The First Regular Session of the 98th Missouri General Assembly will begin at 12:00 noon on Wednesday, January 7, 2015.
Pre-filing of legislation for the 2015 session began on December 1, 2014. Your Missouri Right to Life Legislative Team is reviewing all bills and will be reporting weekly in the weekly lifelines during the legislative session.
Registering at EScrip's Online Mall is your way to support Missouri Right to Life Education Fund every time you shop online. The Online Mall also provides timely money-saving offers as an added benefit to you for shopping with them.
Never miss out on special savings or earnings again! Install Forgetmenot from the Escrip Online Mall website, and you'll be reminded automatically whenever you're shopping with a merchant who gives back. You'll earn for Missouri Right to Life Education Fund even if you've forgotten to go through the eScrip Online Mall first. It's free, saves money and easy to install.
Whether you want to shop the latest fashions from Bloomingdales or Nordstrom, or if you are gearing up with the latest gadgets from the Apple Store, or bargain hunting at eBay, your shopping will make a difference for Missouri Right to Life Education Fund.
Join hundreds of thousands of pro-life people from across the U.S. and other countries to peacefully protest the 1973 Supreme Court's decision to legalize abortion. Travel on one of the Missouri Life Caravan buses, leaving throughout the St. Louis Metro area Jan 21-23.
Click here to download a registration form or contact Missouri Life Caravan at (314) 434-4900 or email: mrl.eastern@yahoo.com.
Live calls are being made to lists of pro-lifers asking if the person is pro-life, pro-choice or mixed. When the person responds pro-life, they are asked to donate to the "Right to Life Committee." When the person questions the caller about the committee they are given a PO Box in Washington, D.C. 20024. When asked about what they do, the caller does not provide any information.
Further, when you Google Right to Life Committee, the first several items that come up are National Right to Life Committee.
These calls are not being made by and the money donated is NOT coming to National Right to Life Committee or Missouri Right to Life. IF you should receive one of these calls, or if you hear from someone who receives one of these calls, it is suggested that you report the call as potential fraud to your state Attorney General's office.
Disclaimer: NRLC and MRL both do telephone fundraising, but the caller will use the full name of the organization at the beginning of the call.
Two very respected neurologists have testified via sworn declarations that she is not now brain dead...read more.
Why Not Get "Stop ICU Child Care OK" in Writing?
Apparently legislation in Missouri is controversial among the bioethics set because it requires written consent to stop ICU care for a child...read more.
The abortion rate keeps dropping. This raises a few important questions...read more.
"NRLC and their Missouri affiliate, Missouri Right to Life are grateful for the many years of service and expertise Jim Bopp has given to the pro-life cause," said Pam Fichter, MRL president...read more .
Every pro-lifer who has ever given any thought to the matter or expressed a view on it acknowledges, indeed proclaims, the difference between a human organism and a human cell that is not a human organism...read more.
January 7, 2015, Statewide - New legislative session begins.
January 21, 22, 23, 2015, Statewide - The 42nd Annual National March for Life. Click here to download a registration form.
March 10, 2015, Statewide - MRL Legislative Action Day. Mark your calendars to come to Jefferson City and lobby for life!


After a short ride from the wondrous time had at Lyra, we found ourselves in good time for the evening kick-off at K.V.Mechelen. To our delight both the Belgian Cup and the first round of Jupiler Pro League fixtures had thrown up several options for a double and K.V. more than fitted the bill.
Tickets ordered in advance online were collected effortlessly from the super efficient kiosk. To give the hosts their full name for once, Yellow Red Koninklijke Voetbalclub Mechelen, would explain the vibrant coloured queues waiting for the gates to swing open at 7pm. Formed in 1904 a mere couple of months after city neighbours Racing Mechelen, KV have a proud history and rejoice in the low matricule number of 25. Today's opposition, Standard de Liège, however, are older still and own matricule 16.
The clubs home ground has the dreaded sponsored name of Argosstadion after Argos Oil paid for the naming rights. Its traditional name is Achter de Kazerne, which literally translated as "behind the barracks", the ground having once been adjacent to a large but now demolished army base. The club has played at Achter since 1911 when the then president Francis Dessain purchased the vacant land from the Chevalier Marin brewery. The club were originally called FC Malinois and the supporters are often still referred to as "Malinwa". The ground itself is quite magnificent. The main grandstand has wooden seating and an unusual slated roof, opposite is a really traditional covered terrace, a large percentage of the 10,402 crowd will gather here. The fans that stand on this side of the ground generate a really first class atmosphere of singing, colour and noise. Behind the far goal is an unusual twin tier stand with benched seating in the top tier and terracing underneath. The other end looks formidable from the outside, tall and cavernous but in truth the twin tier of glazed corporate seating, more than half empty for this opening match of the season, is a tad underwhelming once inside. Aside from that minor quibble a stunning set of traditional floodlight pylons complete a really great ground that is draped liberally in the club's colours of "Geel en Rood". One does wonder whether the redevelopment of the huge covered terrace and the twin tier stand behind the goal at the end of this season will have a deleterious affect on the feel of the stadium. The club does need to progress so lets hope the plans are sympathetic and in keeping with the great history of this venue.
A brass band and anthem singing turn the volume up prior to the kick-off and expectation is high for the start of the new season. The home side toil manfully in the heat but seem to lack quality in the forward department. The visitors show their title credentials with two identical breakaway goals in the second half. In both cases a forward springs the offside trap from a counter attack and slots past the home custodian. On the quality of play alone they are worthy winners.
Belgian football has some really historic old fashioned football grounds indeed the recently opened Ghelamco Arena in Gent is the first totally new stadium in the country in 38 years. Both K.V. Mechelen and Lyra TSV were an absolute pleasure to visit and some more trips to this welcoming corner of Europe will certainly be pushed up the agenda.
1. Wouter Biebauw; 4. Seth De Witte; 6. Sheldon Bateau; 10. Abdul-Yakuni Iddi; 13. Wannes Van Tricht; 14. Benjamin Mokulu; 15. Thomas Enevoldsen; 19. Maxime Biset; 21. Anthony Van Loo; 26. Antonio Ghomsi; 29. Alessandro Cordaro.
28. Tome Pacovski; 3. Seweryn Michalski; 8. Jerry Vandam; 9. Mads Junker; 11. Mats Rits; 16. Victor Prodell (for 10, 67 mins); 18. David Destorme (for 13, 46 mins); 20. Joachim Van Damme (for 14, 78 mins).
1. Elji Kawashima; 4. Daniel Opare; 6. Laurent Ciman; 17. Yoni Buyens; 23. Michy Batshuayi; 25. Antonio Periera Dos Santos; 37. Jelle Van Damme; 39. Imoh Ezekiel; 40. Paul Jose Mpoku Ebunge; 44. Ibrahima Cisse; 63. Geoffrey Mujangibia.
16, Anthony Morris; 2. Alessandro Iandoli (for 40, 69 mins); 7. Raza Ghoochannejahad; 10. Igor De Camargo (for 39, 78 mins); 11. Frederic Bulot (for 63, 65 mins); 36. Dino Arslanagic; 75. Alpaslan Ozturk.
This entry was posted in Travel, Matches & Stadiums and tagged Achter de Kazerne, argosstadion, Belgian Football, Belgium, groundhopping, Jupiler Pro League, KV Mechelen, Standard Liege, Yellow and Reds by peterrmiles. Bookmark the permalink.


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text:
Carollia monohernandezi är en fladdermus i familjen bladnäsor som förekommer i Colombia.

Ett exemplar var 50 mm lång (huvud och bål), hade en 11 mm lång svans, underarmar som var 30,5 mm långa, 11 mm långa bakfötter och 20 mm stora öron. Viktuppgifter saknas. Håren på ovansidan är ljusbruna nära roten och mörkbruna vid spetsen. Pälsen på undersidan är mellanbrun. Svansen är helt omsluten av svansflyghuden. På nedre läppen finns vårtiga utskott som bildar en U. Hudflikarna på näsan har en rund grundform och en lång spjutformig uppsats. Ett annat kännetecken är trekantiga öron.

Individerna lever i låglandet och i bergstrakter mellan 30 och 2660 meter över havet. Ett exemplar från södra Panama tillhör antagligen denna art. Exemplaren vistas i regnskogar och i torra tropiska skogar. Andra arter i samma släkte har främst frukter av växter från släktet Piper som föda.

Inget är känt angående populationens storlek och möjliga hot. IUCN listar arten med kunskapsbrist (DD).

Referenser

Bladnäsor
monohernandezi
Däggdjur i neotropiska regionen

redpajama_set_name: RedPajamaWikipedia


This project is designing, developing, and testing an innovative approach to elementary students' learning in the critical areas of multiplicative reasoning, fractions, and proportional reasoning. The project is building on the successful El'Konin-Davydov (E-D) elementary mathematics curriculum that originated in Russia to develop a curriculum framework that can be implemented in U. S. schools. The ultimate product of the research will be a rational number learning progression consisting of carefully articulated and sequenced learning goals.
The Measurement Approach to Rational Number (MARN) project is a collaborative effort by faculty at New York University, Iowa State University, and the Illinois Institute of Technology that is designing, developing, and testing an innovative approach to elementary students' learning in the critical areas of multiplicative reasoning, fractions, and proportional reasoning. The project team is building on the successful El'Konin-Davydov (E-D) elementary mathematics curriculum that originated in Russia to develop a curriculum framework that can be implemented in U. S. schools.
The MARN project addresses five core research questions about how rational number learning can be developed from a measurement perspective and how sociocultural theory and constructivism can contribute to design of effective learning trajectories based on that perspective. The project begins with careful analysis of the E-D curriculum embodied in Russian mathematics materials, of classroom data from a Hawaii implementation of the E-D curriculum, and of relevant prior curriculum development projects in other U. S. contexts. Work is proceeding from development of an initial curriculum framework through intensive teaching experiments to implementation and modification of the framework in the course of classroom design experiments.
The ultimate product of the research and development effort will be a rational number learning progression consisting of carefully articulated and sequenced learning goals. The curriculum framework will also include mathematical tasks to foster learning of each concept, description of predicted student learning in the context of the tasks, a set of assessment items related to each concept, and guidelines for relevant teacher interventions. Thus, the framework will provide a foundation for development of curriculum units.


A BLISTERING first quarter from the England Roses inspired them to victory in the opening match of the Vitality Netball International Series on Friday night, despite an impressive Malawi fight back.
England raced into an eleven goal lead at the end of the opening quarter with Kadeen Corbin and Rachel Dunn impressively dominating the shooting circle.
At the other end, the Queens were struggling to break through the Roses defensive line and were dealt an early blow when Mwai Kumwenda hobbled from the court after just five minutes.
The momentum was with the Roses and they continued to capitalise in the final third to build a 22-11 lead after the opening fifteen minutes.
The return of Kumwenda provided a much needed spark for the Queens and they responded excellently in Q2.
The deficit was down to six almost instantly as the energy through court from the visitors started to pay dividends. A more robust defensive approach from the Queens failed to halt the Corbin streak as she ended the half with 15 goals from 15 attempts.
Despite the continued accuracy of the Roses' shooting duo, the advantage had shrunk to 39-30 at the half-time interval.
The physicality continued in the third quarter with Jade Clarke and Beth Cobden putting in the hard yards to cover Malawian attacks. A number of deflections and steals keeping the away side at bay.
It was matched by a rejuvenated Queens with Loreen Ngwira showing her athleticism with an astonishing sideline intercept to push her side forward.
With five minutes remaining in the quarter Ellie Cardwell made her way into GA with Corbin taking over at GS. The change made an instant impact with the Roses able to stifle their opponents, and the clock, to take a ten goal advantage into the final quarter, 51-41 to the hosts.
With a significant gap to overcome, Malawi had to come out fighting and they certainly did. Turnover goals reduced the Roses' lead and the phenomenal Queens support in the stands ratcheted the noise levels up another notch.
England remained calm and the introduction of Sasha Corbin saw the home fans in full voice to welcome the ever-popular mid-courter onto court.
However, it was sister Kadeen who was stealing all the headlines with a fantastic Player of the Match performance.
A piece of wonderful movement was deservedly spotted by Clarke who unleashed a fabulous feed for the younger Corbin to cap a fine display.
The Queens continued to battle but were ultimately undone by their slow start. There was certainly enough heart shown after that to suggest that Sunday will not necessarily be the coronation that the Roses will be hoping for.


I have not concealed your steadfast love and your faithfulness from the great congregation.
may those who love your salvation say continually, "Great is the LORD!
Today was one of those good days that I hear about. Yeah, how about that?
And, I'm going to bed early!
After several tumultuous days, today felt like a dream. I could go on and list all the reasons why each of these things were awesome. But I won't. I'll just recognize that it was refreshing to have such a good day and to treasure moments like this. Many days may not be like this. I need to remember this day in order to encourage myself when the not so good days come along.


1. It works well with dynamic braking resistors.
2. Helpful in loading resistors.
3. It can also be combined with neutral grounding resistors.
4. Capable of running for long service period.
The wire grid type NGR offered by is globally accepted and acclaimed for higher quality standards, and durability. We are also capable of adding some optional features in the resistor on client's demand.


Geldards are very pleased to announce they have joined forces with The Law Society to support the 2019 LGBT History Month.
To mark LGBT History Month, The Law Society are hosting a speed networking event in Cardiff on Thursday 21st February 2019. The event is a chance to network with LGBT+ solicitors from both in-house and law firms, law students, trainees, barristers and legal executives. This event is open to law students, solicitors and other legal professionals from firms that are South Wales members of the Law Society.
We have been working in conjunction with The Law Society and other various Law Firms in South Wales to support LGBT History Month.
"At Geldards we are very proud to be supporting The Law Society's LGBT History Month and this unique networking opportunity. This event is not just for those that identify as LGBT+, it is an event to raise awareness and to promote better understanding of LGBT issues in the workplace and across all communities. It is open to all regardless of sexual orientation.
For more information on the event and LGBT History Month, please visit The Law Society's website.


The "provider" shall be Stephen Brown t/a Era Video Productions and/or employees/agents representing the provider.
In the case of a limited company, the company registered pursuant to the Companies Act 2006 (or any other enactment or legislation introduced as a supplement or consolidation thereof).The "event" shall refer to the occasion, ceremony, conference, reception, location and any other duty to which the customer has tasked the provider to provide services.
"Service" or "services" shall encompass (but not be limited to): filming of events, provision and utilisation of editing facilities, conversions of all types, production and copying.
The "product" shall be the digital or disc based media produced or created as a result of the service.
The "vendor" or "vendors" shall include (but not be restricted to) any and all third parties providing goods, services, hosting, planning or be a third party in any other way associated with their own independent services/product(s) provided to the customer, either directly or indirectly, at all times before, during and after the event.
The "material" shall refer to all and any material, content, equipment, storage medium or devices supplied/loaned by the customer (or supplied/loaned by a third party under the direction – or by the request - of the customer) to the supplier for the purpose of creating the product.
The "equipment" shall refer to all hardware, vehicles, cameras, microphones, projectors, sound mixers, lenses and ancillary equipment/items belonging to the provider or their agent.
"Commission", when used in the context of reselling, shall refer to the published and agreed commission rate payable by the provider to the customer upon receipt of funds from the third party to which the sale/resell – made by the provider, on behalf of the customer – relates.
The "purchaser" shall be the person or organisation that procures any material subject to resell.
Where the provider has verifiably confirmed the willingness and availability to attend the event, and/or provide the service and/or create and supply the product.
There shall be no variation to this contract without the express written consent and authority of the provider.
This contract will govern the service requested by the customer at the time the contract is entered into and at any future event or provision of any subsequent product by the provider.
Subject to compliance of the terms within paragraph CONTRACT (1) the provider undertakes to attend the event and fulfil his obligations in accordance with the description of the service.
Upon the request of the provider, the customer will furnish the provider with all necessary contact details pertaining to the vendor/vendors associated with the event.
The customer will, wherever necessary, assist and partake in all matters and communication arising between the provider and the vendor.
The provider shall not be liable for any cost or expense, charged or incurred by any vendor, as a result of the provider's attendance, actions, energy usage or any other activity which the vendor sees fit to charge; the customer undertakes and assumes liability in this regard should it occur.
In accordance with paragraph CONTRACT (1) the provider undertakes to provide the service, which has been ordered or requested by the customer.
With the exception of the provider's physical attendance at an event in isolation, time shall not be the essence of contract when providing the service and/or delivering the product; at all times the provider will endeavour to complete the service or supply the product in a timely fashion; however, no set off or deduction can be made by the customer as a result of any delay associated with completion of the service and/or delivery of any product.
Each product shall be delivered in the format stipulated by the customer; the provider will assume no liability in connection with loss, damage or incompatibility should it be found that the stated format is incorrect, not applicable or inadequate. In this event, and upon the creation of a new format, the customer shall be liable for any subsequent cost.
Where applicable the customer shall ensure safe and unencumbered delivery of the material; the provider shall not be liable for any loss or damage at any time during transit or possession. Risk shall remain with the customer at all times and, where appropriate, the customer shall ensure that adequate cover/insurance is in place.
If the material is cine film then there is always the possibility that, during conversion, the film may snap or damaged sprocket holes will prevent feeding through the equipment; in this event the provider may have to cut out the affected portion and splice the material in order for conversion to take place. The provider will not be held accountable for any loss of footage in this regard.
With all material, and in the event of breakage or failure, the provider may seek the assistance of a third party to repair and make good the material concerned; this may incur an additional charge. Should this happen, the provider will consult with the customer and both parties shall agree to this extra expense prior to utilising the assistance of any third party provider; the customer shall be liable for any additional/associated cost.
In accordance with paragraph 7 [SERVICES] the provider will not be held liable for any loss or damage incurred as a result of the actions/inaction of any third party and/or any loss or damage incurred at any time during transit.
The provider reserves the right to refuse production/reproduction or copying of any material which is considered to be illegal, harmful, inciting, insulting or, in any way, likely to offend others.
The provider will convert material for the sole private use of the customer and - where the material is of a highly personal nature involving the customer or any other person captured within the material - the customer confirms their own consent together with that of any third party (and/or any other person captured or involved within material involving footage or scenes of a highly personal nature - originally intentional or otherwise) and that the relevant third party or person has raised no objection to the service being provided by the provider (i.e. the duplication/conversion of the material). In any event, the customer undertakes not to disseminate, copy or publish any product without the express consent of any other party involved in the initial creation of - or likely to be identified/affected by - the material and/or the ensuing product.
Any and all material supplied or loaned by the customer shall be free from third party copyright.
The customer will not at any time, under any circumstances, seek any recompense from the provider in respect of copyright or duplication hereinafter.
The provider is at liberty to use material supplied by the customer for marketing purposes unless the customer expressly prohibits this at the time of placing the order.
Copyright of the product (where not owned or claimed by the customer or any validated third party) will belong to the provider.
The licence supplied by PRS is subject to strict limitations concerning duplication and distribution; the customer shall respect the terms of the licence and shall not copy, distribute, disseminate or broadcast the product in any way, which is in breach of the conditions of the licence.
The customer hereby indemnifies the provider from all and any breaches of copyright, by the customer and/or any other third party, and shall assume full liability in connection with any subsequent or consequential civil action or criminal prosecution brought about by the copyright owner(s), the appropriate licensing authority and/or any law enforcement agency regardless of jurisdiction.
The customer shall be liable for any additional cost associated with renewal or amendment of any licence linked to the product.
It is the customer's responsibility to ensure that the relevant vendor has the appropriate public performance licence.
Where the event is a church wedding (including hymns) the customer will be responsible for all church copyright fees and will be expected to arrange this directly with the church concerned.
War or threat of war.
Civil disobedience/disorder/riots, strike, threat of strike and/or industrial action.
Acts or negligence of any postal or courier provider.
Adverse weather conditions/acts of nature.
Equipment breakdown/failure resultant in partial or total loss of enjoyment.
Payment is to be made immediately upon completion of the order in all instances.
The provider strongly recommends that all media/material is sent by recorded delivery (or other means of delivery requiring signature) by the customer; the provider accepts no liability for loss or damage to the material in transit.
Where the product is a digital download the customer will be provided with a login and password to the hosted service; the customer shall be expected to keep this information secure and undertakes not to disclose it to any unauthorised party. The customer shall inform the provider immediately in the event of unauthorised access to the hosted service. Equally, the customer shall ensure that, in the event that the information is disclosed to a trusted source and a breach occurs at, or via, this source, the customer shall immediately inform the provider of the breach. The provider will not be liable for any breach or unauthorised access; the customer shall – at all times - be liable for the actions or any breach committed by the trusted source(s).
The product shall remain on the hosted service and be available for download for a period of 30 (thirty) days from the date of payment being received from the customer; thereafter, the provider reserves the right to remove the product from the hosted service without prior notice.
i) The deposit (where only the deposit has been paid by the customer).
ii) The value of the contract (where the full contract price has been paid for by the customer).
The customer shall indemnify, and keep indemnified, the provider from any and all consequential loss caused by death, injury, damage to equipment and property, acts committed by third parties and/or agents or suppliers appointed by the provider, accident, equipment failure, loss of material, loss of profit, loss of production, acts committed/unwillingness to co-operate by any vendor or any person or corporation attending any event.
The customer shall indemnify, and keep indemnified, the provider from all or any loss of enjoyment howsoever caused.
The Contracts (Rights of Third Parties Act) 1999 – including any subsequent amendment or consolidation - shall not apply to this contract.
Deposits (when requested by the provider) are payable immediately and are integral to the commencement of contract in accordance with paragraph 2.1 (ii); the deposit shall represent 30% of the approximated cost of the service. Deposits are non-refundable.
Full payment in respect of the product is due upon receipt of the provider's invoice.
Where the customer is acting in the course of business - charge Compensation, costs and Interest per invoice, pursuant to the Late Payment of Commercial Debts (Interest) Act 1998, as amended and supplemented by the Late Payment of Commercial Debts Regulations 2013.
Seek the recovery of all costs associated with the utilisation of debt collection agencies and/or solicitors.
Charge the customer £25.00 for any dishonoured or unpaid cheque.
These terms shall be subject to scrutiny pursuant to the Unfair Contract (Terms) Act 1977.
The contract shall be subject to English Law and both parties shall submit to the exclusive jurisdiction of England.


My third cousin, a "Locking." She would have been under 100 years old today.
My third cousin once removed, Inga June Nordby. She would have been 112 years old today.
First cousin four times removed, Frederick Walton. He would have been 151 years old today.
The third cousin, an "Anderson."
The husband of my aunt, a "Driver."
My fifth great grandmother, Kirsten Larsdotter.


1501-1505 N OCCIDENTAL BLVD – SOLD $240K OVER ASKING W/ MULTIPLE OFFERS!
This stunning Spanish in the hills of Silver Lake will take your breath away. A well-appointed up and down duplex, this gated property with views and amazing light will be delivered entirely vacant. Both sizeable units consist of two bedrooms and one bath — and feature central air/heat, solar power, hardwood floors and original details throughout. The charm has been retained while bringing the kitchens, bathrooms, plumbing and electrical up to date. A huge and high-ceiling lower storage area conjures up visions of a gracious home office, media room or a future master suite. A quaint front courtyard and terraced backyard with flat grassy areas offers wonderful entertaining options as well as being home to a giant palm and prolific fruit trees. Just blocks from LAMill Coffee, L&E Oyster Bar, MILK as well as everything on Sunset. Park your car in the two car garage and take advantage of the walkability score of this incredible neighborhood.


text:
Post-Election Immigration Policy Advocacy Efforts Begin at YMF
On behalf of Youman, Madeo & Fasano, LLP on Friday, February 3, 2017.
During the week before the presidential inauguration in January 2017, Monica E. Ahmad-Yee, who is the Managing Associate Attorney of the Jackson Heights, Queens office of YMF and the YMF Immigration Policy Advocacy Coordinator, submitted letters to numerous federal officials in support of the continued existence of Deferred Action for Childhood Arrivals (DACA). DACA is a program implemented under an order of the former U.S. Secretary of Homeland Security in 2012 allowing work authorization for certain individuals who entered the U.S. as minors. The correspondence was sent to U.S. Secretary of Homeland Security General John Kelly, U.S. Senate Minority Leader Charles Schumer, U.S. Democratic Whip Senator Dick Durbin, the Congressional Hispanic Caucus, and U.S. Representative Adriano Espaillat-the first person elected to Congress who was once undocumented. The correspondence highlighted the positive effects of DACA in the fields of real estate and architecture as the incoming administration considers whether to allow DACA to persist. DACA helps the U.S. to retain talent that promotes financial growth in the fields of real estate and architecture, areas in which President-elect Trump has shown a clear interest for decades. The purpose of the correspondence to various parties was to ensure that if it did not reach General Kelly directly, it could at least perhaps be forwarded to him or others close to him by Democratic elected officials who have demonstrated a commitment to immigrants' rights.
There are DACA holders now in their twenties who are pursuing successful careers in the fields of architecture and real estate. YMF clients have declined to allow the details of their cases to be profiled in this correspondence, for fear of being targeted by the U.S. government in retribution for advocating in favor of a certain immigration policy. DACA-holding professionals in the fields of architecture and real estate worry about the future of DACA, and have recently applied for renewal of their DACA approvals. They are sure that they will lose their jobs with her current employers if DACA is revoked. These are college graduates who have received honors for their outstanding achievements in architecture and real estate. They have no arrest history anywhere in the world and no history of immigration fraud. As the correspondence sent to U.S. officials asked, "Would the U.S. Department of Homeland Security be serving the interests of the U.S. by repealing DACA and rendering professionals such as these unemployed?"
The submission included a New York Times article profiling a DACA recipient who currently works as an architect; a study calculating that ending DACA would wipe away at least $433.4 billion from the U.S. gross domestic product, or GDP, cumulatively over a decade; and a similar study of the Center for American Progress stating, "At a time when the U.S. economy is finally emerging from the Great Recession, a loss of this magnitude is something the nation cannot afford."
All of our Attorneys are active members of the American Immigration Lawyers Association
Life After a Voluntary Departure Overstay:
Some Light in the Darkness: Hope after Matter of A-B- Domestic Violence Asylum Claim Granted
A Long Path to a Green Card
© 2020 by Youman, Madeo & Fasano, LLP. All rights reserved. Disclaimer

redpajama_set_name: RedPajamaCommonCrawl


At Altitude701 we specialise in discovering high quality wines, beers and ciders from small, family owned growers across Australia. Our goal is to bring joy to the palate of the consumer by presenting these fantastic products via our valued partners in the land of restaurants, small bars, gastro pubs, cafes and the odd groovy independent bottle shop. No mass market stuff here. Just artisan producers that love crafting products for a lucky audience to experience.
Just a few of the reasons to give Altitude701 a call.
• Exceptional products that deliver value across multiple price ranges from the major regions of Australia with a focus on NSW • Specialising on products not found in mass market bottle shops • Wine list creation and consultancy services • Customer satisfaction orientation across the sales and supply chain • Next day delivery in metro areas Why not try something different – something unique!
Michael loves wine, craft beer, good cider and the occasional G&T. He loves drinking it, selling it, preaching about it, teaching about it, making it and brewing it. Once caught up in corporate land in various sales and marketing roles, the lure of creating something unique centred around his passion for the underdog broke through and altitude701 was formed in 2009.
Jason joined the Altitude701 team in 2012. His great appreciation and taste for wines from all over the world he owes to living in the UK for six years – a country that imports it all! He is always interested in the story and the history as well as the juice. With 10 years as a Chef in a previous life and now 13 years in wine… Jason knows where the fun is.


text:
Retroflex lateral flap
The retroflex lateral flap is a type of consonantal sound, used in some spoken languages. It has no dedicated symbol in the International Phonetic Alphabet, but may be represented as ⟨ɭ̆⟩ or with a dot diacritic as ⟨ɺ̣⟩.
ɭ̆
ɺ̣
Features of the retroflex flap:
Its manner of articulation is flap, which means it is produced with a single contraction of the muscles so that one articulator (usually the tongue) is thrown against another.
Its place of articulation is retroflex, which prototypically means it is articulated subapical (with the tip of the tongue curled up), but more generally, it means that it is postalveolar without being palatalized. That is, besides the prototypical subapical articulation, the tongue contact can be apical (pointed) or laminal (flat).
Its phonation is voiced, which means the vocal cords vibrate during the articulation.
It is an oral consonant, which means air is allowed to escape through the mouth only.
It is a lateral consonant, which means it is produced by directing the airstream over the sides of the tongue, rather than down the middle.
The airstream mechanism is pulmonic, which means it is articulated by pushing air solely with the lungs and diaphragm, as in most sounds.
OccurrenceEdit
Iwaidja [ŋaɭ̆uli] 'my foot'
Kannada ಕೇಳಿ [keːɭ̆iː] 'to ask' Can be an approximant [ɭ] instead.
Kobon [example needed] — — Subapical. Written ⟨ƚ⟩.
Kresh[1] [example needed] — —
Malayalam വേളി [veːɭ̆iː] 'marriage' Can be an approximant [ɭ] instead.
Marathi केळी [keɭ̆iː] 'bananas' See Marathi phonology
Miyakoan Some dialects[2] [example needed] — —
Norwegian Trøndersk[3] glas [ˈɡɺ̠ɑːs] 'glass' Apical postalveolar;[3] also described as central [ɽ].[4] See Norwegian phonology
O'odham[5] [example needed] — — Apical postalveolar.[5]
Odia ସକାଳ [sɔkaɭ̆ɔ] 'morning' Can be an approximant [ɭ] instead.
Pashto[6][7] ړوند [ɭ̆und] 'blind' Contrasts plain and nasalized flaps.[6][7] Tend to be lateral at the beginning of a prosodic unit, and a central flap [ɽ] or approximant [ɻ] elsewhere.
Tamil குளி [ˈkuɭ̆i] 'bathe' Allophone of /ɭ/. See Tamil phonology
Totoli[8] [example needed] — — Allophone of /ɺ/ after back vowels.[8]
Tukang Besi[9] [example needed] — — Possible allophone of /l/ after back vowels, as well as an allophone of /r/.[9]
Wayuu[10] [example needed] — —
A retroflex lateral flap has been reported from various languages of Sulawesi such as the Sangiric languages, Buol and Totoli,[11] as well as Nambikwara in Brazil (plain and laryngealized), Gaagudju in Australia, Purépecha in Mexico, Moro in Sudan, O'odham and Mohawk in the United States, Chaga in Tanzania, and Kanuri in Nigeria.
Various Dravidian and Indic languages of India are reported to have a retroflex lateral flap, either phonemically or phonetically, including Gujarati, Konkani, Marathi, Odia, and Rajasthani.[12] Masica describes the sound as widespread in the Indic languages of India:
A retroflex flapped lateral /ḷ/, contrasting with ordinary /l/, is a prominent feature of Odia, Marathi–Konkani, Gujarati, most varieties of Rajasthani and Bhili, Punjabi, some dialects of "Lahnda", ... most dialects of West Pahari, and Kumauni (not in the Southeastern dialect described by Apte and Pattanayak), as well as Hariyanvi and the Saharanpur subdialect of Northwestern Kauravi ("Vernacular Hindustani") investigated by Gumperz. It is absent from most other NIA languages, including most Hindi dialects, Nepali, Garhwali, Bengali, Assamese, Kashmiri and other Dardic languages (except for the Dras dialect of Shina and possibly Khowar), the westernmost West Pahari dialects bordering Dardic (Bhalesi, Khashali, Rudhari, Padari) as well as the easternmost (Jaunsari, Sirmauri), and from Sindhi, Kacchi, and Siraiki. It was once present in Sinhalese, but in the modern language has merged with /l/.[13]
^ D. Richard Brown, 1994, "Kresh", in Kahrel & van den Berg, eds, Typological studies in negation, p 163
^ Aleksandra Jarosz, 2014, "Miyako-Ryukyuan and its contribution to linguistic diversity", JournaLIPP 3
^ a b Grønnum, Nina (2005), Fonetik og fonologi, Almen og Dansk (3rd ed.), Copenhagen: Akademisk Forlag, p. 155, ISBN 87-500-3865-6
^ Heide, Eldar (2010), "Tjukk l – Retroflektert tydeleggjering av kort kvantitet. Om kvalitetskløyvinga av det gamle kvantitetssystemet.", Maal og minne, Novus forlag, 1 (2010): 3–44
^ a b Ladefoged, Peter; Maddieson, Ian (1996). The Sounds of the World's Languages. Oxford: Blackwell. p. 213. ISBN 978-0-631-19815-4.
^ a b D.N. MacKenzie, 1990, "Pashto", in Bernard Comrie, ed, The major languages of South Asia, the Middle East and Africa, p. 103
^ a b Herbert Penzl, 1965, A reader of Pashto, p 7
^ a b Nikolaus Himmelmann, 2001, Sourcebook on Tomini-Tolitoli languages, The Australian National University
^ a b Donohue, Mark (1999), "Tukang Besi", Handbook of the International Phonetic Association, Cambridge University Press, p. 152, ISBN 0-521-63751-1
^ Randall Huber & Robert Reed, 1990, Vocabulario comparativo: palabras selectas de lenguas indígenas de Colombia, p 391
^ J. N. Sneddon, 1984, Proto-Sangiric & the Sangiric languages pp 20, 23
^ * Masica, Colin (1991), The Indo-Aryan Languages, Cambridge: Cambridge University Press, ISBN 978-0-521-29944-2
^ Colin Masica, The Indo-Aryan Languages, CUP, 1991
List of languages with [ɺ̺̠] on PHOIBLE
Retrieved from "https://en.wikipedia.org/w/index.php?title=Retroflex_lateral_flap&oldid=895481289"


text:
El ciudadano ilustre (no Brasil, O Cidadão Ilustre) é um filme dramático argentino-espanhol de 2016 dirigido por Gastón Duprat e Mariano Cohn, tendo como roteirista o co-diretor Duprat. Foi selecionado para competir pelo Leão de Ouro no 73º Festival Internacional de Cinema de Veneza. Em Veneza, Oscar Martínez ganhou a Volpi Cup de melhor ator. Foi escolhido para representar a Argentina na seleção de concorrentes ao melhor filme de língua estrangeira no Oscar 2017, mas não foi indicado.

Enredo
Daniel Mantovani é um escritor argentino mundialmente conhecido ganhador do Prêmio Nobel de Literatura. Embora seus romances se caracterizem por retratar a vida na pequena cidade onde ele nasceu, Salas, ele não fez questão de manter laços com as pessoas dali. Na verdade, Mantovani vive na Europa a mais de três décadas sem nunca ter regressado a Salas. Um dia o escritor recebe o convite do prefeito de Salas para receber a condecoração de cidadão ilustre da cidade. Porém, a volta ao seu país, faz com que o protagonista rememore as  semelhanças e diferenças irreconciliáveis com as pessoas da sua cidade natal.

Elenco
 Oscar Martínez ... Daniel Mantovani
 Dady Brieva ... Antonio
 Andrea Frigerio ... Irene
 Belén Chavanne ... Julia
 Nicolás De Tracy  ... Roque
 Nicolás De Tracy  ... Roque
 Nora Navas ... Nuria
 Marcelo D'Andrea ... Florencio Romero

Recepção
O Cinema com Crítica considerou o filme "uma comédia com humor inteligente, irônico e pertinente, gostosa de se assistir e com uma performance central caprichosamente bem controlada".

Ver também

Lista de submissões ao Oscar de Melhor Filme Estrangeiro em 2017

Ligações externas

Filmes em língua espanhola
Filmes da Espanha de 2016
Filmes da Argentina de 2016
Filmes de drama da Argentina


I pondered for a while over what I was going to write my blog on and many things crossed my mind. Topics included the great spiritual journey I have had in Kenya, how I found myself in machine shopping centre while facilitating groups with sheep baaing in the background or in general talking about how BK has indeed, and truthfully, changed my outlook on how to start a business. However while all these things would be wonderful, meaningful and inspiring to the masses I decided that, as the main readership of this will be future fellows, and that all of you will have your own 'finding yourself' experiences and probably do not want to read about another, that there was no better topic then a few words of advice on the dos and do nots of living in Nakuru.
What is this?!? You are about to find out….
Try and find out when Mokimo night is and run away from the Seasons hotel as quickly as possible (I suggest to Java where the source of Western food is plenty). For those of you who do not know what Mokimo is (trust me, it is better to have never experienced it) it can only be described a green potato mash with white maize in it. It is as bizarre in person as it sounds on paper and its existence I have figured to be due to an alien invasion that has mutated British cuisine and then tele-ported it to Africa. The experience of Mokimo is only made worse by the fact that it is the main meal. I love potato as much as the next person but, as one would never have mash potato as a meal in England, I am not sure why it has been deemed as socially acceptable at the hotel. Not even a vat of chilli sauce can save the potato from its dull fate (and trust me I am a big fan of chill sauce). I hope that none of you have to experience it after climbing Mount Kenya like this cohort did, after climbing a mountain, Mokimo is really the last thing you want to appear on your plate.
Try and avoid Patrick. Patrick is harmless bar from his slightly annoying tendency to try and sell you things and exchange foreign currency with you (particularly if your not from that country). From Danish Krones to Australian Dollars Patrick seems to get every currency but Kenyan Shillings. If you are lucky he give you a gift but for the 6 weeks of working in Nakuru it is really better just to avoid him rather then have him hassle you.
Take some time off and visit the infamous Rafikis (though I would highly suggest not on a school night). Rafikis is muzungu central for Nakuru, full of foreigners (well, maybe not full but full in Nakuru terms anyway) wanting to let their hair down after a long week. While my dancing is not one to be desired I believe that Rafikis has appreciated my attempts to wind my bumsie in a semi Africanish like way.
I hope these dos and don'ts has given you a better idea of 'what to expect' in Kenya, maybe not in the most traditional of terms, and that you take them on board. The rest I will let you figure out!
I have to disagree with your outlook on mokimo, it's a delicacy if you ask me.
I would like to change your view on this Kenya traditional food. Let me know when you are next in Nakuru and I will treat to the best mokimo meal ever. It is one of Kenya's traditional foods and is very delicious if made by an expert….like me! It is a mixture of English potatoes ( I prefer the reddish variety with a buttery taste), fresh baby pumpkin leaves and green maize. It is commonly served with fried beef or chicken or some other protein and vegetables(optional). It is truly delicious and very nutritious if you want a break from the empty junk food.


During the winter months, an inviting and warm atmosphere has been provided by WILLow LeaVes when partnering with area churches to bring a blended service, The Cross, to our community. The final winter service will be a little different on Sunday, April 8th.
As always, there will be complimentary drinks and cookies. From 5 to 6 p.m., WILLow LeaVes will also be offering a smoked pork chop dinner or a salad bar with soup as well as several desserts and hot dogs with chips for kids, all at a very reasonable price. And, you might as well take a few minutes to browse around their interesting store.
Around 6 p.m., the Community Children's Choir, under the leadership of Susan & David Brown, will perform. This wonderful choir consists of children in grades one through six, and they have been practicing hard for months. They will also be presenting "Go, Go Jonah" at Hope United Methodist Church on Sunday, April 29th at 6:30 p.m. You will want to mark this date on your calendar too!
Then, Worship Leader Dale Sechrest will lead in some inspirational music with The Cross Band (Instrumentalists Mark Fisher, Tony Garrison, Mark Neafus, & Avery Tallent; Vocalists Marissa Fisher, Sharron Harker, & Brandy Walters; Sound Technicians Ben Cleland & Pat Walters). Pastor Andy Kilps will deliver a short and meaningful message.
Avery Tallent, a young and talented songwriter and performer, will close the service by sharing original songs off of his new CD with The Cross Band, a group he has been a part of for several years.
"Perfect Love" started evolving in Avery's journey following God. Several of his songs were written after a recent Walk to Emmaus. Lately, he has been involved in a prison ministry which has generated even more songs. His CD will be available through a free will donation.
Reservations are not necessary but helpful, 812-546-0640.


text:
Beyond the Standard Model
Octonions and the Standard Model
Thread starter john baez
john baez
A survey of attempts to connect the octonions to the Standard Model - mainly explaining the math and having fun, not advocating any particular theory.
I've slowly been writing a thread on octonions and particle physics, just to explain some facts in a self-contained way, with all the proofs. I don't know where this will lead. I'm certainly not presenting a theory of physics, much less advocating one. Mainly it's just fun.
Octonions and the Standard Model 1. How to define octonion multiplication using complex scalars and vectors, much as quaternion multiplication can be defined using real scalars and vectors. This description requires singling out a specific unit imaginary octonion, and it shows that octonion multiplication is invariant under SU(3).
Octonions and the Standard Model 2. A more polished way to think about octonion multiplication in terms of complex scalars and vectors, and a similar-looking way to describe it using the cross product in 7 dimensions.
Octonions and the Standard Model 3. How a lepton and a quark fit together into an octonion - at least if we only consider them as representations of SU(3), the gauge group of the strong force. Proof that the symmetries of the octonions fixing an imaginary octonion form precisely the group SU(3).
Octonions and the Standard Model 4. Introducing the exceptional Jordan algebra: the 3×3 self-adjoint octonionic matrices. A result of Dubois-Violette and Todorov: the symmetries of the exceptional Jordan algebra preserving their splitting into complex scalar and vector parts and preserving a copy of the 2×2 adjoint octonionic matrices form precisely the Standard Model gauge group.
I didn't give the proof of that result. After a long break I thought it would be good to go about it quite slowly, introducing lots of nice background material:
Octonions and the Standard Model 5. How to think of the 2×2 self-adjoint octonionic matrices as 10-dimensional Minkowski space, and pairs of octonions as left- or right-handed Majorana-Weyl spinors in 10 dimensional spacetime.
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Related Beyond the Standard Model News on Phys.org
Optical computing at sub-picosecond speeds
ohwilleke
Parts 1-3 seem to map only to QCD and not to the SM more generally.
It sounds from your summary like Part 4 picks up the weak force and QED. Is that correct?
The SM is, of course, formulated in three dimensional space plus one dimensional time. How do the ten dimensions of Part 5 or the seven dimensions of Part 3 reduce to the four dimensions of the SM?
Are there any other differences from the ordinary SM? For example, does this approach have right handed neutrinos?
fresh_42
A question from a mathematical point of view: The octonions are closely related to ##G_2##, as Lie group as well as Lie algebra via their automorphisms, resp. derivations. If I understood it right, then ##G_2## is a GUT candidate. Do you say anything about this connection, and if, in which part?
##\mathrm{G}_2## is the automorphism group of the octonions. As I explain in part 3, ##\mathrm{G}_2## contains ##\mathrm{SU}(3)## in a way that's nicely suited to explain how the strong force interacts with a lepton and a quark (and indeed, leptons and quarks come in matched pairs). But ##\mathrm{G}_2## is not a candidate for a grand unified gauge group because it doesn't contain the Standard Model gauge group.
As I explain in part 4, Dubois-Violette and Todorov showed how to get the Standard Model gauge group from the octonions - or more precisely, the exceptional Jordan algebra, which is built using octonions. This is nicely compatible with what I just said about ##\mathrm{G}_2## and the strong force, but it goes further.
None of this stuff adds up to a theory of physics, at present.
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bayakiv
You may be interested to know that the group of gauge symmetries of the standard model can be associated with the compactification of an 8-dimensional space with a neutral metric. Please see the post #11 in the thread Geometry of matrix Dirac algebra
By the way, the prospects for building new physics are clearly visible there.
One of the most interesting functions on the exceptional Jordan algebra is the determinant. The linear transformations that preserve this form the exceptional Lie group ##\mathrm{E}_6##. I just wrote a blog article explaining how to compute this determinant in terms of 10-dimensional spacetime geometry: that is, scalars, vectors and spinors in 10d Minkowski spacetime.
Octonions and the Standard Model 6.
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ohwilleke said:
Yes, and it's exaggeration to say it gets QCD. It just shows:
1) we get SU(3), the strong force gauge group, by taking the symmetries of the octonions that fix a unit imaginary octonion;
2) the resulting representation of SU(3) on the octonions matches what we get from one quark and one lepton.
This is far from QCD: I'm not talking about a Lagrangian yet. It's just a mathematical fact that one could try to exploit. After all, it's a mystery why quarks and leptons come in matched pairs, with quarks having 3 colors and leptons being colorless. I'm just saying this mathematical structure shows up when you take the octonions and pick a unit imaginary octonion.
Again this is an exaggeration: all we get is the Standard Model gauge group arising in a mathematically natural way. We get it from taking the exceptional Jordan algebra and doing two things: 1) picking a copy of 10-dimensional Minkowski spacetime inside the exceptional Jordan algebra, and 2) picking a unit imaginary octonion. The symmetries of the exceptional Jordan algebra that preserves these two choices are the Standard Model gauge group.
Forget the 7-dimensional stuff, that was just for kicks. The important thing is in Part 5 we see a very precise mathematical analogy at work:
4d Minkowski spacetime : 10 Minkowksi spacetime :: complex numbers : octonions
Speaking roughly: picking a unit imaginary octonion not only picks out a copy of the complex numbers in the octonions, it lets us break an octonion into a quark and a lepton, and gives a copy of 4-dimensional Minkowski spacetime sitting inside 10-dimensional Minkowski spacetime.
I am not discussing a theory of physics. I'm discussing some mathematical facts that might help someone come up with a nice theory of physics.
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I know that my comment now is scientifically irrelevant, but whenever I read about possible GUT related structures, it appears to me as if people blow up the groups to an extent such that any symmetry group can be embedded: if we make ##n## large enough then ##SU(n)## will contain enough copies of the smaller ones.
Sorry, this might have been a bit off topic here. It's because I stranded on your articles:
https://golem.ph.utexas.edu/category/2009/02/the_algebra_of_grand_unified_t.html
https://golem.ph.utexas.edu/category/2009/03/the_algebra_of_grand_unified_t_1.html
Allow me a question from a layman here: Do we need the geometric structure of the root systems (i.e. the angles and lengths), or only their skeleton (i.e. possible paths from short to maximal roots)?
Semisimplicity is a true hurdle. I remember that I once asked why it is physically necessary, and received the answer: because of the subsequent metric from the Killing form. This sounded reasonable, but I'm not completely convinced. Are other symmetry groups thinkable? I mean Poincarré and Heisenberg play a role, but neither is semisimple.
fresh_42 said:
Any particular compact Lie group is a subgroup of ##SU(n)## for sufficiently large ##n##. But people working on GUTs aren't just trying to find a huge group. That would be kind of self-defeating, since a huge group means lots of symmetries, and we don't see evidence for so much symmetry. What they're looking for is a group that's big enough for the known particles to naturally appear arise from one, or a few, irreducible representations of that group. In other words, they're seeking "unification".
About the best example is the Spin(10) theory, usually misnamed the SO(10) theory. All the fermions in a single generation fit neatly into one irreducible representation of Spin(10) - together with one extra particle, a "sterile" right-handed neutrino, meaning one that doesn't feel the electroweak force. And this way of packing all those fermions into a single irreducible representation only works because quarks have charges 2/3 and -1/3, and other facts that previously seemed quite remarkable. So it's nice.
John Huerta and I explained it here:
The algebra of grand unified theories.
We need the whole root system to do physics.
There are pretty good arguments in favor of gauge groups being compact. There's no need for them to be semisimple, and indeed the gauge group of the Standard Model, usually taken as ##\mathrm{SU}(3) \times \mathrm{SU}(2) \times \mathrm{U}(1)##, is not semisimple.
It's a theorem that every gauge group is either a product of a semisimple compact group and an abelian compact group, or a quotient of some such group by a finite subgroup. For example ##\mathrm{SU}(3) \times \mathrm{SU}(2) \times \mathrm{U}(1)## is a product of the semisimple ##\mathrm{SU}(3) \times \mathrm{SU}(2)## and the abelian ##\mathrm{U}(1)##, and the "true" gauge group of the Standard Model is ##\mathrm{SU}(3) \times \mathrm{SU}(2) \times \mathrm{U}(1)## modulo a ##\mathbb{Z}/6## subgroup.
As you note, noncompact symmetry groups are important in physics, but their unitary representations tend to be infinite-dimensional, and while this is fine for some purposes it's not so good for others.
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arivero
what I would like of a such model is an interpolation between QCDxEM and SU(3)xSU(2)xU(1)
Point being, mass of W and Z do such interpolation. If masses go to zero, the full unbroken group, with chiral representations and all that, appears. But if masses of W and Z go to infinity, then we get a "vector" (in the sense of non-axial or not needing complex representations) group: colour plus electromagnetism.
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dlgoff
john baez said:
Mainly it's just fun.
I just wrote two more article in my series:
The first describes the symmetry group ##\mathrm{E}_6## of the exceptional Jordan algebra in terms of 10d Minkowski spacetime. The second starts giving a geometrical explanation of why this works. It involves the octonionic projective plane ##\mathbb{O}\mathrm{P}^2##, so as a warmup I look at the complex projective line ##\mathbb{C}\mathrm{P}^1##, which is isomorphic to the 'heavenly sphere': the starry sky you'd see all around you if you were floating in space.
##\mathrm{E}_6## acts on ##\mathbb{O}\mathrm{P}^2## much as the Lorentz group acts on the heavenly sphere.
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Auto-Didact
I just wrote another article in my series:
Octonions and the Standard Model (part 8).
This starts giving a geometrical explanation of why we can describe the symmetry group ##\mathrm{E}_6## of the exceptional Jordan algebra in terms of 10d Minkowski spacetime. It involves the octonionic projective plane ##\mathbb{O}\mathrm{P}^2##, so as a warmup I look at the complex projective line ##\mathbb{C}\mathrm{P}^1##, which is isomorphic to the 'heavenly sphere': the starry sky you'd see all around you if you were floating in space.
John, I'm almost sure you're already aware of this, but your geometrical explanation here of ##\mathrm{E}_6## by analogy with the Lorentz group and the celestial sphere is a natural generalization of twistor theory. To top it off, you start your latest piece off, almost prophetically, with my favorite quote about mathematics by Atiyah, who as you probably know also had an unpublished physical model using octonions which he didn't publish due to his untimely death; is there by any chance something you aren't telling us?
In either case, it feels like Christmas has come early this year.
mitchell porter
Perhaps I lean too eagerly on the work of string theorists, but in seeking to apply this to physics, I would start by looking for a firm connection between the exceptional Jordan algebra (27 dimensions) and e.g. the bosonic string (26 dimensions). Or: Hisham Sati already suggested that there should be a 27-dimensional theory that can manifest as OP2 fibers (16 dimensions) over M-theory (11 dimensions). Can we interpret J3(O) as OP2 fibered over some 11-dimensional space? @kneemo wrote about similar things (including the twistorial aspects) fifteen years ago.
It is impossible to look without regret at the attempts to apply these complex algebraic structures to physics. New algebraic structures should not be the basis of new physics, they should only be a consequence of new physics. In turn, the new physics must be a consequence of the new geometry and the new dynamic principle. Excuse my categorical judgments, but someone had to say that.
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weirdoguy
bayakiv said:
In turn, the new physics must be a consequence of the new geometry and the new dynamic principle.
And what does this "new geometry" and "new dynamic principle" even mean? And why "new geometry" is ok and "new algebraic structure" is not?
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Mitchell Porter wrote:
Can we interpret J3(O) as OP2 fibered over some 11-dimensional space?
I don't think the exceptional Jordan algebra J3(O) (which I'm calling ##\mathfrak{h}_3(\mathbb{O})##) is ##\mathbb{O}\mathrm{P}^2## fibered over some 11-dimensional space, since ##\mathfrak{h}_3(\mathbb{O})## is just a vector space, hence contractible, while ##\mathbb{O}\mathrm{P}^2## is a compact manifold with a lot of interesting topology. That's not a proof yet, but I'd be really shocked to be wrong here.
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mitchell porter said:
I was wondering how long the 26/27 dimensionality would bring out the string believers, but no harm
I suspect you are essentially paraphrasing Archimedes who spoke about creative mathematics saying: "It is easier to supply the proof [i.e. the algebra] when we have previously acquired, by the method [i.e. through geometry and/or dynamics], some knowledge of the questions than it is to find it without any previous knowledge." Given that the non-specific nature of algebra - i.e. that algebra seems to always work completely subject independent, even when we have no clue whatsoever what the subject itself is to which the algebra is applied - is its very strength, it is obvious how this can easily lead one down endless rabbit holes.
Although I somewhat share your reservations with respect to the role of algebra as opposed to the role of geometry and dynamics in creative mathematics, I can not fully share your sentiment. During the creative process, especially in mathematical physics, it is almost impossible to say beforehand whether the geometry, the dynamical principle or the algebra comes or should come first. This is because these things are all so intertwined and interdependent with both unclear borders as well as multiplicity.
An impression of the one (i.e. of some algebra, geometry or dynamics) on the trained mind can and often does naturally evoke the unconscious processing of one or both of the others. Just because by historical precedence this typically was geometry or dynamics does not imply that algebra itself can not be useful. That algebra essentially lacks direct specificity of course makes it a greater risk to take it as a starting point, but that doesn't imply that it should therefore be dismissed out of hand; this argument stands, even after string theory.
As long as one has a clear goal or vision in mind that one is trying to reach toward - be it through algebra, geometry or dynamics - there is reason for hope. The clearer this goal or vision can be stated, the easier it is to delineate it. In other words, the most important thing is to state clearly what one's vision is at the outset of the journey; only then can one say in the end if it was reached or if not, how far one was away from reaching it, what it would take to reach it in the future, make estimates about its general reachability or state definitively whether or not it is reachable at all. If string theory has failed it is precisely because the original vision, even to the main founders themselves, has remained to this very day unclear; if the founder doesn't have the vision in sight what hope do the followers have?
In any case, in the practice of theoretical and mathematical physics, what should and what should not be taken as a starting point is not something to be decided beforehand categorically; one works with what is given and then just does various mathematical experiments to see how far these can take one towards realizing one's own vision or proving it false. As Einstein said: "One should not reproach the theorist who undertakes such a task by calling him a fantast; instead, one must allow him his fantasizing, since for him there is no other way to his goal whatsoever. Indeed, it is no planless fantasizing, but rather a search for the logically simplest possibilities and their consequences."
@ Auto-Didact Thanks for the detailed comment. One can agree with many things in it, but nevertheless, if the Cayley algebra is "grounded", it would be easier to come up with the use of octonions in physics. Why not immediately tell the author that the algebra of complex numbers is the algebra of conformally linear mappings of the plane, the algebra of quaternions is the algebra of conformally linear mappings of a pair of planes and conformally linear mappings of the planes of this pair, and finally, that the algebra of octonions is the algebra of conformally linear mappings of double pairs, pairs of planes and the planes themselves. Then it would be clear that the octonions are somehow related to the 8-dimensional space, which could be tried to be related to the doublet of Minkowski spaces. However, these are my fantasies, speculations.
The octonions and exceptional Jordan algebra are grounded in geometry; I explain that in my paper
The octonions, Bull. Amer. Math. Soc. 39 (2002), 145-205.
The algebra comes in when you want to do computations. Ever since Descartes - if not sooner - it's been clear that algebra is useful for working with geometry.
The octonions arise because in 8-dimensional Euclidean space - and only in 8 dimensions - there's a symmetry between vectors, right-handed spinor and left-handed spinors, called triality. This has big ramifications for 10-dimensional Minkowski spacetime: a vector is a self-adjoint ##2 \times 2## matrix of octonions, while a left-handed or right-handed Majorana-Weyl spinor is a pair of octonions. This underlies a lot of superstring theory, but I'm more interested in other applications - applications that connect more directly to the Standard Model.
The exceptional Jordan algebra can be seen as an "exceptional" 27-dimensional spacetime where the lightcone is defined by a cubic equation instead of a quadratic one. It contains lots of copies of 10-dimensional Minkowski spacetime, and if we pick one of those copies then a point in the exceptional Jordan algebra can be seen a vector in 10d Minkowski spacetime together with a right-handed Majorana-Weyl spinor and a scalar.
Here's the interesting part: the Standard Model gauge group is precisely the subgroup of symmetries of the exceptional Jordan algebra that preserve a copy of 10d Minkowski spacetime and preserve a copy of the complex numbers in the octonions.
Perhaps I lean too eagerly on the work of string theorists, but in seeking to apply this to physics, I would start by looking for a firm connection between the exceptional Jordan algebra (27 dimensions)
Well, it is about physics, to the real game is, as always, three generations of the standard model. That was the sexy aspect of the papers of Dubois-Violette, and the question could be how constrained the assignment of charges is.
What would be clear depends on one's own personal mathematical temperament as well as on one's (not necessarily professional) experience and preference in mathematics. A century ago Hadamard discovered - by directly studying mathematicians themselves - that the two main temperaments among mathematicians are the geometric and the algebraic temperament. One's mathematical temperament is innate while one's mathematical character is pliable, at least it is in youth; it is a shame that such knowledge is not utilized in mathematics education, which explains the persistence of the problem to a certain extent.
As John mentioned, Descartes already solved this dispute between the primacy of algebra and geometry 400 years ago, yet until this very day you can still find naive mathematicians vehemently bickering about this. This is not only because they typically lack the vision and ability to be able generalize his work in any direction by themselves, but simply because they typically deeply believe contrary to Descartes that there is an objective foundational view which has primacy - i.e. there is a fundamental principle - namely the one that they personally subscribe to, whether it be geometry or algebra. To quote Poincaré: "fundamental principles are only conventions - adopted due to some convenience - and it is quite unreasonable to ask whether they are true or false as it is to ask whether the metric system is true or false."
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The octonions
From this celebrated review (1445 citations according to Google Scholar), I have learned that ##\mathbb{O}\mathrm{P}^2## can be realized via equivalence classes of certain elements of ##\mathfrak{h}_3(\mathbb{O})##. The elements of each such equivalence class are simply real scalar multiples of each other. To me this says that there's a 17-dimensional submanifold of ##\mathfrak{h}_3(\mathbb{O})## which can be interpreted (with some extra structure) as ##\mathbb{O}\mathrm{P}^2## fibered along a line.
So I'd amend my original quest. Now the goal is to interpret the whole of ##\mathfrak{h}_3(\mathbb{O})## (with some extra structure) as a fibration, with the fibers along that line being ##\mathbb{O}\mathrm{P}^2##, but something else (deformations of ##\mathbb{O}\mathrm{P}^2##?) elsewhere. The goal being, to seek convergence with Hisham Sati's notion of a 27-dimensional theory which encompasses ##\mathbb{O}\mathrm{P}^2## fibered over M-theory.
Probably I should next study these copies of 10-dimensional Minkowski space inside ##\mathfrak{h}_3(\mathbb{O})##. Maybe ##\mathfrak{h}_3(\mathbb{O})## can be obtained from 17-dimensional fibers over one of these...
The octonions arise because in 8-dimensional Euclidean space - and only in 8 dimensions - there's a symmetry between vectors, right-handed spinor and left-handed spinors, called triality. This has big ramifications for 10-dimensional Minkowski spacetime: a vector is a self-adjoint matrix of octonions, while a left-handed or right-handed Majorana-Weyl spinor is a pair of octonions. This underlies a lot of superstring theory, but I'm more interested in other applications - applications that connect more directly to the Standard Model.
Isn't it possible to define abstract algebra as the algebra of a geometric object? For example, the algebra of complex numbers is easily defined as the algebra of linear vector fields on the Euclidean plane, whose Lie algebra is tangent to the hypercircles of the Euclidean plane. Similarly, the algebra of quaternions is defined as the algebra of linear vector fields of 4-dimensional Euclidean space, whose Lie algebra is tangent to the hyperspheres of the Euclidean space. If we continue the analogy to 8-dimensional Euclidean space, then we have to take the corresponding Clifford algebra. And what place does the octonion algebra occupy in this algebra?
I wrote another installment:
The introduction goes like this:
The Riemann sphere ##\mathbb{C}\mathrm{P}^1## leads a double life in physics. On the one hand it's the set of states of a complex qubit. In this guise, physicists call it the 'Bloch sphere'. On the other hand it's the set of directions in which you can look when you're an inhabitant of 4d Minkowski spacetime — as we all are. In this guise, it's called the 'celestial sphere'. But these two roles are deeply connected! In 4d spacetime a Weyl spinor is described by a complex qubit: that is, a unit vector in $\mathbb{C}^2$. A state - that is, a unit vector modulo phase - simply says which way the spinor is spinning. Its spin can point in any direction, and these directions are points in the celestial sphere.
Last time I started explaining how to generalize some of these ideas from ##\mathbb{C}\mathrm{P}^1## to what I'm really interested in, ##\mathbb{O}\mathrm{P}^2##. Again this has two roles. On the one hand it's the set of states of an octonionic qutrit. On the other hand it's the heavenly sphere in a 27-dimensional spacetime modeled on the exceptional Jordan algebra. This is a funny spacetime where the lightcone is described not by the usual sort of quadratic equation like
## t^2 - x^2 - y^2 - z^2 = 0 ##
but instead by a cubic equation.
It'll be easy for me to get lost in the pleasures of this geometry. But I have a concrete goal in mind. The symmetries of ##\mathbb{O}\mathrm{P}^2## form the group ##\mathrm{E}_6##, and I'm trying to use this to understand a fact about ##\mathrm{E}_6##. Namely, this Lie group has four Lie subgroups:
the double cover of the Lorentz group in 10 dimensions
translations in right-handed spinor directions
translations in left-handed spinor directions
'dilations' (rescalings)
and these give Lie subalgebras whose direct sum, as vector spaces, is all of ##\mathfrak{e}_6##:
## \mathfrak{e}_6 \cong \mathfrak{so}(9,1) \oplus \mathbb{O}^2 \oplus (\mathbb{O}^2)^\ast \oplus \mathbb{R} ##
I proved these facts back in Part 7, but now I'm trying to understand them better. The duality between points and lines in projective plane geometry turns out to be the key!
Likes Greg Bernhardt
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