text:
Q: curl in C without libcurl I try tu run curl in C with this  command (without libcurl)
curl -X GET "https://dex.binance.org/api/v1/klines?symbol=&interval=&limit=&startTime=&endTime=
I created this script (in linux mint)
#include <stdlib.h>
int status = system("curl -X GET \"https://dex.binance.org/api/v1/klines?symbol=&interval=&limit=&startTime=&endTime=\"");

when I compile, I get this error:
test.c:3:14: error: initializer element is not constant
    3 | int status = system("curl -X GET \"https://dex.binance.org/api/v1/klines?symbol=&interval=&limit=&startTime=&endTime=\"");
      |              ^~~~~~

Anyone  can explain me  why return this  error?

A: You need a main function in C. This is covered in the first chapter of your C text book.
You probably want something this:
#include <stdlib.h>

int main()
{
   int status = system("curl -X GET \"https://dex.binance.org/api/v1/klines?symbol=&interval=&limit=&startTime=&endTime=\"");
   ...
}


text:
As Theresa May visits Buhari, she must remember Biafra
By Dave O. Umahi | For Biafra Writers
British Prime Minister, Theresa May, is visiting the killing-field called Nigeria – a contraption created by her country. It is no surprise, Britain is in dire straits (leaving the European Union), and so its top civil obligation is to enslave its past colonies even more.
Nigeria is a British creation, created to exploit the resources in the enclave to benefit its people at the detriment of the owners of the land. For this reason, in visiting the accursed contraption they created, she would not care about the terrible faith facing the Indigenous people forced to live together in the contraption, just to get what she wants.
Like many British officials before her therefore, she would not be minding the faith of millions of Biafrans killed in the process of forcing the disparate peoples into Nigeria. Neither will she care about the millions of others that died because of her country's subsequent, obstinate actions to keep the peoples together in the choking union.
READ ALSO: Biafra: IPOB Declares September 14, a Day of General Strike, Mourning and Resistance across all Parts of Biafraland
It is almost certain that Theresa May will pretend not to know that Biafrans have long refused to be part of the forced union. Without any iota of doubt, Mrs. May will negotiate arms sales to the Buhari dictatorship, and will definitely be pretending that she did not know the arms will be used to kill Biafrans.
What about Nnamdi Kanu, the leader of Indigenous People of Biafra (IPOB) and a British citizen? The British government under Mrs. May has betrayed him in the past, so there is every indication that she will not talk about him.
Kanu had committed no offence. The only thing he only did was ask for the independence of Biafra from Nigeria. He legitimately established a radio station in London – Radio Biafra – and was using it to canvass support for a referendum for Biafra. Then he came back to Nigeria going from place to place in Biafraland canvassing for support for Biafra referendum. But the Nigerian government was not happy with the reception he was receiving all over Biafraland as he journeyed to meet the people. So they contrived Operation Python Dance, invaded his home, and "disappeared" him and his parents.
What else is there to say?
The only thing left is to inform the British Prime Minister that things are different with this dispensation of Biafrans. As she is discussing with her chief stooge, the African Hitler of our time, she should know that the only thing that has meaning to Biafrans today is Biafra referendum as Biafrans resolve to leave the accursed contraption her ancestors cobbled together. Perhaps she is in doubt. Then, let her visit Biafraland this September 14, and she will see the resolve of Biafrans as they Sit-At-Home in protest against Buhari's Python Dance, deaths of Biafrans gruesomely murdered by Nigeria security forces and the disappearance of the leader of Indigenous People of Biafra, Nnamdi Kanu and his parents.
PUBLISHED BY THE BIAFRA TIMES
Follow us onTwitter: @thebiafratimes
Like our Facebook page: https://www.facebook.com/thebiafratimes

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: JSON Jquery to Struts2 action I want to send my JSON object from Javscript to Struts2 Action.
Sample JSON Object
  {
        "lists":["list1","list2","list3","list4","list5"],
        "maps": {
            "key4":"value4","key3":"value3","key5":"value5","key2":"value2","key1":"value1"
        },
        "number1":123456789,
        "numberarray1":[1,2,3,4,5,6,7,8,9],
        "string1":"A",
        "stringarray1":["A1","B1"]
    }

My Jquery Ajax
$.ajax({
    type: 'POST',
    url: 'json/JSON.action',
    data: JSON.stringify(data),
    dataType: 'json',
    async: false ,
    contentType: 'application/json; charset=utf-8',
    success: function(){window.alert('Done');}
});

Struts.xml config
<action name="JSON" class="com.actions.json.JsonAction" method="getJSON">
    <result type="json"/>
</action>

My Action Class
public class JsonAction extends ActionSupport {

    private String data;

    public String getJSON() {

        return ActionSupport.SUCCESS;
    }

    public String getData() {
        return data;
    }

    public void setData(String data) {
        this.data = data;
    }

}

My Problem is how to receive the JSON Object in Action Class.
NOTE: POST OF JSON object is successful.. I just don't know how to receive it via Action Class.. PLEASE HELP
Thank you

A: *

*There is a typo in your struts.xml entry

*Have you defined tiles result and interceptor in struts.xml . Please see this link

*The json you are sending to the server, doesn't contain any data key. So it will be always null.
Since json is denoted as objects. You need to convert JSON into Java objects in this way.

Approach 1.
Create setters for lists,maps,number1,numberarray1,string1 and so on. In the top of this link, is defined the way to do it. Then you can access all the variables in this way.
Approach 2.
In your javascript  define a new object.
 var sentData ={};
 sentData ["sentData "] = data;
// And in your ajax call ,
data: JSON.stringify(sentData),

And in your action class, create getters and setters for this.
Map<K.V> sentData = new HashMap<K,V>();

This will give you whole json object as a Map.

redpajama_set_name: RedPajamaStackExchange


text:
Interwalometr jest urządzeniem bądź funkcją niektórych aparatów fotograficznych, pozwalającą automatycznie robić zdjęcia w określonych odstępach czasu. Interwalometru używa się często do wykonywania filmów poklatkowych, zdjęć lotniczych lub archiwizacji zdarzeń rozciągniętych w czasie (np rozrostu kultury bakterii, wzrost roślin).

Budowa aparatu fotograficznego

redpajama_set_name: RedPajamaWikipedia


text:
City Council approves mayor's choice for Department of Investigation
Updated Feb 4, 2014 ; Posted Feb 4, 2014
By Jillian Jorgensen | jorgensen@siadvance.com
debi-floor.JPG
Councilwoman Debi Rose (D-North Shore) speaks during a City Council meeting from her new seat in front of the room.
(Staten Island Advance/Jillian Jorgensen)
CITY HALL - The City Council affirmed Tuesday Mayor Bill de Blasio's pick to lead the Department of Investigation, Mark Peters - who will choose the new NYPD Inspector General.
During a three-hour hearing last week, some Council members raised concerns that Peters, who served as de Blasio's campaign and transition treasurer, was too close to the mayor to be an independent check on him.
But some of those Council members, including Dan Garodnick, who waged a campaign for Speaker against Speaker Melissa Mark-Viverito, said they were won over by Peters' answers.
"These concerns in this case are outweighed by the professionalism and credentials of this candidate," Garodnick said.
Peters is an attorney who has served as senior staff attorney at Children's Rights, Inc.; chief corruption prosecutor at the state attorney general's office; deputy chief of the civil rights bureau in the attorney general's office; and chief of the public integrity unit.
But Garodnick urged Peters to make his own choice for the new position of Inspector General of the NYPD -- an office created by the Council, appointed by the Department of Investigations Commissioner, and designed to provide additional police oversight.
"I strongly urge you to make your own individual choice of the inspector general of the NYPD without any influence of the mayor," Garodnick said. "The mayor has the privilege of choosing you, he has the privilege of choosing the police commissioner. He should not also have the opportunity to pick the inspector general."
During a vote on Peters' affirmation in the Rules, Privileges and Elections Committee before the full Council vote, Councilman Jumaane Williams, one of the authors of the Community Safety Act creating the NYPD inspector general, abstained. He also abstained during the full floor vote.
He said Peters was well qualified, but he was concerned about the precedent of appointing someone so close to the mayor to an oversight position.
"I supported de Blasio, and I think it's a good pick for DOI. But in 12 years you may have a mayor that everybody doesn't like, and he does something similar, and then what?" Williams told reporters.
He said he didn't mind the mayor have some input in the choice of an inspector general.
"I had a little issue with the significant input," Williams said, "trying to see how much input, how much weight he's going to give the mayor as opposed to everybody else."
Councilwoman Inez Dickens voted in favor of Peters, but said she was "leery."
"I am nervous about your closeness to the mayor, and your ability to really separate yourself from your friendship, and your ties, and the fact that you might have to investigate something that comes before you concerning the mayor's office," Ms. Dickens said during the committee vote.
But Speaker Mark-Viverito and Rules Chair Brad Lander said that closeness had been thoroughly vetted by the committee in its hearing.
"I, too, was comfortable at the end of the day with the line of questioning and the answers that were received," Ms. Mark-Viverito, who herself has been knocked for being too close to the mayor, said.
Staten Island Council members Debi Rose (D-North Shore) and Vincent Ignizio (R-South Shore) both serve on the Rules committee and voted in favor of the affirmation in committee, and when it was before the full Council. Councilman Steven Matteo (R-Mid-Island) also voted yes on the Peters appointment when it came to the floor.
"I think he took that issue head-on at the committee level to my satisfaction, and that he will ensure that his objectivity is maintained," Ignizio said of Peters' closeness to the mayor.
The Council also voted to override six vetoes from former Mayor Michael Bloomberg.
Among them were a bill to require the NYPD to post online quarterly hit and run data; the creation of an animal abuse registry that would prevent those convicted of animal abuse from owning or living with an animal; a bill that included technical fixes to the original paid sick time bill passed last year; a bill requiring the NYPD to report to the City Council about crime in parks and playgrounds larger than acre; a bill to create a voluntary master environmental hazard remediation technician registration program; and a bill to roll back FDNY inspection fees for non-profits.
Ignizio and Matteo voted against overriding the paid sick time veto - both do not support the city requiring employers to provide paid sick time.


text:
Background Information for Russia
<Missing Content: countries:rs:info>
Russian Background
Russia's map
Background: Founded in the 12th century, the Principality of Muscovy, was able to emerge from over 200 years of Mongol domination (13th-15th centuries) and to gradually conquer and absorb surrounding principalities. In the early 17th century, a new Romanov Dynasty continued this policy of expansion across Siberia to the Pacific. Under PETER I (ruled 1682-1725), hegemony was extended to the Baltic Sea and the country was renamed the Russian Empire. During the 19th century, more territorial acquisitions were made in Europe and Asia. Defeat in the Russo-Japanese War of 1904-05 contributed to the Revolution of 1905, which resulted in the formation of a parliament and other reforms. Repeated devastating defeats of the Russian army in World War I led to widespread rioting in the major cities of the Russian Empire and to the overthrow in 1917 of the imperial household. The Communists under Vladimir LENIN seized power soon after and formed the USSR. The brutal rule of Iosif STALIN (1928-53) strengthened Communist rule and Russian dominance of the Soviet Union at a cost of tens of millions of lives. The Soviet economy and society stagnated in the following decades until General Secretary Mikhail GORBACHEV (1985-91) introduced glasnost (openness) and perestroika (restructuring) in an attempt to modernize Communism, but his initiatives inadvertently released forces that by December 1991 splintered the USSR into Russia and 14 other independent republics. Since then, Russia has shifted its post-Soviet democratic ambitions in favor of a centralized semi-authoritarian state whose legitimacy is buttressed, in part, by carefully managed national elections, former President PUTIN's genuine popularity, and the prudent management of Russia's windfall energy wealth. Russia has severely disabled a Chechen rebel movement, although violence still occurs throughout the North Caucasus.
Tot: 0.01s; Tpl: 0.002s; cc: 0; qc: 8; dbt: 0.0056s; 1; m:sid w:www (10.17.0.6); sld: 1; ; mem: 545.4kb


text:
Tornado warning in York County: Was the risk really there?
Parts of the Mid-Atlantic reported severe damage from the strong line of storms.
Tornado warning in York County: Was the risk really there? Parts of the Mid-Atlantic reported severe damage from the strong line of storms. Check out this story on ydr.com: https://www.ydr.com/story/news/2019/04/15/tornado-warning-central-pa-severe-weather-good-bet-dynamic-moist-line-storms/3471182002/
Teresa Boeckel, York Daily Record Published 11:55 a.m. ET April 15, 2019 | Updated 1:35 p.m. ET April 15, 2019
Severe Weather Awareness Week is next week. Sunday night's storm was a prime example to kick it off, meteorologist Matt Steinbugl said.
Emergency alerts with a tornado warning popped up on cellphones Sunday evening for many York County residents.
Some hurried to their basements, fearful of what might come.
In the end, a tornado did not materialize for the county, but two tornadoes have been confirmed elsewhere in Pennsylvania. Parts of the Mid-Atlantic also reported severe damage from the strong line of storms. Meteorologists say the danger was present on the radar for the risk of severe weather locally.
More: Wacky weather in central Pa.: 'Graupel' could fall
A storm cell in northern Maryland showed some rotation with a trajectory into and across York County, so it wasn't surprising that the National Weather Service issued the warning, said Eric Horst, director of the Weather Information Center with Millersville University.
An overnight storm with a possible tornado touchdown caused a trail of damage in southern Delaware. A tornado warning had been issued for York County, Pa. on Sunday night. While one did not materialize, meteorologists say the danger was present. (Photo: Image courtesy: Delaware Electric Cooperative)
"Last night's system was very dynamic and moist ... so severe weather was a good bet," he said Monday.
It's also unusual to have a tornado risk occurring during the late evening and overnight hours, said Matt Steinbugl, a meteorologist with the National Weather Service in State College. Severe storms often happen during the afternoon and early evening hours.
But when these severe storms roll in and people are getting ready for bed or are asleep, they are more vulnerable of being in danger, Steinbugl said.
"You can't see the tornado or any approaching wind damage that's coming at you," said Tom Kines, a senior meteorologist with AccuWeather.com.
More: Start planning your next weekend adventure. Knoebels is getting ready to open for summer
More: 2019 prom schedule, pictures for York and Adams county high schools
Radar can pick up on rotation within the clouds, he said. That's what was happening on Sunday night.
"...they can certainly spawn tornadoes," Kines said.
Not all tornadoes show a hook on the radar, Steinbugl said. With the line of storms that moved through, most of the danger was from straight line wind. What can happen, though, is there can be circulation in the storm that spins up a brief tornado.
The National Weather Service sent survey teams out to look at damage in parts of the state. The tornadoes confirmed were in Union and Warren counties.
Some Facebook users wondered why public sirens were not used on Sunday to alert the public to the severe weather warning.
The testing of the Civil Defense sirens ended some time ago, county spokesman Mark Walters said. Emergency responders now receive alerts through digital technology. Many fire companies would not purchase special equipment to make their sirens compatible with the latest technology.
Many apps are available to alert the public of emergencies, he said in an email. The alerts provide details that a siren could not.
Severe Weather Awareness Week is next week, Steinbugl said. The agency will be reminding residents how to prepare for spring and summer hazards.
"This is a prime example to kick this off," he said.
The National Weather Service recommends:
Check the forecast regularly: See if you're at risk for tornadoes.
Sign up for notifications: Know how your community sends warnings.
Create a communications plan: Have a family plan that includes an emergency meeting place and related information. Pick a safe room in your home, such as a basement, storm cellar, or an interior room on the lowest floor with no windows.
Practice your plan: Conduct a family drill regularly so everyone knows what to do if a tornado is approaching.
Prepare your home: Consider having your safe room reinforced. You can find plans for reinforcing an interior room on the Federal Emergency Management Agency website.
Help your neighbor: Encourage your loved ones to prepare. Take CPR training so you can help if someone is hurt.
Storms do damage in Delaware, tornado touches down near Laurel
The Phillips family home on Seaford Road in Laurel suffered some damage from downed trees after the storm. Maddy Lauria
Some of the heaviest storm damage could be found on Seaford Road in Laurel, where crews from multiple agencies and companies worked to clear debris, limbs and downed power lines on Monday. Maddy Lauria/The News Journal
Trees and power lines were down in parts of western Sussex County on Monday after a storm. Maddy Lauria/The News Journal
A DelDOT worker operates a drone to get an aerial view of storm damage on Seaford Road in Laurel. Maddy Lauria/The News Journal
Scott Phillips looks at the aftermath of storm damage that uprooted this tree planted by his parents in the 1940s. Maddy Lauria/The News Journal
Some roads in the Laurel area remained closed hours after a storm swept through the area overnight. Here, Seaford Road is blocked by emergency crews who said that area was among the hardest hit. Maddy Lauria/The News Journal
A building collapsed as the result of a strong band of storms that passed through Sussex County over night on Monday, April 15, 2019. MEGAN RAYMOND/SALISBURY DAILY TIMES
Multiple homes sustained damage on Seaford Rd. in Laurel, Del. after a strong band of storms passed through Sussex County on Monday, 15, 2019. MEGAN RAYMOND/SALISBURY DAILY TIMES
Buildings near Rt. 13 North in Laurel, Del. sustained damage after a strong band of storms passed through Sussex County on Monday, 15, 2019. MEGAN RAYMOND/SALISBURY DAILY TIMES
A building collapsed on the corner of Waller and Firetower Rd. as the result of a strong band of storms that passed through Sussex County over night on Monday, April 15, 2019. MEGAN RAYMOND/SALISBURY DAILY TIMES
Debris along the side of Rt. 13 North in Laurel, Del. after a strong band of storms passed through Sussex County on Monday, 15, 2019. MEGAN RAYMOND/SALISBURY DAILY TIMES
The UTZ facility located on Sussex Hwy. in Laurel, Del. sustained major damage over night due to a strong band of storms that passed through the area on Monday, April 15, 2019. MEGAN RAYMOND/SALISBURY DAILY TIMES
Downed power lines created a hazardous situation on Seaford Rd. in Laurel, Del. after a strong band of storms passed through Sussex County on Monday, 15, 2019. MEGAN RAYMOND/SALISBURY DAILY TIMES
A crop irrigation system sustained damage after a strong band of storms passed through Sussex County overnight on Monday, April 15, 2019. MEGAN RAYMOND/SALISBURY DAILY TIMES
Multiple crews assess the damage on Seaford Rd. after a possible tornado passed through overnight in Laurel, Del. on Monday, 15, 2019. MEGAN RAYMOND/SALISBURY DAILY TIMES
Downed trees, damaged power lines and damage to multiple homes has Seaford Rd. closed off after a possible tornado passed through overnight in Laurel, Del. on Monday, 15, 2019. MEGAN RAYMOND/SALISBURY DAILY TIMES
Crews clear downed trees from power lines on Seaford Rd. in Laurel, Del. after a strong band of storms passed through Sussex County on Monday, 15, 2019. MEGAN RAYMOND/SALISBURY DAILY TIMES
Debris along the side of Seaford Rd. in Laurel, Del. after a strong band of storms passed through Sussex County on Monday, 15, 2019. MEGAN RAYMOND/SALISBURY DAILY TIMES
Debris litters Seaford Rd. in Laurel, Del. after a strong band of storms passed through Sussex County on Monday, 15, 2019. MEGAN RAYMOND/SALISBURY DAILY TIMES
At least one person was injured in a line of severe thunderstorms that hit Sussex County overnight, tearing roofs off houses and damaging up to two dozen buildings. Laurel Fire Department
Sussex County took a beating from overnight storms, leaving this home battered by winds and trees Monday, April 15, 2019. Courtesy of Nathan Reynolds
Storm damage near Seaford Monday, April 15, 2019, after overnight storms. Courtesy Delaware Electric Cooperative
Workers clear a fallen tree on Seaford Road near Laurel on Monday, April 15, 2019. A major storm ripped though parts of Sussex County early Monday, closing roads and causing damage near Laurel. Megan Raymond/Salisbury Daily Times
The roof was torn from part of a Sussex County home in the storm that left trees down and many without power on Monday, April 15, 2019. Courtesy of Nathan Reynolds
Trees and power lines are entangled in Sussex County Monday, April 15, 2019, after an overnight storm. Courtesy of Nathan Reynolds
Delaware Electric Cooperative crews out early Monday, April 15, 2019, restoring power after severe storms overnight. Courtesy Delaware Electric Cooperative
Workers clear a fallen tree on Seaford Road near Laurel on Monday, April 15, 2019. A major storm ripped though parts is Sussex County early Monday closing roads and causing damage near Laurel. Megan Raymond
Delaware Electric Cooperative shared images Monday morning of some of the damage done by overnight storms to the area of Rt. 20 and Baker Mill Road near Seaford. Delaware Electric Cooperative
Overnight storms left a tree downed on tis Newark home. Courtesy Lauren Lavelle
Delaware Electric Cooperative was out early Monday working to restore power to areas hit by storms overnight. They shared this image of damage near Seaford. Delaware Electric Cooperative
Work crews line the shoulder of Seaford Road near Laurel, Delaware, after major storm ripped through the area on Monday, April 15, 2019. Several homes were affected in the area. Staff photo by Rose Velazquez
Trees block Seaford Road near Laurel, Delaware, after major storm ripped through the area on Monday, April 15, 2019. Several homes were affected in the area. Staff photo by Rose Velazquez
Delaware Electric Cooperative early Monday shared this image of downed trees near Seaford. Delaware Electric Cooperative
Read or Share this story: https://www.ydr.com/story/news/2019/04/15/tornado-warning-central-pa-severe-weather-good-bet-dynamic-moist-line-storms/3471182002/
Penn Waste sold to Canada's Waste Connections


Highly important financial lending services are usually enhanced with quality advisory services by developing a perfect opportunity where the clients can easily personalize their advisory services to a level of assuring clients with the best information that will in the end be helpful in making the most informed decisions as regards to finances. It is incredibly true that highly pleasing financial lending companies often create a good platform where persons seeking for loans can conveniently fill personal forms, be connected with an extensive network of lenders and as well be able to access the loan at a very fast rate. In addition, highly appealing online financial lending companies make to it that they employ effective lending methods that will in the end assure quality services at no additional charges making it easier for clients to be satisfied with quality credit cards, small loans and other varied products.
The beauty about the reliable online financial lenders is the truth that they are always willing to serve the clients at any desired moment to a level of assuring twenty-four hour financial services a day in every week resulting to the provision of prompt financial services during emergencies. More so, highly regarded online financial services are comprised of quality data security systems by embracing the latest data encryption systems that will in the end protect the data from being accessed by unscrupulous persons and as well be able to comply with data protection measures. Highly encouraging online financial lenders are often highly educated professionals who reveal commendable credentials as well as a wide range of experience in offering the most improved online financial lending services to an extent of satisfying clients fully.
It is unbelievably true that highly promising financial lending companies are comprised of excellent websites that hold customer-oriented features to enable clients to identify their best financial service options, be able to book appointments and as well get the latest updates. In a nutshell, highly trusted online financial lending companies are licensed by the government to assure legal operations while the obtained accreditation with regulatory institutions assure premium financial lending services that are fully scrutinized.


The Chromax® M5 is the 5th generation Chromax® golf ball. The M5 takes the best features from our popular M1x, O.V. and Distance golf balls rolled into one in 8 colors. The Optimal Visibility Metallic Neon Green Golf Ball is included in the family of colors, with more prominent markings and larger dimples for more distance.
Why Metallic Neon Green Golf Balls? Why Not?
Add some metallic bling to your golf game. Add some flash. Shouldn't your golf balls look as good as your clubs?
© 2018 Chromax Golf | Easy to see metallic neon green golf balls beneficial for all golfers. Helpful for visually impaired, eye site challenged, glaucoma patients, and senior women. USGA tournament approved golf balls. High visibility from patented metallic neon green reflective chrome coatings. Unique gift idea.


We are so excited about the week ahead! After hearing about the i Can Bike program on the radio, my husband, Tony suggested we sign Olivia up to participate. Now, I have to say that there aren't many things that Olivia can't do or won't try, and we usually figure out a way to make modifications so that she can participate in activities that interest her. But, to be honest, I had been trying very hard to accept the fact that independently riding a two-wheeler might not be within our grasp (due in large part to Olivia's balance and coordination issues). Now I'm not so sure! After Tony's suggestion, I went straight to their website and was SO impressed with what I saw there! An 80% success rate sounded pretty promising to me. We filled out an application right away, and Olivia is set to start tomorrow at 11:40.
The i Can Bike program is part of the larger non-profit i Can Shine organization, which "provides quality learning opportunities in recreational activities for individuals with disabilities. By creating an environment where each person is empowered to maximize their individual abilities, everyone can shine!" I can't wait to document our experience here on the Create Possibilities blog. We will be attending 75 minute sessions every day, Monday through Friday this week. I hope you'll check back in to see our progress!


text:
Nat Rev Dis Primers. 2017 Sep 21;3:17067. doi: 10.1038/nrdp.2017.67.
Severe childhood malnutrition.
Bhutta ZA1,2, Berkley JA3,4,5, Bandsma RHJ1,4,6, Kerac M7, Trehan I8,9,10, Briend A11.
Centre for Global Child Health, Hospital for Sick Children, Peter Gilgan Centre for Research &Learning, 686 Bay Street, Toronto, Ontario, M5G 0A4, Canada.
Center of Excellence in Women and Child Health, Aga Khan University, Karachi, Pakistan.
Clinical Research Department, KEMRI/Wellcome Trust Research Programme, Kilifi, Kenya.
The Childhood Acute Illness &Nutrition (CHAIN) Network, Nairobi, Kenya.
Nuffield Department of Medicine, University of Oxford, Oxford, UK.
Department of Biomedical Sciences, College of Medicine, University of Malawi, Blantyre, Malawi.
Department of Population Health, London School of Hygiene &Tropical Medicine, London, UK.
Lao Friends Hospital for Children, Luang Prabang, Laos.
Department of Pediatrics, Washington University in St. Louis, St. Louis, Missouri, USA.
Department of Paediatrics and Child Health, University of Malawi, Blantyre, Malawi.
Department of Nutrition, Exercise and Sports, Faculty of Science, University of Copenhagen, Copenhagen, Denmark.
The main forms of childhood malnutrition occur predominantly in children <5 years of age living in low-income and middle-income countries and include stunting, wasting and kwashiorkor, of which severe wasting and kwashiorkor are commonly referred to as severe acute malnutrition. Here, we use the term 'severe malnutrition' to describe these conditions to better reflect the contributions of chronic poverty, poor living conditions with pervasive deficits in sanitation and hygiene, a high prevalence of infectious diseases and environmental insults, food insecurity, poor maternal and fetal nutritional status and suboptimal nutritional intake in infancy and early childhood. Children with severe malnutrition have an increased risk of serious illness and death, primarily from acute infectious diseases. International growth standards are used for the diagnosis of severe malnutrition and provide therapeutic end points. The early detection of severe wasting and kwashiorkor and outpatient therapy for these conditions using ready-to-use therapeutic foods form the cornerstone of modern therapy, and only a small percentage of children require inpatient care. However, the normalization of physiological and metabolic functions in children with malnutrition is challenging, and children remain at high risk of relapse and death. Further research is urgently needed to improve our understanding of the pathophysiology of severe malnutrition, especially the mechanisms causing kwashiorkor, and to develop new interventions for prevention and treatment.
10.1038/nrdp.2017.67
Publication type, MeSH terms, Grant support
Malnutrition*/diagnosis
Malnutrition*/epidemiology
Malnutrition*/physiopathology
Malnutrition*/therapy
MR/M007367/1/Medical Research Council/United Kingdom
Malnutrition - MedlinePlus Health Information


Friends of Land Air Water is a non-profit organization that cosponsors (along with the student group Land Air Water) the annual Public Interest Environmental Law Conference at University of Oregon School of Law in Eugene, Oregon. Friends of Land Air Water is composed of graduates of the University of Oregon School of Law who are now practicing environmental attorneys in Oregon. Many of the organization's board are former Land Air Water co-directors and PIELC co-directors. Because of their experience, they also provide Land Air Water with a wealth of historical information and institutional memory.
Friends of Land Air Water also operates an annual Public Interest Environmental Law Summer Stipend Program, which awards stipends to law students to work in public interest environmental law positions. Students receiving grants have worked for organizations all over the world, from as nearby as the Klamath-Siskiyou Wildlands Center in Williams OR, to Foundation La Era Agricola in Venezuela, and the United Nations in Geneva, Switzerland.
Friends of Land Air Water can be contacted at PO Box 11501, Eugene, OR 97440.


text:
Angry Robot Books
Trent Jamieson
Website: www.trentjamieson.com
Trent Jamieson is an Australian Fantasy writer, and winner of two Aurealis Awards, whose Death Most Definite series is being published by Orbit and is already attracting rave notices.
Trent has been writing fiction since he can remember, and selling it since the mid-Nineties… quite a long while after he started. He works as a teacher, a bookseller and a writer and has taught at Clarion South where he was described as "the nicest guy in Australian Spec Fic" shattering the reputation he was trying to build as the "Hard Man of the Australian Writing Community". Trent's latest creation takes us to a dying land of decaying clockwork technology that is being devoured by a great rift in reality, the Roil.
Interview with Rowena Cory Daniells (Aug 2011)
Interview with Kickboxing Roosters (Nov 2011)
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How are we already in the peak heat of Summer? In just weeks, our little man will arrive which is a good thing since this big ol' belly is having a hard time bending over to do much in the garden anymore. We have enjoyed what harvest we have gotten though this summer, are learning from what harvest we didn't yield (yet expected we would), and excited to plan for what's to come for each of the garden beds as we move from Summer to Fall.
What a great month to be sharing more on tomatoes, considering my youngest decided she has learned to like them this past month!
Admittedly, homegrown tomatoes are worlds better than those you buy from the store, but even still - last summer she would bite into them, feel them burst, then spit them out while this summer, she has started to pop them in her mouth and gobble them up!
Some days, she still decides she doesn't want them and skips them when offered or spits them out when served as part of our meal. More often then not though, she helps me "find the red ones" in the garden, eating them as we go, and then willingly initiates eating them when I put some of them on her plate.
I hope we can keep this momentum as our homegrown tomato supply dies off to the summer eat (and pesky squirrels!) and we go back to buying them at the store in the off-season!
There are many kids who are obsessed with ketchup and will use it as a dip for nearly anything. Majority of kids will also chow down on pizza or maybe even spaghetti without any wonder of what the red sauce is made of. Offering a fresh, raw tomato to a child rarely goes over as easily as the above options however.
Make your own spaghetti sauce and let them help squeeze the whole tomatoes!
Make your own pico de gallo and let them use a kid-safe knife to help cut the tomatoes!
What other ways could you offer tomatoes to your kiddos this summer?


Last night I had the opportunity (I almost called it a privilege, but that wouldn't be true) to be at a minor league baseball game in Little Rock, Arkansas where MLB-MVP-turned-laughingstock Jose Canseco would continue his boxing "career" against Gary Hogan, a 60-year old assistant athletic director from a local university.
This baseball season has been marked by frequent no-hitters. In lieu of writing a 2000-word post on no-hitters, I've decided to take a more graphical approach, so here's a timeline of all the no-hitters in pro baseball history with some stats and interesting facts.


J. Tellefsen faced 4 batters in the 5th.
V. Gonzales reached on a fielding error by ss (2-2 BKFB).
S. Salomon hit by pitch (2-2 BKFB).
M. Trezza singled to right center (0-0); S. Salomon advanced to second.
H. Jones singled up the middle, RBI (2-2 BSKB); M. Trezza advanced to second; S. Salomon scored.
D. Resendez hit by pitch (2-1 BBF).
M. Dominguez singled through the left side (0-1 K); D. Resendez advanced to second.
Malia Black singled to shortstop (0-1 K).
C. Hughes walked (3-1 BBBKB).
T. Gonzales singled to shortstop (0-0).
A. Young pinch ran for T. Gonzales.
T. Gonzales to 3b for A. Young.
M. Trezza singled up the middle (1-1 BK).
Mala. Black singled up the middle, RBI (2-1 KBB); M. Diamond scored.
M. Dominguez walked (3-0 BBBB).
S. Smith pinch ran for M. Dominguez.
N. Garcia doubled to left field (3-2 BBFBSF); S. Smith advanced to third.
V. Gonzales walked (3-0 BBBB).
A. Perez doubled to right center, 2 RBI (0-2 SF); V. Gonzales advanced to third; N. Garcia scored; S. Smith scored.
B. McElderry pinch ran for A. Perez.
T. Gonzales singled to right field, RBI (1-1 BS); B. McElderry advanced to third; V. Gonzales scored.
S. Saldivar singled to pitcher, bunt (0-0); T. Gonzales advanced to second.
M. Gilgert to p for J. Tellefsen.
A. Perez to c for B. McElderry.
M. Dominguez to ss for S. Smith.
S. Salomon walked (3-1 BBBKB).
S. Reilly doubled to right center, RBI (1-0 B); S. Salomon scored.
M. Leal to p for C. Bentke.
E. Lynch pinch ran for S. Reilly.
E. Lynch advanced to third on a wild pitch.
M. Trezza singled to shortstop, RBI (1-2 BFSF); E. Lynch scored.
S. Reilly to dp for E. Lynch.
M. Dominguez singled to center field (2-2 SBKFFBF).
L. Mitchell pinch hit for H. Swinney.
H. Swinney to lf for L. Mitchell.
Mala. Black singled to left center (3-2 BBBKF).
Malia Black singled through the right side, RBI (1-2 SFB); Mala. Black scored.
C. Hughes doubled to right field, out at third rf to 2b to 3b, RBI (2-1 KBB); Malia Black scored.
S. Torrence to c for H. Jones.
V. Gonzales doubled to center field (0-2 KF).
S. Saldivar homered to right field, 2 RBI (3-2 BKBFB); V. Gonzales scored.
C. Tart hit by pitch (2-1 BKB).
B. Beck to p for M. Gilgert.
D. Resendez hit by pitch (1-0 B); C. Tart advanced to second.
M. Dominguez hit by pitch (3-2 BBKBFF); D. Resendez advanced to second; C. Tart advanced to third.
L. Harris pinch hit for H. Swinney.


text:
\section{A K\"unneth Formula}

This is \cite[Definition~25]{Hartmann2019b}:
\begin{defn}\name{asymptotic product}
\label{defn:asymptoticproduct}
 If $X$ is a metric space and $Y$ a coarsely geodesic coarsely proper metric space fix points $p\in X$ and $q\in Y$ and a constant $R\ge 0$ large enough. Then the \emph{asymptotic product}
$X\ast Y$ of $X$ and $Y$ is defined by
\[
  X\ast Y:=\{(x,y)\in X\times Y: |d(p,x)-d(q,y)|\le R\}
\]
 as a subspace of $X\times Y$. We define the projection $p_1:X\ast Y\to X$ by $(x,y)\mapsto x$ and the projection $p_2:X\ast Y\to Y$ by $(x,y)\mapsto y$. Note that the projections are coarse maps. In what follows we denote by $d(p,\cdot),d(q,\cdot)$ coarse maps $X\to \R_+,Y\to \R_+$ defined by $x\in X\mapsto d(p,x),y\in Y\mapsto d(q,y)$.
\end{defn}

\begin{rem}
Let $X,Y$ be metric spaces of which $Y$ is coarsely geodesic coarsely proper. Now $X\ast Y$ of Definition~\ref{defn:asymptoticproduct} is determined by points $p\in X,q\in Y$ and constant $R\ge 0$. By \cite[Lemma~26]{Hartmann2019b} the space $X\ast Y$ does not depend on the choice of $p,q,R$ up to coarse quivalence. By \cite[Lemma~27]{Hartmann2019b} the diagram
\[
 \xymatrix{
 X\ast Y \ar[d]_{p_1}\ar[r]^{p_2}
 & Y\ar[d]^{d(q,\cdot)}\\
 X\ar[r]_{d(p,\cdot)}
 &\R_+
 }
 \]
 is a pullback diagram in $\coarse$.
\end{rem}

\begin{lem}
\label{lem:asymptoticproductprops}
Let $X,Y$ be metric spaces with $Y$ coarsely geodesic coarsely proper. The following statements hold:
\begin{enumerate}
\item If $A\s X, B\s Y$ are subsets then $(A\times B)\cap (X\ast Y)$ is bounded if $A$ is bounded or $B$ is bounded.
\item If $(U_i)_i$ is a coarse cover of $X$ and $(V_j)_j$ a coarse cover of $Y$ then $((U_i\times V_j)\cap (X\ast Y))_{ij}$ is a coarse cover of $X\ast Y$
\item Let $\sheaff,\sheafg$ be coarse ultrafilters on $X,Y$ respectively with $d(p,\cdot)_*\sheaff\lambda d(q,\cdot)_*\sheafg$. Choose the constant of $X\ast Y$ large enough. Then
\[
\sheaff\ast\sheafg:=\{(A\times B)\cap (X\ast Y):A\in\sheaff,B\in\sheafg\}
\]
is a coarse ultrafilter on $X\ast Y$.
\end{enumerate}
\end{lem}
\begin{proof}
\begin{enumerate}
\item Suppose $A$ is bounded. Then $(x,y)\in A\ast Y$ implies $x\in A$ and $|d(x,p)-d(y,q)|\le R$. Let $S\ge 0$ be such that $A\s B(p,S)$. Then $y\in B(q,R+S)$. Thus $A\ast Y$ is bounded. Similarly if $B$ is bounded then $X\ast B$ is bounded.
\item Let $E\s (X\ast Y)^2$ be an entourage. Then
\f{
\bigcap_{ij} E[(U_i\times V_j)^c\cap (X\ast Y)]
&\s\bigcap_{ij} E[(U_i\times V_j)^c]\cap (X\ast Y)\\
&=\bigcap_{ij} (E[U_i^c\times Y]\cup E[X\times V_j^c])\cap (X\ast Y)\\
&= (\bigcap_i E[U_i^c\times Y]\cap (X\ast Y))\cup (\bigcap_j E[X\times V_j^c]\cap (X\ast Y))
}
is bounded. Thus $((U_i\times V_j)\cap (X\ast Y))_{ij}$ is a coarse cover of $X\ast Y$.

Alternative proof: $(\iip{p_1}{U_i}\cap \iip{p_2}{V_j})_{ij}$.
\item Let $i:X\ast Y\to X\times Y$ be the inclusion. At first we prove
\[
i_*(\sheaff\ast\sheafg)=\{A\times B:A\in\sheaff,B\in\sheafg\}
\]
is a coarse ultrafilter on $X\times Y$. We check the axioms of a coarse ultrafilter on $i_*(\sheaff\ast\sheafg)$:
\begin{enumerate}
\item If $A_1\times B_1,A_2\times B_2\in i_*(\sheaff\ast\sheafg)$ then $A_1,A_2\in\sheaff,B_1,B_2\in\sheafg$. This implies $A_1\close A_2$ in $X$ and $B_1\close B_2$ in $Y$. Then $A_1\times B_1\close A_2\times B_2$ in $X\times Y$.
\item Let $A_1\times B_1,A_2\times B_2\s X\times Y$ be two subsets with $(A_1\times B_1)\cup (A_2\times B_2)\in i_*(\sheaff\ast \sheafg)$. Since $(A_1\cup A_2)\times (B_1\cup B_2)\z (A_1\times B_1)\cup (A_2\times B_2)$ this implies $(A_1\cup A_2)\times (B_1\cup B_2)\in i_*(\sheaff\ast\sheafg)$. Thus $(A_1\cup A_2)\in\sheaff,(B_1\cup B_2)\in\sheafg$. This implies $A_1\in\sheaff$ or $A_2\in\sheaff$. Then $A_1\times (B_1\cup B_2)\in i_*(\sheaff\ast\sheafg)$ or $A_2\times (B_1\cup B_2)\in i_*(\sheaff\ast \sheafg)$. Suppose $A_1\times (B_1\cup B_2)\in i_*(\sheaff\ast \sheafg)$. Since $A_1\times B_1$ is maximal among factors of two subsets of $X,Y$ contained in $A_1\times (B_1\cup B_2),(A_1\times B_1)\cup (A_2\times B_2)\in i_*(\sheaff\ast\sheafg)$ we obtain $A_1\times B_1\in i_*(\sheaff\ast \sheafg)$.
\item $X\times Y\in i_*(\sheaff\ast \sheafg)$ since $X\in\sheaff,Y\in\sheafg$.
\end{enumerate}
Let $A\times B\in i_*(\sheaff\ast\sheafg)$ be an element. Since $d(p,\cdot)_*\sheaff\lambda d(q,\cdot)_*\sheafg$ the sets $d(p,\cdot)(A),d(q,\cdot)(B)$ are close in $\R_+$. Thus there exists an $R\ge 0$ and unbounded subsets $A'\s A,B'\s B$ with
\[
|d(p,a)-d(q,b)|\le R
\]
for $a\in A',b\in B'$. Thus we have shown $A\times B\close X\ast Y$. Choose the constant of $X\ast Y$ large enough then $X\ast Y\in i_*(\sheaff\ast\sheafg)$. We can thus restrict $i_*(\sheaff\ast \sheafg)$ to $X\ast Y$ and obtain $\sheaff\ast \sheafg=(i_*(\sheaff\ast\sheafg))|_{X\ast Y}$. This way we have shown $\sheaff\ast \sheafg$ is a coarse ultrafilter.
\end{enumerate}
\end{proof}

\begin{thm}
Let $X,Y$ be metric spaces with $Y$ coarsely geodesic coarsely proper. Define
 \[
\corona X\ast \corona Y:=\{(\sheaff,\sheafg)\in\corona X\times \corona Y:\corona {d(p,\cdot)}(\sheaff)=\corona {d(q,\cdot)} (\sheafg)\}
\]
Then the map
\[
\langle\corona{p_1},\corona{p_2}\rangle:\corona{X\ast Y}\to\corona X\ast \corona Y
\]
is a homeomorphism.
\end{thm}
\begin{proof}
We prove $\langle\corona{p_1},\corona{p_2}\rangle$ is well defined: Let $\sheaff$ be a coarse ultrafilter on $X\ast Y$ then $p_{1*}\sheaff,p_{2*}\sheaff$ are coarse ultrafilters on $X,Y$, respectively. Since $d(p,\cdot)\circ p_1,d(q,\cdot)\circ p_2$ are close the coarse ultrafilters $d(p,\cdot)_*p_{1*}\sheaff,d(q,\cdot)_*p_{2*}\sheaff$ are asymptotically alike. Thus we have shown $(p_{1*}\sheaff,p_{2*}\sheaff)\in \corona X\ast\corona Y$.

Now we prove $\langle \corona{p_1},\corona{p_2}\rangle$ is surjective: Let $(\sheaff,\sheafg)\in\corona X\ast\corona Y$ be a point. By Lemma~\ref{lem:asymptoticproductprops} the system of subsets $\sheaff\ast\sheafg$ is a coarse ultrafilter on $X\ast Y$. Denote by $p_1':X\times Y\to X,p_2':X\times Y\to Y$ the projection to the first, second factor, respectively and by $i:X\ast Y\to X\times Y$ the inclusion. Then $p_1=p_1'\circ i,p_2=p_2'\circ i$. Since $i_*(\sheaff\ast\sheafg)=\{A\times B:A\in\sheaff,B\in\sheafg\}$ we obtain the relations $p_{1*}'i_*(\sheaff\ast\sheafg)\lambda \sheaff,p_{2*}'i_*(\sheaff\ast\sheafg)\lambda \sheafg$. Thus we have proved $\langle \corona{p_1},\corona{p_2}\rangle (\sheaff\ast\sheafg)=(\sheaff,\sheafg)$.

Now we prove $(\corona{p_1}(\sheaff))\ast(\corona{p_2}(\sheaff))=\sheaff$ for every point $\sheaff\in\corona{X\ast Y}$: Let $A\in\sheaff$ be an element. Then $(p_1(A)\times p_2(A))\cap (X\ast Y)\in (p_{1*}\sheaff)\ast(p_{2*}\sheaff)$. Since $A\s (p_1(A)\times p_2(A))\cap (X\ast Y)$ we obtain $(p_{1*}\sheaff)\ast(p_{2*}\sheaff)\s \sheaff$. Thus $(p_{1*}\sheaff)\ast(p_{2*}\sheaff)\lambda \sheaff$. This way we have shown $\langle \corona{p_1},\corona{p_2}\rangle$ is bijective.

Since $\corona{X\ast Y}$ is compact and $\corona X\ast\corona Y$ is Hausdorff we obtain that $\langle \corona{p_1},\corona{p_2}\rangle$ is a homeomorphism.
\end{proof}

\begin{lem}
Let $X,Y$ be metric spaces. There is a homeomorphism
\f{
\corona X \times \corona Y &\to \corona{X\times Y}\\
(\sheaff,\sheafg)&\mapsto \sheaff\times \sheafg
}
where $\sheaff\times \sheafg:=\{A\times B:A\in \sheaff,B\in\sheafg\}$.
\end{lem}
\begin{proof}
We already showed in the proof of Lemma~\ref{lem:asymptoticproductprops} that $\sheaff\times\sheafg$ is a coarse ultrafilter on $X\times Y$. It remains to show that the map is bijective and continuous.

Let $\sheaff_1,\sheaff_2\in\corona X,\sheafg_1,\sheafg_2 \in \corona Y$ be coarse ultrafilters. Suppose $(\sheaff_1\times \sheafg_1)\lambda (\sheaff_2\times \sheafg_2)$. Let $A\in \sheaff_1,B\in \sheaff_2$ be elements. Then $A\times Y \in \sheaff_1\times\sheafg_1,B\times Y\in\sheaff_2\times \sheafg_2$. Thus $A\times Y\close B\times Y$. This implies $A\close B$ in $X$, thus $\sheaff_1\lambda \sheaff_2$.

Let $\sheaff\in \corona {X\times Y}$ be a coarse ultrafilter. Define
\[
\sheaff_i:=\{p_i(A):A\in\sheaff\}
\]
for $i=1,2$. Here $p_i$ denotes the projection to the $i$th factor. Then $\sheaff_1$ is a coarse ultrafilter on $X$:
\begin{enumerate}
\item If $A,B\in\sheaff_1$ then $A\times Y,B\times Y\in \sheaff$. This implies $A\close B$.
\item If $A,B\s X$ with $A\cup B\in\sheaff_1$ then $(A\cup B)\times Y\in \sheaff$. Thus $A\times Y\in\sheaff$ or $B\times Y\in \sheaff$. Then $A\in \sheaff_1$ or $B\in \sheaff_1$
\item Since $X\times Y\in\sheaff$ the set $X\in\sheaff_1$ is contained.
\end{enumerate}
Since $A\s p_1(A)\times p_2(A)$ we have an inclusion $\sheaff_1\times\sheaff_2\s \sheaff$. Thus $(\sheaff_1\times\sheaff_2)\lambda \sheaff$.

Fix a coarse ultrafilter $\sheafg\in\corona Y$. We show the map
\f{
\corona X &\to \corona {X\times Y}\\
\sheaff&\mapsto \sheaff\times \sheafg
}
is continuous: Let $\pi_1,\pi_2\s \corona X$ be subsets with $(\pi_1\times \sheafg)\notclose (\pi_2\times \sheafg)$. Then there exist subsets $A,B\s X\times Y$ with $\pi_1\times\sheafg\s \closedop A,\pi_2\times \sheafg\s\closedop B$ and $A\notclose B$. Since the left side is a product we can assume $A=A_1\times A_2,B=B_1\times B_2$ also. Then $\pi_1\s \closedop {A_1},\pi_2\s \closedop {B_1}$ with $A_1\notclose B_1$.
\end{proof}

If $X$ is a metric space we associate to $X$ a Grothendieck topology determined by coarse covers. Sheaf cohomology on coarse covers is coined coarse cohomology with twisted coefficients in \cite{Hartmann2017a}. Now coarse covers on $X$ determine the finite open covers on $\corona X$. Thus sheaf cohomology on $\corona X$ equals twisted cohomology on $X$ as a coarse space. We compose a Künneth formula for coarse cohomology with twisted coefficients.

\begin{thm}\name{Künneth formula}
Let $X,Y$ be metric spaces, $\sheaff$ a sheaf on $X$ and $\sheafg$ a sheaf on $Y$. Define a presheaf $\sheaff'$ on $X\times Y$ by
\[
U\mapsto \sheaff(p_1(U)).
\]
Then $\sheaff'$ is a sheaf on $X\times Y$. Similarly we can define a sheaf $\sheafg'$ on $X\times Y$. There is a homomorphism
\[
\bigoplus_{p+q=n}\cohomology p X \sheaff \otimes \cohomology q Y \sheafg \to \cohomology n {X\times Y} {\sheaff'\otimes \sheafg'}
\]
Here $\sheaff'\otimes\sheafg'$ denotes the sheaf associated to the presheaf $U\mapsto \sheaff'(U)\otimes \sheafg'(U)$ for $U\s X\times Y$. If there is a $\sheaff$-acyclic coarse cover $\ucover$ of $X$ and a $\sheafg$-acyclic coarse cover $\vcover$ of $Y$ such that $\check C^q(\vcover,\sheafg)$ is torsion free for every $q$ and $\cohomology p \ucover\sheaff$ is torsion free for every $p$ then the homomorphism is an isomorphism.
\end{thm}
\begin{proof}
There is a \v Cech cohomology version of the Eilenberg-Zilber theorem. If $\ucover,\vcover$ are coarse covers of $X,Y$, respectively then
\[
\ucover\times\vcover:=\{U_i\times V_i:U_i\in\ucover,V_j\in \vcover\}
\]
is a coarse cover of $X\times Y$. Then there is a homomorphism
\[
\bigoplus_{p+q=n}\check C^p(\ucover,\sheaff)\otimes \check C^q(\vcover,\sheafg)
\to \check C^n(\ucover\times \vcover,\sheaff'\otimes\sheafg')
\]
for every $n\ge 0$ which maps $(s_{i_0\cdots i_p})\in\prod\sheaff(U_{i_0}\cap\cdots\cap U_{i_p}),(t_{j_0\cdots j_q})\in\prod\sheafg(V_{j_0}\cap\cdots\cap V_{j_q})$ to $(s_{i_0\cdots i_p}\otimes t_{j_0\cdots j_q})\in \prod(\sheaff'\otimes\sheafg')((U_{i_0}\cap\cdots\cap U_{i_p})\times (V_{j_0}\cap\cdots\cap  V_{j_q})$. This induces an isomorphism of cochain complexes. We can now apply \cite[Section~2.8, Chapter~1]{Shafarevich1996} which gives the desired result in case of acyclic coarse covers. In the other case taking the direct limit over coarse covers gives the desired homomorphism.
\end{proof}

\section{Introduction}

The corona $\corona X$ of a metric space $X$ has been introduced in \cite{Protasov2003} and studied in \cite{Protasov2005},\cite{Protasov2011},\cite{Banakh2013},\cite{Protasov2015},\cite{Grzegrzolka2018a},\cite{Hartmann2019a}.

The Stone-\v Cech compactification is a functor $\beta$ from the category of completely regular spaces to the category of compact Hausdorff spaces. Note that by \cite[Theorem~2.1]{Baladze2018} if $X$ is a completely regular space and $G$ a group then
\[
\hat H^n_F(X;G)=\cohomology n {\beta X} G
\]
The left side denotes $n$-dimensional \v Cech type functional cohomology based on finite open covers and the right side denote $n$-dimensional \v Cech cohomology.

This resembles \cite[Corollary~35]{Hartmann2019a} where sheaf cohomology based on finite coarse covers of a metric space $X$ is related to sheaf cohomology on the corona $\corona X$. This property and other properties which we are going to discuss in this paper suggest that the corona functor is the Stone-\v Cech boundary version of a space in the coarse category.

We start with the first quite elementary property:

\begin{thma}
If $\mcoarse$ denotes the category of metric spaces and coarse maps modulo close and $\topology$ the category of topological spaces and continuous maps then the functor
\[
\nu':\mcoarse\to \topology
\]
is faithful.
\end{thma}

A direct consequence of this result is that $\nu'$ reflects isomorphisms.

We examine in which way the corona functor $\nu'$ is related to the Higson corona $\nu$ of \cite{Roe2003}. Originally the Higson corona has been defined on a proper metric space $X$ as the boundary of the compactification detemined by an algebra of bounded functions called the Higson functions. Already \cite{Protasov2005} showed that there exists a homeomorphism $\nu (X) =\corona X$. We provide an explicit homeomorphism and show $\nu,\nu'$ agree on morphisms too.

\begin{thma}
If $X$ is a proper metric space then there is a homeomorphism
\[
\corona X\to \nu(X).
\]
Here the right side denote the Higson corona of \cite{Roe2003}. If $f:X\to Y$ is a coarse map between proper metric spaces then $\corona f,\nu(f)$ are homeomorphic (the same map pre-and postcomposed by a homeomorphism).
\end{thma}

The asymptotic product of two metric spaces has been introduced in \cite{Hartmann2019b} as the limit of a pullback diagram in the coarse category. Note \cite[Theorem 1]{Foertsch2003} shows the following: If $X,Y$ are hyperbolic coarsely proper coarsely geodesic metric spaces then $X\ast Y$ is hyperbolic coarsely proper coarsely geodesic and therefore its Gromov boundary $\partial (X\ast Y)$ is defined. There is a homeomorphism $\partial(X\ast Y)=\partial (X) \times \partial (Y)$ which is the main result of \cite{Foertsch2003}.

This paper shows if $X,Y$ are metric spaces then there is a homeomorphism $\corona X \times \corona Y=\corona{X\times Y}$. If $Y$ is coarsely geodesic coarsely proper then $\corona{X\ast Y}$ is the pullback of
\[
\xymatrix{
& \corona Y\ar[d]^{\corona {d(\cdot,q)}}\\
\corona X\ar[r]_{\corona{d(\cdot,p)}}
&\corona {\Z_+}
}
\]
Here $p\in X,q\in Y$ denote fixed points. Thus $\nu'$ preserves limits of this type. We obtain a coarse version of a Künneth formula for coarse cohomology with twisted coefficients:

\begin{thma}\name{Künneth formula}
Let $X,Y$ be metric spaces, $\sheaff$ a sheaf on $X$ and $\sheafg$ a sheaf on $Y$. Define a presheaf $\sheaff'$ on $X\times Y$ by
\[
U\mapsto \sheaff(p_1(U)).
\]
Then $\sheaff'$ is a sheaf on $X\times Y$. Similarly we can define a sheaf $\sheafg'$ on $X\times Y$. There is a homomorphism
\[
\bigoplus_{p+q=n}\cohomology p X \sheaff \otimes \cohomology q Y \sheafg \to \cohomology n {X\times Y} {\sheaff'\otimes \sheafg'}
\]
Here $\sheaff'\otimes\sheafg'$ denotes the sheaf associated to the presheaf $U\mapsto \sheaff'(U)\otimes \sheafg'(U)$ for $U\s X\times Y$. If there is a $\sheaff$-acyclic coarse cover $\ucover$ of $X$ and a $\sheafg$-acyclic coarse cover $\vcover$ of $Y$ such that $\check C^q(\vcover,\sheafg)$ is torsion free for every $q$ and $\cohomology p \ucover\sheaff$ is torsion free for every $p$ then the homomorphism is an isomorphism.
\end{thma}

If $X$ is a hyperbolic proper geodesic metric space its Gromov boundary $\partial (X)$ is defined \cite{Benakli2002}. Since every Gromov function is a Higson function the Gromov boundary arises as a quotient of the Higson corona \cite{Roe2003}. We provide an explicit description of the quotient map and the induced topology on $\partial(X)$.

\begin{thma}
Let $X$ be a proper geodesic hyperbolic metric space. The relation $\sheaff\sim\sheafg$ if $\sheaff,\sheafg\in \closedop {\rho(\Z_+)}$ for some coarsely injective coarse map $\rho:\Z_+\to X$ is an equivalence relation on coarse ultrafilters and the mapping
\f{
q_X:\corona X&\to\partial (X)\\
\sheaff&\mapsto [\rho]\;\;\; \sheaff\in\closedop{\rho(\Z_+)}
}
to the Gromov boundary $\partial (X)$ of $X$ is continuous and respects $\sim$. The induced map on the quotient associated to $\sim$ is a homeomorphism.

If $A\s X$ is a subset then
\[
\partial_X A:=\{[\rho]:\rho(\Z_+)\close A\}
\]
is closed in $\partial (X)$. The $((\partial_X A)^c)_{A\s X}$ constitute a basis for the topology on $\partial (X)$.
\end{thma}

This result implies there is a larger class of morphisms in the coarse category for which the Gromov boundary is a functor. Originally coarse equivalences were shown to induce continuous maps between Gromov boundaries. If $f:X\to Y$ is a coarse map between hyperbolic proper geodesic metric spaces with the property that for every coarsely injective coarse map $\rho:\Z_+\to X$ the map $f\circ \rho$ is coarsely injective coarse then $f$ induces a map between Gromov boundaries.

\section{On Morphisms}

\begin{lem}
\label{lem:coarseproximitymaps}
Let $f:X\to Y$ be a map between metric spaces. Then
\begin{enumerate}
\item $f$ is a coarse map if
\begin{itemize}
\item $B\s X$ is bounded then $f(B)$ is bounded.
\item if for every subsets $A,B\s X$ the relation $A\close B$ implies $f(A)\close f(B)$.
\end{itemize}
\item if $f$ is coarse then $f$ is coarsely injective if $A\notclose B$ implies $f(A)\notclose f(B)$.
\item $f$ is coarsely surjective if the relation $f(X)\notclose B$ in $Y$ implies $B$ is bounded.
\end{enumerate}
\end{lem}
\begin{proof}
\begin{enumerate}
\item First we show $f$ is coarsely proper. If $B\s Y$ is bounded then $B\notclose Y$. This implies $\iip f B\notclose X$. Thus $\iip f B$ is bounded.

Now we show $f$ is coarsely uniform: Suppose $A,B\s X$ are two subsets with $f(A)\bar \lambda f(B)$. Then there is an unbounded subset $S\s f(A)$ with $S\notclose f(B)$ or there is an unbounded subset $T\s f(B)$ with $T\notclose f(A)$. Assume the former. Then $\iip f S\notclose B$. Since $f$ maps bounded sets to bounded sets the set $\iip f S\cap A$ is unbounded. Thus $A\bar\lambda B$. Thus we have shown $A\lambda B$ implies $f(A)\lambda f(B)$. By \cite[Theorem~2.3]{Kalantari2016} we can conclude that $f$ is coarsely uniform.
\item This is \cite[Lemma~41]{Hartmann2019a}.
\item easy.
\end{enumerate}
\end{proof}

\begin{thm}
If $f,g:X\to Y$ are two coarse maps between metric spaces and $\corona f=\corona g$ then $f,g$ are close.
\end{thm}
\begin{proof}
Suppose $f,g$ are not close. By \cite[Proposition~2.15]{Kalantari2016} there is a subset $A\s X$ with $f(A)\bar\lambda g(A)$. This implies there is a subset $S\s A$ with $f(S)\notclose g(S)$. Now by \cite[Proposition~4.7]{Grzegrzolka2018a} there is a coarse ultrafilter $\sheaff$ on $X$ with $S\in\sheaff$. Then $f(S)\in f_*\sheaff$ and $g(S)\in g_*\sheaff$. Since $f(S)\notclose g(S)$ this implies $f_*\sheaff\not= g_*\sheaff$. Thus $\corona f,\corona g$ are not the same map.
\end{proof}

\begin{cor}
\label{cor:faithful}
If $\mcoarse$ denotes the category of metric spaces and coarse maps modulo close and $\topology$ the category of topological spaces and continuous maps then the functor
\[
\nu':\mcoarse\to \topology
\]
is faithful.
\end{cor}

\begin{cor}
\label{cor:nureflectsepisandmonos}
The functor $\nu':\mcoarse\to \topology$ reflects epimorphisms and monomorphisms.
\end{cor}
\begin{proof}
It is general theory that a faithful functor reflects epimorphisms and monomorphisms. This fact can also be found in \cite[Exercise~1.6.vii]{Riehl2017}. Since by Corollary~\ref{cor:faithful} the functor $\nu'$ is faithful the result follows.
\end{proof}

\begin{cor}
\label{cor:nureflectsisos}
The functor $\nu':\mcoarse\to \topology$ reflects isomorphisms.
\end{cor}
\begin{proof}
Suppose $f:X\to Y$ is a coarse map between metric spaces such that $\corona f$ is an isomorphism in $\topology$. Then $\corona f$ is both a monomorphism and an epimorphism. The proof of \cite[Theorem~40]{Hartmann2019a} can be generalized to hold for metric spaces. Then the map $f$ is coarsely surjective. By Corollary~\ref{cor:nureflectsepisandmonos} the map $f$ is a monomorphism in $\mcoarse$. By a proof similar to the one of \cite[Proposition~3.A.16]{Cornulier2016} every monomorphism is coarsely injective. Since $f$ is coarsely injective and coarsely surjective it is a coarse equivalence.
\end{proof}

\begin{thm}
If $X$ is a proper metric space then there is a homeomorphism
\[
\corona X\to \nu(X).
\]
Here the right side denote the Higson corona of \cite{Roe2003}. If $f:X\to Y$ is a coarse map between proper metric spaces then $\corona f,\nu(f)$ are homeomorphic (the same map pre-and postcomposed by a homeomorphism).
\end{thm}
\begin{proof}
Let $X$ be a proper metric space. First we show that $h'(X):=X\sqcup \corona X$ is a compactification of $X$: Closed sets on $h'(X)$ are generated by $(\bar A\cup \closedop A)_{A\s X}$. We show this topology is compact: If $(\bar A_i\cup \closedop{A_i})^c_i$ is an open cover of $h'(X)$ then there is a subcover
\[
(\bar A_1 \cup \closedop{A_1})^c_1,\ldots,(\bar A_n\cup \closedop{A_n})^c
\]
such that $\closedop{A_1}^c,\ldots,\closedop{A_n}^c$ is a cover of $\corona X$. Now this implies $A_1^c,\ldots,A_n^c$ are a coarse cover of $X$. Thus $\bar A_1\cap\cdots\cap \bar A_n$ is both bounded and closed. Then there is a subcover
\[
(\bar A_{n+1}\cup\closedop{A_{n+1}})^c,\ldots,(\bar A_{n+m}\cup\closedop{A_{n+m}})^c
\]
of $(\bar A_i\cup \closedop {A_i})^c_i$ such that $\bar A_{n+1}^c,\ldots,\bar A_{n+m}^c$ covers $\bar A_1\cap\cdots\cap \bar A_n$. Then
\[
(\bar A_1\cup\closedop {A_1})^c,\ldots,(\bar A_{n+m}\cup \closedop{A_{n+m}})^c
\]
are a subcover of $(\bar A_i\cup\closedop{A_i})^c_i$ that cover $h'(X)$.

Now $X,\corona X$ both appear as subspaces of $h'(X)$. We show the inclusion $X\to h'(X)$ is dense:
\f{
\bar X^{h'}
&=\bigcap_{\bar A\cup \closedop A\z X}(\bar A\cup \closedop A)\\
&=X\cup \closedop X\\
&=h'(X).
}

The Higson compactification $h(X)$ is determined by the $C^*$-algebra of Higson functions whose definition we now recall from \cite{Roe2003}: A bounded continuous function $\varphi:X\to \R$ is called \emph{Higson} if the function
\f{
d\varphi:X^2 &\to\R\\
 (x,y)&\mapsto \varphi(y)-\varphi(x)
}
when restricted to $E$ vanishes to infinity for every entourage $E\s X^2$.

Note \cite[Proposition~1]{Protasov2005} shows Higson functions on $X$ can be extended to $h'(X)$. For the convenience of the reader we recall it.

Without loss of generality assume that $X$ is $R$-discrete for some $R> 0$. Then every coarse ultrafilter $\sheaff$ on $X$ is determined by an ultrafilter $\sigma$ on $X$ by the proof of \cite[Theorem~17]{Hartmann2019a}. If $\sigma$ is an ultrafilter on $X$ then a bounded continuous function $\varphi:X\to \R$ determines an ultrafilter $\varphi_*\sigma:=\{A:\iip \varphi A\in\sigma\}$ on $\R$. Since the image of $\varphi$ is bounded and therefore relatively compact the ultrafilter $\varphi_*\sigma$ converges to a point $\sigma-\lim \varphi\in\R$.

If two ultrafilters $\sigma,\tau$ induce asymptotically alike coarse ultrafilters and $\varphi$ is a Higson function then $\sigma-\lim \varphi =\tau-\lim \varphi$: Suppose $\sigma-\lim \varphi\not=\tau-\lim \varphi$. Then there exist neighborhoods $U\ni \sigma-\lim \varphi$ and $V\ni \tau-\lim \varphi$ such that $d(U,V)>0$. Let $E\s X^2$ be an entourage. Then
\f{
d\varphi: \iip \varphi U\times \iip \varphi V\cap E&\to \R\\
(x,y)&\to \varphi(y)-\varphi(x)
}
vanishes at infinity. Since $d(U,V)>0$ this implies that $\iip \varphi U\times \iip \varphi V\cap E$ is bounded. Now $E$ was an arbitrary entourage thus $\iip \varphi U,\iip \varphi V$ are coarsely disjoint. Since $\iip \varphi U\in \sigma,\iip \varphi V\in \tau$ the ultrafilters $\sigma,\tau$ induce coarse ultrafilters which are not asymptotically alike.

If $\sheaff$ is a coarse ultrafilter on $X$ induced by an ultrafilter $\sigma$ and $\varphi$ a Higson function then denote by $\sheaff-\lim \varphi$ the point $\sigma-\lim \varphi$ in $\R$. By the above $\sheaff-\lim \varphi$ is well defined modulo asymptotically alike of $\sheaff$.

If $\varphi:X\to \R$ is a Higson function then there is an extension
\begin{align*}
\hat \varphi:h'(X) &\to \R\\
x&\mapsto \begin{cases}
\varphi(x) & x\in X\\
\sheaff-\lim \varphi & x=\sheaff\in\corona X
\end{cases}
\end{align*}
we have shown $\hat \varphi$ is well defined. Now we show $\hat \varphi$ is continuous: Let $A\s \R$ be a closed set. If $\sheaff-\lim \varphi\in A$ fix an ultrafilter $\sigma$ on $X$ that induces $\sheaff$. Then $\iip \varphi A\in \sigma$. This implies $\sheaff\in\closedop{\iip \varphi A}$. On the other hand if $\sheaff\in\closedop{\iip \varphi A}$ then there is an ultrafilter $\sigma$ on $X$ with $\iip \varphi A\in\sigma$ that induces $\sheaff$. This implies $\sigma-\lim \varphi\in A$, thus $\sheaff-\lim \varphi\in A$. Now
\f{
\iip {\hat \varphi} A
&=\iip \varphi A \cup \{\sheaff:\sheaff-\lim \varphi\in A\}\\
&=\iip \varphi A\cup \closedop{\iip \varphi A}
}
is closed.

Denote by $(C_h(X))^{h'}$ the set of extensions of Higson functions on $X$ to $h'(X)$. By \cite{Ball1983} the $C^*$-algebra of Higson functions $C_h(X)$ determines the compactification $h'(X)$ if and only if $(C_h(X))^{h'}$ separates points of $\corona X$.

We show $(C_h(X))^{h'}$ separates points of $\corona X$: Let $\sheaff,\sheafg\in \corona X$ be two coarse ultrafilters with $\sheaff\bar\lambda \sheafg$. Then there exist elements $U\in\sheaff,V\in\sheafg$ with $U\notclose V$. Without loss of generality assume that $U,V$ are disjoint such that $d(x,U)+d(x,V)\not=0$ for every $x\in X$. Then define a function
\f{
\varphi:X&\to \R\\
x&\mapsto \frac{d(x,U)}{d(x,U)+d(x,V)}
}
By \cite[Lemma~2.2]{Dranishnikov1998} the function $d\varphi|_E$ vanishes to infinity for every entourage $E\s X^2$. Now $\varphi|_U\equiv 0$ and $\varphi|_V\equiv 1$. This implies $\sheaff-\lim \varphi=0$ and $\sheafg-\lim \varphi=1$.

If $f:X\to Y$ is a coarse map between $R$-discrete for some $R>0$ proper metric spaces and $\varphi:Y\to \R$ a Higson function then $\varphi\circ f:X\to \R$ is a Higson function: Since $X$ is $R$-discrete the map $f$ is continuous, therefore $\varphi\circ f$ is continuous. The map $\varphi\circ f$ is bounded since $\varphi$ is bounded. Let $E\s X^2$ be an entourage and $\varepsilon>0$ a number. Then $\zzp f E\s Y^2$ is an entourage. This implies $(d\varphi)|_{\zzp f E}$ vanishes at infinity. Thus there is a compact set $K\s Y$ such that
\[
|d(\varphi(x,y)|<\varepsilon
\]
whenever $(x,y)\in \zzp f E\cap (K^2)^c$. Since $K$ is bounded the set $\iip f K\s X$ is bounded. The set $\iip f K$ is finite since $X$ is $R$-discrete and therefore $\iip f K$ is compact. Then
\[
|d(\varphi\circ f)(x,y)|<\varepsilon
\]
whenever $(x,y)\in E\cap (\iip f K)^2$.

Now we provide an explicit homeomorphism $\nu(X)\to \corona X$: Denote by
\f{
e_{C_h(X)}:Z&\to \R^{C_h(X)}\\
x&\mapsto (\varphi(x))_\varphi
}
the evaluation map for $X$.

 Note $e_{C_h(X)}$ is a topological embedding and $\nu(X):=\overline{e_{C_h(X)}(X)}\ohne e_{C_h(X)}(X)$ by \cite{Ball1983}. A point $p\in\nu(X)$ is represented by a net $(x_i)_i$ such that for every Higson function $\varphi\in C_h(X)$ the net $\varphi(x_i)_i$ converges in $\R$. Define $F_i:=\{x_j:j\ge i\}$ for every $i$. Then $\sigma:=\{F_i:i\}$ is a filter on $X$ such that $\varphi_*\sigma$ converges to $\lim_i\varphi(x_i)$ for every Higson function $\varphi$ on $X$. An ultrafilter $\sigma'$ which is finer that $\sigma$ determines a coarse ultrafilter $\sheaff$. We have shown above that the association $\Phi_X:p\mapsto \sheaff$ is well defined modulo asymptotically alike.

Now we show the map $\Phi_X$ is injective: Let $p,q\in \nu(X)$ be two points. If $\Phi_X(p)=\Phi_X(q)$ then $\Phi_X(p)-\lim \varphi=\Phi_X(q)-\lim \varphi$ for every Higson function $\varphi$. This implies $p=q$ in $\R^{C_h(X)}$.

We show $\Phi_X$ is surjective: If $\sigma$ is an ultrafilter on $X$ that determines a coarse ultrafilter on $X$ then there is a net $(x_i)_i$ on $X$ which constitutes a section of $\sigma$. Since $\varphi(x_i)_i$ is a section of $\varphi_*\sigma$ for every Higson function $\varphi$ the net $\varphi(x_i)_i$ converges to $\sigma-\lim \varphi$ in $\R$. Thus $(x_i)_i$ converges to a point in $\nu(X)$.

Now we show $\Phi_X$ is continuous: If $A\s X$ is a subset then $\iip {\Phi_X} {\closedop A}$ is a subset of $\nu(X)$. We show it is closed. If $p\in \iip {\Phi_X} {\closedop A}$ then there is a net $(x_i)_i\s X$ that converges to $p$. The net $(x_i)_i$ is a section of an ultrafilter $\sigma$ with $A\in\sigma$. Thus there exists $i$ with $x_j\in A$ for every $j\ge i$. If on the other hand $(x_i)_i$ is a net in $X$ and there exists $i$ with $x_j\in A$ for every $j\ge i$ then $(x_i)_i$ is a section of an ultrafilter $\sigma$ on $X$ with $A\in \sigma$. This implies if $(x_i)_i$ converges to $p\in\nu(X)$ then $p\in\iip {\Phi_X}{\closedop A}$. Thus we have shown
\[
\iip {\Phi_X} {\closedop A}=\overline{e_{C_h(X)}(A)}\ohne e_{C_h(X)}(A)
\]
is closed. This way we have obtained that $\Phi_X$ is a homeomorphism.

Now we define a map
\f{
f_*:\R^{C_h(X)}&\to \R^{C_h(Y)}\\
(x_\varphi)_{\varphi\in C_h(X)}&\mapsto (x_{\varphi\circ f})_{\varphi\in C_h(Y)}
}
We show $f_*(\overline{e_{C_h(X)}(X)})\s \overline{e_{C_h(Y)}(Y)}$: If $(x_\varphi)_\varphi\in\overline{e_{C_h(X)}(X)}$ then there is a net $(x_i)_i\s X$ such that $\lim_i\varphi(x_i)= x_\varphi$ for every $\varphi\in C_h(X)$. Then $f(x_i)_i\s Y$ is a net such that $\lim_i\varphi(f(x_i)) = x_{\varphi\circ f}$ for every $\varphi\in C_h(Y)$.

Now $\nu(f):=f_*|_{\overline{e_{C_h(X)}(X)}\ohne e_{C_h(X)}(X)}$. Then
\[
\nu(f)=\ii\Phi_Y\circ\corona f\circ \Phi_X.
\]
\end{proof}

\section{Remarks}

\section{An alternative Description of the Gromov Boundary}

\begin{thm}
Let $X$ be a proper geodesic hyperbolic metric space. The relation $\sheaff\sim\sheafg$ if $\sheaff,\sheafg\in \closedop {\rho(\Z_+)}$ for some coarsely injective coarse map $\rho:\Z_+\to X$ is an equivalence relation on coarse ultrafilters and the mapping
\f{
q_X:\corona X&\to\partial (X)\\
\sheaff&\mapsto [\rho]\;\;\; \sheaff\in\closedop{\rho(\Z_+)}
}
to the Gromov boundary $\partial (X)$ of $X$ is continuous and respects $\sim$. The induced map on the quotient associated to $\sim$ is a homeomorphism.

If $A\s X$ is a subset then
\[
\partial_X A:=\{[\rho]:\rho(\Z_+)\close A\}
\]
is closed in $\partial (X)$. The $((\partial_X A)^c)_{A\s X}$ constitute a basis for the topology on $\partial (X)$.
\end{thm}
\begin{proof}
Note the first part is already \cite[Lemma~6.23]{Roe2003} which shows the Gromov boundary appears as a quotient of the Higson corona by using the property that every Gromov function is a Higson function. The second part is already \cite[Theorem~9.10] {Grzegrzolka2018a} which defines a coarse proximity structure on $X$ that induces the Gromov compactification.

Every point $p$ in the Gromov boundary $\partial (X)$ is represented by a coarsely injective coarse map $\rho:\Z_+\to X$: A point in $\partial (X)$ is represented by a geodesic ray $r:\R_+\to X$ as defined in \cite[page~427]{Bridson1999}. By \cite[Lemma~3.1]{Bridson1999} the point $p$ can be represented by a large-scale embedding $\Z_+\to X$. Since $\Z_+,X$ are large-scale geodesic this is the same as a coarsely injective coarse map.

If $\rho,\sigma:\Z_+\to X$ are two coarsely injective coarse maps then either $\rho(\Z_+),\sigma(\Z_+)$ are finite Hausdorff distance apart or $\rho(\Z_+)\notclose\sigma(\Z_+)$: Suppose $\rho(\Z_+)\close\sigma(\Z_+)$. Then there are subsequences $(j_i)_i,(k_i)_i\s \Z_+$ and a constant $R\ge 0$ such that $d(\rho(j_i),\sigma(k_i))\le R$ for every $i$. By \cite[Theorem~6.17]{Roe2003} there exists $S>0$ such that the geodesic joining $\rho(j_i)$ to $\rho(j_{i+1})$ has Hausdorff distance at most $S$ from $\rho(j_i),\rho(j_i+1),\ldots,\rho(j_{i+1})$ and from $\sigma(k_i),\sigma(k_i+1),\ldots,\sigma(k_{i+1})$ for every $i$. Thus we obtain $d(\rho(\Z_+),\sigma(\Z_+))\le 2S$.

By Lemma~\ref{lem:curay} for every coarse ultrafilter $\sheaff$ there exists a coarsely injective coarse map $\rho:\Z_+\to X$ such that $\sheaff\in\closedop {\rho(\Z_+)}$. This implies $\sim $ is an equivalence relation on coarse ultrafilters. Since the equivalence classes are closed the quotient is T1.

We recall \cite[Definition~6.21]{Roe2003}: If $\varphi:X\to \R$ is a continuous function then it is called \emph{Gromov} if for every $\varepsilon>0$ there exists $K>0$ such that $(x|y)_{x_0}>K$ implies $|f(x)-f(y)|<\varepsilon$. We denote by $C_g(X)$ the algebra of Higson functions on $X$.

Now we provide the mapping $q_X$. Note that by \cite[Lemma~6.23]{Roe2003} every Gromov function is a Higson function. Thus there is a mapping
\f{
\Phi_X:\R^{C_h(X)}&\to\R^{C_g(X)}\\
(x_\varphi)_{\varphi\in C_h(X)}&\mapsto(x_\varphi)_{\varphi\in C_g(X)}.
}
Now $\Phi_X(\overline{e_{C_h(X)}(X)}\ohne e_{C_h(X)}(X))\s\overline{e_{C_g(X)}(X)}\ohne e_{C_g(X)}(X)$. In fact this map is surjective. This map associates a net $(x_i)_i$ that is section of a coarse ultrafilter to a net $(x_i)_i$ such that $\lim_i\varphi(x_i)\in\R$ exists for every Gromov function $\varphi$. By \cite[Lemma~6.24]{Roe2003} every such net arises as $\rho(i)_i$ for some coarsely injective coarse map $\rho:\Z_+\to X$. Thus $\rho(i)_i$ is a section of some ultrafilter inducing $\sheaff$ which translates to $\sheaff\in\closedop{\rho(\Z_+)}$. Note the map $q_X$ maps $\sheaff$ to $[\rho]\in\partial (X)$.

Now $q_X$ respects $\sim$ and by the above it induces a continuous bijection $\corona X/\sim\to \partial (X)$.

We show the second part of the theorem: Denote by $q:\corona X\to \corona X/\sim $ the quotient map associated to $\sim$. Then
\f{
\iip q {\closedop A}
&=\{[\sheaff]:\sheaff\in\closedop A\}\\
&=\{\closedop{\rho(\Z_+)}:\sheaff\in\closedop{\rho(\Z_+)},\sheaff\in \closedop A\}\\
&=\{\closedop{\rho(\Z_+)}:\rho(\Z_+)\close A\}.
}
Then $\{[\rho]:\rho(\Z_+)\close A\}$ is closed in $\partial (X)$. The $\partial_X A=\iip {q_X}{\closedop A}$ generate the closed sets of $\partial (X)$.

We define a topology on $gX:=X\cup \partial (X)$ by declaring
\[
(\bar A\cup \partial_X A)^c
\]
as a base. Then $gX$ is compact: Let $(x_i)_i$ be a net in $gX$. If $(x_i)_i\cap X$ contains a bounded and infinite subsequence then there is a limit point $x\in X$ to which a subsequence converges. If this is not the case and $(x_i)_i\cap X$ is infinite then by \cite[Proposition~22]{Hartmann2019b} there exists a coarsely injective coarse map $\rho:\Z_+\to X$ with $\rho(\Z_+)\close ((x_i)_i\cap X)$. Then a subsequence converges to $[\rho]$. If $(x_i)_i\cap X$ is finite then a subnet of $(x_i)_i$ converges to a point in $\partial (X)$ since $\partial (X)$ is compact.

Now $X,\partial (X)$ appear as subspaces of $gX$. Since $\bar X^g=gX$ the space $gX$ is a compactification of $X$.
\end{proof}

\begin{cor}
If $f:X\to Y$ is a coarse map between hyperbolic proper geodesic metric spaces and if for every coarsely injective coarse map $\rho:\Z_+\to X$ the map
\[
f\circ\rho:\Z_+\to Y
\]
is coarsely injective then $f$ induces a continuous map $\partial (f):\partial (X)\to \partial (Y)$.
\end{cor}
\begin{proof}
Compare this result with \cite[Theorem~2.8]{Dydak2016} where a visual large-scale uniform map induces a continuos map between Gromov boundaries.

Note that $\corona f$ maps equivalence classes of $\sim$ in $\corona X$ to equivalence classes of $\sim$ in $\corona Y$. Thus if $\sheaff\sim\sheafg$ in $\corona X$ then $q_Y\circ \corona f(\sheaff)=q_Y\circ \corona f(\sheafg)$. This implies there is a unique continuous map $\tilde f:\partial (X)\to\partial (Y)$ such that the following diagram commutes:
 \[
 \xymatrix{
 \corona X\ar[r]^{\corona f}\ar[d]_{q_X}
 & \corona Y\ar[d]^{q_Y}\\
 \partial (X)\ar[r]_{\tilde f}
 &\partial (Y)
 }
 \]
 Now the map
 \f{
 \partial (f):\partial X&\to \partial Y\\
 [\rho]&\mapsto [f\circ \rho]
 }
 also makes this diagram commute, thus $\partial (f)=\tilde f$ is continuous by uniqueness.
\end{proof}

\section{Space of Rays}

\begin{defn}\name{space of rays}
 Let $Y$ be a compact topological space. As a set the \emph{space of rays} $\digamma(Y)$ of $Y$ is $Y\times \Z_+$. A subset $E\s Y^2$ is an entourage if for every countable subset $((x_k,i_k),(y_k,j_k))_k\s E$ the following properties hold:
 \begin{enumerate}
 \item The set $(i_k,j_k)_k$ is an entourage in $\Z_+$.
 \item If $(i_k)_k\to \infty$ then $(x_k)_k$ and $(y_k)_k$ have the same limit points.
 \end{enumerate}
 This makes $\digamma(Y)$ a coarse space.
\end{defn}

\begin{thm}
 If $f:X\to Y$ is a continuous map between compact topological spaces
 \begin{itemize}
 \item then it induces a coarse map by
 \f{
  \digamma(f):\digamma(X)&\to \digamma(Y)\\
  (x,i)&\mapsto (f(x),i)
}
\item If $f$ is a homeomorphism then $\digamma(f)$ is a coarse equivalence.
\end{itemize}
\end{thm}
\begin{proof}
 \begin{itemize}
\item We show $\digamma(f)$ is coarsely uniform and coarsely proper. First we show $\digamma(f)$ is coarsely uniform: Suppose $((x_i,n_i),(y_i,m_i))_i$ is a countable entourage in $\digamma(X)$ such that $(n_i)_i$ is a strictly monotone sequence in $\Z_+$ and $(x_i)_i$ converges to $x$. Then $(n_i,m_i)_i$ is an entourage in $\Z_+$ and $(y_i)_i$ converges to $x$. Since $f$ is a continuous map $f(x_i)_i$ and $f(y_i)_i$ both converge to $f(x)$. Thus we can conclude that
\[
((f(x_i),n_i),(f(y_i),m_i))_i
\]
is an entourage in $\digamma(Y)$.

Now we show $\digamma(f)$ is coarsely proper: If $B\s \digamma(Y)$ is bounded we can write $B=\bigcup_i B_i\times i$ with $B_i\s Y,i\in\Z_+$ where the number of $i$ that appear is finite. Then
\[
 \iip f B=\bigcup_i \iip f {B_i}\times i
\]
is bounded.
\item if $f$ is a homeomorphism then there is a topological inverse $g:Y\to X$ of $f$. Now $f\circ g=id_Y$ and $g\circ f=id_X$. Then
\f{
\digamma(f)\circ \digamma(g)
&=\digamma(f\circ g)\\
&=\digamma(id_Y)\\
&=id_{\digamma(Y)}
}
and
\f{
\digamma(g)\circ \digamma(f)
&=\digamma(g\circ f)\\
&=\digamma(id_X)\\
&=id_{\digamma(X)}
}
 \end{itemize}
\end{proof}

\begin{cor}
 Denote by $\ktopology$ the category of compact topological spaces and continuous maps and by $\coarse$ denote the category of coarse spaces and coarse maps modulo close. Then $\digamma$ is a functor
 \[
  \digamma:\ktopology\to \coarse
 \]
\end{cor}

\begin{prop}
\label{prop:unit}
Denote by $\sheaff_0$ a coarse ultrafilter on $\Z_+$, the choice is not important. For every $y\in Y$ denote by $i_y$ the inclusion $y\times\Z_+\to \digamma(Y)$. The map
\f{
 \eta_Y:Y&\to \nu'\circ \digamma(Y)\\
 y&\mapsto \corona{i_y}(\sheaff_0)
 }
for every metric space $Y$ defines a natural transformation $\eta:\mathbb{1}_{\ktopology} \to \nu'\circ \digamma$.
\end{prop}
\begin{proof}
 If $f:Y\to Z$ is a continuous map between compact spaces we show the diagram
\[
 \xymatrix{
 Y\ar[r]^f\ar[d]_{\eta_Y}
 & Z\ar[d]^{\eta_Z}\\
 \nu'\circ \digamma(Y)\ar[r]_{\nu'\circ \digamma(f)}
 & \nu'\circ \digamma(Z)
 }
\]
commutes.
down and then right: a point $y\in Y$ is mapped by $\eta_Y$ to $\corona{i_y}(\sheaff_0)$. Then
\f{
\nu'\circ \digamma(f)(\corona{i_y}(\sheaff_0))
&=\digamma(f)_*\circ i_{y*}(\sheaff_0)\\
&=(\digamma(f)\circ i_y)_*(\sheaff_0)\\
&=i_{f(y)*}(\sheaff_0)
}
right and then down: a point $y\in Y$ is mapped by $f$ to $f(y)$. Then
\[
 \eta_Z(f(y))=\corona{i_{f(y)}}(\sheaff_0)
\]
 The map $\eta_Y$ is continuous for every compact space $Y$: Let $(y_i)_i$ be a net in $Y$ that converges to $y$. Then $(\corona{i_{y_i}}(\sheaff_0))_i$ converges in $\eta_Y(Y)$ to $\corona{i_y}(\sheaff_0)$: Let $A\s \nu'\circ \digamma (Y)$ be a set such that $\corona{i_y}(\sheaff_0)\in\closedop A^c$. Thus there is some $B\in\sheaff_0$ such that $y\times B\notclose A$. Now for almost all $i$ the relation $(y_i\times B)\notclose A$ holds, thus $\corona {i_{y_i}}(\sheaff_0)\in\closedop A^c$ for almost all $i$.
\end{proof}

\begin{lem}
\label{lem:curay}
Let $X$ be a coarsely geodesic coarsely proper metric space. If $\sheaff$ is a coarse ultrafilter on $X$ there is a coarsely injective coarse map $\rho:\Z_+\to X$ such that $\sheaff\in \closedop {\rho(\Z_+)}$.
\end{lem}
\begin{proof}
Fix an ultrafilter $\sigma$ on $X$ that induces the coarse ultrafilter $\sheaff$. Suppose $X$ is $R$-discrete and $c$-coarsely geodesic for $R,c>0$. We will determine a sequence $(r_i)_i$ of points in $X$ and a sequence $(V_i)_i$ of subsets of $X$.

Fix a point $x_0\in X$ and define $r_0:=x_0$ and $V_0:=X$. Then define for every $y\in X$ the number $d_0(y)$ to be the minimal length of a $c$-path joining $x_0$ to $y$. We define a relation on points of $X$: $y\le z$ if $d_0(y)\le d_0(z)$ and $y$ lies on a $c$-path of minimal length joining $x_0$ to $z$.

For every $i\in \N$ do: Denote by $C_i:=\{y\in X:d_0(y)=i\}$ and define $W_y:=\{z:y\le z\}\cap V_{i-1}$ for every $y\in C_i\cap V_{i-1}$. Now $V_{i-1}\in \sigma$ and the $W_y$ cover $V_{i-1}$ except for a bounded set. Then there is one $y$ such that $W_y\in \sigma$. Define $V_i:=W_y$ and $r_i:=y$.

Define a map
\f{
\rho:\Z_+&\to X\\
i&\mapsto r_i.
}
Then $\rho$ is a coarsely injective coarse map with $(\rho(\Z_+))\in \sigma$.
\end{proof}

\section{Metric Spaces}

\label{sec:metric}
\begin{defn}
 Let $(X,d)$ be a metric space. Then the \emph{coarse structure associated to $d$} on $X$ consists of those subsets $E\s X^2$ for which
 \[
  \sup_{(x,y)\in E}d(x,y)<\infty.
 \]
 We call an element of the coarse structure \emph{entourage}.  In what follows we assume the metric $d$ to be finite for every $(x,y)\in X^2$.
\end{defn}

\begin{defn}
 A map $f:X\to Y$ between metric spaces is called \emph{coarse} if
 \begin{itemize}
  \item $E\s X^2$ being an entourage implies that $\zzp f E$ is an entourage \emph{(coarsely uniform)};
  \item and if $A\s Y$ is bounded then $\iip f A$ is bounded \emph{(coarsely proper)}.
 \end{itemize}
 Two maps $f,g:X\to Y$ between metric spaces are called \emph{close} if
 \[
 f\times g(\Delta_X)
 \]
 is an entourage in $Y$. Here $\Delta_X$ denotes the diagonal in $X^2$.
\end{defn}

\begin{notat}
 A map $f:X\to Y$ between metric spaces is called
 \begin{itemize}
 \item \emph{coarsely surjective} if there is an entourage $E\s Y^2$ such that
 \[
  E[\im f]=Y;
 \]
 \item \emph{coarsely injective} if for every entourage $F\s Y^2$ the set $\izp f F$ is an entourage in $X$.
\end{itemize}
  Two subsets $A,B\s X$ are called \emph{not coarsely disjoint} if there is an entourage $E\s X^2$ such that the set
  \[
  E[A]\cap E[B]
  \]
  is not bounded. We write $A\close B$ in this case.

  Two subsets $A,B\s X$ are called \emph{asymptotically alike} if there is an entourage $E\s X^2$ such that
  \[
  E[A]=B.
  \]
  We write $A\lambda B$ in this case.
\end{notat}

\begin{rem}
 We study metric spaces up to coarse equivalence. A coarse map $f:X\to Y$ between metric spaces is a \emph{coarse equivalence} if
 \begin{itemize}
  \item There is a coarse map $g:Y\to X$ such that $f\circ g$ is close to $id_Y$ and $g\circ f$ is close to $id_X$.
 \item or equivalently if $f$ is both coarsely injective and coarsely surjective.
 \end{itemize}
\end{rem}

\begin{defn}
A metric space is called \emph{coarsely proper} if it is coarsely eqivalent to a proper metric space. It is called \emph{coarsely geodesic} if it is coarsely equivalent to a geodesic metric space.
\end{defn}

\begin{notat}
If $X$ is a metric space and $U_1,\ldots, U_n\s X$ are subsets then $(U_i)_i$ are said to \emph{coarsely cover} $X$ if for every entourage $E\s X^2$ the set
\[
E[U_1^c]\cap \cdots \cap E[U_n^c]
\]
is bounded.
\end{notat}

\section{The Corona Functor}

\begin{defn}
\label{defn:cu}
If $X$ is a metric space a system $\sheaff$ of subsets of $X$ is called a \emph{coarse ultrafilter} if
\begin{enumerate}
\item $A,B\in \sheaff$ then $A\close B$.
\item $A,B\s X$ are subsets with $A\cup B\in\sheaff$ then $A\in\sheaff$ or $B\in\sheaff$.
\item $X\in\sheaff$.
\end{enumerate}
\end{defn}

\begin{lem}
\label{lem:cucoarsemap}
If $f:X\to Y$ is a coarse map between metric spaces and $\sheaff$ is a coarse ultrafilter on $X$ then
\[
f_*\sheaff:=\{A\s Y:\iip f A\in\sheaff\}
\]
is a coarse ultrafilter on $Y$.
\end{lem}
\begin{proof}
see \cite{Hartmann2019a}.
\end{proof}

\begin{defn}
\label{defn:asymptoticallyalikecu}
We define a relation on coarse ultrafilters on $X$: two coarse ultrafilters $\sheaff,\sheafg$ are \emph{asymptotically alike}, written $A\lambda B$ if for every $A\in \sheaff,B\in \sheafg$:
\[
A\close B.
\]
\end{defn}

\begin{rem}
By \cite{Hartmann2019a} the relation $\lambda$ is an equivalence relation on coarse ultrafilters on $X$. If two coarse ultrafilters $\sheaff,\sheafg$ on $X$ are asymptotically alike and $f:X\to Y$ is a coarse map to a metric space $Y$ then $f_*\sheaff\lambda f_*\sheafg$ on $Y$.
\end{rem}

\begin{defn}
\label{defn:topologyoncu}
Let $X$ be a metric space. Denote by $\nu'(X)$ the set of coarse ultrafilters modulo asymptotically alike on $X$. The relation $\close$ on subsets of $\corona X$ is defined as follows: Define for a subset $A\s X$:
\[
\closedop A=\{[\sheaff]\in\corona X:A\in \sheaff\}
\]
Then $\pi_1\notclose \pi_2$ if and only if there exist subsets $A,B\s X$ such that $A\notclose B$ and $\pi_1\s \closedop A,\pi_2\s\closedop B$.
\end{defn}

\begin{rem}
The relation $\close$ on subsets of $\corona X$ defines a proximity relation on $\corona X$ which induces a compact topology. By \cite{Hartmann2019a} the mapping $f_*$ between coarse ultrafilters induces a continuous map $\corona f$ between the quotients. Thus $\nu'$ is a functor mapping coarse metric spaces to compact topological spaces.

The topology on $\corona X$ is generated by $(\closedop A)^c_{A\s X}$. Coarse covers determine the finite open covers \cite{Hartmann2019a}.
\end{rem}

redpajama_set_name: RedPajamaArXiv


Senior Fellow Eugene Steuerle examines the "gray area" in tax laws--he concludes that the law requires objective standards even when it is approximating subjective goals. Sometimes there are true dilemmas, so that any choice will raise some costs that we would just as soon avoid. An honest recognition of those dilemmas may not so much resolve them as reduce the constant demand that the law be changed continually in an attempt to remove the inevitable tension.
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text:
List of Surviving Boeing B-29 Superfortresses - Notable Individual Aircraft
Notable Individual Aircraft
Bockscar, serial number 44-27297, was a "Silverplate" (atomic bomb carrier) conversion with the 393d Bomb Squadron, 509th Composite Group. On 9 August 1945 it dropped the "Fat Man" plutonium atomic bomb on Nagasaki, Japan. Bocks Car was stored for many years and then was finally flown on 26 September 1961 to the National Museum of the United States Air Force at Wright-Patterson Air Force Base near Dayton, Ohio. It is the featured exhibit upon entry into the Museum's Air Power gallery.
Serial number 44-69972 served in the Korean War and was later used as a radar trainer and ballistic missile target. The airframe was acquired by the United States Aviation Museum for restoration to flight status. After a great deal of work at the Boeing plant in Wichita, Kansas where it was originally built, the aircraft was moved in March 2007 to the Kansas Aviation Museum.
Enola Gay, serial number 44-86292, was another "Silverplate" conversion for the 393rd Bomb Squadron, 509th Composite Group. On 6 August 1945 it dropped the "Little Boy" uranium atomic bomb on Hiroshima, Japan. For many years it was in storage at Paul Garber facility at National Air and Space Museum (NASM), Washington, D.C. It was recently re-assembled after a lengthy restoration and is currently displayed at the Smithsonian's Steven F. Udvar-Hazy Center at Dulles International Airport.
Fertile Myrtle
Bureau number 84029 (Navy P2B-1S), formerly a USAF B-29 45-21787, was later used to carry the Douglas D-558-II Skyrocket research aircraft. It was donated to an aviation museum in Oakland, California in 1984, and then later sold to Kermit Weeks' Fantasy of Flight museum in Polk City, Florida. It is on the US Civil register as N29KW. It was used in the flying sequences of the 1980 Walt Disney movie The Last Flight of Noah's Ark. The forward fuselage has been restored and is on static display at Fantasy of Flight along with the remainder of the unrestored fuselage on the attraction's new storage facility tour.
Fifi, serial number 44-62070, belongs to the Commemorative Air Force and is the only airworthy B-29 in the world at present. Fifi was grounded in 2006 because of problems with all four engines. In 2008, the Commemorative Air Force and the Cavanaugh Flight Museum announced that Fifi would be re-engined, and returned to flight status. On 15 July 2010 talks with the FAA to sign Fifi's Airworthiness Certificate were completed. Fifi took flight in early August 2010 with its new engines and was flown in the CAF AIRSHO air show in October 2010 and is currently available for rides at select airshows.
Haggerty's Hag
Serial number 44-86408 was delivered to USAAF the day the Enola Gay dropped the first atomic weapon on Hiroshima, Japan. It was later used to collect radioactive samples during postwar atomic tests, and is now on display at Hill Air Force Base Museum, Utah.
Serial number 44-62022 is currently on display inside the Pueblo Weisbrod Aircraft Museum and is named in honor of all the crews who fought in the Pacific Theater. A B-29 by that name was piloted by a native of Pueblo, Lt. Robert T. Haver, who gave it his pet name for a younger sister. The original Peachy flew 35 combat missions into enemy territory from Tinian Island in the Marianas islands chain in the central Pacific. This aircraft was donated to the museum in 1976 by the Naval Air Weapons Station China Lake, CA and in 2005 it was moved indoors.
Serial number 44-70016 originally flew with the 330th Bomb Group, 20th Air Force from Guam, now displayed inside Hangar 4 at the Pima Air & Space Museum in Tucson, Arizona.
T-Square-54
Serial number 44-69729 (No. 54) was assigned to the 875th Bomb Squadron, 498th Bomb Group, 73d Bomb Wing and completed thirty-seven bombing missions before it was converted to a KB-29 aerial refueling tanker in June 1949. In 1986 it was removed from the Naval Air Weapons Station China Lake and transported to the Lowry Heritage Museum at Lowry Air Force Base; now Wings Over the Rockies Air and Space Museum. No. 54 went through its initial level of restoration in 1987 with museum volunteers and was readied for Lowry AFB's 50th anniversary and the 40th anniversary of the USAF on 2 October 1987. It was restored to its 1944 markings with the "T Square 54" on its vertical stabilizer. In 1995 the USAF Museum transferred T-Sq-54 to the Museum of Flight in Seattle, Washington. After another level of restoration and change in its markings, it was displayed again 1996.
Sweet Eloise
Serial number 44-70113 also flew with the 73rd Bomb Wing, 20th Air Force. Eloise was decommissioned in 1956 and stored until the Marietta B-29 Association sponsored restoration in 1994 and put it on display at Dobbins ARB, Georgia.
Read more about this topic: List Of Surviving Boeing B-29 Superfortresses
Famous quotes containing the words notable and/or individual:
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Human Computer Interface
Terms related to list of surviving boeing b-29 superfortresses:
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Wikipedia Aircraft (Creative Commons)


text:
Amari Cooper #19 of the Dallas Cowboys runs with the ball in the first quarter of the game against the Philadelphia Eagles at Lincoln Financial Field on January…
Amari Cooper #19 of the Dallas Cowboys runs with the ball in the first quarter of the game against the Philadelphia Eagles at Lincoln Financial Field on January 08, 2022 in Philadelphia, Pennsylvania. (Photo by Mitchell Leff/Getty Images)
Browns make Amari Cooper, Chase Winovich trades official
Posted: Mar 16, 2022 / 04:35 PM EDT
Updated: Mar 16, 2022 / 04:35 PM EDT
Cleveland keeps Walker, Hubbard
BEREA, Ohio (WJW)– The Cleveland Browns officially announced a few transactions on Wednesday.
The Browns received wide receiver Amari Cooper and the 202th overall pick in the 2022 NLF Draft from the Cowboys in exchange for the 155th and 193th overall selections.
"I am really excited about joining the Cleveland Browns. They have a passionate fan base that I can't wait to play in front of. Winning is the goal, that is what it is all about. That's why we play the game. I'm excited to come in, get to work and contribute to winning," Cooper said in a news release.
Baker Mayfield tweets 'thank you' to Cleveland fans
Cleveland also got defensive end Chase Winovich and sent linebacker Mack Wilson to New England.
The Browns agreed to terms with linebacker Anthony Walker Jr. and tackle Chris Hubbard, while adding defensive tackle Taven Bryan and wide receiver Jakeem Grant.
"Last year when we brought in A-Walk, we knew we were getting a smart and productive linebacker. He proved us right in those areas. He also possesses those leadership qualities that you can't have enough of on your team, and we are thrilled to have him back," head coach Kevin Stefanski said.
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Just a couple of unrelated images which I adore. Thanks to Casapinka for the gorgeous Jackie O image - so beautiful and I love this room by Antonia Hutt via Desire to inspire - my favourite colour combo of the moment - pink and blue!!!
I thought of you when I posted that picture. I knew you'd love it.
I love this picture of Jackie O. Grace Kelley wedding pictures are so beautiful too.
I am a great admirer of Antonia Hutt's work. I love the two yellow Chinese vases in the background.
wow! you have been busy! can't wait to see how the shoot goes, i love the pink and blue combo too!
Great photo. I also love the photo of Jackie with John John in the White House nursery. He is pulling on her pearls and she is smiling and looks so happy and beautiful.
Oh I love that photo too! Jackie Kennedy will always forever be the epitome of class!
I just love your Blog! I found you on Domino and go in every morning to check your newest post!I love pink and blue also, and pink and yello.Your photos and posts are wonderful.
Great way to start my day! Thankyou!
Thanks Susan for your lovely comment aboug my blog - I'm so glad you enjoy your visits here!! Stay in touch!!


text:
Wastewater testing for the virus will provide useful information from Redeemer's campus, which is currently open to students, staff and faculty, but not the general public.
While McMaster's research project is tracking COVID-19 via wastewater to support its re-opening plans, collaboration with Redeemer is expected to provide useful information from a campus that is already open to students, faculty and staff, but closed to the general public. The project will provide Redeemer with specific and regular data about the presence of the virus on campus, serving as an early warning system and allowing for the implementation of remedial measures as necessary.
Read the full story on Redeemer University's website
McMaster to significantly increase wastewater testing designed to track COVID-19
Researchers at McMaster University are ramping up a wastewater testing program designed to quickly detect and track COVID-19 in raw sewage which could serve as an early warning sign for current outbreaks and future pandemics.
While existing clinical tests can identify affected individuals with precision, researchers say wastewater testing is a cost-efficient and quick means to identify the virus and can be narrowed down to identify specific neighborhoods and communities.
"We know COVID-19 can be reliably detected in feces of affected individuals including those with mild to no symptoms, which is an area where clinical tests fall short," says Gail Krantzberg, a professor at the W. Booth School of Engineering Practice and Technology, who is working with colleague and wastewater expert Zobia Jawed on the research project.
"A broad wastewater testing system allows us to constantly monitor, test and accurately report on the spread of disease within communities, which would include nursing homes, schools and universities, to address the crucial need not only for the current pandemic but for future outbreaks," she says.
With support from the Ministry of the Environment, Conservation and Parks (MECP), researchers plan to test samples three times a week and report results within 24 hours to public health agencies in a number of municipalities which include the City of Hamilton, Niagara Region, Haldimand County, Norfolk County and Oxford County. Several universities across Ontario are working with the province on the program.
Read More on the Brighter World news page


Dona Castle is – deluxe hotel located in Kollam Town . Kollam, also known as Quilon or Desinganadu, is the place which takes the credit for being the hub of the country's cashew trading and processing industry. Affording an impeccable blend of scenic surrounding, tradition and hospitality, Kollam is often referred to as the dreamland of Kerala. Dona Castle is one of the leading business class hotels in Kollam. However the hotel is equally suited for the leisure travellers. Warm hospitality and elegant services makes your stay in this hotel memorable experience. Dona Castle offers world class amenities and services which a traveller expects from any hotel of this category.
Dining in Hotel Dona Castle Kollam :At Donacastle, we offer a distinctive dining experience, one that served the finest Indian and international cuisines, serving traditional and contemporary favourites. From casual, all-day eateries to formal, fine dining, guests can look forward to a wide selection of delectable dishes and refreshing drinks.
The Hotel Dona Castle is located 75 Kms distance from Thiruvananthapuram International Airport and nearest Railway Station is Kollam Railway Station only 5 Km and Kollam Bus Station is only 1 Km.
Breakfast will be provided in Multi-cuisine Restaurant as per guest plan.
Pick up & Drop to the Station/Airport is charged and the Taxi/Cab is outsourced.


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Serco Group: How Do You Find the Right People to Deliver Superb Public Services?
Find out how this UK public sector organization transformed its HR function by implementing SAP SuccessFactors solutions. Learn how the software helped it put people at the heart of its business strategy to deliver significantly enhanced 21st-century HR-driven experiences for customers, partners, and employees.