text:
The end of the line beckons. The SWR Class 455s (part 2)…
Posted by Paul Bigland in British Railways, Class 455, History, Photography, Railways
British Railways (BR), Class 455, Photography, Railways
Following on from part 1 I've completely skipped the logical path of documenting the Class 455/8s – for two reasons. One is that the fleet is split between SWR and Southern and the other is that this is the fleet that's also the last that's going to go! Instead, I'm concentrating on the 20 strong Class 455/9 fleet that all work on SWR and are based at Wimbledon Park depot.
The 455/9s were built at York works in 1985. They were identical to the earlier 455/7s apart from the fact they didn't use recycled class 508 TSO trailers and were built as brand-new 4-car units. That said, set 5912 has a TSO formerly part of the prototype Class 210 DEMU (picture later) and set 5913 (now stored) had a MSO which was rebuilt from another former class 210 vehicle after the original was written off by a cement-mixer which fell off a bridge and crushed it at Oxshott in November 2010.
Just four years old, first in class No 5901 in original BR livery and condition leaves Vauxhall and heads for Clapham Junction on the 26th November 1989.
5902 arrives at Kingston-upon-Thames on the 3rd March 2010.
Approaching Clapham Junction on the 30th December 2021 is 5903, paired with a 455/7 unit.
A picture that illustrates the front end difference between the earlier 455/8's and later 455/9s. Here's5855 keeping 5904 company at Waterloo on the 3rd January 2018.
Inside Wimbledon Park depot on the 20th May 2015 where 5905 is receiving fitters attention.
On the same day as the previous picture and a few miles down the road from the depot 5906 and 5871 head for Waterloo wit a service from Guildford.
A sight that will soon be gone forever. A trio of 455s 5907, 5911 and 5912 wait at Waterloo with services to Guildford and (in the case of 5912) Hampton Court on the 30th June 2011.
On a wet 3rd April in 2018 5908 arrives at Guildford on the rear of a working from Waterloo.
5909 passes Wimbledon depot (and 5706 heading in the opposite direction) whilst working a service from Waterloo to Hampton Court on the 20th May 2015.
Forward to the 27th January 2022 and 5910 is pictured at Waterloo after arriving from Woking.
At Guildford London Rd station on the 24th April 2014 5911 arrives with a service to Waterloo via Surbiton.
Sporting the old Stagecoach livery, set 5912 leads a service for Chessington South past Wimbledon on the 12th January 2005.
5913 calls at Clapham Junction on the 28th July 2015. This unit's one of the early casualties and has already been taken out of service and stored.
Back at Waterloo on the 27th January 2022 where 5914's seen waiting to depart platform 2 with a service to Hampton Court.
The 8th January 2022 was a day of torrential rain across the South-East and the aftermath can be seen in this view of Epsom, where 5915 leads 5851 whilst working, 2D43 the 1553 London Waterloo to Effingham Junction.
Back at Clapham Junction on the 27th January 2022 as 5916 leads a Waterloo – Woking service.
It's the 8th September 2009 and set 5917 leads a service out of Waterloo station and across the complicated switches and crossings that make up the station throat.
20th May 2015 was a good day for capturing shots of 455s around Wimbledon. In this view 5918 brings up the rear of a service from Waterloo along with 5733 as it passes the Sutton branch to the left and the severed remains of the M&EE engineers siding.
Clapham Junction on the 27th January 2022 again with 5919 arriving on the rear of a service from Dorking.
It's the 31st August 2021 and the last built Class 455 calls at Clapham Junction whilst working a service to Guildford.
I've a favour to ask…
If you enjoy reading this blog, please click on an advert or two. You don't have to buy anything you don't want to of course (although if you did find something that tickled your fancy that would be fab!), but the revenue from them helps to cover some of the cost of maintaining this site – and right now (because of Covid), us freelances appreciate all the help that we can get to aid us in bouncing back from lockdowns. Remember, 99% of the pictures used in my blogs can be purchased as prints from my other website – https://paulbigland.zenfolio.com/


It was a whole different feel than lunch plus two kids for upscale dinner always adds a level of complication. Additionally, of course we came opening night so it was also pretty busy. Our server was very attentive, some might even say a bit too attentive, but he meant well, so no harm.
I ordered sashimi which was good, including hotate (scallop) tamago (sweet egg omelet) and my favorite at the moment, ama ebi (sweet shrimp) which some with the fried heads as well, which are delicious!
We also had the home-made duck pot stickers, which were great, they were much more delicate than most gyoza you commonly get in restaurants, since very few actually go to the trouble to make them from scratch.
My husband got the pork belly ramen, which as you know from my earlier post, I am a big fan of.
Chef Hesse and Chef McKee were very helpful and personable, while also balancing that with efficient service and seemed to have a complete handle on everything that was going on. I would expect nothing less of two with their experience, however, I was still impressed, because like I mentioned it was their first public dinner service for Masu.
The rest of the photos are just ambiance shots because I really liked the atmosphere. It's a bit more artistic and playful that many of the other Japanese places in town.
I look forward to my next visit to Masu. Maybe I'll see you there for lunch?


text:
Student controversy sparks Westboro protest
Natalie Wickman|December 2, 2014
Margie M. Phelps, left, stands with her husband, the late Pastor Fred Phelps and her daughter Margie J. Phelps during a demonstration outside the federal courthouse in Baltimore, Maryland, Wednesday, Oct. 31, 2007. Photo by Jed Kirschbaum, Associated Press.
The university announced Monday that it will review a widely publicized incident regarding a disagreement between a student and an instructor about homosexuality, a day after the Westboro Baptist Church announced plans to picket campus in response.
When asked about the review, University Spokesman Brian Dorrington responded on behalf of Richard Holz, dean of the College of Arts & Sciences.
"Marquette University is reviewing both a concern raised by a student and a concern raised by a faculty member," Dorrington said in an email. "We are taking appropriate steps to make sure that everyone involved is heard and treated fairly. In compliance with state and federal privacy laws, we will not publicly share details, including the results of the reviews."
The disagreement was first reported Nov. 9 on political science professor John McAdams' blog, Marquette Warrior, before it was picked up nationally. It occurred between philosophy doctoral student Cheryl Abbate and an unidentified student, who reported the incident to McAdams.
McAdams said he was told about the investigation at a meeting with Holz before Thanksgiving break. In the meeting, McAdams said Holz was not clear who was being investigated. However, McAdams concluded that he would be involved in the investigation, even though it was not explicitly stated.
BACKGROUND ON THE INCIDENT
The incident occurred when Abbate's Theory of Ethics class discussed philosopher John Rawls's equal liberty principle, which states that each person has an equal right to the most extensive liberties compatible with similar liberties for all and possible violations of it.
"When one student suggested that a ban on gay marriage violated the principle, Abbate quickly moved on to the next topic, as there were more nuanced examples to discuss before the end of class," according to an article from Inside Higher Education.
Another student approached Abbate after that class and said he was "very disappointed" and "personally offended" that she had not considered his classmate's example about gay marriage, according to the student's recording of the conversation, which Insider Higher Education obtained.
"The student said he had seen data suggesting that children of gay parents 'do a lot worse in life,' and that the topic merited more conversation," according to Inside Higher Education.
Abbate disagreed, according to the student's recording, and the conversation ended with the student saying "it's still wrong for the teacher of a class to completely discredit one person's opinion when they may have different opinions" and that it is the student's "right as an American citizen" to challenge the idea. Abbate said the student didn't "have the right, especially (in an ethics class,) to make homophobic comments or racist comments," according to the recording.
She also invited the student to drop her class if he disagreed.
Abbate said McAdams mis-attributed the quote "everyone agrees with gay rights and there is no need to discuss this" to her in his blog post. The quote is not on the student's recording, according to Inside Higher Education.
McAdams told Inside Higher Education that all of the quotes in the blog post were taken from the student's audio recording, "except his characterization of what had happened before the recording, when the topic of gay marriage was first raised. He shared an email he sent to Abbate for her input the day he published his report, and said he published that evening, after he did not hear back."
"If the instructor had told the student 'I didn't think that was a particularly good use of class time,' no harm no foul," McAdams said. "The instructor has every right to decide what is worth class discussion time and what isn't. If somebody said something in an utterly uncivil way, the teacher has the right to come down on them. But you don't start with the assumption that any argument is going to be offensive. That was my beef and the basis of my blog post."
Abbate did not respond to the Tribune's request for comment.
"As a university, we inform and engage students on a comprehensive view of societal issues," Dorrington said in an email. "Like colleges and universities across the country, debate and discussion are essential elements of our intellectual environment at Marquette, where our faculty and students have the ability to explore ideas, express opinions and participate in discussion."
The story spread throughout November, leading to coverage from Fox News, American Thinker, LGBT Weekly and BizPac Review.
After the wide exposure, The Westboro Baptist Church of Topeka, Kan., publicly known for its anti-homosexual views, announced on Twitter Sunday its plans to protest the incident Dec. 8 from 9 to 9:30 a.m in front of the Church of the Gesu.
WESTBORO'S PICKET PLANS
The tweet, directed at the Tribune and Marquette's twitter accounts, included a press release picture from the church. "Tell us why the media is telling this despicable tale: Teacher to student: 'If you don't support gay marriage, drop my class'? Why are your students publishing junk-law articles on the subject of fag marriage if (Marquette) is a 'Christian' school?" the press release states.
The church describes itself on its website as strongly adhering to the Bible's teachings. "(We) preach against all form of sin (e.g., fornication, adultery [including divorce and remarriage], sodomy), and insist that the sovereignty of God and the doctrines of grace be taught and expounded publicly to all men," its website states.
Some students are planning anti-protests in response. At least two Facebook events have been created and about 200 people plan to go.
"I'm trying to organize an anti-protest for the Westboro Baptist Church protest," said Douglas Floski, a senior in the College of Business Administration. "I think we should go there and remind them that it's 2014 and not 1950."
The Westboro Baptist Church is known for its pickets that have included "God hates fags" signs. Its beliefs and actions have been explored through a few documentaries, including 2007's Fall from Grace.
Tags: Cheryl Abbate, College of Arts & Sciences, controversy, homosexuality, incident, Marquette, marquette controversy, Marquette University, philosophy, Review, Richard Holz, under review
French courses dropped for the fall semester
Explorer challenge awards over 7 million
Ray Eckstein, university alumnus and donor passes
Chemistry professor researches dementia prevention, focus based on conjunction study
Sold Out Run for Freedom to host 5K
Marquette adopts new test-optional policy
Marquette engineering professor awarded $1.4 million grant to lessen inaccuracies in CT scanning
Sen. Ron Johnson discusses immigration proposal, among other topics
First online bachelor program now taking applications
McCormick demolition begins this week
Soup with Substance: Full of Hope shares refugee's story
Campus Ministry trying to put in ablution station
Vida Coffee: student-run business to open in West Allis
Student run business program goes to conference at Harvard
Marquette students work with Project RETURN to serve Milwaukee community

redpajama_set_name: RedPajamaCommonCrawl


When you have been in the security installation industry like I have been since 1984, you sometimes just want to cut to the chase and tell potential customers exactly what works and is inexpensive. Also the practices to avoid when companies are masquerading services that are really there primarily just to make them money.
In this particular blog entry I will explain what in AD Alarms opinion is the best wireless security alarm system on the market at the moment, which provides the best service at the lowest cost.
We recommend Yale Wireless Alarms, which are a fantastic piece of equipment, that does exactly what it's designed to do, by providing an efficient security alarm, which can be installed quickly and easily with an auto dialler.
The auto dialler is particularly useful because it will on all alarm activations ring up any pre-programmed mobile or landline telephone numbers with a pre-programmed message from its owner, which enables the owner, friends or family to act as a free monitoring station of the system. We all think at AD Alarms that this is a very useful and practical accessory to the security system. There are some very well-known large installation companies that offer to install your security system extremely cheaply, so long as you sign up with them for a number of years monitoring service and that's fine except when you think about it you are actually paying every year, every year ! For something your friends and family can do for free by just having their numbers programmed into the alarm system.
Yale Security alarms are entirely wireless with the exception of the main control panel and its auto dialler, but these two units are easily dealt with. The main control panel simply plugs into a socket and then charges rechargeable batteries in case of power failure and the auto dialler has just as one lead from the control panel to the nearest telephone point, where a splitter is plugged in allowing a telephone and the auto dialler to work from the same telephone socket.
It is possible to program up to 40 detectors into the system, which is obviously far more than most people would ever require. We install the average system for £328 throughout the UK. The average system compromises of the main control panel with a built-in 120 DB internal siren, built-in auto dialler, two wireless magnetic door contacts, two wireless passive infrared sensors, one external self acting siren box with LEDs and one dummy siren box at the rear of the property.
Wireless systems are particularly useful for external buildings like garages, workshops and sheds because it's easy to quickly install a passive infrared or magnet ic door contact with the external building, which would trigger the main house alarm if an intruder tried to get in. This allows the customer to be able to arm the entire system during the night which would cover the house and any the remote buildings, but during the daytime switch off the main house if at home, but then rearm any external buildings separately.
all the accessories you could wish for, I shall give you a quick run through of what's available.
Probably the most popular accessory is the remote keypad, because this gives the customer secondary control of the security system from anywhere within 30 meters of the main control panel. This can be particularly useful for example in a garage where it is possible for the customer to arm the entire house and garage during the night but then in the morning switch off the house alarm detectors if they are at home, but then rearming the garage for daytime. Now if say father comes home from work and wants to park the car without going into the house first, he can now do so by simply disarming the garage on the wireless remote keypad and then rearming the garage before going into the house.
There is also a purpose-built wireless panic attack button, which can be put into bedrooms and any other location.
A remote key fob key ring with built-in panic button, can be used to arm the system as the customer leaves his house from outside, which flashes the LEDs on the siren box to visually signal the system is armed.
Wireless smoke detectors can trigger the entire system and they not only give off their own inbuilt loud alarm sound, they also trigger the external siren box and internal loud sounder, sending out a pulsing sound throughout the entire system which signifies it is an alarm alert rather than an intruder alert which is a constant alarm sound.
There are many other features will into the control panel, like the ability to be up to switch on and test your security system from anywhere in the world by telephone or mobile phone.
When you've been in the business as long as I have, you've seen most of the money-making schemes which large companies try to sell as so-called services, which are mostly just money-making schemes for them. Example, cleverly worded contract where you don't actually own the security alarm equipment but are only renting it and are forced to have your system serviced every year for a set period of years. Sometimes the main control panel is programmed so that after an alarm activation the customer cannot reset their system, they have to call for the installation company to come out to investigate and reset the system, but obviously that means they receive a call out fee each time.
So if you're looking for a straightforward wireless burglar alarm installed quickly easily and without damage or mess to your building, that allows you to monitor your own system free of charge and only needs standard replacement batteries every 2 to 3 years, which customers can replace themselves, I would strongly recommend Yale Wireless Alarms.
We are recommended specialist's throughout England for Yale Wireless Alarm installation – Yale Wireless Alarm Servicing – Yale Wireless Alarm Repairs.


text:
China's Aerial Ballet Above the Moon
By Leonard David
Ascender (left) departs orbiter/returner.
Credit: CCTV/Inside Outer Space screengrab
China's Chang'e-5 mission performed an aerial ballet above the Moon, an uncrewed rendezvous and docking of spacecraft and transfer of collected samples in lunar orbit.
At 23:10 (Beijing Time) on December 3, the ascender of Chang'e-5 took off from the lunar surface with its cache of Moon samples.
At 05:42 (Beijing Time) on December 6, the ascender successfully rendezvoused and docked with the orbiter-returner combination on the lunar orbit, and at 06:12, the lunar samples were transferred to the returner of Chang'e-5.
Beyond expectations
"The transfer of lunar samples of the Chang'e-5," said Ye Peijian, the chief director of Chang'e-5 program, "is what has never been done before in the world. The rendezvous and docking of the ascender and the combination of orbiter and returner is also the first time in the world. I think we have done a great job. Actually, it has been completed beyond my expectation," Ye told China Central Television (CCTV).
Yang Yuguang, Vice Chairman, Space Transportation Committee, said the orbiter and re-entry capsule combination has a mass about 2.3 tons while the ascender has a mass about 400 kilograms.
Engineers at China Aerospace Science and Industry Corporation (COSIC) developed techniques and technologies for the automated rendezvous and docking for Chang'e-5 mission.
Credit: COSIC via CGTN
Crash cushions
In a China Global Television Network (CGTN) story, engineers at China Aerospace Science and Industry Corporation (COSIC) detailed the technologies they developed for the Chang'e-5 mission: an accelerometer, crash cushions or dampers to reduce impact of docking, while microwave radar served as the eyes of the ascender-orbiter pair to "look" at each other.
COSIC specialists performed months of experiments and carried out 15 simulations to assure the radars would work as intended, even taking the interference of lunar dust into consideration.
Having completed its mission, the Chang'e-5's ascender separated from the orbiter-sample return vehicle.
Returner spacecraft carries re-entry capsule and its cache of lunar samples.
According to Gao Lei, a CNSA official, the orbiter-returner will orbit the Moon for about six to seven days. It will then enter an Earth-Moon transfer orbit, and experience another three to four days of flight before returning to Earth.
For new videos showcasing the lunar rendezvous and docking tasks, go to:
— Chang'e-5 orbiter-sample return vehicle separates from ascender.
https://youtu.be/6BnA_ms1fIc
— Chang'e-5 – rendezvous and docking explained. Li Gefei (researcher, Beijing Aerospace Control Center) explains the rendezvous maneuvers and Peng Jing (deputy chief designer of the Chang'e-5 probe) explains the docking process.
https://youtu.be/898aiTn23Tg
— Docking, Separation of Chang'e-5 Modules Conquer Technical Difficulties: Experts
https://youtu.be/BsYApf1LBcE


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ITV has announced details of a special one-off television special with Sheridan Smith.
Smith, who is a singer and multi award-winning actress, will headline her own show which is scheduled to air later this year.
The star of ITV shows such as Mrs Biggs and Cilla, Sheridan will showcase exclusive performances of songs from her new album, as well as an array of musical numbers, all accompanied by a live orchestra. She will also discuss her life, career and status as a national treasure.
Made by ITV Studios, the show will celebrate Sheridan and her love of music and performing.
Commenting on the news, she said: "I am so excited to be performing my songs and sharing my journey with my fans, friends and family. It's a dream come true."
Lee Connolly, Creative Director for ITV Entertainment, said: "With such a stellar career as an actor, it's easy to forget that Sheridan is also a wonderful singer. With brilliant performances in ITV's Cilla and as Fanny Brice in Funny Girl it reminded us why Sheridan is such a special and unique performer and we are delighted to be making this one off special with her."
Sheridan will be made by ITV Studios and will air on ITV this autumn. It was commissioned by Head of Entertainment Commissioning ITV, Siobhan Greene. Lee Connolly is the Executive Producer for ITV Studios.


text:
Q: Can't count how many times a word appears in a string I'm trying to solve this problem: Write a program that prints the number of times the string 'bob' occurs in s. But I'm struggling with my loop, if the I find the word in the string it adds 1 for every character in the string, think I might have to add a nested loop but don't know which.
That's my code:
numOfBobs = 0
for word in s:
    if 'bob' in s:
        numOfBobs += 1
print(numOfBobs)

A: s = "bobtestbobabcbob"
numOfBobs = s.count("bob")
print(numOfBobs)

You can use string.count("word") for that

A: for word in s won't really cut it, because while word looks like you mean a "word", Python doesn't know this. It is giving you a character.
def countSubstrings(input, search):
    result = 0
    currentIndex = 0
    while currentIndex + len(search) < len(input):
        if input[currentIndex:len(input)] == search:
            result += 1
    return result

This is a short draft of how it could look like. Since this is a homework question (assumption, sorry), I'm going to leave it up to you to figure out the off-by-one errors and improvements (hint: len(x) is constant in these loops, so maybe pre-compute them).

A: Try this :
for word in s:
    if 'bob' == word:
        numOfBobs += 1
print(numOfBobs)

This will work if your input is list

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text:
Got Dynamite Demi Lovato
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Текст песни Got Dynamite в исполнении Demi Lovato c переводом: I can't take your hand andLead you to the water I can't make you feel what you don't feel. Got Dynamite ukulele tablature by Demi Lovato, free uke tab and chords. Versuri "Got dynamite" de Demi Lovato: I can't take your hand and / Lead you to the water / I can't make you feel / What you don't feel, but you know you wanna.
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I can't take your hand. And lead you to the water. I can't make you feel. What you don't feel but you know you wanna. See All Lyrics. Got Dynamite. Performer: Demi Lovato. Composer: Gary Clark. About Us · Careers · Store · Contact Us · Facebook · Twitter · YouTube · Spotify · Instagram. Print and download Got Dynamite sheet music by Demi Lovato. Sheet music arranged for Piano/Vocal/Guitar in E Minor (transposable). SKU: MN
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Demi Lovato lyrics:: Song lyrics for Got Dynamite. I can't take your hand and Lead you to the water I can't make you feel What you don't feel, but you know you .
Original lyrics of Got Dynamite song by Demi Lovato. Explore 1 meaning or write yours. Find more of Demi Lovato lyrics. Watch official video. Got Dynamite testo canzone cantato da Demi Lovato: I can't take your hand and Lead you to the water I can't make you feel What you don't. Tumblr is a place to express yourself, discover yourself, and bond over the stuff you love. It's where your interests connect you with your people.
15 Jun Гледай всички видеа в плейлиста ``люbiiми пesnii.


Handtribe.com is a curated marketplace for quirky, kitschy fun products, and we're loving the very unusual things on offer.
We are always looking for little curios to jazz up our living spaces, so Handtribe gets major creds for having a lot of very eclectic home décor goodies to choose from.
The range of lighting options feature hanging lamps, and a teapot, and there is a set of monochromatic wall shelves that seem straight out of a noir film. Keeping up with the black and white theme, we also spot very funky hand painted coasters that promise to become conversation starters at the next do we host.
They should also be on your list for easy gifting options- there are some interesting accessories that might earn you brownie points for putting some thought into your gift. We'e digging the bulb that serves as a very chic ash tray and would be just right for that nerdy smoker friends of yours. For fans of the far East, say hello to iPhone cases with a very Tokyo vibe- hello cherry blossoms.
Sign up for the small artist movement, and pick on cool, unusual handcrafted gifts and accessories at this funky new marketplace.


This season, Zinda manages to effortlessly create a slightly wild sit yet is still playful! This python print pump features a delicate trap instep of the foot that we find quite charming. Perfect for spring!


text:
Sheffield United: 'Pressure off' but can Blades produce a miracle after finally winning?
Sheffield United now have five points from 18 games after their first win of the season.
After 186 days of frustration, Sheffield United finally had a sense of achievement that didn't leave them alone, but it seems they've packed their bags and left the country.
Billy Sharp's second penalty was enough to secure all three points against Newcastle on Tuesday night and give the Premier League's bottom side a glimmer of hope of avoiding relegation, which they seemed to be looking to avoid in record time.
The win – Sheffield United's first in 18 attempts in the Premier League this season – took their lead to five points and they now have a nine-point cushion.
Wilder is happy with the first win of the season for the Blades.
The gap is still significant – and they played at least one more game than their closest rivals – but Tuesday's win gave United's players something they felt they were losing – hope.
It feels good, says Blades boss Chris Wilder. We should have had more results, we know that, but the performance was good.
We played the way we have played the past few years.
We've had a lot of tough games and we'll take them. I looked for my car keys and took up another sport when we threw them away to work overtime.
What the bottom of the Premier League table looks like
Can magazines make a big breakthrough?
Sheffield United had the worst start to the season in the English Premier League even after that win, so it will take an incredible turnaround to make another big leap forward.
The team's total in 38 Premier League games is 34 – West Brom survived that mark in 2005.
2004-05 Brom West 38 6 34
2008-09 The city of Hull 38 8 35
2009-10 West Ham 38 8 35
2019-20 Villa Aston 38 9 35
1999-2000 Bradford 38 9 36
The Baggies' six wins this season are also the lowest number the team has ever achieved while staying on top.
To achieve these goals, Sheffield United will need to take 29 points from their last 20 games – a figure which, in itself, means they will probably need more than the Baggies' six wins.
We are all written off – the pressure is off, striker Sharpe told Sky Sports.
We haven't had a good time in the past few months, but now we have to hold our heads high. We're good enough to do it.
West Brom fans stormed out after a 2-0 win over Portsmouth to seal an unlikely rivalry on the final day 2004-05
So the survival rate starts now?
That's the case, although American fans will want to enjoy Tuesday's win a little longer before watching the upcoming games.
Jose Mourinho's team will host Tottenham Hotspur on Saturday and then travel to the United States on Wednesday, January 27 to face Manchester United Premier League leaders before taking on Manchester City at the Etihad Stadium.
They don't get stronger with increasing mileage. But if they manage to get the result of either shock, some may come to believe that the seemingly impossible is possible.
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My Most Memorable Mutt, By Lee Pitts •


Dennis K. "Dennie" Campos passed away June 21, 2004, at his home in Arizona. He was 50 years old. He graduated from Pacific High School in San Leandro in 1973. He owned a successful medical supply business.
He is survived by his wife, Karalee Campos; mother and father, Mr. and Mrs. Frank and Jennie Campos; brother, Ron Campos of Lake County; son, Jason Campos and his two children of Oakley; daughter, Nichole Alch and her two children of Anchorage, Alaska; daughter, Jennie Campos of Atwater; and many nieces and nephews. Dennie was preceded in death by his brother Richard "Rick" Campos.


text:
\section{Introduction}
Recently the problem of constructing differential calculi
on the quantum
{\it special} linear group $SL_q(N)$ \cite{Fad,Dr} has attracted
considerable attention \cite{Wor1}-\cite{IS}. A peculiar attention was
paid to constructing bicovariant differential calculi on these quantum
groups \cite{Wor}-\cite{IS}. Just the requirement of bicovariance, i.e.
invariance under quantum version of right and left group transformations,
aside from the
obvious geometrical meaning has a physical interpretation
\cite{AV}-\cite{ArA}.
As it was recognized the proposed solution reveals some strange
properties. Namely, the bicovariant differential complex involves
an extra element which has no natural classical counterpart in $SL(N)$.
In this paper we construct a quantum algebra of bicovariant forms associated
with
$SL_q(2)$ that is free from this defect.

Let us note that one can say that there are two main approaches to
differential calculus on noncommutative spaces.
The first is the Connes approach \cite{KON} in which
a complex of differential forms is constructed and the operator
$\bf d$ of exterior derivative plays a fundamental role. Such an approach
was used for quantum groups by Woronowicz \cite{Wor1}.

Another approach can be formulated following the  Faddeev idea
that all the objects in the theory of quantum groups
should appear naturally as the result of quantization
of appropriate Poisson
brackets in the theory of Lie groups \cite{FF}.
This point of
view pushes us to start a search for an algebra of quantum forms
with finding natural Poisson-Lie structures on the external
algebra of ordinary differential forms. These Poisson-Lie
structures being quantized should give as a result
algebras of quantum differential forms.
The ${\bf d}$ operator does not play a fundamental role in this approach,
moreover, generally there are no reasons to be sure that quantum
$\bf d$ exists.

Just this point of view was advocated in the paper \cite{AM}.
It was found that
the external algebra on $GL(N)$ can be equipped with the graded
Poisson-Lie structures and just their quantization produces
the bicovariant differential calculi on $GL_q(N)$ \cite{AM}.
This forces us to search directly for
graded Poisson-Lie structures on $SL(N)$ whose subsequent quantization
would give the bicovariant calculi on $SL_q(N)$ rather than to discuss
possible reductions of $GL_q(N)$-calculi to the $SL_q(N)$ case.

We are going to describe all possible graded Poisson-Lie  structures on
the external algebra of $SL(2)$.
We will prove that {\em differential} Poisson-Lie structures prolonging the
Sklyanin brackets do not exist on $SL(2)$. This key observation explains
why does not exist {\it bicovariant } differential calculi on $SL_q (2)$
which is in one to one correspondence with their classical counterpart.
The absence of a unique preferred
Poisson structure
(differential Poisson-Lie structure) provokes the
discussion of different
Poisson brackets on the external algebra
by relaxing some requirements on Poisson
structures and their further quantization. The more natural
possibility which we are going to deal with
in this paper consists in
consideration of a graded Poisson-Lie structure without requiring this
structure to be the differential one.

We will find that there are two and only two graded Poisson-Lie structures
on $SL (2)$. Neither of them can be obtained by a reduction of
graded Poisson-Lie  structures on the external algebra of $GL(2)$.
Then we prove that both of them can be quantized.
As a result we get two graded algebras of quantum right-invariant forms on
$SL_q(2)$. As we could have expected from classical treatment
these algebras of quantum forms on
$SL_q(2)$ do not admit the operator $\bf d$ with standard properties.

The paper is organized as follows. In section 2 we fix our notations
and introduce the notion of a graded Poisson-Lie algebra.
The rest of the section is devoted to the description of all such
structures  on the external algebra of $SL(2)$.
In section 3 the quantization of these  graded Poisson-Lie
structures is presented.

\section{Graded Poisson-Lie structure associated with $SL(2)$}
\subsection{Definitions}
The function algebra ${\cal A}$ on
$SL(2,C)$ is defined as the free unital associative algebra generated by
the entries of the
matrix:
\begin{equation}
T=||t_{m}^{n}||=
\left(\begin{array}{ll}a & b\\ c & d\end{array}\right),
\label{ttt}
\end{equation}
modulo the additional relation  $\det{T}=ad-bc=1.$

Recall, that $\cal A$ has
the natural
Hopf algebra structure
with comultiplication $\Delta$, the counit $\epsilon$
and the antipode $S$:
$$\Delta(T) =T\otimes T,~~\epsilon(T)=I,~~S(T)=T^{-1}.$$
Specifying $T$ as the matrix (\ref{ttt}) we have for the comultiplication
$\Delta$:
\begin{equation}
\Delta \left(\begin{array}{ll}a & b\\ c &
d\end{array}\right)= \left(\begin{array}{ll}a & b\\ c &
d\end{array}\right)\otimes \left(\begin{array}{ll}a & b\\ c &
d\end{array}\right).
\label{uu}
\end{equation}

According to the general theory of Poisson-Lie groups \cite{Dr,Fad,Skl,Sem}
the function algebra on $SL(2)$ can be supplied with the Poisson
structure $\{,\}$ compatible with the comultiplication $\Delta$, {\em i.e.}
satisfying the condition
\begin {equation}
\label {csk}
\Delta\{f,h\}=\{\Delta f, \Delta h\},~~f,h\in \cal A.
\end   {equation}
In terms of generators $t_{i}^{j}$ this Poisson structure  is given by
the Sklyanin bracket \cite{Skl,Skl1}:
\begin{equation}
\begin{array}{lll}
\{a,b\}=-ab, & \{b,d\}=-bd, &  \{c,b\}=0, \\
\{a,c\}=-ac, & \{c,d\}=-cd, &  \{a,d\}=-2bc.
\end{array}
\label{sk}
\end{equation}

Let
\begin{equation}
\theta=\left(\begin{array}{rr}\theta^0 &\theta^1\\ \theta^2
& -\theta^0\end{array}\right)
\label{theta}
\end{equation}
be the canonical right-invariant
one-form on $SL(2)$ taking value in $sl(2)$.
The components
$\theta^i,~i=0,1,2$ being the scalar right invariant one-forms can be
viewed as the generators of the external algebra on $SL(2)$.
In what follows we will refer to
$\theta$ as to the Maurer-Cartan form on $SL(2)$. Note, that the choice of
right-invariant forms is a matter of convention
and they may be replaced by left-invariant ones.

Let us define now the basic object of our study. This is a
$Z_2$-graded algebra
$\cal M$ generated by even $t_{m}^{n}\in {\cal A}$ and
odd $\theta^i$ generators modulo the defining relations:
\begin{equation}
t_{m}^{n}t_{k}^{l}=t_{k}^{l}t_{m}^{n},~~
t_{m}^{n}\theta^i=\theta^it_{m}^{n},~~
\theta^i\theta^j=-\theta^j\theta^i,
\label{hh}
\end{equation}
$$\det{T}=ad-bc=1.$$
Let $\Omega$ (the algebra of external forms) is the subalgebra
of $\cal M$ generated by $\theta^i$.
Clearly, $\cal A$ is also the subalgebra of $\cal M$.

Now our task is to supply $\cal M$ with a coalgebra structure,
{\em i.e.} one needs to define a
homomorphism $\Delta
:{\cal M}\rightarrow{\cal M}\otimes{\cal M}$ which satisfies
the axiom of coassociativity. Obviously, we require $\Delta$
when being restricted on the subalgebra $\cal A$ to coincide with the
comultiplication (\ref{uu}).
Since $\Delta$ when acting on $\Omega$ should encode the
transformation law of the right-invariant
form under the left and right group
multiplications we define two different comultiplications
which we call $\Delta_R$ and $\Delta_L$ \footnote{
In the Woronowicz terminology \cite{Wor} $\Omega$ is called
a bicovariant-bimodule over $\cal A$}:
$$
\Delta_R:\Omega  \rightarrow {\cal A}\otimes \Omega,
$$
$$
\Delta_L:\Omega \rightarrow \Omega \otimes {\cal A}.
$$
Indeed, the components $\theta^i$ of the Maurer-Cartan
form transforms under the left and right group transformations:
$g\rightarrow gg_{1}$ and
$g\rightarrow g_1g$, $g,~g_1\in SL(2)$, as
\begin{equation}
R^{*}_{g_{1}}\theta_{gg_1}=\theta_{g}~~~ \mbox{and}~~~
L^{*}_{g_{1}}\theta_{g_1g}=Ad_{g_1}\theta_{g}
\label{rl}
\end{equation}
respectively. Therefore, in accordance with (\ref{rl})
we define

\begin {equation}
\label {rm}
\Delta_R\theta^i=\theta^i\otimes I
\end   {equation}
and
\begin {equation}
\label {lm}
\Delta_L\theta^i=(Ad_ge_j)^{i} \otimes \theta^j ,
\end   {equation}
where $\{e_j\}$ is a
basis in $sl(2)$.

In addition to $\Delta_{L,R}$ one can consider the comultiplication
$\Delta$ defined as the sum:
\begin{equation}
\Delta_G=\Delta_{L}+\Delta_{R}
\label{dd}
\end{equation}
Concerning this $\Delta_G$ one can supply the $\cal M$
by a counit $\epsilon$ defined on $\theta^i$ as
$\epsilon(\theta^i )=0$. Thus, there are three natural ways to prolong
the comultiplication $\Delta$ from $\cal A$ to the hole algebra
$\cal M$: $\Delta_{L}$, $\Delta_{R}$ and $\Delta_G$. Note, that just the
comultiplication (\ref{dd}) was used for $GL(N)$ \cite{AM}.

Using the notations (\ref{ttt}) for the
generators of $\cal A$ equation  (\ref {lm}) can be rewritten as
\begin{equation}
\Delta_L\theta^0=(1+2bc)\otimes\theta^0-ac\otimes \theta^1
+bd\otimes\theta^2,
\label{df}
\end{equation}
\begin{equation}
\Delta_L\theta^1=-2ab\otimes\theta^0+a^2\otimes \theta^1
-b^2\otimes\theta^2,
\label{df1}
\end{equation}
\begin{equation}
\Delta_L\theta^2=2cd\otimes\theta^0-c^2\otimes \theta^1
+d^2\otimes\theta^2.
\label{df2}
\end{equation}

Let us recall that the graded algebra $\cal M$ becomes a
graded Poisson algebra if we define
a bilinear operation $\{,\}:$ $~{\cal M}\otimes {\cal M}$
 $\to {\cal M}$ which satisfies

i) the super Jacobi identity:
\begin{equation}
(-1)^{\deg{x}\deg{z}}\{\{ x,y\}, z \}+(-1)^{\deg{y}\deg{z}} \{\{ z,x\}, y
\}+ (-1)^{\deg{x}\deg{y}}\{\{ y,z\}, x \}=0,
\label{ya}
\end{equation}

ii) the graded Leibniz rule:
\begin{equation}
\{x\cdot y, z \}=x\{y, z \}+(-1)^{\deg{y}\deg{z}}\{x, z \}y,
\label{ya1}
\end{equation}

iii) the graded symmetry property:
\begin{equation}
\{x, y \}=(-1)^{\deg{x}\deg{y}+1}\{y, x \} ,~~~ \deg{\{x, y
\}}=(\deg{x}+\deg{y})\bmod 2.
\label{ya2}
\end{equation}

The graded Poisson brackets on $\cal M$ can be extended to
the brackets ${\cal M}\otimes{\cal M}$ in a natural way:
\begin{equation}
\{ x\otimes y,z\otimes w\}_{{\cal M}\otimes {\cal M}}=
(-1)^{\deg{y}\deg{z}}\{ x,z\}_{\cal M}\otimes yw+
(-1)^{\deg{y}\deg{z}}xz\otimes \{ y,w\}
\label{zzx}
\end{equation}
for any elements $x,y,z,w\in {\cal M}$.
\begin {defin}
A graded Poisson algebra $\cal M$ is a graded Poisson-Lie algebra if it
 admits a Poisson-Lie structure, i.e. the
following compatibility conditions are satisfied:

1)for any elements $f,h \in \cal A$
\begin{equation}
\Delta\{f,h\}_{\cal M}=\{\Delta f, \Delta h\}_{{\cal M}\otimes{\cal M}},
\label{cova}
\end{equation}

2)the brackets involving the odd generators $\theta^i$ are
covariant with respect to the both actions of $\Delta_L$ and $\Delta_R$, {\em
i.e.}:
\begin{equation}
\Delta_{L,R} \{\theta^i,f\}_{\cal M}=\{\Delta_{L,R}
\theta^i,\Delta f\}_{{\cal M}\otimes{\cal M}},~~i=0,1,2,~~
f\in {\cal A}
\label{*}
\end{equation}
\begin{equation}
\Delta_{L,R} \{\theta^i,\theta^j\}_{\cal M}=\{\Delta_{L,R}
\theta^i,\Delta_{L,R} \theta^j\}_{{\cal M}\otimes{\cal M}},~~i,j=0,1,2.
\label{**}
\end{equation}
\end{defin}

We also say that a graded Poisson-Lie structure is of the first order if
(\ref{cova}) and (\ref {*}) are satisfied, and of the
second order if (\ref{cova}) and (\ref {**}) take place.

Now according to our general strategy
we look for a graded Poisson structure (brackets) on $\cal M$
obeying the natural covariance conditions (\ref {cova}), (\ref{*}) and
(\ref{**}).

One can also search for a graded Poisson
structure covariant under the action of $\Delta_G$ given by (\ref{dd}).
Note that for $GL(N)$ the graded Poisson-Lie structures are covariant with
respect to $\Delta_G$ \cite{AM}, but in
general a Poisson-Lie algebra can appear to be
a $\Delta_G$-noncovariant one.

\subsection{$\{\theta, t\}$ brackets.}
Due to the grading
requirement (\ref{ya2}) we can write down
the general expression for the brackets as
\begin{equation}
\{\theta^i,
a\}=C_{aj}^{i}\theta^j,~~ \{\theta^i, b\}=C_{bj}^{i}\theta^j,~~
\{\theta^i, c\}=C_{cj}^{i}\theta^j,~~
\{\theta^i, d\}=C_{dj}^{i}\theta^j,
\label{rr}
\end{equation}
where $C$-s are unknown structure functions of $a$, $b$, $c$ and $d$.
We omit the cubic terms proportional to $\theta^0\theta^1\theta^2$
from the very beginning since they are forbidden by the covariance
condition (\ref{*}).
Note that one has to take into account that on $SL(2)$ the
matrix elements $a,b,c,d$ are not independent:
$\det{T}=ad-bc=1$. Therefore, one of the relations
in eqs. (\ref{rr}) should follow from the three others.
Considering the coordinate patch on
$SL(2)$ where $d\ne 0$ we find:
\begin{equation}
\{\theta^i, a\}=\{\theta^i,
d^{-1}(1+bc)\}=-d^{-1}a\{\theta^i,d\}+
d^{-1}\{\theta^i,b\}c+d^{-1}\{\theta^i,c\}b.
\label{xx}
\end{equation}

The covariance of eq.(\ref{rr})
with respect to the action of $\Delta_R$ (eq.(\ref{*})) leads to the
system of equations on the coefficients $C$:
$$
\Delta
C_{cj}^{i}=C_{cj}^{i}\otimes a+C_{dj}^{i}\otimes c,
$$
\begin{equation}
\Delta C_{dj}^{i}=C_{cj}^{i}\otimes b+C_{dj}^{i}\otimes d,
\label{rr1}
\end{equation}
$$
\Delta C_{bj}^{i}=d^{-1}\left(-aC_{dj}^{i}
+cC_{bj}^{i}+bC_{cj}^{i}\right)\otimes b+
C_{bj}^{i}\otimes d
$$
for any $i,j=0,1,2$. Since the right tensor multipliers in the r.h.s.
of eq (\ref{rr1}) are linear in $a,b,c,d$ we realize that $C$-s are
also linear functions of matrix elements. Then comparing
eqs.(\ref{rr1}) with eqs.(\ref{uu})
one
can easily find the following solutions:
\begin{equation}
C_{cj}^{i}=\alpha_{j}^{i}a+\beta_{j}^{i}c,~~
C_{dj}^{i}=\alpha_{j}^{i}b+\beta_{j}^{i}d,~~
C_{bj}^{i}=-\beta_{j}^{i}b+\gamma_{j}^{i}d,
\label{rr2}
\end{equation}
where $\alpha_{j}^{i},\beta_{j}^{i},\gamma_{j}^{i}$ are arbitrary numerical
coefficients.  Substituting the coefficients (\ref{rr2}) in eq.(\ref{xx}) we
also get the coefficient $C_{aj}^{i}$:
\begin{equation}
C_{aj}^{i}=-\beta_{j}^{i}a+\gamma_{j}^{i}c.
\end{equation}

Having found the form of structure functions we can now use the covariance
of the brackets with respect to the action of $\Delta_L$. For example,
the equation $\{\Delta_L\theta^0,\Delta a\}=\Delta_L\left(
C_{aj}^{0}\theta^j\right)$ gives
\begin{equation}
4abc\otimes a\theta^0+b(1+3bc)\otimes a\theta^2-a^2c\otimes a\theta^1+
b^2d\otimes c\theta^2+abc\otimes c\theta^1+
\label{rr3}
\end{equation}
$$
(1+2bc)a\otimes C_{aj}^{0}\theta^j+b(1+bc)\otimes C_{aj}^{2}\theta^j-
a^2c\otimes C_{aj}^{1}\theta^j+
$$
$$
b(1+2bc)\otimes C_{cj}^{0}\theta^j+b^2d\otimes C_{cj}^{2}\theta^j-
abc\otimes C_{cj}^{1}\theta^j=
$$
$$
\left[\Delta C_{a0}^{0}(1+2bc\otimes I)-\Delta C_{a1}^{0}(2ab\otimes I)+
\Delta C_{a2}^{0}(2cd\otimes I)\right]\left(I\otimes \theta^0\right)+
$$
$$
\left[-\Delta C_{a0}^{0}(ac\otimes I)+\Delta C_{a1}^{0}(a^2\otimes I)-
\Delta C_{a2}^{0}(c^2\otimes I)\right]\left(I\otimes \theta^1\right)+
$$
$$
\left[\Delta C_{a0}^{0}(bd\otimes I)-\Delta C_{a1}^{0}(b^2\otimes I)+
\Delta C_{a2}^{0}(d^2\otimes I)\right]\left(I\otimes \theta^2\right).
$$
The explicit form of $\Delta$-s is taken from eqs. (\ref{rr1}) and
(\ref{rr2}).
Now supposing all the coefficients of linear independent structures in
this equation to be
equal to zero we obtain the set of conditions on the unknown
numerical
coefficients $\alpha_{j}^{i},\beta_{j}^{i}$ and $\gamma_{j}^{i}$.
The surprising fact is that the coefficients are defined from this single
equation up to one continuous parameter, say, $\eta$ (see Appendix).

It remains to check
that this solution satisfies the other eight equations. This tedious but
pure algebraic task can be done and we arrive to
the one-parameter
system of candidates for the brackets.
Note, that the determinant $\det{T}=ad-bc$ is the
central element of the brackets in question as it was desired.

Next we define the values of this parameter $\eta$
from the part of the super Jacobi identities
that involve one $\theta$-variable
and two functions on $SL(2)$:
\begin{equation}
\{\{\theta^i,f\},h\}+\{\{h,\theta^i\},f\}+\{\{f,h\},\theta^i\}=0.
\label{tfh}
\end{equation}
The result is the following: $\eta=0$ or $\eta=-2$.
\begin{lemma}
There exist two and only two graded
Poisson-Lie structures of the
first order on $SL(2)$. They are given by:\\

{\bf I-type}
\begin{equation}
\begin{array}{lll}
\{\theta^0,a\}=-2 c\theta^1,
& \{\theta^1,a\}=a\theta^1, &
\{\theta^2,a\}=4 c\theta^0 -a\theta^2,\\
\{\theta^0,b\}=-2 d\theta^1, &
\{\theta^1,b\}=b\theta^1, &
\{\theta^2,b\}=4 d\theta^0 -b\theta^2, \\
\{\theta^0,c\}=0, &
\{\theta^1,c\}=-c\theta^1, &
\{\theta^2,c\}=c\theta^2, \\
\{\theta^0,d\}=0, &
\{\theta^1,d\}=-d\theta^1, &
\{\theta^2,d\}=d\theta^2,
\end{array}
\label{qqr1}
\end{equation}

{\bf II-type}
\begin{equation}
\begin{array}{lll}
\{\theta^0,a\}=0,
& \{\theta^1,a\}=-a\theta^1, &
\{\theta^2,a\}=a\theta^2,\\
\{\theta^0,b\}=0, &
\{\theta^1,b\}=-b\theta^1, &
\{\theta^2,b\}=b\theta^2, \\
\{\theta^0,c\}=-2a\theta^2, &
\{\theta^1,c\}=4a\theta^0 +c\theta^1, &
\{\theta^2,c\}=-c\theta^2, \\
\{\theta^0,d\}=-2b\theta^2, &
\{\theta^1,d\}=4b\theta^0+d\theta^1, &
\{\theta^2,d\}=-d\theta^2,
\end{array}
\label{qqr2}
\end{equation}
\end{lemma}

The brackets (\ref{qqr1}) and (\ref{qqr2})
have another interesting property, namely,
{\em they are also invariant with respect to the  comultiplication}
$\Delta_G=\Delta_L+\Delta_R$.

\subsection{$\{\theta,\theta\}$ brackets}
Now we are in a position to determine the bracket
containing two $\theta$-s. Having in mind the grading requirement
(\ref{ya2}) one can
write for this bracket a following representation:
\begin{equation}
\{\theta^i,\theta^j\}=C_{mn}^{ij}\theta^m\theta^n,
\label{gg}
\end{equation}
where the coefficients $C_{mn}^{ij}\in \cal A$ are unknown functions
that can be defined by requiring the bracket (\ref{gg}) to obey the
bicovariance conditions (\ref{**}).
Equation for $\Delta_R$ can be written as
$$
\{\theta^i\otimes I,\theta^j\otimes I\}=\{\theta^i,\theta^j\}\otimes I=
\Delta C_{mn}^{ij}(\theta^m\theta^n\otimes I)
$$
and it is obviously satisfied if all the coefficients $C_{mn}^{ij}$ are
pure numbers.

To write down the equations for coefficients $C$ that follows from the
equation for $\Delta_L$  we start with
the bracket $\{\theta^0,\theta^1\}$.

Applying $\Delta_L$ to it's both sides
\begin{equation}
\Delta_L\{\theta^0,\theta^1\}=C_{01}^{01}\Delta_L(\theta^0\theta^1)+
C_{02}^{01}\Delta_L(\theta^0\theta^2)+
C_{12}^{01}\Delta_L(\theta^1\theta^2),
\end{equation}
and using eq.(\ref{**}) we arrive to
$$
-2ab(1+2bc)\otimes \{\theta^0,\theta^0\}-a^3c\otimes\{\theta^1,\theta^1\}-
b^3d\otimes \{\theta^2,\theta^2\}+
$$
$$
8a^2bc\otimes \theta^0\theta^1+4b^2(1+2bc)\otimes \theta^0\theta^1-
2ab(1+4bc)\otimes \theta^0\theta^1+
$$
$$
a^2(1+4bc)\otimes \{\theta^0,\theta^1\}-b^2(3+4bc)
\otimes \{\theta^0,\theta^2\}+ab(1+2bc)\otimes \{\theta^1,\theta^2\}=
$$
\begin{equation}
C_{01}^{01}(a^2\otimes \theta^0\theta^1-ab\otimes
\theta^1\theta^2+b^2\otimes \theta^0\theta^2)+
\label{yr}
\end{equation}
$$
C_{02}^{01}(c^2\otimes \theta^0\theta^1-cd\otimes
\theta^1\theta^2+d^2\otimes \theta^0\theta^2)+
$$
$$
C_{12}^{01}(-2ac\otimes \theta^0\theta^1+(1+2bc)\otimes
\theta^1\theta^2-2bd\otimes \theta^0\theta^2).
$$

Equating the terms containing the linear independent forms $\theta^i\theta^j$
in the right multiplies of tensor product we obtain the system of equations
for coefficients $C$. The solutions of this system are
collected in the \mbox{Table 1:} \\[5mm]
$$
\begin{array}{llllll}
C_{01}^{01}=-2 & C_{02}^{01}=0 & C_{12}^{01}=0 & C_{01}^{00}=\alpha &
C_{02}^{00}=\beta & C_{12}^{00}=\gamma \\
C_{01}^{02}=0 & C_{02}^{02}=2 & C_{12}^{02}=0 &
C_{01}^{11}=0 & C_{02}^{11}=0 & C_{12}^{11}=0 \\
C_{01}^{12}=2\alpha & C_{02}^{12}=2\beta & C_{12}^{12}=4+2\gamma &
C_{01}^{22}=0 & C_{02}^{22}=0 & C_{12}^{22}=0
\end{array}
$$
\begin{center}
Table 1.
\end{center}
Here $\alpha,\beta,\gamma$ are coefficients that are not fixed from the
system. To find $\alpha,\beta,\gamma$ let us consider, for instance, the
l.h.s. of the following Jacobi identity:
\begin{equation}
\{\{\theta^0,\theta^0\},a\}+\{\{a,\theta^0\},\theta^0\}-
\{\{\theta^0,a\},\theta^0\}=0.
\label{ss}
\end{equation}
By using $\{\theta^0,\theta^0\}=\alpha \theta^0\theta^1+\beta \theta^0
\theta^2+\gamma \theta^1\theta^2$ eq.(\ref{ss}) is reduced to the form
$$
(-\alpha(1+\eta)a+2\eta \gamma + 4\eta c)\theta^0\theta^1)+
\beta\eta c\theta^1\theta^2+\beta(1+\eta)a\theta^0\theta^2=0.
$$
Thus, we find $\alpha=0,\beta=0$ for both $\eta=0$ and $\eta=-2$.
Moreover, $\eta(4+2\gamma)=0$, {\em i.e.} $\gamma=-2$ for $\eta=-2$.
Let us show that when $\eta=0$ we still have $\gamma=-2$.
Clearly, taking the equation
$$
\{\{\theta^0,\theta^0\},c\}+\{\{c,\theta^0\},\theta^0\}-
\{\{\theta^0,c\},\theta^0\}=0
$$
when $\eta=0$ and $\alpha=\beta=0$ we obtain:
$(4\gamma+8)a\theta^0\theta^2=0$, {\em i.e.} $\gamma=-2$.

This means that using the bicovariance
condition for the bracket $\{\theta^0,\theta^1\}$ we determine all
the brackets $\{\theta^i,\theta^j\}$ and, moreover, two systems of brackets
(\ref{qqr1}) and (\ref{qqr2}) with $\eta=0$ and $\eta=-2$,
respectively define
only one candidate for the bracket $\{\theta^i,\theta^j\}$. Thus, we
arrive to the Lemma 2.
\begin{lemma}
There is a unique system of brackets of the second order invariant
with respect to the both $\Delta_L$  and $\Delta_R$ and it is given by
\begin{equation}
\begin{array}{lll}
\{\theta^0,\theta^0\}=-2\theta^1\theta^2,&
\{\theta^0,\theta^1\}=-2\theta^0\theta^1,&
\{\theta^0,\theta^2\}=2\theta^0\theta^2, \\
\{\theta^1,\theta^1\}=0,&
\{\theta^1,\theta^2\}=0,&
\{\theta^2,\theta^2\}=0.
\end{array}
\label{dg}
\end{equation}
\end{lemma}

{\em Proof.}
What we have to do is to show that the system of brackets given by
eqs.(\ref{sk}), (\ref{qqr1}) or  (\ref{qqr2}) and (\ref{dg})
satisfies the super Jacobi identity and the
bicovariance condition (\ref{**}).
This is a matter of direct calculations.

 From Lemma 1 and Lemma 2 follows the
\begin {theor}
There exist two and only two graded  Poisson-Lie structures on
the external algebra of  $SL(2)$ prolonging the Sklyanin
brackets (\ref {sk}). They are given by (\ref {qqr1}) or (\ref {qqr2}) and
(\ref {dg})
\end{theor}

\subsection{Differential Poisson structures}
In the theory of Lie groups the operator ${\bf d}$ of exterior derivative plays
an important role.
There is a natural differential operator $\bf d$ on $\cal M$,
${\bf d}:{\cal M}\to{\cal M}$. ${\bf d}$ is defined
on generators of ${\cal M}$ by:
\begin{equation}
{\bf d}T=\theta T~~~{\bf d}\theta=\theta\theta ,
\end{equation}
($\theta$ is the matrix (\ref{theta}) written in terms of
$\theta^i$-generators) and extended to the hole algebra $\cal M$
by using ${\bf d}^2 =0$ and the Leibniz rule.
In principle, graded Poisson structures are not
connected in any way with the operator ${\bf d}$. However, one can rise a
question if there exist such Poisson structures with respect to which ${\bf d}$
is a differentiation.
\begin {defin}
A graded Poisson structure on $\cal M$
is called a differential one if the operator
${\bf d}$ satisfies the Leibniz-like rule:
\begin {equation}
{\bf d}\{ f,h\}=\{ {\bf d}f,h\} +(-1)^{\deg f}\{ f,{\bf d}h\}
\label {LEB}
\end{equation}
\end{defin}

Now we are going to see whether the Poisson-Lie structures on $SL(2)$ given
by (\ref{sk}), (\ref{qqr1}) or (\ref{qqr2}) and (\ref{dg}) are
differential ones. Let us consider for example the bracket $\{ a,b\}
=-ab$. Then \begin{equation} \{ {\bf d}a,b\}+\{ a,{\bf d}b\}=-2ab\theta^0
-(3+2bc)\theta^1 \label {d1} \end{equation} and \begin{equation} {\bf d}\{
a,b\}=-{\bf d}(ab)= -2ab\theta^0 -(1+2bc)\theta^1 .
\label {d2}
\end{equation}
This shows
that our Poisson-Lie structures on $\cal M$ are not the differential ones.
Hence, we arrive to the
\begin{theor}
Differential Poisson-Lie structures on the external algebra of
$SL(2)$ prolonging the Sklyanin brackets do not exist.
\end{theor}

\section{Quantization}
In this section we show that the Poisson-Lie structures on the external
algebra of $SL(2)$ given by eqs.(\ref{sk}), (\ref{qqr1}) or (\ref{qqr2}) and
(\ref{dg}) can be quantized. One defines the quantization of a commutative
graded Poisson-Lie algebra $\cal M$  as a constructing of a
non-commutative algebra ${\cal M}_q$ ($q=\exp h$)
supplied with comultiplications
$\Delta (h), \Delta_{L,R}(h)$ that obeys the following conditions:

1) ${\cal M}_q$ is a free module over
the ring $k[[h]]$, where $h$ is a parameter of quantization,

2) as a
coalgebra ${\cal M}_q/h{\cal M}_q$ is isomorphic to $\cal M$,

3) one can define on ${\cal M}$ the graded Poisson bracket:
\begin{equation}
\{ x, y \}=\lim_{h\rightarrow 0}\left(
\frac{1}{h}[\hat{x},\hat{y}]\right),~~x,y\in {\cal M},~~\hat{x},
\hat{y}\in {\cal M}_q
\label{ren}
\end{equation}

which should coincide with the original bracket on
$\cal M$ \cite{Dr,Fad}.

First of all, note that the quantization of (\ref{sk}) gives the defining
relations describing the function algebra on the quantum group $GL_q (2)$:
\begin{equation}
\begin{array}{lll}
ab=qba & ac=qca & ad-da=\mu bc \\
bc=cb  & cd=qdc & bd=qdb
\end{array}
\label{yy}
\end{equation}
where $\mu =q-1/q$.
The further factorization of $Fun (GL_q (2))$ modulo the quantum
determinant $\det_q T=ad-qbc$ defines the function algebra ${\cal A}_q =Fun
(SL_q (2))$ on the quantum group $SL_q (2)$. The quantization leaves the
coalgebra structure intact.
The quantization of the relations (\ref{qqr1}) and (\ref{qqr2})
and (\ref{dg}) is given by the following theorem.
\begin{theor} Noncommutative algebras generated by the symbols
$\theta^i,~i=0,1,2$ and the generators of the quantum group
$SL_q(2)$ modulo \\
I-type relations:
\begin{equation}
\begin{array}{lll} \theta^0a=a\theta^0+q^2\mu
c\theta^1,& \theta^1a=\frac{1}{q}a\theta^1,& \theta^2a=qa\theta^2-\mu\lambda
c\theta^0, \\ \theta^0b=b\theta^0+q^2\mu d\theta^1,&
\theta^1b=\frac{1}{q}b\theta^1,&
\theta^2b=qb\theta^2-\mu\lambda d\theta^0, \\
\theta^0c=c\theta^0, &
\theta^1c=qc\theta^1, &
\theta^2c=\frac{1}{q}c\theta^2, \\
\theta^0d=d\theta^0, &
\theta^1d=qd\theta^1, &
\theta^2d=\frac{1}{q}d\theta^2
\end{array}
\label{sss}
\end{equation}
or II-type relations
\begin{equation}
\begin{array}{lll}
\theta^0a=a\theta^0,&
\theta^1a=qa\theta^1, &
\theta^2a=\frac{1}{q}a\theta^2, \\
\theta^0b=b\theta^0,&
\theta^1b=qb\theta^1,&
\theta^2b=\frac{1}{q}b\theta^2, \\
\theta^0c=c\theta^0+\mu a\theta^2, &
\theta^1c=\frac{1}{q}c\theta^1-\frac{\mu\lambda}{q^2}a\theta^0, &
\theta^2c=qc\theta^2, \\
\theta^0d=d\theta^0+\mu \theta^2, &
\theta^1d=\frac{1}{q}d\theta^1-\frac{\mu\lambda}{q^2}b\theta^0, &
\theta^2d=qd\theta^2.
\end{array}
\label{sac}
\end{equation}
with $$\mu=q-1/q,~~\lambda =q+1/q,$$
and the relations
\begin{equation}
(\theta^0)^2=\frac{q^2\mu}{\lambda}\theta^1\theta^2,~~
(\theta^1)^2=(\theta^2)^2=0,~~\theta^1\theta^2=-\theta^2\theta^1,
\label{ww}
\end{equation}
$$
\theta^1\theta^0=-\frac{1}{q^2}\theta^0\theta^1,~~~
\theta^2\theta^0=-q^2\theta^0\theta^2.
$$
represent the quantization of the graded Poisson-Lie algebra
(\ref{qqr1}) or (\ref{qqr2}) and (\ref {dg}), respectively.
The quantum determinant
is the central element of the both algebras introduced
above.
\end{theor}

{\em Remark~~} Since the quantization procedure implies that the
comultiplications survive under quantization the Theorem 3 assumes the
existence of the quantum version of left and right comultiplications $\Delta
_{L,R}(q)$.

{\em Proof} At first, one can easily show that in the quasiclassical limit
($h\to 0$) the relations (\ref{sss}) and (\ref{sac}) produce the
Poisson structures of the first and the second types, respectively. Next, one
needs to check the consistency of the algebras introduced in the
theorem with the defining relations of ${\cal A}_q.$
For this purpose it is enough to
consider the ordering of the cubic monomials. Let us, for example, bring
the monomial $ab\theta^0$ into the form $\theta^0ab$ by two different ways:
$$
ab\theta^0=a(\theta^0b-q^2\mu  d\theta^1)=(\theta^0a-q^2\mu
c\theta^1)b-q^2\mu ad \theta^1=\theta^0ab-q\mu\left(q ad+
bc\right)\theta^1,
$$
$$ ab\theta^0=qb(\theta^0a-q^2\mu c\theta^1)=
q(\theta^0b-q^2\mu d\theta^1)a-q^3\mu bc\theta^1=
\theta^0ab-q\mu\left(q da+q^3bc\right)\theta^1.$$
Due to eqs.(\ref{yy})
the results of passing by two different ways are the same. Analogously,
one can show the consistency of the defining relations (\ref{sss}) and
(\ref{sac}) by considering all the other cubic monomials.

Covariance of (\ref{qqr1}), (\ref{qqr2}) and (\ref{dg}) with respect to
$\Delta_L$ and $\Delta_R$ gives rise to the existence of comultiplications
$\Delta_{L,R} (q)$ being
homomorphisms of the algebra described in the Theorem 3.
On $\theta$ generators the action of $\Delta _L(q)$ reads
\begin{equation}
\Delta _L(q)\theta^0=(ad+\frac{1}{q}bc)\otimes\theta^0-qac\otimes \theta^1
+bd\otimes\theta^2,
\label{df12}
\end{equation}
\begin{equation}
\Delta _L(q)\theta^1=-\frac{\lambda}{q}ba\otimes\theta^0
+a^2\otimes\theta^1 -\frac{1}{q}b^2\otimes\theta^2,
\label{df13}
\end{equation}
\begin{equation}
\Delta _L(q)\theta^2=\lambda dc\otimes\theta^0-qc^2\otimes
\theta^1+d^2\otimes \theta^2.
\label{df14}
\end{equation}
and
\begin {equation}
\Delta _R (q)\theta^i=\theta^i \otimes I
\label {u}
\end   {equation}
Such a coproduct is nothing but the adjoint coaction of ${\cal A}_h$ on
$\theta^i$ generators, representing the quantum analog of components of the
right-invariant Maurer-Cartan form. To make it clear let us introduce a
matrix $\theta$
\begin {equation}
\theta=\parallel \theta_{k}^{~m}\parallel=\left(\begin{array}{rr}\theta^0
&\theta^1\\ \theta^2 & -\frac{1}{q^2}\theta^0\end{array}\right) \label {uuq}
\end   {equation}
with
 the quantum trace $\tr{\theta}_q =\frac{1}{q}\theta_{1}^{~1} +q
\theta_{2}^{~2}=0$. Then one can write
\begin {equation}
\Delta_R(q)\theta^i=\theta^i\otimes I,~~~~
\Delta_L(q)\theta_{i}^{~j}=t_{i}^{~k}S(t_{m}^{~j})\otimes \theta_{k}^{~m}
\label {uuu}
\end   {equation}
Now one can show that $\Delta_{L,R}(q)$ are homomorphisms.
At last, using the defining relations
(\ref{sss}) one can check that the quantum determinant $\det_qT$ is the
central element of the algebra under consideration.

\section   {Concluding Remarks and Discussion}
A few remarks are now in order.

$\bullet$
To make the quantization of the brackets
(\ref{qqr1}) and (\ref{dg}) more transparent it is suitable
to rewrite them using the corresponding classical $r$-matrix.  Introducing
the standard tensor notations we have for the brackets of the first order
eq.(3.15) from \cite{AM} with $\alpha=0=\beta$. In the case of $GL(N)$
group these brackets were forbidden by the total Jacobi identity. For the
brackets (\ref{dg})  one can write:
\begin{equation}
\{\theta _1, \theta _2\} =  -(\theta _1\theta _1+ \theta
_2\theta_2)+ r^{12}_{+}\theta _1\theta _2+ \theta _1\theta_2r^{12}_{+}-
\theta _1r^{12}_{+}\theta _2- \theta_2r^{12}_{-}\theta _1,
\label {t13}
\end{equation}
where  $r_{+}$ is the classical $r$-matrix for $sl(2)$ (see (\ref{rrr}))
and $r_{-}=-r_{+}^{t}$.

Let us note that the corresponding quantum algebra (\ref {ww}) was found
in \cite {IS} in the $R$-matrix form
\begin{equation}
R_{12}\theta_1R_{21}\theta_2+
\theta_2R_{12}\theta_1R_{12}^{-1}=
k_q(R_{12}\theta_1^2R_{21}^2+\theta_2^2),
\label{t14}
\end{equation}
where $k_q=\frac{\mu q^2}{q^3+1/q}$ and the quantum $R$-matrix for
$SL_q (2)$ is given in Appendix B. It is clear that the brackets
(\ref{t13}) are the quasiclassical limit of the relations (\ref{t14}).
It seems natural that taken in the $r$-matrix form the graded Poisson-Lie
structures can be generalized to $SL(N)$.

$\bullet\bullet$ Let us consider the
$*$-involution on $SL_q(2)$ defined by \begin{equation}
a^{*}=d,~~d^{*}=a,~~b^{*}=-qc,~~c^{*}=-\frac{1}{q}b.
\label{gmm}
\end{equation}
In addition to (\ref{gmm}) we can introduce the operation $*$ on
$\theta$-s:
\begin{equation}
(\theta^0)^{*}=-\theta^0,~~(\theta^1)^{*}=-\theta^2,~~
(\theta^2)^{*}=-\theta^1.
\label{gm}
\end{equation}
One can easily check that the relations (\ref{ww}) are invariant
with respect to the operation $*$. However, $*$ operation does not
leave both (\ref{sss}) and (\ref{sac}) invariant but transforms the brackets
(\ref{sss}) into (\ref{sac}) and vice versa.

$\bullet\bullet\bullet $
Let us briefly discuss the issue of existence of an operator ${\bf d}_h$ of
exterior derivative for the noncommutative associative algebras described
in the Theorem 3. First of all we would like to stress that this question
has essentially a classical origin.
Obviously, an operator ${\bf d}_h$ should
be introduced in agreement with the defining relations (\ref{yy}) of
${\cal A}_h$ that in the standard tensor notations  read \cite{Fad}:
\begin{equation}
RT_1T_2=T_2T_1R,
\label{gggg}
\end{equation}
where $R$ is the quantum $R$-matrix for $SL_q(2)$ (see (\ref{RRR})).
This means that
\begin{equation}
R{\bf d}_hT_1T_2+RT_1{\bf d}_hT_2={\bf d}_hT_2T_1R+T_2{\bf d}_hT_1R.
\label{gg2}
\end{equation}
Now let us suppose that $R$-matrix and ${\bf d}_h$ operator are
quasiclassical, {\em i.e.}
\begin{equation} R=1+hr+O(h^2),~~~{\bf d}_h={\bf
d}+h{\bf d}^1+O(h^2),
\label{gge}
\end{equation}
where ${\bf d}$ is the ordinary operator of exterior derivative.
Then by using eq.(\ref{ren})
the quasiclassical version of (\ref{gg}) takes the form
$$
\{{\bf d}T_1,T_2\}+\{T_1,{\bf d}T_2\}=[r_{+}^{12}, {\bf d}(T_1T_2)]=
{\bf d}\left([r_{+}^{12}, T_1T_2]\right),
$$
where $\{T_1,T_2\}=[r_{+}^{12}, T_1T_2]$ is the Sklyanin brackets
(\ref{sk}) expressed via the classical $r_{+}^{12}$ matrix for $sl(2)$
(see (\ref{rrr})).
Thus, we conjecture that {\it any noncommutative algebra of quantum
differential forms admits an exterior derivative if the corresponding
graded Poisson-Lie structure is the
differential one}. As we have seen all
graded Poisson-Lie structures on $SL(2)$
are not differential ones and, therefore, the corresponding algebras of
quantum forms do not admit the exterior derivative.

This situation is quite opposite to what we have for $GL(N)$.
In \cite{AM} it was shown that for all graded Poisson-Lie structures
on $GL(N)$ the ordinary {\bf d} operator has the description
in inner terms, namely
\begin {equation} {\bf d}=\{ \kappa\tr{\theta},\ldots\},
\label {dst}
\end {equation}
where $\kappa$ is a coefficient depending on the choice of a Poisson-Lie
structure.  Then the Leibniz rule eq.(\ref{LEB}) reduces to the graded
Jacobi identity \begin {equation} \{\tr{\theta},\{
f,h\}\}=\{\{\tr{\theta},f\},h\} +(-1)^{\deg f}\{ f,\{\tr{\theta},h\}\}
\end{equation}
and, therefore, all graded Poisson-Lie structures on $GL(N)$ appear to be
the differential ones. Moreover, the
possibility of expressing ${\bf d}$ as in (\ref{dst}) allows one to
define its quantum counterpart via the graded commutator $[,]$ as
$$
{\bf d}_h=\left[\frac{1}{\mu}\tr\mbox{_q}{\theta},\ldots \right].
$$

In general, according to
the Connes definition of differentiation of a noncommutative
graded algebra the operator ${\bf d}$ is expressed as
$$
{\bf d}=[\xi ,\ldots ]
$$
where $\xi$ is some special element of degree one such that $[\xi,\xi]=0$.
For a given noncommutative graded
algebra an appropriate element $\xi$ may or may not exist. In the
last case one can try to extend the algebra in such a way as to
include $\xi$ and, therefore to make the algebra a differential one.
Just this situation takes place in the standard approach to  differential
calculi on quantum special groups \cite{Wor},\cite{Car},\cite{WZ}.
In this case the graded algebras of quantum right(left)-invariant forms
can be supplied with the exterior differentiation but the price we have
to pay for doing this consists in extending these algebras by an extra
element $\xi$ which has no natural classical counterpart in the
corresponding classical group. Note, that many of the constructions of
bicovariant differential calculi of such a type can be obtained by the
reduction of bicovariant differential calculi on $GL(N)$
\cite{Car},\cite{WZ}.

$\bullet\bullet\bullet\bullet $
Let us compare now the graded Poisson-Lie structures on $GL(2)$
with the Poisson-Lie structures on $SL(2)$ in more detail.
Among the graded $GL(2)$ Poisson-Lie brackets of the second order
there is only one natural candidate for $SL(2)$ reduction.
Its choice is dictated
by the compatibility with the condition
$\tr{\theta}=0$. This selected Poisson-Lie bracket is given
by the formula (\ref{t13}) where $\theta$ has
four independent entries.
The corresponding quantum algebra
is compatible with the condition $\tr\mbox{_q}{\theta}=0$
and also can be reduced to $SL_q (2)$. It is not surprising that
it is given just by eq.(\ref{t14}).

The situation drastically changes when we search for a graded Poisson-Lie
structure of the first order on $GL(N)$ that can admit
the $SL(N)$-reduction.
It turns out \cite{IS} that
the reduction of any graded Poisson-Lie structure on $GL(N)$
involves inevitably the additional one-form
generator $\xi=\tr{\theta}$. Thus,
the reduction yields the classical limit
of the standard bicovariant
calculi on quantum special groups \cite{Wor},\cite{Car}.
Note, that the relations (\ref{sss}) and (\ref{sac}) change the
transformation property of (\ref{dg}) as compared with the
$GL_q(2)$ case. Namely, despite the fact that
\begin{equation}
\Delta_G (q)=\Delta_L(q)+\Delta_R(q)
\label{qqq}
\end{equation}
is the homomorphism of the algebras (\ref{sss}) and (\ref{sac}) the
relations (\ref{dg}) in opposite to the $GL(N)$ case do not
respect the action of (\ref{qqq}).

Finally, one can address a question whether it is possible to find for the
algebras (\ref{sss}) and (\ref{sac}) an $R$-matrix formulation. Note,
that the existence of such a formulation can make the generalization
of our $SL(2)$ constructions to $SL(N)$ case straightforward.

$$~$$
{\bf ACKNOWLEDGMENT}
$$~$$
The authors are grateful to I.Volovich for interesting
discussions.
This work is supported in part by RFFR under grant N93-011-147.
$$~$$
\newpage

{\large \bf APPENDIX}

redpajama_set_name: RedPajamaArXiv


text:
Family Retirement Club
White House Could Be Readying Order for Americans to Wear Masks in Public
WOW! Rush Limbaugh On Pelosi - "She Will Never Turn Over the Articles of Impeachment for Acquittal in the Senate" Here's Why...
(FamilyRetirementClub.Com)- President Donald Trump expressed his desire last month to reopen the United States economy by Easter. Listening to expert advice, the president instead chose to extend the "15 Days to Slow the Spread" order by a further 30 days, encouraging Americans to stay at home as much as possible and avoid social interaction.
Now, it seems, the White House may be considering advising the American people to wear masks in public to further reduce the spread of the Chinese coronavirus.
The Washington Post reports that memos from the Centers for Disease Control which discuss the possible measure have been seen in the White House and are being considered by members of the White House Coronavirus Task Force. During a press briefing on Tuesday, President Trump was asked about potentially telling Americans to wear plans in public, but he did not offer a concrete answer.
"My feeling is, if people want to do it, there's certainly no harm to it. I would say do it," the president said. "But use a scarf if you want, you know? Rather than going out and getting a mask or whatever."
The president's comments reflect the fact that the United States, like much of the rest of the world, currently has a shortage of masks. Those who most urgently need masks are people working in the medical field, dealing with coronavirus patients daily. Until a sufficient quantity of masks is available across the country, the president is unlikely to tell everybody to wear masks.
That may soon change, however, if Vice President Mike Pence is right. Responding to CNN's Wolf Blitzer, Pence explained that the Centers for Disease Control is looking into the issuing of masks as a protective move.
"We will have a recommendation for the president at the appropriate time," he said.
@wolfblitzer: Should all Americans be wearing masks?
VP Pence: CDC is looking at the issue of masks as a protective move. We will have a recommendation for the president at the appropriate time.
— Yamiche Alcindor (@Yamiche) April 1, 2020
So, it looks like the government may well soon advise Americans to wear masks. That could only mean that an increased supply of masks is now available, courtesy of the many American companies stepping up and increasing production of personal protective equipment.
Until then, wearing a scarf over the mouth can offer some level of protection against the virus and also stop people from spreading it as easily when exhaling or coughing.
A combination of sensible social distancing measures, and the wearing of masks, could be just what the United States needs to get the economy operating at some level through the summer months.
Trump Says "CRAZY NANCY" Is Responsible for Blocking Coronavirus Aid to American Workers
Kanye West Chooses 57-Year-Old White Woman As Running Mate
Uh, Oh: Democrat Staffer Fired for RACIST and SEXIST Tweets!
Trump Says "CRAZY NANCY" Is Responsible for Blocking Coronavirus Aid to...
Universities Start Giving Out "George Floyd Memorial Scholarships"
New York Times Implies White Suburban Families Are Racist
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text:
Nitsche, Erik (September 7, 1908 - November 10, 1998)
Erik Nitsche (September 7, 1908 - November 10, 1998) was a Swiss-born artist who designed, books, annual reports, and other printed material. Born in Lausanne, Switzerland, Nitsche came from an artistic family. Both his father and grandfather were photographers and the family counted several artists among their friends, including Paul Klee. Nitsche attended the Kunstgewerbeschule in Munich, Germany, instead of the Bauhaus school in Berlin. He worked in Cologne, Germany, after graduating in the early 1930s, and was soon hired by Maximilien Vox to work in Paris. Nitsche moved to the United States in 1934, fleeing the rising tensions in Europe. He arrived in Hollywood before landing in New York City, where he worked as a freelance graphic artist for the next ten years doing work for numerous magazines, including Look, Life, Vanity Fair, and Harper's Bazaar. He became art director of Air Tech and Air News magazines in 1940, where he had total control over the illustrations and format. In the early 1950s, Nitsche left New York for Connecticut, where he began working with The Gotham Agency, which had General Dynamics as a client. By 1955, Nitsche was named art director at General Dynamics, which wanted to portray itself as a purveyor of peace instead of a manufacturer of weapons and other related materials of destruction. In the five short years he worked for General Dynamics, Nitsche created a place for himself in the history of graphic design, with this work being his most well-known legacy. Among the countless posters, brochures, advertisements, and annual reports he created for General Dynamics was a 420-page book entitled 'Dynamic America' that recounted the company's history. In 1960, Nitsche moved back to Geneva, Switzerland, where he founded Erik Nitsche International, which published pictorial history books on myriad topics. After moving around for most of his career, Nitsche was diagnosed with a possibly fatal illness in 1995 and died on November 10, 1998.
1938 Nitsche Board Game Tracing the Events of the Year 1937


I'm sorry, did you just assume MY OPINION?
Maybe a huge Mobile Depot with a ship hangar and a gun on top might do?
Guns on a POS are very relevant outside of the giant Sov entities that throw around entire capital fleets. It is one of the huge areas that Citadels are failing on in highsec, POS defences are far superior to what you can get on a Citadel in highsec, even on an XL Citadel. However that's something that's been beaten to death in other threads relevant to Citadels, which this isn't, so apologies for the slightly off topic post.
That's cool for sov owners, but outside of Sov it might be possible to sneak in a control tower in an area someone "claims," but may not d-scan aggressively enough for new structures.
Either way, someone will notice if they look for it, and won't notice if they don't. Since it doesn't show up on your overview we are talking a very minor difference in the effort you need to put in to find it.
Also, the blue flash thing is counteracted by that you now never need to clear a moon to drop your stager. You can't be moonlocked out and need to announce, two days in advance, you plan to clear a moon and drop a pos as soon as the pos you're clearing comes out of reinforced.
This isn't a real issue.
I think the difference in effort is significant. Just looking at space, as opposed to needing to warp to distant celestials and clicking d-scan. Or using scan probes. If CCP would block the appearance of blue icons in space for citadels that are in the anchoring process, (until after anchoring is completed) that would match what control towers do in non-sov space.
I have my toys and damn everyone else who doesn't do EXACTLY what I do!
CCP Lebowski, I really want to believe you when you say "full feature parity with POS's". I really really do. In particular, the feature of fast setup and fast removal. I can do both of these with a small POS in a single play session. I cannot go so with ANY new structure.
Please, please truly give us "full feature parity with POS's".
1 - they need to be replaced.
3 - They are meeting my overall needs as far as player owned structures are concerned.
Are they perfect? I have a few gripes, (parity of services not withstanding) such as being locked into modules when the structure is damaged. I can appreciate not swapping with a combat timer, but not being able to swap when you do not have a weapons timer or at least between vulnerabilities is no where near parity with POSes.
And this is the other gripe: A viable structure one can deploy, dock in, store things in, have defenses usable, and then remove within a 24 hour period.
If I had to guess this is to make the fitting choices on the Citadels more meaningful, since unlike a POS it's very very easy for a Citadel to store multiple sets of complete fittings and very easy to change them out, so in order for the initial fitting choices to mean something (since first attacks often aren't defended anyway) they lock you in to your fitting at the time of the attack, so you can't just fit for maximum industry and then re-fit for combat when you get reinforced once, either out of fittings in the Citadel or by bringing in a Jump Freighter.
This kind of touches on something that bugs me a little, "feature parity" doesn't mean "will function exactly like POSes with all of the strengths and weaknesses these old things had" it means "fills most of the same niches and meets all the needs a POS did within reason".
No where in any of the designs has CCP said they wouldn't use this as a chance to iterate on the basic POS concept, one of the oldest pieces of Eve's design, and find ways to both make it more interesting and better.
Nope, though I am now assuming you have a stick jammed up there somewhere.
I didn't call anyone out by name, the "you" was pretty clearly second person plural, and I was speaking generally about groups of people categorized by opinions.
So yeah, no, nice try though, 1/10 for effort.
Most POSes serious about defense have multiple weapon modules offlined and ready to online should they be needed. Additionally, modules can still be anchored and onlined (once the reinforce period is over) even during battle. Anyone throwing away the first defense of their citadel by not being there is not serious about defending their citadel or simply baiting for a fight.
Additionally, there is no such thing as this: "maximum industry and then re-fit for combat" as far as modules are concerned. Rigs, yes. High Slot, Medium, and Low Slot: no - they have 0 impact on industry. Service modules, no - they have no impact on citadel defense - except cloning.
So lets fine tune my gripe to be more precise: High, Medium, and low slots should be changeable despite damage to the struture - they simply cannot be changed while you have a weapon timer. Rigs and service modules are locked into place while the structure is damaged. Now you have a structure where you can change between defending against capitals or sub-capitals etc. but if they were industry minded in their Rigs, they are locked in and they cannot 'save' their service modules.
Several off topic posts have been removed, as well as, other posts that violated our forum rules. Please keep it civil, constructive and on topic. Thank you!
What? I'm with him on this one; the amount of negativity toward these changes has been practically non-existent, with most concerns being along the lines of wanting to make sure players don't lose the ability to do much of what they do now. You're going full-Gevlon here, Tom. There won't be any winter of rage, because there is no range. Nullsec, lowsec, and highsec alike are on-board with these changes, and the way they are happening. Hell, even w-space residents seem to be pretty pleased with the way the new structures have been coming out, what with their ability to swap clones now, and there being no asset safety.
just to add my voice, i am utterly satisfied with the way the new structures are working out. once a few minor-but-important issues are resolved they will be better than POS/station trash by a significant margin.
**** still needs to be fixed but the issues there are all well known.
I personally will be fine operating out of an engineering complex.
But, three years ago when I didn't have a good fraction of a trillion ISK behind me, I'd have balked at paying ~1b for a destructible engineering complex that broadcasts its location.
I think there is a need for something smaller than the lowest tier engineering complex, even if it is limited to tech 2 modules and tech 1 ships. Somewhere that a player with two billion in working capital can start to cut their teeth in manufacturing.
Presently I feel the smallest engineering complex requires you to have five to ten billion in working capital to justify its expense. The smallest POS works with two to three billion in working capital and that niche needs filling.
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Is this to do with the rumours of CCP selling bits of the game to new providers? I'm not opposed to new blood, as new blood is new ideas; I'm just being nosy is all.
Yes there aren't currently any industry focused high, medium, or low slot modules, but that doesn't preclude anything like that being included in the future. It also doesn't invalidate my point which is that I think CCP are doing this to make Citadel fitting decisions matter more. If you've fit one way you shouldn't be able to just spontaneously re-fit to another setup because your scouts say the enemy is bringing something else.
Having this sort of locking makes the fitting decision matter more the same way that combat refitting for Caps was nerfed to make fitting decisions matter.
At the risk of going off topic, this rumor seems to have grown weird mutant legs. Nothing has ever been said about CCP "selling bits of the game", the various private companies and individuals that own bits of CCP (as a whole and entire company) are apparently considering offers to buy their stake in CCP.
CCP as a company has basically no say in any of this except possibly the option to buy up the held stake.
Just my .02 USD here.
While I think price point is a very valid concern, and I think structures should probably be expanded in a way that allows a lower price point for some feature, I don't think there's a need for a 100% match in functionality and configurability with POSes.
Specifically I like that fitting decisions on a Citadel matter more than on a POS both for Rigs and the regular fittings. IMO that gives CCP more freedom with their design and makes the game more interesting because now we don't have the possibility of spontaneously swapping things around between fights or even mid-fight.
I'm going to go with a desire on CCP's part to free up resources toward other endeavors. As he said in the same comment, this will actually free up resources towards development of the new features, probably because they won't be as pressed to deal with potential issues with the old ones.