text:
Le parc national de la Lagoa do Peixe est un petit parc naturel créé dans le Sud du Brésil (à environ  de Porto Alegre par la route BR-101) autour de la Lagoa do Peixe (la lagune aux poissons) qui se situe entre l'embouchure de la Lagoa dos Patos (ou lagune des canards) et l'océan Atlantique Sud.

Le parc est reconnu au titre de site Ramsar depuis 1993.

Faune

Le parc accueille principalement une faune aquatique et des oiseaux migrateurs dont les plus représentés sont certainement :

 le flamant rose ;
 l'ibis ;
 le héron ;
 l'otarie.

Économie

Le tourisme et l'éco-tourisme y sont organisés depuis les villes de Mostardas, Tavares et São José do Norte, mais restent limités à quelques milliers de personnes par an seulement du fait de la difficulté d'accès, notamment en période humide.

Liens externes

  Description générale en portugais
  Birding in Rio Grande do Sul

Références

Parc national au Brésil
Tourisme au Brésil
Parc national créé en 1986
Environnement au Rio Grande do Sul
Site Ramsar au Brésil
Site Ramsar en 1993

redpajama_set_name: RedPajamaWikipedia


text:
Diversity Grant Application
Antics, Drift, and Chaos
Thursday, March 29, 2018 - 8:30 am–9:10 am
Lorin Hochstein, Netflix
Large systems evolve from successful, smaller one, an observation predicted by the branch of study known as systems theory. Systems theory also predicts that our systems will inevitably behave, and fail, in unforeseen ways. This talk will draw from the ideas of two very different systems theorists to demonstrate that neither quality architecture nor thorough testing can prevent our software from eventually exhibiting pathological behavior. The first is the safety researcher Sidney Dekker, who proposed a theory of "drift into failure" that describes how seemingly reliable safety-critical systems can still lead to accidents. The second is the late pediatrician John Gall, who coined the "Generalized Uncertainty Principle" about how all types of complex systems behave unexpectedly.
Even though failure is inevitable, there is still hope. Chaos Engineering is an approach that can be used to identify system vulnerabilities before they lead to outages. This talk will cover how to design and run Chaos Engineering experiments, drawing examples from our experiences at Netflix.
Lorin Hochstein is a Sr. Software Engineer on the Chaos Team at Netflix, where he works on ensuring that Netflix remains available. He was previously Sr. Software Engineer at SendGrid Labs, Lead Architect for Cloud Services at Nimbis Services, Computer Scientist at the University of Southern California's Information Sciences Institute, and Assistant Professor in the Department of Computer Science and Engineering at the University of Nebraska–Lincoln.
@lhochstein
SREcon18 Americas Open Access Videos Sponsored by
author = {Lorin Hochstein},
title = {Antics, Drift, and Chaos},
address = {Santa Clara, CA},
View the slides
SREcon is a registered trademark of the USENIX Association.

redpajama_set_name: RedPajamaCommonCrawl


text:
Sarah Haskins and Filip Ospaly Repeat as 2012 St. Anthony's Triathlon Champions
St. Anthony's Hospital
Both Women's, Men's Winners Break Previous Course Records
ST. PETERSBURG, Fla., April 29, 2012 /PRNewswire-USNewswire/ -- Sarah Haskins and Filip Ospaly successfully defended their titles at the 2012 St. Anthony's Triathlon on Sunday. Haskins and Ospaly, who won the titles a year ago, also broke course records in both the men's and women's professional races which drew one of the largest pro fields in the event's 29-year history.
(Photo: http://photos.prnewswire.com/prnh/20120429/DC96924)
Haskins, 31, won her fourth title in the past five years and her third in a row. She was in control for most of the race and bested her nearest competitor by more than two minutes, clocking in at 1:56:55. The previous women's record was 1:57:45.
"Toward the end, people were telling me 'Sprint! Sprint! Sprint!' So I did," Haskins said. "I was just so happy to break the record."
For Haskins, who now lives in Clermont, this is her second win of the year. Earlier this month, she won the Nautica South Beach Triathlon in Miami Beach. She has a busy May planned as she will race in the ITU World Triathlon in San Diego on May 10 and then the Capital of Texas Triathlon in Austin, Texas, on May 24. She also is training to make the 2012 Summer Olympics team.
Ospaly, 36, did what he does best – run fast – and crossed the finish line in 1:45:50. "At the bridge, I made my move," he said. "The run is my strong suit and I knew I could overcome." He passed several leaders on the run portion of the race to come in first. Ospaly, of the Czech Republic, bested the previous course mark of 1:46:10.
Coming in second in the professional women's division was Alicia Kaye, also of Clermont, with a time of1:59:16. The top three was rounded out by Jodie Stimpson of Great Britain, whose time was 1:59:37.
The three top finishers in the professional men's race all beat the old course record. Second place went to Ben Collins of Seattle who crossed the finish line in 1:45:59. Third place went to Timothy O'Donnell of Boulder, Colo., with a time of 1:46:04.
Featuring a number of world champions and past title winners, the St. Anthony's Triathlon boasted one of its strongest fields for the 2012 competition. The international-distance race (1.5K swim, 40K bike and 10K run) is the second event of the 2012 global 5150 Triathlon Series, offering athletes coveted points toward 5150 U.S. Championship qualification.
Known for its scenic course along the downtown St. Petersburg waterfront, St. Anthony's Triathlon also has been named the fourth largest triathlon in the country by USA Triathlon. The regional events qualify the top 33 percent per age group for the USA Triathlon Age Group National Championship.
St. Anthony's Triathlon attracts approximately 3,500 individuals and 125 relay teams each year from more than 45 states and nearly 20 countries. The race weekend also included an extensive event expo and the Meek & Mighty Triathlon, a shorter-distance race for youth ages 7-14 and novice adults. Athletes competed for a professional prize purse totaling $65,000 in addition to $10,000 in prizes for the top male and female competitors in the Elite Amateur division.
The 5150 series is an International distance triathlon consisting of: 1.5K swim, 40K bike and 10K run. It is the largest international distance triathlon series in the world and the first non-drafting international race series of its kind, offering a competitive platform for professional and age-group athletes.
Visit http://www.raceresults360.com/satriathlon12/#/results for all results. Look for news about St. Anthony's Triathlon at www.SATriathlon.com.
About St. Anthony's Hospital
St. Anthony's Hospital is a 395-bed hospital founded in 1931 as a ministry of the Franciscan Sisters of Allegany and is the first and only faith-based hospital in Pinellas County. In its 81st year, the hospital continues its rich history dedicated to improving the health of the community by providing high-quality, innovative and compassionate care.
About BayCare Health System
BayCare Health System is a leading community-based health system in the Tampa Bay area. Composed of a network of 10 not-for-profit hospitals, outpatient facilities and services such as imaging, lab, behavioral health and home health care, BayCare provides expert medical care throughout a patient's lifetime. With more than 200 access points conveniently located throughout Tampa Bay, BayCare connects patients to a complete range of preventive, diagnostic and treatment services for any health care need. BayCare's family of hospitals are: Mease Countryside, Mease Dunedin, Morton Plant, Morton Plant North Bay, St. Anthony's, St. Joseph's, St. Joseph's Children's, St. Joseph's Hospital-North, St. Joseph's Women's, and South Florida Baptist. For more information, visit BayCare on the Web at www.BayCare.org.
SOURCE St. Anthony's Hospital


text:
import os
from subprocess import call
from ..utils.command import BaseCommand
from ..utils import package_json

class Command(BaseCommand):
	name = "run"
	@classmethod
	def decorate_subparser(cls, subparser):
		subparser.add_argument('script', type=str)
	@classmethod
	def run(cls, args):
		cls._run(args.script)
	@staticmethod
	def _run(script):
		script_content = package_json.get_script(script)
		if not script_content:
			print("Unable to find script "+script)
			return
		call("export PYTHONPATH=./python_modules:$PYTHONPATH;"+" "+script_content, shell=True)

redpajama_set_name: RedPajamaGithub


From Cheats, Oh, Flamingo, Daughter, Two Door Cinema Club, and more.
Ahh, summer love. Fun, fleeting, and forever etched in our memories. Do you and your summer love have a song? Or is there a particular song that just makes you look back at all your wonderful summer memories with that special someone? This week, we're sharing a few songs that make us think of summer loves. Click play and give it a listen. And don't forget to follow us on Spotify to get updated whenever we upload a new mix.


text:
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You Are Here: Home > 9 Best Luxury Crossovers for 2020
9 Best Luxury Crossovers for 2020
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With an emphasis on interior refinement, proven versatility, and state-of-the-art tech features — it's no surprise that luxury shoppers are increasingly choosing a premium compact crossover over their sedan counterparts. Due to their compact footprint, these crossovers offer precision handling and surprisingly-spacious interiors to accommodate all of life's essentials. Whether you're headed downtown for dinner and a movie or across state lines for a weekend getaway — there's a compact luxury crossover that's perfectly suited to your lifestyle. Check out the Germain Motor Company's top picks in this segment below.
The perfect solution to navigating city streets, the Audi Q3 impresses with dynamic styling, agile performance, and driver-centric technologies. Equipped with standard quattro® all-wheel drive and a turbocharged 228-horsepower 2.0-liter TFSI® engine — the Q3 delivers inspired power that doesn't sacrifice on efficiency. The optional MMI® touch response system provides available Audi connect®, enabling Google Earth™ with 3D satellite imagery, and a Wi-Fi hotspot for up to eight passenger devices. 12-way heated leather front seats provide the perfect combination of comfort and support on extended journeys. Other impressive interior features available on the Q3 are ambient interior lighting, a panoramic sunroof, and a 60/40 split folding rear seat. No matter where you're headed, you can count on making a memorable first impression with the Audi Q3.
Starting at $34,700 MSRP
Max Cargo Capacity – 48 cubic feet
EPA-Estimated MPG – 19 City / 27 Highway
All-Wheel Drive – Standard
View Audi Q3 Inventory
No matter if you're headed out the door for a quick joyride through the city or across the country for an extended road trip — the BMW X1 will expand your possibilities with the press of a pedal. Standard power comes from a 2.0-liter BMW TwinPower Turbo inline 4-cylinder engine paired with available xDrive all-wheel drive for surefootedness across even the worst road surface conditions. Despite its compact platform, the X1 features spacious headroom and available Sliding and Reclining rear seats for expanded versatility. Key tech features available on the X1 include a Head-Up Display, Apple CarPlay® smartphone integration, Rear View Camera and Park Distance Control, and an 8.8-inch Central Information Display. Standard BMW Navigation ensures that you'll always arrive at your destination safely and on-time with the BMW X1.
Max Cargo Capacity – 58.7 cubic feet
All-Wheel Drive – Available
View BMW X1 Inventory
Offering the commanding exterior presence of an SUV combined with athletic performance and agility, the Cadillac XT4 is not your ordinary crossover. Experience 237 horsepower and 258 lb-ft of torque from its standard 2.0-liter turbocharged engine that's paired with a 9-speed transmission and available twin-clutch AWD. Striking design elements found on XT4 Sport models include a gloss-black mesh grille framed by Galvano accents and gloss-black roof rails. Its inviting interior offers hand-selected materials along with a new Cadillac cut-and-sewn process that spirals the stitching down the armrests on the doors. Available Wireless Charging and a Cadillac 4G LTE built-in Wi-Fi hotspot lets you charge up quickly and stream your favorite entertainment.
View Cadillac XT4 Inventory
A masterful design combined with an exclusive 268-horsepower 2.0-liter Variable Compression Turbo (VCT) engine help illustrate why the Infiniti QX50 remains a favorite among compact luxury crossover buyers. The QX50 displays signature Infiniti DNA in every curve of it's striking exterior design with deep dramatic creases and dynamic LED lighting. Inside the cabin of the QX50, you'll discover a premium atmosphere with luxurious accents including an available Ultrasuede® headliner and available genuine leather seating surfaces. In addition to the incredible refinement of the interior, there's also a massive 65.1 cubic feet of cargo capacity which gives you plenty of room when packing for a weekend getaway. Cutting-edge driver-assistive technologies available on the Infiniti QX50 include Blind Spot Intervention®, the Lane Departure Warning System, and Intelligent Cruise Control.
View Infiniti QX50 Inventory
2020 Jaguar E-PACE
If you're searching for a dynamic yet agile SUV, the Jaguar E-PACE impresses with its sculpted hood and muscular rear haunches. As the first compact SUV from Jaguar, the E-PACE stands out for its enhanced driving dynamics and refinement from a range of available Ingenium engines and standard all-wheel drive. JaguarDrive Control allows you to select Comfort, Eco, Dynamic or Rain / Ice / Snow to adapt to a variety of weather conditions. In addition to a massive 57.2 cubic feet of cargo capacity, the interior of the E-PACE features deep front door pockets which have been sculped to accommodate a range of items including phones, cans, and a 1.5-liter bottle of water. The 10-inch Touch Pro screen at the heart of the center console supports swipe and pinch gestures and delivers rich audiovisual entertainment.
View Jaguar E-Pace Inventory
Chiseled character lines, a dramatically styled front fascia, and a road-hugging stance help you make a memorable first impression with the Lexus NX. Experience exhilarating performance from NX F SPORT models or unparalleled fuel economy from the NXh. Peace of mind comes standard with the NX thanks to the Lexus Safety System+, an integrated suite of class-leading standard active safety equipment. An available 10.3-inch high-resolution split-screen multimedia display is your centralized hub for Lexus Enform Dynamic Navigation, perfect for finding a new restaurant or theater to visit. The optional eight-speaker Lexus Premium Sound System allows you to hear your favorite songs with outstanding clarity and depth.
View Lexus NX Inventory
Offering a sporting soul and a compact footprint, the Mercedes-Benz GLC offers turbocharged engine power which makes it both adventurous and adaptable. Taut, trim, and muscular — the GLC stands out with an eye-catching front grille and elegant LED taillamps. The standard power liftgate opens to reveal plenty of cargo capacity featuring unique underfloor storage compartments. Quench your thirst for performance with a potent 255-horsepower turbocharged 2.0-liter engine and a 9G-TRONIC transmission. From a 10.25-inch central touchscreen display to standard Apple CarPlay™ smartphone, the Mercedes-Benz GLC helps you stay connected on the go. Groundbreaking safety innovations also position the GLC as one of the safest luxury crossover vehicles in its segment.
View Mercedes-Benz GLC Inventory
2020 Porsche Macan
Engineered for drivers who never make compromises, the Porsche Macan combines sportiness, design, and everyday practicality. Experience race-inspired performance from its standard 2.0-liter turbocharged 4-cylinder engine which delivers 248 horsepower. Standard all-wheel drive and a 7-speed Porsche Doppelkupplung (PDK) transmission provide an exciting combination of response and poise across all types of weather conditions. A new 10.9-inch touchscreen display in Porsche Communication Management (PCM) boasts full-HD resolution and a personalized start screen. Premium genuine leather sport seats provide superior support while cornering. Driving a Macan means that you'll experience sports-car exhilaration in the form of a compact SUV.
View Porsche Macan Inventory
2020 Range Rover Evoque
Constructed with an emphasis on minimalism and reduction, the Range Rover Evoque redefines the meaning of driving a premium compact crossover. Characterized by its sloping roofline and rising beltline, the Evoque captures the attention of onlookers with its seductive styling. A testament to the legendary capabilities of Range Rover vehicles, the Evoque includes standard All-Terrain Progress Control (ATPC) for confidence in challenging conditions. Impressive standard features on the Evoque include 12-way grained leather seats, InControl® Touch™ with an 8-inch touchscreen, and projected puddle lights. You can personalize the interior with premium touches like twin-needle stitched leather, aluminum accents, or wood veneer finishes.
View Range Rover Evoque Inventory
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Due to financial hardship, I've lost most of my possessions during the past year and sadly, this included a lot of my writing and equipment and recordings. Unlike the furniture that will be auctioned off, personal irreplaceable items are usually callously destroyed or thrown out despite the storage company reportedly requesting personal items be left with them.
I'm finding that I remember at least the bones of a lot of the things I've written & maybe some of them will improve in the re-writing. Anyway, at least I can "save" them here.
Consider these works in progress.


text:
Columns and Views
MagazinesNewsletterCustomer Service
Columns & Views
Home › Tech and Gear
Interference: Define and Conquer
Cases should be evaluated individually; some may involve considerable effort
Thomas G. Osenkowsky ⋅ Sep 20, 2010
Broadcasters encounter interference in two forms: that which someone may accuse the broadcaster of causing, and that which the broadcaster experiences.
The most familiar type of the former is a consumer complaint that the broadcaster's signal is being received on a device not intended to do so. Typical devices are telephones, home sound systems and radio receivers.
Broadcasters may face complaints from other broadcasters, commercial and government entities. A broadcaster also may receive interference on its RPU, STL, EAS and off-air monitoring receivers.
Locating the source of interference often is a challenge, especially if the problem is intermittent.
Curing interference requires a combination of art and science; the same solution may not be effective in similar cases. A typical arsenal of components used to remedy consumer gear interference is shown in Fig 1. Ferrite devices, inductors, capacitors, AC power line filters, DSL filters and ground wire may be employed to reduce or eliminate unwanted reception.
Fig. 1: Curing interference is a combination of art and science; the same solution may not be effective in similar cases. A typical arsenal of components used to remedy consumer gear interference is shown.
A common consumer complaint is reception of an AM station on a stereo or public address amplifier. This can also occur in a house system where the studio and transmitter are collocated.
Typical cures involve placing a .1 µf capacitor across the speaker output terminals on the amplifier and/or the speaker itself. An inductor in series with the speaker output terminal may help, as can twisted (not zip cord type) speaker cable. Try wrapping several turns of the speaker cable through a toroidal ferrite choke.
With ferrite products, use the proper suppression material for the offending frequency band. Fair-Rite #31 and 73 are effective at AM frequencies, whereas #43 and 44 are effective at FM frequencies; #61 is effective at UHF frequencies (see sidebar for Fair-Rite link).
RF entering through the audio input terminal of an audio amplifier may be cured by placing a small capacitor across the hot lead(s) to ground, or across the balanced hot pins. A small inductor may also be used. For VHF/UHF frequencies a ferrite choke may be placed around the input terminal(s) inside the unit. A small value capacitor placed across a tape head can remedy FM/VHF/UHF interference. Take care to select the lowest value of capacitor possible to eliminate the RF while still preserving the audio frequency response.
Unwanted reception of RF in telephones often can be treated effectively by installing a DSL filter in series with the telephone line. Determine whether RFI is heard on the incoming telephone line; just plug in a Western Electric 500 or 2500 set into the demark jack with the customer's equipment disconnected. If the incoming line has RFI on it, the matter should be referred to the telephone service provider. If the line is free of RFI, the issue lies with the customer's equipment. If a DSL filter does not solve the problem, refer the complainant to the telephone manufacturer's website for technical support.
Many telephones lack RFI protection; however, the manufacturer may offer external filters. Third-party vendors like K-Y Filter Co. also offer such filters.
Receivers in close proximity to transmitter sites may experience front-end overload with the resulting inability to receive other stations. A notch filter from a supplier like Tin Lee Electronics Ltd. may be helpful for FM reception where an external antenna is employed. These are also helpful in resolving television interference.
The FCC has a resource page that may be helpful to consumers, headlined "Interference: Defining the Source" (see sidebar).
It is not advisable to attempt repairs to consumer equipment; some states require licensure to do so, and you also may face liability issues. An engineer or station may stand accused of causing damage to the device or be blamed for its unrelated improper operation. Advise consumers on how to purchase filters; refer them to local licensed repair shops or the manufacturer for resolution.
Unhappy FAA
Here are several cases of interference complaints and how they were resolved.
I received a call from the chief air traffic controller at a local airport claiming that our Class A FM station was interfering intermittently with the tower frequency, 119.4 MHz.
I asked if he could hear our audio and whether aircraft could hear the interference. He checked and said the problem had been heard by listeners in aircraft and separately on the ground via a portable receiver. The audio was unintelligible but our station was suspected because the antenna of the FAA's direction finding van pointed toward our tower. Yet this also could mean that the offender was someone else, located between the van and our tower or beyond us on that bearing.
I invited the FAA technician to visit our site. Not having a spectrum analyzer, I brought along a Potomac FIM-71 and Icom R-7100 receiver.
I raised/lowered transmitter and exciter power; I mistuned the IPA and PA. But I could not produce any of our audio on 119.4 MHz. I could hear the tower and aircraft, but no evidence of our signal, other than on our licensed frequency.
Asked for a recording of the interference, the chief controller produced a GPS time-indexed DAT tape as the worst example.
We listened to 8 minutes of pure garble, akin to wideband FM detected on an AM receiver. According to our music log, our station at the time had been playing "Run" by Collective Soul. Listening to the tape, he and I agreed we could hear no change in tempo or cadence, and no voice. Also, "Run" was not an 8 minute song.
One aircraft trying to call in during this time had been diverted to a secondary frequency, and no wonder. I would not want to listen to that garble all day. This was a safety issue. I told the controller to call me if the interference reappeared.
It did so the next morning at 9:30; so I turned off our transmitter/exciter. This produced no change at all; the interference remained. Our station, it appeared, was not the offender.
I offered my assistance to the FAA not only as the chief engineer of the station but as a pilot who earned his license at that airport. I never heard back from the controller but I did meet the airport manager at a local restaurant some months later and asked if they'd ever found the cause of the interference.
The FAA technician finally had identified an SUV from which the signal was emanating. The owner had installed an FM booster to improve his reception. Removing the fuse to the booster cured the problem.
In another case, a local police department called to report that our 850 kHz station was interfering with their 45 MHz repeater.
They could not hear our audio, only beeps and tones at all hours of the day and night; but we stood accused because their radio technician had examined FCC records and identified ours as the most powerful transmitter licensed to that town.
Useful Info An FCC resource page
"A Ham's Guide to RFI, Ferrites, Baluns and Audio Interfacing"
Fair-Rite Products Corp. (material data sheets)
K-Y Filter Co.
Tin Lee Electronics Ltd.
"Interference: Defining the Source" (FCC)
I explained that the source probably was a paging transmitter at their multi-user site miles away. When the lieutenant told me the problem had been very bad a few days earlier at 4 a.m., I also pointed out that we were a daytimer and not on the air until 6 a.m.
I never heard back.
Playing against the house
At a Class A FM station, we received a complaint of interference to the CSPAN-2 channel on the local cable system at a nearby residence.
The resident was not home when the head-end chief technician and I visited. The center frequency of the CSPAN-2 was 800 kHz removed from our licensed frequency. The problem remained even after the drop cable and a trunk section were replaced.
I asked the technician if he could see our signal on a spectrum analyzer at various nearby tap points if the CSPAN-2 modulator was turned off. He said yes. Clearly this was a cable leakage issue.
It turns out the source was the neighbor's house. Aluminum siding recently had been installed there, and the drop cable's shield had been punctured and stapled in three places. The siding was acting as a receive antenna.
In another instance, this same FM station was said to be interfering with one 800 kHz up the dial. We cured this by installing double shielded coax cable between the audio processor/stereo generator located in a rack and the exciter composite input. Our collocated AM station operates on 800 kHz.
In another such case, we realized that when the station's ATU had been installed, its ground strap had never been connected to the base ground strap at the tower. In fact we found the strap coiled up inside the ATU. When we connected it, the problem was solved.
Interference has many variations, causes and cures. Evaluate and treat each case individually. Some remedies are simple, where others may involve considerable effort to locate and cure.
Tom Osenkowsky is a broadcast engineering consultant and long-time contributor to Radio World.
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Will the U.S. Sit Back or Attack? Who Will Start?
We asked 11 soccer obsessives to tell us what they were hoping to see the U.S. men's national team do against Guatemala in Livestrong Park. Here's what they told us.
BY Various Posted
The worst thing that could happen Tuesday night in Kansas City? The U.S. loses and crashes out of World Cup qualifying before they even reach the Hex.
The second-worst thing that could happen? The U.S. settles for a complacent draw, thereby ensuring passage but also disappointing fans desperate for a showpiece win.
So, how should Jurgen Klinsmann play it?
Korey Donahoo
President, American Outlaws
I'd love to see Jermaine Jones on the bench, which we have a pretty good chance of seeing, considering he broke the one rule he had on Friday night in Antigua—to not get a yellow card—as a second-half substitute. Give the tireless Zusi a starting spot in the middle, which he has more than earned. I'd also love to see another goal or two from Eddie. Let's cash in on him while he's hot, with Zusi serving up delicious crosses for him all day long. Last on my wish list: a two-goal cushion.
Freelance soccer writer
Clint Dempsey needs to be briefed on what his role is in the American team. In Dempsey the U.S. has an exceptional talent, even by the high measure of the English Premier League, yet Klinsmann doesn't seem sure how to make the best of him. Dempsey himself also needs to fully commit to the international cause. Too often he makes it easy for fans to angle accusations that he doesn't care about the U.S. team. Unlike club soccer, international soccer is about utilizing the players you have been given. The U.S. has been given Dempsey. They need to use him.
National Lead Writer, Bleacher Report
"Get to the Hex" sounds like a bad action comedy with Russell Brand, but that's the only goal for Klinsmann on Tuesday. The U.S. can get to the Hex with a draw (or a loss and some help), but it's important for Klinsmann to play for the win. Guatemala is the type of team the U.S. must dominate if a serious run is to be expected in the World Cup. Still, both teams advance with a draw, so expect a defensive formation (4-1-3-1-1) with an offensive mentality. I'm okay with that, as long as the U.S. plays to win.
Luis Bueno
The United States' World Cup qualifier against Guatemala is not a must-win—Eddie Johnson saw to that when he scored a last-gasp winner in Antigua on Friday. However, the U.S. must approach this game as such. Too often throughout this semifinal round, the Americans have lacked urgency. The team slogged through away games in Jamaica and Antigua, and were not clinical in their finishing against their Caribbean rivals at home either. Urgency from the start and goals against a team that will be bent on escaping with a nil-nil draw would be a solid way to close out this round.
Dan Wiersema
Founder, Free Beer Movement
While it has been a welcome change to see the U.S. possess the ball better (and not have to chase the game even against inferior opposition) we've yet to see Jurgen Klinsmann's master plan lead to sustained pressure in the final third, shots, and goals… please… several goals. The opening half hour against Jamaica in Columbus gave us a nibble of what it should look like, but great goalkeeping and the post left American fans unfulfilled. Against Guatemala I'd like to see possession turn to pressure, turn to shots, turn to goals… no matter from whom or from where they come from.
Co-host, Best Soccer Show
If the U.S. is going to assuage any fears that 2014 could be the first World Cup they miss since 1986, the effort in Kansas City needs to take several steps forward from what we saw in Antigua. Unfortunately, a draw will do for both teams, and it's possible we see an underwhelming walk to the finish line. But Klinsmann should do everything he can to raise his team's level by insisting on a comprehensive win. To this point, he's struggled to find a balance within his lineup. Tuesday in Kansas City would be a good place to end the struggle.
Brian Blickenstaff
I'd like the U.S. to win against Guatemala, but I want a good performance, too. I want the team to attack with width, defend against the counterattack, and generally play like a coherent unit. After the Antigua and Barbuda match, SI's Grant Wahl critiqued Klinsmann's tenure as national team coach, arguing that "this team has regressed during the German's 14 months in charge." Like every American soccer fan, I'd like to disagree, but where's the evidence?
Phil Schoen
Announcer, beIN Sport
With Fabian Johnson still out, there's a good chance Michael Parkhurst pushes Carlos Bocanegra inside after his rough outing against Antigua. Another possibility is sitting a struggling Hercules Gomez, pushing a red-hot Eddie Johnson inside and inserting someone to get width on the left. Clint Dempsey only shined in flashes against Antigua, but I fully expect Jurgen Klinsmann to start him, though I wouldn't be surprised in a quick hook if he continues to disappear. Graham Zusi should have a good showing at home, and I wouldn't be surprised if Alan Gordon gets some extended minutes in the second half.
Jared DuBois
Who knows more about Wizards than KC? So what better place to test out magic than Livestrong Park? Is Alan Gordon a witch? Is Klinsy the Rain Man of roster selection? I don't know, but it's going to take more than mysticism to beat Guatemala. The U.S. will need to be smart in not giving up cheap fouls and overcommitting to the attack. I'm excited to see the Bradley/Zusi dynamic build.
Sayra Moran
Founding Member, Women United FC
What I would like for Tuesday's qualifier is more team cohesiveness. Klinsmann obviously loves to tinker with the roster and has tough decisions to make on what the starting lineup will be. Guatemala is always hungry to win and the USMNT should make a strong case in why they deserve to advance. Our back line is stacked with talent so they should stifle chances that Guatemala attempts to create. Eddie Johnson was indisputably great against Antigua and Barbuda: I'd like to see him, the rest of the forwards, and the attacking midfielders possess more and set up solid plays.
Luke Lohr
Founder, MLSReserves.com
Win. Simple as that. While we'd all like to see glorious passing and beautiful goals, none of it will matter if the squad does not win in Kansas City. Ninety minutes separate the United States from a fresh start, and if they win past performances will be forgotten when looking back. Fight hard, get dirty, and win. We can complain and analyze over the rest afterwards. That said, I'd like to see Zusi in the midfield with Bradley once again, with Johnson and Gomez up top. The duo has potential but needs time to develop.
We want to hear your take too. Post your thoughts on the game—in 100 words or less—below.


Montgomery County Parks and Recreation is asking residents to complete an online survey that will help shape its master plan.
This survey, which is available through Oct. 16, is available to all County residents, including those living in Blacksburg or Christiansburg, and students attending Virginia Tech. The master plan will give the department a vision and goals for the next 20 years.
Please enter this link into your web browser, http://bit.ly/mcprfall2015, or scan the accompanying QR code, to take the survey. For more information, please visit www.nrvrc.org or contact Jennifer Wilsie or Michael Gottfredson at (540) 639-9313.


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La qüestió de determinar si un nombre donat n és primer es coneix com el problema de la primalitat. Un test de primalitat, test de primeritat (o revisió de primalitat) és un algorisme que, donat un nombre d'entrada n, no aconsegueix verificar la hipòtesi que n és compost.

Per tant, un test de primalitat només afirma que "davant de la falta de verificació de la hipòtesi: n és compost, es pot tenir certa confiança de què es tracta d'un nombre primer". Aquesta definició implica un grau menor de confiança que amb una prova de primalitat (o test verdader de primalitat), que n'ofereix la seguretat matemàtica (confiança=1).

Motivació
El problema de la Factorització és un problema per al qual no s'ha trobat una solució de Temps polinòmic.

D'altra banda, algunes aplicacions com ara en criptografia necessiten una sèrie de nombres primers molt grans escollits de forma aleatòria. L'algorisme per obtenir un nombre primer aleatori molt gran pot ser així:

El temps d'acabament d'aquest algorisme és, de mitjana:

On  és el temps de trobar un nombre aleatori més el temps de verificar si aquest nombre és primer (o verificar que no és compost) i  és la probabilitat que un nombre a l'atzar entre n i 2n sigui primer.

La probabilitat que un nombre triat a l'atzar entre n i 2n sigui primer es pot estimar a partir del teorema dels nombres primers en:

Aquesta probabilitat és força gran, fins i tot per a nombres molt grans, per exemple la probabilitat que un nombre entre  i  sigui primer, resulta ser aproximadament d'un 1%.

Per tant la clau està en el temps necessari per a determinar si un nombre és primer o no. L'interès dels tests de primalitat radica en la possibilitat d'utilitzar algorismes que tenen un temps inferior al de les proves de primalitat i al mateix temps una probabilitat d'error (acceptar com a primer un nombre que no ho és) molt baixa.

Història del problema de la primalitat
Els problemes de la factorització d'un nombre donat i la determinació de nombres primers són molt antics. Els registres històrics sobre l'estudi de nombres primers es remunten a Euclides () encara que hi ha evidències que el coneixement de l'existència d'aquests nombres es remunta a Pitàgores ().
Tanmateix, el primer procediment matemàtic conegut per a determinar-los es remunta a Eratòstenes (segle II aC), el garbell d'Eratòstenes: Per a obtenir els nombres primers més petits que un  donat, primer es col·loquen els nombres de l'1 a l' en una llista i es ratllen totes les posicions parelles tret de la primera (el 2). Després, es ratllen tots els que són múltiples de tres tret del tres (a partir del primer nombre no ratllat, el 3, comptant de tres en tres). Després, els que són múltiples de cinc tret del cinc (el següent nombre de la llista sense ratllar després del 3, comptant de cinc en cinc). I així successivament. Un cop s'ha arribat a un nombre que sigui més gran que  s'atura l'algorisme. Els nombres que han quedat sense ratllar, són tots els nombres primers més petits que .

La versió original de l'algorisme del garbell d'Erastòstenes no s'acabava en . Va ser el matemàtic àrab Ibn al-Bannà qui va proposar aquesta millora.

L'algorisme del garbell d'Estòstenes troba tots els nombres primers més petits que un nombre donat. Però de vegades el que es necessita saber és només si un nombre donat és primer o no. Això es pot determinar amb el garbell, però el temps de càlcul és molt llarg (i el resultat diu més del que es necessita).

Els primers registres escrits de l'estudi dels nombres primers a l'Europa medieval, corresponen al matemàtic italià Leonardo de Pisa (Fibonacci). Fibonacci va presentar un algorisme per a determinar si un nombre donat és primer o no sense necessitat d'haver de determinar tots els nombres primers més petits que el nombre en qüestió. L'algorisme de Fiboncci consisteix a comprovar que cap altre nombre primer més petit que  divideix a .
El bolonyès Pietro Antonio Cataldi fou el primer a utilitzar les relacions observades entre els nombres per a determinar la primalidad en el seu treball sobre els nombres perfectes.

Un nombre perfecte és el que és igual a la suma dels seus divisors propis. Per exemple 6 és perfecte, ja que la suma dels seus divisors (1 + 2 +3) és igual a 6. Els set primers nombres perfectes són: 6, 28, 496, 8128, 33550336, 8589869056 i 137438691328.

Cataldi va determinar que si  és primer llavors  ha de ser primer i  ha de ser perfecte. Aquest teorema introdueix una família de nombres especialment important per a la història de la primalidad: els anomenats nombres de Mersenne en honor del filòsof Marin Mersenne (1588-1665), que són nombres de la forma  on p és un nombre primer. Mersenne va comprovar que dels 257 primers nombres de la família que porta el seu nom, només 11 són primers (són els  per a p =2, 3, 5, 7, 13, 17, 19, 31, 67, 127 i 257).
De fet Mersenne va cometre alguns errors perquè  no és primer per a p=67 ni 257 i sí que ho és per a p=61, 89 i 107.

Contemporani de Mersenne va ser Pierre de Fermat (1607-1665). Fermat va establir el teorema conegut com a Petit teorema de Fermat o PTF), estableix el següent:

Un corolari d'aquest teorema diu que si  és primer, llavors quealsevol nombre primer  que divideixi a  ha de ser de la forma  per algun . També es pot demostrar que si  és el nombre més petit tal que , llavors  sempre que .

Fermat s'adonà que el teorema anterior era útil para a detectar possibles nombres primers  tales que . Fermat també va suggerir que els nombres de la forma  (anomenats nombres de Fermat i representats per ) havien de ser primers i ho va comprovar per a tots els n més petits que 4. No ho va poder demostrar per a  i avui se sap que  és compost, com ho són tots fins a  (i potser tots els altres, tot i que això encara és una conjectura).

Leonhard Euler va trobar un divisor de  (contradient la conjectura de Fermat sobre la primalitat de ). Va enunciar el teorema que diu que tot divisor primer de  ha de ser de la forma  per a algun .

François Éduard Anatole Lucas va treballar sobre els nombres de Fibonacci i de Mersenne, va obtenir resultats sobre la divisibilitat dels de Fibonacci i va crear una prova de primalitat per als nombres de Mersenne (que va fer servir per a comprovar la primalitat de ).

Definicions de Test de primalitat i de prova de primalitat
El problema de la factorització (trobar factors, primers o no, que multiplicats donen el nombre) i el de primalitat (saber si un nombre és primer) estan relacionats però tenen una naturalesa molt diferent. Per a saber que un nombre es pot descompondre en factors, n'hi ha prou en conèixer una descomposició, a partir d'aquí és fàcil comprovar que la factorització és correcta, només cal multiplicar els factors, no cal conèixer els mètodes per a trobar els factors. Però saber que un nombre és primer (que no es pot descompondre en factors) és molt més complicat. Com digué el matemàtic del  Fortuné Landry tret que es coneguin els mètodes de comprovació i es realitzin el càlculs, l'expressió "és primer" només és qüestió de fe. Una test (o revisió) de primalitat és un algorisme que, a partir d'un nombre n, en no aconseguir verificar que és compost, fa que augmenti la credibilitat de l'afirmació "n és un nombre primer".

Aquesta és la visió matemàtica. En les aplicacions en enginyeria, per exemple en criptografia, el risc de considerar que un nombre és primer quan en realitat no ho és, consisteix en el fet que el grau de seguretat baixa en la mesura en què sigui més o menys fàcil descompondre el nombre. Hi ha dos enfocaments, per una banda si la probabilitat que el nombre sigui compost és molt petita i les claus es canvien molt sovint, l'efectivitat d'un criptoanàlisi que pretengui explotar aquesta feblesa pot ser menstenible, per altra banda, per explotar la feblesa cal tenir un algorisme que pugui descompondre el nombre en un temps de càlcul acceptable, per tant si el nombre no es pot descompondre amb els algorismes coneguts que tenen un temps de càlcul acceptable, encara que no sigui primer ofereix un nivell de seguretat acceptable.
Per tot això cal definir formalment els conceptes de tests (o revisions) i de proves.

Definició: Un test (o revisió) de primalitat és un algorisme que, donat un nombre d'entrada n, no aconsegueix verificar la hipòtesi que diu "n és compost".

És a dir, abans de passar el test de primalitat, la probabilitat que un nombre escollit a l'atzar en un determinat conjunt sigui primer és el quocient entre la quantitat de nombres primers que hi ha al conjunt i la quantitat total de nombres que té el conjunt. Després de passar el test de primalitat, la probabilitat que el nombre sigui primer és el quocient entre la quantitat de nombres primers i la quantitat de nombres que passen el test (siguin o no primers). Si la quantitat de nombres que no sent primers passen el test és petita comparada amb la quantitat de nombres primers, aquesta probabilitat pot ser propera a 1.

Definició: Un algorisme de prova de primalitat (o test verdader de primalitat) és un algorisme determinístic que, donat un nombre d'entrada n, verifica que és cert el teorema: "n és primer". Una prova de primalitat és la verificació computacional d'aquest teorema.

Així doncs una diferència entre els tests i les proves és el grau de certesa: les proves de primalitat ofereixen la certesa total (probabilitat que el nombre sigui primer = 1) els test ofereixen una certesa parcial (probabilitat que el nombres sigui primer <1).

Test verdaders de primalitat
Tot seguit s'estudien les proves de primalitat.

Prova de Lucas-Lehmer per a nombres de Mersenne
L'exemple clàssic de test verdader de primalitat és la Prova de Lucas-Lehmer per a nombres de Mersenne. La prova LL s'aplica als nombres de Mersenne (l'entrada és l'índex p del nombre de Mersenne del qual es vol comprovar la primalitat). La definició de l'algorisme és la següent:

Aquest resultat és important, ja que presenta la prova com una seqüència senzilla de passos, lineal en n, on totes les operacions bàsiques (productes, restes, mòduls, comparacions) són computables en temps polinòmic.
El problema obvi que té aquesta prova és la manca de generalitat, ja que només es pot aplicar als nombres de Mersenne.

Prova basada en el teorema de Pocklington
Aquest algorisme de prova de primalitat s'aplica a nombres n genèrics i suposa que es coneix una factorització parcial de n -1. Es basa en el teorema de Pocklington.
Dit teorema estableix el següent:

Teorema:  tal que  i , on  té una factorització en nombres primers coneguda.

Si per a cada factor primer  de  tal que:

(i)
(ii) .
Llavors , primer, divisor de n, ; per tant, si  llavors n és primer.

Així, si es coneix la factorització d'un divisor de F es poden concloure per la comprovació de les condicions (i) i (ii) que un nombre donat és primer.
Exemple de prova per Pocklington per al nombre n=57283:
 Se suposa coneguda la factorització parcial n-1 = 6 x 9547 i també conegut el fet que F=9547 és un nombre primer, per tant q és únic i igual a F. Ja que , i , es pot concloure que n és primer.
L'algorisme és senzill. Es limita a realitzar una sèrie de càlculs amb aritmètica modular i comprovar-ne el resultat. La contrapartida és que es necessita una factorització parcial de n.

Prova basada en el teorema de Pepin
L'última prova en aquest apartat es deu a Pepin (1877). El teorema de Pepin s'enuncia com segueix:

Teorema: , el nombre de Fermat enèsim, definit per  és primer si i nomé si .
La constant 3 de la prova de Pepin en realitat es pot substituir per qualsevol enter positiu per al qual l'operador anomenat símbol de Jacobi sigui igual a -1. Això inclou als valors 3, 5 i 10.
Així com la prova de Lucas-Lehmer (LL) només es pot aplicar als nombres de Mersenne, la prova de Pepin només es pot aplicar als nombres de Fermat, pel que el seu ús (com en el cas de LL) queda bastant restringit.

Tests probabilístics
Els tests probabilístics tot i que no proven la primalitat amb total certesa resulten d'interès en tenir un temps de còmput més curt i en ser computacionalment més estables i predictibles.

Si l'nvers del Petit Teorema de Fermat (PTF) fos cert (és a dir, si la comprovació de la condició an-1≡1 (mod n), per a qualsevol nombre a primer respecte de n impliqués la primalitat de n) la prova de primalitat seria un assumpte molt senzill. Però, existeix una família de nombres compostos que compleixen la condició, per tant la prova per l'invers del Petit Teorema de Fermat (PTF) no és vàlida; aquest nombres s'anomenen Nombres de Carmichael en honor del matemàtic que els va descobrir. Un exemple de nombre de Carmichael és n=561.

Els test probabilístics estan basats en la idea de relaxar la correcció de la prova per aconseguir un comportament de resposta polinòmic o subpolinòmic. Es basen bé en l'ús del PTF, bé en l'ús dels verificadors i falsadors d'Euler.

Test de primalitat de Fermat
El primer exemple de test probabilístic que es veurà és el test de Fermat. L'esmentat test està basat en el PTF. L'algorisme basat en aquest test s'aplica elegint diversos enters aleatoris a entre 2 i n-2 i calculant . Si algun valor de  és diferent d'1 l'algorisme torna compost, en cas contrari torna primer. La fortalesa d'aquest test rau en el fet que després d'un nombre normalment petit de repeticions la probabilitat que un nombre compost passi com a primer és molt petita.

Com s'ha comentat abans, el test de Fermat pateix d'un conegut problema: els nombres de Carmichael. Els nombres de Carmichael passen la condició de Fermat per a tots els possibles valors d'a; això implica que si el candidat a nombre primer fos un nombre de Carmichael, no importa quantes vegades es passi el test de Fermat, el resultat sempre serà negatiu i en conseqüència el resultat del test serà un fals positiu. Tanmateix, els nombres de Carmichael són relativament escassos (n'hi ha 105.212 menors de 1015) pel que la probabilitat d'elegir-ne algun és realment baixa. El test de Fermat és d'ampli ús en el camp de la criptografia.

Test de Solovay-Strassen
Un altre test molt conegut i utilitzat en criptografia és el test de primalitat de Solovay-Strassen (SS). Aquest test està basat en el criteri d'Euler que estableix que si n és un nombre primer senar, llavors  per a tots els enters que satisfan que el mcd(a, n)=1, on  representa el símbol de Jacobi definit per

On cada  és un nombre primer diferent,  i  és el símbol de Legendre definit per

Els valors d'a que compleixen el criteri d'Euler s'anomenen verificadors d'Euler per a la primalitat de n i els que no el compleixen es denominen falsadors d'Euler per a la primalitat de n.

El test SS es podria codificar de la següent manera:

El test SS té una probabilitat d'encert de ½ per cada pas de j. Això implica que la probabilitat que l'entrada sigui un nombre compost havent estat declarat com a "possible primer" és menor que ½t. Aquest test va ser descobert el 1978 i va ser modificat el 1982 per Atkin i Larson, però ara com ara està en desús. El motiu és que el test que s'estudia tot seguit és més eficient i, pel cap baix, té el mateix nivell de correcció.

Test de Miller-Rabin
El test més implantat en l'actualitat és el  Miller-Rabin  (també conegut com a test fort del pseudoprimer). El test de Miller-Rabin (MR) està basat en el següent fet: Si es té un nombre primer n i  on r és senar, es compleix que , llavors o bé  o bé .

El test MR es pot codificar de la següent manera:

L'error comès en cada pas d'iteració és de ¼, (el disseny fa que existeixin més falsadors d'Euler que en SS) pel que la probabilitat que l'entrada sigui un nombre compost quan es declara com a "possible primer" és menor que ¼t. D'altra banda, en utilitzar l'exponenciació binària les operacions necessàries es realitzen ràpidament.

Dels tres test probabilístics aquí presentats, el millor des del punt de vista tècnic i pràctic és el de Miller-Rabin. El test SS és computacionalment pitjor i més difícil d'implementar, ja que cal calcular el símbol de Jacobi. D'altra banda ambdós tenen l'avantatge davant el de Fermat que es pot augmentar la confiança de la primalitat assignant a t un valor arbitràriament alt (Fermat té el límit definit pels nombres de Carmichael).

Avenços recents
Des dels anys 70 s'ha estat treballant en la millora dels algorismes clàssics per obtenir millors proves de primalitat. Per a això s'ha treballat en la factorització de formes polinòmiques de n. Entre aquests algorismes destaquen el degut a Adleman, Pomerance i Rumely (APR) i la millora que sobre aquest varen fer Cohen i Lenstra (APR-CL) que obtenen complexitats gairebé polinòmiques.

També s'està avançant en aquest camp utilitzant altres formes més senzilles de treball amb grups matemàtics en lloc de l'aritmètica modular dels grups de Galois.

En aquest sentit s'estan fent avenços en el treball amb corbes el·líptiques mòdul n. Una corba el·líptica és una funció que es defineix de la següent forma:

En corbes d'aquest tipus han estat treballant des de 1986 Goldwasser, Kilian i Atkin. Aquest últim va definir el mètode ECPP, que té diverses implementacions i que s'ha provat que és d'ordre polinòmic per a gairebé totes les entrades.

Moltes de les proves i tests de primalidad que s'han vist fins ara es resolen en temps polinòmic.

Durant anys els sistemes criptogràfics han estat utilitzant-los per a la generació de claus segures. Tanmateix tenen limitacions. Alguns no són proves de primalidad i en conseqüència no tornen un certificat de primalidad: existeix una probabilitat (encara que petita) de què un nombre sigui considerat primer quan en realitat és compost; són els que es coneixen com a algorismes probabilístics d'ordre P (RP). D'altres sí que certifiquen la primalidad, però no es garanteix que el test acabi en temps polinòmic; són els que es coneixen com a algorismes deterministes de temps polinòmic probabilístic (ZPP). Alguns necessiten factoritzacions parcials o totals de n+1 i, com ja s'ha vist, la factorització és un problema que no es pot resoldre en temps polinòmic en el cas general. Per a d'altres, l'acabament en temps polinòmic es basa en certes conjectures no provades.

Per exemple, el test de Miller és polinòmic si la hipòtesi estesa de Riemann (o conjectura ERH) és certa. Hi ha una creença generalitzada en la conjectura ERH, però en faltar una demostració matemàtica no es pot concloure el seu acabament polinòmic.

Test verdader de primalitat AKS

El recent descobriment d'un algorisme determinista de temps polinòmic que no es basa en cap conjectura no provada ha de ser considerat una fita important. Concretament l'agost de l'any 2002 tres acadèmics de la Universitat de Kanpur (Agrawal, Kayal i Saxena) varen presentar un algorisme determinista de classe P per a la determinació de la primalitat d'un nombre. La clau de l'algorisme és una versió simplificada del PTF això és la condició:

Els autors se les varen arreglar per a formular el següent algorisme, que s'ha provat que pot executar-se en un temps de complexitat màxima de .

Els autors varen demostrar a més, que si determinats nombres primers (anomenats nombres primers de Sophie Germain) tenen la distribució conjecturada per Ardí, l'exponent 12 que apareix en l'expressió de complexitat pot reduir-se a 6. El que implica que el temps estimat d'execució seria equivalent al d'alguna test de primalidad, com ara el mètode ECPP comentat més amunt, que es basa en les corbes el·líptiques.

En realitat aquest descobriment no té implicacions pràctiques en la computació moderna. El cert és que les parts constants de la complexitat de l'algorisme són molt més costoses que en els actuals algorismes probabilístics. És d'esperar que en el futur proper s'obtinguin millores en aquestes constants, però el cert és que els algorismes actuals de generació de nombres primers cobreixen bastant bé les necessitats actuals i, possiblement, les futures (i és poc probable que la línia proposada millori en temps d'execució als algorismes probabilístics existents). Tanmateix sí que té una importància fonamental des del punt de vista teòric, ja que suposa la primera prova de primalitat d'aquestes característiques que s'ha demostrat matemàticament.

Referències
 Cormen, Thomas H.; Leiserson, Charles E.; Rivest, Ronald L.; Stein, Clifford: Introduction to Algorithms. Sección 31.8: "Primality testing", pp.887–896. MIT Press & McGraw-Hill, 2a edición, 2001. (.)
 Crandall, Richard & Pomerance, Carl: Prime Numbers: A Computational Perspective Capítol 3: "Recognizing Primes and Composites", pp.109–158. Capítol 4: "Primality Proving", pp.159–190. Secció 7.6: "Elliptic curve primality proving (ECPP)", pp.334–340. Springer, 1a edició, 2001. (.)
 Knuth, Donald. The Art of Computer Programming, Volum 2: Seminumerical Algorithms. Pàgines 391–396 de secció 4.5.4. Addison-Wesley, 3a edició, 1997. (.)
 Williams, H.C.: Édouard Lucas and Primality Testing. John Wiley & Sons, 1998. (.)

Notes

Vegeu també
 Complexitat computacional
 Criptografia
 Édouard Lucas
 Petit teorema de Fermat

Enllaços externs
 En català
 Facultat d'informàtica de Barcelona: Primalitat
 Publicacions de l'Institut d'Estudis Catalans: L'algorisme de primalitat AKS
 Marc Masdeu: Algorisme AKS

En anglès
 Agrawal, Kayal & Saxena: Primes is in P  Instituto de Tecnología Kanpur, India.
 Bernstein, D.J.: Distinguishing prime numbers from composite numbers
 Caldwell, Chris: The Prime Pages Universitat de Tennessee.


Washington, DC — Students from throughout the state of Idaho are interning in the regional and Washington, D.C. offices of Senator Jim Risch this summer. The students will assist with legislative research and constituent services, as well as learn about the workings of the federal government.
Stephen Parrott, of Buhl, is a senior at the University of Idaho majoring in agricultural business. He is the son of Dan and Cally Parrott.
Alex Semanko, of Eagle, is a senior at Regis University majoring in peace and justice. She is the daughter of Norm and Lana Semanko.
Phil Thurston, of Sugar City, is a senior at Brigham Young University majoring in geography. Phil is the son of Russell and Arlene Thurston.
Taryn Wheeler, of Moscow, is a junior at George Washington University majoring in political science. She is the daughter of Michelle Wheeler.
Shannon Sullivan, of Coeur d'Alene, is a senior at the University of Idaho majoring in English. She is the daughter of Colleen Sullivan.
Jordyn Cziep, of Rexburg, is a senior at Brigham Young University – Idaho majoring in political science. She is the daughter of Becky Bochenek-Boyle and Shane Boyle.
For more information about internships, interested applicants can go to Senator Risch's website. Applications for the fall session, which runs from September to December, must be received in the Senator's office by July 10.


Glasstec 2014... Smart-Builder will be there! Will you?
Smart-Builder will be returning to Glasstec, with the latest version of their award-winning software, for the fourth consecutive time.
For those who don't know yet, the Smart-Builder software suite makes it easier to sell glass and glass related products.
With the different Smart-Builder modules you can design and estimate showers, shopfronts, splashbacks, partitions and balustrades.
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Have you been thinking about using software to look more professional, save time or increase sales? Perhaps you want to design showers in under a minute? If so, then come and see Smart-Builder at hall 10, stand A53.
For more information about Smart-Builder Software, explore the website or email info@smart-builder.com. Alternatively speak to our German reseller, Joachim Fischinger by calling +49 (0) 7404-914 440.


We all get stretch marks some time or the other. Stretch marks are often caused during puberty, pregnancy, and gym (bodybuilding). They are not harmful in any way but are very embarrassing and make us feel self-conscious a lot! There are cosmetic procedures to treat stretch marks like a laser. But home remedies are practiced and advised more commonly. Why? Simply because home remedies do not cause any side effects or pain and are economical! However, you can not get rid of them permanently even with a laser because they can come back in certain situations. But you can lighten them and reduce them to the point where they look kind of non-existence in appearance. In this post, I will be sharing- a concoction which will help you to reduce stretch marks, a regime for stretch marks and some tips. So hop in to learn and try!


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Owning real estate is an important part of mastering your destiny. We can help you. Click below to find out more.
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We've simplified the buying process with straightforward, easy-to-read contracts. Of course, we encourage you to hire a professional if you think it's necessary, but we've done our best to make the process easy for anyone to understand.
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text:
When a Reddit User Fell Pregnant With Her Sister's Ex-Fiancé's Baby, She Asked Her Infertile Sister to Throw Her Baby Shower, Now the Redditor Wants to Know AITA?
February 6, 2020 September 14, 2020 / Getting Pregnant, Pregnancy, Relationships / By Sara Vallone
(Trigger Warning: This article talks frankly about infertility.)
Shortly after this Reddit user's 29-year-old sister broke up with her 28-year-old boyfriend of three years, she started dating him. The Reddit user admitted that she knows "there's a whole thing surrounding dating a sibling's ex but please hear me out."
As the 20-year-old continued, Lucy and Josh were once engaged in 2018 before they ended their relationship in 2019 when Lucy learned that she couldn't have kids. "I don't know exactly what went on but after the infertility diagnosis Lucy became very depressed, she went on antidepressant medicine and started therapy."
AITA for asking my sister to throw my baby shower party when she is suffering from infertility? https://t.co/KNZeg7Pk31 pic.twitter.com/uKdiBaKhQl
— Am I the Asshole? (@AITA_reddit) January 29, 2020
RELATED: AITA: Woman Claims Her Husband and Father-In-Law Are Convinced She's Going to Die During Childbirth, to the Point Where They Want Her to Pack up Her Pre-Baby Clothes and Put Them in Storage
The Reddit user continued, "A few weeks after starting therapy she and Josh broke up, mutually apparently. Josh lives just down the road from us so I see him out and about on the farm quite often." She admitted that their relationship "just kind of happened naturally."
Woman Wonders If She's Wrong for Asking Her Infertile Sister to Plan Her Baby Shower
They went on a few dates, grew closer together, and then unexpectedly, she learned she was pregnant with her sister's ex-fiancé's baby. "I kept it secret from Lucy because she is still very down and depressed."
Two months later, she decided it was time to tell Lucy. "In my opinion Josh can't just never move on, and someone shouldn't be forever off-limits because your sibling briefly dated them."
But in a twist that shouldn't surprise anyone, when Lucy learned her little sister was expecting a child with her ex-fiancé, "sh*t. hit. the. fan."
"I sat her down and said, 'I have some news.' I told her I was with Josh and that I'm expecting, I told her it would mean the world to me if she would be godmother to the baby and asked if she would like to plan the shower for me as I know she absolutely thrives on parties."
According to the Reddit user, Lucy didn't react, just simply asked her sister to leave. "I made the point that it's our parents' house."
Being the self-aware sister that she is, she wrote, "I know on paper this sounds bad, it really does, but I should be allowed to live my life and so should Josh." The following morning, the user received a text from Lucy that read:
"Thanks for letting me know you're dating Josh, oh and that you're pregnant with his child. Congratulations, you achieved what I could not. I am in such a bad place and you will never understand. Josh and I agreed I needed time and medication and then we would try again, but I guess he never told you that did he? As for your baby shower, all I can say is well done, you always were good at telling jokes. I hope you rot in hell, you evil b*tch."
The Reddit user said that she confronted Josh who said everything her sister said about him was true, but that after they started hanging out, he fell in love with her. The 20-year-old went on to ask if she's "the a**hole in this situation," because she really wants her sister's support.
One commenter wrote, "I hope this is fake. If it is not, you are one of the biggest AH I have seen on this site." Another added, "YTA ALL THE WAY. This is so bad. I hope it's not real. How could anyone be so terrible?"
RELATED: This Mother-in-Law Gave Her Future Daughter-in-Law the Very Lingerie She Wore on Her Wedding Night… and Yeah, Yikes!
And someone else commented, "'Briefly dated?' Three years is not brief, and they were engaged? Six months apart is nothing. And you should NEVER have asked her to throw you a party celebrating not only a baby that she is mourning that she couldn't conceive but to her very recent ex who she was planning a life with. You don't sound like you've been supportive or understanding of your sister at all. It is extremely common for people to mourn their loss when they find out they have fertility problems, it sounds like your sister is still mourning and you expect her to celebrate you? Nah."
Sara Vallone
Sara Vallone has been a writer and editor for the last four and a half years. A graduate of Ohio University, she enjoys celebrity news, sports, and articles that enhance people's lives.


text:
Eulitoma est un genre de mollusques gastéropodes au sein de la famille Eulimidae. Les espèces rangées dans ce genre sont marines et parasitent des échinodermes ; l'espèce type est Eulitoma nitens.

Distribution
Certaines espèces sont présentes dans l'océan pacifique, notamment sur le littoral australien ; d'autres espèces se rencontrent dans l'océan Atlantique Nord-Est.

Liste d'espèces
Selon  :
 Eulitoma akauni (Habe, 1952)
 Eulitoma arcus Bouchet & Warén, 1986
 Eulitoma insignis (Dautzenberg & H. Fischer, 1896)
 Eulitoma josephinae Bouchet & Warén, 1986
 Eulitoma langfordi (Dall, 1925)
 Eulitoma nishimurai (Habe, 1958)
 Eulitoma nitens Laseron, 1955
 Eulitoma obtusiuscula Bouchet & Warén, 1986

Références taxinomiques

Notes et références

Genre de gastéropodes (nom scientifique)