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late 14c. (from c.1100 as a surname), "a worker in any sort of lead" (roofs, gutters, pipes), from Old French plomier "lead-smelter" (Modern French plombier) and directly from Latin plumbarius "worker in lead," noun use of adjective meaning "pertaining to lead," from plumbum "lead" (see plumb (n.)). Meaning focused 19c. on "workman who installs pipes and fittings" as lead water pipes became the principal concern of the trade. In U.S. Nixon administration (1969-74), the name of a special unit for investigation of "leaks" of government secrets.
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Try a plunger: If it's a double sink, use a wet rag or rubber stopper to block the other drain. Place the plunger directly over the drain until it forms an air-tight seal. If you have trouble forming an air-tight seal with the plunger, run it under some hot water to make it more flexible. Move the plunger up and down to dislodge the clog from the drain.
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A conventional water heater is recognized as a cylindrical storage tank ranging in size from 20 to 80 gallons in capacity. This tank is typically insulated with one or two elements that heat the water to the temperature set on the thermostat. Conventional water heaters have been used for decades in residential and commercial buildings. However, this method of constantly heating or keeping the tank of water hot is not very energy efficient, especially if you don’t have a need for hot water 24 hours a day.
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Try a plunger: If it's a double sink, use a wet rag or rubber stopper to block the other drain. Place the plunger directly over the drain until it forms an air-tight seal. If you have trouble forming an air-tight seal with the plunger, run it under some hot water to make it more flexible. Move the plunger up and down to dislodge the clog from the drain.
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Saint George S.C.

Saint George Sports Club (Amharic: ቅዱስ ጊዮርጊስ ስፖርት ክለብ, Kidus Giorgis Sport Club) is an Ethiopian football club based in Addis Ababa, Ethiopia. They are members of the Ethiopian Football Federation and play in the top division of Ethiopian football, the Ethiopian Premier League. Founded in 1935, the club was the first in Ethiopia and was established as a symbol of Ethiopian nationalism and resistance against the occupying forces of fascist Italy.

History

Establishment
The club was founded on 1935 at Doro Manekia in George Dukas's family house by Ethiopian Ayele Atnash and Greek George Ducas. Established in the Arada (Arada Giorgis) neighborhood of Addis Ababa during Fascist Italy's invasion of Ethiopia, the club quickly became the symbol of Ethiopian nationalism in the midst of Italian occupation. The patriotic struggle of the 1930s left an indelible mark on the club and the Arada neighborhood, defining both for centuries to come. The history of the club is often thought to be heavily influenced by this neighborhood. St George was said to have started with only 2 Tegera Birr, 1 ball, goal posts and a stamp.

Often finding it hard to play football on local pitches due to restrictions placed on them by the Arada police, the club had to constantly move from place to place. In one instance the club members tried carrying goal posts to 'Filwehameda' ( presently located next to Custom Authorities Head Office), but were ultimately chased away by authorities. Attempts to play at  'Aroge Kera' on the 'Etege Menen' field were also unsuccessful as unhappy local villagers chased them away. Then they went to 'Belay Zeleke' 'Zebegna Sefer' village, but Arada police came and chased them away once again.

Matches were organized against other local teams or groups in the area such as those of the Armenian community of Addis Ababa. However, because the club was short handed in the number of players they had they ended up recruiting others to play. This is how  Yidnekachew Tessema came to be a part of the team, he was found on the streets of Addis and was asked to join them for the match. It was said that he was spotted while crossing Berad Mekonnen bridge and since he went to Teferi Mekonnen School where all club members went to school,  they were familiar with him. After agreeing to join them, St. George was able to beat the Armenian team 2-0 thanks to two goals by Yidnekachew himself.

The club's first jerseys were brown and white, affordable cloth for the cash strapped club at the time. One of the founders, George Ducas, used scrap together money from his parents to support the club. Others in the club would go around knocking at doors singing traditional songs like "Hoya Hoye" in order to earn money for the club. The customary reward for their singing efforts was bread, not money, but they were able collect this bread in a sacks to sell it in laborers' villages to earn the money. Once the club was able to find some funds they were able to get a New Jersey that implies their unity with the Ethiopian flag colors.  They gave the first jersey to the second team and started wearing the new ones until pressure from the occupying police force made them have to hide this New Jersey underneath their clothing.

After buying jersey with the money, the club bought food for the players with the rest of the money. The members and players of the club would to eat bread and tea after matches and training sessions.

Connection to the Ethiopian Struggle
When Italian efforts to directly destroy St. George didn't work, they forced the club to change its name and play matches against a club the Italians had created called '6 kilo'. This club was purposely created by Italians to weaken and demoralize St. George. Sponsored by the nearby factory 'Cugnac Alovo', 6 Kilo (also called 'Cenco Maje' to mean July 5), had more money and supplies than St. George. They beat St. George on multiple occasions and St. George also did the same however those matches nearly always ended with beatings by the Arada (Italian) police.

The ongoing Guerrilla warfare during this time was of  the utmost importance to the club and its members. Knowing this the Italians trying using the club as a propaganda tool for their own administration in order to confuse and entrap the guerilla fighters. The Italians sent a messages to resistance leaders like Ras. Abebe Aregay to "come and see the people is in peace" inviting him to watch a football match at JanMeda, a popular field in Addis Ababa.

Hearing this the guerilla fighters took an Italian General as leverage not trusting the Italians and Ras. Abebe Aregay sent Demissie W/Michael to investigate the situation. Having been warned before hand to peacefully play the match, St. George was picked to play against "6 Kilo". The game quickly turned into a physical fight after kickoff with spectators often cheering and whistling to encourage the fight rather than the game. Then the game was interrupted and the Italians' plan foiled.

In 1941 when Ethiopia was liberated from fascist Italian control and Haile Selassie I had returned, it was us the club supporters along with fellow Addis Ababians that sang the national anthem "Ethiopia hoy des Yebelesh"(to mean, Rejoice Ethiopia) to welcome him back. An anthem that was written by a huge St. George supporters Yoftahe Nigussie and produced by Captain Nalbadin.

Ethiopian League Football
The first officially recognized version of an Ethiopian football league was established in 1944. Originally five teams representing the various communities of Addis Ababa including St. George (Ethiopian), Fortitudo (Italian), Ararat (Armenian), Olympiakos (Greek) and the British Military Mission in Ethiopia (BMME) contested for the title which was won by the BMME. In 1947, the country's formal national league kicked off with three teams; St. George, Mechale and Ke'ay Bahir. The club remained within the league for twenty-five years before the Derg reorganized the football leagues, and forced all existing clubs to shut down. In this process the club had its name changed to Addis Ababa Brewery in 1972 only to change it back four years later. The club switched its name back an forth for 19 years until the fall of the Derg in 1991 when the club officially changed its name back to St. George.

St. George enjoyed some dominance in the late 60's after which the league went through a period of relative parity in the 70's and 80's. However, during the premier league era no club has been more dominant than St. George S.C., amassing an impressive 14 titles since the start of the era in the 1997-98 season. As of 2017, the club has a combined 29 top division titles which is by far the most in Ethiopian football.

Ownership
The club is owned by the St. George Football Association. It is also financially supported by prominent Saudi Businessman Mohammed Hussein Al Amoudi and Ethiopian businessman Abenet Gebremeskel, who is also chairman of the club.

In June 2018 it was announced that the club would sell most of its shares to fans.

Supporters
Saint George have one of the largest fan bases in all of Ethiopian football and are known for their fervent displays during home matches. Often singing the club's anthem and waving yellow and orange checkered flags, the supporters of Saint George provide some of the most festive atmospheres in Ethiopian football.

The ultras of the club are known to be involved in hooliganism, which is a very prevalent phenomenon in the Ethiopian football. Clashes with rival support groups are common, especially during derby matches such as in the "Sheger Derby".

In the early days chants supporters of the club used to repeat went as follows:

In reference to their early rivals "6 kilo":

«ይጫወቱ ነበር በቴስታ በጋንባ፣
መገን 6 ኪሎ ተሸንፎ ገባ።» meaning "6 kilo, although playing with their legs and kicking players with headers, they always lose"

In reference to founder Ayele Atnash.

«ግጥም አይነቃነቅም የብረት ዲጂኖ፣
እንዴት ነህ አየለ የአራዳ ተርሲኖ?» meaning "firm as a metal steal, how are you Ayele Atnash, Arada's Tersino?"

In reference to outstanding players Elias (who later became a pilot) and Yidnekachew.

«በሰማይ ኤልያስ በምድር ይድነቃቸው፣
ለመታሰቢያነት እግዜር ፈጠራቸው።»meaning "Elias on the sky, Yidnekackew on land, God created them in tribute."

Academy
In 2017, Saint George finished construction on Yidnekahew Tessema Sport Academy, the club's first youth academy, in the city of Bishoftu (Debre Zeyit). The academy is named after Yidnekahew Tessema, a former Saint George and Ethiopian national team player who rose to prominence in African football as CAF president (1972 -1987). The academy, built at a cost of over 60 million ETB, lies on 24,000 hectares of land and is expected to accommodate over 100 youth players at one time. The facilities at the academy include: two football pitches, a cafeteria, a conference center, a game room, dressing rooms,a modern medical center, a gym, and  dormitories.

Grounds
Saint George plays its home matches at Addis Ababa Stadium, also known as Yidnekachew Tessema Stadium. Due to it being the largest international standard stadium in the area, the ground is shared with many other Addis Ababa-based clubs including Ethiopian Coffee, Defense, Addis Ababa City, EEPCO, and formerly CBE SA.

Since 1999, fee-paying supporters have owned St. George. In November 2007, the club had finished raising funds and would begin construction of a new stadium. Budgeted at 312 million Birr, 80% of the cost would be covered by Sheik Mohammed Al Amoudi with the balance to be contributed by the club's supporters.

Honors

Domestic Titles
Ethiopian Premier League: 29

1950, 1966, 1967, 1968, 1971, 1975, 1985, 1986, 1987, 1990, 1991, 1992, 1994, 1995, 1996, 1999, 2000, 2002, 2003, 2005, 2006, 2008, 2009, 2010, 2012, 2014, 2015, 2016, 2017

Ethiopian Cup: 12
1952, 1953, 1957, 1973, 1974, 1975, 1977, 1993, 1999, 2009, 2011, 2016

Ethiopian Super Cup: 16
1985, 1986, 1987,1994, 1995, 1996, 1999, 2001, 2002, 2003, 2005, 2006, 2009, 2010, 2015, 2017

Regional Titles
Addis Ababa City Cup: 6
2009, 2010, 2011, 2013, 2017, 2019

Performance in CAF competitions
CAF Champions League: 9 appearances

1997 – First Round
2000 – First Round
2001 – First Round

2003 – Preliminary Round
2004 – First Round
2006 – First Round

2007 – First Round
2010 – Preliminary Round
2011 – Preliminary Round
2013 – Preliminary Round
2015 – Preliminary Round
2016 – First Round
2017 - Group Stage

 African Cup of Champions Clubs: 10 appearances

1967 – Semi-Final
1968 – First Round
1969 – First Round
1972 – Second Round

1976 – First Round
1986 – Second Round
1991 – withdrew in First Round
1992 – Preliminary Round

1993 – Preliminary Round
1996 – Second Round

CAF Confederation Cup: 1 appearance
2012 – First Round

CAF Cup: 1 appearance
2002 – Second Round

CAF Cup Winners' Cup: 3 appearances
1975 – First Round
1978 – Preliminary Round
1994 – Second Round

Players

First-team squad
As of 12 January 2020

Club Officials
President:  Ato Abinet Gebremeskel

Secretary:  Neway Beyene

Director of Sport:  Kasshun Gezaw

Team Leader:  Tafess Bekele

Coaching and Medical Staff
Head Coach: Srdan Zivojhov

Assistant Coach:  Zerihun Shengeta

Medical Staff:  Bekele Zenebe

References

External links
 Latest Ethiopian Football News
 Official Web Site

Category:Football clubs in Ethiopia
Category:Football clubs in Addis Ababa
Category:Association football clubs established in 1935
Category:1935 establishments in Ethiopia


Confession Bear

i don't think consumerism is the problem...

people are just flipping idiots

these captions aren't guaranteed to be correct


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FOUNDATION (BUILDING CONSTRUCTION).

A foundation is that part of a building which is in direct contact with the ground and its primary aim is to transmit and spread the loads (dead and live) from the building over a sufficient area of soil to avoid undue settlement because of the failure of the underlying soil. A good foundation should satisfy the following requirements: a) It shall safely sustain and transmit to the ground the loads (dead, live and wind) in such a way as not to cause any settlement or other movement which would impair stability or cause damage to the whole or any part of the buildings or both.
b) It shall be taken down to such a depth or be so constructed as safeguard the building from swelling, shrinking of freezing of the subsoil.
c) The materials used must be capable of adequately resisting any attack by sulphates of any other deleterious matter and chemicals present in the subsoil.

FACTORS AFFECTING THE CHOICE OF FOUNDTION
The following are the factors affecting the choice of foundation: ^ Soil type
^ Site condition (topography/slope, water content/flood plain) ^ Type of construction
^ Magnitude of the load and intensity
^ Economic and other constructionak considerations
^ Type of building
^ The possible effect of weather element e.g. rain.

TYPES OF FOUNDATION
The major types of foundation are:

^ STRIP FOUNDATION: This is the commonest type of foundation used or adopted in building one or two storey building and at most four storeys on firm non-shrinkable sub-soils such as gravel or laterite. It consists of continuous strip of concrete either in ratio 1:3:6 or 1:2:4.
Strip foundation
can be normal, Deep or Wide.
~NORMAL STRIP FOUNDATION: is when the width of the foundation footing is not more than three times the wall thickness
~DEEP STRIP FOUNDATION: is when the depth of the foundation is up to 900mm. It is used especially in shrinkable clayey soil to counteract the variations of soil conditions at different seasons.
~WIDE STRIP FOUNDATION: is used to spread the load over a larger area of soil; it is used in soil with low bearing capasity such as clayey, marshy ground, silt and build-up soils. The concrete is usually reinforced in both the transverse and longitudinal direction.

^ PAD FOUNDATION
These are isolated foundations constructed of reinforced concrete to support columns and mostly used in framed building construction. They can be used to carry point loads or can be designed so that the loads of the walls and the buildings are transferred through ground beams that rest on pad foundations. The pad foundation transfers the loads to a lower level where soil of sufficient load bearing strata exists. Pad foundation can be inform of isolated column foundation, continuous column foundation or combined column foundation.

^ RAFT FOUNDATION
A raft foundation is one which covers the entire area of the buildings may extend beyond it. It consits of concrete that is suitably reinforced and up to 300mm thick. It is best suited for use on soft natural ground, soft clay, alluvial deposits. Compressible fill or on ground that is liable to subsidence as in mining areas. Their advantage over strip foundation is in the ability to act as a single unit thus eliminating differential settlement.
Major forms of raft foundation
SOLID RAFT FOUNDATION: This consists primarily of reainforced concrete slab up to 300mm thick which is often thickend under load bearing walls.
BEAM AND SLAB RAFT FOUNDATION: This is like inverted reinforced concrete floor with upstand beams between the bases of columns. The beams collected the beams and slab spreading the loads over the whole area. However, if the surface of the slab is to serve as a floor, then the raft with downstand beams is used.
CELLULAR RAFT FOUNDATION: This is mostly used in basement
construction and can be constructed either as bouyancy, basement or box raft foundation.

^PILE FOUNDATION
This is frequently used where the subsoil is poor or uncertain bearing capacity of where there is likely to be appreciable ground movement as with firm or where it is necessary to transmit the building load through a weak and unstable soil conditions to a lower stratum of sufficient bearing capacity. The choice of the type to be used depends on the soil and advice of foundation experts while the distribution of the piles is influencfd by the design of the building, the loads to be carried and the load bearing capacity or the strenght of the piles.
Pile may be constructed of reinforced concrete, timber, steel or combination of any two.


Q:

jQuery KeyUp causes page to refresh

So working with an area with enter should add a result, it works but it also refreshes the page afterwards.
var targetX, targetY;
var tagCount = 0;
$(function(){
$('#tag').live('click', function(){
    var iid = $(this).attr('p');
    var img = $('#img-'+iid);
    $(img).wrap('

');
    $('#tag-wrapper').css({width: $(img).outerWidth(), height: $(img).outerHeight()});
    $('#tag-wrapper').append('

Name<input type="text" id="tag-name">Save Cancel
');
    $(img).click(function(e){
        mouseX = e.pageX - $('#tag-wrapper').offset().left;
        mouseY = e.pageY - $('#tag-wrapper').offset().top;

        targetWidth = $('#tag-target').outerWidth();
        targetHeight = $('#tag-target').outerHeight();

        targetX = mouseX - targetWidth/2;
        targetY = mouseY - targetHeight/2;

        inputX = mouseX + targetWidth/2;
        inputY = mouseY + targetHeight/2;

        if($('#tag-target').css('display')=='block'){
            $("#tag-target").animate({left: targetX, top: targetY}, 500);
            $("#tag-input").animate({left: inputX, top: inputY}, 500);
        }else{
            $("#tag-target").css({left: targetX, top: targetY}).fadeIn();
            $("#tag-input").css({left: inputX, top: inputY}).fadeIn();
        }

        $('#tag-name').focus();
        $('#canceltag').click(function(){
                closeTagInput();
        });
        $('#savetag').click(function(){
            alert($('#tag-name').val());
        });
        $('#tag-name').live('keyup', function(e){
            if (e.keyCode == 13){
                $('#savetag').click();
                return false;
            }
        });
    });
});
});

A:

As we don't see your HTML markup, I can only guess, but most probably you've got your <input> element wrapped in a <form>. Even if you don't specify any attributes on it, it defaults to a GET request to the current URL, and it WILL submit as soon as you press the Enter key.
The solution would be to bind a handler to the form's submit event and call preventDefault().
$('form').submit(function(e){
    e.preventDefault();
});


M+N Architecture proudly announces the completion of the new Flash Entertainment Offices at twofour54 in Abu Dhabi.

The space consists of a big open office area,
where the main feature is the two big white tables which replace traditional work stations and can accommodate more than 50 employees.
Thanks to their special design, the tables rise and bend, allowing people to pass through special “bridges” and move freely around the space.

We congratulate with the design team and we thank all involved parties (in particular our client, Flash Entertainment, and the fitout contractor, Life Space interiors) for such a successful project and outstanding result.


I fail to see how extending the royalty 'freeness' through 2016 helps Mozilla, or any of the h.264 detractors. It's more likely a devious way to entrench the standard, then hold the world hostage six years from now. The Mozilla VP is exactly right.

I see maybe two options:

1. A white knight (Google) buys the license and open-source's it. Unfortunately, probably extremely unlikely.

2. The open-source world bands together and improves the Ogg codec (or invents something new) to the point it can compete with h.264 in terms of quality and compression.


import { Scalar, CustomScalar } from '@nestjs/graphql';
import { ApolloError } from 'apollo-server-express';
import { StringValueNode } from 'graphql/language/ast';

@Scalar('Mac')
export class MacScaler implements CustomScalar<string, string> {
  description = 'Mac properly validates numbers to be valid mac number or not';

  parseValue(value: string): string {
    if (!value.match('[0-9a-f]{2}([-:]?)[0-9a-f]{2}(\\1[0-9a-f]{2}){4}$')) {
      throw new ApolloError('invalid mac number');
    }
    return value;
  }

  serialize(value: string): string {
    if (!value.match('[0-9a-f]{2}([-:]?)[0-9a-f]{2}(\\1[0-9a-f]{2}){4}$')) {
      throw new ApolloError('invalid mac number');
    }
    return value;
  }

  parseLiteral(ast: StringValueNode): string {
    return ast.value;
  }
}


Epidermal growth factor is a potent inhibitor of renin secretion.
Epidermal growth factor (EGF) is not only a cell mitogen but a potent vasoconstrictor that shares many properties with angiotensin II. Because EGF is localized in the kidney, we have studied the direct effects of EGF on renin secretion using both static incubations and perifusions of rat renal cortical slices. EGF at 5 x 10(-9) M significantly inhibited renin secretion in static incubations (control, 100 +/- 3%; EGF, 72 +/- 3%; p < 0.001). When added to perifusions, EGF acted rapidly, reducing renin secretion at the earliest time period (10 minutes). Similarly, transforming growth factor-alpha, which can bind to the EGF receptor, also inhibited renin secretion (control, 92 +/- 8%; transforming growth factor-alpha [2 x 10(-9) M], 63 +/- 4%; p < 0.02). Because both prostaglandins and lipoxygenase products of arachidonic acid have been shown to play a role in some EGF-mediated actions, we examined these possible mechanisms of EGF action. Meclofenamate, a cyclooxygenase blocker, and BW755c and baicalein, both lipoxygenase blockers, were studied. None of these agents altered EGF-mediated renin inhibition. EGF action has also been coupled to the stimulation of tyrosine kinase activity; therefore, we examined the effects of the tyrosine kinase inhibitors genistein and quercetin. Both genistein (10(-5) M) and quercetin (10(-5) M) abolished the inhibition of renin by EGF (control, 100 +/- 3%; EGF, 82 +/- 4%; EGF plus genistein, 110 +/- 7%; p < 0.01; EGF, 75 +/- 4%; EGF plus quercetin, 92 +/- 4%; p < 0.01).(ABSTRACT TRUNCATED AT 250 WORDS)


The Sevilla 16-17 third kit introduces a stunning design, officially launched today. It is inspired by the sands of Sevilla’s La Maestranza de Caballería bullring, bringing the city’s competitive heritage to the European stage.

Sevilla defender Coke said: “We’re very excited for the new challenges we face in Europe next season and we think this kit is great. We think the fans will really like the design. We all can’t wait to wear this on Europe’s biggest football stage.”

Sevilla 16-17 Third Kit

This is the new New Balance Sevilla 2016-17 third shirt.

The New Balance Sevilla 2016-17 third shirt combines a citrus base with red, used for all logos as well as the stunning collar.

The Sevilla crest on the front of the yellow Sevilla 16-17 third shirt is colored in monochromatic red.

Richard Wright, General Manager of New Balance Football said: “Sevilla FC has had incredible success in Europe and we’ve developed this kit in conjunction with the club to ensure they are ready for the next European challenge. It’s heavily influenced by the city and it completes a really strong kit collection for Sevilla for the 16/17 season.”

The Sevilla 16-17 third kit shorts and socks wil feature the same color as the shirt.

Do you like the new Sevilla 2016-2017 third jersey? Let us know in the comments below.


The present invention relates in general to the reclosable bag art, wherein bags made from sheet material and more particularly plastic film are equipped with reclosable extruded zipper means wherein one bag wall has adjacent to the bag opening a zipper strip which has profile means interlockable with complementary profile means on the opposite bag wall. More particularly, the invention relates to the zipper means and new and improved profile structure therefor.
The present invention is particularly directed to extruded zippers of the kind wherein a single generally hook-shaped profile rib on one zipper strip is releasably interlockable within a single generally channel shaped or grooved complementary profile having confronting spaced generally hook-shaped lip means releasably interlockable with the hook-shaped rib profile. A prior art example of such zipper structure is seen in U.S. Pat. No. 4,101,355.
The foregoing zipper structure is distinguishable from zipper structures of the multi-hook and groove type as exemplified in U.S. Pat. No. 4,430,070, wherein both of the releasably interlockable profile strips have similar profile rib hooks and complementary grooves shaped for mating with the profile hooks of the companion strip.
A problem encountered with the single rib and groove profile zipper strips that is not encountered with the multicomplementary rib and groove zipper strip resides in that whereas the multi groove profile presents a fairly stable, generally square or rectangular shape resisting deformation in handling, the single hooked rib profile has heretofor generally lacked such stability, though some attempts have been made to correct this problem, as in copending application U.S. Ser. No. 866,917 filed May 27, 1986.


Q:

Searching for the last instance of data in a list

I have an assignment to write a function that searches for the last instance of data (integer in this case) in a list. The function breaks with access violation on the line with if statement.
Node* List::SearchLast (int val)
{
    Node* pLast=NULL;
    Node* pNode=pHead;
    while (pHead!=NULL)
    {
        if (pNode->data==val)
            pLast=pNode;
        pNode=pNode->next;
    }
    return pLast;
}

I tried watching what happens with pNode.Here it becomes zero as it should.But then just passes the while statement. What am i doing wrong?

A:

Your while is an infinite loop, change to:
Node* List::SearchLast(int val)
{
    Node *pLast = NULL;
    Node *pNode = pHead;
    while (pNode != 0) {
        if (pNode->data == val) pLast = pNode;
        pNode = pNode->next;
    }
    return pLast;
}


Q:

Taking signs out of columns of matrix

My textbook presents the following matrix and asks to find its determinant:
$$d=\left|\begin{array} --1&1&-2\\-1&-1&-4\\-1&1&-7\end{array}\right|$$
And then says that it takes the negative sign from the first column and the negative sign from the third column so that the matrix becomes:
$$d=\left|\begin{array}11&1&2\\1&-1&4\\1&1&7\end{array}\right|$$
I understand that it is possible to multiply any row by -$1$, but if I were to multiply every row by $-1$ then the second column would have the signs inverted. Any hints on how this is possible to take the negative signs out of the matrix?

A:

Rather than premultiplying the matrix, try post multiplying the matrix by $diag(-1, 1, -1)$ to achieve that result.
$$\begin{bmatrix}-1 & 1&-2\\-1&-1&-4\\-1&1&-7\end{bmatrix}\begin{bmatrix}-1 & 0&0 \\ 0&1&0\\0&0& - 1\end{bmatrix}= \begin{bmatrix}1&1&2\\1&-1&4\\1&1&7\end{bmatrix}$$
In terms of determinant, we can perform elementary column operations. You can view it as taking transpose (transpose doesn't change the determiant), perform row operations, then taking transpose back again.


Q:

Questions of 'Designing for Performance' document at Android Developer site

In the Avoid Creating Objects section of the page Designing for Performance in the Android Developer documentation I read some paragraphs for which I am not able to visualize a code representation:
An array of ints is a much better than an array of Integers, but this also generalizes to the fact that two parallel arrays of ints are also a lot more efficient than an array of (int,int) objects. The same goes for any combination of primitive types.

How would these 'parallel arrays of ints' look like? Would it be something like instead of having a method with a signature such as getData():int[][] returning

   [a][b]
   [c][d]
   [e][f]

... it would be better to have two methods, each returning one of the 'columns' of data? as in:
getFirstDimensionData():int[]

   [a]
   [c]
   [e]

and a second one getSecondDimensionData():int[]

   [b]
   [d]
   [f]

What is an 'array of (int,int) objects? ... something like an array of objects of a-type-not-yet-defined that has two int member instances defining its state?

The immediate next paragraph:
If you need to implement a container that stores tuples of (Foo,Bar) objects, try to remember that two parallel Foo[] and Bar[] arrays are generally much better than a single array of custom (Foo,Bar) objects.
... makes me think that the author is making up some sort of notation. I guess my key question is: is the author of the page using this (somethingX, somethingY) notation to refer to an arbitrary class that 'wraps' the elements inside the parentheses?
Finally, is this a standard notation or just something the author of the page created by himself and omitted to explain?
Can anyone, please, shed some light? :)
Thanks in advance,
Y

A:

What they're saying is that
class foo {
    int a;
    int b;
}

foo[] bar;

Is slower than
int[] foo;

With foo[row*2] being a and foo[row*2+1] being b.
The notation (foo, bar) is trying to symbolize a class that contains foo and bar (like (a,b) in my above example).
I don't believe it's a standard notation, but it wouldn't be the first time I've been proven wrong.


A common ancestor for Candida tropicalis and dehydrogenases that synthesize antibiotics and steroids.
Candida tropicalis peroxisomes contain a 905-residue trifunctional enzyme with hydratase-dehydrogenase-epimerase activity that is important in fatty acid beta-oxidation. At its amino terminus are two tandem copies of an approximately 280 residue domain of unknown function. We provide evidence that this domain is homologous to oxidoreductases used for metabolizing sugars and synthesizing antibiotics and steroids such as estradiol, androstenedione, corticosterone, and hydrocortisone. The trifunctional enzyme shows no sequence similarity to the bifunctional hydratase-dehydrogenase found in animal peroxisomes and plant glyoxysomes, which are homologs of each other. We suggest that the C. tropicalis trifunctional enzyme and the animal and plant bifunctional enzymes have different ancestors.


Protect yourself from the elements from chin to finger tips, proving that you can be styling and cozy at the same time. An elegant cable panel and flattering shaping complement the generous cowl neck and extra-long sleeves.

Julie’s Sweater is worked in the round from the bottom up. Set-in sleeves are picked up from the armholes and worked down to the cuff, using short rows to form a sleeve cap. A cowl collar is picked up from the top edge and optional thumbholes are worked in the extra long sleeves.


Subscribe to our weekly newsletter and be kept up to date on the latest Linux releases. Your email address
will only be used for this newsletter, and you can unsubscribe at any time with a single click.

GhostBSD is a simple, user-friendly operating system, based on the legendary security and stability of FreeBSD operating system. Within the BSD community, FreeBSD itself is renowned for being exceptionally stable, robust, and lightweight operating system that provides an excellent base for Desktop. However, FreeBSD is aiming at servers, router, storage appliance, and it is also considered to be beyond the reach of those who lack the technical expertise required to use it.

GhostBSD provides all the benefits of the FreeBSD operating system combined with a focus on simplicity for newcomers. GhostBSD is ship with a simple installer, including MATE or XFCE desktop environments, pre-installed, with a graphical application to easily install software and update your system, codecs to play multimedia files is also pre-installed. GhostBSD is suitable for newcomers to BSD as well as *nix experienced users. With modest hardware requirements, GhostBSD is ideal for modern workstations, and single board computers 64-bit hardware.


The Television Critics Association gave out its annual TCA Awards Saturday night, and 'Mad Men,' 'Game of Thrones' and 'Modern Family' were among the winners.

'Friday Night Lights' was named Program of the Year, and several of the show's actors stood on the stage with executive producer Jason Katims as he gave a heartfelt speech about how hard it was to let the show go after five seasons.

'Game of Thrones' was named Outstanding New Program, 'Mad Men' won as Outstanding Drama and for the second year in a row, 'Modern Family' won as Outstanding Comedy.

The full list of winners, plus five awesome things that happened during the ceremony, is below.

'Mad Men' cast members John Slattery, Jon Hamm, Christina Hendricks and Elisabeth Moss turned up at the TCA Awards, as did creator Matthew Weiner and other writers and producers from the show. After the awards, Slattery happened to mention that he's directing the fifth episode of the season. He directed two episodes last season, and of course it was announced some time ago that Jon Hamm will be directing an episode of the show for the first time when it goes into production on Monday. (It'll be a while until we see those episodes. AMC hasn't given an exact date for 'Mad Men's' return -- the network has only said it would be back in "early 2012." Weiner said after the ceremony that he was told the show could return in March -- but that date wasn't certain.)

Much of the cast of 'Modern Family' turned up as well, but 'Game of Thrones' producer Carolyn Strauss picked up the award for the HBO show. She said that executive producers David Benioff and D.B. Weiss and the show's cast had wanted to be at the ceremony at the Beverly Hilton, but they were were in Belfast working on the second season of 'Thrones.' which went into production July 25.

It was a most enjoyable night, and here is a very subjective list of Five Awesome Things That Happened at the TCA Awards:

• Comedy legend Carl Reiner came to the ceremony, and he got a standing ovation when 'The Dick Van Dyke Show,' which he created, got the Heritage Award. In his acceptance speech, he told the story of how he came to write a comedy about his own life (he was a writer for a variety show who lived in New Rochelle, N.Y., and had a wife and two kids), and how the pilot he shot with himself as the star wasn't that great. His agent wanted to revive the project, but Reiner said he didn't want to fail twice with the same material. His agent's response, according to Reiner: "You won't fail, because we'll get a better actor to play you." That line got one of the biggest laughs of the night.

• Rose Marie, who also came to the ceremony, got a standing ovation when Reiner talked about her contributions to the show. When Rose Marie spoke, she said she was proud of having been the one to suggest Morey Amsterdam for the role of Buddy. (And yes, if you're wondering, the actress was sporting that famous black bow in her hair.)

• Oprah mocked herself! She couldn't be at the ceremony to receive her Career Achievement award, so she sent a pre-taped acceptance speech, in which she threatened to talk for 19 minutes -- one minute longer than the 18-minute Oprah filibuster that was delivered in response to a question at the January TCA press tour. Oh, Oprah, you jokester. Of course, she didn't speak that long -- her speech was short and sweet and gracious. (Yet by not coming, she denied me the chance to say, as drug-addled Liz Lemon once did, "I'm snitting next to Borpo!")

• Host Nick Offerman was a hoot and a half. He showed a short film about what it took for him to get into character -- it began with a boy who looked about 10 (allegedly that is who he is before he's been fully Offermanized). The boy ate mountains of bacon, drank a bacon shake and then worked on his car, all of which helped his burgeoning mustache grow. Finally he engaged in bare-knuckle boxing, which was the final step of the transformation in to the Full Offerman. Later, to show his range as an actor, he recited famous lines from movies ("You had me at hello.") in a very Ron Swanson-esque monotone. (After every recitation, which included Yoda's "Judge me by my size, do you?" speech, Offerman paused and deadpanned, "Powerful stuff.") He sang a funny song set to the tune 'Walk the Line' about reading mean commenters on the Internet (because he has a delicate ego, "he should stay offline"). And that was great, but Offerman doing Yoda lines had to be the high point of his hosting gig. It doesn't get much better than that. (Offerman needs to take that show on the road -- preferably to Comic-Con).

• Jason Katims took the stage with many of the writers and several cast members (including Connie Britton and Kyle Chandler) from 'Friday Night Lights' to accept the Program of the Year award (and they got a standing ovation as well). He spoke about how much critics had done to help the show survive, and he said he had run into people in recent months who said they hadn't watched the 'FNL' finale because they didn't want to say goodbye to that world. He said he'd walk away from those conversations thinking that those people should just go ahead and watch the finale and give themselves closure, but then he said he'd actually been afflicted by the same problem, in slightly different form. He said he spent so many weeks editing the show's series finale that movers actually came and started taking furniture and equipment and away from the editing room he was in. Eventually that development forced him to come up with the final cut of the finale.

Just the 'FNL' theme music playing as the cast and crew walked up to the stage had gotten many of the critics in the room misty, and by the time Katims ended his speech with "Texas forever," eyes were being dabbed all over the place.

Update: Critic Alan Sepinwall has even more highlights from the evening here.

Friday Night Lights is the best family show which we followed every week. Great acting by the cast and story by the writers. It was a welcome break from all the reality shows and cops & robbers. If another channel would pick up this show they would gain not only us and many more viewers. And that translate into more sponser's.

I think this is the wrong way to look at it. Given its ratings, any fan of FNL should be *extremely* grateful that we managed to get five* seasons of the show.

(*Four, if we pretend that Season 2 never happened...which we should.)

NBC initially tried airing the show on Tuesdays and Wednesdays before moving it to Friday. People just didn't watch. A lot of blame can often be laid at the feet of networks when it comes to how they handle quality programming, and maybe NBC more than any other. But this is one example where it should be applauded for keeping a quality show on the air despite all odds.


Quote From now on, we expect trading relationships to be fair and to be reciprocal.

YEARS OF UNFAIR TRADE PRACTICES: China has consistently taken advantage of the American economy with practices that undermine fair and reciprocal trade.

For many years, China has pursued industrial policies and unfair trade practices—including dumping, discriminatory non-tariff barriers, forced technology transfer, over capacity, and industrial subsidies—that champion Chinese firms and make it impossible for many United States firms to compete on a level playing field.

China’s industrial policies, such as its “Made in China 2025” plan, harm companies in the United States and around the world.

China imposes much higher tariffs on United States exports than the United States imposes on China. China’s average tariff rate is nearly three times higher than the average United States rate. Certain products are even more imbalanced, for instance the United States charges a 2.5 percent tariff on Chinese cars, while China currently maintains a 25 percent tariff on cars from the United States.

China has banned imports of United States agricultural products such as poultry, cutting off America’s ranchers and farmers from a major market for their goods.

China has dumped and unfairly subsidized a range of goods for the United States market, undermining America’s domestic industry. In 2018 alone, the Trump Administration has found dumping or unfair subsidies on 13 different products, including steel wheels, cold-drawn mechanical tubing, tool chests and cabinets, forged steel fittings, aluminum foil, rubber bands, cast iron soil pipe and fittings, and large diameter welded pipe.

In January 2018, the Trump Administration found that China’s overproduction of steel and aluminum, and the resulting impact on global markets, is a circumstance that threatens to impair America’s national security.

The United States has run a trade in goods deficit with China for years, including a $375 billion deficit in 2017 alone.

UNDERMINING AMERICAN INNOVATION AND JOBS: China has aggressively sought to obtain technology from American companies and undermine American innovation and creativity.

The cost of China’s intellectual property theft costs United States innovators billions of dollars a year, and China accounts for 87 percent of counterfeit goods seized coming into the United States.

United States Trade Representative’s (USTR) Section 301 investigation identified four of China’s aggressive technology policies that put 44 million American technology jobs at risk: Forced technology transfer; Requiring licensing at less than economic value; Chinese state-directed acquisition of sensitive United States technology for strategic purposes; and Outright cyber theft.

China uses foreign ownership restrictions, administrative review, and licensing processes to force or pressure technology transfers from American companies. China requires foreign companies that access their New Energy Vehicles market to transfer core technologies and disclose development and manufacturing technology. China imposes contractual restrictions on the licensing of intellectual property and technology by foreign firms into China, but does not put the same restrictions on contracts between two Chinese enterprises.

China directs and facilitates investments in and acquisitions of United States companies to generate large-scale technology transfer.

China conducts and supports cyber intrusions into United States computer networks to gain access to valuable business information so Chinese companies can copy products.

STANDING UP TO CHINA’S UNFAIR TRADE PRACTICES: President Trump has taken long overdue action to finally address the source of the problem, China’s unfair trade practices that hurt America’s workers and our innovative industries.

In January 2018, the President announced his decision to provide safeguard relief to United States manufacturers injured by surging imports of washing machines and solar products. This was the first use of Section 201 of the Trade Act of 1974 to impose tariffs in 16 years. These actions responded to injurious trade practices by China and other countries, including attempts to avoid legally imposed antidumping and countervailing duties. Following the decision, Whirlpool announced 200 new jobs in Ohio.

USTR and the Department of Commerce are working together to defend the right of the United States to continue treating China as a non-market economy in antidumping investigations until China makes the reforms it agreed to when it joined the World Trade Organization (WTO).

President Trump’s Administration has successfully litigated WTO disputes targeting unfair trade practices and upholding our right to enforce United States trade laws. In February 2018, USTR won a WTO compliance challenge against China’s unfair antidumping and countervailing duties on United States poultry exports and China announced the termination of those duties.

PROTECTING AMERICAN INNOVATION AND CREATIVITY: President Trump has worked to defend America’s intellectual property and proprietary technology from theft and other threats.


Q:

How do I implement matrix.Transpose() for my non-static Transpose function?

I have been given the following code in a test.cpp file to implement:
cout << "Case 2: the non-static Transpose function" << endl;
{
    double column[4] = {2, 1, 0, -1};
    double row[3] = {2, 0, -1};
    Matrix matrix = Matrix::Toeplitz(column, 4, row, 3);
    cout << "The original Matrix = " << endl;
    cout << matrix << endl;  //This part of the code works

    matrix.Transpose();  //How do I implement this?
    cout << "The transposed version = " << endl;
    cout << matrix << endl;
    cout << "Press any key to continue ..." << flush;
    system("read");
    cout << endl;
}

The way Matrix::Toeplitz(column, 4, row, 3) works is as follows:
Matrix Matrix::Toeplitz(const double* column, const int noOfRows, const double* row, const int noOfColumns){
    Matrix outT(column, noOfRows, row, noOfColumns);
    return outT;
}

So how would I implement matrix.Transpose()?  My code so far is as follows:
Matrix& Matrix::Transpose () {

double newrow[noOfRows];
for(int i=0; i<noOfRows; i++){
    int index = GetIndex(i,0);
    newrow[i] = data[index];
}

double newcol[noOfColumns];
for(int i=0; i<noOfColumns; i++){
    int index = GetIndex(0,i);
    newcol[i] = data[index];
}

Matrix outT(newcol, noOfColumns, newrow, noOfRows);
}

This has no effect on cout<<matrix<<endl;
I was thinking that Matrix outT(newcol, noOfColumns, newrow, noOfRows); should give new information (i.e. switching the column and row arrays) to the matrix object when implementing matrix.Transpose but it hasn't been working.
Is this the correct format Matrix& Matrix::Transpose () for implementing matrix.Transpose()?

A:

Matrix::Transpose can't return a reference to a locally declared object. This will lead to many problems.
See C++ Returning reference to local variable.
It must return by copy (then, function can be const, as current object is not being modified):
Matrix Matrix::Transpose() const
{
    double newrow[noOfRows];
    for(int i=0; i<noOfRows; i++){
        int index = GetIndex(i,0);
        newrow[i] = data[index];
    }

    double newcol[noOfColumns];
    for(int i=0; i<noOfColumns; i++){
        int index = GetIndex(0,i);
        newcol[i] = data[index];
    }

    return Matrix(newcol, noOfColumns, newrow, noOfRows);
}

Then, you use it this way:
Matrix transposed = matrix.Transpose(); // does not modify matrix object
cout << "The transposed version = " << endl;
cout << transposed << endl;

If returning Matrix&, you need to have your method transpose the current object and return it (return *this), only useful to help caller to chain many operators (like doing m.Transpose().Transpose() for instance).
Then, it could be (not tested):
Matrix& Matrix::Transpose()
{
    // backup old content
    double* backupData = new double[noOfRows*noOfColumns];
    memcpy( backupData, data, sizeof(double)*noOfRows*noOfColumns );

    // change matrix geometry
    int oldRowCount = noOfRows;
    noOfRows = noOfColumns;
    noOfColumns = oldRowCount ;

    // transpose matrix by copying from backup content
    for ( unsigned int line = 0; line < noOfRows ; ++line )
    {
        for ( unsigned int col = line; col < noOfColumns; ++col )
        {
            data[line * noOfColumns + col] = backupData[col * noOfRows  + line];
        }
    }

    delete [] backupData;

    return *this;
}

Then, you use it this way:
matrix.Transpose(); // modifies matrix object
cout << "The transposed version = " << endl;
cout << transposed << endl;


INTRODUCTION
============

Heart failure (HF) is increasingly prevalent worldwide and is associated with significant morbidity and mortality. The lifetime risk of developing HF is one in five at the age of 40 years \[[@R1]\]. Over 5 million individuals in the United States have HF, and more than 550, 000 are diagnosed annually \[[@R2]\]. It is becoming a burden in health care, which results in greater \$39 billion annual cost in North American and £716 million (1.8% of the total NHS budget) in the United Kingdom \[[@R3]\]. HF is a global epidemic, but clinical characteristics and treatment may vary for patients with HF across geographic regions \[[@R4]\].

In China, 4.2 million individuals have HF, and cardiovascular disease is the leading cause of death \[[@R5]-[@R6]\]. In Japan, 1.0 million individuals were estimated to have HF in 2005, and this figure is expected to rise to 1.3 million by 2035 \[[@R7]\].

During the last 20 years, changes in society and economy in East Asia countries, such as the aging of the population and medical progress, have led to changes in the epidemiology of HF \[[@R8]\]. Some region-specific, epidemiological studies have been conducted in East Asia, especially in China and Japan \[[@R9]-[@R26]\]. These research studies included the populations in both urban and rural areas, and investigated the epidemiology of different age-groups of patients.

The present review based on recent evidence, aims to update the epidemiology and management of HF in East Asian countries, including the prevalence/incidence, aetiology/comorbidities, treatment, prognosis, HF with preserved ejection fraction (HFPEF), and HF in older patients in East Asia.

SEARCH STRATEGY
===============

We searched PUBMED between 1 January 1990 and 30 June 2012 for articles concerned with the epidemiology of HF, risk factors for HF, drug treatment and prognosis of HF in populations in East Asia. The search terms were: HF, PEF, prevalence, incidence, aetiology, risk factor, drug management, prognosis, outcome, mortality, rehospitalization, China, Chinese, Japan, Japanese, Taiwan, Hong Kong, Korea, Mongolia, Malaysia, Singapore, Thailand, East Asia or the combination of these key words. We included epidemiological studies and clinical trials. Study populations of fewer than 720 people and duplicates were excluded. The articles meeting the eligibility criteria with full text were selected for data extraction. A total of 324 articles were retrieved by literature searches for reports on the epidemiology and treatment of HF in East Asia. Of these, 42 articles qualified for inclusion.

PREVALENCE AND INCIDENCE OF HF
==============================

The prevalence of HF was 6.7% in Malaysia, 4.5% in Singapore, and 1.3% in China respectively \[[@R16],[@R19],[@R20]\]. The reported incidence of HF in the Chinese population is 0.7 to 0.9 per 1000 \[[@R13],[@R15]\]. There are 1.8 million individuals with congenital cardiac abnormalities in China and 500, 000 new cases of HF every year \[[@R27]\]. A hospital-based study showed that the prevalence of Chinese patients with HF by age \< 40, 40 -- 49, 50 - 59, 60 -- 69, and 70 - 79 years was 6.7%, 10.7%, 18.8%, 23.5%, and 30.8% respectively (p\<0.01), while community-based studies demonstrated approximately doubling prevalence with each decade of age with 0.3% at age 35- 44 years, 0.6% at age 45-54 years, 1.3% at age 55-64 years, 2.6% at age 65-74 years, and 4.1% at age ≥75 years \[[@R11],[@R13]\]. On the other hand, the age of Chinese patients admitted for HF has significant reduced in recent years: 66.4 ± 14.1 years between 2000 and 2003, 64.9 ± 14.4 years between 2004 and 2006, and 64.2 ± 14.8 years between 2007 and 2010 (P \< 0.01) \[[@R11]\]. Age-adjusted hospital admission rates for HF increased by 38% in 1990s in Singapore \[[@R19]\], and hospital admissions for HF were about 35% higher in Malaysians than in Chinese in this study \[[@R19]\].

AETIOLOGY AND COMORBIDITIES OF HF
=================================

In recent decades, the ischemic aetiology for HF has increased in East Asia populations but not as greatly as in Western populations. In a USA national registry, out-patients with HF had a relatively higher proportion of ischaemic aetiology (52.6%, 71.1% and 72.9% for those aged \<65, 65-76 and \>76 years, respectively) and prior myocardial infarction (MI) (34.3%, 42.8% and 41.5% for the respective ages) \[[@R28]\]. Asian Americans were reported to have higher prevalence of HF after acute MI \[[@R29]\].

Aetiology and comorbidities of HF in East Asia are given in Figure [1](#F1){ref-type="fig"}. The proportion of coronary artery disease (CAD) ranged from 25% to 47% in HF populations in mainland China, Taiwan, Hong Kong, Malaysia, and Japan \[[@R9]-[@R26]\]. Hypertension was the most likely comorbidity in Japanese patients with HF, with the highest rate of 74% \[[@R25]\], however, the lowest rate of hypertension (19%) was in Malaysia \[[@R15]\]. The prevalence of hypertension in HF was 23%-47% in mainland China \[[@R9]-[@R11],[@R14]\], 38.3%-41.3% in Taiwan \[[@R15]\], and 37% in Hong Kong \[[@R10]\]. Moreover, valvular disease appears to be a less common aetiology of HF in East Asia, reported in 15% - 35% of patients with HF in most of countries, but only 4% in Malaysia \[[@R18]\]. Diabetes and atrial fibrillation (AF) are also common comorbidities, with 12%-36% and 21%-42% prevalence respectively among HF patients \[[@R9]-[@R26]\]. Furthermore, renal dysfunction and anaemia are risk factors of HF. A hospital-based study of patients with HF in Canada indicated that Chinese patients had the highest rates of renal disease compared to white populations \[[@R30]\].

Data about comorbidities of HF were consistent in one community-based study and three hospital-based studies in China \[[@R9]-[@R11],[@R14]\]. The most common comorbidities were CAD, hypertension, and diabetes mellitus. Dilated cardiomyopathy, valvular heart disease, and AF were common comorbidities in these Chinese populations with HF. A 10-year survey of hospital in-patients with HF showed rheumatic valvular heart disease was the most frequent cause in patients aged less than 40 years old and dilated cardiomyopathy was most likely in patients aged 40-59 years \[[@R11]\]. Renal dysfunction was also common in Chinese patients with CHF, and the China Heart Survey showed that 34.3% patients with CHF had chronic kidney disease \[[@R12]\]. AF was another main cause of Chinese HF patients in 1990s and early 2000s, with the rate of 20.6%-23.2%9.

Two Japanese studies (CHART-1, CHART-2) showed that an increasing trend towards ischemic aetiology (26.4%-47.1%) and comorbidities with diabetes (19.5-23.3%) and hypertension (47.4%-74.3%) in Japanese HF patients \[[@R20],[@R24],[@R25],[@R31]\], confirmed by the JCARE-CARD which revealed a prevalence of CAD in 32% of patients \[[@R22]\]. In the CHART-1 study between 2000 and 2005, CAD accounted for only 26.4% and the proportion of patients older than 65 years was 66% \[[@R20]\], but in the CHART-2 study between 2006 and 2010, CAD as a comorbidity increased to 47.1%, hypertension was 74.3%, and diabetes was 23.3% \[[@R22]\]. Additionally, JCARE-CARD showed that 57% patients with HF had anaemia \[[@R23]\], and the prevalence of AF was common (40%) in hospital-HF patients \[[@R21]\].

DRUG TREATMENT FOR HF IN EAST ASIA
==================================

In East Asian countries, diuretics were the most common treatment, used in between 50.9% and 96.9% of patients, followed by renin-angiotensin system (RAS) inhibitors (59.2-76.5%). Prevalence of angiotensin-converting enzyme inhibitor (ACEI) and angiotensin-2 receptor blocker (ARB) use was 31.5-52.2% and 30.9-44.4% respectively. Nitrate use was variable (23.3-80.0%), and β-blocker use varied from 19.5-49.0% in China, Taiwan, and Japan, to only 9.3% in Malaysia. Aspirin was used in 41.2% of HF patients in Taiwan, 47.2% in Japan, and 55.7% in Malaysia. Warfarin was reported to be used in 40.8% Japanese patients with HF \[[@R9]-[@R26]\] (Fig. **[2](#F2){ref-type="fig"}**). The relatively high rates of aspirin and warfarin usage may reflect the underlying high prevalence of CAD and AF in these populations, but population-based data are lacking.

Nitrates, diuretics, digitalis, ACEI, and β-blocker were the most commonly used agents in Chinese patients with chronic HF. Nearly half of patients with NYHA (New York Heart Association) Class III-IV were treated with the combination of ACEI and β-blocker, or diuretic, digitalis, ACEI and β-blocker. β-blocker therapy was most likely used in patients with NYHA Class II-III \[[@R14]\]. Although the administration of ACEI and β-blockers increased in recent years, their application in clinical practice did not achieve the level proposed by recent guidelines for HF management \[[@R32],[@R33]\]. Diuretics were the most commonly used drugs, in both younger (74·4%) and older (76·9%) patients in Taiwan, followed by ACEI and/or ARB and aspirin15.

β-blocker use increased in the last decade, whilst diuretics and digitalis decreased in Japanese cohorts with HF. The usage of RAS inhibitors and β-blockers for overt HF patients in the CHART-1 and CHART-2 studies increased from 69.1% to 72.3% and from 27.9% to 49.0%, respectively. In contrast, the usage rate of loop diuretics and digitalis decreased from 76.3% to 50.9% and from 48.1% to 23.5%, respectively.

New pharmacological therapies proposed by recent consensus guidelines for the management of HF \[[@R33]\], such as eplerenone and ivabradine, are less likely to be used in clinical practice in East Asia. There is very limited research data on these drugs in East Asian patients, who are under-represented in recent clinical trials in HF, e.g. only 8% of Asian patients in the SHIFT trial \[[@R34]-[@R35]\].

ANTITHROMBOTIC TREATMENT IN HF IN EAST ASIA
===========================================

The comorbidities related to HF (such as CAD, AF) lead to a high risk of thromboembolic events, including stroke, pulmonary embolism and peripheral arterial embolism, whilst coronary ischaemic events also contribute to the progression of heart failure. CAD as a major aetiology of HF has increased with the societal and epidemiologic transition in East Asian countries and the prevalence of AF among patients with HF was 21-42% in those countries \[[@R9]-[@R26]\]. In a Japanese cohort study, 15% of HF patients were reported to suffer stroke \[[@R23]\]. The rate of aspirin use was consistent across Japan, Malaysia, and Taiwan (41.2-55.7%) \[[@R15],[@R18],[@R23]\].

Warfarin was used in 40.8% patients with HF in Japan, while 35% patients had AF and 15% patients suffered the stroke in this cohort \[[@R23]\]. However, only 5.1-5.2% patients with HF used warfarin in Malaysia and Taiwan \[[@R15],[@R18]\]. There were limited epidemiologic data from East Asia to evaluate the prevalence of comorbidities related to HF which may increase risk of thrombosis. Further research is required to provide such data in order to inform use of antithrombotic treatment for stroke prevention in HF patients.

To date, four major randomized controlled trials of antithrombotic therapy in HF have been performed \[[@R36]-[@R39]\]. There was no significant overall difference in the composite end point of ischemic stroke, intracerebral hemorrhage, or death between warfarin and aspirin in WARCEF and there is no evidence to support routine anticoagulant therapy in HF patients without AF. As in other clinical trials, Asian patients are greatly under-represented.

DEVICE THERAPY
==============

Cardiac resynchronization therapy (CRT) and implantable cardioverter-defibrillator (ICD) therapies have not been widely used in treatment of HF in East Asia. CRT with defibrillator (CRT-D) became available in Japan in 2006 \[[@R40]\]. Large-scale epidemiological data regarding CRT-D, CRT-P and ICD are lacking in East Asian countries, and prospective data are required.

CARDIAC REHABILITATION AND TELEMONITORING IN HF
===============================================

There are scarce data on cardiac rehabilitation and telemonitoring or telemedicine in the management of HF in East Asia. A nationwide survey on the implementation of cardiac rehabilitation following acute myocardial infarction (AMI) showed that 0-9% of Japanese hospitals provided outpatient cardiac rehabilitation programs \[[@R41]\]. A Japanese study including 442 patients with AMI or coronary artery bypass graft surgery (CABG) suggested less favourable physiological and psychosocial outcomes in women than men \[[@R42]\]. Small studies suggest that short educational programmes in the outpatient setting can improve long-term outcomes in HF \[[@R43]-[@R44]\], but other studies show mixed results, and that cardiac rehabilitation may increase patient anxiety \[[@R45]-[@R47]\]. There may be a role for Chinese qigong exercise in cardiac rehabilitation \[[@R48]\].

PROGNOSIS AND OUTCOME OF HF
===========================

Total mortality from HF was 2.2-8.8% in China, Taiwan, Singapore, Thailand, and Japan \[[@R19],[@R22],[@R23],[@R49]\]. 30-day mortality was similar in mainland China and Taiwan at 5.3% and 3.9% respectively \[[@R15]\]. In a 15-year trend analysis (from 1993 to 2007) in China, mortality of young patients with HF reduced \[[@R9]\], however, 30-day mortality in those individuals aged over 80 years increased from 9.8% to 20.0%. In this Chinese population, the 30-day hospital mortality showed a downward trend in HF patients with CAD, decreasing significantly from 9.3% in 1993-1997 to 3.8% in 2003-2007 (P\<0.001) \[[@R50]\]. In another Chinese cohort with chronic HF, including 6453 patients with mean follow-up of 3 years, HF mortality was 30.1% in CAD, 44.9% in dilated cardiomyopathy (DCM), 36.2% in hypertensive heart disease (HHD), and 13.1% in rheumatic heart disease (RHD). Chronic systolic HF due to CAD, DCM and HHD carried a worse prognosis than that of RHD \[[@R51]\]. A higher hospital mortality rate was associated with an increased number of comorbidities10. Mortality from HF decreased from 7.3 per 10 000 in 1991 to 6.1 per 10 000 in 1998 in Singapore, and the decline was greater in women19. But, Indians and Malays had a worse outcome compared to the Chinese, probably due to higher mortality and HF readmission rates. A possible explanation for the worse outcomes in Indians could be due to the higher prevalence of diabetes mellitus and atherosclerotic vascular disease \[[@R52]\].

The rehospitalisation rate was 23.4% to 40% in three Japanese HF cohorts. In Thailand, the rehospitalisation rate within 30 days after discharge was 14.1% \[[@R50]\]. The length of hospital stay (LOS) \> 5 days was the predictor of early readmission. Prognosis of HF in East Asia is shown in Table **[1](#T1){ref-type="table"}**.

The prognosis and risk factors of HF in East Asia may be comparable with Western populations \[[@R53]\], although prospective data are lacking. Although survival after HF diagnosis has improved over time in North America, the death rate remains high, with nearly 50% of people diagnosed with HF dying within 5 years1. The reported 30-day in-hospital mortality of patients with HF ranged from 1.7-7.2% in North America \[[@R54]\]. The 30-day, 1-year, and 5-year case fatality rates after hospitalization for HF were 10.4%, 22%, and 42.3%, respectively \[[@R55]\]. Three-fourths of all HF hospitalizations are due to exacerbation of symptoms in patients with known HF. One-half of hospitalized HF patients experience readmission within 6 months \[[@R56],[@R57]\].

Consistent with the data from North America, diabetes was a significant prognostic risk factor in Japanese population. Age was also associated with higher risks of adverse outcomes. In one study, 70% patients were over 65 years, and women were mostly over 70 years \[[@R21]\]. Anaemia and lower haemoglobin were independently associated with long-term adverse outcomes, including all-cause death, cardiac death, and rehospitalisation \[[@R22]\]. Japanese HF patients with reduced eGFR had a higher incidence of all-cause death and re-admission because of worsening CHF \[[@R24],[@R26]\], whilst renal dysfunction was independently associated with advanced NYHA classes in a Chinese population \[[@R12]\]. Ventricular tachycardia or atrial fibrillation could impact the prognosis of patients with HF \[[@R58]\].

Advanced HF has an extremely high mortality and morbidity and is associated with poor quality of life. Future research is needed to identify high-risk individuals in order to improve patient outcomes.

HFPEF IN EAST ASIA
==================

The majority of data from East Asia regarding HFPEF is from Japanese studies. Several multicentre-studies demonstrated the prevalence of HFPEF from 26% to 45% in Japan \[[@R24],[@R59]\]. Patients with PEF (EF ≥50%) were more likely to be older and female. Hypertension and hypertrophic cardiomyopathy were more common in HFPEF, whilst MI or CAD were less common (JCARE-CARD data) \[[@R20]-[@R22]\]. Patients with HFPEF had higher prevalence of AF, and anaemia was also common (20-30%) and associated with higher mortality in HF patients. Renal failure and diabetes mellitus were the common comorbidities in patients with HFPEF. Calcium channel blockers (CCB) were used commonly in patients with HFPEF, whilst ACEI and β-blocker were less likely to be administered in those patients \[[@R60]\].

In-hospital mortality of HFPEF patients was 4.6% in Thailand and 2.2% in Singapore \[[@R50],[@R50]\]. CHART studies showed that all-cause mortality of Japanese patients with HFPEF at 1, 2, and 3 years was 7%, 16%, and 22%, respectively \[[@R24]\]. HFPEF patients had in-hospital mortality of 6.5%, which was not different from patients with reduced EF (\<40%) after multivariable adjustment (JCARE-CARD data) \[[@R22]\]. There was no significant difference in survival analysis for all-cause mortality or cardiac mortality between patients with reduced and preserved EF. Rehospitalization rates were 23.7% and 25.7% in reduced and preserved EF patients respectively, with no difference between groups (p=0.47).

ELDERLY HF IN EAST ASIA
=======================

The prevalence of HF increased in proportion with aging. Hospital-based studies showed that the prevalence of HF in patients aged 60 years was 23.5-30.8% in China. The annual incidence of HF was 14 per 1000 in men and 20 per 1000 in women older than 85 years in Hong Kong \[[@R16]\], and 22 per 1000 population in elderly people in Taiwan \[[@R15]\]. Hypertension was the most common cause of patients aged 60 years in a Chinese HF cohort, and multiple comorbidities were predominant in the elderly compared to the younger patients \[[@R8]\]. Therapy with nitrates, ACEI and ARB was most common in patients aged over 60 years compared to the patients aged less than 60 years. Combination therapy with diuretic, digitalis, ACEI, and β-blockers was common in the elderly with CHF. β- blocker use was used with equal frequency in elderly and young Chinese patients with HF. Patients greater than 85 years have a 25-fold higher risk of heart failure hospitalization, longer length of in-hospital stay, higher total medical expenditure and higher in-hospital mortality \[[@R15]\]. The 1-year mortality rate increased with age, reaching 40% for patients older than 85 years in Hong Kong \[[@R16]\]. The mortality of young patients with HF reduced during recent years in mainland China, but the mortality of very elderly patients (aged over 80 years) did not significantly decrease (Fig. **[3](#F3){ref-type="fig"}**).

The proportion of elderly population is high in Japan. The prevalence of HFPEF patients older than 65 years was 66% (CHART-1 study) \[[@R24]\]. 70% of patients with HF were over 65 years, and women with HF were mostly over 70 years in Japan \[[@R21]\]. Among patients aged over 70 years with HFPEF, valvular heart disease was the most frequent aetiology in CHART-1 study in the early 2000s. However, subsequent Japanese studies, including CHART-2, JCARE-GENERAL and JCARE-CARD, showed that hypertension in patients with HF increased in prevalence and became the most common comorbidity. Older age was also associated with the adverse outcome and 1-year mortality rate was 9.1% in HF patients with mean age of 74 years \[[@R21]\].

Further detailed data from individual studies regarding the epidemiology and management of HF in East Asia are shown in the Appendix.

CONCLUSION
==========

The prevalence of HF ranged from 1.3 to 6.7% in East Asian countries, with increasing prevalence with age. In terms of aetiology of HF, ischemic heart disease has increased and valvular disease decreased in this region during the last 20 years. Patients with HF and preserved EF were more likely to be older, female, and to have hypertensive heart disease. The mortality of HF remains high, and increasing age, diabetes, anaemia, renal dysfunction, and AF are associated with adverse outcome. Although the usage of ACEI, ARB, and β-blocker therapy has increased in recent years, diuretics, nitrates, and digitalis are the most commonly used drugs. The increased usage of ACEI, ARB, and β-blocker may reflect the increasing role of coronary artery disease as the aetiology of HF and increasing adherence to international guidelines. However, more evidence is needed in East Asian settings for novel drugs such as eplerenone and ivabradine. Antithrombotic treatment for prevention of thromboembolism in patients with HF in East Asia requires further research.

Declared none.

CONFLICT OF INTEREST
====================

The authors confirm that this article content has no conflict of interest.

Appendix
========

Table 1.Epidemiology and management of HF in East AsiaStudyCountry and SettingPopulation (n) Age, Mean (SD) Male, %Study Design and DatePrevalence/Incidence,% Mortality,% Rehospitalizaiton,%Aetiology/comorbidities, %DrugPei *et al*. 2011 \[6\]China7,319 CHF patients Age:59.6(16.9) Male:62.1%Retrospective 1993-200730-day mortalities: 5.3% Male: 5.4% Female: 5.2%1993-1998: Coronary heart disease: 37.2%\
Hypertension: 23.3%\
Diabetes mellitus: 12.3% Rheumatic vulvar disease:35.2%\
2003-2007: Coronary heart disease : 46.8%\
Hypertension: 46.7%\
Diabetes mellitus: 21.1%\
Rheumatic vulvar disease: 16.6%Yin *et al*. 2011\[7\]China Beijing (Urban)6,949 patients with HF Male:4344 Female: 2605Retrospective 1993-2007Coronary artery disease: 45.0%\
Hypertension: 38.7%\
Valvular disease:27.5%\
Rheumatic valvular disease:21.8%\
Nonrheumatic valvular disease: 5.7%\
Diabetes mellitus: 18.3%Yu *et al*. 2011\[8\]China Hubei (Urban, rural)12,450 patients Age: 62 (15) Male: 7166, 57.6%Retrospective 2000-2010 12 hospitals\<40 years: 6.67% (830/12 450)\
40-49 years: 10.7% (1336/12 450)\
50-59 years: 18.8% (2342/12 450)\
60-69 years: 23.5% (2920/12 450)\
70-79 years: 30.80% (3835/12 450)\
≥80 years: 9.53% (1187/12 450)\
NYHA class I: 0.60%,II: 23.20%,III:50.31%,IV: 26.50%Hypertension: 31.5%\
Coronary heart disease:28.2%\
Dilated cardiomyopathy: 26.6% Rheumatic valvular heart disease: 17.5% Aetiology: Age\<40: rheumatic valvular heart disease Age40-59 : dilated cardiomyopathy Age≥60 years: hypertensionDigitalis :47.5% Diuretics:68.8% ACEI:50.7% β-blocker:44.1% aldosterone antagonist :53.1%Liu, *et al*. 2011 \[9\]China1006 patients with CHF Age: 71.3(9.9) Male: 63.7%Retrospective 2005Chronic kidney disease: 34.3%Yang, *et al*. 2010 \[10\]China Xinjiang (6 localities, random sampling)8459 adults Age: 35 years overRetrospective Communities-basedHF: 1.26% Male: 1.61%; Female: 0.93% (p\<0.05) Age35- 44:0.29% Age45-54:0.60% Age55-64:1.32% Age65-74:2.55% Age≥75 years:4.10%Ma, *et al*. 2007 \[11\]China5189 patients with CHF Age: 62.9(13.4) Male: 49.5%Retrospective 1973-2002Aetiology Coronary heart disease:44.2% Rheumatic heart disease: 24.1% Pulmonary heart disease :19.0% Cardiomyopathy:4.8%Nitriate:80.0% Diuretics:71.8% Digitalis:68.1% ACEI:52.2% β-blockers:19.5%Tseng, *et al*. 2011 \[12\]Taiwan2692 patients with HF Age: 73(13) Male: 55%Retrospective Random sample of insurant 2005HF incidence: Age 20-60 years:88/100,000 Age≥65 years:21.8/100,000 In-hospital mortality: Total:3.9% Age 20-60 years: 2.7% Age≥65 years:4.2%Comorbidities: Age≥65 years: Hypertension:38.3% Infection:32.0% Ischemic heart disease:31.9% Age 20-60 years: Hypertension:41.3% Diabetes:35.5% Ischemic heart disease:29.8%Diuretics:76.3% ACEI:50.8% Aspirin:41.2% Digoxin:32.4% CCB:29.3% β-blockers:25.4% Clopidogrel:13.2% Warfarin:5.1%Hung, *et al*. 2000 \[13\]Hong Kong6203 patients with HF Male age: 72.4 Female age: 77.5 Male: 44%Retrospective 11 hospitals 1997Total incidence: 0.7 per 1000 Age\> 85: 20 per 1000(women); 14 per 1000 (men) Mortality:32%Sanderson, *et al*.1995 \[14\]Hong Kong730 patients with HF Male: 44%ProspectiveIncidence Women: 3.8/1000 Men: 3.0/1000Hypertension:37% Ischemic heart disease:31% Valvular heart disease:15%Chong, *et al*. 2003 \[15\]Malaysia1435 acute medical admissions Male: 62.9% Mean age: 63.6 yearsRetrospective Single-center6.7%(97/1435)Ischaemic heart disease: 49.5%(48) Hypertension: 18.6%(18) Dilated cardiomypathy: 4.1%(4) Valve disease: 4.1%(4) Anaemia:3.1%(3)Aspirin: 55.7%(54) Warfarin:5.2%(5) Diuretics:96.9%(94) β-blocker:9.3%(9) Digoxin:13.4%(13) Nitrate:54.6%(53) ACEI: 43.3%(42) Statin:2.2%(2)Ng, *et al*. 2003 \[16\]Singapore15774 admissions\
Age≥65 years\
Male: 46.6%\
Female: 53.4%Retrospective\
1991-1998HF:4.5%\
HF 1991: 1436\
HF 1997: 2457\
Mortality:2.5%Koseki, *et al*. 2003 \[17\]Japan721 patients with HFPEF (EF≥50%)\
Age≥20years\
Male: 67.1%Prospective multicenter1-year mortality:8%Tsutsui, *et al*. 2007 \[18\]Japan2685 HF patients Age: 74(12)\
Male: 46%Prospective multicenter 2004-2005Mortality: 6.3%\
All-cause death:\
Hospital-HF:6.7%\
GP-HF:5.9%\
Cardiac death:\
Hospital-HF:2.9%\
GP-HF:1.7%Aetiology:\
Ischemic: 30%\
Hypertension:35% Valvular:26% Cardiomyopathic:15%\
Comorbidities:\
AF: 40%\
Prior history of HF:83%ACEI:31.5%\
ARB:30.9%\
ACEI or ARB:59.2%\
ACEI and ARB:3.3%\
β-blocker:27.4% Diuretics:62.0% Digitalis:43.0%\
CCB: 37.1%Hamaguchi, *et al*. 2009 \[20\]Japan\
164 hospitals2675 patients with HF\
Age: 71.5(13)\
Male: 58.1%Prospective\
2004-2007\
Average follow-up:2.4 years57% patients with HF had AnemiaTsuchihashi-Makaya, *et al*. 2009 \[19\]Japan1692 patients with HF\
Age ≥65: 69.3%\
Male: 59.7%Prospective\
2004-2007\
Average follow-up: 2.4 yearsAetiology:\
Reduced EF:\
Ischemic:39.8%\
Hypertensive:21.6%\
Cardiomyopathic, dilated:36.3%\
Preserved EF:\
Ischemic:25.4%\
Hypertensive:44.3%\
Cardiomyopathic, dilated:5.1%\
(p\<0.001)\
Comorbidities:\
Reduced EF:\
Hypertension:50.4%\
Hyperlipudemia:28.8%\
Atrial fibrillation:24.5%\
Preserved EF:\
Hypertension:68.3%\
Hyperlipudemia:22.8%\
Atrial fibrillation:38.3%\
(p\<0.005)Shiba, *et al*. 2008 \[21\]Japan1,278 HF patients Age: 68.3(13.4) Male: 66%Prospective 2000-2005 Mean follow-up:3.5 yearsAetiology: Coronary artery disease:25.4% Valvular heart disease: 26.4% Non-ischemic cardiomyopathy:28.6% Comorbidities: Hypertension:47.4% Diabetes:18.9% Dyslipidemia:16.7% AF:41.8%Shiba, *et al*. 2008 \[21\]Japan1,278 HF patients Age: 68.3(13.4) Male: 66%Prospective 2000-2005 Mean follow-up:3.5 yearsAetiology: Coronary artery disease:25.4% Valvular heart disease: 26.4% Non-ischemic cardiomyopathy:28.6% Comorbidities: Hypertension:47.4% Diabetes:18.9% Dyslipidemia:16.7% AF:41.8%Shiba, *et al*. 2011 \[22\]Japan10,219 HF patients Age: 68.2(12.3) Male: 69.8%Prospective Multicenter 2006-2010Aetiology: Coronary artery disease: 47.1% Comorbidities: Hypertension:74.3% diabetes:23.3%RAS inhibitors: 72.3% Diuretics :50.9% β-blockers:49.0% Digitalis23.5%Hamaguchi, *et al*. 2011 \[23\]Japan2,675 patients with AF Age: 71(13) Male: 59.7%Prospective 2004-2005 Average follow-up:2.1 yearsNYHA class I:35.2%, II:55.2%, III:6.0%, IV: 3.6% All-cause death 14.7%(247) Cardiac death 8.8%(148) Rehospitalization 33.1%(557)Aetiology: Ischemic:32% Valvular:27.7% Hypertensive:24.6% Dilated cardiomyopathy:18.2% Comorbidities: Hypertension：52.9% Hyperuricemia:46.8% Diabetes mellitus：29.9% Dyslipidemia:24.8% Prior stroke:15.0% COPD:6.7% Smoking:37.7% Prior MI:26.9% AF:35.2%Aspirin: 47.2% Warfarin:40.8% Diuretics:88.2% β-blocker:48.6% Digitalis:30.9% Nitrate:23.3% ACEI: 37.4% ARB:44.4% ACEI/ARB:76.5% CCB:25.2% Statin:19.9%[^1]

![Aetiology and comorbidities in studies of HF in East Asia. CAD: coronary artery disease. AF: atrial fibrillation.](CCR-9-112_F1){#F1}

![Drug treatment or HF in East Asia. CCB: calcium channel blocker; ACEI: angiotensin-converting enzyme inhibitor; ARB: angiotensin- converting enzyme receptor inhibitor; RAS: renin-angiotensin system.](CCR-9-112_F2){#F2}

![Prevalence and mortality of HF in Chinese population with age.](CCR-9-112_F3){#F3}

######

Prognosis of HF in East Asia

  Author                          Country     Patients (n)   Year        30-day Mortality   1-year Mortality   Mortality   Rehospitalization
  ------------------------------- ----------- -------------- ----------- ------------------ ------------------ ----------- -------------------
  Pei *et al*. \[[@R5]\]          China       7319           1993-2007   5.30%              \*                 \*          \*
  Tseng *et al*. \[[@R11]\]       Taiwan      2692           2005        3.90%              \*                 \*          \*
  Ng *et al*. \[[@R15]\]          Singapore   15774          1991-1998   \*                 \*                 2.50%       \*
  West *et al*. \[[@R39]\]        Singapore   1029(HFPEF)    2005-2009   \*                 \*                 2.20%       \*
  West *et al*. \[[@R39]\]        Thailand    989(HFPEF)     2005-2009   \*                 \*                 4.60%       \*
  Koseki *et al*. \[[@R16]\]      Japan       721(HFPEF)     2003        \*                 8%                 \*          23.4%
  Tsutsui *et al*. \[[@R17]\]     Japan       2685           2004-2005   \*                 \*                 6.30%       40%
  Hamaguchi *et al*. \[[@R19]\]   Japan       2675           2004-2005   \*                 \*                 8.8%        33.1%

HFPEF: Heart failure with preserved ejection fraction. \*: Non-available data.

[^1]: GP: general practice; COPD: chronic obstructive pulmonary disease; CHF: chronic heart failure; HFPEF: heart failure with preserved ejection fraction; CCB: calcium channel blocker; ACEI: angiotensin-converting enzyme inhibitor; ARB: angiotensin-converting enzyme receptor inhibitor; RAS: renin-angiotensin system


Q:

Finding Galois group of a separable polynomial

The question asks the following:

Let $E$ be the splitting field of $x^4-10x^2-20$ over $\mathbb{Q}$. Find $Gal(E/\mathbb{Q})$.

Since this polynomial is irreducible by Eisenstein's criterion, we know that the Galois group acts transitively on the set of four distinct roots of this polynomial. However, after that, I am very lost as to how should I proceed. One approach which I thought of is to check the transitive subgroups of $S_4$, but that seems to make things more complicated. I would appreciate hints on this problem.

A:

Let $\alpha_1=\sqrt{5+3\sqrt{5}},\alpha_2=\sqrt{5-3\sqrt{5}}$, then the splitting field of $f$ is $E=\mathbf{Q}(\alpha_1,\alpha_2)$. As $f$ is irreducible, we know that $\alpha_1$ has degree $4$ over $\mathbf{Q}$. In particular, $\mathbf{Q}(\alpha_1)$ and $\mathbf{Q}(\alpha_2)$ are quadratic extensions of $\mathbf{Q}(\sqrt{5})$. They are equal if and only if $\alpha_1\alpha_2=\sqrt{-20}\in \mathbf{Q}(\sqrt{5})$, which is not the case (see comment in this answer). Now, $\alpha_2$ is a zero of $X^2+\alpha_1^2-10\in \mathbf{Q}(\alpha_1)[X]$, so $$|\operatorname{Gal}(E/\mathbf Q)|=[E:\mathbf{Q}]=[\Omega:\mathbf{Q}(\alpha_1)][\mathbf{Q}(\alpha_1):\mathbf{Q}]=2\cdot 4=8.$$
As $D_8$ is the only transitive subgroup of order 8 of $S_4$, we conclude $\operatorname{Gal}(E/\mathbf{Q})\cong D_8$.


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Educational wooden toys - it is an ideal toy for young children. They are happy to take on, as soon as they are able to withstand the tests which they are subjected to little pranksters. In this case you can be sure that the toy does not bring them any harm. Quality toys for children are covered by health safe for colors, so even if the baby will try them "to the tooth", nothing will happen to him. Large wooden toy expressive, whose main goal - prompting the baby to make their first "steps". It is great to push forward on any surface and it does not matter whether it is a smooth floor or carpet. Inside rattle plates, gently tapping the side of each other . And to reach the cherished goal can be great to make a noise, try to touch the ball inside and rolled on itself. You can play with your mother, "Who faster", can be used katalochku and for older children in the game of words, when meeting with the guests - just let your imagination run wild! Toy wonderful polished, very robust and reliable. Size: Length: 11 cm Diameter 7 cm

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