The untold need for not only having an online platform but also the need to interact with other digital features seamlessly is on the rise because people are interested in high quality results in all aspects of business. However, people are reluctant to learn the more detailed terminologies yet they require to learn these basic technological skills. Since use of presentations is among the methods which people use to convey their ideas, they can only capture the attention of such an audience if the presentation is made using a presentation software that generates high results. If you are interested, do check it out!
This means that there is need for business to come up with way in which they can make their presentations more appealing, what leads to the development of presentation software. This is because meetings are very common with most of the managers a great majority of their time in meeting. Meetings in their very nature are costly to the organization considering that they take up time as well as financial resources of the organization. In a bid to reduce these costs, there has also been developed software which allows for presentations to be conducted remotely. This makes it possible for participants to engage in meeting by just logging in to a designated site where they can view the presentation.
Cost reduction is the most evident benefit of utilizing a remote presentation software because it cut on the travel and accommodation expenses allowing more capital to be channeled to other sectors of the organization. The use of the software also frees up the managers time to attend to other areas that equally require their attention which in consequence will lead to better performance. The recipients of such a presentation that makes use of these software are able to have higher productivity levels as they can obtain maximum value from the presentation thus improving the performance of such a business. These benefits give the business a competitive edge over its competitors making them outperform them. Go to this website if you want to learn more.


15th Anniversary Race for Autism at Balboa Park!
Fragile X syndrome is a leading genetic cause of autism. About one in three people with the syndrome also has autism. But even those who do not have autism often share certain autistic traits, such as avoidance of eye contact and difficulties in social situations. Mutations in the gene FMR1, which cause fragile X syndrome, account for up to 5 percent of autism cases.
Costumes, Halloween parties, trick-or-treating and spooky decorations are fun for most kids, but for a child with Sensory Processing Disorder (SPD), Halloween celebrations can be overwhelming. A child with SPD processes input from the five senses differently. What is background music to others may be loud and distracting to a kid with SPD, costumes may feel itchy, make-up may feel sticky, and masks may have a strong scent or be too restricting for kids with Sensory Processing Disorder.
There is a steady slowdown of cars in front of us on our way to a swim meet. My son, who was diagnosed with autism spectrum disorder (ASD) at an early age, starts to show his agitation. Anxiety violently announces itself in the form of rapid-fire questions.
"Are we going to be late for warm-ups?"
This is the question many, including myself in the disability field, are starting to ask.
Historically, transition programs of most school districts have been geared toward students with disabilities staying on the high school campus, not graduating with a high school diploma and instead getting a certificate of attendance. Such a certificate is practically worthless when it comes to employers or college admissions, but these certificates were and still are, offered as an easier track for those who cannot complete the requirements to obtain a diploma.
This unique one-on-one Private Santa Experience is designed for your child to have a more quiet and casual time with Santa. As a father of a 14 y.o. boy on the Spectrum, I know all too well that the crowds, long lines, and the awful dreaded judgmental stares at the mall are far too overwhelming for those with special needs (and for us ASD parents)! PortrArt Creations will be creating a more intimate setting so your child can have a rare opportunity with Santa and we will capture every moment.
There will be more information at a later date on this incredible experience so please sign up below if you are interested in knowing more about the Sensory Santa Experience.
Trumpet Behavioral Health and Regus is putting on a Sensory Friendly Trick or Treat event for families the day before Halloween. Kids with Special Needs and without are invited to participate. PLEASE register here: www.tbh.com/events (scroll down to find the San Diego Trick or Treat event, click the "register button", and follow the prompts to include your contact name and information).
We will have activities and refreshments in the lobby for families and children!
The La Mesa Library is proud to present an Autism-Friendly playtime event every first Sunday of the month. The library staff provide a friendly, judgement-free space in their lovely space with a variety of sensory and educational activities. All families are welcome to enjoy and explore the library an hour before it opens to the public every month - we hope you can join us!
Eager to learn more? The County of San Diego put together a beautiful intro video you can find here!
*Please note this is a family event best suited for children ages 3-10. Individuals without children will not be granted entry until the library opens for its public hours. We appreciate your understanding!
Learn about the research and practical guidelines for using evidence-based practices to promote inclusion throughout the lifespan.
Click here to read their latest newsletters for all the info and updates!!!
As some of you know, I am Editor in Chief of the Carlat Child Psychiatry Report, a practice newsletter that stands independently from pharmaceutical industry and other influences to give clinicians practical guidance in child and adolescent mental health. As part of that work, I have just co-authored The Child Medication Fact Book for Psychiatric Practice. It is written for clinicians and Val asked me if parents might find it useful too. Maybe so. The book talks about the practicalities of medication, with an eye toward avoiding too much medication, watching out for side effects, and, overall, keeping medication in it's proper place - medication should never be the whole story but something that supports overall treatment. You can download sample pages from the Carlat website and see what you think. https://thecarlatchildreport.com/ChildMedFactbook I am interested in feedback!
Attention Team Captains - here's a great way to form a team for the Race for Autism! Take advantage of our Justice League pricing package for the 15th anniversary!
Justice League Special - $25 flat rate for 15 persons! This includes timing fees and larger T-shirt sizes.
To apply or learn more, please contact us at 858-679-8800.


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141 (сто четиридесет и първа) година преди новата ера (пр.н.е.) е година от доюлианския (Помпилийски) римски календар.

Събития

В Римската република
 Консули са Гней Сервилий Цепион и Квинт Помпей.
 Квинт Фабий Максим Сервилиан и армията му са победени и обкръжени от вожда Вириат. Двамата сключват договор, който признава териториите на бунтовниците, а самият Вириат е обявян за "приятел и съюзник" на Рим. Римският народ потвърждава договора.
 Сенатът признава Симон Хасмоней за независим владетел.

В Азия
 Хан Уди става император на Китай.
 Царят на партите Митридат I окупира Южна Месопотамия.

Родени

Починали
 Хан Дзинди, император от династията Хан (роден 188 г. пр.н.е.)

Бележки:

Източници

redpajama_set_name: RedPajamaWikipedia


A visit to the Forbidden City can be overwhelming.
It allows you to explore the former heart of the Middle Kingdom and a glimpse to its rich history.
A visit to the Forbidden City is the top must-do for anyone traveling in Beijing.
Located in the heart of Beijing city. This is China's largest and best-preserved cluster of ancient buildings and is very easy to access. I advise you spent a full day to visit, or perhaps several separate trips if you are enthusiastic about Chinese history.
Chinese people prefer to call it "Gu Gong" (??), which refers to the former palaces. It has been home to Ming and Qing Dynasties of emperors for over 500 years, since the 3rd emperor of Ming Dynasty moved the capital to Beijing in 1421.
The complex is not one stately building but rather like a city within city, like the Vatican in Rome. There are over 9,000 rooms in 800 buildings in the city separated by passages.
There are 4 gates located on each side of the place, north, south, east and west of the Forbidden City. Each stands for a special meaning and can only be accessible by particular people in ancient time.
Audio guides are available here to help those who have no guide. However, I still recommend you to have a local guide as you can ask any questions you are interested in but not just simply listen.
Now the entrance for travelers is located in the south of this city, just on the opposite of the famous Tiananmen Square. Before entering the Forbidden City, you need to walk through the Gate of Heavenly Peace, where you will see the famous portrait of Mao Zedong that has hung here for years.
Behind it is the huge port-red walls that thrust out from either side of the Meridian Gate (Wumen). This is where you obtain your ticket.
As you walk through the Palace you will encounter some of these key sights.
The highlights are the Three Great Halls, which lie along a line bisecting the complex, running south to north. The first you can see and also the largest is the imposing Hall of Supreme Harmony.
Raised on a 3-tiered platform, the hall was recently the tallest building in Beijing for many years. During the ancient time, it represented the supreme power of the emperor and no one could look down upon this most sacred of imperial buildings.
Behind the Hall of Supreme Harmony is the smaller Hall of Middle Harmony (Zhonghedian), where ministers from the ministry of Rites were received. The rectangular Hall of Preserving Harmony (Baohedian) was used to be the place where the emperor oversaw the final stages of the civil service examinations.
As you reach the north, you will see the Gate of Heavenly Purity (Qiangqingmen), where you can see a carving on the huge marble slab showing a dragon flying through the clouds.
The courtyards behind the Gate of Heavenly Purity is called the Inner City. It used to be the place for the imperial courts live. Here offers a great photography chance as you will find well designed gardens, elaborate pavilions, ponds and stone bridges.
Like the nearby Temple of Heaven, almost all of the palaces structures are built of wood, and mainly adorned with red walls and imperial yellow tiles. You will be astonished by the wisdom and skills of ancient Chinese people as most of these wooden structures were constructed without any nails.
However, fire has always been a constant hazard to the Forbidden City. Many buildings were regularly destroyed and rebuilt. To prevent the fires, large cauldrons were placed throughout the city to supply water in the case of a fire. In the winter small fires were maintained under each to prevent the water from freezing.
The Forbidden City in the weekends or holidays will be crowded with people. I recommend you to have a travel agency to book and ticket and arrange the itinerary for you. Waiting in an endless line to buy the ticket might be the last thing you want to experience during your trip.
There is no denying that the Forbidden City is China's most popular travel destination.
Do not miss it when you travel to Beijing!


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Moczydlnica Dworska


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It's possible for us to display blocks before or after a region in our theme. This allows us to insert content outside of a region in our theme. This is particularly useful for jQuery Mobile Panels.
By utilizing the _prefix or _suffix object variable on a region's settings, we can display blocks before or after a region.
Learn more about creating custom blocks.
We can then optionally use block visibility rules to control when this block should be rendered.


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National Safety Council News and Alerts, 2/13/09
Congress again pushes for combustible dust bill
House Democrats reintroduced a bill that would force OSHA to promulgate a rule regulating combustible dust.
The Worker Protection Against Combustible Dust Explosions and Fires Act of 2009 (H.R. 849) was introduced Feb. 4 by Reps. George Miller (D-CA), John Barrow (D-GA) and Lynn Woolsey (D-CA).
The bill comes one day after six workers were injured in a coal dust blast at a Milwaukee power plant, and nearly one year after a sugar dust explosion that killed 14 workers at the Imperial Sugar facility in Port Wentworth, GA.
"While OSHA turned a blind eye to this issue under President [George W.] Bush, I know that the new administration will confront this threat with the urgency that it deserves," Woolsey said in a statement. Obama has, in the past, expressed support for a combustible dust standard.
An identical bill was introduced and passed in the House in the previous Congress last year in a 247-165 vote. It was referred to the Senate in May, but never made it out of the Health, Education, Labor and Pensions Committee.
MSHA issues alert on man lifts, bucket trucks
The Mine Safety and Health Administration has issued a safety hazard alert (.pdf file) to provide guidance for workers who use man lifts and bucket trucks.
Since 1995, 13 workers have died from incidents associated with the devices, including five fatalities at coal mines, MSHA said. The fatalities resulted from falls, rollovers, electrocutions and crushing incidents, the agency said, noting that man lifts and bucket trucks are different types of equipment but often are used for the same purpose and have similar hazards.
MSHA advises workers to use equipment only for its intended purpose and to operate in tight quarters only when stated in the manufacturer's recommendations.
TRANSPORTATION SAFETY NEWS
International conference focuses on road safety
Highway safety experts from around the world will gather in Washington Feb. 16-18 to discuss strategies to prevent roadway traffic crashes – the leading cause of workplace death and injury.
The International Conference on Road Safety at Work (.pdf file) is the first international conference dedicated to preventing roadway traffic crashes. Experts from government, business, labor, the research community and the National Safety Council will be present.
The event is co-sponsored by the World Health Organization, Pan American Health Organization, International Labor Organization and U.S. Department of State.
HOME AND COMMUNITY NEWS
Home filled with danger for teens: study
The home can be a very dangerous place for adolescents, according to a study from the University of Alabama at Birmingham.
According to a study abstract, psychologists from UAB inspected the homes of a diverse sample of 42 teens age 14-16 and found:
29 percent of homes had an unlocked firearm. 15 percent of rifles and 18 percent of handguns were stored loaded. 31 percent of homes had unsecured alcohol. 21 percent had exposed electrical cords. 6 percent had unlocked fireworks. More than 90 percent had no working carbon monoxide detector. According to the researchers, more than 30 percent of fatal injuries sustained by adolescents occur in the home.
Results were published in the January issue of International Emergency Nursing.

redpajama_set_name: RedPajamaCommonCrawl


Can I download the manual as a PDF?
Can I install Duplicate Cleaner Pro on another computer?
Can I use System Restore to back up/recover deleted or moved files?
How do I remove deleted tracks from iTunes?
I have lots of duplicate files found- which ones should I delete?
Where can I download version 3 of Duplicate Cleaner Pro?


Civic Charter is a global movement of people working together for democracy and human rights. The Civic Charter is a document which outlines the rights that all people have to participate, based off of laws and conventions that their governments have agreed to. Signing the Civic Charter is your way to join a transnational community of activists who support one another to build campaigns and take action when their rights are violated.
If you believe that everyone should have the right to speak up for what they believe in, this movement is for you. Learn more about our campaigns and add your name to the Civic Charter at civiccharter.org.


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Facebook Seeks Blockchain Talent for Five New Company Roles
Facebook has listed five new blockchain-related jobs on its careers page within the past three weeks, two of which were first listed Dec. 5 and 6.
The positions currently open for applicants are two software engineer roles, a data scientist post and a data engineer — all full-time roles at the company's headquarters in Menlo Park, California.
In the job description for blockchain engineer at the Facebook Blockchain Data Engineering team, the ad characterizes the position as "technically" and "intellectually challenging" work, which "will have massive global impact."
The most recently listed role — Product Marketing Lead for the Facebook blockchain team — outlines that the team is vital to the company's mission of problem solving and community building, and specifically in "exploring the opportunity the blockchain will bring."
While the precise details of Facebook's planned — or extant — blockchain initiatives are kept under wraps, the ad for "Data Scientist, Blockchain" indicates that:
"We're exploring areas of interest across all facets of blockchain technology. Our ultimate goal is to help billions of people with access to things they don't have now — that could be things like equitable financial services, new ways to save, or new ways to share information."
The ads for the two "Software Engineer, Blockchain" roles indicate that blockchain specialists joining the existing Software Engineering (Infrastructure) team would help build the "large distributed components that run Facebook," which need to scale to serve "millions of requests per second," and to do so "with sub-second latency and in a fault tolerant manner."
Preferred qualifications include "[e]xperience with distributed computing (Hive/Hadoop)" (for the role of "Data Scientist, Blockchain") and coding experience in a range of languages such as "C, C++, Java, C#, Perl, PHP, Hack and/or Python" ("Software Engineer, Blockchain").
In early May, the head Facebook's messaging app Messenger, David Marcus — who has been a board member of major United States crypto exchange Coinbase as of December 2017 — announced the company had set up a group "to explore how to best leverage blockchain across Facebook, starting from scratch."
In July, Facebook's director of engineering of three years, Evan Cheng, joined the blockchain team to fulfill a parallel role dedicated to exploring the technology's applications.
As reported this October, the average earnings of a blockchain engineer have soared to between $150,000 and $175,000 per year, 400 percent higher than in 2017, according to Hired's "2018 State of Salaries Report." Hired's report cited demand fueled by the interest of global tech giants such as Facebook, Amazon, IBM and Microsoft, all of whom are currently advertising for specialists from the emerging sector.
Analytics Blockchain In the world Interesting News people Main, News
South Korea's Second Largest Bank Begins Blockchain Record-Keeping to Reduce Human Error
PayPal Launches Blockchain-Based Innovation Reward System for Employees


Wayanad Social Service Society (WSSS) is selected as the State Nodal Agency for the promotion of the website in Malayalam. The Malayalam portal logo is launched on 10th Oct.2014 by the Hon'ble Dist. Collector.Mr. Kesavendrakumar.I.A.S in a function presided over by His Excellency, Bishop Jose Porunnedam in the presence of, the State Minister for Welfare of Scheduled Tribe and YouthAffairs, Kumari. P.K.Jayalakshmi and other Govt.Officials.


I really cut down on the number of books I bought this past year. Most books I read come from the library. The books I did buy are ones my library doesn't have, but I really wanted to read. Above is every single book I've gotten so far this year. Some were gifts. Most are manga. Books on the right I've read already. I still need to read the books in the (much larger) left pile.


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A new Yu Yu Hakusho smartphone game in the works?! It's REI-GAN time once more! | TGS 2017
Cosplayer Ki-Chan
Heads up, anime fans, get ready for some big news coming your way straight from Tokyo Game Show 2017! KLab Inc. and AXEL GameStudio Inc. have announced an upcoming Yu Yu Hakusho mobile game for smartphones, titled Yu Yu Hakusho 100% Maji Battle!
That's right, everyone, you read that right!
The one and only spirit Detective Yusuke Urameshi and his comrades are returning for an all-new battle tournament! But they're not the only ones coming back – a whole slew of heroes and villains from the hit anime series will be available for selection! Players can form their own dream team of five (5) characters and fight other combatants in epic PVP battles!
To top it all off, the voice actors from the original anime series will be reprising their roles for this game! Sasaki Nozomu, Chiba Shigeru, Megumi Ogata and Nobuyuki Hiyama will be bringing Yusuke, Kuwabara, Kurama and Hiei back to life – can you imagine all the nostalgia feels that will bring?! Because, I can't!
First Rurouni Kenshin's new manga, then Cardcaptor Sakura's new anime, and now this! Seems like the 90's anime are really making a comeback!
Yu Yu Hakusho 100% Maji Battle is still currently under development, but hopefully it will be 100% completed soon and to be released on iOS and Android so we can relive the intense action of the anime all over again!
Previous articleSound-Based VR Game "Stifled" Resonates a New Kind of Horror | TGS 2017
Next articleDynasty Warriors 9 First Impressions – Witnessing the Birth of a New Dynasty! | TGS 2017
https://www.facebook.com/kichan.cosplayer/
Cosplayer, collector and fan of most everything related to cartoons, mainly Vocaloid and My Little Pony. Also a dabbler in board games and an aspiring illustrator on deviantArt. Has an unhealthy obsession for plushies.
Mobile Suit Gundam: Hathaway gets a new trailer ahead of May 2021 release


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Undefeated Filipino Jhack Tepora picked up an excellent win on the road, scoring a second-round knockout of Lusanda Komanisi in South Africa on 22 September. The 24-year-old claimed the WBO International featherweight bauble in the process and is a youngster worth remembering. The feat is even more remarkable given Tepora suffered an HIV scare before the bout which thankfully proved to be false.
A few hours later Genesis Servania gave WBO featherweight champion Oscar Valdez a real fright in their meeting at the Convention Center in Tucson Arizona. Valdez began well, showing a nice variety in his work and he looked to have more dimensions to his game. Servania was strong and pressed the action and looked to counter Valdez.
The champion dropped his hands in round four and paid the price as he was dropped by the challenger. Valdez repaid the complement in round five and by now we had a real firefight on our hands. Servania continued to land hard shots but as the bout moved in to the second half Valdez moved a lot more and attempted to keep his distance where possible.
The two traded in an exciting last stanza but it was the Mexican who retained his title by scores of 116-110, 115-111 and 117-109. Despite the fan-friendly nature of the contest Valdez showed defensive frailties that will need to be addressed if he's to compete with the rest of the top fighters at featherweight.
As for Servania his reputation was massively enhanced despite the loss and he can certainly come again at either super bantamweight or featherweight. Also in Arizona Uzbekistan's Fazliddin Gaibnazarov scored a shutout over eight rounds versus Victor Rosas.
Romero Duno won an eight-round decision over Juan Pablo Sanchez on 23 September on the undercard of Jorge Linares' bout with Luke Campbell at the Forum in LA. All three scorecards read 78-74.
On the same day over in Texas, Nonito Donaire claimed a unanimous ten-round points victory against Ruben Garcia Hernandez with scores of 100-90, 97-93 and 99-91.
Mark Anthony Barriga came through his toughest test to date with flying colours as he scored a shutout over ten versus Samartlek Kokietgym for the vacant WBO International strawweight strap in Beijing on 29 September. Also on this card unbeaten Filipino Ronnie Baldanado impressively halted Iwan Zoda in six and Chinese debutant Lu Bin vanquished Chatchai Or Benjamas in three.
Japanese southpaw Satoshi Shimizu captured the OPBF featherweight crown in just his fourth pro bout by destroying Sa Myung Noh in five rounds at the Korakuen Hall on 2 October. Shimizu established the distance from the off and his left hand was landing with regularity. The Korean tried to get inside but was met with some sickening body shots for his trouble. Shimizu scored a knockdown in the fourth and Noh did well to survive the round. There was no such luck for the champion in the fifth as Shimizu brought an end to proceedings. The Ohashi Gym fighter is now on the hunt for world titles in 2018.
Super flyweights Rex Tso and Kohei Kono were expected to provide plenty of entertainment in their 7 October encounter at the Hong Kong Convention and Exhibition Center. The duo went at it from the opening bell with Tso's extra youth and speed proving the difference in the first round.
A huge clash of heads occurred in round two, leaving Tso with a swelling. The injury seemed to drive Kono on and the man from Japan increased the tempo and the swelling was rapidly becoming worse and Tso's left eye was also beginning to shut. The bout was called off in round seven with the injuries to the home man resulting in him being unable to continue.
After a ridiculously long delay we went to the cards. Unusually they weren't read out by the MC but eventually they came in and Tso was ahead 68-66 on all three, thus giving him the technical decision victory. Hopefully a rematch can be arranged to settle the score conclusively as the fight was thoroughly enjoyable.
A couple of hours earlier unbeaten Shuya Masaki scored a stunning opening round KO of Ciso Morales at the Korakuen Hall. The Filipino looked relatively comfortable until a crippling right hand to the body left him out for the full ten count and the Teiken super featherweight is now set for a title fight next with the OPBF route looking most likely.
Hinata Maruta's daring attempt to claim the OPBF super bantamweight strap in just his sixth pro bout didn't pay off as he was outworked by the experienced Hidenori Otake at the Korakuen Hall on 13 October. The first four rounds were closely contested with Maruta looking to use his height and reach whilst Otake tried to make it an inside battle.
Otake took control between rounds five and eight, forcing the challenger in to his type of fight. Maruta responded well in the championship rounds and showed glimpses of the talent that has excited many in Japanese boxing but it was the champion who got the deserved points decision at the final bell with scores of 116-112 twice and 117-111. This will have been a great learning experience for Maruta though and he can certainly come again. As for Otake there are a number of interesting domestic bouts available to him.
Felix Alvarado ploughed through Fahlan Sakreerin Jr in three rounds in an IBF light flyweight eliminator that took place in Nicaragua on 14 October. The hard hitting Nicaraguan flew out of the gate immediately forcing the Thai on to the ropes and at the end of round one Fahlan was down. The ferocious attacks continued in round two and Alvarado finished proceedings in round three with a thumping right hand that left Fahlan flat on his back and needing attention. Alvarado recently gave both Kazuto Ioka and Juan Carlos Reveco all they could handle despite being outpointed by both and he is a genuine threat to all the champions at 108lbs.
A busy weekend of action involving Asian fighters kicked off on 20 October with a Japan vs China card which was held at the Korakuen Hall. Headlining the bill was Rikki Naito, who narrowly outpointed unbeaten Baishanbo Nasiyiwula over eight rounds by scores of 77-75, 77-76 and 75-79.
Still at the Korakuen Hall on 21 October we had a new Japanese lightweight champion crowned as Shuichiro Yoshino stopped Spicy Matsushita in seven rounds. Yoshino moves to 6-0 (4 KOs) and looks a promising fighter. He will make his first defence in February 2018.
A few hours later in Belfast Ryan Burnett and Zhanat Zhakiyanov put their respective bantamweight world titles on the line in the first ever unification clash to take place in Ireland. The Kazakh employed his usual pressure tactics, swarming all over Burnett from the outset. Burnett, a talented and smooth boxer was forced in to an inside tussle which lead to a rough, gritty, messy encounter which was full of holding and clinching during the first half.
As Zhakiyanov slowed down in the second half there was more space available for Burnett to land nice combinations which he duly did. The man from Northern Ireland did enough down the stretch to take it and judges' totals of 119-109, 118-110 and 116-112 gave him the victory. The 25-year-old has had a fantastic 2017.
The next day saw the focus switch to Tokyo as the rematch between Ryota Murata and Hassan N'Dam headlined a solid triple header. Murata was out for revenge after being on the wrong end of a dreadful decision to N'Dam in May. The first couple of rounds saw N'Dam throw more but Murata land with the heavier shots.
The man from Japan continued to apply educated pressure and he made a concerted effort to target the body and by the end of round four he was in full control. N'Dam took an absolute pummeling in rounds five and six and the French-based Cameroonian was coming apart at the seams. The beating continued in round seven and at the end of the stanza N'Dam was pulled out by his corner giving Murata the redemption he deserves The bout was a huge hit in Japan, leading on many of the sports pages and being watched by an average audience of around 13.7 million viewers.
On the same bill, Daigo Higa made it 14 wins from 14, maintaining his 100 per cent KO ratio in the process as he easily saw off Thomas Masson to retain his WBC flyweight belt. Despite having the height and reach advantages Masson was unable to make use of these attributes and Higa had no issues getting inside from the off. Round after round the champion chipped away at the challenger who was pretty resilient but that was about it. The Frenchman took a knee in round seven and was stopped by the doctor due to an eye injury soon afterwards. Next up for Higa could be a defence in Okinawa in January or February.
The third title bout on this card saw WBC light flyweight champion Ken Shiro face a tough assignment against Pedro Guevara. The Mexican got off to a really bright start and was ahead on the open scoring after four rounds. Knowing he needed to change things Shiro upped the ante and gave Guevara a cut eye.
After eight rounds there was split scoring with also one card level. Both men went for it in the last third of the contest but it was the champion who prevailed via majority decision with scores of 115-113, 116-112 and 114-114. Next up for Shiro is an ordered rematch with Ganigan Lopez, with no time frame specified at the moment.
There is still no word from the WBC regarding the failed drugs test of Luis Nery after his win over Shinsuke Yamanaka in August. The Mexican in the meantime takes on Arthur Villanueva in a non-title contest in Tiajuana on 4 November.
Wanheng Menayothin makes his latest WBC strawweight title defense on 24 November in Nakhon Ratchasima against recently deposed world champion Tatsuya Fukuhara. The Thai would move to 49-0 with a win and could reach the magic 50 if he were to overcome mandatory challenger Leroy Estrada sometime in 2018.
After being upgraded to full WBO champion due to the retirement of Katsunari Takayama, Fukuhara was outpointed by Ryuya Yamanaka in August in his first defence. Given their styles this should be a decent contest but Japanese boxers have an appalling record in world title fights in Thailand.
OPBF bantamweight champion Mark John Yap makes another defence of his title at the EDION Arena in Osaka against Seizo Kono on 3 December.
Also in December, on a date and venue to be confirmed at time of writing, Kenichi Ogawa squares off against Tevin Farmer for the vacant IBF super featherweight belt. Ogawa made five defences of the national 130lbs crown and showed inconsistent form during this period. He looked strong and powerful in his first encounter with Rikki Naito and against Hirotsugu Yamamoto but was pushed incredibly close by both Naito and Satoru Sugita in their respective rematches. Ogawa does have power but the 29-year-old has limitations and can look very one dimensional at times. He also isn't the hardest to hit which could be his downfall against a slickster like Farmer.
Talking of the American, after going 7-4-1 at the beginning of his career he has strung together 18 straight wins and has defeated the likes of Gamaliel Diaz and Ivan Redkach in a remarkable turnaround. His last loss came five years ago to former super featherweight belt holder Jose Pidraza in a contest that Farmer took at late notice. The 27-year-old southpaw was shot earlier this year and was lucky not to be seriously injured but now has the big chance he has been craving for and should prevail in his first world title tilt.
Finally, WBC flyweight boss Srisaket Sor Rungvisai will square off against Juan Francisco Estrada on 24 February 2018 in Los Angeles, while IBF 108lbs champion Milan Melindo has been ordered to rematch Hekkie Budler after their exciting clash that took place in September.


text:
Journal of Heat Transfer (16)
Journal of Thermal Science and Engineering Applications (1)
Heat Transfer and Thermal Engineering (1)
Special Section Photogallery (1)
Evaporation (8)
Condensation (7)
Resolution (Optics) (6)
Visualization (6)
Chang Kyoung Choi
Surface Plasmon Resonance Imaging: A Technique to Reveal the Dropwise Condensation Mechanism
Shahab Bayani Ahangar, Jeffrey S. Allen, Seong Hyuk Lee, Chang Kyoung Choi
Journal: Journal of Heat Transfer
Article Type: Photo Gallery
J. Heat Transfer. March 2020, 142(3): 030903.
Paper No: HT-20-1045
To understand the physics behind dropwise condensation, a microscopy technique must be able to measure a sub-nanometer film at a high temporal resolution (>1,000 FPS). In this work, automated Surface Plasmon Resonance imaging (SPRi) is used as a tool to study the existence of a thin film between the dropwise condensate. SPRi is a label-free imaging technique that works based on the attenuated total internal reflection. SPRi can detect changes in the refractive index (RI) of the test medium in the thin region (<300 nm) above the sensing gold layer. The automated, angle-scanning SPRi instrument was developed by integrating linear and rotating motorized stages. This instrument improves conventional SPRi by enhancing the resolution of angle probing, increasing the speed of angle scanning, and minimizing the angle-dependent image artifacts. As a proof of concept, we visualized the three stages of coalescence at 10,000 FPS, including bridge formation, composite peanut-shape droplet formation, and the relaxation stage. Furthermore, we probed the solid-vapor interface during the dropwise condensation to evaluate the existence of a thin film on the substrate. The results of our visualization show that the area between droplets is covered by an adsorbed film with a thickness of a monolayer (0.275 nm) and a surface coverage of less than one ( m 2 / m 2 ). Moreover, the results reveal a dry region forms on the substrate when part of the substrate is exposed to ambient conditions due to the coalescence. The dry zone on the substrate has higher surface energy, as compared to the surrounding area. Therefore, the exposed area serves as a favorable site for vapor molecules to strike the surface and form new nuclei.
Topics: Condensation, Imaging, Surface plasmon resonance, Drops, Instrumentation, Resolution (Optics), Thin films, Vapors, Bridges (Structures), Composite materials
A Very Low-Cost, Labor-Efficient, and Simple Method to Block Scattered Ultraviolet Light in PDMS Microfluidic Devices by Inserting Aluminum Foil Strips
Shuo Wang, Peter Shankles, Scott Retterer, Yong Tae Kang, Chang Kyoung Choi
Journal: Journal of Thermal Science and Engineering Applications
J. Thermal Sci. Eng. Appl. February 2019, 11(1): 014501.
Paper No: TSEA-18-1288
Opto-microfluidic methods have advantages for manufacturing complex shapes or structures of micro particles/hydrogels. Most of these microfluidic devices are made of polydimethylsiloxane (PDMS) by soft lithography because of its flexibility of designing and manufacturing. However, PDMS scatters ultraviolet (UV) light, which polymerizes the photocrosslinkable materials at undesirable locations and clogs the microfluidic devices. A fluorescent dye has previously been employed to absorb the scattered UV light and shift its wavelength to effectively solve this issue. However, this method is limited due to the cost of the materials (tens of dollars per microchip), the time consumed on synthesizing the fluorescent material and verifying its quality (two to three days). More importantly, significant expertise on material synthesis and characterization is required for users of the opto-microfluidic technique. The cost of preliminary testing on multiple iterations of different microfluidic chip designs would also be excessive. Alternatively, with a delicate microchannel design, we simply inserted aluminum foil strips (AFS) inside the PDMS device to block the scattered UV light. By using this method, the UV light was limited to the exposure region so that the opto-microfluidic device could consistently generate microgels longer than 6 h. This is a nearly cost- and labor-free method to solve this issue.
Topics: Aluminum foil, Integrated circuits, Microfluidics, Plasma desorption mass spectrometry, Strips, Ultraviolet radiation, Microchannels
Neutron attenuation analysis of cryogenic propellants
Kishan Bellur, Daniel Hussey, David Jacobson, Jacob Lamana, Ezequiel Medici, James Hermanson, Dr. Jeffrey S. Allen, Chang Kyoung Choi
Neutron imaging enables direct visualization of evaporation and condensation of cryogenic propellants in metal containers such as aluminum and stainless steel. CFD models of propellant behaviors inside the large tanks have shown that a thin liquid film is formed along the interior surface, but this had not been verified experimentally. In the present study, neutron imaging is used to study evaporation and condensation rates of liquid methane inside a cylindrical 10 mm, Al 6061 cell. The liquid meniscus is clearly shown, but the spatial resolution is insufficient to directly image thin liquid films that may be on the interior surface. Optical density (neutron attenuation) analysis enables quantitative measurements of these liquid films. An optical density image is formed by removing the background noise and normalizing the liquid image with that of the empty cell. Optical densities are then transformed into a liquid transmission thickness using the Beer-Lambert law. This technique enables measurement of film thicknesses smaller than the spatial resolution of the imaging system. The above graphic shows an optical density image during condensation of methane and the corresponding horizontal scan which suggests that a 11 μm film exists on the wall. The images indicate that methane undergoes film-wise condensation and is perfectly wetting to aluminum. These experiments were conducted at the NIST Center for Neutron Research in the Neutron Imaging Facility and the relevant work is supported by an Early stage Innovations Grant from NASA's Space Technology Research Grants Program (Grant # NNX14AB05G).
Topics: Neutrons, Propellants, Imaging, Condensation, Density, Methane, Aluminum, Evaporation, Lubrication theory, Resolution (Optics)
Electron Mobility across Grain Boundaries in Graphene Synthesized using Chemical Vapor Deposition Process
Fei Long, Chang Kyoung Choi
J. Heat Transfer. August 2017, 139(8): 080901.
Chemical vapor deposition (CVD) is currently the only method for large-scale synthesis of graphene. However, the CVD process introduces grain boundaries (GBs) when individual grains coalesce with various mismatch angles. These GBs contain atomic dislocations and defects, which are believed to alter graphene's mechanical, electrical, and thermal properties. Specifically, the GBs can act as "potential barriers" when charges move from one grain to neighboring grains. This barrier effect will not only change the electrical conductivity but also the thermal conductivity of graphene. Besides high-resolution, 3-dimensional topography images, Atomic force microscopy (AFM) can also obtain the electrical properties at the nanoscale. In this report, the potential barrier effect of graphene GBs is studied with AFM. During the experiment, the probe is brought into contact with the graphene while positively (or negatively) biased. This process injects net charges into the graphene. The electrostatic potential across the GBs can be measured by AFM as an indication of the potential barrier effect. GBs with lower potential difference correspond to lower potential barrier, and vice versa. The dependency of the barrier effect on the mismatch angles was also measured. Considering the 6 folds' symmetry of graphene atomic lattice, the mismatch angle is in the range of 0° ∼ 30°, with 30° the maximum mismatch angle. Our results can be well fitted with a sinusoidal function with π /3 period, which supports our hypothesis that higher mismatch angle contains higher density of dislocations and defects that increase the potential barrier of GBs.
Topics: Chemical vapor deposition, Electron mobility, Grain boundaries, Graphene, Potential barrier, Atomic force microscopy, Dislocations, Density, Electric potential, Electrical conductivity
Atomic Force Microscopy (AFM) as a Powerful Tool to Study Temperature-Dependent Polymer Film Formation
J. Heat Transfer. February 2017, 139(2): 020904.
Published Online: January 6, 2017
Atomic force microscopy (AFM) is one of the most effective tools in nanotechnology researches. Using the raster scanning method with a soft cantilever, three dimensional sample surface topography can be obtained with a sub-nanometer resolution. In this study, AFM is employed to characterize the nanostructures of polymer film under two temperature treatments. 3-aminopropyltriethoxysilane (APTES) is selected as a model polymer molecule due to its wide applications for amino-functionalization of Si/SiOx based surfaces, such as silicon and mica. The APTES molecule has three ethoxy groups that can react with surface hydroxyl groups or with another APTES molecule through a siloxane bond. The self-assembled APTES self-assembly film has typically three configurations, namely uncrosslinked monolayer, crosslinked monolayer, and multilayer. Ten percent aqueous solution is used to cover the entire mica surfaces. Then the surfaces are rinsed with DI water and dried with N 2 to remove left over solution. Two hours incubation was followed in 80°C or 140°C, respectively. At 80 °C (below the boiling point), the uniform APTES film is obtained. On the other hand, at 140 °C (above the boiling point), the film exhibits multilayer structure, as confirmed by AFM images. Contact angle measurement shows that the multilayer film is less wettable than the monolayer film by 20°. It seems that the evaporation rate of the water layer on the substrate is the key to various film configurations.
Topics: Atomic force microscopy, Polymer films, Temperature, Phase transition temperature, Self-assembly, Water, Cantilevers, Evaporation, Nanostructures , Nanotechnology
High Speed SPR Visualization of Frost Propagation Inside a Subcooled Water Droplet
Chan Ho Jeong, Seong Hyuk Lee, Dong Hwan Shin, Vinaykumar Konduru, Jeffrey S. Allen, Chang Kyoung Choi
A surface plasmon resonance (SPR) imaging microscopy coupled to a high-speed camera is used to visualize the frost propagation inside a subcooled liquid droplet. The SPR experimental setup consists of a 50 nm thick gold-coated cover glass placed on a BK7 dove prism and optically matched using index matching liquid. Collimated monochromatic light of 600 nm wavelength is incident on the gold-glass interface at 71.8°, which corresponds to the SPR minima angle for ice (RI 1.309). Images are captured using Photron APS-RS camera at 1000 fps with a shutter speed of 1 ms. The prism and the gold film are cooled using a thermo-electric cooler (TEC). A water droplet is placed on the gold film and the temperature of the droplet is decreased from room temperature (23.0 ± 1 °C) to below 0 °C. Adjacent to the water droplet, the vapor condensates to form tiny droplets. The tiny condensate droplets would freeze first and the frost propagates through the condensate region. During this period the central droplet is in a subcooled state. The speed of frost propagation through the condensates is slow and takes tens of seconds to cover the gold film with ice. Within a single condensate droplet, however, the frost propagation velocity is expected to be considerably higher. Eventually the frost line reaches the central droplet. There is a delay of few seconds between the frost line reaching the droplet and frost propagation inside the droplet. The point at which frost touches the subcooled droplet acts as a nucleation site for the droplet and the frost propagates in the droplet at high speed. The average velocities of frost propagations in the subcooled liquid droplet were calculated to be 5.2 ± 0.3 cm/s and 7.4 ± 0.5 cm/s, when the gold film temperature was -5.0 ± 1 °C and -7.8 ± 1 °C respectively.
Topics: Drops, Subcooling, Visualization, Water, Condensed matter, Temperature, Glass, Ice, Prisms (Optics), Delays
Examining Liquid Hydrogen Wettability Using Neutron Imaging
Vinaykumar Konduru, Kishan Bellur, Ezequiel F. Médici, Jeffrey S. Allen, Chang Kyoung Choi, Daniel S. Hussey, David Jacobson, Juscelino B. Leão, John McQuillen, James C. Hermanson
The control of propellant boil-off is essential in long-term space missions. However, a clear understanding of propellant cryogenic condensation/evaporation in microgravity is lacking. One of the key factors in designing such systems is the location of liquid surfaces and the relation to wettability. The BT-2 Neutron Imaging Facility located at the National Institute of Standards and Technology (NIST), Gaithersburg, MD, is used to image evaporation and condensation of hydrogenated propellants inside of an aluminum 6061 container. Liquid hydrogen has larger neutron cross-section area than the aluminum, allowing the visualization of the liquid-vapor interface. The test cell has a conical section that enables determination of a contact angle with enhanced accuracy. If the contact angle is equal to the angle of the cone, a flat liquid-vapor interface is expected. The test cell has the cone angle of 10o and a flat interface was not observed. Using the Laplace-Young equation to fit the interface, the contact angle for hydrogen and aluminum was between 0° and 4°. The theoretical Laplace curves with contact angles of 2o and 10o are plotted on the liquid-vapor interface. The of 2o curve is a closer fit as compared to the 10o curve. The uncertainty arises from resolution limits of the neutron imaging setup and edge detection. More details on the neutron imaging mechanism and relevant physics can be found from the authors' other publication of Cryogenics, 74, pp131-137, 2016: doi:10.1016/j.cryogenics.2015.10.016.
Topics: Hydrogen, Imaging, Neutrons, Aluminum, Propellants, Vapors, Condensation, Cryogenics, Evaporation, National Institute of Standards and Technology
High-Speed Surface Plasmon Resonance (SPR) Reflectance Imaging of Drop Coalescence during Condensation and Evaporation
Vinaykumar Konduru, Dong Hwan Shin, Jeffrey S. Allen, Chang Kyoung Choi, Seong Hyuk Lee, Young-Ki Choi, Sosan Cheon, Kenneth D. Kihm
Drop condensation and coalescence is visualized using high-speed Surface Plasmon Resonance (SPR) reflectance microscopy. SPR microscopy is a label-free technique that can characterize thin films (less than 1µm) by detecting the changes in the refractive index of the test medium. The sensing surface is a 50 nm thick gold film on a 2.5 nm thick Ti layer is deposited on a borosilicate substrate. P-polarized monochromatic light (632 nm) is incident on the gold film in a total internal reflection mode. Free electrons in the gold film are excited by the incident light when a resonance condition is met. The result is a decrease in the reflected intensity. Resonance depends upon wavelength, incident angle, and refractive index of prism and test medium. To induce condensation, a water bridge is created between the SPR gold film and an ITO coated glass slide. When the ITO coated slide is heated water evaporates from the bridge and condenses on the gold film. The sequence of images on the process of droplet deposition and drop coalescence are captured at 1500 frames per second. Experiments were conducted at an SPR angle of 44o, which is slightly above the minimum intensity angle for air at 43.8o. Therefore, the brightest and darkest regions correspond to the areas on the gold film covered with bulk water and a very thin film of water, respectively. The thickness of the film is proportional to the intensity of reflected light.
Topics: Condensation, Evaporation, Imaging, Reflectance, Surface plasmon resonance, Water, Microscopy, Refractive index, Resonance, Thin films
Wettability Effect on Droplet Growth Behaviors During Dropwise Condensation
Jae Bin Lee, Seong Hyuk Lee, Chang Kyoung Choi, Jungho Lee
Proc. ASME. IMECE2015, Volume 8B: Heat Transfer and Thermal Engineering, V08BT10A053, November 13–19, 2015
The present study examines the transient characteristics of droplet growth and heat transfer during dropwise condensation process on different hydrophobic surfaces. The self-assembled monolayer (SAM) of n-octadecyl mercaptan was coated on the surface to change the surface wettability with the contact angles of 148° and 124°. A Canon EOS 7D camera and an Infinity K2 lens were used to capture the spontaneous images during condensation. From the experiment, three regimes were observed: in the first regime where the droplets were formed with nearly homogenous pattern, the heat transfer coefficient increased rapidly. In the second regime, both the droplet size and the liquid area fraction increased. In the third regime, coalescence among larger droplets was dominant, causing the decrease in the liquid area fraction with time. Moreover, the measured fall-off time was faster in the case with higher contact angle because of relatively low surface energy.
Topics: Condensation, Drops, Heat transfer, Heat transfer coefficients, Lenses (Optics), Self-assembly, Surface energy, Transients (Dynamics)
Contact Angle Measurement of Liquid Hydrogen (LH 2 ) in Stainless Steel and Aluminum Cells
Kishan Bellur, Vinaykumar Konduru, Manan Kulshrestha, Daanish Tyrewala, Ezequiel Medici, Jeffrey S. Allen, Chang Kyoung Choi, Daniel S. Hussey, David C. Jacobson, Juscelino B. Leão, John McQuillen, James Hermanson, Arun Tamilarasan
One of the key limitations to long-term space missions is to avoid propellant boil-off in a microgravity space environment. Even with the use of active and passive controls of propellants, boil off is inevitable. Long-term CFD simulations on propellant behaviors depend on evaporation/condensation coefficients (known as accommodation coefficients) which are in turn dependent upon the wetting characteristics. Phase change experiments were conducted in the BT-2 neutron imaging facility at the National Institute of Standards and Technology (NIST) by introducing vapor H 2 in 10 mm Al6061 and SS316L test cells placed inside the 70mm 'orange' cryostat. Condensation is achieved by lowering the cryostat temperature below the saturation point and vice versa for evaporation. The high neutron cross-section of liquid H 2 in comparison to both the vapor and the test cell materials allows for visualization of a distinct liquid-vapor interface. Multiple images are stacked to increase the signal-to-noise ratio and the meniscus edge is obtained by detecting the pixels with largest gradients in intensities at the liquid meniscus. The contact angle is obtained by curve fitting of the Young-Laplace equation to the detected meniscus. The contact angle for Al6061 and SS316 is found to be between 0° and 4°. The uncertainty arises from edge detection, magnification, and resolution limits of the neutron imaging setup. The test was conducted at a saturation temperature of 21K (1.215 bar). The results from the neutron experiments will be then used in conjunction with FEA thermal models and kinetic phase change models to extract accommodation coefficients.
Topics: Aluminum, Boiling, Computational fluid dynamics, Condensation, Curve fitting, Edge detection, Engineering simulation, Evaporation, Finite element analysis, Hydrogen
Frosting Characteristics on Hydrophilic and Superhydrophobic Copper Surfaces
Chan Ho Jeong, Jae Bin Lee, Seong Hyuk Lee, Jungho Lee, Seung Mun You, Chang Kyoung Choi
The main objective of this study is to examine the frosting characteristics affected by the surface wettability. Two different copper surfaces – bare and nano structured - were prepared for the experiments. Their static contact angles are 74° (bare: without surface treatment) and 154° (nano-structured), respectively. The temperature of the copper substrate was measured by using resistance temperature detector (RTD) sensors embedded inside small holes drilled at 1 mm underneath the surface. During the phase change, the temperature of the copper substrates remained -7.8±0.6°C and the ambient temperature was set as 24±0.5°C with the relative humidity of 45%. Images were captured by using the CMOS camera with the 5 second time interval. Film condensation occurred because of higher wettability of the bare copper surface. Film condensates were frozen at the early stage and frost crystal grew in the vertical direction. On the other hand, dropwise condensates formed on the nano-structured copper surface remained as the supercooled liquid phase for 44 minutes owing to its low wettability. After 4 minutes, frosting on the bare copper substrate was triggered and propagated until it covered the whole surface. The frosting was significantly delayed on the superhydrophobic copper surface due to the lower surface free energy. The different porous media composed of frost which directly influence the heat transfer characteristics was formed on each surfaces. Therefore, additional investigation for heat transfer phenomenon on superhydrophobic surface should be conducted.
Topics: Copper, Temperature, Heat transfer, Complementary metal oxide semiconductors, Crystals, Film condensation, Porous materials, Resistance thermometers, Sensors, Surface finishing
Visualization in the Contact Line Region of an Evaporating Nanofluid Drop
Dong Hwan Shin, Jeffrey S Allen, Chang Kyoung Choi, Seong Hyuk Lee
Photogallery Entry 13
Topics: Evaporation, Heat, Mass transfer, Nanofluids, Visualization
Dependency of Condensation Forms on Wettability
Jae Bin Lee, Jin Woon Lee, Seong Hyuk Lee, Yong Tae Kang, Chang Kyoung Choi
Topics: Condensation, Heat, Mass transfer
Detection & Collection of Bacteria in an Evaporating Sessile Droplet
Jung-Yeul Jung, Yong Tae Kang, Chang Kyoung Choi
Photogallery Entry 2
Topics: Bacteria, Drops, Evaporation, Heat, Mass transfer
Dynamics of a non-Newtonian Droplet Impact on a Micro-Textured Surface
Joo Hyun Moon, Dong Hwan Shin, Seong Hyuk Lee, Chang Kyoung Choi
Topics: Drops, Dynamics (Mechanics)
Biological Temperature Sensing of Focal Contacts
Jen-Yung Chang, Brian Plunger, Jong-Min Kim, Chang Kyoung Choi
Topics: Adhesion, Biomechanics, Biomedical measurement, Biophysics, Cancer, Lung, Optical microscopy, Refractive index, Temperature
Dynamic Spreading of a Droplet Impinging on Micro-Textured Surfaces
Jae Bong Lee, Seong Hyuk Lee, Chang Kyoung Choi
Topics: Aluminum, Density, Drops, Flow visualization, Hydrophobicity, Microfluidics, Milling machines, Surface energy, Surface roughness, Surface texture
Evaporation Characteristics of Sessile Droplets on Nano-Patterned Hydrophobic Surfaces
Dong Hwan Shin, Seong Hyuk Lee, Scott Retterer, Chang Kyoung Choi
Topics: Drops, Evaporation, Flow visualization, Hydrophobicity, Two-phase flow, Water, Wetting


text:
\section{Introduction}

The Bethe--Salpeter (BS) equation \cite{Bet51} is usually considered
the rigorous framework in which to approach the bound state problem in QED.
The increasing precision of the experimental data concerning
QED bound states (e. g. decay rate, energy levels, etc. for some
recent reviews we refer the reader to \cite{Kin90}) makes more and more
urgent to effort the evaluation of physical quantities
by handling the BS equation with a systematic and unified formalism.

In this paper we will focus our attention to the bound
state energy levels in QED and will discuss the so-called
Barbieri--Remiddi (BR) formalism. This formalism was first suggested
for positronium \cite{Bar78,Cas78} (for a clarifying quanto-mechanical
example see also \cite{Her95}), but has been used in recent years
also for hydrogenic atoms \cite{Cav94}, QCD bound states \cite{Kum94}
and scalar-scalar bound states \cite{Moe96}. The main idea
is to solve exactly the BS equation for a suitable
zeroth-order kernel containing the relevant binding interaction
(i. e. the Coulomb potential) and then to perform a perturbative
expansion in terms of the difference between the complete two-body
kernel and the zeroth-order one. What is appealing in this approach
is that the zeroth-order solution is completely known in analytic
closed form. Therefore the perturbative expansion obtained in this
way is completely self-contained and does not need to be improved
for higher correction in the fine structure constant $\alpha$.

In the following the BR formalism will be derived in the general
case of muonium (i. e. different masses). This result is new
and contains the positronium and hydrogenic case as a particular one.
Moreover it furnishes a way to treat radiative and
recoil corrections in the same theoretical framework, which
seems to be very promising.

The paper contains two main sections. In section 2
we derive the perturbative expansion of the energy levels
from the BS equation in the so-called Kato
formalism. In section 3 we derive in some detail the BR
solution for muonium. Section 4 is devoted to some comments and
conclusions.

\section{The Bethe--Salpeter equation}

In this section we review some basics concerning the
Bethe--Salpeter equation in QED and set up the theoretical
background for the next section. The main result will be the perturbative
expansion of the energy levels of the two fermion bound state
given by Eq. (\ref{energy}).

\begin{figure}[htb]
\vskip 0.8truecm
\makebox[0.2truecm]{\phantom b}
\epsfxsize=14.8truecm
\epsffile{g.ps}
\vskip 0.3truecm
\caption{{{\small \it Four point Green function $G$: graphs up to
two loops.}}}
\label{psg}
\vskip 0.8truecm
\end{figure}

Let us consider a system of two fermions (of mass $m_1$ and $m_2$
and electric charge $-e$ and $Ze$ respectively) like muonium.
The four point Green function $G$ is the sum of the Feynman graphs
shown in Fig. \ref{psg} (notice that for a particle-antiparticle system,
like positronium, one has to add the annihilation graphs).
Let us define $G_0$ the two fermions free propagator:
\begin{equation}
G_0(E;p) = S_F^{(1)}(E_1;p) S_F^{(2)}(-E_2;p)^T, \qquad\quad
S_F(E_j;p) = {i \over E_j\gamma^0 + {p\kern-1ex {/}} -m +i\epsilon},
\label{G0}
\end{equation}
where $^{(1)}$ and $^{(2)}$ refer to the two fermion lines,
$E_j \equiv  E ~m_j / (m_1+m_2)$, $E$ is the bound state energy
and $p$, $q$ are the relative momenta of the outcoming and incoming
particles in the centre-of-mass reference frame
\footnote{
Let $p^{(1)}$ and $p^{(2)}$ be the momenta of the
outcoming particles, and
$$
P \equiv  p^{(1)} + p^{(2)}, \qquad\quad
p \equiv {\mu \over m_1}p^{(1)} - {\mu \over m_2}p^{(2)},
$$
with $\mu = m_1 m_2 / (m_1 + m_2)$ the reduced mass of the two particles.
In the centre-of-mass frame ${\vec p}^{~(1)} = - {\vec p}^{~(2)}$  implies
$P = (p^{(1)}_0+p^{(2)}_0,\vec 0~)$ $= (E,\vec 0~)$.
From the previous equations we obtain
\begin{eqnarray}
p^{(1)} &=&  p + {m_1 \over m_1+m_2}P = ( p_0 + E_1, {\vec p}~),
\nonumber\\
p^{(2)} &=& -p + {m_2 \over m_1+m_2}P = (-p_0 + E_2,-{\vec p}~),
\nonumber
\end{eqnarray}
where $E_j = E~m_j / (m_1+m_2)$ and therefore
$$
E = E_1+E_2  .
$$
Finally, we note that in the static limit
$$
E  \rightarrow m_1+m_2, ~~~~ E_j \rightarrow m_j .
$$
In the same way we can treat the incoming momenta.}.
It is found that the Green function $G$ satisfies the equation:
\begin{equation}
G(E;p,q)=
G_0(E;p){\Bigg[} (2\pi)^4\delta^{4}(p-q) + \int\ftt{4}{k}K(E;p,k)G(E;k,q)\Bigg].
\label{bs_eq}
\end{equation}
This equation (for simplicity we have neglected the spinor indices)
is known as the Bethe--Salpeter equation \cite{Bet51}. The kernel $K$,
describing the interaction between the two fermions, is not known
in analytic closed form and is given by all the two particle irreducible
graphs without external legs shown up to two loop in Fig. \ref{psk}.
Graphically the BS equation can be represented as in Fig. \ref{psbs_g}.

\begin{figure}[htb]
\vskip 0.8truecm
\makebox[0.2truecm]{\phantom b}
\epsfxsize=14.8truecm
\epsffile{k.ps}
\vskip 0.3truecm
\caption{{{\small \it The interaction kernel $K$.} }}
\label{psk}
\vskip 0.8truecm
\end{figure}

$G$, as a function of $E$,  has simple poles in the bound
state energy levels $E_{n...}$ \cite{Ede53} ($n...$ is a convenient set
of quantum numbers which classifies the levels). Since the Coulomb interaction
is contained in $K$,  $E_{n...}$ (without mass terms) has to coincide
with the Bohr levels at the leading order in $\alpha$.
Therefore for any ${n...}$, we can write
\begin{equation}
G(E) = {R_{n...} \over E-E_{n...}} + \hat G_{n...}(E) \,,~~~~~~~~
E_{n...} = m_1 + m_2 -{\mu \over 2}
\left( {{Z\alpha} \over n} \right)^2 ~+~ \cdots ~,
\label{G_pol}
\end{equation}
where $R_{n...}$ is the residuum at the pole, $\hat G_{n...}$ is non singular
in the limit $E \to  E_{n...}$ and $\mu$ is the reduced mass
of the two particle system. From now on we will neglect the explicit
indication of the momenta in the argument of the functions, where considered
not strictly necessary.

\begin{figure}[htb]
\vskip 0.8truecm
\makebox[2truecm]{\phantom b}
\epsfxsize=11truecm
\epsffile{bs_g.ps}
\vskip 0.3truecm
\caption{{{\small \it Inhomogeneous BS equation:
$G(E) = G_0(E) + G_0(E) K(E) G(E)$.}}}
\label{psbs_g}
\vskip 0.8truecm
\end{figure}

Inserting (\ref{G_pol}) into the BS equation and comparing the residua,
we obtain:
\begin{equation}
R_{n...} = G_0(E_{n...})K(E_{n...})R_{n...} ,
\label{bs2_eq}
\end{equation}
which is known as the homogeneous Bethe--Salpeter equation.
Moreover, from the comparison of the non singular parts in $E-E_{n...}$
we obtain the normalization condition \cite{Man56}:
\begin{equation}
R_{n...} = R_{n...}~\pd{E} \left( G_0^{-1} - K \right) (E_{n...})~R_{n...}~.
\label{norm}
\end{equation}

The BS equation (\ref{bs_eq}) is, up to now, not solvable in
analytic closed form. Let $K_c$ be an interaction kernel satisfying
the following two properties:
\begin{description}
\item{$i)$} ~~$K_c$ reproduces the same non relativistic limit of $K$, i.e.
the Coulomb potential $V = -4\pi Z\alpha/p^2$ times some spinorial factors;
\item{$ii)$} ~~the BS equation for $K_c$:
\begin{equation}
G_c(E) = G_0(E) + G_0(E) K_c(E) G_c(E) ,
\label{Gc_eq}
\end{equation}
is analytically solvable in closed form.
\end{description}
With these assumptions it is possible to solve the BS equation for $G$
at least perturbatively in terms of $\delta K \equiv K - K_c$ and to give
a perturbative expansion for the bound state energy levels (the poles of $G$).

From the property $i)$ it follows that $G_c$ has simple poles for $E=E_n^c$.
These poles are surely more degenerate than the poles of the
complete Green function $G$ and give back, at the leading
order in $\alpha$, the Bohr levels:
\begin{equation}
G_c(E) = {\sum R^c_{n...} \over E-E^c_n } + \hat G^c_n(E) \,,~~~~
E^c_n = m_1+m_2-{\mu \over 2}\left( {{Z\alpha} \over n} \right)^2 ~+~ \cdots ~,
\label{Gc_pol}
\end{equation}
where $R^c_{n...}$ is the residuum at the pole
and $\hat G^c_n$ is non singular in the limit $E \to E^c_n$.
The sum is extended over all the degenerate states for each $n\in {\hbox{\s@ l\kern-.5ex N}}$.
The residuum $R^c_{n...}$ satisfies the analogous of equations
(\ref{bs2_eq}) and (\ref{norm}):
\begin{eqnarray}
R^c_{n...} &=& G_0(E^c_n)K_c(E^c_n)R^c_{n...}~,
\label{gc2_eq}\\
R^c_{n...} &=& R^c_{n...} ~\pd{E}
\left( G_0^{-1} - K_c \right) (E^c_n) ~R^c_{n...}~.
\label{normc}
\end{eqnarray}

From the definition of $\delta K$ and from (\ref{bs_eq}) and (\ref{Gc_eq})
we obtain the perturbative expansion of $G$ in terms of $\delta K$:
\begin{equation}
G(E) = G_c(E) + G_c(E) \delta K(E) G_c(E)
+ G_c(E) \delta K(E) G_c(E) \delta K(E) G_c(E) + \cdots .
\label{expG}
\end{equation}
In order to obtain from (\ref{expG}) the perturbative expansion of the poles
$E_{n...}$ we will use the so-called Kato perturbation theory \cite{Kat49}.
Since the energy levels are the poles of $G$ we can write:
\begin{equation}
E_{n...} =
{\displaystyle \oint_{\kern 1pt \Gamma_n}
{dz ~z ~{\rm Tr}\left\{ G(z)O_{n...} \right\}} \over \displaystyle
\oint_{\kern 1pt \Gamma_n} {dz    ~{\rm Tr}\left\{ G(z)O_{n...} \right\}}},
\label{Egamma}
\end{equation}
where $\Gamma_n$ is a closed curve in ${\hbox{l\kern-1.2ex C}}$
which contains only the poles $E_{n...}$ and $E^c_n$ of $G$ and $G_c$
respectively, $O_{n...}$ is an operator which does not vanish on
$R_{n...}$ and $R^c_{n...}$ and  ${\rm Tr}$ means the trace over the spinor
indices. A convenient choice is
$$
O_{n...} \equiv  \pd{E} \left( G_0^{-1} - K_c \right)(E^c_n) ~ R^c_{n...} ~
\pd{E} \left( G_0^{-1} - K_c \right)(E^c_n).
$$
Inserting (\ref{expG}) in (\ref{Egamma}) integrating in $z$ and taking
into account (\ref{normc}), we obtain (up to order $\delta K^4$):
\begin{eqnarray}
E_{n...} &=& E^c_n + {1 \over D_{n...}} \left< \delta K(E^c_n) \right>_{n...}
+ {1 \over D^2_{n...} } \left< \delta K(E^c_n) \hat G_c(E^c_n)
\delta K(E^c_n) \right>_{n...}
\nonumber\\
&+& {1 \over D^2_{n...} } \left< \delta K(E^c_n) \right>_{n...}
\left< \pd{E} \delta K(E^c_n) \right>_{n...}
\nonumber\\
&+& {1 \over D^3_{n...} } \left< \delta K(E^c_n) \hat G_c(E^c_n)
\delta K(E^c_n) \hat G_c(E^c_n) \delta K(E^c_n) \right>_{n...}
\nonumber\\
&+& {1 \over D^3_{n...} } \left< \delta K(E^c_n) \hat G_c(E^c_n)
\delta K(E^c_n) \right>_{n...} \left< \pd{E} \delta K(E^c_n) \right>_{n...}
\nonumber\\
&+& {1 \over D^3_{n...} } \left< \pd{E} \left(\delta K \hat G_c \delta K \right)
(E^c_n) \right>_{n...} \left< \delta K(E^c_n) \right>_{n...}
\nonumber\\
&+& {1 \over D^3_{n...} } \left< \delta K(E^c_n) \right>_{n...}
\left[ \left< \pd{E} \delta K(E^c_n) \right>_{n...} \right]^2
\nonumber\\
&+& {1\over 2} {1 \over D^3_{n...} }
\left[ \left< \delta K(E^c_n) \right>_{n...} \right]^2
\left< {\partial^2~ \over \partial E^2} \delta K(E^c_n) \right>_{n...}
+ ~O(\delta K^4),
\label{energy}
\end{eqnarray}
where
$$
\left< A \right>_{n...} \equiv {\rm Tr}\left\{ A ~R^c_{n...} \right\} =
\int \ftt{4}{p} \int \ftt{4}{q}
{\rm Tr}\left\{ A(p,q) ~R^c_{n...}(p,q) \right\}.
$$
$D_{n...}$ is the degeneracy of the $E=E_{n...}$ level and is defined to be
\begin{equation}
D_{n...} \equiv
\left< \pd{E} \left( G_0^{-1} - K_c \right) (E^c_n) \right>_{n...}.
\label{DDD}
\end{equation}

Equation (\ref{energy}) expresses the bound state energy $E_{n...}$
as an expansion in $\delta K$. Since $\delta K$ is the difference between
the sum of the infinit series of Feynman graphs drawn in Fig. \ref{psk}
and the kernel $K_c$, $\delta K$  is not known in closed form.
Each graph of Fig. \ref{psk} contributes to (\ref{energy}) with
a series of powers of $\alpha$, because the dependence of the residuum $R^c_n$
on the fine structure constant (like in the well-known non-relativistic
case where the hydrogen wave-functions depend on $\alpha$). For consistency
with $i)$ the explicit calculation must exhibit that to an increasing order in
$\delta K$ it corresponds an increasing leading order in $\alpha$
in the contributions to the energy levels. In this sense
expansion (\ref{energy}) can be interpreted as a perturbative expansion in the
fine structure constant. Once $K_c$ is explicitly given and the
corresponding BS equation is solved (this means we have an analytic
expression for $E^c_n$, $R^c_{n...}$ and $\hat G^c_n$) the expansion
(\ref{energy}) allows to obtain without any ambiguity the energy levels
up to a given order in $\alpha$ for all the two-fermions bound states in QED.
We emphasize that, in absence of an exact solution of Eq. (\ref{Gc_eq}),
expression (\ref{energy}) could be evaluated only for an approximate choice of
$G_c$ to improve at any increasing of the requested precision.

\section{The Barbieri--Remiddi solution}

In this section we work out with some detail the so-called Barbieri--Remiddi
solution of equation (\ref{Gc_eq}) (for and exhaustive description
see \cite{Vaibo}). With this name we mean a zeroth order kernel $K_c$
which satisfies the previous given properties $i)$ and $ii)$ (in other words
$K_c$ should describe correctly at the leading order in $\alpha$
the bound state and make solvable the corresponding BS equation
(\ref{Gc_eq})) as well as the solution of the corresponding BS equation.
The BR solution was first given for the positronium \cite{Bar78}.
In the following we will give the generalization of that solution
for a bound state of two fermions with different masses, i. e. muonium.
Once $K_c$ is given, we solve the equation for $G_c$ and
work out the poles $E^c_n$ and the residua $R^c_{n...}$.
At that point the perturbative expansion of the energy levels (\ref{energy})
will be completely defined.

Let us define the energy projectors
\begin{equation}
\Lambda_{\pm}({\vec p},m_j) \equiv { E_{pj} \pm (m_j-{\vec p}\cdot\vec\gamma)\gamma^0 \over
2 E_{pj}};
\end{equation}
with $E_{pj} \equiv \sqrt{{\vec p}^{~2}+m_j^2}$.
In terms of $\Lambda_{\pm}$ the free fermion propagator $S_F$ can be written as
$$
S_F(E_j;p) =
i \left( {\Lambda_{+}({\vec p},m_j)\gamma^0 \over p^0+E_j-E_{pj}+i\epsilon}
+        {\Lambda_{-}({\vec p},m_j)\gamma^0 \over p^0+E_j+E_{pj}-i\epsilon} \right).
$$
Moreover, we define
\begin{eqnarray}
\Lambda({\vec p},{\vec q}~) &\equiv& \left(
{16 E_{p1}E_{p2}E_{q1}E_{q2} \over (E_{p1}+m_1)(E_{p2}+m_2)(E_{q1}+m_1)
(E_{q2}+m_2)} \right)^{1\over 2}
\label{LL}\\
&\times&
\left(\gamma^0\Lambda_+({\vec p},m_1){1+\gamma^0 \over 2}
\Lambda_+({\vec q},m_1)\right)^{(1)}
\left(\gamma^0\Lambda_-({\vec q},m_2){1-\gamma^0 \over 2}
\Lambda_-({\vec p},m_2)\right)^{(2)T}.
\nonumber
\end{eqnarray}

The zeroth order BR interaction kernel for the muonium is
\begin{equation}
K_c(E;{\vec p},{\vec q}~) \equiv i R(E;{\vec p}~)R(E;{\vec q}~)V({\vec p}-{\vec q}~)\Lambda({\vec p},{\vec q}~),
\label{Kc}
\end{equation}
with
\begin{equation}
R(E;{\vec p}~) = \left( {8\mu E^2 \over
(E+E_{p1}+E_{p2})(E-E_{p1}+E_{p2})(E+E_{p1}-E_{p2})} \right)^{1\over2}.
\end{equation}
We assume (\ref{Kc}) as a definition. In the following we will verify
that this choice satisfies the properties $i)$ and $ii)$ given in the previous
section.

In the static limit ($E\rightarrow m_1+m_2$, $E_j\rightarrow m_j$
and ${\vec p}, {\vec q} \rightarrow 0$),
$$
K_c(E;{\vec p},{\vec q}~) \rightarrow -i~V({\vec p}-{\vec q}~)
\left( {1+\gamma^0 \over 2} \right)^{(1)}\left( {1-\gamma^0 \over 2} \right)^{(2)T},
$$
i. e. $K_c$ reproduces the Coulomb potential times some spinorial factors.

In order to verify that the choice (\ref{Kc}) makes solvable the BS
equation (\ref{Gc_eq}) it is useful to express the Green function $G_c$
in terms of a new function $H_c$ \footnote{
In general $H_c$ could depend on each component of the momenta
$p$ and $q$. The explicit calculation, however, will show
that $H_c$ does not depend on $p_0$ and $q_0$ (see Eq. (\ref{hh_eq3})).}:
\begin{equation}
G_c(E;p,q) \equiv G_0(E;p) + iR(E;{\vec p}~)R(E;{\vec q}~)H_c(E;{\vec p},{\vec q}~)
G_0(E;p)\Lambda({\vec p},{\vec q}~)G_0(E;q).
\label{Hc_def}
\end{equation}
Including (\ref{Hc_def}) and (\ref{Kc}) in (\ref{Gc_eq}), we have
\begin{eqnarray}
H_c(E;{\vec p},{\vec q}~) = V({\vec p}-{\vec q}~) &-&i\int\ftt{4}{k}
{R(E;{\vec k}~)^2 \over (k^0+E_1-E_{k1}+i\epsilon)(k^0-E_2+E_{k2}-i\epsilon)}
\nonumber\\
&\times& V({\vec p}-{\vec k}~)H_c(E;{\vec k},{\vec q}~).
\nonumber
\end{eqnarray}
Integrating on $k^0$ we obtain
\begin{equation}
H_c(E;{\vec p},{\vec q}~) = V({\vec p}-{\vec q}~) + \int\ftt{3}{k}
{1\over E^* - k^2 /2 \mu } V({\vec p}-{\vec k}~)H_c(E;{\vec k},{\vec q}~),
\label{eqhc2}
\end{equation}
where
$$
E^* \equiv {(E-m_1-m_2)(E-m_1+m_2)(E+m_1-m_2)(E+m_1+m_2) \over 8\mu E^2}.
$$
Equation (\ref{eqhc2}) is nothing else than the Schr\"odinger
equation for the propagator of a non relativistic particle in
an external Coulomb field. Therefore its solution is known.
A way to express it is by means of the Gegenbauer polynomia
$C^\lambda_j$ (for the definition and some properties see \cite{Ter80})
\cite{Sch64}:
\begin{equation}
H_c(E;{\vec p},{\vec q}~) = V({\vec p}-{\vec q}~)
- {16\pi\mu(Z\alpha)^2\gamma \over (p^2+\gamma^2) (q^2+\gamma^2) }
\sum_{j=0}^{\infty}{1\over j+1-\mu Z\alpha/\gamma}
C^1_j\left({\hat\xi}({\vec p}~)\cdot{\hat\eta}({\vec q}~)\right),
\label{hh_eq3}
\end{equation}
where $\gamma\equiv \sqrt{-2\mu E^*}$.
Substituting Eq. (\ref{hh_eq3}) in (\ref{Hc_def}) we obtain the
explicit analytic expression of the Green function corresponding
to the kernel $K_c$ given by (\ref{Kc}).
As we will see, once $G_c$ is given, it is straightforward to work out
the poles $E^c_n$, the residua $R^c_{n...}$ and $\hat G^c_n$.

From (\ref{hh_eq3}) we have immediately that $G_c$ has poles in
\begin{equation}
E^* = -{\mu\over 2}\left({{Z\alpha}\over n}\right)^2 \Rightarrow
E = E^c_n = \sqrt{m_1^2-(\mu{Z\alpha}/n)^2} + \sqrt{m_2^2-(\mu{Z\alpha}/n)^2}
~~~ n\in {\hbox{\s@ l\kern-.5ex N}} .
\label{Enc}
\end{equation}
Notice that up to order $\alpha^2$
$$
E^c_n \approx m_1 + m_2 - {\mu\over 2}\left({{Z\alpha}\over n}\right)^2.
$$
The poles of $G_c$ give back the mass terms plus the Bohr levels,
i. e. the physically correct levels up to order $\alpha^2$.
Moreover we have
$$
E_j(E^c_n) = E^c_n{m_j \over m_1+m_2} \approx m_j
- {m_j \over m_1+m_2}{\mu\over 2}\left({{Z\alpha}\over n}\right)^2.
$$

The residuum at the pole $E = E^c_n$, as defined in (\ref{Gc_pol}), is
\begin{eqnarray}
\sum R^c_{n...}(p,q) &=& {i\over 4\mu}
{E^c_n \over \sqrt{m_1^2-(\mu{Z\alpha}/n)^2}\sqrt{m_2^2-(\mu{Z\alpha}/n)^2}}
R(E^c_n;{\vec p}~)R(E^c_n;{\vec q}~)
\nonumber\\
&\times& \left( p^2+(\mu{Z\alpha}/n)^2 \right)
\left( q^2+(\mu{Z\alpha}/n)^2 \right)
r_n({\vec p},{\vec q}~)
\nonumber\\
&\times& G_0(E^c_n;p)\Lambda({\vec p},{\vec q}~)G_0(E^c_n;q) ,
\label{sumRc}
\end{eqnarray}
where
\begin{equation}
r_n({\vec p},{\vec q}~) \equiv 64\pi n \left(\mu{Z\alpha} \over n\right)^5
{C^1_{n-1}\left({\hat\xi}({\vec p}~)\cdot{\hat\eta}({\vec q}~)\right)
\over \left[p^2 + (\mu{Z\alpha} /n)^2\right]^2
\left[q^2 + (\mu{Z\alpha} /n)^2 \right]^2} = \sum_{l=0}^{n-1}\sum_{m=-l}^{l}
\varphi_{nlm}({\vec p}~) \varphi^*_{nlm}({\vec q}~).
\label{rr_def}
\end{equation}
$\varphi_{nlm}({\vec p}~) \equiv R_{nl}(p)Y_{lm}(\hat p)$ are
the well-known hydrogen atom wave functions \cite{Bet57}.
Moreover, we can write
\begin{eqnarray}
&~&
\left(\Lambda_+({\vec p},m_1){1+\gamma^0 \over 2}
\Lambda_+({\vec q},m_1)\gamma^0\right)^{(1)}
\left(\Lambda_-({\vec q},m_2){1-\gamma^0 \over 2}
\Lambda_-({\vec p},m_2)\gamma^0\right)^{(2)T}  =
\nonumber\\
&~&
\left(\Lambda_+({\vec p},m_1){1+\gamma^0 \over 2}
\Lambda_+({\vec q},m_1)\gamma^0\right)_{\alpha\beta}
\left(\Lambda_-({\vec q},m_2){1-\gamma^0 \over 2}
\Lambda_-({\vec p},m_2)\gamma^0\right)_{\gamma\delta} =
\nonumber\\
&~&
\left( \Lambda_+({\vec p},m_1)       \right)_{\alpha\rho}
\left( {1+\gamma^0 \over 2}  \right)_{\rho\sigma}
\left( \Lambda_+({\vec q},m_1)\gamma^0 \right)_{\sigma\beta}
\left( \Lambda_-({\vec q},m_2)       \right)_{\gamma\nu}
\left( {1-\gamma^0 \over 2}  \right)_{\nu\tau}
\left( \Lambda_-({\vec p},m_2)\gamma^0 \right)_{\tau\delta}
\nonumber\\
&~&
= {1\over 2}\sum_{Ss}
\left(\Lambda_+({\vec p},m_1)\Gamma_{Ss}\Lambda_-({\vec p},m_2)\gamma^0\right)_{\alpha\delta}
\left(\Lambda_-({\vec q},m_2)\Gamma^{\dagger}_{Ss}
\Lambda_+({\vec q},m_1)\gamma^0\right)_{\gamma\beta} ~,
\label{llfie}
\end{eqnarray}
where we have used the Fiertz identity:
$$
\left( {1+\gamma^0 \over 2}  \right)_{\rho\sigma}
\left( {1-\gamma^0 \over 2}  \right)_{\nu\tau} =
{1\over 2}\sum_{Ss} \left( \Gamma^{\dagger}_{Ss} \right)_{\nu\sigma}
\left( \Gamma_{Ss} \right)_{\rho\tau} ~~~ S\in{{0,1}}, ~~~s\in{{-S,...,S}} ~;
$$
with the definitions:
\begin{eqnarray}
\Gamma_{00} &=& {1+\gamma^0 \over 2} \gamma^5, ~~~
\Gamma_{1s}  = i{1+\gamma^0 \over 2}\vec v_s\cdot \vec \gamma ~,
\nonumber\\
\Gamma^{\dagger}_{00} &=& {1-\gamma^0 \over 2} \gamma^5, ~~~
\Gamma^{\dagger}_{1s}  = i{1-\gamma^0 \over 2}\vec v^{~*}_s\cdot \vec \gamma ~,
\nonumber\\
\vec v_0 &=& (0,0,1) ~~~~~~ \vec v_{\pm 1} = -{1\over \sqrt{2}}(\pm 1,i,0) ~.
\nonumber
\end{eqnarray}
Eqs. (\ref{rr_def}) and (\ref{llfie}) allow to identify the quantum numbers
${n...}$ with the principal quantum number $n$, with
the numbers $S,s$ describing the spin of the bound state and
with the numbers $l,m$ describing the angular momentum.
The corresponding states $R^c_{nlmSs}$ are
\begin{eqnarray}
\left( R^c_{nlmSs}(p,q) \right)_{\alpha\beta\gamma\delta}
&=& {i\over 2\mu}
{E^c_n \over \sqrt{m_1^2-(\mu{Z\alpha}/n)^2}\sqrt{m_2^2-(\mu{Z\alpha}/n)^2}}
R(E^c_n;{\vec p}~)R(E^c_n;{\vec q}~)
\nonumber\\
&\times&
\left( { E_{p1}E_{p2}E_{q1}E_{q2} \over
(E_{p1}+m_1)(E_{p2}+m_2)(E_{q1}+m_1)(E_{q2}+m_2) }\right)^{1\over 2}
\nonumber\\
&\times&
{\left( p^2+(\mu{Z\alpha}/n)^2 \right)
\over (p^0+E_1(E^c_n)-E_{p1}+i\epsilon)(p^0-E_2(E^c_n)+E_{p2}-i\epsilon)}
\nonumber\\
&\times&
{\left( q^2+(\mu{Z\alpha}/n)^2 \right)
\over (q^0+E_1(E^c_n)-E_{q1}+i\epsilon)(q^0-E_2(E^c_n)+E_{q2}-i\epsilon)}
\nonumber\\
&\times&
\varphi_{nlm}({\vec p}~) \varphi^*_{nlm}({\vec q}~)
\nonumber\\
&\times&
\left(\Lambda_+({\vec p},m_1)\Gamma_{Ss}\Lambda_-({\vec p},m_2)\gamma^0\right)_{\alpha\delta}
\left(\Lambda_-({\vec q},m_2)\Gamma^{\dagger}_{Ss}\Lambda_+({\vec q},m_1)\gamma^0\right)_{\gamma\beta}.
\label{Rc}
\end{eqnarray}
These states are not degenerate (how it is possible to verify directly by
calculating $D_{nlmSs}$). Sometimes in the literature the residua
at the poles of the Green function are written as
$$
\left( R^c_{nlmSs}(p,q) \right)_{\alpha\beta\gamma\delta}
 = \left( \psi^c_{nlmSs} (p) \right)_{\alpha\delta}
   \left( \overline{\psi}^c_{nlmSs} (q) \right)_{\gamma\beta};
$$
the functions $\psi^c_{nlmSs}$ and $\overline{\psi}^c_{nlmSs}$
are called the BR wave functions of the bound state:
\begin{eqnarray}
\left( \psi^c_{nlmSs}(p) \right)_{\alpha\delta}
&=& \left( {i\over 2\mu}
{E^c_n \over \sqrt{m_1^2-(\mu{Z\alpha}/n)^2}
\sqrt{m_2^2-(\mu{Z\alpha}/n)^2}} \right)^{1\over 2}
R(E^c_n;{\vec p}~)
\nonumber\\
&\times&
\left( { E_{p1}E_{p2} \over
(E_{p1}+m_1)(E_{p2}+m_2)}\right)^{1\over 2}
\nonumber\\
&\times&
{\left( p^2+(\mu{Z\alpha}/n)^2 \right)
\over (p^0+E_1(E^c_n)-E_{p1}+i\epsilon)(p^0-E_2(E^c_n)+E_{p2}-i\epsilon)}
\nonumber\\
&\times&
\varphi_{nlm}({\vec p}~)
\left(\Lambda_+({\vec p},m_1)\Gamma_{Ss}\Lambda_-({\vec p},m_2)\gamma^0\right)_{\alpha\delta} ~,
\label{psic}\\
\overline{\psi}^c_{nlmSs} &=& \gamma^0 \left( \psi^c_{nlmSs} \right) ^{\dagger}
\gamma^0 ~.
\label{psicbar}
\end{eqnarray}
Actually there are no reasons to introduce
the bound state wave functions: from the formalism developed in the
previous section it is clear that all the physical quantities
can be expressed in terms of residua.

Finally, we obtain $\hat G^c_n$ subtracting from $G_c$ the
singular part:
\begin{eqnarray}
\hat G^c_n(E^c_n;p,q) &=& (2\pi)^4\delta^{4}(p-q)G_0(E^c_n;p) +
G_0(E^c_n;p)K_c(E^c_n;{\vec p},{\vec q}~)G_0(E^c_n;q)
\nonumber\\
&+& \hat H_c(E^c_n;p,q) ,
\label{hatGc}
\end{eqnarray}
where $\hat H_c$ takes into account all the contributions non singular
in $E = E^c_n$ which come from the second term in (\ref{hh_eq3}).
For an explicit expression of $\hat H_c$ in the positronium
case we refer the reader to \cite{Buc80b}.

\section{Conclusions}

From the above given expressions we can recover some interesting
limiting cases.

Putting $Z=1$ and $m_1 =m_2 \equiv m$ ($\mu = m / 2$ and
$E_1 = E_2 = E /2$) the above given zeroth-order solution of the BS equation
reduces to the original BR solution given in \cite{Bar78} for positronium.
The main difference with the muonium case is that for positronium
also annihilation graphs contribute to the interaction
kernel $K$. In the literature the singlet state ($S =0$) is usually referred
as {\it parapositronium} and the triplet state ($S =1$) as
{\it orthopositronium}. Some applications can be found in
\cite{Vaibo,Buc80b,Buc80a,Hil89,Vaied}.

Taking the limit of one particle mass to infinity the case of a particle
in an external Coulomb field is recovered.
In this case (e. g. $m_2 \rightarrow \infty$ ) $\mu = m_1 \equiv m$,
the difference ~$E_2-m_2$ ~is finite and the bound state energy $E$
is given by
$$
E = {\lim_{m_2 \rightarrow \infty}} (E_1+E_2-m_2).
$$
This case has been extensively studied in \cite{Cav94,Vaibo,Rem84}
for the evaluation of the pure radiative corrections to the
energy levels of hydrogenic atoms.

As a conclusive remark, we stress that all these systems
and muonium can be studied now in the same framework.
In particular the formalism provides a powerful tool in dealing
simultaneously with radiative, recoil and radiative-recoil corrections.
Extremely interesting seems also to be the study of the infinit mass limit
of one particle in the energy expansion (\ref{energy}) evaluated on
muonium states. This should eventually clarify how this limit works
in a purely off mass-shell context.

redpajama_set_name: RedPajamaArXiv


We had an indoor plan, but we lucked out with a dry day for Kendra's senior session - Yaaaay!
I love a good "urban" shoot. There's something seriously fun about discovering all of the spots of color and texture that always seem to be hiding around the next corner (or down the next smelly alleyway).
Kendra - thanks for being up for anything and for being so much fun!


text:
West Hills Mall not cause of Weija-Gbawe floods – Management
Wed, 14 Oct 2020 Source: Spike Consult
The attention of the Management of West Hills Mall has been drawn to a comment in the media (purported to have been made by the Honourable MP for the Weija-Gbawe Constituency, Madam Tina Naa Ayeley Mensah), suggesting that the incidence of flooding in parts of her constituency is the result of the construction of West Hills Mall.
Although the claim is spurious and was obviously made without reference to the topography and flood history of the area, we feel obliged to react to correct the erroneous impression the Honourable MP's comments might have created among uninformed members of the public.
The point must be made in no uncertain terms, that the Old Barrier/Atala stretch of the Accra- Winneba highway (which lies more than one kilometre away from Dunkonah where West Hills Mall is located) is a low-lying platform and has for many years always suffered flooding. Early residents of the area would confirm that as far back as in the 1990s' and even before the string of private developments, including ATALA, sprung up along the route, this stretch had been prone to flooding. As always, the degree of flooding depended on the intensity and duration of the rains.
In 2009/10, when the idea of building a shopping mall was conceived, the Developers took account of two key issues which had to be addressed as integral aspects of the project design: One was to ensure that the flow of traffic to the mall was independent of the run of traffic on the Accra Winneba highway and that driving into and out of the mall did not impose any conflict or interruptions to traffic flow on the highway. A thorough traffic impact assessment (TIA) was conducted by a joint team of experts comprising the Developer and the Ghana Highway Authority, resulting in the commitment of an enormous amount of resources and engineering to build what is now the West Hills Mall Interchange.
This reference becomes relevant here because immediately the mall was completed, certain individuals who commuted to Kasoa and beyond on a daily basis, frantically sought to blame the near proverbial rush-hour traffic generated by the Weija Toll Booth along the Kasoa road, on the construction of the mall.
The other issue of concern to the Developer was drainage, being fully aware of what happens whenever there is a heavy downpour one kilometre away on the Accra-bound track of the highway. The topography of the Dunkonah area was critically studied. The area, as residents may remember, experienced minimum flooding, but the Developer took no chances; two existing drains (one at the SCC traffic light and the other behind the building which now houses Melcom) were expanded and a new Storm Drain built to contain all run-off rainwater from the entire mall area. This storm drain is connected to the already existing drain behind the Melcom Building and to the relief of residents, has, since 2014, changed the story of flooding in that part of Dunkonah and the immediate environs of West Hills Mall. Needless to mention that engineering designs used by the Developer for neutralising the contingency of flooding in the Dunkonah area were all vetted, approved and the works duly inspected by authorized state agencies.
Whiles we are full of admiration for the Honourable MPs zeal to do something about the problem of flooding in her constituency, we would advise that she relies on the result of a proper technical study which takes full account of the natural topography of the area, the impact of the string of new private developments along the highway and the suitability or otherwise, of existing drainage systems (if any at all) in that area. It would do nobody any good if we shied away from the fact that the low-lying nature of the area in question (Old Barrier area) and the poor drainage system there, was simply too fragile for the intensive overnight rains of October 8th and 9th and the all- day-long rains the community experienced on October 10th.
West Hills Mall
Source: Spike Consult


"Sparky" at Amelia Island in early March with 16″ 928 wheels.
The information on how to tell the tire size is very helpful, especially when combined with speed ratings. One size number that they don't put on the tire is the overall diameter of the tire. The article mentions Tire Rack, and I have them bookmarked as I go there often. Diameter is a handy thing to know. For example, our 924S – Sparky – had 16″ Porsche 928 wheels on it until after the Amelia Island shows, where I discovered that the inside rear tires were both slightly hitting the inside wheel well on compression. I switched back to the original 15″ phone dials that had fairly new tires until I can sort out the 16″ dilemma. (I really like the look of those wheels.) So just to see what I was getting into, I checked Tire Rack for the overall diameters of the tires – the 15″ were all 215/65 – 15's, and a check on Tire Rack told me that the diameter was 25.9″ tall. My 16″ tires were 24.9″ tall, so the car was 1/2″ taller with the 15's on it. Not that you would actually notice, but…a half inch is a half inch.
When putting either the 928 wheels or the Design 90 (D90) 16″ wheels on a 924S, we typically stagger front to rear. I go with 7″ fronts and 8″ rears. Therefore, the tire width is different front to rear, and when your tires are directional, that means that you cannot rotate the tires. Most will see that the tire on the front is a 205/55-16, and the rear is a 225/50-16 – and both are the same diameter of 24.9″. So the car will ride somewhat level on the same diameter tires, although the fronts and rears are different widths.
With all that said, the other thing to look for is mentioned at the end of the article – the date of manufacture. When you go fishing in the used market, you find cars that will have what looks like great tires, but how old are they? At the Nort Northam Collection, we recently picked up a nice, low-miles 1999 Boxster. The tires had little wear on them, but a check of the date showed that the rear tires were new in 2010, but the fronts were new in 2003. Since the car was going to be used for some spirited mountain driving and some auto crossing, replacement was indicated, even though they looked to be okay. Time is not kind to tires, and having a tire come apart on you on the road isn't a pleasant experience.
245/35-15 Hoosiers. Treadwear rating? 00.
Tire treadwear rating – a number between "0" and "600" – indicates to us how "sticky" a tire will be against the road. The lower the number, the better the grip. However, lower numbers wear out faster, and that is indicated by the treadwear rating when compared to the warranty. An eighty-four month warranty tire will carry a treadwear number somewhere north of 500, meaning that it is made out of plastic, not rubber. It will last a long time, but possibly not handle like you would want. On the other hand, a treadwear rating of 200 will give you great grip, but you will be looking for rear tires at about 10-12,000 miles. (Don't ask me how I know this.) DOT race tires carry treadwear ratings of as low as "0" and as high as "40." Not great for wear, but really sticky.
So that is our take on tires, selection, and decision-making. Check the date of manufacture on your tires and don't get into a situation where you find out that you are on tires that were made before you got out of grammar school.
My 1988 924S Special Edition on the trailer to go to its new home, wearing D90 16″ wheels – 7's on the front, 8's on the back. They didn't hit the inner fenders on the rear, and we will figure out why really soon! I like the look of the 16″ wheels on a 924S!


text:
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{
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+ (void)setError:(NSError **)errorPtr withError:(NSError *)error
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redpajama_set_name: RedPajamaGithub


text:
In a sudden turnaround, it's reported Roma have beaten Juventus to the signing of FC Dallas defender Bryan Reynolds.
The Giallorossi had been the first to chase him down several weeks ago, then Juve emerged as the favourites, sending him on loan to Benevento first.
They had to take this step, because the Bianconeri have already filled their non-EU slots.
However, there were delays in getting the deal done and FC Dallas were more inclined to work with Roma than Juventus.
According to Il Tempo reporter Filippo Biafora this evening, Roma have turned the situation on its head and agreed a loan with obligation to buy at the end of the season.
It's believed the Giallorossi offered immediate playing time in Serie A as well as an improved contract.
Lazio and Parma are eager to bring Juventus defender Daniele Rugani back to Serie A, midway through his loan with Stade Rennais.
The 26-year-old was sent to France on loan in October after struggling for playing time in Turin.
His situation hasn't really improved their either, with just two competitive games for the club, largely due to thigh issues.
According to Sportitalia, Lazio and Parma have asked Juve about picking up Rugani in the January transfer window for the remaining six months of that loan.
Lazio are seeking a defender after news Luiz Felipe would be out until March following ankle surgery.
Parma are also looking towards Roma's Federico Fazio, but are put off by his wages.
Arkadiusz Milik might finally be on his way to Olympique Marseille after Napoli agreed to drop legal action against the striker.
That was the obstacle holding up both this transfer and the one in September towards Roma.
According to Sportitalia and Sky Sport Italia, that has now been resolved, because Napoli accepted they were in a no-win situation with his contract due to expire in June.
Milik needs to sign a new contract with Napoli before he can be allowed to join Marseille on loan with obligation to buy.
The club had outstanding issues with the Poland international, specifically suing him – and all the players who took part in the 'mutiny' that sparked Carlo Ancelotti's dismissal – for image rights and docking their wages.
Marseille are expected to pay €9m plus €4m in add-ons and a 20 per cent sell-on clause included in the agreement.
It's reported Roma have fired team manager Gianluca Gombar and Global Sport Officer Manolo Zubiria after the embarrassing substitution error.
They didn't read the rules correctly for the Coppa Italia and made a sixth substitution during extra time in their 4-2 defeat to Spezia.
Only five changes were allowed, the regulation stated that an extra 'slot' was allowed in extra time to make changes, but not an extra substitution.
The five substitutions in 90 minutes can be made in three 'slots' to ensure time isn't wasted.
Because of the howler, Roma would've been eliminated from the Coppa Italia even if they hadn't lost on the field.
This isn't even the first time this season that Roma have been penalised for not sticking by the rules, as they already had a 3-0 defeat given to them by default against Hellas Verona for fielding Amadou Diawara when he was ineligible.
Spezia had a private meeting with Pope Francis in the Vatican today and he congratulated them for the Coppa Italia win against Roma.
The club will remain in Rome for the next few days, as they will face Roma again in Serie A this weekend.
So they took the opportunity to visit Pope Francis at the Vatican and he was given his own Spezia jersey.
"First of all, congratulations, because you did so well yesterday," His Holiness told the players.
"In Argentina, we dance the tango, and the tango is the 4-2 music. You won 4-2, so that's good. Congratulations and courage!
"And thank you for visiting me, because I love to see the efforts of young people in sport. Sport is a marvellous thing, it brings out all the best we have in ourselves.
"Continue like this, because it brings you to a great nobility. Thank you for your efforts."
Complimenti e coraggio!
Con queste parole, @Pontifex_it ha accolto lo #SpeziaCalcio al gran completo, ricevuto questa mattina in udienza privata nelle stanze vaticane
https://t.co/saNErz4HU4 pic.twitter.com/87Rc8jLXWZ
— Spezia Calcio (@acspezia) January 20, 2021


Nathan Grimoulas is a Greek-Australian Stage Manager who has worked in several industries within arts and entertainment, now working and exploring his passion within circus. Originally studying Sound Engineering at JMC Academy and always maintaining the view that one doesn't need to go to university or private school to be good at something he has grown to challenge himself and others on all fronts.
Global Citizen and forever a student at the School of Life (so lame, so great) he spends most of his time lost in critical thought, at the gym and eating.
Nathan sees the Stage Manager as one who should make life easier for everyone, a facilitator for the manifestation of the dreams and passions of the thousands of creative individuals that surround us. He is contributing to TAL to share his sometimes alternative views on ambition, materialism, society and self-development to further enrich the diversity of information available to those in and out of the creative industry.


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