text:
About The Convention
About the Queen City
Charlotte Host Committee
B-Roll Download
OUR TEAM MEET THE LEADERSHIP
Ronna McDaniel
Chairwoman, Republican National Committee
Ronna McDaniel is the second woman ever elected Chair of the RNC. During the 2016 election, Ronna McDaniel helped deliver Michigan for Donald Trump and the GOP for the first time in decades. She was elected as the State Chairman from Michigan in February of 2015. Ronna served as a Trump delegate and chaired the Michigan Delegation to the 2016 Republican National Convention. She has served as a Precinct Delegate, as a District Committee Executive Member and State Committeewoman in Michigan and served as National Delegate to the Tampa Convention representing Michigan's 11th District.
In 2013, she served as Co-Chair for the Mackinac Leadership Conference and was appointed by Governor Rick Snyder to serve on the Board of Marriage and Family Therapists. In her local community of Northville, Ronna has served on land planning and public safety committees and is actively involved in her local PTA. She received her B.A. in English from Brigham Young University. Ronna is married to Patrick McDaniel and has two children, Abigail and Nash.
Marcia Lee Kelly
Marcia Lee Kelly is the President and CEO of the 2020 Republican National Convention. Most recently, Kelly was the Assistant to the President, Director of White House Management and Administration and Director of the Office of Administration, which provides operational support for the President. In that capacity, she oversaw 390 personnel supporting the White House, Office of Administration and the Executive Residence. She was also an official member of the USA Presidential Delegation to the Olympics in South Korea.
Over the course of her almost 30-year career, she has worked on two presidential transition teams and three Republican National Conventions in Minneapolis, Tampa and Cleveland. As Director of Operations for the 2016 Convention, she managed overall logistics, including build-outs of convention venues.
A first generation Korean-American, Kelly started her career in the New York City Mayor's Office, produced the Yankees ticker-tape parade and directed the two-year long NYC Millennium celebration that included 26-hours of non-stop live broadcasting to a global audience. Among a list of large-scale commemorations organized by Kelly: the Princess Diana Memorial, World Cup Host Committee, Inauguration of Mayor Giuliani and a Sting Concert in Central Park. Kelly was nominated for a daytime Emmy award for the "Prayer for America" which was the first memorial for the victims of 9/11. She and her work have been featured in the New York Times and Los Angeles Times.
Toni Anne Dashiell
Chairwoman, Republican National Convention
Toni Anne Dashiell is the Chairwoman for the RNC Committee on Arrangements for the 2020 Republican National Convention, and continues to serve as the Republican National Committeewoman for Texas.
Dashiell has been active in politics, grassroots advocacy and leadership training for more than 40 years. She is a leader among leaders, who was awarded the 2009 Ronald Reagan Leadership Award by the National Federation of Republican Women for her distinctive performance as the President of the Texas Federation of Republican Women (TFRW). She has traveled to Bosnia, Nigeria, Sri Lanka and Burma on behalf of the Women's Democracy Network to train women and men seeking public office. She co-authored with Rachel Woods "Leading for Freedom: Leadership Skills for Republicans" and conducts workshops across the nation on the topics addressed in the book.
Dashiell's service as a volunteer grassroots leader dates back to 1968, when she first worked on a presidential campaign as a member of Teenage Republicans. Since that time, she has been a consistent leader in numerous Republican campaigns and organizations both in Texas and across the nation. Dashiell was proud to serve as Kendall County Chair from 2010 to 2013 and as a Vice Chair of the Texas for Trump Coalition in 2016. She has served on the RNC since 2013, and was re-elected to the Budget Committee in January 2019.
Together, she and her husband, Tom, are small business owners in Boerne, Texas, working in both real estate and insurance.
Stephen "Max" Everett
Vice President and Chief Information Officer
Max Everett is the Vice President and Chief Information Officer for the 2020 Republican National Convention. This is Everett's sixth convention, having previously served as the Chief Information Officer for the 2004 and 2016 conventions. In these roles, he is responsible for the management, strategy and execution of major convention programs, while overseeing the convention's IT infrastructure and operations.
Everett brings over two decades of experience in providing innovative solutions and managing risk for both public and private sector organizations. Everett was most recently the Chief Information Officer for the U.S. Department of Energy, overseeing the Department's information technology (IT) portfolio, serving as an advisor to the Deputy Secretary and Secretary and leading various functions within the Office of the Chief Information Officer.
Everett received a bachelor's degree from the University of Texas and a J.D. from the University of Houston.
OUR TEAM MEET THE LEADERSHIP STAFF
Whitney Andersen –Chief of Program
Luke Bullock – Deputy Director of Buildout
Christina "CC" Cobaugh – Chief of Staff and Director of Ticketing
Kelly Eaton – Deputy Director of Operations
Blair Ellis – Director of Communications
Tatum Gibson – National Press Secretary
Kelsey Gorman – Director of Signature Events Coordination
Susan Haney – Deputy Director of External Affairs
Dustin Hendrix – Director of Transportation
Doug Hochberg – Digital Director
Jinger Kelley – Deputy Director of Finance
Andy King – Deputy Director of Logistics Flow & Signage
Thomas Krol – Deputy Director of Transportation
Edith "Dee Dee" Lancaster – Director of Logistics Flow & Signage
Joy Lee – Counsel
Christine "Chris" Lesko – Chief of Infrastructure
Diandra Lopez – Director of Delegate Experience
Thomas Maxwell – Chief Financial Officer
Dan McCarthy – Chief Public Affairs Officer
Mallory McGough – Director of Administration
Robert "Bob" O'Donnell – Director of Security
Jonathan "Jonny" Oringdulph – Chief Logistics Officer
Yandrick Paraison – Director of Special Projects
Russell Peck – Director of Community Affairs
Max Poux – Deputy Director of Security
Christopher Reese – Director of Executive Operations
James Sample – Director of Operations
Megan Schenewerk – Deputy Director of Administration
Lisa Shoemaker – Director of Media Operations
Rebecca Wasserstein – Director of Hotels and Venues
External Logo Use Policy
Paid for by the Committee on Arrangements for the 2020 Republican National Convention. Not authorized by any candidate or candidate's committee.
© 2020 Republican National Convention. All rights reserved
Pagado por el Comité de Acuerdos para la Convención Nacional Republicana 2020. No está autorizado por ningún candidato o comité de candidatos.
© 2020 Convención Nacional Republicana. Todos los derechos reservados


text:
ACCEPTED

#### According to
Index Fungorum

#### Published in
Syll. fung. (Abellini) 5: 747 (1887)

#### Original name
Pholiota magna Sacc.

### Remarks
null

redpajama_set_name: RedPajamaGithub


text:
ACCEPTED

#### According to
The Catalogue of Life, 3rd January 2011

#### Published in
null

#### Original name
Schoenus acutus Labill.

### Remarks
null


text:
DO YOU STILL FEEL HOPE?
Tell me, because I've forgotten, what does hope feel like? I'm not trying to be sarcastic, really. I just don't remember.
See, while I am totally for saving the environment, I think it's not the most important thing out there these days. What do I think is more important than the environment? One thing - US. Not the U.S., not our economy, not our bank accounts, our SUVs or even our way of life. But our life itself. You see because WE are the problem and the solution - well, we WILL be the solution, but for now, we're just the problem. Here are some things I've observed about us wacky and not-so-lovable humans:
1) People are interested in maintaining their own lifestyles as they are. OR, improve their lifestyles by making more money.
2) People are so interested in 1) that they will perform all manner of mental rationalization in order to make it happen. Whether it be taking a crappy job that makes them hate life, or by stepping on people to get ahead.
3) There are way too many people who can't see past what's on TV tonight. (Oo! The Sopranos!)
4) There are also way too many people who say things like "sure, I'm all for the environment!" but then drive around an SUV in a major American city. (With no plans to ever take their vehicle off-road. Hauling is no excuse - why do you think God invented the mini-van?)
5) People are so afraid of risk, pain or ANY kind of suffering that if a disaster happened and our leaders took every last one of their rights away from them 'in exchange for their safety', they would sit down in their easy chair and smile, feeling safe again to watch Family Feud in 'peace'.
6) Movers and shakers in the world are happy to overlook the fact that marketing campaigns have effectively become brainwashing campaigns. Calling them 'propaganda' doesn't go far enough.
7) Movies, TV, media, politicians and other public figures set examples that only serve to enforce the above points in every member of the Western World.
8) Millions of people have died around the world in the name of profits, the bottom line. (See 1) And we hear barely word one of any of it on any of the mainstream news media outlets. The Sudan, Bosnia, Columbia, the Middle East, areas of Asia. All of these places are focal points for oil and death. Don�t believe me? Do a Google search for any of those locations. You�ll find oil or violence-related stories for all of them.
My point in a nutshell is this: The environment will never be saved until the majority of humans on this planet stop treating each other with less respect than they do the environment.
Sure, 'education' is up compared to one hundred years ago, but lets compare the education the poor folks get to the education the white-- I mean the *rich* folks get. Let's check out health care. If you're rich, you get to pay for the procedures you need... until you need more procedures. Even the rich don't escape the fact that our health care industry is set up so that we're not *cured* we're just perpetuated. In the end, I don't care who is really behind 911, nor do I care about the Palestinians or the Israelis. I couldn't care less about famine in Africa or genocide in the Sudan, or the myriad lies we are told and tell ourselves here in the US.
All I want is for us to stop being so shitty to one another.
And no, I didn't just have a bad day, I'm just trying to point out that while I don't feel we are a suicidal animal, I do think we are incapable of respecting ourselves and others any less than we already do. And until this changes, THIS is the reason the environment can NEVER be the most important thing on our minds.
Humans have the potential to achieve great things. Explore the universe (both literally and figuratively) create works of art so grand they cause spontaneous tears of joy and/or sadness to fall, we are capable of such wonder, and yet most of what Humans do is one of three things:
1) Figure out how to make other people give you their money.
2) Figure out what you need to do to get the money you'll give to person #1.
3) Survive.
Granted, there are exceptions (I did say 'most' of what humans do), but the generalization is that all we really want to do is have money so we can live the way we want to live. We're an entire species dedicated to the get-rich-quick-scheme. And when it comes to the people polluting the environment? Guess what kind of people they are. #1, #2 and #3.
This has been "Life According to ThePete: Sucks Doesn't It?" and I'm your host, ThePete saying good night and suck less!
Crap, I forgot to try to suggest a solution. Okay, here goes:
We need a new group. Maybe a political party even. This group would work quietly, subtly, working it's way into society's most powerful corners. From there, each member would illicit change. Right now, I am on a path to do just that. I am trying to change things with my writing. I work positive, environmentally responsible messages into everything I write. (Maybe that's why I've not sold more.) In my opinion, this is the only way a sweeping change can occur - gradually, over the span of many years. Long-term investment isn't easy, but I'm doing it.
By doing this, I know I'm opening myself up for an attack from people more cynical than I (if such a person can exist) for being stupid and thinking I can change the world with my writing but I don't give a crap. I'm putting myself out there. We all need to do more of what we believe is right, not what's right for our bank accounts. And that INCLUDES how we treat each other and our environment can come after that. Think about it - if we just save the environment, the people who were in power before are still there. What's to stop them from polluting the environment all over again? But if we get humans to treat each other with respect, then automatically, the environment will be saved, because, after all, hurting the environment is hurting ourselves.
You know, I think I do remember what hope feels like.
Labels: TheCriticalPete
Crazy World, TheKey Passes 1600 Pages
Hey there... things have been crazy the past couple of days. Just passed page 1600 in TheKey a couple of days ago. It's been tough to pull myself from world events. Things are so crazy what with people just not getting what's going on with the US Government. It's some pretty scary stuff and frankly I haven't been able to figure out where to come at it from. But watch GDF.C (TheBitch Page) for stuff... so much to assimilate, but I'm getting there. Hopefully this weekend, I'll be back on the weekly bitch schedule... wish me luck!
Labels: In TheNews
PLAN FOR A NEW AMERICAN EMPIRE
First off, I've added a new Real Media clip in TheMedia of the Moment section. It's of our fearless leader flubbing furiously a famous old phrase about being fooled... ironic.
But the REAL news is this article:
HERE!!!
It claims to have uncovered a document that is the Bush 2 Administration's plan for an Iraq Attack and then followed by a global domination-type deal. If that's not enough for you, this document is dated September 2000. Talk about the power of positive thinking. Although I think it's more negative thinking from the world's point of view... If this article is legit, which it appears to be, there's some serious bad things in front of us... anyway, enjoy your day!! Click here to watch a Real Video presentation on how the world is running out of oil! COOL!
Labels: TheCriticalPete, ThePoliticalPete
PROBLEMS WITH BUSH'S ADDRESS TO THE UN
A year after terrorists struck American soil, the Bush II Administration is using this attack as part of it's reasoning for a new Iraq Attack. However, there doesn't appear to be any evidence that Iraq has helped Al Qaida out. Speaking to the UN, President Bush tried to address concerns of an Iraq Attack and the justifications to have one. You can read the whole speech here. What follows are my problems with his address. (I refer to the United States Government as the USG.)
Had Saddam Hussein been appeased instead of stopped, he would have endangered the peace and stability of the world.
Can I ask just what Saddam was supposed to do to threaten this so-called world peace and stability? (I didn't realize we had it!)
In 1991, Security Council Resolution 688 demanded that the Iraqi regime cease at once the repression of its own people, including the systematic repression of minorities - which, the Council said, "threaten(ed) international peace and security in the region."
Oh, I see, so he's trying to build on a mis-statement of the UN in the first place. I wonder who originally decided at the UN Iraq's oppression of minorities somehow equated a threat to world peace...
Tens of thousands of political opponents and ordinary citizens have been subjected to arbitrary arrest and imprisonment, summary execution, and torture by beating, burning, electric shock, starvation, mutilation, and rape. Wives are tortured in front of their husbands; children in the presence of their parents - all of these horrors concealed from the world by the apparatus of a totalitarian state.
Hm, this sounds a little like the USG's ally Saudi Arabia. Not a perfect comparison, granted, but close enough to wonder how the USG can point the finger at one without pointing it at it's own friend. Hell, that also sounds a bit like the US! (I said a BIT.)
In 1991, the U.N. Security Council, through Resolutions 686 and 687, demanded that Iraq return all prisoners from Kuwait and other lands. Iraq's regime agreed. It broke its promise. Last year the Secretary-General's high-level coordinator of this issue reported that Kuwaiti, Saudi, Indian, Syrian, Lebanese, Iranian, Egyptian, Bahraini, and Omani nationals remain unaccounted for - more than 600 people. One American pilot is among them.
Nice try - ONE person constitutes a violation? Come on, man! Give them a break. You try being a government and keeping track of ONE person. Hell, the USG couldn't keep track of FOUR PLANES on 911 and you get mad because the Iraqi's miss ONE GUY? (Don't get me wrong, they should release that one guy immediately, but this should not be considered a full violation.)
In 1991, the U.N. Security Council, through Resolution 687, demanded the Iraq renounce all involvement with terrorism, and permit no terrorist organizations to operate in Iraq. Iraq's regime agreed. It broke its promise. In violation of Security Council Resolution 1373, Iraq continues to shelter and support terrorist organization that direct violence against Iran, Israel, and Western governments. Iraqi dissidents abroad are targeted for murder. In 1993, Iraq attempted to assassinate the Emir of Kuwait and a former American President. Iraq's government openly praised the attacks of September 11th. And al-Qaida terrorists escaped from Afghanistan are known to be in Iraq.
Uh, ya want proof with that? Jeez, I've heard better arguments on Limbaugh's show. Last I heard, the terrorists were hanging out in the northern territories where I thought Saddam didn't have a whole lot of control over. Just my understanding - please correct me if I'm wrong.
U.N. inspectors believe Iraq has produced two to four times the amount of biological agents it declared, and has failed to account for more than three metric tons of material that could be used to produce biological weapons.
So, isn't this saying that Iraq *doesn't* have chemical weapons? "Could be used to produce" suggests they haven't produced them yet.
Right now, Iraq is expanding and improving facilities that were used for the production of biological weapons.
Again, how about some proofy-woofy with my Big Mac?
United Nations inspections also reveal that Iraq likely maintains stockpiles of VX, mustard, and other chemical agents, and that the regime is rebuilding and expanding facilities capable of producing chemical weapons.
WHICH UN inspectors? Because I know of at least one (COUGHscottritterCOUGH) that thinks nothing even close to this.
And in 1995 - after four years of deception
Pick your reaction:
1)Oh THAT'S rich.
2)Talk about the pot calling the kettle black!
3)Well, if anyone knows anything about deception, it certainly would be Mr. Bush!
Iraq finally admitted it had a crash nuclear weapons program prior to the Gulf War. We know now, were it not for that war, the regime in Iraq would likely have possessed a nuclear weapon no later than 1993.
Uh-huh, that's nice. Um, Georgie? Why don't you go back to your room until you have some actual evidence that Iraq needs to be invaded, m'kay? You can watch a little TV if you want, but please try and finish your homework before taking up the UN's time... in other words, what the hell does this have to do with Saddam having nukes NOW? It only speaks to the likelihood that he has nukes now, but this is hardly proof. That's like assuming every guy who gets out of jail WILL commit a crime again. Sure, it's possible, even likely, but do we arrest these guys again, just in case?
Today, Iraq continues to withhold important information about its unclear program
How's that for an ironic typo?
Iraq's state-controlled media has reported numerous meetings between Saddam Hussein and his nuclear scientists, leaving little doubt about his continued appetite for these weapons.
Why doesn't Bush just say "I saw on TV that Saddam was meeting with really mean guys and that's not fair, since he said he wouldn't. And it's his own TV station, so you know they're telling the truth!" So, just because he's meeting with nuke scientists they've instantly got nukes...
Iraq was allowed to use oil revenues to buy food
Of course, Bushie-poo fails to mention that buying oil from Iraq is a LOT like supporting an enemy government. If Iraq were so bad, wouldn't we want to avoid Iraqi oil all together? (I know the answer, I'm just being rhetorical.)
{Saddam} blames the suffering of Iraq's people on the United Nations, even as he uses his oil wealth to build lavish palaces for himself, and arms his country.
And this means that we should invade his country? I'm not sure I see how a leader being a dickweed to his citizens means we need to play schoolground protector. Besides, shouldn't we march into Saudi Arabia with the same attitude?
In 1991, Iraq promised U.N. inspectors immediate and unrestricted access to verify Iraq's commitment to rid itself of weapons of mass destruction and long-range missiles. Iraq broke this promise, spending seven years deceiving, evading and harassing U.N. inspectors before ceasing cooperation entirely.
Again, this is not what Scott Ritter said.
As we meet today, it has been almost four years since the last U.N. inspectors set foot in Iraq - four years for the Iraqi regime to plan and build and test behind a cloak of secrecy.
Pick your criticism:
1) Isn't this an admission that we have no intelligence regarding Iraqi weapons capabilities? (i.e. we have no evidence that they have WOMD so we can't really invade.)
2)So much for US intelligence sources... I thought we could find out a lot about them by watching those who sell stuff to them...
Saddam Hussein's regime is a grave and gathering danger.
Can't the same be said about the USG?
To suggest otherwise is to hope against the evidence.
WHAT evidence? You mean that list of things you think suggest evidence, Bush?
To assume this regime's good faith is to bet the lives of millions and the peace of the world in a reckless gamble.
I know that life has been a pretty stable thing for you Bush - what with your daddy making so much happen for you, but LIFE is a gamble. By marching into Iraq, YOU are GUARANTEEING the deaths of American soldiers and the expenditure of a BUTTLOAD of American tax dollars. Thanks, I'd rather wait for real proof to emerge from intel sources before we do that.
The first time we may be completely certain he has nuclear weapons is when, God forbid, he uses one.
Wow - even Bush's speech writers are idiots. "we may be completely certain" when "he uses one"?? I think there would be pretty much no doubt at that point, Bright Eyes. The catch is, there are many things we can find out about Iraq and their weapons capabilities in the meantime. Just look at the folks over at Janes.com - do you think opposing governments just hand out information on their own forces? But Jane's has been publishing intel on America's enemies since the cold war (or before, I'm not honestly sure). So, you tell me how they can know all this stuff about enemy forces, yet we can't tell if Iraq has bought the parts needed for a nuke.
Iraq has answered a decade of U.N. demands with a decade of defiance.
That may be, but are there no other alternatives?
If the Iraqi regime wishes peace, it will immediately and unconditionally forswear, disclose and remove or destroy all weapons of mass destruction, long-range missiles and all related material.
Sounds fair enough. Won't we need to send in weapons inspectors to make sure they're not lying? D'OH! Guess we can't invade then!
If the Iraqi regime wishes peace, it will immediately end all support for terrorism and act to suppress it, as all states are required to do by U.N. Security Council resolutions.
WHAT a crock!! The US supported terrorism in the past by calling it "resistance". PLEASE.
If the Iraqi regime wishes peace, it will release or account for all Gulf War personnel whose fate is still unknown.
All one of them!
If all these steps are taken, it will signal a new openness and accountability in Iraq. And it could open the prospect of the United Nations helping to build a government that represents all Iraqis - a government based on respect for human rights, economic liberty and internationally supervised elections.
JUST LIKE SAUDI ARABIA... I mean.. no wait...
The United States has no quarrel with the Iraqi people
But we'll kill them when we invade, just like we did in Afghanistan.
Liberty for the Iraqi people is a great moral cause and a great strategic goal.
Oh, sure! Yes, yes. Hm-hm... that's why we didn't kill Saddam ten years ago - because we wanted to liberate the Iraqi people... If anything, it's about the money the Iraqi people will spend on Coca-Cola and McDonalds once our corporations colonize Iraq.
Free societies do not intimidate through cruelty and conquest and open societies do not threaten the world with mass murder.
But it's okay when WE do it! :D
We can harbor no illusions. Saddam Hussein attacked Iran in 1980,
!!! WITH OUR HELP YOU MORON! WE GAVE HIM THE MONEY/WEAPONS TO DO IT!!! IF IT WASN'T FOR THE USG, SADDAM WOULDN'T BE IN POWER RIGHT NOW!! (Shouldn't the world be more concerned that the USG keeps propping up seriously dangerous people as leaders of countries?)
and Kuwait in 1990. He has fired ballistic missiles at Iran, Saudi Arabia, Bahrain and Israel. His regime once ordered the killing of every person between the ages of 15 and 70 in certain Kurdish villages in Northern Iraq. He has gassed many Iranians and 40 Iraqi villages.
Sure, and we knew about all this back when we were supporting Saddam's regime with American Tax Dollars. Has the USG suddenly grown a conscience? Or are the war profiteers that run the USG looking to put some really big presents under their Christmas trees this year?
My nation will work with the U.N. Security Council on a new resolution to meet our common challenge.
Read: We've got a plan, you want to come along? Fine. But, uh, we're going to invade. Just an FYI...
The Security Council resolutions will be enforced
Even if the Security Council doesn't want them enforced.
the just demands of peace and security will be met - or action will be unavoidable.
WITH WAR!! YEAAAH!! KILL 'EM ALL! ahem... I mean, uh...
And a regime that has lost its legitimacy will also lose its power.
Wait, so YOU'RE RESIGNING?? COOL!!
Events can turn in one of two ways.
Again, choose your reply:
1)My way or my way...
2)Ah... black or white, the ONLY two ways to look at the world!
If we fail to act in the face of danger, the people of Iraq will continue to live in brutal submission.
Isn't it cute how he continues to pretend to care about the Iraqi people? He doesn't care about the AMERICAN people! It's ADORABLE!!
And if an emboldened regime were to supply these weapons to terrorist allies, then the attacks of September 11th would be a prelude to far greater horrors.
Yeah and Ben Kenobi was telling Luke the truth when he said Vader killed Luke's dad from a certain point of view.
We must choose between a world of fear and a world of progress.
And WAR is the correct choice?? Is pot free when you live in the White House?
We must stand up for our security, and for the permanent rights and hopes of mankind.
While eroding the rights of our own citizens...
Sigh... I wonder at this point why Bush is even caring what everyone thinks. In the end, he will have to invade anyway. If he doesn't, watch for his administration to slowly move away from Saddam as a real target, just like they did with Osama. Personally, I hope the latter happens. Invasion now would just mean that "W" will try to use the momentum to continue his world conquest and invade other countries as well. My guess is that if an Iraq Attack does happen, it'll be at one of three times: the end of September 2002, the end of November 2002 or January of 2003. I've read that the US Government has claimed all three dates to foreign powers, yet to the citizens of it's own country, the USG has made no such clear declarations...
Let's keep our fingers crossed...
MY 911 TRIBUTE
Okay, so TheBlurb lies - but not entirely. My 911 tribute is in TheMedia of the Moment section - specifically in the Real Media section. Click TheMedia link above (not NOW, you boob! Finish reading this first!) and then click on the three videos in the top section. The bottom two have been up for a few days. But, they're all examples of how our WONDERFUL government has let us down.
The third clip down is a clip from an episode of the failed X-Files spin-off scifi show The Lone Gunmen. It follows the adventures of three conspiracy geeks as they foil a plot to remotely pilot a passenger airplane into the World Trade Center. The episode the clip is from aired March 4, 2001.
The second clip down is a clip from a recent episode of Donahue featuring a clip from a BBC documentary about how botched the 2000 election was.
The first clip is the best of the bunch - it's a clip of George Bush as he is told in front of a school room full of kids that a second plane has just struck the Twin Towers. At this point, we didn't know if there would be more planes falling from the sky or what. Yet, what does he do upon discovering the country HE'S leading is under attack? He sits back and continues with the school kids for another 20 minutes. To which, I say: "Why did we elect you, again? OH THAT'S RIGHT, WE DIDN'T!"
How do you like THAT 911 tribute...
Oh yeah and you can check out the other stuff too. There's a new fun wav clip and I've added a new mp3 that you should listen to and try to name it. Use the tag board for your ideas for what the track is. Oh yeah and the Gatchaman clip is still up just cuz I think it's so damn cool... :D
JFK DIED FOR MONEY? MAYBE
Wondering what those two $5 bills are when you go to ThePete.Com? (I recently moved them here.) The bottom one is a standard $5 bill before the new ones came out a couple years back. The top one, with the red seal is a United States Note ordered into existence by John F Kennedy on June 4, 1963. It was a silver certificate, which meant that you could go to the US government and ask for silver in exchange for the note. Before 1963 and since JFK's death, this is NOT the way US money works. US money today is worth something ONLY because the US Government (and the citizens it governs) agree that it is 'worth something'. In actuality, it isn't worth anything at all. Just a little FYI to confuse the crap out of you during an otherwise 'normal' day. To TOTALLY blow your mind, check out this thread at one of my favorite forums to post to. It will open your eyes and knock you on your ass. ENJOY! (But, be warned - it's a tough read - make sure to stretch out your brain before because you don't want to sprain it like I did... ow! I think I pulled a lobe!)
Back from the East & Lone Gunman Clip
What a crazy couple of weeks it's been. First off, check out the new Real Media clip in TheMedia of the Moment - it's a clip of the failed "X-Files" spin-off called "The Lone Gunmen". The episode the clip came from was aired March 4, 2001 and in it, the lead characters foil a plot that may seem familiar to anyone who watches TV. Check it out. Last week I had to fly back east to my mom and step-dad's place because they're moving. This meant that I had to save my old toys from oblivion. I also brought my cat from high school back with me, so we've now got THREE cats and four mice... pictures of all are coming soon! Anyway, lots more going on. More soon - I PROMISE... like you care ;) Oh yeah, I'll have a new Bitch by the end of the day, too. Lataz...

redpajama_set_name: RedPajamaCommonCrawl


text:
The Road to Maxwell's Demon
Conceptual Foundations of Statistical Mechanics
Meir Hemmo, University of Haifa, Israel
Orly R. Shenker, Hebrew University of Jerusalem
Date Published: July 2014
Time asymmetric phenomena are successfully predicted by statistical mechanics. Yet the foundations of this theory are surprisingly shaky. Its explanation for the ease of mixing milk with coffee is incomplete, and even implies that un-mixing them should be just as easy. In this book the authors develop a new conceptual foundation for statistical mechanics that addresses this difficulty. Explaining the notions of macrostates, probability, measurement, memory, and the arrow of time in statistical mechanics, they reach the startling conclusion that Maxwell's Demon, the famous perpetuum mobile, is consistent with the fundamental physical laws. Mathematical treatments are avoided where possible, and instead the authors use novel diagrams to illustrate the text. This is a fascinating book for graduate students and researchers interested in the foundations and philosophy of physics.
Provides new solutions to long-standing problems in the foundations of statistical mechanics
Addresses fundamental concepts such as measurement, the second law of thermodynamics and Maxwell's Demon
Avoids mathematical treatments so readers do not have to wade through complex mathematics
'The Road to Maxwell's Demon is an exceptionally clear and readable book, intended for readers without physics or philosophy backgrounds. It is also a highly original and important contribution to the foundations of physics. It goes against much of the received wisdom and offers novel solutions to many problems: among them, discussions of time asymmetry in classical mechanics, an empiricist alternative to typicality, a criticism of the role of ergodicity, the notion of a physical observer and the irrelevance of information theory to the foundations of statistical mechanics. Readers interested in the foundations of physics will welcome such a fresh outlook on these topics.' Amit Hagar, Metascience
contains: 105 b/w illus.
2. Thermodynamics
3. Classical mechanics
5. Macrostates
6. Probability
7. Entropy
8. Typicality
9. Measurement
10. The past
11. Gibbs
12. Erasure
13. Maxwell's Demon
Meir Hemmo is an Associate Professor in the Department of Philosophy, University of Haifa. He has written on various issues in the foundations of quantum mechanics and statistical mechanics.
Orly Shenker is a Senior Lecturer for the Program in History and Philosophy of Science at the Hebrew University of Jerusalem. She has written on the foundations of classical and quantum statistical mechanics and on the rationality of science.
Time, Chance, and Reduction
Philosophical Aspects of Statistical Mechanics
Physics Meets Philosophy at the Planck Scale
Contemporary Theories in Quantum Gravity
Conceptual Foundations of Quantum Field Theory
Pauli's Exclusion Principle
The Origin and Validation of a Scientific Principle
Electric Waves
Being an Adams Prize Essay in the University of Cambridge


Average regular pay in the UK, for example, may have risen marginally. Globalisation has allowed corporates to source cheap labour from around the world, enabling companies to increase profit margi.
Yet as overall, historically, rates are now still incredibly cheap, I thought it worth running through. Only borrow for a one-off, planned, necessary purchase, eg, paying for annual car insurance a.


If I didn't have to go, angelis and amaretto, I would tangle with you all morning , but alas..
aw,bye for now One Song,so sad you're leaving me in last place!!!!
hmm does a wink count as being last?!!
Sorry did I say I was threw here ???
Is it too early to be last?
so this is where it went.
Everyone gets one shot at TRUE love, I have had mine.


text:
Malawi's drone battlefield is on the humanitarian front
Ra'eesa Pather 29 Jun 2017 12:32
The residents of Kasungu are introduced to drone technology, which is being tested for transporting items such as medical supplie and to survey disaster stricken areas. (Pictures: Unicef/Malawi/2017/Chisiza)
The first humanitarian drone corridor in Africa has been launched in Kasungu, Malawi, creating a real-life testing ground to use drones to deliver medicine or even wi-fi.
The Malawian government and Unicef announced the official opening of the corridor on Thursday at the idle Aerodome airfield in Kasungu – a district north of the capital Lilongwe. Transport and Public Works Minister Jappie Mhango said Malawi's willingness to embrace technological innovation led to the development of the corridor
"We have already used drones as part of our flood response and we can see the potential for further uses, such as transportation of medical supplies, which could transform lives in remote rural communities," he said.
The corridor was developed as a partnership between the government and the children's fund.
In March last year, Unicef used drones to transport dried blood samples from infants for HIV testing in laboratories. The study showed that drones are feasible to provide additional support for transporting medical supplies.
This was backed up in April when drones were deployed to support emergency efforts when floods engulfed parts of Malawi.
Pictures from drones showed disaster areas where relief was necessary.
The success of both incidents led to further excitement from the Malawian government to pursue a humanitarian corridor and to invite companies and individuals to apply to use the location to test their drones.
The three uses for the drones in the corridor include:
Imagery of locations that could be used for monitoring during floods or other disasters
Providing wi-fi connectivity to schools or remote areas
Transporting light-weight medical supplies and samples to clinics or laboratories
The corridor has a 80km distance around the Aerodome airfield and covers 5000km2, making it one of the biggest in the world. Unicef says it would benefit 301 schools inside the corridor and 486 health services points.
To gain access to the corridor, applicants would need to commit that their drones would be used for humanitarian aid. This would be in an agreement signed with the Malawian government's civil aviation department, which would include a code of conduct.
Johannes Wedenig, head of Unicef Malawi, said at the official opening that the corridor would reimagine drones as tools for relief rather than weapons.
"This is our opportunity to shape a new technology in a positive direction. To take something that is known for military and commercial purposes, and make it a tool for development and humanitarian response," he said.
But, to get support from locals, Malawian officials have had to do extensive work convincing people that drones are not harmful. The government's information and communication department embarked on roadshows, briefed traditional leaders and local government officials and drove vans with loudspeakers to make public announcements.
Some of the concerns Malawians had were that drones would violate their privacy and they associated the flying objects with witchcraft or satanism.
"Before we did the sensitisation people thought we were introducing satanism. After we did the sensitisation, they said it's for the common good," Wallace Chipete, deputy co-ordinator for development in the ministry of information told the Mail & Guardian.
On Wednesday, a final drone demonstration was held before the opening of the corridor. Groups of school children excitedly ran to the drone as it landed.
"We were told about these drones and how they would help bring medicine," said one 16-year-old scholar.
The corridor is open for a year until July 2018.
This article was produced with support from Unicef.
Ra'eesa Pather
Ra'eesa Pather is a Cape Town-based general news and features journalist. Read more from Ra'eesa Pather
@raediology
MalawiWiFimedicinedronesDrone deliveryUnicef
New Malawi water scheme is in the interest of a few, not the country
Facts around Malawi water scheme don't wash


text:
Q: Controlling the number of parallel tasks running simultaneously I have a Windows service application that has a number of different jobs that need to be done in parallel and are spawned on three different schedules. However I want to make sure that at no point of time more than N tasks are running.
This is not a duplicate of this question, because that is about limiting the number of tasks that are started per second, not the number that are running concurrently.  Also not a duplicate of this because my tasks are on separate schedules so cannot be queued simultaneously.
Here is some code to provide context:
namespace WindowsService1
{
    public partial class Service1 : ServiceBase
    {
        List<Task> ServiceTasks;
        private List<Timer> ServiceTimers;
        private static int N = 10;

        public Service1()
        {
            InitializeComponent();
        }

        protected override void OnStart(string[] args)
        {
            List<double> Times = new List<double>(){1000d,2000d,5000d};
            for(int i = 0; i<3 ; i++)
            {
                 var t = new Timer(Times[i]);
                 t.AutoReset = true;
                 ServiceTimers.Add(t);
            }
            ServiceTimers[0].Elapsed += Timer1Elapsed_DoSomething;
            ServiceTimers[0].Start();
            ServiceTimers[1].Elapsed += Timer2Elapsed_DoSomething;
            ServiceTimers[1].Start();
            ServiceTimers[2].Elapsed += Timer3Elapsed_DoSomething;
            ServiceTimers[2].Start();
        }

         private void Timer1Elapsed_DoSomething(object sender, ElapsedEventArgs e)
         {
            ServiceTasks.Add(Task.Factory.StartNew(() => ServiceWork.DoTask1()));
         }

         private void Timer2Elapsed_DoSomething(object sender, ElapsedEventArgs e)
         {
            ServiceTasks.Add(Task.Factory.StartNew(() => ServiceWork.DoTask2()));
         }

         private void Timer3Elapsed_DoSomething(object sender, ElapsedEventArgs e)
         {
            ServiceTasks.Add(Task.Factory.StartNew(() => ServiceWork.DoTask3()));
         }
    }
}

How can I modify this code to ensure that only N tasks will be running at any given time?

A: SemaphoreSlim is a class that allows you to do just that. It's a lock for N simultaneous "threads".
Like that:
SemaphoreSlim s = ...;
async Task F() {
 await s.WaitAsync();
 DoWork();
 s.Release();
}

You can use the synchronous API as well if you don't mind 1MB of stack usage per thread waiting.

This:
 Task.Factory.StartNew(() => ServiceWork.DoTask3())

becomes:
Task.Run(async () => {
 await s.WaitAsync();
 try {
  ServiceWork.DoTask3();
 } finally {
  s.Release();
 }
});

And you can start an unlimited number of these and they will self-throttle.
The list of tasks is still required so that you can shut down the service cleanly by waiting for all tasks to complete and handling their errors.

redpajama_set_name: RedPajamaStackExchange


text:
AP source: Mavs adding Kidd-Gilchrist after Charlotte buyout
by: SCHUYLER DIXON, Associated Press
Posted: Feb 11, 2020 / 12:22 AM CST / Updated: Feb 11, 2020 / 12:22 AM CST
DALLAS (AP) — The Dallas Mavericks are set to add veteran Michael Kidd-Gilchrist to their young core as they close in on the franchise's first trip to the playoffs in four years.
Kidd-Gilchrist, the No. 2 pick in the 2012 draft, has agreed to sign with the Mavericks after taking a buyout from the Charlotte Hornets, a person with direct knowledge of the situation said Monday night.
The Mavericks plan to waive Ryan Broekhoff to make room for Kidd-Gilchrist, the person told The Associated Press on condition of anonymity because the moves are not yet official.
The 26-year-old Kidd-Gilchrist, drafted by Charlotte behind former Kentucky teammate Anthony Davis, had fallen out of the rotation with the Hornets. The agreement with the Mavericks came two days after Kidd-Gilchrist was waived.
At 6-foot-6 and 230 pounds in his eighth season, Kidd-Gilchrist gives Dallas the size and experience to help defend some of the elite forwards in the Western Conference.
Offense will be the bigger question in a scheme that relies heavily on 3-point shooting even from most of Dallas' frontcourt players, including 7-foot-3 forward Kristaps Porzingis.
Kidd-Gilchrist struggled with his shooting despite efforts to improve his form. He is shooting 47.5% from the field and 28% from 3-point range for his career.
After playing in just 12 games with Charlotte this season, Kidd-Gilchrist has career averages of 8.6 points and 5.5 rebounds.
Led by 20-year-old sensation Luka Doncic, the Mavericks are in strong position to end their longest stretch without making the playoffs in 20 years.
Dallas has a realistic shot at finishing as high as fourth in the West and is seven games clear of ninth with 28 games remaining.
Broekhoff was in his second season with the Mavericks after the Australian joined them as a 28-year-old rookie. Broekhoff averaged 4.0 points in 59 career games while shooting 40% from 3 for Dallas. He missed a month this season with a broken left fibula.
by Jason Logan, Covers / Jan 18, 2021
DALLAS (COVERS) -- The wildest NFL season in history is down to its final four teams with betting lines for the AFC and NFC Championships hitting the board Sunday.
But just when you thought the 2020-21 campaign couldn't get any nuttier, the best player in the league is a question mark for Championship Weekend. That could leave the odds for the AFC title game looking very different come Sunday.
Tom Brady will take on Aaron Rodgers in a matchup of quarterback legends in the NFC title game.
The AFC championship could feature two of the top young QBs if Patrick Mahomes is healthy enough to start for Kansas City against Buffalo's Josh Allen.


When Sales And Marketing Should Be Out Of Sync Four Quadrant Blog Sales & Marketing Plan Uploaded by patriotjobs on Saturday, April 6th, 2019 in category Marketing.
See also Sales & Marketing Plan 8 Sales And Marketing Plan Templates Doc Pdf Free Premium from Marketing Topic.
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NJPW's Strong Style Evolved UK weekend wrapped up in the Manchester area on Sunday.
O-Khan won with Mongolian chops off the middle rope. Oka's gimmick is some sort of mystical wizard type thing, but people weren't buying it and kept chanting "genie pants."
Nagata submitted him with a crossface. Nagata came off like a total superstar and Umino did really well.
They had a comedy/nothing match, ending when Desperado rolled up Gedo. Yano was really over.
WALTER hit a powerbomb for the finish. There were lots of stiff chops from both guys, but it was a pretty one-sided match.
Taichi picked up the win with a roll-up after Kanemaru interfered. Ospreay was crazy over, but with this being a Taichi match there wasn't much to it.
The crowd loved everyone but were really into Tiger Mask.
White hit the Blade Runner for the victory. Fletcher was a replacement for Chris Brookes, who was announced as being ill. The match was really good -- the best of the night until the two top matches. The crowd was hot for both guys.
Sabre rolled up Okada and pinned him, which amazed everyone. The fans loved Sabre, but Okada was on a different level as a superstar. The audience gave him a standing ovation at the end. I'd put this at 4.5 stars.
Amazing match -- I'd go 4.75 stars. Suzuki was the clear favorite and won with a Gotch piledriver. There were standing ovations at multiple points, with the crowd popping huge for the title change.
WALTER came out and booted Ishii after the match before having a staredown with Suzuki.


A completely natural and organic hydrating cream, NAVEEN Chamomile Moisturising Cream is an effective plant based formula that's gentle, pure and efficacious. This beautiful formulation is ideal for all those concerned about dryness, dullness, fine lines and redness. Infused with botanical powerhouses including extracts of certified organic chamomile flower water, organic macadamia nut oil, jojoba oil and olive oil, this cocktail of oils and botanicals boosts elasticity and retains moisture. It helps in rejuvenating skin cells, lessens visibility of fine lines, retains moisturize and improves skin tone, texture and clarity over time. The beautiful texture of this cream is not sticky and easily blends onto the skin.
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canada goose uk outlet So it is with tool using in animals, from canada goose outlet jackets chimpanzees to crows to the cactus finches of the Galapagos: canada goose outlet in usa animals can put their already evolved equipment to new uses. And so it is with the human brain. https://www.canadagoosejacketca.ca It hasn changed much in the last couple million years, but oh what we have done with it canada goose uk outlet.


text: Q: How to define the integral over boundary in R^n(n>3) I am a math undergraduate. While learning the theory of PDEs, I find many textbooks(evans' for instance) just cite formula and conclusions related to the integral of a function with n variables over the boundary of a open set U in R^n, without proof or explaining. But when I Studied basic analysis, we only       learned how to deal with the R^3 case(integral over surface in R^3) and I Don't know what it means when it comes to n>3. I just want to know which or what kind of textbooks  will discuss this kind of integral issues, such as exact definition and how to calculate or understand it. Thanks.


text:
Dalida. La Danze de Zorba (Zorba's Dance) English Version / La Danze de Zorba (Zorba's Dance) French Version
La Danse de Zorba (Zorba's Dance) by Dalida.
This 45 rpm record on 20th Century Fox Records is a promotional copy. It is a international copy with the same song on both sides one in French and the other in English.
Iolanda Cristina Gigliotti born in 1933, and was known professionally as Dalida. a French singer and actress, born in Egypt to Italian parents. She won the Miss Egypt beauty contest in 1954 and began a 31 year singing career in 1956. In her musical career she was credited with selling 170 million albums and singles worldwide.
In June 1965, Dalida recorded "La danse de Zorba", a song from 1964 comedy movie Zorba the Greek, which became her biggest international success since "24 mille baisers" in early 1961. The song once again brought Dalida to seven international charts, entering the top three in six and topping in two countries. Surpassing a million copies, it also earned Dalida two more golden discs; in France, and in Brazil where it was also awarded with the Cico Viola award for the best selling record of the year.
This record is in very good plus condition,


text:
Q: How do I configure WebLogic 10.3 Web App To Use SAML 2 SSO and Identity Provider? I have several Web applications all running in WebLogic 10 and I want to authenticate the users using SSO and WebLogic's built-in SAML 2 SSO support.
I configured a SAML2IdentityAsserter on the security realm and created a Web SSO Identity Provider Partner that uses the meta-data from the identity provider that I set up earlier.  That all seemed to go fine.
I deployed a simple web app that I'm using for testing that is configured to use this realm.  However, when I try to log in to the web app, it doesn't seem to even try to use the identity provider.  I set the  to both BASIC and CLIENT-CERT but both acted as if the SAM2IdentityAsserter wasn't set up.  I played with changing the order of the asserters and tried removing the default asserter but none of this has made a difference.
Has anyone had any success doing this under WLS 10.3?

A: Maybe you could have a look at Implementing SAML2 SP-initiated use case with Weblogic 10.3.4. and ADFS
Best regards,
Luis
ps: now, It seems that we have got the right configuration, we are able to sign in our SSO System but we get and error from our Idp. You need to set up the security in your app through your descriptors (web.xml and weblogic.xml). Take a look at the configuration of your weblogic app console: $WEBLOGIC_HOME/wlserver/server/lib/consoleapp/webapp/WEB-INF/web.xml and $WEBLOGIC_HOME/wlserver/server/lib/consoleapp/webapp/WEB-INF/weblogic.xml)


text:
\section{Statement of the Problem and Result}

In the late eighties, W.\ Kirsch \cite{Kir87, Kir89} investigated
the relative eigenvalue counting function $\xi_L (E)$ for compactly-supported
nonnegative perturbations $V$ of the nonnegative Laplacian $- \Delta_L \geq 0$ on cubes $\Lambda_L := ] -L / 2, L /2 [^d \subset \mathbb{R}^d$ with Dirichlet boundary conditions.
The cubes $\Lambda_L$ of edge length $L>0$ are centered about the origin in $d$-dimensional Euclidean
space $\mathbb{R}^{d}$. The real-valued local perturbation $V$ is
a compactly-supported, nonnegative potential $0 \le V \in
\mathrm{L}^{\infty}(\mathbb{R}^d)$. We emphasize that $V$ does not depend on
$L$ and, of course, $L$ is large enough so that $\supp(V) \subset
\Lambda_{L}$.

The finite-volume spectral shift function (SSF) or relative
eigenvalue counting function $\xi_L (E)$ for the pair of
self-adjoint operators $( - \Delta_L / 2 + V , - \Delta_L / 2)$ on the Hilbert space
$\mathrm{L}^2 (\Lambda_L)$, with Dirichlet boundary conditions on $\partial
\Lambda_L$, is defined as the real-valued function of $E\in\mathbb{R}$ given by
 \begin{equation}
 \xi_L (E) := \# \bigg\{\begin{array}{l} \text{eigenvalues of $-\Delta_{L}/2$}\\
  \text{(counting\ multipl.)~ $\le E$}\end{array}\bigg\} - \# \bigg\{\begin{array}{l} \text{eigenvalues of $-\Delta_{L}/2 + V$}\\
  \text{(counting multipl.)~ $\le E$}\end{array}\bigg\} .
 \end{equation}
Kirsch was interested in the limit of $\xi_{L} (E)$ as $L \to\infty$. Perhaps surprisingly, Kirsch
proved \cite{Kir87} that if $d \in\mathbb{N}\setminus\{1\}$ and if $\int_{\mathbb{R}^{d}}\d x\,
V(x) >0$, then
  %
  \begin{equation}\label{unbdd1}
    \sup_{L > 0} \xi_L (E) = \infty  \qquad\quad \text{for every~} E>0.
  \end{equation}
  %
  Furthermore, he proved the existence of a countable dense set of
  energies $\mathcal{E} \subset [0, \infty[$ so that
  %
  \begin{equation}\label{unbdd2}
    \sup_{L \in \mathbb{N}} \xi_L (E) = \infty  \qquad\quad \text{for every~} E \in
  \mathcal{E}.
  \end{equation}
Clearly, the reason for this divergence is the growing degeneracy of
eigenvalues of the Laplacian in $d\ge 2$ dimensions as $L\to\infty$, which is
lifted by the perturbation $V$. In contrast, in $d=1$ space dimension, and also for
corresponding lattice systems in arbitrary dimension, the spectral shift function remains bounded in this limit,
as follows from a finite-rank-perturbation argument.

More generally, if one replaces the sequence $L_{n} =n \in\mathbb{N}$ in \eqref{unbdd2} by another diverging sequence of lengths,
one would expect the set of ``bad'' energies $\mathcal{E}$ to change.
One might conjecture, however, that the largest set of energies $\mathcal{E}$, on which $\xi_{L}$ explodes, still has zero Lebesgue measure.
Although still unproven in this generality, this conjecture is strongly supported by Theorems~\ref{HiMu-1} and~\ref{HiMu-2} below.

In order to state these theorems, we need to list the hypotheses.
We write $\mathcal{K}(\mathbb{R}^{d})$ and $\mathcal{K}_{\mathrm{loc}} (\mathbb{R}^d)$ to denote the Kato class and the local
Kato class, respectively \cite{AiSi82, Sim82}. We say $U$ is Kato decomposable, $U\in\mathcal{K}_{\pm}(\mathbb{R}^d)$, if
$\max\{0, U\} \in \mathcal{K}_{\mathrm{loc}}(\mathbb{R}^{d})$ and $\max\{0, -U\} \in \mathcal{K}(\mathbb{R}^{d})$.
In the following we consider two real-valued potential functions $U$ and $V$ on $\mathbb{R}^{d}$ such that
\begin{equation}
  \label{ass}
  \tag{$\star$}
  U \in \mathcal{K}_{\pm}(\mathbb{R}^{d}), \qquad  0\le V \in\mathcal{K}_{\mathrm{loc}}(\mathbb{R}^{d}) , \quad \supp (V) \subseteq \Lambda_{\ell} \text{~ for some~} \ell>0.
\end{equation}
 We also introduce the
corresponding infinite-volume self-adjoint Schr\"odinger operators $H_{0} :=
-(\Delta/2) + U$ and $H_{1}:= H_{0} + V$ on $\mathrm{L}^{2}(\mathbb{R}^{d})$.
Their self-adjoint finite-volume Dirichlet restrictions $H_{0}^{(L)}$ and
$H_{1}^{(L)}$ to $\mathrm{L}^{2}(\Lambda_{L})$ have compact resolvents and, therefore, discrete spectrum. For a given energy $E \in \mathbb{R}$,
let $N_0^{(L)}(E)$, resp.\ $N_1^{(L)}(E)$, denote the number of eigenvalues,
including multiplicity, for $H_0^{(L)}$, resp.\ $H_1^{(L)}$, less than or
equal to $E$.  These are both monotone increasing functions of the energy $E$.
We define the relative eigenvalue counting function by
\begin{equation}\label{ssf2}
  E \mapsto \xi_L (E) \equiv \xi (E; H_1^{(L)}, H_0^{(L)})
  := N_0^{(L)}(E) -N_1^{(L)}(E) \geq 0
\end{equation}
for all $E \in \mathbb{R}$.  It is known that this function is equal to the (more
generally defined) \emph{spectral shift function} for the pair $(H_1^{(L)},
H_0^{(L)})$, see e.g.\ \cite{Yaf92, BiYa93} or Eq.\ (5.1) in the Appendix of \cite{HiMu10}.

\begin{thm}
 \label{HiMu-1}
  Let $d\in\mathbb{N}$ and assume \eqref{ass}. Then, we have
  %
  \begin{equation}\label{ssf-bound2}
    \lim_{L \rightarrow \infty} \int_\mathbb{R} \!\d E\; \xi_{L}(E) \, f(E) =
    \int_\mathbb{R}\!\d E \; \xi(E)\; f(E)
  \end{equation}
  %
 for every function $f$ of the form $f=\raisebox{.4ex}{$\chi$}_{I} g$, where $g \in C(\mathbb{R})$ is continuous and $\raisebox{.4ex}{$\chi$}_{I}$ is the indicator function of a (finite) interval $I \subset\mathbb{R}$. In particular, for Lebesgue-almost all $E \in \mathbb{R}$ we have
  %
  \begin{equation}\label{eq-ssf4}
  \lim_{\delta \downarrow 0} \lim_{L \rightarrow \infty}
    \frac{1}{\delta} \int_{E}^{E+\delta} \!\d E'\, \xi_{L}(E') = \xi(E).
  \end{equation}
\end{thm}

We refer to \cite{HiMu10} for a proof of the theorem, see also \cite{GeKoSc95}.
Kirsch's result \eqref{unbdd1} shows that one cannot get rid of the
energy smoothing in \eqref{eq-ssf4}, that is, the limits $\delta \downarrow
0$ and $L\to\infty$ must not be interchanged. The best one could hope for is
convergence Lebesgue-almost everywhere  of $(\xi_{L_{j}})_{j\in\mathbb{N}}$ for
sequences of diverging lengths. The next theorem is a
partial result in this direction.
\begin{thm}
  \label{HiMu-2}
  Let $d\in\mathbb{N}$ and assume \eqref{ass}. Then, for every sequence of lengths
  $(L_{j})_{j\in\mathbb{N}}$ $\subset \, ]0,\infty[$ with $\lim_{j\to\infty} L_{j} =
  \infty$ there exists a subsequence $(j_{i})_{i\in\mathbb{N}} \subset\mathbb{N}$ with
  $\lim_{i\to\infty} j_{i} =\infty$ such that for every subsequence
  $(i_{k})_{k\in\mathbb{N}} \subset\mathbb{N}$ with $\lim_{k\to\infty} i_{k} =\infty$ we
  have
  \begin{equation}
    \label{ces-in}
    \lim_{K\to\infty} \frac{1}{K} \sum_{k=1}^{K} \xi_{\wtilde{L}_{k}}(E) \leq \xi(E)
  \end{equation}
  for Lebesgue-almost all $E\in\mathbb{R}$. Here we have set $\wtilde{L}_{k}
  :=L_{j_{i_{k}}}$ for all $k\in\mathbb{N}$.
\end{thm}

The simple proof \cite{HiMu10} of Theorem~\ref{HiMu-2} relies on Theorem~\ref{HiMu-1}, the fact that $V$, and hence $\xi_{L}$, has a definite sign, and a deep result of Koml\'os. For one-dimensional systems, equality in (\ref{ces-in}) has recently been shown in \cite{BoMa09}. We refer to the literature cited in \cite{HiMu10} for further estimates of spectral shift functions.

In this note we are interested in refining the convergence in Theorem~\ref{HiMu-1} for the case where the background potential $U$ is periodic with period $p = (p_{1}, \ldots, p_{d}) \in\mathbb{R}^d$. In this situation, one can consider the potential
$V$ centered at any point $x_0 + x \in \Lambda_{L}$, with $x \in p\mathbb{Z}^d$ and $x_0 \in \Lambda_L$, so that $
\Lambda_\ell (x_0) \subset \Lambda_L$.
One expects that the limit in \eqref{ssf-bound2} is independent of the shift $x \in p \mathbb{Z}^d$. We prove that this is true and that the
convergence in \eqref{ssf-bound2} is uniform in the shift vectors $x \in p \mathbb{Z}^d$.

To formulate this precisely, we introduce some more notation.
Recall that $\ell >0$ was defined by $\supp(V) \subseteq \Lambda_{\ell}$.
We choose a security distance function $D$ with the properties  $D(L) \le (L -\ell)/2$ for
all $L\ge \ell$ and $\lim_{L\to\infty} D(L) =\infty$.
For $x_{0} \in\mathbb{R}^{d}$ we define the set of allowed shifts
\begin{equation}
\label{shift}
 A_{L}(x_{0}) := \Big\{ x_{0}+ x : x \in p\mathbb{Z}^d \text{~and~} \dist\big(\Lambda_{\ell}(x_{0} + x), \mathbb{R}^{d} \setminus \Lambda_{L}\big) > D(L) \Big\}
\end{equation}
in the box $\Lambda_{L}$. Here we used the notation $\Lambda_{\ell}(y)$ to indicate that the cube is centered about $y\in\mathbb{R}^d$ instead of the origin. Shifts in $A_{L}(x_{0})$ differ only by a multiple of the period of $U$, and it is enough to consider $x_{0} \in \raisebox{-1pt}{\Large$\times$}_{j=1}^{d} [0, p_{j}[$ in the periodicity cell of $U$.
Given $y\in\mathbb{R}^{d}$ we write $V_{y} := V(\,\pmb{\cdot}\, -  y)$ for the shifted perturbation potential and note that if $y\in A_{L}(x_{0})$, then $\supp(V_{y})$ respects the security distance $D(L)$ to the boundary of $\Lambda_{L}$. Finally we define the Schr\"odinger operator $H_{1,y} := H_{0} + V_{y}$ with the shifted perturbation potential along with its finite-volume Dirichlet restrictions $H_{1,y}^{(L)}$. We do not require $V\ge 0$ any more.

\begin{thm}
  \label{uniform}
    Let $d\in\mathbb{N}$ and let $U,V \in \mathcal{K}_{\pm}(\mathbb{R}^d)$. Assume that $U$ is periodic with period $p\in\mathbb{R}^d$ and $\supp(V) \subseteq \Lambda_{\ell}$ for some $\ell >0$. Fix an arbitrary point $x_{0} \in \raisebox{-1pt}{\Large$\times$}_{j=1}^{d} [0, p_{j}[$ in the periodicity cell of $U$ and a sequence $(L_{n})_{n\in\mathbb{N}} \subset[\ell, \infty[$ of diverging lengths, $\lim_{n\to\infty} L_{n} = \infty$.
Then,
  %
  \begin{equation}\label{ssf-uniform}
    \lim_{n \rightarrow \infty} \int_\mathbb{R} \!\d E\; \xi\big(E; H_{1, x_{L_{n}}}^{(L_{n})}, H_{0}^{(L_{n})}\big) \, f(E) =
    \int_\mathbb{R}\!\d E \; \xi(E; H_{1, x_{0}}, H_{0})\; f(E)
  \end{equation}
  %
holds uniformly in $(x_{L_{n}})_{n\in\mathbb{N}} \in \raisebox{-1pt}{\Large$\times$}_{n\in\mathbb{N}}  A_{L_{n}}(x_{0})$ for every given function $f$ of the form $f=\raisebox{.4ex}{$\chi$}_{I} g$, where $g \in C(\mathbb{R})$ is continuous and $\raisebox{.4ex}{$\chi$}_{I}$ is the indicator function of a (finite) interval $I \subset\mathbb{R}$.
\end{thm}

The proof of Theorem~\ref{uniform} relies on a suitable continuity theorem for Laplace transforms, Theorem \ref{cont-laplace}, proven in the next section. We prove Theorem \ref{uniform}  in Section \ref{sec:assumptions1} by verifying the assumptions
of Theorem \ref{cont-laplace} using the Feynman-Kac representation for Schr\"o\-ding\-er semigroups.

\begin{rem}
 Theorem~\ref{uniform} also works in the context of ergodic random Schr\"o\-dinger operators, if we replace the periodic potential $U$ by a random potential $U_{\omega}$ that is ergodic with respect to a subgroup $G$ of the translation group $\mathbb{R}^d$. In this case the group $G$ replaces $p\mathbb{Z}^d$ in the definition \eqref{shift} of the sets $A_{L}(x_{0})$ of allowed shift vectors. In addition, we have to replace the spectral shift functions in \eqref{ssf-uniform} by their expectations $\IE$ over randomness. In fact, our original motivation for Theorem~\ref{uniform} stems from the construction of a strictly positive lower bound on the density of states for alloy-type random Schr\"odinger operators  in the continuum \cite{HiKlMu10}, where it will be needed. As is apparent already in the lattice case of this problem \cite{HiMu08}, one needs to control a Ces\`aro sum
\begin{equation}
\label{cesaro}
 \frac{1}{(L/\ell)^{d}} \sum_{j \in \ell \mathbb{Z}^d \cap \Lambda_{L}} \int_{\mathbb{R}}\!\d E\, f(E) \, \IE \big[\xi\big(E; H_{1,j}^{(L)}, H_{0}^{(L)}\big) \big]
\end{equation}
 in the limit $L\to\infty$ for some given function $f$ as allowed by Theorem~\ref{uniform}. We apply Theorem~\ref{uniform} with the distance function $D(L) = (1/2)\log(L -\ell +1)$ to \eqref{cesaro}. Then the asserted uniformity of the convergence in $j$ implies
\begin{equation}
    \lim_{L\to\infty}\frac{\ell^{d}}{L^{d}} \sum_{j \in \ell \mathbb{Z}^d \cap \Lambda_{L}} \int_{\mathbb{R}}\!\d E\, f(E) \, \IE \big[\xi  \big(E; H_{1,j}^{(L)}, H_{0}^{(L)}\big) \big]
    = \int_{\mathbb{R}}\d E\, f(E)\, \IE \big[\xi\big(E; H_{1,0}, H_{0}\big) \big].
\end{equation}
\end{rem}

\section{An abstract uniform convergence result for measures}

The uniform convergence of the finite-volume spectral shift
functions will follow from a more general result, Theorem \ref{cont-laplace}, on the continuity of the Laplace transform of Borel measures.
We begin with a simple observation:

\begin{lmm} \label{wonderland}
 For given sets $A_{n}$, $n\in \mathbb{N}$, define $\AA := \raisebox{-1pt}{\Large$\times$}_{n \in\mathbb{N}} A_{n}$. Consider a family of sequences in $\mathbb{C}$ which is indexed by $a \equiv (a_{n})_{n\in\mathbb{N}}\in \AA$ and has the property that the $n$-th sequence element depends only on $a_{n}$, but not on $a_{m}$ for $m\neq n$. We denote a sequence of this family by $(x_{n}^{a_{n}})_{n\in\mathbb{N}}$. Suppose that for every $a\in\AA$  the limit
\begin{equation}
 x := \lim_{n\to\infty} x_{n}^{a_{n}}
\end{equation}
exists in $\mathbb{C}$ and is independent of $a\in \AA$. Then the sequence $(x_{n}^{a_{n}})_{n\in\mathbb{N}}$ converges to $x$ uniformly in $a\in\AA$.
\end{lmm}

\begin{proof}
 We argue by contradiction. Assume that the limit $x$ is not approached uniformly in $a$. Then there is $\varepsilon >0$ such that for every $N\in\mathbb{N}$ there is $n \ge N$ and $\alpha_{n} \in A_{n}$ such that $|x_{n}^{\alpha_{n}} - x| > \varepsilon$. In other words, there exists $\varepsilon >0$, a subsequence $(n_{j})_{j\in\mathbb{N}}$ with $\lim_{j\to\infty}n_{j} = \infty$ and $\alpha_{n_{j}} \in A_{n_{j}}$ for all $j\in\mathbb{N}$ such that
\begin{equation}
\label{contra}
 |x_{n_{j}}^{\alpha_{n_{j}}} - x| > \varepsilon \qquad\quad\text{for all~} j\in\mathbb{N}.
\end{equation}
Define $a\in\AA$ by setting $a_{n_{j}} := \alpha_{n_{j}}$ for all $j\in\mathbb{N}$ and $a_{k}$ arbirtrary for $k \notin \{n_{j}: j\in\mathbb{N} \}$. But then $\lim_{n\to\infty} x_{n}^{a_{n}} = x$ by hypothesis, and hence $\lim_{j\to\infty} x_{n_{j}}^{a_{n_{j}}} = x$, contradicting \eqref{contra}.
\end{proof}

\begin{dfn}
 Let $\mu$ be a Borel measure on $\mathbb{R}$. If there is $t_{0} \in\mathbb{R}$ such that the integral
\begin{equation}
    \wtilde{\mu}(t) := \int_{\mathbb{R}}\!\d\mu(x)\, \e^{-t x} < \infty
\end{equation}
 is finite for all $t \ge t_{0}$, we say that the \emph{(two-sided) Laplace transform} of $\mu$ exists for $t\ge t_{0}$.
\end{dfn}

We will need the following version of a continuity theorem for Laplace transforms.

\begin{thm} \label{cont-laplace}
Let $(\mu_{n}^{a_{n}})_{n\in\mathbb{N}}$ be a sequence of Borel measures on $\mathbb{R}$ for every $a \equiv(a_{n})_{n\in\mathbb{N}} \in \AA$. Assume that for every $a\in\AA$ there exists $t_{a} \in\mathbb{R}$ such that for all $n\in\mathbb{N}$ the Laplace transform of $\mu_{n}^{a_{n}}$ exists for $t \ge t_{a}$. Suppose further that for every $a\in\AA$ and every $t \ge t_{a}$ the limit
\begin{equation}
 \wtilde{\mu}(t) := \lim_{n\to\infty} \wtilde{\mu}_{n}^{a_{n}}(t)
\end{equation}
 exists in $\mathbb{R}$ and is independent of $a\in \AA$. Then $\wtilde{\mu}$ is the Laplace transform
of a Borel measure $\mu$ on $\mathbb{R}$ and $\mu_{n}^{a_{n}}$ converges vaguely to $\mu$ as $n\to\infty$, the convergence being uniform in $a\in\AA$. In other words,
\begin{equation} \label{cont-claim}
 \lim_{n\to\infty} \int_{\mathbb{R}}\!\d\mu_{n}^{a_{n}}(x)\, f(x) =
  \int_{\mathbb{R}}\!\d\mu(x)\, f(x)
\end{equation}
holds uniformly in $a\in\AA$ for every given function $f$ of the form $f=\raisebox{.4ex}{$\chi$}_{I} g$, where $g \in C(\mathbb{R})$ and $\raisebox{.4ex}{$\chi$}_{I}$ is the indicator function of a (finite) interval $I \subset\mathbb{R}$ whose endpoints are not charged by the measure $\mu$.
\end{thm}

\begin{proof}
Existence of the limiting measure $\mu$ and pointwise convergence for every $a\in\AA$ of the limit in \eqref{cont-claim} for every given $f$ of the specified form is a standard continuity theorem for Laplace transforms, see for example \cite[Thm.\ 2a in Sect.\ XIII.1]{Fel71} and replace one-sided by two-sided Laplace transforms there. Uniformity of the convergence in $a\in \AA$ then follows from Lemma~\ref{wonderland} applied to the sequence $\big(\int_{\mathbb{R}}\!\d\mu_{n}^{a_{n}}(x)\, f(x)\big)_{n\in\mathbb{N}}$.
\end{proof}

\section{Proof of Theorem~\ref{uniform}}\label{sec:assumptions1}

We prove Theorem \ref{uniform} on the uniform convergence of the finite-volume spectral shift
functions using Theorem \ref{cont-laplace}.

\begin{proof}[Proof of Theorem~\ref{uniform}]
1. We verify the assumptions of Theorem~\ref{cont-laplace}.
To this end we fix $x_{0}$ in the periodicity cell of $U$ and a
sequence $(L_{n})_{n\in\mathbb{N}}$ of diverging lengths. Thanks to Dirichlet-Neumann bracketing and since both $U$ and $V$ are Kato decomposable, we have
$\mathrm{inf\,spec\,} H_{1, x_{L_{n}}}^{(L_{n})} \ge \mathrm{inf\,spec\,} H_{1, x_{0}} > -\infty$ for all $x_{L_{n}} \in  A_{L_{n}}(x_{0})$ and all $n\in\mathbb{N}$. From this we infer that for every $n\in\mathbb{N}$ and for
every shift $x_{L_{n}} \in  A_{L_{n}}(x_{0})$ the two-sided Laplace
transform
\begin{equation}
\begin{split}
 \wtilde{\xi}^{(n)}_{x_{L_{n}}}(t) &:= \int_{\mathbb{R}}\!\d E\, \e^{-tE} \,
 \xi\big(E; H_{1,x_{L_{n}}}^{(L_{n})}, H_{0}^{(L_{n})}\big) \\
 &\phantom{:}=  \frac{1}{t} \;\tr_{\mathrm{L}^{2}(\Lambda_{L_{n}})}
\left[ \exp\big(-t H_{0}^{(L_{n})} \big) - \exp\big(-t H_{1, x_{L_{n}}}^{(L_{n})} \big) \right]
\end{split}
 \end{equation}
exists for every $t >0$. So fix $t>0$ from now on.

\par\noindent
2. The standard Feynman--Kac representation \cite{Sim79} of the heat kernel gives
\begin{equation}
\begin{split}
   \varphi^{(n)}_{x_{L_{n}}}(t) &:=  t (2 \pi t)^{d/2} \; \wtilde{\xi}^{(n)}_{x_{L_{n}}}(t)\\
  &\phantom{:}= \int_{\Lambda_{L_{n}}} \!\d x \;
  ~\mathbb{E}\mkern2mu_{x,x}^{0,t} \left[ \raisebox{.4ex}{$\chi$}_{\Lambda_{L_{n}}}^{\,t} (b) \, \e^{- \int_0^t \d s \,
      U(b(s) )} \left( 1 - \e^{- \int_0^t \d s \, V_{x_{L_{n}}}(b(s)) } \right) \right]  \\
   &\phantom{:}= \int_{\Lambda_{L_{n}}} \!\d x \;
  ~\mathbb{E}\mkern2mu_{x,x}^{0,t} \left[ \raisebox{.4ex}{$\chi$}_{\Lambda_{L_{n}}}^{\,t} (b) \,  \mathcal{U}_{t}(b) \,\mathcal{V}_{t}(b- x_{L_{n}}) \right].
\end{split}
 \end{equation}
Here, $\mathbb{E}\mkern2mu_{x,y}^{0,t}$ denotes the normalized expectation over all Brownian
bridge paths $b$ starting at $x\in\mathbb{R}^d$ at time $s=0$ and ending at
$y\in\mathbb{R}^d$ at time $s=t$. The Dirichlet boundary condition is taken into
account by the cut-off functional $\raisebox{.4ex}{$\chi$}_{\Lambda}^{\,t}(b)$, which is equal to
one if $b(s) \in \Lambda$ for all $s \in [0, t]$, and zero otherwise.
Moreover, we have introduced the Brownian functionals
$\mathcal{U}_{t}(b) := \e^{- \int_0^t \d s \, U(b(s))}$ and $\mathcal{V}_{t}(b) := 1- \e^{- \int_0^t \d s \, V(b(s))}$.

\par\noindent
3. We shift the integration variables $x \rightarrow x + x_{L_{n}}$ and $b \rightarrow b + x_{L_{n}}$. This and the periodicity of $U$ results in
\begin{equation}
\label{conv-start}
\begin{split}
   \varphi^{(n)}_{x_{L_{n}}}(t)  &= \int_{\mathbb{R}^d} \!\d x \, \raisebox{.4ex}{$\chi$}_{\Lambda^{n}}(x) \; \mathbb{E}\mkern2mu_{x,x}^{0,t} \left[
   \raisebox{.4ex}{$\chi$}_{\Lambda^{n}}^{\,t} (b) \, \mathcal{U}_{t}(b+x_{0}) \, \mathcal{V}_{t}(b) \right]
   = \int_{\mathbb{R}^d} \!\d x \, \raisebox{.4ex}{$\chi$}_{\Lambda^{n}}(x) \, F_{n}(x)
\end{split}
\end{equation}
where we have introduced the abbreviations $\Lambda^{n} := \Lambda_{L_{n}}(-x_{L_{n}})$ and
\begin{equation}\label{eq:functional1}
 F_{n}(x) := \mathbb{E}\mkern2mu_{x,x}^{0,t} \left[
   \raisebox{.4ex}{$\chi$}_{\Lambda^{n}}^{\,t} (b) \, \mathcal{U}_{t}(b+x_{0}) \, \mathcal{V}_{t}(b) \right]  .
\end{equation}

\par\noindent
4. We evaluate the limit as $n \rightarrow \infty$ of $F_n (x)$  in (\ref{eq:functional1}).
We observe that $\Lambda^{n} \supseteq \Lambda_{\ell +2 D(L_{n})}$,
independently of $x_{L_{n}} \in A_{L_{n}}(x_{0})$ for every $n\in\mathbb{N}$, whence
\begin{equation}
 \lim_{n\to\infty} \raisebox{.4ex}{$\chi$}_{\Lambda^{n}}(x) = 1 \qquad \text{and} \qquad
 \lim_{n\to\infty} \raisebox{.4ex}{$\chi$}^{\,t}_{\Lambda^{n}}(b) = 1
\end{equation}
for every $x\in\mathbb{R}^d$, $\mathbb{P}_{0,0}^{0,t}$-a.e.\ Brownian bridge path $b$ and every choice of shifts
\begin{equation}
 (x_{L_{n}})_{n\in\mathbb{N}} \in \mathop{\raisebox{-1.5pt}{\LARGE $\times$}}\limits_{n \in\mathbb{N}} A_{L_{n}}(x_{0}) =: \AA(x_{0}).
\end{equation}
Here, we have exploited the $\mathbb{P}_{0,0}^{0,t}$-a.s continuity of $s \mapsto b(s)$.
Next, the expectation of the functiona $\mathcal{U}_t (b)$ is controlled
using \cite[Eqs.\ (6.20), (6.21)]{BrHuLe00} that state that
\begin{equation}
    \label{BHL}
 \sup_{x\in\mathbb{R}^d} \mathbb{E}\mkern2mu_{x,x}^{0,t} \big[ \e^{- \int_0^t \d s \, W(b(s))}\big] < \infty
\end{equation}
for every $W \in\mathcal{K}_{\pm}(\mathbb{R}^d)$. This bound (\ref{BHL}) and dominated convergence yield the existence of
\begin{equation}
\label{inner-limit}
 F(x) := \lim_{n\to\infty} F_{n}(x) =  \mathbb{E}\mkern2mu_{x,x}^{0,t} \big[ \mathcal{U}_{t}(b+x_{0}) \, \mathcal{V}_{t}(b) \big]
\end{equation}
for every $x\in\mathbb{R}^d$ and every $(x_{L_{n}})_{n\in\mathbb{N}} \in \AA(x_{0})$.

\par\noindent
5. Finally, for every $x\in\mathbb{R}^d$, every $n\in\mathbb{N}$ and every $x_{L_{n}} \in A_{L_{n}}(x_{0})$ we have the estimate
\begin{equation}\label{eq:upperbd1}
    |F_{n}(x)| \le  G(x) := \mathbb{E}\mkern2mu_{x,x}^{0,t} \left[  \raisebox{.4ex}{$\chi$}_{\Xi_{x}^{t}}(b) \, \mathcal{U}_{t}(b+x_{0}) \, \Big( 1 +  \e^{- \int_0^t \d s \, V(b(s))} \Big) \right] ,
\end{equation}
where $\Xi_{x}^{t}$ denotes the event that $\sup_{s \in [0,t]} |b(s) -x| > \dist\big(x, \supp(V)\big)$.
The Cauchy-Schwarz inequality and \eqref{BHL} then imply
\begin{equation}\label{eq:upperbd2}
 G(x) \le c \left(\mathbb{P}_{x,x}^{0,t}[\Xi_{x}^{t}] \right)^{1/2}=  c \left(\mathbb{P}_{0,0}^{0,t} \bigg[ \max_{s \in [0,t]} |b(s)| > \dist\big(x, \supp(V)\big) \bigg] \right)^{1/2}
\end{equation}
for an $x$-independent constant $c \in ]0,\infty[$. The probability
in the last line is the complement of the distribution function for
the maximum of a $d$-dimensional Bessel bridge \cite{YoZa04} and has
a Gaussian decay, see, for example, \cite[p.~341, Lemma 1]{kirsch88}
or \cite[p.~438]{GrSh96}. This yields $G \in \mathrm{L}^{1}(\mathbb{R}^d)$.

\par\noindent
6. We now combine (\ref{inner-limit}) and the upper bound (\ref{eq:upperbd1}), (\ref{eq:upperbd2})
to evaluate the limit of \eqref{conv-start}. Dominated convergence applied to \eqref{conv-start} gives for
all $(x_{L_{n}})_{n\in\mathbb{N}} \in \AA(x_{0})$
\begin{equation}
\label{limit}
   \lim_{n\to\infty} \varphi^{(n)}_{x_{L_{n}}}(t)  = \int_{\mathbb{R}^d}\!\d x\, \lim_{n\to\infty}
   F_{n}(x) = \int_{\mathbb{R}^d}\!\d x\, \mathbb{E}\mkern2mu_{x,x}^{0,t} \big[ \mathcal{U}_{t}(b) \, \mathcal{V}_{t}(b-x_{0}) \big],
\end{equation}
where we have used another change of variables. Therefore Theorem~\ref{uniform} follows from
\begin{equation}
\begin{split}
\lim_{n\to\infty}   \wtilde{\xi}^{(n)}_{x_{L_{n}}}(t) &=  \frac{1}{t} \; (2\pi t)^{-d/2}  \int_{\mathbb{R}^d}\!\d x\, \mathbb{E}\mkern2mu_{x,x}^{0,t} \big[ \mathcal{U}_{t}(b) \, \mathcal{V}_{t}(b-x_{0}) \big] \\
     &=  \frac{1}{t} \;\tr_{\mathrm{L}^{2}(\mathbb{R}^d)} \left[ \exp(-t H_{0}) - \exp(-t H_{1, x_{0}}) \right] \\
 &= \int_{\mathbb{R}}\!\d E\, \e^{-tE} \,
 \xi\big(E; H_{1,x_{0}}, H_{0}\big)
\end{split}
\end{equation}
for all $(x_{L_{n}})_{n\in\mathbb{N}} \in \AA(x_{0})$ and from Theorem~\ref{cont-laplace}.
\end{proof}

\begin{acknowledgement}
  PM would like to thank Nariyuki Minami, Shu Nakamura, Fumihiko Nakano and
  Naomasa Ueki for their splendid hospitality during the \emph{Kochi School on Random
  Schr\"odinger operators} and the RIMS-workshop \emph{Spectra of Random Operators and Related Topics}
  in Kyoto in November and December 2009. PM also acknowledges Edgardo Stockmeyer and Ingo Wagner
  for interesting discussions. The authors thank the Centre
  Interfacultaire Bernoulli in Lausanne, Switzerland, for hospitality and the Swiss NSF for
  partial financial support during the time this work was finished.
\end{acknowledgement}

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