text:
IDF Intelligence Chief: Iran Is Continually Surprised and Impressed by Israeli Determination
(Jerusalem Post) Yonah Jeremy Bob - Iran recently weighed initiating a terrorist attack at the World Cup soccer tournament and was only dissuaded out of concern for how Qatar, the host country, might respond, IDF Intelligence head Maj.-Gen. Aharon Haliva said Monday. Haliva said Iran would likely soon carry out at least a symbolic enrichment of uranium to the 90% weaponized level, and the world will be tested as never before. He expressed doubt about the West's determination on the Iran nuclear issue, noting that the West still does not comprehend the sustained challenge that Iran presents to it directly. Regarding the conflict between Iran and Israel in different parts of the region, Haliva said: "The vision of [IRGC Quds Force commander Qasem] Soleimani has fallen. There are very few Iranians in southern Syria. The number of Iranian personnel also in Syria [generally] is getting smaller. Iran sees the determination of Israel to deal with them. Most of the time, if Iran pushes, most of the world retreats." He said Iran is continually surprised and impressed by Israeli determination.


text:
package com.hubspot.singularity.hooks;

import com.hubspot.singularity.SingularityTaskHistoryUpdate;
import com.hubspot.singularity.SingularityWebhook;
import com.hubspot.singularity.data.WebhookManager;

public class SingularityTaskWebhookAsyncHandler extends AbstractSingularityWebhookAsyncHandler<SingularityTaskHistoryUpdate>  {

  private final WebhookManager webhookManager;

  public SingularityTaskWebhookAsyncHandler(WebhookManager webhookManager, SingularityWebhook webhook, SingularityTaskHistoryUpdate taskUpdate, boolean shouldDeleteUpdateDueToQueueAboveCapacity) {
    super(webhook, taskUpdate, shouldDeleteUpdateDueToQueueAboveCapacity);

    this.webhookManager = webhookManager;
  }

  @Override
  public void deleteWebhookUpdate() {
    webhookManager.deleteTaskUpdate(webhook, update);
  }

}

redpajama_set_name: RedPajamaGithub


text:
George Washington and the Continental Congress
Stephen J. Field
Courtesy of the Library of Congress, Washington, D.C.
(1816–99). U.S. lawyer Stephen Field was an associate justice of the Supreme Court of the United States from 1863 to 1897. His 34 years of service was the second longest term in the court's history (after that of William O. Douglas).
Stephen Johnson Field was born on Nov. 4, 1816, in Haddam, Conn. He graduated from Williams College in Williamstown, Mass., in 1837 and then practiced law in New York City with one of his brothers, the legal reformer David Dudley Field. In 1849 he moved to California, where he bought land in the Sacramento River gold-mining area, organized a town government, and became a state legislator and then a state supreme court justice.
President Abraham Lincoln appointed Field to the U.S. Supreme Court in 1863. Field supported the constitutional approach that largely freed the rapidly expanding industry of the United States from governmental regulation after the American Civil War. He found that the 14th Amendment, which had been passed as a civil-rights measure, provided for the protection of private enterprise. In his interpretation, the privileges and immunities of citizens secured by the amendment included the right to run a business without government interference, a view that prevailed in the court from the 1890s until the 1930s.
In 1880 and 1884 Field was a serious contender for the Democratic presidential nomination. He died on April 9, 1899, in Washington, D.C.

redpajama_set_name: RedPajamaCommonCrawl


you edit a segment of BBC Motion Gallery's Living Colour documentary. Completely revised for Final Cut Pro 6 and featuring all-new footage, this best-selling, Apple-certified guide provides a strong foundation in all aspects of video editing. Renowned author Diana Weynand starts with basic video editing techniques and takes you all the way through Final Cut Pro's powerful advanced features. Each chapter presents a complete lesson in an aspect of video editing and finishing, using actual broadcast footage. After marking and editing clips to create a rough cut, you'll learn how to trim and refine the cut before moving on to complex tasks such as mixing sound, adding titles, creating transitions and motion effects, applying filters, real-time color correcting, and working with multi-format and multi-camera footage.


Archives|Why Do New Yorkers Leave Auto Carcasses to Be Picked Clean?
Why Do New Yorkers Leave Auto Carcasses to Be Picked Clean?
As a Californian living in New York for a year, I am puzzled about several common New York practices, but one has perplexed me completely. It concerns a car, smashed up from a fairly bad accident, that my husband and I came across while walking along Broadway, very near Columbia University. The car was unattended, and my husband noticed that the flares had already burned out.
We continued on. Returning an hour later, I had my answer. The radio was gone. So was the steering wheel. We stood discussing the situation with another passerby. The police drove up while we were there, making sure we weren't going to steal anything. Apparently, the car was under limited surveillance.
I marveled, ''Wouldn't it just be easier to tow the car to a lot?'' I would have asked them, but they left before I could.
Mind you, this is right on Broadway. You'd think the police would have the car towed simply for being an obstruction to the roadway.
I mentioned this at a party the other night, and one person explained to me that in New York even cars are bio-degradable. Another told me it was the police who strip the cars at night. I expressed disbelief, but he assured me it was true. He also said the insurance company would pay more if the car were dismantled; if the parts were intact, the insurance would pay only to reconstruct the car.


In 2017, Norway and Germany entered into a partnership to both acquire submarines of the same design to boost maritime operations and cooperation with each other. Norway and Germany are looking to finalize the details of the partnership and sign an agreement in 2019. German-based ThyssenKrupp Marine Systems was selected to provide a total of six Type 212 CDs, beating out France's DCNS (currently Naval Group). There will be opportunities for Norwegian-based defense firms, namely Kongsberg, to work on the submarines and further cooperation between indigenous defense firms in each country. ThyssenKrupp is in the process of creating a joint-venture with Kongsberg, in which the latter will supply the submarines with a combat system. Norway is replacing its fleet of Ula-class submarines which have been operational since the early 1990s with four new submarines, while Germany is acquiring two submarines, with all six submarines to be delivered in the mid-2020s-2030. The Type 212 is currently in service with the German navy.
ThyssenKrupp is boasting that the new Type 212s will have increased speed, longer range, and increased underwater endurance. Previous variants of the Type 212 have a top speed of 20 knots, slowing down to eight knots when submerged. However, it's speculated that the new Type 212 CDs could have more power if ThyssenKrupp incorporates a second generator. But the acquisition of the submarine doesn't stop at Norway and Germany. The Italian Navy also has an older variant of the Type 212s in its fleet which are expected to be retired in the early 2020s, though Italy is moving forward with upgrading the hull instead of opting to purchase the new CD-variant. Poland's submarine competition (dubbed Orka) is considering the Type 212 alongside the A26 and the Scorpene-class submarine, while the Netherlands is also searching for new submarines and considering between the Type 212 or the A26. Norway and Germany have offered to extend the joint agreement with the Netherlands to encourage the Dutch to acquire the Type 212 CD, with the incentive that doing so would yield cost savings to the country.
On February 1, the Indian government released an interim, federal budget before national elections in early May. New Delhi allocated over $61 billion to the military. The figure represents a nominal 6.6 percent over last year, or a 3.5 increase in real terms. India's defense community was largely critical of the proposed defense budget, however, citing declining toplines as a percentage of GDP. Aside from defense, the overall budget included populist measures targeting key voting blocs, including $2.8 billion in payments to Indian small farmers and $2.6 billion worth of tax breaks to the country's middle class. The FY2020 budget release comes as Prime Minister Modi's government has been accused of politicizing economic data in the run-up to the elections, as well as undermining the autonomy of the country's central bank by calling for lower interest rates.
On January 31, the German government decided to delay the planned purchase of new fighter aircraft. The German military is seeking to replace its aging fleet of Tornado fighters with a new nuclear-capable aircraft. A plan was being put forward to buy $17 billion worth of aircraft from the United States, but center-left elements of the German government requested additional time and information before approving it. The primary contenders for this requirement were the Lockheed Martin F-35, the Boeing F/A-18, and the Airbus Eurofighter Typhoon – with the German Air Force specifically requesting the F-35. However, France has made it clear that choosing the F-35 would cause problems for future collaboration between France and Germany regarding the fighter development. As a result, there is a distinct chance that Germany will purchase the F/A-18 and the Eurofighter, but currently no firm commitments have been made.
Airbus and Dassault will be jointly awarded the first contract in the French-led Future Combat Air System (FCAS). The contract is a two-year €65 million ($74 million) contract that will set out the structure of the program and industrial cooperation. The funds will be split evenly between the two companies. Subsequent contracts for the development of the engines on the fighter component of the FCAS will likely go to Safran and MTU Aero Engines. Spain will also be inducted as a full partner into the program this summer, though it is not yet clear how costs will be divided once Spain is added to the project.


Table lamp designed in 1967 by German designer Ingo Maurer and manufactured by M Design. It consists of a simple support for the bulb which swivels an adjustable light source. Chrome and black metal. Adjustable. can be used as a table lamp or mounted to the wall.


If Trailer 2 is equipped with spring brakes, the parking brakes will be "On. Far as i know this is completely possible in GTA online on the ps4. Close the Pintle hook safety latch and hook the safety chain from the dolly onto Trailer 1's O-ring. When the tractor turns sharply, it must not hit the landing gear.
Also if you have a reefer, check the fuel levels and make sure the zones are set right. That doesn't sound very gay. If Trailer 2 does not have spring brakes, connect the air lines and the electrical cable from the dolly to Trailer 2. Truck drivers are doing whatever they have to do in order to not lose their jobs to drones.
Two dudes getting married? In addition, videos can be downloaded bolivia colombia online dating HD quality.
That's the joke, amigo. Never drive with the legs only part way up.
Test if you have done everything correctly. It must be able to take an amount of force, from various directions.
The first and second trailers are coupled with a converter, or dolly -- a fifth wheel on an axle. Open the air tank petcock -- or depress the air release valve. Make sure to lock and secure it properly. If i back up to a trailer it auto hooks onto the truck.
Is that part of the trailer for Fast and Furious 8? Please remove the copyrighted content within 24 hours. This lowers the suspension of the semi-truck significantly.
All you have to do is click on the appropriate format and download it now. Open the shut off valves on the back of Trailer 1. Place the dolly so its fifth wheel touches the front of Trailer 2 and its fifth wheel jaws are in line with Trailer 2's king pin.
Although it is highly unlikely that you will get it on your first try, you will surely be able to master it with a little practice.
References About the Author Devorah Fox has been writing professionally since Remove the kingpin lock. Don't forget to verify the cargo seal against your manifest. Ideally, the trailer touches the fifth wheel. He may be referring to the 20, lb semi-truck drifting around like a sx.
Close the dolly's petcock drain valve and Trailer 2's shut-off valves.
What's gay about that? However, aligning them gets the best results. You can download it in many different formats, whether audio format MP3 or video format MP4. But drones are robots in da skies.
If you are a truck driver, it is important that you know how to couple and uncouple a trailer and semi-truck. Hook the dolly eye hook onto the Pintle hook of Trailer 1, the trailer hooked to the tractor.
Longer-ranging music or video is also available to spend up to 8 hours of time. It's important to know that you are responsible for downloading the legal responsibility!
The semi-truck will not couple properly with the trailer if the kingpin lock is still there. You can do this easily with the buttons below.
When you are happy with the position, release the brake. Its a horrible noise you'll never forget, not to mention is shakes the whole building Missed the part where the trucker got out and connected the glad hands and then released the air brakes of the container so its wheels would roll.
They may catch on railroad tracks and objects in the road.
Secure the fifth wheel locking lever. Some owners forget to remove it.
It can also be a lot of hassle to your shipment. Came just to see this gif again. To do this, simply dump some air.
Except for the use of the dolly, coupling doubles is essentially the same as coupling a tractor and one semitrailer. In the lower corner of the browser, you will see how much time is left back from downloading.
Non of that is required to physically move the trailer though.


Home In evidenza Workshop Digital Threats to Democracy: Comparative Lessons and Possible Remedies, New York City June 13-14 2019.
Workshop Digital Threats to Democracy: Comparative Lessons and Possible Remedies, New York City June 13-14 2019.
The Media & Democracy program at the Social Science Research Council is pleased to announce a call for proposals for the "Digital Threats to Democracy: Comparative Lessons and Possible Remedies" workshop. This workshop will bring together social science and humanities scholars to present comparative research on how countries adapt and respond to digital threats to democracy.
The workshop, organized in collaboration with Cristian Vaccari (Loughborough University), will be held at the Social Science Research Council in New York City on June 13-14, 2019. Accepted participants' travel and accommodation costs will be covered by the organizers.
We welcome applications from both junior and senior scholars across all disciplines. However, the focused nature of the workshop demands that we limit participation to 10–12 authors. Thus, our selection will be determined not only by the quality of submissions, but also by their thematic fit and complementarity.
A selection of the papers presented at the workshop will be invited to submit full manuscripts of up to 8,000 words for publication in a special issue of the International Journal of Press/Politics, subject to peer-review.
To apply, please submit a current C.V. and an abstract of up to 500 words to mdapplications@ssrc.org by February 3, 2019.
Processi, istituzioni e politiche nell'Italia contemporanea, organizzato dal Centro "Papa Luciani" di Santa Giustina (Belluno) e patrocinato dallo Standing group SISP Politica e Storia. 10-13 luglio 2019.


Elegant Enamel filled Sterling Silver Menorah pendant has enamel filled swirl accents by its base.
Sterling silver Menorah pendant outline is filled with green speckled Enamel. Sterling Silver outlined swirls are filled with blue speckled enamel at each side of the menora base.


PRAIRIE RONDE — With his team trailing by three touchdowns, Northwest High head coach Chris Edwards took the necessary action..
It was all quite simple, Edwards said.
Just give the ball to Chris Lee.
Lee placed a sputtering Raiders' offense on his shoulders Friday night as he helped lift Northwest to a 20-18 victory over Peabody Magnet School in a bi-district Class 3A playoff game.
The senior running back scored all three of the Raiders' unanswered touchdowns during the final 14 minutes as seventh-seeded Northwest (9-2) advanced to the regional round to host No. 10 Marksville.
Lee, who rushed for all but 10 of Northwest's 169 first half rushing yards, finished the game with 314 of the Raiders 320 team rushing yards on his 36 carries.
"If we were going to win, we knew that we had to ride the one that got us here and we certainly weren't going to stop doing that (Friday night)," said Edwards.
Peabody (6-5), the No. 26 seed, led 18-0 with two minutes and 55 seconds remaining in the third quarter.
Northwest's comeback began immediately after the War Horses scored the final Peabody touchdown on a six-yard Bruce Price run.
The Raiders set up the first TD on a 36-yard pass from quarterback Terrel Guillory to wide receiver Dylan Guillory. Lee scored on a 20-yard on the next snap (2:18).
Peabody was flagged on 15-yard penalties on the Raiders' next drive and that helped set up Lee's second touchdown run, a 2-yarder with 8:34 left in the game.
Then Lee finalized the game's final touchdown possession when he scored on a 5-yard run with 64 seconds remaining. That drive took nearly four minutes and consumed nine plays.
Peabody head football coach Benny Vault Jr. said his team self-destructed throughout the game.
The War Horses lost three fumbles inside the Northwest 10 and the Raiders also intercepted two passes.
Also affecting Peabody were an array of penalties — 12 for 110 yards.
Vault said the cumulative problem of penalties and turnovers were too much to overcome.
"We gave it away, just gave it away. Our kids played well, but we had the fumbles and then all the penalties.
"Those fumbles were all at inopportune times. Our kids played hard, but we didn't have that killer instinct we needed," Vault said.
Northwest defensive back Tavin Gant intercepted two passes. Recovering fumbles for the Raiders were Matthew Rideau and Anthony White.
Peabody took a 4-point lead quickly as Lee was tackled for safeties twice in the end zone twice during the first 14 minutes for a pair of safeties.
The War Horses lost a chance to establish a dominant advantage with a fumble at the Raiders' one-yard line late in the first quarter and aagain at the Northwest 8 early in the second period.
Peabody led 12-0 at halftime after the only first half touchdown when the War Horses' Robert Perry intercepted a pass at the Raiders' 46.
Seven plays later Peabody scored on a 3-yard run by quarterback Sadrick Kirklin.
Despite trailing by 12 after two quarters, Edwards said he felt somewhat comfortable starting the second half.
"We dug ourselves a little hole, but we knew (Peabody) had eight guys going both ways. I thought they kind of starting dropping late in the game and our defense played great with some late stops.
"I think winning like this will help us down the line. I don't think we can start off playing any worse," Edwards said.


Site de soutien international à Íngrid Betancourt.
It is useful to look more carefully into the intellectual and moral dimensions – in addition to the political ones – of the EELV (French Greens) crisis.
The following ten theses outline how ecologist parties can strengthen their bases by re-imagining a new kind of political platform and adopting a cooperative approach.
[2014d] "The Anthropological Crisis and the Social and Solidarity Economy", L'Option de Confrontations Europe, n°33, janvier 2014.
Home > Économiste, auteur > Écologie > France : Epicenter of the "Malbouffe" Crisis.
en France : Epicenter of the "Malbouffe" Crisis.
[2013h] (with Natalie Gandais) "France : epicenter of the 'Malbouffe" Crisis", Green European Journal, Vol 5, March 2013.
Atelier annuel de l'Euromemo Group sur la crise et les politiques alternatives pour l'Europe. J'interviens à la première session « L'état de l'Union » et à la session spéciale « Croissance économique et développement soutenable ».
Home > Vie publique > Articles et débats > Icelanders owe nothing.
By calling voters to a referendum on the subject of Icelandic taxpayers taking on the debt of Icesave bank, President Grimsson caused shock waves to break out in the world's financial community. For the first time during this global financial crisis, a country was challenging its "sovereign" debt - the debt of a nation represented by its government.
Ce rapport analyse la place de la "crise énergie" dans la crise économique mondiale actuelle et les moyens d'y faire face.
European Parliament resolution on the Annual Policy strategy for 2009.
Home > Député européen (Verts, France) > Mes initiatives > Sécurité collective et environnement > Présentation du rapport "Changements climatiques et sécurité internationale"
en Présentation du rapport "Changements climatiques et sécurité internationale"
Good afternoon everyone. My name is Victoria Brereton and I work in the Research Unit at the Brussels Headquarters of International Crisis Group. I would first like to thank the conference organizers for inviting to what promises to be a wide ranging debate. I think what we can see from today's agenda and the discussion thus far is the central position that climate change now occupies at the heart of EU policy and strategic thinking. As the European Commission's recent paper on Climate Change and International Security indicates, we have begun to engage with a breadth of potential impacts – encompassing diminishing resources, mass migration, severe socio-economic stress and increased political instability in some of the world's most fragile states. There is recognition that these threats demand a concerted and international response.
It is my honour and a privilege to welcome you to this energy and security conference. Energy policy is security policy, or to be more precise, what we want is peace policy. In the 21st century security policy is a cross-cutting task – and everything else but pure military policy.
Le rapport propose de ne pas étendre cette garantie des prêts de la Banque européenne d'investissement aux pays (comme l'Ouzbékistan) sous le coup de sanctions de l'Union européenne pour violation des droits de l'Homme.
Home > Député européen (Verts, France) > Économie > Divers economie > Background note on "Measurement beyond GDP"
en Background note on "Measurement beyond GDP"
Preliminary remark: On a regular basis, if there were to be political will in the EP, the question of "going beyond GDP" could stand high on the political agenda of the EP, through the adoption of various reports: adoption of the Sustainable Development Strategy or the renewal of the Lisbon Strategy. The fact that the renewed European Sustainable Development Strategy (EU SDS) identifies Sustainable Consumption and Production  (SCP) as one of the key challenges to be addressed to meet the challenges of sustainable development presents another occasion to address, through the coming European action plan on SCP, this key issue for the Greens. To feed our reflections within the Green group on this issue, and in view of the context of the European electoral campaign of next year, here is a summary of the conference "Beyond GDP" which was organised in Brussels in November 2007, with the following objective: to analyse the shortcomings of GDP and to see which indicators could serve as a new base for measuring progress and the well-being of nations. This background note aims to give an overview of the key issues debated, and on the opportunities/shortcomings of other indicators which go beyond growth.
Green MEPs called on the European Commission to waive the 10% target for agro-fuels and to put forward a proposal for an obligatory food security impact assessment within the framework of the Common Agricultural, Energy and Trade Policy.
A postscript to "What is political ecology"
[2003d-en2] "Johannesburg and beyond : A political ecology perspective" in Joachim H. (ed.) Sustainable development - Past Conflicts and Future Challenges. Taking Stock of the Sustainable Discourse, Westfälisches Dampfboot, Mûnster, 2008.
It should be noted that we became a democracy for the first time in April 1994, a mere 13 years ago. The legislation which established the Truth and Reconciliation Commission (TRC) in South Africa, the Promotion of National Unity & Reconciliation Act (The Act) was promulgated in 1995.


The listing of India's first REIT by Blackstone-backed Embassy Group has been in the offing for quite some time, but it now finally appears that it will be listed within the first half of 2019. As REITs await their official deployment in India, investors hoping to cash on this new avenue for generous ROI growth seek to understand what exactly is in store for them - and for the real estate market.
The post 50% of Indian office stock qualifies for REITs appeared first on Track2Realty.
The post Adani forays in Pune with luxury residential project appeared first on Track2Realty.
The post Quality talent not attracted to real estate appeared first on Track2Realty.
It would be pertinent to note that raging infernos spared no one - be it rich or poor, residents of newly-built high-rises or the squalid slums, all fell victim to the scourge of flames which enveloped their structures, turning their cherished homes into death traps.
The post Growing incidence of fires in Mumbai high-rises appeared first on Track2Realty.
National Real Estate Development Council (NAREDCO has requested Government to address the key concerns of the real estate industry and home buyers, offer tax incentives across housing segments and boost buyer's confidence through a slew of measures in the upcoming interim Union Budget 2019-20.
The post NAREDCO presents its pre-budget memorandum to the government appeared first on Track2Realty.
The post Office leasing touches 50 million square feet in 2018: Colliers appeared first on Track2Realty.
The post Interim budget & feasibility of realty appeasement appeared first on Track2Realty.
The post Sobha strengthens its best practices, Embassy jumps into top 3 appeared first on Track2Realty.
» Any hope for commercial realty with interim budget?
The post Any hope for commercial realty with interim budget? appeared first on Track2Realty.
The post NRIs – Know the Score Before Buying a Property in India appeared first on Track2Realty.
StayAbode Ventures has announced Asia's largest co-living project in partnership with CP Developers. This will be the largest A grade co-living project in India with 1400 people living in a community environment, in the heart of Bengaluru's Whitefield - a professional hub neighbouring ITPL and large MNCs with a working population of over 50,000 millennials.
The post StayAbode announces Asia's largest co-living project appeared first on Track2Realty.
The post NCLT Delhi Court issued contempt of court Notice to Rohtas Goel, CMD, Omaxe appeared first on Track2Realty.
This growth is witnessed across five major cities – Mumbai, Gurugram, Noida, Bengaluru and Pune, where 4000 homebuyers were surveyed by 360 Realtors to understand buying trends. One of the key driving factors for the increase in investor interest is the impact of policies such as RERA. Assured rentals and EMI payouts after possession, offered by developers have also significantly boosted investor confidence.
The post 2018 marks steady rise in investor interest in Indian housing appeared first on Track2Realty.
The share of mid-market houses costing INR 20-50 lakh in the overall residential sales in the country has been progressively rising, touching an all-time high of 42 percent of total transactions in the second half of the current financial year 2018-19, according to data released today by India's largest marketplace for new homes Square Yards.
The post Mid-market housing mainstay of residential sales appeared first on Track2Realty.
Year 2018 was a veritable roller-coaster ride for the Indian real estate. Despite signs of recovery across segments, the liquidity crunch – further exacerbated by the NBFC crisis – put all industry stakeholders on tenterhooks.
The post The highs and lows of Indian real estate in 2018 appeared first on Track2Realty.
With high expectations from 2018, it was anticipated that the teething problems around policy initiative introduced in 2017 (RERA and GST) would ease out by the end of the year, bringing a new order of transparency and efficiency.
The post 2018: A year of renewed hope appeared first on Track2Realty.
The post Smartworks leases new facilities in Pune and Chennai appeared first on Track2Realty.
The Government's decision to allow 51% FDI in multi-brand retail and 100% FDI in single-brand retail under the automatic route was a definite crowd-pleaser that attracted giants like Walmart to make forays into the country.
The post Review of retail realty in 2018 & predictions for 2019 appeared first on Track2Realty.
The low consumer confidence has been linked as much to peoples' lack of confidence in their own ability to pay as with the employment uncertainties. Collectively, the buyers' risk aversion in today's economy as well as the developers' unfair business practices have eclipsed real estate like never before.
The post Consumer confidence in real estate hits 10-year low appeared first on Track2Realty.
While 2018 lived up to a fair number of expectations, there were a few misses too, particularly in the case of clarity on GST norms. Key highlights of 2018 were the creation of positive sentiments in the market by way of a robust office space absorption by emerging segments, as well as increase in the number of new launches and sales in the affordable housing sector.
The post Expectations & road ahead for 2019 appeared first on Track2Realty.


We describe an identity based key encapsulation mechanism (ID-KEM). It is possible to use this ID-KEM to build a secure identity based encryption scheme using the techniques of Bentahar et al. The resulting encryption scheme has a number of performance advantages over existing methods.


Git allows to signed commits. This PR enables displaying those commits.
The development of this MR is sponsored by @siemens (/cc @bufferoverflow).
## What does this MR do? 1. Shows gpg signed commits (excl. tags) 1. If the gpg key is verified (= the gpg was added to GitLab and the user's email matches the key's email) a "Verified" batch is displayed 1. If the gpg key is not verified or does not exist on GitLab an "Unverified" batch is displayed 1. If the commit is not signed, the behaviour is unchanged 1. Allows the user to add gpg keys to his profile ## Are there points in the code the reviewer needs to double check? - ## Why was this MR needed? Git allows to signed commits. This PR enables displaying those commits. The development of this MR is sponsored by @siemens (/cc @bufferoverflow). ## Screenshots (if relevant) **Commits list:** ![Commits___signed_commits___nannie_bernhard___gitlab_test___GitLab_3_](/uploads/3626b483fe6fc4d43631eb2e035ed49f/Commits___signed_commits___nannie_bernhard___gitlab_test___GitLab_3_.png) **Commit details:** ![signed_commit_by_nannie_bernhard__0f44cd1d____Commits___nannie_bernhard___gitlab_test___GitLab](/uploads/5c3f5f30fb1e8d88db595c2a8f0b3f17/signed_commit_by_nannie_bernhard__0f44cd1d____Commits___nannie_bernhard___gitlab_test___GitLab.png) **Badge popovers:** ![Commits___signed_commits___nannie_bernhard___gitlab_test___GitLab_5_](/uploads/be231431396aab800a1d058d29bc9cdf/Commits___signed_commits___nannie_bernhard___gitlab_test___GitLab_5_.png) ![Commits___signed_commits___nannie_bernhard___gitlab_test___GitLab_4_](/uploads/a7fb39ca0a76492d1515462050ef256d/Commits___signed_commits___nannie_bernhard___gitlab_test___GitLab_4_.png) **User settings > GPG key:** ![GPG_Keys___User_Settings___GitLab_2_](/uploads/f91a08bc669a33117875a7e07ae32280/GPG_Keys___User_Settings___GitLab_2_.png) ## Does this MR meet the acceptance criteria? - [x] [Changelog entry](https://docs.gitlab.com/ce/development/changelog.html) added - [x] [Documentation created/updated](https://gitlab.com/gitlab-org/gitlab-ce/blob/master/doc/development/doc_styleguide.md) - [ ] API support added - Tests - [x] Added for this feature/bug - [x] All builds are passing - [x] Conform by the [merge request performance guides](http://docs.gitlab.com/ce/development/merge_request_performance_guidelines.html) - [x] Conform by the [style guides](https://gitlab.com/gitlab-org/gitlab-ce/blob/master/CONTRIBUTING.md#style-guides) - [x] Branch has no merge conflicts with `master` (if it does - rebase it please) - [x] [Squashed related commits together](https://git-scm.com/book/en/Git-Tools-Rewriting-History#Squashing-Commits) ## What are the relevant issue numbers? Closes https://gitlab.com/gitlab-org/gitlab-ce/issues/20268.


At J & A we believe that the correct installation of your equipment is as essential. If you've just bought a new Bang & Olufsen or require a re-installation our certified engineers will help install your system so you can start to enjoy your audio and video equipment.
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text:
\section{Introduction}

Let $\{X,X_n,n\geq 1\}$ be a sequence of independent and identically distributed (i.i.d.) random variables in a probability space $(\Omega,\mathcal{F},P)$. Define $S_n=X_1+\cdots+X_n$, $n\in\mathbb{N}$. If $E|X|<\infty$, then by the law of large numbers, we know that $\frac{S_n}{n}\stackrel{a.s.}{\longrightarrow} \mu$, where $\mu=E[X]$. In fact, we also have $\frac{S_n}{n}\stackrel{L^1}{\longrightarrow} \mu$ by the martingale theory.

Hsu and Robbins (1947) introduced a new kind of convergence named ``{\it complete convergence}''. Let $\{Y,Y_n,n\geq 1\}$ be a sequence of  random variables. $\{Y_n,n\geq 1\}$ is said to completely converge to $Y$, if for any $\varepsilon>0$,
\begin{eqnarray*}
\sum_{n=1}^{\infty}P(|Y_n-Y|>\varepsilon)<\infty,
\end{eqnarray*}
which is denoted by $Y_n\stackrel{c.c.}{\longrightarrow} Y$. Obviously, $Y_n\stackrel{c.c.}{\longrightarrow} Y\Rightarrow Y_n\stackrel{P}{\longrightarrow} Y$. In fact, by  the Borel-Cantelli lemma, we know that  $Y_n\stackrel{c.c.}{\longrightarrow} Y \Rightarrow Y_n\stackrel{a.s.}{\longrightarrow} Y$.

 Hsu and Robbins (1947) proved that if $E[X^2]<\infty$ and $E[X]=\mu$, then
$\frac{S_n}{n}\stackrel{c.c.}{\longrightarrow} \mu$. Erd\"{o}s (1949) proved the converse result. Baum and Katz (1965) extended the Hsu-Robbins-Erd\"{o}s theorem. Below is
a special case of the Baum-Katz theorem.

\begin{thm} {\rm (Baum and Katz (1965))}. Let $\alpha\geq 1$. Suppose that $\{X, X_n,n\geq 1\}$ is a sequence of i.i.d.
random variables with partial sum $S_n=\sum_{i=1}^n X_i$,
$n\in\mathbb{N}$. Then the condition $E|X|^{\alpha}<\infty$ and
$EX=0$ is equivalent to
$
\sum_{n=1}^{\infty}n^{\alpha-2}P\left(|S_n|>n\varepsilon\right)<\infty,\ \
\forall\varepsilon>0.
$
\end{thm}
Lanzinger (1998), Gut and Stadtm\"{u}ller (2011),
Chen and Sung (2014) extended the results of Baum and Katz (1965).

Chow (1988) first investigated the complete moment
convergence and obtained the following result. Let $\alpha\geq 1$,
$p\le \alpha$ and $p<2$. Suppose that $\{X, X_n,n\geq 1\}$ is a
sequence of i.i.d. random variables with $E[X]=0$. If
$E[|X|^{\alpha}+|X|\log^+|X|]<\infty$, then
\begin{eqnarray*}\label{Chow-a}
\sum_{n=1}^{\infty}n^{\frac{\alpha}{p}-\frac{1}{p}-2}E\left[\left(|S_n|-\varepsilon
n^{\frac{1}{p}}\right)^{+}\right]<\infty,\ \forall
\varepsilon>0,
\end{eqnarray*}
where $x^+=\max\{0,x\}$. Chow's result has been generalized in various directions. Refer to Qiu and Chen (2014), Li and Hu (2017) and the references therein.

Li and Hu (2017) introduced a new convergence called ``{\it strong $L^p$-convergence}''. Let $\{Y,Y_n,n\geq 1\}$ be a sequence of random variables, and $p>0$. $Y_n$ is said to strongly $L^p$-converge to $Y$ if
$
\sum_{n=1}^{\infty}E[|Y_n-Y|^p]<\infty,
$
which is denoted by $Y_n\stackrel{S\mbox{-}L^p}{\longrightarrow} Y$. Obviously, $Y_n\stackrel{S\mbox{-}L^p}{\longrightarrow} Y\Rightarrow Y_n\stackrel{L^p}{\longrightarrow} Y$.
 By Markov's inequality, $Y_n\stackrel{S\mbox{-}L^{p}}{\longrightarrow} Y\Rightarrow Y_n\stackrel{c.c.}{\longrightarrow} Y$. Then for $p\geq 1$, we have the following diagram:
\begin{eqnarray*}
\begin{array}{ccccccc}
Y_n\stackrel{c.c.}{\longrightarrow} Y&\Rightarrow& Y_n\stackrel{a.s.}{\longrightarrow} Y&\Rightarrow &Y_n\stackrel{P}{\longrightarrow} Y&\Rightarrow &Y_n\stackrel{d}{\longrightarrow} Y\\
\Uparrow & & & & \Uparrow & &\\
Y_n\stackrel{S\mbox{-}L^{p}}{\longrightarrow} Y&\Rightarrow &Y_n\stackrel{L^{p}}{\longrightarrow} Y&\Rightarrow &Y_n\stackrel{L^1}{\longrightarrow} Y&&
\end{array}
\end{eqnarray*}
In particular, for $p>1$,  $Y_n\stackrel{S\mbox{-}L^{p}}{\longrightarrow} Y$ implies both $Y_n\stackrel{a.s.}{\longrightarrow} Y$  and $Y_n\stackrel{L^1}{\longrightarrow} Y$.

Recently, Hu and Sun (2018) studied convergence rates in the law of large numbers for i.i.d. random variables. They obtained a strong $L^p$-convergence version and a strong almost sure convergence version of the law of large numbers in a probability space.

The motivation of this note is to study convergence rates in the law of large numbers for i.i.d. random variables under sublinear expectations, and extend some results in a probability space to a sublinear expectation space.

Motivated by the risk measures, superhedge pricing and modeling uncertainty in finance, Peng (2006, 2007, 2008a, 2008b, 2009, 2010) initiated the notion of i.i.d. random variables under sublinear expectations, and proved the central limit theorems and the weak law of large numbers among others.

 Hu and Zhou (2015) presented some multi-dimensional laws of large numbers under sublinear expectations without the requirement of identical distribution.  Chen (2016) proved a
 strong law of large numbers (SLLNs) for i.i.d. random variables
 under capacities induced by sublinear  expectations.  Hu and Chen (2016)
 presented three laws of large numbers for independent random
 variables without the requirement of identical distribution.    Zhang (2016) showed that Kolmogorov's SLLNs holds for i.i.d. random variables under a continuous sublinear expectation if and only if the corresponding Choquet integral is finite. Chen et al. (2017)  investigated some SLLNs for sublinear expectation without independence. Hu and Yang (2017) obtained  a SLLNs for i.i.d. random variables under one-order type moment condition. Hu (2018) obtained a SLLNs for a sequence of independent random variables satisfying a controlled 1st moment condition under sublinear expectations. Chen et al. (2019) established a kind of SLLNs for capacities with a new notion of exponential independence for random variables under an upper expectation.

 We refer to Marinacci (1999), Maccheroni and Marinacci (2005), Cozman (2010), Li and Chen (2011), Chen (2012), Chen et al. (2013), Agahi et al. (2013), Zhang and Chen (2015), Hu et al. (2016), Wu and Jiang (2018) for more results on SLLNs for capacity, nonlinear expectations or sublinear expectations.  We also refer to  Hu and Zhou (2019) and Zhang (2019) for some recent results on the convergence of random variables  under sublinear expectations.

The rest of this note is organized as follows. In Section 2, we recall some basic notions and  results on sublinear expectations. In Section 3, we present our main results and give the proofs. In the final section, we mention some questions.

\section{Sublinear expectations}\setcounter{equation}{0}\label{sub-e}

  In this section, we introduce some basic definitions and notations about sublinear expectation. Refer to Peng (2010) for more details.

Let $\Omega$ be a given set and let $\mathcal{H}$ be a linear space of real functions defined on $\Omega$ such that for any constant number $c$, $c \in \mathcal{H}$; if $X \in \mathcal{H}$, then $|X| \in \mathcal{H}$; if $X_1,\cdots ,X_n \in \mathcal{H}$, then for any
$\varphi \in C_{l,lip}(\mathbb{R}^n)$, $\varphi(X_1,\cdots ,X_n) \in \mathcal{H}$, where $ C_{l,lip}(\mathbb{R}^n)$ denotes the linear space of functions $\varphi$ satisfying
 \begin{eqnarray*}
 |\varphi(x)-\varphi(y)| \leq C(1+|x|^m+|y|^m)|x-y|, \ \ \forall x, y \in\mathbb{R}^n
 \end{eqnarray*}
for some $C>0$, $m\in \mathbb{N}$ depending on $\varphi$.
For $n \in \mathbb{N}$, let $\mathcal{H}^{n}=\{X=(X_1,\cdots,X_n), X_i\in \mathcal{H}, \forall i=1,\cdots,n\}$ denote $n$-dimensional random vector space.
\begin{defi} {\rm (Definition 1.1 of Peng (2010))}  A sublinear expectation $\hat{E}$ on $\mathcal{H}$ is a functional $\hat{E}:\mathcal{H} \rightarrow \mathbb{R}$ satisfying the following properties $:\forall$ $X,Y\in \mathcal{H}$,

(i) Monotonicity: $\hat{E}[X] \geq \hat{E}[Y] ,\  \mbox{if}\ X \geq Y$;

(ii) Constant preserving: $\hat{E}[c]=c ,\  \forall \ c \in \mathbb{R}$;

(iii) Sub-additivity:  $\hat{E}[X+Y] \leq \hat{E}[X] + \hat{E}[Y]$;

(iv) Positive homogeneity:  $\hat{E}[\lambda X] = \lambda \hat{E}[X], \  \forall \lambda \geq 0$.\\
The triple $(\Omega,\mathcal{H},\hat{E})$ is called a sublinear expectation space.

\end{defi}
In the following, we assume that $\Omega$ is a complete separable metric space and let $\cal{B}(\Omega)$ denote
the Borel $\sigma$-algebra of $\Omega$. Further we assume that there exists a family $\mathcal{P}$ of probability measures on $(\Omega,\cal{B}(\Omega))$ such that
\begin{eqnarray*}
\hat{E}[X]=\sup\limits_{P\in \mathcal{P}}{E_P}[X],\ \ \forall X \in \mathcal{H}.
\end{eqnarray*}
Suppose that for any $A \in \cal{B}(\Omega)$, $I_{A}\in \mathcal{H}$. A pair of capacities associated with $\hat{E}[\cdot]$ are defined by
\begin{eqnarray*}
V(A):=\hat{E}[I_{A}],\  v(A):=-\hat{E}[-I_{A}],\ \forall A\in \cal{B}(\Omega).
\end{eqnarray*}
It is easy to check that
\begin{eqnarray*}
V(\emptyset)=0, \ V(\Omega)=1 , V(A)+v(A^{c})=1,
\end{eqnarray*}
where $A^{c}$ is the complementary set of $A$, $A\in \cal{B}(\Omega)$.
For $p\in [1,+\infty)$, the map
\begin{eqnarray*}
\left\|\cdot\right\|_{p}:X\in \mathcal{H} \mapsto (\hat{E}[|X|^{p}])^{\frac{1}{p}}
\end{eqnarray*}
forms a seminorm on $\mathcal{H}$.

\begin{defi}{\rm (Definition I.3.1 of Peng (2010))}  Let $(\Omega_i,\mathcal{H}_i,\hat{E}_i),i=1,2$ be two sublinear expectation spaces and $X_i\in \mathcal{H}_i^{n},i=1,2$. $X_1$ and $X_2$ are called identically distributed, which is denoted by $X_1\stackrel{d}{=}X_2$, if
\begin{eqnarray*}
\hat{E}_{1}[\varphi(X_1)]=\hat{E}_{2}[\varphi(X_2)] ,\forall \varphi \in C_{l,lip}(\mathbb{R}^n).
\end{eqnarray*}
\end{defi}

\begin{defi}{\rm (Definition I.3.10 of Peng (2010))}  Let $(\Omega,\mathcal{H},\hat{E})$ be a sublinear expectation space, and $X \in \mathcal{H}^m$, $Y\in \mathcal{H}^n$, $n,m\in\mathbb{N}$. $Y$ is said to be independent to  $X$ under $\hat{E}[\cdot]$, if for each test function $\varphi \in C_{l,lip}(\mathbb{R}^{n+m})$, we have
\begin{eqnarray*}
\hat{E}[\varphi(X,Y)]=\hat{E}[\hat{E}[\varphi(x,Y)]_{x=X}],
\end{eqnarray*}
whenever $\bar{\varphi}(x):=\hat{E}[|\varphi(x,Y)|]<\infty$ for all $x$ and $\hat{E}[|\bar{\varphi}(X)|]<\infty$.
\end{defi}

\begin{defi}{\rm (Proposition I.3.15 of Peng (2010))}  A sequence of random variables $\{X_n,n\geq 1\}$ on $(\Omega,\mathcal{H},\hat{E})$ is said to be independent and identically distributed, if $X_i\stackrel{d}{=}X_1$ and $X_{i+1}$ is independent to $(X_1,\cdots,X_i)$ for each $i\geq 1$.
\end{defi}

\begin{defi}{\rm (Definition II.1.4 of Peng (2010))}  A $d$-dimensional random vector $X=(X_1,\cdots,X_d)^{T}$ on a sublinear expectation space $(\Omega,\mathcal{H},\hat{E})$ is called (centralized ) G-normal distributed if
\begin{eqnarray*}
aX+b\bar{X}\stackrel{d}{=} \sqrt{a^2+b^2}X\ \ \mbox{for any}\ a,b\geq0,
\end{eqnarray*}
where $\bar{X}$ is an independent copy of $X$ ($\bar{X}\stackrel{d}{=}X$ and $\bar{X}$ is independent to $X$).
\end{defi}

\section{Convergence rates in the law of large numbers}\setcounter{equation}{0}

In this section, we will study convergence rates in the law of large numbers under sublinear expectations. Let $(\Omega,\mathcal{H},\hat{E})$ be a sublinear expectation space as introduced in Section \ref{sub-e}, and  $\{X,X_n,n\geq 1\}$ be a sequence of random variables in $\mathcal{H}$. We have the following convergences:
\begin{description}
\item[(1)] $\{X_n,n\geq 1\}$ is said to quasi surely converge to $X$, if there exists a set $N \subset \Omega$ such that $\hat{E}[I_{N}]= 0$ and $\forall \omega\in \Omega\backslash N$, $\lim_{n \to \infty}X_n(\omega)=X(\omega)$, which is denoted by $X_n\stackrel{q.s}{\longrightarrow} X$.

\item[(2)] $\{X_n,n\geq 1\}$ is said to converge to $X$ in capacity, if for all $\varepsilon > 0$, $\lim_{n \to \infty}V(\{|X_n-X|\geq \varepsilon\})=0$, which is denoted by $X_n\stackrel{V}{\longrightarrow}X$.

\item[(3)] $\{X_n,n\geq 1\}$ is said to $L^p$ converge to $X~(p >0)$, if $\lim_{n \to \infty}\hat{E}[|X_n-X|^p]=0$, which is denoted by $X_n\stackrel{L^p}{\longrightarrow}X$.

\item[(4)] $\{X_n,n\geq 1\}$ is said to completely converge to $X$, if for any $\varepsilon >0$, $\sum_{n=1}^{\infty}V(\{|X_n-X|\geq \varepsilon\})<\infty$, which is denoted by $X_n\stackrel{c.c.}{\longrightarrow}X$.

\item[(5)] $\{X_n,n\geq 1\}$ is said to $S\mbox{-}L^p$ converge to $X~(p >0)$, if $\sum_{n=1}^{\infty}\hat{E}[|X_n-X|^p]<\infty$, which is denoted by $X_n\stackrel{S\mbox{-}L^p}{\longrightarrow}X$.

\item[(6)] $\{X_n,n\geq 1\}$ is said to strongly quasi surely converge to $X$ with order $\alpha$~($\alpha >0$), if $\sum_{n=1}^{\infty}|X_n-X|^{\alpha}<\infty$ q.s.,
which is denoted by $X_n\stackrel{S_{\alpha}\mbox{-}q.s.}{\longrightarrow}X$.
\end{description}
Generally, we have
\begin{eqnarray*}
\begin{array}{ccccccccc}
&&&&X_n\stackrel{S_{p}\mbox{-}q.s.}{\longrightarrow}X & \Rightarrow & X_n\stackrel{q.s}{\longrightarrow} X&&\\
&&&&\Uparrow & &\Uparrow&&\\
X_n\stackrel{V}{\longrightarrow}X&\Leftarrow& X_n\stackrel{L^p}{\longrightarrow}X&\Leftarrow& X_n\stackrel{S\mbox{-}L^p}{\longrightarrow}X& \Rightarrow& X_n\stackrel{c.c.}{\longrightarrow}X&\Rightarrow&X_n\stackrel{V}{\longrightarrow}X\\
\end{array}
\end{eqnarray*}
If $\hat{E}$ has the monotone continuity property (\cite[Definition 2.2(vii)]{CJP11}), i.e. for any $X_n\downarrow 0$ on $\Omega$,  $\hat{E}[X_n]\downarrow 0$, then
we have (see Hu and Zhou (2019))
\begin{eqnarray*}
 X_n\stackrel{q.s.}{\longrightarrow} X \Rightarrow  X_n\stackrel{V}{\longrightarrow} X \Rightarrow  X_n\stackrel{d}{\longrightarrow} X.
\end{eqnarray*}

Let $\{X_n,n\geq 1\}$ be a sequence of i.i.d. random variables such that $\hat{E}[X_n]=-\hat{E}[-X_n]=\mu$. Denote $S_n=X_1+ X_2\cdots+X_n$, $\tilde{S}_n=\sum_{i=1}^{n}(X_i-\hat{E}[X_i])$. Then
$
\frac{S_n}{n}-\mu=\frac{\tilde{S}_n}{n}.
$

\subsection{Strong $L^p$ convergence version of the law of large numbers}

\begin{thm}\label{thm3.4}

Suppose that $\hat{E}[|X_1|^{\alpha}]<\infty$ for some $\alpha>2$. We have

(i) if $0< p\leq 2$, then
$
\frac{S_n}{n}\stackrel{S\mbox{-}L^{p}}{\nrightarrow} \mu;
$

(ii) if $2<p\leq \alpha$,  then
$
\frac{S_n}{n}\stackrel{S\mbox{-}L^p}{\longrightarrow} \mu.
$
\end{thm}

To prove Theorem \ref{thm3.4}, we need one lemma.

\begin{lem}\label{lem3.5} {(Theorem II.3.3, Lemma II.3.9 of Peng (2010), Theorem 3.2 of Hu (2011))} \\
 Let $\{X_i\}_{i=1}^{\infty}$ be a sequence of $\mathbb{R}^{d}$-valued i.i.d. random variables, satisfying $\hat{E}[X_i]=-\hat{E}[-X_i]=0$ and $\hat{E}[|X_i|^{2+\beta}]<\infty$ for some $\beta>0$. Then the sequence $\{\overline{S_n}\}$ defined by $\bar{S}_n:=(\sum_{i=1}^{n}X_i)/\sqrt{n}$ converges in law to $\xi$, i.e.,
\begin{eqnarray*}
\lim_{n\to\infty}\hat{E}[\varphi(\overline{S_n})]=\hat{E}[\varphi(\xi)],
\end{eqnarray*}
for any continuous function $\varphi\in C(\mathbb{R}^{d})$ satisfying the growth condition that $|\varphi(x)|\leq C(1+|x|^p)$ for some constants $C>0,~p>0$, where $\xi$ is  G-normal distributed with the law $N(\{0\}\times [\underline{\sigma}^2,\bar{\sigma}^2])$, $\underline{\sigma}^2=-\hat{E}[-X_i^2],\bar{\sigma}^2=\hat{E}[X_i^2]$.
\end{lem}

\noindent {\bf Proof of Theorem \ref{thm3.4}.}
Set $\tilde{X}_i=X_i-\mu$, $i\geq 1$. Then we have $\hat{E}[\tilde{X}_i]=\hat{E}[-\tilde{X}_i]=0,\forall i\geq 1$.

(i) Let $\hat{E}[\tilde{X}_i^2]=\bar{\sigma}^2$. Then $\bar{\sigma}^2>0$ by the assumption. By the  positive homogeneity of $\hat{E}$, we have
\begin{eqnarray*}
\hat{E}\left[\left|\frac{\tilde{S}_n}{n}\right|^{p}\right]
=\frac{1}{n^{p/2}}\hat{E}\left[\left|\frac{\tilde{S}_n}{\sqrt{n}}\right|^{p}\right].
\end{eqnarray*}
By Lemma \ref{lem3.5}, we have
\begin{eqnarray}\label{proof-lem3.4-a}
\hat{E}\left[\left|\frac{\tilde{S}_n}{\sqrt{n}}\right|^p\right]\to \hat{E}[|\xi|^p], \ \ \mbox{as}\ \ n\to\infty,
\end{eqnarray}
where $\xi$ is $G$-distributed with $\hat{E}[\xi^2]=\bar{\sigma}^2>0$. It follows that $V(\{\omega\in \Omega| |\xi(\omega)|>0\})>0$, which implies that $\hat{E}[|\xi|^p]>0$ for any $p>0$. Denote $c_p=\hat{E}[|\xi|^p]$.  Then by (\ref{proof-lem3.4-a}), there exists  $N\in \mathbb{N}$  such that
\begin{eqnarray*}
\hat{E}\left[\left|\frac{\tilde{S}_n}{\sqrt{n}}\right|^{p}\right]\geq\frac{c_p}{2}, \ \ \forall\ n\geq N.
\end{eqnarray*}
Therefore, for any $0< p \leq 2$, we have
\begin{eqnarray*}
\sum_{n=1}^{\infty}\hat{E}\left[\left|\frac{\tilde{S}_n}{n}\right|^p\right]\geq \sum_{n=N}^{\infty}\frac{1}{n^{p/2}}\hat{E}\left[\left|\frac{\tilde{S}_n}
{\sqrt{n}}\right|^{p}\right]\geq \frac{c_p}{2}\sum_{n=N}^{\infty}\frac{1}{n^{p/2}}=\infty.
\end{eqnarray*}

(ii) By the assumption, we know that for any $k\geq 1$, $X_{k+1}$ is independent to $(X_1,\ldots,X_k)$, which implies that $X_{k+1}$ is negatively dependent to $(X_1,\ldots,X_k)$ (see Zhang (2016, Definition 1.5) for the definition of {\it negative dependence}).  By the Marcinkiewicz-Zygmund inequality under sublinear expectations (see Zhang (2016, (2.13)),  the fact that $\hat{E}[\tilde{X}_i]=\hat{E}[-\tilde{X}_i]=0,\forall i\geq 1$, and Minkowski's inequality (see Peng (2010, Proposition I.4.2),  we have
\begin{eqnarray}\label{thm3.4-c}
\hat{E}\left[\left|\tilde{S}_n\right|^{\alpha}\right]
&\leq& \hat{E}\left[\max\limits_{k\leq n}\left|\tilde{S}_k\right|^{\alpha}\right]\nonumber\\
&\leq& C_{\alpha}\left\{\left(\sum_{k=1}^{n}\left(\left(\hat{E}\left[\tilde{X}_k\right]\right)^{+}
+\left(\hat{\mathcal{E}}\left[\tilde{X}_k\right]\right)^{-}\right)\right)^{\alpha}
+\hat{E}\left[\left(\sum_{k=1}^{n}\tilde{X_k}^2\right)^{\frac{\alpha}{2}}\right]\right\}\nonumber\\
&=&C_\alpha\hat{E}\left[\left(\tilde{X}_1^2+\cdots+\tilde{X}_n^2\right)^
{\alpha/2}\right]\nonumber\\
&=&C_\alpha\left\|\tilde{X}_1^2+\cdots+\tilde{X}_n^2\right\|_{\alpha/2}^{\alpha/2}\nonumber\\
&\leq&C_\alpha\left(\left\|\tilde{X}_1^2\right\|_{\alpha/2}+\cdots+\left\|\tilde{X}_n^2\right\|_{\alpha/2}\right)^{\alpha/2}\nonumber\\
&=&C_\alpha n^{\alpha/2}\hat{E}\left[\left|\tilde{X}_1\right|^{\alpha}\right],
\end{eqnarray}
where $x^+=\max\{0,x\}$, $x^-=\max\{0,-x\}$, and $C_\alpha$ is a positive constant depending only on $\alpha$. It follows that
\begin{eqnarray*}
\sum_{n=1}^{\infty}\hat{E}\left[\left|\frac{\tilde{S}_n}{n}\right|^{\alpha}\right]
\leq C_\alpha\sum_{n=1}^{\infty}\frac{\hat{E}[|\tilde{X}_1|^{\alpha}]}{n^{\frac{\alpha}{2}}}<\infty .
\end{eqnarray*}

For any $2<p<\alpha$, by H\"{o}lder's inequality under sublinear expectations (see Peng (2010, Proposition I.4.2)) and (\ref{thm3.4-c}),  we obtain that
\begin{eqnarray*}
\sum_{n=1}^{\infty}\hat{E}\left[\left|\frac{\tilde{S}_n}{n}\right|^p\right]
&\leq&\sum_{n=1}^{\infty}\frac{1}{n^p}\left(\hat{E}\left[\left|\tilde{S}_n\right|^{\alpha}\right]\right)^{p/\alpha}\\
&\leq&\sum_{n=1}^{\infty}\frac{1}{n^p}\left(C_\alpha n^{\alpha/2}\hat{E}\left[\left|\tilde{X}_1\right|^{\alpha}\right]\right)^{p/\alpha}\\
&=&\left(C_\alpha\hat{E}\left[\left|\tilde{X}_1\right|^{\alpha}\right]\right)^{p/\alpha}
\sum_{n=1}^{\infty}\frac{1}{n^{p/2}}<\infty.
\end{eqnarray*}
\hfill\fbox

In Chow (1988), the author also obtained the following result. Let $\{X,X_n,n\geq 1\}$ be a sequence of i.i.d. random variables with $E[X]=0$ in a probability space $(\Omega,\cal{F},P)$. Suppose that $1<\alpha<2$. If $E[|X|^{\alpha}\log^{+}|X|]<\infty$, then
\begin{eqnarray*}\label{Chow-a}
\sum_{n=1}^{\infty}n^{-2}E[|S_n|^{\alpha}]<\infty.
\end{eqnarray*}

As a consequence of Theorem \ref{thm3.4} and its proof, we obtain the following two corollaries.

\begin{cor}
Suppose that $\alpha>2$, $\hat{E}[|X_1|^{\alpha}]<\infty$, and $\hat{E}[X_1]=-\hat{E}[-X_1]=0$. Then, for any $2<p\leq\alpha$ and $\beta>(p+2)/2,$ we have
\begin{eqnarray*}
\sum_{n=1}^{\infty}n^{-\beta}\hat{E}[|S_n|^{p}]<\infty .
\end{eqnarray*}
\end{cor}

\begin{cor}
Suppose that  $X_1 \not \equiv \mu$ q.s.,  $\hat{E}[|X_1|^{\alpha}] <\infty$ for any $\alpha >0 $, and $p>0$. Then
\begin{eqnarray*}
\frac{S_n}{n}\stackrel{S-L^p}{\longrightarrow} \mu \Leftrightarrow p>2 \ .
\end{eqnarray*}
\end{cor}

\subsection{Strongly quasi sure convergence version of the law of large numbers}

\begin{pro}\label{thm3.10}
Suppose that $\hat{E}[|X_1|^{\alpha}]<\infty$ for some $\alpha>2$. Then for any
 $\beta>2$, we have
\begin{eqnarray*}
\frac{\tilde{S}_n}{n}\stackrel{S_{\beta}\mbox{-}q.s.}{\longrightarrow} 0,
\end{eqnarray*}
i.e., $\frac{S_n}{n}\stackrel{S_{\beta}\mbox{-}q.s.}{\longrightarrow} \mu$.
\end{pro}
{\bf Proof.} By Theorem \ref{thm3.4}(ii), we know that  for $2<\beta\leq \alpha$, it holds that $\frac{S_n}{n}\stackrel{S\mbox{-}L^{\beta}}{\longrightarrow} \mu,$ i.e.
$$
\sum_{k=1}^{\infty}\hat{E}\left[\left|\frac{S_n}{n}-\mu\right|^{\beta}\right]<\infty,
$$
which together with  the monotone convergence theorem (Cohen et al. (2011)) and the sublinear property implies that
\begin{eqnarray*}
\hat{E}\left[\sum_{k=1}^{\infty}\left|\frac{S_n}{n}-\mu\right|^{\beta}\right]
&=&\lim_{m\to\infty}\hat{E}\left[\sum_{k=1}^m\left|\frac{S_n}{n}-\mu\right|^{\beta}\right]\\ &\leq&\lim_{m\to\infty}\sum_{k=1}^m\hat{E}\left[\left|\frac{S_n}{n}-\mu\right|^{\beta}\right]\\
&=&\sum_{k=1}^{\infty}\hat{E}\left[\left|\frac{S_n}{n}-\mu\right|^{\beta}\right]<\infty.
\end{eqnarray*}
It follows that
\begin{eqnarray}\label{thm3.10-a}
\sum_{k=1}^{\infty}\left|\frac{S_n}{n}-\mu\right|^{\beta}<\infty,\ q.s.\ \ \mbox{for any}\ \  2<\beta\leq \alpha.
\end{eqnarray}

By the strong law of large numbers (see Theorem 1 of Chen (2016)), there exists a set $N\subset \Omega$ such that $V(N)=0$ and for any $\omega\in \Omega\backslash N$, there exists $M(\omega)\in \mathbb{N}$ such that for any $n\geq M(\omega)$,
\begin{eqnarray*}\label{thm3.10-b}
\left|\frac{S_n}{n}-\mu\right|<1.
\end{eqnarray*}
It follows that  for $\beta>\alpha$ and $\omega\in \Omega\backslash N$,
$$
\sum_{n=M(\omega)}^{\infty}\left|\frac{S_n}{n}-\mu\right|^{\beta}\leq
\sum_{n=M(\omega)}^{\infty}\left|\frac{S_n}{n}-\mu\right|^{\alpha},
$$
which together with (\ref{thm3.10-a}) implies that for any $\beta>\alpha$,
$$
\sum_{k=1}^{\infty}\left|\frac{S_n}{n}-\mu\right|^{\beta}<\infty,\ q.s.
$$
\hfill\fbox

\section{Some questions}\setcounter{equation}{0}

In this section, we present some questions for further research.

\noindent {\bf Question 1.} Can we extend the Hsu-Robbins theorem from a probability space to a sublinear expectation space?

\noindent {\bf Question 2.} If the answer to Question 1 is affirmative, can we prove the converse result?

In fact, we can ask more questions. As to the results on the convergence rates in the law of large numbers in a probability space, we can consider the corresponding questions in a sublinear expectation space.

\bigskip

{ \noindent {\bf\large Acknowledgments} \quad   This work was
supported by National Natural Science Foundation of China (Grant
No. 11771309, 11871184).}

redpajama_set_name: RedPajamaArXiv


text:
April Fools: Selector Infected WIXOSS Live Action Adaptation & Cat Expansion Announced
2015, Anime, Images, Japanese News, News, Other
The official website of the Selector Infected WIXOSS franchise has revealed that there will be a live action film based on the popular card game and anime. Additionally, a brand new expansion pack for the card game titled Tama Limited Edition was also revealed.
Takara Tomy, the producers of the card game, have revealed that the film will be a high budget production where the entire cast itself costs a grand total of ¥2,300 (~ $19.10 USD). The film will also use maximise the use of visual effects, utilising free software found on the internet to surpass the animation of the anime. The first promotional video for the live action film was released, showcasing the wonderful visuals and budget:
A brand new expansion to the card game has been announced. Tama Limited Edition is the next major update to the game, bringing new cat cards to the series. Furthermore, it will also increase the exposure of the game to felines.
Here is an image from the new expansion being used in a recent tournament:
There is also one more announcement, a Summer Camp where in order to attend you must: wear a swimsuit, have goggles, wear a swimming cap and are an expert in gymnastics.
Selector Infected WIXOSS is an original anime series animated by J.C. Staff (Toradora!, Sakurasou no Pet na Kanojo) and directed by Takuya Satou (Steins;Gate, Seitokai no Ichizon). A card game based on the series titled WIXOSS was produced from Takara Tomy in April this year. The series received a second anime adaptation last year titled Selector Spread WIXOSS.
WIXOSS is a card game that's popular with teenagers. Supposedly there exist "LRIG Cards," female character cards with wills of their own. Special girls can hear the voices of the LRIGs, and those who possess them are called Selectors. These Selectors have card battles in a dimension that other humans cannot access. It's said that whoever triumphs in these battles will have their wish granted. Ruko Kominato is the latest girl to find an LRIG card. She names her card Tama, and without any further explanation is thrown into her life as a Selector.
The live action Selector Infected WIXOSS film will be coming out in Japanese theatres on Smarch 35th next year. More information will follow in the next eon.
You can visit the franchise's website here: http://www.takaratomy.co.jp/products/wixoss/
You can visit the anime's website here: http://selector-wixoss.com/
And follow their Twitter here: @selector_anime
Source Article and Images – WIXOSS Website
"Selector Infected WIXOSS", "Selector Spread WIXOSS", images, video and all associated brands and titles © 2015 J.C. Staff and Project Selector
Tags: april April Fools film Fools j.c. staff live action movie promotional video PV Selector Infected WIXOSS Selector Spread WIXOSS selector_anime video Wixoss セレクター infected WIXOSS


text:
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text:
[Docs] [txt|pdf] [Tracker] [Email] [Diff1] [Diff2] [Nits] [IPR]
Versions: 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 RFC 4906
Network Working Group                                       Luca Martini
Internet Draft                                           Nasser El-Aawar
Expiration Date: October 2002               Level 3 Communications, LLC.
Steve Vogelsang                                            Daniel Tappan
John Shirron                                               Eric C. Rosen
Toby Smith                                                 Alex Hamilton
Laurel Networks, Inc.                                Jayakumar Jayakumar
Vasile Radoaca                                  Dimitri Stratton Vlachos
Nortel Networks                                      Mazu Networks, Inc.
Andrew G. Malis                                       Chris Liljenstolpe
Vinai Sirkay                                            Cable & Wireless
Vivace Networks, Inc.
Giles Heron
Dave Cooper                                          PacketExchange Ltd.
Kireeti Kompella
Transport of Layer 2 Frames Over MPLS
draft-martini-l2circuit-trans-mpls-09.txt
This document is an Internet-Draft and is in full conformance with
all provisions of Section 10 of RFC2026.
Task Force (IETF), its areas, and its working groups. Note that other
groups may also distribute working documents as Internet-Drafts.
http://www.ietf.org/ietf/1id-abstracts.txt.
Martini, et al.                                                 [Page 1]
Internet Draft draft-martini-l2circuit-trans-mpls-09.txt      April 2002
http://www.ietf.org/shadow.html.
This document describes methods for transporting the Protocol Data
Units (PDUs) of layer 2 protocols such as Frame Relay, ATM AAL5,
Ethernet, and providing a SONET circuit emulation service across an
MPLS network.
1      Specification of Requirements  ..........................   3
3      Tunnel Labels and VC Labels  ............................   3
4      Protocol-Specific Details  ..............................   5
4.1    Frame Relay  ............................................   5
4.2    ATM  ....................................................   5
4.2.1  ATM AAL5 VCC Transport  .................................   5
4.2.2  ATM Transparent Cell Transport  .........................   5
4.2.3  ATM VCC and VPC Cell Transport  .........................   6
4.2.4  OAM Cell Support  .......................................   6
4.2.5  ILMI Support  ...........................................   7
4.3    Ethernet VLAN  ..........................................   7
4.4    Ethernet  ...............................................   7
4.5    HDLC  ...................................................   7
4.6    PPP  ....................................................   8
5      LDP  ....................................................   8
5.1    Interface Parameters Field  .............................  10
5.2    C Bit handling procedures  ..............................  11
5.2.1  VC types for which the control word is REQUIRED  ........  11
5.2.2  VC types for which the control word is NOT mandatory  ...  11
5.2.3  Status codes  ...........................................  13
5.3    LDP label Withdrawal procedures  ........................  13
5.4    Sequencing Considerations  ..............................  14
5.4.1  Label Mapping Advertisements  ...........................  14
5.4.2  Label Mapping Release  ..................................  14
6      IANA Considerations  ....................................  15
7      Security Considerations  ................................  15
8      References  .............................................  15
9      Author Information  .....................................  16
1. Specification of Requirements
document are to be interpreted as described in RFC 2119.
In an MPLS network, it is possible to carry the Protocol Data Units
(PDUs) of layer 2 protocols by prepending an MPLS label stack to
these PDUs. This document specifies the necessary label distribution
procedures for accomplishing this using the encapsulation methods in
[7]. We restrict discussion to the case of point-to-point transport.
QoS related issues are not discussed in this draft. This document
describes methods for transporting a number of protocols; in some
cases, transporting a particular protocol may have several modes of
operation.  Each of these protocols and/or modes may be implemented
independently.
An accompanying document [8] also describes a method for transporting
time division multiplexed (TDM) digital signals (TDM circuit
emulation) over a packet-oriented MPLS network. The transmission
system for circuit-oriented TDM signals is the Synchronous Optical
Network (SONET)[5]/Synchronous Digital Hierarchy (SDH) [6]. To
support TDM traffic, which includes voice, data, and private leased
line service, the MPLS network must emulate the circuit
characteristics of SONET/SDH payloads. MPLS labels and a new circuit
emulation header are used to encapsulate TDM signals and provide the
Circuit Emulation Service over MPLS (CEM).
3. Tunnel Labels and VC Labels
Suppose it is desired to transport layer 2 PDUs from ingress LSR R1
to egress LSR R2, across an intervening MPLS network. We assume that
there is an LSP from R1 to R2. That is, we assume that R1 can cause a
packet to be delivered to R2 by pushing some label onto the packet
and sending the result to one of its adjacencies. Call this label the
"tunnel label", and the corresponding LSP the "tunnel LSP".
The tunnel LSP merely gets packets from R1 to R2, the corresponding
label doesn't tell R2 what to do with the payload, and in fact if
penultimate hop popping is used, R2 may never even see the
corresponding label.  (If R1 itself is the penultimate hop, a tunnel
label may not even get pushed on.)  Thus if the payload is not an IP
packet, there must be a label, which becomes visible to R2, that
tells R2 how to treat the received packet.  Call this label the "VC
label".
So when R1 sends a layer 2 PDU to R2, it first pushes a VC label on
its label stack, and then (if R1 is not adjacent to R2) pushes on a
tunnel label.  The tunnel label gets the MPLS packet from R1 to R2;
the VC label is not visible until the MPLS packet reaches R2.  R2's
disposition of the packet is based on the VC label.
Note that the tunnel could be a GRE encapsulated MPLS tunnel between
R1 and R2. In this case R1 would be adjacent to R2, and only the VC
label would be used, and the intervening network need only carry IP
packets.
If the payload of the MPLS packet is, for example, an ATM AAL5 PDU,
the VC label will generally correspond to a particular ATM VC at R2.
That is, R2 needs to be able to infer from the VC label the outgoing
interface and the VPI/VCI value for the AAL5 PDU. If the payload is a
Frame Relay PDU, then R2 needs to be able to infer from the VC label
the outgoing interface and the DLCI value. If the payload is an
Ethernet frame, then R2 needs to be able to infer from the VC label
the outgoing interface, and perhaps the VLAN identifier. This process
is unidirectional, and will be repeated independently for
bidirectional operation. It is REQUIRED to assign the same VC ID, and
VC type for a given circuit in both directions. The group ID (see
below) MUST NOT be required to match in both directions. The
transported frame MAY be modified when it reaches the egress router.
If the header of the transported layer 2 frame is modified, this MUST
be done at the egress LSR only.
Note that the VC label must always be at the bottom of the label
stack, and the tunnel label, if present, must be immediately above
the VC label. Of course, as the packet is transported across the MPLS
network, additional labels may be pushed on (and then popped off) as
needed. Even R1 itself may push on additional labels above the tunnel
label. If R1 and R2 are directly adjacent LSRs, then it may not be
necessary to use a tunnel label at all.
This document does not specify a method for distributing the tunnel
label or any other labels that may appear above the VC label on the
stack. Any acceptable method of MPLS label distribution will do.
This document does specify a method for assigning and distributing
the VC label. Static label assignment MAY be used, and
implementations SHOULD provide support for this. When signaling is
used, the VC label MUST be distributed from R2 to R1 using LDP in the
downstream unsolicited mode; this requires that an LDP session be
created between R1 and R2. It should be noted that this LDP session
is not necessarily transported along the same path as the Layer 2
PDUs. [1] In addition, when using LDP to distribute the VC label,
liberal label retention mode SHOULD be used. However, as required in
[1], the label request operation (mainly used by conservative label
retention mode) MUST be implemented. VC labels MUST be allocated from
the per-platform label space.
Note that this technique allows an unbounded number of layer 2 "VCs"
to be carried together in a single "tunnel".  Thus it scales quite
well in the network backbone.
While this document currently defines the emulation of Frame Relay
and ATM PVC services, it specifically does not preclude future
enhancements to support switched service (SVC and SPVC) emulation.
4. Protocol-Specific Details
4.1. Frame Relay
The Frame Relay PDUs are encapsulated according to the procedures
defined in [7]. The MPLS edge LSR MUST provide Frame Relay PVC status
signaling to the Frame Relay network. If the MPLS edge LSR detects a
service affecting condition as defined in [2] Q.933 Annex A.5 sited
in IA FRF1.1, it MUST withdraw the label that corresponds to the
frame relay DLCI. The Egress LSR SHOULD generate the corresponding
errors and alarms as defined in [2] on the egress Frame relay VC.
4.2. ATM
4.2.1. ATM AAL5 VCC Transport
ATM AAL5 CSPS-SDUs are encapsulated according to [10] ATM AAL5 CPCS-
SDU mode. This mode allows the transport of ATM AAL5 CSPS-SDUs
traveling on a particular ATM PVC across the MPLS network to another
ATM PVC.
4.2.2. ATM Transparent Cell Transport
This mode is similar to the Ethernet port mode. Every cell that is
received at the ingress ATM port on the ingress LSR, R1, is
encapsulated according to [10], ATM cell mode, and sent across the
LSP to the egress LSR, R2. This mode allows an ATM port to be
connected to only one other ATM port. [10] allows for grouping of
multiple cells into a single MPLS frame. Grouping of ATM cells is
OPTIONAL for transmission at the ingress LSR, R1. If the Egress LSR
R2 supports cell concatenation the ingress LSR, R1, should only
concatenate cells up to the "Maximum Number of concatenated ATM
cells" parameter received as part of the FEC element.
4.2.3. ATM VCC and VPC Cell Transport
This mode is similar to the ATM AAL5 VCC transport except that cells
are transported. Every cell that is received on a pre-defined ATM
PVC, or ATM PVP, at the ingress ATM port on the ingress LSR, R1, is
LSP to the egress LSR R2. Grouping of ATM cells is OPTIONAL for
transmission at the ingress LSR, R1. If the Egress LSR R2 supports
cell concatenation the ingress LSR, R1, MUST only concatenate cells
up to the "Maximum Number of concatenated ATM cells in a frame"
parameter received as part of the FEC element.
4.2.4. OAM Cell Support
OAM cells MAY be transported on the VC LSP. When the LSR is operating
in AAL5 CPCS-SDU transport mode if it does not support transport of
ATM cells, the LSR MUST discard incoming MPLS frames on an ATM VC LSP
that contain a VC label with the T bit set [10]. When operating in
AAL5 SDU transport mode an LSR that supports transport of OAM cells
using the T bit defined in [7], or an LSR operating in any of the
three cell transport modes MUST follow the procedures outlined in [9]
section 8 for mode 0 only, in addition to the applicable procedures
specified in [6].
4.2.4.1. OAM Cell Emulation Mode
AN LSR that does not support transport of OAM cells across an LSP MAY
provide OAM support on ATM PVCs using the following procedures:
A pair of LSRs MAY emulate a bidrectional ATM VC by two uni-
directional LSPs.  If an F5 end-to-end OAM cell is received from a
ATM VC, by either LSR that is transporting this ATM VC, with a
loopback indication value of 1, and the LSR has a label mapping for
the ATM VC, then the LSR MUST decrement the loopback indication value
and loop back the cell on the ATM VC. Otherwise the loopback cell
MUST be discarded by the LSR.
The ingress LSR, R1, may also optionally be configured to
periodically generate F5 end-to-end loopback OAM cells on a VC. If
the LSR fails to receive a response to an F5 end-to-end loopback OAM
cell for a pre-defined period of time it MUST withdraw the label
mapping for the VC.
If an ingress LSR, R1, receives an AIS F5 OAM cell, fails to receive
a pre-defined number of the End-to-End loop OAM cells, or a physical
interface goes down, it MUST withdraw the label mappings for all VCs
associated with the failure. When a VC label mapping is withdrawn,
the egress LSR, R2, MUST generate AIS F5 OAM cells on the VC
associated with the withdrawn label mapping. In this mode it is very
useful to apply a unique group ID to each interface. In the case
where a physical interface goes down, a wild card label withdraw can
be sent to all LDP neighbors, greatly reducing the signaling response
4.2.5. ILMI Support
An MPLS edge LSR MAY provide an ATM ILMI to the ATM edge switch. If
an ingress LSR receives an ILMI message indicating that the ATM edge
switch has deleted a VC, or if the physical interface goes down, it
MUST withdraw the label mappings for all VCs associated with the
failure. When a VC label mapping is withdrawn, the egress LSR SHOULD
notify its client of this failure by deleting the VC using ILMI.
4.3. Ethernet VLAN
The Ethernet frame will be encapsulated according to the procedures
in [12].  It should be noted that if the VLAN identifier is modified
by the egress LSR, according to the procedures outlined above, the
Ethernet spanning tree protocol might fail to work properly. If the
LSR detects a failure on the Ethernet physical port, or the port is
administratively disabled, it MUST withdraw the label mappings for
all VCs associated with the port.
4.4. Ethernet
in [12].  If the LSR detects a failure on the Ethernet physical port,
or the port is administratively disabled, the corresponding VC label
mapping MUST be withdrawn.
4.5. HDLC
HDLC frames are encapsulated according to the procedures in [11]. If
the MPLS edge LSR detects that the physical link has failed, or the
port is adminstratively disabled, it MUST withdraw the label mapping
that corresponds to the HDLC link.
4.6. PPP
PPP frames are encapsulated according to the procedures in [11]. If
that corresponds to the PPP link.
5. LDP
The VC label bindings are distributed using the LDP downstream
unsolicited mode described in [1]. The LSRs will establish an LDP
session using the Extended Discovery mechanism described in [1,
section 2.4.2 and 2.5], for this purpose a new type of FEC element is
defined. The FEC element type is 128. [note1] Only a single VC FEC
element MUST be advertised per LDP VC label.  The Virtual Circuit FEC
element, is defined as follows:
|    VC tlv     |C|         VC Type             |VC info Length |
|                      Group ID                                 |
|                        VC ID                                  |
|                       Interface parameters                    |
|                              "                                |
- VC Type
A 15 bit quantity containing a value which represents the type of
VC. Assigned Values are:
VC Type  Description
0x0001   Frame Relay DLCI
0x0002   ATM AAL5 VCC transport
0x0003   ATM transparent cell transport
0x0004   Ethernet VLAN
0x0005   Ethernet
0x0006   HDLC
0x0007   PPP
0x8008   CEM [8]
0x0009   ATM VCC cell transport
0x000A   ATM VPC cell transport
- Control word bit (C)
The  highest  order bit (C) of the VC type is used to flag the
presence  of  a  control  word  ( defined in [7] ) as follows:
bit 15 = 1 control word present on this VC.
bit 15 = 0 no control word present on this VC.
Please see the section "C Bit handling procedures" for further
explenation.
- VC information length
Length of the VC ID field and the interface parameters field in
octets. If this value is 0, then it references all VCs using the
specified group ID and there is no VC ID present, nor any
interface parameters.
- Group ID
An arbitrary 32 bit value which represents a group of VCs that is
used to create groups in the VC space. The group ID is intended
to be used as a port index, or a virtual tunnel index. To
simplify configuration a particular VC ID at ingress could be
part of the virtual tunnel for transport to the egress router.
The Group ID is very useful to send wild card label withdrawals
to remote LSRs upon physical port failure.
- VC ID
A non zero 32-bit connection ID that together with the VC type,
identifies a particular VC.
- Interface parameters
This variable length field is used to provide interface specific
parameters, such as interface MTU.
5.1. Interface Parameters Field
This field specifies  interface specific parameters. When aplicable,
it MUST be used to validate that the LSRs, and the ingress and egress
ports at the edges of the circuit, have the necessary capabilities to
interoperate with each other. The field structure is defined as
|  Parameter ID |    Length     |    Variable Length Value      |
|                         Variable Length Value                 |
|                             "                                 |
The parameter ID is defined as follows:
Parameter   ID Length    Description
0x01         4       Interface MTU in octets.
0x02         4       Maximum Number of concatenated ATM cells.
0x03   up to 82      Optional Interface Description string.
0x04         4       CEM [8] Payload Bytes.
0x05         4       CEM options.
The Length field is defined as the length of the interface parameter
including the parameter id and length field itself.
- Interface MTU
A 2 octet value indicating the MTU in octets. This is the Maximum
Transmission Unit, excluding encapsulation overhead, of the
egress packet interface that will be transmitting the
decapsulated PDU that is received from the MPLS network. This
parameter is applicable only to VC types 1, 2, 4, 5, 6, and 7,
and is REQUIRED for these VC types. If this parameter does not
match in both directions of a specific VC, that VC MUST NOT be
enabled.
- Maximum Number of concatenated ATM cells
A 2 octet value specifying the maximum number of concatenated ATM
cells that can be processed as a single PDU by the egress LSR. An
ingress LSR transmitting concatenated cells on this VC can
concatenate a number of cells up to the value of this parameter,
but MUST NOT exceed it. This parameter is applicable only to VC
Martini, et al.                                                [Page 10]
types 3, 9, and 0x0a, and is REQUIRED for these VC types. This
parameter does not need to match in both directions of a specific
VC.
- Optional Interface Description string
This arbitrary, OPTIONAL, interface description string can be
used to send an administrative description text string to the
remote LSR. This parameter is OPTIONAL, and is applicable to all
VC types. The interface description parameter string length is
variable, and can be from 0  to 80 octets.
- Payload Bytes
A 2 octet value indicating the the number of TDM payload octets
contained in all packets on the CEM stream, from 48 to 1,023
octets. All of the packets in a given CEM stream have the same
number of payload bytes. Note that there is a possibility that
the packet size may exceed the SPE size in the case of an STS-1
SPE, which could cause two pointers to be needed in the CEM
header, since the payload may contain two J1 bytes for
consecutive SPEs. For this reason, the number of payload bytes
must be less than or equal to 783 for STS-1 SPEs.
- CEM Options.  An optional 16 Bit value of CEM Flags. See [8] for
the definition of the bit values.
5.2. C Bit handling procedures
5.2.1. VC types for which the control word is REQUIRED
The Label Mapping messages which are sent in order to set up these
VCs MUST have c=1. When a Label Mapping message for a VC of one of
these types is received, and c=0, a Label Release MUST be sent, with
an "Illegal C-bit" status code. In this case, the VC will not come
5.2.2. VC types for which the control word is NOT mandatory
If a system is capable of sending and receiving the control word on
VC types for which the control word is not mandatory, then each such
VC endpoint MUST be configurable with a parameter that specifies
whether the use of the control word is PREFERRED or NOT PREFERRED.
For each VC, there MUST be a default value of this parameter. This
specification does NOT state what the default value should.
If a system is NOT capable of sending and receiving the control word
on VC types for which the control word is not mandatory, then it
behaves as exactly as if it were configured for the use of the
control word to be NOT PREFERRED.
If a Label Mapping message for the VC has already been received, but
no Label Mapping message for the VC has yet been sent, then the
procedure is the following:
-i. If the received Label Mapping message has c=0, send a Label
Mapping message with c=0, and the control word is not used.
-ii. If the received Label Mapping message has c=1, and the VC is
locally configured such that the use of the control word is
preferred, then send a Label Mapping message with c=1, and
the control word is used.
-iii. If the received Label Mapping message has c=1, and the VC is
not preferred or the control word is not supported, then act
as if no Label Mapping message for the VC had been received
(i.e., proceed to the next paragraph).
If a Label Mapping message for the VC has not already been received
(or if the received Label Mapping message had c=1 and either local
configuration says that the use of the control word is not preferred
or the control word is not supported), then send a Label Mapping
message in which the c bit is set to correspond to the locally
configured preference for use of the control word.  (I.e., set c=1 if
locally configured to prefer the control word, set c=0 if locally
configured to prefer not to use the control word or if the control
word is not supported).
The next action depends on what control message is next received for
that VC.  The possibilities are:
-i. A Label Mapping message with the same c bit value as
specified in the Label Mapping message that was sent. VC
setup is now complete, and the control word is used if c=1
but not used if c=0.
-ii. A Label Mapping message with c=1, but the Label Mapping
message that was sent has c=0. In this case, ignore the
received Label Mapping message, and continue to wait for the
next control message for the VC.
-iii. A Label Mapping message with c=0, but the Label Mapping
message that was sent has c=1. In this case, send a Label
Withdraw message with a "Wrong c-bit" status code, followed
by a Label Mapping message that has c=0. VC setup is now
complete, and the control word is not used.
-iv. A Label Withdraw message with the "Wrong c-bit" status code.
Treat as a normal Label Withdraw, but do not respond.
Continue to wait for the next control message for the VC.
If at any time after a Label Mapping message has been received, a
corresponding Label Withdraw or Release is received, the action taken
is the same as for any Label Withdraw or Release that might be
received at any time. Note that receiving a Label Withdraw should not
cause a corresponding Label Release to be sent.
If both endpoints prefer the use of the control word, this procedure
will cause it to be used. If either endpoint prefers not to use the
control word, or does not support the control word, this procedure
will cause it not to be used. If one endpoint prefers to use the
control word but the other does not, the one that prefers not to use
it is has no extra protocol to execute, it just waits for a Label
Mapping message that has c=0.
5.2.3. Status codes
RFC 3036 has a range of Status Code values which are assigned by IANA
on a First Come, First Served basis. These are in the range
0x20000000-0x3effffff [note 2]. The following new status codes are
defined:
0x20000001 "Illegal C-Bit"
0x20000002 "Wrong C-Bit"
5.3. LDP label Withdrawal procedures
As mentioned above the Group ID field can be used to withdraw all VC
labels associated with a particular group ID. This procedure is
OPTIONAL, and if it is implemented the LDP label withdraw message
should be as follows: the VC information length field is set to 0,
the VC ID field is not present, and the interface paramenters field
is not present. For the purpose of this document this is called the
"wild card withdraw procedure", and all LSRs implementing this design
are REQUIRED to accept such a withdraw message, but are not required
to send it.
The interface parameters field MUST NOT be present in any LDP VC
label withdrawal message or release message. A wildcard release
message MUST include only the group ID.A Label Release message
initiated from the imposition router must always include the VC ID.
5.4. Sequencing Considerations
In the case where the router considers the sequence number field in
the control word, it is important to note the following when
5.4.1. Label Mapping Advertisements
After a label has been withdrawn by the disposition router and/or
released by the imposition router, care must be taken to not re-
advertise (re-use) the released label until the disposition router
can be reasonably certain that old packets containing the released
label no longer persist in the MPLS network.
This precaution is required to prevent the imposition router from
restarting packet forwarding with sequence number of 1 when it
receives the same label mapping if there are still older packets
persisting in the network with sequence number between 1 and 32768.
For example, if there is a packet with sequence number=n where n is
in the interval[1,32768] travelling through the network, it would be
possible for the disposition router to receive that packet after it
re-advertises the label. Since the label has been released by the
imposition router, the disposition router SHOULD be expecting the
next packet to arrive with sequence number to be 1. Receipt of a
packet with sequence number equal to n will result in n packets
potentially being rejected by the disposition router until the
imposition router imposes a sequence number of n+1 into a packet.
Possible methods to avoid this is for the disposition router to
always advertise a different VC label, or for the disposition router
to wait for a sufficient time before attempting to re-advertised a
recently released label. This is only an issue when sequence number
processing at the disposition router is enabled.
5.4.2. Label Mapping Release
In situations where the imposition router wants to restart forwarding
of packets with sequence number 1, the router shall 1) Send to
disposition router a label mapping release, and 2) Send to
disposition router a label mapping request. When sequencing is
supported, advertisement of a vc label in response to a label mapping
request MUST also consider the issues discussed in 5.3.1
As specified in this document, a Virtual Circuit FEC element contains
the VC Type field. VC Type value 0 is reserved. VC Type values 1
through 10 are defined in this document. VC Type values 11 through 63
are to be assigned by IANA using the "IETF Consensus" policy defined
in RFC2434. VC Type values 64 through 127 are to be assigned by IANA,
using the "First Come First Served" policy defined in RFC2434. VC
Type values 128 through 32767 are vendor-specific, and values in this
range are not to be assigned by IANA.
the Interface Parameters field, which is a list of one or more
parameters, and each parameter is identified by the Parameter ID
field. Parameter ID value 0 is reserved. Parameter ID values 1
through 5 are defined in this document.  Parameter ID values 6
through 63 are to be assigned by IANA using the "IETF Consensus"
policy defined in RFC2434. Parameter ID values 64 through 127 are to
be assigned by IANA, using the "First Come First Served" policy
defined in RFC2434. Parameter ID values 128 through 255 are vendor-
specific, and values in this range are not to be assigned by IANA.
This document does not affect the underlying security issues of MPLS.
[1] "LDP Specification." L. Andersson, P. Doolan, N. Feldman, A.
Fredette, B. Thomas. January 2001. RFC3036
[2] ITU-T Recommendation Q.933, and Q.922 Specification for Frame
Mode Basic call control, ITU Geneva 1995
[3] "MPLS Label Stack Encoding", E. Rosen, Y. Rekhter, D. Tappan, G.
Fedorkow, D. Farinacci, T. Li, A. Conta. RFC3032
[4] "IEEE 802.3ac-1998" IEEE standard specification.
[5] American National Standards Institute, "Synchronous Optical
Network Formats," ANSI T1.105-1995.
[6] ITU Recommendation G.707, "Network Node Interface For The
Synchronous Digital Hierarchy", 1996.
[7] "Encapsulation Methods for Transport of Frame-Relay Over IP and
MPLS Networks", draft-martini-frame-encap-mpls-00.txt. ( work in
progress )
[8] "SONET/SDH Circuit Emulation Service Over MPLS (CEM)
Encapsulation", draft-malis-sonet-ces-mpls-05.txt ( Work in progress
[9] "Frame Based ATM over SONET/SDH Transport (FAST)," 2000.
[10] "Encapsulation Methods for Transport of ATM Cells/Frame Over IP
and MPLS Networks", draft-martini-atm-encap-mpls-00.txt. ( work in
[11] "Encapsulation Methods for Transport of PPP/HDLC Frames Over IP
and MPLS Networks", draft-martini-ppp-hdlc-encap-mpls-00.txt. ( work
in progress )
[12] "Encapsulation Methods for Transport of Ethernet Frames Over IP
and MPLS Networks", draft-martini-ethernet-encap-mpls-00.txt. ( work
[note1] FEC element type 128 is pending IANA approval.  [note2]
Status codes assigment is pending IANA approval.
9. Author Information
Luca Martini
Level 3 Communications, LLC.
1025 Eldorado Blvd.
Broomfield, CO, 80021
e-mail: luca@level3.net
Nasser El-Aawar
e-mail: nna@level3.net
PacketExchange Ltd.
The Truman Brewery
LONDON E1 6QL
e-mail: giles@packetexchange.net
Dimitri Stratton Vlachos
Mazu Networks, Inc.
125 Cambridgepark Drive
e-mail: d@mazunetworks.com
Dan Tappan
250 Apollo Drive
Chelmsford, MA, 01824
e-mail: tappan@cisco.com
Jayakumar Jayakumar,
225, E.Tasman, MS-SJ3/3,
e-mail: jjayakum@cisco.com
Alex Hamilton,
285 W. Tasman, MS-SJCI/3/4,
e-mail: tahamilt@cisco.com
Eric Rosen
e-mail: erosen@cisco.com
Steve Vogelsang
Laurel Networks, Inc.
Omega Corporate Center
1300 Omega Drive
e-mail: sjv@laurelnetworks.com
John Shirron
e-mail: jshirron@laurelnetworks.com
Toby Smith
e-mail: tob@laurelnetworks.com
Andrew G. Malis
2730 Orchard Parkway
Email: Andy.Malis@vivacenetworks.com
Vinai Sirkay
e-mail: sirkay@technologist.com
Vasile Radoaca
600  Technology Park
Billerica MA 01821
e-mail: vasile@nortelnetworks.com
Chris Liljenstolpe
e-mail: chris@cw.net
960 Hamlin Court
e-mail: dcooper@gblx.net
1194 N. Mathilda Ave
e-mail: kireeti@juniper.net


Portland Thorns FC topped Utah Royals FC 2-0 on Friday night in front of a crowd of 15,113 at Providence Park in Portland, Oregon. The win moved the Thorns into second place in the NWSL, one point ahead of Seattle Reign FC, who play Saturday night.
With the win, the Thorns are now 4-3-3 (15 points). Thorns coach Mark Parsons became the third coach in NWSL history to reach 50 regular season wins, joining Reign coach Vlatko Andonovski and Utah coach Laura Harvey. Utah Royals FC fell to 2-2-5 (11 points) with their first road loss in franchise history.
In the 18th minute, Christine Sinclair scored the first goal of the game for the Thorns, her league-leading sixth goal of the season. Sinclair started the play at midfield, serving a lob over the top to Tobin Heath, and then continuing her run towards goal. Heath threaded the pass back to Sinclair, who took a touch to her left before shooting and beating Utah goalkeeper Abby Smith.
Lindsey Horan doubled the lead in the 39th minute, finishing a cross from Meghan Klingenberg with her knee to give Portland a 2-0 lead. The goal is Horan's fourth of the season, pulling her into a tie for second in the NWSL.
The Thorns had a great chance to score just a few moments earlier, but Smith made a kick save and then Utah defender Becky Sauerbrunn blocked a shot with her face.
Not ?ne, but tw? close chances from inside the area.
Utah had a chance to pull one back near the end of the first half, but Klingenberg cleared Amy Rodriguez's shot off the line.
Sinclair and Heath nearly connected again for another goal late, but Sinclair's shot bounced off the crossbar.
It's the second straight shutout for the Thorns. It's also the second clean sheet for goalkeeper Britt Eckerstrom, who made two saves in the match, including one on a hard Rodriguez shot moments before the final whistle.
Rodriguez played all 90 minutes for the first time this season, after returning from the ACL tear she suffered last year.
The Thorns will next be in action on Wednesday night when they host the unbeaten North Carolina Courage. Utah Royals FC will visit Sky Blue FC (0-6-1) on June 2.
Match ends, Portland Thorns 2, Utah Royals 0.
Second Half ends, Portland Thorns 2, Utah Royals 0.
Attempt saved. Amy Rodriguez (Utah Royals) right footed shot from outside the box is saved in the centre of the goal.
Attempt missed. Amy Rodriguez (Utah Royals) right footed shot from the centre of the box is close, but misses to the right. Assisted by Gunnhildur Yrsa Jonsdottir with a cross.
Corner, Portland Thorns. Conceded by Abby Smith.
Attempt saved. Christine Sinclair (Portland Thorns) right footed shot from outside the box is saved in the top centre of the goal. Assisted by Tobin Heath.
Ifeoma Onumonu (Portland Thorns) wins a free kick on the left wing.
Substitution, Portland Thorns. Ifeoma Onumonu replaces Ana Maria Crnogorcevic.
Foul by Angela Salem (Portland Thorns).
Offside, Utah Royals. Katrina-Lee Gorry tries a through ball, but Gunnhildur Yrsa Jonsdottir is caught offside.
Angela Salem (Portland Thorns) wins a free kick in the defensive half.
Offside, Portland Thorns. Angela Salem tries a through ball, but Ana Maria Crnogorcevic is caught offside.
Attempt blocked. Katrina-Lee Gorry (Utah Royals) right footed shot from outside the box is blocked. Assisted by Amy Rodriguez.
Attempt saved. Ana Maria Crnogorcevic (Portland Thorns) header from the centre of the box is saved in the centre of the goal. Assisted by Tobin Heath with a cross.
Rachel Corsie (Utah Royals) is shown the yellow card.
Lindsey Horan (Portland Thorns) is shown the yellow card.
Corner, Utah Royals. Conceded by Kelli Hubly.
Substitution, Portland Thorns. Kelli Hubly replaces Ellie Carpenter.
Substitution, Utah Royals. Elise Thorsnes replaces Erika Tymrak.
Substitution, Portland Thorns. Angela Salem replaces Andressinha.
Erika Tymrak (Utah Royals) wins a free kick on the left wing.
Delay in match Ana Maria Crnogorcevic (Portland Thorns) because of an injury.
Delay in match Becky Sauerbrunn (Utah Royals) because of an injury.
Attempt blocked. Ana Maria Crnogorcevic (Portland Thorns) left footed shot from the centre of the box is blocked. Assisted by Christine Sinclair with a through ball.
Second Half begins Portland Thorns 2, Utah Royals 0.
First Half ends, Portland Thorns 2, Utah Royals 0.
Attempt missed. Desiree Scott (Utah Royals) right footed shot from outside the box is high and wide to the right following a set piece situation.
Attempt blocked. Amy Rodriguez (Utah Royals) left footed shot from the centre of the box is blocked.
Attempt blocked. Erika Tymrak (Utah Royals) right footed shot from the centre of the box is blocked.
Goal! Portland Thorns 2, Utah Royals 0. Lindsey Horan (Portland Thorns) right footed shot from very close range to the centre of the goal. Assisted by Meghan Klingenberg with a cross.
Attempt blocked. Lindsey Horan (Portland Thorns) left footed shot from the centre of the box is blocked.
Attempt saved. Christine Sinclair (Portland Thorns) right footed shot from the centre of the box is saved in the centre of the goal. Assisted by Ana Maria Crnogorcevic.
Offside, Utah Royals. Amy Rodriguez tries a through ball, but Erika Tymrak is caught offside.
Attempt missed. Brooke Elby (Utah Royals) right footed shot from the right side of the box is too high. Assisted by Diana Matheson.
Attempt saved. Erika Tymrak (Utah Royals) right footed shot from outside the box is saved in the top centre of the goal.
Offside, Utah Royals. Erika Tymrak tries a through ball, but Gunnhildur Yrsa Jonsdottir is caught offside.
Goal! Portland Thorns 1, Utah Royals 0. Christine Sinclair (Portland Thorns) left footed shot from the centre of the box to the bottom left corner. Assisted by Tobin Heath.
Meghan Klingenberg (Portland Thorns) wins a free kick in the attacking half.
Offside, Utah Royals. Amy Rodriguez tries a through ball, but Gunnhildur Yrsa Jonsdottir is caught offside.
Amy Rodriguez (Utah Royals) wins a free kick on the left wing.