Did you take a beautiful photograph, but the backlighting is washing everyone out? Or is the photograph too dark to tell what's going on in it? Photoshop can rescue good photos from bad lighting.
How can Photoshop redeem bad lighting?
Here are a few quick fixes.
Go to Image > Adjustments > Brightness/Contrast to alter the brightness or darkness of an image. For an image that is too dark, increase the brightness. However, be careful not to increase the brightness to expose the graininess of an image. For an image that is too light, turn down the brightness.
You can also adjust the color hue. When you brighten or darken an image, it may become discolored. Adjusting the hue of image can restore the color scheme of the original while maintaining improved lighting.
On a photograph that is washed out and too bright, turning up the contrast can help define some of the darker points of the image. The only danger to increasing contrast is that it can create images that appear too stark. Compare the original side by side with the altered image to avoid a too-shocking contrast.
Auto-adjusting a photograph would of course be the simplest route to take. While auto-adjust does not catch all the issues with a photo, it can identify and reduce some of the most obvious photographic indiscretions.
For better photographs and the resulting images created from the background images, you can use quick Photoshop hacks. Keep reading our blog for more Photoshop posts throughout the month of January. And if you are interested in working with our expert team of designers, give us a call.


Hours: 9 a.m.-9 p.m. Mon.-Thu., 9 a.m.-10 p.m. Fri.-Sat.
Less a taco truck than a snack bar that also has a few Mexican offerings. They do sell tacos, flautas, and mega-tortas, but to find them, you'll have to search the menu, past the chili dogs, cheeseburgers, frito pies, barbecue chicken sandwiches and Doritos nachos -- yes, the cheesy, orange triangles come topped with yet another cheese-like substance and jalapenos. No seating.


Experience Adventure at Nae Limits!
With over 14 Water & Land Adventure Activities to choose from there really are "Nae Limits" to your Highland Perthshire adventure. Nae Limits 4* Activity Centre is centrally located on the A9, open all year round, providing you with all the facilities and equipment you need for your day of adventure.
White Water Rafting, Canyoning, Tubing and Quad Biking are just some of the adventure activities on offer for all you adrenalin junkies out there! For a fun filled family day out that you will never forget then Family Rafting or Gorge Walking is a must. Or if Mum & Dad want a day "off" then bring the kids along to Wee Limits – Outdoor Adventure Days just for "wee adventurers" aged 6-12 running during the school holidays.
Multi Activity Breaks are also on offer, perfect for stag & hen do's, birthday bashes or a unique team building event with your very own Highland Games.
After your action-packed day of adventure, visit the on-site café Rivers Meet for a tasty bite to eat – the Nachos come highly recommended. Not forgetting the paw-dorable doggy menu for your furry friends, the Sausage Sizzler is a firm favourite.
Ps Loch Tay Highland Lodges guests get 10% off Nae Limits Water Activities – just enter code "LTHL10" at the checkout.
Now the only decision left is which activity to pick?


Server Assistant $25-30/hour with tips!
Hiring Unrivaled Server Assistants for our beautiful waterfront location in downtown Seattle.
Job responsibilities will include running food, ongoing table maintenance, clearing and resetting of tables. Must have food and beverage knowledge along with hospitality and service skills. Must have a flexible schedule and weekend availability is required.
Minimum wage + tips (average $25-30/hour with tips).
Since opening in 1975, Elliott's Oyster House has delighted taste buds with impeccably fresh seafood. Through the years, we've earned a national reputation for our seafood specialties: sustainable Dungeness crab, wild salmon from thriving runs, Alaskan halibut, and Pacific Northwest shellfish - including our star attraction, oysters. Sustainability is particularly important to us. So Elliott's works with local oyster growers and fishery partners who share our commitment to preserving the planet.


Welcome to the Seattle's Backyard, the hidden gem of the Pacific Northwest. Have you heard about Seattle Southside? If you've ever traveled to Western Washington, odds are you've visited here and didn't even know it. Whether you're a local or a visitor, there's just so much to love about this area that it's difficult to choose just ten. Here's a list of ten reasons to love Seattle Southside.
Nestled along Puget Sound in Western Washington, Seattle Southside is centrally located between Seattle and Tacoma. The three cities of SeaTac, Tukwila, & Des Moines compromise the area also known as "Seattle's Backyard." There's plenty to experience here, not to mention, everything else that's just a stone's throw away from the airport. Take a short trip up north to Downtown Seattle on the Link Light Rail, take a tour with Tours Northwest to Mount Rainier National Park, or take a tour of the San Juan Islands on a Victoria Clipper.
Seattleites love their festivals, and that feeling extends to Seattle Southsiders as well. Do you like comicons? Every year, the DoubleTree in SeaTac hosts Aki Con for anime enthusiasts, Crypticon for horror buffs and since 1978, Norwescon has been a comicon juggernaut for fans of fantasy & sci-fi. There's the Poverty Bay Blues & Brews Fest every summer on the shores of Puget Sound, the delicious Des Moines Waterfront Farmers Market, the stellar UFO Festival in Burien, Hops & Props at The Museum of Flight, 4th of July at Fort Dent Park, and that's not even scratching the surface of all the exciting events in Seattle Southside and Western Washington.
Shopping 'till you drop is quite possible in Seattle Southside. In fact, that feat could probably be accomplished at one place: Westfield Southcenter. Westfield Southcenter is the largest shopping center in Washington State, and is home to dozens of boutique shops, big box stores, restaurants, and even an AMC theatre. Step out of Westfield and the shopping options continue in the Southcenter area with jewelry, books, recreation and sports stores and so much more.
This sort of goes along with location. You really don't need a car in Seattle Southside to get to where you want to go. The Link Light Rail goes as far south as Angle Lake and as far north as Husky stadium, making travel to downtown Seattle a breeze. Staying in a hotel in SeaTac? Take the free Southside Express mall shuttle to Westfield Southcenter for all your shopping and entertainment needs. If you're looking to get out into the evergreen side of the Evergreen State, take a tour with Tours Northwest or Customized Tours to Mount Rainier or Snoqualmie Falls.
There's no doubt about it, downtown Seattle is expensive. Whether you're talking about parking fees, hotel rates, or anything travel related, it's going to cost you a bit more up there. Seattle Southside has over 50 value-priced hotels, with rates typically 20-30% less than their downtown counterparts. Even if downtown Seattle is your priority, you're just a quick light rail ride away. The Seattle Southside Regional Tourism Authority also offers the free Do More-Save More Passport to Savings, which functions like digital coupon book to the area's top attractions, restaurants, and even some hotels.
Sports are a big deal in Seattle Southside. Head down to the sports megacomplex, Starfire Sports, and watch the Seattle Sounders practice or play a game yourself! Also, coming to Seattle Southside in 2018, Starfire Sports will be home to the Seattle Seawolves, one of the founding teams of Major League Rugby in the United States. If you're a thrill seeker, you need to try indoor skydiving at iFLY Seattle. Looking for a leisurely game of golf? Play 18 holes at Foster Golf Links along the Duwamish River. Of course, if you want to catch a Seahawks or Mariners game, hop on the light rail and you'll be there in no time.
Seattle Southside has always been a great destination for families. The hotels are family friendly, there's a great selection of restaurants, but the main draw for families and kids would have to be the attractions. You can take to the skies on one of The Museum of Flight's flight simulators, or iFLY Seattle's vertical wind tunnel (they cater to ages 3-103). Spend a day at Family Fun Center with go-karts, batting cages, mini golf, and more. Bowl and game to your heart's desire at ACME Bowl and Round 1 Entertainment, experience the future of laser tag and virtual reality at Virtual Sports, take a sweet factory tour of Seattle Chocolates and sample some delectable delights. After a day of fun, head to California Pizza Kitchen or Bahama Breeze for a dinner the whole family can agree on.
Speaking of dinner, Seattle Southside is home to a world-class dining scene. The emphasis should be on "world," as the international dining scene is booming! Try Din Tai Fung's famous Taiwanese dumplings, Arashi Ramen's savory tantan men, shrimp & chorizo tacos at Moctezuma, sweet crispy garlic chicken at Bai Tong, rich Ethiopian coffee at Star Coffee and so much more. Not to mention, you can't come to the Pacific Northwest and not try some fresh seafood. Try the chowder at Salty's at Redondo, Anthony's HomePort, Wally's Chowder House, and Duke's Chowder House and see which one's your favorite.
The number one reason to love Seattle Southside just about combines all previous items on this list as Seattle Southside is home to a unique blend of nature and urban land/cityscapes. They've got the giant mall, but there's also beautiful Des Moines Beach Park on the shores of Puget Sound. There are 50+ hotels all sitting in the shadow of Mount Rainier. There's plenty of indoor recreation like bowling and gaming, but there's also plenty of hiking trails and beaches for walking. Seattle Southside is close to Seattle, close to the mountains, close to the water…they've got it all! Spend a vacation or staycation in Seattle Southside and experience this natural/urban wonderland called Seattle's Backyard.


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Photos: Explosive wildfires rage across California stoked by fierce winds
by: The Associated Press and Nexstar Media Wire
Posted: Sep 9, 2020 / 07:44 AM PDT / Updated: Sep 9, 2020 / 06:51 AM PDT
Flames lick above vehicles on Highway 162 as the Bear Fire burns in Oroville, Calif., on Wednesday. The blaze, part of the lightning-sparked North Complex, expanded at a critical rate of spread as winds buffeted the region. (AP Photo/Noah Berger)
Firefighters watch the Bear Fire approach in Oroville, Calif., on Wednesday. (AP Photo/Noah Berger)
A firefighter watches flames ignite a tree at the Bear fire in Oroville, California on September 9, 2020. Dangerous dry winds whipped up California's record-breaking wildfires and ignited new blazes, as hundreds were evacuated by helicopter and tens of thousands were plunged into darkness by power outages across the western United States. (Photo by JOSH EDELSON/AFP via Getty Images)
Firefighters monitor the Bear Fire burning in Oroville, Calif., on Wednesday. (AP Photo/Noah Berger)
Embers fly across a roadway as the Bear Fire burns in Oroville, Calif., on Wednesday. The blaze, part of the lightning-sparked North Complex, expanded at a critical rate of spread as winds buffeted the region. (AP Photo/Noah Berger)
Flames surround a segment of Lake Oroville as fire continues to spread at the Bear fire in Oroville, California on September 9, 2020. – Dangerous dry winds whipped up California's record-breaking wildfires and ignited new blazes, as hundreds were evacuated by helicopter and tens of thousands were plunged into darkness by power outages across the western United States. (Photo by JOSH EDELSON / AFP) (Photo by JOSH EDELSON/AFP via Getty Images)
SHAVER LAKE, CA – SEPTEMBER 8: A community of forest homes lies in ruins along Auberry Road in the Meadow Lakes area after the Creek Fire swept through on September 8, 2020 near Shaver Lake, California. California Gov. Gavin Newsom has declared a state of emergency in five California counties after record heatwave temperatures fueled numerous wildfires over the Labor Day weekend. The state of emergency applies to Fresno, Madera and Mariposa, San Bernardino and San Diego counties. (Photo by David McNew/Getty Images)
A burned Valero gas station smolders during the Creek fire in an unincorporated area of Fresno County, California. (Photo by JOSH EDELSON/AFP via Getty Images)
A home is completely destroyed after the Creek Fire swept through the area near Shaver Lake, California.(Photo by David McNew/Getty Images)
Butte county firefighters watch as flames tower over their truck at the Bear fire in Oroville, California. (Photo by JOSH EDELSON/AFP via Getty Images)
A storage tank sits near a destroyed home after the Creek Fire swept through the area near Shaver Lake, California. (Photo by David McNew/Getty Images)
A melted slide smolders as a playground continues to burn at Pine Ridge school during the Creek Fire. W(Photo by JOSH EDELSON/AFP via Getty Images)
High-tension power lines are seen against a burning landscape in the Tollhouse area of unincorporated Fresno County, California.(Photo by JOSH EDELSON/AFP via Getty Images)
A home is completely destroyed after the Creek Fire swept through the area near Shaver Lake, California. California Gov. Gavin Newsom has declared a state of emergency in five California counties after record heatwave temperatures fueled numerous wildfires over the Labor Day weekend. The state of emergency applies to Fresno, Madera and Mariposa, San Bernardino and San Diego counties. (Photo by David McNew/Getty Images)
SHAVER LAKE, Calif. (AP) — Wildfires raged unchecked throughout California Wednesday, and gusty winds could drive flames into new ferocity, authorities warned.
Diablo winds in the north and Santa Ana winds in the south were forecast into Wednesday at a time when existing wildfires already have grown explosively.
On Tuesday, 14 firefighters were forced to deploy emergency shelters as flames overtook them and destroyed the Nacimiento Station, a fire station in the Los Padres National Forest on the state's central coast, the U.S. Forest Service said. They suffered from burns and smoke inhalation, and three were flown to a hospital in Fresno, where one was in critical condition.
In the past two days, helicopters were used to rescue hundreds of people stranded in the burning Sierra National Forest, where the Creek Fire has destroyed 365 buildings, including at least 45 homes, and 5,000 structures were threatened, fire officials said.
Flames threatened the foothill community of Auberry between Shaver Lake and Fresno.
In Southern California, fires burned in Los Angeles, San Bernardino and San Diego counties, and the forecast called for the arrival of the region's notorious Santa Anas. The hot, dry winds could reach 50 mph at times, forecasters said.
People in a half-dozen foothill communities east of Los Angeles were being told to stay alert because of a fire in the Angeles National Forest.
"The combination of gusty winds, very dry air, and dry vegetation will create critical fire danger," the National Weather Service warned.
The U.S. Forest Service on Monday decided to close all eight national forests in the southern half of the state and shutter campgrounds statewide.
More than 14,000 firefighters are battling fires. Two of the three largest blazes in state history are burning in the San Francisco Bay Area, though they are largely contained after burning three weeks.
California has already set a record with nearly 2.3 million acres (930,800 hectares) burned this year — surpassing a record set just two years ago — and the worst part of the wildfire season is only beginning.
"It's extraordinary, the challenge that we've faced so far this season," Gov. Gavin Newsom said.
The threat of winds tearing down power lines or hurling debris into them and sparking a wildfire prompted Pacific Gas & Electric, the state's largest utility, to shut off power to 172,000 customers over the weekend. More outages were expected Wednesday, with power not expected to be completely restored until Wednesday night.
To the south, Southern California Edison warned roughly 55,000 customer accounts may lose power while San Diego Gas & Electric said 16,700 customers are at risk of a preemptive outage.
In the Sierra National Forest east of Fresno, dozens of campers and hikers were stranded at the Vermilion Valley Resort after the only road in — a narrow route snaking along a steep cliff — was closed Sunday because of the Creek Fire.
Well before dawn Tuesday, the sound of helicopter blades chopping through the air awoke Katelyn Mueller, bringing relief after two anxious nights camping in the smoke.
"It was probably the one time you're excited to hear a helicopter," Mueller said. "You could almost feel a sigh of relief seeing it come in."
The use of military helicopters to rescue a large number of civilians for a second day — 164 before dawn Tuesday and 214 people from a wooded camping area on Saturday — is rare, if not unprecedented.
"This is emblematic of how fast that fire was moving, plus the physical geography of that environment with one road in and one road out," said Char Miller, a professor of environmental analysis at Pomona College who has written extensively about wildfires. "Unless you wanted an absolute human disaster, you had to move fast."
Numerous studies in recent years have linked bigger wildfires in America to global warming from the burning of coal, oil and gas, especially because climate change has made California much drier, making plants more flammable.
"The frequency of extreme wild fire weather has doubled in California over the past four decades, with the main driver being the effect of rising temperature on dry fuels, meaning that the fuel loads are now frequently at record or near-record levels when ignition occurs and when strong winds blow," Stanford University climate scientist Noah Diffenbaugh said in an email.
Stanislaus County to open more locations in push to vaccinate more residents
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Sycamore Trust
Alumni & Friends Protecting Notre Dame's Catholic Identity
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Talking about matters related to our fight for an authentic Catholic renewal at Notre Dame.
Whether or not you agree with the views we express, we encourage you to join us online or by phone to discuss our bulletins and other matters related to Notre Dame's Catholic identity.
Upcoming Discussion
On Wednesday, March 22 (7:30-8:45 PM EDT), Bill Dempsey, Sycamore Trust President, will discuss Fr. Jenkins's decision to break with tradition by not inviting President Trump to deliver this year's commencement address at Notre Dame – a decision which belies his defense against charges of scandal caused by President Obama's 2009 commencement address. Click below to register.
Read all about it in our current bulletin, The Ghost of Commencement Past.
Like the ancient Sycamore tree standing watch over the Grotto, Sycamore Trust, with its broad base of supporters within the Notre Dame Family, seeks to protect the school's formative heritage — its Catholic identity and its sustaining relationship to the Church
NDCatholic.com is a a project of Sycamore Trust which provides information to present and future students on how to obtain an authentic Catholic education at Notre Dame.
Click on the image above to purchase "For Notre Dame: Battling for the Heart & Soul of a Catholic University" by Wilson D. Miscamble, C.S.C.
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Sycamore Trust provides a source of information, a means of communication, and a collective voice to Notre Dame alumni and others in the Notre Dame family who are concerned about preserving the Catholic identity of the University.
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Tag: Edinburgh
Remembering former Hibernian and Congolese cult hero Dominique Malonga
With the African Cup of Nations having kicked off at the weekend, NTOF are looking at some of the most interesting African players to grace Scottish fo…
Abdessalam Benjelloun - Hibs' Moroccan marksman
With the African Cup of Nations kicking off this week, NTOF will be looking at some of the most interesting African players to grace Scottish football.…
Other clubs must follow Hibs and Leeann Dempster's lead according to MSPs
Hibernian CEO Leeann Dempster has rightly been commended for looking to eliminate bad behaviour at one of the biggest clubs in the country. The section…
Hearts' Hibs draw was secured by the man who scored for opponents
It wasn't the prettiest game, but Hearts managed to grind out a 1-1 draw away to rivals Hibs. It means they have went undefeated at Easter Road this se…
Four former Hearts and Hibs players to have crossed the Edinburgh divide
The two top Edinburgh sides will lock horns for the final time this season on Sunday as Hibs host Hearts at Easter Road. There has been one win for ea…
Three Neil Lennon raids on Celtic as Hibs manager
Hibs haven't looked back since being relegated to the Championship in 2013-14. Since then the Hibees spent three seasons in Scotland's second tier and …
Hibernian winger achieved something that hasn't been seen for 34 years on Saturday
Hecky's at the wheel rang out at full time in Gorgie on Saturday. Hibernian managed to beat their rivals Hearts at Tynecastle for the first time in 6 y…
Former Hibs hitman can't stop scoring for the Hatters
As the weeks go by, it looks more and more likely that Luton Town will be playing Championship football next season. It's a remarkable tale for the Hat…
How former Hearts hitman Bjørn Johnsen has blossomed
After scoring Norway's opener in their Euro 2020 qualifying clash with Sweden last night, Bjørn Johnsen provided an unwelcome reminder for Hearts fans.…
Three notable Hearts vs Aberdeen clashes - another classic to come?
The big Premiership fixtures don't stop with the third Old Firm league clash of the season this weekend, while fifth placed Hearts host third placed Ab…


Plus playing the exact same level for 8 hours seeking bugs can drive you up the wall, to the point you believe you're head is likely to spin. Communication skills refer to the ability to convey data in a very clear and understandable fashion, the capability to engage with diverse people and personalities and the capacity to listen and comprehend what others are saying. Vocational skills typically refers to occupations you could learn with some simple training or on-the-job in lieu of a university degree. You will also require strong interpersonal skills to create a rapport with students. Alternatively, you must demonstrate that you've got the capacity to draw in a crowd.
A universal comprehension of the full business is critical in order to completely appreciate the duties of the offered role. The experience is priceless and if it's possible to can receive ONE job for a game tester another firm will hire you later. Teaching experience is preferred, but it's not always required.
A letter of reference explains the abilities and achievements of a particular individual. A cover letter is also where you can at times compensate for lack of knowledge or education, by explaining how you'd still be a great choice because of different strengths. Your cover letter is typically the very first point of interaction involving you and the prospective employer, and that's why it is critical that cover letters are written with careful consideration. Therefore, in the event the cover letter doesn't impress him, he might not even bother to appear further, even if your resume is stellar.
A master's degree and training in the hottest computational design and simulation computer computer software tools might enhance your odds of locating a job. Students have an assortment of rights they may not know about, including the right of disabled students to acquire reasonable accommodations. Some colleges may require the level to coincide with the courses being taught, or else they may use that as a means to weed out applicants if there are too many who apply to get a position.
CPR training is normally a perquisite too. Technical leads commonly do the job for software businesses and information technology consulting firms. Engineering is a profession which uses computers in many ways.
A journalist's starting salary often is dependent upon the sort of publication or broadcast business you work for as well as economic aspects that influence the business. In case the employer employs scanning software, the computer software might not be in a position to read your resume and that may damage your odds for an interview. Some could discover that it's easy, while some still find it difficult to acquire their resume to get read by their prospective employers. Be certain to highlight your strengths, showing your prospective employer what you could offer.
If you're asking for an engineering job, your stint for a dogwalker might not be relevant. When writing an expert narrative, list all appropriate background experience you've got for the job accessible. A whole lot of testing jobs are temp to employ, or only temp. Most likely if you become hired to a testing job you aren't going to be officially working for that company, you're going to be hired beneath a staffing firm, or you'll have a contract with the organization. If you're prepared for hard work then you're well prepared to be a leasehand.
When applying for employment, particularly in the era of technology, it's always an excellent idea to supply the skills that employers may search for in potential candidates. Writing targeted, employer-specific and beneficial cover letters is one proven means to do it. The exact same can be said for positions in fields like accounting, in which knowledge of the several software programs that exist will be useful and show a possible employer that you're ready to learn a program quickly. Being between jobs isn't ideal. Make certain to get any technical kinks out ahead of time so you're not struggling with them when it is time to conduct the interview. The very last things you would like to happen come interview time are technical issues that delay the beginning of the interview.
Making an educated decision in a timely manner is a skill that demands the ability to appraise all feasible options and pick the best possible approach concerning functionality and feasibility. As the work search procedure gets increasingly internet-based, a growing number of companies are conducting job interviews over Skype. You then go ahead to send several applications to different schools on account of the simple fact that admission is quite competitive in Germany due to the dearth of tuition fees, and hence you wouldn't wish to risk putting all your eggs in 1 basket. If you haven't used Skype before, it is essential that you get acquainted with the software before you get started conducting the interview.
Your letter should explain what you can do to help your customer,' not what it is you're selling, she explained. For a more customary company, a normal three-paragraph letter is going to do. Therefore, writing an excellent letter has to be your aim to become noticed by the recruiter. Essential things are application letter should be original and ought to represent you. At the moment, application letter for hiring managers should be accomplished especially for each application.
If you wish to receive a job in a well-known company, do your very best to fulfill their standards and to present yourself accordingly. Just concentrate on the roles you've had that are related to the job which you're applying for. Or if you're young and searching for your first professional job then it would be suitable to compose a cover letter. When searching for someone, there's normally a particular job in mind, but it doesn't necessarily indicate that's the only thing we're searching to fill. Some decide that more is better, sending as many works since they canand that is only one of the biggest mistakes that can be made.
To find more information about resume and cover letter writing services have a peek at the ideal internet page. Choosing how to deal with your letter can be hard, particularly if you're not quite certain who will be reading it. In truth, it's much better than OK to polarizing. Among the toughest things about cover letters is they must be catchy, informative, and short at the exact same moment. The whole idea of a very good cover letter is the fact that it isn't generic but specific to the job which you are applying for! As soon as it is not super fun thinking of writing a letter to each prospective employer about all of the explanations for why they need to interview you, it's a necessary evil that may help determine the hiring manager's interest (positively or negatively) in meeting you.
Don't be lazy in regards to writing a cover letter! In years past cover letters were the only means to acquire an awareness of a candidate's personality. If you are able to write a great cover letter, it may be an immediate ticket to your job.
Cover letters are a valuable part of the application procedure, and an excellent way to ensure your resume speaks for you as well as your abilities. If you do this, you may as well not send any cover letter whatsoever. In reality, the cover letter is a great chance for you to picture what the employer most wants to hear dependent on the work advertisement and your own company research, then determine what would work best to assist you in getting that job. Drafting a cover letter can be among the most stress inducing facets of the work search. In any case, reading cover letters that worked is a terrific method of getting inspiration. Standard cover letters are written for a particular job or position you're applying to.
Simply following some basic strategies and making certain adjustments could be sufficient to make your cover letter much superior than before. A cover letter is your opportunity to generate a positive first impression on a possible new employer, therefore it's important to devote some time making sure yours is like it can get. Today, a great cover letter isn't a full-page letter.
You locate a letter you desire after browsing through several sites. It's rather easy to be sure your cover letter is error-free. The cover letter is the main tool to entice the recruiters' interest. In addition to that, your cover letter might even make it in the hands of the individual you addressed it to! Internal cover letter help online is a simple method of getting beyond the very first stage as it is possible to see cover letters and resumes of one candidate and find out how they've been in a position to compose the two independently.
The easiest way to create a cover letter is to write in a way that explains to the possible employer as to why you're a great fit. It is much more than what you can do or have done in the past. It does not need to be long either, each paragraph only needs to be a couple sentences to get the point across. A special cover letter ought to be written for each individual job which you are applying for. An excellent cover letter is a chance to explain any shortcomings you may have.
The most common sort of cover letter is the conventional cover letter, sometimes referred to as an application letter. The cover letter is a chance to begin a conversation and for us to get to understand what makes you tick. A video cover letter ought to be between 30 seconds to a single minute.


All 5 pieces bolt on to existing mounting points with no welding or fabricating required.
Low hanging exhaust crossover pipe is protected with a smooth sheet of steel or aluminum.
NOTE: If you order this set in aluminum, the crossmember will be powder coated black and made of steel. If you have a diff drop, you will need to get spacers from the maker of your diff drop to space your skid plates.
Strength without the weight. Our 5052 laser cut aluminum alloy has the same strength levels as our 3/16" steel, but at a faction of the weight. We recommend aluminum where the application sees regular off-roading, yet limited potential for dragging on hard surfaces like rocks. While 1/4" aluminum has the strength to handle heavy rock impacts, it is much more susceptible to galling than steel, when dragged over rocks. Galling results in what looks like fine aluminum shavings by the rock that was dragged down the plate. Another way of thinking about this is by first stating that aluminum has no problem at impacting an obstacle, it's what happens after impact that matters. After impact, if your driving style is to reassess the trail and choose a better line, aluminum is the right choice. If your driving style is to continue on the same line, as in rock crawling applications, we would recommend our 3/16" steel systems. Aluminum does not require prepping and repainting impact areas to prevent rust.


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Concussion Effects May Linger More Than a Year After Return to Play
Brain Concussion
New research published in Neurology has found athletes' brains may still not be fully recovered 1 year after being allowed to return to play. The study involved 24 college athletes with concussion college athletes and 122 athletes without concussions. Men and women were equally represented in both groups. Participants competed in the following sports: volleyball, hockey, soccer, football, rugby, basketball, lacrosse, and water polo.
When compared to athletes without concussions, those returned to play after a concussion had significantly reduced blood flow in the brain 1 year later. Specifically, athletes with concussions had an average decrease in blood flow of 10 mL/100 g of blood per minute compared to athletes without concussions. When examining diffusion weighted imaging (DTI) of white matter tracts, researchers also found the brains of athletes with concussions still showed possible signs of tissue swelling 1 year after return to play. No changes in resting brain activity in grey matter or white matter tractography differences were seen, however.
"There is growing evidence that recovery from a concussion may not be complete when symptoms such as headache and dizziness are gone and the athlete is allowed to return to play, so it is important to determine if various aspects of the brain injury resolve over time or are perhaps permanent," said study author Nathan W. Churchill, PhD, of St. Michael's Hospital in Toronto, Canada. "Our research looked at the brain one year after return to play in a group of college athletes and found that evidence of brain injury from concussion remained in some parts of the brain."
"The principal finding of this study was that different aspects of brain physiology have different patterns of long-term recovery," said Dr. Churchill. "These findings significantly enhance our understanding of the natural course of brain recovery after a concussion. Future studies are needed to look beyond one year after return to play to see if these longer-term brain injuries eventually heal or remain permanent."
For athletes with concussions, the first brain MRI was performed an average of 4 days after injury. The second occurred when the athlete was cleared to return to play. The third scan was performed 1 year after return to play. Athletes who did not have concussion also had a brain MRI at the start of their seasons. Brain scans of the athletes with concussions were then compared to the brain scans of the healthy athletes.
A limitation of the study is no athletes had baseline brain MRI done before injury and comparisons were age-, sex-, and concussion-history matched instead.
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Home Business COVID-19 puts private school teachers on life support
COVID-19 puts private school teachers on life support
"The coronavirus pandemic has really affected me financially. I have emptied my savings account at the moment and I am really struggling to survive. My school paid me full salary for the month of March, but told me I wouldn't be paid anything from April since there is no money coming in," a private school teacher who has four dependents and wants to only be known as Gabriel told the B&FT.
Many private school teachers can identify with the situation of Gabriel narrated above. Some have been told point-blank not to expect anything called money from their employers, as the closure of schools in March to contain the coronavirus pandemic has stopped all incoming revenues – namely school fees, extra classes fee, feeding fee, among others.
For most of these teachers, even though they appreciate the restriction from government as well-intentioned, the hardship it has brought on their lives and those of their dependents is unbearable and has put them in desperate situations. Some, this Paper is reliably informed, have even sent their families to their villages; as the standard and cost of living there is far lower than the city.
For others, the situation has disrupted their planned projects for the year. For example, Jonathan, also a private school teacher in Accra, says he was saving toward marriage by end of the year. But with the disruption to his income, he has no option other than to dip his hands into his savings – essentially, meaning the marriage plans must be put on hold till further notice.
What makes the situation more dispiriting for these private school teachers is that most of them survive on salaries of less than GH¢1,000 (about US$180) monthly. Gabriel, for example, says he takes home an income of less than GH¢700 monthly. And it is with this meagre salary that his mother, two nephews and one niece depend – such a nerve-racking ordeal for a young man in his early 30s.
To buffer their scanty salary, most private school teachers also depend on extra class fees to survive. Without this, Jonathan says, the teachers can't stay on the job even with their full salaries. In the school where he teaches, in a very good week he takes home GH¢250 as extra income he makes from extra classes organised by the school.
So, the issue clearly goes beyond salaries that have either ceased coming or been cut by 50 percent. It tresspasses into other mini benefits that teachers get to cushion their small income. For Gabriel and Jonathan, the pandemic and its impact on their livelihoods have got them thinking lately as to whether their future lies with a teaching job. Like many of their colleagues, they would quickly, without thinking twice, jump at any opportunity in other sectors that may come their way after this whole pandemic episode is over.
The hardship faced by the schools has pushed its body, the Conference of Heads of Private Schools (CHOPSS), to call on government to include them among businesses that must be given stimulus packages to revive their operations; or else it will be difficult for them to rise again even after the ban is lifted.
Should schools re-open?
Though the two teachers interviewed are hard-hit by the closure of schools, lifting the restrictions now at a time when the number of confirmed cased has surpassed 6,400 would be very dangerous; especially, as it would be difficult to observe some of the safety protocols such as social distancing. "The lives of students and teachers are at stake here. I don't think the time is due for us to go back to school. The rate of infection is still high," says Gabriel.
"We all know how dangerous it would be for this nation should schools reopen. The disease would spread like wildfire since no school in Ghana can safely practice social distancing. We are not sure of how to handle the situation," Jonathan said. For private school teachers, they can only hope a vaccine can be found soon so life can return to normal; or else they will be plunged into abject poverty.
VIAthebftonline | Ghana
SOURCEObed Attah YEBOAH
Conference of Heads of Private Schools (CHOPSS)
Schools in Ghana
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text:
package com.yujian.util;

import java.math.BigDecimal;
import java.text.DecimalFormat;

/**
 * @Author:俞尖坚
 * @Description: 用来进行bidDecimal的加减乘除
 * @createTime : 16-11-29
 * @Modified By:
 */

public class ArithUtil {
  private static final int DEF_DIV_SCALE = 5;//保留6位小数
  private static final DecimalFormat decimalFormat = new DecimalFormat("0.00");

  private ArithUtil() {
  }

  /**
   * decimal加法
   */
  public static double add(double d1, double d2) {
    BigDecimal b1 = new BigDecimal(Double.toString(d1));
    BigDecimal b2 = new BigDecimal(Double.toString(d2));
    return b1.add(b2).doubleValue();

  }

  public static BigDecimal add(BigDecimal d1, BigDecimal d2) {
    return d1.add(d2);
  }

  /**
   * decimal减法
   */
  public static double sub(double d1, double d2) {
    BigDecimal b1 = new BigDecimal(Double.toString(d1));
    BigDecimal b2 = new BigDecimal(Double.toString(d2));
    return b1.subtract(b2).doubleValue();

  }

  public static BigDecimal sub(BigDecimal d1, BigDecimal d2) {
    return d1.subtract(d2);
  }

  /**
   * decimal 乘法
   */
  public static double mul(double d1, double d2) {
    BigDecimal b1 = new BigDecimal(Double.toString(d1));
    BigDecimal b2 = new BigDecimal(Double.toString(d2));
    return b1.multiply(b2).doubleValue();
  }

  public static BigDecimal mul(BigDecimal d1, BigDecimal d2) {
    return d1.multiply(d2);
  }

  /**
   * decimal 除法
   */
  public static double div(double d1, double d2) {
    return div(d1, d2, DEF_DIV_SCALE);
  }

  public static BigDecimal div(BigDecimal d1, BigDecimal d2) {
    return div(d1, d2, DEF_DIV_SCALE);
  }

  public static double div(double d1, double d2, int scale) {
    if (scale < 0) {
      throw new IllegalArgumentException("The scale must be a positive integer or zero");
    }
    BigDecimal b1 = new BigDecimal(Double.toString(d1));
    BigDecimal b2 = new BigDecimal(Double.toString(d2));
    return b1.divide(b2, scale, BigDecimal.ROUND_HALF_UP).doubleValue();
  }

  public static BigDecimal div(BigDecimal d1, BigDecimal d2, int scale) {
    if (scale < 0) {
      throw new IllegalArgumentException("The scale must be a positive integer or zero");
    }
    return d1.divide(d2, scale, BigDecimal.ROUND_HALF_UP);
  }

  /**
   * 四舍五入保留2位小数
   */
  public String formatNumber(BigDecimal number) {
    double temp = number.doubleValue();
    return formatNumber(temp);
  }

  /**
   * 四舍五入保留2位小数
   */
  public String formatNumber(double number) {
    number = (double) (Math.round(number * 100) / 100.0);
    return decimalFormat.format(number);
  }

  /**
   * 四舍五入保留4位小数
   */
  public String format(double number) {
    DecimalFormat df = new DecimalFormat("0.0000");
    return df.format(number);
  }

  public static void main(String[] args) {
    ArithUtil arithUtil = new ArithUtil();
    String format = arithUtil.format(0.88885);
    System.out.println(format);
  }

}

redpajama_set_name: RedPajamaGithub


…..news letter #524 – holy sit…..
finally! new releases are starting to trickle in. a bunch of stuff this week and more on the way for monday. now that you've finished with valentines day, you can get back to spending money on yourself….
– expanded reissue of their second album, remastered by bob weston. cd copies include 16 bonus tracks and new cover art re-imagined by graphic artist jay ryan. the limited edition lps pressed to green vinyl. 'vee vee' was a slight departure from the bombastic noisepop that characterized archers of loaf's previous work, and the album's success proved that the band wasn't just a flash in the pan. the album became their best-selling album to date.
– back in stock! didn't expect any more of this one but here they are…. this is your last notice, don't continue to sleep on these caretaker records folks!!
– recorded in the same two week session as 2011's 'angels of darkness, demons of light I', 'II' carries on in the freely improvised, folkloric vein of the title track from their last release. tape was rolled and spontaneous composition occurred. striking in many ways, not least, in the wildly improvised nature of this particular recording. this new earth material brings forth some highly original and deeply mesmerizing tones throughout, at times more hopeful and less dark and death oriented than previous work.
– grimes' fourth release in less than two years. incorporating influences as wide as enya, tlc and aphex twin, drawing from genres like new jack swing, idm, new age, k-pop, industrial and glitch – this approach has marked grimes as a curator of culture, allowing the project to remain flexible and evolving. despite an upbeat demeanour, an urgency permeates the album. calling between our history and the future, it uses the pleasure of minimal rhythms and dance to entice. yet beyond its rich, software-sculpted cohesiveness and vocal energy, runs a very real and odd world.
– continues the band's penchant for crafting adventuresome and infectious state of the art pop music. but this time band leader nick thorburn has infused the songs with a personal introspection that gives the record a new and powerful emotional resonance. produced in less than two weeks, the 11 songs recorded live with hardly a single overdub. it's a stripped down process and beautifully understated sound which only reinforces the confessional content of the lyrics.
– the eighth album overall from this okkervil river off shoot. on animal joy, meiburg ditches the expansive approach of his recent records particularly the epic trilogy of palo santo, rook and the golden archipelago to create a record that seems shockingly direct, immediate and intensely personal. he's no stranger to lush, crafted recordings, but this one sounds like no prior shearwater incarnation.
– besides having an excellent name, this man, a luminary of algerian music, possessed a unique musical sense, able to transcend the borders of musical cultures to create a distinctive fusion of arabo-andalusian and european styles. recorded in 1965 in paris, it is a solo piano album presenting a trans-mediterranean crossover based on traditional algerian vocal pieces known as istikhbars. comes with an insert with liner notes in english and japanese. limited edition of 200 pressed on vinyl.
– in december 1975, waits entered the studios of kqrs minneapolis for his first ever fm broadcast, floated across the airwaves by that very station and syndicated by many others nationwide. now considered the holy grail of waits broadcasts amongst serious collectors of the great man's work, this performance featuring tom waits alone at his piano with just his magnificent voice as accompaniment, the way he should be heard, is nothing short of staggering. limited to 1000 copies.
– over the course of a year, whitman performed a piece of live electronic music a few dozen times entitled "generator." this lp covers the final two performances of the piece over two consecutive evenings; these recordings show the piece in two different iterations, taking two different trajectories entirely. they're considered the definitive versions of the piece. composed for, and realized with a scalable selection of digital and analog modular synthesis equipment, an attempt to wrest a viable performance-based music out of what had until then been a solitary set of sound-design tools.
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Ross grew up in Woburn, MA, about 10 miles Northwest of Boston. His father, Jim, works as a farmer, leading the now fifth-generation family greenhouse business. He grew up attending The Church of the Open Bible in Burlington, MA and was schooled at its Open Bible Academy. Upon graduation, Ross attended Northland Baptist Bible College, receiving his Bachelor's in Bible with a math minor. After completing a pastoral internship at Capitol Hill Baptist Church in Washington D.C., Ross moved to Louisville, KY where he finished a Master of Divinity degree from the Southern Baptist Theological Seminary. Before coming to First Baptist in the Spring of 2011, Ross served on the staff at Kenwood Baptist Church in Louisville, KY. Ross and his wife Suemi welcomed their daughter Lily in August 2011, their son Owen in January 2014, their daughter Nora in January 2016, and their son Jack in December 2017.
Kevin grew up in southeast Michigan as the second of twelve children. After graduating from Bob Jones University with a degree in Health, Fitness, and Recreation, he served for four years at a Christian school and church in Chattanooga, TN. From 2007-2015, Kevin and his wife Isetta lived in Dunbar, WI, where he served as the Operations and Junior Camp Director at Northland Camp. God used those experiences to sharpen their desire for service and give them experience with children, youth, and adult ministry. During those years, Kevin joined the pastoral staff at Grace Baptist Church, where his areas of oversight included Sunday School, children's ministry, and corporate worship. He and his family moved to Lapeer in 2015 to serve with First Baptist Church. Kevin is committed to God's Word and continuing the life-touching-life discipleship philosophy that has impacted him for Christ. In addition to his graduate studies, he also enjoys running, sports, reading, and spending time with Isetta and their four children (Caleb, Jacqueline, Luke, and Elizabeth).
The church staff, pastors, and deacons serve the church body by working alongside the congregation in the various ministries of the church: Our pastors provide spiritual leadership and teaching to equip the church, and deacons serve those leading and working in our ministries. Pastors and deacons are called by the church based on qualifications found in 1 Timothy 3 and Titus 1.


We lead the initiative in GIS enterprise system design, including capacity planning, configuration, and optimization.
We implement real-time situational awareness planning and decision support using advanced Geocoding/Geolocation and remote sensing data.
When it comes to data processing, we are always compliant with Federal Geographic Data Committee (FGDC) standards.
NiyamIT modernizes and maintains Hazus for FEMA as part of Risk MAP Program. FEMA's Hazus Program provides a nationally standardized methodology for the estimation of structural damage and economic loss caused by earthquakes, hurricanes, floods, and tsunamis.
Comprehensive Data Management System will streamline and automate processing of raw data. Updated datasets can be shared between user communities for common use, instead of each user community having to make its own updates.
The methodology is captured in a series of GIS-based spatial and analytic tools. Hazus uses a spatial interface to overlay a hazard with a geographic area, including the area's building inventory and demographic data.
FEMA, state and local government, academia, private sector, partner federal agencies, and international research groups use Hazus to predict damage and economic loss due to a specific disaster.
We are changing the database engine to take advantage of the 64 bit architecture. To maintain tight security and protection of the systems registry, Hazus will now utilize its own configuration file and leave the systems registry untouched.
Manages flood maps, mitigated flood risks and communicated flood risk to homeowners. Provides decision making tools to reduce flood losses in 22,000+ communities within USA.
Developed and deployed intelligent and intuitive location based (zip code) dashboards with geo targeted alerts to retrieve status of mitigation actions in the event of a natural hazard.
Integrates with DHS' Homeland Infrastructure Foundation-Level Data (HIFLD) for Hazus. HIFLD program provides common geospatial data of the highest possible quality and currency to planners, managers and responders throughout Homeland Security Enterprise and comprises of over 450 datasets/topics.
Architected, implemented and manages a highly scalable National Flood Hazard Layer (NFHL) GIS services that support 55M+ requests per month.
Leads the development of US DOT National Pipeline Mapping System (NPMS) to assist general public query information related to gas transmission and hazardous liquid pipelines, liquefied natural gas plants, and breakout tanks through a GIS based Map Viewer.


text:
package me.hatter.tools.jsspserver.auth;

import java.lang.annotation.ElementType;
import java.lang.annotation.Retention;
import java.lang.annotation.RetentionPolicy;
import java.lang.annotation.Target;

@Target(ElementType.TYPE)
@Retention(RetentionPolicy.RUNTIME)
public @interface CSRFMark {

    String csrfToken() default "__csrf";
}


text:
Q: $3$ never divides $n^2+1$ Problem: Is it true that $3$ never divides $n^2+1$ for every positive integer $n$? Explain.
Explanation: If $n$ is odd, then $n^2+1$ is even. Hence $3$ never divides $n^2+1$, when $n$ is odd.
If $n$ is even, then $n^2+1$ is odd. So $3$ could divide $n^2+1$.
And that is where I am stuck. I try to plug in numbers for $n$ but I want a more general form of showing that $3$ can't divide $n^2+1$ when $n$ is even.

A: Another way: $ $ notice that $\,3\,$ divides one of $\ \color{#0a0}{n\!-\!1,\,n,\,n\!+\!1}.\ $ Therefore
$\ \ \ \color{#c00}{3\mid n^2\!+1}\Rightarrow\ 3\mid 2 = (\color{#c00}{n^2\!+1})(2\!-\!n^2)+\color{#0a0}{(n\!-\!1)n^2(n\!+\!1)},\ $ contradiction.
Remark $\ $ The above implies coprime $\,n^2\!+1\,$ and $\,n^3\!-n = (n\!-\!1)n(n\!+\!1),\,$ except when $\,n\,$ is odd, when they have gcd $= 2.\,$ The above linear relation between them is simply the Bezout identity for their gcd, considered as a polynomial over $\Bbb Q$ (which can be computed mechanically using the extended Euclidean algorithm). Though this approach is not as efficient as using modular arithmetic, it highlights an interesting viewpoint that often proves useful: often properties of integers (numbers) are special cases of properties of polynomials (functions).

A: Hint: What are the only squares modulo $3$? Put another way, look at the expression $n^{2}+1$ modulo $3$. What is true of $n^{2} \pmod 3$ for any $n \in \mathbb{N}$?

A: If $3$ divides $n^2+1$ then it must have solution modulo $3$. But clearly
$0^2+1\equiv 1 \pmod 3$
$1^2+1 \equiv 2 \pmod 3$
$2^2+1 \equiv 5 \equiv 2 \pmod 3$
Otherwise put $n=3k,3k+1,3k+2$ and see that $3$ never divides it

A: Instead of considering whether $n$ is even or odd, consider the remainder when $n$ is divided by $3$; as an example, if the remainder is $1$, we have $$n = 3k + 1 \implies n^2 + 1 = 9k^2 + 6k + 2$$
which is not divisible by $3$. There are two more cases.

A: $n= 0 \pmod3  \implies n^2 + 1 = 1\pmod3$,
$n = 1\pmod3 \implies n^2 + 1 = 2\pmod3$,
$n = 2\pmod3 \implies n^2 + 1 = 2\pmod3$.
So $n^2 + 1$ is not a multiple of $3$ for any $n$.

A: Every integer $n$
can be written in the form
$3m+k$,
where $m$ is a non-negative integer
and $k = 0, 1, $ or $2$.
(This is a particular case of
the result that
for any positive integer $j$,
every integer $n$
can be written in the form
$jm+k$, where  $m$ is a non-negative integer
and $k$ is an integer such that
$0 \le k < j$.)
Therefore
$n^2+1
=(3m+k)^2+1
=9m^2+6mk+k^2+1
=3(3m^2+2mk)+k^2+1
$.
If $3 \mid n^2+1$,
then $3 \mid k^2+1$.
But
the possible values of
$k^2+1$ are
$1, 2, $ and $5$
(for $k = 0, 1, 2$, respectively),
and $3$ does not divide any of them.
Therefore $3$ does not divide $n^2+1$.

A: Divide $n$ by $3$ and let $Q$ be the quotient and $R$ the remainder. So
$$ n = 3\,Q + R$$
$$n^2+1 = 9\,Q^2 + 6 \, Q\, R + R^2 +1$$
$R$ can only be $0$, or $1$ or $2$. Now argue that in all cases $n^2+1$ is not divisible by $3$.
Not divisibility depends only on $R$ i.e. only on $n \mod 3$. From your question, it looks like you are just starting on number theory. You will soon realize that most problems require you to look only at the remainder.

A: Since $n-1,n,n+1$ are three successive integers so one of them must be divisible by 3 hence there product must be divisible by $3$ i.e. $3|(n-1)n(n+1) \implies 3|n^3-n$ , now
$3|n^2+1 \implies 3|n(n^2+1) \implies 3|n^3+n \implies 3|n^3+n-(n^3-n) \implies 3|2n$ , since 3 does
not divide $2$ so $3|n \implies 3|n^2 \implies 3|n^2+1-n^2 \implies 3|1$ , contradiction !

A: Note that the statement mathematically means: $$ 3 \mid (n^2 + 1) \implies n^2 + 1 \equiv 0 \pmod 3 \equiv n^2 \equiv -1 \equiv 2 \pmod 3. $$ Is this ever possible?

A: $\newcommand{\+}{^{\dagger}}%
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 \newcommand{\bracks}[1]{\left\lbrack #1 \right\rbrack}%
 \newcommand{\ceil}[1]{\,\left\lceil #1 \right\rceil\,}%
 \newcommand{\dd}{{\rm d}}%
 \newcommand{\ds}[1]{\displaystyle{#1}}%
 \newcommand{\equalby}[1]{{#1 \atop {= \atop \vphantom{\huge A}}}}%
 \newcommand{\expo}[1]{\,{\rm e}^{#1}\,}%
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 \newcommand{\half}{{1 \over 2}}%
 \newcommand{\ic}{{\rm i}}%
 \newcommand{\iff}{\Longleftrightarrow}
 \newcommand{\imp}{\Longrightarrow}%
 \newcommand{\isdiv}{\,\left.\right\vert\,}%
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 \newcommand{\partiald}[3][]{\frac{\partial^{#1} #2}{\partial #3^{#1}}}
 \newcommand{\pp}{{\cal P}}%
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 \newcommand{\sech}{\,{\rm sech}}%
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 \newcommand{\totald}[3][]{\frac{{\rm d}^{#1} #2}{{\rm d} #3^{#1}}}
 \newcommand{\ul}[1]{\underline{#1}}%
 \newcommand{\verts}[1]{\left\vert\, #1 \,\right\vert}$
For $n = 1$, it's obvious since $3 \not|\ 2$. Let's assume $3 \not|\ n^{2} + 1$. Then, $n^{2} + 1 = 3p + \delta$ for $p, \delta$ integers and $\delta = 1, 2$:
$$
\pars{n + 1}^{2} + 1 = n^{2} + 1 + 2n + 1 = 3p + \delta + 2n + 1
$$
If $\delta = 1$, $\delta + 2n + 1 = 2\pars{n + 1}$ which is even.
If $\delta = 2$, $\delta + 2n + 1 = 2n + 3\quad\imp\pars{n + 1}^{2} + 1 = 3\pars{p + 1} + 2n$: The first term is a multiple of $3$ but the second is even.

redpajama_set_name: RedPajamaStackExchange


text:
\section{Introduction: the general setting}
We fix a prime number $p$, a prime number $\ell \neq p$, and a nontrivial $\overline{{\mathbb Q}_\ell}^\times$-valued additive character $\psi$ of ${\mathbb F}_p$. For $k/{\mathbb F}_p$ a finite extension, we denote by  $\psi_k$ the nontrivial additive character of $k$ given by $\psi_k :=\psi\circ {\rm Trace}_{k/{\mathbb F}_p}$. In perhaps more down to earth terms, we fix a nontrivial ${\mathbb Q}(\mu_p)^\times$-valued additive character $\psi$ of ${\mathbb F}_p$, and a field embedding of
${\mathbb Q}(\mu_p)$ into  $\overline{{\mathbb Q}_\ell}$ for some $\ell \neq p$.

Given an integer $D \ge 3$ which is prime to $p$, we form the local system ${\mathcal F}_{p,D}$ on ${\mathbb A}^1/{\mathbb F}_p$ whose trace function, at $k$-valued points $t \in {\mathbb A}^1(k) = k$, is given by
$$t \mapsto -\sum_{x \in k}\psi_k(x^D + tx).$$
This is a geometrically irreducible rigid local system, being the Fourier Transform of the rank one local system ${\mathcal L}_{\psi(x^D)}$. It has rank $D-1$, and each of its $D-1$ $I(\infty)$-slopes is $D/(D-1)$. It is pure of weight one.  [It is the local system  ${\mathcal F}({\mathbb F}_p,\psi, {\mathds{1}}, D)$ of \cite{Ka-RLSA}.]

Let us further fix a choice of $\sqrt{p} \in \overline{{\mathbb Q}_\ell}^\times$. For each finite extension $k/{\mathbb F}_p$, we then use this choice of$\sqrt{p}$ to define $\sqrt{\#k} := \sqrt{p}^{\deg(k/{\mathbb F}_p)}$. We then define the ``half"-Tate twisted local system
$${\mathcal G}_{p,D} := {\mathcal F}_{p,D}(1/2)$$
whose trace function, at  at $k$-valued points $t \in {\mathbb A}^1(k) = k$, is given by
$$t \mapsto -\sum_{x \in k}\psi_k(x^D + tx)/\sqrt{\#k}$$

The local system ${\mathcal G}_{p,D}$ is pure of weight zero.
\begin{lem} The determinant $\det({\mathcal G}_{p,D})$ is arithmetically of finite order. More precisely,  $\det({\mathcal G}_{p,D})^{\otimes 4p}$ is arithmetically trivial.
\end{lem}
\begin{proof}It suffices to show that after extension of scalars from ${\mathbb F}_p$ to its quadratic extension ${\mathbb F}_{p^2}$, the $2p$'th power is trivial, i.e.,
that if $k/{\mathbb F}_p$ is a finite extension of even degree $2d$, then the determinant takes values in $\mu_{2p}$.To see this, note that the twisting factor $\sqrt{p}^{2d}=p^d \in {\mathbb Q}$, so this determinant has values in ${\mathbb Q}(\mu_p)$ which are units at all finite places of residue characteristic not $p$ (use the $\ell$-adic incarnations) and which have absolute value $1$ at all archimedean places of ${\mathbb Q}(\mu_p)$. Because there is a unique $p$-adic place of ${\mathbb Q}(\mu_p)$, the product formula shows that the determinant has values which are also units at $p$, and hence are roots of unity in ${\mathbb Q}(\mu_p)$, i.e., they are $2p$'th roots of unity.
\end{proof}

When we view the local system ${\mathcal G}_{p,D}$ as a representation
$$\rho_{{\mathcal G}_{p,D}}: \pi_1({\mathbb A}^1/{\mathbb F}_p) \rightarrow GL(D-1,\overline{{\mathbb Q}_\ell}),$$
the Zariski closure of the image of $\pi_1({\mathbb A}^1/{\mathbb F}_p) $ is defined to be the arithmetic monodromy group $G_{arith}$. The Zariski closure of the image of the normal subgroup $\pi_1^{geom}:=\pi_1({\mathbb A}^1/\overline{{\mathbb F}_p}) $ is defined to be the geometric monodromy group $G_{geom}$.
Thus we have inclusions of algebraic groups over $\overline{{\mathbb Q}_\ell}$: $$G_{geom}\lhd G_{arith} \subset GL(D-1).$$

Applying \cite[8.14.5, $(1) \iff (2) \iff (6)$]{Ka-ESDE} in the particular case of ${\mathcal G}_{p,D}$, we have
\begin{prop}\label{arithfin}The following conditions are equivalent.
\begin{itemize}
\item [(1)] ${\mathcal G}_{p,D}$ has finite $G_{geom}$.
\item [(1bis)] ${\mathcal F}_{p,D}$ has finite $G_{geom}$.
\item [(2)] ${\mathcal G}_{p,D}$ has finite $G_{arith}$.
\item [(3)] All traces of ${\mathcal G}_{p,D}$ are algebraic integers.
\end{itemize}
\end{prop}

When $D \ge 3$ is odd (and prime to $p$), the local system  ${\mathcal F}_{p,D}$ is symplectically self-dual. As shown in \cite[Proposition 4 and Corollary 6]{R-L}, its $G_{geom}$ is either finite or it is the full symplectic group  ${\rm Sp}(D-1)$. When $D \ge 3$ is even (and prime to $p$),  the same reference shows that $G_{geom}$ is either finite or is $SL(D-1)$. The proof of \cite[Proposition 4 and Lemma 5]{R-L} also shows
that when $D$ is not of the form $1+q$ for $q$ a power of $p$, then ${\mathcal F}_{p,D}$  is not induced (i.e., the given representation of its
$G_{geom}$ is not induced). Indeed, by the result  \cite[11.1]{Such} of  \v{S}uch, if the representation were induced, it would be Artin-Schreier induced, and that is what is ruled out when $D$ is not of the form $1+q$. [When $D=1+q$, then $G_{geom}$ is, by Pink \cite[20.3]{Ka-RLSA}, a finite $p$-group, and (hence) the representation is induced.]

When $D \ge 3$ is prime to $p$, the trace function of ${\mathcal G}_{p,D} $ takes values in ${\mathbb Z}[\mu_p]$. If moreover $p$ is $1$ mod $4$, then
we can choose either quadratic Gauss sum, a quantity which itself lies in ${\mathbb Z}[\mu_p]$, as our $\sqrt{p}$, and hence all traces of ${\mathcal G}_{p,D}$ lie in ${\mathbb Z}[\mu_p][1/p]$.  If $p$ is not $1$ mod $4$, this remains true for traces of the pullback of ${\mathcal G}_{p,D}$ to ${\mathbb A}^1/{\mathbb F}_{p^2}$. In either case, the traces of ${\mathcal G}_{p,D}$ in question are algebraic integers if and only if they all have
${\rm ord}_p \ge 0$.

\begin{rmk}\label{tracefld}When $D \ge 3$ is prime to $p$ and {\bf odd}, then the traces of ${\mathcal F}_{p,D} $ lie in the real subfield ${\mathbb Q}(\mu_p)^+$.
If in addition $p$ is $1$ mod $4$, then either quadratic gauss sum is $\pm \sqrt{p}$ also lies in this field, and hence  ${\mathcal G}_{p,D} $ has traces in
 ${\mathbb Q}(\mu_p)^+$.
 \end{rmk}

Results of Kubert, explained in  \cite[4.1,4.2,4.3]{Ka-RLSA} and discovered independently in \cite[Cor. 4, Cor. 5]{R-L}, show that $G_{geom}$ and $G_{arith}$ for ${\mathcal G}_{p,D}$ are finite when $q$ is a power of $p$ and $D$ is any of
$$q+1,\ \ \frac{q+1}{2} {\rm \ with \ odd \  }q,  \frac{q^n+1}{q+1} {\rm \ with \ odd \ }n.$$
Let us call these the Kubert cases.
In \cite[17.1, 17.2]{Ka-RLSA} and \cite[3.4]{Ka-Ti-RLSMFUG} their $G_{geom}$ groups are  determined for all odd $q$.

Both authors have given numerical criteria for ${\mathcal G}_{p,D}$ to have finite $G_{geom}$ and $G_{arith}$, cf. \cite[first paragraph after 5.1]{Ka-RLSA} and \cite[Thm. 1]{R-L}. The second author did extensive computer experiments to find other $(p,D)$ than the Kubert cases for which ${\mathcal G}_{p,D}$ seemed to have finite $G_{geom}$ (i.e., where many many traces were all algebraic integers). For primes $p \le 11$ and $D \le 10^6$, there was only one non-Kubert candidate, the case $p=5,\  D=7$.

In the first part of this paper, we prove that ${\mathcal F}_{5,7}$ has finite $G_{geom}$ (and hence, by Proposition \ref{arithfin},  that ${\mathcal G}_{5,7}$ has finite $G_{geom}$ and finite $G_{arith}$). In the second part, we show that
 $G_{geom}=G_{arith}= 2.J_2$ in one of its two six-dimensional irreducible representations. These two representations are symplectic. Their character values lie in ${\mathbb Z}[\sqrt{5}]$ and are Galois-conjugates of each other. As Guralnick and Tiep point out \cite[Table 1]{G-T}, the group $2.J_2$, sitting inside $Sp(6,{\mathbb C})$, has the exotic property that it has the same moments $M_n$ (dimension of the space of invariants in the $n$'th tensor power of the given six-dimensional representation) as the ambient group ${\rm Sp}(6,{\mathbb C})$ for $M_1$ through $M_{11}$; one needs $M_{12}$ to distinguish them.

 It is not clear whether there ``should" be infinitely many $(p,D)$ other than the Kubert cases for which ${\mathcal G}_{p,D}$ has finite $G_{arith}$, or finitely many, or just this one $(5,7)$ case. Much remains to be done.

\section{Finiteness of the monodromy}

In this section we will prove that the sheaf $\mathcal F_{5,7}$ has finite geometric monodromy. We will do so by applying the numerical criterion proven in \cite[Theorem 1]{R-L}, which we recall here. For a prime $p$ and an integer $x \ge 0$, we define
$$[x]_{p,\infty}:={\rm \ the\  sum \ of \ the\  digits \ of\  the \ }p{\rm -adic\  expansion\ of\ }x,$$
using the usual digits $\{0,1,2,...,p-1\}$.

For every $r\geq 1$ we define $[x]_{p,r}=[x]_{p,\infty}$ if $1\le x \le p^r-1$, and we extend the definition to every integer $x$ by imposing that $[x]_{p,r}=[y]_{p,r}$ if $x\equiv y$ (mod $p^r-1$).[Thus we are using $\{1,2,...,p^r-1\}$ as representatives of ${\mathbb Z}/(p^r - 1){\mathbb Z}$.]

From \cite[Thm. 1]{R-L}, we have

\begin{thm}\label{numcrit}
The sheaf $\mathcal F_{p,d}$ has finite geometric monodromy if and only if the inequality
 $$
 [dx]_{p,r}\leq [x]_{p,r}+\frac{r(p-1)}{2}
 $$
holds for every $r\geq 1$ and every integer $0<x<p^r$.
\end{thm}

Let us enumerate some basic properties of the functions $[-]_{p,\infty}$ and $[-]_{p,r}$.

\begin{prop}
 For strictly positive integers $x$ and $y$, and for $r\in\mathbb N\cup\{\infty\}$, we have:

 \begin{enumerate}
 \item $[x+y]_{p,r}\leq [x]_{p,r}+[y]_{p,r}$
 \item $[x]_{p,r}\leq [x]_{p,\infty}$
 \item $[px]_{p,r}=[x]_{p,r}$
 \end{enumerate}
\end{prop}

\begin{proof}
 We first prove (1) for $r=\infty$. Note that $[x]_{p,\infty}$ is the minimal number of terms in any decomposition of $x$ as a sum of powers of $p$. By taking the sum of the $p$-adic expansions of $x$ and $y$ we see that $x+y$ can be written as a sum of $[x]_{p,\infty}+[y]_{p,\infty}$ powers of $p$, and the inequality follows.

 For (2) we proceed by induction on $x$: for $0<x<p^r$ it is obvious by definition. If $x \ge p^r$, let $s$ be the largest integer such that $p^s\leq x$. Then $s\geq r$ and $[x-p^s]_{p,\infty}=[x]_{p,\infty}-1$. Since $x\equiv x-p^s+p^{s-r}$ (mod $p^r-1$), while $x > x-p^s+p^{s-r} > 0$,
 we have, by induction on $x$ and (1)$_\infty$,
 $$
 [x]_{p,r}=[x-p^s+p^{s-r}]_{p,r}\leq[x-p^s+p^{s-r}]_{p,\infty}\leq[x-p^s]_{p,\infty}+[p^{s-r}]_{p,\infty}=
 $$
 $$
 =[x]_{p,\infty}-1+1=[x]_{p,\infty}.
 $$

 In order to prove (1) for finite $r$ we can assume that $x,y<p^r$. Then by (2) and (1)$_\infty$, we have
 $$
 [x+y]_{p,r}\leq [x+y]_{p,\infty}\leq [x]_{p,\infty}+[y]_{p,\infty}=[x]_{p,r}+[y]_{p,r}.
 $$

 Finally, (3) is obvious for $r=\infty$. For finite $r$, note that if $x=a_{r-1}p^{r-1}+\cdots+a_1p+a_0$ is the $p$-adic expansion of $x<p^r$, then $px\equiv a_{r-2}p^{r-1}+\cdots+a_1p^2+a_0p+a_{r-1}$ (mod $p^r-1$), so $[px]_{p,r}=[x]_{p,r}=a_{r-1}+\cdots+a_1+a_0$.

\end{proof}

We now fix $p=5$ and $d=7$.

\begin{lem}\label{l1}
 Let $r$ be a positive integer and $0 \le x<5^r$ an integer such that $x\not\equiv 2 \mod 5$. Then $[7x]_{5,\infty}\leq[x]_{5,\infty}+2r$.
\end{lem}

\begin{proof} We proceed by induction on $r$. For $r=1$ and $r= 2$ one checks it by hand.

Now let $r\geq 3$ and $0 \le x<5^r$ with $x\not\equiv 2 \mod 5$.
If $0 \le x<5^{r-1}$ the stronger inequality $[7x]_\infty\leq [x]_\infty+2r-2$
holds by induction, so we may assume that $5^{r-1}\leq x<5^r$. Consider the $5$-adic expansion of $x$, which has $r$ digits, the last one being $\neq 2$ by hypothesis. We distinguish two cases:

\emph{Case 1:} The constant term is not $2$, and there is some other digit $\neq 2$, say the one multiplying $5^s$, for some $s$ with $r >s >0$. Write $x=5^sy+z$, with $0 \le z<5^s$, $0 \le y<5^{r-s}$ (that is, split the first $r-s$ and the last $s$ $5$-adic digits of $x$). Then by induction on $r$ we get
$$
[7x]_{5,\infty}=[7\cdot 5^s y+7z]_{5,\infty}\leq [7\cdot 5^sy]_{5,\infty}+[7z]_{5,\infty}=
$$
$$
=[7y]_{5,\infty}+[7z]_{5,\infty}\leq [y]_{5,\infty} + 2(r-s)+[z]_{5,\infty} +2s=[x]_{5,\infty}+2r.
$$

\emph{Case 2:} All other digits are $=2$, that is, $x=(222...22a)_5$ with $a\in\{0,1,3,4\}$. Note that $7\cdot(222...220)_5=(322...2140)_5$ (where there are two fewer $2$'s on the right hand side). Then
$$
[7x]_{5,\infty}=[7\cdot(22...220)_5 + 7a]_{5,\infty}\leq[7\cdot(22...220)_5]_{5,\infty}+[7a]_{5,\infty}=
$$
$$
=[(322...2140)_5]_{5,\infty}+[7a]_{5,\infty}
=2(r+1)+[7a]_{5,\infty}\leq 2(r+1)+a+2 =
$$
$$
= 2(r-1)+a+6\le 2(r-1)+a+2r = |(222...22a)_5]_{5,\infty}+2r=[x]_{5,\infty}+2r.
$$
\end{proof}

\begin{rmk}Although it will not be used, it follows from the lemma that for every $r \ge 1$ and for every integer $x$ with $0 \le x <5^r$, we have
$$[7x]_{5,\infty}\leq[x]_{5,\infty}+2r+2.$$
Indeed, for $0 \le x <5^r $, the quantity $5x$ is $<5^{r+1}$ and is not $2$ mod $5$. So by the lemma applied to $5x$ with $r+1$, we have
$$[7\cdot 5x]_{5,\infty}\leq[5x]_{5,\infty}+2r+2.$$
But $[7\cdot 5x]_{5,\infty}=[7x]_{5,\infty}$ and $[5x]_{5,\infty}=[x]_{5,\infty}$.
\end{rmk}
\begin{thm}\label{finmono} The geometric monodromy of $\mathcal F_{5,7}$ is finite.
\end{thm}
\begin{proof} By Theorem \ref{numcrit}, we need to show that $[7x]_{5,r}\leq[x]_{5,r}+2r$ for $r\geq 1$ and $0<x<5^r$.

If $x=\frac{5^r-1}{2}$, then $x=(22...22)_5$, so $[x]_{5,r}+2r=4r$ and the inequality is clear, since $4r$ is an absolute upper bound for the function $[-]_{5,r}$.

Otherwise, some $5$-adic digit of $x$ is $\neq 2$. Since multiplying $x$ by $5$ cyclically permutes the digits of $x$ modulo $5^r-1$ and does not change the values of $[x]_{5,r}$ or of $[7x]_{5,r}$, we may assume that the last digit of $x$ is $\neq 2$. Then
$$
[7x]_{5,r}\leq [7x]_{5,\infty}\leq[x]_{5,\infty}+2r=[x]_{5,r}+2r
$$
by Lemma \ref{l1}.
\end{proof}

\section{Determination of the monodromy groups}
We first give a general descent construction, valid for general ${\mathcal F}_{p,D}$ with $D \ge 3$ prime to $p$.
On ${\mathbb G}_m/{\mathbb F}_p$, consider the rank $D-1$ local system ${\mathcal H}_{p,D}$ whose trace function, for $k/{\mathbb F}_p$ a finite extension, and $t \in {\mathbb G}_m(k)=k^\times$, is
$$t \mapsto -\sum_{x \in k}\psi_k(x^D/t + x).$$
The pullback of  ${\mathcal H}_{p,D}$ by the $D$'th power map $[D]$ is (the restriction to ${\mathbb G}_m$ of) the local system ${\mathcal F}_{p,D}$: simply repace $t$ by $t^D$ and make the change of variable $x \mapsto tx$ inside the $\psi$.

View  ${\mathcal F}_{p,D}$ as the Fourier Transform $FT([D]^\star({\mathcal L}_{\psi(x)})$. Then we see from \cite[9.3.2]{Ka-ESDE}, cf. also \cite[2.1 (1)]{Ka-RLSA}, that this ${\mathcal H}_{p,D}$ is geometrically isomorphic to the Kloosterman sheaf formed with all the nontrivial multiplicative characters of order dividing $D$.

\begin{rmk}\label{traceflddesc}Exactly as in Remark \ref{tracefld}, when $D \ge 3$ is odd and prime to $p$, and $p$ is $1$ mod $4$, the field of traces of ${\mathcal H}_{p,D}$ lies in ${\mathbb Q}(\mu_p)^+$.
\end{rmk}
This descent has all of its $I(\infty)$-slopes equal to $1/(D-1)$ (either from its identification with a Kloosterman sheaf of rank $D-1$,
or because its $[D]$-pullback, ${\mathcal F}_{p,D}$, has all its  $I(\infty)$-slopes equal to $D/(D-1)$).

Either from the fact that its pullback is geometrically irreducible, or from the Kloosterman description, or just from the fact of having all $I(\infty)$-slopes $1/(D-1)$, we see that ${\mathcal H}_{p,D}$ is geometrically irreducible.

\begin{lem}\label{tensorindec}Let $d \ge 2$, $\ell \neq p$, and $M$ a $d$-dimensional continuous $\overline{{\mathbb Q}_\ell}$-representation $\rho_M$ of $I(\infty)$ all of whose slopes are $1/d$. Suppose that $d$ is not divisible by $p^2$. Then there does not exist a factorization of $d$
as $d=ab$ with $a,b$ both $< d $, together with algebraic groups $G_1 \subset SL(a,\overline{{\mathbb Q}_\ell})$ and $G_2 \subset SL(b,\overline{{\mathbb Q}_\ell})$ such that
$$Image(\rho_M) \subset {\rm the \ image \ }G_1\otimes G_2 \ {\rm of\ }G_1\times G_2 \ {\rm \ in\ }SL(ab,\overline{{\mathbb Q}_\ell}).$$
\end{lem}
\begin{proof}We argue by contradiction. The map $G_1\times G_2 \rightarrow G_1\otimes G_2$ has finite kernel, ${\mathcal K}$, which is a subgroup of
the group $\mu_{\gcd(a,b)}$ (this being the kernel of $SL(a)\times SL(b) \rightarrow SL(ab)$). Because $I(\infty)$ has cohomological dimension one, the group $H^2(I(\infty), {\mathcal K})=0$, and therefore there exists a lift of $\rho_M$ to a homomorphism
$$\rho_{a,b}:I(\infty) \rightarrow G_1\times G_2,$$
compare \cite[7.2.5]{Ka-ESDE}.
Because the kernel ${\mathcal K}$ has order prime to $p$, the upper numbering subgroup $I(\infty)^{\frac{1}{d} +}$, which acts trivially on $M$,
lies in the kernel of $\rho_{a,b}$ (simply because $I(\infty)^{\frac{1}{d} +}$ is a pro-$p$ group which maps to the finite group ${\mathcal K}$ which has order prime to $p$, cf. \cite[7.1.4]{Ka-ESDE}).
Then the homomorphisms
$$\rho_a:= pr_1  \circ \rho_{a,b}: I(\infty) \rightarrow G_1$$
and
$$\rho_b:= pr_2 \circ \rho_{a,b}: I(\infty) \rightarrow G_2$$
are  each trivial on  $I(\infty)^{\frac{1}{d} +}$, i.e., each has all slopes $\le 1/d$. Therefore their Swan conductors have $Swan(\rho_a)\le a/d < 1$ and $Swan(\rho_b)\le b/d < 1$. But Swan conductors are nonnegative integers. Therefore both $\rho_a$ and $\rho_b$ have $Swan=0$, i.e., both are tame. But then $M$ is tame, contradiction.
\end{proof}

When $D \ge 3$ is odd and prime to $p$, the half-Tate twist ${\mathcal H}_{p,D}(1/2)$ is symplectically selfdual.

We now turn our attention to the particular case of ${\mathcal H}_{5,7}$ and its half-Tate twist ${\mathcal H}_{5,7}(1/2)$. We know from
Theorem \ref{finmono} that its $G_{geom}$ (and hence also its $G_{arith}$, by Proposition \ref{arithfin}) is a finite irreducible subgroup of $Sp(6, \overline{{\mathbb Q}_\ell})$. By Remark \ref{traceflddesc}, the field of traces of  ${\mathcal H}_{5,7}(1/2)$ lies in ${\mathbb Q}(\mu_5)^+ ={\mathbb Q}(\sqrt{5})$. Computing the trace at $t=1 \in {\mathbb F}_5^\times$, we see that its field of traces is in fact ${\mathbb Q}(\sqrt{5})$ (and not just ${\mathbb Q}$).

\begin{lem}The group $G_{geom} \subset Sp(6, \overline{{\mathbb Q}_\ell})$ is primitive, i.e.,  the given six-dimensional representation is not induced.
\end{lem}
\begin{proof}By Pink's theorem \cite[Lemma 12]{Ka-MG}, if a Kloosterman sheaf is (geometrically) induced, its list of characters is Kummer induced. So for our Kloosterman sheaf, formed with the nontrivial characters of order $7$, being induced would imply that, for some divisor $n \ge 2$ of $6$, its characters are all the $n$'th roots of some collection of $6/n$ characters. In particular, some ratio of
distinct characters of order $7$ would be a character of order dividing $n$, for some divisor $n$ of $6$, which is not the case: all such ratios have order $7$.

Another proof is to observe that if ${\mathcal H}_{5,7}$ were induced, then its pullback  ${\mathcal F}_{5,7}$ would be induced (a system of imprimitivity for a group remains one for any subgroup). But by \cite[11.1]{Such}, if ${\mathcal F}_{5,7}$ were induced, it would be Artin-Schreier induced, so its rank, $6$, would be a multiple of $p=5$.
\end{proof}

\begin{thm}The local system ${\mathcal H}_{5,7}(1/2)$ has $G_{geom}=G_{arith} =2.J_2$.
\end{thm}
\begin{proof}
Our situation now is that we have a primitive (by Lemma \ref{tensorindec}) irreducible subgroup $G$ (the $G_{geom}$ for ${\mathcal H}_{5,7}(1/2)$) in
$Sp(6, \overline{{\mathbb Q}_\ell})$ such that the given six-dimensional representation is not contained in the tensor product of two lower dimensional representations of $G$. Therefore the larger finite group $G_{arith}$ is a fortiori itself primitive and irreducible inside $Sp(6)$.

We now appeal to the work \cite[\&3, Theorem]{Lind} of Lindsey, as stated in \cite[Theorem 3.1]{C-S}. This gives
the list of irreducible primitive subgroups of $SL(6,{\mathbb C})$. Those whose given six-dimensional representation is not contained in a nontrivial tensor product are either
\begin{itemize}
\item[(1)]$2.S_5$ or $S_7$.
\item[(2)]a quasisimple group.
\item[(3)] a group containing a quasisimple group of index two on which the representation remains irreducible.
\end{itemize}

The first case is subsumed by the third, as $2.S_5=2.A_5.2$ contains $2.A_5$, and $S_7$ contains $A_7$.
The quasisimple groups in question are
$$2.A_5 =SL(2,5), 3.A_6, 6.A_6, A_7, 3.A_7, 6.A_7, PSL(2,7), SL(2,7), SL(2,11), $$
and
$$SL(2,13), PSp(4,3) \cong PSU(4,2), SU(3,3), 6.PSU(4,3), 2.J_2, 6.PSL(3,4).$$

Of these, those which lie as an index two subgroup of a larger group inside $SL(6,{\mathbb C})$ are
$$SL(2,5), 3.A_6, A_7, PSL(2,7), PSp(4,3),$$
$$SU(3,3),  6.PSU(4,3),6.PSL(3,4).$$

Of the listed quasisimple groups, the only ones with irreducible symplectic representations of degree six are
$$SL(2,5),\ SL(2,7),\ SL(2,13),\ SU(3,3), \ 2.J_2.$$.

Of these, the only ones whose field of character values (for any of its six-dimensional irreducible symplectic representations) lies in ${\mathbb Q}(\sqrt{5})$ are $SL(2,5)$,  $SU(3,3)$ and $2.J_2$. For $SL(2,5)$ and $SU(3,3)$, the field of traces is ${\mathbb Q}$; for $2.J_2$ it is  ${\mathbb Q}(\sqrt{5})$.
So the only possibilities for $G_{arith}$ other than $2.J_2$ are the groups $G.2$ for $G$ either $SL(2,5)$ or $SU(3,3)$. But for neither of these two groups does the given representation extend to a symplectic representation (or a selfdual one), as one checks by looking in the Atlas \cite{ATLAS}.

Therefore $G_{arith}$ for ${\mathcal H}_{5,7}(1/2)$ must be $2.J_2$. As $G_{geom}$ is a normal subgroup of $G_{arith}$ with cyclic quotient (namely some finite quotient of $\mathrm{Gal}(\overline{{\mathbb F}_p}/{\mathbb F}_p)$), we must also have $G_{geom}=G_{arith} =2.J_2$.
\end{proof}

\begin{cor} For the local system ${\mathcal G}_{5,7}$, we have $G_{geom}=G_{arith} =2.J_2$.
\end{cor}
\begin{proof}Neither $G_{geom}$ nor $G_{arith}$ changes when we pass from ${\mathbb A}^1$ to the dense open set ${\mathbb G}_m$. Restricted to ${\mathbb G}_m$,
${\mathcal G}_{5,7}$ is the $[7]$ pullback of ${\mathcal H}_{5,7}(1/2)$. This pullback replaces the  $G_{geom}$ and $G_{arith}$ of ${\mathcal H}_{5,7}(1/2)$ by normal subgroups of themselves of index dividing $7$. But $2.J_2$ has no such proper subgroups.
\end{proof}

\section{Appendix: Relation of $[x]_{p,r}$ to Kubert's $V$ function}
We denote by $({\mathbb Q}/{\mathbb Z})_{{\rm prime \ to\ }p}$ the subgroup of ${\mathbb Q}/{\mathbb Z}$ consisting of those elements whose order is prime to $p$.
We denote by ${\mathbb Q}_p^{n.r.}$ the fraction field of the Witt vectors of $\overline{{\mathbb F}_p}$. For ${\mathbb F}_{q}$ a finite extension of ${\mathbb F}_p$, we have
the Teichmuller character
$$Teich_{{\mathbb F}_q}: {\mathbb F}_{q}^\times \cong \mu_{q-1}( {\mathbb Q}_p^{n.r.}),$$
whose reduction mod $p$ is the identity map on ${\mathbb F}_{q}^\times $.
For an integer $d$, consider the Gauss sum over ${\mathbb F}_q$,
$$G(\psi_{{\mathbb F}_ q},Teich^{-d}) := \sum_{x \in {\mathbb F}_q^\times}\psi_{{\mathbb F}_q}(x)Teich^{-d}(x).$$
If we write $q=p^r$, then by Stickelberger's theorem,
$${\rm ord}_q(G(\psi_{{\mathbb F}_ q},Teich^{-d}) )=(1/r)\sum_{j=0}^{r-1}<p^j \frac{d}{p^r-1}>.$$
As explained in \cite[p. 206]{Ka-G2hyper}, standard properties of Gauss sums show that there is a unique function
$$V:  ({\mathbb Q}/{\mathbb Z})_{{\rm prime \ to\ }p} \rightarrow {\rm the\ real\  interval \ }[0,1)$$
such that for $q=p^r$ and $d$ an integer, we have
$$V\left(\frac{d}{p^r-1}\right)=(1/r)\sum_{j=0}^{r-1}<p^j \frac{d}{p^r-1}>.$$
As noted in \cite[line before Theorem 1]{R-L}, we thus have the identity
$$V\left(\frac{d}{p^r-1}\right) = \frac{1}{r(p-1)}[d]_{p,r}$$
{\bf provided} that $1 \le d \le p^r-2$ (i.e., provided that $\frac{d}{p^r-1}$ is nonzero in $({\mathbb Q}/{\mathbb Z})_{{\rm prime \ to\ }p}$). However, for $d=0$, $V(\frac{d}{p^r-1})=0$, while
$$ \frac{1}{r(p-1)}[0]_{p,r}=1.$$

This ``reversal" of the values at $0$, together with the identity for Kubert's $V$ function
$$V(x) + V(-x) =1, \ {\rm \ for \ } x \neq 0,$$
means precisely that for any integer $d$ and any power $p^r$ of $p$, we have the identity
$$\frac{1}{r(p-1)}[d]_{p,r} =1 - V\left(\frac{-d}{p^r-1}\right).$$
With this identity, one sees easily that the criterion \cite[Theorem 1]{R-L} for ${\mathcal F}_{p,D}$ to have finite geometric monodromy, namely
that
$$[Dx]_{p,r} \le [x]_{p,r} +r(p-1)/2$$
for all $r \ge 1$ and all integers $x$, is equivalent to the criterion \cite[first paragraph after 5.1]{Ka-RLSA}
that for all $y \in ({\mathbb Q}/{\mathbb Z})_{{\rm prime \ to\ }p}$, we have
$$V(Dy) + 1/2 \ge V(y).$$

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The Caribbean island nation of Antigua and Barbuda has again protested to the World Trade Organization regarding the United States' failure to offer fair restitution in the online-gambling trade dispute between the two countries. In the latest hearing before the WTO's Dispute Settlement Body, held on Friday, Antigua's representative, Sir Ronald Saunders, again protested the ongoing failure of the US to make a legitimate to offer the dispute, in which Antigua is now due roughly $270 million from the US in alternate consideration.
The dispute between the two countries over the US's failure to allow Antigua-based online-gambling companies to market their services freely to US customers has gone on since 2003. The WTO has repeatedly found the US in violation of the applicable trade agreements, which it signed in the late '90s. Roughly a decade ago, the WTO ruled that Antigua was due $21 million annually by the US, but not in direct money. Instead, the WTO ruled that Antigua could make its own versions of various US intellectual-property goods, and abrogate ("ignore" having to pay those US-based copyright holders until that $21 million cap was reached.
Between the difficulty of manufacturing and marketing WTO-approved knockoff goods of such items as music, movies and software, and the US applying significant pressure to Antigua to not go ahead with what the US has termed "state-authorized piracy," it's been tough for Antigua to attempt to collect that $21 million annual stipend in the way the WTO allows. Antigua has threatened to do so several times, as a way of forcing the US to the bargaining table, but it's really just been a decade-long of chicken. Antigua does receive other aid from the US, and the US has repeatedly threatened to cut off some of that aid should Antigua go ahead and collect its WTO-mandated award.
If there was one thing new in Saunders' WTO speech, it was that the US had indeed made a lowball offer last year of $2 million. That's actually less than one percent of the $270 million Antigua is owed. It's also the second such chicken-feed offer the US has made; several years back, the US offered a few hundred thousand plus "other considerations".
As gambling-world soap operas go, the Antigua-v-US tale shows no signs of being resolved any time soon. The WTO is like most international organizations in that it's all but toothless when a dispute arises between economically mismatched nations. The US has little reason not to go right on ignoring Antigua's pleas and threats, and until something changes, it's the current status quo.
It continues to be most unfortunate that, despite 14 long years of deprivation, Antigua and Barbuda has to appear before this body, year after year, to report that the United States has not seen it possible to offer fair and equitable terms to my small country for the significant losses in trade revenues that it has suffered as a result of U.S. violation of the General Agreement on Trade in Services (GATS).
At the last meeting of this body on 23rd November 2016, at which this matter was discussed, the delegation of the United States indicated that it had offered "a broad range of useful suggestions to settle this dispute in November 2013, only to have Antigua ignore the U.S. offer for a long period of time before finally indicating that it was not acceptable".
For the record, Chair, my delegation is compelled to advise that, in accordance with the award made to my country by the Arbitration Panel established by this Body, the trade losses to Antigua and Barbuda now stands at more than US$200 million.
The U.S. offer that my Government found "not acceptable" did not amount to $2 million.
It should be no surprise, therefore, that my Government could not accept the offer.
It cost my small country much more than $2 million simply to bring the trade dispute to the attention of this Body and to seek redress in conformity with established and binding rules.
The U.S. delegation also told this body last November that "pursuant to Article XXI of the GATS", the U.S. offered "a generous package of services concessions as compensation for removing internet gambling from the U.S. schedule", adding that "Antigua is the only Member to block the United States from completing this process".
My delegation is further obliged to point out that my Government has not "blocked" the United States from removing its commitment from its schedule.
We have acted to safeguard our rights.
And at such time as the U.S. makes a fair, equitable and just offer to Antigua and Barbuda for the extreme harm done to our economy, we stand ready to act in an appropriate manner consistent with the rules of this Organization that the U.S. helped to fashion.
Chair, other countries – not named by the U.S. delegation last year – have released the U.S. from its GATS obligations in this particular matter because, although these countries did not pay the cost of bringing it before this Body, the U.S. has settled their losses in ways that remain undisclosed to this Body and to my government.
It can hardly be fair or just that the U.S. has reached settlements with other countries and not with my small country which was the principal victim of losses in trade revenues and employment.
The delegation of the United States also told this Body last year that "the regulation of cross-border gambling is a matter of public morality".
Consequently, my delegation is obliged to point out that in April 2005, the Appellate Body of this organization found that the U.S. could not invoke a "morals defense" to its violation of the GATS.
What is more, while the U.S. has banned internet gaming from foreign providers, domestic gambling service providers continue to operate and thrive.
Last November, the U.S. delegation advised this body that the government was reviewing "the most recent communication" from my government and that it "will continue to work expeditiously toward finding a realistic settlement".
It is with profound regret that my delegation has to advise that 10 months later, my Government has not received a response from the U.S. despite many overtures, including our most recent letter of 5th June 2017 to the US Trade Representative which has gone unanswered.
Chair, my delegation points out that the size of Antigua and Barbuda's economy is a mere US$1.4 billion; the size of the US economy is US$18 trillion.
Further, over the 14 years in which my small country has suffered trade revenue losses in this particular matter, exceeding US$200 million, we have in no way taken any hostile or retaliatory action against the U.S.
Indeed, the contrary is the truth.
For, over that same period, the U.S. enjoyed a trade surplus with Antigua and Barbuda of U$2 billion, as we continue to purchase almost 70 per cent of goods and services from the U.S.
We have not diverted our purchases away from the U.S. market.
Therefore, while the trade revenues losses to my small country is almost 20 per cent of our Gross Domestic product, settling with us would represent only .0011% of one year of the GDP of the United States.
Chair, my country has just suffered enormously from the ravages of Hurricane Irma.
Three weeks ago, the island of Barbuda, our second most populous island, was completely decimated by the Category 5 hurricane's battering which left all the inhabitants homeless and with no potable water, no electricity, no hospital and no school.
My government was forced to declare the island a disaster and to evacuate all the residents to Antigua where they are now being maintained in difficult and cramped circumstances despite our best efforts with limited resources.
For the first time in 300 years, there is not a single permanent resident on Barbuda, and Antigua is faced with an unexpected and unscheduled increase of 3 percent of its population and all the demands that such a sudden influx of people entails.
Additionally, we are confronted with an estimated cost of more than US$250 million to rebuild Barbuda and to resettle its inhabitants in their homeland.
There would be no better time than now, for the United States to settle this long-running issue which mars an otherwise friendly relationship between our two countries that has existed for generations.
Of course, Chairman, Antigua and Barbuda has the option of implementing suspension of U.S. intellectual property rights which is the award given by the Arbitral Bodies of this Organization.
Over these many years, we have not done so, not because we can't, or because we haven't had offers to help us implement the award in a transparent way and consistent with the DSB's authorization.
We have not done so because we have too high a regard for the U.S. owners of intellectual property who have contributed much to the enjoyment and advancement of the world.
We had hoped that the U.S. government would respond to our restraint in ways that would settle this issue without causing any loss of income to U.S. copyright holders.
Chair, we are aware that in 2010, Brazil was awarded the right to suspend payment of U.S. intellectual property rights in compensation for trade losses.
The US settled with Brazil by cash payments of over US$440 million and other ways in 2010 and 2014.
It would be very regrettable, Chair, if tiny Antigua and Barbuda were compelled to be the first country to have to suspend payment of U.S. intellectual property rights despite its best efforts to reach a settlement with the U.S., its largest and richest neighbour to whom it has always been – and remains – a friend.


The optic nerve transmits visual information from the retina to the brain. The optic nerve's function includes special somatic afferent, which carries the sensory modality of vision.
The images below of the optic nerve were captured using the Richter Optica U2 biological microscope at 400x magnification.
Optic Nerve under a brightfield microscope.
The images were captured using a 5 mega pixel microscope camera.
Optic Nerve captured under epi fluorescent microscope.
The optic nerve prepared slide can be found in the Histology Musculoskeletal slide kit.


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Q: c# datagridview set new row position on top is there any way to set the last empty row on the top of the DataGridView ?
it annoys with large dataset to scroll to the last row to add a new one.

A: There is no way to move the add new row to the top of a datagridview.  There is a control called the bindingSource which has methods like MoveLast to make it easier to navigate to last row of data.
    private void Form_Load(object sender, EventArgs e)
    {
        BindingList<DataInfo> data = new BindingList<DataInfo>();
        for (int x = 1; x <= 100; x++)
        {
            data.Add(new DataInfo()
            {
                id = x,
                Name = $"User{x}"
            });
        }

        this.bindingSource1.DataSource = data;
        this.dataGridView1.DataSource = bindingSource1;
    }

    private void button1_Click(object sender, EventArgs e)
    {
        bindingSource1.MoveLast();
    }
}

public class DataInfo
{
    public int id { get; set; }
    public string Name { get; set; }
}

A: Be aware of the difference between an "Empty row" and the "Add new Row", which seems to be an empty row, but which in fact is not part of your data yet.
Real Empty Rows on top
Suppose our DataGridView shows several properties of a sequence of Customers.
To get the empty rows on top, you'll have to define "Empty row":

*

*Is it the row where every displayed Customer property has a null value?

*Or should I check all Customer properties, even the non-displayed ones?

*And what about value types? When are they considered to be empty? If they have a value 0?

*And what about a displayed DateTime?

Questions, questions. Apparently you need to extend your Customer with a property IsEmpty:
public bool IsEmpty => ... // TODO code that returns true if customer is "Empty".

In order to sort such that the Empty Customers are on top, you need to create a CustomerComparer class, a class that implements IComparer<Customer>,
and tell the DataGridView to sort using this comparer:
IComparer<Customer> customerComparer = ...
this.DataGridView1.Sort(customerComparer);

An example of a Customer Comparer class:
class CustomerComparer<Tproperty> : Comparer<Customer>
{
    public bool EmptyRowsFirst {get; set;} = true;

    // sort the non-empty customers ascending or descending:
    public SortDirection SortDirection {get; set;} = SortDirection.Ascending;

    // which property to use to sort the non-empty customers:
    public Func<Customer, TProperty> PropertySelector

    public override int Compare (Customer x, Customer y)
    {
         if (this.EmptyRowsFirst)
         {
             if (x.IsEmpty)
                return y.IsEmpty ? 0 : +1
             else
                return y.IsEmpty ? -1 : this.CompareByProperty;
         }
         else
             return this.CompareByProperty;
    }
}

Method CompareByProperty:
private int CompareByProperty(Customer x, Customer y)
{
    IComparer<TProperty> propertyComparer = Comparer<T>.Default;
    TProperty propertyX = this.PropertySelector(x);
    TProperty propertyY = this.PropertySelector(y);
    int compareResult = propertyComparer(propertyX, propertyY);
    if (this.SortDirection == SortDirection.Descending)
        compareResult = -compareResult;
    return compareResult;
}

Usage:
// Sort by Customer.BirthDay, Ascending, empty rows First:
IComparer<Customer> customerComparer = new CustomerComparer<DateTime>
{
     EmptyRowsFirst = true,
     SortDirection = SortDirection.Ascending,
     customer => customer.BirthDay,
};
this.DataGridView.Sort(customerComparer);

// Sort by Customer.City, rest as default:
IComparer<Customer> customerComparer = new CustomerComparer<String>
{
     customer => customer.City,
};
this.DataGridView.Sort(customerComparer);

A: It's possible to create an empty DataGridView (Dgv) with possibility to add new data.
The typical code for Dgv is (considering BindingSourceOject is assigned to ContextObject.DataSource):
    ContextObject.DBSetObject.Load();
    BindingSourceOject.DataSource = ContextObject.DBSetObject.Local.ToBindingList();

If do not load DBSet (remove the first line), Dgv will appear empty but connected to DBSetObject. It will show the data entry row only. New rows will appear here while being added.
The solution for the hole data processing form is to put two Dgvs on it. The first one is 'empty' as described above for data adding and another one with no data entry (AllowUserToAddRows = false) to view/edit existing data.
This solution deliver us from creating a set of controls to add data. Two Dgvs can share same event handlers for data validation, formatting etc.


text:
#ifndef READLINE_READLINE_H
#define READLINE_READLINE_H

char *readline(const char *prompt);

#endif  /* READLINE_READLINE_H */