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Difference between revisions of "Great white shark"
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[[Image:Great_white_shark.jpg|right|thumb|350px|A 12-foot long Great white shark photographed off the coast of Mexico]]
{{Taxonomy
|name=Great White Shark
|image=white_shark.jpg
|domain=Eukaryota
|kingdom= Animalia
|subkingdom=Bilateria
|superphylum=
|phylum=Chordata
|subphylum=Vertebrata
|infraphylum=Gnathostomata
|microphylum=
|superdivision=
|division=
|subdivision=
|superclass=
|class=Chondrichthyes
|subclass=Elasmobranchii
|infraclass=Euselachii
|superorder=
|order=Lamniformes
|suborder=
|infraorder=
|superfamily=
|family=Lamnidae
|subfamily=
|supertribe=
|tribe=
|subtribe=
|genera=
|genus=Carcharodon
|subgenus=
|species=C. carcharias
|binomialname=
|sub=
|regionimg=
|pop=Unknown
|conservation=Vulnerable<ref>http://www.iucnredlist.org/apps/redlist/details/3855/0/full</ref>
The '''great white shark''' (''Carcharodon carcharias'') is a species of [[shark]] in the order [[Lamniformes]], and the only member of the genus ''Carcharodon''. Known variously around the world as "white pointer", "white death" (Australia), "blue pointer" (South Africa), and "man-eater" (worldwide), the white shark has brought extensive scientific and media attention to investigate its habits and behavior.
The '''great white shark''' (''Carcharadon carcharias'') is a large carnivorous fish considered to be dangerous to humans. Although the average size of the shark is 13 to 15 feet, sightings of sharks 20 feet long and larger are common. According to the [[Guinness Book of World Records]], the largest great white ever caught was 37 feet in length. The only larger [[shark]]s are the [[plankton|planktivorous]] [[basking shark]] and [[whale shark]].
The white shark is the third-largest fish on record, exceeded in size only by the plankton-feeding [[whale shark|whale]] and [[basking shark]]s. It is a large-bodied, robust animal with an average length between 13–15 feet, and weigh between 1,500-2,450 pounds.<ref>http://www.jawshark.com/great_white_recorded_sizes.html</ref> Larger individuals have been caught from time to time,<ref>http://news.nationalgeographic.com/news/2011/05/110506-biggest-great-white-sharks-apache-caught-animals-science/</ref> with 21 feet the largest length currently recorded for two individual, one caught in Cuba in the 1940s, and one caught off the Azores in 1978.
== Habits ==
The white shark has a coloration pattern shared by the [[orca]] and [[penguin]]s in that it is generally a dark grey above, and a pale cream to white underside, thought by scientists to be a [[camouflage]] pattern. Its large crescent tail provides quick bursts of speed when needed.
Great white sharks are found worldwide in tropical and temperate waters. They can regulate their body temperature to some degree, so as to remain active in cold water. Feeding particularly on marine mammals such as [[fur seal]]s and [[sea lion]]s, great white sharks typically capture their prey by giving a single devastating bite, then retreating and circling until the victim has bled to death.
== Attacks on humans ==
Most attacks on surfers and bathers are believed to cases of mistaken identity, and they are generally not finished off, their [[flavor]] comparing poorly with that of a [[blubber]]y [[pinniped]]. However, although it is rare, there are cases of rogue individuals who were purposely attack humans. The book and film ''[[Jaws]]'' is based on these rogue individuals.
Most attacks on surfers and swimmers are believed to cases of mistaken identity, and they are generally not finished off, their [[flavor]] comparing poorly with that of a [[blubber]]y [[pinnipedia|pinniped]].
The book and film ''[[Jaws]]'' is based on the inaccurate theory of a "rogue shark," a theory that is widely considered to be inaccurate.<ref>https://en.wikipedia.org/wiki/1992_Cageless_shark-diving_expedition</ref>
Great white sharks have recently become rare due to human persecution, and are now protected in [[South Africa]] and [[Australia]].
{{DEFAULTSORT:Shark, great white}}
[[Category:Sharks]]
[[Category:Fish]]
[[Category:Dangerous animals]]
[[Category:Carnivores]]
==links==
*[http://homepage.mac.com/mollet/Cc/Cc_list.html White shark summary]
Domain Eukaryota
Subkingdom Bilateria
Phylum Information
Sub-phylum Vertebrata
Infraphylum Gnathostomata
Class Chondrichthyes
Sub-class Elasmobranchii
Infra-class Euselachii
Order Lamniformes
Family Lamnidae
Genus Information
Genus Carcharodon
Species C. carcharias
Population Unknown
Conservation status Vulnerable[1]
The great white shark (Carcharodon carcharias) is a species of shark in the order Lamniformes, and the only member of the genus Carcharodon. Known variously around the world as "white pointer", "white death" (Australia), "blue pointer" (South Africa), and "man-eater" (worldwide), the white shark has brought extensive scientific and media attention to investigate its habits and behavior.
3 Attacks on humans
The white shark is the third-largest fish on record, exceeded in size only by the plankton-feeding whale and basking sharks. It is a large-bodied, robust animal with an average length between 13–15 feet, and weigh between 1,500-2,450 pounds.[2] Larger individuals have been caught from time to time,[3] with 21 feet the largest length currently recorded for two individual, one caught in Cuba in the 1940s, and one caught off the Azores in 1978.
The white shark has a coloration pattern shared by the orca and penguins in that it is generally a dark grey above, and a pale cream to white underside, thought by scientists to be a camouflage pattern. Its large crescent tail provides quick bursts of speed when needed.
Great white sharks are found worldwide in tropical and temperate waters. They can regulate their body temperature to some degree, so as to remain active in cold water. Feeding particularly on marine mammals such as fur seals and sea lions, great white sharks typically capture their prey by giving a single devastating bite, then retreating and circling until the victim has bled to death.
Attacks on humans
Most attacks on surfers and swimmers are believed to cases of mistaken identity, and they are generally not finished off, their flavor comparing poorly with that of a blubbery pinniped. The book and film Jaws is based on the inaccurate theory of a "rogue shark," a theory that is widely considered to be inaccurate.[4]
Great white sharks have recently become rare due to human persecution, and are now protected in South Africa and Australia.
↑ http://www.iucnredlist.org/apps/redlist/details/3855/0/full
↑ http://www.jawshark.com/great_white_recorded_sizes.html
↑ http://news.nationalgeographic.com/news/2011/05/110506-biggest-great-white-sharks-apache-caught-animals-science/
↑ https://en.wikipedia.org/wiki/1992_Cageless_shark-diving_expedition
White shark summary
Retrieved from "https://www.conservapedia.com/index.php?title=Great_white_shark&oldid=1453195"


What do you do if your ammonia probe is not working properly? Symptoms are low slopes, erratic readings, error messages during calibrations, and impossible answers.
Whether you just received the probe, or if you have had it for several years, the first thing you need to do is run an "Inner Body Check". This test will tell whether the sensor system itself is operating correctly. If you just received the probe and are having trouble and call the manufacturer or your dealer, the first thing they will ask for are your results from the Inner Body Check before they consider an in-warranty replacement.
Even if the probe is several years old, and therefore out of warranty, this simple test will save you a lot of headaches. If the probe fails this test, it will not work regardless of how many times you re-calibrate or remake your standards.
This applies to both Thermo Scientific Ammonia Probes.
Note: Before you run this test: If the probe has been dry for more than a few days, you should disassemble the probe as per step #2 below and soak the inner body in regular pH 7.00 buffer overnight. If you neglect to do this, the probe will probably fail the test regardless of whether it is actually good or not!
Pour 50-100 ml of each into a beaker and label each beaker.
Disassemble your Ammonia probe. If you have a Pinnacle ammonia probe, simply unscrew the cap at the bottom. If you have an Orion ammonia probe, unscrew the top and pull the inner body out of the top of the probe.
Once you have disassembled the probe, be careful with it because the glass at the bottom of the inner body is very fragile. If you break it, you WILL be buying a new probe.
Make sure the probe is connected to the meter and put the meter into the millivolt (mv) mode.
Place the beaker containing the pH 7.00 buffer with NaCl on a stir plate. Add a 1" stir bar and stir at slow to medium speed.
Clamp the inner body into a probe holder and immerse the probe in the beaker on the stir plate, being careful not to lower it so far that it is hit by the stir bar.
The reading should stabilize within two minutes. A "stable" reading is a reading which drifts 0.1 mv/minute or less. Record this reading, paying attention to the minus sign (-), if present.
Remove the inner body from the solution, rinse it with DI water, and repeat steps 5-7 above using pH 4.00 buffer with NaCl.
From the two mv readings obtained, calculate the difference in millivolts. Remember to take any minus signs into account. For example, if the reading in the 7 buffer was -25 mv, and the reading of the 4 buffer was 145 mv, the difference is 160 mv.
The ideal difference is 175 mv. Normally we consider any difference over 150 mv to be satisfactory. Usually, if the sensor is bad, the difference will be 2 mv or less, so it should be pretty obvious whether the sensor is good or not.
If the probe fails the Inner Body Check, there is NOTHING you can do to make it work. If you just received it, call your dealer for a replacement as an out-of-box failure. If you have used the probe for some period of time, but it is still under warranty, contact the manufacturer for an in-warranty replacement. If it is out of warranty, you still MUST replace it. You are wasting your time if you continue to play with it.
If the probe passes the Inner Body Check, chances are at least 99% that the problem lies elsewhere: bad membranes, bad filling solution, or improper lab technique.


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The Flash Podcast On The Mixx – November 2016
Posted by :The Flash Podcast On : November 27, 2016
Tags:DC Comics, DC TV, The CW, The Flash, The Flash Podcast
2016 is almost over as television will soon be on a hiatus, including the CW's The Flash TV show. But until then, one of our geekiest shows on The Mixx Radio Network, The Flash Podcast, is going to keep itself busy with tons of great episodes. If you missed any of the airings of the podcast this month on The Mixx, do not fear as we have all the episodes for you to catch up!
The Flash Podcast Season 3 – Episode 5: Monster
On this week's episode of The Flash Podcast, Andy Behbakht, Brittany Rivera and special guest host, Britney Moane (host of DC TV Classics) get together to review the fifth episode of The Flash Season 3 titled "Monster". In this episode, Caitlin Snow reaches out to her mother, Dr. Carla Tannhauser (guest star Teen Wolf's Susan Walters) to get some help with her meta-human powers.
Meanwhile, Barry has to face a giant monster who has invaded Central City while Team Flash gets to know the new Harrison Wells from Earth-19 who may or may not have a few secrets of his own. The gang also read listener feedback about "Monster" before going on to the preview session for the next episode titled "Shade" which will air on Tuesday, November 15. That and more on the latest episode of The Flash Podcast!
Official CW Episode Description for The Flash 3.05: "Monster" | CAITLIN CALLS ON HER MOTHER FOR HELP WITH HER GROWING META POWERS — Desperate to understand what is happening to her, Caitlin (Danielle Panabaker) visits her mother, Dr. Tannhauser (guest star Susan Walters), a renowned biomedical researcher, in the hopes that her mother can provide some answers about Caitlin's growing meta-human powers. However, when Dr. Tannhauser treats her daughter like a test subject, Caitlin grows cold and brings up past wounds causing the two to have a major blowout. Meanwhile, after a mysterious new meta-human attacks Central City, Barry (Grant Gustin) tries to convince Julian (Tom Felton) to let him assist on the case. Kim Miles directed the episode written by Zack Stentz (#305). Original airdate 11/1/2016."
http://traffic.libsyn.com/theflashpodcast/TFP_S3_005.mp3
The Flash Podcast Special Edition: Invasion! & Predictions For 4-Show Crossover
On a special edition episode of The Flash Podcast, with you wait for The Flash to return next week, Andy Behbakht and Andrew Dyce get together to do a discussion on the DC Comics storyline "Invasion!". This is the book that will be adapted for the upcoming four-show crossover event between The CW DC TV shows, Supergirl, The Flash, Arrow and DC's Legends of Tomorrow that airs in just a couple of weeks from now!
In addition to reviewing and discussing the iconic DC storyline, the duo also talks about their predictions and anticipation for the crossover event in terms of how "Invasion!" will be adapted and what they hope to see throughout CW's mega-crossover. During the news session, Andy and Andrew discuss the reveal of the Vibe and Killer Frost costumes, the Young Justice Season 3 news as well as the recent development on The Flash movie. That and more on this special edition of The Flash Podcast – don't forget to tune in for The Flash next week on Tuesday, November 15 at 8/7c on The CW with 3.06 "Shade"! If you are interested in checking this book out before the TV crossover, you can purchase "Invasion!" on Amazon or digitally through Read DC Entertainment or Comixology.
http://traffic.libsyn.com/theflashpodcast/TFP_SP18.mp3
The Flash Podcast Season 3 – Episode 6: Shade
On this week's episode of The Flash Podcast, Andy Behbakht, Amy Marie and Brittany get together to review the sixth episode of The Flash Season 3 titled "Shade". In this episode, Wally West begins to remember his life as Kid Flash in the Flashpoint Universe when he starts having dreams of being the yellow-red suited speedster. Barry has no choice but tell the whole West family what happened to Wally in the Flashpoint Universe, however Doctor Alchemy is after Wally and another big villain makes his debut.
In the news session, the gang discusses the two first TV spots for the upcoming crossover event between all the four CW DC shows, "Invasion!". The gang also read listener feedback about "Shade" before going on to the preview session for next week's episode titled "Killer Frost" which was directed by filmmaker and returning Flash director, Kevin Smith! That and more on the latest episode of The Flash Podcast!
As mentioned on the podcast, Amy's dog Roan is getting a surgery to fix his leg this weekend and she could use your help to fund the financial fees for the operation. Click here to read Roan's story, more about his crooked leg and how you can donate to Roan's Go Fund Me page.
Official CW Episode Description for The Flash 3.06: "Shade" | WALLY HAS VISIONS OF BEING KID FLASH — When Wally (Keiynan Lonsdale) starts having dreams about being Kid Flash, Barry (Grant Gustin) realizes he has to tell Wally, Iris (Candice Patton) and Joe (Jesse L. Martin) about what happened to Wally in Flashpoint in order to keep him safe. JJ Makaro directed the episode written by Emily Silver & David Kob (#306). Original airdate 11/15/2016."
The Flash Podcast Season 3 – Episode 7: Killer Frost
On this week's episode of The Flash Podcast, Andy Behbakht, Amy Marie and Andrew Dyce get together to review the seventh episode of The Flash Season 3 titled "Killer Frost". In this episode, which was directed by Kevin Smith, Caitlin Snow's ice powers begin to consume her as the villainous ice queen come to life on Earth-1. As Caitlin gets colder, Barry must go through the impossible and fight his fellow team member.
The gang also read listener feedback about "Killer Frost" before going on to the preview session for next week's episode titled "Invasion!" which is part of the 4-show crossover! In addition to that, find out about the big exciting live podcast crossover event between this podcast, Supergirl Radio, Legends Of Tomorrow Podcast and Quiver: The Green Arrow Podcast! That and more on the latest episode of The Flash Podcast!
Official CW Episode Description for The Flash 3.07: "Killer Frost" | KEVIN SMITH DIRECTS; KILLER FROST EMERGES — Caitlin (Danielle Panabaker) uses her powers to save Barry (Grant Gustin) but as her mother predicted, the effort unleashes her inner Killer Frost. Killer Frost goes on a rampage looking for Dr. Alchemy, kidnapping Julian (Tom Felton) and battling both The Flash and Vibe (Carlos Valdes). Meanwhile, Joe (Jesse L. Martin) and H.R. (Tom Cavanagh) have a heart to heart talk. Kevin Smith directed the episode with story by Judalina Neira and teleplay by Andrew Kreisberg & Brooke Roberts (#307). Original airdate 11/22/2016."
The Flash airs on Tuesday nights at 8/7c on The CW!
The Flash Podcast
The Flash Podcast On The Mixx – October 2016
The Flash Podcast On The Mixx – December 2016

redpajama_set_name: RedPajamaCommonCrawl


Many of us are really fed up with the fact that few things are worse than receiving unwanted calls. Well, it's not that bad either, but it's a very annoying thing that we can not easily block on iPhones, since Apple does not allow any third-party application to access call logs .
For that reason and after a long period of "fighting" with the Indian government, Apple (or a developer with authorization from Apple) is making an application capable of blocking spam in calls and text messages , thus avoiding any call or message not desired .
It is true that iOS could already block numbers and chats of iMessage, in addition to iOS 10 added a new API that allowed developers to create applications that allow blocking incoming calls . But this time it seems that they are going to take this a little further.
Unfortunately, Apple has reported that many of the functions proposed by the Indian government for the new application will not be possible . For example, there is no way to make third-party software access recent calls.
It is also logical to think that Apple will not allow anyone to create an application that accesses private information of users , not even an application created by the same Indian government under the supervisor of Apple since if this happens, other governments will begin to ask the same after.
Anyway, the immediate and early denial of Apple received by the Indian government after the proposal of an anti-spam application, sat pretty bad several Indian representatives . It was then that Apple decided to send different executives to discuss the proposal and study the options with the Indian regulators.
The Reuters website tells us that Apple ended up agreeing to help create an anti-spam application with limited functions , but the Indian regulator remained quite frustrated after the meeting on this issue.
Do you think Apple should allow an anti-spam application to be created for iOS? Are you worried about your privacy? Tell us in the comments!


Your new LG G5 just got even better with a SUPER case from SUPCASE. Choose from a versatile Case Line that gives you the protection you need in a slim, sleek profile you'll love. Our cases are crafted to fit and provide the protection you need in a slim profile you will love. Choose from a diverse product line that is sure to add style, function, and durability to your new device.
Your LG G5 just got even better with a SUPER case from SUPCASE. Choose from a versatile Case Line that gives you the protection you need in a slim, sleek profile you'll love. Our cases are crafted to fit and provide the protection you need in a slim profile you will love. Choose from a diverse product line that is sure to add style, function, and durability to your new device.
Sporty, clear, protective what's not to love? LG G5 Unicorn Beetle Case is a sleek, clear casew that lets you show off the original design of your phone. Added shock resistant bumpers give you the protection you need.
One of our most beloved cases the Unicorn Beetle Pro is equipped to get the job done. Protect your investment with a case that is heavy duty and functional on the go.
Finally, remember that we're here for you. Always feel free to reach out if there is something you'd like to say. We're always available on our Facebook or Twitter for a quick chat about any issues you may have, or just to geek out about the latest news in the tech industry. Reach out - we promise, we're even more fun that you think!
You're only a few clicks away from owning industry-leading products designed to maximize your phone's most attractive attributes.


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Q: How to extend the rows of a matrix in MATLAB filling the added rows with the first row's values efficiently I have a matrix myVel that is of size [1 501] meaning 1 row and 501 columns.
I want to extend this matrix so that the matrix will be of size [N 501], where N is an arbitrary number.
Each of the values in the columns need to be the same (meaning that all the values in the first column are all say, x and all of the values in the second column are say, y and so on).
This means that each row would consist of the same values.
How can I achieve this efficiently?

A: Divakar's solution is one way to do it, and the link he referenced shows some great ways to duplicate an array.  That post, however, is asking to do it without the built-in function repmat, which is the easiest solution.  Because there is no such restriction for you here, I will recommend this approach.  Basically, you can use repmat to do this for you.  You would keep the amount of columns the same, and you would duplicate for as many rows as you want.  In other words:
myVelDup = repmat(myVel, N, 1);

Example:
myVel = [1 2 3 4 5 6];
N = 4;
myVelDup = repmat(myVel, N, 1);

Output:
>> myVel

myVel =

  1     2     3     4     5     6

>> myVelDup

myVelDup =

  1     2     3     4     5     6
  1     2     3     4     5     6
  1     2     3     4     5     6
  1     2     3     4     5     6

In general, repmat is called in the following way:
out = repmat(in, M, N);

in would be a matrix or vector of values you want duplicated, and you would want to duplicate this M times horizontally (rows) and N times vertically (columns).  As such, for your case, as you have an array, you will want to duplicate this N times vertically and so we set the first parameter to N.  The second parameter, the columns stay the same so we specify this to be 1 as we don't want to have any duplications... and thus the call to repmat you see above.
For more information on repmat, check out this link: http://www.mathworks.com/help/matlab/ref/repmat.html

redpajama_set_name: RedPajamaStackExchange


Reaching the hedonistic heights of luxury, Capitol Grand and LK Tower embody the pinnacle of architectural achievement. Realised through the pioneering vision of LK Property Group and world renowned architects Bates Smart, elliptical forms of elegant simplicity create an unmistakable vision of beauty.
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Home to the fortunate few, admired by all.
Capitol Grand, incorporating LK Tower, will be the tallest landmark building outside of the Melbourne CBD.
Rising above the iconic crossroads of Toorak Rd and Chapel St, two landmark structures celebrate the sculptural splendour of geometry and form. The voluptuous curves of Capitol Grand house 3 levels of luxury retail, matched by a suitably sophisticated collection of residences above.
Set back from Toorak Rd, the landmark LK Tower soars skyward with luxury residences, tapering as the tower rises towards its breathtaking summit.
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LK Tower offers spectacular vistas across Melbourne from Albert Park Lake to Port Phillip Bay and south-east to the picturesque Dandenong Ranges.
Enjoy quiet contemplation or evening celebrations, with the glittering city skyline, lush green Botanic Gardens and the shimmering Yarra River as a breathtaking backdrop.


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Brazilian Jazz Jam by Vinicius Gomes & Friends
Palabra, Imagen y Escena / Literary & Visual Arts Series.
Maya Burns / Singer songwriter
Concerts, Songwriting
40-19 Gleane St. Elmhurst, NY
terraza7.com
Presented by Mexico Now Festival & Terraza 7
Monday January 16th, 2023 at 8:00 pm.
$15 cover charge for mezzanine.
Maya Burns / Voice; Piano; Guitar; Saxophone.
Join us for an evening with the singer, composer and multi-instrumentalist Maya Burns, whose music ties cultures together through a powerful message of unification. Burns will play at jazz club Terraza 7, deemed by The New York Times as "a beloved fixture in one of the most ethnically diverse neighborhoods in the country."
Burns travelled around California with her parents, crafters at music festivals such as Live Oak, and grew up in Ensenada, Mexico, since she was four. Her bicultural upbringing played a big role in her musical education and shaped her style as a combination of ranchero, rock, folk, funk and jazz. She has played at festivals such as Whole Earth, Live Oak, Irvine Lake Festival, and was the headliner of the 2018 Jazzatlán Festival. In 2016, she was the musical director for eXtras, a play by the writer and journalist Sabina Berman and performed by the Bichir brothers that won the LA Critics Choice Award.
Maya constantly explores diverse genres with her voice, piano, guitar, and saxophone. At a very young age, she has managed to craft a fascinating multicultural identity that continues to captivate audiences all over.


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Q: How to hide web-page scrolls preserving scrolling functionality I have a specific task, which requires to hide web-page scrollbars in Chrome, but preserve scrolling functionality (with keys and mousewheel). Currently I use
document.documentElement.style.overflow = 'hidden';
but this effectively disables scrolling.
Does anyone can suggest another way to fulfil the task via javascript or WinAPIs?
The code is actually placed inside a Chrome extensions (content script), so many things impossible for ordinary pages can be involved. Also I have a plugin which does already subclass Chrome window (Chrome_RenderWidgetHostHWND) for other purposes, so even more complicated methods are also welcomed.
According to MS Spy the Chrome window contains WS_EX_RIGHTSCROLLBAR style even when the scripted style.overflow is set to hidden. This makes me think, that the restriction is applied by the browser internally, and can not be removed by WinAPI calls.
EDIT:
I overlooked that WS_EX_RIGHTSCROLLBAR = 0x00000000, so it is implied by default and can not be eliminated.
EDIT2:
I came across ::-webkit-scrollbar CCS styles, and it allows me for changing scrollbars width to 0! The scrollbar is not visible (just to distinguish this state to hidden) and works. Now the question is how can I change this style from javascript notation?

A: On the css way...
I tried inserting some css on an allready loaded page and the scrollbars never changed?
chrome.tabs.insertCSS(tab.id,{code:"::-webkit-scrollbar {width: 0 !important; height: 0 !important}"});

...even tried attaching it to the head and that didnt work either....
insertNoScrollBars=function (){
 if(document.getElementById('HideScrollBars') == null){
      var headID = document.getElementsByTagName("head")[0];
      var cssNode = document.createElement('style');
      cssNode.setAttribute('id','HideScrollBars');
      cssNode.innerText="::-webkit-scrollbar {width: 0 !important; height: 0 !important}"
      headID.appendChild(cssNode);
   }
}

chrome.tabs.query({'active': true, 'windowId': chrome.windows.WINDOW_ID_CURRENT},
   function(tab){
    chrome.tabs.executeScript(tab.id,{code:"("+insertNoScrollBars+")()"});
    //chrome.tabs.insertCSS(tab.id,{code:"::-webkit-scrollbar {width: 0 !important; height: 0 !important}"});
   }
);

Looking around it seems the scrollbars wont get updated unless theres some kind of refresh?....
http://userscripts.org/scripts/show/117089
One thing that did work tho (altho it might not suit your needs) was to inject the css using content script settings in the manifest....
manifest.json
{
  "name": "Hide scrollbars",
  "version": "1.0",
  "description": "As the name says",
  "permissions": [
    "bookmarks", "tabs", "<all_urls>"
  ],
  "content_scripts": [
    {
      "matches": ["<all_urls>"],
      "css": ["mystyles.css"],
      "run_at" : "document_start"
    }
  ]
}

mystyles.css
::-webkit-scrollbar {width: 0 !important; height: 0 !important}

Or
If the only reason you want to inject it programmaticly is so you only inject it if your settings say to then you could inject it with a content script at document start.....
manifest.json
 {
  "name": "Hide scrollbars",
  "version": "1.0",
  "description": "As the name says",
  "permissions": [
    "<all_urls>"
  ],
  "content_scripts": [
    {
      "matches": ["<all_urls>"],
      "js": ["content.js"],
      "run_at" : "document_start"
    }
  ]
}

content.js
// Do a check here to see if your settings say to hide the scrollbars or not
 if(document.getElementById('HideScrollBars') == null){
      var headID = document.documentElement;
      var cssNode = document.createElement('style');
      cssNode.setAttribute('id','HideScrollBars');
      cssNode.innerText="::-webkit-scrollbar {width: 0 !important; height: 0 !important}"
      headID.appendChild(cssNode);
   }

A: jsFiddle is apparently having some issues, but this is a good start for you. I used jQuery here as it cuts a lot of corners, but this can be translated into pure javascript. I believe you will need to bind to both html and body because of some browser quirks. I don't feel like doing the work for you, but if you need guidance let me know. Or if others want to take the time to write it they can feel free to co-opt my code.
//simulate mouse wheels. We us DOMMouseScroll for FF and mousewheel for all others
$('body').bind('mousewheel DOMMouseScroll', function(e) {
    var scrollTo = null;

    if (e.type == 'mousewheel') {
        scrollTo = (e.originalEvent.wheelDelta * -1);
    }
    else if (e.type == 'DOMMouseScroll') {
        scrollTo = 40 * e.originalEvent.detail;
    }

    if (scrollTo) {
        $(this).scrollTop($(this).scrollTop() + scrollTo);
    }
});

//monitor keypresses (you may want to use keypress or keydown instead).
//remember that spacebar/shift-spacebar can also scroll screen full length.
$(document).keydown(function(e) {
    console.log(e.keyCode);
    var scrollTo = 120;

    if (e.keyCode == 40) {
        console.log('down');
    }
    else if (e.keyCode == 38) {
        console.log('up');
        scrollTo *= -1;
    }
    else if (e.keyCode == 32) {
        console.log('spacebar');
        scrollTo = $(window).height();
    }

    $('body').scrollTop($('body').scrollTop() + scrollTo);
});

A: I don't know anyhing about chrome extension programming. If i had to do it on a webpage i'd try to use the jquery plugin jScrollPane http://jscrollpane.kelvinluck.com/ with some custom css.

A: Do you mean like this?
 http://jsfiddle.net/DerekL/wZ5r2/
What it does?
What it does is simply locked the scrollTop to a specific Y (or X if you want).
var scr = {
    ini: 0,
    locked: false,
    dis: function() {
        scr.ini = document.body.scrollTop;
        scr.locked = true;
        $(window).scroll(function() {
            if (scr.locked) {
                window.scrollTo(0, scr.ini);
            }
        })
    },
    en: function() {
        scr.locked = false;
    }
};

Advantage

*

*Very light;

*Very easy to understand too;

*100% users will not able to scroll the page.

Hope it helps you out.


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Maximise your multi-tasking with these go to tri shorts for all things swim, bike and run. With the advantage of the FOHER Tridimensional Performance fabric, our (and your!) favourite tri short has you covered. With breathable, compression and comfort as priority functions, you'll be 100% focused on your performance.
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You must not overlook the essentiality of turning your home into a rental Airbnb if you are among the people who travel a lot for business or leisure reasons. It is apparent that you will have a means of getting some more cash into your pocket when you place your home or property in the Airbnb market. Nevertheless, it is possible that you will feel confused about where you should start with that idea. The article focuses on the tips that will assist you to be a successful Airbnb host.
You have to understand that the Airbnb guests look for the most beautiful rentals in the market. It is for this cause that you have to do all that you can to make your house look like it leaped off the screen of HGTV. It implies that installing ambient lights, investing in arts, excellent floral arrangements, and many others are some of the things you cannot afford to overlook. You must not forget that the guests are willing to spend their vacation in the house they saw on the pictures, and thus you have to confirm that all the elements will remain. Furthermore, it is necessary that you think of having a pool in the premises since it can pull a lot of vacationers to your property. You should view options on this site when you want to create a pool in your home.
It is advisable that you do not feel burdened to meet the guests at the entrance of the property or even go for them at the airport. You must go an extra mile of carrying some of their bags and even helping them to arrange their rooms as a way to show them your hospitality. Besides, you have to ensure that you will not leave the premises until you show the visitors some of the things available at the place.
You should know that Airbnb will demand that the guests accept the terms of the rental property before finishing the booking. You thus have to testify to it that you will be straightforward when writing the rules of residing in your premises. Nevertheless, you should not be too strict when writing the rules so that you do not make it quite cumbersome for the guests to comply with them.
Confirm that you will be helpful when communicating with the guests beforehand so that you can figure out some of their needs. Confirm you will want to know if the guests have food allergies or sensitivity to particular materials. It is even necessary that you do not make the error of not leaving a manual on how to utilize the electronics in the home for the renters so that they will not have a hard time living in the premises.


St. John's Law Review (1939) "Copyrights--Right to Maintain Infringement Suit--Sufficiency of Compliance with Section 12, Copyright Act 1909 (The Washington Publishing Company, Inc. v. Drew Pearson, Robert S. Allen and Van Rees Press, Inc., 306 U.S. 30 (1939))," St. John's Law Review: Vol. 14 : No. 1 , Article 16.


For over 30 years, Jeff Dedrick has been a successful entrepreneur. From owning a DJ service in college to eventually owning five restaurants and two fitness clubs, Jeff has enjoyed the freedom that comes from being self employed.
In February, 2005 Jeff decided to completely sell all his offline businesses and move 100% online. He made that decision before he even started his first website or captured his first email subscriber!
Less than a year later, Jeff had a rapidly growing online business and in the next few years created some of the hottest sites in Internet Marketing.
In 2011 Jeff decided to take his new expertise for online marketing and apply it back in the real world by opening a brand new business, a medical weight loss clinic. In its second year, by using all his past sales and marketing knowledge, he was able to triple the sales from it's first year. In 2013 he opened a second location.
Jeff has been very selective over the years when working one on one with businesses to help them increase their customers and grow their sales. It wasn't until 2018 that Jeff has decided to open up his coaching to the public for the first time ever with the goal of doubling the sales of 500 businesses in the next few years.
Jeff is still very selective with whom he works with. If you have a positive attitude and really want to have your business succeed then you are invited to apply for one of his coaching programs.
What would it mean for your business and your personal life if you could double your sales in ten months?


We rent the property via The Thinking Traveller, an agency based in London and offering the most desirable holiday-villas in Sicily, Puglia and the Greek islands. In 2002, its founders, Rossella, a Sicilian cell-biologist, and Huw, a Londoner marketing-manager, gave up their jobs to start the business and offer the best villas with pool, sea-front houses, old masserie and romantic rural properties... The local Sicily team on site has the same passion. "Our" Federica is immediately hands-on when it comes to re-arrange last-minute details for our Etna-trip.


Works by the iconic Maine artist are on display at Fort Williams Park.
"Luando Morning," 1994, oil on linen, 30 by 48 inches.
A knight in full armor rides his fancifully-dressed steed on a stage-like path through the forest with his retinue – a proudly prancing pony and a baby rhino – while the inhabitants (monkeys, toucans, a zebra, etc.) look on. It's a childhood fantasy, playful and dreamy. You can practically hear the staccato visual rhythms, a sweet but triumphant little march.
"Return Home" is a 1971 watercolor by the late great Maine artist and illustrator Dahlov Ipcar, long one of America's most recognizable artists. "Return Home" isn't soaked in her puzzle-board geometrics, but we do see it in the fabric draped on the knight's mount. And even that offers a hint to what Ipcar is all about. Her paintings set to these complex patterns comfortably reach out to the idea of fabric design. They are rich, decorative and, yes, even a little homespun. They are playful, comfortable and homey.
But they are also highly sophisticated responses to some of the leading intellectual art movements of Modernism, particularly Cubism and Surrealism. The surreal content was revolutionary not long ago, but we're now so comfortable with the Freudian notion of the unconscious that it's hard for us to be startled by imagined or dreamed scenes, however irrational. The cubist aspects of Ipcar's work are easier to spot, but ultimately more difficult to parse. The obvious element, particularly in paintings like Ipcar's large scenes of African animals, such as her 1994 "Luando Morning," is the flat presentation of objects on the surface with clearly intentional disregard for the regular spatial rules. Ipcar's cubism, however, is not the heady stuff of Picasso and Braque, but the more decorative and geometrical cubism of Max Weber and Juan Gris.
Ipcar takes her geometrical structure and layout logic from Gris. She breaks up the canvas like a quilt and sets different groups in their own geometrical sections. Here are zebras. Here is a scene of a cheetah chasing its speedy prey. Here are hyenas, and so on. From Weber, Ipcar takes a density that spreads over the surface with an almost pulsing energy, abundant and everywhere apparent.
In her 2012 "Equine Pinwheel," Ipcar uses something like playing-card logic to present a painting that could be seen from any direction. It practically dares us to lay it flat, like a card – or a quilt. But this is no mere wish to be decoration. This is the history of landscape painting: flat vertical things that depict flat horizontal things. It's Cubism, and not simply something that looks like Cubism: It's about how painting works. And this is the key to Ipcar: If you underestimate her sophistication behind her homey veneer, you're going to miss out on some great art.
"Equine Pinwheel," 2012, oil on linen, 30 by 30 inches.
While her humble and hardworking home is often featured in her work, it was hardly a house of cultural naivete. Ipcar was the daughter of Marguerite and William Zorach – two of America's greatest artists. (One of the strongest paintings in the show is a warm and appealing portrait of Ipcar's father.) Both Zorachs have been remembered well and often in recent shows at the Portland Museum of Art and the Farnsworth Art Museum, for example. To find her own way, Ipcar married at 19 and took her husband's name. This might not be a point of interest except that she had a solo show at the Museum of Modern Art (MoMA) when she was 21 years old under the name of Ipcar, not Zorach, an already impressive brand.
That was in 1939. MoMA opened to the public in 1929 and has long been known as a boys' club.
Ipcar was born in 1917 and passed away in February 2017 at the age of 99. She was still showing and painting up until the year before she passed away.
Ipcar will be always be known as an illustrator (an excellent exhibition of her illustrations just came down from the Portland Public Library's Lewis Gallery), but she was a great American artist, draftsman, designer and painter.
Rachel Walls' gallery space at Fort Williams is an ideal space to see Ipcar's work. It's an authentic Maine place, mired in history and the tough-nut truth of the fortressed coast. (Fortress ruins, after all, are places where the imaginations of young people run wild.) Walls' sense of place and history, as well, is handled with a quiet sense of time that fits the ephemeral flashes of Ipcar's work: At moments, it feels dated, but then it pulls itself out to timelessness and back. It's Blake's Tyger, then Rousseau, Dali, cartoon and so on. But within any sense of design calendar, Ipcar comes back again and again until it's obvious that she was always in the right place, holding our pulse, even if only through the beat of our children's hearts.
Walls has scores of Ipcar's iconically recognizable paintings. And in the handsome old building, the experience to a casual viewer is that of a large and excellent museum (without the price tag). These are joined by quirky older paintings, extraordinary flat fiber works and fabric sculptures of incomparable wit and whimsy. We also see that Ipcar's illustrations are works of unusual depth and observation rather than the typical saccharine visual bonbons to occupy the young. Walls has, for example, works from a series of Ipcar's farm illustrations, and these challenge our understandings and sensibilities. A factory farm in the 1950s, for example, is a model of clean efficiency exuding an obvious moral benefit for society.
"Lady and Tiger," 1936, oil on hardboard, 7 by 7 inches.
Ipcar's 1936 "Lady and Tiger," a tiny tondo on beaverwood, might spin with the clarity of an illustration, but it's hardly a puritanical object. Certainly, Ipcar's work is great for families with children, but I wouldn't suggest a close reading of a work like this. A child might see a tiger eating a lady in a dreamlike moment of fantasy, but a teen won't. I saw it both ways, of course, but it made me blush.
Like the nearby Portland Head Light, Ipcar is iconic. But we should be careful not to overlook her qualities just because we've seen glimpses of her work again and again through the years. There is far more to her work than has ever been discussed. And now that she's passed to the better angels of our nature, maybe it's time we look a little more closely.


Home & Garden pressure washers | Kaercher Inc.
Kills 99.99 % bacteria without chemicals. Anti-mess and anti-stress.
Whether indoors or outdoors, here you will find a wide range of tips and examples for getting your home into shape.
As the world's largest cleaning machines manufacturer, comprehensive customer service is a key priority for Kärcher.
Unbeatable versatility – high-pressure cleaning with Kärcher.
We have an extensive range of cleaning machines that meets your needs.
Experience exciting stories with Kärcher. Join us on our journey through the world of Kärcher.
You will be supported by our customer service over the entire service life of your Kärcher machine.
Why Kärcher makes a difference Whether gentle treatment or powerful cleaning – Kärcher high-pressure cleaners offer the perfect solution for every cleaning task. Where previously dirt dominated, now there is nothing but cleanliness. Kärcher adds value to your environment and gives back value: old becomes new, shabby becomes chic. Passionate engineering, the highest quality requirements and decades of experience in the development of innovative high-pressure cleaners make this possible.
The "K5 Premium" high-pressure cleaner with water-cooled motor and hose reel is designed for ease of use. Ideal for moderate dirt, e.g. large vehicles, stone walls and bicycles.
The "K4" – for occasional removal of moderate soiling, e.g. on small vehicles, garden fences or bicycles. This high-pressure cleaner features a water-cooled motor.
Especially compact, robust and effective high-pressure cleaner with extra long-lasting water-cooled motor. Ideal for regular use for moderate soiling.
The extremely practical "K2 Compact" high-pressure cleaner is ideal for removal of normal dirt around the home and is also easy to store and transport.
Compact, powerful and economical: the entry-level high pressure cleaner for occasional use. Suitable for applications such as car washing or patio cleaning.
Pressure washers are the most effective way to clean outdoors and are extremely easy to use: connect the device to the water supply and power outlet, turn on the tap, switch on the pressure washer and let the cleaning fun begin! With matching special accessories, the devices are transformed into real all-rounders: whether for wet blasting, pipe cleaning, terrace cleaning or gutter cleaning, the application possibilities are virtually unlimited. On top of that, the water pressure is always greatest in the immediate vicinity of the nozzle. This means that stubborn dirt is cleaned away more easily with lower nozzle clearance. The clearance is increased accordingly for light dirt and sensitive surfaces. Our practical examples show how you can achieve the best results with your pressure washer.
Pressure washers offer the right solution for every cleaning task!
Since moss not only forms a thick layer on paved surfaces, but remains in the pores of the paving stones, the dirt blaster is used to remove moss. It produces a rotating jet, which combines the cleaning power of a concentrated jet with the area performance of a flat stream. Hold the high-pressure jet vertically to the paved surface and slowly clean from one edge of the moss-covered area to the other at a distance of around 20 to 30 cm.
Kärcher special accessories and cleaning agents ensure thorough and gentle vehicle care. To make your vehicle sparkle in just a few simple steps, and ensure that it stays that way, first remove coarse dirt with a high-pressure jet, then spray Kärcher insect remover onto the radiator grille, bumper and windscreen. Spray Kärcher rim cleaner onto the wheel rims. Cover the vehicle with the cleaning agent function or the special foam jet with Kärcher car shampoo and allow to work in. Finally, clean your vehicle with the power brush from top to bottom in order to make optimal use of the cleaning agent's power.
Our T-Racer terrace cleaners ensure optimum cleaning results with a gentle action, even over large areas. The innovative combination of height-adjustable propellers and two high-pressure nozzles create a hovercraft effect which allows the T-Racer to hover above the ground. An integrated protective guard protects the propeller and high-pressure nozzles from damage from small stones. The device delivers a higher cleaning performance and uniform cleaning results. The casing prevents splashback, thereby protecting both you and the walls from spray.
Say goodbye to scrubbing! Dirt and earth can be removed efficiently from plant and flower pots, spades, shovels, rakes, wheelbarrows, etc. in next to no time using a Kärcher pressure washer. The Vario Power and Multi Power Jet spray lances are particularly suited to this task. Working in the garden has never been easier!
Easily tackle unsightly marks on garden furniture – as a result of air pollution or the previous winter – with the Kärcher garden cleaning set. The Kärcher wash brush and detergent are recommended for cleaning stubborn dirt.
Before cleaning close the shutters. Set the spray lance to low pressure and apply the cleaning agent. Start at the lowest section of the shutters. Leave the cleaning agent to work in for a few minutes so that the dirt is loosened completely. Remove the dissolved dirt with the wash brush and finally rinse with the high-pressure jet.
The performance class is the key differentiator for pressure washers and the main parameter in terms of the cleaning time required. The right device makes cleaning considerably easier. Different technical features, which are fine-tuned in line with the cleaning requirements, are linked to the different performance classes to make work even easier and more efficient.
The cleaning performance of a pressure washer is determined by how the water pressure and water volume are used in combination. The better these two factors are aligned, the easier it is to remove stubborn dirt and the quicker large surface areas can be cleaned. Kärcher puts its devices into specific performance classes based on different cleaning requirements. The larger the surface area to be cleaned and/or the more stubborn the dirt, the higher the performance class recommended. To clean large surface areas such as façades, a K5 device with matching accessories is recommended. As well as offering better performance, higher unit classes also offer other practical functions. These include longer hose lengths for a considerably extended working radius and better hose quality to improve twist resistance and flexibility. This ensures short set-up times and considerably more comfort, especially in the case of frequent use.
Pressure in a normal household water supply is around 4 bar. Water supplied into the pressure washer via a garden hose, passes through a booster pump which generates water pressure of up to 145 bar. The water is ejected through a small high-pressure nozzle as a concentrated jet with a high cleaning effect.
Why buy a Kärcher pressure washer?
For over 60 years, Kärcher has been perfecting the art of high-pressure cleaning and is constantly in the spotlight on account of its outstanding innovations. More than 1,300 patents and utility models are evidence of the company's inventive spirit and make Kärcher the world's leader. Our focus is always on the needs of our customers.
The rotating high-pressure jet combines the power of a narrow jet with the area performance of a flat stream. Thanks to their patented nozzle technology, Kärcher's dirt blasters outperform the competition and enable faster and more efficient cleaning thanks to maximum stripping performance.
As the global market leader we offer the most reliable pressure washers on the market. For over 80 years, Kärcher has stood for quality and innovation that is "Made in Germany". We manufacture all of our devices in our own factories to the highest production standards. Before the products leave the factory, they are fully tested for their functionality and performance. That is why we can always guarantee to our customers that they are purchasing perfect products, which speak for themselves in terms of their performance capabilities and long service life.
The whole package counts. With the right combination of device, accessories and cleaning agent, even the most stubborn dirt won't stand a chance. The right accessories increase the cleaning possibilities significantly and make the cleaning even more effective, efficient and comfortable.
Kärcher offers a wide range of accessories and cleaning agents. This allows us to solve every cleaning problem, no matter how specific. Our accessories can be connected effortlessly to any pressure washer with the simple bayonet system.
When you buy a Kärcher pressure washer, the basic accessories – Vario Power spray lance, a dirt blaster, high-pressure gun, high-pressure hose and a water filter – are already included for selected items.
Your device can be equipped with an additional car kit or home kit on request so that you can fulfil your individual cleaning needs for car and home in a targeted way. The car kit, for example, includes a wash brush, foam brush and car cleaning agent. The home kit includes surface cleaner as well as a special cleaning agent.
With Kärcher special accessories, available separately, you can increase the functionality of your pressure washer even further and solve all your cleaning needs. Surface cleaner, for example, enables quick, efficient and splash-free cleaning of all outside surfaces.
The new generation of Kärcher cleaning agents is creating quite a stir with their 3-in-1 active principle. As well as perfect cleaning effect, these new multi-talented products provide gentle care and reliable protection, saving the operator lots of time and effort. By using renewable and natural resources, Kärcher is also placing an even stronger emphasis on sustainability. What's more, the smart bottle design is a winner too. Whether it is for connection (Plug 'n' Clean), for filling the detergent tank or as a container for suction via the detergent suction hose, the new detergents are universally suitable for all Kärcher pressure washers.
In our cleaning agent finder you will find the right cleaning agent for your Kärcher pressure washer.


Security threat reports are be finding mobile malware to be an ongoing and growing threat, but malware researcher Hitesh Dharmdasani has some simple advice for those concerned about getting infected by nasty, insidious, and occasionally downright surprising malware.
"The best way to keep yourself protected is to not go on third-party market stores or download apps that are not from a recognised marketplace," Dharmdasani told CSO Australia.
Dharmdasani should know: as part of the malware research team within security vendor FireEye, he is at the front line of the fight against the mobile-malware invasion. He's seen and analysed a steady stream of mobile malware – including, most recently, an Android strain called Android.HeHe that disconnects calls and blocks SMS messages received from certain phone numbers, then removes any trace of the numbers from the device's logs.
The list of blocked numbers is unknown as it is retrieved from a remote command-and-control server on request by the malware. Since the malware is written in Korean, it is also tricker to work with than some other malware.
Code like Hehe, Dharmdasani said, is "quite different from what we usually see" as it's not focused on damaging or stealing data – as in MisoSMS, another Android malware recently discovered by FireEye Labs.
The vulnerability of Android devices to malware continues to be a source of concern across the industry, with the Cisco 2014 Annual Security Report the latest study to confirm that Android is a significant and growing target for malware – with the Andr.SMSSend family comprising 98 per cent of observed Android malware families and Andr/Qdplugin-A the most common specific strain.
Fully 99 per cent of mobile malware targeted Android devices in 2013, the report found, while noting that Android users have the highest encounter rate – 71 per cent – with all forms of Web-delivered malware (users of Apple's iOS operating system, by contrast, comprised 14 per cent of all Web malware encounters).
Mobile devices introduce other security issues, the Cisco report notes, with the loss of intellectual property an ever-present threat and historical experience showing the use of wireless channels to eavesdrop on data being exchanged wirelessly.
Mobile malware targeting specific malware made up 1.2 per cent of all Web malware encounters in 2013, Cisco found, noting that with increasing efforts to monetise Android malware during 2013 it's clear that mobile malware is "an emerging – and logical – area of exploration for malware developers".
Whether that exploration eventually turns mobile malware into an unmanageable problem remains to be seen, but for now he's confident that he and his colleagues – working tirelessly in research labs at security firms around the world – can keep up with the torrent of new mobile malware.


If you use this API for something cool, please let us know, we like looking at interesting uses of the data. If you have any suggestions/requests for endpoints, please email: scott.wainstock@gmail.com. If you have any patches that you'd like to submit to the API, please check out: github.com/scottwainstock/pbm.


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text:
Join me in wishing Alabama member Michael Darst a happy birthday. Member for over 3 years
maey (Maggie Aey) January 11, 2023, 4:48pm #1
Happy birthday @mdarst! Michael has been with InterNACHI® for over 3 years!
kleonard (Kevin Leonard, CPI/CMI) January 11, 2023, 5:07pm #2
Happy Birthday Michael.
pgiannino (Peter Giannino, CMI®) January 11, 2023, 5:17pm #3
Happy Birthday Michael !!!
jfudge (JR Scott Fudge) January 11, 2023, 5:20pm #4
wforrest (William Forrest, CMI) January 11, 2023, 5:42pm #5
Happy Birthday Michael!!
gromicko (Nick Gromicko, CMI) January 11, 2023, 5:56pm #6
ryoung7 (ROBERT YOUNG, CMI) January 11, 2023, 9:40pm #7
Happy Birthday to you, Michel.
Wishing you many more annual InterNACHI Birthday greetings
rmckay (Randy McKay, CMI, CPI Ab. #332322) January 12, 2023, 1:31am #8


By adopting a Comprehensive Regional Protection and Solutions Framework at a conference in Honduras last year, the region has taken a new approach to addressing forced displacement in Central America.
The initiative, which UNHCR, the U.N. Refugee Agency and its partners support, goes beyond simply keeping forcibly displaced people safe. It seeks to allow them to be more self-reliant and to integrate into the communities that welcome them while contributing to their host countries by paying taxes and even starting successful businesses.
The framework, known by its Spanish acronym, MIRPS, brings together refugees' countries of origin, transit and destination to ensure a regional focus spanning national borders. This geographical breadth is complemented by a whole-of-society approach, welding together steps taken by governments, civil society, international organizations, the private sector, financial institutions and academics to ensure a truly comprehensive response to the dynamics of forced displacement in Central America and Mexico.
You can see it at work in Mexico and Guatemala, which I visited last year, where civil society groups, including the church and human-rights defenders, have risen to the occasion. They are present all along the main routes for individuals and families escaping violence, providing essential, life-saving services and support. When those who flee reach their destination, the framework facilitates access to the asylum system, minimizes the use of detention and ensures a fair and effective determination of the asylum claim.
It also looks to address the conditions that are causing displacement in countries of origin. This is a multi-faceted effort that includes improving security for people by strengthening institutions, as well as assisting governments in providing the kind of front-line protection that, when absent, leaves people with few options but to flee.
No one country can do this alone. Regional cooperation and shared responsibility together are the best way to generate success stories from these human tragedies.
The framework complements other regional initiatives, such as the Alliance for Prosperity Plan, a road map developed by the governments of El Salvador, Guatemala and Honduras. It aims to sow the conditions for a more sustainable development model, offering citizens the opportunities and conditions to stay in their countries. USAID and other development actors have made initial financial contributions to this plan, but such investments need time and nurturing to bear fruit.
Central America has done a lot to help itself, but these countries deserve more international support. We are seeing too many examples of prevention gone wrong, of small investments not made that have led, down the road, to costly exercises in peacekeeping. Let this effort in the Americas be an example of international and regional cooperation done right — not politics gone wrong.
Filippo Grandi is the United Nations High Commissioner for Refugees.


text:
\section{Introduction}

Consider the Nevanlinna class
\[
 N=\bigl\{f\in H({\mathbb D}):\lim_{r \to 1}\int_{0}^{2\pi} \log^+|f(re^{i\theta})|\; \frac{d\theta}{2\pi}<+\infty\} ,
\]
which is a complete metric space with the distance defined by
\[
d(f,g)=\lim_{r \to 1}\int_{0}^{2\pi}  \log(1+|f(re^{i\theta})-g(re^{i\theta})|)\;  \frac{d\theta}{2\pi}\ .
\]

\begin{definition*}
A sequence $\Lambda\subset{\mathbb D}$ is a (free) interpolating sequence for $N$ if the space of traces $N|\Lambda$ is ideal, that is, whenever $f\in N$ and $\{\omega_\lambda\}_{\lambda\in\Lambda}$ is a bounded sequence there exists $g\in N$ such that $g(\lambda)=\omega_\lambda f(\lambda)$, $\lambda\in\Lambda$. We shall write $\Lambda\in \Int N$.
\end{definition*}

Since $N$ is an algebra, it is easily seen that $\Lambda\in \Int N$ if and only if for every bounded sequence $\{v_\lambda\}_{\lambda\in\Lambda}$ there exists $f\in N$ such that $f(\lambda)=v_\lambda $, $\lambda\in\Lambda$.
In particular, if $\Lambda\in \Int N$ there exist functions $f_\lambda\in N$ interpolating the values
\[
\delta_{\lambda,\lambda'}=
\begin{cases}
1\; & \textrm{if $\lambda^\prime=\lambda$}\\
0\;  & \textrm{if $\lambda^\prime\neq\lambda$}\ .
\end{cases}
\]
Moreover this can be achieved with functions $f_\lambda$ such that $\sup_{\lambda\in\Lambda} d(f_\lambda,0)<\infty$, as can be seen by going through the details of the proof of \cite[Theorem 1.2]{HMNT}.

Note that for other algebras of holomorphic functions the analogous size control of these $f_\lambda$ is an immediate consequence of the open mapping theorem applied to the
restriction operator. This is the case for $H^\infty$, the algebra of bounded holomorphic functions,
the Korenblum algebra $A^{-\infty}$, or the Smirnov class $N^+$ (see below).
However, $N$ is not even a topological vector space \cite{ShSh}, so no open mapping theorem can be used here.

Conversely, for $H^\infty$ and $A^{-\infty}$ (and for other Banach spaces), the existence of functions $f_\lambda$ with uniform control of their size and interpolating the values $\delta_{\lambda,\lambda'}$ implies that $\Lambda$ is an interpolating sequence (see \cite[Chap.VII]{Gar}, \cite[Lemma 2.3]{Ma}). We provide an example showing that this is not the case for $N$ nor $N^+$. For the Nevanlinna class, we have:

\begin{theorem}\label{thN}
Let $\Lambda$ be a sequence in ${\mathbb D}$.  Then,
\begin{itemize}
\item [(a)] If $\Lambda \in \Int N$, then there exist $C>0$ and functions $f_\lambda\in N$ such that
\begin{itemize}
\item[(i)] $d(f_\lambda,0)\leq C$ ,
\item[(ii)] $f_\lambda(\lambda^\prime)=\delta_{\lambda,\lambda'}$, $\lambda'\in\Lambda$.
\end{itemize}

\item [(b)] The converse fails: there is a sequence $\Lambda\notin \Int N$ for which there exist $C>0$ and  $f_\lambda\in N$ satisfying (i) and (ii).
\end{itemize}

\end{theorem}

On the other hand, the Smirnov class $N^+$ is defined by
\[
N^+=\bigl\{f\in N:\lim_{r \to 1}\int_{0}^{2\pi}\log^+|f(re^{i\theta})|\;  \frac{d\theta}{2\pi}=\int_{0}^{2\pi} \log^+|f^*(e^{i\theta})|\;  \frac{d\theta}{2\pi}\bigr\}\ ,
\]
where $f^*(e^{i\theta})=\lim\limits_{r \to 1} f(re^{i\theta})$ (which exists a.e. $\theta\in [0,2\pi)$).

Since $N^+$ is an $F$-space (\cite[Lemma 1]{Ya}), an application of the open mapping theorem for such spaces (see \cite[2.11, p.47]{Ru}) shows  that there exist $C>0$ and functions $f_\lambda\in N^+$ satisfying (i) and (ii) from Theorem \ref{thN}.
But more can be said. Denote by $\mathcal F$ the class of convex, increasing functions $\psi:[0,+\infty)\longrightarrow[0,+\infty)$ such that $\lim\limits_{t\to +\infty} \psi(t)/t=+\infty$. It is known that if $f\in N^+$, there exists $\psi\in\mathcal F$,
depending on $f$, such that
\[
\int_{0}^{2\pi}
 \psi\left[  \log(1+|f^*(e^{i\theta})| \right)]\;  \frac{d\theta}{2\pi}<+\infty\ .
\]

\begin{theorem}\label{thS}
Let $\Lambda$ be a sequence in ${\mathbb D}$.  Then,
\begin{itemize}
\item [(a)] If $\Lambda \in \Int N^+$, then there exist $\psi\in\mathcal F$, $C>0$ and functions $f_\lambda\in N^+$ such that
\begin{itemize}
\item[(i)] $\displaystyle\int_{0}^{2\pi} \psi\left[  \log(1+|f_\lambda^*(e^{i\theta}) | ) \right]\;  \frac{d\theta}{2\pi}\leq C$ ,
\item[(ii)]  $f_\lambda(\lambda^\prime)=\delta_{\lambda,\lambda'}$, $\lambda'\in\Lambda$.
\end{itemize}

\item [(b)] The converse fails: there is a sequence $\Lambda\notin \Int N^+$ for which there exist  $\psi\in\mathcal F$, $C>0$ and  $f_\lambda\in N^+$ satisfying (i) and (ii).
\end{itemize}

\end{theorem}

As in the Nevanlinna case, part (a) is implicit in the proof of \cite[Theorem 1.3]{HMNT}, while part (b) will follow from an explicit example.

\section{Preliminaries. Interpolation in the Nevanlinna and Smirnov classes}

A complete description of the
interpolating sequences for $N$ and $N^+$, including a characterisation of the traces, was given in \cite [Theorems 1.2 and 1.3]{HMNT}.  In particular, we will make use of the following geometric characterisation.

Let $b_\lambda(z)=\frac{z-\lambda}{1-\bar\lambda z}$ be a Blaschke factor and
$B_\lambda(z):= \prod_{\lambda'\neq \lambda} \left( -\frac{|\lambda'|}{\lambda'}\right) b_{\lambda'}(z)$ the Blaschke product with one factor omitted. Given a finite measure $\mu$ in ${\mathbb T}$, let
\[
P[\mu](z)=\int_0^{2\pi}\frac{1-|z|^2}{|z-e^{i\theta}|^2} d\mu(\theta)\
\]
denote its Poisson transform.

\begin{TheoremA} \cite{HMNT} \label{thA}
Let $\Lambda\subset{\mathbb D}$.
\begin{itemize}
 \item [(a)] $\Lambda\in \Int N$ if and only if
there exists $\mu$  positive measure with finite mass on ${\mathbb T}$ such that
\begin{equation*}\label{condN}
|B_\lambda(\lambda)|\geq e^{-P[\mu](\lambda)}\ ,\quad \lambda\in\Lambda .
\end{equation*}

\item [(b)]  $\Lambda\in \Int N^+$ if and only if
there exists $w\geq 0$, $w\in L^1({\mathbb T})$ , such that
\begin{equation*}\label{condS}
|B_\lambda(\lambda)|\geq e^{-P[w](\lambda)}\ ,\quad \lambda\in\Lambda .
\end{equation*}
\end{itemize}
\end{TheoremA}

In classical terminology, when  $w$ is a positive function in $L^1({\mathbb T})$, the harmonic function $u=P[w]$ is called \emph{quasi-bounded}. According to \cite[Theorem 1.3.9, p.10]{ArGa}, for any such functions there exists $\psi\in \mathcal F$ such that
\begin{equation}\label{qb}
\sup_{r<1}\int_0^{2\pi} \psi[ u (re^{i\theta})]\; \frac{d\theta}{2\pi}=\int_0^{2\pi} \psi[ w (e^{i\theta})]\; \frac{d\theta}{2\pi}< +\infty\ .
\end{equation}

\section{Proof. Necessity.}

As said before, the necessity of conditions (i) and (ii) in Theorems \ref{thN} and \ref{thS} is implicit in \cite{HMNT}. We briefly recall how this goes.

Assume $\Lambda\in \Int N$ and let $\mu$ be the measure given by Theorem A (a). Consider the function
\[
g(z)=\int_0^{2\pi}\frac{e^{i\theta}+z}{e^{i\theta}-z}\; d\mu(\theta)\ .
\]
Since $\Real g(z)=P[\mu](z)\geq 0$ we see that $g\in N^+$ and also $ e^g\in N$.  Letting $H=(2+g)^2$ we have $H\in N^+$ and
\[
|H(\lambda)|\geq \bigl(2+\Real g(\lambda)\bigr)^2\geq \bigl(2+\log\frac 1{|B_\lambda(\lambda)|}\bigr)^2=
 \bigl(1+\log\frac e{|B_\lambda(\lambda)|}\bigl)^2\ ,
\]
whence letting $\phi(t)=(1+t)^{-2}$ we obtain, for any $\lambda' \in \Lambda$,
\begin{align*}
|\delta_{\lambda\lambda'}| & \leq |B_\lambda(\lambda)|\ \phi \bigl(\log\frac e{|B_\lambda(\lambda)|}\bigr)\
e^{P[\mu] (\lambda)} |H(\lambda)|\ .
\end{align*}

\begin{theorem*} \cite[Theorem 4]{Gar2}
Let $\phi:[0,\infty)\longrightarrow [0,\infty)$ be a decreasing function such that $\int_0^\infty \phi(t)\; dt<\infty$. There exists $C>0$ such that if $\{v_\lambda\}_\lambda$ is a sequence with
\[
|v_\lambda|\leq |B_\lambda(\lambda)|\ \phi \bigl(\log\frac e{|B_\lambda(\lambda)|}\bigr) \quad \lambda\in\Lambda,
\]
then there exists $F\in H^\infty$ with $F(\lambda)=v_\lambda$, $\lambda\in\Lambda$, and $\|F\|\leq C \int_0^\infty \phi(t)\; dt$.
\end{theorem*}

Aplying Garnett's theorem to the sequence $\bigl\{ \dfrac{\delta_{\lambda\lambda'}}{e^{P[\mu] (\lambda)} |H(\lambda)| }\bigr \}_{\lambda\in\Lambda}$ we obtain a constant $C(\phi)$ and functions $F_\lambda\in H^\infty$ with $\|F_\lambda\|_\infty\leq C(\phi)$ and
\[
F_\lambda(\lambda')=\dfrac{\delta_{\lambda\lambda'}}{e^{P[\mu] (\lambda)} |H(\lambda)| }\ .
\]
Defining
\[
f_\lambda (z)=F_\lambda(z) e^{g(z)} H(z)
\]
we finally have (ii) and
\[
\log^+|f_\lambda(z)|\leq \log C(\phi)+ P[\mu](z) +\log^+ |H(z)|\ ,
\]
which implies (i).

The same proof for the Smirnov case provides interpolating functions $f_\lambda \in N^+$ with
\[
\log^+|f_\lambda(z)|\leq \log C(\phi)+ P[w](z) +\log^+ |H(z)|\ ,
\]
where $w$ is given by Theorem A(b).
Since $H\in N^+$, the subharmonic function $\log^+ |H(z)|$ has a quasi-bouded harmonic majorant, and
 (i) in Theorem~\ref{thS} follows from \eqref{qb}.

\section{Proof. Lack of sufficiency.}
In order to construct examples of non-interpolating sequences satisfying (i) and (ii) in Theorems \ref{thN} and \ref{thS}, consider the dyadic intervals on ${\mathbb T}$:
\[
I_{n,k}=\{e^{2\pi i\theta} : k 2^{-n}\leq\theta< (k+1) 2^{-n}\}, \quad n\in{\mathbb N},\ k=0,\dots,2^n-1\ .
\]

Let us prove first Theorem 1.1 (b).

Consider the sequence $A$ defined in the following way: on the ray terminating at an end of a dyadic interval of the $n$-th generation  (and which is not and end of an interval in a previous generation) consider the dyadic sequence with radii $1-2^{-m}$, starting at $m=2n$. Explicitly
\[
A=\{a_{m}^{n,k}\}_{
\begin{subarray}{l}
n\in{\mathbb N}\\
0\leq k<2^n-1\textrm{, $k$ odd}\\
m\geq 2n
\end{subarray} }
\qquad a_{m}^{n,k}=(1-2^{-m}) e^{2\pi i k2^{-n}}\ .
\]

\begin{figure}[htb]
\centering
\includegraphics[width=0.95\textwidth]{seqA.pdf}
\caption{Representation of the points of $A$ ``above'' the interval $I_{n,k}$}
\label{fig:awesome_image}
\end{figure}

Now, to each $a\in A$ associate a point $b$ on the same ray and so that
\begin{equation}\label{sepN}
\varrho(a,b):=\left|\frac{a-b}{1-\bar a b}\right|\simeq \exp\left(-\frac{1}{1-|a|}\right)\ .
\end{equation}
We thus obtain a sequence $B$, which can be explicitly given by
\[
B=\{b_{m}^{n,k}\}_{
\begin{subarray}{l}
n\in{\mathbb N}\\
 0\leq k<2^n-1 \textrm{, $k$ odd}\\
m\geq 2n
\end{subarray} }
\qquad b_{m}^{n,k}=(1-e^{-2^m})a_{m}^{n,k}\ .
\]

\begin{lemma}\label{intH}
The sequences  $A$ and $B$ are both interpolating for $H^\infty$.
\end{lemma}

Recall that $A\in \Int H^\infty$ means that there exists $C>0$ (the interpolation constant) such that for every bounded sequence $\{v_a\}_{a\in A}$ there is $F\in H^\infty$ with $\|F\|_\infty\leq C \|\{v_a\}\|_\infty$ and $F(a)=v_a$, $a\in A$.

\begin{proof}
Let us see that $A\in \Int H^\infty$.
By Carleson's theorem (\cite[Theorem 1.1, Chap.VII]{Gar}) it is enough to see that $A$ is separated in the pseudo-hyperbolic metric $\varrho$, which is obvious from the definition, and that $\nu=\sum_{a\in A} (1-|a|) \delta_a$ is a Carleson measure.

Let us see first that $A$ is a Blaschke sequence:
\begin{align*}
\sum_{a\in A} 1-|a|=\sum_{n=1}^\infty \sum_{k=0}^{2^n-1}\sum_{m\geq 2n} 2^{-m}
\simeq \sum_{n=1}^\infty 2^n 2^{-2n}<+\infty
\end{align*}

In order to see that $\nu$ is a Carleson measure we have to prove that there exists $C>0$ such that $\nu(Q(I))\leq C |I|$ for all $I$ interval in ${\mathbb T}$, where $Q(I)=\{re^{i\theta} : 1-r<|I|\ ,\, e^{i\theta}\in I\}$ is the associated Carleson box.  It is enough to consider the case where $I$ a dyadic interval. Thus let $I=I_{n,k}$ and
\[
Q(I_{n,k})=\{re^{i\theta} : r>1-2^{-n}\ ,\, \theta\in 2\pi[k2^{-n}, (k+1)2^{-n})\}\ .
\]
By construction, in $Q(I_{n,k})$ there are  $2^j$ rays of the $(n+j)$-th generation. Hence
\[
\sum_{a\in A\cap Q(I_{n,k})} 1-|a|\simeq \sum_{j=1}^\infty 2^j \sum_{m\geq 2(n+j)} 2^{-m}\simeq
\sum_{j=1}^\infty 2^{-2n-j}\lesssim 2^{-n} =|I_{n,k}|\ .
\]
\end{proof}

Define $\Lambda=A\cup B$.
Let us see first that there exist $C>0$ and $f_\lambda$ satisfying (i) and (ii) in Theorem~\ref{thN}.

Fix $\lambda=a_m^{n,k}$ and denote by $\tilde\lambda=b_m^{n,k}$ its ``twin". As just seen, there exist $C>0$ and $P_\lambda^A\in H^\infty$ such that
\begin{itemize}
\item $\| P_\lambda^A \|_\infty \leq C$,
\item $P_\lambda^A (\lambda)=1$ and $P_\lambda^A(a_{m^\prime}^{n^\prime,k^\prime}) =0\quad \forall(n^\prime,k^\prime,m^\prime)\neq (n,k,m)$\ .
\end{itemize}

As in the proof of Lemma~\ref{intH}, we can see that $(B\setminus\{\tilde\lambda\})\cup \{\lambda\}$ is also in $\Int H^\infty$, and with interpolation constant $C>0$ independent of $\lambda$. Therefore there exist  $P_\lambda^B\in H^\infty$ such that
\begin{itemize}
\item $\| P_\lambda^B \|_\infty \leq C$,
\item $P_\lambda^B (\lambda)=1$ and $P_\lambda^B(b_{m^\prime}^{n^\prime,k^\prime}) =0\quad \forall(n^\prime,k^\prime,m^\prime)\neq (n,k,m)$\ .
\end{itemize}

Define finally
\begin{equation}\label{fl}
f_\lambda:= c_\lambda P_\lambda^A  P_\lambda^B b_{\tilde\lambda} e^{g_\lambda}\ ,
\end{equation}
where
\[
g_\lambda(z)=\frac{\lambda^*+z}{\lambda^*-z} \qquad  (\lambda^*=\lambda/|\lambda|)\
\]
and $c_\lambda$ is chosen so that $f_\lambda(\lambda)=1$.

Notice that, by construction, (ii) in Theorem~\ref{thN} holds. In order to see (i) notice that \eqref{sepN} gives
\[
|c_\lambda|=\frac{1}{|b_{\tilde\lambda}(\lambda)|}\exp\left(-\frac{1+|\lambda|}{1-|\lambda|}\right)\simeq
\exp\left(\frac 1{1-|\lambda|}- \frac{1+|\lambda|}{1-|\lambda|}\right)\lesssim 1\ .
\]
Then
\begin{align*}
\log|f_\lambda(z)|=
\log|c_\lambda|+\log|P_\lambda^A(z)|+\log|P_\lambda^B(z)|+\log| b_{\tilde\lambda}(z)|+\Real g_\lambda(z)
\end{align*}
and therefore
\[
\log^+|f_\lambda(z)|\leq \log \|c\|_\infty + 2\log C+ \Real g_\lambda(z)\ .
\]
Since
\[
\sup_{r<1}\int_0^{2\pi}   \Real g_\lambda(r e^{i\theta}) \frac{d\theta}{2\pi}=
\sup_{r<1} \int_0^{2\pi} \frac{1-r^2}{|r e^{i\theta}-\lambda^*|^2}\frac{d\theta}{2\pi}=1\  ,
\]
we have (i), as desired.

Let us see now that $\Lambda\notin \Int N$ by seeing that there is no $\mu$ satisfying the condition of Theorem A(a). Since
\[
\log\frac 1{|B_\lambda(\lambda)|}\simeq \frac 1{1-|\lambda|}\qquad \lambda\in\Lambda ,
\]
such $\mu$ should satisfy in particular  (fixed any $n,k$)
\[
1\lesssim (1-|a_{m}^{n,k}|)  P[\mu] (a_{m}^{n,k}), \quad \forall m\geq 2n\ .
\]
This would force the measure $\mu$ to satisty $1\lesssim \mu\{e^{2\pi ik2^{-n}}\} $ for all $n,k$ (\cite[Theorem 2.2]{ShSh}), and therefore $\mu({\mathbb T})$ could not be finite.

Let us prove now Theorem 1.2 (b). In the same construction done for $N$ consider a sequence made of the ``first" couple of points of each ray, and with a slightly bigger separation. More precisely, let $\tilde\Lambda=\tilde A\cup\tilde B$, where
\[
\tilde A=\{a_{n,k}\}_{
\begin{subarray}{l}
n\in{\mathbb N}\\
0\leq k<2^n-1,\ \textrm{$k$ odd}
\end{subarray} }
\qquad a_{n,k}=(1-2^{-2n}) e^{2\pi i k2^{-n}}\ .
\]
and $\tilde B=\{b_{n,k}\}_{n,k}$ is so that $a_{n,k}$ and $b_{n,k}$ are on the same ray and
\begin{equation}\label{sepS}
\varrho(a_{n,k},b_{n,k})=\exp\left(-\frac 1{(1-|a_{n,k}|)\log_2(\frac 1{1-|a_{n,k}|})}\right) =\frac{2^{2n}}{2n}\ .
\end{equation}

As in Lemma~\ref{intH}, $\tilde A$ and $\tilde B$ are $H^\infty$-interpolating sequences, so there exist bounded peak functions $P_\lambda^{\tilde A}$, $P_\lambda^{\tilde B}$ with the same properties as before.

Given $\lambda\in\tilde\Lambda$, let $I_\lambda$ denote the Privalov ``shadow" of $\lambda$ on ${\mathbb T}$, that is
\[
I_\lambda=\{e^{i\theta} : |e^{i\theta}-\lambda|\leq 2(1-|\lambda|)\}\ .
\]
Let
\[
w_\lambda(\theta)=\frac {C_0}{(1-|\lambda|)\log_2(\frac 1{1-|\lambda|})}  \chi_{I_\lambda}(e^{i\theta}) ,
\]
where $c$ is a universal constant to be chosen later, and consider
\[
g_\lambda(z)=\int_0^{2\pi} \frac{e^{i\theta}+z}{e^{i\theta}-z}\; w_\lambda(\theta)\; \frac{d\theta}{2\pi}\ .
\]
Notice that $\|w_\lambda\|_{L^1({\mathbb T})}\simeq c (\log_2(\frac 1{1-|\lambda|}))^{-1}\lesssim 1$ and
\[
\Real g_\lambda(\lambda)=P[w_\lambda](\lambda)\simeq\frac 1{1-|\lambda|}\int_{I_\lambda} w_\lambda(\theta)\; d\theta \ge \frac {C_1 C_0}{(1-|\lambda|)\log_2(\frac 1{1-|\lambda|})}\ .
\]

Now define $f_\lambda$ as in \eqref{fl}, with these new $g_\lambda$. Again, it is clear that (ii) in Theorem~\ref{thS} holds.
Also, $\{c_\lambda\}_{\lambda\in\Lambda}$ is bounded if $C_0$ is chosen appropriately: if $\lambda=a_m^{n,k}$,
\[
\log|c_\lambda|=\log\frac 1{\varrho(a_{n,k},b_{n,k})}-\Real g_{a_{n,k}}(a_{n,k})\leq\frac {1-{C_1 C_0}}{(1-|a_{n,k}|)\log_2(\frac 1{1-|a_{n,k}|})}\leq 0\ .
\]
In order to see (i) notice that, as before, there exists $\tilde C>0$ such that
\begin{align*}
\log^+|f_\lambda|&\leq \log \|c\|_\infty+2 \log C +P[w_\lambda]\leq \tilde  C +P[w_\lambda]\ .
\end{align*}
Therefore, by \eqref{qb}, for $\lambda=a_m^{n,k}$ and taking $\psi(t)=(1+t)\log(1+t)\in\mathcal F$ we get (i):
\begin{align*}
\int_0^{2\pi} \psi[\log^+|f_\lambda^*(e^{i\theta})|]\, \frac{d\theta}{2\pi}&\leq
\int_0^{2\pi} \psi[ \tilde C+\frac {{C_0}\chi_{I_\lambda}(\theta)}{(1-|\lambda|)\log_2(\frac 1{1-|\lambda|})} ]\, \frac{d\theta}{2\pi}\\
&=\int_{\theta\notin I_\lambda} \psi(\tilde  C) \, \frac{d\theta}{2\pi}
+\int_{I_\lambda}\psi \bigl[\tilde C+\frac {C_0}{(1-|\lambda|)\log_2(\frac 1{1-|\lambda|})}\bigr] \, \frac{d\theta}{2\pi}\\
&\lesssim 1+ (1-|\lambda|) \psi \bigl[\frac {2{C_0}}{(1-|\lambda|)\log_2(\frac 1{1-|\lambda|})}\bigr]\\
&\lesssim 1+\frac {1}{\log_2(\frac 1{1-|\lambda|})}\log_2 \left(\frac {2{C_0}}{(1-|\lambda|)\log_2(\frac 1{1-|\lambda|})}\right)
\lesssim 1\ .
\end{align*}

Let us finish by proving that $\Lambda\notin \Int N^+$. Assume that there is $w\in L^1({\mathbb T})$ satisfying Theorem A (b). Then
\begin{align*}
\frac 1{(1-|a_{n,k}|)\log_2(\frac 1{1-|a_{n,k}|})}&=\log\frac 1{\varrho(a_{n,k}, b_{n,k})}\leq \log\frac 1{|B_{a_{n,k}}(a_{n,k})|}\\
&\leq P[w](a_{n,k})=\int_0^{2\pi}\frac{1-|a_{n,k}|^2}{|a_{n,k}-e^{i\theta}|^2}\; w(\theta)\; \frac{d\theta}{2\pi}\ ,
\end{align*}
and therefore
\[
\sum_{n\geq 1} \sum_{k=0}^{2^n-1}\frac 1{2n}\simeq \sum_{n\geq 1} \sum_{k=0}^{2^n-1}\frac 1{\log_2(\frac 1{1-|a_{n,k}|})}\lesssim
\int_0^{2\pi}\sum_{n,k}\frac{(1-|a_{n,k}|^2)^2}{|a_{n,k}-e^{i\theta}|^2}\; w(\theta)\; \frac{d\theta}{2\pi}\ .
\]
We will have a contradiction as soon as we prove that
\[
\sup\limits_{\theta\in[0,2\pi)}\sum_{n,k}\frac{(1-|a_{n,k}|^2)^2}{|a_{n,k}-e^{i\theta}|^2}<\infty\ .
\]
With no loss of generality assume that $e^{i\theta}=1$ and that the dyadic intervals $I_{n,k}$, $0\leq k<2^n-1$,  are ordered so that $e^{i\theta}\in I_{n,0}$. Then we have
\begin{align*}
|e^{i\theta}-a_{n,k}|^2 &=|1-a_{n,k}|^2\simeq (1-|a_{n,k}|)^2 + |e^{2\pi i k2^{-n}}-1|^2\\
& \simeq (2^{-2n})^2 + (k 2^{-n})^2= 2^{-2n} (2^{-2n}+k^2)\ .
\end{align*}
Since for each $e^{i\theta}$ there is only one $a_{n,k}$ with $1-|a_{n,k}|\simeq |e^{i\theta}-a_{n,k}|$, we have then
\begin{align*}
\sum_{n,k}\frac{(1-|a_{n,k}|^2)^2}{|a_{n,k}-e^{i\theta}|^2}&\simeq
\sum_{n\geq 1} \sum_{k=1}^{2^n-1} \frac{2^{-4n}}{2^{-2n} k^2}\simeq \sum_{n\geq 1} 2^{-2n}\ .
\end{align*}

redpajama_set_name: RedPajamaArXiv