Forest Management Plans are typically submitted by licensed foresters on behalf of their clients. MNAP reviews Forest Management Plans to determine if rare, threatened, or endangered species or sensitive habitats are present. Management recommendations are made where appropriate.
You can request a Forest Management Plan review by sending a map showing the property location via email (maine.nap@maine.gov), regular mail (93 State House Station, Augusta, ME, 04333-0093), or FAX (207-287-8040).
We hope that the Maine Data Checker has been a useful tool in developing your forest management plans. Technology evolves rapidly, including the settings on your web browser and on your computers, and many of you have experienced issues using the Data Checker. It seems there have been recent updates to Internet Explorer and Firefox that have caused more users to have problems using the Data Checker (Data Checker has never worked in Chrome or Safari). Unfortunately the coding behind the Data Checker is old, and we are unable to update it to make it usable in current web browsers. In addition to changing frequently, technology is expensive.
We are exploring options for a new tool that will perform the same function, which is to answer the single question: Is there a natural resource feature present or near your lot? This tool needs to produce a map for the user, maintain user confidentiality to other users, allow us to know who is using the tool, and keep the data hidden. We will keep you posted, but it is likely to be a while before such a tool is available.
In the meantime, please submit requests for review for your lot to maine.nap@maine.gov. The Maine Natural Areas Program works with Maine Department of Inland Fisheries and Wildlife to provide you with the most up-to-date information for any natural resource features that may be on or near your lot, and to provide management recommendations should any be present. You will receive a letter, checklist, and map with the response. Requests should include a map of the property, and these can be sent in an email (maine.nap@maine.gov), via FAX (287-8040), or via regular mail (MNAP, 93 SHS, Augusta, ME 04333). If you would like the landowner name on the response, please include that with your request.
See also Forestry Technical Assistance.


Enterprise growth and IT equipment have become so closely linked that planning and building a high performance data room is one of the critical issues for IT managers today.
With the core technologies of power electronics, the expert teams at Delta Electronics have developed a new generation of data center infrastructure solutions: InfraSuite.
Delta InfraSuite includes power management, rack & accessories, and environmental management system.


text:
Behind the US war drive against North Korea
The test firing by North Korea of a short-range missile on Monday, the latest in a series of similar missile trials, has provoked another round of condemnations and warnings by Washington and its allies, amid a continuing US military build-up near the Korean Peninsula. The US Navy announced last week that it was deploying the USS Nimitz and its battle group to the region, bringing to three the number of aircraft carriers able to direct their massive fire power against North Korea.
President Trump responded to the missile test by tweeting that North Korea had shown "great disrespect" towards its neighbour China, which was "trying hard" to compel Pyongyang to bow to US demands to abandon its nuclear and missile programs. Washington has placed immense pressure on Beijing, above all through the threat of a war on its doorstep, to use its economic muscle to rein in the Pyongyang regime.
Speaking on CBS's "Face the Nation" on Sunday, US Defence Secretary James Mattis made clear that China had limited time. He condemned North Korea as "a direct threat to the United States," adding: "We don't have to wait until they have an intercontinental ballistic missile with a nuclear war head on it." Mattis warned that any war with North Korea would be "catastrophic" and involve "probably the worst kind of fighting in most people's lifetimes."
The US war drive against North Korea has been accompanied by an incessant campaign in the media vilifying the Pyongyang regime and the alleged threat posed by its tiny nuclear arsenal. Mattis has already indicated that any attempt by North Korea to use a nuclear weapon would be met with an "effective and overwhelming" response—that is, annihilation, using America's huge nuclear armoury.
Like the US-led conflicts in the Middle East, North Korea's "weapons of mass destruction" and its gross human rights abuses have become convenient pretexts for preparing a war against a small, isolated and economically backward country. US imperialism has other, predatory, economic and geo-strategic objectives. Above all, a war to destroy the Pyongyang regime would be aimed at weakening and undermining China, which has always regarded North Korea as an important buffer against the US and its allies in North East Asia—Japan and South Korea.
Nor is the sudden rise in tensions on the Korean Peninsula solely due to Trump and his administration's militaristic propensities. Rather Trump's aggressive and menacing stance against North Korea is a product of rapidly sharpening geo-political rivalries in Asia and throughout the world, fuelled by the ever worsening capitalist breakdown in the wake of the global financial crisis of 2008.
Ever since the collapse of the Soviet Union in 1991, the chief objective of US strategy has been to prevent any economic or military challenge from its rivals and, in particular, to prevent the Eurasian landmass from being dominated by one or more competitors.
Former US national security adviser Zbigniew Brzezinski spelled out the rationale in 1997 in Foreign Affairs: "What happens with the distribution of power on the Eurasian landmass will be of decisive importance to America's global primacy and historical legacy … In a volatile Eurasia, the immediate task is to ensure that no state or combination of states gains the ability to expel the United States or even diminish its decisive role."
Between 1950 and 1953, the US waged a criminal war on the Korean Peninsula against China, which cost the lives of millions, in order to ensure its dominant position in North East Asia. Washington's attitude to Pyongyang, with which it never signed a peace treaty, has, ever since, been one of unremitting hostility. After the demise of the Soviet Union, American strategy has been based upon regime change and the incorporation of North Korea into its sphere of influence, at China's expense. The US failed to live up to its side of the agreements, struck in 1994 and 2007 with North Korea, to denuclearise.
The rising danger of a US attack on North Korea coincides with a barely disguised civil war over foreign policy raging within the American political establishment and state apparatus. The differences are, in reality, tactical: whether in its drive for dominance of Eurasia, the US should focus first on Russia or on China. The constant barrage of accusations against the Trump administration's alleged links to Russia is driven by opposition to his efforts to reorient US foreign policy towards a confrontation with Beijing, rather than Moscow.
Washington's unrelenting pressure on Beijing over North Korea is, in part, a response to growing signs that the Obama administration's "pivot to Asia"—which was intended to isolate and militarily encircle China—is unravelling. The tilt by the Philippines, under President Rodrigo Duterte, away from Washington and towards closer relations with Beijing, is the most obvious sign of similar drifts elsewhere in Asia and internationally to take advantage of economic opportunities in China.
The US is also facing challenges in Europe, most openly from Germany, where Chancellor Angela Merkel declared, after the weekend's G7 meeting, that "we Europeans must really take our destiny into our hands," rather than relying on the US. Earlier this month, China formally launched its ambitious One Belt, One Road initiative—a plan for massive infrastructure spending on roads, ports, pipelines, rail links and telecommunications across Eurasia, linking China to Europe. Significantly Germany and Britain, which have both looked to boost economic relations with China, were strongly represented at the gathering in Beijing.
Unable to outbid China economically, the US is preparing to use its military might to undermine a potential competitor and disrupt the relations of its rivals with Beijing—and not for the first time. In 2002, President Bush tore up an agreement with North Korea to denuclearise and branded it part of an "axis of evil," along with Iran and Iraq. In doing so, he effectively sabotaged South Korea's so-called "Sunshine Policy" which, with the backing of China and the European powers, was a plan to transform the Korean Peninsula into a transport and pipeline conduit to link Europe and East Asia.
Fifteen years later, the stakes are far higher and the threat of war much greater. Facing a mounting political crisis and acute social tensions at home, the Trump administration is resorting to more and more reckless measures to try to assert US dominance. Whether on the Korean Peninsula or another flashpoint, such as the South China Sea, US imperialism is being driven to take military measures that would threaten to precipitate a war between nuclear armed powers and a catastrophic conflagration.
Peter Symonds
North Korean-US tensions rise as end-of-year deadline approaches
US renews insults and threats against North Korea
Japanese and South Korean parliamentarians broach talks over trade dispute
US-North Korean nuclear talks stall again
Trump meets North Korean leader as part of broader anti-China agenda
The East China Sea Crisis
Japan plans for massive military build-up aimed at China
US navy sends destroyer to challenge China in South China Sea
Japan scrambles fighter to intercept Chinese military aircraft
Japan plans missile deployment in East China Sea

redpajama_set_name: RedPajamaCommonCrawl


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BOOK: Piaget J. (1962, original edition 1945) Play, dreams and imitation in childhood, London, Heinemann.
BOOK CHAPTER: Aziz-Zadeh L. & Ivry R. B. (2008) The Human Mirror Neuron System and Embodied Representations, in Sternad D. (ed.) Progress in Motor Control, New York, Springer, pp. 355-377.
ONLINE MATERIAL: Accessed April 23, 2014.
In-text references should be cited by giving the author's name, year of publication (Smith, 2001) and specific page numbers after a direct quotation. If there is more than one reference, the list of references should be in chronological order (Smith, 2005; Peterson, 2014). In case of more than ., the first name should be followed by et al. and the names should be listed in full in the References. Throughout the article authors should be careful in maintaining authorial anonymity; where authors cite their own works in the text, they should cite them as 'author's own' in both text and bibliography until publication (Authors' own, 2007).
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Browse other questions tagged support tag .
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Education plays a pivotal role in shaping the personality of a child into a healthy mind and happy soul. It tones an individual's aptitude for academic excellence and helps him/her to face the challenges of life in a balanced and harmonious way.
At Anekant English Medium School, Baramati, we seek to create a holistic learning environment and make teaching a joyful process. Our mission is to nurture individual potential. We believe in cultivating multiple intelligence's and talents of students. We constantly evaluate and re-evaluate so as to make the process of learning interesting, effective and result oriented.
We seek to accomplish all this with your constant support and confidence in us. We assure you that in this journey towards excellence, we will continue to inspire and motivate learners to become empowered, independent and thinking individuals, who are able to make a mark for themselves in society in the days to come.


The Michigan music community as well as the international metalcore scene was hit with a hard loss yesterday upon the announcement of Kyle Pavone, vocalist and keyboardist of Michigan native band We Came As Romans, passed away at a young age of 28.
Pavone joined the band in 2008, and is featured on all five of their full length albums.
The band included the lyrics to "Promise Me" in their statement. The lyrics were one of Pavone's final tweets. In addition, "Promise Me" is a song that he opened up to the public about it's deeply personal meaning to him.
Pavone has touched many lives in the music community. Not only through his immense lyricism and talented vocals; his role in We Came as Romans played a huge part in inspiring young musicians in the Michigan music community.
We Came As Romans provided unconditional support and opportunities to the local scene. Their Christmas show at The Crofoot Ballroom invited a select few local bands the opportunity to open for them in the ballroom, an opportunity not many may have experienced without the band's hospitality.
In addition, their stop at The Crofoot last year on their headlining tour provided many locals to open for them, creating a mini festival out of the entire complex.
On stage, Pavone was noting short of smiles and interactions with fans. He was known for climbing various stage elements or hopping onto a pool float and crowd surfing while he sang.
"Since the first time I put "To Plant A Seed" in my car radio, I was absorbed by the sound and the lyrical content. The words that Kyle spoke moved mountains, and sometimes I feel that the only reason musicians like myself have a chance to stand tall is because of the shoulders we stand on, Kyle being one of them to me and to many others. Kyle gave us joy, relief, and even opportunity. The world will never forget him, and his words will forever live on through his lyrics, those of which we will always hold close to our hearts. Rest easy, Kyle." said Robbie Hunt, vocalist of As We Divide, one of the local bands that had the opportunity to share the stage with Pavone.
Pavone was a symbol to those small bands starting out that they too can make it. Aspiring artists learned from Pavone and We Came As Romans, and strived to achieve in the same way.
Musicians across the community are sharing their memories of Pavone across social media, joining together to mourn one of Michigan's most talented.
"We will miss his smiles, his sincerity, his concern for others, and his impressive musical talent. In lieu of flowers, we will be providing information regarding charity donations this coming week. The family and the band wish to thank their fans and the music community for all of their love and support as they navigate their grief." the band stated.


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Stay Tuned: 'The Good Doctor' is a good show
Melissa Crawley More Content Now
Nov 7, 2017 at 10:23 AM Nov 7, 2017 at 10:23 AM
Focusing on Dr. Shaun Murphy (Freddie Highmore), a young surgical resident who has autism and savant syndrome, �The Good Doctor� shines a light on what life is like for adults with similar characteristics. It�s a medical drama with a universal message about how we should define ourselves beyond our limitations, no matter what those might be. Well-paced, with solid performances from a diverse cast, the show is both thoughtful and entertaining.
Richard Schiff (�Ballers,� �The West Wing�) plays Dr. Aaron Glassman, President of San Jose St. Bonaventure Hospital and mentor to Shaun. He hires Shaun before seeking the approval of the hospital�s board members and in a contentious meeting, one accuses him of making Shaun�s hire personal. He snaps back: �Letting things get personal is how we make it matter.� It�s an idea that sets the stage for the show�s doctor/patient interactions.
A running theme in almost every case is the boundary between the personal and the medical. In one episode, a woman has a cancerous tumor in her abdomen. Shaun�s fellow surgical resident Dr. Jared Kalu (Chuku Modu) sees the difficult and life-threatening procedure as an opportunity to test his skills while their colleague Dr. Claire Browne (Antonia Thomas) reacts emotionally and offers the woman hope, promising her that she will live to see her son�s wedding. Which one is being a �good� doctor?
Shaun�s response to the woman�s case is to suggest matter-of-factly that she will probably die but they could remove one of her kidneys to more easily extract the cancerous mass. It�s an unconventional approach with no promise of success and one he offers with no empathy. Yet, Shaun�s inability to personalize is countered with flashback scenes to his childhood. We learn that his father was abusive, his younger brother was his best friend and he became a surgeon because he saw his brother die in an accident when they were young. He may not appear to others to be capable of emotional connection but the flashbacks offer a glimpse into his inner life. Shaun feels things just not in a way that his colleagues understand. It�s an impactful way to both personalize the character and depict autism.
Shaun�s boss, Dr. Neil Melendez (Nicholas Gonzalez), accepts that Shaun has extraordinary medical skills but is less accommodating about his inability to communicate with patients. Gonzalez plays Neil as the typical arrogant attending surgeon but adds a few layers to make him less predictable. Hill Harper (�CSI: NY�), as Dr. Marcus Andrews, the head of surgery, is a highlight, and his alpha male performance adds tension to the story. He wants Glassman�s job and is even less accepting of Shaun than Neil is.
Highmore is well cast as Shaun, delivering a natural performance that allows him to disappear into the character. He makes you want to watch Shaun�s journey and root for him along the way. Despite a somewhat predictable pattern of Shaun�s genius ideas saving lives, �The Good Doctor� is a good show that offers a unique take on the medical drama.
�The Good Doctor� is on Mondays at 10 p.m. EDT on ABC.
� Melissa Crawley is the author of �Mr. Sorkin Goes to Washington: Shaping the President on Television�s �The West Wing�� and the recently released �The American Television Critic.� She has a Ph.D. in media studies and is a member of the Television Critics Association. To comment on Stay Tuned, email her at staytuned@outlook.com or follow her on Twitter at @MelissaCrawley.


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The Pakistan national cricket team toured South Africa from 20 November 2013 to 30 November 2013. The tour included three One Day Internationals (ODIs) and two Twenty20 Internationals (T20I) between South Africa cricket team and Pakistan. The Twenty20 series was drawn 1-1 while Pakistan won the ODI series 2-1. This was Pakistan's first ever ODI series win over South Africa and became the first Asia team to beat the Proteas in an away series.

Squads

T20I series

1st T20I

2nd T20I

ODI series

1st ODI

2nd ODI

3rd ODI

References

International cricket competitions in 2013–14
2013–14 South African cricket season
2013-14
2013 in South African cricket
2013 in Pakistani cricket

redpajama_set_name: RedPajamaWikipedia


This snack can be served with a sprinkling of icing sugar or with warm custard.
I particularly like eating it as a serving with cream on a stack of warm pancakes.
The following recipe has been provided by Loretta Lee, a Malaysian living in Lincolnshire, who blogs at Nyonya Recipe.
Mix all the ingredients together until you get a soft dough.
Drop spoonfuls of the mixture and fry till golden brown, turning frequently.
Next Post Does fawning over Nick Clegg still have a place in the party?


text:
Victorian leadership on renewable energy to deliver higher jobs and lower power prices
The six successful wind and solar projects announced under the Victorian Government's reverse auction scheme today will deliver a massive boost for jobs and investment in regional Victoria while driving down power prices, the Clean Energy Council said.
Clean Energy Council Chief Executive Kane Thornton said the Victorian Government's support for these projects and a new commitment to 10,000 home battery systems were great examples of political leadership that would drive down electricity costs and put power back into the hands of all Victorians.
"The Victorian Renewable Energy Target (VRET) is providing long-term certainty for investors that is resulting in the lowest cost renewable energy projects. Combined with the recent announcement to support rooftop solar and today's commitment to 10,000 home battery systems, it is clear the Victorian Government is taking a leadership role on energy policy," Mr Thornton said.
"Renewable energy such as solar and wind is now the lowest cost power generation that can be built today. As coal-fired power plants continue to retire from the system, the 928 MW of new renewable energy which will be built under the Victorian Renewable Energy Target (VRET) will help to push down power prices while creating hundreds of regional jobs and $1.1 billion of investment.
"The Victorian reverse auction scheme is a well-designed policy that will ultimately save consumers money on their bills while providing much-needed certainty for the investors in the three wind farms and three large-scale solar plants announced today.
"Reducing power bills and emissions while securing the reliability of the power supply is achievable, and states like Victoria are showing it can be done with a mix of policies that are ambitious but achievable.
"Our industry is excited to continue working with the state government to transform the economy to one which is smarter and cleaner," he said.


I was quite interested to see this book very favorably reviewed in the International Journal of Intelligence and Counterintelligence (IJIC), the top journal in the field, so it was with some disappointment that I found it to be less robust than I expected.At one level, that of a very basis reference, it could be a solid four-star effort, and I give the author and publisher credit for having conceptualized and executed this on-going endeavor. Especially bothersome is its limited coverage–a directory such as this, especially in the aftermath of 9-11, must be comprehensive and include countries like Colombia, Nigeria, Qatar, Saudi Arabia, and the Central Eurasian "stans" to name a number that are not covered.
I found both the updates and the further readings to be a very mixed bag, with too many countries that I am familiar with suffering from what appears to be either an over-reliance on one or two primary sources or somewhat random notation. It is clear to me that this book does *not* benefit from a systematic literature review, nor is it really current with the great web sites that are available, both in general terms as well as with specific country orientations–on top of the limited coverage, less than a third of the world, this really reduces its value.
1) Create a broader board of advisors. The author performs heroically for one man, but clearly does not have the global network of true experts that is needed to make sure his coverage is world-class.
2) Add a State of Intelligence report to the front of the book, with regional overviews. The emergence of a European intelligence community, the impact of the Kosovo war on this movement as well as NATO, NATO's publication of an open source intelligence handbook, etc., the specific points of failure for 9-11 as well as the Afghan campaign that failed to capture the Al Qada leadership, all should be in there, together with the Homeland Security initiative and new relations among nations now quasi-committed to improved cooperation against terrorism–while decapitating their programs against crime. To be a proper reference work, this book must also take care in the overview to tease out the threads of progress among the varied intelligence communities that exist-national civilian, military, law enforcement, investigative journalism, business intelligence, and academic studies on intelligence. The fact that it does not reference such vital organizations as the Society of Competitive Intelligence Professionals, or the International Association of Law Enforcement Intelligence Analysts, for example, suggests that the book is being put together along very old lines of thinking, and is not yet coming to grips with the dramatic changes occurring in the real world of intelligence.
3) The publisher, or a non-profit foundation, must fund a proper literature review. Even for the United States, the most obvious country, most of the intelligence reform books published between 1999 and 2002 and listed by the Council on Intelligence do not appear in this reference work, nor does it retain the Aspin-Brown Commission Report or the House Permanent Select Committee Report on IC21, as references of continuing relevance.
4) The index must be expanded to include all authors and organizations.
5) The acronyms must be expanded to be truly comprehensive. A one page listing that is mostly military ranks and failed to include the acronyms PfP (Partnership for Peace), OSINT (open source intelligence), or C4I (command, control, communications, and intelligence–a vital aspect of understanding where intelligence fits in the larger picture) is simply not serious.
Bottom line: I will keep this book as a light-weight reference, but I will not buy it again unless the publisher gets serious about producing a quality product that is truly international and reflective of the intelligence reform and intelligence failure lines of inquiry that are well-known to serious professionals who understand that intelligence is the core competency of both governments and organizations in the age of information.


Samford University's annual musical celebrations of Christmas will begin Nov. 29 with a free concert by the Bells of Buchanan handbell ensemble. The concert, sponsored by Patty McDonald, will begin at 7:30 p.m. in Samford's Brock Recital Hall.
The annual Hanging of the Green celebration will feature music by University Chorale Dec. 1 at 6:00 p.m. in Reid Chapel. The event is free-of-charge and open to the public.
The Michael J. and Mary Anne Freeman Theatre and Dance Series, in partnership with Merrill Lynch, will present the beloved Irving Berlin musical "White Christmas" Dec. 1-3. Performances will be Dec. 1 at 10 a.m. (for schools,) Dec. 2-3 at 7:30 p.m. and Dec. 3 at 2:30 p.m., all in Samford's Wright Center Concert Hall. The Dec. 2 performance is sponsored by Merrill Lynch. Tickets are $12 (adults,) $9 (55+) and $6 (students/children). Purchase tickets online at arts.samford.edu or call (205) 726-2853.
The Davis Architects Guest Artists Series will present a concert by Boston Brass Dec. 6 at 7:30 p.m. in Brock Recital Hall. The event will include Classical and Christmas music, a performance by the University Wind Ensemble and a premiere by composer and Samford music professor Sarana Chou. Tickets are $20 (adults,) $15 (55+) and $10 (students/children). Purchase tickets online at arts.samford.edu or call (205) 726-2853.
Finally, Patty McDonald will sponsor a free Christmas Band Concert Dec. 8 at 7:30 p.m. in Brock Recital Hall.


That, I am not alone in the struggle to bring conscience, faith and the Bible itself back into the national psyche offers little consolation because, God seems to have required this at a time when it is anything but vogue. But of all the absurd attempts to remove any mention of God from the public, perhaps the latest effort tops anything that has happened to date.
District Judge, Ronald Lagueux ruled that Cranston High School in Rhode Island must remove a placard that has been in the school for decades because it ends with the word "Amen." The authoritarian 'out with it' was supposedly dignified by the judge in a forty page opinion stating all his learned and wise reasons to oust the placard.
Seventy percent of voters expressed their view that Sharia law should not be practiced in the great state of Oklahoma, but the opinion of one has prevailed. The appeals court decided to stand behind Judge Vicki Miles — Lagrange, who said "When the law that voters wish to enact is likely unconstitutional, their interests do not outweigh Mr. Awad's in having his constitutional rights protected." Awad is the executive director of the Council on American-Islamic Relations in Oklahoma; who would have guessed?
Perhaps we have taken the fight against terror in the wrong direction. Maybe we need only send a few Christians to Muslim nations and go region by region asking for our civil rights and religious freedoms to be given place as it is here in the U.S. How successful would we be at that?
Besides raising the question of whether this judge ever heard the sage wisdom of Forest Gump's Mom, we can only guess that she has read nothing about honor killings, decapitations and limb removals that are commonly practiced, sanctioned and demanded under Sharia Law. Some say the nation is going down, who could imagine that some would want us to stop and pause in the seventh century just long enough to cast a few of our children off, before we slide the rest of the way down.
How dare we get cranky with Newt Gingrich for suggesting that federal judges be reined in, to be honest, some of them should be impeached, and others jailed. Give us some good ole American jurisprudence based on the Constitution, balance, equity and a good helping of common sense, and who knows, maybe even an apology from Newt's critics!
In Arizona a judge has told students they have a right to sue their school districts for bouncing La Raza that some see as an organization that is racially bent, hate mongering and anti-American. Arizona's HB 2281 was passed to ensure that no racially inclined courses can be taught in schools. The opinion of one judge is now calling for the students to ignore, fight against and overturn the law if it is their opinion that it is not fair. Here is a case of an opinion that is meant to spawn other opinions and change the law. How do you spell confusion?
When leaders begin to trust their own judgment above the laws of God or our own Constitution what happens is perhaps best seen in a statement made by one of the most ancient of biblical figures. Job, a man well tested and tried in the crucible of suffering, emerged as one who earned the approval of God. Job declared, "He leadeth counsellors away spoiled, and maketh the judges fools." (Job 12: 17) Should we be rift with Newt for noticing that in America, today, this principle is still alive and well?
In many ways we are all becoming fools for thinking that getting one conservative president to replace Barack Obama will solve all the nations' problems. What have we done to bring the nation back around? How many of us are willing to return to the values we were once connected to and willing to live and die for if need be?
In a generation that is history challenged, morally decadent and socially operating on the pure power of liberal magic fairy dust it seems that we now believe that America is to be ruled by opinion rather than law. The Constitution may be an idea whose time has gone and if President Obama's adherence to that revered document is any example, we are all now free to float into the new charter for American jurisprudence and governance which we might call, the great doctrine of "I did it my way."
This is neither satire nor tongue in cheek, but it is the liberal rap of the day. The only thing more disturbing is that the polls tell us that millions will still vote both the president and the liberal judges' right back into office if they can. Is anyone listening, can we pull ourselves away from American Idol and the Good Wife long enough to change the channel to some relatively reliable unbiased news source. (If you could actually find one) God forbid we actually visited a watchdog site and spent a few minutes studying the actual records of both the president and the current field of candidates.
Benjamin Disraeli said "The youth of a nation are the trustees of posterity," but unless they are taught to discern the truth before the sands of time run out on them or their generation's moment in time, they may as well be the trustees of a mess of porridge. Opinions are endless, but the rule of law is the foundation, the walls and the protective roof over any nation. Nations swayed by the trends of the day, have according to history's immutable record, all failed and ceased to be.
Opinion seems to have cheated the evangelicals out of an evangelical candidate. Who can explain why they did not rally behind Michele Bachmann and Rick Perry who were without doubt the only true evangelicals to have tried for the GOP nomination. Perhaps they were depending on some opinion rather than the very criterion they so readily espouse which is their own faith and doctrine. Are they now the proof of America's confusion and the very line of demarcation between a good church member and a poor disciple? If I believe that to be true, will they counter with the proverbial; that's only your opinion? Isn't it disturbing how easily one opinion can cancel or simply eliminate another?
It seems that this is not only the day of the petted opinion, but it has become a day of the consensus of opinions. If more people think it is more important to fix the economy than to fix America's dying and gasping morality, does that consensus equal a sure path for Mitt Romney? Or is it the day of opinions that yield up the best return for a nation clamoring for more creature comforts and security rather than some ethics, morality and Godliness which come at such a high price in personal commitment?
Can we suspend some opinions for others based on the personal gain factor? Can we ignore our opinions about flip flops, Bain Capital, offshore accounts in the Cayman Islands, and a promise to leave Obama's 'don't ask don't tell' policy in place in our military, all because we think our jobs, bank accounts, retirement plans and Social Security will have a better chance to survive?
Can evangelicals suspend their opinions about Mormonism's doubtful 'Book of Mormon' polygamy and a Christology that reeks of error and bad exegetical bible interpretation, all because of some other opinion that is anything but evangelical? God knows, I don't want to know what that opinion might be.
Even as churches in the Middle East are being firebombed, Muslim converts to Christianity are being killed and threatened with execution and Christianity is under a full attack from every liberal from high school students to judges both in America and abroad, the truth is this, if you are a Christian your opinion counts for absolutely nothing. Christians have a Savior who we also call our Master, which means that we gave up our opinions at the foot of the cross. Whatever is antichrist we are against: regardless of how much wealth, security or comfort it might promise.
Wanting what is right, Godly and good for the country is a stand not an opinion. It will not be the shifting sand of trends and pop culture inclinations that will produce the best president in 2012. The founders, pioneers, statesmen and industrious of this nation were men and women whose legacy of conviction and moral fortitude did not waver through adversity, economic problems and times of uncertainty, it is the only stuff that can produce a legacy. They were men and women who counted the cost, (Lk 14: 28) rather than counting their wealth.
We have gay military personnel that gave up our secrets, occupy movements invigorated by union mobsters, high school students who are fighting the dreaded word 'amen,' and evangelicals that seem to have completely lost touch with what actually defines them. We have a president that is choking free enterprise, and rallying around the gay agenda like it was the greatest single cause in last two centuries, but isn't it just great, that we still have our opinions?
In the end will we be glad to have one last opinion about which way a great nation should fall? Some would say all at once, while others would insist it is better if it collapses slowly. We can fill the blogs and toast the endless editorials that say everything anyone has ever said about it; all the while they are saying nothing at all?
When opinions become the golden calf that we worship it is apparent that we are nearing the place where all standards are disappearing, in the ancient world that spelled the end of entire civilizations. Little in human nature has changed since then and nations and civilizations don't seem to have learned a thing. This is not an opinion but a historical fact, you know, one of those things we're doomed to repeat if we don't learn from it.
Only one generation has passed to come to the realization that religion is not after all the "opiate of the masses" as stated by Karl Marx, but it turns out that opinions are the real opiates. Can we vet, debate, discern, discuss and then decide on a president under the influence of something that by any other name is still, dope? Let's do our homework America and choose based on solid facts and nothing more.


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text:
What Happened to Macbeth Shoes?
by Jacky Chou
Shoe lovers around the world were devastated when Macbeth Shoes closed its doors in 2018. But what exactly happened to this beloved brand?
The History of Macbeth Shoes
Macbeth shoes were a popular brand of footwear in the early 1900s. The company was founded in 1890 by John Macbeth, and the shoes were known for their quality and durability. The company began to decline in the 1920s, and by the early 1930s, it was out of business.
There are several theories about what happened to Macbeth shoes. One theory is that the company simply could not compete with larger shoe companies that had more money to invest in marketing and advertising. Another theory is that the quality of the shoes declined as the company tried to cut costs.
Whatever the reason, Macbeth shoes are no longer being made. However, there are still many people who remember the brand fondly and are curious about its history.
The Decline of Macbeth Shoes
Macbeth shoes were once a popular brand of footwear, known for their durability and stylish designs. However, in recent years, the company has seen a decline in sales and popularity. There are several possible explanations for this decline.
First, Macbeth shoes have been losing market share to other brands. This is likely due to a combination of factors, including competition from other companies and changes in consumer preferences. Second, the quality of Macbeth shoes has decreased over time. This has led to customer dissatisfaction and further declining sales.
Finally, Macbeth shoes have been hit hard by the recession. Many consumers are now looking for cheaper alternatives to name-brand products. As a result, Macbeth shoes are no longer seen as a good value for the price.
It is unclear what the future holds for Macbeth shoes. The company will need to make some changes if it wants to regain its position in the marketplace.
The End of Macbeth Shoes
Macbeth shoes was a footwear company based in Scotland. The company was founded in 2001 by Gordon Fraser and Danny Strassner. The company produced a range of shoes, including running shoes walking shoes, and casual wear.
In 2009, the company ran into financial difficulties and was forced to close its doors. The company's assets were sold off, and the brand name was bought by a US-based company. The new owners have since relaunched Macbeth as a lifestyle brand, selling a range of clothing and accessories.
The Legacy of Macbeth Shoes
Macbeth shoes were once a widely known brand of skateboarding shoes. The company was founded in the early 1990s by Mike McGill and Gavin Odell, two professional skateboarders from Southern California. McGill and Odell were fed up with the poor quality of skateboarding shoes on the market and decided to start their own company to make better shoes for themselves and their friends.
The company quickly gained a following among other professional skateboarders, and within a few years, Macbeth was making shoes for some of the biggest names in skateboarding, including Tony Hawk and Bam Margera. The company's popularity continued to grow throughout the 2000s, and by 2006, Macbeth was bringing in $40 million in annual sales.
However, in 2007, the company was sold to Globe International, a large sporting goods conglomerate based in Australia. Under Globe's ownership, Macbeth began to lose its identity as a skateboarding-specific brand, and many professional skaters who had been loyal to the brand for years began to look elsewhere for their footwear needs.
By 2010, Globe had stopped manufacturing Macbeth shoes entirely, and the once-popular brand became little more than a memory for many people. While it's unclear what exactly led to the downfall of Macbeth shoes, it's safe to say that the loss of its identity as a skateboarding brand was a major factor.
What Happened to the Macbeth Brand?
The Macbeth brand was started in 2001 by entrepreneur Ethan Beers. The company was named after his favorite novel, Macbeth by William Shakespeare. The company initially sold shoes and other accessories through an online store. In 2003, the company expanded its product line to include clothing and eventually opened its own physical retail stores.
The company grew quickly and by 2006, it had over 60 stores in the United States. However, in 2007, the company began to experience financial difficulties. It closed many of its stores and laid off a large number of employees. In 2009, the company filed for bankruptcy and was acquired by Dick's Sporting Goods. The Macbeth brand was relaunched in 2012 but it has not regained its previous level of popularity.
Where are Macbeth Shoes Made Now?
Macbeth shoes are now made in China. Previously, they were made in the United States. The company outsourced its manufacturing to save costs.
Are Macbeth Shoes Still Popular?
It seems like only yesterday that Macbeth shoes were all the rage. The funky designs, bright colors, and comfortable materials made them a favorite among young people everywhere. But lately, it seems like Macbeth shoes have fallen out of favor. So what happened?
There are a few theories floating around. One is that the company simply lost touch with its target market. Young people's tastes change quickly, and Macbeth failed to keep up with the times. Another theory is that the quality of Macbeth shoes has declined in recent years, leading consumers to look elsewhere for their footwear needs.
Whatever the reason, it's clear that Macbeth is no longer the powerful force in the shoe industry that it once was. But who knows? With a few changes, perhaps the company can make a comeback and recapture its former glory.
The Macbeth Shoe Company Today
The Macbeth Shoe Company is no longer in business. Its last store closed in 2017. The company was founded in 1874 by John Macbeth and was originally headquartered in Toronto, Canada. In its early years, the company specialized in handcrafted leather shoes and boots. By the early 1900s, Macbeth had become one of the largest shoe manufacturers in Canada, with a network of stores across the country. In the 1950s, the company expanded into the United States and opened a factory in New York.
The company continued to grow throughout the second half of the 20th century. In the 1980s, it was sold to a private equity firm and went public on the Toronto Stock Exchange. In the 1990s, Macbeth was bought by a holding company controlled by British billionaire Lord Astor.
In 2006, Lord Astor's holding company went bankrupt and Macbeth was sold to an investment firm based in Hong Kong. The new owners restructured the company and closed many of its stores. In 2010, they filed for bankruptcy protection and announced that they were discontinuing the Macbeth brand. All of its remaining stores were closed by 2017.
The Future of Macbeth Shoes
In October of 2019, it was announced that Macbeth shoes would be discontinuing its production line. This came as a shock to many, as the brand had been popular among alternative and punk subcultures for nearly two decades. The company released a statement saying that they "decided to close [their] doors and move on to other projects."
So, what does this mean for the future of Macbeth shoes?
For starters, it means that the brand will no longer be producing any new shoes. This means that, although you may still be able to find Macbeth shoes for sale online or in stores, the selection will dwindle over time as existing inventory is sold off. Additionally, it's likely that prices for Macbeth shoes will increase as they become more scarce.
If you're a fan of Macbeth shoes, it's important to remember that there are other brands out there that may fill the void left by Macbeth's departure. While no brand is likely to completely replicate Macbeth's unique style, there are certainly other companies out there producing quality alternative and punk footwear. So don't despair – just do some research and you're sure to find a new favorite brand!
After decades of success, Macbeth shoes is no more. The company announced its closure in 2019, bringing an end to a footwear brand that was once beloved by skaters and punk rockers alike.
What happened? In short, the company failed to adapt to changing tastes and trends. While Macbeth had a loyal following, it didn't have the same mass appeal as some of its competitors. In the end, that proved to be its downfall.
Jacky Chou
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text:
\section{Introduction}

The large-scale structure of the universe as observed in redshift
surveys displays a complicated geometry.  This complex structure
referred to as the "cosmic web", is characterized by the presence of
clusters, filaments, sheets and voids. More than 30 years ago galaxy
surveys found evidence of filaments \citep{1981ApJ...243..411G}
and analyses of modern surveys find hundreds of filaments and
pancakes \citep{costa-duarte2011}.  Numerical simulations complement
the obserations, and find that sheets (which include walls and
pancakes) may occupy over half of the volume \citep{Hahn2007a}.

The structure of the cosmic web is the result of the gravitational
growth of the small amplitude primordial density and velocity
perturbations.  \citet{1970A&A.....5...84Z} first suggested the
anisotropic nature of gravitational collapse leading to Zeldovich
Pancakes, which are formed when an overdense region collapses first
along one of its principal axes. The pancake picture was further
developed in \citet{1982GApFD..20..111A} and \citet{shandarin1989}.
Various papers have simulated Zeldovich pancakes under controlled
conditions
\citep{1984ApJ...281....1F,1998ApJ...509...62T,Binney-2004,Schulz-2013}
which typically involve simulations of particles only along a fixed
axis perpendicular to the pancake.

The dynamics of pancakes has been studied extensively with large
numerical $N-$body simulations, where pancakes have been observed over
the last almost 20 years \citep{1995PhRvL..75....7S}. The dynamical
importance of these sheets, expressed through the mass fraction of
sheets in the cosmic web is rather uncertain, and varies in the range
$(6\% - 36\%)$, while the volume fraction varies from $(5\% - 54\%)$
\citep{cautun2014,forero-romero-2009,hoffman2012,Hahn2007a,Shandarin2012,
2010MNRAS.408.2163A,Shen06,Doroshkevich70}.

There are several ways of defining whether a structure in the cosmic
web is a filament, sheet, void or halo.  Often, structures are
differentiated on the basis of eigenvalues of the second derivative of
the tidal tensor $T_{ij}$, for a sheet $T_{ij}$ has only one positive
eigenvalue. Alternatively the sheets can be defined through the shear
tensor, which is a rescaled derivative of the velocity field.
\citep{2007MNRAS.381...41H, forero-romero-2009,
  2010MNRAS.409..156B,costa-duarte2011,hoffman2012}.  In recent
studies, the entire 6 dimensional phase space information is taken into
account for recognizing structures \citep{Shandarin2012, abel2012,
Neyrinck12, Neyrinck2012b}.

Direct observations of pancakes is extremely difficult whereas
identifying halos is straight forward. This is due to their planar nature
and their low contrast with the background \citep{Aragon07,
2010MNRAS.408.2163A, cautun2014}.  Generally,
there is a non uniform mass distribution along the area of the sheet,
since most of the sheet mass is located in a few very massive regions
whereas many of the remaining regions have very low density with no
massive halos in them.  Observations of high-density regions in
galaxy observations were pioneered 60 years ago
\citep{devaucouleurs53,abell58}, and have today led to the detection
of hundreds of sheets \citep{costa-duarte2011}.  All these sheets are,
however, based on overdensities in phase-space only, and it has still
not been clearly established to which extent the sheets have infact
collapsed along the one dimension only.  This is one of the
concerns of the present paper, to consider whether such overdensities
in phase-space are indeed sheets.

Recently it was shown, that certain pancakes may be useful as tools to measure
the mass of massive galaxy clusters \citep{Falco_Paper}. These
pancakes are positioned at 3-10 virial radii from the cluster. The cluster mass
is measured by considering the small perturbation to the Hubble flow,
which the galaxy cluster will induce on the observable line of sight
velocity of the galaxies in the pancake. One thing missing in this
analysis is, however, to confirm that the structures used are indeed
pancakes. In this paper we will confirm that this is indeed the case.

Another aspect of pancakes are their density profile perpendicular to
the pancake.  In the papers \citep{Binney-2004, Schulz-2013} it was
shown that cold collapse leads to final equilibria that are close to a
universal power-law density profile, with an exponent less than 1/2.
Here we have compared the power law density profile for the sheet
observed in a cosmological simulation, and we find that the
theoretical prediction are in fair agreement with the result from the
cosmological simulation, however, with a slightly more shallow central
profile.

Observationally, when a pancake is seen face-on, it is not possible to
extract the density profile. However, we derive an equivalent to the
Eddington method \citep{Eddington1916, BinneyBook} in one
dimension, which in principle may allow one to extract information
about the line of sight density profile, by using the observable
distribution of velocities.

\section{Numerical Simulation of Sheets}
\label{Numerical_Simulation}

In order to consider the equilibration level of a pancake, we need to
extract a real pancake from a cosmological simulation.  A series of
recent papers \citep{Shandarin2012, abel2012, Vogelsberger:2008, White:2009, Vogelsberger:2011} developed
powerful cosmological simulation techniques to analyze the
evolution of dark matter sheet.
In this paper, we have analysed
  the sheet at a fixed redshift, $z=0$.  We consider a few of the pancakes used
in \citet{Falco_Paper}, which are based on the N-body simulation
described there (for more details, see
\citep{kravtsov97,gottloeber2008}).
These pancakes were used to demonstrate a new method
of measuring the cluster mass, but it was not quantified if these were
truly  sheets (equilibrated along only one dimension) or instead
filaments (equilibrated along two dimensions).

The reason for considering these particular pancakes is that they have
been found through a detection method, which will work on directly
observable data.  As observational quantities one uses only the
two-dimensional position on the sky and the line of sight
velocity. Here we will, however, analyze these structures using all the
information available from the numerical simulation.

The pancakes are pointing almost radially from a large galaxy cluster,
and lie at a distance of the order 10-40 Mpc from the cluster.
The pancakes are extracted by considering a
slice on the sky ($\pi/4$), and then looking for overdensities in the
phase-space of projected radius and line of sight velocity, ($R,
v_{\rm los}$).  A sheet produces an almost straight line in that
space.

In Figure~\ref{fig:1b.every5} we show the phase-space plot for the cluster
and the extracted sheet. The cluster is a (normal) dense collection of galaxies
at projected radii smaller than 2 Mpc, whereas the sheet forms a dense, and
fairly narrow strip at projected distances between 6 and 16 Mpc. The
velocities are centered at the cluster, and the sheet particles have
projected velocities between 500 and 2500 km/sec. Only every 5th point is
plotted.

\begin{figure}
\includegraphics[scale=0.7,keepaspectratio=true]{1bevery5.pdf}
\caption{Phase space plot for the extracted sheet. The green points
at projected radii smaller than 2 Mpc belong to the central cluster, and
the dense, narrow strip between 6 and 16 Mpc is the sheet.}
\label{fig:1b.every5}
\end{figure}

Now, having these sheets, we can rotate them according to their major
axes (X,Y,Z), in such a way that X is an axis along the longest axis
of the sheet, and Z is an axis along the shortest axis. The latter
axis, Z, thus corresponds to the direction perpendicular to the sheet,
namely the direction where we anticipate that the collapse has already
happened.

This is demonstrated in Figure~\ref{fig:2b.every5} where we show
the real-space projection of the sheet. The x-axis is the distance
from the cluster, and we see that the sheet sits in real space
at a distance between 10 and 30 Mpc from the cluster. Visually we
clearly see, that the sheet is very uniform and broad in the
non-collapsed dimension (Y, upper panel), whereas it is much more
compact and dense in the collapsed dimension (Z, lower panel).

\begin{figure}
\includegraphics[scale=1.,keepaspectratio=true]{fig2new.pdf}
\caption{Real space projection of the extracted and rotated sheet.
  The X-axis corresponds to the distance from the cluster, which is
  the green points at radius below a few Mpc. The sheet are the red
  points at distances between 10 and 30 Mpc.  We clearly see visually
  that the one dimension (Z, lower panel) is closer to equilibration
  than the other dimension (Y, upper panel).}
\label{fig:2b.every5}
\end{figure}

As a first test, we compare the density profiles along these
directions.  We confirm that the profile along the Z-direction does
appear fairly ``\emph{gaussian}'', whereas the profiles along the
other directions (which are expected to not have collapsed yet) are
still fairly top-hat shaped, in agreement with the similar findings of
\citep{boys}.

We also need a selection of galaxies to compare with, a background.
For that we consider the same slice on the sky as the signal, however,
for the velocity we extract the region with the opposite sign. This
means that if the sheet is positioned beyond the cluster (with
positive line of sight velocity), then the background is selected as
the symmetric region, but in front of the cluster (with negative line
of sight velocities).

The largest sheet is not a homogeneous box, so we divide it into 10
radial bins (each bin containing equal number of particles) along the
X (radial) direction, and the bins are numbered in ascending order of
their distance from the cluster.  We discard the extreme bins (1 and
10).  This may in particular allow us to consider different levels of
virialization as a function of distance from the cluster.  Similar
binning is performed in the background region.
We have analysed another two sheets from the numerical simulation.
Their properties are qualitatively similar to the sheet discussed
in this paper, however, because of a lower number of particles in those
sheets, no additional interesting lessons were learned from them.

\begin{figure*}
\includegraphics[scale=1.0,keepaspectratio=true]{2x3.pdf}

\caption{A sheet has been extracted using only observational data, and
here we analyse the full phase-space properties of that sheet.
The phase space plots for the 7th radial bin of the
  largest sheet in X,Y,Z directions. The origin of each plot is
  separately chosen such that mean coordinate and mean velocity of the
  particular direction are both zero.  Also, the Phase Space plots for
  the background region are provided for comparison.
The difference in levels of
  equilibration along various axes of the sheet is clearly seen.
The green line shown in the diagrams represents the
  Hubble Flow.}

\label{fig:Phase_Space_Complete}

\end{figure*}

\section{Stability analysis using Phase Space Plots}
\label{Phase_Space_Stability}

\subsection{Equilibration along different axes}

The structure of phase space along different axes can be used to
understand the level of equilibration along the particular axes of the
structure.  For a structure which has reached equilibrium in all the
three directions, a phase space plot in any direction will show a
semi-gaussian blob.  On the contrary, for a structure which remains
non-equilibrated along a particular direction, the Hubble flow would
completely dominate over the gravitational attraction, and its phase
space plot along that direction will show a straight line
corresponding to the Hubble expansion.

Phase space plots for one of the radial bins of the largest
sheet are shown in figure (\ref{fig:Phase_Space_Complete}) along with
the phase space plots for the background region along the three axes.
First of all, the background region (lower panels) is clearly seen to
follow the Hubble expansion fairly accurately along all 3 directions.
Instead, the signal region (upper panels) clearly shows variation from
almost following the Hubble flow (X-direction, right-most panel) to
almost being completely equilibrated (Z-direction, left-most
panel). The Y-direction is in the early stage of equilibration, only
starting to depart from the Hubble flow.

We therefore see, that the sheet candidate indeed is a real 2
dimensional sheet, and therefore differs from a filament, which should
be collapsed along 2 dimensions.

A similar analysis for the other radial bins indicate, that the outer
bins (6-9) are all in a state which have collapsed along only one
dimension, whereas the innermost bins (2-5) are in a more advance
state, where either the equilibration has happened along 2 dimensions
for some bins, or the presence of substructure is more pronounced.
This effect can also be observed by looking at the surface mass
density values for the outermost bins(6-9) being (0.2625 to 0.39375)
$M_{\sun}/pc^2$ which is lower than the density of innermost bins(2-5)
which is (0.4375 to 0.875) $M_{\sun}/pc^2$.  We will therefore limit
our analysis to the outermost bins (6-9) for the rest of this paper.

\subsection{Phase space structure}
\label{Phase_space_structure}

\begin{figure}
\includegraphics[scale=0.7,keepaspectratio=true]{Bin_7_parts.pdf}
\caption{When we remove the Hubble flow, the phase space plot of one
  radial bin (bin 7) is seen to be divided into an almost equilibrated
  elliptical part, and 2 infalling streams of galaxies.}
\label{fig:Bin7_Parts}
\end{figure}

In this section we will consider some additional aspects of the phase
space plots along the X,Y,Z directions.  Considering their dynamic
behaviour, the simple Hubble motion of the galaxies is perturbed by
the gravitational effect of the cluster mass and the gravitational
field of the sheet itself. Thus the total velocity of each paticle
(galaxy) is the combination of two terms
\begin{equation}
\bar{v}_{r} (r) = \textup{H}\bar{r} + \bar{v}_{p} (r) \, ,
\label{eqn:Velocity_Components}
\end{equation}
which are the pure Hubble flow and an infall term $v_{p}$.  We remind
that we have rotated the sheet in such a way, that the X-direction
points radially out from the cluster.  Considering the motion along
the radial X-direction, the corresponding infall term $v_{p} (x)$ is
governed by the gravitational force of the massive nearby cluster
(which naturally acts only in the X-direction), and the contribution
from the mass of the sheet can be neglected as a first
approximation. Outside the region where the Hubble flow starts to
dominate, namely outside 3-4 times the virial radius
\citep{prada,custa}, the infall term can be approximated to be
\begin{equation}
 \overline{v}_{p} (r) \approx -v_{0} \Big(\frac{r}{r_{v}}\Big)^{-b} \, ,
\end{equation}
where $r_{v}$ is the virial radius and $v_{0}$ is an appropriate
constant (\citet{Falco_Paper}).  Thus, $\overline{v}_{p} (r)$ will
give the slight deviation from the linear Hubble flow in the slope of
the phase space plots in the X-direction for both the sheet and the
background regions, seen in the right-most panels in figure
\ref{fig:Phase_Space_Complete}. For the Y-direction, the sheet has
just started to equilibrate, so, deviation caused by the mass of the
sheet itself will be small compared to the Hubble flow, as seen in the
middle panel for the sheet.

If we subtract the Hubble flow from the velocity of each particle we
obtain the phase space figure (\ref{fig:Bin7_Parts}) for the radial bin 7.
This phase-space plot of the perpendicular direction shows the
essentially equilibrated central part, and 2 streams of galaxies in
the process of falling into the sheet.  Each radial bin in the sheet
seems to have collapsed into a
nearly equilibrated elliptical part and two streams of infalling
galaxies which are not part of the virialized structure.
We emphasize that only directly observational data was used to
identify the sheets (2 position in projected space, and the
line of sight velocity), whereas we now, subsequently, consider the
full detail of all of phase-space.

By removing the particles in the two streams, we can get the density
profile of the equilibrated structure as a function of distance from
the center.  The profiles are somewhat noisy due to substructures
which are not fully equilibrated.  The structure of the equilibrated
elliptical part in the plots is similar to the plots derived from one
dimensional simulations in the paper \citep{Schulz-2013}.  This is
shown in figure (\ref{fig:Tremaine_Comparison}). We have also plotted
a smooth function given by
\begin{equation}
\rho_{z} \left ( z \right ) \sim \left | z \right |^{-\gamma } \exp\bigg(-\Big(\frac{|z|}{z_{0}}\Big)^{1-\gamma }\bigg) \, ,
 \label{eqn:fitting_function}
\end{equation}
as a fit to the curve.  From the fitting curve we find that $\gamma
= 0.2$. This can be compared to various analytical predictions:
$\gamma = 0.47$ in the paper \citep{Schulz-2013} and $\gamma = 0.5$ in
\citet{Binney-2004}.

\begin{figure}
\includegraphics[scale=0.7,keepaspectratio=true]{log_log_bin_7.pdf}
\caption{The density profile $\rho \left (| z |\right )$ is plotted
  for the radial bins numbered 6, 7, 8, 9 on a logarithmic scale. The blue
  fitting curve shows the model in equation
  (\ref{eqn:fitting_function}) with the value of $\gamma = 0.2$}
\label{fig:Tremaine_Comparison}
\end{figure}

\subsection{Behavior of Infalling Streams}

The streams in figure (\ref{fig:Bin7_Parts}) can be compared to the
stages of early equilibration as described in the papers
\citet{Binney-2004,Schulz-2013}.  The potential energy
of the sheet can be calculated from the density profile using equation
(\ref{eqn:Poisson_Equation}).
To make a better estimation of the potential energy profile,
at distances away from its center, we have taken into account the
approximations to be made for a \emph{finite} sheet.

Thus, we have estimated the total energy ($K.E + P.E$) of the
infalling particles by comparing the change in kinetic energy of the
particles in the 2 streams with the profile of potential energy due to
the sheet itself.  Energy conservation holds as long as the potential
is stable in time.  Such a constant total energy curve is given in
figure (\ref{fig:Energy Fit}). The kinetic energy of particles in both
in +Z and -Z streams are compared with the constant total energy
curve.

The galaxies in the +Z stream follow this prediction very accurately.
The stream on the other side of the sheet clearly has a component of
particles (galaxies) which do not follow this simple behaviour. These
particles are at distances 1-3 Mpc from the sheet, and have an
additional energy of approximately 150 km/sec. In figure 4 we see that
these are more dense particles, with a non-zero velocity dispersion.
A potential origin of this discrepancy may be related to the
non-equilibrated substructures, which are mainly seen in the -Z
direction, implying that the -Z stream galaxies could be in a peculiar
stage in the equilibration process rather than in a completely free
fall motion.

\begin{figure}
\includegraphics[scale=0.7,keepaspectratio=true]{V__2_vs_z_7bin.pdf}
\caption{The kinetic energy distribution function $1/2 \,
  v_{z}^{2}\left ( z \right )$ of bin 7 are plotted.  The fitting
  function has been derived from the density profile of this bin.}
\label{fig:Energy Fit}
\end{figure}

\section{Eddington Model for one dimension}
\label{1D Eddington Model}

In this section, we derive an equivalent of the Eddington
model \citep{Eddington1916, BinneyBook} for its application on
isotropic sheets with an infinite area.

We shall consider self-consistent systems in which the density
distribution determines the potential through Poisson's equation, and
the potential must also determine the density consistently through the
collisionless Boltzmann equation.

As we will see, an equivalent of the Eddington
model for 3 dimensions can be used approximately for sheets along their
perpendicular direction (Z- axis).  These sheets are assumed to have
uniform spatial distribution along the X-Y plane and to be completely
equilibrated along the Z-axis.  The change in gravitational potential
or the total energy of galaxies along X and Y axis is considered to be
negligible as compared to their change along Z axis.  Thus we consider
only the Z axis values of potential and total energy of the galaxies
for our analysis.  We define the relative potential $\Psi $, and the
relative energy $\xi$ of a galaxy by
\begin{equation}
 \Psi = -\Phi  + \Phi _{0}  \hspace{5 mm} {\rm and} \hspace{5 mm} \xi = \Psi - \frac{\upsilon^{2} }{2} \,
 \label{eqn:new_variables}
\end{equation}
where $\Phi_{0}$ is a constant such that the conditions $f > 0$ for
$\xi > 0$, and $f = 0$ for $\xi \leq 0$ are satisfied.

We can now derive a unique ergodic distibution function (DF) as a
function of relative energy $f(\xi)$ from the given density profile of
the sheet $\rho(|z|)$ with an infinite extension in the x- and y-
direction as
\begin{equation}
f\left ( \xi  \right ) =
\frac{1}{\sqrt{2}\pi }  \int_{0}^{\xi }\frac{d\Psi }{\sqrt{\xi - \Psi }}
\frac{\mathrm{d} \rho }{\mathrm{d} \Psi } \, ,
\label{eqn:Eddington_1D}
\end{equation}
where $\Psi$ is the relative potential. The derivation is shown in
detail in Appendix-(\ref{Apdx1}), and this result is similar to
\citet{Eddington1916}.

We can obtain the velocity distribution function $P(v)$ along the line
of sight, by integrating $f\left ( \xi \right )$ as :
\begin{equation}
P \left ( \upsilon  \right ) = \int_{-z_{\textup{max}}}^{z_{\textup{max}}}f\left ( \xi  \right )dz \,
\end{equation}
where $z_{max}$ is computed such that $\xi > 0$ is always valid.
$P(v)$ is directly observable, and hence this model can in principle
be used to extract the density profiles of sheets from the observation
of the line of sight velocities of the galaxies belonging to the
sheet, even though this practically may never be possible.

\section{Application to analytical models}
\label{Analytical Models}

Let us first consider a few simple and analytical models.  We will
here assume a known density profile for a sheet and calculate the
associated phase space distribution function and velocity distribution
function, $P(v)$, using equation (\ref{eqn:Eddington_1D}).  The spirit
behind this analysis is that direct observations of the sheets give us
their velocity distribution function and surface density ($\Sigma$)
only.  The detailed properties of the VDF of the sheets, obtained from
the observations, can then be compared to the computed profiles which
have the same surface density ($\Sigma$) and from it the density
profile could be deduced.  The analysis in this section is done for
idealized sheets with infinite area.

\subsection{Model 1 : An Isothermal sheet}
\label{isothermal_sheet}
First a sheet with a density profile, which is often used in the
simulations of the galaxy discs, is examined
\begin{equation}
\rho \left ( z \right ) = \begin{cases}
\frac{1}{2a}\Sigma sech^{2}\left ( \frac{z}{a} \right ) & \text{ : } \left | z \right |< z_{max}\\
 0& \text{ : otherwise } \, .
\end{cases}
\label{eqn:sech_density2}
\end{equation}
The scale length of the sheet is a, and the value of surface density $\Sigma$ is normalized such that $2\pi G\Sigma = 1$.

By using equation (\ref{eqn:Eddington_1D}), the phase space
distribution function is -
\begin{eqnarray}
 f\left ( \xi  \right )
 &=& k_{1}\int_{0}^{\xi }\frac{1}{\sqrt{\xi -\Psi }} e^{-\frac{2}{a}\left ( \Psi _{0} - \Psi \right )} d\Psi \\
 &=& k_{2}  e^{\frac{2}{a}\xi } erf\left ( \sqrt{\frac{2}{a} \xi} \right ) \, .
 \label{eqn:sech_f(e)}
\end{eqnarray}

Here `erf' represents the error function and $k_{1}$,$k_{2}$ are
normalization constants. The derivation and the approximations
involved in calculating $\Sigma$ are given in the
Appendix-(\ref{Apdx2}). In order to derive the velocity distribution
function.

\begin{equation}
P \left ( v  \right ) = k' \int_{-z_{max}}^{z_{max}}e^{\frac{2}{a}\left ( \Psi - \frac{v^{2}}{2} \right )} \times  \textup{erf}\Bigg(\sqrt{{\frac{2}{a} ( \Psi - \frac{v^{2}}{2} )}}\Bigg) dz
 \label{eqn:sech_P(v)}
\end{equation}
where $k'$ is the constant for normalization, we substitute

\begin{equation}
\Psi = \Psi _{0} - a   \ln\left ( \frac{e^{\frac{z}{a}} + e^{-\frac{z}{a}}}{2} \right ) \,  .
\end{equation}

The definite integral can be computed to get the distribution of
velocities.  The resulting profile obtained is shown in figure
(\ref{fig:Sech_VDF}) for different values of $a$.

\begin{figure}
\centering
\includegraphics[scale=0.7,keepaspectratio=true]{sech_VDF.pdf}
\caption{The velocity distribution functions for density
  profile represented by equation (\ref{eqn:sech_density2}) for
  different values of constant $a$.  The value of mass per unit area
  $(\Sigma)$ is kept constant for all the curves.}
\label{fig:Sech_VDF}
\end{figure}

\par
\subsection{Model 2 : A core with a power law cutoff}
Another density profile with convenient analytical properties is
\begin{equation}
  \rho \left ( z \right ) = \begin{cases}
    \Sigma \frac{a^{2}}{2}\left ( z^{2} + a^{2} \right )^{-\frac{3}{2}} & \text{ : } \left | z \right |< z_{max}\\
    0& \text{ : otherwise }  \, .
\end{cases}
\label{eqn:Power_Law}
\end{equation}
The scale length of the sheet is $a$ and it's surface density is
($\Sigma$). The equation for the relative potential becomes
\begin{equation}
 \Psi_{0} - \Psi = 2\pi G \Sigma (\sqrt{z^{2}+a^{2}} - a)
\end{equation}

Similar to the previous example, the value of surface density
($\Sigma$) is considered such that $2\pi G\Sigma = 1$.  The phase
space distributions function for two values of $a$ are given below.

\subsubsection{\textbf{a = 1}}

\begin{eqnarray*}
  f(\xi ) &=& \frac{\sqrt{\xi }}{648(3-\xi )^{3}}\Big(8\xi^{2} - 78\xi +297 \Big) +\\
  && + \frac{5}{8(3-\xi )^{\frac{7}{2}}}\tan^{-1} \Big(\sqrt{\frac{\xi }{3-\xi }}\Big)
\end{eqnarray*}

\subsubsection{\textbf{a = 2}}

\begin{eqnarray*}
  f(\xi ) &=& \frac{\sqrt{\xi }}{1536(4-\xi )^{3}}\Big(8\xi^{2} - 104\xi +528 \Big) +\\
  && + \frac{5}{8(4-\xi )^{\frac{7}{2}}}\tan^{-1} \Big(\sqrt{\frac{\xi }{4-\xi }}\Big)
\end{eqnarray*}

\begin{figure}
\centering
\includegraphics[scale=0.7,keepaspectratio=true]{Powerlawcutoff_VDF.pdf}
\caption{The velocity distribution
  functions for density profile represented by equation
  (\ref{eqn:Power_Law}) for different values of constant $a$.  The
  value of mass per unit area $(\Sigma)$ is kept constant for all the
  curves.}
\label{fig:Power_Law_VDF}
\end{figure}

Further, the velocity distribution profile can be obtained by direct
integration and resulting profiles obtained are shown in figure
(\ref{fig:Power_Law_VDF}).

\section{Application to simulations}

\begin{figure*}
\vbox to 80mm {
\hbox {\includegraphics[scale=1.0,keepaspectratio=true]{Application-Eddington.pdf}}
}

\vspace{0.5cm}
\caption{This figure shows the comparison between the observed
  velocity distribution curves (in green) and the curves derived from
  the application of Eddington model (in red).
  The observed velocity distribution curve falls
  less steeply than the calculated one which implies that the sheet
  isn't completely equilibrated yet. }

\label{fig:Application-Eddington}
\end{figure*}

In this section we will present a comparison between the derived
Eddington Model given by the equation (\ref{eqn:Eddington_1D}) on the
simulated CDM sheet described earlier section. We will apply the
Eddington formula separately on the 7th, 8th \& 9th radial bins of the
largest sheet and compare to the analytically calculated velocity
distribution curves with the observed VDFs for each of the bins.  The
calculation is quite tedious due to various approximations and
complicated functions are involved in it.

First of all, for the density distribution
 along the perpendicular axis of the sheet, we will estimate the best-fit parameters
for the symmetric analytical model presented in section (\ref{isothermal_sheet}).
In this step, we have ignored the anisotropies present in the sheet along its perpendicular direction (Z-axis).
The gravitational potential
function of the sheet is then calculated from the density
distribution using the Poisson's
equation (\ref{eqn:Poisson_Equation}).
In this analysis, we are dealing with particles with z coordinates less than
the dimensions of the sheet in the xy plane so we can perform the potential energy calculations
similar to the simplified calculation for a sheet of infinite area.

For Eddington formula to be applicable, a structure must be completely
equilibrated so that the ergodic hypothesis is valid.  The radial bins
of the sheet are divided into structures as discussed in section
\ref{Phase_space_structure}.

To make a proper comparison between
calculated and observed VDFs, we will take into consideration only the
particles which lie in equilibrated regions of the sheet for plotting
the observed VDF and we will neglect the particles lying in the
infalling streams. Using these particles, we can also fix an
appropriate value to the width ($z_{max}$) of the sheet which is an
input parameter needed for performing the integration in equation
(\ref{eqn:sech_P(v)}).

The computed and observed
total velocity distribution curves for each of the bins 7,8,9 are
compared separately in the figure (\ref{fig:Application-Eddington}).
The constraints on $z _{max}$ can be used to roughly calculate $v_{max}$
which turns out to be almost $120 \, km/s$ in these cases.
These curves can be observed to be similar within an order of magnitude.
The discrepancies between the calculated and observed VDFs can be attributed
to the various approximations which are elaborated in this section.

\section{Conclusions}
Zeldovich pancakes are cosmological structures which have collapsed
and equilibrated only along the one dimension.  These pancakes can be
identified at redshift zero using only observational parameters and
have recently received renewed interest, since they can be used to
measure cluster masses.

We consider the phase-space properties of pancakes from a cosmological
numerical simulation, which were detected using the observational
technique.  We demonstrate how these objects are in the process of
equilibrating mainly along the one dimension, and are much less
equilibrated along the other two. We extract the density profiles of
these structures, and we find fair agreement with theoretical
predictions.

\section*{Acknowledgments}
It is a pleasure thanking Martina Falco, Radek Wojtak, Martin Sparre, Thejs Brinckmann and
Mikkel Lindholmer for discussions.
The Dark Cosmology Centre is funded by the Danish National Research Foundation.

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redpajama_set_name: RedPajamaArXiv