text:
Buried in the sweeping executive order President Trump signed this week to undo critical climate and public health protections was a provision seeking to overturn limits on methane pollution from the oil and gas industry.
As Trump launches an all-out assault on his predecessor's climate initiatives, this little-noticed methane provision may seem like a side note. Unfortunately, it could have major implications for our nation.
Rules benefit taxpayers and industry
The U.S. Environmental Protection Agency finalized common-sense clean air standards for new and modified oil and gas operations in May 2016 after a multi-year public and technical review. The Bureau of Land Management followed with a similar rule late last year that addresses methane pollution on federal and public lands.
The EPA's nationwide safeguards, now targeted by the Trump administration, were modeled after methane initiatives already implemented in Colorado and Ohio – programs that have been popular with the public and proven cost-effective for the industry. California followed suit in late March 2017 when it adopted strong rules to cut methane from the state's oil and gas sector.
The main ingredient in natural gas, methane is a potent greenhouse gas with 84 times the warming power of carbon dioxide over the first 20 years after it is emitted. America's oil and gas industry currently releases nearly 10 million metric tons of methane a year, enough to cover the gas needs of more than 7 million homes.
In addition to mitigating a potent climate pollutant, methane protections would capture and reduce smog-forming and toxic air pollution that is released along with methane.
Unsurprisingly, efforts to weaken these rules have run into public and political resistance, also from constituents in key energy-producing states.
America's oil and gas industry currently releases nearly 10 million metric tons of methane a year.
According to a national poll conducted just last month, 73 percent of Americans support state and federal action requiring the oil and gas industry to reduce gas leaks.
In light of such public sentiment it's especially troubling that Trump's executive order would roll back BLM limits on methane waste and pollution on our nation's federal and tribal lands. Oil and gas development in these areas is widespread and natural gas waste is mounting.
Such waste contributes not just to climate and public health risks, but also to millions of dollars in lost royalties that could benefit states, tribes and federal taxpayers.
Congress has even taken the attack against the BLM methane standards a step further. Industry allies in the U.S. Senate are trying to use a blunt, arcane law called the Congressional Review Act to completely kill these protections – potentially blocking future administrations from addressing methane waste on public lands.
These efforts all share a common theme: Favoring the oil and gas polluter lobby at the expense of citizens and our environment. This, surely, is not what America is about.
We are told, "methane is a potent greenhouse gas with 84 times the warming power of carbon dioxide over the first 20 years after it is emitted."
Felice Stadler should be asking scientists, "If you double methane how much will that run up the temperature in actual degrees, and how long will that take?" Because telling us that it's 84 times more powerful than CO2, doesn't really tell anyone anything.
Steve Case - Milwaukee, WI
That's a good point. We'd have to know how much CH4 so we'd know the equivalent CO2 effect. Then we'd have to divide that by the CO2 actually admited. Then we'd know how much greater the warming effect would be. Might be pretty small; certainly not above 1%. Still, it wouldn't be zero.
In reply to We are told, "methane is a by Steve Case
BINGO! Let's say you doubled CH4 from 2 parts per million [ppm] to 4 ppm. An equivalent mass of CO2 would be about 0.7 ppm increasing it from 400 ppm to 400.7 ppm. That would cause a very small increase, in temperature and 84 times that would still be rather small. Turns out to be about 0.2°C. And at the rate CH4 is increasing today, it would take nearly 300 years to happen.
In reply to That's a good point. We'd by Greg
Hi Steve and Greg,
For context, emissions of methane from human activities currently account for about one-quarter of the excess heat trapped in the atmosphere; CO2 emissions account for about one-half. Natural gas activities, in particular, are responsible for more than a quarter of our methane emissions. Therefore, reductions of methane from natural gas activities can play a major role in reducing warming.
Further, we can reduce these methane emissions using existing technology and at a relatively cheap cost. Therefore, this is one of the most feasible and effective climate change mitigation options.
Ilissa Ocko, EDF climate scientist
In reply to That's a good point. We'd by Greg
It's a good question, but one that can't be answered in precise numbers. Climate is a chaotic system - like weather.
Forecasters may not be qable to tell you exactly how warm it will be, or how many inches of rain you'll see - but they're getting pretty good at seeing the general trends.
Climatologists aren't magicians. They can't tell us how much CO2 or Methane will be needed to raise global temperatures by 1 degree - but they can definitely tell us that an enormous amount of Methane being released is likely to accelerate climate change far faster than CO2 levels alone.
It's like a busload of scientists, politicians, and oil execs are driving through a dense fog, toward a cliff. The scientist are saying "Slow down, there's a cliff!" Oil companies are saying "It's not a cliff, it's just a dip in the road - and we'll see it through the fog in plenty of time." Politicians are saying "It won't affect MY kids, living behind a wall of Police, financially secure, and able to move to wherever the weather is fine. The oil companies have more money than the scientists, so I'll listen to THEM."
In reply to We are told, "methane is a by Steve Case
Methane is an even larger problem in the Arctic. See Arctic News which states humanity will be extinct by 2026 without a drastic reduction in fossil fuels.
24/7 solar powered, engines, capable of replacing fossil fuels are in development. They will replace conventional power plants, as they can scale to large sizes.
Eventually cluster of engines at utility sub-stations can replace wind farms & solar farms.
To the surprise of almost everyone, engines can run 24/7 on ambient heat, a huge untapped reservoir of Solar Energy, larger than Earth's fossil fuel reserves. A Ford engine conversion proved the concept. See aesopinstitute.org
"The thermal energy content of the atmosphere, ocean, and upper crust is estimated to be more than 10,000 times that of the world's fossil fuel reserves, making it a potentially inexhaustible reservoir of green energy." Prof. Daniel Sheehan, University of San Diego
Most parts can be 3-D printed. Since there is no combustion, polymers (plastics) can be used to make many components.
They will create no chemical emissions and will cool the surrounding area. Contrast with carbon dioxide and heat produced by combustion engines.
Solar powered engines – once verified by an independent laboratory – will be produced using 3-D printing.
Rants by an anonymous individual posing as a (fake) Physics Board uses some truth mixed with blatant lies and distortions, to deflect support for new science, which is traditionally slow to gain acceptance.
Inexpensive engines running 24/7 on ambient heat can soon become as common as solar panels.
"See Arctic News which states humanity will be extinct by 2026 without a drastic reduction in fossil fuels."
Seriously? I have only nine years to live, and how is Arctic methane going to do me in?
Solar engines running off of ambient heat? There needs to be a temperature gradient to get some power out of it. But it does indeed sound interesting. I'll have to Google Prof. Daniel Sheehan and his 3D printed engines and have a look.
Best regards
Global warming is releasing methane from melting permafrost etc. Let's hope Arctic News is wrong! But,you may want to look at the extensive data on their site.
The temperature gradient needed to run engines on ambient heat is created in converted engines by filling them with propane, which acts as a refrigerant, changing from a liquid to a gas. It is not consumed.
These engines extract the heat and become very cold. They can air condition a home as a side effect.
See aesopinstitute.org to learn more.
In reply to "See Arctic News which states by Steve Case
I grew up near Charleston, WV. There was a sign there for "The Chemical Valley" re. all the chemical plants in the area. Methane was produced there and we had several scares back in the 1960's and beyond. Carbide was a huge employer and we still have chemical plants there. We had several frightening incidents and I can still hear the warning sirens going off.
No, humanity will not be extinct in nine years.
Alarmist propaganda just makes serious discussion about climate change difficult or impossible. If we don't stay grounded in science, and avoid outlandish exaggerations, we can't really claim any greater degree of impartiality than those who deny it altogether.
This is incredibly important, and we really need to approach the issue with deep understanding and unwavering honesty.
Thank you for your thoughtful comment, Mark. We fully agree that the debate over, and solutions to, the climate change problem must be based on good science.
In reply to No, humanity will not be by Mark E. Rhoads
Methane has a shorter lifespan than carbon dioxide in the atmosphere, about 12 years. But it is a potent amplifier of the effects of other greenhouse gases. See NASA: https://www.giss.nasa.gov/research/features/200409_methane/
How much of the 10 million metric tons of methane emitted from the oil and gas industry is emitted as methane and how much of it is burned in the flares shown in the picture associated with this article?
Those flares, often shown to alarm the public, are designed to destroy the methane by burning it, which does emit CO2 but does not emit methane. Let us use good science to evaluate the problem and not alarm the public by comparing apples and oranges. Also be mindful of the very large natural emissions of methane from geological sources as well as huge sources from cows and other livestock.


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What to Know
- Evan Kitz-Miller, 16, was taken to an area hospital after he was found unresponsive at around 7:51 p.m., authorities said
- Kitz-Miller, of Mundelein, was attending the Lollapalooza music festival, city officials confirmed
- The first three days of Lollapalooza saw a combined total of seven arrests and 119 attendees taken to area hospitals
A suburban Chicago teenager died after being found unresponsive at the Lollapalooza music festival Sunday night, authorities said.
Evan Kitz-Miller, 16, was found unresponsive at around 7:51 p.m. in the 300 block of East Randolph Street, according to Chicago police and the Cook County Medical Examiner's office.
Kitz-Miller, of the 21000 block of West Bittersweet Drive in Mundelein, was taken via private ambulance to Northwestern Memorial Hospital where he was pronounced dead just before 9 p.m., officials said.
Further details surrounding the incident were not immediately available and a death investigation remained ongoing, according to Chicago police.
Kitz-Miller was attending the music festival in Grant Park, according to Chicago's Office of Emergency Management and Communications.
"The safety and security of festival attendees is our top priority," OEMC spokeswoman Melissa Stratton said in a statement.
"We are saddened to learn that an individual transported from the event in critical condition last night due to a medical emergency has since passed away," she continued, adding, "Our thoughts and prayers are with his family and friends at this time."
"We are saddened to learn of the death of an individual who attended Lollapalooza on Sunday," a spokeswoman for the festival said in a statement. "The individual's family and loved ones are in our thoughts during this difficult time. We have no further information at this time."
The first three days of Lollapalooza saw a combined total of seven arrests and 119 attendees taken to area hospitals, officials said. Statistics on the fourth day were not immediately available.
Each of the first three days saw more than 100,000 attendees apiece, officials said, for a total of 325,930 people.

subset: commoncrawl


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Just considering and looking at options for corps to join. Not interested in 0.0 blobfests or straight up gate ganking/camping or training corps. I definitely enjoy good even fights or even fighting against the odds. I am open to wormholes as I have started exploring them myself recently, however must have pvp available. I am in CST in the US, mainly playing late night (11 pm CST and later) during the week and pretty open on weekends. Really just want a group to play with again.
Started playing Eve again 4-5 months ago with a new toon. I have only ever been in Einherjar Rising(Cry Havoc) which I have held directors roles and one of the top fcs and participated in a few alliance tourneys. This was from late 2004 to about 2010 when I quit playing.
So far I've mainly played solo with a little small gang work figuring out all the changes and relearning everything else. I can fly sabres, confessor, svipul, caldari and minny hacs and recons as well as the Loki. Ready to train minny and amarr inty and af anytime, skill books injected just not trained. Also just started training on alt account currently maxing out cover ops scanning.


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Black family to sue American Airlines after being kicked off plane in Charlotte, N.C.
Allan Ali and his newborn-holding partner, Kamia Hoilett, had a negative interaction with a flight attendant Sunday on Philly-bound plane.
A Black family traveling with a newborn baby was kicked off an American Airlines flight on Sunday as they headed home to Philadelphia from Charlotte, North Carolina. They plan to take legal action.
As seen in a now-viral video, Allan Ali and his partner, Kamia Hoilett, were asked to leave a Sunday afternoon flight before departure after a brief, negative interaction with a white male passenger and a white female flight attendant.
The Shade Room interviewed Ali, who said the incident escalated when he and his infant-holding partner stood to let a man who was sitting in their row into his seat. Ali said the man aggressively spoke to them, saying, "Y'all have to get up."
According to Ali, the couple tried to exit the row to let the man in, but the flight attendant was blocking the path. He said Hoilett asked her for space, but the airline employee responded, "Is this going to be a problem?"
The situation then escalated when the same flight attendant told Hoilett to sit down and buckle her seatbelt in what they describe as "a passive-aggressive tone."
Hoilett told the attendant she didn't like the manner in which she was being spoken to, and the employee then "stormed off" to report the incident to the captain, who instructed the flight attendants to remove the family from the flight.
In the now-viral video posted to Instagram, Hoilett is heard repeatedly saying, "I didn't do anything." Her partner then recaps the incident, saying that they were being asked to leave the flight with their child.
The couple left the 1 p.m. flight and were finally able to depart Charlotte at 8:20 p.m.
American Airlines told the Grio Tuesday afternoon that the company is investigating the incident and has reached out to Ali as well as the other involved passengers and employees.
"Our values demand that all customers are treated fairly and with respect, and we find the video posted by the family concerning," the company said in an emailed statement. "This matter has our full attention and we will take appropriate action as necessary."
Ali and Hoilett feel that despite being put on another flight, they were treated unfairly. Ali told The Shade Room that he has spoken to an attorney and plans to file an official complaint.
Another couple recently took legal action against American Airlines because they were kicked off a flight in August after they refused to place a bag containing a sacred prayer shawl on the floor.
Roberto and Elana Birman, a Jewish couple married 52 years, were carrying a Tallit bag — a clear, 8.5 inch-by-8.5-inch plastic carrier — for Mr. Birman's prayer book and shawl, which was placed in the overhead bin. According to reporting from The New York Post, an attendant on their flight from Miami threw the bag into his lap and told him it had to go under the seat.
When Birman told the attendant that the religious item could not go on the floor, the flight attendant reportedly responded, "It doesn't matter." He and his wife refused, with Mrs. Birman calling the request akin to asking a Christian to "throw a cross on the floor" where it could be stepped on.
Per Post reporting, "The pilot came over but didn't speak to them, the Birmans said. Eventually, a ground crew member was called and urged them to follow him off the plane, they said." The Birmans recently filed a suit against the airline.
"My clients were ejected from the flight based on the prejudices and complete lack of sensitivity of American Airlines employees for reasons wholly unrelated to security," said their lawyer, Brad Gerstman. "The flight attendant and pilot's conduct was as offensive as it was illogical."
American Airlines is reportedly reviewing the Birmans' suit, and has not yet issued a response to the incident involving Ali and Hoilett.
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In mathematics, the greatest common divisor (GCD) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest common divisor of x and y is denoted . For example, the GCD of 8 and 12 is 4, that is, .[1][2]
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In the name "greatest common divisor", the adjective "greatest" may be replaced by "highest", and the word "divisor" may be replaced by "factor", ví that other names include highest common factor (hcf), etc.[3][4][5][6] Historically, other names for the same concept have included greatest common measure.[7]
This notion can be extended vĩ đại polynomials (see Polynomial greatest common divisor) and other commutative rings (see § In commutative rings below).
The greatest common divisor (GCD) of two nonzero integers a and b is the greatest positive integer d such that d is a divisor of both a and b; that is, there are integers e and f such that a = de and b = df, and d is the largest such integer. The GCD of a and b is generally denoted gcd(a, b).[8]
This definition also applies when one of a and b is zero. In this case, the GCD is the absolute value of the non zero integer: gcd(a, 0) = gcd(0, a) = |a|. This case is important as the terminating step of the Euclidean algorithm.
The above definition cannot be used for defining gcd(0, 0), since 0 × n = 0, and zero thus has no greatest divisor. However, zero is its own greatest divisor if greatest is understood in the context of the divisibility relation, ví gcd(0, 0) is commonly defined as 0. This preserves the usual identities for GCD, and in particular Bézout's identity, namely that gcd(a, b) generates the same ideal as {a, b}.[9][10][11] This convention is followed by many computer algebra systems.[12] Nonetheless, some authors leave gcd(0, 0) undefined.[13]
The GCD of a and b is their greatest positive common divisor in the preorder relation of divisibility. This means that the common divisors of a and b are exactly the divisors of their GCD. This is commonly proved by using either Euclid's lemma, the fundamental theorem of arithmetic, or the Euclidean algorithm. This is the meaning of "greatest" that is used for the generalizations of the concept of GCD.
The number 54 can be expressed as a product of two integers in several different ways:
Thus the complete list of divisors of 54 is . Similarly, the divisors of 24 are . The numbers that these two lists have in common are the common divisors of 54 and 24, that is,
Of these, the greatest is 6, ví it is the greatest common divisor:
Computing all divisors of the two numbers in this way is usually not efficient, especially for large numbers that have many divisors. Much more efficient methods are described in § Calculation.
Coprime numbers[edit]
Two numbers are called relatively prime, or coprime, if their greatest common divisor equals 1.[14] For example, 9 and 28 are coprime.
A geometric view[edit]
For example, a 24-by-60 rectangular area can be divided into a grid of: 1-by-1 squares, 2-by-2 squares, 3-by-3 squares, 4-by-4 squares, 6-by-6 squares or 12-by-12 squares. Therefore, 12 is the greatest common divisor of 24 and 60. A 24-by-60 rectangular area can thus be divided into a grid of 12-by-12 squares, with two squares along one edge (24/12 = 2) and five squares along the other (60/12 = 5).
Reducing fractions[edit]
The greatest common divisor is useful for reducing fractions vĩ đại the lowest terms.[15] For example, gcd(42, 56) = 14, therefore,
Least common multiple[edit]
The least common multiple of two integers that are not both zero can be computed from their greatest common divisor, by using the relation
Using prime factorizations[edit]
Greatest common divisors can be computed by determining the prime factorizations of the two numbers and comparing factors. For example, vĩ đại compute gcd(48, 180), we find the prime factorizations 48 = 24 · 31 and 180 = 22 · 32 · 51; the GCD is then 2min(4,2) · 3min(1,2) · 5min(0,1) = 22 · 31 · 50 = 12 The corresponding LCM is then 2max(4,2) · 3max(1,2) · 5max(0,1) = 24 · 32 · 51 = 720.
In practice, this method is only feasible for small numbers, as computing prime factorizations takes too long.
Euclid's algorithm[edit]
The method introduced by Euclid for computing greatest common divisors is based on the fact that, given two positive integers a and b such that a > b, the common divisors of a and b are the same as the common divisors of a – b and b.
So, Euclid's method for computing the greatest common divisor of two positive integers consists of replacing the larger number by the difference of the numbers, and repeating this until the two numbers are equal: that is their greatest common divisor.
For example, vĩ đại compute gcd(48,18), one proceeds as follows:
So gcd(48, 18) = 6.
This method can be very slow if one number is much larger than thở the other. So, the variant that follows is generally preferred.
Euclidean algorithm[edit]
A more efficient method is the Euclidean algorithm, a variant in which the difference of the two numbers a and b is replaced by the remainder of the Euclidean division (also called division with remainder) of a by b.
Denoting this remainder as a mod b, the algorithm replaces (a, b) by (b, a mod b) repeatedly until the pair is (d, 0), where d is the greatest common divisor.
For example, vĩ đại compute gcd(48,18), the computation is as follows:
This again gives gcd(48, 18) = 6.
Lehmer's GCD algorithm[edit]
Lehmer's algorithm is based on the observation that the initial quotients produced by Euclid's algorithm can be determined based on only the first few digits; this is useful for numbers that are larger than thở a computer word. In essence, one extracts initial digits, typically forming one or two computer words, and runs Euclid's algorithms on these smaller numbers, as long as it is guaranteed that the quotients are the same with those that would be obtained with the original numbers. The quotients are collected into a small 2-by-2 transformation matrix (a matrix of single-word integers) vĩ đại reduce the original numbers. This process is repeated until numbers are small enough that the binary algorithm (see below) is more efficient.
This algorithm improves tốc độ, because it reduces the number of operations on very large numbers, and can use hardware arithmetic for most operations. In fact, most of the quotients are very small, ví a fair number of steps of the Euclidean algorithm can be collected in a 2-by-2 matrix of single-word integers. When Lehmer's algorithm encounters a quotient that is too large, it must fall back vĩ đại one iteration of Euclidean algorithm, with a Euclidean division of large numbers.
Binary GCD algorithm[edit]
The binary GCD algorithm uses only subtraction and division by 2. The method is as follows: Let a and b be the two non-negative integers. Let the integer d be 0. There are five possibilities:
- a = b.
As gcd(a, a) = a, the desired GCD is a × 2d (as a and b are changed in the other cases, and d records the number of times that a and b have been both divided by 2 in the next step, the GCD of the initial pair is the product of a and 2d).
- Both a and b are even.
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Then 2 is a common divisor. Divide both a and b by 2, increment d by 1 vĩ đại record the number of times 2 is a common divisor and continue.
- a is even and b is odd.
Then 2 is not a common divisor. Divide a by 2 and continue.
- a is odd and b is even.
Then 2 is not a common divisor. Divide b by 2 and continue.
- Both a and b are odd.
As gcd(a,b) = gcd(b,a), if a < b then exchange a and b. The number c = a − b is positive and smaller than thở a. Any number that divides a and b must also divide c ví every common divisor of a and b is also a common divisor of b and c. Similarly, a = b + c and every common divisor of b and c is also a common divisor of a and b. So the two pairs (a, b) and (b, c) have the same common divisors, and thus gcd(a,b) = gcd(b,c). Moreover, as a and b are both odd, c is even, the process can be continued with the pair (a, b) replaced by the smaller numbers (c/2, b) without changing the GCD.
Each of the above steps reduces at least one of a and b while leaving them non-negative and ví can only be repeated a finite number of times. Thus eventually the process results in a = b, the stopping case. Then the GCD is a × 2d.
Example: (a, b, d) = (48, 18, 0) → (24, 9, 1) → (12, 9, 1) → (6, 9, 1) → (3, 9, 1) → (3, 3, 1) ; the original GCD is thus the product 6 of 2d = 21 and a= b= 3.
The binary GCD algorithm is particularly easy vĩ đại implement on binary computers. Its computational complexity is
The computational complexity is usually given in terms of the length n of the input. Here, this length is and the complexity is thus
- .
Other methods[edit]
If a and b are both nonzero, the greatest common divisor of a and b can be computed by using least common multiple (LCM) of a and b:
- ,
but more commonly the LCM is computed from the GCD.
Using Thomae's function f,
which generalizes vĩ đại a and b rational numbers or commensurable real numbers.
Keith Slavin has shown that for odd a ≥ 1:
which is a function that can be evaluated for complex b.[16] Wolfgang Schramm has shown that
is an entire function in the variable b for all positive integers a where cd(k) is Ramanujan's sum.[17]
The computational complexity of the computation of greatest common divisors has been widely studied.[18] If one uses the Euclidean algorithm and the elementary algorithms for multiplication and division, the computation of the greatest common divisor of two integers of at most n bits is This means that the computation of greatest common divisor has, up vĩ đại a constant factor, the same complexity as the multiplication.
However, if a fast multiplication algorithm is used, one may modify the Euclidean algorithm for improving the complexity, but the computation of a greatest common divisor becomes slower than thở the multiplication. More precisely, if the multiplication of two integers of n bits takes a time of T(n), then the fastest known algorithm for greatest common divisor has a complexity This implies that the fastest known algorithm has a complexity of
Previous complexities are valid for the usual models of computation, specifically multitape Turing machines and random-access machines.
The computation of the greatest common divisors belongs thus vĩ đại the class of problems solvable in quasilinear time. A fortiori, the corresponding decision problem belongs vĩ đại the class P.. of problems solvable in polynomial time. The GCD problem is not known vĩ đại be in NC, and ví there is no known way vĩ đại parallelize it efficiently; nor is it known vĩ đại be P-complete, which would imply that it is unlikely vĩ đại be possible vĩ đại efficiently parallelize GCD computation. Shallcross et al. showed that a related problem (EUGCD, determining the remainder sequence arising during the Euclidean algorithm) is NC-equivalent vĩ đại the problem of integer linear programming with two variables; if either problem is in NC or is P-complete, the other is as well.[19] Since NC contains NL, it is also unknown whether a space-efficient algorithm for computing the GCD exists, even for nondeterministic Turing machines.
Although the problem is not known vĩ đại be in NC, parallel algorithms asymptotically faster than thở the Euclidean algorithm exist; the fastest known deterministic algorithm is by Chor and Goldreich, which (in the CRCW-PRAM model) can solve the problem in O(n/log n) time with n1+ε processors.[20] Randomized algorithms can solve the problem in O((log n)2) time on processors[clarification needed] (this is superpolynomial).[21]
- For positive integers a, gcd(a, a) = a.
- Every common divisor of a and b is a divisor of gcd(a, b).
- gcd(a, b), where a and b are not both zero, may be defined alternatively and equivalently as the smallest positive integer d which can be written in the size d = a⋅p + b⋅q, where p and q are integers. This expression is called Bézout's identity. Numbers p and q lượt thích this can be computed with the extended Euclidean algorithm.
- gcd(a, 0) = |a|, for a ≠ 0, since any number is a divisor of 0, and the greatest divisor of a is |a|.[2][5] This is usually used as the base case in the Euclidean algorithm.
- If a divides the product b⋅c, and gcd(a, b) = d, then a/d divides c.
- If m is a positive integer, then gcd(m⋅a, m⋅b) = m⋅gcd(a, b).
- If m is any integer, then gcd(a + m⋅b, b) = gcd(a, b). Equivalently, gcd(a mod b,b) = gcd(a,b).
- If m is a positive common divisor of a and b, then gcd(a/m, b/m) = gcd(a, b)/m.
- The GCD is a commutative function: gcd(a, b) = gcd(b, a).
- The GCD is an associative function: gcd(a, gcd(b, c)) = gcd(gcd(a, b), c). Thus gcd(a, b, c, ...) can be used vĩ đại denote the GCD of multiple arguments.
- The GCD is a multiplicative function in the following sense: if a1 and a2 are relatively prime, then gcd(a1⋅a2, b) = gcd(a1, b)⋅gcd(a2, b).
- gcd(a, b) is closely related vĩ đại the least common multiple lcm(a, b): we have
- gcd(a, b)⋅lcm(a, b) = |a⋅b|.
- This formula is often used vĩ đại compute least common multiples: one first computes the GCD with Euclid's algorithm and then divides the product of the given numbers by their GCD.
- The following versions of distributivity hold true:
- gcd(a, lcm(b, c)) = lcm(gcd(a, b), gcd(a, c))
- lcm(a, gcd(b, c)) = gcd(lcm(a, b), lcm(a, c)).
- If we have the unique prime factorizations of a = p1e1 p2e2 ⋅⋅⋅ pmem and b = p1f1 p2f2 ⋅⋅⋅ pmfm where ei ≥ 0 and fi ≥ 0, then the GCD of a and b is
- gcd(a,b) = p1min(e1,f1) p2min(e2,f2) ⋅⋅⋅ pmmin(em,fm).
- It is sometimes useful vĩ đại define gcd(0, 0) = 0 and lcm(0, 0) = 0 because then the natural numbers become a complete distributive lattice with GCD as meet and LCM as join operation.[22] This extension of the definition is also compatible with the generalization for commutative rings given below.
- In a Cartesian coordinate system, gcd(a, b) can be interpreted as the number of segments between points with integral coordinates on the straight line segment joining the points (0, 0) and (a, b).
- For non-negative integers a and b, where a and b are not both zero, provable by considering the Euclidean algorithm in base n:[23]
- gcd(na − 1, nb − 1) = ngcd(a,b) − 1.
- An identity involving Euler's totient function:
- where is the p-adic valuation.
Probabilities and expected value[edit]
In 1972, James E. Nymann showed that k integers, chosen independently and uniformly from {1, ..., n}, are coprime with probability 1/ζ(k) as n goes vĩ đại infinity, where ζ refers vĩ đại the Riemann zeta function.[24] (See coprime for a derivation.) This result was extended in 1987 vĩ đại show that the probability that k random integers have greatest common divisor d is d−k/ζ(k).[25]
Using this information, the expected value of the greatest common divisor function can be seen (informally) vĩ đại not exist when k = 2. In this case the probability that the GCD equals d is d−2/ζ(2), and since ζ(2) = π2/6 we have
This last summation is the harmonic series, which diverges. However, when k ≥ 3, the expected value is well-defined, and by the above argument, it is
For k = 3, this is approximately equal vĩ đại 1.3684. For k = 4, it is approximately 1.1106.
In commutative rings[edit]
The notion of greatest common divisor can more generally be defined for elements of an arbitrary commutative ring, although in general there need not exist one for every pair of elements.
If R is a commutative ring, and a and b are in R, then an element d of R is called a common divisor of a and b if it divides both a and b (that is, if there are elements x and y in R such that d·x = a and d·y = b). If d is a common divisor of a and b, and every common divisor of a and b divides d, then d is called a greatest common divisor of a and b.
With this definition, two elements a and b may very well have several greatest common divisors, or none at all. If R is an integral domain name then any two GCD's of a and b must be associate elements, since by definition either one must divide the other; indeed if a GCD exists, any one of its associates is a GCD as well. Existence of a GCD is not assured in arbitrary integral domains. However, if R is a unique factorization domain name, then any two elements have a GCD, and more generally this is true in GCD domains. If R is a Euclidean domain name in which euclidean division is given algorithmically (as is the case for instance when R = F[X] where F is a field, or when R is the ring of Gaussian integers), then greatest common divisors can be computed using a size of the Euclidean algorithm based on the division procedure.
The following is an example of an integral domain name with two elements that bởi not have a GCD:
The elements 2 and 1 + √−3 are two maximal common divisors (that is, any common divisor which is a multiple of 2 is associated vĩ đại 2, the same holds for 1 + √−3, but they are not associated, ví there is no greatest common divisor of a and b.
Corresponding vĩ đại the Bézout property we may, in any commutative ring, consider the collection of elements of the size pa + qb, where p and q range over the ring. This is the ideal generated by a and b, and is denoted simply (a, b). In a ring all of whose ideals are principal (a principal ideal domain name or PID), this ideal will be identical with the phối of multiples of some ring element d; then this d is a greatest common divisor of a and b. But the ideal (a, b) can be useful even when there is no greatest common divisor of a and b. (Indeed, Ernst Kummer used this ideal as a replacement for a GCD in his treatment of Fermat's Last Theorem, although he envisioned it as the phối of multiples of some hypothetical, or ideal, ring element d, whence the ring-theoretic term.)
Xem thêm: định lý pitago
See also[edit]
- Bézout domain
- Lowest common denominator
- Unitary divisor
- ^ a b Long (1972, p. 33)
- ^ a b c Pettofrezzo & Byrkit (1970, p. 34)
- ^ Kelley, W. Michael (2004), The Complete Idiot's Guide vĩ đại Algebra, Penguin, p. 142, ISBN 978-1-59257-161-1.
- ^ Jones, Allyn (1999), Whole Numbers, Decimals, Percentages and Fractions Year 7, Pascal Press, p. 16, ISBN 978-1-86441-378-6.
- ^ a b c Hardy & Wright (1979, p. 20)
- ^ Some authors treat greatest common denominator as synonymous with greatest common divisor. This contradicts the common meaning of the words that are used, as denominator refers vĩ đại fractions, and two fractions bởi not have any greatest common denominator (if two fractions have the same denominator, one obtains a greater common denominator by multiplying all numerators and denominators by the same integer).
- ^ Barlow, Peter; Peacock, George; Lardner, Dionysius; Airy, Sir George Biddell; Hamilton, H. P..; Levy, A.; De Morgan, Augustus; Mosley, Henry (1847), Encyclopaedia of Pure Mathematics, R. Griffin and Co., p. 589.
- ^ Some authors use (a, b),[1][2][5] but this notation is often ambiguous. Andrews (1994, p. 16) explains this as: "Many authors write (a,b) for g.c.d.(a, b). We bởi not, because we shall often use (a,b) vĩ đại represent a point in the Euclidean plane."
- ^ Thomas H. Cormen, et al., Introduction vĩ đại Algorithms (2nd edition, 2001) ISBN 0262032937, p. 852
- ^ Bernard L. Johnston, Fred Richman, Numbers and Symmetry: An Introduction vĩ đại Algebra ISBN 084930301X, p. 38
- ^ Martyn R. Dixon, et al., An Introduction vĩ đại Essential Algebraic Structures ISBN 1118497759, p. 59
- ^ e.g., Wolfram Alpha calculation and Maxima
- ^ Jonathan Katz, Yehuda Lindell, Introduction vĩ đại Modern Cryptography ISBN 1351133012, 2020, section 9.1.1, p. 45
- ^ Weisstein, Eric W. "Greatest Common Divisor". mathworld.wolfram.com. Retrieved 2020-08-30.
- ^ "Greatest Common Factor". www.mathsisfun.com. Retrieved 2020-08-30.
- ^ Slavin, Keith R. (2008). "Q-Binomials and the Greatest Common Divisor". INTEGERS: The Electronic Journal of Combinatorial Number Theory. University of West Georgia, Charles University in Prague. 8: A5. Retrieved 2008-05-26.
- ^ Schramm, Wolfgang (2008). "The Fourier transform of functions of the greatest common divisor". INTEGERS: The Electronic Journal of Combinatorial Number Theory. University of West Georgia, Charles University in Prague. 8: A50. Retrieved 2008-11-25.
- ^ Knuth, Donald E. (1997). The Art of Computer Programming. Vol. 2: Seminumerical Algorithms (3rd ed.). Addison-Wesley Professional. ISBN 0-201-89684-2.
- ^ Shallcross, D.; Pan, V.; Lin-Kriz, Y. (1993). "The NC equivalence of planar integer linear programming and Euclidean GCD" (PDF). 34th IEEE Symp. Foundations of Computer Science. pp. 557–564. Archived (PDF) from the original on 2006-09-05.
- ^ Chor, B.; Goldreich, O. (1990). "An improved parallel algorithm for integer GCD". Algorithmica. 5 (1–4): 1–10. doi:10.1007/BF01840374. S2CID 17699330.
- ^ Adleman, L. M.; Kompella, K. (1988). "Using smoothness vĩ đại achieve parallelism". 20th Annual ACM Symposium on Theory of Computing. Thành Phố New York. pp. 528–538. doi:10.1145/62212.62264. ISBN 0-89791-264-0. S2CID 9118047.
{{cite book}}: CS1 maint: location missing publisher (link)
- ^ Müller-Hoissen, Folkert; Walther, Hans-Otto (2012), "Dov Tamari (formerly Bernhard Teitler)", in Müller-Hoissen, Folkert; Pallo, Jean Marcel; Stasheff, Jim (eds.), Associahedra, Tamari Lattices and Related Structures: Tamari Memorial Festschrift, Progress in Mathematics, vol. 299, Birkhäuser, pp. 1–40, ISBN 978-3-0348-0405-9. Footnote 27, p. 9: "For example, the natural numbers with gcd (greatest common divisor) as meet and lcm (least common multiple) as join operation determine a (complete distributive) lattice." Including these definitions for 0 is necessary for this result: if one instead omits 0 from the phối of natural numbers, the resulting lattice is not complete.
- ^ Knuth, Donald E.; Graham, R. L.; Patashnik, O. (March 1994). Concrete Mathematics: A Foundation for Computer Science. Addison-Wesley. ISBN 0-201-55802-5.
- ^ Nymann, J. E. (1972). "On the probability that k positive integers are relatively prime". Journal of Number Theory. 4 (5): 469–473. Bibcode:1972JNT.....4..469N. doi:10.1016/0022-314X(72)90038-8.
- ^ Chidambaraswamy, J.; Sitarmachandrarao, R. (1987). "On the probability that the values of m polynomials have a given g.c.d." Journal of Number Theory. 26 (3): 237–245. doi:10.1016/0022-314X(87)90081-3.
- Andrews, George E. (1994) [1971], Number Theory, Dover, ISBN 978-0-486-68252-5
- Hardy, G. H.; Wright, E. M. (1979), An Introduction vĩ đại the Theory of Numbers (Fifth ed.), Oxford: Oxford University Press, ISBN 978-0-19-853171-5
- Long, Calvin T. (1972), Elementary Introduction vĩ đại Number Theory (2nd ed.), Lexington: D. C. Heath and Company, LCCN 77171950
- Pettofrezzo, Anthony J.; Byrkit, Donald R. (1970), Elements of Number Theory, Englewood Cliffs: Prentice Hall, LCCN 71081766
Further reading[edit]
- Donald Knuth. The Art of Computer Programming, Volume 2: Seminumerical Algorithms, Third Edition. Addison-Wesley, 1997. ISBN 0-201-89684-2. Section 4.5.2: The Greatest Common Divisor, pp. 333–356.
- Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. Introduction vĩ đại Algorithms, Second Edition. MIT Press and McGraw-Hill, 2001. ISBN 0-262-03293-7. Section 31.2: Greatest common divisor, pp. 856–862.
- Saunders Mac Lane and Garrett Birkhoff. A Survey of Modern Algebra, Fourth Edition. MacMillan Publishing Co., 1977. ISBN 0-02-310070-2. 1–7: "The Euclidean Algorithm."


text:
Holger Winnemöller1 Jan Eric Kyprianidis2 Sven C. Olsen
1Adobe Systems, Inc., United States
2Hasso-Plattner-Institut, Germany
Computers & Graphics, 2012
Recent extensions to the standard difference-of-Gaussians (DoG) edge detection operator have rendered it less susceptible to noise and increased its aesthetic appeal. Despite these advances, the technical subtleties and stylistic potential of the DoG operator are often overlooked. This paper offers a detailed review of the DoG operator and its extensions, highlighting useful relationships to other image processing techniques. It also presents many new results spanning a variety of styles, including pencil-shading, pastel, hatching, and woodcut. Additionally, we demonstrate a range of subtle artistic effects, such as ghosting, speed-lines, negative edges, indication, and abstraction, all of which are obtained using an extended DoG formulation, or slight modifications thereof. In all cases, the visual quality achieved by the extended DoG operator is comparable to or better than those of systems dedicated to a single style.
Winnemöller, H., Kyprianidis, J. E., & Olsen, S. C. (2012). XDoG: An eXtended difference-of-Gaussians compendium including advanced image stylization. Computers & Graphics, 36(6), pp. 740-753.
@ARTICLE{ Winnemoeller:2012:XED, author = { Winnem{\"o}ller, Holger and Kyprianidis, Jan Eric and Olsen, Sven C.}, title = { XDoG: An eXtended difference-of-Gaussians compendium including advanced image stylization }, journal = { Computers \& Graphics }, volume = { 36 }, number = { 6 }, pages = { 740--753 }, year = { 2012 }, doi = { 10.1016/j.cag.2012.03.004 } }


text:
05-25-2012, 04:21 AM (This post was last modified: 06-02-2012, 01:23 PM by Ice Queen Zero.)
Obviously a fake...
Even if it's really working, hope you got a lot of patience running your games at 0.00000001 FPS
I think you mean PCSX in your post right?? Coz there is no such thing as ePCSXe..
or maybe PCSX + ePSXe = ePCSXe...
05-25-2012, 04:27 AM (This post was last modified: 06-02-2012, 01:24 PM by Ice Queen Zero.)
I think this was already discussed in some threads in this forum..Can't remember it clearly...
I'm lazy to use the "search function"
About your question, I think I'll leave it to PCSX2 coders or someone expert who are willing to post here..And seriously, my amateur knowledge ends here..
Anyway I found something:
technically, no.
you're running pieces of software on an architecture that wasn't made for it.
an emu is a kind of real time translator.
if the machine's architecture is close to the original hardware, the emu won't have a lot of "translating" to process (i.e : Dolphin)
PS2 & PS3 's hardware are so far from PC's hardware that this "translating process" will require more raw power.
BTW, I removed your link to avoid any further problem.
CPU : AMD Ryzen 7 3800X
Mobo : Asus PRIME B450-PLUS
GPU : NVIDIA GeForce RTX 3070
RAM : 16 Go
05-25-2012, 04:46 AM (This post was last modified: 05-25-2012, 04:46 AM by Ice Queen Zero.)
well, you just came to understand the difference between a port and an emu...
CPU : AMD Ryzen 7 3800X
Mobo : Asus PRIME B450-PLUS
GPU : NVIDIA GeForce RTX 3070
RAM : 16 Go
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text:
Patriots Have Not Yet Begun to Fight: Here's How to Protect Your Vote via the Electoral College
There's only one thing worse than grief and that's discouragement. I've been dismayed to see my fellow MAGA patriots slipping into discouragement this week courtesy of the Devil's own Mainstream Media.
Hey, you! Snap out of it! There are more "checks and balances" on the Electoral College Vote than you can shake a stick at so take heart! (Scroll down to Section 3 to read the encouraging details!!!)
We're Americans, dammit. Even better than that, we're Christians and God did not gives us a spirit of fear, but of Power! Of Love! And of a Sound Mind! (2 Timothy 1:7)
We are the people of John Paul Jones' famous quote: "I have not yet begun to fight."
We are the people of General McAuliffe who responded "NUTS" to a Nazi surrender demand.
We are the people of Valley Forge who left bloody footprints in the snow.
We Americans "can beat the world at anything from war to tiddlywinks." (Meet John Doe)
Compared to all the adversity we've faced since the 1700s and all we've overcome, the pathetic blatant, in-your-face, well documented ballot box Benedict Arnolds are well within our perview to conquer as well.
C'mon man! Buck up, me buckos! President Trump is still feeding rope to the traitors who are still counting phony ballots. He's still building his arsenal of ammunition for winning this election legally and fairly. His legal team has an embarrassment of riches in their quiver. And the Senate is Republican.
President Trump wouldn't have done fourteen (14!!!) rallies in three days at the age of seventy-four if he hadn't spent the last four years quietly shoring up the election process for just this moment! He kept us in the dark because he never shows his hand. Yes it hurt, but surely we can bear these labor pains necessary for our Glorious Republic to drain the election process swamp.
President Trump has not yet begun to fight and neither have we.
As it turns out, even after casting our ballots there's something we can do to protect the accuracy of the Electoral College. There are a lot of steps, a lot of "checks and balances," a lot of flexibility to protect the integrity of the Electoral College Vote from fraud with precedents already in place! Representative Mo Brooks (R-AL) explained it to Breibart on Thursday while I was researching another angle, but we concur.
So read on, Patriots! Onward Christian Soldiers!
Click here to learn more about Lenora Thompson: wife, writer, patriot.
This website is 100% patriot supported.
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text:
Congratulations to 4th year MLS student Emily Gates who was recently awarded a Johns Hopkins Tuition Subsidy Scholarships for the 2020-2021 academic year. Over the course of her tenure at Stevenson University, Emily has been .
Medical Laboratory Science News
Sunday, April 19 marks the beginning of Medical Laboratory Professionals Week, or put more simply, Lab Week.This year's Lab Week comes at an unprecedented time in history, when healthcare professionals in Maryland, throughout.
Mary Moorhouse (MLS '07), Manager of the Blood and Tissue Banks at Sinai and Northwest Hospitals and Melissa Fisher (MLS '17), Blood Bank, Sinai Hospital are making a difference for those infected with COVID-19. The Sinai.
A 16-year-old female presents to the hospital with a burning sensation in her leg. There is a noted ulcer that she has been trying to alleviate with antibiotics.
Human infection with parasitic worms can be devastating. Over a quarter of all humans are infected by parasites.


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The Maine Legislature's Education Committee held a public hearing May 12 on legislation that would establish a public charter school program in Maine.
Maine is one of 10 states that don't allow charter schools.
Education Commissioner Stephen Bowen delivered the following testimony supporting L.D. 1553, An Act To Create a Public Charter School Program in Maine.
Testimony of Stephen Bowen, Commissioner of Education
Senator Langley, Representative Richardson, and Members of the Joint Standing Committee on Education and Cultural Affairs:
My name is Stephen Bowen, I am the Commissioner of Education, and I am here representing the Department of Education and the State Board of Education, testifying in favor of the revised L.D. 1553 An Act To Create a Public Charter School Program in Maine. There will be plenty of charter school experts here today to discuss the details of the bill before you, so I'd like to take this opportunity to talk with you about charter schools as a public policy issue, and I'll leave the details of the bill to the others that will follow.
There will likely be a great deal of discussion this afternoon about what charter schools are, but I'd like to begin today by talking about what charter schools are not.
To begin, charter schools are not private schools. Charter schools are public schools that are simply governed and managed in a way that is different than conventional public schools.
Charter schools are not religious schools. The bill before you spells out clearly that "a public charter school may not engage in any religious practices in its educational program, admissions or employment policies or operations."
Despite what you are likely to hear today, charter schools are not exclusionary or elitist. Charter schools must accept all applicants for whom they have space. While they may specialize or have a specific focus, they may not discriminate against certain types of students, may not charge tuition, may not use entrance exams or otherwise bar entry to students, and must use a lottery system to fill slots if they have too many applicants. The bill before you also requires that charter schools produce a plan to meet the transportation needs of students, in order to assure that all students are able to have access to charter schools.
Indeed, charter schools today serve a more diverse population than conventional public schools. Nationally, more than 60 percent of students served by charter schools are non-white, compared to just over 40 percent of the student in conventional public schools. Forty-three percent of charter school students are eligible for free or reduced lunch, compared to only 40 percent in the nation's traditional public schools. Charter schools also serve about the same percentage of special education students as conventional public schools, and a quarter of all charter schools are not in cities or suburbs, but in the more rural areas of the nation.
Charter schools are also not a new idea. Today, 1.7 million students attend 5,400 charter schools in 40 states, and enrollments continue to grow. Critics of the charter school model might like you to think that public support for privately-managed schools is a new and unproven idea, but here in Maine, the Town Academies, governed by private boards of trustees, have been educating students at public expense for generations. As with charter schools, the academies are not governed or managed by local school boards, yet they continue to attract students and families year after year and generation after generation.
In fact, one thing charter schools are is overwhelmingly popular with parents and families. Today, there are 420,000 students on charter school waiting lists nationwide. Last school year, 27,000 students attended charter schools in nearby Massachusetts, and another 26,700 were on waiting lists. 20,000 students are on charter school waiting lists in North Carolina, 35,000 are on waiting lists in Florida, and 56,000 are on waiting lists in Texas. In total, two-thirds of the charter schools in the nation have students waiting to get in.
Why? Because charter schools offer students and families what we all want in so many other aspects of our lives, which is options. Think for a moment about what we ask our public schools to do. We draw lines on a map, and then we tell educators that they, and they alone, must meet the learning needs of every single child who lives within the lines on the map. Our schools often do an excellent job of meeting those needs, but families across the nation are lining up to get into charter schools because they want a different kind of educational approach, one that is simply not found in many of the nation's schools.
It is that student and family choice which brings accountability to public charter schools. Remember, no child can be required to attend a charter school – they are public schools of choice. If charter schools do not succeed in meeting the educational needs of students, the schools close. That is a degree of accountability that far exceeds the accountability measures we have in place for conventional public schools.
Do charter schools drain funding from conventional public schools, as is likely to be suggested today? Under the law before you, money would indeed follow the student from their local school district to the charter school, but only if the student and his or her family make the choice to leave – if they decide that the charter school better meets their educational needs. In this example, then, the money is being spent to buy students the education that best meets their needs, which is precisely what we should want as a matter of public policy. The education dollars we spend are used to provide the student with the education that best meets his or her needs.
It is important to point out that there is one other thing that charter schools are not, and that is some kind of silver bullet that will solve all our education problems. Charter schools are a promising reform, they will give educators a model of schooling to work with that may indeed allow them to be more innovative, and they may improve student outcomes for the students that attend them. However, though we may learn from the reforms implemented by charter schools – and we have learned much over the past few years from reforms, like extended learning time, that were pioneered by charter schools – we still must take steps to make every school better, and that effort will take far more than simply enacting charter school legislation.
Charter schools can be a part of that effort. However, hundreds of thousands of children are being educated in charter schools across this country – all of them there because parents and families decided that such schools were the best options for their children. Thousands of students on waiting lists are waiting to have that option as well.
It is an option we should offer Maine's students and families. For these reasons, the Department of Education and the State Board of Education support the passage of L.D. 1553 An Act To Create a Public Charter School Program in Maine.
Before I finish, I'd like to quickly address the issue of carrying over the bill, which I know has been talked about. Simply put, the Department and the State Board would like to see the bill passed during this session, because waiting another year puts us another year behind in implementing this reform. I would urge the Committee to remember that if the bill passes this Session and is signed by the Governor, it would not take effect until the fall. Before any charter school was authorized, rules and policies around charter schools would need to be developed and adopted, the State Charter School Commission proposed in the bill would need to be formed, and charter school authorizers would need to be trained and their procedures established. In short, there is virtually no chance that a charter school would be operational by this fall, even if the bill was passed today. Waiting another year on the bill simply means waiting two more years for charter schools to open.
I thank you for your time and attention, and I am happy to answer any questions the Committee may have and will be available for work session on this bill.


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Incremental creep and massive holes in universal health coverage (think dental care) have left many Australians questioning whether there's any such thing as "free health care". One recent study estimated households now pay directly for almost 25% of the nation's health costs.
Into this existing mess of user charges has stepped yet another proposal to cost shift from government to households. The Australian Centre for Health Research (ACHR), a small "think tank" set up by the smaller private health funds, has proposed a new A$6 co-payment for access to bulk-billed general practitioner services.
Mandatory payments for GP visits
The ACHR claims to build on the abortive 1991 Hawke government attempt to impose a similar charge. Like the Hawke proposal, it aims to relieve the federal budget by shifting part of the cost of primary care to patients. Around 80% of GP services are currently bulk billed, with no upfront charge.
The ACHR claims consumers wouldn't notice a A$6 charge as it's "less than the price of two cups of coffee". But at the same time it would change behaviour, sending "clear price signals to Australians that their basic health-care services are not free goods" and will be better "valued by consumers if they come with a price signal".
The proposal recommends freezing GP rebates paid by Medicare, which would prompt GPs to charge the co-payment to maintain their incomes. Consumers would have a new incentive to think twice about going to the GP with a minor complaint. They would look after their own health and, to avoid the A$6 charge, move to more healthy lifestyles.
This would, the ACHR claims, save the federal budget up to A$750 million.
However, despite arguing for a clear and direct price signal to consumers, the ACHR suggests that private health insurers should be allowed to cover co-payments for GP services. This extension of insurance sits oddly with the ACHR claim that the co-payment would end the "moral hazard" of consumers cushioned from the real cost of services.
Co-payments paid out of insurance would quickly increase. Australia's private insurers have a poor record of resisting fee increases and can rely on government subsidies to cover much of the rise in premiums. Medicare is likely to come under greater pressure to raise rebates as the gap widens (especially for the uninsured).
Insured co-payments would weaken bulk billing, undermining one of the major restraints on medical costs.
What does the evidence say?
This has been all been tried before. In the first term of the Howard government, GP rebates were frozen, and there was a large decline in bulk billing, as GPs made up the lost income by charging their patients. This ended in a political crisis, as consumers turned on the government.
Tony Abbott entered the health ministry in 2001 with the task of restoring bulk billing and fixing a major political sore, vowing to become "Medicare's greatest friend".
The ACHR relies on heroic assumptions about consumer behaviour. The only piece of evidence cited is an experiment in the effects of different levels of co-payment carried out in the United States in the early 1970s by the RAND Corporation.
The RAND experiment found that co-payments (the lowest was at 25% of service costs) did influence demand for services across the board, without a significant impact on health outcomes. It has become the main source of justifications for increased co-payments as a budget control.
Even at the time these results were criticised. The study excluded people over 65 – a serious defect if its results are applied to the Australian context. Even in the 1970s, US health care was far more expensive and patients more heavily serviced than their Australian equivalents. A lot of fat could be cut from the American system without it affecting basic health outcomes.
So, is there evidence of unnecessary demand for Australian GP services?
The Bettering the Evaluation and Care of Health (BEACH) study, which has been collecting data on primary care services since 1998, shows there has been an increase in use of GP services. But this is explained by the increased age of patients and the growing complexity of the issues GPs handle. Both are linked to the rise in chronic illness.
Chronic illnesses such as diabetes 2 are not better managed by discouraging contact with the health system. We need to improve health literacy and self-management but there is no evidence that this will occur through the financial pain of a A$6 co-payment.
The larger private health insurance funds are now investing considerable resources in prevention as they see this as a major component of their costs. Their response has not been blunt financial penalties, but encouragement to live healthier lifestyles.
Reining in health costs
Our health system shouldn't be immune from possible expenditure cuts. But primary care is a poor starting point.
The RAND study did offer one way forward. One consumer group was recruited into a "free" Health Management Organisation, which employed salaried doctors and tried to integrate care across the system – from primary care to hospitals.
Like groups that paid co-payments for fee-for-service care, the HMO group recorded major cost savings. But rather than an across-the-board effect, the HMOs saved money by reducing hospitalisation (a 39% fall).
The Chronic Care Model of Care, which is widely used in the US, is similarly focused on broader treatment, bringing community based primary and hospital care together and reducing unnecessary hospital admissions. "Self-management support" plays a big part in this model – but co-payments do not figure.
Australian governments and health-care providers have been making a slow journey towards integrating care across the system. The fruits are being seen in fewer hospitalisations and better care. But attempts to revive discredited models of co-payment distract from the real problems facing Australia's health.
Jim Gillespie's latest book Making Medicare: The Politics of Universal Health Care in Australia, co-authored with Anne-Marie Boxall, was published in September by UNSW Press.


text:
By Professor Pat Hanscom, Mathis Wackernagel, Ph.D., and Nicola Horsburgh
Scotland may be close to running a biocapacity reserve, becoming a biocapacity leader in its own right, new research from the University of Stirling has found. Scotland has about 3.6 gha (global hectares) of biocapacity per resident. This juxtaposes with an Ecological Footprint per resident of possibly 4.2. gha (2018 UK data), assuming that the Scottish Footprint is similar to that one of the UK as a whole.
This contrasts with the average biocapacity of the UK as a whole, which stands at just 1.2 gha per person (Global Footprint Network, National Footprint and Biocapacity Accounts 2022 Edition, based on 2018 UN data). In other words, with only 8% of the UK population, Scotland makes up 27% of the country's biocapacity. At the global scale, Scotland's position is also quite notable when considering that the biocapacity on our planet is about 1.6 gha per person.
These findings are based on a preliminary analysis of Scotland's biocapacity that researchers from the University of Stirling recently completed, with methodological guidance from Global Footprint Network. Lead researcher Nicola Horsburgh used various land classification systems as an entry point and estimated each land type's biological productivity. This allowed her to calculate how many global hectares (gha) of biocapacity Scotland harbors.
Preliminary Biocapacity Results for Scotland
Researchers estimated the various components of Scotland's biocapacity. The data, in table 1 below are shown in global hectares per person.
|Scotland (gha/person)
|United Kingdom including Scotland (gha/person)
|Grazing land
|Marine/inland fishing grounds
|Built-up land
|Total Biocapacity
|Ecological Footprint*
|Resulting Biocapacity Deficit
Table 1: Biocapacity of Scotland by area type. The Scotland data, sourced from Scottish statistics, are for 2018; the UK data, sourced from UN statistics, are for 2016.
*To compare the biocapacity to the respective Ecological Footprints, we assume that people in Scotland have a similar Footprint to the general population of the United Kingdom. Due to past decarbonization, Scotland's per person Footprint may already be lower, and may drop even further given Scotland's commitment to reaching a 75% reduction in its carbon emissions against 1990 levels by 2030. Therefore, Scotland may have the opportunity to leave its biocapacity deficit situation in the near future, if managed well.
Future Scottish Footprint reduction
Even though Scotland's Ecological Footprint has never been comprehensively assessed, it is a safe initial assumption that, per person, it is similar to that of the UK average. That's commonly the case in many high-income countries that Global Footprint Network has studied: the difference of Ecological Footprints per person among regions is typically not large.
However, the situation might be somewhat different in Scotland, not only because GDP per person is slightly lower than the UK average, potentially implying lower levels of consumption. This may even be compensated by the fact that colder winters in Scotland compared to the rest of the U.K may lead to higher energy consumption per person.
Probably the most significant driver behind Scotland's expected lower Ecological Footprint, as compared to the rest of the UK, is the fact that the region has been on a rapid decarbonization path. Since 1990, it has cut its carbon emissions 47%. Currently, 75% of its electricity is generated from renewable sources. Given that currently 64% of the UK's Ecological Footprint is carbon, this may indicate that Scotland's per person Footprint may be reaching a level close to its own biocapacity. Given its continued decarbonization effort, supported by the strong commitment of Scotland's government, this increases the possibility that Scotland may be exiting its biocapacity deficit in the foreseeable future. Hopefully, there will be a Scottish Ecological Footprint study soon to test this possibility.
Additionally, the Scottish Government's Climate Change Plan (2018) goes beyond aggressive decarbonization targets. It also embraces other policy instruments to increase and preserve natural resources, like peatland restoration and afforestation. Horsburgh estimates that peatland's biocapacity alone might constitute an additional 0.1 gha of biocapacity per resident.
"Preparing oneself for a future with climate change and resource constraints also has other benefits since every country that invests in its own long-term success makes it more likely for other countries to follow," the researchers state in their report. "There are several mechanisms which amplify this positive sum game: exchange of information and joint learning; reduction in overall demand on the planet; and building capacity to support others. It becomes a positive-sum game."
This biocapacity assessment reflects a most encouraging development. Because it has been acting out of its own accord, despite the global morass that is global climate "action", Scotland is building the future it needs, guided by one-planet prosperity. Any government would benefit if it recognized that one-planet prosperity is not just good for humanity, but necessary for themselves to be able to operate in the future. This recognition would certainly amplify climate action and give a boost to the upcoming UN climate conference, COP26, held in Glasgow next year. Dinna Fash!
For more information
To download the University of Stirling's 2020 initial biocapacity report, click here.
For an expanded, academically published version, consult: Nicola Horsburgh, Andrew Tyler, Scot Mathieson, Mathis Wackernagel, David, Lin, 2022, Biocapacity and cost-effectiveness benefits of increased peatland restoration in Scotland, Journal of Environmental Management, Volume 306, 15 March 2022, 114486, https://doi.org/10.1016/j.jenvman.2022.114486
(updated March 2022)


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IVAN BEGOVIC, age 52. Beloved son of Pavo and Manda (deceased); dear brother of Ana Begovic-Juhant (deceased), Mary Headley and Nada Wardeiner; loving father of Paul and Roseanna; adored "Dede" of Melissa, Dominic and Jaedyn. He lived a life of many challenges, both mental and physical hardships, but always overcame them to help all his family. He will be missed and loved dearly. Friends received at DeJOHN-FLYNN-MYLOTT FUNERAL HOME OF WILLOUGHBY HILLS, 28890 CHARDON RD. (BETWEEN BISHOP RD. Continue reading
Archives for March 2014
Arlene Dotson
Friends and family are invited to meet at Holy Cross Cemetery Monday, March 31, 2014 at 12 noon for a Graveside Service to honor and celebrate Arlene's life. Continue reading
Gloria Kluk
GLORIA M. KLUK (nee Smargiassi) age 84; beloved wife of the late Martin; loving mother of David (wife Patricia), Sandra, Debra Nelson (husband Michael), Laura Koch (husband Robert) and Robert (wife Denise); devoted grandmother of Jennifer and Stephanie, Aron, Jason and Seth, Adrienne, Anthony, Heather, Ilona and Anna, Martin and Chelsea, and great-grandmother of Lauren, Jason, Daniel, Milo, Olive and Anthony; dearest daughter of the late Jennie (nee Yafanaro) and Santino Smargiassi; dear sister Continue reading
Rosalia Likozar
ROSALIA "ZALKA" LIKOZAR age 83, passed away on March 25, 2014 at her residence. She was born September 12, 1930 in Polje, Slovenia and was forced to emigrate to Spittal, Austria after WW II in one of the many displaced persons' camps due to the imposition of communism in Slovenia. She came to the US and lived in the St. Clair Avenue neighborhood. In 1955, she married Joseph (Joze) Likozar in St. Vitus Church and settled on Norwood Rd. until moving to Highland Heights, Ohio. Mrs. Likozar was Continue reading
Sylvia Seneviratne
SYLVIA SENEVIRATNE (nee De Silva), aged 93 years, went to be with the Lord on March 23, 2014, beloved wife of the late Shirely, loving mother of Shanthi Samarasekera (husband Lallith – deceased), Elias Parakrama Seneviratne (wife Nimali), Ernest Priyanath Seneviratne (wife Christine), Charles Sunil Seneviratne (wife Kumarani), and Elizabeth Srima Ranasinghe (husband Gerard Chanaka Ranasinghe), dearest grandmother of 13 and great-grandmother of 11. Contributions in memory of Sylvia suggested Continue reading
Marian Randa
MARIAN A. RANDA (nee Specht) age 89. Beloved wife of the late Paul J. Cherished daughter of the late Charles F. and Marie V. (nee Kristofeck) Specht. Dear sister of Wilford Specht and the late Bernard, Francis and Harold Specht. Dearest aunt of Kathy Leciejewski, Karen Zannella, Kimberly Collister, Karla Rosada and many other nieces and nephews. Retired after 47 years at Chase Brass and Copper. Contributions may be made in Marian's memory to Geauga Humane Society Rescue Village, 15463 Continue reading
Jean Amato
JEAN D. AMATO (nee Salvatore), age 100; beloved wife of the late Vincent; loving mother of Joseph of California; devoted grandmother of Christine, Laura Androsko and great-grandmother of Melissa, John and Jacqueline; Dearest sister of the late Emma DiFiori and Irene Ianiaro and John Salvatore; dear sister-in-law, aunt, great-aunt and friend of many. Jean enjoyed playing bingo and crafts. She was also a huge fan of the Cleveland Indians. Her family remembers her as a classy lady who was very Continue reading
Dorothy Lucas
Dorothy J. Lucas. Beloved wife of the late Anthony. Loving daughter of the late Joseph and Julie (nee Tudor). Beloved sister of Judge Alfred Lucas and the late Donald (Barbara). Dearest aunt and great-aunt of many. The family suggests contributions may be made in Dorothy's memory to St. Jerome Catholic Church, 15000 Lake Shore Blvd. Cleveland, OH 44110. A Mass of Christian Burial will be held on Tuesday, March 25, 2014 at St. Jerome Church at 10:00 AM. Interment All Souls Cemetery. The Continue reading
Ernest McDaniel
ERNEST MITCHELL MCDANIEL. age 65; beloved husband for 42 years of Dolores M. (nee Alioto); loving father of Charles and Lynnette Stollard (husband Clint); devoted grandfather of Samuel and Allison Stollard; cherished son of the late Charles and Joyce (nee Bess); dearest brother of the Tim (wife Beverly) and Dwayne; dear nephew, brother-in-law, uncle and great-uncle of many. Ernest was a veteran of the U.S Army serving in Vietnam. He was a recipient of the Purple Heart. He was retired from BF Continue reading