Regardless of your bug issue-- be termites, cockroaches, or rodents-- no one enjoys the sight of a pest scooting across their walls and hallways. After all, lots of pests are known to provide a variety of health dangers, with some even understood for bring illness into your house. Sadly, when you identify one pest that frequently indicates there are numerous them concealing somewhere and ready to further infest your house. When this happens, you'll want to deal with the best pest control operator around to secure your property.
When the bed bugs remain in your house, they'll be going from 1 place to another. Bed bugs are intrusive insects Centerburg, OH that might be tough to spot. They are best treated by an experienced expert.
Bed bugs are rather more resistant and resistant than each insect, consisting of rats and cockroaches in Centerburg, OH . Unless a bed bug was identified, the first sign of an problem is typically the presence of skin inflammation. Once bed bugs have actually invaded your home, they can be somewhat hard to get rid of. They can be harder to deal with than other home insect insects for a couple of reasons. Because they are hard to see, utilize a magnifying glass. They don't stay on the human that they are feeding on and so they will normally conceal in clothes and attempt to get to a brand-new location. They are unable to endure heats, making heat a highly effective treatment method .
Charge of bed bugs can take some time and numerous follow-up treatments. Overall control takes a thoroughly planned and developed integrated strategy. Bed bug control does not have to be expensive Centerburg, OH .
You will have to know the signals of a insect problem. An invasion is something which can occur to any person Centerburg, OH . As an example, be particular to take a look at where you need to take care of your bed bug infestation. If you're concerned you own a bed bug infestation, begin trying to find physical indicators of their presence. Bed bug invasions can impact a single bed in 1 room or a entire house or home. Chemical techniques aren't the only method to control bed bug invasions.
Ways To Get Going with Bed Bugs Exterminator or Pest Control Expert Centerburg, OH ?
Generally, experienced bug control service will employ a couple of choices of treatment approaches like vacuuming, cleansing, steaming and other mechanical methods to completely get rid of the bed bug problem. There are a number of pest control business that may help you for the exact very same. Typically speaking, most excellent insect control companies will initially send down a specialist to run a visual evaluation of your house before estimating you a rate Centerburg, OH .
If you're not needed to leave your home for more than a few hours during the extermination, or in case you are getting ready for the pest control specialist, there are a number of approaches to prevent taking bed bugs with you. As soon as you have the ability to observe that bed bugs have actually undoubtedly entered your home, it's not ever prematurely to attempt and locate an exceptional bed bugs pest control man Centerburg, OH Centerburg, OH . During a fumigation, your home will be dealt with in tarpaulin, which is usually anchored utilizing big containers of water you should supply. Whether a full home is plagued, it might be needed to spray listed below the home, which would increase the overall price tag of services. Your home does not have to be plagued that you get bed bugs. Try to bear in mind that DIY insecticides alone are not likely to rid your home of bed bugs, particularly items which do not keep eliminating after they dry.


text:
Cartel claims against surgeons to be investigated
By Julia Medew
Updated November 4, 2016 — 1.39pm first published at 12.32pm
Concerns about potential cartel behaviour among Australian surgeons has been referred to the Australian Health Ministers' Advisory Council for further investigation.
In September, Fairfax Media revealed claims that overseas-trained surgeons were facing anti-competitive behaviour that reached into the Royal Australasian College of Surgeons - a powerful group that largely controls the supply of surgeons in Australia and, allegedly, the level of competition and fees they can charge.
NSW Health Minister Jillian Skinner said after discussing the issue at the Council of Australian Governments' meeting of health ministers last month, concerns about unprofessional behaviour had been referred to the ministers' advisory council.
The council is made up of state and territory health department secretaries and chief executives, and it has a Victorian-based committee that works on workforce issues, including ideas for strategic reform.
An American surgeon who says he was bullied, harassed and discriminated against when he tried to have his skills recognised in Australia. Credit:Brian Cassey
Fairfax Media understands all health ministers at the COAG meeting were worried about the potential for surgeons to be protecting their lucrative private markets.
Last year, a report commissioned by the college of surgeons said commercial gain and protection of market share was driving bad behaviour among surgeons, and that conflicts of interest were potentially compromising the assessment of overseas-trained doctors and preventing fair complaints management.
The college recently denied claims it was implicated in any anti-competitive behaviour, saying patient safety was its only consideration when deciding who practises surgery in Australia.
In September, two former chiefs of the Australian Competition and Consumer Commission said governments had been too fearful of powerful medical lobby groups in the past, and that they needed to investigate the college of surgeons for potentially restricting the supply of surgeons to Australia.
"Governments have been reluctant to take strong action because of a fear of the surgeons' lobby and because of some ill-advised concerns that the more surgeons, the more operations, and the more costs to government," said Professor Allan Fels, chairman of the ACCC during the 1990s.
Professor Graeme Samuel, head of the ACCC during the 2000s, said medical colleges were "closed shops", and that health ministers needed to open them up to more scrutiny to create a transparent competitive market for patients.
Julia Medew
Julia Medew is Health Editor at The Age.

redpajama_set_name: RedPajamaCommonCrawl


Puttin: The puttin is a small pullout on the left side of 178 heading north just passed Camp McCall. Follow the trail leading from the pullout until you see the gorge of Reedy Cove Creek. From there bushwack down to the rivers edge.
Takeout: This site has some info on how to get to the Falls/Takeout.
The trail to above the waterfall is on river left of the creek before you get to twin falls at a point when the trail is close to the creek, cross the creek an head up hill to the top. This trail continues alongside the creek for most of the way up to camp McCall.
I have not run all of the creek just from the slide above Twin Falls down. I am also fairly sure that no one has run this creek.
10 or so slides that run on for about 100 yds, a no brainer and a lot of fun. Just watch out for the low hanging rhododendron. Directly below this is a good sized pool take out at this pool.
Don't run it! The portage trail is on river left and is fairly steep.


Situated between River Valley and Orchard Road, Lloyd Sixty Five is ideally placed; and above all, a smart, high end residential development.
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2+ Study (with Loft, Powder Room and Private Lift) 1808/ 1819 SF, and comes with/ without Interior Design unit.
Contact Rain hp: 86117777 by SMS/ WhatsApp/ Call to appreciate this rare and beautiful project!


We use the latest technology in CNC machining to maximize efficiency and keep your costs within budget. We have 40 and 50 taper vertical and horizontal machine tools with capacity up to 126" in X-Axis Travel, 95" in Y-Axis Travel, and 35" in Z-Axis Travel. See our facilities list to learn more.


Pastor Monametsi Bahudi in Gabarone, Botswana recently shared with us what has become a familiar story that I often hear in my travels.
"It's a joy to close 2017 with a report of a sinner that turned from sin and self to Christ. Pako is 24 years old, a graduate of University of Botswana with a combined major in Environmental Science and Sociology. His parents, especially his mother, are staunch members of a Zionist church. She has insisted that all her children should attend her church. When Pako was a teenager he began to resent the church and questioned many of their practices. He did not know the truth himself, but he increasingly questioned the church's practices and teachings.
One of his friends who attended another church asked him to watch a sermon on YouTube which could answer some of his questions. The sermon was by Pastor Paul Washer, the "Shocking Youth Message." He watched it and agreed with many points in the sermon. He began to follow Mr. Washer on both Sermon Audio and YouTube. He desired to know more about Mr. Washer's preaching and he went to the HeartCry website. He looked through the website and discovered that HeartCry was supporting a missionary in Botswana. He tracked us down and found us last October.
His parents had been worried about him and did not want him missing church. He began attending our Bible studies and I set up a meeting with him. I took him out for coffee, where we studied the Bible together and I shared the gospel with him. He told me a week later that he is now a believer. He sent me a text, "Pastor, I now know that I am a Christian. Can you meet my parents to share the gospel with them too?" I have assigned him to Brother Kenosi for discipleship."
Please pray for Pako's spiritual growth and the salvation of his parents, as well as for Pastor Bahudi and the church in Gabarone as they share the gospel with others like Pako.


Many artists have created albums around an idea, called "concept albums". The Antlers, an indie-rock group from Brooklyn, New York, created an incredible concept album in 2009. Hospice, The Antlers's third studio album, features the story of a husband and wife – but the wife is terminally ill with bone cancer. Their relationship slowly spirals downward throughout the album, as she begins to be overcome by her fears and the disease. Peter Silberman, the lead singer, has described the album as the story of an emotionally abusive relationship, as told via the analogy of a hospice worker and a terminally ill cancer patient.
The opening track, Prologue, is an instrumental song with wavering notes and haunting melodies. Kettering, the next track, shows off Silberman's falsetto with lyrics about how Sylvia rejects any form of kindness, as shown through the lyrics, "When I was checking vitals, I suggested a smile/you didn't talk for a while, you were freezing". There is foreshadowing when Silberman sings, "I didn't believe them when they told me there was no saving you" as the last line in the song. Sylvia is a song about Sylvia being uncooperative, even suicidal, and the hospice worker's heartbreaking consent that allows her to continue abusing him. Atrophy, a song as well as the word for "the partial wasting away of the body", discusses how the worker struggles with wanting to take away some of Sylvia's pain as well as being unhealthily attached to her. Bear, the next song, is not wrapped into the hospice worker/Sylvia metaphor, but instead talks about Silberman and his girlfriend, and the pregnancy/abortion that further tore them apart. The abortion weakens their relationship, as evidenced in the line "when we get home, we're bigger strangers than we ever were before". Thirteen is the track that splits the first half from the darker half of the album, where the relationship begins to go even farther downhill and both relationships and people begin to die. Two, the next song, is about the emotionally abusive and destructive behaviors of both people involved in the relationship. In this song, the metaphorical doctor (in the "version" of Silberman and his girlfriend's relationship, it is his voice of reason) telling him that there is no saving Sylvia and she will die soon. Shiva, the third to last song, describes the moment when Sylvia dies and the worker's grief over it. The word "shiva" also comes from a Jewish tradition involving the mourning process of seven days, which keeps with the theme of her death. Wake also fits with the theme of "death"-involved words and mourning-words, and in the first half of the song, it's the narrator speaking to a friend and apologizing, and in the second half, the narrator is speaking to himself (or anyone), according to Silberman. The final track, Epilogue, is the track that causes it to come full-circle. In the chorus, "You're screaming/and cursing/and angry/and hurting me/and then smiling/and crying/apologizing" shows how (in the relationship meaning) Silberman's girlfriend is trying to get back together after the breakup. It also discusses how he sees Sylvia (in the hospital metaphor) in his nightmares and he's afraid.
I was first introduced to the Antlers by my older brother, a few years ago. His friends then proceeded to ask him why he would "ruin my life" by letting me listen to something as absolutely heartbreaking as Hospice. I do love the album, and it is clear to see that Silberman and his co-musicians are extremely talented, it is terribly sad.
I would rate this, overall, a 8/10.


Aerospace Floor Panels Market Share « Global Market Insights, Inc.
Rapidly increasing air traffic resulting from worldwide expansion of the aviation sector has propelled the aerospace floor panels market with key manufactures speeding up the production of commercial aircrafts. Constituting a major portion of any aircraft's weight, floor panels need to be light for reducing the overall mass and also should be durable to tolerate the brunt of thousands of passengers or tons of cargo load over a period of time. The introduction of efficient materials and designs to manufacture lightweight panels and structures has supplemented cost savings for airlines along with meeting stringent norms mandated by aviation authorities. As such, the aerospace floor panels market has hugely transformed due to consistent focus on enhancing the quality of panels, which form an integral component of the all-round safety within the aircraft.
Speaking of efficient panels, a prominent design that has critically altered the aerospace floor panels industry is the honeycomb sandwich assembly, which has allowed the production of lighter and highly durable floor paneling. Applicable in a variety of segments such as railways, marine, construction and energy, the honeycomb sandwich design offers exceptional strength-to-weight ratio and panels can be modified according to the type of use. In terms of improving interior aesthetics of an aircraft, the surfaces of these panels can be customized depending on the face sheet material. With the use of high-quality honeycomb sandwich panels to ensure a strong floor base, the global aerospace floor panels market surpassed a revenue of USD 174 million in 2017. Aluminium honeycomb panels, in particular, are increasingly being utilized in aircraft production and demand for these panels is expected to rise steadily over the next few years.
In terms of feasibility, Aluminium offers remarkable strength-to-weight properties to floor panel designers along with flexibility and considerably low processing cost, as compared to other robust materials like Titanium. Other notable features of Aluminium are corrosion resistance, easy to machine and cut as per required specifications and the ability to enhance the durability of structural components. Since the alloy is also described as being almost 90% recyclable, Aluminium honeycomb sandwich panels are expected to become immensely popular in the aerospace floor panels market. Major aircraft manufacturers are already treading in the direction of adopting aluminium honeycomb cores in flooring to reduce the structural weight and cost of production. Interesting predictions regarding growth of the aircraft segment has evidently spurred the development of the aerospace floor panels industry.
Recently, the American multinational airplane maker Boeing released a statement in which it mentioned that the aircraft industry has been witnessing a prolific growth trend over the past eight years. The company also revealed certain estimates, according to which the global demand for new passenger jets will reach approx. 42,730 by 2037. The total value of these new planes is projected to be around USD 6.3 trillion, indicating the massive earning potential of the aerospace floor panels market from new aircraft production. Boeing attributes the growing demand to the continuous economic growth worldwide and the rising consumer spending, especially by the working middle class population. Expansion of the tourism sector has additionally boosted air traffic in emerging economies, strengthening the aerospace floor panels industry stance.
Besides the passenger segment, use of cargo planes for transporting heavy commercial or military equipment and to undertake product delivery between multiple countries has grown tremendously due to progressive pricing trends. As a result, not only new cargo-carrying aircrafts are being made but old and new commercial jet builds are also being converted to freight planes, signifying a lucrative emerging avenue for the aerospace floor panels market. For instance, Dresden-based Elbe Flugzeugwerke (EFW), a joint venture between Airbus and Singapore Technologies (ST) Engineering's Aerospace arm, is involved with converting passenger jet to freight aircrafts. In August 2018, EFW delivered an Airbus A330-200 Passenger-to-Freighter converted plane to EgyptAir Cargo, while reports indicate that EFW has further contracts in the pipeline to convert ten A321-200s for lessor Vallair.
As cargo freighters need to be light for traversing large distances with heavy loads, sturdy flooring and lighter frame is essential for guaranteeing safe transportation and better fuel-efficiency. With projects like EFW, production of floor panels suitable for commercial logistics will see tremendous increase and substantially bolster the aerospace floor panels industry. Anticipated to register a 4% CAGR from 2018 to 2024, the aerospace floor panels market is spearheaded by companies like EFW, The Gill Corp., Rockwell Collins, Zodiac Aerospace, Nordam Group, Euro Composites and Avcorp Corporation.
This entry was posted in Automotive & Transportation and tagged Aerospace Floor Panels Market, Aerospace Floor Panels Market Analysis, Aerospace Floor Panels Market Research, Aerospace Floor Panels Market Share, Aerospace Floor Panels Market Size, Aftermarket, Aircraft, Aluminum Honeycomb, Business Jet, Commercial Aircraft, Distribution Channel, Helicopter, Nomex Honeycomb, OEM, Raw Material, Regional Jet.


If you're carefree and classically cool (the type we all want to be, honestly), chances are you've considered a pixie haircut. And we say: Take the plunge, because we can't think of anything chicer than a properly sculpted short haircut. Here's a roundup of the ten best ways to rock this resurged trend and show off that bone structure your mama gave ya.


I have entered the realm of stop motion animation! After a rare critique in 2012, I showed artist Brad Biancardi my rope drawings and he suggested I utilize my photography and drawing skills to make some video work. Pretty good idea.
In graduate school, I worked with photography AND cinema students, so many of my artist friends are filmmakers. I always marveled at my friend's work, especially their stop motion animation pieces. Check out my friend Aygul's work and Kate's work. I really admire Aygul and Kate. I expect big things to come from them.
I also decided to check out what the Internetz has to say about stop motion and found this.
If short on time, I recommend the chess stop motion video (very good), Human Tetris (a crowd pleasure but obviously took a lot of coordination), and Sia's Breathe Me video.


READERS' PICK: Walking into Frank's is a ticket to a down-home breakfast with down-home service with a smile. This greasy spoon gets a unanimous thumbs up for its reliable comfort food: omelets, hotcakes, home fries and the strongest coffee mere glass can hold (ask for the special "Double Blend"). You might have to wait for a table, as the dining area is so cozy every table feels like it's right in the kitchen. The sizzle of the grill has been known to interrupt many a glazed-eye morning conversation. Dining at Frank's is one of life's simple pleasures: good food, good company, cash only.
READERS' POLL RUNNER-UP: Millie's Pancake Haus, 7053 N Oracle Road; 6530 E. Tanque Verde Road. If you guessed that a restaurant with "haus" in the name would have cute patterned wallpaper, natural wood finishes and, er, adorable stuffed sheep, perhaps you've been to Millie's. If so, you have also dined on pancake recipes from around the globe: potato pancakes, Russian blintzes, Swedish pancakes, and of course, old-fashioned buttermilk pancakes, all lovingly prepared and served in tandem with a traditional contingent of eggs, bacon and sausages. Enjoy a pancake of distinct national origin every day of the week. Millie is in the haus!
MORE MANIA: Marlene's Hungry Fox, 4637 E. Broadway Blvd. If you believe in the beauty, even magic, of a true country breakfast, live out your gluttonous fantasies at the family-owned Marlene's. In this land of tiny foxes, where biscuits float in white gravy and French toast glitters in maple syrup, all your dreams of double-yolked eggs and frosted cinnamon buns will come true. These platters are so laden down with good things, they're delivered to your booth on a rolling cart.
MORE MANIA: The Garland Restaurant, 119 E. Speedway Blvd. Like any breakfast place, The Garland features a good selection of the standard egg-toast-bacon breakfast fare. What sets them apart, however, are their ethnic-influenced and vegetarian breakfast creations. Many feature eggs, vegetables, cheeses and sauces in tantalizing combinations and hearty portions. One of our personal favorites is the fresh-fruit crepe, served with orange yogurt sauce and the Garland's homemade whipped cream.


Mimecast knows email security and the nasty things that lurk behind the surface better than most. With more than 24,900 customers, the company concentrates on providing cloud security, archiving and continuity services for 24,900 customers.
SecurityBrief talked to Dave Hood, Mimecast's director of product marketing. His mission is to help organisations become more cyber resilient, particularly across Office 365, Continuity and the Mimecast API.
The company recently conducted a study called the Email Security Risk Assessment (ESRA), which showed that everything from spam, dangerous file types, malware and impersonation attacks are making it through organisations' own security and email providers.
"Some take a set and forget approach to email and only make changes need to be made such as a migration or there is a catalyst event like a security breach or service disruption. Our research shows that if organisations aren't using next generation email security solutions and reviewing their defences then they are vulnerable," he says.
Why are email security breaches still happening?
"First, it's important to recognise that email is the number one way that organisations are being attacked. 9 in 10 hacks begin with email, because it's a communication channel that employees use all the time and trust. Hackers exploit that trust with sophisticated attacks," Hood says.
Echoing the calls of many security expert, he says that legacy technologies like antivirus and antispam will no longer work anymore because the threats are evolving – and fast.
"Organisations need to deploy protection against payload-based attacks such as malicious links and attachments, and impersonation attacks that do not have a malicious payload but are instead trying to create an action such as a fraudulent wire transfer," he says.
It's not just attacks from outside the organisation that are worrying, as Hood says that internal threats can come from compromised or malicious insiders.
Hood says that email from internal users can show lateral threat movement, whether it be malware, URLs or impersonation emails, throughout the organisation.
"The bottom line is, internally generated email, whether staying inside or going out, needs to be part of every organisation's threat detection and cyber resilience strategy," he says.
Why - and where - are IT professionals lacking?
But one single ESRA study is not enough. To take testing even further, Mimecast teamed with Vanson Bourne and found that while IT departments are wary of malicious URLs or emails, they are still left vulnerable.
The studies showed that IT professionals were surprised at how poor their email security is, and Hood says that it's not only a case of the 'she'll be right' ignorance, it's also about insufficient training that doesn't occur often enough.
"Traditional annual training may give a false sense of security that employees will be able to spot attacks, but the truth is that these attacks are well crafted to get past even the most vigilant employee," he says.
Hood says that modern email security technologies need to be able to rewrite links before the email even lands in an employee's inbox. This provides protection across all devices and all locations.
"Secondly, at the time of click, whether that is one minute after the email is received, an hour after the email is received or five years later when the email has been archived, the link must be checked in real-time. Checking a block list is not enough as many targeted attacks use malicious websites that were previously unknown," he says.
The final piece in the puzzle is what Hood calls the 'human firewall' at the organisation. Whether administrators use tools to identify those who need more training, or employees take it on themselves, it is all about identifying risky emails and links.
The company built its own Internal Email Protect service to help deal with email threats, and unlike other vendors, Mimecast brings together security, continuity and data replication capabilities.
Internal Email Protect can prevent email-borne attacks, make sure that employees have access to email during attacks, and store data in third-party archives to make sure that it's not lost after an attack.
"Together, these services allow organisations to adopt a posture of cyber resilience, ready to manage any attack without damage to their operations or brand," Hood says.
So beyond all the statistics and services, what lies ahead for Mimecast in 2017? Hood says the company is growing rapidly, with 3Q results showing 30% YOY growth.
Closer to home, he says that Australia is an important factor in its APAC operations, with its Melbourne head office acting as APAC headquarters.
"Ongoing investment in Australia cybersecurity expertise, local partnerships and regional technology infrastructure has been instrumental in our growth. We've migrated hundreds of customers to our Australian data centres to serve their local data sovereignty requirements," he says.
"A key differentiator in the market for Mimecast has always been our commitment to customer success and we're proud of the program we've built. Our growth plans into new markets reflect this commitment," Hood concludes.


On July 20, 2018, Sarar USA, Inc. (the "Debtor") filed a voluntary petition for relief under Chapter 11 of the United States Bankruptcy Code in the United States Bankruptcy Court for the District of New Jersey. The case is pending before the Honorable John K. Sherwood.
A hearing on the Debtor's First Day Motions was held on July 24, 2018 before the Honorable John K. Sherwood, United States Bankruptcy Court for the District of New Jersey, Martin Luther King, Jr. Federal Building, 50 Walnut Street, 3rd Floor, Courtroom 3D, Newark NJ, 07102. A final hearing on certain of the First Day Motions was held on August 28, 2018 at 11:00 a.m. (ET).
Notice of Chapter 11 Bankruptcy Case. Filed by Jeffrey Vanacore on behalf of Sarar USA, Inc. Meeting of Creditors: September 12, 2018 at 10:00 a.m.


1 Discovering Affordable Dental Implants in Davenport, Iowa– Why So Expensive?
5 How Do I Get Dental Implants in Davenport IA?
You assumed whatever was great. No person appeared to notice that you were missing out on a few teeth, as well as then someone went across the line. You were given granny sandals and a crocheted blanket for Xmas, the recommendation being that it was time to curl up on the couch with your cat and a glass of warm milk.
Discovering Affordable Dental Implants in Davenport, Iowa– Why So Expensive?
Shedding your teeth has begun to make you look old. You rarely talk to any individual any longer anyway, so why not work out in for a very early nap? Nonsense! When affordable dental implants are simply a phone call away, you don't have to settle.
Maybe member of the family will be more straight and tactful concerning it, however somebody has to inform you that affordable dental implants could be life-altering. Discovering affordable dental implants begins with a net search and also the readiness to travel a bit. Chances are you will certainly need to go to a major city to discover a dentist that makes it his organisation to provide cost effective dental services to individuals that require them. It could appear like incorrect economy if you have to spend for train tickets or gas, but simply note the distinction in cost as well as it quickly ends up being clear: traveling is well worth the effort to have your smile once again.
The reason dental implants are so expensive is that lots of people get associated with making them, placing them and finishing them. Add this to the price of products plus the dental professional's helicopter fees, and quickly you will certainly need to sell your cars and truck to be able to consume steak once again.
How Do I Get Dental Implants in Davenport IA?
Dental professionals could reduce expenses by doing just what every customer does to save loan: purchasing wholesale. Since there is no such point as a poor dental practitioner, it is clear that these procedures take place often sufficient for an expert to buy products in advancement. If he is educated, he can do even more of the job himself rather compared to sending you to a various person to deal with each part of the procedure. Every one of this could save you money, after you request for a strong sedative to get you with the procedure.
The majority of these oral practices promote services online. Net advertising assists to maintain prices down and get to more people, while widening their customer base at the exact same time. More customers and lower media prices add up to savings we can pass on to consumers. When you see one of our dental professionals, make certain to request a price evaluation for the dental implants.
Consider benefiting from these services prior to any individual has to motivate you. Shock them with a new smile. The benefits start with self esteem, which is essential to living a complete life. Not every person who sheds teeth will certainly be senior. Lots of youngsters experience dental conditions or injuries which cause tooth loss. When you could not grin or talk openly, this cuts you off from individuals as well as hinders your possibilities of success, especially if you intend to operate in a client service ability.
Worse still, your jaw needs teeth in it to remain healthy. Without anything to support, your jaw begins to run out like a muscle that never obtains utilized. Your mouth will certainly transform form to ensure that, even if you intend to obtain dentures eventually, they will not fit. Act swiftly to stop this from occurring and offer us a call today.
The advantage of choosing affordable dental implants over dentures is that they will assist you to maintain bone mass, whereas dentures do not. You have simply as excellent an opportunity of losing bone if you use dentures as you do without teeth.
Even dentures can be put in your mouth semi-permanently. Your dental expert will repair them to a variety of messages so that you take hip hop lessons without shedding them. While the yelling of your fellow dancers or the target market as they go flying can be interesting, the guideline of 'finders caretakers' can mean your downfall for locating affordable dental implants.
Pay little focus to the cost of your friend's treatment. Her mouth is various from yours, so the solutions you need will certainly not cost the very same amount. It might take much longer for your treatment to be finished. Extra materials might be required. Bone grafting may be essential before any type of more work can be done. Try not to be discouraged, though.
When picking affordable dental implants, simply learn what sort of anesthetic services are provided at the same time. This must put you at your convenience. You could be asleep during. If your major concern about going to the dentist is that you are merely scared, this is particularly convenient. A phobia of dental experts is typical, however is in some cases avoidable. Do not watch 'Little Shop of Horrors' or 'Marathon Guy,' and you can be simply great.
Maybe family members will certainly be much more direct as well as tactful concerning it, however somebody requires to tell you that affordable dental implants could be life-changing. Discovering affordable dental implants starts with a net search and the willingness to travel a little bit. While the yelling of your other dancers or the target market as they go flying can be exciting, the rule of 'finders keepers' might mean your downfall for finding affordable dental implants.


Universal Bike Mount (BM1) is designed to hold your smartphone securely on your bike, so you can enjoy your cycling experience. The BM1 fits on handlebars and bike stems ranging from 18-30mm in diameter. Easily adjust the position of your smartphone for different cycling conditions.


text:
Natural Diet and Pesticides
By A'ndrea Elyse Messer, for Phys.Org
Feeding honey bees a natural diet of pollen makes them significantly more resistant to pesticides than feeding them an artificial diet, according to a team of researchers, who also found that pesticide exposure causes changes in expression of genes that are sensitive to diet and nutrition.
Honey bees are exposed to hundreds of pesticides, while they are foraging on flowers and also when beekeepers apply chemicals to control bee pests," said Christina Grozinger, professor of entomology and director of the Center for Pollinator Research, Penn State. "Our study demonstrates that exposure to non-lethal doses of at least two of these pesticides causes large changes in the expression of genes involved in detoxification, immunity and nutrition-sensing. This is consistent with results from previous studies that have found that pesticide exposure compromises bees' immune systems. Furthermore, our study reveals a strong link, at the molecular level, between nutrition, diet and pesticide exposure
Exploring this link further, the researchers found that diet significantly impacts how long bees can survive when given lethal doses of a pesticide.
"This interaction between pesticide exposure and nutrition is likely what's at play in our finding that feeding bees a complex diet of pollen—their natural diet—makes them significantly more resistant to lethal doses of a pesticide than feeding them a more simple, artificial diet," said Daniel Schmehl, postdoctoral researcher, University of Florida.
To determine the impact of pesticide exposure on gene expression patterns in honey bees, the scientists first fed one of two miticides—coumaphos or fluvalinate, the two most abundant and frequently detected pesticides in the hive—to bees for a period of seven days. On the seventh day, the researchers extracted RNA from the bees, attached a fluorescent marker to the RNA and examined differences in gene expression patterns—indicated by changes in patterns of fluorescence—between the pesticide-treated bees and the control bees.
"We found significant changes in 1,118 transcripts—or pieces of RNA—among the bees that were fed either of the two miticides compared to the control group," said Schmehl. "These transcripts included genes involved in detoxification, immunity and nutrition."
Based upon the results, the team performed several subsequent analyses aimed at understanding the impact of pesticides on honey bee physiology. One of these subsequent analyses examined the susceptibility of bees to pesticide stress after consuming a pollen diet or an artificial diet—either a soy protein or no protein diet. The team fed the bees these diets while simultaneously feeding them a lethal dose of the pesticide chlorpyrifos, an insecticide that is frequently used to control pests in agricultural crops and commonly detected in honey bee hives. They then recorded bee mortality daily for each of the treatment groups for a period of 16 days.
The researchers found that the bees that were fed a pollen-based diet exhibited reduced sensitivity to chlorpyrifos compared to the bees that were fed an artificial diet.
The results appear in the online issue of the Journal of Insect Physiology.
"This is the first time such a strong link between pesticide exposure and diet has been demonstrated at the molecular level, and the first time the effects of artificial versus natural diets have been explored in terms of resistance to pesticides," said Grozinger. "Diet and nutrition can greatly impact the ability of bees to resist pesticides, and likely other stressors. However, agriculture and urbanization have reduced the amounts and diversity of flowering plants available to bees, which likely nutritionally stresses them and makes them more sensitive to these other stressors. If we can figure out which diets and which flowering plants are nutritionally optimal for honey bees, we can help bees help themselves."
Read more at: http://phys.org/news/2014-11-diet-affects-pesticide-resistance-honey.html#jCp
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CATCH THE BUZZ – Honey Program Non-Recourse Marketing Assistance Loan and LDP Program Overview.
The Agricultural Act of 2014 (2014 Farm Bill) authorizes nonrecourse marketing assistance loans (MALs) and loan deficiency payments (LDPs) for the 2014 through 2018…


As part of the New Mexico Statutes, the beneficiary of an interest in property may renounce the gift, either in part or in full (Uniform Disclaimer of Property Interests Act NMSA 1978 46-10-1 to 46-10-17). Note that the option to disclaim is only available to beneficiaries who have not acted in any way to indicate acceptance or ownership of the interest ( 46-10-13).
The disclaimer must be in writing and include a description of the interest, a declaration of intent to disclaim all or a defined portion of the interest, and be signed by the disclaimant ( 46-10-5 (c)).
Deliver the disclaimer within nine months of the transfer (e.g., the death of the creator of the interest) to the personal representative of the decedent's estate or the trustee, or file it with the court having authority to appoint such a person or to enforce the trust ( 46-10-12). If real property is involved, record a copy of the disclaimer in the office of the county clerk in the county in which the property or interest disclaimed is located. This helps avoid any ambiguity regarding the chain of title ( 46-10-15).


Made in soft and fluffy Buttercup yarn, this tunic will be loved by little girls everywhere! Switch up the stripe colors to her favorites to be sure to make a top she'll want wear all the time.
Gauge/Tension: 11 sts = 4" [10 cm]; 17 rows = 4" [10 cm] in St st. CHECK YOUR GAUGE. Use any size needles to obtain the gauge given.


Valentine's Day is just a month away. After Christmas, Valentine's Day is our second favorite holiday of the year. After all, very few of us can resist those heart melting and gushingly sweet wishes exchanged on the holiday of love! 💖 At the same time, Valentine's day is also a retail occasion for all eCommerce marketers, as people are willing to spend a little more for their loved ones on this special day. (Keep in mind that the average spend in the US for Valentine's gifts is $140). That's why we are bringing you a set of lovely Valentines Day email templates to help inspire your next V-day campaigns. Simply grab, customize and send with ContactPigeon (or your own email client – we're not judging)!
Wrap up your Valentine's Day offer with an eye-catching bow. This minimalistic template with a moving red gift bow will sure be able to attract your recipient's attention. Add an attractive offer on top, and you'll be on way to win the hearts of your customers this February.
Planning a special event on Valentine's Day? Whether if it's an in-store event, give-away, or online sales, this Valentines Day email template can help make your announcement more memorable. Send it in advance to your subscribers as a reminder to mark down the special date.
A simple "Happy Valentine's Day" goes a long way. Pair it with a theme in red, a color of passion, for a strong message on this romantic holiday.
Bring out the sparkle of your next email campaign with the next Valentines Day design, filled with sparkling hearts of gold.
What's more classic for Valentine's Day wish than a candy sweetheart? The following design takes inspirations from the classic candy with the signature color of pink pastel. The design goes perfectly with any candy, hand-crafts or stationaries merchandise with a lady-like appeal.
A dreamy heart with romantic backlight fills our hearts with coziness, as it will for many recipients. This email design will generate a romantic yet warm appeal to go along with your valentine's day promotion.
Chocolate, champagnes and rose petals. Things that remind us of love in the air. The following email template design showcases the petals of love in love shaped moldings. We can say that it certainly brings out the celebratory spirit of Valentine's Day.
Featuring a colorful display of hanging paper hearts, this design sends the impression of love notes or greeting cards from someone special.
Customizing the template to fit your business brand and audience. If you are already logged into your ContactPigeon account, click on the respective link to start editing the template directly using our drag & drop email editor.
And you're all set to send. For more inspirations on how to make your Valentine's Day email campaign stand out, check out a previous Valentine's Day post that covers the strategy and ideas for Subject Lines.
As always, we wish you all the love on this Valentine's Day!


text:
NGC 5338 (również PGC 49353 lub UGC 8800) – galaktyka soczewkowata (SB0), znajdująca się w gwiazdozbiorze Panny. Odkrył ją Lawrence Parsons 3 maja 1877 roku.

W galaktyce tej zaobserwowano supernową SN 2006E.

Zobacz też
 Lista obiektów NGC

Przypisy

Linki zewnętrzne

Galaktyki soczewkowate
Gwiazdozbiór Panny
5338
Obiekty astronomiczne odkryte w 1877

redpajama_set_name: RedPajamaWikipedia


Logic Analyzers are expensive and are less well supported by development tools, but can often capture trace at higher speeds than is possible with a TPA. Most developers capture trace using a TPA or on-chip trace buffer.
The CoreSight ETB and ETR is an ATB slaves and connects to the CoreSight system directly to enable capture of trace data on-chip. A TPA or Logic Analyzer must connect to the pins of a trace port, that is driven by a TPIU.
Most systems implement either one ETB or one TPIU. However, it is possible to implement multiple trace sink components using a CoreSight Replicator. See Systems with an ETB and a TPIU.
Figure 5.1 shows a system that implements an ETB and a TPIU connected to a TPA.


I'm sure that many of you already know Richard's work but, if you don't I urge you to pay a visit to his site. The poem I'm sharing with you today has incredible power. It is deeply moving but, at the same time, is brutally real…..you'll see what I mean; I really hope you like it….
Wow. An amzing poem, very emotional. I loved it.
Hmmm that's odd, I can't open it either. Sorry I don't know what's broken….
How strange. Perhaps he didn't like the fact that I reblogged the post. Normally I'd message but not possible on Richard's site unfortunately. Sorry you didn't get to read the poem, it was extremely powerful.


Beck/Arnley Premium Fully Synthetic Hydraulic Fluid is a superior quality formulation of high performance, carefully selected, synthetic base oils. State-of-the-art additives are formulated for specific European vehicles. Specifically developed for use in hydraulically supported lever control, power steering and shock absorbers.
Formulated for: Audi, BMW, Jaguar, Land Rover, Mercedes-Benz, Mini, Porsche, Saab, Volkswagen, and Volvo.


– When you attend for your appointment.
enquiry in as efficient manner as possible.
form part of your medical record and will be used to provide you with the most effective treatment.
done with your prior consent.
to receive marketing, you may opt out at a later date.
If you no longer wish to be contacted for marketing purposes please contact the clinic.
you link to other websites you should read their own privacy policies.


I'd like to take this opportunity to welcome you to our new site, Kool Campers. Our aim is quite simple; to provide the best resource available for everyone interested campervan rentals.
Whether you're a holidaymaker looking for your next big adventure or an owner looking for a place to promote your van, Kool Campers is here to help.
We have years of experience in providing solutions for holiday rentals and recently we noticed an increase in the number of campervan rental companies using our bookalet.co.uk booking system. That set us thinking. Why not combine our interest in campervans with bookalet and launch a dedicated free to list portal to help promote van rentals, with an option to add a booking system should that be required?
Enter Kool Campers. But we wanted to be different! So, we've decided to make listing your van on the site entirely free of charge. No subscription fees for the owner to pay and no outrageous booking fees for the guest to contend with.
Rob, our lead developer on this project is already well immersed in this world having set up and run the respected pre67vw.com website for the last 15 years. He's the man to point the finger at should you find anything not working properly!
We'd love for you to join our community and add your campervan. You get your own page for each van you list, an availability calendar, rate card and enquiry form.
There's no obligation to add a booking system but should you decide to do so, you'll then be able to take online bookings and payments as well as managing all the bookings via the online management console. You even be able to add these calendars and booking forms to your own website and sync calendars to ensure you avoid potential double bookings.


Awesome Con is Washington DC's comic con! We celebrate all aspects of Geek Culture, including comic books, sci-fi, fantasy, horror, anime, gaming, TV, movies, animation, music, comedy, art, science, and more! You can get all the information about Awesome Con at awesomecon.com, and follow us on Facebook, Instagram and Twitter.
Club Awesome is the coolest way to experience Awesome Con. Membership in Club Awesome includes access to the exclusive Club Awesome Lounge, the first seating group for the Main Stage, and more! See all our Club Awesome details here! Make sure to read up on all the benefits before you purchase.
A weekend or single day ticket gets you into 99% of everything that's awesome at Awesome Con, but if you want to get in early and get your hands on some sweet swag, you've got to go VIP!
Any pass purchased by March 12 can be mailed to the address you provided. BADGES WILL NOT BE MAILED IMMEDIATELY AFTER YOUR ORDER. Badges will be mailed to US addresses only, with all international orders held for pick up. Special Event tickets and merchandise orders will also all be held for pick up at Awesome Con. Merchandise will not be mailed and must be picked up at Awesome Con.
All attendees three-years-old and up need a ticket to Awesome Con. We recommend all children under 18 attend with an adult, and all children under 13 must have an adult with them while attending Awesome Con.
Guest-specific VIPs (the "Dave Bautista VIP," for instance) provide guaranteed, pre-paid autographs and photo ops, plus admission to the con - all in one bundle - plus a few extra perks like swag.
Autograph sales, photo op sales, and the programming schedule will be release about 3-4 weeks before Awesome Con 2019.


1,159 of 3,036,198 websites are using Shift JIS, which is 0.04 percent of all analysed websites, providing information about the charset technology. There is a decrease of 16 websites using Shift JIS, which is 1.4 percent less than last month. The major competitors are GBK and ISO-8859-15.


The moment guests step into the Oryx Rotana, they will be enchanted by its unique blend of traditional Arabian hospitality and the breathtaking opulence of modern and contemporary luxury. The iconic architectural design of the hotel has turned Oryx Rotana into Doha's premier meeting place, ideal for both business and leisure. Our facilities include a total of 11 meeting rooms with 2 ballrooms. Meeting room 1, 2, 3 and 4, Jade A&B, Topaz A&B and Pearl 1, 2 and 3 at the Business Centre. These venues can be further divided into 2 rooms each when required. All meeting rooms has been designed for companies looking for an outstanding, modern meeting and conference venue with state-of-the-art audio visual equipment and latest technological services and support A Business centre with secretarial support is also available for any of your meeting requests in addition to a dedicated team to attend for your needs.
Doha International Airport (www.dohaairport.com/) Car rentals are available. Passengers with international driving licenses can drive for seven days. Minimum fare for airport taxi starts at 25QAR and charged per kilometer at 1.20QAR. Many hotels in Doha offer transportation from airport to hotel.
Qatar National Convention Centre (www.qatartourism.gov.qa) Dedicated multi purpose hall for 4,200 guests. 2,500 seat auditorium and 500 seat theatre Approximately 15-20 minute drive from major hotels and the West bay business precinct.


Stop drug makers from gaming the system.
Urge the state assembly to require greater transparency for drug prices by supporting Senate Bill 17.
California drug makers are using their monopoly power against the people of California. Right now, these corporations have free reign to hike up drug prices at a moment's notice and keep drug purchasing data secret, leaving Californians in the dark.
Sen. Hernandez has introduced Senate Bill 17, which will hold drug makers accountable by demanding greater transparency. This bill has already made it through the state Senate, and the the Assembly is considering the measure right now.
Require drug makers to publish data about purchasing trends, including drug prescription and pricing data.
Prevent drug companies from dramatically raising prices without warning by requiring drug companies to give 60 days' notice to purchasers before making major increases to drug prices.
Require health insurance companies to disclose what portion of premiums go towards prescription drugs.
This legislation will empower purchasers to make cost-effective health care decisions based off newly-available information pharmaceutical companies have to provide. With more transparency, SB 17 will help keep costs down for Californians.
Act Now: Write your state assemblymember and urge them to support Senate Bill 17.


Tien Tzuo was the featured speaker for the Executive's Club of Chicago inaugural program of its 2018-2019 Signature Series earlier this month. The topic, of course, was the subscription economy and Tien's new book, Subscribed. Being one of very few consulting firms that has a practice dedicated to subscription and recurring revenue businesses, Navint sponsored the event.
The old way of doing business was about how to come up with a hit product and sell as many units of that product through as many channels as possible. We certainly had customers, but often we didn't know who they were. We just knew somebody bought what we were producing.
A subscription model puts the customer, not the product, in the center of every interaction. We can see how the customer is interacting with and using our service, therefore we have no choice but to make them happy. The customer feedback creates a better product and a healthier relationship. We can deliver the outcome the customer wants, not just a product. It's not about the song, it's about entertainment; it's not about the cars, it's about getting from point A to point B; it's not about excavators, it's about moving dirt. And this is the magic—the customer will take you where you want to go.
This means getting into the marketplace really quickly, getting to know your customers really well, and iterating your products and services. The keys to the subscription business model are agility and iteration, which seems counter-intuitive to businesses that have historically focused on reproduction and scale.
Changing the pricing and packaging is a never-ending journey. A good example familiar to everyone is the telecom industry, which is constantly changing its packaging and pricing in innovative bundles based on customer usage. This is a great example of a dynamic marketplace in which competitors and alternatives arrive all the time. So, the ability to have iteration and agility, again, is key to making their subscription business successful.
While Tien believes that subscription services are the way of the future, he stated that we are still very early in its evolution. Each year, Zuora produces the Subscription Economy Index, which reflects the growth metrics of hundreds of companies around the world. This year's index showed that subscription businesses grew revenues five times faster than both the S&P 500 revenues and U.S. retail sales from 2012 to 2018. With these numbers, he said, it's hard to imagine any industry not interested in that kind of growth.
Some surprising businesses are getting into the subscription world by being creative with their services. One example Tien shared is Fender Guitar. The new CEO decided to focus on the customer and, through research, realized that half of their sales are to first-time guitar buyers. However, 90% of these buyers quit playing after three months because learning to play guitar is hard. If the customer is still playing after twelve months, they are a customer for life. The CEO realized that Fender needed to do something to help these new players keep playing from months four to twelve.
So, Fender launched digital services targeted to first-time players. The first was a tuning app to give the company a sense of which customers were playing and which were not. Then they launched Fender Play, which was a series of videos that teach you how to play. But these videos do not teach how to play "Mary Had a Little Lamb," but instead taught songs by Bob Marley, U2, and Maroon 5 because Fender knew that what new players really want are to be rock stars. These new apps gave Fender unique insights into their customers' usage. Even if just a few players make it to month twelve, that significantly and positively impacts their revenues.
Fender is a good example of putting their customers in the center and being creative with providing value to customers to improve business outcomes.
These were just a few insights in the hour-long discussion on the subscription economy. Jeff Wissink will be publishing an extended Q&A with Tien in Forbes in the coming weeks. We'll be sure to share it when it becomes available.
If you are interested in learning more about how Navint helps businesses focus on the customer journey, enable dynamic packaging and pricing, or transition to recurring revenue, contact us. We will be happy to have the conversation.


Registration forms are available to download or from reception at any of our surgeries. If you are registering for your family you will need a registration form for each person.
If you live outside of our practice area but would like to register with us please speak to a member of our reception team.


text:
\section{Introduction}
Recently, there has been considerable
progress in understanding the properties of strongly coupled
gauge theories with supersymmetry
\cite{seibergwitten,seiberg,maldacena}. In particular, there
are a number of supersymmetric gauge theories that are believed
to be interconnected through a web of strong-weak coupling dualities.
Although existing evidence for
these dualities is encouraging, there is still an urgent need
to address these issues at a more fundamental level. Ideally,
we would like to solve for the bound states of these
theories directly, and at any coupling.

Of course, solving a field theory from first principles
is typically an intractable task. Nevertheless, it has been
known for some time that $1+1$ dimensional field theories
{\em can} be solved from first principles via a straightforward
application of
DLCQ  (see \cite{bpp98} for a review).
In more recent times, a large class of supersymmetric
gauge theories in two dimensions was studied using
a supersymmetric form of DLCQ  (or `SDLCQ'), which is known to
preserve supersymmetry \cite{sakai95,klebhash,alp98a,alp98b,
alpp98,alpp99,alp99}.

We have recently been able to extend
the SDLCQ algorithms to solve higher-dimensional theories \cite{alp99b}.
One important difference between two-dimensional and
higher-dimensional theories is the phase diagram induced by
variations in the gauge coupling. The
spectrum of a $1+1$ dimensional gauge theory
scales trivially with
respect to the gauge coupling, while a theory in higher dimensions
has the potential of exhibiting a complex phase structure,
which may include a strong-weak coupling duality.
Ref.~\cite{alp99b} seemed to provide hints of the latter.
It is therefore interesting to study
the phase diagram of gauge theories in $D \geq 3$ dimensions.

Towards this end, we consider  three dimensional SU($N_c$) ${\cal N}=1$
super-Yang-Mills   compactified on the space-time ${\bf R} \times S^1 \times
S^1$. The calculations are all done in the large $N_c$ limit.  In
particular, we
compactify the light-cone coordinate
$x^-$ on a light-like circle via DLCQ, and wrap the remaining  transverse
coordinate $x^{\perp}$ on a spatial circle.   We are able to solve
for bound state
wave functions and masses numerically by diagonalizing the  discretized
light-cone supercharge. We have shown that the SDLCQ procedure   extends
naturally to $2+1$ dimensions, resulting in an exactly supersymmetric
spectrum.

The contents of this paper are organized as follows.
In Section \ref{formulation}, we formulate
SU($N_c$) ${\cal N}=1$ super-Yang-Mills
defined on the compactified space-time ${\bf R} \times S^1 \times S^1$.
Explicit expressions are given for the light-cone supercharges,
which are then discretized via the SDLCQ procedure.
Quantization of the theory is carried out by imposing
canonical \mbox{(anti-)}commutation relations for boson and fermion
fields. We also
discuss the two discrete symmetries of the theory in this section. In Section
\ref{numerical}, we present our numerical results. We present plots of the
spectrum as  a function of the longitudinal and transverse  resolution and
show that it convergences very rapidly in both.
We plot the spectrum also as a
function of the coupling and find a very stable strong-coupling spectrum. We
identify several states that appear to be unphysical and disappear at high
transverse resolutions. Finally we discuss the infrared spectrum of the theory
and present evidence that it is entirely determined by the dimensionally
reduced theory. We conclude our analysis with a discussion of our results and a
list of important related future projects in Section \ref{summary}.

\section{Light-Cone Quantization and SDLCQ}
\label{formulation}

Discrete light cone quantization has proven to be a very powerful method of
studying the mass spectra of various theories \cite{bpp98}.
It is well known that in $1+1$ dimension one can define a new version of DLCQ
which preserves supersymmetry \cite{sakai95,alp99}. In higher dimensions a
supersymmetric prescription is also possible \cite{alp99b}. We begin by
introducing light-cone coordinates
$x^{\pm} = (x^0 \pm x^1)/\sqrt{2}$, and compactifying the $x^-$ coordinate on a
light-like circle. In this way, the conjugate light-cone momentum
$k^+$ is discretized.
To discretize the remaining (transverse) momentum $k^{\perp} = k^2$, we may
compactify $x^{\perp} = x^2$ on a spatial circle.  Of course, there
is a significant
difference between the discretized light-cone momenta $k^+$ and the discretized
transverse momenta
$k_{\perp}$; namely, the light-cone momentum $k^+$ is always positive, while
$k_{\perp}$ may take on positive or negative values. The positivity
of $k^+$ is a key
property that is exploited in DLCQ calculations;  for any given light-cone
compactification, there are only a finite number of choices for $k^+$
-- the total
number depending on how finely we discretize the  momenta. The `resolution'
of the discretization is usually characterized by a positive integer
$K$, which is called
the `harmonic resolution'
\cite{pb85,yamawaki}; for a given choice of $K$, the light-cone
momenta $k^+$ are
restricted to positive integer multiples of $P^+/K$, where $P^+$ is
the total light-cone
momentum of a state. In the context of two-dimensional theories,
this implies a finite
number of Fock states \cite{pb85}.

In the case of interest here, we include
an additional transverse
dimension, and the number of Fock states is no longer finite,
since there is an arbitrarily large number of transverse momentum
modes defined on the transverse spatial circle.
Thus, an additional truncation of the transverse momentum
modes is required to render the total number of Fock states
finite and the problem numerically tractable.
This truncation procedure, which is characterized by a transverse
resolution T, is
analogous to the truncation of $k^+$  imposed by the `harmonic resolution' $K$.
Thus the transverse momentum $k_\perp$ range from zero to $\pm\frac{2
\pi T}{L}$ ,
where $L$ is the size of the transverse circle.

Let us now review these ideas in the context of a specific
super-Yang-Mills theory.
We start with $(2+1)$-dimensional ${\cal N}=1$ super-Yang-Mills theory
defined on a space-time with one transverse dimension
compactified on a circle:
\begin{equation}
S=\int d^2 x \int_0^L dx_\perp \mbox{tr}(-\frac{1}{4}F^{\mu\nu}F_{\mu\nu}+
{\rm i}{\bar\Psi}\gamma^\mu D_\mu\Psi).
\end{equation}
After introducing the light--cone coordinates
$x^\pm=\frac{1}{\sqrt{2}}(x^0\pm x^1)$, decomposing the spinor $\Psi$
in terms of chiral projections
\begin{equation}
\psi=\frac{1+\gamma^5}{2^{1/4}}\Psi,\qquad
\chi=\frac{1-\gamma^5}{2^{1/4}}\Psi,
\end{equation}
and choosing the light--cone gauge $A^+=0$, we obtain
\begin{eqnarray}\label{action}
S&=&\int dx^+dx^- \int_0^L dx_\perp \mbox{tr}\left[\frac{1}{2}(\partial_-A^-)^2+
(D_+\phi+\partial_\perp A^-)\partial_-\phi+ {\rm i}\psi D_+\psi+ \right.\nonumber \\
& &
\left.
         \hspace{15mm} +{\rm i}\chi\partial_-\chi+\frac{{\rm i}}{\sqrt{2}}\psi
D_\perp\chi+
\frac{{\rm i}}{\sqrt{2}}\chi D_\perp\psi \right].
\end{eqnarray}
A simplification of the
light--cone gauge is that the
non-dynamical fields $A^-$ and $\chi$ may be explicitly
solved from their Euler-Lagrange equations of motion:
\begin{equation}
A^-=\frac{1}{\partial_-^2}J=
\frac{1}{\partial_-^2}\left(ig[\phi,\partial_-\phi]+2g\psi\psi -\partial_\perp \partial_-\phi
\right), \quad
\chi=-\frac{1}{\sqrt{2}\partial_-}D_\perp\psi.\nonumber
\end{equation}
These expressions may be used to express any operator
in terms of the physical degrees of freedom only.
In particular, the light-cone energy, $P^-$, and momentum
operators, $P^+$,$P^{\perp}$,
corresponding to  translation
invariance in each of the coordinates
$x^\pm$ and $x_\perp$ may be calculated explicitly:
\begin{eqnarray}\label{moment}
P^+&=&\int dx^-\int_0^L dx_\perp\mbox{tr}\left[(\partial_-\phi)^2+
{\rm i}\psi\partial_-\psi\right],\\
P^-&=&\int dx^-\int_0^L dx_\perp\mbox{tr}
\left[-\frac{1}{2}J\frac{1}{\partial_-^2}J-
            \frac{{\rm i}}{2}D_\perp\psi\frac{1}{\partial_-}D_\perp\psi\right],\\
P_\perp &=&\int dx^-\int_0^L dx_\perp\mbox{tr}\left[\partial_-\phi\partial_\perp\phi+
            {\rm i}\psi\partial_\perp\psi\right].
\end{eqnarray}
The light-cone supercharge in this theory
is a two component Majorana spinor, and may be conveniently
decomposed in terms of its chiral projections:
\begin{eqnarray}\label{sucharge}
Q^+&=&2^{1/4}\int dx^-\int_0^L dx_\perp\mbox{tr}\left[\phi\partial_-\psi-\psi\partial_-
                   \phi\right],\\
\label{sucharge-}
Q^-&=&2^{3/4}\int dx^-\int_0^L dx_\perp\mbox{tr}\left[\partial_\perp\phi\psi+
            g\left({\rm
i}[\phi,\partial_-\phi]+2\psi\psi\right)\frac{1}{\partial_-}\psi\right].
\end{eqnarray}
The action (\ref{action}) gives the following canonical
(anti-)commutation relations for
propagating fields for large $N_c$ at equal $x^+$:
\begin{equation}
\left[\phi_{ij}(x^-,x_\perp),\partial_-\phi_{kl}(y^-,y_\perp)\right]=
\left\{\psi_{ij}(x^-,x_\perp),\psi_{kl}(y^-,y_\perp)\right\}=
\frac{1}{2}\delta(x^- -y^-)\delta(x_\perp -y_\perp)\delta_{il}\delta_{jk}.
\label{comm}
\end{equation}
Using these relations one can check the supersymmetry algebra
\begin{equation}
\{Q^+,Q^+\}=2\sqrt{2}P^+,\qquad \{Q^-,Q^-\}=2\sqrt{2}P^-,\qquad
\{Q^+,Q^-\}=-4P_\perp.
\label{superr}
\end{equation}

We will consider only states which have vanishing transverse momentum,
which is possible since the total transverse momentum operator
is kinematical\footnote{Strictly speaking, on a transverse
cylinder, there are separate sectors with total
transverse momenta $2\pi n/L$; we consider only one of them, $n=0$.}.
On such states, the light-cone supercharges
$Q^+$ and $Q^-$ anticommute with each other, and the supersymmetry algebra
is equivalent to the ${\cal N}=(1,1)$ supersymmetry
of the dimensionally reduced ({\em i.e}.\ two-dimensional) theory
\cite{sakai95}.
Moreover, in the $P_{\perp} = 0$ sector,
the mass squared operator $M^2$ is given by
$M^2=2P^+P^-$.

As we mentioned earlier, in order to render the bound state equations
numerically tractable, the transverse
momentum of partons must be truncated.
First, we introduce the Fourier expansion for the fields $\phi$ and $\psi$,
where the transverse space-time coordinate $x^{\perp}$ is periodically
identified:
\begin{eqnarray}
\lefteqn{
\phi_{ij}(0,x^-,x_\perp) =} & & \nonumber \\
& &
\frac{1}{\sqrt{2\pi L}}\sum_{n^{\perp} = -\infty}^{\infty}
\int_0^\infty
         \frac{dk^+}{\sqrt{2k^+}}\left[
         a_{ij}(k^+,n^{\perp})e^{-{\rm i}k^+x^- +{\rm i}
\frac{2 \pi n^{\perp}}{L} x_\perp}+
         a^\dagger_{ji}(k^+,n^{\perp})e^{{\rm i}k^+x^- -
{\rm i}\frac{2 \pi n^{\perp}}{L}  x_\perp}\right]
\nonumber\\
\lefteqn{
\psi_{ij}(0,x^-,x_\perp) =} & & \nonumber \\
& & \frac{1}{2\sqrt{\pi L}}\sum_{n^{\perp}=-\infty}^{\infty}\int_0^\infty
         dk^+\left[b_{ij}(k^+,n^{\perp})e^{-{\rm i}k^+x^- +
{\rm i}\frac{2 \pi n^{\perp}}{L} x_\perp}+
         b^\dagger_{ji}(k^+,n^\perp)e^{{\rm i}k^+x^- -{\rm i}
\frac{2 \pi n^{\perp}}{L} x_\perp}\right]
\nonumber
\end{eqnarray}
Substituting these into the (anti-)commutators (\ref{comm}),
one finds
\begin{equation}
\left[a_{ij}(p^+,n_\perp),a^\dagger_{lk}(q^+,m_\perp)\right]=
\left\{b_{ij}(p^+,n_\perp),b^\dagger_{lk}(q^+,m_\perp)\right\}=
\delta(p^+ -q^+)\delta_{n_\perp,m_\perp}\delta_{il}\delta_{jk}.
\end{equation}
The supercharges now take the following forms:
\begin{eqnarray}\label{TruncSch}
&&Q^+={\rm i}2^{1/4}\sum_{n^{\perp}\in {\bf Z}}\int_0^\infty dk\sqrt{k}\left[
b_{ij}^\dagger(k,n^\perp) a_{ij}(k,n^\perp)-
a_{ij}^\dagger(k,n^\perp) b_{ij}(k,n^\perp)\right],\\
\label{Qminus}
&&Q^-=\frac{2^{3/4}\pi {\rm i}}{L}\sum_{n^{\perp}\in {\bf Z}}\int_0^\infty dk
\frac{n^{\perp}}{\sqrt{k}}\left[
a_{ij}^\dagger(k,n^\perp) b_{ij}(k,n^\perp)-
b_{ij}^\dagger(k,n^\perp) a_{ij}(k,n^\perp)\right]+\nonumber\\
&&+ {{\rm i} 2^{-1/4} {g} \over \sqrt{L\pi}}
\sum_{n^{\perp}_{i} \in {\bf Z}} \int_0^\infty dk_1dk_2dk_3
\delta(k_1+k_2-k_3) \delta_{n^\perp_1+n^\perp_2,n^\perp_3}\nonumber\\
&&\times\left\{
     {1 \over 2\sqrt{k_1 k_2}} {k_2-k_1 \over k_3}
[a_{ik}^\dagger(k_1,n^\perp_1) a_{kj}^\dagger(k_2,n^\perp_2)
b_{ij}(k_3,n^\perp_3)
-b_{ij}^\dagger(k_3,n^\perp_3)a_{ik}(k_1,n^\perp_1)
a_{kj}(k_2,n^\perp_2) ]\right.\nonumber\\
&&+{1 \over 2\sqrt{k_1 k_3}} {k_1+k_3 \over k_2}
[a_{ik}^\dagger(k_3,n^\perp_3) a_{kj}(k_1,n^\perp_1) b_{ij}(k_2,n^\perp_2)
-a_{ik}^\dagger(k_1,n^\perp_1) b_{kj}^\dagger(k_2,n^\perp_2)
a_{ij}(k_3,n^\perp_3) ]\nonumber\\
&&+{1 \over 2\sqrt{k_2 k_3}} {k_2+k_3 \over k_1}
[b_{ik}^\dagger(k_1,n^\perp_1) a_{kj}^\dagger(k_2,n^\perp_2)
a_{ij}(k_3,n^\perp_3)
-a_{ij}^\dagger(k_3,n^\perp_3)b_{ik}(k_1) a_{kj}(k_2,n^\perp_2) ]\nonumber\\
&&+({ 1\over k_1}+{1 \over k_2}-{1\over k_3})
[b_{ik}^\dagger(k_1,n^\perp_1) b_{kj}^\dagger(k_2,n^\perp_2)
b_{ij}(k_3,n^\perp_3)
+b_{ij}^\dagger(k_3,n^\perp_3) b_{ik}(k_1,n^\perp_1) b_{kj}(k_2,n^\perp_2)]
         \left. \frac{}{}\right\}. \nonumber \\
\end{eqnarray}
We now perform the truncation procedure; namely, in all sums over the
transverse momenta $n^{\perp}_{i}$ appearing in the above expressions for the
supercharges, we restrict summation to the following allowed momentum
modes: $n^{\perp}_{i}=0,\pm 1 ... \pm T$.  Note that this prescription is
symmetric, in the sense that there are as many positive modes as there are
negative ones. In this way we  retain parity symmetry in the transverse
direction.

How does such a truncation affect the supersymmetry properties of the
theory? Note first that an operator relation $[A,B]=C$ in the  full
theory is not
expected to hold in the truncated formulation.  However, if A is quadratic in
terms of fields (or in terms of creation and  annihilation operators), one can
show that the relation $[A,B]=C$ implies
$$
[A_{tr},B_{tr}]=C_{tr}
$$
for the truncated operators $A_{tr}$,$B_{tr}$, and $C_{tr}$.  In our
case, $Q^+$
is quadratic, and so the relations
$\{Q_{tr}^+,Q_{tr}^+\}=2\sqrt{2}P_{tr}^+$ and
$\{Q_{tr}^+,Q_{tr}^-\}=0$ are true
in the $P_\perp=0$ sector of the truncated theory.  The anticommutator
$\{Q_{tr}^-,Q_{tr}^-\}$,
however, is not equal to $2\sqrt{2}P_{tr}^-$. So the diagonalization of
$\{Q_{tr}^-,Q_{tr}^-\}$ will yield a different bound-state spectrum
than the one
obtained after diagonalizing $2\sqrt{2}P_{tr}^-$. Of course, the two spectra
should agree in the limit
$T\rightarrow\infty$. At any finite truncation, however, we have the liberty to
diagonalize either of these operators. The choice of $\{Q_{tr}^-,Q_{tr}^-\}$
specifies our regularization scheme.

Choosing to diagonalize the light-cone
supercharge $Q_{tr}^-$ has an important advantage:
{\em the spectrum is exactly supersymmetric for
any truncation}. In contrast, the spectrum of the Hamiltonian $P_{tr}^-$
becomes supersymmetric only in the infinite resolution limit.

Let us discuss the discrete symmetries of $Q^-$. There are three commuting
$Z_2$ symmetries, one of them is the parity in the transverse direction:
\begin{equation}\label{defparity}
P: a_{ij}(k,n^\perp)\rightarrow -a_{ij}(k,-n^\perp),\qquad
        b_{ij}(k,n^\perp)\rightarrow b_{ij}(k,-n^\perp).
\end{equation}
Note that $P$ does not commute with $Q^+$ or with $P_\perp$:
\begin{equation}
PQ^+=-Q^+P, \qquad PP_\perp=-P_\perp P.
\end{equation}
The second symmetry is given by a generalization of the T--symmetry defined in
\cite{kutasov93} (we will call it S to avoid the confusion with transverse
truncation parameter):
\begin{equation}
\label{defz2}
S: a_{ij}(k,n^\perp)\rightarrow -a_{ji}(k,n^\perp),\qquad
        b_{ij}(k,n^\perp)\rightarrow -b_{ji}(k,-n^\perp).
\end{equation}
It commutes with all the Noether charges (\ref{moment})--(\ref{sucharge-}).
Since $P$ and $S$ commute with each other one needs only one additional
symmetry $R=PS$ to close the group.

Since $Q^-$, $P$ and $S$ commute with each other we can diagonalize them
simultaneously. This allows us to diagonalization of the supercharge
separately
in the sectors with fixed $P$ and $S$ parities and thus will reduce the size
of matrices. Doing this one finds that the roles of $P$ and $S$ are different.
While all the eigenvalues are usually broken into non-overlapping $S$--odd and
$S$--even sectors \cite{bdk93}, the $P$ symmetry leads to a double
degeneracy of massive states (in addition to usual boson--fermion degeneracy
due to supersymmetry). To demonstrate this, let us start from the massive
bosonic state $|M+\rangle$:
\begin{equation}
\left(Q^-\right)^2|M+\rangle=M^2|M+\rangle,\qquad
P|M+\rangle=+|M+\rangle.
\end{equation}
If $M\ne 0$ then the bosonic state $Q^+Q^-|M+\rangle$ has nonzero norm and it
is also an eigenstate of $\left(Q^-\right)^2$ with eigenvalue $M^2$. This state
however has a negative parity:
\begin{equation}
PQ^+Q^-|M+\rangle=-Q^+PQ^-|M+\rangle=-Q^+Q^-P|M+\rangle=-Q^+Q^-|M+\rangle.
\end{equation}
Thus we found one more nice feature of SDLCQ: in addition to preserving
supersymmetry in the truncated theory it also preserves the degeneracy of the
spectrum related to parity. We believe that this degeneracy will be lost
in the usual DLCQ approximation but currently have no proof of that.

To summarize, we have introduced a truncation procedure
that facilitates a numerical study of the bound state problem, and
preserves supersymmetry.
The interesting property of the light-cone supercharge $Q^-$
(\ref{Qminus}) is the
presence of a gauge coupling constant as an independent variable,
which does not appear in the study of two-dimensional theories.
In the next section, we will study how
variations in this coupling affects the bound states
in the theory.

\section{Numerical Results}
\label{numerical}
In order to implement the DLCQ formulation of the bound-state problem -- which
is tantamount to imposing periodic boundary conditions
$x^- = x^- + 2 \pi R$ \cite{yamawaki} -- we simply restrict the
light-cone momentum variables $k_i$ appearing in the expressions for $Q^+$
and $Q^-$ to the following discretized set of momenta:
$\left\{ \frac{1}{K} P^+, \frac{2}{K} P^+, \frac{3}{K} P^+,\dots,
\right\}$. Here, $P^+$ denotes the total light-cone momentum of a
state, and may be thought of as a fixed constant, since it is
easy to form a Fock basis that is already diagonal with respect to the
operator $P^+$ \cite{pb85}.
The reciprocal of the harmonic resolution $K$
measures the coarseness of our discretization.
The continuum limit is then recovered by taking the limit
$K \rightarrow \infty$. Physically, $1/K$ represents the smallest
positive unit of longitudinal momentum fraction allowed for each
parton in a Fock state.

\begin{figure}[ht]
\centerline{
\psfig{file=testII.eps,width=10.0true cm,angle=0}
}
\caption{{\small Plot of bound state mass squared $M^2$
in units of $2 \pi^2 / L^2$
as a function of the dimensionless coupling $0 \leq g' \leq 10$,
defined by $(g')^2 = g^2 N L/4 \pi^3$,
at $N=1000$ and $K=5$. Note that there are massless states.} \label{old}}
\end{figure}

Of course, as soon as we implement the SDLCQ procedure, which is  specified
unambiguously by the harmonic resolution $K$,  and cut off transverse  momentum
modes via the constraint $|n_i^{\perp}| \leq T$,  the integrals  appearing in
the definitions  for $Q^+$ and $Q^-$ are replaced by finite sums, and so  the
eigen-equation
$2P^+P^-|\Psi\rangle = M^2 |\Psi\rangle$ is reduced to a finite  matrix
diagonalization problem. In this last step we use the fact that $P^-$ is
proportional  to the square of the light-cone supercharge\footnote{ Strictly
speaking, $P^- =
\frac{1}{\sqrt{2}}(Q^-)^2$ is an identity in the continuum theory, and a {\em
definition} in the compactified theory, corresponding to the SDLCQ prescription
\cite{sakai95,alp99}.} $Q^-$. Previously \cite{alp99b} we studied
this theory with
$K$ up to $5$, but with only one unit of transverse momentum corresponding to
$T=1$.  In Figure \ref{old} we show the spectrum we obtained in
that study as a function of a dimensionless coupling
$g'=g\sqrt{NL/4\pi^3}$.  This figure shows several striking
features that we want to analyze in more detail. First, we want to know
whether the well defined strong-coupling spectrum, observed in
Figure \ref{old},
persists at higher values of transverse resolution $T$ and study its
convergence in $T$. The other striking feature of the $K=5$, $T=1$ spectrum is
the state that is falling rapidly at large coupling. We will analyze the
behavior of analogous states at different values of longitudinal and
transverse resolutions and in particular we will be interested in the fate of
the asymptotic (as $g\rightarrow\infty$) massless state in the continuum
limit.
In addition to this state there are many states that stay exactly massless
at all values of coupling. As we have shown in \cite{alp99b}, the number of
such states does not depend on the value of the transverse resolution.  The new
numerical data support this result. The massive state at $g=0$ are just the
discrete approximation the a continuum of free particles and is extactly
calculable analytically.

Our previous SDLCQ calculations were done using a code written in
Mathematica and performed on a PC. This code has now been rewritten in
C++ and some of the present work was done on supercomputers. We were able
to perform numerical diagonalizations for $K=2$ through 7 and for values of
$T$ up to $T=9$ at
$K=4$ and $T=1$ at $K=7$.

\begin{figure}[ht]
\centerline{
\psfig{file= plot_K4g10FINAL.ps,width=8.0true cm,angle=0}
\psfig{file= plot_K5g10FINAL.ps,width=8.0true cm,angle=0}
}
\caption{{\small Plot of bound state mass squared $M^2$
in units of $2 \pi^2/ L^2$  as a function of the transverse
resolution $T$ for a coupling
$g'=10$ and for longitudinal resolutions $K=4$ (a) and $K=5$ (b).
Boson and fermion masses are identical. }
\label{perpmom}}
\end{figure}

\begin{figure}[ht]
\centerline{
\psfig{file= plot_K4t9.ps,width=8.0true cm,angle=0}
\psfig{file= plot_K6t1.ps,width=8.0true cm,angle=0}
}
\caption{{\small  Plot of bound state mass squared $M^2$
in units of $4 \pi^2 / L^2$  as a function of the coupling
$g'$.  We show the plots for $K=4$, $T=9$ (a) and $K=6$,
$T=1$ (b).}
\label{coupling}}
\end{figure}

\subsection{Strong Coupling: Massive Spectrum}
There are very few theories, other than in $1+1$ dimensions, where we have good
information about the  strong-coupling
spectrum. In $1+1$ dimensions the concept of strong coupling has
very little meaning since the coupling only comes in as an overall
multiplicative
constant in the Hamiltonian. There are a few lattice results but
most of what we
know comes from theories that have dualities with weakly coupled theories. For
the $(2+1)$-dimensional ${\cal N}=1$ SYM
theory we are considering, there is no  known duality between strong
and weak coupling. Using SDLCQ, however, we can directly uncover the
behavior of
the theory at strong coupling.

In Figure \ref{perpmom}, we plot the bound state mass squared
$M^2$, in units of $4 \pi^2 /L^2$, as a function of the transverse
resolution $T$\ for $K=4$ and $K=5$ in the strong-coupling
regime. We see that
these curves are amazingly flat, showing that this theory converges
very rapidly with
the transverse cutoff.  We saw previously in $(1+1)$-dimensional
models \cite{alp98a} that SDLCQ  converges much
faster than DLCQ, and this
appears to persist for the transverse momentum
in $2+1$ dimensions. From these figures it
appears that we get sensible results by $T=2$ and good results already
for  $T=3$.

Given this rapid convergence, a sensible procedure is to remove the
transverse cutoff by extrapolating the masses of the low lying
bounds states to
large transverse resolution at each value of the longitudinal resolution
(thus constructing the SDLCQ spectrum of the complete three dimensional theory)
and then extrapolating to large longitudinal resolution K for each of the
states to find the spectrum as a function of the coupling.  For $K=6$ and $7$
we simply take the masses at the largest transverse momentum since there are
not enough transverse moment points to make a meaningful extrapolation.

Let us look at the bound state mass as a
function of the coupling.
Fig.~\ref{coupling}(a) shows an example of states completely settled down
in transverse resolution, namely $K=4, T=9$. In contrast,
Fig.~\ref{coupling}(b) has only $T=1$ at $K=6$. Notice that nevertheless
both plots show extremely stable states as a function of the coupling $g$,
irrespective of their status of convergence in $T$.
As we found in our preliminary study \cite{alp99b} of this theory, all
the masses in the strong-coupling region are independent of the coupling. We
see that by a coupling of $g'=20$ a stable strong-coupling spectrum has
appeared. We have
looked as high as  couplings of 1000 and we see this same behavior for all
longitudinal and transverse resolutions.

\begin{figure}[ht]
\centerline{
\psfig{file= plot_K.ps,width=10.0true cm,angle=0}
}
\caption{{\small  Plot of bound state mass squared $M^2$
in units of $2 \pi^2 / L^2$  as a function of $1/K$ for coupling
$g'=10$.  For $K=3, 4$ and $5$ we plot the value
of the mass obtained by extrapolating in the transverse resolution $T$. For
$K=6$ and $7$ we
take the values at the highest resolution $T$.}
\label{long}}
\end{figure}

In Figure \ref{long}  we plot the bound state mass as a function of $1/K$ .
These results are the first calculation of the
strong-coupling  bound states of ${\cal N}=1$
SYM in $2+1$ dimensions. As we increase
the resolution we are able to see states that have,
as their primary component,
more and more partons, and, as we have seen in other supersymmetric
theories, many
of these states appear at low energies.  This accumulation of
high-multiplicity
low-mass states
appears to be a unique property of SUSY theories. In non-SUSY theories the
new states appear at increasing  energies. In the dimensionally reduced
version of this theory we saw that the
accumulation point of these low-mass states
appeared to be at zero mass
\cite{alp99b,ahlp99}. Here again we see clear evidence of an
accumulation of low
mass states, however we don't have sufficient information to say whether an
accumulation point exists.

\begin{figure}[ht]
\centerline{
\psfig{file= plot_K5special.ps,width=10.0true cm,angle=0}
}
\caption{{\small  Plot of bound state masses falling rapidly with
increasing coupling. The mass squared $M^2$ of these states
in units of $4 \pi^2/ L^2$  are plotted as a function of $g' = g \sqrt{N L}/4
\pi^{3/2}$ for $K=5$ at the transverse resolutions $T=1$ (solid lines),
$T=2$ (dashed lines), $T=3$ (short dashed line) and
$T=4$ (long dashed line)}.}
\label{falling}
\end{figure}

At this point we have not attempted to follow a specific bound state as a
function of $K$. The appearance of new low mass as we increase $K$ makes this
difficult, however a careful study of the wavefunction should make it
possible. Also the accuracy of the extrapolation to infinite $K$ would be
greatly impoved by addition of one or two additional transverse resolution at
the largest values of $K$.

\subsection{Strong Coupling: Unphysical States}

In our preliminary study of this model we found one state that was particularly
striking. It was very heavy at small coupling and approached zero mass at
strong coupling, {\em cf.}~Figure \ref{old}.  We have now been
able to look at this state at higher values of both transverse and
longitudinal resolutions. We now believe that this state is
most likely not a physical one.

We are now able to identify two states with irregular coupling dependence
which  are shown in Figure
\ref{falling} at various transverse resolution for $K=5$. We see that as we
increase the transverse cutoff these
states move up rapidly  in mass, leading us to conclude that as $T \rightarrow
\infty$, they decouple. One of these irregular states falls down to
$M=0$ and then
moves up, while another one has the same type of behavior, but with finite
minimal mass. The fact that the first state touches zero is of some interest: a
similar behavior was noted in a supersymmetric
scalar matrix model in \cite{klebhash} and in that model the authors
conjecture that this behavior might signal the existence of a critical
coupling. Here the point where the mass
goes to zero would appear to move to infinity as we remove the transverse
cutoff, and it is not at all clear that those ideas carry over here.

At $K=6$ and $K=4$ we do not see these states, at least not at the same masses
but at $K=7$ we again see such states. We believe that this is strong evidence
that these are unphysical states. Clearly a real normalizable bound state must
be visible at both even and odd resolutions, which is not the case here.
Recently we have seen unphysical massless states of this type in a two
dimensional theory with  $(8,8)$ supersymmetry \cite{ahlp99}.
In that theory we had an independent theoretical
evidence for them to be unphysical.

\subsection{ Massless States}
In Figure \ref{old} we see a number of states that become massless
as $g' \rightarrow0$. We already explained this property in \cite{alp99b}.
Namely at zero coupling only the first term survives in the supercharge
(\ref{Qminus}) and then all the partons with $n_\perp=0$ (anti-)commute with
$Q^-$. Thus any state constructed from such partons only becomes massless.
The inverse statement is also true: at $g'=0$ a massless state cannot contain
any parton with $n_\perp\ne 0$. Thus the set of massless states at $g'=0$
coincides with a Hilbert space of the theory dimensionally reduced to $1+1$.
Moreover, the whole infrared spectrum of SYM$_{2+1}$ at small coupling is
governed by the dimensionally reduced theory (see \cite{alp99b} for details).

Previously \cite{alp99b,alp98b} we commented on the existence of
exactly massless states and in \cite{alp99b} on the one-to-one correspondence
between them and massless states of the $(1+1)$-dimensional model. Actually
this fact provides an easy way to construct massless states for
three-dimensional theories; the matrices to be
diagonalized have a size much smaller
than the ones used in the straightforward approach. The counting of
massless states
in three dimensions is also reduced to the analogous problem in $1+1$
dimensions.
For finite $N_c$, even the $(1+1)$-dimensional case is not easily handled
\cite{alp98b}; however, for large $N_c$ the multi-trace states decouple, and
one needs to count only single-trace massless states. At resolution $K$ there
are $2(K-1)$ of them. As a numerical check of the correspondence between
massless sectors of $(2+1)$ and $(1+1)$-dimensional
theories, we can count the massless states
at different values of transverse resolution and as anticipated we found this
number to be independent of $T$.
These massless states are BPS states in the
sense that they are destroyed by one super-charge, $Q^-$, and not the
other, $Q^+$, and
the BPS bound, which is zero here, is saturated.

In \cite{alp99b} it appeared that there were additional states that became
massless as $g \rightarrow \infty$ but now we believe that these states are
unphysical. Therefore the only massless states at nonzero coupling are the
same $2(K-1)$ BPS states we saw in the dimensionally reduced model.

\section{Discussion}
\label{summary}
In this work, we considered the bound states of three dimensional  SU($N$)
${\cal N}=1$ super-Yang-Mills defined on the compactified space-time ${\bf R}
\times S^1 \times S^1$. In particular, we compactified the light-cone
coordinate
$x^-$ on a light-like circle via DLCQ, and wrapped the remaining  transverse
coordinate
$x^{\perp}$ on a spatial circle. We showed explicitly that SDLCQ,  employed
in recent studies of $(1+1)$-dimensional supersymmetric gauge theories, extends
naturally to $2+1$ dimensions. The supersymmetry becomes
${\cal N}=(1,1)$ because we can always chose $P_\perp$ to be zero in  a
light-cone quantized field theory, and SDLCQ provides a regularization
scheme  that preserves this supersymmetry. The supersymmetric theory considered
here is finite  and requires no renormalization.

By retaining a finite number of transverse and longitudinal modes, we were
able to solve for bound-state wave functions and masses numerically by
diagonalizing
the discretized light-cone supercharge.  The theory clearly has a stable
spectrum at both small and large couplings. In Figure \ref{perpmom} we
see that the theory converges very rapidly in the transverse
resolution. We have
seen in reference \cite{alp98b} that SDLCQ  gives very smooth behavior in the
longitudinal resolution. In Figure \ref{falling} we see that the states with
irregular coupling dependence move off rapidly to high mass with increasing
transverse resolution. They also do not seem to appear at resolutions 4 and 6.
We therefore conclude that they are not physical states.
We see that there are no new massless states at strong coupling,
and the complete massless sector of SYM$_{2+1}$ is determined by the
two-dimensional model. The number of exactly massless states at any coupling is
$2(K-1)$, with no dependence on the transverse resolution. In addition, some
states become massless as $g$ goes to zero, but their behavior is
also described
by the theory in
$1+1$ dimensions. Consequently, we conclude that
the entire massless spectrum of the $(2+1)$-dimensional model is determined by
the dimensionally reduced model.

In previous work
\cite{alp99b} we saw that the average number of particles
in the massless states increases with
$g$ and quickly becomes equal to the maximum number allowed by the resolution.
We also see  here that the number of low-mass states increases with resolution.
Together this implies that at strong coupling the light states of this theory,
and other SUSY theories, have a huge number of degrees of freedom. No doubt,
it is this fact that allows for the possibility that
these SUSY theories can contain all of the physics of dual theories in a
different number of space-time dimensions.
It would be interesting to relate this observation with the recent
claim that strongly coupled super-Yang-Mills theory corresponds to string
theory in an anti-de Sitter background \cite{maldacena}. Of course, the
techniques we have employed here may be applied to any supersymmetric gauge
theory defined on a suitably compactified space-time. This should facilitate a
more general study of the strongly coupled dynamics of super-Yang-Mills
theories, and in particular, allow us to scrutinize the string-like properties
of Yang-Mills theories.

We have neglected the zero modes totally in this calculation. It remains an
important problem to include these modes. We already know a
great deal about zero modes \cite{alpt98} which are, after all, really only
a few extra quantum mechanical degrees of freedom. It has recently been
conjectured by Witten \cite{witten} that including these zero modes leads to
spontaneous supersymmetry breaking in this theory.

Let us briefly comment on the  $L$ dependence of the spectrum. For large
$L$ the appropriate dimensionless $L$ independent mass scale is;
\[
{M^2 \over g^4 N^2} \propto {M^2 L^2/4\pi^2 \over(g')^4}
\]
At large $g'$ the spectrum is constant in terms of $M^2
L^2/4\pi^2$, therefore in terms of this dimensionless mass scale the entire
spectrum would go
to zero as $g' \rightarrow \infty$. A possible interpretation of this result is
that in the continuum limit this theory approaches a conformal field
theory. There are however very massive states in our spectrum, that we did not
study, that could remain massive in the contimuum limit.

    The code that we are currently using is a newly
written C++ version  of the Mathematica code that we used in much of
our earlier
work. Our large runs  for matrix generation are currently performed
at the Ohio Supercomputer Center.  Matrix diagonalization is
done using standard Lapack routines \cite{Lapack} on supercomputers at the Ohio
Supercomputer Center and the Minnesota Supercomputing Institute. This is
our first  project with this new configuration, and we are currently working
on several  analytical and numerical improvements that we expect will
allow us to increase by several factors of 10 the size of the problems we
will be able to address in the future. Among these are $N=4$ SYM in $3+1$ and
$N=1$ SYM in $2+1$ with a Chern-Simons term \cite{witten}.

\medskip
{\large \bf Acknowledgments}
This work is supported in part by the US Department of Energy. We would like to
acknowledge the Ohio Supercomputer Center and the Minnesota Supercomputing
Institute for grants of computing time. We also would like to
acknowledge David G.~Robertson of the Ohio Super Computing Center
for his valued assistance and Aki Hashimoto for valuable conversations.

redpajama_set_name: RedPajamaArXiv