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Volunteers Bring Blessings After the Floods
Crisis & Disaster Response | 2:57 DR-170702_Wisconsin_Flood_Relief_2__FINAL_REV_ALT_END_h264.mp4
Laura Fissinger's basement flooded due to historic rainfall in southeastern Wisconsin. Samaritan's Purse volunteers are helping Laura's family and many others in the area start over after devastating storms.
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Listen to a preview of this week's future favorite and then give it a thumbs up or thumbs down.
You are here: Home / Heard On 20 / Jon's Future Favorite – For King & Country "Fix My Eyes"
One of our most requested specials is the tribute we've aired about the late, great Rich Mullins. You can listen to the show using the player … [Read More...]
20 The Countdown Magazine has secured exclusive permission to show two wonderful Rich Mullins films. The first is Homeless Man: The Restless Heart of … watch now
20 airs on great radio stations all over the world including AM and FM signals, satellites and networks and online outlets. To carry the show on your … Continue Reading

subset: commoncrawl


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The question
Let $f$ be a nonconstant polynomial over $\mathbb{C}$. Let's say that a point $c \in \mathbb{C}$ is unusual for $f$ if every root $x$ of $f(x) - c$ is repeated. Can $f$ have more than one unusual point?
Short remarks
There can be exactly one unusual point, e.g. if $f(x) = x^2$. There can be none, e.g. if $f(x) = x^3 + 3x$.
There are at most $\deg(f) - 1$ unusual points, since every unusual point is the image under $f$ of a critical point.
The hypotheses "nonconstant" and "over $\mathbb{C}$" could be varied. I added them to rule out cases like the following: over a field $k$ of characteristic $p$, every point of $k$ is unusual for $x^p$ (since the derivative of $x^p$ is $0$). I'd be happy to change the hypotheses to "nonconstant polynomial over an algebraically closed field of characteristic 0". Maybe something like "polynomial whose derivative is nonzero, over an algebraically closed field" would also be sensible.
Weak reason to expect the answer to be "no"
Perhaps there's a very short answer to my question: I could be overlooking something elementary. But in case it's not so easy, I'll give a flimsy argument for why we might expect the answer to be "no" - that is, for why we might expect every polynomial to have at most one unusual point.
My question is equivalent to: is there a nonconstant polynomial $f$ over $\mathbb{C}$ for which $1$ and $-1$ are both unusual? For $1$ to be unusual means that every root of $f(x) - 1$ is also a root of $f'(x)$. Writing $d = \deg(f)$, this is equivalent to $$ (f(x) - 1) \mid f'(x)^d. $$ Similarly, for $-1$ to be unusual means that $(f(x) + 1) \mid f'(x)^d$. Both together are equivalent to $$ (f(x)^2 - 1) \mid f'(x)^d, $$ that is, $$ (f(x)^2 - 1)\cdot g(x) = f'(x)^d $$ for some $g(x) \in \mathbb{C}[x]$. This forces $\deg(g) = d(d - 3)$ (and so $d \geq 3$).
So, can we find $f$ and $g$ satisfying the last displayed equation? Comparing coefficients, what we have here is a system of $d(d - 1) = d^2 - d$ equations in $(\deg(f) + 1) + (\deg(g) + 1) = d^2 - 2d + 2$ unknowns. There are $d - 2$ more equations than unknowns, and $d \geq 3$, so a first guess is that it can't be done.


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Samsung is making its tablet computers look more like its hit Galaxy phones in the hope that the success of the smartphones can boost tablet sales.
Samsung Electronics Co., the second-largest maker of tablets after Apple, is putting three new tablets in the Galaxy Tab 3 series on sale in the U.S. on July 7. The cheapest, $199 device will have a screen that measures 7 inches diagonally. An 8-inch model will go for $299 and a 10-inch one for $399.
"Our goal is to attract Galaxy smartphone users, and to make it the ultimate smartphone accessory," said Shoneel Kolhatkar, director of product planning at Samsung Mobile.
The "Tab" line is Samsung's value brand, undercutting the price of similar Apple models. Samsung's premium tablets are in the "Note" line, which include styluses.
The new tablets have the same three buttons on the front as the Galaxy smartphones. Last year's Tab 2 had no physical buttons on the front, as encouraged by Google, which supplies the Android software.
The 10-inch model is the first Android-powered Samsung tablet to use an Intel processor. That's a significant win for the Santa Clara, Calif., chipmaker, which has been trying to break into the market for cellphone and tablet chips now that PC sales are slumping. Other smartphones and tablets run chips made by a variety of companies, all based on designs from ARM Holdings PLC, a British company.
Samsung had 18 percent of the global tablet market in the first quarter this year, according to research firm IDC. Apple had 40 percent. In smartphones, the figures are nearly reversed, with Samsung dominating, largely because of its Galaxy line. Apple came in second with a 17 percent market share for the iPhone.
Even though the tablets have bigger screens than Samsung's flagship Galaxy S4 smartphone, their screen resolution is lower. The 10-inch tablet has a resolution of 1280 by 800 pixels, compared with 1920 by 1080 for the phone. The smartphone packs in three times more detail in a square inch than the tablet does. Competitors Google and Apple have similarly-sized tablets with higher-resolution screens.


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Notice to Members 06-02
Broker-Dealer, Investment Adviser Firm, Agent and Investment Adviser Representative Renewals for 2006
The 2006 NASD Broker-Dealer and Investment Adviser Renewal Registration Program is in its final phase this month. NASD is issuing this Notice to help firms review, reconcile and respond to their Final Renewal Statements and reports that are currently available on Web CRD/IARD.
Questions regarding this Notice may be directed to the Gateway Call Center at (301) 869-6699.


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About Double Jeopardy
In this thriller, Ashley Judd plays Elizabeth Parsons, who is convicted of murdering her husband and sentenced to a long stretch in prison. After Elizabeth has spent six years behind bars, it turns out that her husband is still alive: he faked his own death as part of an insurance scam, and Elizabeth is soon released. However, Elizabeth's feelings for her husband can hardly be described as warm, and she wants custody of her son. Elizabeth's parole officer (Tommy Lee Jones) wonders if she might try to make his murder a real thing after all, especially since the law states a person cannot be convicted of the same crime twice.


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Guests cook with wild Mediterranean herbs gathered from behind the house, salad greens and vegetables from local markets, olives from the abudant groves, and prepare unique Mediterranean, Spehardic, and Mozarabic dishes. Guests will visit Europe's highest viticultural region, the up-and-coming Vinos de la tierra Norte de Granada and meet with wine makers.
Classes are available by the hour on a fllexible schedule, November-April each year.
An optional two-week English language program can includes hands-on cooking and food culture sessions led by Vaughn Perret & Charles Leary, as well as guided visits to markets, vineyards, shops, and local restaurants. All cooking programs take place in the afternoons, allowing for morning Spanish classes if desired.
Mr. Perret studied history as an undergraduate at Loyola University, pursued graduate studies in cultural anthropology at Tulane University, and received his J.D. from Cornell University.
Charles Leary holds a PhD and MA in history from Cornell University, and received his A.B. magna cum laude from Kenyon College.
Both Perret & Leary have taught the Nova Scotia Seafood cooking school since 2000.
|Albaycin historic district
|0 km
|Alhambra Palace
|25 mins
|Plaza Nueva
|25 mins
|starting at 25 euros per person
|charges are per hour


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Last Week's Poll Results: Favorite Grocery Stores
Here are the results to last week's poll: What's Your Favorite Grocery Store? »
Trader Joe's 33% Wegmans 23% Whole Foods 18% Publix 8% Central Market 8% Safeway 5% Fairway 4% Giant 2 % Fred Meyer 2% Stew Leonard's 2%
It was a controversial topic but Trader Joe (or Jose, Ming, Giotto, Johann, or Joe-San, depending on the product) wins it! Honorable mentions go out to all the markets we couldn't squeeze into the poll, including: New Seasons, Copps, C-Town, Piggly Wiggly, Market Basket, Hannaford, Nugget, Cub Foods, Harris Teeter, H-Mart, Byerly's, Dierbergs, Buehler's, and Henry's.
One person who clearly did not vote for Trader Joe's had this to say in the comments:
I've never understood the Trader Joe's phenomenon. Can a store with a frozen foods section that's significantly bigger than any other section really be considered a "supermarket"? Isn't Trader Joe's just a glorified convenience store? Or are the Trader Joe's in Boston and NY significantly different from those in other areas? Is it the ridiculously cheap but really low-quality cheese and wine sections that people lust for? The Hawaiian shirts? What?!?
This post may contain links to Amazon or other partners; your purchases via these links can benefit Serious Eats. Read more about our affiliate linking policy.


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If you have received a request for a medical review and/or knowledge and road test from us, it means we have received information regarding your ability to safely operate a motor vehicle.
The information we received likely came from law enforcement, medical professionals, insurance companies or concerned citizens.
If the requested information is not received within 45 days of the notice date, your driving privilege will be suspended and/or revoked until the information is received.
If you have received a Corrective Action Notice that states you must complete any one of the following tests: written, vision, or road test with us, you do not need an appointment. You may visit any MVD office during normal business hours.
If you have direct knowledge of a person's medical status that would affect his or her ability to safely operate a motor vehicle, you may complete a Driver Condition / Behavior Report. Information received by the Medical Review Program is subject to disclosure in accordance with state and/or federal law. Once we receive the form, our only contact will be with the driver. We will not notify you of any outcome.
You must submit a copy of the vehicle registration and a letter from your physician, stating the medical reason for the request. The information must include your name and license number. Please note this exemption does not include the front windshield of the vehicle.
It is the driver's responsibility. As soon as a driver's medical condition allows, the driver must notify the Medical Review Program (in writing or by telephone) that he or she has, or may have, a medical condition not previously reported, which affects the ability to safely operate a motor vehicle.
No, but if a physician reports a driver in good faith, the physician is immune from civil or criminal liability for making the report.
You must be seizure-free for 90 days, but you must report the seizure to the Medical Review Program as soon as the medical condition allows. At the end of the 90 days, you will be mailed a Medical Examination Report to complete and submit to determine eligibility.
Yes, for a noncommercial license only.
Arizona Department of Transportation
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Copyright © Arizona Department of Transportation – All rights reserved.


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CBS Renews "The Big Bang Theory' for Three More Seasons
Surprise, surprise, and a hearty "bazinga" to fans everywhere. CBS' unstoppable juggernaut 'The Big Bang Theory' continues to reign supreme as one of the most-watched series on television, and the CBS empire has no intention of letting it go quietly into the night. The nerd comedy has been renewed for an additional three seasons, keeping Sheldon, Leonard, Penny, Howard, Raj, Bernadette and Amy Farrah Fowler on the air through at least 2017.
Despite its sheer scope, the move can hardly be considered a surprise, given the ratings and awards 'The Big Bang Theory' continues to rake in each season. Not only that, but this is actually the CBS comedy's second three-season renewal, further strengthening relations with sitcom magnate Chuck Lorre overall. Worth noting is that the licensing renewal does not include cast salary negotiations for series stars and original cast members Johnny Galecki, Jim Parsons, Kaley Cuoco-Sweeting, Simon Helberg and Kunal Nayyar, the former three of which will no doubt secure a major payday for their involvement.
Says CBS Entertainment Chairman Nina Tassler of the renewal:
Comedy is a big part of our schedule, and 'The Big Bang Theory' is the biggest comedy force on television. This multi-year deal further strengthens our network's position for future seasons and marks another chapter in the great partnership CBS enjoys with Warner Bros. Television for delivering audiences the best in comedy. We're proud to work with and showcase the incredible talents of Chuck Lorre, Steve Molaro and this amazing cast every week.
Currently in its seventh season, 'The Big Bang Theory averages 19.79 million viewers in most current ratings, garnering a 6.1/19 scoring among adults 18-49. The nerds are certainly here to stay, so tell us what you want to see from future seasons of 'The Big Bang Theory' in the comments!


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We help drive more business to your website!
We will correct all of the above points and more to help your website rank better in search engines.
You found us because we are ranking for what you typed in to Google.
If we rank for the most competitive keywords right now, then we can get your website to page #1 too and help you get the organic traffic from Google that your competitors are getting right now.
See what people like you really think about our SEO Coventry services.
The adjacent graph shows what generally happens to our clients' websites after 6 months of SEO. The organic, relevant traffic increases by at least x4.
*Please note, the numbers are there for a guide but are accurate percentages on an average of 10 websites we have performed SEO on.
We guarantee to rank on page #1 for your chosen keywords ** We will not charge after pre-agreed timescale until we get you on page #1
SEO pricing is different for every keyword but if you fill out the SEO discovery form below, we will be in touch regarding the health of your website and price for SEO.
We would love to help everyone that requests our services as we have assisted hundreds of business achieve high-levels of success. We select the clients we work with very carefully and have reasonable criteria that needs to be met in order for us to proceed.
We only work with a limited amount of clients at any given time to ensure maximum attention to detail and your company´s ultimate success.
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Great question! Just because you now have a website, it does not mean people are going to visit it. In our opinion SEO for start-ups is crucial. The best anaolgy we always use is that it is like having a lovely well stocked shop in the middle of the desert. People will come, if they know it is there, but if no one knows about it, very few will find it and therefore very few will come. So to explain that, someone types in what you do in to Google, and your website is not on the first page, how do they know your website exists!
To an extent yes. But maybe not how or what you would think for. Just because you have had a web design done for you by us or by anyone, doesn't guarantee it will rank. There are many facets to SEO and this is what we specialise in.
Yes. However the timeframe is not guaranteed and will be different per client, per keyword, per SEO project.
By stating we guarantee means that we will have a pre-agreed timescale for the keywords you require and if you are not on page #1 at the expiry of this timescale, we will continue to do SEO for free until page #1 is acheived. However some SEO projects require ongoing SEO, in this case we will just switch focus on keywords and contine improving rankings of the new keywords.
Yes, of course. We don't just do local SEO, we have many clients from the UK, EU countries and the US and can rank you whereever you are in the world for whatever you want to rank for.
Yes of course, we not only can send them to you direct in email as often as you want but we have an App where you can view your keyword progress at any time.
All you need to do is fill in our SEO discovery form, information request and then we can begin.
Again this depends on the keyword, the niche, the competition but to generalise, we would say things will start to happen around the 6 month mark.
Don't panic! This is very normal, we always advise to allow 6 months before seeing anything significant. Not to say it won't happen quicker but google indexes slow these days in 2019 and it takes time for links pointing to your website to pass the juice or power.
The answer is yes you will for some time, depending on the competitiveness of the niche and keyword. If you drop down a few positions we will analyse and tell you why. If you have stopped SEO, you may need to restart if your competitors are doing SEO.