm pp'hh'}z_{\rm pp'hh'}a^\dag_{\rm p}a^\dag_{\rm p'}a_{\rm h'}a_{\rm h},
\end{eqnarray}
where $|{\rm HF}\rangle$ is the Hartree-Fock (HF) ground state and
$z_{\rm pp'hh'}$ is antisymmetric under the exchanges of ${\rm p} \leftrightarrow {\rm p'}$ and ${\rm h} \leftrightarrow {\rm h'}$.
We refer to the truncation scheme given by eqs. (\ref{purt1}) and (\ref{purt2}) as TDDM1. In the applications of TDDM1 to the Lipkin model
it was found that
although TDDM1 effectively suppresses excess two-body correlations in small $N$ systems,
it overestimates the contributions of the three-body correlation matrix in large $N$ systems.
To make TDDM1 applicable to large $N$ systems, we modified the truncation scheme \cite{ts2017} to
\begin{eqnarray}
C_{\rm p_1p_2h_1p_3p_4h_2}&=&\frac{1}{\cal N}\sum_{\rm h}C_{\rm hh_1p_3p_4}C_{\rm p_1p_2h_2h},
\label{purt11}\\
C_{\rm p_1h_1h_2p_2h_3h_4}&=&\frac{1}{\cal N}\sum_{\rm p}C_{\rm h_1h_2p_2p}C_{\rm p_1ph_3h_4}.
\label{purt22}
\end{eqnarray}
The factor ${\cal N}$ is given by
\begin{eqnarray}
{\cal N}&&=1+\frac{1}{4}\sum_{\rm pp'hh'}C_{\rm pp'hh'}C_{\rm hh'pp'},
\label{norm}
\end{eqnarray}
which plays a role in reducing the three-body correlation matrix in strongly interacting regions of the Lipkin model.
We refer to the truncation scheme given by eqs. (\ref{purt11}) and (\ref{purt22}) as TDDM2.
The conservation of the total energy and total particle number is not affected by the above approximations
for the three-body correlation matrix because its anti-symmetry properties under the exchange of single-particle indices is respected.

\section{Results}
\subsection{Two-level Lipkin model}
First we consider the usual two-level Lipkin model.
The Lipkin model \cite{Lip} describes an $N$-fermions system with two
$N$-fold degenerate levels with energies $\epsilon/2$ and $-\epsilon/2$,
respectively. The upper and lower levels are labeled by quantum number
$p$ and $-p$, respectively, with $p=1,2,...,N$. We consider
the standard Hamiltonian
\begin{equation}
{H}=\epsilon {J}_{z}+\frac{V}{2}({J}_+^2+{J}_-^2),
\label{elipkin}
\end{equation}
where the operators are given as
\begin{eqnarray}
{J}_z&=&\frac{1}{2}\sum_{p=1}^N(c_p^{\dag}c_p-{c_{-p}}^{\dag}c_{-p}), \\
{J}_{+}&=&{J}_{-}^{\dag}=\sum_{p=1}^N c_p^{\dag}c_{-p}.
\end{eqnarray}
The HF ground state where the lowest single-particle states given by the operators $\{a_{-p}\}~~(p=1,2,\cdot\cdot\cdot N)$ are fully occupied
\begin{eqnarray}
|{\rm HF}\rangle=\prod_{p=1}^Na^\dag_{-p}|0\rangle
\end{eqnarray}
is obtained by the transformation
\begin{eqnarray}
\left(
\begin{array}{c}
a^\dag_{-p}\\
a^\dag_{p}
\end{array}
\right)=\left(
\begin{array}{cc}
\cos\alpha&\sin\alpha\\
-\sin\alpha&\cos\alpha
\end{array}
\right)
\left(
\begin{array}{c}
c^\dag_{-p}\\
c^\dag_{p}\\
\end{array}
\right).
\nonumber \\
\label{2l-trans}
\end{eqnarray}
The HF energy is given by
\begin{eqnarray}
E(\alpha)&=&-\frac{N\epsilon}{2}+N\epsilon \sin^2\alpha
\nonumber \\
&+&VN(N-1)\sin^2\alpha\cos^2\alpha.
\end{eqnarray}
Using $\chi=|V|(N-1)/\epsilon$, we can express $E_{\rm HF}$ which minimizes $E(\alpha)$ as
\begin{eqnarray}
E_{\rm HF}=\left\{
\begin{array}{c}
-\frac{N\epsilon}{2}~~~~~(\chi\le 1)\\
\frac{N\epsilon}{4}(-\chi-1/\chi)~~~~~(\chi> 1),
\end{array}
\right .
\end{eqnarray}
where $\cos2\alpha=1/\chi$ is satisfied.

Since the solution in TDDM is closely related to that in the deformed Hartree-Fock theory (DHF) as shown below,
we discuss some properties of the DHF solution.
In DHF the occupation matrix is given by
\begin{eqnarray}
n_{-p}(n_{-p-p})&=&\cos^2\alpha,
\label{low}\\
n_{p}(n_{pp})&=&1-n_{-p}=\sin^2\alpha,
\label{up} \\
n_{p-p}&=&\cos\alpha\sin\alpha.
\end{eqnarray}
In DHF higher reduced density matrices have no correlated parts. For example the 2p--2h element of the two-body density matrix is expressed with
the occupation matrices as
\begin{eqnarray}
\rho_{pp'-p-p'}&=&\langle{\rm DHF}|c^{\dag}_{-p}c^{\dag}_{-p'}c_{p'}c_p|{\rm DHF}\rangle
\nonumber \\
&=&n_{p-p}n_{p'-p'}=\cos^2\alpha\sin^2\alpha.
\label{2p2h}
\end{eqnarray}
Similarly, the ph--ph element is given by
\begin{eqnarray}
\rho_{p-p'-pp'}(p\neq p')&=&\langle{\rm DHF}|c^{\dag}_{-p}c^{\dag}_{p'}c_{-p'}c_{p}|{\rm DHF}\rangle
\nonumber \\
&=&n_{p-p}n_{-p'p'}=\cos^2\alpha\sin^2\alpha.
\label{phph}
\end{eqnarray}
The three-body density matrix is also expressed as the antisymmetrized products of three occupation matrices
such that
\begin{eqnarray}
\rho_{p-p'p''pp'-p''}=\cos^2\alpha\sin^4\alpha,
\end{eqnarray}
which is the same as $n_{pp}\rho_{-p'p''p'-p''}$. This means that the correlated part of the three-body density matrix
$C_{p-p'p''pp'-p''}$ vanishes in DHF.

In TDDM (also in TDDM1 and TDDM2) the ground state is obtained using the adiabatic method \cite{toh2005,mazz2006} starting from the non-interacting "spherical" HF state
where the occupation matrix $n_{\alpha\alpha'}$ has no off-diagonal elements. Since the TDDM equations eqs. (\ref{n1}) and (\ref{r2})
maintain the symmetry, $n_{\alpha\alpha'}$ always has no off-diagonal elements. Similarly, $\rho_{pp'-p-p'}$ and $\rho_{p-p'-pp'}~(p\neq p')$
have no uncorrelated parts in TDDM. As shown below, there are strong similarities between the TDDM and DHF solutions such that
$C_{pp'-p-p'}$ and $C_{p-p'-pp'}$ correspond to eqs. (\ref{2p2h}) and
(\ref{phph}), respectively. The diagonal elements eqs. (\ref{low}) and (\ref{up}) in DHF
also correspond to those in TDDM. This suggests the following relation for the expectation value of an operator $\hat{Q}$
\begin{eqnarray}
\langle \hat{Q}\rangle_{\rm TDDM}&\approx&\langle \Psi_{\rm DHF}|\hat{Q}|\Psi_{\rm DHF}\rangle
\nonumber \\
&\approx&\frac{1}{2} (\langle{\rm DHF}(\alpha)|\hat{Q}|{\rm DHF}(\alpha)\rangle
\nonumber \\
&+&\langle{\rm DHF}(-\alpha)|\hat{Q}|{\rm DHF}(-\alpha)\rangle),
\label{<q>}
\end{eqnarray}
where $|\Psi_{\rm DHF}\rangle$ is a 'spherical' wavefunction given by
\begin{eqnarray}
|\Psi_{\rm DHF}\rangle=\frac{|{\rm DHF}(\alpha)\rangle+|{\rm DHF}(-\alpha)\rangle}{\sqrt{2}}.
\end{eqnarray}
Here $|{\rm DHF}(\alpha)\rangle$ means the deformed HF ground state with $\alpha$.
In fact the following relations hold
\begin{eqnarray}
 \langle{\rm DHF}(\alpha)|{\rm DHF}(-\alpha)\rangle&=&(\cos^2\alpha-\sin^2\alpha)^N
 \nonumber \\
 \\
 \langle{\rm DHF}(\alpha)|c^\dag_\alpha c_\beta|{\rm DHF}(-\alpha)\rangle&\propto& (\cos^2\alpha-\sin^2\alpha)^{N-1}
 \nonumber \\
 \\
 \langle{\rm DHF}(\alpha)|c^\dag_\alpha c^\dag_\beta c_{\beta'} c_{\alpha'}|{\rm DHF}(-\alpha)\rangle&\propto& (\cos^2\alpha-\sin^2\alpha)^{N-2}.
 \nonumber \\
\end{eqnarray}
Since $0<(\cos^2\alpha-\sin^2\alpha)<1$, the above expectation values between $|{\rm DHF}(\alpha)\rangle$ and $|{\rm DHF}(-\alpha)\rangle$ become
quite small for large $N$, justifying eq. (\ref{<q>}).
\begin{figure}
\resizebox{0.5\textwidth}{!}
\includegraphics{12e.eps}
}
\caption{Ground-state energy in TDDM (solid line)
as a function of $\chi=|V|(N-1)/\epsilon$ for $N=12$.
The results in TDDM1 where the three-body correlation matrix is given by eqs. (\ref{purt1}) and (\ref{purt2}) are shown with the dashed line.
The green (gray) line depicts the results in TDDM2 where the three-body correlation matrix is given by eqs. (\ref{purt11}) and (\ref{purt22}).
The results in HF and DHF($\chi>1$) are shown with the dotted line. The open circles (DTDDM) indicate the results in TDDM calculated using the 'deformed'
single-particle states and the DHF ground state.
The exact values are given by the dot-dashed line.}
\label{12e}
\end{figure}
\begin{figure}[h]
\resizebox{0.5\textwidth}{!}{
\includegraphics{12n.eps}
}
\caption{Same as fig. \ref{12e} but for the occupation probability $n_{p}$ of the upper state.}
\label{12n}
\end{figure}

\begin{figure}[h]
\resizebox{0.5\textwidth}{!}{
\includegraphics{12c.eps}
}
\caption{Same as fig. \ref{12e} but for the 2p--2h element $C_{pp'-p-p'}$ of the two-body correlation matrix.
The results in DHF show $n_{p-p}^2$. }
\label{12c}
\end{figure}

\begin{figure}
\resizebox{0.5\textwidth}{!}{
\includegraphics{50e.eps}
}
\caption{Ground-state energy in TDDM (solid line)
as a function of $\chi$ for $N=50$.
The exact values are given by the dot-dashed line.
The dashed line depicts the results in TDDM1.
The results in TDDM2 lie between the TDDM results and the exact values and are not shown here.
The results in HF and DHF($\chi>1$) are shown with the dotted line but cannot be distinguished from the exact values
in the scale of the figure except for the region $\chi\approx 1$.
}
\label{50e}
\end{figure}
\begin{figure}[h]
\resizebox{0.5\textwidth}{!}{
\includegraphics{50n.eps}
}
\caption{Same as fig. \ref{50e} but for the occupation probability $n_{p}$ of the upper state.
}
\label{50n}
\end{figure}

\begin{figure}[h]
\resizebox{0.5\textwidth}{!}{
\includegraphics{50c.eps}
}
\caption{Same as fig. \ref{50e} but for the 2p--2h element $C_{pp'-p-p'}$ of the two-body correlation matrix.
The results in DHF show $n_{p-p}^2$. }
\label{50c}
\end{figure}

\begin{figure}[h]
\resizebox{0.5\textwidth}{!}{
\includegraphics{200ex1.eps}
}
\caption{Excitation energy of the first excited state calculated in TDDM (dots) a function of $\chi$ for $N=200$. The exact values are shown with the dot-dashed line.
The dotted line depicts the results in RPA.}
\label{200ex1}
\end{figure}

\begin{figure}[h]
\resizebox{0.5\textwidth}{!}{
\includegraphics{200ex2.eps}
}
\caption{Same as fig. \ref{200ex1} but for the second excited state. The dotted line depicts the RPA results for the first excited state.}
\label{200ex2}
\end{figure}
To illustrate how TDDM, TDDM1 and TDDM2 behave in small $N$ regions, we first present the results for $N=12$.
The ground-state energy $E_0$ calculated in TDDM (solid line) is shown in fig. \ref{12e} as a function of $\chi$.
The results in TDDM1 where the three-body correlation matrix is given by eqs. (\ref{purt1}) and (\ref{purt2}) are shown with the dashed line.
The results in TDDM2 where the three-body correlation matrix is given by eqs. (\ref{purt11}) and (\ref{purt22}) are shown with the green (gray) line.
The results in HF and DHF ($\chi>1$) and the exact values are shown with the dotted and dot-dashed lines, respectively.
The open circles indicate the results in TDDM calculated using the 'deformed' (symmetry broken)
single-particle states and the DHF ground state as the starting ground state. We refer to this scheme as the deformed TDDM (DTDDM). When the 'deformed' basis is used,
the two-body correlation matrix is so small that both DTDDM and the deformed TDDM1 give similar results.
The exact values are given by the dot-dashed line.
In this small $N$ system
TDDM overestimates two-body correlations \cite{ts2014,ts2017} and TDDM1 underestimates them in strongly interacting regions. TDDM2 cures this problem and
the agreement with the exact solutions is much improved.  DTDDM also provides the additional correlation energy missing in DHF.
The occupation probability $n_{p}$ of the upper state and the 2p--2h element $C_{pp'-p-p'}$ of the correlation matrix calculated in TDDM
are shown in figs. \ref{12n} and \ref{12c}, respectively. In DHF $n_{p-p}^2$ is shown as a quantity corresponding to $C_{pp'-p-p'}$.
TDDM1 and TDDM2 describe well $E_0$, $n_{p}$ and $C_{pp'-p-p'}$ in the transition region $\chi\approx 1$, where DHF fails to reproduce the exact values.
Figures \ref{12n} and \ref{12c} indicate that the improvement in $E_0$ from TDDM to TDDM2 is due to the appropriate reduction of $C_{pp'-p-p'}$.
Figures \ref{12e}--\ref{12c} also show that DHF becomes good approximation with increasing interaction strength and that the improvement in $E_0$ from DHF to DTDDM
is brought by that in $n_p$. The deviation of $n_p$ and $C_{pp'-p-p'}$ in DTDDM at $\chi=1.5$ is due to the fact that the deformed state becomes unstable in DTDDM near $\chi=1$.

Now we present the TDDM results for $N=50$.
The ground-state energy $E_0$ calculated in TDDM (solid line) is shown in fig. \ref{50e} as a function of $\chi$.
The results in TDDM1 are given by the dashed line.
The dotted and dot-dashed lines depict the results in HF and DHF ($\chi>1$) and the exact values, respectively.
The results in HF and DHF cannot be distinguished from the exact values in the scale of the figure except for the region $\chi\approx 1$.
The results in TDDM2 lie between the TDDM results and the exact values and are not shown here.
In this large $N$ system, the ground-state energies in TDDM and TDDM2 agree well with the exact solutions and the DHF energies also become close to the exact values including the transition region.
This is also seen in $n_p$ and $C_{pp'-p-p'}$ shown in figs. \ref{50n} and \ref{50c}, respectively.
The factor ${\cal N}$ in eqs. (\ref{purt11}) and (\ref{purt22}) plays a role in drastically reducing the three-body correlation matrix,
which makes TDDM2 almost equivalent to TDDM \cite{ts2017}. In DHF the three-body density matrix has no correlated parts. The fact that DHF becomes good approximation for the ground
state of the Lipkin model with
increasing number of particles explains that TDDM which has no three-body correlation matrix becomes good approximation for large $N$.
We checked that TDDM gives the almost exact ground state for much larger $N$.

Finally we present the excitation energies of the first and second excited states calculated in TDDM for $N=200$ where TDDM gives the almost exact ground-state.
The energy of the first excited state is calculated using the TDDM equations eqs. (\ref{n1}) and (\ref{r2}) and assuming $n_{p-p}$, $C_{pp'-pp'}$ and
$C_{-p-p'-pp'}$ are small. The second excited state which has the same symmetry as the ground state is calculated in a different manner.
In the adiabatic method used for the ground-state calculations there is a small mixing of excited states which have the same symmetry as
the ground state. The excitation energy of the second excited state can be estimated from the frequency of the small oscillation
of $n_{pp}$ in the adiabatic method. The obtained results for the first and second excited states are compared with the exact solutions (dot-dashed line) in figs. \ref{200ex1}
and \ref{200ex2}, respectively. The dots in figs. \ref{200ex1} and \ref{200ex2} depict the TDDM results.
The results in RPA for the first excited state are shown in figs. \ref{200ex1} and \ref{200ex2} with the dotted line. In contrast to RPA
TDDM describes the decreasing excitation energy of the first excited state with increasing interaction strength beyond $\chi=1$. For $\chi>1.073$ TDDM does not give an oscillating solution to the first excited state.
This indicates that the three-body correlation matrix plays some role in the first excited state.
With increasing $\chi$ the RPA results for the first excited state approach the exact results for the second excited states as shown in fig. \ref{200ex2}.
The agreement of the TDDM results with the exact values is good for both the first and second excited states. This is related to the fact that
TDDM becomes exact with increasing number of particles.

In this subsection we found out that in the two-level Lipkin model the three-body
correlation matrix vanishes in the large $N$ (thermodynamic) limit and that TDDM solves the ground state of
this model exactly staying in the symmetry unbroken description. How far our
findings can be transposed to other models of this type of a one site spin
model is an open question but our studies may help to analyze the situation
also in other cases.
We now will turn to the case of the three-level Lipkin model.

\subsection{Three-level Lipkin model}
Next we consider the three-level Lipkin model \cite{li} with the single-particle levels labeled 0, 1 and 2.
Since the number of unoccupied states is larger than that of the occupied states, the three-level Lipkin model may be more realistic than the
two-level Lipkin model and it has often been used to test extended mean-field theories \cite{hol,hagino,delion}.  We choose the Hamiltonian which is invariant under the exchange of 1 and 2:
\begin{eqnarray}
H=\epsilon(\hat{n}_1+\hat{n}_2)+\frac{V}{2}\left(K_1^2+K_2^2+(K_1^\dag)^2+(K_2^\dag)^2\right),
\label{3lH}
\nonumber \\
\end{eqnarray}
where
\begin{eqnarray}
\hat{n}_\alpha=\sum_{i=1}^N c^\dag_{\alpha i}c_{\alpha i}~~~~~~~~~~\alpha=~0,~1,~2,
\label{spq}
\\
K_\alpha=\sum_{i=1}^N c^\dag_{\alpha i}c_{0i}~~~~~~~~~~\alpha=~1,~2.
\end{eqnarray}
The HF ground state where the lowest single-particle states given by the operators $\{a_{0i}\}~~(i=1,2,\cdot\cdot\cdot N)$ are fully occupied
\begin{eqnarray}
|{\rm HF}\rangle=\prod_{i=1}^Na^\dag_{0i}|0\rangle
\end{eqnarray}
is obtained by the transformation
\begin{eqnarray}
\left(
\begin{array}{c}
a^\dag_{0i}\\
a^\dag_{1i}\\
a^\dag_{2i}
\end{array}
\right)=\left(
\begin{array}{ccc}
\cos\alpha&\cos\beta\sin\alpha&\sin\beta\sin\alpha\\
-\sin\alpha&\cos\beta\cos\alpha&\sin\beta\cos\alpha\\
0&-\sin\beta&\cos\beta
\end{array}
\right)
\left(
\begin{array}{c}
c^\dag_{0i}\\
c^\dag_{1i}\\
c^\dag_{2i}
\end{array}
\right).
\nonumber \\
\label{3l-trans}
\end{eqnarray}
The HF energy is independent of $\beta$ and given by
\begin{eqnarray}
E(\alpha,\beta)=N\epsilon \sin^2\alpha+VN(N-1)\sin^2\alpha\cos^2\alpha.
\end{eqnarray}
Using $\chi=|V|(N-1)/\epsilon$, we can express $E_{\rm HF}$ which minimizes $E(\alpha,\beta)$ as
\begin{eqnarray}
E_{\rm HF}=\left\{
\begin{array}{c}
0~~~~~(\chi\le 1)\\
\frac{N\epsilon}{4}(2-\chi-1/\chi)~~~~~(\chi> 1).
\end{array}
\right .
\end{eqnarray}
The ground-state wavefunction which has the symmetry under the exchange of 1 and 2 may be written as
\begin{eqnarray}
|\Psi\rangle=\frac{1}{\pi}\int_{-\pi/2}^{\pi/2}|{\rm DHF}(\alpha,\beta)\rangle d\beta,
\label{total}
\end{eqnarray}
where $|{\rm DHF}(\alpha,\beta)\rangle$ is the DHF ground state with $\alpha$ and $\beta$. In the following we show that eq. (\ref{total})
gives a non-vanishing three-body correlation matrix.
To evaluate an expectation value of an operator $\hat{Q}$ using eq. (\ref{total}), we need the overlap $\langle{\rm DHF}(\alpha,\beta')|\hat{Q}|{\rm DHF}(\alpha,\beta)\rangle$.
We show some examples of the overlaps using $X=\cos^2\alpha+\cos(\beta'-\beta)\sin^2\alpha$ \cite{hol}:
\begin{eqnarray}
&\langle{\rm DHF}&(\alpha,\beta')|{\rm DHF}(\alpha,\beta)\rangle=X^N,\\
&\langle{\rm DHF}&(\alpha,\beta')|c^\dag_{11}c_{11}|{\rm DHF}(\alpha,\beta)\rangle
\nonumber \\
&=&\cos\beta'\cos\beta\sin^2\alpha X^{(N-1)},\\
&\langle{\rm DHF}&(\alpha,\beta')|c^\dag_{01}c^\dag_{02}c_{12}c_{11}|{\rm DHF}(\alpha,\beta)\rangle
\nonumber \\
&=&\cos^2\beta\cos^2\alpha\sin^2\alpha X^{(N-2)},\\
&\langle{\rm DHF}&(\alpha,\beta')|c^\dag_{01}c^\dag_{12}c_{02}c_{11}|{\rm DHF}(\alpha,\beta)\rangle
\nonumber \\
&=&\cos\beta'\cos\beta\cos^2\alpha\sin^2\alpha X^{(N-2)},\\
&\langle{\rm DHF}&(\alpha,\beta')|c^\dag_{11}c^\dag_{12}c^\dag_{03}c_{13}c_{02}c_{11}|{\rm DHF}(\alpha,\beta)\rangle
\nonumber \\
&=&\cos^2\beta'\cos^2\beta\cos^2\alpha\sin^4\alpha X^{(N-3)},
\end{eqnarray}
where $01,~11,~\cdot\cdot\cdot$ mean the quantum number $(\alpha,i)$ for the single-particle state given in eq. (\ref{spq}). All components of the density matrices
do not depend on the quantum number $i$.
Since $X^N$ for large $N$ is sharply peaked at $\beta'-\beta\approx 0$, the diagonal assumption $\beta'=\beta$ is justified for the overlaps.
Then the density matrices obtained with eq. (\ref{total}) are given as follows after the $\beta$ integration
(we choose magnetic quantum numbers so that the expressions are general but in the end there will, of course, be no dependence on magnetic states):
\begin{eqnarray}
n_{\rm pp}&=&\langle\Psi|c^\dag_{11}c_{11}|\Psi\rangle=\frac{1}{2}\sin^2\alpha,
\label{npp}
\\
C_{\rm pp'hh'}&=&\langle\Psi|c^\dag_{01}c^\dag_{02}c_{12}c_{11}|\Psi\rangle
\nonumber \\
&=&\frac{1}{2}\cos^2\alpha\sin^2\alpha,
\label{pphh}
\\
C_{\rm ph'hp'}&=&\langle\Psi|c\dag_{01}c\dag_{12}c_{02}c_{11}|\Psi\rangle
\nonumber \\
&=&\frac{1}{2}\cos^2\alpha\sin^2\alpha,
\label{cphph}
\\
\rho_{\rm ph'p''pp'h''}&=&
\langle\Psi|c^\dag_{11}c^\dag_{12}c^\dag_{03}c_{13}c_{02}c_{11}|\Psi\rangle
\nonumber \\
&=&\frac{3}{8}\cos^2\alpha\sin^4\alpha.
\end{eqnarray}
Since $\rho_{\rm ph'p''pp'h''}$ contains four particle-state indices, the $\beta$ integration makes it impossible to express $\rho_{\rm ph'p''pp'h''}$
by the product of $n_{\rm pp}$ and $C_{\rm ph'hp'}$ which respectively have two particle-state indices.
From the above expressions we obtain the correlated part of the three-body density matrix as
\begin{eqnarray}
C_{\rm ph'p''pp'h''}&=&C_{11,02,13,11,12,03}
\nonumber \\
&=&\langle\Psi|c^\dag_{11}c^\dag_{12}c^\dag_{03}c_{13}c_{02}c_{11}|\Psi\rangle
\nonumber \\
&-&\langle\Psi|c^\dag_{11}c_{11}|\Psi\rangle\langle\Psi|c^\dag_{12}c^\dag_{03}c_{13}c_{02}|\Psi\rangle
\nonumber \\
&=&\frac{1}{8}\cos^2\alpha\sin^4\alpha.
\label{c3dhf}
\end{eqnarray}
Similarly, the three-body correlation matrix $C_{\rm ph'h''p'hh''}=C_{11,02,03,12,01,03}$ corresponding to eq. (\ref{purt2}) is
evaluated using the DHF wavefunction eq. (\ref{total}) and it is found that $C_{11,02,03,12,01,03}=0$
as is the case of the two-level Lipkin model. This is because $\rho_{\rm ph'h''p'hh''}$ contains only two particle-state indices, which allows us to express it as $n_{\rm hh}C_{\rm ph'hp'}$.
On the other hand, the three-body correlation matrix of the form
$C_{\rm pp'p''hp'h''}$,
which enters the equation of motion for $C_{\rm ph'p'h}$, is also non-vanishing because it contains four particle-state indices. Using eq. (\ref{total}) it is
evaluated to be the same as eq. (\ref{c3dhf}) that is ($\cos^2\alpha\sin^4\alpha/8$).
The above analysis indicates that the three-body correlation matrix in the strongly interacting region $(\chi>1)$ of the three-level Lipkin model is quite different from that of the two-level Lipkin model
and that it should be properly treated. However,
extending the truncation scheme to include the equation of motion for the three-body correlation matrix is a difficult task and is not pursued in this work.
In the following we just point out
that there exists a simple truncation scheme for the three-body correlation matrix which gives a good description of the ground state
for the whole range of the interaction strength. In this approach the quadratic approximation for the pph--pph type three-body correlation matrix given by eq. (\ref{purt1}) is used
and the phh--phh type given by eq. (\ref{purt2}) is omitted considering the above analysis based on the DHF wavefunction.
We refer to this truncation scheme as TDDM1-b. We first present the results in TDDM1-b and then discuss why TDDM1-b works.

\begin{figure}
\resizebox{0.5\textwidth}{!}{
\includegraphics{20e3l.eps}
}
\caption{Ground-state energy of the three-level Lipkin model calculated in TDDM1-b (solid line)
as a function of $\chi$ for $N=20$. The dashed, dot-dashed and two-dot-dashed lines depict the results in TDDM, TDDM1 and TDDM2, respectively.
The results in HF and DHF($\chi>1$) are shown with the dotted line.
The exact values are given by the dots.}
\label{20e3l}
\end{figure}
\begin{figure}
\resizebox{0.5\textwidth}{!}{
\includegraphics{200e3l.eps}
}
\caption{Ground-state energy of the three-level Lipkin model calculated in TDDM1-b (solid line)
as a function of $\chi$ for $N=200$. The exact values are given by the dots.
The dashed and dot-dashed lines depict the results in TDDM and TDDM1, respectively.
The results in HF and DHF($\chi>1$) are shown with the dotted line but cannot be easily distinguished from the TDDM1-b results in the scale of the figure.
}
\label{200e3l}
\end{figure}

\begin{figure}
\resizebox{0.5\textwidth}{!}{
\includegraphics{20n3l.eps}
}
\caption{Occupation probability of the state 1 of the three-level Lipkin model calculated in TDDM1-b (solid line)
as a function of $\chi$ for $N=20$. The dot-dashed line depicts the results in TDDM1.
The results in HF and DHF($\chi>1$) given by eq. (\ref{npp}) are shown with the dotted line.
The exact values are given by the dots.}
\label{20n3l}
\end{figure}

\begin{figure}
\resizebox{0.5\textwidth}{!}{
\includegraphics{20c3l.eps}
}
\caption{Same as fig. \ref{20n3l} but for $C_{\rm pp'hh'}$. The results in HF and DHF are given by eq. (\ref{pphh}).}
\label{20c3l}
\end{figure}

\begin{figure}
\resizebox{0.5\textwidth}{!}{
\includegraphics{200n3l.eps}
}
\caption{Same as fig. \ref{20n3l} but for $N=200$.}
\label{200n3l}
\end{figure}

\begin{figure}
\resizebox{0.5\textwidth}{!}{
\includegraphics{200c3l.eps}
}
\caption{Same as fig. \ref{20c3l} but for $N=200$.}
\label{200c3l}
\end{figure}

The ground-state energy calculated in TDDM1-b (solid line) is shown in figs. \ref{20e3l} and \ref{200e3l} as a function of $\chi$
for $N=20$ and $200$, respectively. The exact values are given by the dots. The dashed and dot-dashed lines depict the results in TDDM and TDDM1, respectively.
The results in HF and DHF($\chi>1$) are shown with the dotted line but in the case of $N=200$ they cannot be easily distinguished from the TDDM1-b results in the scale of the figure.
The results in TDDM2 are given with the two-dot-dashed line in fig. \ref{20e3l}. In the case of $N=200$ they are close to those in TDDM as in the case of the two-level Lipkin model
and are not shown in fig. \ref{200e3l}.
In contrast to the case of the two-level Lipkin model TDDM strongly overestimates two-body correlations in the three-level Lipkin model even for $N=200$.
This is due to the fact that the three-body correlation matrix cannot be neglected in the three-level Lipkin model as discussed above.
DHF gives a good description of the ground-state energy for $N=200$ as in the case of the two-level Lipkin model. The results in
TDDM1-b agree well with the exact solutions both in $N=20$ and $200$. TDDM1 underestimates the correlation effects for large $\chi$ because the phh--phh
component of the three-body correlation matrix given by eq. (\ref{purt2}) is non-vanishing.
The occupation probability $n_1$ of the single-particle level labeled 1 and the 2p--2h element of the two-body correlation matrix calculated in TDDM1-b are also in good agreement with the exact values as
shown in figs. \ref{20n3l}--\ref{200c3l}. We have checked that the agreement of the TDDM1-b results with the exact solutions extends at least to $\chi=10$ in the case of $N=200$.
The results in TDDM1 are not so good as those in TDDM1-b but the agreement with the exact values are reasonable in the transition region ($\chi\approx1$).
In the case of the two-level Lipkin model the ground state energies calculated in TDDM1-b approximately come in the middle between the results in TDDM and TDDM1.

In the following we try to explain why TDDM1-b gives good results for the three-level Lipkin model.
In the large $N$ case of the three-level Lipkin model (and also the two-level Lipkin model) the coupling of $C_{\rm pp'hh'}$ and $C_{\rm hh'pp'}$
to $C_{\rm ph'p'h}$ described by the $H_{\alpha\beta\alpha'\beta'}$ term in eq. (\ref{r2}) is dominant (see eq. (\ref{h-term})).
The three-body correlation matrix of the form
$C_{\rm pp'p''hp'h''}$,
which enters the equation of motion for $C_{\rm ph'p'h}$, is neglected in TDDM1-b(and also in TDDM1). This is because such an element of the three-body correlation matrix
is of higher order than eq. (\ref{purt1}) in the perturbative regime. In the strongly interacting region of the three-level Lipkin model $C_{\rm pp'p''hp'h''}$ becomes non-vanishing as discussed above.
As a consequence of the neglect of $C_{\rm pp'p''hp'h''}$, $C_{\rm ph'p'h}$ is overestimated in TDDM1-b.
If $C_{\rm pp'p''hp'h''}$ is assumed to be $n_{\rm p'p'}C_{\rm pp''hh''}/2$ using eqs. (\ref{npp}) and (\ref{pphh}), the overestimation in eq. (\ref{r2}) for $C_{\rm ph'p'h}$ can be evaluated to be
$n_{1}C_{\rm pp'hh'}/(n_0-2n_1)$, where $n_0$ is the occupation probability of the single-particle level labeled $0$.
It is impossible to analytically calculate its contribution to
$C_{\rm ph'p'h}$ but comparison of $C_{\rm ph'p'h}$ in TDDM1-b and that in DHF
which is given by eq. (\ref{cphph}) shows that the deviation of $C_{\rm ph'p'h}$
is well expressed as
\begin{eqnarray}
\frac{C_{\rm pp'hh'}^2}{2(n_0-n_1)}.
\label{over}
\end{eqnarray}
The quadratic form is understandable because $n_1$ is determined by $C_{\rm pp'hh'}$ in eq. (\ref{n1}).
In the equation of motion for $C_{\rm pp'hh'}$ in TDDM1-b one of the four terms in eq. (\ref{r2}) which include the three-body correlation matrix ($C_3$) cancels the overestimated part of $C_{\rm ph'p'h}$:
eq. (\ref{over}) is multiplied by $-2(n_0-n_1)$ due to the occupation factors in eq. (\ref{h-term}).
Consequently,
the three remaining $C_3$ terms in TDDM1-b play a role as the effective $C_3$ terms.
In fig. \ref{200c33l} the three quarters of eq. (\ref{purt1}) calculated in TDDM1-b (solid line) are compared with the exact values of $C_3$ (dots)
and the DHF values (dotted line) given by eq. (\ref{c3dhf}). The TDDM1-b values well simulates the $\chi$ dependence of the exact $C_3$.
This is the reason behind why the simple truncation scheme eq. (\ref{purt1}) gives good results.

Our study of the three-level Lipkin model has shown that contrary to the two-level
case the three-body correlation matrix cannot be neglected in the large $N$ (thermodynamic)
limit. Working in the symmetry unbroken basis, the cumulant approximation to
the correlated part of the three body density matrix works very well for the
ground state energy if only the pph--pph term is retained. We gave arguments why
the phh--phh particle contribution must be discarded.
However, the validity of TDDM1-b remains
restricted to the particularities of the model and conclusions for the general
case cannot be made.
On the other hand, staying
in the symmetry unbroken description, one cannot describe the rotational
spectrum which emerges in the three-level Lipkin model \cite{li} if the two upper levels
become degenerate as is the case of eq. (\ref{3lH}).
For such cases with a spontaneously broken
symmetry it is in general better to start with a symmetry broken basis and to
recover good symmetry with projection techniques.
DTDDM which consists of the simplest truncation scheme for $C_3$ and the symmetry broken single-particle basis
may be applicable for such cases.
In the past we applied our cumulant approximation eqs. (\ref{purt1}) and (\ref{purt2}) to the more realistic
case of $^{16}$O with promising results \cite{toh2015}. In these
examples the symmetry unbroken (spherical) description is certainly the choice
to be used.

\begin{figure}
\resizebox{0.5\textwidth}{!}{
\includegraphics{200c33l.eps}
}
\caption{Three-body correlation matrix $C_{11,02,13,11,12,03}~(C_3)$ used in TDDM1-b (solid line) multiplied by a factor $3/4$
as a function of $\chi$ for $N=200$.
The results in HF and DHF($\chi>1$) are shown with the dotted line. The exact values are given by the dots.}
\label{200c33l}
\end{figure}

The excited states of the three-level Lipkin model can be calculated in the same manners as those used for the two-level Lipkin model.
The results obtained from the TDDM1-b based approaches are shown in figs. \ref{200e13l} and \ref{200e23l}.
The exact eigenstates are labeled by the quantum number $\langle L_0^2\rangle=0,~1,~2,\cdot\cdot\cdot$ where $L_0=i(K_{12}-K_{21})$ \cite{delion}
with $K_{12}(=K_{21}^\dag)=\sum_i c^\dag_{1i}c_{2i}$, and the ground state has $\langle L_0^2\rangle=0$.
In fig. \ref{200e23l} the exact values for the lowest excited state with the same quantum number as the ground state are shown.
Both the first and second excited states in TDDM1-b have $\chi$ dependence which is similar to the case of the two-level Lipkin model. The first excited state in TDDM1-b collapses beyond $\chi=1.045$.
A more accurate treatment of the three-body correlation matrix than TDDM1-b is required.
\begin{figure}
\resizebox{0.5\textwidth}{!}{
\includegraphics{200e13l.eps}
}
\caption{Excitation energy of the first excited state in TDDM1-b (open squares) as a function of $\chi$ for $N=200$. The results in
RPA are shown with the dotted line and the exact values are given by the dots.}
\label{200e13l}
\end{figure}
\begin{figure}
\resizebox{0.5\textwidth}{!}{
\includegraphics{200e23l.eps}
}
\caption{Excitation energy of the second excited state in TDDM1-b (open squares) as a function of $\chi$ for $N=200$. The results in
RPA for the first excited states are shown with the dotted line. The dots depict
the exact values for the lowest excited state with $\langle L_0^2\rangle=0$.}
\label{200e23l}
\end{figure}

\section{Summary}
We studied the time-dependent density-matrix theory ( TDDM) in the large $N$ and strong coupling limits of the Lipkin models.
It was found that in the two-level Lipkin model the ground state calculated using the original truncation scheme of TDDM
where the three-body correlation matrix is completely neglected
approaches the exact solution with increasing number of particles. It was pointed out that this is related to the fact that the deformed Hartree-Fock approximation (DHF)
gives the exact ground-state energies in the large $N$ limit. The relation between the occupation matrix in DHF and the correlation matrix in TDDM was also discussed.
The small amplitude limit of TDDM was also found to describe the excited states of the two-level Lipkin model
very well in the 'spherical' region. In the 'deformed' region the first excited state falls to zero as it should.
However, it falls to zero with a finite slope contrary to the exact solution which goes to zero asymptotically.
It indicates that the three-body correlation matrix neglected in TDDM still plays some role in excited states.

It was shown that in the three-level Lipkin model a simple truncation scheme where the three-body correlation matrix
is approximated by the square of the two-body correlation matrix gives good results for the ground-state properties.
Also the first two excited states are quite well reproduced far into the strongly correlated (deformed) region working in the symmetry unbroken basis.

We pointed to the fact that the influence of the three-body correlation matrix in the two- and three-level Lipkin models is quite different.
While in the former model the genuine three-body correlations totally disappear in the large $N$ limit, they partially vanish in the latter model.
We gave reasons for this different behavior and suggested that for other spin models similar studies could eventually also give insight into the role of three-body correlations there.

The fact that three-body correlation matrix in the strong coupling ('deformed') regions
is apparently quite model dependent is perturbing and sheds some doubt of the 'blind' applicability
of the cumulant approximation (TDDM1) to the three-body correlation matrix in 'deformed' regions while working in the spherical basis.
On the other hand more realistic applications to $^{16}$O \cite{toh2015} and other models \cite{ts2014}
where the three-body correlation matrix does not disappear have shown in the past
that the cumulant approximation is quite powerful for symmetry unbroken systems. It was also shown that TDDM1 gives reasonable results for the three-level Lipkin model
as long as the interaction is not so strong.
Therefore we think that the cumulant approximation is applicable to realistic systems.

redpajama_set_name: RedPajamaArXiv


text:
Health/Environment
Post News Group
anne-daniel
oaklandpost_y7kt4e
Home Health Healthcare Racial Disparities Continue Despite ACA
Healthcare Racial Disparities Continue Despite ACA
Oakland Post
More Californians than ever before have health insurance, but coverage isn't care, and the Affordable Care Act (ACA) has magnified the deep racial, ethnic and cultural disparities in accessing quality health care in California.

Latino and African Americans especially remain heavily uninsured and struggle to receive health care.
Language and cultural barriers, lack of Internet or an email address, a lack of experience in using health insurance, a shortage of doctors and clinics in poor and rural communities, and high costs are preventing many from receiving health care and medications.
A new report "Breaking Barriers: Improving health insurance enrollment and access to health care in California," reveals a deep divide between social class, income, culture and ethnicity emerging under the state's Covered Care.
"It's unconscionable that so many have been left out of something as basic as the chance to enjoy good health," said Gary Delgado, author of Breaking Barriers. "Lack of Internet access or speaking another language is not a reason to be locked out of a health system that purports to be open to all.
"Obamacare did not cause the widespread racial disparities we found, but neither did it solve them. Now we have to take them on directly," said Delgado.
"Breaking Barriers" is a year-long study that includes a survey of nearly 1,200 low-income people in 10 states in Spanish, Cantonese, and English. They were contacted at food banks, health clinics, and homeless centers.
Alfredo DeAvila did surveys and interviews for the Breaking Barriers California report.
"If the ACA is going to be successful, we need to help people transition not only into the health insurance system, but also into the health care system," he said. "We must invest in public education about how to get ongoing preventive care."
The Korean America community, especially seniors are struggling because of costs, said DJ Yoon, executive director of NAKASEC (National Korean American Service and Education Consortium.)
"California can be a leader in assuring quality health care for all people. We have let people of color again slip through the cracks in our system, we can do better – and here is a roadmap for how we get there," said Delgado.
Key recommendations in the report include:
Improve language access. Make provider directories available in multiple languages and list addresses, phone numbers, languages spoken, hospital affiliations, and specialties;
Simplify the insurance-shopping experience. Make cost information transparent and communicate clearly about deductibles, co-pays, and preventive services that are included;
Covered California should enforce and impose penalties on insurers who do not reduce racial health care disparities within required timeframes;
Assure that primary care providers are within 30 minutes driving or public transit time. Enrollees who must travel further should be offered free transportation;
Expand school-based health centers, especially in medically underserved communities;
Address underlying causes of poor health, especially in poor communities, (mold, infestations, domestic violence) Expand medical-legal partnerships as an avenue toward addressing poor health in low-income communities;
Reinforce the ACA-mandated "well-woman preventive" care and provide education about the value of preventive care for all. Ensure that all plans include reproductive health care services.
The full Breaking Barriers in California report is available at http://allianceforajustsociety.org/wp-content/uploads/2015/04/BBReport_CALIF.pdf
Latino and African Americans especially remain heavily uninsured and struggle to receive health care.
"Breaking Barriers"
racial disparities
Previous articleOP-ED: Baltimore-Don't Get It Twisted
Next articleOP-ED: Marilyn Mosby: Without Fear or Favor
Moms 4 Housing Evicted from Vacant Home By Deputies After Verdict Favored Owners
Advocates and Unhoused Residents Seek Community Help to Build Small Homes on MLK Weekend
Oakland Moves to Prohibit Landlords from Considering Criminal Histories in Rental Housing
Supervisor Carson Opposes Oakland Coal Terminal
California Charter Stories Bring Hard Data, First-Hand Experience to National School...
Richmond Gets Ready for Music on the Main
Oakland's Public Banking Feasibility Study Released
Lee Commemorates Black History Month
Mayor's Brooklyn Basin Project Shortchanges Black Workers, Taxpayers and Minority Contractors
Oakland Moms4Housing Say 'Housing is a Human Right,' but the Judge...
Report: Marin's Beach Water Mostly Excellent
Moms 4 Housing Evicted from Vacant Home By Deputies...
Advocates and Unhoused Residents Seek Community Help to Build Small...
Oakland Moves to Prohibit Landlords from Considering Criminal Histories in Rental...
OP-ED: Education Activism Picking Up Across Country
Oakland 12th Grader Gema Quetzal Cardenas Appointed to State Board of...
School District, AC Transit Reach Agreement to Save Bus Service to...
Oakland2631
City Government784
San Francisco622
The Oakland Post is one of eight weekly newspapers Serving the San Francisco Bay Area. Each paper seeks to provide awareness of issues and current events of concern in Bay Area minority communities.
© Post News Group. All Rights Reserved. Powered by Embtel Solutions, Inc.
Single-Payer Health Care Bill to be Introduced in California Senate
Clergy Warn of Dangers of Coal


text:
Q: Is there a formula for the periodicity of a^b mod n? I am looking for a formula for the minimum p for which
$$Mod[a^{p+1},n]=a$$ for all $a<n$.
I am aware of Euler's formula, $Mod[a^{\phi(n)},n]=1$ when (a,n) are coprime, which implies that $Mod[a^{k\phi(n)+1},n]=a$. But I'm looking for the minimum periodicity that applies to all $a<n$ and the conditions under which such periodicity exists.
If n is prime, then Euler tells us that the periodicity is just EulerPhi[n] which is n-1.
But $n=15$ has a periodicity of 4 for all $a<15$ even though the EulerPhi[15]=8 and 15 is non-coprime with several a's. $Mod[a^{4k+1},15]=a$
And if $n=12$, no value of p works for $a\epsilon\{2,6,10\}$
So is there a general formula for determining the periodicity and whether it exists?  I want to be clear that individual a's might have different periodicities, but I'm looking for lowest the p over which the entire set $a<n$ is periodic.

A: You are right, Eulers totient function $\varphi(n)$ is only an upper bound on the periodicity. The precise answer is given by the "Carmichael function" $\lambda(n)$, which is also sometimes called "reduced totient function". Check https://en.wikipedia.org/wiki/Carmichael_function for remarks on that. Your examples are totally correct:

*

*For any prime $p$ it is $\varphi(p)=\lambda(p)=p-1$

*For $n=15$ it is $\varphi(15)=8$ but $\lambda(15)=4$.

In terms of group theory, $\varphi(n)$ is the order of the group $(\mathbb{Z}/n\mathbb{Z})^*$, and $\lambda(n)$ is the exponent of the group $(\mathbb{Z}/n\mathbb{Z})^*$.

redpajama_set_name: RedPajamaStackExchange


The muscles that stiffen and open the throat tend to relax during sleep, causing the throat's opening to narrow slightly. In people with Obstructive Sleep Apnea Syndrome (OSAS), this narrowing is so great that breathing becomes difficult. Eventually the person is awakened and falls back to sleep dozens to hundreds of times each night.
OSAS often occurs in overweight people, as fatty tissue in the neck affects the size or shape of the breathing passage. OSAS is not exclusive to overweight people. If you have OSAS, you may not be getting enough oxygen during sleep and probably don't sleep soundly.
A pattern of snoring interrupted by pauses, then gasps, is a sign that breathing stops and restarts.
Trouble concentrating, or becoming forgetful, irritable, anxious or depressed.
Certain birth defects that affect size/shape of throat, face or chin such as Down Syndrome.
While asleep, children may snore or squeak, have difficulty breathing, or sleep fitfully.
May seem sluggish or have daytime hyperactivity.
Find out your snore score.
To get a free brochure or to learn more about OSAS please call 262-928-4043.


Conductive tracks were laid on PVC film with lands at each end. Two sets of three were used; painted tracks, painted tracks with additional paint blobbed on the lands, and tracks with blobbed paint allowed to dry before additional blobs were added.
One set was dried for 12 hours, the other for 30 minutes under a fan and then both were covered in 1mm hot-melt EVA. 0.2mm tinned copper wire leads were pushed through from the PVC side and the resistance measured with a bench multimeter.
The fresher tracks were unreliable, exhibiting infinite resistance except for the plain painted track which was intermittent between 60 and 160 ohms.
The older tracks had an extremely intermittent single track, 17-50 ohm blobbed track, and 5-6 ohm for the double-blobbed track.
These results suggested that the earlier PCB experiment should be redone with double-blobbed lands and that the silver paint is allowed to cure overnight before embedding in EVA.
support, and can also run on windows!!"
B.V. All rights reserved. 13 Refs.
We had thought of a half-way-house in powder-printing machines where a powder-filled cavity in the part is vacuumed out half way through a build and filled with another material, such as Wood's metal, or silicone rubber.
15 April 2005: Vik has just sent us a draft copy of his report. It's also available from Reports and Documentation at www.reprap.org.
An extrusion head that co-extrudes a thin copper wire filament together with a polymer (like a miniature version of the way that ordinary electrical wires are made) to form electrical connections. The extrusion would bind in with the rest of the RP part.
Polymorph might be a useful material. It's a nylon-like polymer that melts around 60oC.
We quite like the idea of building an extra head into an FDM system to dispense polydimethylsiloxane (PDMS - bathroom sealant) together with an optically-triggered crosslinking agent; that way we could make components from rigid insulators, rigid conductors, and a synthetic rubber all integrated together.
Another powder-printing possibility: inkjet pure water onto hemihydrated calcium sulphate (i.e. plaster of paris - or maybe instead even Portland cement... possibly mixed with a fibre filler for strength). The CaSO4 solidifies in a few minutes.
Alternatively inkjet a solvent to fuse a powder; PVA and water might work quite well, or virtually any thermoset and a corresponding organic solvent for it. Thermosets dissolving in propanone (acetone) might be good, as propanone has a high vapour pressure and so would evaporate quickly and is not that toxic in a well-ventilated area (it's nail varnish remover).


1968: Dark Shadows' Joe & Guthrie tried to break into Laura's tomb.
1984: Guiding Light's Mindy considered an abortion.
1990: General Hospital's Julian pulled a gun on Paget ("Duke").
1992: Days of our Lives' Vivian arrived in Salem."History speaks to artists. It changes the artist's thinking and is constantly reshaping it into d ifferent and unexpected images."


Are your Predator Pro Slip On Exhausts too loud? We have a solution that'll bring them down a notch: the British Customs Predator Pro Quiet Core. Simply insert them into the ends and they'll go down a few decibels; that simple. Available in Brushed or Polished finish and made with 304 Stainless Steel meaning it's built to last.
Does not fit original Predator Exhausts; only fits newer Predator Pro mufflers. If you are unaware which Predator exhaust you have please contact us prior to ordering.


Zoe was instantly transported to a place she had never been to before. She knew she was still somewhere in heaven, as the glorious presence of the Lord was all around her. But it was dark, and she couldn't see where she was. She was lying on something squashy and soft, and it was moving, bump, bump-bump. Up and down the floor moved. Zoe pressed her hands against it. It was warm and living and moved as though it were breathing! She could feel life flowing through the floor, like a giant, powerful, living stream.
Where am I? she thought.
Before Zoe could answer, it grew lighter. She was in a vast chamber. It was like a majestic cathedral, but made of living tissue instead of stone and glass. Blood flowed through giant veins and arteries that were the pipes and structures supporting the massive chamber. Valves opened and closed like some massive industrial factory. Instead of steam and gas being emitted as the valves moved, sparks of energy and filled the air. It resonated and vibrated through the giant chamber like the most beautiful earthly choir you could ever imagine, only magnified a thousand trillion times. The effect of the heavenly music made Zoe want to laugh and cry, all at the same time, and to love everything—especially God. Zoe could have listened to the music forever.
In the center of the chamber was a magnificent tree. It was beautiful. Its leaves were the greenest of greens, and the fruit on it sparkled and shone. The tree looked very holy and was full of life. Then, before Zoe's very eyes, the tree began to change color. It turned brown and then black. The leaves withered and fell, and the fruit shriveled and dropped to the chamber floor. The strong branches disintegrated into ash and drifted to the floor. Within moments, all that was left of the magnificent tree was a withered stump. Blood ran down the stump, pooled on the floor, and then slowly seeped into the floor of the chamber. The beautiful music ceased. Zoe gasped. She had just witnessed something catastrophic.
She held her breath. All she could hear was the giant heart beating faster. She knew that this tree was the most precious tree that had ever existed … and now it was dead!
Maybe an angel will come and heal the tree, she thought.
But no angel came and nothing happened. After a long wait, which seemed to last forever, the voice spoke again.
The figure of a man entered through a door in the chamber. He walked reverently, with purpose and direction over to the tree stump. His features were not clear, as they shifted and shimmered as he moved. As he walked, his feet did not always touch the ground, hovering a few inches above it. He glided like an eagle as he walked, and yet he was strong and powerful like an ox or a lion. The beauty and radiance about him was like a thousand fluid rainbows and exploding sunsets. Words could not adequately describe the man's utter beauty and holiness. He was off the Richter scale! Zoe was captivated by this person—unable to remove her gaze from him. He must be Holy Spirit, she thought. He's so beautiful, powerful … so awesome!
Holy Spirit bent down and picked up a seed that had fallen to the ground, where the tree had died. He examined it very carefully, turning it over lovingly with his fingers. Then he opened his mouth and sang, the chamber itself vibrating in unison with him. The song was beautiful, filling the chamber.
It was a song of love and hope being awakened again. It was the heart-cry of the Father for his beloved son, his one and only son. Zoe was inside the heart of Father God—sometime long ago, even before the courts of heaven existed. Zoe heard the voice again; the one she had first heard when she had entered the chamber. It was Father who had spoken to her! He sang about how much he loved his son. Holy Spirit responded and sang back to him. Back and forth in duet they continued to sing over the seed.
"How precious, how wonderful is my love for you, my son," Father sang.
"You are the Father to all fathers, the compassionate one to all mothers, the friend to all children," sang Holy Spirit.
Zoe trembled as she realized that she was being shown one of the greatest mysteries and privileges in all of heaven. The Father's heart was the chamber prepared for his precious son. The Father was also going to look for a Bride for his son. When the Bride was found and ready, Jesus would bring her back to this most intimate place. They would be together forever.
Zoe wanted to look away. She felt that she was witnessing something so intimate, so holy that she should not be seeing it. But then the Lord had brought her here, to witness this great and ancient mystery. Zoe stood, weeping and trembling.
The tears rolled down her face. How could anybody be found worthy enough to come to such a holy place, to the place of the Father's heart, to be with Jesus? Why had she even been allowed to be here?
He then bent over and tenderly placed the seed he was still holding into the flesh of the Father's heart. The seed was black and dead. When it touched the living flesh of the Father's heart, death radiated out from the seed in all directions. It was like black ink in water as it was sucked up into the veins and arteries. Once vibrant and red, the pulsating chamber of life became black and died. The Father let out a cry of pain and anguish for his tree that had died. Father wept.
Zoe fell to her knees. She too was overcome by the grief that the Father felt. She cried with her head between her knees.
How long she cried, Zoe did not know. But then she felt droplets of water falling on her. At first she thought that she was imagining it, but no. Zoe looked up and saw rain falling from the roof of the chamber. Father God was crying. Father's tears formed small pools. The tears ran into the crevice where the seed had been planted. The pool of tears touched the seed. Then the miracle happened!
There was a rumbling sound like a giant earthquake. An explosion of light filled the chamber.
"The seed…the seed, it moved!" shouted Zoe, momentarily forgetting she was in the most holy place. "It's moving, changing …" but Zoe didn't finish what she was saying.
One moment it was a dead seed and the next, there stood… a Lamb!
This was the most ancient of mysteries. This was the great secret within the heart of the Father, before the foundation of the world. This was the secret plan of Father, Son, and Holy Spirit. The Son had willingly sacrificed himself out of his exceedingly great love for his Father. He was the sacrifice that had been prepared before time began, so that all people, from every tribe, tongue, and nation, could be brought home to his Father's house.
But then, on that most gruesome day, the day that the Son of Man would be murdered on the cross, it would all be turned around. Redemption day! It would become the day of the greatest victory—the Son of God who took on human form, left his majesty in heaven, and became the perfect man. He was totally God and man all at the same time … and sinless! He was the Lamb that was sacrificed before the beginning of the world, the mystery hidden in the Father's heart. He was the perfect guilt offering that took away the sin of his precious, fallen Bride. Now she could be restored to the Father, Holy Spirit, and to Jesus himself. Death could not hold the Son of God, nor could Satan. Jesus was perfect—sinless. There were no legal rights for Death and Satan to claim him, because he was faultless and perfect. No human since the fall of Adam and Eve in the garden paradise had ever achieved this. It had been impossible … until now. God had shown up as the son of Man in human form, and he was awesome! He would strip bare and plunder the kingdom of darkness. He was about to rescue the righteous ones who had died before he was born on earth, who were waiting for his return. Jesus would rise from the grave, from the bowels of the earth, and return to heaven.
The Lamb stood, hidden in the center of the Father's heart. He was also the tree, the tree of Life that would bring life to his Bride. He was the One who would give his leaves to bring healing to the nations. For the moment though, this too was hidden, a secret in the heart of the Father, waiting, waiting patiently for the right time to be revealed.
Zoe shook. She was seeing the most holy secret of all, right before her very eyes. What had she done to deserve this?
Tears ran down Zoe's face. She had still not given up hope for her family, who were still trapped within the wreckage of the car. With all that was going on, she had not dared ask the Lord about them, but she was also his friend. Could she ask him now?
The tenderness in the Lamb's eyes told her everything. She knew in that instant that he cared more about them than she could ever do. The Lamb nodded. Reassured, Zoe knew everything would be fine. The Lamb grinned and then smiled. The smile became a laugh. Zoe had never seen a Lamb laugh before! But it appeared to be the most natural thing in the world.


Original artwork adds to the appeal of the classy kitchen.
Gorgeous blue shapes the exterior of the renovated hollywood craftsman bungalow.
Turning a 1918 abondoned home into a modern delight before shots.
Statue from jamaica in the dining room.
Natural materials like recycled beer bottle kitchen countertop used in the kitchen renovation.
A look at the kitchen before renovation.


text:
Children's /
Children's Theatre Plays /
Aladdin and His Sister
Book By: Janice Rider
Cast: 4 m, 2 w, 3 flexible. Some doubling possible.
This play presents a new, fun version of the story of Aladdin! While Aladdin is a lazy, unmotivated young man, his sister, Maliha, is resourceful, courageous, and compassionate, looking after him upon the death of their parents. One day an unscrupulous sorcerer pretends to be their long-lost uncle. He cons Aladdin into retrieving a buried lamp and traps him in the bowels of the earth. Thanks to Maliha and a friendly snake, Aladdin is rescued by rubbing the ring the stranger lent him. The Genie of the Ring becomes Aladdin's slave but is befriended and freed by Maliha. Later, Aladdin remembers the old lamp which the "uncle" had wanted originally. Aladdin polishes it and the Genie of the Lamp appears—just in time to help Aladdin gain the hand of the beautiful and exotic sultan's daughter. But there's not a happy ending yet because the sorcerer returns to kidnap her. The grateful Ring Genie reappears to help Aladdin and Maliha rescue the princess as the story progresses towards a happy ending for all—except the sorcerer! About 45 minutes.
CENTRAL LAFOURCHE HIGH SCHOOL 4 Performance(s)
RACELAND, LA 6/21/2016
ST. JOHN LUTHERAN SCHOOL 2 Performance(s)
GRAND HAVEN, MI 11/10/2011
Canadian Playwright Janice Rider
Talks About "Aladdin and His Sister"
Q: WHAT INSPIRED YOU TO WRITE THIS PLAY?
I first became acquainted with the story of Aladdin from a children's book, "The Thousand Nights and One Night." Later on, when my children were small, we would re-enact these tales together using items we found in the house as props. Last year, when I was looking for a new idea for a story, I visited the library and found a number of tales adapted from that book. I read through them and talked to my two sons, now teenagers. We were excited about the idea of trying a play with an exotic flavour. I also felt that Aladdin was the kind of story whose plot could go in a number of different directions. The original Aladdin is unmotivated and, it seemed to me, that he would benefit from a family member whose personality was strikingly different from his. This is how Maliha, Aladdin's sister, was born.
Q: WHAT IS YOUR FAVOURITE LINE IN THE PLAY?
My favourite line in the play is one Maliha says. "Just because something has always been done a certain way does not mean that it cannot be improved upon." It seems to me that things only improve when we recognize that maintaining the status quo limits our ability to see the situations in the world where change is needed. Maliha recognizes the needs and desires of others. She is empathetic and caring. She could focus on her own agenda, and attempt to improve her own status, but she chooses to look after others. Maliha mothers her brother, finds a way to help the poor and hungry, and frees the Genie of the Ring from his bondage.
Q: WHERE DID THE CHARACTERS COME FROM? ARE THEY BASED ON PEOPLE YOU KNOW?
I was lucky to be raised in a family where girls were highly valued. My mother is a strong person who has the courage of her convictions, and my father has always taken great pride in his two daughters and his wife. He certainly believes in the equality of women. Maliha has many of my mother's qualities, and really believes in herself. Maliha's belief in herself allows her to stand up to Aladdin in a male-dominated world. She is also responsible, someone whom Aladdin can always count on to come through for him. The princess, Badra, is another strong female character who attempts to fend for herself against a domineering father and is anything but a feminist. The genies are playful characters, and have many of the characteristics of my two sons and their friends. For instance, the genies have a sense of humour, zest for life and living, and the ability to form strong bonds of friendship.
Q: WHAT DID YOU TRY TO ACHIEVE WITH THIS PLAY?
Whenever I write a play, one of my primary goals is to engage the children and youth who perform in it. I want them to have fun acting, I want them to enjoy the audience's reaction, and I want them to feel a sense of connection with the characters they dramatize. Secondly, I want the audience to be really focused during the performance, and leave feeling energized. Thirdly, I like to have something unexpected in each play, something the audience has never seen us do before. In this case, a genie on stilts two-feet high, and a short genie with karate skills appeared amidst clouds of "smoke." No one was expecting such a huge Genie of the Ring, and no one was expecting the Genie of the Lamp to be so much shorter than the first genie. Fourthly, I want to send a positive message in a way which is not preachy.
Q: DO YOU HAVE ANYTHING ELSE YOU'D LIKE TO ADD?
I should make a point of noting that my youngest son, Matthew, told me that I should be trying to publish my plays, since I am writing them all the time. He has been a source of inspiration, and his persistence encouraged me to submit this play. His older brother, Nathan, was the one who told me that I should start a drama club, and he has provided ideas and feedback throughout the club's existence. Both of my boys have always participated in my plays. My husband, Dave, is the one on the sidelines who is ever on-side with me, my own personal advocate.


text:
Cash Sent From the US Is Guatemala's Lifeline During the Pandemic
Migrants living in the U.S. are sending more money home than ever before.
Jeff Abbott
Planned Parenthood Just Got Officially Shut Out of Guatemala
"It is impossible to even have a debate about abortion here," said one observer.
Sandra Cuffe
Genocide Survivors Say Guatemalan Government is Blocking Their Fight for Justice
Institutional peace bodies are being shut down in the Central American nation. The move is seen by victims as a retreat by the government on promises it made as part of peace accords that ended the civil war.
Cash-Stuffed Suitcases Discovered in Guatemala Have Authorities Hunting a Former Minister
Luggage tickets on the cases containing cash worth $16 million had not been removed, and an arrest warrant has been issued for an official suspected of corruption.
A Massive Migrant Caravan Headed for the U.S. Just Got Dismantled in Guatemala
The exodus was stopped by Guatemalan soldiers days after they left Honduras. The government said the caravan was a COVID-19 contagion risk.
Maya Averbuch , Jeff Abbott
Coyotes Are Now Smuggling Migrants Back Home After They've Given Up on America
Travel restrictions around COVID-19 across Latin America mean some of those who want to get back home have to do it illegally.
Bryan Avelar, Deborah Bonello
COVID Has Caused Extra Harm for Guatemala's Victims of Gendered Violence
"Women will file a complaint of gender violence and the hearings will not happen until a year later. You can imagine the impact."
Miranda Mazariegos, Melisa Rabanales
Mayan Ruins in Guatemala Could Become a U.S.-Funded-Tourist Attraction
The development would include hotels, restaurants, and a miniature train to transport tourists along ancient Mayan highways.
Julia Lindau
Migrants Take Out Huge Loans to Pay Coyotes. Coronavirus Could Cause Them to Default.
Many Guatemalan migrants use their homes as collateral to pay smugglers. Unable to work, they're at risk of losing everything.
Megan Janetsky, Victoria Stunt
A Pregnant Guatemalan Woman Fell to Her Death After Attempting to Climb the Border Wall
She fell more than 19 feet and landed on her back, according to authorities. She was 8 months pregnant.
Trone Dowd
Why Guatemala's President Inked an Impossible Asylum Deal with Trump
"We don't think he is negotiating this in the name of Guatemala. We think he is negotiating impunity for him and his family"
Inside the Allegedly Exploitative Farm Owned by One of Canada's Richest Families
A group of Guatemalan women have come forward alleging they were sexually harassed and threatened with deportation at a company owned by the Aquilini family, who also own the Vancouver Canucks.
Jamie Maxwell


text:
Royal British International School
MD Welcome
School Mission & Vision
Charity Clinic
Directories & Departments
Classroom Experience
Primary Years
Secondary Years
Senior Years
RBIS Summer Camps
Real Madrid Campus
Ms. Ariel A Mar Tun
Ms Ariel (V.P./IB Coordinator)
Ms Ariel is both our Vice Principal and IB Coordinator. As IB Coordinator, she facilities weekly collaborative planning sessions with all of our Primary Faculty members. Ms Ariel has been working in International Education for over 6 years, holding posts as STEM (Science, Technology, Engineering, & Maths) Teacher, Primary Social Studies Teacher, and Primary Science teacher.
Supplementary to her BA in English, Ms Ariel hold U.K. teaching certification (Cambridge, L.T.T.C.) and has attended a comprehensive range of STEM courses, International Baccalaureate workshops, and other professional development courses.
Mr. Alexander Briseno
Mr. Alexander Briseno is the RBIS's primary years English teacher. He hails from Texas of the USA and found his way to Myanmar through his passion of being an educator. He has an extensive background in teaching international students of varying ages and well versed in the intricacies of the English language.
Mr. Alexander Briseno background in business management also allows him to bring more practical lessons and knowledge to the students. It is his personal goal to ensure all students leave the classroom each day having more knowledge academically and socially compared to when they entered. Having lived abroad for more than half of his life, he is well adapted to communicating with people of varying cultural backgrounds and am always happy to share his experiences with students.
Mr. Myat Thu
Mr. Myat Thu (V.P./IB Coordinator)
Mr. Myat Thu received his bachelor degree, B.Sc. (Physics) from the Yangon University in 1979 and a master degree, M.Sc.(Nuclear Physics) in 1985. Then he worked as a demonstrator and tutor in the Department of Physics, Yangon University from 1980 to 1989. In 2002, Mr. Myat Thu successfully completed the three-semester hour graduate level course in "Research on classroom learning and teaching course, Educ 594" from the State University of New York.
In 2015, Mr. Myat Thu attended a technology workshop at the Thomas Jefferson High School for Science and Technology, Virginia state, USA. Now Mr. Myat Thu is working in the Sciences and ICT department at the Royal British International School Yangon.
Ms. Wanzu
Ms Wan Zu, who comes to us from Malaysia, has a very strong academic background, having held positions as a teacher, coordinator, and primary head-mistress in Malaysia. Furthermore, Ms Wan Zu has also enjoyed tenure as an English teacher for both Preschool and Special-Needs children, giving her an excellent insight into early years and primary education, the difficulties faced by pupils, and early indications of learning difficulties.
Further to her educational Bachelor's and Master's, Ms Wan Zu is currently pursuing her Doctorate (Phd) in Education, specializing in Social Foundation and Educational Leadership. She sees young learners as constructivists when it comes to learning and encourages students to become lifelong learners both inside and outside of the classroom.
Accounts Department
No. 15 Thukhitar Street. Moe Kaung Road
Yankin Township, Myanmar
Tel: (95) 015 794 92/09950257208
Email: accounts@royalbritishinternational.com
Email: support@royalbritishinternational.com
Admissions Department
Email: admissions@royalbritishinternational.com
Marketing/Enquiry
Email: info@royalbritishinternational.com
Email: qa@royalbritishinternational.com
Email: hr@royalbritishinternational.com
Email: principal@royalbritishinternational.com
15 Thukhitar Street, , Moe Kaung Road, Yankin Township, Yangon Myanmar
Copyright © Royal British International School Yangon 2019 -2020


text:
Kaliban (Uran XVI) – zewnętrzny, nieregularny księżyc Urana, poruszający się ruchem wstecznym. Został nazwany od imienia postaci ze sztuki Burza Szekspira.

Kaliban został odkryty 6 września 1997 roku przez Bretta J. Gladmana, Philipa D. Nicholsona, Josepha A. Burnsa i Johna J. Kavelaarsa przy pomocy 200-calowego teleskopu Hale'a. Zespół ten w tym samym czasie odkrył też większy księżyc Sykoraks.

Zobacz też
 Chronologiczny wykaz odkryć planet, planet karłowatych i ich księżyców w Układzie Słonecznym

Przypisy

Linki zewnętrzne

Księżyce Urana
Obiekty astronomiczne odkryte w 1997

redpajama_set_name: RedPajamaWikipedia