Parishioners dealing with extended recuperation experience a sense of loss in many areas. Among them is the loss of independence which includes their ability to drive themselves to church, receive the sacraments, and partake in the fellowship that a true community of people provides. The Convalescent Home Mass Ministry at St. Vincent's seeks to lessen that loss and assist our parishioners in continuing to feel connected to the flock. One Tuesday a month, a priest from our parish visits one of the four convalescent homes in Petaluma, presides at a Mass, and offers Communion to these folks. In addition, a volunteer from the ministry brings the gift of the Eucharist every week to the Convalescent Homes. The ministers offer the sacrament, and the gift of friendship and fellowship to feed the spiritual needs of these parish members. We thank those who give of themselves to this ministry, and offer the opportunity to anyone interested in giving their time and talent to the community in this special way. You may call Carole Giacomini at the church rectory, 762-4278, (leave a message and she will call you back), she will gladly guide you through this call to stewardship.


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Apotheosis magazine handles setbacks this year
Knight Errant Screenshot
This year Apotheosis will be published solely online instead of the traditional magazine.
Connor Rahill, Staff Writer
At the end of almost every school year since 2002, BSM has released the Apotheosis magazine, a collection of artwork created and submitted by students. However, this year, due to the COVID-19 outbreak and Extended Online School (EOS) coming into effect, the magazine will not be produced. Instead, the editorial board will only put the accepted artwork on the BSM Apotheosis website.
This isn't the first year Apotheosis has had to abandon the print publication. In 2014, due to increasing printing costs, Apotheosis cancelled the magazine and created a website to publish submissions. It wasn't until 2018 when English Teacher Ms. Kaia Preus and then art teacher Ms. Nan Onkka took the lead of Apotheosis that the print edition was picked back up. "Only in the past three or so years have we made it a magazine as well as a website… it was only online for a number of years before Ms. Onkka and I came on the scene," Preus said.
The editorial board of Apotheosis consists of student volunteers, and EOS has made it difficult for editors to meet and discuss the future of Apotheosis. With the adjustment to EOS, production of this year's edition has been slightly delayed. "What has been impacted is our ability to dedicate focus to this project when there are so many other things going on," Preus said.
Because of the COVID-19 outbreak, a physical print was clearly not an option this year. The editorial board had to decide to either design and publish a digital magazine or only upload artwork to the website. "Creating a digital spread was too much with online school and the stressors of COVID-19, so we will focus on making a website as we have in past years," Preus said.
At this time, all submissions have been judged and the accepted artwork has been edited. The Apotheosis website is still being developed and is currently in production. "I think it is possible for us to get the website out before the end of the school year, but I'm also trying to have a lot of patience and grace…sometimes, when there is a major pandemic going on…things don't get done or don't get done in the same way, and that is okay," Preus said.
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redpajama_set_name: RedPajamaCommonCrawl


Never stop learning. Continuous professional development feeds your mind, fulfils you and keeps you employed in the best jobs.
I had no clue what to do and just knew I did NOT want to be a teacher. I was probably around 16 when Mum made me do one of those career multi-choice question things and up popped PR as something that might suit. Turns out it was a pretty good match and I decided to study a subject area that has since turned into a bit of a passion for me.
It would be easier to answer how things haven't changed! Digital technology has revolutionised the comm's industry and will continue to do so for the foreseeable future. Smart PR practitioners have grasped the nettle, are retraining and understand that organisations need to tell their brand story in a coherent and compelling way. That job sits squarely with us and complements our skills perfectly.
What's not to be optimistic about? It's a hugely exciting time to be in comm's. After all, change brings opportunity and the industry is crying out for people with digital skills. What's more, as we climb out of recession, businesses are looking for more support. We celebrated five years in business this August and these past twelve months have been our best yet.
Behavioural change is one of the greatest benefits. It requires significant investment in time and resource if you are to properly engage with your audiences and is not something that can be achieved overnight but when you're pushing a message that can change lives (such as something health, education or enterprise-related), there is nothing more rewarding than seeing a campaign successfully come to fruition. Never fails to give me a buzz.
Business acumen, perseverance, honesty and a slight touch of nosiness.
Don't put so much pressure on yourself. Things happen when they do for a reason. You always have choices, even when you feel like you don't.
I'm leading work at the CIPR on the gender pay gap (research shows there is an average salary discrepancy between men and women practitioners of £12k). As a female dominated industry, we need to find a way to lead on this issue and become an exemplar for other industries.
Lethargy is something that concerns me. In the past we have collectively been slow to react to the changing world around us – and that is a criticism of our sector bodies as well as us as individuals. We need to start looking more at the bigger picture and not just focus on the day to day. We also need to shout louder as we work in a worthy industry and we have a clear role in helping organisations to achieve commercial success.
Maggie Gyllenhaal for sure. Although some of my mates would be shouting Kristen Wiig right now as they think we look like each other #winning.
Have a few but today I'm going with High Fidelity. I'm a big John Cusack fan.


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Parents outraged over sexual assault on minor
Hundreds of outraged parents Thursday stormed into a private school here, protesting against the alleged sexual assault on a six-year-old student by two teachers during school hours.
"We have detained the accused for interrogation after a complaint was filed against them Wednesday on the incident, which is reported to have occurred July 2," deputy commissioner of police (east) Satish Kumar told IANS here.
Though the victim told her parents and teachers July 9 that she was physically abused by the sports teacher and physical instructor in the school premises, the Vibgyor High School authorities failed to act against the accused and tried to hush up the incident.
"The incident came to light Tuesday after the parents brought it to our notice. We registered the case under section 376 of the Indian Penal Code on their complaint...," Kumar said.
Seeking stringent action against the accused, protesting parents sought security for their children studying in the school where the tuition fee alone is Rs.1.5 lakh a year.
"We have told the school management to file a separate complaint with the police against the accused so that the case could be investigated properly and the guilty punished," said Nandish Reddy, the parent of a student.
Incidentally, Reddy is a former BJP lawmaker from the K.R. Puram assembly segment in the city's eastern suburb.
Earlier, the agitated parents and guardians of the wards stormed into the school premises after pulling down the gate and smashing the window glass panes of the building after they were denied entry to meet the school management.
"We are not shielding the accused. We are cooperating with police in the case," school chairman Rustom Kerawalla told reporters.
"We have also handed over the CCTV footage of the class room to the investigation officer. If they are found guilty, they should be hanged."
According to the parents, the accused committed the crime when the child was alone in the class room.
"We have also learnt that the two instructors are not employees of the school but are working on contract. They have been hired without any background check or profiling of their conduct," said another parent.
The school remained shut Thursday in view of the protest by parents and guardians. - IANS


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'Suicide Squad': Most disappointing movie of summer. Maybe of all time.
The joke's on us.
By Jeff Sneider on August 3, 2016
What are we -- some kind of ... 'suicide squad'? Credit: Clay Enos
> Entertainment > Movies
Last summer, Warner Bros. released the first trailer for Suicide Squad, driven by a creepy cover of the Bee Gees song "I Started a Joke." With the would-be savior of the DCU blasting into theaters a line from the song is all too appropriate: "Oh if I'd only seen that the joke was on me."
Arriving amid a flurry of Sno-cone-colored hype -- much of it mistakenly centered around Jared Leto's cranked-to-11 performance as the Joker -- Suicide Squad follows "the worst of the worst."
Unfortunately, that term applies more to director David Ayer's appalling screenplay than its motley crew of semi-charming antiheroes.
SEE ALSO: 17 infuriating, logic-defying plot holes in 'Batman v Superman'
Leading the way are Will Smith's hitman-with-a-conscience Deadshot and Margot Robbie's demented ex-shrink Harley Quinn, both of whom are doing hard time at Belle Reve, a beyond-maximum security prison facility containing a handful of metahuman criminals including the fiery-yet-remorseful El Diablo (Jay Hernandez) and a BET-loving cannibalistic creature named Killer Croc (Adewale Akinnuoye-Agbaje).
Killer Croc is hangry. Credit: Clay Enos
This fearsome foursome, along with poster-boy soldier Rick Flag (Joel Kinnaman), his soul-sucking sword-wielding bodyguard Katana (Karen Fukuhara), Australian thief Captain Boomerang (Jai Courtney) and "a man who can climb anything" named Slipknot (Adam Beach), are called upon by den mother/bad mutha Amanda Waller (Viola Davis) to stop a terrorist threat that has laid siege to Midway City in exchange for the half-hearted promise of freedom.
If it sounds like Escape From New York, that's because it is, but with a star-studded ensemble filling Kurt Russell's Snake Plissken boots. That dastardly threat is the evil Enchantress, an ancient witchy woman who possesses the body of young archaeologist June Moone (Cara Delevingne) and sets out to create an army of what appear to be ashy rock zombies so she can build a machine that will destroy all of mankind -- which, in her expert opinion, must pay the ultimate price for coming to worship machines more than gods.
I'll never telllllll Credit:
Waller keeps the Enchantress' heart in a briefcase (because she's bad-ass like that!) and stabs it whenever she wants Enchantress to stop enchanting and just be June, who happens to be sleeping with Flag. Oh, and Enchantress has a bad-CGI brother named Incubus (I only know his name thanks to Twitter) who has lava-like tentacles.
Are you sensing how ridiculous all of this sounds?
At least things are rough from the start, so it doesn't feel like Ayer pulls the rug out from under you with a lousy third act -- though make no mistake, the third act is lousy. The director uses the film's first few minutes to introduce his main characters with a barrage of on-the-nose music cues that are apparently supposed to double as character development.
There are more than 20 songs on the soundtrack and the first half of the film plays like a medley of music videos. At one point, Waller sends the Squad on a mission to save a HVT -- a high value target, because Ayer loves military-speak -- and it turns out to be Waller herself. As soon as she's saved, she promptly kills a bunch of co-workers (the same average, innocent citizens she's trying to protect in the first place) because they aren't "cleared" to know the Squad even exists.
Will Smith's movie star status, not in danger here. Credit: Clay Enos
Ayer wants to have his cake and eat it too, but this action makes little sense within the context of the movie. If Ayer gets anything right here, it's the casting: Smith makes it out of Suicide Squad alive, delivering a fairly strong and sympathetic portrait of a father who will do whatever it takes to see his little girl.
Robbie doesn't fare quite as well, for as transfixing as she is as the ever-unpredictable Harley Quinn, her performance rings hollow at times and her exaggerated Brooklyn accent grows irksome. That brings us to Jared Leto's turn as the Joker, which amounts to an extended cameo that barely gives the Oscar-winner a chance to put his stamp on the character.
The performance he does give is dialed way up, though Leto excels during the Joker's quieter moments. It's actually laughable how Leto has been front-and-center throughout this year-long publicity campaign, but kudos to the Warners team for realizing early on that they had little else to sell.
Hernandez gets the closest thing to an arc in the movie as El Diablo, who is cursed with more than just a hot temper. He almost steals the picture -- but he's not an A-list actor, so his character isn't given enough time to pull off the heist.
It burns! Credit:
The generally under-appreciated Akinnuoye-Agbaje stands out as the well-designed Killer Croc, though you can expect to hear plenty about his "BET" line near the end of the film.
Delevingne does herself no favors whether she's playing an archaeologist (ha!) trapped in a ho-hum romance with Flag, or Enchantress, the god-awful "villain" of this movie. How ironic that a movie about a group of villains suffers from the very lack of a good villain.
Courtney barely makes an impression in his latest disappointing studio film, though he can take solace in the fact that he isn't disposable like Slipknot, who doesn't even merit his own introduction before Waller and Flag wring his selfish neck. But hey, someone had to take the fall to prove that the threat was real.
Meanwhile, Common and Scott Eastwood are treated like walking, talking props -- and let's not forget Fukuhara, whose character isn't given much to do and whose face is mostly obscured by a completely unnecessary mask. Ben Affleck returns for a cameo as Batman, seemingly only to have an excuse to kiss Harley Quinn ... errr, save her life with CPR (after punching her in the face underwater).
NEW YORK, NY - AUGUST 01: Director David Ayer attends the "Suicide Squad" World Premiere at The Beacon Theatre on August 1, 2016 in New York City. (Photo by Jamie McCarthy/Getty Images) Credit: Getty Images
The elephant in the room is Ayer, who's the right guy at the wrong place at the wrong time. He seemed like a good choice on paper despite the fact that his resume never exactly screamed Comic Book Movie. Suicide Squad works overtime to have a sense of humor, but Ayer has a dark sensibility and can't have it both ways. The film wants to be gritty, but instead it's just goofy.
Suicide Squad is hamstrung by its PG-13 rating, a noticeable limitation that Marvel's Deadpool didn't have, and not only is the film poorly structured (too many flashbacks, montages and whiplashing twists) and edited, but the storytelling itself is inept. You can bet that Ayer will no doubt be hyping a Director's Cut version of this in the coming months, because you can practically see the editing room battles on the screen.
It's well known that the film underwent extensive reshoots, but you can see studio executives' fingerprints all over this movie. Everyone at Warners is under pressure for the film to deliver, and while it is poised to open huge this weekend, there's no telling what the true cost of the movie is. Not only was "Suicide Squad" supposed to save a DCU in utter free-fall, but it was supposed to save the summer for Hollywood, which has apparently forgotten how to make blockbusters.
This year has been particularly insulting between Batman v Superman: Dawn of Justice, Independence Day: Resurgence, Alice Through the Looking Glass, Warcraft, The Huntsman: Winter's War, The Legend of Tarzan and now Suicide Squad, all of which boast a Rotten Tomatoes score below 36.
It's clear that the made-by-committee approach to tentpoles just isn't working as well as it used to, if it ever worked in the first place.
To call Suicide Squad a disappointment would be an affront to your intelligence. It may in fact be the most disappointing movie of all time. It could go down as The Disappointment. I don't know if WB's marketing and publicity executives deserve a raise or if its DCU brain trust should be fed to Killer Croc.
Who is going to step up and take responsibility for this CGI nonsense? It was supposed to be the movie that signaled WB/DC could do something outside of their typical comic book movie formula, but instead it falls victim to that very formula, robbing the unique premise of any originality. Even the mid-credits tag is poorly conceived.
Not since the first Star Wars prequel has a film hit theaters with such high expectations and failed to deliver on even a fraction of that potential. At this point, the future of the DCU remains unclear, but what is clear is that this one isn't on Zack Snyder.
It appears that saving the DCU is a job that calls for Wonder Woman and the rest of the Justice League, because Suicide Squad simply puts the "bad" in "bad-ass."
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Leah has been covering the unfolding drama at the Consumer Financial Protection Bureau, a powerful and shockingly unaccountable agency designed by Elizabeth Warren created by Democrats' Dodd-Frank bill. Its longtime director -- who, finally, was legitimately confirmed in 2013 after President Obama's unconstitutional and unanimously-overruled 2012 recess appointment -- resigned from the CFPB late last week, ahead of an expected gubernatorial run in Ohio.
Some legal questions are tough. The question of who should lawfully be considered the acting director of the Consumer Financial Protection Bureau is not one of them. President Trump unquestionably has the power to name Mick Mulvaney (his Senate-confirmed budget director) to the position, and he has done so. The lawsuit seeking to block this appointment, filed by the CFPB's deputy director Leandra English — who hopes to take the job herself — is frivolous and offensive...Cordray was quite explicitly attempting to ensure that he, rather than the president, would choose his successor. Under the aforementioned CFPB statute, the deputy director serves as the director "in the absence or unavailability of the director." Cordray was paving the way for English to argue that his resignation as director creates an "absence or unavailability" that makes her the director as a matter of law.
Interestingly, English is being represented by private counsel. According to Reuters, CFPB general counsel Mary McLeod, who was appointed by Cordray in 2015, thinks the Trump administration has the stronger legal claim and has written a memo to this effect.
Got that? CFPB's own lawyer is siding with the Trump administration in this fight, which is why Ms. English was reduced to obtaining outside counsel in her lawsuit. Mary McLeod was hand-selected by the recently-departed, aggressively 'left-wing' director, who heaped praise upon her "tested judgment" and "wealth of experience" in 2015. The law is pretty clear in this case, yet many Leftists are latching onto this quixotic stunt as their latest means of signaling hair-on-fire "resistance" to the Trump presidency. They frequently lament how the president's actions are "NOT NORMAL!" and shouldn't be treated as such. Well, attempting to usurp the president's statutory power to fill executive vacancies is not normal.
I wonder if the folks trying to block Mulvaney's designation as Acting CFPB Director realize that this episode actually *highlights* why the Supreme Court should hold the CFPB's structure unconstitutional, as the DC Circuit panel did in PHH v. CFPB.
The people defending this scheme look very silly.


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Water and Food Security
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- Country -AlgeriaBahrainComorosDjiboutiEgyptIraqJordanKuwaitLebanonLibyaMauritaniaMoroccoOmanPalestineQatarSaudi ArabiaSomaliaSudanSyriaTunisiaUnited Arab EmiratesYemen
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- Topic -Banking and FinanceEnvironmentGovernanceICTYouthHealthDemographyEducationEnergyGenderLabor and EmploymentMacroeconomyPovertyWater and Food SecurityTrade
Arab Region's Youth in Figures
The United Arab Emirates, Qatar and Saudi Arabia ranked the highest at the regional level at 27, 30 and 39, respectively, and out of 140 economies. Read More
All countries from WHO's Eastern Mediterranean Region (which contains all Arab countries except Algeria, Mauritania and Comoros) collectively approved the UHC2030 Global Compact. Read More
The percentage of individuals (% of total population) using the internet in the Arab region
The percentage of individuals (% of total population) using the internet in the Arab region has more than doubled in 2018 at 54.7% in 2018 up from 24% in 2010. Read More
Multidimensional Poverty
In 2013, 40% (9.8 million people) of the population were multi-dimensionally poor, while an additional 22.4% (around 5.5 million) lived near multidimensional poverty.Read More
Crude Oil Export
The country relies heavily on its large oil and natural gas resources to support its economy and is considered a major oil producer and exporter. In 2016, UAE produced 1.1 billion barrels of crude oil up from 693.6 million barrels in 2002. In addition, the UAE exported 2.41 million barrel per day of crude oil in 2016.Read More
Trade and economic integration have played significant roles in Tunisia's economic development. In 2016, trade of goods and services reached 90% of Tunisia's GDP.Read More
The spread and amplification of Syria's armed conflict have led to a humanitarian crisis with 6.5 million internally displaced persons and 4.8 million refugees by the end of 2015, according to the United Nations High Commissioner for Refugees (UNHCR).Read More
The majority of Sudan's population is rural, with an urban population of just 34% in 2016.Read More
The under-five years and maternal mortality rates in Somalia are amongst the highest in the world; one out of every seven Somali children dies before reaching 5 years old and the maternal mortality rate was 732 deaths per 100,000 live births in 2015 down from 1080 per 100,000 live births in 2000.Read More
The country is the largest exporter of total petroleum liquids in the world and one of the World's largest producers of crude oil, producing 3.6 billion barrels in (2017).Read More
Cash Surplus
The cash balance recorded a surplus of 16% of GDP in 2015, up from 14.2% of GDP in 2014, coupled with a slight decrease in Government revenues by 1.8% between 2014 and 2015, and a drop in expenditures by 10.3% over the same period.Read More
Improved Water
Palestinians continue to face severe water shortages with the decline in access to improved water sources to 58.4% in 2015, down from 90.9% in 2000.Read More
Primary Enrollment Rate
The gross primary enrollment rate grew up to 110% in 2015, from 93.4% in 2000; at the primary level, the Gender Parity has been achieved.Read More
Tertiary Enrollment
The tertiary enrollment noticeably increased from 10.2% in 2000 to 28.14% in 2015.Read More
Cash Deficit
The inflation rate remained relatively low at 3.5% in 2014 but declined to 0.5 in 2015 and the cash deficit shrunk from MRO minus 53.8 billion in 2013 to MRO minus 24.74 billion in 2014.Read More
In Libya, like other Arab countries, it is the women who are severely affected by unemployment. Women unemployment rate more than doubled in recent years, where it rose from 11.3% in 2010 to 24.7% in 2018.Read More
The health system is quite developed with a high life expectancy of 79.5 years in 2015 and low levels of maternal mortality and infant mortality, reaching 15 per 100,000 and 7.1 per 1,000, respectively.Read More
Trade has always had a significant weight in Kuwait's economy, with international trade-to-GDP ratio moderately increasing over the last fifteen years from 86.6% in 2000 to 95% in 2016.Read More
Adult Literacy Rate
Jordan recorded the highest adult literacy rate among the Arab countries in 2012, averaging at 98%.Read More
The tertiary gross enrollment ratio in Iraq has been on the rise since 2006, it reached 19.4% in 2015.Read More
Egypt is the most populous country among Arab countries with a population of 91.5 million in 2015, growing at an annual rate of 2%. The population is dense around the Nile basin with a global population density of 92 inhabitants per square kilometer in 2015 up from 69 inhabitants per square kilometer in 2000. The Egyptian population is young with almost 77% of its population below 30 years.Read More
The majority of the population in Djibouti is urban, with 77% of the total population living in urban areas in 2015.Read More
Comoros is one of the least populous countries in the world with a population of 788,000 in 2015, growing at an average annual rate of 2.4% since 2000. However, it is densely populated, its density increased from 284 inhabitants per square kilometer in 2000 to 404 inhabitant per square kilometer in 2014.Read More
The overall unemployment rate in Bahrain reached 1.3% in n 2018.Read More
education attainment in Algeria has been on the rise, resulting in a 37% tertiary gross enrollment ratio in 2015. Read More
Lack of public expenditure on the healthcare system in middle-income and poor countries is one of the main problems facing the healthcare sector.Read More
Banks in the Arab Region
More than 330 Arab banking and financial institutions operate in the Arab region today.Read More
Forest Area in the Arab Region
Comoros scored the highest % of forest area of the total land area (2015).Read More
Energy Consumption Per Capita in GCC Countries
GCC countries scored the highest energy consumption per capita in the Arab region. Read More
Copyright © United Nations Development Programme


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IELTS Fever
The Table Below Shows Information About Age, Average Income per Person and Population Below the Poverty Line
The table below shows information about age, average income per person and population below the poverty line in three states in the USA. Summarise the information by selecting and reporting the main features and make comparisons where relevant.
The table illustrates the details of four categories: aged under 18, over 60, average income per person, calculated in dollars and the population below the poverty line in three states, California, Utah and Florida in the United States.
Overall, In the case of people, the percentage for age under 18, Utah has the highest proportion, which is 28%, comparatively California and Florida have less in portion, 17% and 6%, respectively. Whereas in the case of aged people over 60 years, Florida got 23% which is considerably above the other states.
Indeed, California has the highest average income per person, which is 23000$, slightly above that of Florida's income which is 22000$ and considerably higher than Utah, which is only 17000$ per person average income.
Unlike the above details, the population below the poverty line makes a huge difference in that California has the highest per cent of 16 despite its average income. At the same time, in Florida, only 12% of the population is under the poverty line. Furthermore, it can be seen that Utah has the least per cent in this case, with only 9% of people under the poverty line.
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The Table Below Shows the Proportion of Different Categories of Families Living
In "ACADEMIC WRITING TASK 1"
The Table Below Shows the Proportion of Different Categories of Families Living in Poverty
IELTSFever FREE Online Mock Test Day 492 Recent IELTS Exam Tests
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Are Dabs, or hash oil, or wax illegal?
On behalf of Yeretsian Law posted in blog on Monday, April 16, 2018.
Dabs, BHO and wax, hashish and shatter are just some names for concentrated cannabis. These are the extracted resin from the cannabis plant and can be inhaled many ways including vaping.
Can you be convicted of a crime you didn't know about?
On behalf of Yeretsian Law on Monday, April 2, 2018.
When it comes to corporate operations the president or chief officer can be convicted of a crime he or she did not commit or even know about based on precedence.


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The Kimberley Diamond Cup was an annual skateboarding event held at the beginning of each Southern Hemisphere Spring in Kimberley, South Africa. The event featured the largest single-event prize purse in skateboarding - $100,000 for first prize in the Street competition - and is the largest skateboarding competition in Africa.

The 2015 Kimberley Diamond Cup featured skaters from more than 50 countries. In the Street World Championships final, Nyjah Huston of the U.S. edged out Luan Oliveira of Brazil to capture the $100,000 first prize.

The 2014 Kimberley Diamond Cup Skateboarding World Championships featured skaters from 37 countries. Kelvin Hoefler from Brazil placed first in the Street competition. Fellow competitor Nyjah Huston, generally regarded as "the best contest street skateboarder in the world", won the Street Competition in 2013.

Kimberley Diamond Cup championships were webcast worldwide. SuperSport, the leading sports provider in South Africa, broadcasts the event.

The Kimberley Diamond Cup replaced the Maloof Money Cup, a skateboarding event held in South Africa in 2011 and 2012.

Background

In 2013, the Kimberley Diamond Cup World Skateboarding Championships replaced the Maloof Money Cup World Championships, previously held in South Africa in 2011 and 2012.

The 2013 skateboarding competition was held from September 27–29 at the Kumba Skate Plaza in Kimberley, capital of the Northern Cape Province in South Africa. The event was named in homage to the Kimberley's history as the location of the first diamond mine in South Africa, and for its reputation as "The Diamond City".

World Skateboarding Grand Prix

The 2013 and 2014 Kimberley Diamond Cup championships were produced by World Skateboarding Grand Prix (WSGP) and presented in partnership with the Northern Cape Provincial Government and Kumba Iron Ore, the fourth-largest iron ore producer in the world and the largest in Africa.

WSGP CEO Tim McFerran founded the company in 2013. McFerran previously served as vice president at Maloof Skateboarding and ran the Maloof Money Cup World Championships from 2008 to 2012. In 2009, McFerran was named one of the "Hot 25 best and brightest business professionals" in the Orange County, California region by OC Metro.

Community outreach

In 2013 and 2014, WSGP conducted skateboarding clinics throughout South Africa, given away hundreds of skateboards, and employed a full-time skateboarding mentor at the Kumba Skate Plaza.

Communities located around Kimberley Diamond Cup Sponsor Kumba Iron Ore's mines own a stake in the company and receive twice-yearly dividend payments that are used for community development projects such as clinics, schools, and infrastructure development. Kumba Iron Ore has also a stated commitment to turn South Africa Northern Cape Province into a world-class extreme sport destination.

Economic impact

In 2013, John Block, Member of the Executive Council (MEC) for Finance, Economic Development and Tourism in the Northern Cape Province of South Africa, said "hotels in Kimberley were at capacity and the flights were sold out" during the 2013 Kimberly Diamond Cup." Patrick Seboko, head of the Northern Cape Province Department of Economic Development and Tourism, said the Kimberley Diamond Cup will help "promote the province as attractive destination for mega events, 'high octane' sports, and adventure tourism."

Mission

WSGP's stated mission is to "help stimulate local economies through tourism and support youth development, especially those in underserved or impoverished communities, through skate clinics, demos, pro tours and more."

Kimberley Diamond Cup competition results

2015 Kimberley Diamond Cup

Skaters from more than 50 countries were represented in the 2015 Kimberley Diamond Cup skateboarding competition, which was held October 7–10 at the Kumba Skate Plaza. In the Street World Championships final, twelve finalists from eight countries competed for the world title and $100,000 top prize. Nyjah Huston of the U.S. was the third-place qualifier for the event and first-place winner in 2013. In the final, Huston edged out Luan Oliveira of Brazil to capture first prize. In the Vert World Championships, Jimmy Wilkins reclaimed the title he won in 2014 and the $35,000 first place prize.

2014 Kimberley Diamond Cup

The 2014 Kimberley Diamond Cup was held from October 2–5 at the Kumba Skate Plaza. Skaters from 37 countries participated.

Kelvin Hoefler from Brazil placed first in the Street competition and took home first prize, which came with $100,000. Hoefler performed a switch-frontside blunt down the rail and 360 flip lipslide down the rail. Nyjah Huston, 2013 winner in the Street event, was the top qualifier but he was eliminated in the final rounds of the head-to-head Street competition.

In the Mini MegaBig Air World Championships, 14-year-old Alana Smith of the U.S. became the first female to successfully perform a backflip in competition.

Eight 4-man teams of skateboarders, including several teams from South Africa, competed in the Rider Cup Team Championships during Kimberley Diamond Cup. The South African team 4 Staxx took the Rider Cup Team Championship 2014 title.

2013 Kimberley Diamond Cup

The total prize purse at the 2013 Kimberley Diamond Cup was R5,000,000, approximately $500,000 in US dollars at the time, and was the largest single-event prize purse in skateboarding that year.

During the summer of 2013, professional skateboarders Ryan Decenzo and Adam Dyet joined the WSGP's Skateboarding for Hope tour in the Northern Cape province and participated in skateboarding clinics and demonstrations in Kathu, Kuruman, Postmasburg and Kimberley.

American professional street skateboarder Nyjah Huston won the Pro Street Contest at the Kimberley Diamond Cup, and $100,000 in prize money. Huston's highlights included a nollie heelflip backlip, switch frontside blunt, fakie five-o on high flat bar. Huston has been called "the best contest street skateboarder in the world" and is a 4-time X Games gold medalist. During practice, Huston was filmed performing a 270-degree "kickflip lipslide" on a rail, a difficult skateboarding trick that had never been on a full-sized handrail.

"Vert legend" Andy MacDonald won the Vert/BigAir Overall (combined results from 50% Vert and 50% Big Air competition scores). MacDonald holds the record for the most X Games medals in vert skateboarding and was crowned as skateboarding's World Champion nine times in the World Cup Skateboard Series.

External links
 Kimberley Diamond Cup
 World Skateboarding Grand Prix

References

2013 in South African sport
World championships
Skateboarding competitions

redpajama_set_name: RedPajamaWikipedia


text:
Pterodactylus (from Greek  () meaning 'winged finger') is an extinct genus of pterosaurs. It is thought to contain only a single species, Pterodactylus antiquus, which was the first pterosaur to be named and identified as a flying reptile.

Fossil remains of Pterodactylus have primarily been found in the Solnhofen limestone of Bavaria, Germany, which dates from the Late Jurassic period (early Tithonian stage), about 150.8 to 148.5 million years ago. More fragmentary remains of Pterodactylus have tentatively been identified from elsewhere in Europe and in Africa.

Pterodactylus was a generalist carnivore that probably fed on a variety of invertebrates and vertebrates. Like all pterosaurs, Pterodactylus had wings formed by a skin and muscle membrane stretching from its elongated fourth finger to its hind limbs. It was supported internally by collagen fibres and externally by keratinous ridges. Pterodactylus was a small pterosaur compared to other famous genera such as Pteranodon and Quetzalcoatlus, and it also lived earlier, during the Late Jurassic period, while both Pteranodon and Quetzalcoatlus lived during the Late Cretaceous. Pterodactylus lived alongside other small pterosaurs such as the well-known Rhamphorhynchus, as well as other genera such as Scaphognathus, Anurognathus and Ctenochasma. Pterodactylus is classified as an early-branching member of the ctenochasmatid lineage, within the pterosaur clade Pterodactyloidea.

Discovery and history

The type specimen of the animal now known as Pterodactylus antiquus was the first pterosaur fossil ever to be identified. The first Pterodactylus specimen was described by the Italian scientist  in 1784, based on a fossil skeleton that had been unearthed from the Solnhofen limestone of Bavaria. Collini was the curator of the , or nature cabinet of curiosities (a precursor to the modern concept of the natural history museum), in the palace of Charles Theodore, Elector of Bavaria at Mannheim. The specimen had been given to the collection by Count  around 1780, having been recovered from a lithographic limestone quarry in . The actual date of the specimen's discovery and entry into the collection is unknown however, and it was not mentioned in a catalogue of the collection taken in 1767, so it must have been acquired at some point between that date and its 1784 description by Collini. This makes it potentially the earliest documented pterosaur find; the "Pester Exemplar" of the genus Aurorazhdarcho was described in 1779 and possibly discovered earlier than the Mannheim specimen, but it was at first considered to be a fossilized crustacean, and it was not until 1856 that this species was properly described as a pterosaur by German paleontologist .

In his first description of the Mannheim specimen, Collini did not conclude that it was a flying animal. In fact, Collini could not fathom what kind of animal it might have been, rejecting affinities with the birds or the bats. He speculated that it may have been a sea creature, not for any anatomical reason, but because he thought the ocean depths were more likely to have housed unknown types of animals. The idea that pterosaurs were aquatic animals persisted among a minority of scientists as late as 1830, when the German zoologist Johann Georg Wagler published a text on "amphibians" which included an illustration of Pterodactylus using its wings as flippers. Wagler went so far as to classify Pterodactylus, along with other aquatic vertebrates (namely plesiosaurs, ichthyosaurs, and monotremes), in the class Gryphi, between birds and mammals.

The German/French scientist Johann Hermann was the one who first stated that Pterodactylus used its long fourth finger to support a wing membrane. Back in March 1800, Hermann alerted the prominent French scientist Georges Cuvier to the existence of Collini's fossil, believing that it had been captured by the occupying armies of Napoleon and sent to the French collections in Paris (and perhaps to Cuvier himself) as war booty; at the time special French political commissars systematically seized art treasures and objects of scientific interest. Hermann sent Cuvier a letter containing his own interpretation of the specimen (though he had not examined it personally), which he believed to be a mammal, including the first known life restoration of a pterosaur. Hermann restored the animal with wing membranes extending from the long fourth finger to the ankle and a covering of fur (neither wing membranes nor fur had been preserved in the specimen). Hermann also added a membrane between the neck and wrist, as is the condition in bats. Cuvier agreed with this interpretation, and at Hermann's suggestion, Cuvier became the first to publish these ideas in December 1800 in a very short description. However, contrary to Hermann, Cuvier was convinced the animal was a reptile. The specimen had not in fact been seized by the French. Rather, in 1802, following the death of Charles Theodore, it was brought to Munich, where Baron Johann Paul Carl von Moll had obtained a general exemption of confiscation for the Bavarian collections. Cuvier asked von Moll to study the fossil but was informed it could not be found. In 1809 Cuvier published a somewhat longer description, in which he named the animal Petro-Dactyle, this was a typographical error however, and was later corrected by him to Ptéro-Dactyle. He also refuted a hypothesis by Johann Friedrich Blumenbach that it would have been a shore bird. Cuvier remarked: "It is not possible to doubt that the long finger served to support a membrane that, by lengthening the anterior extremity of this animal, formed a good wing."

Contrary to von Moll's report, the fossil was not missing; it was being studied by Samuel Thomas von Sömmerring, who gave a public lecture about it on December 27, 1810. In January 1811, von Sömmerring wrote a letter to Cuvier deploring the fact that he had only recently been informed of Cuvier's request for information. His lecture was published in 1812, and in it von Sömmerring named the species Ornithocephalus antiquus. The animal was described as being both a bat, and a form in between mammals and birds, i.e. not intermediate in descent but in "affinity" or archetype. Cuvier disagreed, and the same year in his Ossemens fossiles provided a lengthy description in which he restated that the animal was a reptile. It was not until 1817 that a second specimen of Pterodactylus came to light, again from Solnhofen. This tiny specimen was that year described by von Sömmerring as Ornithocephalus brevirostris, named for its short snout, now understood to be a juvenile character (this specimen is now thought to represent a juvenile specimen of a different genus, probably Ctenochasma). He provided a restoration of the skeleton, the first one published for any pterosaur. This restoration was very inaccurate, von Sömmerring mistaking the long metacarpals for the bones of the lower arm, the lower arm for the humerus, this upper arm for the breast bone and this sternum again for the shoulder blades. Sömmerring did not change his opinion that these forms were bats and this "bat model" for interpreting pterosaurs would remain influential long after a consensus had been reached around 1860 that they were reptiles. The standard assumptions were that pterosaurs were quadrupedal, clumsy on the ground, furred, warmblooded and had a wing membrane reaching the ankle. Some of these elements have been confirmed, some refuted by modern research, while others remain disputed.

In 1815, the generic name Ptéro-Dactyle was latinized to Pterodactylus by Constantine Samuel Rafinesque. Unaware of Rafinesque's publication however, Cuvier himself in 1819 latinized the name Ptéro-Dactyle again to Pterodactylus, but the specific name he then gave, longirostris, has to give precedence to von Sömmerring's antiquus. In 1888, English naturalist Richard Lydekker designated Pterodactylus antiquus as the type species of Pterodactylus, and considered Ornithocephalus antiquus a synonym. He also designated specimen BSP AS.I.739 as the holotype of the genus.

Description

Pterodactylus is known from over 30 fossil specimens, and though most belong to juveniles, many preserve complete skeletons. Pterodactylus antiquus was a relatively small pterosaur, with an estimated adult wingspan of about , based on the only known adult specimen, which is represented by an isolated skull. Other "species" were once thought to have been smaller. However, these smaller specimens have been shown to represent juveniles of Pterodactylus, as well as its contemporary relatives including Ctenochasma, Germanodactylus, Aurorazhdarcho, Gnathosaurus, and hypothetically Aerodactylus if this genus is truly valid.

The skulls of adult Pterodactylus were long and thin, with about 90 narrow and conical teeth. The teeth extended back from the tips of both jaws, and became smaller farther away from the jaw tips, this was unlike the ones seen in most relatives, where teeth were absent in the upper jaw tip, and were relatively uniform in size. The teeth of Pterodactylus also extended farther back into the jaw compared to close relatives, and some were present below the front of the nasoantorbital fenestra, which is the largest opening in the skull. Another autapomorphy that Pterodactylus has is that the skull and jaws were straight, which are unlike the upwardly curved jaws seen in the related ctenochasmatids.

Pterodactylus, like related pterosaurs, had a crest on its skull composed mainly of soft tissues. In adult Pterodactylus, this crest extended between the back edge of the antorbital fenestra and the back of the skull. In at least one specimen, the crest had a short bony base, also seen in related pterosaurs like Germanodactylus. Solid crests have only been found on large, fully adult specimens of Pterodactylus, indicating that this was a display structure that became larger and more well developed as individuals reached maturity. In 2013, pterosaur researcher S. Christopher Bennett noted that other authors claimed that the soft tissue crest of Pterodactylus extended backward behind the skull; Bennett himself, however, didn't find any evidence for the crest extending past the back of the skull. Two specimens of P. antiquus (the holotype specimen BSP AS I 739 and the incomplete skull BMMS 7, the largest known skull of P. antiquus) have a low bony crest on their skulls; in BMMS 7 it is 47.5 mm long (1.87 inches, more or less 24% of the estimated total length of its skull) and has a maximum height of 0.9 mm (0.035 inches) above the orbit. Several specimens previously referred to P. antiquus preserved evidence of the soft tissue extensions of these crests, including an "occipital lappet", a flexible, tab-like structure extending from the back of the skull. Most of these specimens have been reclassified in the related species Aerodactylus scolopaciceps, which may however be nothing more than a junior synonym. Even if Aerodactylus were valid, at least one specimen with these features is still considered to belong to Pterodactylus, BSP 1929 I 18, which has an occipital lappet similar to the proposed Aerodactylus definition, and also possesses a small triangular soft tissue crest with the peak of the crest positioned above the eyes.

Paleobiology

Life history

Like other pterosaurs (most notably Rhamphorhynchus), Pterodactylus specimens can vary considerably based on age or level of maturity. Both the proportions of the limb bones, size and shape of the skull, and size and number of teeth changed as the animals grew. Historically, this has led to various growth stages (including growth stages of related pterosaurs) being mistaken for new species of Pterodactylus. Several detailed studies using various methods to measure growth curves among known specimens have suggested that there is actually only one valid species of Pterodactylus, P. antiquus.

The youngest immature specimens of Pterodactylus antiquus (alternately interpreted as young specimens of the distinct species P. kochi) have a small number of teeth, as few as 15 in some, and the teeth have a relatively broad base. The teeth of other P. antiquus specimens are both narrower and more numerous (up to 90 teeth are present in several specimens).

Pterodactylus specimens can be divided into two distinct year classes. In the first year class, the skulls are only  in length. The second year class is characterized by skulls of around  long, but are still immature however. These first two size groups were once classified as juveniles and adults of the species P. kochi, until further study showed that even the supposed "adults" were immature, and possibly belong to a distinct genus. A third year class is represented by specimens of the "traditional" P. antiquus, as well as a few isolated, large specimens once assigned to P. kochi that overlap P. antiquus in size. However, all specimens in this third year class also show sign of immaturity. Fully mature Pterodactylus specimens remain unknown, or may have been mistakenly classified as a different genus.

Growth and breeding seasons

The distinct year classes of Pterodactylus antiquus specimens show that this species, like the contemporary Rhamphorhynchus muensteri, likely bred seasonally and grew consistently during its lifetime. A new generation of 1st year class P. antiquus would have been produced seasonally, and reached 2nd-year size by the time the next generation hatched, creating distinct 'clumps' of similarly-sized and aged individuals in the fossil record. The smallest size class probably consisted of individuals that had just begun to fly and were less than one year old. The second year class represents individuals one to two years old, and the rare third year class is composed of specimens over two years old. This growth pattern is similar to modern crocodilians, rather than the rapid growth of modern birds.

Daily activity patterns
Comparisons between the scleral rings of Pterodactylus antiquus and modern birds and reptiles suggest that it may have been diurnal. This may also indicate niche partitioning with contemporary pterosaurs inferred to be nocturnal, such as Ctenochasma and Rhamphorhynchus.

Diet
Based on the shape, size, and arrangement of its teeth, Pterodactylus has long been recognized as a carnivore specializing in small animals. A 2020 study of pterosaur tooth wear supported the hypothesis that Pterodactylus preyed mainly on invertebrates and had a generalist feeding strategy, indicated by a relatively high bite force.

Paleoecology

Specimens of Pterodactylus have been found mainly in the Solnhofen limestone (geologically known as the Altmühltal Formation) of Bavaria, Germany. The main composition of this formation is fine-grained limestone that originated mainly from the nearby towns Solnhofen and Eichstätt, which is formed by mud silt deposits. The Solnhofen Limestone is a diverse Lagerstätte that contains a wide range of different creatures, including highly detailed fossilized imprints of soft bodied organisms such as jellyfishes. Abundant specimens of pterosaurs similar to Pterodactylus were also found within the formation, these include the rhamphorhynchids Rhamphorhynchus and Scaphognathus, several gallodactylids such as Aerodactylus, Ardeadactylus, Aurorazhdarcho and Cycnorhamphus, the ctenochasmatids Ctenochasma and Gnathosaurus, the anurognathid Anurognathus, the germanodactylid Germanodactylus, as well as the basal euctenochasmatian Diopecephalus. Fossil remains of the dinosaurs Archaeopteryx and Compsognathus were also found within the limestone, these specimens were related to early evolution of feathers, since they were some of the only ones that had them during the Jurassic period. Various lizard remains were also found alongside those of Pterodactylus, with several specimens assigned to Ardeosaurus, Bavarisaurus and Eichstaettisaurus. Crocodylomorph specimens were widely distributed within the fossil site, most were assigned to the metriorhynchid genera Cricosaurus, Dakosaurus, Geosaurus and Rhacheosaurus. These genera are colloquially called as marine or sea crocodiles due to their similar built. The turtle genera Eurysternum and Paleomedusa were also found within the formation. Fossils of the ichthyosaur Aegirosaurus also appeared to be present in the site, as well as fish remains, with many specimens assigned to ray-finned fishes such as the halecomorphs Lepidotes, Propterus, Gyrodus, Mesturus, Proscinetes, Caturus, Ophiopsis and Ophiopsiella, the pachycormids Asthenocormus, Hypsocormus and Orthocormus, as well as the aspidorhynchid Aspidorhynchus, and the ichthyodectid Thrissops.

Classification

Initial classifications for Pterodactylus started when paleontologist Hermann von Meyer used the name Pterodactyli to contain Pterodactylus and other pterosaurs known at the time. This was emended to the family Pterodactylidae by Prince Charles Lucien Bonaparte in 1838. However, this group has more recently been given several competing definitions.

Beginning in 2014, researchers Steven Vidovic and David Martill constructed an analysis in which several pterosaurs traditionally thought of as archaeopterodactyloids closely related to the ctenochasmatoids may have been more closely related to the more advanced dsungaripteroids, or in some cases, fall outside both groups. Their conclusion was published in 2017, in which they placed Pterodactylus as a basal member of the suborder Pterodactyloidea.

As illustrated below, the results of a different topology are based on a phylogenetic analysis made by Longrich, Martill, and Andres in 2018. Unlike the previous results above, they placed Pterodactylus within the clade Euctenochasmatia, resulting in a more derived position.

Formerly assigned species

Numerous species have been assigned to Pterodactylus in the years since its discovery. In the first half of the 19th century any new pterosaur species would be named Pterodactylus, which thus became a "wastebasket taxon". Even after clearly different forms had later been given their own generic name, new species would be created from the very productive sites, throughout Europe and North America, often based on only slightly different material.

The earliest reassignments of pterosaur species to Pterodactylus started in 1825, with the description of Rhamphorhynchus; fossil collector Georg Graf zu Münster alerted the German paleontologist Samuel Thomas von Sömmerring about several distinct fossil specimens, Sömmerring thought that they belonged to an ancient bird. Further fossil preparations had uncovered teeth, to which Graf zu Münster created a skull cast. He later sent the cast to Professor Georg August Goldfuss, who recognized it as a pterosaur, specifically a species of Pterodactylus. At the time however, most paleontologists incorrectly consider the genus Ornithocephalus () to be the valid name for Pterodactylus, and therefore the specimen found was named as Ornithocephalus Münsteri, which was first mentioned by Graf zu Münster himself. Another specimen was found and described by Graf zu Münster in 1839, he assigned this specimen to a new separate species called Ornithocephalus longicaudus; the specific name means 'long tail', in reference to the animal's tail size. German paleontologist Hermann von Meyer in 1845 officially emended that the genus Pterodactylus had priority over Ornithocephalus, so he reassigned the species O. münsteri and O. longicaudus into Pterodactylus münsteri and Pterodactylus longicaudus. In 1846, von Meyer created the new species Pterodactylus gemmingi based on long-tailed remains; the specific name honors the fossil collector Carl Eming von Gemming. Later, in 1847, von Meyer finally erected the generic name Rhamphorhynchus () due to the distinctively long tails seen in the specimens found, which are much longer than those seen in Pterodactylus. He assigned the species P. longicaudus as the type species of Rhamphorhynchus, which resulted in a new combination called Rhamphorhynchus longicaudus. The species R. münsteri was later changed to R. muensteri by Lydekker in 1888, due to the ICZN rule that prohibits non-standard Latin characters, such as ü, in scientific names.

Beginning in 1846, many pterosaur specimens were found near the village of Burham in Kent, England by British paleontologists James Scott Bowerbank and Sir Richard Owen. Bowerbank had assigned fossil remains to two new species; the first was named in 1846 as Pterodactylus giganteus; the specific name means 'the gigantic one' in Latin, in reference to the large size of the remains, and the second species was named in 1851 as Pterodactylus cuvieri, in honor of the French scientist Georges Cuvier. Later in 1851, Owen named and described new pterosaur specimens that have been found yet again in England. He assigned these specimens to a new species called Pterodactylus compressirostris. In 1914 however, paleontologist Reginald Hooley redescribed P. compressirostris, to which he erected the genus Lonchodectes (), and therefore made P. compressirostris the type species, and created the new combination L. compressirostris. In a 2013 review, P. giganteus and P. cuvieri were reassigned to new genera; P. giganteus was reassigned to a genus called  Lonchodraco ('lance dragon'), which resulted in a new combination called L. giganteus, and P. cuvieri was reassigned to the new genus Cimoliopterus ('chalk wing'), creating C. cuvieri. Back in 1859, Owen had found remains the front part of a snout in the Cambridge Greensand, and assigned it into the species Pterodactylus segwickii; in honor of Adam Sedgwick, a British geologist. This species however, was reassigned to the genus Camposipterus in 2013, therefore creating the new combination Camposipterus segwickii. Later, in 1861, Owen had uncovered multiple distinctively looking fossil remains yet again in the Cambridge Greensand, these were assigned to a new species named Pterodactylus simus, though the British paleontologist Harry Govier Seeley had created a separate generic name called Ornithocheirus, and reassigned P. simus as the type species, which created the combination Ornithocheirus simus. Between the years 1869 and 1870, Seeley had reassigned many pterosaur species into Ornithocheirus, while also creating several new species. Many of these species however, are now reclassified to other genera, or considered . In 1874, further specimens were found in England, again by Owen, these ones were assigned to a new species called Pterodactylus sagittirostris, this species however, was reassigned to the genus Lonchodectes in 1914 by Hooley, which resulted in an L. sagittirostris. This conclusion was revised by Rigal et al. in 2017, who disagreed with Hooley's reassignment, and therefore created the genus Serradraco, which afterwards resulted in a new combination called S. sagittirostris.

Assigning new pterosaur species to Pterodactylus was not only common in Europe, but also in North America; paleontologists such as Othniel Charles Marsh in 1871 for example, described several toothless pterosaur specimens, which were accompanied by teeth that belonged to the fish Xiphactinus, which Marsh assumed that these teeth belonged to the pterosaur specimens he found, since all pterosaurs discovered at the time had teeth. He then assigned these specimens to a new species called "Pterodactylus oweni", but this was changed to Pterodactylus occidentalis because "P. oweni" was found to have been preoccupied by a pterosaur species described with the same name back in 1864 by Seeley. In 1872, American paleontologist Edward Drinker Cope also found various pterosaur specimens in North America, he assigned these to two new species known as Ornithochirus umbrosus and Ornithochirus harpyia, Cope attempted to assign the specimens he found to the genus Ornithocheirus, but misspelled forgetting the 'e'. In 1875 however, Cope reassigned the species O. umbrosus and O. harpyia into Pterodactylus umbrosus and Pterodactylus harpyia, though these species had been considered  ever since. Paleontologist Samuel Wendell Williston unearthed the first skull of the pterosaur, and found that the animal was toothless, this made Marsh create the genus Pteranodon (lit. 'toothless wing'), and therefore reassigned all the American pterosaur species, including the ones that he named, from Pterodactylus to Pteranodon.

Later, in the 1980s, subsequent revisions by Peter Wellnhofer had reduced the number of recognized species to about half a dozen. Many species assigned to Pterodactylus had been based on juvenile specimens, and subsequently been recognized as immature individuals of other species or genera. By the 1990s it was understood that this was even true for part of the remaining species. P. elegans, for example, was found by numerous studies to be an immature Ctenochasma. Another species of Pterodactylus originally based on small, immature specimens was P. micronyx. However, it has been difficult to determine exactly of what genus and species P. micronyx might be the juvenile form. Stéphane Jouve, Christopher Bennett and others had once suggested that it probably belonged either to Gnathosaurus subulatus or one of the species belonging to Ctenochasma, though after additional research Bennett assigned it to the genus Aurorazhdarcho. Another species with a complex history is P. longicollum, named by von Meyer in 1854, based on a large specimen with a long neck and fewer teeth. Many researchers, including David Unwin, have found P. longicollum to be distinct from P. kochi and P. antiquus. Unwin found P. longicollum to be closer to Germanodactylus and therefore requiring a new genus name. It has sometimes been placed in the genus Diopecephalus because Harry Govier Seeley based this genus partly on the P. longicollum material. However, it was shown by Bennett that the type specimen later designated for Diopecephalus was a fossil belonging to P. kochi, and no longer thought to be separate from Pterodactylus. Diopecephalus is therefore a synonym of Pterodactylus, and as such is unavailable for use as a new genus for "P." longicollum. "P." longicollum was eventually made the type species of a separate genus Ardeadactylus.

Controversial species

The only well-known and well-supported species left by the first decades of the 21st century were P. antiquus and P. kochi. However, most studies between 1995 and 2010 found little reason to separate even these two species, and treated them as synonymous. More recent studies of pterosaur relationships have found anurognathids and pterodactyloids to be sister groups, which would limit the more inclusive group Caelidracones to just two clades. In 1996, Bennett suggested that the differences between specimens of P. kochi and P. antiquus could be explained by differences in age, with P. kochi (including specimens alternately classified in the species P. scolopaciceps) representing an immature growth stage of P. antiquus. In a 2004 paper, Jouve used a different method of analysis and recovered the same result, showing that the "distinctive" features of P. kochi were age-related, and using mathematical comparison to show that the two forms are different growth stages of the same species. An additional review of the specimens published in 2013 demonstrated that some of the supposed differences between P. kochi and P. antiquus were due to measurement errors, further supporting their synonymy.

By the 2010s, a large body of research had been developed based on the idea that P. kochi and P. scolopaciceps were early growth stages of P. antiquus. However, in 2014, two scientists began publishing research that challenged this paradigm. Steven Vidovic and David Martill concluded that differences between specimens of P. kochi, P. scolopaciceps, and P. antiquus, such as different lengths of neck vertebrae, thinner or thicker teeth, more rounded skulls, and how far the teeth extended back in the jaws, were significant enough to separate them into three distinct species. Vidovic and Martill also performed a phylogenetic analysis which treated all relevant specimens as distinct units, and found that the P. kochi type specimen did not form a natural group with that of P. antiquus. They concluded that the genus Diopecephalus could be returned to use to distinguish "P". kochi from P. antiquus. They named the new genus Aerodactylus for P. scolopaciceps as well. So, what Bennett considered early growth stages of one species, Vidovic and Martill considered representatives of new species.

In 2017, Bennett challenged this hypothesis, he claimed that while Vidovic and Martill had identified real differences between these three groups of specimens, they had not provided any rationale that the differences were enough to distinguish them as species, rather than just individual variation, growth changes, or simply due to crushing and distortion during the fossilization process. Bennett pointed in particular to the data used to distinguish Aerodactylus, which was so different from the data for related species, it might be due to an unnatural assemblage of specimens. As a result, Bennett continued to consider Diopecephalus and Aerodactylus simply as year-classes of immature Pterodactylus antiquus.

List of species
During its over-200-year history, the various species of Pterodactylus have gone through a number of changes in classification and thus have acquired a large number of synonyms. Additionally, a number of species assigned to Pterodactylus are based on poor remains that have proven difficult to assign to one species or another and are therefore considered  (). The following list includes names that were used to identify new pterosaur species that now have been reclassified, or until recently thought to be pertaining to Pterodactylus proper, and names based on other material that has as yet not been assigned to other genera. This list also includes species that are  ('naked names'), which are species that were not published formally. Species that are  ('forgotten names') are the ones that have been disused, and species that are  ('rejected names') are the ones that have been rejected because a more preferable name had been accepted instead.

{| class="wikitable sortable"
|-
! Name
! Author
! Year
! Status
! class="unsortable" | Notes
|-
|Pterodactylus antiquus
|(Sömmerring)
|(1812)
|Valid
|Designated as the type species of Pterodactylus, and replacing Ornithocephalus antiquus due to being an obsolete name
|-
|Pterodactylus "suevicus"
|Oken
|1816
|Nomen nudum
|
|-
|Pterodactylus brevirostris
|(Sömmerring)
|(1817)
|Synonym of Ctenochasma elegans
|Reclassified from Ornithocephalus brevirostris
|-
|Pterodactylus giganteus
|(Oken)
|(1819)
|Nomen dubium
|Synonym of Rhamphorhynchus muensteri; reclassified from Ornithocephalus giganteus
|-
|Pterodactylus longirostris
|Cuvier
|1819
|Synonym of Pterodactylus antiquus
|
|-
|Pterodactylus grandis
|Cuvier
|1824
|Nomen dubium
|Synonym of Rhamphorhynchus muensteri
|-
|Pterodactylus crocodilocephaloides
|Ritgen
|1826
|Synonym of Pterodactylus antiquus
|
|-
|Pterodactylus nettecephaloides
|Ritgen
|1826
|Nomen oblitum
|Synonym of Aurorazhdarcho micronyx
|-
|Pterodactylus macronyx
|Buckland
|1829
|Reclassified as Dimorphodon macronyx
|
|-
|Pterodactylus (Rhamphorhynchus) macronyx
|(Buckland)
|(1829)
|Synonym of Dimorphodon macronyx
|Reclassified from Dimorphodon macronyx
|-
|Pterodactylus banthensis
|(Theodori)
|(1830)
|Reclassified as Dorygnathus banthensis
|Reclassified from Ornithocephalus banthensis
|-
|Pterodactylus (Rhamphorhynchus) (ensirostris) banthensis
|(Theodori)
|(1830)
|Nomen oblitum
|Synonym of Dorygnathus banthensis
|-
|Pterodactylus goldfussi
|Theodori
|1830
|Synonym of Dorygnathus banthensis
|
|-
|Pterodactylus crassirostris
|Goldfuss
|1831
|Reclassified as Scaphognathus crassirostris
|
|-
|Pterodactylus macronyx
|Meyer non Buckland
|1831 non 1829
|Synonym of Dorygnathus banthensis
|
|-
|Pterodactylus medius
|Münster
|1831
|Nomen dubium
|Synonym of Altmuehlopterus rhamphastinus
|-
|Pterodactylus muensteri
|(Goldfuss)
|(1831)
|Synonym of Rhamphorhynchus muensteri
|Reclassified from Ornithocephalus muensteri
|-
|Pterodactylus (Rhamphorhynchus) muensteri
|(Goldfuss)
|(1831)
|Synonym of Rhamphorhynchus muensteri
|Reclassified from Pterodactylus muensteri
|-
|Pterodactylus bucklandi
|Meyer
|1832
|Indeterminate rhamphorhynchine
|Once assigned to the genus Rhamphocephalus
|-
|Pterodactylus longipes
|Münster
|1836
|Synonym of Ardeadactylus longicollum
|
|-
|Pterodactylus kochi
|Wagner
|1837
|Reclassified as Diopecephalus kochi
|Reclassified from Ornithocephalus kochi; possible synonym of Pterodactylus antiquus
|-
|Pterodactylus lavateri
|Meyer
|1838
|Synonym of Rhamphorhynchus muensteri
|
|-
|Pterodactylus (Ornithopterus) lavateri
|(Meyer)
|(1838)
|Synonym of Rhamphorhynchus muensteri
|Reclassified from Pterodactylus lavateri
|-
|Pterodactylus longicaudus
|Münster
|1839
|Reclassified as Rhamphorhynchus longicaudus
|
|-
|Pterodactylus meyeri
|Münster
|1842
|Synonym of Diopecephalus kochi
|
|-
|Pterodactylus secundarius
|Meyer
|1843
|Nomen dubium
|Synonym of Rhamphorhynchus muensteri
|-
|Pterodactylus cliftii
|Mantell
|1844
|Synonym of Palaeornis cliftii
|Reclassified from Palaeornis cliftii
|-
|Pterodactylus diomedeus
|(Owen)
|(1846)
|Synonym of Cimoliornis diomedeus
|Reclassified from Cimoliornis diomedeus
|-
|Pterodactylus gemmingi
|Meyer
|1846
|Synonym of Rhamphorhynchus muensteri
|
|-
|Pterodactylus (Rhamphorhynchus) gemmingi
|(Meyer)
|(1846)
|Synonym of Rhamphorhynchus muensteri
|Reclassified from Pterodactylus gemmingi
|-
|Pterodactylus giganteus
|Bowerbank non Oken
|1846 non 1819
|Reclassified as Lonchodraco giganteus
|
|-
|Pterodactylus ornis
|Giebel
|1847
|Synonym of Palaeornis cliftii
|
|-
|Pterodactylus conirostris
|Owen
|1850
|Synonym of Lonchodraco giganteus
|
|-
|Pterodactylus cuvieri
|Bowerbank
|1851
|Reclassified as Cimoliopterus cuvieri
|
|-
|Pterodactylus compressirostris
|Owen
|1851
|Reclassified as Lonchodectes compressirostris
|
|-
|Pterodactylus redenbacheri
|(Wagner)
|(1851)
|Synonym of Aurorazhdarcho micronyx
|Reclassified from Ornithocephalus redenbacheri
|-
|Pterodactylus rhamphastinus
|(Wagner)
|(1851)
|Reclassified as Altmuehlopterus rhamphastinus
|Reclassified from Ornithocephalus rhamphastinus
|-
|Pterodactylus giganteus
|Morris non Oken non Bowerbank
|1854 non 1819 non 1846
|Synonym of Cimoliornis diomedeus
|
|-
|Pterodactylus longicollum
|Meyer
|1854
|Reclassified as Ardeadactylus longicollum
|
|-
|Pterodactylus wuerttembergicus
|Quenstedt
|1854
|Nomen oblitum
|Synonym of Cycnorhamphus suevicus
|-
|Pterodactylus suevicus
|Quenstedt
|1855
|Reclassified as Cycnorhamphus suevicus
|
|-
|Pterodactylus micronyx
|Meyer
|1856
|Reclassified as Aurorazhdarcho micronyx
|
|-
|Pterodactylus crassipes
|Meyer
|1857
|Nomen rejectum
|Reclassified as Ostromia crassipes
|-
|Pterodactylus (Rhamphorhynchus) crassipes
|(Meyer)
|(1857)
|Nomen rejectum
|Synonym of Ostromia crassipes; reclassified from Pterodactylus crassipes
|-
|Pterodactylus eurychirus
|Wagner
|1857
|Synonym of Cycnorhamphus suevicus
|
|-
|Pterodactylus (Ornithocephalus) eurychirus
|(Wagner)
|(1857)
|Synonym of Cycnorhamphus suevicus
|Reclassified from Pterodactylus eurychirus
|-
|Pterodactylus suevicus eurychirus
|(Wagner)
|(1857)
|Synonym of Cycnorhamphus suevicus
|
|-
|Pterodactylus hirundinaceus
|Wagner
|1857
|Synonym of Rhamphorhynchus muensteri
|
|-
|Pterodactylus (Rhamphorhynchus) hirundinaceus
|Wagner
|1857
|Synonym of Rhamphorhynchus muensteri
|
|-
|Pterodactylus (Ornithocephalus) propinquus
|Wagner
|1857
|Nomen dubium
|Possible synonym of Altmuehlopterus rhamphastinus
|-
|Pterodactylus propinquus
|(Wagner)
|(1857)
|Nomen dubium
|Reclassified from Pterodactylus (Ornithocephalus) propinquus; possible synonym of Altmuehlopterus rhamphastinus
|-
|Pterodactylus propinquus medius
|Wagner
|1857
|Nomen dubium
|Synonym of Altmuehlopterus rhamphastinus
|-
|Pterodactylus (Ornithocephalus) vulturinus
|Wagner
|1857
|Synonym of Ardeadactylus longicollum
|
|-
|Pterodactylus vulturinus
|(Wagner)
|(1857)
|Synonym of Ardeadactylus longicollum
|Reclassified from Pterodactylus (Ornithocephalus) vulturinus
|-
|Pterodactylus liasicus
|Quenstedt
|1858
|Reclassified as Campylognathoides liasicus
|
|-
|Pterodactylus fittoni
|Owen
|1859
|Nomen dubium
|Reclassified as either Ornithocheirus fittoni or Anhanguera fittoni; possible synonym of Cimoliopterus cuvieri
|-
|Pterodactylus sedgwickii
|Owen
|1859
|Reclassified as Camposipterus sedgwickii
|
|-
|Pterodactylus silvestris
|Owen
|1859
|Synonym of Palaeornis cliftii
|
|-
|Pterodactylus cerinensis
|Meyer
|1860
|Nomen dubium
|
|-
|Pterodactylus grandipelvis
|Meyer
|1860
|Nomen dubium
|
|-
|Pterodactylus scolopaciceps
|Meyer
|1860
|Reclassified as Aerodactylus scolopaciceps
|
|-
|Pterodactylus elegans
|Wagner
|1861
|Reclassified as Ctenochasma elegans
|
|-
|Pterodactylus pulchellus
|Meyer
|1861
|Synonym of Aurorazhdarcho micronyx
|
|-
|Pterodactylus simus
|Owen
|1861
|Reclassified as Ornithocheirus simus
|
|-
|Pterodactylus spectabilis
|Meyer
|1861
|Synonym of Pterodactylus antiquus
|
|-
|Pterodactylus woodwardi
|Owen
|1861
|Nomen dubium
|Reclassified as Ornithocheirus woodwardi
|-
|Pterodactylus hopkinsi
|Seeley
|1864
|Nomen nudum
|
|-
|Pterodactylus oweni
|Seeley
|1864
|Synonym of Ikrandraco machaerorhynchus
|Not to be confused with the preoccupied species "Pterodactylus oweni"
|-
|Pterodactylus longispinis|Cope
|1866
|Reclassified as Rhabdopelix longispinis|
|-
|Pterodactylus macrurus|Seeley
|1869
|Reclassified as Gnathosaurus macrurus|
|-
|Pterodactylus nobilis|Owen
|1869
|Nomen dubium|Reclassified as Ornithocheirus nobilis|-
|Pterodactylus curtus|Owen
|1870
|Nomen dubium|Reclassified as Ornithocheirus curtus|-
|"Pterodactylus oweni"|Marsh
|1871
|Preoccupied
|Reassigned as Pterodactylus occidentalis prior to being preoccupied
|-
|Pterodactylus ingens|Marsh
|1872
|Synonym of Pteranodon longiceps|Reclassified as Pteranodon ingens|-
|Pterodactylus occidentalis|Marsh
|1872
|Nomen dubium|Reclassified from the preoccupied species "Pterodactylus oweni"; reclassified as Pteranodon occidentalis|-
|Pterodactylus velox|Marsh
|1872
|Nomen dubium|Reclassified as Pteranodon velox|-
|Pterodactylus suprajurensis|Sauvage
|1873
|Nomen dubium|
|-
|Pterodactylus aclandi|Owen
|1874
|Nomen dubium|Possible synonym of Rhamphocephalus depressirostris|-
|Pterodactylus daviesii|Owen
|1874
|Nomen dubium|
|-
|Pterodactylus duncani|Owen
|1874
|Nomen dubium|Possible synonym of Rhamphocephalus bucklandi|-
|Pterodactylus kiddii|Owen
|1874
|Nomen dubium|Possible synonym of Rhamphocephalus bucklandi|-
|Pterodactylus manseli|Owen
|1874
|Nomen dubium|
|-
|Pterodactylus marderi|Owen
|1874
|Synonym of Dimorphodon macronyx|
|-
|Pterodactylus pleydelli|Owen
|1874
|Nomen dubium|
|-
|Pterodactylus sagittirostris|Owen
|1874
|Reclassified as Serradraco sagittirostris|
|-
|Pterodactylus umbrosus|Cope
|1874
|Nomen dubium|Reclassified from Ornithochirus umbrosus|-
|Pterodactylus validus|Owen
|1875
|Reclassified as Doratorhynchus validus|
|-
|Pterodactylus montanus|Marsh
|1878
|Reclassified as Dermodactylus montanus|
|-
|Pterodactylus suevicus|Fraas non Quenstedt
|1878 non 1855
|Synonym of Ardeadactylus longicollum|
|-
|Pterodactylus fraasi|(Seeley)
|(1901)
|Synonym of Ardeadactylus longicollum|Reclassified from. Cycnorhamphus fraasi|-
|Pterodactylus cristatus|Wiman
|1925
|Reclassified as Germanodactylus cristatus|
|-
|Pterodactylus westmani|Wiman
|1925
|Synonym of Pterodactylus antiquus|
|-
|Pterodactylus cormoranus|Döderlein
|1929
|Synonym of Pterodactylus antiquus|
|-
|Pterodactylus arningi|Reck
|1931
|Nomen dubium|
|-
|Pterodactylus brancai|Reck
|1931
|Nomen dubium|Reclassified as Dsungaripterus brancai|-
|Pterodactylus maximus|Reck
|1931
|Nomen dubium|
|-
|Pterodactylus raptor|Owen vide Ingles & Sawyer
|1979
|Nomen nudum|
|-
|}

Cultural significancePterodactylus is regarded as one of the most iconic prehistoric creatures, with multiple appearances in books, movies, as well as television series and several videogames. The informal name "pterodactyl" is sometimes used to refer to any kind of animal belonging to the order Pterosauria, though most of the times to Pterodactylus, as it's the most well-known member of the group. The popular aspect of Pterodactylus consists of an elongated head crest, and potentially large wings. Studies of Pterodactylus however, conclude that it may even lack a bony cranial crest, though several analysis have proven that Pterodactylus may in fact have a crest made up of soft tissue instead of bone.Pterodactylus is the star character of the 2005 horror film Pterodactyl, where it is identified with the informal name "pterodactyl", hence the name of the film. In the film, the "pterodactyls" resemble the aspect of the distantly related genus Pteranodon due to the elongated bony cranial crest, and their enormous size. One peculiar feature that Pterodactylus had in the film is the possession of teeth, while this is generally accurate for Pterodactylus, the overall appearance of the creatures in the film is similar to that of Pteranodon, as well as the large size, this makes them resemble some kind of pterosaur identical to Pteranodon, but with the possession of teeth.

Another appearance of Pterodactylus-like creatures is in J. R. R. Tolkien's Middle-earth legendarium. In this novel, the Nazgûl, introduced as the Black Riders, are nine characters who rode flying monsters that looked similarly built to Pterodactylus''. Christopher Tolkien, the son of the author, described the flying monsters as "Nazgûl-birds"; his father described the appearance of the steeds as somewhat "pterodactylic", and acknowledged that these were obviously "new mythology".

See also
 List of pterosaur genera
 Timeline of pterosaur research

References

External links

Late Jurassic pterosaurs of Europe
Pterodactyloids
Solnhofen fauna
Taxa named by Constantine Samuel Rafinesque
Fossil taxa described in 1809


Wellington-Greer Fire Protection District responded to eight calls in 2017 - 20 percent less than the previous year, according to data from the National Fire Incident Reporting System.
Come out Friday night as we kick off our summer concert series!
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Beginning May 24th thru September, Aroma Park United Methodist Church will hold their Farmer's Market on Thursdays from 4:00 - 7:00 P.M.
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Bourbonnais Elementary School District No. 53 Board of Education met Tuesday, June 12.


text:
\section{Introduction}
We work with a class $\Omega^{*}_{\infty,\,loc}$ of differential
forms on $\mathbb{R}^{n}$, those with coefficients locally in
$L_{\infty}$, with differential satisfying the same condition.
``Locally'' will mean ``on a neighborhood with compact closure'',
as usual. Classes $\Omega^{*}_{\infty}$ and
$\Omega^{*}_{\infty,\,loc}$ are invariant under bi-Lipschitz
coordinate changes and therefore are naturally defined on any
Lipschitz manifold. In context of his geometric theory of
integration Whitney in his book \cite{W} considered a class of
so-called flat forms, invariant under Lipschitz maps, and proved a
Poincar\'e lemma for them \cite[Th IX.12A]{W} using an elaborate
geometric construction.
We give a different shorter proof below, based on the techniques
from \cite{GKS}.
Differential forms of class $\Omega^{*}_{\infty,\,loc}$ are
nothing but locally flat forms in the sense of Whitney.

The second author is grateful to the first author for introducing
him to the subject and would also like to acknowledge the support
of the Skirball foundation and hospitality of the Center of
Advanced Studies in Mathematics at Ben Gurion University.

\section{Class $\Omega^{*}_{\infty,\,loc}$}
The differential forms we consider are not the ones in the smooth
category, they belong properly in the Lipschitz category and are
defined as follows.

On an open domain $U\subset\mathbb{R}^{n}$ a $k$-form is an almost
everywhere defined map
$$w:U\rightarrow\Lambda^{k}(\mathbb{R}^{n})$$
Two maps are considered equivalent and define the same form if
they coincide almost everywhere. Denote by $\mathcal{F}^{k}(U)$ a
vector space of differential forms of degree $k$, defined on $U$.
Vector spaces $\mathcal{F}^{k}(U)$ form a graded ring,
$\mathcal{F}^{*}(U)$ with respect to addition and exterior
product.

By $\mathcal{L}^{k}_{\infty}$ we denote the space of $k$-forms
with bounded coefficients. The union of these for all $k$ make up
a graded ring $\mathcal{L}^{*}_{\infty}$.

The ring of smooth forms with compact support in $U$ will be
denoted $\mathcal{D}^{*}(U)$. According to de Rham \cite{dR},
\emph{$k$-currents} on $U$  are linear continuous functionals on
$\mathcal{D}^{n-k}(U)$, denoted $\mathcal{E}^{k}(U)$. For each
current $w\in\mathcal{E}^{k}(U)$ one can define its exterior
differential $dw\in\mathcal{E}^{k+1}(U)$ by the formula:
$$<dw,\alpha>=(-1)^{k+1}<w,d\alpha>,\quad\quad \forall\alpha\in\mathcal{D}^{n-k-1}(U)
$$
Define
$$\Omega^{*}_{\infty}(U)=\{w\mid w\in\mathcal{L}^{*}_{\infty}(U),\,dw\in\mathcal{L}^{*}_{\infty}(U)\}\ ,$$
where by $dw\in\mathcal{L}^{*}_{\infty}(U)$ we mean that $dw$ as a
functional has an integral representation with an
$\mathcal{L}^{*}_{\infty}$-kernel:
$$<dw,\alpha>=\int_{U}dw\wedge\alpha,
$$
where we abuse notation: the $dw$ under the integral means the
form $dw\in\mathcal{L}^{*}_{\infty}(U)$, same notation as the
original functional it represents. Using a multi-index
$$\vec{i}=(i_{1},i_{2},...,i_{k})\quad\quad i_1<...<i_{k}\,,$$ we shall write
a $k$-form $w$ as follows:
$w=\displaystyle{\sum_{\vec{i}}a_{\vec{i}}dx^{\vec{i}}}$.\\On
every compact $K$ in $U$ consider a seminorm:
$$|w|_{K,\infty}=\max_{\vec{i}} \textrm{ess}\sup_{x \in K}|a_{\vec{i}}(x)|
$$
We will use $\sup$ to denote essential supremum from now on. In
$\Omega^{*}_{\infty}$ consider\\seminorms
$$|w|_{K,\infty,\infty}=|w|_{K,\infty}+|dw|_{K,\infty}
$$
With these seminorms $\mathcal{L}^{k}_{\infty}(U)$ and
$\Omega^{k}_{\infty}(U)$ become locally convex
topological vector spaces.

We will compare now the forms of class $\Omega^{*}_{\infty,\,loc}$
with locally flat forms in the sense of Whitney \cite[IX.6]{W}. We
recall some definitions.

If $P$ is an $s$-dimensional plane in $\mathbb{R}^{n}$, and $A$ - a
measurable set in $P$, then $|A|_s$ shall stand for the
$s$-dimensional Lebesque measure of $A$.

Given a form $w\in\mathcal{F}^{k}(U)$ and a set $Q\subset U$, a
simplex $\sigma^s\subset U$ $(s\geq k)\ $ is said to be
$Q$-\emph{good} for $w$, if all coefficients of $w$ are measurable
on $\sigma^s$ and $|\sigma^s\backslash Q|_s=0$. Simplex $\sigma^s$
is said to be $Q$-\emph{excellent} if $\sigma^s$ and each of its
faces of dimension $\geq k$ is $Q$-good.

A form $w=\displaystyle{\sum_{\vec{i}}a_{\vec{i}}dx^{\vec{i}}}\in
\mathcal{F}^{k}(U)$ is said to be \emph{flat} if:

(a) coefficients $a_{\vec{i}}$ are measurable in $U$,

(b) $\displaystyle{\sup_{x\in U}|a_{\vec{i}}(x)|\leq N}$ for some
$N$,

(c) there exist such $Q\subset U$ and $N'$, that $|U\backslash
Q|_n=0$, and for every\\ $Q$-excellent for $w$ simplex
$\sigma^{k+1}\subset U$: $$|\int_{\partial \sigma^{k+1}}w|\leq
N'|\sigma^{k+1}|_{k+1}\ .$$
\begin{thm}
\label{thm:1.5} Class $\Omega^{*}_{\infty,\,loc}(U)$ coincides
with the space of all locally flat forms in $U$. The exterior
differential of an arbitrary form $w\in
\Omega^{*}_{\infty,\,loc}(U)$ coincides with the differential of
$w$ in the sense of Whitney \cite[IX.12]{W}.
\end{thm}
{\bf Proof}\quad See \cite[Theorem 1.5]{GKS} $\Box$

\section{$\Omega^{*}_{\infty,\,loc}$-morphisms}
A map $f:U\rightarrow \mathbb{R}^{m}$, $U\subset \mathbb{R}^{n}$, is called
locally Lipschitz if for every compact $K \subset U$ there exists
a constant $C$, satisfying: $$|f(x)-f(x')|\leq C|x-x'|$$ for any
$x, x' \in K$ . Every locally Lipschitz function $f:U\rightarrow
\mathbb{R}^{1}$ is differentiable almost everywhere on $U$, its
partial derivatives are generalized partial derivatives. Hence,
the exterior differential $df$ of a locally Lipschitz function
$f$, considered as a form of degree $0$, has a coordinate
representation $$df=\frac{\partial f}{\partial
x^1}dx^1+...+\frac{\partial f}{\partial x^n}dx^n\ .$$

Locally Lipschitz map $\varphi: U\rightarrow V$ will be called an
$l$-map, if for any point $x\in U$ there exist a neighborhood $W$
of $x$ and a constant $C$, such that $$|\varphi^{-1}(A)\cap
W|_n\leq C|A|_m$$ for any open $A\subset V$. Preimage of a measure
zero set under an $l$-map has measure zero. Hence for any $l$-map
$\varphi: U\rightarrow V$ there is a well-defined homomorphism
$\varphi^*: \mathcal{F}^*(V)\rightarrow \mathcal{F}^*(U)$.

According to Rademacher theorem \cite[IX.11]{W} any locally
Lipschitz map is differentiable almost everywhere, therefore any
$l$-map $\varphi$ satisfies:
$$\varphi^*(\mathcal{L}^{*}_\infty(V))\subset
(\mathcal{L}^{*}_\infty(U))\ .$$
\begin{thm}
\label{thm:2.2} If $\,\varphi: U\rightarrow V$, $U\subset \mathbb{R}^{n}$,
$V\subset \mathbb{R}^{m}$ - an $\,l$-map, $w\in
\Omega^{*}_{\infty,\,loc}(V)$, then $$\varphi^* w\in
\Omega^{*}_{\infty,\,loc}(U) ,\quad d(\varphi^* w)= \varphi^* dw\
.$$ The map
$$\varphi^*: \Omega^{*}_{\infty,\,loc}(V) \rightarrow \Omega^{*}_{\infty,\,loc}(U)$$
is continuous.
\end{thm}
{\bf Proof}\quad See \cite[Theorem 2.2]{GKS} $\Box$
\begin{rem}
A homeomorphism $\varphi: U \rightarrow V\,,\,U,\,V \subset \mathbb{R}^{n} $
is called Lipschitz if $\varphi$, $\varphi^{-1}$ are locally
Lipschitz. For Lipschitz homeomorphisms Theorem \ref{thm:2.2} is
satisfied, since they are $l$-maps.\end{rem} Whitney defines
homomorphism $\varphi^*$ on classes of flat forms for any locally
Lipschitz $\varphi: U \rightarrow V\,,\,U\subset \mathbb{R}^{n},\,V  \subset
\mathbb{R}^{m}$ \cite[X.9]{W} . Due to Theorem \ref{thm:1.5} the
construction of Whitney defines a homomorphism $\varphi^*:
\Omega^{*}_{\infty,\,loc}(V) \rightarrow
\Omega^{*}_{\infty,\,loc}(U)\,$. If $\varphi$ is a Lipschitz
homeomorphism then $\varphi^*$ in the sense of Whitney
\cite[X.9]{W} coincides with the $\varphi^*$ introduced above.

\section{Lemma Poincar\'e for bounded forms}
Lemma Poincar\'e for forms with $p$-summable coefficients for
finite $p$ is proven in \cite[Lemma 3.4]{GKS}. The case $p=\infty$
(locally flat forms) is treated in \cite{W} via nontrivial
explicit geometric construction. We use analytic technique similar
to that used in \cite{GKS} to obtain a short alternative proof for
$p=\infty$ case. We start with the following key observation.
\begin{lem}
\label{lem:3.2} Let $I$ be a cube in $\mathbb{R}^{n}$ and $w$ an
arbitrary smooth $k$-form on $I$. There exists a smooth closed
$w'\ (dw'=0)$, such that:
$$|w-w'|_{I,\infty}\leq
C|dw|_{I,\infty}$$ for some constant $C$ depending only on $n$,
$k$ and $I$.
\end{lem}
{\bf Proof}\quad We can assume $I=I^{n}$ in $\mathbb{R}^{n}$. For
$k\geq n$ the statement is true for $C=0$, for other cases we will
proceed by induction on $n$. For $n=1$ we only need to consider
$k=0$. In this case $w=f(x)$ and we have:
$$\sup_{x\in I}|f(x)-f(0)|=\sup_{x\in I}|\int_{0}^{x}f'(\tau)d\tau|\leq\int_{0}^{1}|f'(\tau)|d\tau\leq\sup_{x\in
I}|f'(x)|\ .$$ In other words, $$|f(x)-f(0)|_{I,\infty}\leq
|df|_{I,\infty}\ .$$ Suppose now $n>1$. An arbitrary smooth form
$w$ can be represented in the following way:
$$w=w_{1}\wedge dx^{n}+w_{2}\ ,$$
where forms $w_1$ and $w_2$ do not contain $dx^n$ in their
coordinate representations. Clearly:
\begin{equation}
\label{eq:9}
|w|_{I,\infty}=\max(|w_1|_{I,\infty},|w_2|_{I,\infty})
\end{equation}
Forms $w_1$ and $w_2$ can be considered as those on the cube
$I'=I^{n-1}$, depending on a parameter $x^n$. Differentials of
these in $I'$ we will denote by $d'w_1$ and $d'w_2$. Then
$$
dw=d'w_1\wedge dx^n + (-1)^k\frac{\partial w_2}{\partial
x^n}\wedge dx^n + d'w_2\ ,$$ where by $\frac{\partial
w_2}{\partial x^n}$ we mean a form, whose coefficients are the
partial derivatives of $w_2$ with respect to $x^n$. We have:
\begin{equation}
\label{eq:10} (dw)_1=d'w_1+(-1)^k\frac{\partial w_2}{\partial
x^n}\ ,\ (dw)_2=d'w_2
\end{equation}
Denoting $$d'w_2=\sum_{i_1<...<i_{k+1}<n}a_{\vec{i}}dx^{\vec{i}}$$
we have:
$$|d'w_2|_{I,\infty}=\max_{\vec{i}=(i_1,...,i_{k+1})}
\sup_{x \in I}|a_{\vec{i}}(x)|=\max_{\vec{i}}\sup_{x^n \in
[0,1]}\sup_{x \in I'}|a_{\vec{i}}(x)|=\sup_{x^n \in
[0,1]}|d'w_2|_{I',\infty}
$$
Hence for some $n^{\textrm{th}}$ coordinate value $\tau \in
[0,1]$:
\begin{equation}
\label{eq:11} |d'w_2(\tau)|_{I',\infty}\leq |d'w_2|_{I,\infty}
\end{equation}
Consider a form $$\bar{w}=\int_{\tau}^{x^n}w_1(\sigma)d\sigma\ ,$$
with the integration carried out over the $n^{\textrm{th}}$
coordinate. Its differential is
\begin{equation}
\label{eq:12}
d\bar{w}=(-1)^{k+1}w+\int_{\tau}^{x^n}(dw)_1dx^n+(-1)^k w_2(\tau)\
.
\end{equation}
The induction step gives us a closed form $\tilde{w}$ on $I'$ such
that:
\begin{equation}
\label{eq:13} |w_2(\tau)-\tilde{w}|_{I',\infty}\leq
C|d'w_2|_{I',\infty}\ .
\end{equation}
Let us define $w'=(-1)^{k-1}d\bar{w}+\tilde{w}$. Here $\tilde{w}$
is considered as a form on $I$, independent of $x^n$. According to
(\ref{eq:12})
\begin{equation}
\label{eq:14}
w-w'=(-1)^k\int_{\tau}^{x^n}(dw)_1dx^n+w_2(\tau)-\tilde{w}\ .
\end{equation}
Let us estimate the norm of
$\displaystyle{\int_{\tau}^{x^n}(dw)_1dx^n}$. Since the integral
is taken separately of each coefficient $a_{\vec{i}}$ of the form
$(dw)_1$ we have:
$$|\int_{\tau}^{x^n}(dw)_1dx^n|_{I,\infty}=\max_{\vec{i}}\sup_{I}|\int_{\tau}^{x^n}a_{\vec{i}}dx^n|$$
$$\leq \max_{\vec{i}}\sup_{I}\int_{0}^{1}|a_{\vec{i}}|dx^n\leq
\max_{\vec{i}}\sup_{I}\sup_{x^n}|a_{\vec{i}}|=|(dw)_1|_{I,\infty}
$$
Hence, from (\ref{eq:14}), (\ref{eq:13}), (\ref{eq:11}),
(\ref{eq:10}), (\ref{eq:9}):
$$
|w-w'|_{I,\infty}\leq |(dw)_1|_{I,\infty} +
C|(dw)_2|_{I,\infty}$$
$$\leq C'(|(dw)_1|_{I,\infty}
+|(dw)_2|_{I,\infty})\leq 2C'\max(|(dw)_1|_{I,\infty}
,|(dw)_2|_{I,\infty})\ ,
$$ where $C'=\max(1,C)$. \\Now notice that
$$|dw|_{I,\infty}=|(dw)_1\wedge dx^n +
(dw)_2|_{I,\infty}=\max(|(dw)_1|_{I,\infty},|(dw)_2|_{I,\infty})\
.
$$
Thus $|w-w'|_{I,\infty}\leq 2C'|dw|_{I,\infty}$ which concludes
the proof.
 $\Box$
\begin{cor}
\label{cor:3.3} For any smooth closed $k$-form $w$ ($k>0$) on any
cube $I \subset \mathbb{R}^{n}$ \\there exists such smooth
"primitive" $\theta$ ($d\theta=w$) that
$$|\theta|_{I,\infty}\leq C|w|_{I,\infty}
$$
for some constant $C$.\end{cor} {\bf Proof}\quad According to the
(usual) Lemma Poincar\'e for smooth forms, there exists a smooth
$\theta_1$, such that $d\theta_1=w$. Lemma \ref{lem:3.2} then
provides for existence of a smooth closed $\theta_2$ satisfying
$|\theta_1-\theta_2|_{I,\infty}\leq C|w|_{I,\infty}$. The form
$\theta=\theta_1-\theta_2$ is the desired primitive. $\Box$
\begin{lem
\label{lem:3.4} Any $x \in \mathbb{R}^{n}$ has a neighborhood $V$
such that any closed\\ $\mathcal{L}^{k}_{\infty}$-form $w$ on $V$
is exact: for $k>0$ $\exists \theta \in
\mathcal{L}^{k-1}_{\infty}(V): d\theta=w$. \\If $k=0$, then $w$ is
a locally constant function.
\end{lem}
{\bf Proof}\quad A function which has all of its generalized
derivatives vanish is locally constant. For $k>0$ consider an open
cube $I$, centered at $x$. According to \cite[Lemma 1.3]{GKS} and
the Remark following it, it is possible to choose a sequence of
smooth closed $k$-forms that weakly converges to $w$.

Using Mazur's theorem \cite[Theorem V.1.2]{Y} we can construct
another sequence \{$w_s$\} (of finite convex combinations of the
elements of the original sequence) that will satisfy:
$$|w-w_s|_{I,\infty}\leq \frac{1}{2^s}\ ,$$ and $dw_s=0$ on $I$.

From Corollary \ref{cor:3.3} it follows that there exist such
forms $\theta_s$ on the cube $I$, that
$$
d\theta_1=w_1\ ,\ d\theta_s=w_s-w_{s-1}\ \textrm{ for }s>1\
\textrm{ and }\ |\theta_s|_{I,\infty}\leq
C|w_s-w_{s-1}|_{I,\infty}\ .
$$
Since $$|\theta_s|_{I,\infty} \leq C|w_s-w_{s-1}|_{I,\infty} \leq
C(|w-w_{s}|_{I,\infty}+|w-w_{s-1}|_{I,\infty})\leq
\frac{C}{2^s}+\frac{C}{2^{s-1}}\ ,$$ the series
$\displaystyle{\sum_{s=1}^{\infty}\theta_s}$ converges in
$\mathcal{L}^{k-1}_{\infty}(I)$. Let
$\theta=\displaystyle{\sum_{s=1}^{\infty}\theta_s}$. \\Since
$$|w-\sum_{s=1}^{N}d\theta_s|_{I,\infty}=|w-w_{N}|_{I,\infty}\leq \frac{1}{2^N}\ ,
$$
we see that $d\theta=w$, as required. $\Box$\\

Denote by $H^*_{\infty,\,loc}(M)$ the cohomology of the cochain
complex $\{\Omega^{*}_{\infty,\,loc},d\}$ on a manifold $M$.
\begin{thm}[De Rham Theorem]
\label{thm:dR} For any Lipschitz manifold $M$\\ the cohomology
groups $H^*_{\infty,\,loc}(M)$ are canonically isomorphic to the
cohomology groups $H^*(M;\mathbb{R})$ of the manifold $M$.
\end{thm}
Denote by $\lambda : H^{*}_{\infty,\,loc}(M)\rightarrow
H^*(M;\mathbb{R})$ the canonical isomorphism above.
\begin{thm}
\label{thm:3.6} If $f: M \rightarrow N$ is a Lipschitz map then
$f^* \lambda=\lambda f^*$ .
\end{thm}
The last two theorems follow from Lemma \ref{lem:3.4}, \cite[Lemma
3.1]{GKS} and the general theorems of sheaf theory \cite[11.4.6,
11.4.16]{G}.

It turns out that after relaxing the locality requirement, de
Rham Theorem
above is in general no longer valid for $H^{*}_{\infty}(M)$. In
other words $H^*_{\infty}(M)$ provides a genuinely different (in
fact metric rather than topological) invariant. De Rham theorem
for $H^{*}_{\infty}(M)$ still holds on compact manifolds. This
leads us to ask the following questions.

Do compact manifolds form the maximal class of spaces $M$ for
which the de Rham theorem holds? When is $0 < \dim H^*_{\infty}(M)
< \infty$ for non-compact $M$ ?

redpajama_set_name: RedPajamaArXiv


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Black rice is a source of iron, vitamin E, and antioxidants.
The bran hull (outermost layer) contains one of the highest levels of anthocyanins found in food! The grain has a similar amount of fibre to brown rice and, like brown rice, has a mild, nutty taste.
Black rice has a deep black colour and usually turns deep purple when cooked. Its dark purple colour is primarily due to its anthocyanin content, which is higher in weight than that of other coloured grains.