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Tag Archives: Lady Edith Crawley
Choice-CONTAINS SERIES 4 SPOILERS-READ AT YOUR OWN RISK
*- These characters, with the exception of Harry Crawley, belong to Julian Fellows and Carnival Productions.
*-Based on what spoilers I know of Edith's story line for the 4th series. If you prefer to withhold reading until the series has ended, I understand.
"Mama, look" Harry proudly showed her the tower of blocks he had constructed.
Edith smiled approvingly on her son.
Within a moment, the tower crumbled to the floor and Harry eagerly began to rebuild.
As much as Edith loved her son, she knew of the realities of his life. It was true that he was the grandson of an earl, but he also a bastard.
While his cousin would one day become the Earl of Grantham and inherit both the land and the family fortune, Harry would have to make due with much less. Her London flat was far from the glamour and prestige of her childhood home.
It was a simple flat, containing two bedrooms, a kitchen and living room. There were no housemaids to do the cleaning or help them dress, no nanny to take care of Harry while she worked and no Mrs. Patmore to do the cooking. Edith did it all and surprised herself how accustomed she had become to doing it without help.
Not that Edith was without support. Robert and Cora loved their grandson and were willing to support their daughter. But outside of the confines of the Abbey, she knew that they would be confronted with whispers and stares.
"There goes poor Lady Edith" they would whisper "First she is abandoned at the altar and then she finds herself pregnant by her married editor".
"You don't have to leave, there is room enough for the both of you" her mother pleaded when Edith announced her decision to leave Downton permanently.
"I know, Mama, but we can't stay in Yorkshire".
"There will be a little bit of money, your welcome to come home whenever you want to".
"Thank, you papa".
Edith watched her parents become smaller and smaller as the train left Downton. London was the best place for her and Harry. She could work either from home or at the office; Aunt Rosamund was more than willing to watch Harry if she was needed.
In London, the gossips focused their attention elsewhere. She was simply Edith Crawley, journalist for the Sketch. The fact that her father was an Earl or that her child was born out of wedlock was unimportant.
But still something was missing and that was Michael. But she knew what she was getting into when they started this relationship. The only thing that was unexpected was their son.
"Mama sad?" Harry put down his blocks and crawled to his mother, noticing the tears beginning to dot her eyelashes.
"No, darling, mama is not sad".
"Mama, love".
"I love you too" it was hard to deny that Harry was Michael's son. Harry had the same inquisitive brown eyes, the blond curls that flopped in between his eyes. On Michael it was sexy, on Harry it was adorable.
Edith didn't know when or if Michael would ever return. But she would carry on as she did before Michael, surviving and living her life as she knew how.
Filed under Downton Abbey, Fanfiction
Tagged as Carnival Productions, Downton Abbey, Downton Abbey Fanfiction, Downton Abbey Series 4 fanfiction, Edith Crawley, Fanfiction, Harry Crawley, Julian Fellows, Lady Edith, Lady Edith Crawley, Michael Gregson
Missing-Series 4 Spoiler READ AT YOUR OWN RISK
*-These characters belong with love and respect; belong to Julian Fellows, Carnival, etc. I am simply a humble admirer borrowing the characters.
*-The story contains a spoiler based for series 4, episode 1. Read at your own risk.
It all happened so fast. George's birth and Matthew's accident.
There were nearly a 100 bedrooms for Mary to choose from after Matthew died. But she chose to stay in the bedroom that she shared with him during their short marriage, to sleep in the bed where their son, their only child was created.
It took three months of coaxing from Anna and Cora to convince to Mary to allow the sheets to be washed.
Mary's depression caused her parents to be concerned. She had never been melancholy sort, but loosing Matthew seemed to have broken her.
She might have not left her room, if it wasn't for Georgie. George Matthew Crawley, Mary and Matthew's son and heir to his grandfather's title was the light of her life. Her grandmother kept insisting that Mary hire a nursemaid, but Mary declined. The only person to nurse her son was his mother.
Tonight was a party being thrown in her honor. Robert and Cora hoped that some new faces might bring a smile to their eldest daughter's face.
When Sybil died, Mary missed her sister and sympathized with her husband. Tom had become part of the family and Sybee was adored by the adults around her. But until Matthew died, she did not understand the magnitude of such a loss, to parent your child without the one person who you loved above all others.
Tom had been her rock in past six months; she didn't know what she would do without him.
"Are you ready?" Cora gently knocked before stepping into the room while Anna put the finishing touches on Mary's hair.
"As I will ever be".
"Will there be anything else, milady" Anna asked.
"No, Anna, that will be all, thank you" with a final curtsy, Anna left the room.
"You look lovely, my darling".
"I hope so, mama".
As Mary began to ascend down the stairs, she heard George cry.
"Georgie".
"Mary, I checked on Georgie and Sybie. They are both sleeping".
"Mama, please, I will be right down, I promise".
Entering the nursery, Mary found both her son and niece sleeping peacefully.
"I do the same thing" Tom came up behind her.
"Sybil would be proud of you, Tom, the way you've built your life here".
"I think Matthew would say the same thing about you. He's fine boy, Mary, you should be very proud of him".
"I am, every day".
"Tom, Mary, are you coming?" Now it was Edith's turn to call out.
"Yes, we're coming".
The party was a great success. Mary's smile started to slowly return that evening. Though she would never truly get over the loss of her husband, she knew that everything would be alright in the end.
Tagged as Downton Abbey, Downton Abbey AU Fanfiction, Downton Abbey fanfiction spoilers, Downton Abbey Series 4 fanfiction, Fanfiction, Lady Cora Crawley, Lady Edith Crawley, Lady Mary Crawley, Lady Sybil Crawley, Matthew Crawley, Tom Branson
*-These characters are not my own, they belong to Julian Fellows, Carnival, etc.
*Story takes place a year after season 3, episode 2.
*-This story was written before Michael Gregson was introduced to the American audience.
It was bound to happen eventually. The shopping district in Ripon was small enough; Edith knew that the day would come when she and Anthony would meet. That day was today.
The invitation from Tom had come the day before; he needed to run into Ripon to purchase some things for the house. The house remained in the same state since he and Sybee moved in a year ago, it was time to spruce it up. Mary was occupied, so Edith was happy to join her brother in law for the afternoon; a woman's touch was exactly what the house needed.
"Good day, Mr. Branson, Lady Edith" they were greeted by the shop keeper. Between them was Sybee, who had recently started to walk. She was determined to go as fast and as far as she could, fighting any attempts by her father or any other adult to keep her out of trouble.
Tom handed the clerk a list of supplies while Edith took it up herself to entertain her young niece.
"What do you think, Sybbie? Should we ask papa if your old Aunt Edith can buy it for you?" Edith held out the small doll.
Sybbie reached for the doll, hugging it tightly.
"Tom" Edith called out, pointing to the doll.
"I'll pay for it".
"No" Edith protested "Let me spoil her a little; it's my pleasure".
The bell above the door rang to reveal Sir Anthony.
"Sir Anthony, this is a pleasure, what can I do for today?" the shop keeper asked.
"My niece had her first child last week. I would like to send a gift for the child, but I am just clueless as to what to get".
"I think I know what will do" the shopkeeper directed her clerk to direct Sir Anthony to the appropriate gift.
Tom instantly turned to Edith, knowing that she had not quite gotten over being publicly jilted at the alter. Today was the first time that Edith and Anthony had been with close proximity since their aborted wedding.
"Mr. Branson, Lady Edith" Sir Anthony turned to greet them.
Then Sybbie let out a cry and Edith said a silent thank you.
"Pay me back another time; he doesn't deserve your time or your tears" Tom whispered to her, taking the doll to the front to include in the final bill. He might be a bit rash every now and then, but he had a good heart.
"Papa?" Sybbie asked, realizing the doll was no longer in her grasp.
"Why don't you take her outside, I will be there in a minute?".
As she waited for Tom, Edith took a moment to reflect on her life. She was not Lady Strallan, she might never marry or have children of her own. But this was her life and she was determined to make the most of it.
Tagged as Downton Abbey, Downton Abbey AU Fanfiction, Downton Abbey series 3 fanfiction, Fanfiction, Lady Edith Crawley, Sir Anthony Strallen, Sybee Branson, Tom Branson


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In South Africa a new AI-based project offers the opportunity for a large corpus of scientific terms to be translated into six indigenous languages
Published in: Artificial intelligence, Language advocacy, Languages/Linguistic curiosities, Translation industry, Translation technology
by Pisana Ferrari – cApStAn Ambassador to the Global Village
Language really matters when it comes to scientific communication and education. How can you have conversations about science when the scientific terms you wish to talk about do not exist in your own language? Sibusiso Biyela is a science communicator and journalist from South Africa, based in the Johannesburg Metropolitan Area, who is trying to bring science closer to people by reporting in an indigenous African language. Biyela says he can speak to his friends and family about a whole host of topics in his mother tongue, isiZulu, but is forced to switch to English when talking about science. Despite the fact that Zulu — or isiZulu, as the language is called in South Africa — is spoken by some 10 million people, it simply doesn't have the words for communicating science, he says. To write about DNA — a word for which there is no Zulu counterpart — a writer would have to go back and explain terms like molecules, cells, and genetic codes, which themselves have no Zulu counterparts. One of Biyela's recent science assignments was about a new fossil discovery in South Africa. As there are no words for dinosaur in his language he decided to go with the more general term isilwane sasemandulo, Zulu for ancient animal. He described Ledumahadi mafube as a creature of elephant-like size and shape, with a head and neck resembling a stiff, tiny-headed snake and a tail resembling that of a monitor lizard. Other seemingly simple words required similarly careful treatment, eg. origin of nature or creatures, for evolution, old bones found in the ground, for fossils. In the final story, he says he spent as many words explaining the meanings of scientific terms as he did describing the discovery itself. "So my news piece wasn't just a news piece. It was an attempt to tell a science story in a language that science overlooked — to help right a societal wrong". A new AI project may help to bridge the science language divide in South Africa and improve trust and confidence in science. This is of course all the more essential in times of the COVID-19 pandemic.
Consequences of the science language divide
The issue is not so much that the people one is communicating with cannot speak or understand English, Biyela claims, but that discussing science in your own language makes it easier to culturally "own" it. He quotes a prominent sociology professor and fervent proponent for the "decolonization" of knowledge, Kwesi Kwaa Prah, in a 2007 report to the Foundation for Human Rights in South Africa, who says that "without literacy in the languages of the masses, science and technology cannot be culturally-owned by Africans. Africans will remain mere consumers, incapable of creating competitive goods, services and value-additions in this era of globalization." The language divide has its roots in the colonial history of South Africa. For most of the 20th century, English was the country's only language of science. During apartheid, the government invested funds to "transform" Afrikaans into a language of science, a privilege which was not given to the other indigenous languages. Still today, science examinations in public schools are conducted only in English and Afrikaans, says Biyela. The language divide has therefore alienated large parts of South Africa's population from scientific education and enterprise, he adds.
New AI project for six indigenous languages
Today, Biyela is one of the partners of the 'Masakhane MT: Decolonise Science' project, an initiative aimed at building a multilingual parallel corpus of African research by translating African pre-print research papers into six African languages: siZulu, Northern Sotho, Yoruba, Hausa, Luganda, Amharic. Masakhane is a grassroots organisation whose mission is to strengthen and spur natural language processing (NLP) research in African languages. The data to be translated will be pre-print papers published on AfricArxiv, a community-led digital archive for African research, which currently has around 600 articles in a number of different fields (life sciences, engineering, law, social sciences, mathematics). The aim of the dataset is to facilitate tools and products being developed (e.g. translation models and tools, teaching aids, etc) and the creation of glossaries and new terminology. A pilot run is due to be performed; the translations from the pilot will be assessed by the project's linguistic partners and data curators to ensure quality and format of translations and allow for feedback, before work continues.
Bringing science closer to people in COVID-19 times
As Biyela rightly points out, understanding science in one's own language not only makes it easier to trust the institution of science but can go a very long way to reaching the people that need science the most. During the pandemic, many African governments did not communicate information about COVID-19 in all the languages in their countries, or not in a timely manner (this has regrettably happened in many other countries around the world, see our blog post at this link). This means that people risked missing out on potentially life saving information and this is turn can affect compliance to containment measures or travel restrictions, critical in order to protect not only individuals but also the community at large. Right now, information is needed more than ever because there is an alarming amount of vaccine hesitancy, Biyela says.
Pichon, A. The language of science. Nat. Chem. 13, 1025–1026 (2021)
"Masakhane MT: Decolonise Science"
"Decolonizing Science Writing in South Africa", Sibusiso Biyela, TheOpenNotebook, February 12, 2019
See also our other articles about the language of science and decolonization of knowledge
In South Africa a new movement seeks to "decolonise" the teaching of mathematics
Letting English become the lingua franca in science means that studies in other languages often go unread
Today, more than 90% of the indexed articles in the natural sciences are published in English, that wasn't always the case
Photo credit Hands intertwined against with colours and backdrop of South African flag, Hasanov Jeyhun at Shuttertock

redpajama_set_name: RedPajamaCommonCrawl


October's total was perhaps a bit disappointing following the increase in films watched during September, but with 36 new films viewed, we have now passed the 400 mark and with two months to go, reaching the target is still achievable. As you might expect from the month that ends with Halloween, there were plenty of horror films watched during October, from classics such as Halloween to new releases like IT, Happy Death Day and Gerald's Game.
Below are the stats for the month, including our picks for best and worst films of the month. You can also scroll down to see the reviews written by each team member for every film watched in October.


NOW THE SECRET IS OUT !!!!!
Features The two identical 2-bedroom houses both have open plan living, bathroom and large front verandas that run the length of the house.
Opportunity There is also a 20 ft Islander boat for sale:- 60 hp Yamaha, 4 stroke , 200 hours for $30,000.
Located on the northern side of Vanua Levu the second largest of over 300 islands that make up the Fiji group, you will find this special paradise of unspoilt beauty. Surfing, fishing and diving on the great sea reef on Fiji's North side (the fifth largest barrier reef in the world) with its numerous tropical game fish and crystal-clear waters, is as pristine as it gets.
Once part of a large coconut plantation this 4-acre freehold property at Narewa is roughly 50 minutes from Labasa, 40 minutes from Labasa Airport and 1.5 hours from Savusavu. The country side is beautiful and the people and villages nearby will provide an enriching experience to witness the Fijian culture firsthand.
The houses are built to capture views that stretch up to the mountains of rocky outcrops and ridges and out to sea to little islands and reefs that dot the horizon and most importantly, the surfing sites. The top house is the only house in Northern Fiji with a view of the surf spots and it is only a 35 minute boat ride to Twin Pass.
The two identical 2-bedroom houses both have open plan living, bathroom and large front verandas that run the length of the house. The main house has a 2 Car garage (22X24ft) and a utility bathroom. The property is landscaped with plenty of fruit trees, solar panels, 24 volts system with generator back up and Bore Hole.
Only one Resort (Nukubati) goes out there. Check out their web page.
- Twin Pass which has a right and a left.
The right at Twins is one of the best high-performance waves in Fiji. An easy take off with tube sections and cutback sections that ends in deep water. No closeouts and a dry hair paddle back out. The left up to six feet is like Restaurants on Tavarua, at eight foot plus it's like a miniature Teahupoo, thick and hollow and it ends in deep water.
The article is about Rob Machado, Ross Williams and Pat Oconnell surfing at Twins. Absolutely empty surf and plenty of spots no one has ever surfed yet.
There is also a 20 ft Islander boat for sale:- 60 hp Yamaha, 4 stroke , 200 hours for $30,000.
This is undoubtedly a rare opportunity to live out your dreams. Call for more details.


All in all the experience was better than I expected. The crew worked in horrible weather; minus 30's and later on, deep clay mud. They were professional, polite and a great crew.
Our sales person was fabulous. He worked with us continually through any and all problems/delays that we had. Some of the issues we had with the project were significant delays, a broken front window (that was replaced) and a breakdown in some communication resulting in us having to take days off work with no workers ending up coming.
All in all the work that was done was excellent, our sales person was on top of everything and even though it took a year from start to finish he stayed with this project until the end.
I found dealing with your company was a positive experience. The sales rep was very informative and listened to my concerns and requirements. The installation crew was great and they explained thoroughly what they were doing and answered my questions and concerns.
used Basement Systems of Winnipeg before, your company seems to have replaced them. So, 'took a chance' on you guys.
Exceptional crew... Nat was very informative every step of the process. Great crew she leads and works with.
Nat was a very experienced & caring person who obviously takes great pride in her work & the customer's wants & needs. She went above & beyond in my opinion, even securing the cord for the pump so it won't get in the way of anything.
The installation crew did a great job, we are very happy with the outcome. They were efficient and friendly.


Release v0.13.0 is fresh from the oven.
This release ships with major improvements in the xrootd implementation and a few fixes in rootio.
rootio has been updated to v2 of pierrec/lz4 library to decode LZ4 compressed ROOT files.
$> xrd-cp -r root://server.example.com/some/dir .
Command xrd-ls lists directory contents on a remote xrootd server.
a convenience xrootd/xrdio.File type, implementing various io.Xyz interfaces has been introduced as well.


Most useful learnings: How to do TDD.
Exercise improvements: The Spy exercise contains many more files than necessary which was confusing at first.
Start tomorrow: At home yes. At work non-technical elements stand in the way.
Challenges to applying: Cannot gain permission to install and use an off the shelf unit test framework.


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Aurore Martin née à Oloron-Sainte-Marie le , est une femme politique, militante du parti basque indépendantiste Batasuna. Un mandat d'arrêt européen a été émis en octobre 2010 à son encontre par la justice espagnole dans le cadre d'une enquête liées à des « faits de participation à une organisation terroriste, et terrorisme » à la suite d'apparitions publiques au sein de Batasuna, parti illégalisé en Espagne mais légal en France.
Cela a conduit à une tentative d'arrestation avortée en 2011, puis à son arrestation par la gendarmerie française le  novembre 2012 et à sa remise immédiate aux autorités judiciaires espagnoles. Elle est cependant libérée sous caution le 22 décembre 2012.

Aurore Martin était en 2012 la première citoyenne française extradée vers l'Espagne dans le cadre du conflit basque.

Biographie
Née en 1979 à Oloron-Sainte-Marie (ville béarnaise limitrophe du Pays Basque), au sein d'une famille peu militante ne parlant pas le basque, Aurore Martin a été scolarisée dans une ikastola, école associative dans laquelle l'enseignement est dispensé en basque.

Elle s'engage progressivement en faveur de l'identité basque en participant à la vie associative et en établissant des maisons de jeunes (gaztetxe). Son engagement militant s'affirme progressivement ; après l'évasion d'un militant pro-basque du commissariat de Bayonne, elle est arrêtée en janvier 2003 pour association de malfaiteurs et incarcérée à Fleury-Mérogis, avant de bénéficier d'un non-lieu. Devant ce qu'elle considère comme une injustice, elle se radicalise en adhérant à Batasuna, parti défendant la création d'un État basque souverain et un projet de société très marqué à gauche.

L'affaire Aurore Martin

Émission d'un mandat d'arrêt européen
Le 13 octobre 2010, le tribunal central d'instruction  à l'audience nationale de Madrid émet un mandat d'arrêt européen à son encontre, en vue de poursuites pénales pour des « faits de participation à une organisation terroriste, et terrorisme », commis en France et en Espagne en 2006 et 2007.

Il lui est précisément reproché « trois séries de faits :

 - des faits commis en Espagne, à Pampelune et à Alava, consistant en la participation, en qualité de membre du parti politique Batasuna, à des manifestations publiques qui se sont tenues les 24 mars et 26 avril 2006, 3 mars et 14 septembre 2007, ainsi que la rédaction d'un articule publié dans le journal Gara dans lequel elle se présente comme membre du parti Batasuna ;

 - des faits commis sur le territoire français, à Bayonne et à Ustaritz consistant en la participation à des manifestations publiques du parti Batasuna les 21 septembre 2006 et 28 janvier 2007 ;

 - des faits commis en Espagne, afférents à son inscription en qualité d'employée du EHAK (parti communiste des terres basques) depuis le 2 novembre 2006 et la réception le 17 février 2007 de deux virements de  chacun sur ses comptes personnels en provenance d'un compte bancaire ouvert à la « caja de ahorros de pensiones » de Barcelone dont le titulaire est le EHAK ».

Ces faits sont qualifiés de participation à une organisation terroriste et terrorisme par les autorités judiciaires requérantes et sont punissables d'une peine de douze ans d'emprisonnement en Espagne.

En application des dispositions instituant le mandat d'arrêt européen, introduites en droit français à l'article 695-23 du code de procédure pénale, les faits relevant de certaines incriminations, dont le terrorisme, punissables de plus de trois années d'emprisonnement par l'État émetteur du mandat, n'ont pas à faire l'objet d'un contrôle dit de la double incrimination visant à vérifier qu'ils sont répréhensibles à la fois dans l'État émetteur et dans l'État chargé d'exécuter le mandat .

Participation à Batasuna
Ce mandat d'arrêt européen fonde ainsi sa remise aux autorités espagnoles sur le fait qu'elle milite activement au sein du mouvement indépendantiste basque Batasuna. Cette organisation a été déclarée illégale en Espagne du fait de ses liens avec  (ETA)  et ne dispose pas d'existence juridique en France. Batasuna apparaissait jusqu'en 2009 sur la liste officielle des organisations terroristes de l'Union européenne, mais n'y figure plus depuis 2010.

Passage dans la clandestinité
Le 21 décembre 2010, à la suite du rejet de ses recours devant la justice française contre l'exécution du mandat d'arrêt européen, Aurore Martin annonce par communiqué qu'elle décide de se cacher pour échapper à une arrestation et à un transfert vers l'Espagne. Depuis la clandestinité, elle annonce dans une lettre adressée au Journal du Pays basque (Euskal Herriko Gazeta) qu'elle est candidate aux élections cantonales de mars 2011 dans le canton de Tardets-Sorholus dans les Pyrénées-Atlantiques, sous l'étiquette d'Euskal Herria Bai (Pays basque Oui), en tant que suppléante de Gilen Iriart.

Le 3 juin 2011, Aurore Martin explique dans un entretien accordé au Journal du Pays basque et à Mediapart son désir de « recommencer une vie publique normale ». Le 18 juin 2011, à l'occasion d'un colloque sur le thème du mandat européen qui se tient à Biarritz, elle sort de la clandestinité.

Première tentative avortée, puis arrestation et remise à l'Espagne
Le 21 juin 2011, lors d'une tentative d'arrestation par la police française, rue des Basques à Bayonne, des militants et sympathisants de la gauche abertzale empêchent son arrestation au cours d'une confrontation musclée avec la police. Après cet échec, le ministre français de l'Intérieur, Claude Guéant réaffirme que « cette dame est sous le coup d'un mandat d'arrêt européen. Il est du devoir de la police française de mettre en œuvre ce mandat d'arrêt. Et il sera mis en œuvre ».

Aurore Martin est finalement arrêtée par les gendarmes à Mauléon-Licharre (Pyrénées-Atlantiques) le  novembre 2012 au cours d'un contrôle routier, puis remise aux autorités judiciaires espagnoles. Des élus locaux protestent contre ce transfert en affirmant « que les faits visés par l'Espagne ne sont pas répréhensibles en France ».

Le 2 novembre 2012, après sa remise à l'Espagne, le mouvement Batasuna accuse publiquement le ministre de l'intérieur français Manuel Valls d'avoir rompu un « accord tacite avec les nationalistes basques » et d'être « un simple relais de Madrid à Paris ».

Libération
Elle est libérée le 22 décembre 2012, avec le versement d'une caution de , payée notamment grâce à des collectes de fonds organisées par Batasuna. Aurore Martin devra, en outre, se présenter entre le  et le 5 de chaque mois devant la justice espagnole, sans que cette disposition ne l'oblige à vivre en Espagne.

Le 13 janvier 2016, l'Espagne renonce à toutes ses poursuites et amnistie Aurore Martin de sa peine d'un an et huit mois de prison. En effet, en vertu d'un accord judiciaire entre l'Etat et 35 indépendantistes inculpés, ils sont libérés sans peine après avoir reconnu leur « délit de participation à une organisation terroriste » et signé un « engagement à renoncer à toute activité en lien avec l'usage de la violence, en souhaitant que cette reconnaissance contribue à la réparation des dommages et souffrances qui ont été causés aux victimes du terrorisme ».

Notes et références

Voir aussi

Articles connexes
 Batasuna
 Mandat d'arrêt européen

Liens externes

Naissance en janvier 1979
Naissance à Oloron-Sainte-Marie
Nationaliste basque
Personnalité politique liée aux Pyrénées-Atlantiques
Femme politique française

redpajama_set_name: RedPajamaWikipedia


Colbitzer Pils is an ideal pleasurable experience for all Pils connoisseurs who prefer a fine dry hopped and tangy beer Pilsner type . The liveliness and the fresh taste are characteristics of this product.
33 cl can 4x6 pack click here!
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Every year, I send my family a reminder that we do not want any plastic toys or clothes made from synthetic fibers. I wish I could say that they always followed our wishes, but somehow, the message flies out the window when they see some "adorable" plastic thing they think my children can't live without. My husband has changed the motto to "No More Toys" this year, but the grandparents have already scoffed at the idea. Perhaps I should try sending my family Alicia Daniel's list to help them make appropriate gift selections. If we are going to tell our children to reduce, reuse, recycle, shouldn't our holiday gift giving and receiving reflect this practice?
How can I subtly send this to everyone I know… especially the grandparents!
Thanks for the list of questions, it's a great starting point.
I am with you 100%. I wrote a blog post about it and said, hands down- no more JUNK toys. My rule is: only give gifts that are hand made or make a donation to my favourite charities. We have too much stuff!
As always, we'll see who listens- some people need to fill their devoid souls through shopping and don't actually care about what you NEED.


text:
Acrocercops karachiella is een vlinder uit de familie van de mineermotten (Gracillariidae). De wetenschappelijke naam van de soort werd voor het eerst geldig gepubliceerd in 1968 door Amsel.

Gracillariinae


text:
Clifford Henry Dyment FRSL (20 January 1914 – 5 June 1971) was a British poet, literary critic, editor and journalist, best known for his poems on countryside topics. Born to Welsh parents, his mother was widowed when Dyment was four years old.

Born in Alfreton, Derbyshire, he spent his early childhood in Caerleon-on-Usk but was educated at Loughborough Grammar School in Leicestershire.

His poem "The Son" was occasioned by his discovery of a letter written by his conscripted father prior to his death in World War I. Another Dyment poem "From Many a Mangled Truth a War is Won" laments the tendency to invent pretexts and justifications for wars.

His first published collection was First Day (1935). During the latter part of the 1930s he was a literary figure in London. During World War II he was engaged to make films, working for the British government.  His poem As a boy with a richness of needs I wandered was included by Philip Larkin in The Oxford Book of Twentieth Century English Verse, in 1971.

The poem Mouse was set to music by Betty Roe as part of her song cycle of Cat and Mouse (1987).

He received a Rockefeller Foundation Atlantic Award in 1950.

Works

First Day (1935)
Straight or Curly (1937)
The Axe in the Wood (1944)
Thomas Hood, Selected Poems (1948, Grey Walls Press) editor
Poems 1935–1948 (1949)
Experiences and Places (1955)
The Railway Game: An Early Autobiography (1962)
C. Day-Lewis (1963 biography)
Collected Poems (1970)
'The Encounter'

References

External links
Filmography

1914 births
1971 deaths
People educated at Loughborough Grammar School
People from Alfreton
Fellows of the Royal Society of Literature
20th-century British poets
British male poets
20th-century British male writers


Franz Julian Paetzold is a passionated German carp angler. He is a real carp food specialist. Franz likes to fish in small hidden lakes. Most of his fishing consists of short overnighters between work. His strategy is mainly spending a lot of time at the bank, watching and observing. Paying attention and the ability to adapt are the key to being successful in short sessions. Franz also dedicates a lot of his time working with kids in his local fishing club.


text:
Adjuvant Low-Dose Interleukin-2 (IL-2) Plus Interferon-alpha (IFN-alpha) in Operable Renal Cell Carcinoma (RCC): A Phase III, Randomized, Multicentre Trial of the Italian Oncology Group for Clinical Research (GOIRC)
There is currently no standard therapy to reduce the recurrence rate after surgery for renal cell carcinoma (RCC). The aim of this study was to assess efficacy and safety of adjuvant treatment with low doses of interleukin-2 (IL-2) + interferon-alpha (IFN-alpha) in operable RCC. The patients were randomized 1:1 to receive a 4-week cycle of low-dose IL-2 + IFN-alpha or observation after primary surgery for RCC. Treatment cycles were repeated every 4 months for the first 2 years and every 6 months for the subsequent 3 years. The primary endpoint was recurrence-free survival (RFS); safety; and overall survival (OS) were secondary endpoints. ClinicalTrials.gov registration number was NCT00502034. 303/310 randomized patients (156 in the immunotherapy arm and 154 in the observation group) were evaluable at the intention-to-treat analyses. The 2 arms were well balanced. At a median follow-up of 52 months (range, 12-151 mo), RFS, and OS were similar, with an estimated hazard ratio (HR) of 0.84 [95% confidence interval (CI), 0.54-1.31; P = 0.44] and of 1.07(95% CI, 0.64-1.79; P = 0.79), respectively in the 2 groups. Unplanned, subgroup analysis showed a positive effect of the treatment for patients with age 60 years and younger, pN0, tumor grades 1-2, and pT3a stage. Among patients with the combined presence of >= 2 of these factors, immunotherapy had a positive effect on RFS (HR = 0.44; 95% CI, 0.24-0.82; P <= 0.01), whereas patients with <2 factors in the treatment arm exhibited a significant poorer OS (HR = 2.27; 95% CI, 1.03-5.03 P = 0.037). Toxicity of, immunotherapy was mild and limited to World Health Organization grade 1-2 in most cases. Adjuvant immunotherapy with IL-2 + IFN-alpha showed no RFS or OS improvement in RCC patients who underwent radical surgery. The results of subset analysis here presented are only hypothesis generating.
Adjuvant Low-Dose Interleukin-2 (IL-2) Plus Interferon-alpha (IFN-alpha) in Operable Renal Cell Carcinoma (RCC): A Phase III, Randomized, Multicentre Trial of the Italian Oncology Group for Clinical Research (GOIRC) / Passalacqua, R; Caminiti, C; Buti, S; Porta, C; Camisa, R; Braglia, L; Tomasello, G; Vaglio, A; Labianca, R; Rondini, E; Sabbatini, R; Nastasi, G; Artioli, F; Prati, A; Potenzoni, M; Pezzuolo, D; Oliva, E; Alberici, F; Buzio, C. - In: JOURNAL OF IMMUNOTHERAPY. - ISSN 1524-9557. - 37:9(2014), pp. 440-447. [10.1097/CJI.0000000000000055]


text:
Robert 'Buddy' Shaw
| Filmography
Robert 'Buddy' Shaw was an American actor.
Robert 'Buddy' Shaw was born Wilfred Shaw on March 29th, in California, United States. His zodiac sign was Aries.
He died on Sunday, August 29th, 1976 at the age of sixty-nine (69) in Los Angeles, California, United States.
As an actor, Robert 'Buddy' Shaw has been seen in movies such as Twisted Rails, released in 1934 in which he plays Tommy McGuire, Monsieur Beaucaire (1946), Turnabout (1940), Easy Living (1949), Rumba (1935), and One Night of Love (1934).
Sunrise at Campobello
Directed by: V. J. Donehue, starring R. Bellamy, G. Garson, H. Cronyn, J. Hagen...
Directed by: L. Milestone, starring F. Sinatra, D. Martin, S. Davis Jr., P. Lawford...
Ice Palace
Directed by: V. Sherman, starring R. Burton, R. Ryan, M. Hyer, J. Backus...
The Miracle of Our Lady of Fatima
Directed by: J. Brahm, starring S. Whitney, S. Jackson, C. Milletaire, S. Ogg...
Jim Thorpe -- All-American
Directed by: M. Curtiz, starring B. Lancaster, C. Bickford, S. Cochran, P. Thaxter...
Directed by: G. Douglas, starring F. Lovejoy, D. Hart, P. Carey, J. Millican...
Directed by: S. Heisler, starring G. Cooper, R. Roman, S. Cochran, R. Massey...
Directed by: D. Butler, starring D. Day, G. MacRae, G. Nelson, E. Arden...
Directed by: J. Tourneur, starring V. Mature, L. Ball, L. Scott, S. Tufts...
Monsieur Beaucaire
Directed by: G. Marshall, starring B. Hope, J. Caulfield, P. Knowles, M. Reynolds...
Robert 'Buddy' Shaw ➤ Filmography
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Robert 'Buddy' Shaw ➤ Message Board
1 message - lee if you read this you will know right away who i am , hi new years eve motley crew hi sweety...
A letter from a dear friend, Robert Michael Crofoot,GOD, to Simon Cowell
1 message - Dear Simon,...
Photos of Robert Downey Jr. from "Due Date" (2010), a film by Todd Phillips
1 message - «Due Date» is a Comedy film directed by Todd Phillips, and written by Alan R. Cohen, Alan Freedland, Adam Sztykiel and Todd Phillips,...
[PHOTOS] Robert Downey Jr., Jude Law in "Sherlock Holmes: A Game of Shadows", a film by Guy Ritchie
1 message - Starring Robert Downey Jr., Jude Law, Noomi Rapace, Jared Harris, Stephen Fry and Kelly Reilly, «Sherlock Holmes: A Game of Shadows» (also...
An American actor
An English actor, and writer
Robert 'Buzz' Henry
Robert 'Bones' Hamilton
Resources: contributions from movie fans. Anyone can submit additionnal information and corrections, you can post a message into the forum, or you can contact me by e-mail. Information and materials are submitted by users and thus may not always contain up-to-date and correct information, so do not hesite to report mistakes, and submit corrections.Thank you!. Direct editing is no longer available, sorry.
theiapolis PEOPLE


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EY's Omar Ali: Why UK financial services will look beyond Europe in 2022
Omar Ali is the Regional Managing Partner for Emeia Financial Services at EY 2021 has not been an easy year, but we have seen some landmark developments in financial services in Europe, including record profits, record high M&A levels, the first significant wave of European …	Read More
Gov. Hochul proposes radical changes in politics and tone in the 1st State of the State speech
ALBANY – In her first State of the State speech, Gov. Kathy Hochul proposed a dramatic expansion of New York's health care staff, tax breaks for small businesses, a new ethics agency, and a new era of cooperation between her office and other elected officials. …	Read More
Gov. Kathy Hochul sets the agenda at the 1st State Of The State Address – CBS New York
ALBANY, NY (CBSNewYork) – Governor Kathy Hochul gave her first State of the State speech on Wednesday, setting out programs and priorities as she tried to distance herself from her scandal-ridden former deputy, Andrew Cuomo. As CBS2's Marcia Kramer reported before the speech, the governor …	Read More
Cramer says it is impossible to recommend Chinese shares in a hostile communist regime
CNBC's Jim Cramer said on Wednesday that he can not recommend investors to buy Chinese shares because the communist government there is a "total wild card". Chinese President Xi Jinping "does not like capitalism," Cramer told the "Squawk Box," saying the leader of the world's …	Read More


Belle Harbor! 1 Block to the Beach!! Detached Brick High Ranch, meticulously maintained. Main level has beautiful hardwood floors throughout, XL bright & airy LR that connects to a Formal DR. The main floor has a full kitchen, full bath, 2 bdrs and a master suite with a 3/4 bath, garden view from bedrooms. Lower level is fully finished with 2 more bdrs, full bath, dinette and rec room, capacity for wet bar. Access to built in garage and laundry area. Private drive, front porch and spacious rear yard, gardeners dream.
I was searching for a Property and found this listing (MLS® #425901). Please send me more information regarding 255 Beach 131, Belle Harbor, New York, 11694. Thank you!
I'd like to request a showing of 255 Beach 131, Belle Harbor, New York, 11694 (MLS® #425901). Thank you!


text:
Singapore Gallery
UltraSuperNew
Digi Salon
in partnership with Mutek.jp
Fri, Oct 19 - Thu, Nov 01 2018
Sat, Oct 19, 6:00pm - 10:00pm
The Digi Salon is an international exhibition of digital creativity co-hosted by MUTEK.JP and UltraSuperNew Gallery. The exhibit will feature innovative projects at the intersection of technology, art and music. In addition, several artist talks, live music events, and panel discussions will be held throughout the exhibition period to explore the creative interpretation of new technologies.
Digi Salon will also feature an installation and collection of prints called 'dyebirth,' designed and constructed by artist collective, nor. 'dyebirth' explores organic patterns through a controlled variable involving digital computations. Inspired by the works of Ilya Prigogine, a Belgium physicist, who proposed a theory called 'dissipative structure,' a concept that theorizes life as an exchange between energy and matters within its surrounding. The installation visualizes the concept by using ink droplets and digitally controlled variables to express the complex idea diversity in life. The installation will be complimented with a DJ mix produced by Yui Onodera & Robert Lippok.
We cordially invite you to join us in the ambitious explorations in the field of art, music, and technology.
nor is a Japanese art collective made up of architects, designers, musicians, engineers, and more. nor pushes creative boundaries by designing installations and products that interweave hardware and software integration. Their work uses creative means in hopes to understand undefined and unexplored areas.
https://nor.tokyo/
Dyebirth
MUTEK.JP
MUTEK.JP is a cultural association that is dedicated to the dissemination and development of digital creativity in sound, music, and audio-visual art. In 2016, Tokyo joined the burgeoning family of MUTEK events all over the world. Established with the same curatorial vision as its Montréal headquarters, including a mandate to cultivate local talent in a global context, MUTEK.JP provides a platform for the most original and visionary artists currently working in their fields.
http://mutek.jp/
Digi Salon Events
2018/10/20 (sat) 14:00 - 19:00
Digi Beats presents several local DJs who are fully committed to taking you to another dimension through euphonic rhythms and silky cadences.
Digi Lab: Artist Talk with nor
2018/10/25 (Thu) 18:30 - 22:30
On a Thursday night, we will invite artist collective, nor, to share more about 'dyebirth,' on display and their future artistic endeavors.
Digi Lab: Artist Talk & Live set with Intriguant
2018/10/26 (Fri) 18:00 - 22:00
On a Friday night, we will invite Singapore-based electronic music producer and DJ, Intriguant, to share more about his music that has arrested many fans world wide.
Experience presents several local DJs who are fully committed to taking you to another dimension through euphonic rhythms and silky cadences. Drop in and bask in tunes that knows no creative boundaries.
Digi Lab: Panel Discussion on Art x Blockchain
2018/10/31 (Wed) 18:00 - 22:00
In this panel discussion we invite a multidisciplinary collection of people to exchange thoughts on the topic of digital art and the blockchain.
Mutek Match
2018/11/1 (Thurs) 14:00 - 17:00
Develop your professional network, get expert advice, explore avenues for collaboration and coproduction, and pitch your ideas or projects!
Sign up to hear about our upcoming exhibitions and events
©2020 UltraSuperNew Gallery All Rights Reserved.


text:
Bread and Fallen Angels
Have you ever stopped to think about the origins of bread? It's such a familiar food that we rarely give it much thought outside of buying more, or deciding which sandwich filling to use.
Bread is supposed to be one of the oldest foods known to humanity, dating back approximately 30,000 years when flatbread was made from starch extracted from pounded plant roots. Grain-based bread apparently emerged around 10,000 BC, made by Neolithic peoples who used also used air-borne yeast, or yeast already found on the grains themselves, to make the dough rise a little. If some of this dough was kept until the next day then added to a fresh batch, the yeast was passed on - as with sourdough. The Gauls and Iberians figured out how to take foam off beer to increase the yeast content. Elsewhere in Europe, grains were soaked in wine to access yeast.
Who was the first person to walk past a patch of wild grasses and think, "Hey, I can do something with this..?"
There is a huge jump in technology between a person who chews grains, and someone who figures out how to dry those grains, sift off the husks, grind the grains to make flour, how to store that flour so it didn't become damp and spoil, and how to add fat and water in the right quantities, how to knead it, use yeast, let it rise, knead again and rise again, then bake (or fry or steam). Having achieved this much, they then cross-pollinated wild grasses to create more useful kinds of grains - and all this was done when, according to conventional history, we were supposed to be simple hunter-gathers with a penchant for grunting and sharing fleas.
It might be argued that the end result - bread - was arrived at through experimentation. Yet experiments usually already have a specific end result in mind. How does a person set out to invent bread when no-one's heard of bread before, when the very concept of bread has yet to exist?
Similar historical puzzles exist about the origins of pottery, weaving, writing, herbal cures and metal tools.
One interesting theory is that knowledge of these skills was handed to the hunter-gatherers by survivors of an older civilisation whose history is buried in myth and legend. Stories tell of Atlantis, Eden, Tir naNog, Elysium and similar idealised places whose citizens were allegedly far superior in scientific - or magical - ability, or who dwelt in a paradisaical, pastoral Happy Land. With all such tales there is an associated big disaster. Usually this results in a lack of access to such places, due to geological cataclysms or magical retribution of some sort.
If knowledge is power then power certainly rested with those survivors, who could live very comfortably in comparison with the Neolithic peoples. The principle of 'work for me, in return for a better life' would have evolved readily, and positions within these communities would have been sought eagerly by many who would have been content to be exploited in return for an improved standard of living. Imagine if you'd only ever crunched grains, and then someone handed you a slice of bread. Wouldn't that bread seem magical? Wouldn't you be favourably impressed and be willing to exchange work for more yummy bread?
But nobody likes to be exploited too much. Sooner or later someone probably realised that anything the Big Wigs could do, they could do too.
Or maybe some Big Wigs felt that the status quo was unfair to the Neolithic people, and so decided to share their 'how to' knowledge. This decision would have caused uproar among the ranks of the power-holders, as traditionalists would have strongly disagreed with sharing the knowledge that had given them a relatively comfortable life. The resulting political schism would have had far-reaching ramifications, and those who broke with tradition would have been viewed either as heroes or rebels depending on which side you were on. Some people believe an occurance like this lies behind the story of angels and fallen angels, a myth which dates back at least to ancient Sumeria.
Of course, this alternative to popular history does not explain where the Big Wigs originated from, or where their knowledge originated from. However, archaeologists and historians keep pushing back the probable dates of how old humanity really is. It's all just educated guesswork, and many readily admit this. Some suspect there have been a succession of world populations followed by devastations then re-populations, time and time again. Such a theory is possible.
Labels: history, philosophy


This entry was written by admin, posted on 05/27/2015 at 6:35, filed under Motorcycle & ATV Gloves and tagged Black/Red, Gloves, Medium, Motorcycle, Olympia, Reflector, SPORT. Bookmark the permalink. Follow any comments here with the RSS feed for this post. Both comments and trackbacks are currently closed.
I can't tell you how often I wear my gloves. OK, just about every ride! The Hi-Viz was a fantastic choice for Olympia to make. I just wish that they made a M/L size because that would be the exact fit for me. The generous was just a hair to huge on the extension of my fingers, thus why I originally returned my first pair. A very, very minor inconvenience but! When the time is right, or just because, I'll certainly return for more Olympia gloves! You also get used to the Velcro strapping underneath, but, every now and then, it would be nice to have it on top.
I was slightly disappointed in the quality of the gloves. I have bought a few of these over the years and this order (year) was lacking. The stitching was poor mainly on the fore and index fingers and become annoying even on small rides. The trembling dampening has also decreased – I am not sure if they used less gel or what the issue is but my older gloves (same type) are surpass (thicker gel). I do like the style subdue the velco is enough to make them fit but not obnoxious as in many full gauntlet types. Hopefully they will get surpass over time, I just hope Olympia pays more attention to quality in the future.


With such widespread ages at work, is it an insurmountable problem carving a suitable common space for everyone to communicate and to mix in well?
In a recent article, a self-confessed "oldie" expressed surprise at his younger colleagues' tech and romance styles. On the one hand, he felt liberated from having to prove himself on the lunch choice and tech fronts (there's millennials to handle the latter) but on the other, he couldn't believe the Tinder-style decisions they were making in their social lives. His surprise was especially surprising because every so-called generation has had their own way of hooking up.
But differences in dating styles aside, how can businesses create workplaces that all generations feel comfortable in? What are the dos and don'ts of working with baby boomers, Generation X, Generation Y and millennials?
This can vary depending on your office fitout, but not everyone likes chewing the fat in an open-plan area (even if it has funky pot plants and standing desks). By providing quiet places to work and have confidential discussions (some meeting rooms just don't feel sufficiently private), everyone gets the best of both: conviviality when it's welcome and a cone of silence for other times.
Encourage ways to share ideas and develop open forums (making it clear they need to be respectful and moderated); it's an opportunity for new relationships and ideas to take root.
Bring in guest speakers who represent different stages of life (make sure they're engaging, as well as insightful), and try out some new approaches to existing work methods.
Neither age nor youth has a monopoly on agility, adaptiveness, or better ways of doing things. Listening, tolerance and greater acceptance of difference must be mutual if you really want "generational glide" and workplace harmony and collaboration.
Attention-grabbing headlines and pigeonholing may suit demographers and marketers, but many people don't care to be categorised in this superficial fashion. Just because we all tend to apply the Duck test to each other doesn't mean we should stick to it. See everyone as an individual, not a set of generalised characteristics.
Don't assume everyone loves social media, texting, and meetings. Everyone is different in how they like to communicate and while there are some similarities for certain age groups, it is never safe to assume.
And what about the term "digital natives"? It is not in itself patronising terminology, but some people make an assumption that fluency in apps and programs does not make for critical thinking skills. These need to be developed no matter what age or generation you are. The key point is never assume anything, simply based on age, in assessing skills.
Being closed to ideas or training in new ways of doing things swings both ways. Older generations can learn new software and workplace approaches; younger generations can absorb better ways to contextualise and draw from experience. Everyone can benefit from being open and persisting with new ideas and new strategies.
This is a problem in many workplaces, less so because of age and more so because we are all different in our likes and dislikes about how we spend our time socialising. At work this needs to develop organically, perhaps through collaborating on a project or pitching for new business.


Early viewing advised on this well presented mid terraced house comprising of lounge, living room, modern kitchen with oven & hob, two bedrooms and first floor bathroom.
Front and rear gardens together with double glazing and gas combi central heating.
Available now - a well presented mid terraced house conveniently located for Treorchy Town Centre. Comprising of entrance lobby, cloaks/wc, lounge/diner, refitted modern kitchen with oven & hob, three bedrooms and first floor bathroom. There is a forecourt and rear garden together with double glazing and gas combi heating. Recommended.
Available now - a three bedroom mid terraced house convenient for local amenities and comprising of entrance hall, lounge/diner, kitchen with built in oven and hob and refitted first floor bathroom. There is a paved forecourt and terraced rear garden with lane access. Gas combi central heating and double glazing.
A well presented first floor flat comprising of lounge, modern kitchen/breakfast room, two bedrooms and bathroom. The property benefits from gas central heating and double glazing and is located in a convenient location for amenities and main roads. Offered unfurnished and available immediately.
Convenient for town centre and transport links, a modern top floor apartment comprising of entrance hall, lounge with open modern open plan fitted kitchen with built in oven, hob, fridge and freezer, one bedroom and modern shower room. The property has electric heating and is offered unfurnished.
*** Available now *** A three bedroom well presented property comprising of entrance lobby, lounge, modern kitchen/breakfast room with oven & hob, utility, modern bathroom and first floor cloaks/WC. There is an enclosed rear garden together with double glazing and gas combi central heating.


Something to cheer you up!
Well, the weather is pretty shocking here at the moment, which for us makes planting and picking more challenging…but our thoughts and best wishes go out to the farmers in other areas, including Somerset, who are having an extremely tough time.
We have a few new things in the Farm Shop to brighten things up, and some great ideas for eating well on a budget…so see you soon!
Layla has been busy creating some new cake recipes…first out were these delicious Red Velvet cupcakes, especially for Valentine's Day, light as air sponge with a creamy cream cheese topping! She has also been baking Chocolate and Beetroot Brownies, which are available in our cafe now, and in the farm shops next week. Don't be put off by the concept of veg in cakes…look at the carrot cake and how we were all sceptical at first! The beetroot works a treat, adding a sweet earthy flavour which really compliments the chocolate…and of course the beetroot is homegrown! Watch out for more delicious cakes coming this way!
In Season and Fresh from the Farm!
Our homemade Seville Orange Marmalade is available in the farm shop now…but be quick as it's only around for a few weeks, and it is really rather special!
We have a lovely new range of high quality, attractive kitchenware…including some from the Jamie Oliver range! Items include mashers, garlic crushers, knives, graters, peelers and lots more. Happy cooking…!
Have you been watching 'Food and Drink' on Tuesday nights? They've been looking at how to cook up cheaper, but no less tasty food, using different cuts of meat. They've cooked a beef steak called 'mouse' (because it has a pointed nose!) This is also known as Eye of Silverside, which we sell as a whole joint or which Tony can slice into steaks for you! Delicious pan fried for a couple of minutes each side, and is a change from rump or sirloin. Here is a link to another recipe using breast of lamb – BBC Two – Food & Drink http://t.co/uonc1sUT8v Breast of Lamb recipe…delicious, inexpensive and even better using our homereared lamb!
Anglesey Farmers Market is at Ysgol David Hughes on Saturday the 15th February from 9am – 1pm…and a great opportunity to buy fresh and local!


As part of the Subism team I helped organise the Subism Glug Networking events in Nottingham & London.
Glug #8 at Brownes Nottingham – Subism hosted a gallery & live drawing.
Glug #11 at The Queen of Hoxton – Subism arranged illustrators to work on the stairwell walls and upstairs on the roof.


Alt-poppers iDKHOW But They Found Me will be following their Slam Dunk Festival appearances with a run of dates across the UK and Europe! Straight after the festival, they will be embarking on three UK dates before hitting mainland Europe in June!
Slam Dunk Festival, UK Tour.


text:
\section{Introduction}

Recent research in fractional differentiation has produced an operator whose results intersect with past fractional derivatives, and also allows for an extension to fractional derivatives \textit{in the sense of distributions} and \textit{fractional derivatives of distributions} \cite{Camrud}. The operator is defined formally as:

\begin{Definition}

	Let $f\in X_t(\Omega)\subseteq X^{-c}(\Omega)$ a distributional function space with trivial constant, and let $z_0\in\partial \Omega$ (note $z_0$ may be infinite).

	For $\alpha\in\mathbb{C}$, the $\alpha^{th}$ distributional differintegral of $f(z)$, with respect to the variable $z$, is

	\begin{equation}
	\begin{split}
	\text{\LARGE\S}_z ^\alpha f(z)&=\frac{1}{\Gamma(\alpha)}\int_{z_0}^z f(\zeta)(z-\zeta)^{\alpha-1}d\zeta\\
	&=\frac{1}{\Gamma(\alpha)}\oint_{\gamma} f(\zeta)(z-\zeta)^{\alpha-1}H(z-\zeta)d\zeta
	\end{split}
	\end{equation}
	where $\gamma$ is a simple closed curve in $\Omega$ containing the points $z_0$ and $z$, with $H(z-\zeta)$ becoming the real-valued Heaviside step function when $\gamma$ is parameterized by a real variable.\footnote{That is, if $\gamma(t):[t_0,t_1]\to \Omega$ with $\gamma(t_0)=\gamma(t_1)=z_0$ and $\gamma(t')=z$ for $t'\in[t_0,t_1]$, then $H(z-\zeta)=H\big(z-\gamma(t)\big)=1$ if $t\in[t_0,t')$ and $H(z-\zeta)=H\big(z-\gamma(t)\big)=0$ if $t\in(t',t_1]$.}
\end{Definition}

However, in an applied setting, it is much easier to view the definition as

\begin{Definition}
	For a test function $\phi\in\mathcal{D}(\mathbb{R})$, the distributional differintegral is
	\begin{equation}
	\phi^{(-\alpha)}(x)=\int_{\mathbb{R}}\phi(t)\delta^{(-\alpha)}(x-t)dt
	\end{equation}
	where $\delta^{(-\alpha)}(x)=\frac{x^{\alpha-1}}{\Gamma(\alpha)}H(x)$, with $H(x)$ the Heaviside step function.
\end{Definition}
For functions in a space that are not test functions, one defines $f^{(-\alpha)}(x)=\lim_{n\to\infty}\phi_n^{(-\alpha)}(x)$ where $\{\phi_n\}$ is a sequence of test functions converging to $f$ in norm. Similarly, one defines the fractional differintegral of distributions via $T^{(-\alpha)}[\phi]=e^{-i\pi \alpha}\cdot T[\phi^{(-\alpha)}]$ for all test functions $\phi$.

To ensure that the operator satisfies the index law, that is $\text{\Large\S}_x^\alpha\text{\Large\S}_x^\beta=\text{\Large\S}_x^{\alpha+\beta}$, the derivative direction of the operator needs to be injective. This causes a problem when dealing with constants since $\frac{d}{dx}1=\frac{d}{dx}0=0$. To sidestep this issue, integer-valued derivatives of constants are given a ``label'' that keeps them identifiable in the codomain of the operator. These are called the \textit{Zero Functions} and they occur in the form

\begin{equation}
\emptyset(x)=\frac{d}{dx}1=\frac{x^{-1}}{\Gamma(0)}
\end{equation}
and more importantly as a fractional differintegral
\begin{equation}
\emptyset^{(-\alpha)}(x)=\frac{x^{\alpha-1}}{\Gamma(\alpha)}
\end{equation}
such that $\delta^{(-\alpha)}(x)=\emptyset^{(-\alpha)}(x)H(x)$. Since the operator is linear, one may use the above to define the differintegral of an arbitrary constant.

\section{Fractional Fourier series}

It is well known that if $f\in C(\mathbb{T})$ then the Fourier series $\sum_{n=-\infty}^\infty c_n e^{i n x}$ with $c_n=\int_{\mathbb{T}}f(x)e^{-i n x}dx$ uniformly converges to $f$ on $\mathbb{T}$. Furthermore, if one restricts the functions to $L^2(\mathbb{T})$, then the sequence $\{e^{i n x}\}_{n=-\infty}^\infty$ forms an orthonormal basis for the Hilbert space.

It seems natural to ask whether fractional derivatives of the exponentials can serve as linearly dense subset for the natural derivative extension of $L^2(\mathbb{T})$, namely the Sobolev space $W^{\alpha,2}(\mathbb{T})$.

First note that from the above definition of the differintegral, we have
\begin{equation}
\text{\LARGE\S}_x^\alpha e^{i n x}=(i n)^{-\alpha} e^{i n x}=n^{-\alpha} e^{i (nx-\alpha\frac{\pi}{2})}
\end{equation}
where any necessary branch cuts are taken along the negative imaginary axis: $\arg z\in (-\frac{\pi}{2},\frac{3\pi}{2})$.

If we allow ourselves linear combinations with complex coefficients, however, it may be seen that
\begin{equation}
\sum_{n=-\infty}^\infty c_n (in)^{-\alpha} e^{inx}=\sum_{n=-\infty}^\infty d_n e^{inx}
\end{equation}
for $d_n=(in)^{-\alpha}c_n$. Therefore any linear combination of $\Big\{\text{\Large\S}_x^\alpha e^{inx}\Big\}_{n=-\infty}^\infty$ is also a linear combination of $\{e^{i n x}\}_{n=-\infty}^\infty$, which is an orthonormal subset of $W^{\alpha,2}(\mathbb{T})$.

\begin{Theorem}
	The set $\{e^{i n x}\}_{n=-\infty}^\infty$ forms an orthonormal basis for $W^{\alpha,2}(\mathbb{T})$. More importantly, the series $f^{(\beta)}(x)=\sum_{n=-\infty}^\infty d_n e^{inx}$ is uniformly convergent for all $\beta\in[0,\alpha]$ and the coefficients are of the form $d_n=(in)^\beta \int_{\mathbb{T}}f(x)e^{-inx}dx$.
\end{Theorem}
\begin{proof}

It is trivial to show that $\{e^{i n x}\}_{n=-\infty}^\infty$ is orthonormal, and since $W^{\alpha,2}(\mathbb{T})\subset L^2(\mathbb{T})$ we know that $\{e^{i n x}\}_{n=-\infty}^\infty$ is a basis.

Let $f\in W^{\alpha,2}(\mathbb{T})$ and $\beta\in[0,\alpha]$. Then $f^{(\beta)}\in L^2(\mathbb{T})$.

Since $\{e^{i n x}\}_{n=-\infty}^\infty$ is an orthonormal basis for $L^2(\mathbb{T})$ there exists $d_n=\int_{\mathbb{T}}f^{(\beta)}(x)e^{-inx}dx$ such that $\sum_{n=-\infty}^\infty d_n e^{inx}=f^{(\beta)}(x)$ uniformly.

Since the sum converges uniformly, by the integral definition of $\text{\Large\S}_x^\beta$ we have that
\begin{equation}
\begin{split}
f(x)&=\text{\LARGE\S}_x^\beta f^{(\beta)}(x)=\text{\LARGE\S}_x^\beta\bigg[\sum_{n=-\infty}^\infty d_n e^{inx}\bigg]=\sum_{n=-\infty}^\infty d_n\text{\LARGE\S}_x^\beta e^{inx}\\
&=\sum_{n=-\infty}^\infty d_n (in)^{-\beta}e^{inx}=\sum_{n=-\infty}^\infty c_n e^{inx}
\end{split}
\end{equation}
where $c_n=(in)^{-\beta}d_n$ or rather $d_n=(in)^\beta c_n=(in)^\beta\int_{\mathbb{T}}f(x)e^{-inx}dx$.

\end{proof}

In the sense of distributions, as $\sum_{n=-\infty}^\infty e^{inx}=\delta(x)$ we may also assert the following:

\begin{Theorem}
	\begin{equation}
	\sum_{n=-\infty}^\infty n^{\alpha}e^{i(nx+\alpha\frac{\pi}{2})}=\delta^{(\alpha)}(x)
	\end{equation}
	in the sense of distributions.
\end{Theorem}

\begin{proof}
	Since $\int_{\mathbb{R}} \phi(t)\delta^{(\alpha)}(x-t)dt=\phi^{(\alpha)}(x)$ for all test functions $\phi\in\mathcal{D}(\mathbb{T})$, and since the series $\phi(x)=\sum_{n=-\infty}^\infty c_n e^{inx}$ (for $c_n=\int_{\mathbb{T}}\phi(x)e^{-inx}dx$) is uniformly convergent, we have that

	\begin{equation}
	\begin{split}
	\phi^{(\alpha)}(x)&=\int_\mathbb{R} \phi(t),\delta^{(\alpha)}(x-t)dt=\int_{\mathbb{R}}\bigg[ \sum_{n=-\infty}^\infty c_n e^{int},\delta^{(\alpha)}(x-t)\bigg]dt\\
	&=\sum_{n=-\infty}^\infty c_n\cdot\bigg[\int_{\mathbb{R}} e^{int}\delta^{(\alpha)}(x-t)dt\bigg]=\sum_{n=-\infty}^\infty c_n n^\alpha e^{i(nx+\alpha\frac{\pi}{2})}
	\end{split}
	\end{equation}
	Since this property holds for all $\phi\in\mathcal{D}(\mathbb{T})$ we have convergence in the sense of distributions.
\end{proof}

\section{Differintegral of Fourier transforms}

It is often the case that Fourier transforms serve as a gateway for fractional differentiation, as a multiplication operator $T_{\alpha}[\widetilde{f}(\omega)]=(i\omega)^\alpha \widetilde{f}(\omega)$ in Fourier space is equivalent to differentiation in the domain space. One would hope that a similar result follows from the above differintegral. Indeed we see the following:

\begin{Theorem}
	\begin{equation}
	\mathcal{F}[f^{(\alpha)}(t)]=(i\omega)^\alpha \widetilde{f}(\omega) \text{ and } \mathcal{F}^{-1}[\widetilde{f}^{(\alpha)}(\omega)]=(-it)^\alpha f(t).
	\end{equation}
\end{Theorem}

\begin{proof}
	\begin{equation}
	\begin{split}
	\mathcal{F}[f^{(\alpha)}(t)]&=\frac{1}{\sqrt{2\pi}}\int_\mathbb{R} f^{(\alpha)}(t)e^{-i\omega t}dt=\frac{1}{\sqrt{2\pi}}\int_{\mathbb{R}}\bigg[ \int_{\mathbb{R}}f(\tau)\delta^{(\alpha)}(t-\tau)d\tau \bigg]e^{-i\omega t} dt\\
	&\frac{1}{\sqrt{2\pi}}=\int_{\mathbb{R}} f(\tau)\bigg[\int_{\mathbb{R}}\delta^{(\alpha)}(t-\tau)e^{-i\omega t}dt\bigg]d\tau =\frac{1}{\sqrt{2\pi}}\int_{\mathbb{R}}f(t)(i\omega)^\alpha e^{-i\omega t}dt\\
	&=(i\omega)^\alpha \frac{1}{\sqrt{2\pi}}\int_{\mathbb{R}}f(t)e^{-i\omega t}dt=(i\omega)^\alpha \widetilde{f}(\omega).
	\end{split}
	\end{equation}
	The exchange of integration is justified by Fubini. The reverse direction follows by the same process.
\end{proof}

These results follow with what has been surmised, and often used to develop fractional operators. It should be mentioned, however, that in the case of the fractional Laplacian (developed from an inverse Fourier transform), these results differ. Often, a fractional Laplacian may be defined as $(-\Delta)^\alpha =\mathcal{F}^{-1}|\omega|^{2\alpha}\mathcal{F}$ since $\mathcal{F}[-\Delta]=-\mathcal{F}[\Delta]=-(i\omega)^2=\omega^2=|\omega|^2$. It should be noted, however, that for fractional powers, $\omega^{2\alpha}\neq |\omega|^{2\alpha}$ (certainly for any $\omega\notin[0,\infty)$) and this is where the two definitions differ, as the power of the differintegral may be extend to all $\alpha\in\mathbb{C}$ giving $\mathcal{F}[(-\Delta)^{\alpha}]=-(i\omega)^{2\alpha}\neq |\omega|^{2\alpha}$.

\section{Fractional wave equation}

While all of the above might seem ``nice'', it is always important to ask the question, ``How can this be applied?''. Fractional differential equations have recently been increasing in popularity due to their ability to model complex systems.

We observe the wave equation
\begin{equation}
\frac{\partial^2 f}{\partial t^2}-\frac{\partial^2 f}{\partial x^2}=0
\end{equation}
which when utilizing the change of variables $u=x+t$, $v=x-t$ becomes
\begin{equation}
\frac{\partial^2 f}{\partial u\partial v}=0.
\end{equation}

Since the differintegral defines the fractional integral and derivatives of distributions, we seek a fundamental solution to the above. By observation, this fundamental solution is $\frac{1}{2}H(u)H(v)$ since $\frac{\partial^2}{\partial u\partial v}\frac{1}{2}H(u)H(v)=\frac{1}{2}\delta(u)\delta(v)=\delta(u,v)$. Shifting back with the change of variables, we receive the fundamental solution of $\frac{1}{2}H(x+t)H(x-t)$.

\subsection{Fractionalization in $u,v$ space}

Since the equation is easier to solve in the $u,v$ variables, we fractionalize that part, giving the equation
\begin{equation}
\frac{\partial^\beta}{\partial u^\beta}\frac{\partial^\alpha }{\partial v^\alpha}f=0.
\end{equation}
This may be equivalently written as
\begin{equation}
\int_{\mathbb{R}}\bigg[\int_{\mathbb{R}}f(z,y)\delta^{(\alpha)}(v-y)dy\bigg]\delta^{(\beta)}(u-z)dz=0.
\end{equation}
In this form, it is easy to find a fundamental solution, namely
\begin{equation}
\frac{1}{2}\delta^{(-\beta)}(u)\delta^{(-\alpha)}(v)=\frac{u^{\beta-1}v^{\alpha-1}}{2\Gamma(\beta)\Gamma(\alpha)}H(u)H(v)=\frac{(x+t)^{\beta-1}(x-t)^{\alpha-1}}{2\Gamma(\beta)\Gamma(\alpha)}H(x+t)H(x-t).
\end{equation}
We see as $\alpha,\beta\to 1$ we achieve the fundamental solution for the regular wave equation.

Utilizing this fundamental solution we recover a final solution of the form
\begin{equation}
f(x,t)=\frac{(x-t)^{\alpha-1}}{\Gamma(\alpha)}\phi(x+t)+\frac{(x+t)^{\beta-1}}{\Gamma(\beta)}\psi(x-t)
\end{equation}
where $\phi,\psi$ are arbitrary and fixed for specific initial/boundary conditions. Note the following cases:

\begin{enumerate}
	\item When $\alpha=\beta=1$ we recover D'Alembert's formula,
	\begin{equation}
	f(x,t)=\phi(x+t)+\psi(x-t).
	\end{equation}
	\item When $\alpha=1,\beta=0$ we recover
	\begin{equation}
	f(x,t)=\phi(x+t)
	\end{equation}
	which is equivalent to the solution of the differential equation $\frac{\partial f}{\partial t}-\frac{\partial f}{\partial x}=0$.
	\item When $\alpha=0,\beta=1$ we recover
	\begin{equation}
	f(x,t)=\psi(x-t)
	\end{equation}
	which is equivalent to the solution of the differential equation $\frac{\partial f}{\partial t}+\frac{\partial f}{\partial x}=0$.
	\item When $\alpha=\beta=0$ we recover
	\begin{equation}
	f(x,t)=0
	\end{equation}
	which is equivalent to the solution of the differential equation $f=0$. No surprise there.
\end{enumerate}

From the above we recognize that the equivalence between fractional equations of

\begin{equation}
\frac{\partial^\beta}{\partial u^\beta}\frac{\partial^\alpha}{\partial v^\alpha}f=0\iff\Big(\frac{\partial}{\partial x}+\frac{\partial}{\partial t}\Big)^\beta\Big(\frac{\partial}{\partial x}-\frac{\partial}{\partial t}\Big)^\alpha f=0
\end{equation}
and hence we must utilize the generalized binomial formula to understand the fractional differential equation of the form
\begin{equation}
\bigg[\sum_{k=0}^\infty \frac{\Gamma(\beta+1)}{\Gamma(\beta-k+1)\Gamma(k+1)}\frac{\partial^{\beta-k}}{\partial x^{\beta-k}}\frac{\partial^k}{\partial t^k}\bigg]\bigg[\sum_{k=0}^\infty \frac{(-1)^k\Gamma(\alpha+1)}{\Gamma(\alpha-k+1)\Gamma(k+1)}\frac{\partial^{\alpha-k}}{\partial x^{-k}}\frac{\partial^k}{\partial t^k}\bigg]f=0.
\end{equation}
Observe that since these sums contain infinite (positive and negative) powers of partial derivatives, solutions to fractional differential equations are forced to be infinitely differentiable. Of course, this is always possible when searching for a distributional solution, but sometimes a classical solution may be very difficult to find.

Let us observe one solution to the fractional wave equation with prescribed initial conditions.

\begin{Theorem}
	For $\alpha\in(0,1]$ and $\beta\in(1-\alpha,1]$ for uniqueness, the solution to the fractional wave equation
	\begin{equation}
	\Big(\frac{\partial}{\partial t}+\frac{\partial}{\partial x}\Big)^\beta\Big(\frac{\partial}{\partial t}-\frac{\partial}{\partial x}\Big)^\alpha f=0
	\end{equation}
	with initial conditions $f(x,0)=g(x)$ and $f_t(x,0)=h(x)$ is
	\begin{equation}
	\begin{split}
	f(x,t)&=\frac{1}{2}\Big(\frac{x+t}{x-t}\Big)^{1-\alpha}\bigg[g(x+t)+\int_0^{x+t}h(y)+y^{\alpha+\beta-3}\bigg(\int_0^y (\alpha-\beta)z^{2-\alpha-\beta}g'(z)+(\alpha+\beta-2)z^{2-\alpha-\beta}h(z)dz\bigg)dy\bigg]\\
	&+\frac{1}{2}\Big(\frac{x-t}{x+t}\Big)^{1-\beta}\bigg[g(x-t)-\int_0^{x-t}h(y)+y^{\alpha+\beta-3}\bigg(\int_0^y (\alpha-\beta)z^{2-\alpha-\beta}g'(z)+(\alpha+\beta-2)z^{2-\alpha-\beta}h(z)dz\bigg)dy\bigg]
	\end{split}
	\end{equation}
	where the integrals $\int_0^x (\circ)dy$ are considered as inverse derivatives.
\end{Theorem}
\begin{proof}
Note
\begin{equation}
f(x,0)=(-x)^{\alpha-1}\phi(x)+x^{\beta-1}\psi(-x)=g(x)
\end{equation}
\begin{equation}
f_t(x,0)=(\alpha-1)(-x)^{\alpha-2}\phi(x)+(-x)^{\alpha-1}\phi'(x)+(\beta-1)x^{\beta-2}\psi(-x)+x^{\beta-1}\psi'(-x)=h(x)
\end{equation}

Noting that for $\alpha=\beta=1$ the solution comes in the form
\begin{equation}
\phi(x+t)=\frac{1}{2}\bigg[g(x+t)+\int_0^{x+t}h(y)dy\bigg] \text{ and }\psi(x-t)=\frac{1}{2}\bigg[g(x-t)-\int_0^{x-t}h(y)dy\bigg]
\end{equation}
so we surmise that for arbitrary $\alpha,\beta$ we recover a solution in the form
\begin{equation}
f(x,t)=\frac{1}{2}\Big(\frac{x+t}{x-t}\Big)^{1-\alpha}\bigg[g(x+t)+\int_0^{x+t}h(y)+\eta(y)dy\bigg]+\frac{1}{2}\Big(\frac{x-t}{x+t}\Big)^{1-\beta}\bigg[g(x-t)-\int_0^{x-t}h(y)+\nu(y)dy\bigg]
\end{equation}
for some functions $\eta,\nu$ dependent on $\alpha,\beta$. We utilize the first identity, giving
\begin{equation}
f(x,0)=g(x)+\int_0^x h(y)+\eta(y)dy-\int_0^x h(y)+\nu(y)dy=g(x)+\int_0^x\eta(y)-\nu(y)dy=g(x).
\end{equation}
Hence it is clear that $\eta=\nu$. The second identity leads to
\begin{equation}
f_t(x,0)=h(x)+\eta(x)+\frac{(1-\alpha)}{x}g(x)+\frac{(1-\alpha)}{x}\int_0^x h(y)+\eta(y)dy+\frac{(\beta-1)}{x}g(x)+\frac{(1-\beta)}{x}\int_0^x h(y)+\eta(y)dy=h(x)
\end{equation}
or rather
\begin{equation}
x\eta(x)+(2-\alpha-\beta)\int_0^x \eta(y)dy=(\alpha-\beta)g(x)+(\alpha+\beta-2)\int_0^x h(y)dy
\end{equation}
which becomes the differential equation
\begin{equation}
(3-\alpha-\beta)\eta(x)+x\eta'(x)=(\alpha-\beta)g'(x)+(\alpha+\beta-2)h(x).
\end{equation}
Elementary methods (as this is a first order linear differential equation) give the solution of this equation to be
\begin{equation}
\eta(x)=x^{\alpha+\beta-3}\int_0^x (\alpha-\beta)y^{2-\alpha-\beta}g'(y)+(\alpha+\beta-2)y^{2-\alpha-\beta}h(y)dy.
\end{equation}
Note that we consider $\int_0^x (\circ) dy$ as the \textit{inverse derivative} rather than an integral. This side-steps requiring that the integral converges at the lower bound. See \cite{Camrud} for the definition of inverse derivative.
\end{proof}

We now compute this result for $f(x,0)=\sin(x)$ and $f_t(x,0)=\cos(x)$. Then
\begin{equation}
\begin{split}
f(x,t)&=\frac{1}{2}\Big(\frac{x+t}{x-t}\Big)^{1-\alpha}\bigg[\sin(x+t)+\int_0^{x+t}\cos(y)+2(\alpha-1)y^{\alpha+\beta-3}\bigg(\int_0^y z^{2-\alpha-\beta}\cos(z)dz\bigg)dy\bigg]\\
&+\frac{1}{2}\Big(\frac{x-t}{x+t}\Big)^{1-\beta}\bigg[\sin(x-t)-\int_0^{x-t}\cos(y)+2(\alpha-1)y^{\alpha+\beta-3}\bigg(\int_0^y z^{2-\alpha-\beta}\cos(z)dz\bigg)dy\bigg]
\end{split}
\end{equation}

Figures 1,2,3,4 show a three-dimensional graph of $Re[f]$ versus time and space for chosen values of $\alpha=\beta=0,\frac{1}{2},\frac{3}{4},1$ respectively.

\subsection{Fractionalized in $x,t$ space}

Instead of fractionalizing the wave equation as
\begin{equation}
\frac{\partial^\beta}{\partial u^\beta}\frac{\partial^\alpha}{\partial v^\alpha}f=0
\end{equation}
we can fractionalize it as
\begin{equation}
\frac{\partial^\beta}{\partial t^\beta}f-\frac{\partial^\alpha}{\partial x^\alpha}f=0.
\end{equation}

\begin{Theorem}
	A general solution to the fractional wave equation
	\begin{equation}
	\frac{\partial^\beta}{\partial t^\beta}f-\frac{\partial^\alpha}{\partial x^\alpha}f=0.
	\end{equation}
	is
	\begin{equation}
	f(x,t)=\sum_{k=0}^\infty c_k e^{\omega^\alpha t+\omega^\beta x}.
	\end{equation}
\end{Theorem}

\begin{proof}

Since $e^{\omega y}$ is an eigenfunction of $\text{\Large\S}_y^\alpha$ with eigenvalue $\omega^{-\alpha}$, we assume that our solution is time-periodic. That is
\begin{equation}
f(x,t)=e^{\omega t}g(x)
\end{equation}
and we recover the eigenvalue equation
\begin{equation}
\frac{\partial^\beta}{\partial t^\beta}f-\frac{\partial^\alpha}{\partial x^\alpha}f=0\iff \frac{\partial^\alpha}{\partial x^\alpha}f(x,t)=\omega^{\beta}f(x,t).
\end{equation}
Of course this may be manipulated further into
\begin{equation}
\frac{d^\alpha}{dx^\alpha}g(x)=\omega^{\beta}g(x)
\end{equation}
which has the solution
\begin{equation}
g(x)=c\cdot e^{\omega^{\beta/\alpha}x}
\end{equation}
for $c\in\mathbb{C}$. Therefore the solution to the differential equation is of the form
\begin{equation}
f(x,t)=\sum_{k=0}^\infty c_k e^{\omega^\alpha t+\omega^\beta x}
\end{equation}
where we took $\omega\mapsto\omega^\alpha$ to simplify the expression.

\end{proof}

\begin{Remark}
	For any $\alpha,\beta\notin\mathbb{Z}$ the expressions $\omega^\alpha,\omega^\beta$ are multivalued. Even further, for $\alpha,\beta\notin\mathbb{Q}$ the expressions $\omega^\alpha,\omega^\beta$ have infinitely many values. For this reason, it is important to study the possibilities for the function $f(x,t)=\sum_{k=0}^\infty c_k e^{\omega^\alpha t+\omega^\beta x}$, as this is not a simple Fourier series.

	Further, even for $\alpha,\beta\in\mathbb{Z}$, alternate solutions are of the form
	\begin{equation}
	f(x,t)=\sum_{k=0}^\infty c_k e^{\omega t+\omega^{\beta/\alpha} x} \text{ and }
	f(x,t)=\sum_{k=0}^\infty c_k e^{\omega^{\alpha/\beta} t+\omega x}
	\end{equation}
	where in both cases $\omega^{\beta/\alpha}=(\omega^\beta)^{1/\alpha},\omega^{\alpha/\beta}=(\omega^\alpha)^{1/\beta}$ are multivalued expressions. This is precisely the case for $\alpha=\beta=2$ (the regular wave equation) when we recover solutions in the form
	\begin{equation}
	f(x,t)=\sum_{k=0}^\infty c_k e^{i\omega (x+t)}+\sum_{k=0}^\infty c_k e^{i\omega (x-t)}=F(x+t)+G(x-t)
	\end{equation}
	D'Alembert's formula.
\end{Remark}

We compute this result for $f(x,0)=\sin(x)$. This, along with assuming periodicity, provides a well-defined solution:

\begin{equation}
f(x,t)=\frac{1}{2i}\Big[e^{i^{\alpha/\beta} t+i x}-e^{(-i)^{\alpha/\beta} t-i x}\Big]
\end{equation}

Figures 5,6,7 show a three-dimensional graph of $f$ versus time and space for chosen values of $\alpha/\beta<1,\alpha/\beta>1,\alpha/\beta=1$ respectively.

redpajama_set_name: RedPajamaArXiv


So you're thinking about cycling the Danube River, huh? It's a pretty incredible journey to do on two wheels and definitely one for the courageous. I know because I cycled it myself this summer – all 420kms of it. As the Danube cycle path is such a big journey, it's super important to have everything you need before you put those legs to work, as there's no going back once you start. Being prepared will bring you peace of mind knowing that you're as organised and ready as you can ever be to do this epic ride. So here I am with the answers to all your questions. You can thank me later.
The Danube River may not take the title for the longest river in Europe, but it is definitely the most visited. Stretching from Germany to the Ukraine and crossing through 10 countries, the Danube is home to many ecosystems, beautiful landscapes and cyclists – both those kitted out in lycra and the adventurous, inexperienced a.k.a. mwah. With around 40,000 cyclists cycling the Danube River every summer, the paths and signage are well maintained, making it easy to move in between towns.
The path is predominately flat, apart from a few hillside villages. This makes it suitable for everyone and although it can be difficult riding up hills with luggage on the back, it is manageable. You've just got to think of how much fun it will be when you are cruising back down.
Where to start and finish?
The most popular section of the Danube River starts from Passau in Germany and ends in Vienna, Austria. This is by far the easiest, most organised and busiest section of the river making it a great introduction to bicycle touring. You can also opt for another country and ride an extra 60km to Bratislava in Slovakia – this gives you a taste of what the paths are like away from the main section.
To ride from Passau to Bratislava is approximately 420km, with most of the distance covered overland in Austria. It can be done in a week but to really make the most of the journey, two weeks is a perfect amount of time. This allows you time for a day off your bike in places you really enjoy and not have to be rushing to get to the final destination.
Where can I get a bike from?
Unless you're lucky to have your own bike, then you'll be faced with the decision of whether you should hire or buy a bike for the journey. Both are fair options, it really depends on what your plans are at the end of the bike ride.
After much deliberation, I decided to buy a second-hand bike when I was in Munich – and named her Gertie. Ideally, I was chasing freedom over anything and knew that I would rather not have to worry about something that wasn't actually mine. As soon as I started the bike ride I put everything for sale online and was able to sell it pretty quickly at the end of my ride.
In the cities, hostels are the way to go. They give you a spot to comfortably rest your head, provide peace of mind with your belongings when you go out exploring during the day and are a great place to meet other travellers. I stayed in a private room at both Wombats Munich and Wombats Vienna, which were both awesome hostels that I highly recommend. In Bratislava, I stayed at Hostel Blues which was within walking distance to all of the sights, including plenty of street food vans.
For the smaller towns in between, you have the option of carrying a tent and camping or staying in a bed and breakfast. There are plenty of options but it's important to book in advance, especially if you plan on attempting the journey between July and September.
How do I carry my luggage?
The true cycling tourist carries their bags on the back of their bike. In saying this, it's possible to arrange a pickup and drop-off bag service if you decide to hire a bike with Velotours. Carrying your gear on the back of the bike isn't problematic if you pack light, which is highly advisable.
If you buy your own bike, make sure you buy bags for both the front and back wheel, to balance the weight out. This will make it easier to move the bike around and may reduce the number of falls you have.
This really depends on your priorities when travelling. If you value comfort and want to stay in private rooms in hostels and bed and breakfasts, then allow up to €50. Whereas, campsites range from €9- 15 a night. Be aware that some sites may also charge per person which is usually an extra €3- 6.
To reduce costs, go grocery shopping in the bigger towns and cities to stock up on staple ingredients. You'll always be able to find fresh fruit and vegetables in the small towns, which will only set you back a Euro or two.
Water: free – but BYO bottle.
Is cycling the Danube River suitable for solo travellers?
In terms of safety, the Danube River is solo travel friendly for both male and female cyclists. Coming from someone who did the journey all by herself, it's important to note that it does get lonely. Although the cycle path can be busy in the peak season, you'll sometimes ride for a few kilometres without seeing anyone. I would advise inviting a friend along for the journey, that way you can have someone to go through the good and the bad with and laugh about all the silly things that happen along the way. It also means that you can split the gear between you, cut down on food costs and it also makes set up and pack up a lot quicker.
I'm not a cyclist. Can I still do it?
Of course you can. If I did it, so can you. I should mention that I have never actually owned a bike in my adult life and was always that person that would hang back on a biking day tour, so I wouldn't have to do any indicating. So, yes, it's definitely possible.
Just because you haven't got yourself a lycra kit, own the hottest Garmin watch or are yet to nail the one hand bike riding, it doesn't mean you can't go cycling along the Danube bike trail. All you need is a reasonable amount of fitness and an adventurous spirit.
Munich is a great city to get yourself organised for the big cycle, especially if you plan on buying a bike. While you are there, go rest your legs in the Englischer Garden, which has got to be one of the most beautiful city parks.
Catch the train from Munich to Passau, which only takes two hours and costs start from €7. This is the main starting point for most cycling tourists and it's a gorgeous, pastel coloured town that is worthy of a wander through.
Schlogen is one of the smaller towns along the river but it's the well-known location of the right-angle bend in the Danube River. If your legs are up to it, you can walk just 20 minutes up to the viewpoint to see it from above.
One of the bigger towns along the Danube, Linz is absolutely stunning and is not only a great place to stop in for a coffee, but to try a Linz cake which is almond based with a dollop of redcurrant jam. I highly recommend trying it at Jindrak Café.
A place of serenity and by far my favourite campsite along the river. If you don't spend the night here, be sure to pop in to try their homemade strawberry soft serve. It's to die for and is the perfect quencher after sweating it out on the bike.
Grein is one of the most beautiful towns that you'll pass through on the bike ride. Be sure to either stay here overnight or at least stop and lock your bike up so you can explore on foot. Walk up to Schloss Greinburg to get a gorgeous view over the town – if you stay the night, this is an awesome spot to watch either the sunset or sunrise.
The most popular tourist attraction along the Danube is the Melk Abbey and it's easy to see why. As well as taking time to go up and see what all of the fuss is about, be sure to get your hands on some apricot dumplings, a local, sweet delicacy of the region.
For all of those wine fanatics out there, this will be your favourite part of the bike ride (actually, even if you don't like wine, this will still be your favourite part). The scenery of the Wachau region is absolutely stunning and will give your camera a run for its money and test your 'drink riding' ability. I definitely recommend wine tasting at Eigl wines in Joching.
Krems is a university town bursting at the seams with restaurants, cafes and a whole lot of students. Although big, there isn't too much to do here and is best used as a food stop or last-minute rest for the night.
There weren't many times that I got lost, but this was a big one. There were roadworks happening leaving Krems which meant detours. After riding almost 400km, the word detour haunted me and still does to this very day. Most of the time, the signs have been super helpful, but this was the one case where they weren't. There were signs pointing in both directions and of course the one I took first (right side) left me at a dead end having to backtrack.
If the roadworks are still going on when you arrive, make sure you go left, in towards the town. It adds on about 4km to the trip but you will be greeted with your first sunflower field on the journey, which definitely makes up for it.
Home to the Austrian painter Egon Schiele, Tulln is a gorgeous, green riverside town that has a unique charm to it. This is the last town before Vienna and is a perfect place to spend the night.
Vienna is a city full of picture-perfect pastel buildings and is overloaded with art galleries and museums. There's plenty to see and do in Vienna and is worthy of a few nights stay. Make sure you explore Shonbrunn Palace, eat to your heart's content at Nacschmarket and live out your Beauty and the Beast dreams at the National Austrian Library.
Soph recommends staying at: Wombats Hostel at The Lounge.
The ride from Vienna to Bratislava is guaranteed to test your patience, bike balance skills and endurance but it's also one of the greatest days on the trip. Not only do you come to the realization that you have just ridden over 400km on a push bike, but you pass through fields full of sunflowers.
Bratislava is an awesome city that is still considered off the beaten track in relation to its neighbouring cities of Vienna, Prague and Budapest. The food scene is remarkable here, which is great considering you will be craving all things naughty yet yummy. Be sure to have breakfast at Urban House in the old town.
Even if the weather forecast looks perfect, make sure you come prepared for some rain too. I didn't, and I ended up riding a whole day in a 65L black, makeshift garbage bag raincoat #fashionista.
This was the hardest day on my cycling journey and quite possibly one of the hardest travel days ever. The night before this day, a huge storm rolled in and the rain was so heavy that it made my tent cover slip and fill with water. Everything inside was damp, including myself, my mattress and passport. I had to pack everything up in the rain and then jump back on my bike and ride 45km to get to the next destination…in a garbage bag.
This is why you need to be prepared, no matter how beautiful the weather forecast is – you never know what mother nature is really going to do. Although it was the toughest day, it was also the most memorable. Whilst packing up in the morning, I had two people that were staying in motor homes come over to me and invite me in for coffee. One lady even offered to pay for a night's accommodation, so I didn't have to rough it out in the rain for another night.
I know it's tempting to bring nice clothes and shoes for the bigger cities, but it's much better to have less when you are cycling. This doesn't mean you can't pack anything jazzy, just limit it.
I was relying on the campsites to have guest kitchens, but these aren't available. Therefore, to cut down costs, bring a portable stove so you can not only whip up a beautiful meal, but you can make yourself a coffee or cup of tea in the morning. It will make a huge difference to both your mood and budget.
If you can, plan to do your ride in May, June or October as this is when it's less busy. Not only will you find more serenity, but accommodation is generally cheaper and with more options if you aren't camping. The peak season starts at the end of June and goes until October.
Aim to start riding before 9am every day as this will help you avoid most of the bike traffic, particularly tour groups. Plus, the more time you have you have up your sleeve to get to the next destination will mean more time for both exploring and relaxing.
I can guarantee that this trip will be one to remember, both for the good, the bad, the ugly and the downright hilarious. Plus, I'm sure you'll make your friends jealous with all your incredible photos of castles, Sound of Music lookalike landscapes and an increased leg muscle definition. After all, from jealousy stems inspiration and that's what we all crave at the end of the day.
Sophie Spencer is an Australian travel blogger who lives for adventure and thrives off breaking out of that pesky comfort zone. She created Adventures of Soph to inspire travellers to live their boldest life, full of courage, change and a whole lot of colour. But as with the good, she also shares the ugly yet realistic side of travel, talking openly about mental health, her travel mishaps and hardest times both on and off the road.
The post Get wild on two wheels: a beginner's guide to cycling the Danube River appeared first on Hostelworld Blog.


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STRONG TAKES
TV + FOOD + TRAVEL + MAKEUP +EVERYTHING ELSE
Tag: top chef
What I've been watching this week – October 15
Drag Race UK RuPaul's Drag Race has finally made it across the pond. The first two episodes have been a lot of fun. I am biased because I feel like a British (or Northern Irish!) accent makes everything better. I think the cast has been […]
by haleystrong28
What I've been watching this week – October 1
Hustlers I know, I went to go see a movie in theatres, I can't believe it either. With all the hype surrounding the movie, and with the absolutely unreal, star-studded cast, I felt like I couldn't miss it. Especially now that I have Tuesdays free […]
Movies, Pop Culture, Television
What I've been watching this week – May 13
I am so glad that my favourite show is back. In the 9th season of Taskmaster, 5 comedians/presenters/general brits on tv come together to complete tasks and then watch each other complete the tasks. Sounds not great in concept, but holy F is it funny. I genuinely laugh out loud at many points throughout the episode. The first episode of the new season was great. Of course it was. I don't know the cast super well, but I am excited to see where it goes.
I've been really enjoying The Challenge this season, for the most part at least. I am super over Paulie and Cara's storyline. The Brits have been great, and I've completely changed my mind about Big Brother contestants being on the show. They have been a lot of fun over the last few seasons. I chat more about this latest episode on the MTV Reality RHAP Up.
Top Chef Canada
Boy has this season been a drag. I just can't get into the Canadian version of one of my favourite shows, which I hate to say. I'm hoping it's just this season. Nearly all of the women went home, pretty well right off the bat. And I'm pretty sure the season started with less women than men, but I'm not fact-checking myself on that one. The challenges have been fine, and the guest judges have been great, but we spend almost no time with the guest judges. The regular judging panel seem to take this all too seriously. I'm going to finish out the season, but it's not appointment viewing.
Drag Race Season 11
Yet another disappointment on the tv front. Season 11 has just not been incredibly compelling for me. The cast is good, but it's like the editors haven't done a great job at conveying the story. Some of the eliminations seem completely out of whack, and I don't totally find myself rooting for anyone in particular
Okay, so this new season hasn't started yet, but it's about to! You can catch our draft podcast on the newest cast here.
April Reads
Buttermilk Graffiti by Edward Lee I was wandering around a bookstore recently and came across Buttermilk Graffiti, a book about Top Chef Texas Alumni Ed Lee's journey through the impact that immigrants have had on the food culture of the USA. He explores pockets of […]
What I've been watching this week – March 18
Top Chef Kentucky – The latest season of Top Chef came to an end this week, and it was one of my favourite finales. Maybe because my favourite cheftestant from the very beginning took the whole thing, which rarely happens for me. The season overall […]
What I've been watching this week – February 25
Top Chef 4 & 5 – I'm just getting deeper and deeper into my Top Chef binge.
Season 4 was one of my favourites so far. I still have 2 episodes left in that season, my boyfriend wanted to watch it with me because he is a big Richard Blais fan. There are obviously some familiar faces, including Richard, and two of my favourites, Antonia Lofasso and Stephanie Izard. The challenges are great, and I love the cast.
Season 5 was a little bit of a snooze compared to season 4. I wasn't super satisfied with the winner, and there were some unlikeable people on the cast. And I guess after watching the powerhouse that was season 4, season 5 just couldn't hold up to it.
Game of Clones – Yes this show is terrible. What is it? Some vaguely recognizable faces from other MTV shows tell producers their celeb crush and then they find 7 people who look like that. I believe it's a British concept. The first episode featured Jersey Shore's Pauly D and Teen Mom 2's Kail Lowry. It's weird and insane, and I guess watch it if you have nothing better to do.
Teen Mom 2 – I really never thought I'd be back here, watching Teen Mom regularly. Last season of Teen Mom OG was my first season back in a loooong time. Naturally, I also came back to watching Teen Mom 2. It's nice background noise while I'm working.
What I've been watching this week – February 4
FYRE: The Greatest Party That Never Happened – Everyone was talking about it. This doesn't usually mean that I am into watching things everyone is talking about. I usually avoid those things because I don't feel like having an opinion about it and then someone […]
What I've been watching this week – January 28
Top Chef Season 11 – I couldn't stop the Top Chef train this week. After I finished Season 10, I moved right onto Season 11, New Orleans. This is such a fun season. I love New Orleans and I really enjoy seeing the city as […]
What I've Been Watching This Week – January 7
Are You the One Season 5 – I hadn't seen this season since it originally aired. A couple of cast members from this season have moved on to other shows including Ex on the Beach and The Challenge. I forgot what hot messes all these people are. It's interesting to go back and watch (SPOILER ALERT) the only losing cast in Are You the One history, and see where they went wrong, and where maybe they had some decks stacked against them. In earlier seasons, the cast was helped a lot more. In this season, especially near the end, there was almost a feeling that production wanted them to lose this. The last challenge was completely random who would being going into the truth booth. I think this season is where I started to love this show a little less.
Top Chef Kentucky – This week we saw the conclusion to the two-part episode of the infamous Restaurant Wars challenge. It was early in the season because they wanted to use a three-team format. I quite liked the three teams format because often times during Restaurant Wars, the challenge is a blow out, and you more or less know which team is going to lose, and who is going to go home. In this iteration, you could tell which team was doing better, but no team was pulling ahead of the others. I didn't think it was a bad choice to have two people go home in this episode, I feel like it made a lot of sense. The underperformer of the two losing teams each went home. I was sad because one of my favourite cheftestants this season went home so early, but it was clear they were going to based on what was happening.
RuPaul's Drag Race Season 9 – Drag Race has been my bedtime show for a couple of months now. Since all the seasons are now on Netflix, it's super easy to just keep them playing. I have been watching season 9 the last week. It wasn't my favourite season when it was on, and it's not my favourite season in a rewatch. I think the challenges are a little odd, and don't really show the queens' skills off. Also one queen had to be MEDEVACED FOR THE FIRST TIME IN DRAG RACE HISTORY!!!!
What I've been watching this week – December 17
RuPaul's Drag Race All Stars 4 – We have had 3 iterations of RPDR (plus a holiday special!!) in one calendar year, which is truly insane. But that does not mean I wasn't super excited for the premiere. The episode followed what has become the […]
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haley strong • culinary bad boy • casual wine enthusiast • z-list podcaster • here for the wrong reasons • IG: @hstrong_ Twitter: @hstrong_