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Death by Degrees Updated Hands-On
We get an updated look at Namco's upcoming solo adventure for everyone's favorite voluptuous assassin.
By Ricardo Torres | @GS_RT on November 3, 2004 at 3:29PM PST
Death by Degrees is the upcoming third-person action game from Namco that puts you in the role of Nina Williams, the buxom assassin from the Tekken series. The game is set during Nina's formative killing years when she plied her trade as a special covert agent. While we've gotten a few looks at rough work-in-progress versions of the game at E3 and the Tokyo Game Show, Namco showed off a more solid version of the upcoming release at a recent gaming industry event. Naturally, we took the opportunity to take a look at the game to see how it's coming together.
The sniper rifle is one of many weapons you'll have at your disposal.
The version of Death by Degrees we saw at the event let us hop around and check out a variety of levels that showed off the different styles of gameplay contained in the title, in addition to snippets of its story. The game's story revolves around Nina's assignment to track down a secret weapon, which leads her to investigate a shadowy organization. The specifics of her mission get a little vague thanks to the fact that Nina's superiors aren't big on providing a lot of information. As a result, it falls on you to gather intel as you progress through the game, which ultimately helps you. You'll find a hefty amount of clues and bits of useful information as you go about your business. One of the key ways of discovering things in the game involves cutscenes. Rather than craft pretty computer-generated or real-time sequences that are more or less disposable, DbD's cinematics offer up useful bits of info and clues that can help your investigation...if you pay attention to them.
The gameplay in Death by Degrees is a combination of your standard third-person-action antics, which include exploration and combat, a good dose of puzzle-solving, and some specialized gameplay. The exploration sequences seem to be done fairly well, because the ones we played gave our brains workouts that forced us to be very detail-oriented in our investigations. Besides looking around and finding our ways through different locations, we also triggered cutscenes that dropped bits of info that we'd follow up on, such as the locations of items, and more. These investigations led us to the game's solid combat system, which gives you an array of deadly moves to use when putting the hurt on baddies. Besides Nina's hand-to-hand skills--and critical-strike attacks that let you home in on enemies' weak points to deliver some serious damage--you'll find a wide variety of weapons to use when facing off with enemies. The game's unique Rise to Honor-ish control scheme, which makes use of the analog sticks for targeting and the shoulder buttons for attacking, actually works well...once you get used to it. The system isn't perfect, and it does have its fair share of issues, but it's a fairly solid setup once you're acquainted with it.
After you've defeated your enemies, you can check them out to see if they've dropped any precious items you'll need in your investigation. An interesting twist to the game is Nina's use of a fingerprint scanner to copy her fallen enemy's prints, which she can use to access new areas.
Besides the standard gameplay elements mentioned above, you'll find some minigame-style sequences that put you in the water (while swimming in first-person view no less) to access new areas. Additionally, there are segments where you're in control of some cool gadgets while exploring areas you can't physically access. For instance, the Stingray is a flying robotic minion we used to explore a locked room we couldn't access in hopes of retrieving a code for a door.
The final piece of the gameplay puzzle is that it appears Nina will gain experience as she goes through the game, in addition to building up her skills and attributes. While the system isn't as deep as a role-playing game, you do have the ability to let Nina evolve over the course of the game.
The graphics in the game are shaping up pretty well. Nina is rendered nicely by the capable engine, which readily handles her curves and bounciness. You'll see her lovingly rendered in a variety of different outfits that each sports a high amount of detail. Some of the nonplayable characters we saw match Nina's level of quality, while others are noticeably a few steps below. The environments you'll explore are a little more consistent and offer a varied playground for you to go about your business in. The camera system varies, making it difficult to get your bearings in certain situations. However, the frame rate is pretty solid.
With the Stingray, you'll be able to explore locations that are inaccessible to Nina.
It was a little tough to pick out the audio in the game at the event, but we were able to suss out some of the voice, which ran the gamut from decent to somewhat campy. (The "campy" came courtesy of one of the bosses we encountered.) The bits of music we heard were a little on the bland side, falling squarely into tunes that are to be expected for this kind of game. The sound effects are well done, especially those used for Nina's critical-strike attacks, which really help sell the painful, bone-shattering goings-on.
Overall, Death by Degrees is shaping up to be a unique action title from Namco that should appeal to fans of the genre as well as to gamers who enjoy Nina. The game's graphics and unique gameplay add up to offer a solid enough combination. We'd like to see some of the mechanics tightened up some (such as those that handle swimming), as well as elements of the fighting system, but overall, there's a good amount of potential here. Death by Degrees is currently slated to ship early next year for the PlayStation 2. For more on the game, check out an exclusive interview on our media page.
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This Nebbiolo is grown on the sunny and steep vineyards of the Roero region – in between the left bank of the Tanaro river and some areas in the nearby Langhe region – where full-bodied and fruity wines are produced. The loose and sandy soil is rich in minerals and gives to the wine heady perfumes and rich sensations which linger the mouth. Grape Variety: Nebbiolo subvarieties Lampia, Michet and Rosé.
Maturation and aging: the wine matures in big Slavonian oak barrels for at least 9 months – which give to the Nebbiolo a good balance, ripe tannins and a delicate and captivating bouquet; a short aging in the bottle follows before being sold.
Characteristics: garnet red colour with orange shades which get more evident with aging; its perfumes are delicate, ethereal, intense, round and lingering; the flavours are warm, full-bodied, complex, dry and harmonious. Ripe and complex tannins make the Nebbiolo a powerful wine.
Vini d'Italia - Gambero Rosso 2015 No media download found.
Annuario dei migliori vini italiani - Luca Maroni 2015 No media download found.
I vini di Veronelli - Guida Oro 2014 87 No media download found.
Annuario dei migliori vini italiani - Luca Maroni 2014 87 No media download found.
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Hemp Flower Pre-Rolls
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North Dakota Hemp Laws: Hemp Cigarettes Their Benefits, and State Laws
Posted on November 25, 2020 January 6, 2021 by Mr.HempFlower
It's no secret that hemp is a vastly-growing industry in the U.S., especially in states with lots of growing potential.
And as one of the highest hemp-growing states in the country, North Dakota's made a massive splash with hemp oils as well as hemp cigarettes, which have gained quite a bit of traction as a highly bioavailable CBD source.
But in some states, hemp cigarettes have gained a bit of a legal gray area. For instance, some states have allowed CBD tinctures but banned hemp smokables.
So what's the case for the state of North Dakota?
If you're feeling a bit confused, Mr. Hemp Flower is here for you.
In this guide, we'll cover:
Benefits and Uses of Hemp Cigarettes
Is It Legal To Buy and Sell Hemp Cigarettes in North Dakota?
Choosing Quality: Mr. Hemp Flower's Hemp Cigs
Attentive Craftsmanship & Customer Service
Proof in the Results: Lab Tests, Results and Terpenes
Cannabis sativa, more commonly known as hemp/industrial hemp, is closely related to marijuana, but it doesn't possess nearly as much of the psychoactive component tetrahydrocannabinol, or THC. In fact, some strains of hemp contain almost no THC at all!
What does hemp have instead? Cannabidiol! Also known as CBD.
While hemp shares some physical characteristics with cannabis, they do have one distinction: unlike weed, hemp won't get you high since it possesses significantly less THC.
However, hemp is rich in cannabidiol, or CBD, among several other cannabinoids, terpenes, and flavonoids, which many a rapidly growing number of individuals are beginning to turn to in order to relieve their pain, anxiety, and lack of sleep.
Additionally, growing research suggests that it possesses components that make it a strong candidate for soothing chronic pain.
Now, while it should be clarified that inhaling any kind of plant matter may pose health risks, hemp cigarettes are a non-carcinogenic, nicotine-free alternative to tobacco products. Plus, the lack of nicotine in hemp cigs makes them non-addictive and has even helped individuals quit smoking.
For instance, research from a blind study at University College London showed that nicotine-dependent subjects who were given CBD reduced cigarette usage by 40%, while those who took placebos noticed no difference.
Plus, you're still getting the same benefits of CBD and terpenes that you'd enjoy from any other CBD product, but more quickly and without the digestion process of tinctures or edibles.
Hemp Cigarettes | High CBD Hemp Flower and Kief Blend
Is It Legal To Buy Hemp Cigarettes in North Dakota?
So now you're probably wondering: are hemp cigarettes legal in the state of North Dakota?
Hemp has been grown in North Dakota for several years now, but now that the state's aligned itself with the 2018 Farm Bill, industrial hemp is now explicitly legal, and regulation programs are beginning to emerge.
Last year, Governor Doug Burgum signed Bill 1349 into law, which defines industrial hemp as "…the plant Cannabis sativa l. and any part of the plant, including the seeds and all derivatives, extracts, cannabinoids, isomers, acids, salts, and salts of isomers, whether growing or not, with a delta-9 tetrahydrocannabinol concentration of not more than three-tenths of one percent on a dry weight basis."
The Bill also states that hemp growers in North Dakota must obtain a license from the agriculture commissioner, and that producers and processors must pay a licensing fee that may vary, but won't exceed $350. And while this used to apply to hemp growers as well, they now only have to pay a $150 fee.
Choosing Quality: Where to Buy the Best CBD Cigarettes in North Dakota
Since hemp flower can be legally possessed in the state of North Dakota, residents will be able to find CBD cigarettes wherever CBD products are available.
But sometimes, you'd rather shop from the comfort of your home, and we totally understand the appeals there as well.
Wherever you shop, make sure that the brand is reputable. If you're shopping in-store, check the label for the:
Supplement & ingredient facts
Full-spectrum, broad-spectrum, or isolate
Batch number or QR code
Manufacturer/distributor information
With that said, let's talk about the easiest, safest way to guarantee quality hemp cigs: by shopping online with Mr. Hemp Flower.
Have you tried hemp cigarettes from other brands, and found that they were…just fine? We have too! But we don't want our hemp cigs to be just fine, we want our customers to have a spectacular smoke.
That's why we put the utmost care in every step of our manufacturing process; from the growing and sourcing of our hemp, to the testing, all the way to the moment when those cigs are rolled.
Our hemp is only sourced from the best growing locales in America, including Washington State, Colorado, and Oregon, and you can smell and taste the difference. This noticeable quality is especially thanks to the experience of our growers, who have years of knowledge under their belts.
We don't stop at great hemp, though, while some brands do. Instead of just hemp flower, we roll our hemp cigarettes with premium flower and kief.
Kief is what comes from the resinous trichomes found in hemp, and it's loaded with the terps. Terpenes give hemp strains their unique profiles in aroma, flavor, and even effects, so you know you want these in a good smoke!
And with the addition of kief, you get not just that extra punch of terps, but a phenomenally smooth smoke, to boot!
Our customer service representatives are easy to reach with any inquiries you might have, which you can submit here. On a typical business day, we usually answer our customers' questions within 3-4 hours.
For vendors in North Dakota, we invite you to drop by our wholesale page here.
Proof in the Results: Terpenes in Mr. Hemp Flower CBD Cigarettes
In case we haven't made it clear already, we're crazy about those terpenes and the unique qualities they can provide hemp. More than that though, we love the full-spectrum properties that can occur when you have a flood of terps, cannabinoids, and flavonoids. Because when you're enjoying hemp in its full-spectrum form, you have a better chance of achieving the entourage effect.
But not all hemp strains are made equal, and let's be honest: not all hemp cigarette brands put in the care and attention that's worthy of our customers. That's why our Hemp Cigarettes are made only ith US-grown hemp, which is grown exclusively by experienced farmers throughout Colorado, Washington State, and Oregon, making for the perfect smoke break.
Alpha-Bisabolol-1.31 mg/g (.13%)
Known for its delicate, floral fragrance, alpha-bisabolol is notably found in Roman chamomile and is known for its calming, soothing properties throughout traditional herbal medicine.
Additionally, one 2014 study also showed that alpha-bisabolol may work as an anti-inflammatory agent, which has garnered its interest in chemical and pharmaceutical industries. Studies have also shown that alpha-bisabolol may possess analgesic and antioxidant properties, just to name a few.
Guaiol-1.02 mg/g (.10%)
While the research is still fairly new, guaiol has been prominent in traditional herbal medicine for years; especially as a component in plants like cypress, rose, and pine. Guaiol is known for its clean, evergreen scent, and some studies such as this one highlight its potential aptitude for treating pain.
Beta-Pinene-.626 mg/g (.06%)
Known for its warm, piney aroma, beta-pinene possesses some unique properties, and may be useful for combating the common cold. This has been suggested by studies observing its expectorant properties, meaning that it can help clear nasal and throat passage ways to help relieve coughs.
Trans-Caryophyllene .464 mg/g (.05%)
Found in hops, rosemary, and cloves, caryophyllene is known to possess a spicy, herbaceous aroma and bold flavor. Research on trans-caryophyllene is more extensive than any other terpene, and it's been shown to act as a neuroprotective agent by interacting with the CB1 and CB2 receptors to bring down inflammation.
What happens when you smoke hemp cigarettes?
While hemp cigarettes contain copious amounts of CBD, there's very little THC, which means that you won't feel high or intoxicated. However, many consumers report that smoking hemp cigarettes deliver a calming effect for them, and some even report feeling more focused.
Do hemp cigarettes get you high?
CBD oil and hemp cigarettes can be legally purchased within the state of North Dakota.
Do hemp cigarettes contain nicotine?
Unless otherwise stated on packaging, hemp cigarettes do not contain nicotine, which renders them without the highly addictive properties of traditional cigarettes.
This entry was posted in Hemp Flower and tagged CBD Cigarettes North Dakota.
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Papírová chromatografie je dříve často užívaná, experimentálně jednoduchá, chromatografická technika dělení směsí látek, v planárním (plošném) uspořádání. Jedná se o rozdělovací chromatografii, kdy o pohyblivosti jednotlivých složek dělené směsi chromatogramem rozhoduje rozdělovací koeficient dělených látek. Dělené látky jsou unášeny kapalnou mobilní fází přes zakotvenou kapalnou stacionární fázi. Uspořádání papírové chromatografie může být dle směru pohybu mobilní fáze vzestupné, sestupné nebo i horizontální. Dělicí schopnost je zde ve srovnání s modernějšími metodami nižší a slouží spíše pro orientační měření složení směsí. Papírová chromatografie byla postupně vytěsněna metodou TLC.

Stacionární fází je nejčastěji voda absorbovaná na nosič z atmosféry ve vyvíjecí nádobě. Nosičem stacionární fáze je čistá celulóza ve formě papíru.

Mobilní fáze je omezeně mísitelná až nemísitelná se stacionární fázi. Je to buď čistá látka, nebo směs látek různé polarity.

Historie
Princip papírové chromatografie byl objeven v roce 1943 britskými chemiky Archerem Martinem a Richardem Syngem. Tato metoda umožnila separaci a identifikaci jednotlivých složek rostlin, díky tomu došlo k jejímu prudkému rozvoji po roce 1945.

Instrumentace

Chromatografický papír
je vyrobený z celulózy vysoké čistoty. Má přesně definovanou tloušťku, přesně definovanou pórovitost, přesně definované uspořádání vláken, má předepsaný směr toku mobilní fáze (komerčně dodávaný arch chromatografického papíru má obdélníkový tvar a mobilní fáze musí proudit ve směru delší strany).

Nanášení analytů nebo standardů na chromatografický papír se provádí pomocí kapiláry nebo mikropipety. Kapilárou se nanáší pro kvalitativní analýzu, mikropipety se používá pro  kvantitativní analýzu.

Vyvíjecí zařízení
Vyvíjení se provádí v uzavřeném prostoru (vyvíjecí tank nebo jiná vhodná uzavíratelná nádoba). Důvodem je zamezení odpařování mobilní fáze a nasycení nosiče stacionární fázi

Techniky vyvíjení

Sestupná technika
Mobilní fáze se pohybuje seshora dolů.

Vzestupná technika
Mobilní fáze se pohybuje zdola nahoru. Nevýhodou je snižování rychlosti pohybu mobilní fáze.

Technika opakovaného vyvíjení
Používá několik mobilních fázi.

Technika dvourozměrného vyvíjení
Papír je čtvercového tvaru. Provede se chromatografie první mobilní fází v jednom směru.

Chromatogram se vysuší a pak se provede chromatografie druhou mobilní fází, ve druhém směru, kolmém na první.

Kruhová technika
Vzorek se nanese na střed kruhového filtračního papíru. Mobilní fáze se přivádí knotem do středu chromatogramu, odkud se pohybuje k obvodu a složky se rozdělí do soustředných kruhů.

Vyhodnocení chromatogramu

Kvalitativní vyhodnocení
Kvalitativním ukazatelem analýzy je poloha skvrny analytu anebo standardu na chromatogramu, vyjádřená retenčním faktorem.

Retenční (retardační) faktor RF je dán poměrem vzdálenosti středu skvrny a od startu ku vzdálenosti čela mobilní fáze m od startu.

Kvantitativní vyhodnocení
Kvantitativním ukazatelem je plocha nebo intenzita zabarvení skvrny analytu na chromatogramu. Tyto hodnoty se vždy srovnávají s plochou nebo intenzitou zabarvení skvrny, kterou vytvořilo známé množství standardů za stejných podmínek chromatografie. Měření intenzity zabarvení skvrny se provádí spektrofotometricky.

Odkazy

Reference

Externí odkazy

 Chromatografie na papíře

Chromatografie

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What landlocked Austria lacks in oceanic coastline, it makes up in in great measure with its abundance of outstanding lakes. We have picked out 10 lakeside highlights from the vast choice of beautiful lakes.
With the mountains and lakes, castles and villages, historic towns and idyllic villages, Austria is bar none when it comes to variety of holiday features. While the mountains are the main attraction in Austria, summer or winter, we would like to put the spotlight on the country's wonderful lakes. Swimming, bathing, boat trips, water sports or simply a hike on the shores are some off the many lakeside highlights. You can have it all. Moreover, not to have to worry about huge waves and dangerous currents, is a big bonus. The list of lovely lakes in Austria could at least 4-5 times longer. However, we've tried to find ten different lakes spread over the country. All with their own unique characteristics and in a random order.
Bregenz occupies most of the Austrian shoreline on the Bodensee. The lakeside towns main feature is the promenade, between the port and the Festival area. It's a great place to bask in the sun, romantic evening strolls or just sit down at a café and contemplate about life.
Nostalgic steam train trips, cruising the lake or hiking in alpine nature. A gem among the lakeside highlights is Achensee (Lake Achen) in Tyrol – much more than a picture perfect alpine paradise. With its turquoise blue water and steep cliffs, the northwestern shore almost reminds us of an greek island.
The almost 17 kilometer long lake in Carinthia is one of Austria's warmest lakes and often reaches 25 °C. Wörthersee is Austria's answer to the French Riviera. You find a posh casino in Velden, and it's a popular playground for the rich and famous in Austria. Nonetheless, there are plenty of place for people with a normal income as well, who want to enjoy a lakeside vacation.
Weissensee is beautifully situated in a valley in southeastern Carinthia. The alpine lake is one of Austria's cleanest with drinking water quality. There are awesome hiking and biking trails all around the lake. Enjoy bathing, fishing our cruise on the lake in summer. Winter time the lake usually freezes over and becomes a huge ice-skating rink.
The Millstätter See (Lake Millstatt) in Carinthia, southern Austria is a summer paradise. Watersports, biking, hiking or simply relaxing seaside, you can have it all. We recommend: taking your kids out on the lake and accompany a professional fisher taking up fishingnets or go for a guided rowing boat trip.
The Mondsee in Upper Austria, is easily accessable from the main motorway between Vienna and Salzburg, A2. On the waterfront you can rent electric- or sailboats. Not a sailor! Hour-long guided boat tours around Mondsee run all day from the same place. The village by the same name at the northern lakeshore is really nice and is home to a large Abbey.
For more info, check the website from Mondsee Tourism.
Austria's largest lake, the Neusiedler See is located 40 minutes by car from Vienna in the state of Burgenland. The southern end of the lake, roughly 20%, belongs to Hungary. Europe's second-largest steppe lake is surrounded by the flattest landscape in Austria. Windsurfing are among the most popular watersports on the maximum 1,8 meter deep lake.
For more info, check the website from Neusiedler See Tourism.
Not far from the Mozart City Salzburg there is a lovely lakedistrict. Four pretty lakes, the Wallersee, the Mattsee, the Grabensee and the Obertrumersee, are embedded in the undulating countryside, amongst well-kept meadows and forests. Dotted around the lakes you find idyllic villages and hamlets that offer accommodation and other tourist services.
In northwestern Styria you find the states largest lake, the Grundlsee. Around the lake you find several pebble beaches and a section reserved for nudist bathers. At the far end of the lake there are good hiking trails into the mountains. The Grundlsee is set amidst a stunning alpine landscape, just a 30 minute drive from the World Heritage site Hallstatt.
Little Pillersee in Tyrol, not far from the biathlon arena in Hochfilzen, is a small "undiscovered" gem. In the flat lane around the lake there is a walking and cycling path that is well suited for children or wheelchairs. There are several lawns by the water for swimming, and you can hire pedal boats and stand up paddle boards.


Alert Media, a platform for interactive mass notification, announced Tuesday that it has raised $4.16 million in a Series A funding round.
The Austin-based startup plans to use the money for product development and to hire more sales and business development employees.
Silverton Partners led the founding round which included participation from ATX Ventures and Capital Factory. Alert Media's customers include several large companies in the telecom, manufacturing, shipping, energy and healthcare industries.
"Every large or complex organization that sees our platform in action gets very excited about the possibilities," Brian Cruver, founder and CEO of Alert Media, said in a news release.
Alert Media offers its customers a cloud-based platform that lets them access and send notices from anywhere using any kind of device. A lot of customers use the platform for emergency communications, but it's also being used for more common business notices, according to the company.


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Poetry from an Indigenous Perspective
Francine Simon Public Presence and Online Links Author of THUNGACHI (uHlanga 2017) & SHARK (uHlanga 2019)
Ja. Edition 2020 Ja. Edition 20
uHlanga Press Thungachi: uHlanga Press Thungachi
uHlanga Press Shark: uHlanga Press Shark
Thungachi Book Review:
Previous interview published online:uHlanga Press Thungachi
08 Mar 'There's no single meaning': Poet Francine Simon speaks about her debut collection, 'Thungachi': Interview with Gabriella Pinto
Digitally Published Poems 2020
Ja. Magazine: Poetry-two-poems
The Poetry Foundation: Francine Simon
Ja. Magazine: Poetry
Kalahari Review: Francine Simon
The Johannesburg Review of Books: Francine Simon
Type/Cast: Francine Simon
Instagram: @francinesimon13
Twitter: @WriterGirlRose
Data Sharing: Terms of Use and Restrictions The following is a list of conditions given to the researcher as per agreement with the participant (stated on the participant consent form), and as per agreement between the researcher and the Wits Ethics Committee. The ethics application form and clearance certificate thereof, is attached. • Confidential sections of the interview to be edited out and deleted. Submitted data files are final and do not contain confidential material. • Photographs taken at the discretion of the participant on the days of the interviews. Use of the photographs in the dissertation is permitted, although they were not used. • The interviewee/participant, Francine Simon, reserves the right to request the transcripts, audio files and photographs at any point during or after the research. The final transcripts and photographs were emailed to Simon prior to the final ETD submission, and no objections were raised. • Excerpts of the interview transcripts are used in the dissertation, however, due to length and relevance, the majority of the transcripts were not used. The Wits Ethics Committee permits the researcher to use any part of the original transcribed material for future academic publications, and need not be limited to the excerpts used in the dissertation only. • The following individuals are allowed access to the aforementioned data files, as per the Wits Ethics Committee: Arushani Govender (the researcher), Francine Simon (the participant), Prof. Denise Newfield and Associate Prof. Barbara Boswell (supervisors), and the relevant examination committee. Presently the ethical clearance certificate granted does not cover data access permissions for any other member. • In order for access to be granted to the NRF or any other individual, a new consent form must be drawn up stipulating new terms of use, and is to be signed by the participant and submitted to the Ethics Committee. O
Exploring a South African Indian Woman Poet and her Poetry from an Indigenous Perspective: Interviews with Francine Simon and Readings of Selected Poems from Thungachi.
(University of the Witwatersrand, 2019-07-30) Govender, Arushani
This dissertation executes a critical reading of Francine Simon's poetry in relation to contemporary perspectives of indigenous knowledge (IK), and against the political background and socio-cultural context of the poet's lived experiences. Simon is an emerging South African Indian (SAI) woman poet in the contemporary poetry scene, and has recently published a debut poetry collection titled Thungachi. I unpack instances of IK from selected poems in Thungachi, through use of an indigenous language of critique. Linda Tuhiwai Smith conceptualises indigenous language of critique as a form of theory that indigenous research scholars should engage with, by combining questions of indigeneity with attributes of decolonisation (24). Framed by decolonial theory, this study serves the interests of decolonising research praxis, and thereby the nature of the knowledge produced. I have executed in-depth interviews with the poet to determine how she came to acquire IK and how such knowledge is conveyed and dealt with in her poetry. The interviews are presented as an experiential montage, countering the "objective" nature of academic research that distances the knower from the known. The dissertation is thus composed of theoretical analysis and creative reflections, which together offer a textured exploration of the selected poems and an experience of the poetry. Using the interview data as a supplementary device, I conduct the poetry analysis with the following questions, which pertain to examining the data from an indigenous perspective: What indigenous worldviews are prevalent in Simon's poetry? To what culture/s may those worldviews be attributed? How is IK affected by diaspora, gender and cultural hybridity? This study finds that it is necessary to critique Simon's poetry from an indigenous perspective in order to uncover its cultural complexities, ontological insights and social commentary. Additionally, Simon's poetry demonstrates artistry, experimentation with language and form, and innovates a genre of decolonised feminist poetics that creates room for the heterogeneity of South African Indian women.
Changes in how English FAL learners appreciate poetry when indigenous poetry is brought into the classroom: a practitioner case study of grade 11 learners in Gauteng
(2019) Mavhiza, Grace
A vigorous poetry tradition has existed throughout South African history. It represents in many ways a truly original contribution to the literature in the English first additional language (FAL) classroom. The benefits of poetry in enhancing intellectual, emotional social and linguistic development in learners are well documented. Surprisingly, there is a negative attitude towards poetry by learners and teachers as they prefer other literary genres particularly in a secondary school where this research was carried out. I have realised that the oral traditional poetry which is an African form of poetry practice is largely absent in the classroom today. Through a practitioner case study, this research sought to elicit the Grade 11 learners' changes in appreciation of classroom poetry when indigenous poetry is brought into the English FAL classroom. This study presents previous research regarding perceptions accorded to classroom poetry. This is a qualitative study in which data gathered through questionnaires, face-to-face interviews, poetry texts analysis and reflective writing was presented to answer the primary question; what could be the changes in the appreciation of classroom poetry if indigenous poetry is brought into the classroom? The findings show that learners of English FAL do not appreciate classroom poetry due to the reasons that; classroom poetry is distant from the learners' life experiences making them struggle to interpret the poetry prescribed for them. Learners also said that classroom poetry is boring and this is due to the teaching methods employed in the classroom which are book centred and assessment driven. However, this study concluded through the intervention that encouraging learners to respond to poetry by presenting poems in a range of modes is more likely to boost their interest than focusing on the "traditional" line by line analysis of poems. The other important finding is that if indigenous poetry is brought into the classroom, learners' attitudes towards classroom poetry will positively change
The problem of audience: a study of Durban worker poetry.
(1993) Kromberg, Steve
This dissertation shows how both poets and their audiences have played a central role in the emergence of Durban Worker poetry. A review of critical responses to worker poetry concludes that insufficient attention has been paid to questions of audience. Performances of worker poetry are analysed, highlighting the conventions used by the audience when participating in and evaluating the poetry, Social, political and literary factors which have influenced the audience of worker poetry are explored, as are the factors which led to the emergence of worker poetry. In discussing the influence of the Zulu izibongo (praise poetry) on worker poetry, particular attention is paid to formal and performative qualities. The waye in Which worker poetry has been utilised by both poets and audience as a powerful intellectual resource are debated. Finally, the implications of publishing worker poetry via the media of print, audio-cassettes and video-Cassettes are discussed.
Aesthetics and resistance: aspects of Mongane Wally Serote's poetry.
(1990) Frielick, Frielick Stanley
The literature produced by writers who align themselves with national liberation and resistance movements presents a serious challenge to dominant standards of literary . aesthetics. Resistance writing aims to break down the assumed division between art and politics. and in this view literature becomes an arena of conflict and struggle. This dissertation examines certain aspects of the poetry of Mongane Wally Serote in order to explore the relationship between aesthetics and resistance in his writing. Over the last two decades, Serote has made a significant contribution to the development of South African literature, and his work has important implications for literary criticism in South Africa. Chapter 1 looks at some of these implications by discussing the concept of resistance literature and the main issues arising from the debates and polemics surrounding the work of Serote and other black political writers. Perhaps the most important here is the need to construct a critical approach to South African resistance literature that can come to terms with both its aesthetic qualities and political effects. This kind of approach would in some way attempt to integrate the seemingly incompatible critical practices of idealism and materialism. Accordingly, Chapter 2 is a materialist approach to aspects of Serote's early poetry. The critical model used is a simplified version of the interpretive schema set out by Fredric Jameson in The Political Unconscious. This model enables a discussion of the poetry in relation to ideology, and also suggests ways of examining the discursive strategies and symbolic processes in this particular phase of Serote's development. Serote's later work is 'characterised by the attempt to create a unifying mythology of resistance. Chapter 3 thus looks at Serote's long poems from an idealist perspective that is based on the principles of myth-criticism, As this is a complex area, this chapter merely sketches the main features of Serote' s use of myth as a form of resistance, and then suggests further avenues of exploration along these lines. The dissertation concludes by pointing towards some of the implications of recent political developments in South Africa for Serote and other resistance writers.
Investigating a multimodal, groupwork approach to poetry teaching in a secondary school English classroom
(2016) Pillay, Kubashini
This report explores the ways in which meaning is constructed, adapted or altered as Grade 9 English Home Language learners redesign the meaning of a poem multimodally in the English classroom in a state secondary school in Johannesburg. A unit of poetry work was designed to explore how learners, working together in groups and independently of the teacher, 'shift' across and within modes in the process of redesigning meaning. An array of prescribed poems chosen from official sources – one selected per group – which served as a foundation for designing and creating multimodal artefacts and ensembles, was set as primary texts. The main purpose of this report, then, is to determine how meaning is constructed in learners' responses through their products and presentations in a pedagogic approach that is informed by both multimodality and multiliteracies. The two core concepts in this report – design and modes – are recognised as significant concepts in analysing learners' multimodal artefacts in this chain of semiosis and compared with the characteristics of the original 'poem on paper'. A multiliteracies pedagogy and multimodal artefact design are used to provide the Grade 9 learners the support to 'unlock' their potential and encourage resources to emerge from which they can construct meaning in innovative ways. Since the learners work collaboratively in groups to redesign the meaning of a poem multimodally, findings suggest that this strategy fostered the interaction of ideas, learner activity and engagement and learner verbalisation of ideas. Learners' ideas were developed, articulated, clarified and transformed within the groupwork discussion and were made visible in their multimodal artefacts. Learners' final products in the chain of semiosis were of good quality. In the process of redesign, as agents of meaning making, learners used semiotic resources and the integration of modes to represent their poem multimodally. The words themselves had to be extracted from the poem, redesigned and represented in another form or mode. Finally, this pedagogy demonstrates that it is possible for learners to be active designers of meaning while remaining within the prescriptive parameters of the relatively recent Curriculum and Assessment Policy Statement (CAPS) curriculum. Learners were able to successfully reshape and resemiotise the primary text into other modal artefacts, which one could taste, smell, touch, see or hear.
Grant Information: The National Research Foundation (NRF), through grant-holder linked student support, funded this research. The grant falls within the NRF Indigenous Knowledge Systems funding instruments. • Grant Number: 105159 • Grant-holder Project Title: "Reconceptualising Poetry Education for South African Classrooms through infusing Indigenous Poetry Texts and Practices." • Project Commencement Date: January 2017 • Principle Investigator: Prof. Denise Newfield. Email: newfield@iafrica.com Coordinator of the South African Poetry Project (ZAPP). • Application Institution: University of the Witwatersrand • ZAPP Website is currently under construction. A URL will be provided once it is launched.


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Journal Buddies Jill | June 10, 2022 July 23, 2018 | Creative Writing
Short Story Prompts for Students
Short Story Prompts for Students— Journaling is a wonderful way to help students become more comfortable in their writing and in expressing their own ideas—and its benefits are even more incredible when kids begin journaling at a young age.
That's why we've designed a new set of 32 short story prompts especially for elementary school students. Practicing short story writing helps kids to develop a number of important skills, including critical thinking, cause and effect, empathy, and of course, writing and communication.
In order to maintain the interest of young, easily distracted students, these prompts are designed to be both fun and relatable. You and your students can choose from silly fantastical topics like a story about Freddy, the friendly fire-fighting dragon—or stick to topics that are grounded in the student's daily reality, like a story about the perfect snow day. For extra fun, be sure to have the class share their stories with one another at the end of the day so they can see just how many incredible possibilities they and their classmates came up with!
Use these elementary school short story prompts to get young students writing and exploring their creativity this school year.
32 Short Story Prompts to Get Elementary School Students Writing
Write a story about a leopard named Lily who loves leaping, libraries, loud noises, and lizards.
Write a story about a dog that digs up a dinosaur bone.
Write a story about a family who lives on a boat.
Write a story about a grandma who makes the world's best cookies.
Write a story about a gorilla named Gus.
Write a story about a boy who has an unexpected adventure while walking his dog.
Write a story about an artist who creates very realistic paintings.
Write a story about a made-up reason why the leaves change color and fall each year.
Write a story about a young girl who wants to be a singer when she grows up.
Write a story about an old man who lives by the beach.
Write a story about someone who accidentally shares a secret they weren't supposed to.
Write a story about a beautiful, multi-colored butterfly.
Write a story about the perfect snow day.
Write a story about a boat with a very special mission.
Write a story about a magical pencil that makes doing homework much easier.
Write a story about a young boy who is a very talented chef.
Write a story explaining how Calvin the Cowardly Cow got his name.
Write a story about a magical forest and the creatures that inhabit it.
Write a story about a girl who accidentally loses the class pet.
Write a story about a penguin parade.
Write a story about a family who chooses to live with no Internet at home.
Write a story about a pair of sisters who are always getting into trouble.
Write a story about a girl who invents a magic ice cream dispenser that gives you any flavor you can think of.
Write a story about a cat and a dog that are the best of friends.
Write a story about a cowboy who comes to live in the big city.
Write a story about a magic umbrella.
Write a story about a secret tunnel under the school.
Write a story about Freddy, the friendly fire-fighting dragon.
Write a story about a silly board game where every player gets to make a new rule.
Write a story about a malfunctioning time machine.
Write a story about a pair of brothers who are very best friends.
Write a story about a group of friends who get trapped in a maze.
More Short Story Prompts
Short Story Ideas for Kids
Short Story Ideas & Advice
Writing Prompts for Elementary School Students
Until next time, write on…
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please share them on Facebook, Twitter, and/or Pinterest.
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Tags class, Elementary, elementary school short story prompts, Elementary School Students, elementary writing, Grade 1, Grade 2, Grade 3, Grade 4, Grade 5, help kids writing, journaling, prompts, short story prompts, short story writing, stories, Story Prompts, students, students writing, topics, write a story, writing


text:
\section{Introduction}\label{Sec1}
In this paper we will investigate a generalised two-component Camassa-Holm equation with fractional order inertia operator, given by the system:
\begin{equation}\label{s1:eq1}
\begin{split}
	&m_t = \alpha u_x - au_xm-um_x - \kappa\rho\rho_x,\quad m = Au\\
	&\rho_t = -u\rho_x - (a-1)u_x\rho,\qquad a\in \RR\setminus \{1\}\\
    &\alpha_t = 0
\end{split}
\end{equation}
where the inertia operator $A=(1-D^2)^s$ belongs to the class of fractional Sobolev norms with $s>1$ and $D=\frac{d}{dx}$, and where $u$ and $\rho$ are defined on the circle $\Circle$ and $\alpha$ is a constant. The meaning of these (dependent) variables will be explained later on. Finally $a$ and $\kappa$ are real parameters. In Section \ref{Sec2} it will be shown that the system in equation \eqref{s1:eq1} corresponds to a metric induced geodesic flow on the infinite dimensional Lie group $\DiffS\circledS \CS\times \RR$, when the parameter $a=2$. We denote by $\DiffS$ the group of orientation preserving diffeomorphisms of the circle, $\CS$ denotes the space of smooth function on $\Circle$ while $\circledS$ denotes an appropriate semi-direct product between the pair. In Section \ref{Sec3} we also present rigorous criteria ensuring the existence of global solutions to the system in equation \eqref{s1:eq1}, for a class of nonlocal inertia operators subject to $s>1$ in the general case $a\neq1$. As a consequence of these general investigations we obtain the following result:
\begin{theorem}[Geodesic completeness]\label{thm:gc}
Let $s>3/2$ and $\kappa\ge 0$ be given and assume that $a=2$. Then the solution to \eqref{s1:eq1} emerging from any initial condition $(u_0,\rho_0)\in \CS\times\CS$ is smooth and exists globally in time, i.e.
\begin{equation*}
    (u,\rho)\in \mathrm{C}^{\infty}([0,\infty),\CS\oplus\CS),
\end{equation*}
meaning that the corresponding flow is geodesically complete.
\end{theorem}

In \cite{EHKL2014} the authors, with collaborators, presented a hydrodynamical derivation of the system \eqref{s1:eq1} with $s=1$ and $\kappa>0$, as a model for water waves with $\alpha$ a constant incorporating an underlying vorticity of the flow, following the works \cite{Iva2009} and \cite{Joh2003}. Additionally it was  shown that the hydrodynamical model obtained when $a=2$ corresponds with the Arnold-Euler equation of a right-invariant metric on the infinite dimensional Lie group $\GS = \DiffS\circledS \CS\times \RR$. Moreover, in line with the work of \cite{EM1970}, local uniqueness and existence of the geodesics on $\GS$ were proven, thus ensuring the well posedness of the system \eqref{s1:eq1} with $s=1$. Furthermore a priori estimates were obtained which established criteria for the global existence of solutions for the hydrodynamical system when $a\neq1$.

The system in \eqref{s1:eq1} incorporates a number of remarkable partial differential equations arising as approximate hydrodynamical models. In the case of irrotational flow ($\alpha = 0$), with $\rho\equiv0$ and $s=1$, the system above reduces to a family of equations parameterised by $a\neq1$, the so-called $b$-equations. This class of $b$-equations share several common structural features investigated in \cite{EY2008, Hen2008, Hen2009b} among other works. There are two scenarios in which the $b$-equations yield integrable models, specifically when $a=2$ corresponding to the Camassa-Holm equation \cite{CHH1994,CH1993}, and $a=3$ giving the Degasperis-Procesi equation \cite{DP1999}. Both systems arise as hydrodynamical models of shallow water waves c.f. \cite{Con2011,Joh2002}, possessing both global solutions and solutions which display wave-breaking in finite time, c.f. \cite{Con2000, CE1998b, CE1998a}.

All of these hydrodynamical models have a geometrical interpretation in terms of a geodesic flow on an appropriate infinite dimensional Lie group. The seminal work of Arnold \cite{Arn1966} reformulated the Euler equation describing an ideal fluid, as a geodesic flow on the group of volume preserving diffeomorphisms of the fluid domain. Following this, Ebin and Marsden reinterpreted this group of volume preserving diffeomorphisms as an inverse limit of Hilbert manifolds, c.f. \cite{EM1970}. The crucial aspect of this approach is that it allows one to reformulate the hydrodynamical model governed by a PDE, namely the Euler equation, in terms of the geodesic equation on the Hilbert manifolds, which is an ODE. The question of well-posedness of the Euler equation may then be reformulated in terms of the local existence and uniqueness of solutions to the geodesic equation.
In this manner well-posedness of the system in \eqref{s1:eq1} was established for the specific case $s=1$ and $a\neq1$ in the work \cite{EHKL2014}, and these results may be extended to ensure the well-posedness of the general system when $s>1$ and $a\in\RR\setminus\{1\}$.

In Section \ref{Sec2} of this paper we demonstrate that the system in \eqref{s1:eq1} can be recast as the flow of a right-invariant metric on the Fr\'{e}chet Lie group $\GS$, when $a=2$. This result is shown to be true for a general class of nonlocal inertia operators of the form $A=(1-D^2)^s$ with $s>1$. The well-posedness of the system remains valid for this general class and the reader is referred to the results presented in \cite{EHKL2014} \S 5, and also \cite{EK2014a} for further relevant discussions. Lastly in Section \ref{Sec3} we establish rigourous criteria ensuring global solutions for the system \eqref{s1:eq1} when $A$ induces a fractional Sobolev norm, for general $a\neq1$. In this regard, the pseudo-differential form of the inertia operator generates additional terms requiring careful analysis of the \textit{a priori} estimates necessary to ensure the existence of global solutions. We close our study by giving a proof of Theorem \ref{thm:gc}.

\section{Geometric Formulation}\label{Sec2}
The work undertaken in \cite{CK2002} investigated the  geodesic equation on $\DiffS$ associated with the right-invariant $H^{1}$ metric, namely the Camassa-Holm equation, which is a reduction of the system being currently being investigated. Meanwhile, in \cite{Esc2012} the short-wave limit of \eqref{s1:eq1}, namely $m=-u_{xx}$ and $s=1$, is shown to correspond to a geodesic flow on a symmetric right-invariant connection on a suitable semi-direct product, when $\alpha = 0$. Moreover it was shown in the case $a=2$ that this connection is associated with a metric induced by the norm
\[\norm{u_{xx}}_{L^2}+\norm{\rho}_{L^2},\]
with $u\in\CS/\RR$ and $\rho\in\CS$. It was shown in \cite{EHKL2014} that the system \eqref{s1:eq1} could be recast as a geodesic flow of a right invariant metric on a suitable semi-direct product, when $s=1$ and $a=2$. In Theorem \ref{s1:thm1} it will be shown that these results extend to the case when $A$ belongs to a general class of nonlocal inertia operators.

Given a Lie group $G$ with corresponding Lie algebra $\mathfrak{g}$, then any inner product on $\mathfrak{g}$ may be extended to a \textit{right-invariant metric} in $G$ by right translation of this inner-product. We may represent the inner product on the Lie algebra by an invertible operator
\[\mathbb{A}:\mathfrak{g}\to\mathfrak{g}^{*}.\]
Then a path $g(t)\subset G$ is a geodesic of the $\mathbb{A}$-induced right-invariant metric of $G$ if and only if the Eulerian velocity of $g(t),$ namely
\[ u(t) := TR_{g(t)^{-1}}\dot{g}(t)\]
satisfies the Arnold-Euler equation given by
\begin{equation*}
\begin{split}
    u_t = -\BB(u,u),\qquad  \BB(u_1,u_2) \deq \frac{1}{2}\left(\ad^{\top}_{u_1}u_2+ \ad^{\top}_{u_2}u_1\right)
\end{split}
\end{equation*}
where $u_{i}\in\mathfrak{g}$ for $i=1,2$ and $\ad_{u}^{\top}$ is the adjoint of $\ad_u$ with respect to $\AA.$ That is to say, given $\Lambda\in \mathcal{L}\left(\mathfrak{g},\mathfrak{g}\right),$ we define the adjoint $\Lambda^{\top}$ with respect to the norm $\langle\cdot,\cdot\rangle$ as follows
\begin{equation*}
    \langle u_1,\Lambda^{\top} u_2\rangle = \langle \Lambda u_1,u_2\rangle, \qquad \langle u_1,u_2\rangle = \int_{\Circle} u_1\AA u_2.
\end{equation*}
In what follows it will be demonstrated that the general system \eqref{s1:eq1} with $a=2$ and $s>1$ may be reformulated as the geodesic flow of a right invariant metric on the infinite dimensional Lie group $\GS:=\DiffS\circledS\CS\times\RR$.

Moreover we denote by $H^s(\Circle)$, where $s\ge 0$, the usual Sobolev spaces over $\Circle$, equipped with the norm
\begin{equation*}
\Vert u\Vert_{H^s}:=\left(\sum_{k\in\mathbb{Z}}(1+\vert k\vert^2)^s\hat u_k^2\right)^{1/2},\qquad u\in L_2(\Circle),
\end{equation*}
where $\hat u_k:= (u\vert \mathrm{\mathbf{e}}_k)_{L_2}$ is the $k$-th Fourier coefficient with respect to the standard
\footnote{For simplicity we normalise the length of the circle $\Circle$ to the value $1$, so that $\mathrm{\mathbf{e}}_k=\exp{ikx}$.}
orthonormal basis $\{\mathrm{\mathbf{e}}_k\,;\, k\in\mathbb{Z}\}$ of $L_2(\Circle)$. We observe that
\begin{equation}\label{eq:sob}
\Vert u\Vert_{H^s}=\int_{\Circle} u Au\,dx.
\end{equation}
Furthermore we note that with $\mathds{1}:=\mathrm{\mathbf{e}}_0$ we have
\begin{equation}\label{eq:A1}
A\mathds{1}=\sum_{k\in\mathbb{Z}}(1+\vert k\vert^2)^s(\mathds{1}\vert \mathrm{\mathbf{e}}_k)_{L_2}\mathrm{\mathbf{e}}_k=(\mathds{1}\vert \mathrm{\mathbf{e}}_0)_{L_2}\mathrm{\mathbf{e}}_0=\mathds{1}.
\end{equation}
The latter observation and the fact that $A$ is self-adjoint particularly implies that
\begin{equation}\label{eq:Ainv}
\int_{\Circle} A^{-1} w\,dx=(A^{-1} w\vert A\mathds{1})_{L_2}=(w\vert\mathds{1})_{L_2}=\int_{\Circle} w\,dx,\quad w\in L_2(\Circle).
\end{equation}
After the above preparations we can state the following result:

\begin{theorem}\label{s1:thm1}
Given $\kappa > 0$ and $a=2$ it is possible to write the system (\ref{s1:eq1}) as the Arnold-Euler equation on the Lie algebra $\gs$ of the Fr\'{e}chet Lie group $\GS$ with an associated inner product
\begin{multline}\label{s2:eq1}
    \langle(u_1,\rho_1,\alpha_1),(u_2,\rho_2,\alpha_2)\rangle = \int_{\Circle}u_1Au_2dx  + \kappa\int_{\Circle}\rho_1\rho_2dx \\ -\frac{1}{2}\int_{\Circle}\left[\alpha_2u_1+\alpha_1u_2\right]dx + \frac{1}{2}\alpha_1\alpha_2
\end{multline}
with $u_i,\rho_i\in\CS$ and $\alpha_i\in\RR$ for $i=1,2$.
\end{theorem}

\begin{proof}
  We may write the inner product in (\ref{s2:eq1}) as
\begin{equation}\label{s2:eq2}
    \langle(u_1\,\rho_1,\alpha_1),(u_2,\rho_2,\alpha_2)\rangle = \int_{\Circle}(u_1,\rho_1,\alpha_1)\cdot\mathbb{A}(u_2,\rho_1,\alpha_2)dx,
\end{equation}
where $\cdot$ is the usual dot product in $\RR^3$. The inertia operator $\AA$ is given by
\begin{equation}\label{s2:eq3}
    \AA(u,\rho,\alpha) = \left(Au - \frac{\alpha}{2},\kappa\rho,\frac{1}{2}\Big(\alpha-\int_{\Circle}u\,dx\Big)\right)
\end{equation}
With $U_i = (u_i,\rho_i,\alpha_i)\in \gs$, where $i=1,2,$ we have
\begin{equation}\label{s2:eq4}
    \ad_{U_1}U_2 = \left(u_{1,x}u_2-u_1u_{2,x},\rho_{1,x}u_2 -\rho_{2,x}u_1,0\right)
\end{equation}
and so upon returning (\ref{s2:eq3}) and (\ref{s2:eq4})  to (\ref{s2:eq2}) we find
\begin{align*}
    \langle\ad_{U_1}U_2,U_3\rangle =& \int_{\Circle}\left(u_{1,x}u_2-u_1u_{2,x},\rho_{1,x}u_2-\rho_{2,x}u_1, 0\right)\cdot\AA(u_3,\rho_3,\alpha_3)\\
                                   =& \int_{\Circle}(u_{1,x}u_2-u_1u_{2,x})Au_3 dx +\kappa\int_{\Circle}\left(\rho_{1,x}u_2-\rho_{2,x}u_1, \right)\rho_3dx\\
                                   &-\frac{\alpha_3}{2}\int_{\Circle}(u_{1,x}u_2-u_1u_{2,x})dx
\end{align*}
Integration by parts along with $[A,D]= 0$ yields
\begin{equation}\label{s2:eq5}
\begin{split}
    \langle\ad_{U_1}U_2,U_3\rangle = & \int_{\Circle}u_2\left(u_{1,x}Au_3 +(u_1Au_{3})_x+ \kappa\rho_{1,x}\rho_3-\alpha_3u_{1,x}\right)\\
    &+ \kappa\int_{\Circle}\rho_2(u_1\rho_3)_x \\
    \deq&\int_{\Circle}(u_2,\rho_2,\alpha_2)\cdot(f,g,0)\\
    \deq & \int_{\Circle}(u_2,\rho_2,\alpha_2)\cdot\AA(\tilde{u},\tilde{\rho},\tilde{\alpha}).
\end{split}
\end{equation}
which defines $\tilde{U} = (\tilde{u},\tilde{\rho},\tilde{\alpha})$ in terms of $U_1$ and $U_3$. Thus we are looking for the unique solution of
\begin{equation*}
A\tilde{u} - \frac{\tilde{\alpha}}{2} = f\qquad \kappa\tilde{\rho} = g\qquad \tilde{\alpha} - \int_{\Circle}\tilde{u}dx = 0,
\end{equation*}
which, invoking \eqref{eq:A1}, is found to be
\begin{equation}\label{s2:eq5.1}
    \tilde{u} = A^{-1}f + \int_{\Circle}fdx\qquad \tilde{\rho} = \frac{1}{\kappa}g\qquad \tilde{\alpha} = 2\int_{\Circle}fdx,
\end{equation}
However by definition we also have
\[\langle\ad_{U_1}U_2,U_3\rangle = \langle U_2,\ad_{U_1}^{\top}U_3\rangle = \int_{\Circle}(u_2,\rho_2,\alpha_2)\cdot\AA(\tilde{u},\tilde{\rho},\tilde{\alpha})\]
in which case it follows that $\ad_{U_1}^{\top}U_{3} = (\tilde{u},\tilde{\rho},\tilde{\alpha})$.
Explicitly we have
\begin{equation}\label{s2:eq6}
\begin{split}
    \tilde{u} =& A^{-1}\left(u_{1,x}Au_3 +(u_1Au_{3})_x+ \kappa\rho_{1,x}\rho_3+\alpha_3u_{1,x}\right)\\
               &+\int_{\Circle} \left(u_{1,x}Au_3 + \kappa\rho_{1,x}\rho_3\right)dx\\
    \tilde{\rho} =& (u_1\rho_3)_x\\
    \tilde{\alpha} =&  -2\int_{\Circle}\left(u_{1,x}Au_3 + \kappa\rho_{1,x}\rho_3\right)dx
\end{split}
\end{equation}
Lastly we note by the symmetry of $A$ along with its commutativity with $D$, that
\begin{equation}\label{s2:eq7}
\int_{\Circle}u_{1,x}Au_3 = -\int_{\Circle}u_1Au_{3,x} = -\int_{\Circle}Au_1u_{3,x}
\end{equation}
and so the integral is antisymmetric in $u_1$ and $u_3.$
Hence substituting  $U=(u,\rho,\alpha)$ in (\ref{s2:eq6}) and employing (\ref{s2:eq7}) yields
\begin{equation}\label{s2:eq8}
\begin{split}
 \BB(U,U) =& \ad_{U}^{\top}U
          = \left(A^{-1}\left[u_xAu + (uAu)_x -\alpha u_x + \kappa\rho\rho_x\right], (u\rho)_x,0\right).
\end{split}
\end{equation}
Consequently the Arnold-Euler equation $U_{t} = -\BB(U,U)$
corresponds precisely with the system (\ref{s1:eq1}) when $a=2.$
\end{proof}
\begin{remark}
Note that the bilinear form given by \eqref{s2:eq1} is positive definite for any choice of $\kappa\ge 0$ and $\alpha\in\mathbb{R}$.
\end{remark}
\begin{proof} Define
\begin{equation*}
\Vert (u,\rho,\alpha)\Vert_{\mathbb{A}}^2:=\int_{\Circle}u Au\,dx+\kappa\int_{\Circle}\rho^2\,dx-\alpha\int_{\Circle}u\,dx+\frac{\alpha^2}{2}
\end{equation*}
for $u,\;\rho \in \CS$ and $\alpha\in\mathbb{R}$. Invoking $\int u^2\le \Vert u\Vert_{H^s}=\int uAu$, we get
$$
\Vert (u,\rho,\alpha)\Vert^2_{\mathbb{A}}\ge \int_{\Circle}(u-\frac{\alpha}{2})^2dx+\kappa\int_{\Circle}\rho^2dx.
$$
Thus $\Vert (u,\rho,\alpha)\Vert^2_{\mathbb{A}}>0$ for all $(u,\rho,\alpha)\in \gs$ with $u\ne\alpha/2$ or $\rho\ne 0$. But
$$
\Vert (\frac{\alpha}{2},0,\alpha)\Vert^2_{\mathbb{A}}=\frac{\alpha^2}{4},
$$
which completes the proof.
\end{proof}
\begin{remark} Given $u\,\;\rho\in\CS$ and $\alpha\in\mathbb{R}$, we have that
\begin{equation}\label{eq:aprio}
\frac{3}{4}\Vert u\Vert_{H^s}^2+\kappa\Vert\rho\Vert_{L_2}^2\le\Vert(u,\rho,\alpha)\Vert^2_{\mathbb{A}} +
\frac{\alpha^2}{2}.
\end{equation}
\end{remark}
\begin{proof}
Using the elementary inequality $-u\alpha\ge -u^2/4 - \alpha^2$, we get
$$
-\int_{\Circle}u\alpha\, dx\ge - \frac{1}{4}\int_{\Circle}u^2 dx-\alpha^2\ge - \frac{1}{4}\Vert u\Vert_{H^s}^2-\alpha^2
$$
which readily gives the assertion.
\end{proof}
\begin{remark}\label{rm:3}
Consider the case $a=2$ and let $(u,\rho)$ be a solution to \eqref{s1:eq1} on the time interval $J$. Then the quantity
$
\Vert (u,\rho,\alpha)(t)\Vert_{\mathbb{A}}
$
is constant on $J$.
\end{remark}
\begin{proof}
We have
\begin{equation}\label{eq:tvar}
\frac{1}{2}\frac{d}{dt} \Vert (u,\rho,\alpha)(t)\Vert_{\mathbb{A}}^2=\int_{\Circle}u_tAu\,dx+\kappa \int_{\Circle} \rho_t\rho\,dx - \alpha\int_{\Circle} u_t\,dx.
\end{equation}
Invoking \eqref{s1:eq1} we find because of $[A,D]=0$:
\begin{align*}
    \int_{\Circle} u_t Au =& \int_{\Circle}m_t u\\
                                   =&\ \alpha\int_{\Circle}uu_x- 2\int_{\Circle}u u_x Au-\int_{\Circle}u^2 Au_x-\kappa\int_                                      {\Circle}\rho\rho_x\\
                                   =&\ \frac{\alpha}{2}\int_{\Circle}(u^2)_x- \int_{\Circle}(u^2)_xAu +
									  \int_{\Circle}(u^2)_xAu
										-\kappa\int_{\Circle}\rho\rho_x u\\
								   =&\ -\kappa\int_{\Circle}\rho\rho_x u.
\end{align*}
For the second integral of the right-hand side of \eqref{eq:tvar} we get
$$
\kappa\int_{\Circle}\rho_t\rho =-  \kappa\int_{\Circle}(\rho u)_x\rho =  \kappa\int_{\Circle}\rho\rho_x u.
$$
Thus $\int u_t Au+\kappa\int\rho_t\rho=0$ and we are left to show that $\int u_t=0$. Using \eqref{eq:Ainv} we obtain
\begin{align*}
    \int_{\Circle} u_t  =&\ \alpha\int_{\Circle} A^{-1}u_x - 2\int_{\Circle}A^{-1}(u_x Au)-
							\int_{\Circle}A^{-1}(uAu_x)-\kappa\int_{\Circle}\rho\rho_x\\
                        =&\ \alpha\int_{\Circle} u_x - 2\int_{\Circle}u_x Au-
							\int_{\Circle}uAu_x-\kappa\int_{\Circle}(\rho^2)_x.
\end{align*}
Recalling $[A,D]=0$, integration by parts yields $\int u_t=\int uAu_x$. But $\int u Au_x=0$ by \eqref{s2:eq7} and the proof is complete.
\end{proof}
Following the work of Arnold \cite{Arn1966}, Ebin \& Marsden \cite{EM1970} considered the group of smooth diffeomorphisms as an inverse limit of Hilbert manifolds.  This essentially allows one to recast classes of PDEs, namely the Euler equation, in terms of an ODE, that is to say the geodesic equation on these Hilbert manifolds. These techniques were applied in \cite{Mis2002,CK2003} for the periodic Camassa-Holm equation, while in \cite{EK2011} the Degasperis-Procesi equation was recast as a non-metric geodesic flow. Moreover in \cite{CK2003a, EK2014} these methods were extended to right-invariant metrics induced by fractional Sobolev norms, following from \cite{Kol2009}. In \cite{EHKL2014} the same techniques were applied to the hydrodynamical reduction of \eqref{s1:eq1}, namely $s=1$,  thereby establishing well-posedness of that system. Having reformulated the system \eqref{s1:eq1} as a right-invariant metric flow on the Fr\'{e}chet Lie group $\DiffS\circledS\CS\times\RR$ when $a=2$ and $s>1$, these same techniques also ensure the well-posedness of the system for this general class of fractional Sobolev norms with $a\in\RR\setminus\{1\}$.

\section{Global Solutions}\label{Sec3}
As was pointed out in Section \ref{Sec1}, the Camassa-Holm equation arises as a reduction of the system \eqref{s1:eq1}, namely when $\rho\equiv0$, $a=2$, $\alpha=0$ and $s=1$, and given the classical results of \cite{Con2000, CE1998a,CE1998b} it is clear that not all solutions of either system should exist globally. However that is not to say that global solutions for the class of systems currently being investigated  do not exist. A reduction of the system to the two-component Camassa-Holm equation, namely $s=1$, $\alpha =0$ and $a=2$, was found to possess several notable features in the works \cite{CI2008, Hen2009}, including global solutions, thus providing motivation for the investigation of global existence criteria for the general system \eqref{s1:eq1}.

The solutions $(u,\rho)$ to the system in equation \eqref{s1:eq1}, with associated initial data $(u_0,\rho_0)$, correspond to smooth paths in
\begin{equation*}
    (u,\rho)\in \mathrm{C}^{\infty}(J,\CS\oplus\CS),
\end{equation*}
where $J$ is the maximal time interval of their existence. In what follows we present a collection of \textit{a priori} estimates which establish criteria for the existence of global solutions for \eqref{s1:eq1} when $A$ induces a class of fractional Sobolev norms.

\begin{lemma}\label{s3:lem1} We have
\begin{equation}\label{s3:eq1}
	(\rho\circ\phi)(t)\cdot\phi_x^{a-1}(t) = (\rho\circ\phi)(0)\cdot\phi_x^{a-1}(0)\quad \forall t\in J.
\end{equation}
\end{lemma}

\begin{proof} Let $\phi$ be the flow of the vector field $u$. Then we have
\begin{equation}\label{s3:eq1a}
\phi_t = u\circ\phi
\end{equation}
and so it follows
\begin{equation}\label{s3:eq2}
\begin{split}
	\frac{d}{{d}t}(\rho\circ\phi\cdot\phi_x^{a-1}) &=\left((\rho_t+u_x\rho+(a-1)\rho u_x)\circ\phi\right)\cdot\phi^{a-1}_x=0,
\end{split}
\end{equation}
since $(u,\rho)$ solves the system (\ref{s1:eq1}).
\end{proof}

\begin{corollary}\label{s3:cor1}
If $\rho_0 > 0$, it follows that $\rho(t) > 0$ for all $t\in J$.
\end{corollary}

\begin{proof}
It follows from Lemma \ref{s3:lem1} that
\begin{equation}\label{s3:eq3}
\begin{split}
    (\rho\circ\phi)(t)\cdot\phi_x^{a-1}(t) &= (\rho\circ\phi)(0)\cdot\phi_x^{a-1}(0)\\
     (\rho\circ\phi)(t) &=  (\rho\circ\phi)(0)\cdot\frac{\phi_x^{a-1}(0)}{\phi_x^{a-1}(t)}
\end{split}
\end{equation}
However since $\phi(t)$ is an orientation preserving diffeomorphism we must have
\[\frac{\phi_x(0)}{\phi_x(t)} > 0\quad \forall\ t\in J,\]
in which case if $\rho(0)>0$ it follows from (\ref{s3:eq3}) that
\begin{equation}\label{s3:eq4}
(\rho\circ\phi)(t) >0
\end{equation}
for all $t\in J.$
\end{proof}

\begin{corollary}\label{s3:cor2}
 If $\norm{u_x(t)}_\infty$ is bounded on any bounded subinterval of $J$ then $\norm{\rho(t)}_\infty$ is also bounded on any bounded subinterval of $J.$
\end{corollary}

\begin{proof}
Define $\phi$ as the flow of  the time dependent vector field $u$ and set
\[\gamma(t) = \max_{x\in\Circle}\frac{1}{\phi_x(t)}\]
where we also note $\gamma(t)$ is continuous. Let $I \subset J$ where $I$ is bounded and denote
\begin{equation}\label{K}
K = \sup_{t\in I}\norm{u_x(t)}_\infty.\end{equation}
Given (\ref{s3:eq1a}) we see that
\begin{equation}\label{s3:eq5}
    \left(\frac{1}{\phi_x}\right)_t = -\frac{\phi_{tx}}{\phi_x^2}= -\frac{(u\circ\phi)_x}{\phi_x^2} = -\frac{u_x\circ\phi}{\phi_x}
\end{equation}
which following an integration, and using the definition of $\gamma$ and the bound \eqref{K} leads us to the inequality
\begin{equation}\label{s3:eq7}
    \gamma(t) - \gamma(0) \leq K \int_{0}^{t}\gamma(s)\rm{d} s.
\end{equation}
A subsequent application of Gronwall's Lemma ensures
\begin{equation}\label{s3:eq8.0}
    \gamma(t)\leq\gamma(0)e^{Kt},
\end{equation}
that is to say $\frac{1}{\phi_x(t)}$ is bounded on $I.$
It follows from Lemma \ref{s3:lem1} that $\norm{\rho(t)}_{\infty}$ is bounded on $I$.
\end{proof}

\subsection{Estimates for fractional Sobolev norms}\label{Sec3.1}
When we generalise the inertia operator according to $A = (1-D^2)^{s}$ and $s\in(1,\infty)$, the quantity $u_xm$ can no longer be written as a total derivative and so the \textit{a priori} estimates obtained in \cite{EHKL2014} \S6, must be generalised to account for this term.
The operator $\Lambda^{s}=(1-D^2)^{\frac{s}{2}}$ is a topological isomorphism of $H^{s}(\Circle)$ onto $L^2(\Circle)$.
Providing $H^{s}(\Circle)$ with a Hilbert space structure makes $\Lambda^{-s}(\Circle)$ an isometric isomorphism of $L^2(\Circle)$ onto $H^s(\Circle)$.
That is to say, if $(u,v)\in H^s(\Circle)\times H^s(\Circle),$ their inner product may be written as
\begin{equation}\label{s3:eq8}
    \langle u,v\rangle_{H^s} = \langle \Lambda^{s} u,\Lambda^{s} v\rangle_{L^2}.
\end{equation}
Moreover since $\Lambda^{s} \in \mathcal{L}\left(H^s,L^2\right)$ it follows
\begin{equation}\label{s3:eq9}
    \norm{\Lambda^{s}u}_{L^2}\lesssim\norm{u}_{H^s}.
\end{equation}
The Sobolev imbedding $H^s(\Circle)\hookrightarrow L_\infty(\Circle)$ for $s>1/2$ implies the following bound
\begin{equation}\label{e3:eq10}
    \norm{u}_\infty\lesssim \norm{u}_{H^s} \qquad \forall u\in H^s(\Circle),
\end{equation}
while the fact $D\in\mathcal{L}\left(H^{s+1}(\Circle),H^{s}(\Circle)\right)$ ensures $\norm{D u}_{H^s} \leq C\norm{u}_{H^{1+s}}$
and consequently we have the following estimate for $u_x$
\begin{equation}\label{s3:eq11}
    \norm{u_x}_\infty\lesssim \norm{u}_{H^s},\qquad\text{if}\ s>\frac{3}{2}.
\end{equation}
Finally we note that
\begin{equation}\label{u - m}
\Vert u_x\Vert_{L_\infty}\le \Vert u\Vert_{H^{2s}}=\Vert Au\Vert_{L_2}=\Vert m\Vert_{L_2},\quad u\in \CS,
\end{equation}
by the Sobolev embedding theorem based on the assumption $s>3/2$.

\noindent
In addition to the aforementioned estimate for $\norm{u_x}_{\infty}$, we have the related result bounding $\norm{m}_{H^{k}}+\norm{\rho}_{H^{k+1}}$ given by the following:
\begin{lemma}\label{s3:lem2}
Suppose $\norm{u_{x}}_{\infty}$ is bounded on any bounded subinterval of $J.$ Then
\[\norm{m}_{H^k}^2 + \norm{\rho}_{H^{k+1}}^2\]
is also bounded, on any bounded subinterval of $J$ for all integers $k\geq0$.
\end{lemma}

\begin{proof}The proof begins by demonstrating that the quantity $\norm{m}_{L^2}+\norm{\rho}_{H^1}$ remains bounded when $\norm{u_x}_{\infty}$ remains bounded on a bounded subset of $J$.
\begin{equation}\label{s4:eq12}
\begin{split}
\frac{d}{dt} \left(\norm{m}_{L^2}^2 + \norm{\rho}_{H^1}^2\right)&=\int_{\Circle} mm_tdx + \int_{\Circle}(\rho\rho_t+\rho_x\rho_{xt})\\
                                                                &= \int_{\Circle} m(\alpha u_x - au_xm-um_x -\kappa\rho\rho_x)\\
                                                                &\quad+\int_{\Circle}\rho_x(-u\rho_{xx} - au_x\rho_x -(a-1)\rho u_{xx} )\\
                                                                &\qquad +\int_{\Circle}\rho(-u\rho_x - (a-1)u_x\rho) \\
\end{split}
\end{equation}
Integration by parts yields
\[-\int_{\Circle}umm_xdx= \frac{1}{2}\int_{\Circle}u_xm^2\qquad -\int_{\Circle}u\rho\rho_{x}dx=\frac{1}{2}\int_{\Circle}u_x\rho^2dx\]
which in conjunction with the Cauchy-Schwarz inequality provides the following estimate
\begin{equation}\label{s3:eq13}
\frac{d}{dt}\left(\norm{m}_{L^2}+\norm{\rho}_{H^2}\right)
\lesssim\int_{\Circle}\alpha u_{x}mdx+
\left(1+\norm{u_x}_{\infty}+\norm{\rho}_{\infty}\right)\left(\norm{m}_{L^2}^2+\norm{\rho}_{H^{1}}^2\right).
\end{equation}
Meanwhile, H\"{o}lder's inequality applied to the remaining term yields
\begin{equation*}
\int_{\Circle}\alpha u_xm\leq\abs{\alpha}\norm{u_x}_{\infty}\int_{\Circle}\abs{m}dx\lesssim\norm{u_x}_{\infty}\norm{m}_{L^2}\\
\end{equation*}
and it follows at once that
\begin{equation}\label{s3:eq14}
    \int_{\Circle}\alpha u_{x}mdx\lesssim \norm{u_x}_{\infty}^2 + \norm{m}_{L^2}^2.
\end{equation}
Upon combining these estimates we find
\begin{equation}\label{s3:eq15}
\frac{d}{dt}\left(\norm{m}_{L^2}^2 +\norm{\rho}_{H^1}^2\right)\lesssim \norm{u_x}_{\infty}^2+ \left(1+\norm{u_x}_\infty +\norm{\rho}_\infty\right)\left(\norm{m}_{L^2}^2+\norm{\rho}_{H^1}^2\right).
\end{equation}
A straightforward application of the integral form of Gronwall's inequality ensures that the quantity $\norm{m}_{L^2}^2 +\norm{\rho}_{H^1}^2$ is bounded for all $t \in J$ when $\norm{u_x}_{\infty}$ is bounded in $J$.
\begin{remark}
Gronwall's Lemma requires that the functions $m$ and $\rho$ be continuous, however these functions are in fact smooth and so an application of the lemma is permitted.
\end{remark}

At the next iteration, we wish to show the quantity $\norm{m}_{H^1}^2 + \norm{\rho}_{H^{2}}^2$
is also bounded under the same conditions. Specifically we want to show
\begin{equation}\label{s3:eq16}
\frac{d}{dt}\left(\norm{m}_{H^1}^2+\norm{\rho}_{H^{2}}^2\right)\lesssim\norm{m}_{L^2}^2+\left(1+\norm{m}_{L^2}
+\norm{\rho}_{H^{1}}\right)\left(\norm{m}_{H^1}^2+\norm{\rho}_{H^{2}}^2\right).
\end{equation}
We already have
\begin{equation*}
\begin{split}
\frac{d}{dt}\left(\norm{m}_{L^2}^2+\norm{\rho}_{H^1}^2\right)&\lesssim\norm{u_x}_{\infty}^2+\left(1+\norm{u_x}_\infty +\norm{\rho}_\infty\right)\left(\norm{m}_{L^2}^2 +\norm{\rho}_{H^1}^2\right)\\
&\lesssim\norm{m}_{L^2}^2+\left(1+\norm{m}_{L^2}+\norm{\rho}_{H^{1}}\right)\left(\norm{m}_{H^1}^2+\norm{\rho}_{H^{2}}^2\right),
\end{split}
\end{equation*}
with the second relation being a consequence of the imbeddings $H^2\hookrightarrow H^1$ and $H^1\hookrightarrow L_\infty,$
and the estimate \eqref{u - m}. As such we need only show
\begin{equation}\label{s3:eq17}
\frac{d}{dt}\left(\norm{m_x}_{L^2}^2+\norm{\rho_{xx}}_{L^2}^2\right)\lesssim\norm{m}_{L^2}^2+\left(1+\norm{m}_{L^2} +\norm{\rho}_{H^{1}}\right)\left(\norm{m}_{H^1}^2+\norm{\rho}_{H^{2}}^2\right).
\end{equation}
Considering the first term of \eqref{s3:eq17} we have
\begin{equation}\label{s3:eq18}
\begin{split}
\frac{d}{dt}\norm{m_x}_{L^2}^2
	&=\int_{\Circle} m_x(\alpha u_{xx}-au_{xx}m-au_xm_x - u_xm_x - um_{xx} - \kappa\rho_x^2 - \kappa\rho\rho_{xx})dx.\\
\end{split}
\end{equation}
Integration by parts yields $-\int_{\Circle} um_xm_{xx}dx = \frac{1}{2}\int_{\Circle} u_xm_x^2dx$; thus the Cauchy-Schwarz inequality provides a bound for the norm $\norm{m_x}_{L^2}$ according to
\begin{equation}\label{s3:eq19}
\begin{split}
\frac{d}{dt}\norm{m_x}^2 &\lesssim \norm{u}_{H^2}\norm{m}_{H^1} + \norm{u}_{H^2}\norm{m}_{H^1}^2 + \norm{u_x}_\infty\norm{m}_{H^1}^2 \\
&\quad + \norm{m}_{H^1}\norm{\rho_x^2}_{L^2} + \norm{\rho}_\infty\norm{\rho}_{H^2}\norm{m}_{H^1},
\end{split}
\end{equation}
where we have  used the fact that $\HH{q}$ is a multiplicative algebra for $q>\frac{1}{2}$ thus ensuring
\[\int_{\Circle} u_{xx}mm_xdx \lesssim \norm{u}_{H^2}\norm{m}_{H^1}^2.\]
Moreover in line with the previous iteration, the Cauchy-Schwarz inequality ensures
\begin{equation}
    \int_{\Circle}\alpha u_{xx}m_xdx\lesssim\norm{u}_{H^2}\norm{m}_{H^1} \lesssim \norm{u}_{H^2}^2+\norm{m}_{H^1}^2 .
\end{equation}
Thus upon implementing the estimates
\begin{equation*}
\norm{u}_{H^2}\lesssim \norm{m}_{L^2},\quad \norm{u_x}_{\infty} \lesssim \norm{m}_{L^2},\quad
\norm{\rho}_{\infty}\lesssim\norm{\rho}_{H^1},\quad \norm{\rho_x^2}_{L^2} \lesssim\norm{\rho}_{H^1}\norm{\rho}_{H^2}
\end{equation*}
we obtain
\begin{equation}\label{s3:eq20}
\frac{d}{dt}\norm{m_x}^2 \lesssim \norm{m}_{L^2}^2+\left(1 + \norm{m}_{L^2}+\norm{\rho}_{H^1}\right)\left(\norm{m}_{H^1}^2 + \norm{\rho}_{H^2}^2\right).
\end{equation}
Meanwhile the term $\frac{d}{dt}\norm{\rho_{xx}}_{L^2}^2$ may be written according to
\begin{multline}\label{s3:eq21}
\frac{d}{dt}\norm{\rho_{xx}}_{L^2}^2 = \int_{\Circle}\rho_{xx}(-u\rho_x-(a-1)u_x\rho)_{xx}dx\\
= \left(a-\frac{1}{2}\right)\int_{\Circle}\left(u_{xxx}\rho_x^2-u_x\rho_{xx}^2\right)dx + (a-1)\int_{\Circle}u_{xxx}\rho\rho_{xx}dx.
\end{multline}
The Cauchy-Schwarz inequality in conjunction with the estimate $\norm{u}_{H^3}\lesssim\norm{m}_{H^1}$ yields
\begin{equation}\label{s3:eq22}
\begin{split}
\frac{d}{dt}\norm{\rho_{xx}}_{L^2}^2 & \lesssim \norm{u_x}_{\infty}\norm{\rho}_{H^2}^2 + \norm{m}_{H^1}\norm{\rho}_{\infty}\norm{\rho}_{H^2} + \norm{m}_{H^1}\norm{\rho_{x}^2}_{L^2} +  \norm{u_x}_\infty\norm{\rho}_{H^2}^2 \\
\end{split}
\end{equation}
which can be further simplified using $\norm{\rho_x^2}_{L^2}\lesssim\norm{\rho}_{H^1}\norm{\rho}_{H^2}$
allowing us to write
\begin{equation}\label{s3:eq23}
\begin{split}
\frac{d}{dt}\norm{\rho_{xx}}_{L^2}^2 &\lesssim (1+\norm{m}_{L^2}+ \norm{\rho}_{H^1})(\norm{m}_{H^1}^2+\norm{\rho}_{H^2}),
\end{split}
\end{equation}
having also used $\norm{\rho}_{\infty}\lesssim \norm{\rho}_{H^1}$ and $\norm{u_x}_{\infty}\lesssim\norm{m}_{L^2}$.
It follows that
\begin{equation}\label{s2eq24}
\frac{d}{dt}(\norm{m}_{H^1}^2+\norm{\rho}_{H^2}^2)\lesssim \norm{m}_{L^2}^2+(1+\norm{\rho}_{H^1}+\norm{m}_{L^2})(\norm{m}_{H^1}^2+\norm{\rho}_{H^2}^2),
\end{equation}
thus confirming $\norm{m}_{H^1}^2 + \norm{\rho}_{H^2}^2$ remains bounded in $J$ if $\norm{u_x}_\infty$ is bounded in $J.$

To demonstrate the  general case we must show that the quantity $\norm{m}_{H^k}^2 + \norm{\rho}_{H^{k+1}}^2$
is also bounded on any bounded subinterval of $J$ for all positive integers $k$, when $\norm{u_x}_{\infty}$ is bounded. To demonstrate this we use proof by induction and so want to show if the expression is bounded for some $k>1$ then the same is true for $k+1.$ We note

\begin{equation}\label{s3:eq25}
\begin{split}
	\frac{d}{dt}(\norm{m}_{H^{k+1}}^2 + \norm{\rho}_{H^{k+2}}^2) = \frac{d}{dt}(\norm{m}_{H^{k}}^2 + \norm{\rho}_{H^{k+1}}^2)+\frac{d}{dt}\int\left( (m^{(k+1)})^2  + (\rho^{(k+2)})^2\right)
\end{split}
\end{equation}
and so it is only required that we show the integral on the right hand side remains bounded on $J$ if $\norm{u_x}_\infty$ remains bounded on $J.$

We have
\begin{multline}\label{s3:eq26}
\int\left(m_{t}^{(k+1)}m^{(k+1)} + \rho_t^{(k+2)}\rho^{(k+2)}\right) =\\
\int m^{(k+1)}\left(\alpha u_x^{(k+1)} - a (u_xm)^{(k+1)} - (um_x)^{(k+1)}-\kappa(\rho\rho_x)^{(k+1)}\right)\\
-\int\rho^{(k+2)}\left((u\rho_x)^{(k+2)}+(a-1)(u_x\rho)^{(k+2)}\right).
\end{multline}
The Leibniz rule combined with the Cauchy-Schwarz inequality ensures
\begin{multline}\label{s3:eq27}
	\abs{\int(fg)^{(n+1)}h^{(n+1)}}\lesssim \norm{f}_{H^{n}}\norm{g}_{H^{n+1}}\norm{h}_{H^{n+1}}\\
                                                                        + \abs{\int fg^{(n+1)}h^{(n+1)}} + \abs{\int f^{(n+1)}gh^{(n+1)}},
\end{multline}
which may be applied to the above expression yielding
\begin{multline}\label{s3:eq28}
\frac{d}{dt}(\norm{m}_{H^{k+1}}^2+\norm{\rho}_{H^{k+2}}^2)
\lesssim (1+\norm{m}_{H^{k}}+\norm{\rho}_{H^{k+1}})(\norm{m}_{H^{k+1}}^2+\norm{\rho}_{H^{k+2}}^2)\\
+\int_{\Circle}\alpha m^{(k+1)}u_x^{(k+1)}dx.
\end{multline}
The Cauchy-Schwarz inequality applied to the remaining integral provides the estimate
\begin{equation}\label{s3:eq29}
    \int_{\Circle}\alpha m^{(k+1)}u_x^{(k+1)}dx\lesssim \norm{m}_{H^{k+1}}\norm{u}_{H^{k+2}}\lesssim \norm{m}_{H^{k+1}}^2 + \norm{m}_{H^k}^2,
\end{equation}
having used $\norm{u}_{H^{k+2}}\leq \norm{m}_{H^k}.$
It follows at once that we may write
\begin{equation}\label{s3:eq30}
\begin{split}
\frac{d}{dt}(\norm{m}_{H^{k+1}}^2+\norm{\rho}_{H^{k+2}}^2)\lesssim\norm{m}_{H^k}^2+(1+\norm{m}_{H^k}+\norm{\rho}_{H^{k+1}})(\norm{m}_{H^{k+1}}^2+\norm{\rho}_{H^{k+2}}^2)
\end{split}
\end{equation}
and with Gronwall's Lemma this ensures the quantity $\norm{m}_{H^{k+1}}^2 + \norm{\rho}_{H^{k+2}}^2$ remains bounded, thus Lemma \ref{s3:lem2} has been verified.
\end{proof}

\subsection{Proof of Theorem \ref{thm:gc}}\label{Sec3.2}
\begin{proof}
Let $u_0,\ \rho_0\in\CS$ be given, and denote by
\begin{equation*}
    (u,\rho)\in \mathrm{C}^{\infty}(J,\CS\oplus\CS)
\end{equation*}
the unique non-extendable solution to \eqref{s1:eq1} emerging from $(u_0,\rho_0)$. Assume that $J$ is bounded and write $T^+:=\sup J$. Then there must exists a $k_0\in\mathbb{N}$ such that
\begin{equation}\label{eq:blowup}
    \limsup_{t\to T^+}\Vert u(t)\Vert_{H^{k_0}}=\infty\qquad\text{or}\qquad\limsup_{t\to T^+}\Vert \rho(t)\Vert_{H^{k_0}}=\infty.
\end{equation}
Recalling that by assumption $\kappa\ge 0$ and $a=2$, Remark \ref{rm:3} in conjunction with \eqref{eq:aprio} and \eqref{s3:eq11} implies that $\Vert u(t)\Vert_{L_\infty}$ is bounded on $J$. Invoking Lemma \ref{s3:lem2} this contradicts \eqref{eq:blowup}.
\end{proof}

\section*{Acknowledgements}
Both authors are grateful to Boris Kolev for several helpful discussions. The authors would like to thank the referees for several helpful comments.

redpajama_set_name: RedPajamaArXiv


Twice a year (in the spring and the fall), Distributed Lab - one of the leading blockchain technology companies in Ukraine - holds the BlockchainUA conference. This an educational and networking event that brings together industry experts, IT developers, entrepreneurs, investors, students and everyone interested in blockchain and FinTech innovations. During the event, prominent world and Ukrainian experts share their experience and discuss all the aspects of using blockchain technology in different spheres.
After the conference an All-Ukrainian Blockchain hackathon is usually held, where software engineers and crypto enthusiasts work together to solve the challenges with Blockchain technology.
This year, the fifth All-Ukrainian Blockchain hackathon was particularly exciting event for all employees of Anadea as our colleague Dmitriy Selin participated in this hackathon and won! Dmitriy took the first place in the NEM nomination.
On the 15-16th of September, 2018, the hackathon gathered participants from all over Ukraine in an amazingly great place - UNIT.City, Kiev. The goal of the hackathon was to build prototypes of new products based on Blockchain technology. For solving problems, participants were asked to use products of one of sponsors - Remme, NEM, Bloqly, Kuna - as a part of solution. They also were free to apply their own tools and products to solution of their own problem.
The only drawback of the event was that food breaks consisted mainly of pizza (though there were fruits once). After that I couldn't eat pizza for a week, recalls Dmitriy ;) All the rest was perfect!
The start was given at about 11am, teams started coding at about 3-4pm on Saturday (day 1) and first demos were presented at 4:30pm on Sunday (day 2). From 27 ideas pitched at the start, only 20 survived to the finish.
The idea which Dmitriy decided to implement was a simple copyright protection service - IP (intellectual property) proof.
Dmitriy used their wallet to save NEM timestamps signed with hash of anything in blockchain, which makes it possible to hash and anchor in blockchain any block of information. In practice, you can take a text, a picture, a font, etc. freshly invented by you, create a hash and store it in blockchain. Then, in case of a dispute over who invented this object of intellectual property first, you can pull out your hash, that exact transaction, its time and confirm when it happened.
The NEM blockchain, already has Apostille service with a similar purpose, but it does not allow you to search for hashes. Dmitriy created a solution compatible with Apostille which allows searching for hashes.
As a result, Dmitriy won the first place in the nomination from NEM. The guys with the wallet took the second place.
Besides the nomination from NEM, there were also nominations from Remme, Kuna, Bloqly and the organizers themselves.
Blockchain voting from some team which name we unfortunately don't know.
These projects got 1-2 awards each in different nominations.
Here is what Dmitriy says about his project.
Since this is a blockchain project, in this particular prototype I wanted to have only the frontend, which directly interacts with blockchain so that all personal data would not leave the user's browser.
At first, as a proof of concept, I implemented an application that takes a file or text, calculates a hash, and, with the help of the MetaMask browser extension, which establishes connection with the Ethereum blockchain, sends the required hash and metadata to the pre-written smart contract.
Then, the same behavior was reproduced to work with the NEM blockchain. There are no smart contracts in NEM, but they are not required for such application. The main point is that based on data, a hash is created, based on hash - a private key, based on private key - a public key, based on a public key - an address for it, a specific transaction-message is sent to this address and the payload of this transaction contains data about the hash. Later on, you can compute the address by any hash and check the first transaction to this address. If it has the needed information, then this is the confirmation of ownership. As Jeff, one of the NEM's tops who was an invited guest on the hackathon, said, such "pointer accounts" have a very wide potential for application.
Cheers! And our sincere greetings to all participants!


This is our slogan, loosely translated from Marathi (displayed above)! Striving continuously to live up to our slogan, with limited manpower and resources we have successfully organized various projects in nature conservation, protection and education.
Nature conservation through field protection, awareness, education and scientific based action.
Sahyadri Nisarga Mitra was born when a few likeminded people wanted to do more than sigh away their pangs of conscience about the rampant abuse of nature. The day was 12th Feb. 1992. Out of the brain storming of these individuals, the aim to "Broaden the vision of nature conservation" was taken up as the mission of this Organisation.
Indian Swiftlets on Vengurla Rocks is one of the commendable projects. A timely action by the SNM team and alerting the forest department resulted into arresting of smugglers of Indian Swiftlet's nests within a week's time. Subsequent observations revealed increased number of nesting in this area.
White bellied sea eagle survey in districts Ratnagiri and Sindhudurg helped to get crucial data related to their habitat, nesting and threats.
Such activities in the initial years contributed to build a solid base of volunteers in the Konkan region. These volunteers became the eyes and ears of the organization to sense and resolve the local environmental problems. The data collected through such activities proved crucial for taking up our long-term projects like Vulture Conservation, Marine Turtle Conservation, Homestay and Alternate livelihood options for locals .
Membership is open to all nature lovers who are interested in nature conservation.


I don't always have gluten-free bread on hand, and to buy it at my local gluten-free bakery often seems like a hassle when I can just make my own at home. However, sandwiches do need some sort of exterior structure to be called sandwiches, so I've been thinking recently about bread alternatives.
First, bake the marinated tempeh. Do this at 350' in a deep container that can hold the juices (I prefer a stoneware baking item) for 1 hour, turning the tempeh every 20-25 minutes or so.
Meanwhile, wash and pat dry the lettuce leaves, and lay them out on a plate (I used one leaf for each side of the bun). Add toppings.
When the tempeh has finished baking, let it cool for a little while, then lay on top of the lettuce. Assemble and enjoy.
Mix all ingredients together well and pour over tempeh. Store in a airtight container in the fridge for up to 24 hours, turning the tempeh every few hours or so.
Serve the sandwich with potato salad, potato chips, or another starchy side (to make sure you get all those carbs in somehow). It is suitable to eat by hand, but if you must, cut it up and eat it with a fork (like I had to).


text:
Muckraker / scandal and investigations
DOJ Dismisses Alleged Census Case Bombshell As 'Meritless' And 'Inflammatory'
WASHINGTON, DC - SEPTEMBER 17: Acting Assistant Attorney General for Civil Rights John Gore speaks at the Justice Department September 17, 2018 in Washington, DC. Attorney General Jeff Sessions spoke about Department... WASHINGTON, DC - SEPTEMBER 17: Acting Assistant Attorney General for Civil Rights John Gore speaks at the Justice Department September 17, 2018 in Washington, DC. Attorney General Jeff Sessions spoke about Department of Justice efforts to support free speech on college campuses at the event. (Photo by Aaron P. Bernstein/Getty Images) MORE LESS
June 3, 2019 7:37 p.m.
The Justice Department came out guns blazing in a court filing Monday evening denying many of the claims of new evidence and alleged false testimony in the census citizenship case.
The Justice Department called the ACLU's allegations "meritless" and "inflammatory," while comparing the ACLU's arguments to the "conjuring " of a "conspiracy theory involving a deceased political operative that essentially hinges on wordplay."
"The [ACLU's] motion borders on frivolous, and appears to be an attempt to reopen the evidence in this already-closed case and to drag this Court into Plaintiffs' eleventh-hour campaign to improperly derail the Supreme Court's resolution of the government's appeal," the Department said. "The Court should not countenance Plaintiffs' tactics."
The Justice Department denied that its December 2017 formal request that a citizenship question be added to the census was at all connected to a 2015 study by a Republican consultant who said such a question could facilitate a redistricting overhaul that would boost the GOP's electoral advantages.
The Justice Department said any insinuation of similarities between the 2017 request, written by DOJ official John Gore, and the consultant's study were false.
The ACLU has accused Gore and another person involved in the push to add the question of lying about their testimony.
The ACLU's argument about Gore's alleged lack of candor did not hinge on whether he based the formal request on the 2015 study, but rather whether he had received a draft of the request that included a paragraph ghostwritten by the now-deceased consultant, Tom Hofeller. Gore admitted in a congressional interview earlier this year to receiving the draft from Mark Neuman, an outside advisor on census issues and the other witness who has been accused of lying by the ACLU.
In its court filing Monday, the Justice Department blamed the challengers in the case for not asking the specific questions of Gore in his deposition that would have produced that answer. The Department also pointed out, in what was perhaps the strongest argument in its filing, that it produced the draft for the challengers in discovery in October with the representation that it was among the "materials collected from" Gore. The ACLU, in its initial filing making the allegations, had conceded that the draft had been produced in discovery. But the group claimed that it had been produced by Neuman and that "neither Neuman nor Gore had disclosed that Neuman gave this draft to Gore."
Furthermore, the Department argued, the request written by Gore "bears no resemblance to anything in the Neuman Letter, including the nonsensical paragraph allegedly written by Hofeller."
A hearing in the dispute has already been scheduled in front of the trial court judge for Wednesday. It is not clear whether the challengers will seek to try to put the new evidence in front of the Supreme Court — which heard the case in April — and what procedural mechanism would be available for them to do so.
The challengers were able to connect Hofeller to the draft that Neuman provided Gore because of files on his back-up hard drive that had been found by his estranged daughter after his death last year. The Hofeller's files were provided for a separate partisan gerrymander case in North Carolina, where the challengers were represented by the same law firm as those in the Census case.
Read the filing as well as the relevant exhibits below:
2020 Censuscensus citizenship questionJustice Department
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