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Q: Efficicient algorithm to check if $az+1=(xz+1)(yz+1)$ Given two positive integers $a$ and $z$ with $z$ prime, consider the problem of determining whether the integer $az+1$ can be factored as $az+1=(xz+1)(yz+1)$, where $x, y$ are positive integers and $xz+1$ is prime. This problem can be solved by checking if $yz+1 \ | \ az+1$ for some integer $y$, $yz+1 \le \sqrt{az+1}$.
Trial division however is too slow when $a/z$ is large. Is there an efficient algorithm for solving this problem or a particular case. (Note that we are not interested in finding factors of $az+1$, only to determine if it can be factored this way).
A related but different question is here Prove that the diophantine equation $(xz+1)(yz+1)=az^{3} +1$ has no solutions in positive integers $x, y, z$ with $z>a^{2} +2a$.

A: I'll give a heuristic argument for the following claim: any algorithm that solves this problem cannot be faster than factoring $az+1$.
From there it is well known what the asymptotic complexity is, plus what algorithms are actually faster when implemented in a programming language and so on.
Consider the first few cases with small $z$:
$z=2$
The algorithm returns true if and only if $az+1$ is composite. I proved this a couple days ago here.
$z=3$
Let the factorization of $az+1$ be the following:
$$az+1=\prod_i p_i^{a_i}\prod_i q_i^{b_i}$$
Where $p_i\equiv 1 \mod 3$ and $q_i\equiv 2 \mod 3$. We have that $\sum b_i \equiv 0 \mod 2$ since $az+1\equiv 1 \mod 3$. The factorization is impossible again if $az+1$ is prime but also in the case where $\sum b_i = 2$ and there are no $a_i$ i.e. when it is the product of two primes $\equiv 2 \mod 3$. It's easy to see that all other cases allow you to group the primes into two factors that are $\equiv 1 \mod 3$, all of which get you a valid factorization.
The case $z=4$ is very similar to the previous one. But when $\varphi(z)$ starts getting larger it gets more complicated. The case $z=5$ is as follows:
Let
$$az+1=\prod_i p_i^{a_i}\prod_i q_i^{b_i}\prod_i r_i^{c_i}\prod_i s_i^{d_i}$$
Where the classes of prime numbers are those congruent to $1,2,3,4$ mod 5 respectively. Let also $A=\sum_i a_i$ and the same for the other three residue classes. Then $az+1$ is of the form $(5x+1)(5y+1)$ when all of the following are false:

*

*It is prime;

*$A=C=D=0$ and $B=4$;

*$A=D=0$ and $B=C=1$;

*$A=C=0$ and $B=2$ and $D=1$;
As you can see, these are increasingly complicated statements about the prime factorizations of $az+1$. So I don't think your question can be answered faster than actually factoring it.

A: As GerryMyerson writes, "$az+1=(xz+1)(yz+1)=xyz^2+xz+yz+1,\ a=xyz+x+y,$ so a restatement of the question is whether, given $a,z,$ there is an efficient way to decide whether there exist $x,y$ such that $a=xyz+x+y.$"
Then, a restatement of this is whether, given $a,z$ and $a=qz+r,$ there exist $x,y$ such that $xy=q$ and $x+y=r.$ But this corresponds to solving $x(r-x)=q$ which has solutions
$$
2x = r \pm \sqrt{r^2-4q}.
$$
Thus, we need to decide whether $r^2-4q$ is a square number, say $s^2.$
Now, $r^2-4q=s^2$ is equivalent to $(r+s)(r-s)=4q$ which means that we need to find all factorizations of $4q.$

A: Taking in account GerryMyerson comment, easily to get the system in the form of
\begin{cases}
az+1=(xz+1)(yz+1) = 1+ z(x+y) + z^2xy\\
a=xyz+x+y=(xz+1)y+x=(yz+1)x+y\\
x\le y\\
a,x,y,z\in\mathbb N,\tag1
\end{cases}
where $\;x,y\;$ are unknowns and $\;a,z\;$ are parameters.
Denote $\;s=x+y,\;$ then
$$4(az+1) = 4+4zs+z^2s^2-z^2s^2+4z^2x(s-x) =(zs+2)^2-z^2(s-2x)^2,$$
$$4(a-s) = z(s^2-(s-2x)^2),$$
$$a = zx(s-x)+s,$$
\begin{cases}
y=s-x\\[4pt]
s\in\left\{z\left\lfloor\dfrac{2\sqrt{1+az}-2}{z^2}\right\rfloor+(k-1)z+(a \mod z),\; k\in\mathbb N\right\}\cap\{1,2\dots a\}\\[4pt]
2x=s-\sqrt{s^2-\dfrac{4a-4s}z}.\tag2
\end{cases}
Therefore, the integer variable $\;s\;$ should change the values with the step $\;z.\;$
If $\;z\;$ is too small, then can be used analysis on the unused simple residue classes.
For example, the parity anlysis of $(1)$ gives the next additional constraints.

*

*If $\;\mathbf{(2\!\not|\;z)\wedge(2\!\not|\;a)},\;$ then $\;(2\,|\;az+1),\;(2\!\not|\;x)\vee(2\!\not|\;y).\;$

*If $\;\mathbf{(2\!\not|\;z)\wedge(2\,|\;a)},\;$ then $\;(2\!\not|\;az+1),\;(2\,|\;x)\wedge(2\,|\;y).\;$

*If $\;\mathbf{(2\,|\;z)\wedge(2\!\not|\;a)},\;$ then $\;(2\!\not|\;az+1),\;(2\,|\;x+y).\;$

*If $\;\mathbf{(2\,|\;z)\wedge(2\,|\;a)},\;$ then $\;(2\!\not|\;az+1),\;(2\!\,\not|\;x+y).\;$
Similar schemes allow to improve the computational complexity of the algorithm.
However, there are not a good simple algorithm for big numbers.

redpajama_set_name: RedPajamaStackExchange


CHICAGO (WLS) -- Charges were filed late Friday in a deadly hit-and-run that happened almost six years ago.
Police say Carlos Castillo, 28, has been identified as the driver who struck and killed 25-year-old Rachel Gilliam in the 4300-block of North Lincoln in November 2009.
Castillo is charged with one felony count of leaving the scene of an accident involving a death.


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Iran 'disqualifies' EU from talks
Filed under: Latest, Politics News — Tags: Ahmadinejad, Britain, China, diplomatic, elections, EU, France, Germany, Iran, Libya, nuclear, Russia, United States — expressyoureself @ 6:09 pm
Britain has denied allegations of involvement in the Iranian riots
The EU is no longer qualified to take part in talks on Iran's nuclear programme, Iran's military chief says.
Maj Gen Hassan Firouzabadi, Iran's chief of staff, accused the EU of "interference" in riots which followed June's disputed presidential elections.
The EU has for the past few years been involved in talks to try to persuade Iran to abandon its nuclear ambitions.
EU states, meanwhile, are considering withdrawing their ambassadors from Iran in a growing diplomatic row.
Britain has proposed the step, after Iran detained nine of its embassy staff in Tehran last week. Eight have since been released.
The diplomatic correspondent says the diplomatic signalling seems to have had an effect, and EU governments will now be looking for the remaining detained staff member to be released.
He adds that the problem more generally is that any external pressure tends to be used by the Iranian government to bolster its own narrative of outside interference.
In the wake of mass street protests against President Mahmoud Ahmadinejad's relection, Iran's Basij militia has called for the defeated opposition candidate Mir Hossein Mousavi to be prosecuted.
'Nine offences'
The semi-official Fars news agency said the militia – a volunteer force of Islamic government loyalists – had accused Mr Mousavi of nine offences, including propaganda against the state, and complicity in disrupting national security.
It is our historic responsibility to continue our complaint and make efforts not to give up the rights of the people
Mir Hossein Mousavi
Iranian presidential candidate
In a letter to the chief prosecutor, the militia said Mr Mousavi had been involved in the street protests, in which about 17 protesters and a number of militia members were killed.
The Iranian presidential elections, held on 12 June, returned President Ahmadinejad to power for a second term in office.
But the opposition disputed the result, saying the vote had been rigged.
Both Mr Mousavi, and another defeated opposition candidate Mehdi Karoubi, have issued statements on their websites describing any government led by President Ahmadinejad as "illegitimate".
Mr Mousavi wrote: "It is our historic responsibility to continue our complaint, and make efforts not to give up the rights of the people."
And he called for the release of the "children of the revolution" – a reference to the hundreds of reformist figures detained during the unrest.
'Hostility'
In his statement, reported by Fars, army chief of staff Gen Firouzabadi accused some EU members of supporting the riots, and demonstrating their hostility to the Iranian people.
The EU has yet to comment, but earlier urged Iran to avoid conflict with the international community.
Previously, Iran had aimed its allegations at Britain in particular and at the weekend detained the local employees of its embassy. Five were released on Monday, and a further three on Wednesday.
Iran says it is enriching uranium for power plants, but some Western countries suspect it plans to build nuclear weapons.
Three EU countries – Britain, France and Germany – have led negotiations over Iran's nuclear programme, along with the United States, Russia and China.
'Non-negotiable'
At their last talks, they offered Iran a package of incentives if it would stop its nuclear activities.
But Iran insists that its right to enrich uranium is non-negotiable.
In a separate development, officials in Tehran said President Ahmadinejad had cancelled his trip to an African Union summit in Libya.
Mr Ahmadinejad's office did not give any reason for the decision.
Libya compensates terror victims
Filed under: Business News, Latest, Politics News — Tags: $, America, Art, August, barack obama, Berlin, Berlin disco, blogging, books, Business, Christianity, Condoleezza Rice, culture, David Welch, disco, economics, economy, education, election, election-2008, entertainment, events, faith, family, fashion, film, food, friends, God, history, home, humor, inspiration, john mccain, Libya, life, Lockerbie, Lockerbie bombing, love, McCain, Media, movies, music, nature, news, Obama, people, personal, philosophy, photography, photos, pictures, poetry, Politics, random, relationships, religion, Reviews, Sarah Palin, school, sports, state department, technology, terror attack, thoughts, Travel, Tripoli, TV, US, US diplomat, US secretary of state, US secretary of state Condoleezza Rice, UTA, victims, video, videos, Washington, weapons of mass destruction, writing — expressyoureself @ 5:17 am
Most of those killed in the Lockerbie bombing were Americans
Libya has paid $1.5bn into a US compensation fund for relatives of victims of terror attacks blamed on Tripoli, the US state department says.
The fund was agreed in August to settle remaining lawsuits in the US.
The attacks include the 1988 Lockerbie bombing that killed 270 people and the 1986 bombing of a Berlin disco which killed three and wounded more than 200.
Under the deal, Libya did not accept responsibility for the attacks, but agreed to compensate victims.
It is the final step in a long diplomatic process, which has seen Libya come back into the international fold.
US contribution
The first $300m Libyan payment into the fund was made on 9 October, shortly after an historic visit to Tripoli by US Secretary of State Condoleezza Rice.
Its second payment of $600m was received on Thursday and a final installment of $600m was made on Friday, said David Welch, the US diplomat who negotiated the settlement.
In exchange, President Bush has signed an executive order restoring the Libyan government's immunity from terror-related lawsuits and dismissing pending compensation cases in the US, the White House said.
The US and Libya agreed to the compensation deal in August
Our correspondent says it is unclear why it took so long for the money to be paid into the fund.
She adds that there may have been contributions by American companies lured by business opportunities in Tripoli and keen to expedite the process of normalising ties.
The US State Department, however, has insisted that no money from the American taxpayer will be used for the US portion of the fund.
Libya has already paid the families of Lockerbie victims $8m (£4m) each, but it owes them $2m more.
The fund will also be used to compensate relatives of seven Americans who died in the bombing of a French UTA airliner over Chad in 1989.
In 2004, Libya agreed to pay $35m in compensation to non-US victims of the 1986 Berlin bombing.
In the same year, relatives of non-US victims of the UTA bombing accepted a payment of $1m each from the Gaddafi International Foundation for Charity Associations.
Relations between Libya and the US improved in 2003 when Tripoli stopped working on weapons of mass destruction.
The decision led to the restoration of US diplomatic ties with Libya in 2006.
In turn, it was removed from America's list of countries sponsoring terrorism.
Tourist kidnappers 'shot dead
Filed under: Business News, Latest, Politics News, Travel — Tags: Chad, Egypt, European, European tourists, German, Gilf al-Kebir, Libya, Sawarmy Khaled, Sudanese, tourist, tourists — expressyoureself @ 5:37 pm
Tourist kidnappers 'shot dead'
Sudanese officials say their forces have shot and killed six of the kidnappers who abducted a group of European tourists in Egypt last week.
Two other suspected kidnappers have been taken into custody, but the tourists themselves remain in captivity in Chad, officials in Sudan said.
The hostages – 11 tourists and eight Egyptian guides – were taken on 19 September and are said to be unharmed.
They include five Germans, five Italians and a Romanian.
A spokesman for Sudan's military told The Associated Press that the kidnappers were killed following a high-speed desert chase.
Sawarmy Khaled said the missing Europeans, who were abducted in Egypt but thought to have been taken first to Sudan and are now being held in neighbouring Chad.
Leader 'dead'
Mr Khaled said the Sudanese military forces were near the Libyan border when they encountered a white sports utility vehicle carrying eight armed men, AP reported.
Gilf al-Kebir is a popular destination for adventurous tourists
"The armed forces called for it to stop, but they did not respond and there was pursuit in which six of the armed men were killed," he said, adding that the group's leader, who he identified as a Chadian named Bakhit, was among the dead.
The remaining two gunmen were captured and they confessed to being involved in kidnapping the tourists and their guides, who were on desert safari in southwest Egypt.
The tourists, who were seized while near Gilf al-Kebir in Egypt, are being held by 35 other gunmen in the Tabbat Shajara region of Chad, Mr Khaled added.
The shootings come as negotiations continue for the release of the hostages.
An Egyptian official told the AFP news agency that the kidnappers and German negotiators had agreed to a deal but that "negotiations were still ongoing to work out details."
The kidnappers have demanded that Germany take charge of payment of an $8.8m ransom.
German officials have declined comment.
Rice making historic Libya visit
Filed under: Latest, Politics News — Tags: abandoned weapons of mass destruction, Algeria, America, Assistant Secretary of State Paula DeSutter, avid Welch, Col Gaddafi, Condoleezza Rice, diplomacy, Gaddafi, historic Libya visit, Libya, Libya visit, Lisbon, Lockerbie, Lockerbie aircraft bombing, Morocco, Ms Rice, Muammar Gaddafi, news conference in Lisbon, North African country, Paula DeSutter, political, Portugal, Reuters, Rice, Rice making historic Libya visit, state department, terrorism, Tripoli, Tunisia, United States, US Assistant Secretary of State for Near Eastern Affair, US secretary of state, US secretary of state Condoleezza Rice, US state department, US-Libyan relations, visit, visits, weapons of mass destruction, west — expressyoureself @ 5:31 pm
The US state department described the visit as a "new chapter" in relations
US Secretary of State Condoleezza Rice hailed as "historic" her visit to Libya to meet its leader Muammar Gaddafi.
But she pointed out the "suffering" caused by the North African country's long stand-off with the West.
Libya was on the US state department list of sponsors of terrorism until 2003, when it abandoned weapons of mass destruction and renounced terrorism.
Ms Rice will be the first US secretary of state to visit Libya since 1953.
"It is a historic moment and it is one that has come after a lot of difficulty, the suffering of many people that will never be forgotten or assuaged," Ms Rice told a news conference in Lisbon, Portugal, before leaving for Libya.
Her trip will also include visits to Tunisia, Algeria and Morocco.
But the visit could be overshadowed by Libya's failure so far to honour a deal offering compensation to families of victims of the 1988 Lockerbie bombing.
Six years ago, such a visit would have seemed far-fetched, but diplomacy and political will have overcome the obstacles.
The US State Department have described it as a "new chapter" in relations between the two countries, following on from the restoration of diplomatic ties in 2006.
'Way forward'
Earlier this month, Libya agreed to pay compensation to families of the victims of the Lockerbie aircraft bombing, for which it formally accepted responsibility in 2003.
The deal includes compensation for Libyan victims of the United States' retaliatory bombing raid over Libya in 1986.
Ms Rice's visit was partly intended to be a reward for successful completion of the deal, but Libya has not yet transferred the promised hundreds of millions of dollars into a humanitarian account.
The US Assistant Secretary of State for Near Eastern Affairs, David Welch, told Reuters that he was optimistic the transfer would happen soon but that Ms Rice would press Libya on this issue.
Col Gaddafi has stopped short of referring to America as a friend, but in a televised speech this week he said improved relations were a way for both countries to leave each other alone.
Assistant Secretary of State Paula DeSutter told a briefing in Washington on Thursday that the visit would show other countries they have "a way forward" if they change their behaviour and co-operate with the US.
Our correspondent says that although the visit is largely symbolic diplomacy, many in Libya hope that US-Libyan relations will only improve in the long-run.
What do you think about Condoleezza Rice's visit to Libya? Send us your comments
Italy seals Libya colonial deal
Filed under: Latest — Tags: Africa, African country, America, American, ancient statue of Venu, Benghazi, Benghazi palace, Berlusconi, Coastal motorway, Col Gaddafi, colonial, colonial deal, colonial era, colonial master, Condoleezza Rice, Cyrene, Deal, diplomatic, diplomatic cold, Egypt, Egyptian, Europe, former Ottoman territory, Gaddafi, gesture, goodwill gesture, infrastructure projects, Italian, Italian colonial administration, Italian Prime Minister Silvio Berlusconi, Italy, Italy seals Libya colonial deal, Libya, Libyan leader Col Muammar Gaddafi, Motorway, Mr Berlusconi, Muammar Gaddafi, occupied, Ottoman, pay Libya $5bn, Reuters, Rice, Rome, Silvio Berlusconi, states, Tripoli, Tunisia, Tunisian, US secretary of state, US secretary of state Condoleezza Rice, Venus, Venus of Cyrene, weapons, weapons of mass destruction — expressyoureself @ 4:40 pm
Mr Berlusconi (left) and Col Gaddafi shook hands
Italian Prime Minister Silvio Berlusconi has signed an agreement to pay Libya $5bn as part of a deal to resolve colonial-era disputes.
Libyan leader Col Muammar Gaddafi said the settlement signed in the city of Benghazi opened the door to partnership between the two states.
Mr Berlusconi said the deal, which sees the money being released over 25 years, ended "40 years of misunderstanding".
Libya was occupied by Italy in 1911 before becoming a colony in the 1930s.
The former Ottoman territory became an independent country in 1951.
This is the first African country to be compensated by a former colonial master.
The question is, she adds: will this latest move set precedents for other former African countries to follow suit?
Coastal motorway
Mr Berlusconi explained that $200m would be paid annually over the next 25 years through investments in infrastructure projects, the main one being a coastal motorway between the Egyptian and Tunisian borders.
The headless statue was displayed when the two leaders met
There will also be a colonial-era mine clearing project.
As a goodwill gesture, Italy also returned an ancient statue of Venus, the headless "Venus of Cyrene", which had been taken to Rome in colonial times.
The settlement was a "complete and moral acknowledgement of the damage inflicted on Libya by Italy during the colonial era", the Italian prime minister said.
"In this historic document, Italy apologises for its killing, destruction and repression against Libyans during the colonial rule," Col Gaddafi said for his part.
The agreement was signed in the Benghazi palace which once housed the Italian colonial administration, Reuters news agency reports.
Rome and Tripoli have spent years arguing over compensation for the colonial period.
Mr Berlusconi's one-day trip was his second since June when illegal immigration from Africa to Europe was the key issue of talks.
Italy has been swamped by thousands of African migrants trying to reach its shores by boat.
Libya has come in from the diplomatic cold since 2003 when it abandoned efforts to acquire weapons of mass destruction.
Next week, US Secretary of State Condoleezza Rice is scheduled to make the first high-ranking American visit to Libya since 1953.
Italy to seal Libya colonial deal
Filed under: Latest — Tags: Add new tag, Africa, African migrants, Berlusconi, colonial, colonial deal, Condoleezza Rice, Deal, Egyptian, Europe, illegal immigration, immigration, Italian PM Silvio Berlusconi, Italy, Italy to seal Libya colonial deal, Libya, Libyan leader Col Muammar Gaddafi, Motorway, Mr Berlusconi, Muammar Gaddafi, Rice, Rome, Silvio Berlusconi, Tripoli, Tunisian, US secretary of state, US secretary of state Condoleezza Rice, weapons, weapons of mass destruction — expressyoureself @ 11:48 am
Mr Berlusconi is making his second trip to Libya since June
Italy is to provide billions of dollars to Libya as part of a deal to resolve colonial-era disputes, Italian PM Silvio Berlusconi has announced.
At least $5bn will go to help Libyan infrastructure projects over the next 25 years.
Mr Berlusconi is in the port of Benghazi to meet Libyan leader Col Muammar Gaddafi and seal a bilateral friendship and cooperation accord.
It became independent in 1951.
Mr Berlusconi said: "The accord will provide for $200m a year over the next 25 years through investments in infrastructure projects in Libya."
The main project will be a coastal motorway between the Egyptian and Tunisian borders.
The Italian leader had earlier said he wanted the agreement to "turn the page on the past".
Libya has accused Italy of killing thousands of its citizens and expelling thousands more from their homes in three decades of occupation.
Mr Berlusconi's trip is his second since June when illegal immigration from Africa to Europe was the key issue of talks.
Gaddafi son retires from politics
Filed under: Latest — Tags: civil societies, Col Gaddafi, Col Gaddafi's sons, desert town of Sebha, diplomatic, e Gaddafi Foundation, foreign policy, Gaddafi, Gaddafi son, Gaddafi son retires from politics, government Tripoli, Hannibal, Libya, Libyan leader Muammar Gaddafi, Muammar Gaddafi, oil shipments, political life, power, Sayf al-Islam Gaddafi, Sebha, Switzerland, Tripoli — expressyoureself @ 3:51 pm
Sayf al-Islam said he was not at odds with his father
The son of Libyan leader Muammar Gaddafi has announced his retirement from political life.
Sayf al-Islam Gaddafi has been a leading proponent of reform through his charity, The Gaddafi Foundation.
He said he had been obliged to intervene politically, but this was no longer necessary, as Libya now had institutions and systems it had lacked.
He has previously denied reports he was being groomed to take power and said there was no rift with his father.
He has no official role in government but in the past four years he has come into the limelight internationally because of his interventions.
The situation has changed and if I continue there will be a problem
Sayf al-Islam Gaddafi
In an hour-long televised speech, Sayf al-Islam Gaddafi took some credit for the rehabilitation of Libya's reputation.
"I intervened extensively in everything: our foreign policy, in a lot of problems, in development, in housing. Because there were no institutions or an administrative system that were able to do so," he told a crowd in the desert town of Sebha.
"But now the situation has changed and if I continue there will be a problem."
He said the decision-making process should not be held in the hands of a few people and again urged the creation of more civil societies, an independent media and a judiciary enshrined in a new constitution.
These goals were the responsibility of all Libyans, he said, to a standing ovation in Sebha, where he was addressing a crowd of thousands of young supporters.
Sayf al-Islam is one of seven of Col Gaddafi's sons.
The Libyan leader's youngest son, Hannibal, has caused a diplomatic row with Switzerland after being charged with assaulting two of his servants last month.
Libya's state shipping company halted oil shipments to Switzerland in protest.
US-Libya compensation deal sealed
Filed under: Latest — Tags: Ahmed al-Fatroui, America, Benghazi, Berlin, Berlin disco, Bush, David Welch, diplomatic, diplomatic relations, Gaddafi, George W Bush, international Humanitarian Settlement Fund, Libya, Libyan, Lockerbie, Lockerbie bombing, Middle East, Mr Fatroui, Muammar Gaddaf, Pan Am Flight, Pan Am Flight 103, Relations, relationship, Scotland, Tripoli, US, US assistant secretary of state, US attacks, US President, US President George W Bush, US-Libya, Washington — expressyoureself @ 7:21 am
The signing comes after a long process of negotiation
The US and Libya are set to renew diplomatic relations after signing a deal to compensate all victims of bombings involving the two countries.
The agreement will fully compensate victims of the 1988 Lockerbie bombing, and of the bombing of a Berlin disco two years earlier.
It will also address Libyan claims arising from US attacks on the Libyan capital, Tripoli, and Benghazi in 1986.
The deal was signed in Tripoli by US and Libyan officials.
David Welch, US assistant secretary of state and Washington's top Middle East diplomat, met Ahmed al-Fatroui, head of America affairs, in Libya's foreign ministry to seal the agreement.
When fulfilled, the agreement will permit Libya and the US to develop their relations
David Welch
US assistant secretary of state
Mr Fatroui told reporters it was "the crowning of a long process of exhausting negotiations".
Mr Welch said it was a very important agreement that "turns a new page in our relationship".
"Under this agreement each country's citizens can receive fair compensation for past incidents. When fulfilled, the agreement will permit Libya and the US to develop their relations," he said.
Libyan state media said US President George W Bush had sent a message to the Libyan leader, Muammar Gaddafi, saying he hoped relations between the two countries would continue to improve.
The agreement does not constitute an admission of fault by either party.
An international Humanitarian Settlement Fund will be set up in Libya to compensate all American and Libyan claimants.
Foreign companies and international institutions operating in Libya, which include some American companies, will contribute to the fund.
The deal also paves the way for a full restoration of relations, including the opening of a US embassy in Tripoli and direct US aid.
In all, there were 26 lawsuits filed by American citizens against Libya and three by Libyan citizens against the US.
The 1988 bombing of Pan Am Flight 103 over Lockerbie, Scotland, killed 270 people and the 1986 bombing of a Berlin disco killed three people and wounded more than 200.
Libya says at least 40 people died in the US air strikes.
Relations between Libya and the US have improved dramatically since 2003, when Libya accepted responsibility for the Lockerbie bombing.
Migrants rescued off Italy coast
Filed under: Latest — Tags: Africans, coast, coastguard, emergency, Eritrea, Ethiopia, Europe, government, Greece, immigrants, Italian, Italian government, Italian media, Italy, Italy coast, journey, Lampedusa, Lampedusa island, Libya, Libyan, Malta, Migrants, navy, refugee, Somalia, Spain, state, U.N, UN refugee agency, UNHCR, vessels, women — expressyoureself @ 11:17 am
Some 12,000 people have arrived in Lampedusa since January
Italian vessels have rescued at least 250 would-be migrants from boats and vessels off the coast of Italy.
The navy rescued at least 175 people, believed to be from Eritrea, Ethiopia and Somalia from three vessels, 190km (120 miles) south of Lampedusa island.
A further 72 people – including seven women and a child – were rescued from a rubber dinghy by the coastguard.
Local politicians say Lampedusa is facing a crisis with 12,000 would-be migrants brought ashore since January.
The Italian navy agreed to rescue those onboard the three vessels after they ran out of fuel and water in Libyan territorial waters.
The UN refugee agency, the UNHCR, had appealed to Malta, Libya and Italy to rescue the stranded vessels.
A UNHCR spokesman told Reuters news agency he believed some 25 women and six children were among those on board.
Those rescued from the dinghy 80km south of Lampedusa included seven women and a child, Italian media report.
Thousands of Africans risk their lives to make the perilous journey each year, many leaving in makeshift vessels from Libya hoping to gain entry to Europe via Italy or Malta.
Last year, according to rights watchdog the Council of Europe, some 51,000 migrants arrived by boat in Italy, Spain, Greece and Malta, many of them asylum seekers and refugees who lack legal avenues to enter Europe.
Emergency services in Italy have warned that crowded holding centres in the country are on the verge of collapse, worsening a state of emergency declared by the Italian government over immigrants.

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: Byte to Binary String I need to convert an 8-bit byte of 1's and 0's to a string reading the same thing.  This is what I have
string binstring(byte N) {
string sN(8,'0');
int temp;
for (int i = 0; i < 8; i++){
temp = (N >> i);
if ((temp%2) == '0') {sN[i] = 0;}
else {sN[i] = 1;}
}
return sN + '0';
}

My problem is the conversion is not happening.  Nothing is being outputted.


text:
+ About– About
DW Legacy Design
+ Work– Work
Campus/Institutional
Parks/Open Space
Regional/Urban Planning
Residential Gardens
Resort/Tourism
Urban Design/Mixed-Use
+ Ideas– Ideas
LAF Case Studies
Design Symposia
Interview with Emily McCoy
What place has the most potential to be transformed by landscape architecture?
Areas rich with natural resources and of cultural significance that need to balance growth and development with conservation and preservation. As landscape architects, we need to continue to find creative strategies that allow humans to have more positive relationships with our environment and with each other through environmental and equity planning. For example, we are working on several projects on the North Carolina and South Carolina coasts that are seeing and will continue to see significant impacts of climate change. These areas traditionally are also where marginalized groups have lived for many generations, and now are places of significant growth- where tensions around gentrification, land rights, resiliency, and economics intersect. Couple this with the fact that these areas are also places rich in history and culture, there is critical need to plan and design in a socially and environmentally responsible way. Our charge as designers and planners is to balance all the voices of a community with environmental and cultural resource protection, while considering the future scenarios of climate change and its impact to human safety and economic development – not an easy task. Landscape architects are trained to navigate these complex problems, but we can't do it alone. We need our allied disciplines and our community partners to rally around a commitment to responsible and sustainable planning and design in order to have significant impact. Amongst all these serious issues, it is important to not lose sight that outdoor spaces should be fun and inspiring for the people we design for. It has been a fascinating process working with these communities and I continue to learn from them every day, including acknowledging my own biases and challenging business-as-usual practices in the profession.
What is the greatest challenge facing landscape architects today?
Due to the COVID-19 pandemic, public spaces are more valuable than ever before- they provide places for safe active recreation and mental restoration, and thus should be a part of a comprehensive public health strategy for every community. Due to closures of indoor facilities and social distancing guidelines, we are encouraged to gather outdoors to stay healthy. Therefore, it is even more important to ensure that we gather public insight from all members of the community that will be utilizing these outdoor spaces. This was challenging to do prior to the pandemic and now it is even harder. Our industry had shifted to rely on digital tools – email and social media – to gather public feedback. Yet, due to broadband issues and other challenges prohibiting people from having internet access in some of our communities, we are seeing a shift back to a more analog approach. Think mailers and phone calls. For a project I am currently working on that has experienced some delays due to the pandemic, we are trying something really exciting – temporary art installations. The goal is to keep people connected to the space even though it has stalled. On this same project, which happens to be an area where families have lived in the same homes for generations, we are calling residents and collecting oral histories. It's fascinating to learn about the families that have lived here for decades and their memories of the neighborhood. We are digitizing these histories and going to use them for a permanent art installation.
What is on the horizon for the landscape architecture industry?
With my STEM-based education prior to becoming a landscape architect, I have always been fascinated by the confluence of design, planning and technology. My latest obsession is uncrewed aerial systems, also known as drones. Drones are becoming less expensive and more sophisticated. They have become one of our go-to tools for evaluating existing conditions quickly and accurately. However, drones are much more than a way to take photographs from above, they can also capture other information about the environment through sensors that allow us to track changes such as flooding or soil erosion over time. Before it would take months to evaluate existing conditions, now we can do it in a matter of hours. It's so much faster and efficient than before. I think our reliance on drones as a helpful tool in our landscape architect's toolbox will only grow. The interesting thing to watch will be how much more regulated they become and how that impacts our usage of them. Either way, I expect drones to continue to be an integral part of our work allowing us to assess exiting conditions, and monitor and measure our landscapes in real time, particularly the impact of climate change and the urban heat island, and how and why people use different spaces. This will allow us to assess the success and failure of our design and planning decisions quickly, when it once took years, in order build more sustainable spaces for future generations.
LAF Board of Directors Press Release
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The Washington Redskins announced Tuesday that they've re-signed OL Zac Kerin.
Kerin, 27, originally signed on with the Vikings as an undrafted free agent out of Toledo back in 2014. He spent just over three years in Minnesota before being claimed off of waivers by the Lions at the start of the 2017 season.
Kerin had brief stints with the Giants and Falcons before the Redskins signed him to a contract last December.
In 2018, Kerin appeared in two games for the Redskins.


A new study by AberdeenGroup (Boston), "The Supply Chain Integration Benchmark Report: Warehouse Without Walls," reports that top-performing distribution operations follow a "dynamic" philosophy to reduce cycle time and inventory within their supply chains and still provide high levels of customer service. The research organization likens the dynamic distribution network to lean initiatives in manufacturing designed to root out waste and time and improve responsiveness to customer demands.
On-time delivery performance and order fill rates for best-in-class operations far exceed others responding to the survey.
"Departmental rivalries, misaligned goals and performance metrics, and poor partner management policies all contribute to a company's inability to create more fluid and flexible fulfillment operations," said John Fontanella, the report author and sr. v.p. of research for Aberdeen.


text:
Columbus, Ohio, United States
Lilbourn, Missouri, United States
4.2 km from Lilbourn (2.2 miles)
East Prairie, Missouri, United States
11.2 km from East Prairie (7.2 miles)
Dyersburg, Tennessee, United States
12.2 km from Dyersburg (7.2 miles)
Tiptonville, Tennessee, United States
9.2 km from Tiptonville (6.2 miles)
Ridgely, Tennessee, United States
4.2 km from Ridgely (2.2 miles)
Caruthersville, Missouri, United States
3.2 km from Caruthersville (2.2 miles)
Manila, Arkansas, United States
6.2 km from Manila (3.2 miles)
Portageville, Missouri, United States
10.2 km from Portageville (6.2 miles)
Wickliffe, Kentucky, United States
10.2 km from Wickliffe (6.2 miles)
Bardwell, Kentucky, United States
10.2 km from Bardwell (6.2 miles)
9.2 km from Wickliffe (6.2 miles)
10.2 km from Tiptonville (6.2 miles)
La Center, Kentucky, United States
14.2 km from La Center (9.2 miles)
Doniphan, Missouri, United States
15.2 km from Doniphan (9.2 miles)


text:
Autosomal dominant leukodystrophy with autonomic disease is a rare neurological condition of genetic origin which is characterized by gradual demyelination of the central nervous system which results in various impairments, including ataxia, mild cognitive disability and autonomic dysfunction. It is part of a group of disorders called "leukodystrophies".

Signs and symptoms

Unlike other leukodystrophy syndromes, whose typical age of onset is during childhood, individuals with this condition typically start showing symptoms between their early 40s and late 50s, once they appear, they slowly progress in severity and new symptoms start appearing.

These symptoms first start out with dysfunctions of the autonomic nervous system which result in symptoms such as abnormal functioning of both the bladder and bowel, recurrent blood pressure drops whenever patients stand up, and male erectile dysfunction.

Rarely, anhidrosis might also occur alongside these symptoms.

After these symptoms start, movement impairments develop; they start off at the legs but then progress and move to the arms and the face, these impairments include either muscular spasticity or weakness, intention tremors, ataxia, dysmetria, and dysdiadochokinesis.

In some individuals, progressive dementia is present.

Complications

There are various complications associated with the symptoms that ADLD causes.

Due to the ataxia and it's associated coordination impairments, people might have difficulties with movements such as walking by themselves.

Treatment

Treatment is focused on the symptoms themselves

The ataxic movement impairments can be treated with walking support systems such as canes or wheelchairs, physical therapy, and speech therapy.

Diagnosis

This condition is diagnosed mainly through MRIs and genetic testing of the LMNB gene and the areas surrounding it, although symptom examination is also important for the diagnosis.

Causes

This condition is caused by a duplication of the LMNB1 gene, this gene takes part in the production of the lamin B1 protein, which is essential for determining the nucleus' shape within the cells, the replication of DNA, and the way certain genes express themselves.

When the gene is duplicated (as seen in patients with ADLD), there is an excess of lamin B1 protein, this leads to the underexpression of genes that are important for the production of myelin and an increased hardening of the nuclear envelope, which results in a progressive reduction of myelin production and maintenance as one ages.

Like the name of the condition implies, this condition is inherited following an autosomal dominant pattern, which means that only one copy of a certain mutation (in this case, the duplication of the LMNB1 gene) is needed for a trait or disorder to be expressed, in familial cases, offspring have a 1 in 2, or 50% chance of inheriting a copy of said mutation from one of their affected parents.

Although very rarely, this disorder can be caused by deletions near the LMNB1 gene, only one such family has been described in medical literature: they had a deletion upstream the same gene.

Pathophysiology

In patients with the condition, demyelination (that is, a loss of myelin) starts occurring in both the brain and the spinal cord years before symptoms show up, this abnormality has been identified to be a contributing factor to the development of the first symptoms individuals with this condition show during the early stages of it.

Phenotype-genotype

In a 2018 study done by Naomi Mezaki and 18 other colleagues, it was found that ADLD patients with a deletion near the LMNB1 gene (2 patients from a single family) started showing symptoms at an earlier age, had less autonomic dysfunctions and had more noticeable cognitive deficits than other ADLD patients with duplication of the LMNB1 gene (4 patients from 3 families).

Prognosis

This condition is progressive and fatal.

While the quality of life might be improved with treatment, the life expectancy can't be improved easily: individuals diagnosed with ADLD typically live for another 10 to 20 years after their diagnosis before their death.

Prevalence

At least 70 cases from 35 families around the world have been described in medical literature, most of these were from families of Caucasian descent.

History

This condition was first discovered in 1964 by E Zerbin-Rüdin et al. when they described (what they thought to be) a familial autosomal dominant variant of Pelizaeus-Merzbacher disease with onset in adulthood.

In 2006, Padiath et al. found the LMNB1 duplication involved in ADLD in 4 families, of which 1 was previously described in medical literature. Haplotype studies revealed that the family mentioned beforehand and another Irish-American family shared a common ancestor. The lamin B1 protein was found to be overly expressed in brain tissues of family members affected with ADLD.

See also

Hypomyelination-congenital cataract syndrome
Leukodystrophy
Demyelination

References

Rare genetic syndromes

redpajama_set_name: RedPajamaWikipedia


1. Use today's idioms in a sentence, or write a short dialogue.
2. Do you have any interesting idioms in your language that mean the same as these? Talk about them.
3. What do you know about Julius Caesar, or about Alexander the Great? Talk about them, or learn more if you need to.


The Parliamentary Select Committee on Local Government, has hailed the quality of job done by the contractors working on the Kejetia-Central Market Re-development Project.
This was after they had inspected the project, accompanied by the Kumasi Metropolitan Chief Executive (MCE), Mr. Osei Assibey-Antwi.
Its Chairman, Mr. Osei Nyarko, said they were satisfied with what they saw and promised strong backing for the implementation of the phase two of the project.
The phase one has now been finished and feasibility studies had also been completed for the start of construction works on the next phase[G1] [G2] .
Mr. Nyarko indicated that there could not be any doubt about the economic viability of the project and therefore the need for the government to hasten its effort to get things done without delay.
Another member of the Committee, Mr. Nii Lantey Vanderpuye, gave the assurance that parliament would soon approve the funding for the phase two of the project.
The project, awarded to Brazilian Contractors – Contracta Engineering Company Limited, suffered delays because of the ligation over some structures that needed to be leveled to pave way for its smooth implementation.
The matter was finally determined by Kumasi High Court in January, this year.
Mr. Vanderpuye appealed to traders dislocated by the project to continue to show good understanding and said all should be prepared to make some sacrifices to bring development to the metropolis.
Mr. Assibey-Antwi denied rumors that modifications had been made to the project and said nothing in the original plan had changed.
He expressed optimism that its successful completion would restore sanity to the streets of Kumasi and boost its economy.


the diet, either from organic compounds that are in animal products, such as retinyl esters , or from compounds in plants, most notably β- carotene (see Figure 1). Retinol and its derivatives are collectively called retinoids.
Chemically, retinol is an isoprenoid; isoprenoids are a group of compounds that includes vitamins E and K and cholesterol, which are synthesized from isoprene units. As shown in Figure 1, retinol is a hydrocarbon molecule with a single hydroxyl group at one end. This hydroxyl group can be oxidized to form an aldehyde group (yielding retinal), or to a carboxylic acid group (yielding retinoic acid). Retinal and retinoic acid are the biologically active forms of retinol. In addition to these different oxidation states, retinol occurs as a number of different isomers . The retinol structure shown in Figure 1 is all-trans -retinol, as all of the double bonds are in the trans configuration. Many cis isomers also occur. Two important examples are 11-cis -retinal, which is required for vision (see Figure1), and 13-cis -retinoic acid (or isotretinoin), which is used as an anti-acne drug.
One of the symptoms of vitamin A deficiency is night blindness. If the deficiency persists over time, the eyes will eventually deteriorate, and permanent blindness will result. In specialized cells of the eye, 11-cis -retinal is linked covalently to the enzyme opsin. Opsin is also a membrane protein; it comprises approximately 95 percent of the membrane protein of disks in the outer segments of the eye's rod cells. The disks in a rod cell are circular layers of membrane stacked on top of each other. Each cell contains hundreds to thousands of these disks. This greatly increases the membrane surface area, and thus the amount of opsin, in these light-detecting cells. The combination of 11-cis -retinal and opsin is called rhodopsin. Visible light is absorbed by the 11-cis -retinal, causing it to isomerize to all-trans -retinal (see Figure 1). The resulting shape change in the rhodopsin initiates a series of reactions that ultimately sends signals to the brain.
The other active form of vitamin A is retinoic acid. Retinoic acid exerts its physiological functions via its interactions with a family of nuclear receptors called the retinoic acid receptors (RARs). RARs are members of a superfamily of nuclear receptors that include steroid hormone and thyroid hormone receptors. RARs are involved in regulating the transcription of many genes, including genes involved in the cell growth and cell differentiation of developing organisms. Because of this link between retinoic acid and development, female patients taking isotretinoin (13-cis -retinoic acid) must not become pregnant due to the considerable risk to offspring of severe birth defects.
Maden, Malcolm (1998). "Vertebrate Development: A Nervous Vitamin." Current Biology 8(23): R846–849. Also available from <http://www.bmn.com>.
Zubay, Geoffrey (1998). Biochemistry, 4th edition. Dubuque, IA: Wm. C. Brown Publishers.
Centers for Disease Control. Information available from <http:www.cdc.gov>.
National Institutes of Health. Information available from <http://www.nih.gov>.
"Retinol." Chemistry: Foundations and Applications. . Encyclopedia.com. 18 Apr. 2019 <https://www.encyclopedia.com>.
retinol A diterpene compound, composed of four isoprene units structurally related to carotenes, which is involved in the synthesis of the visual pigments. A deficiency of this compound results in a number of symptoms, including cessation of growth, cornification of epithelial structures, and, most notably, night blindness.
"retinol." A Dictionary of Zoology. . Encyclopedia.com. 18 Apr. 2019 <https://www.encyclopedia.com>.
ret·i·nol / ˈretnôl; -ˌōl/ • n. Biochem. a yellow compound, C20H29OH, found in green and yellow vegetables, egg yolk, and fish-liver oil. It is essential for growth and vision in dim light. Also called vitamin A.
"retinol." The Oxford Pocket Dictionary of Current English. . Encyclopedia.com. 18 Apr. 2019 <https://www.encyclopedia.com>.
retinol: see Vitamin A under vitamin.
"retinol." The Columbia Encyclopedia, 6th ed.. . Encyclopedia.com. 18 Apr. 2019 <https://www.encyclopedia.com>.
retinol (ret-in-ol) n. see vitamin A.
"retinol." A Dictionary of Nursing. . Encyclopedia.com. 18 Apr. 2019 <https://www.encyclopedia.com>.
"retinol." A Dictionary of Food and Nutrition. . Encyclopedia.com. 18 Apr. 2019 <https://www.encyclopedia.com>.
"retinol." A Dictionary of Biology. . Encyclopedia.com. 18 Apr. 2019 <https://www.encyclopedia.com>.
Retinol (RET-uh-nol) is the scientific name for vitamin A, a vitamin found only in animals. It occurs as a yellowish to orange powder with a slight brownish cast and is a relatively stable compound. Retinol is converted in the body from an alcohol to the corresponding aldehyde, retinal (C20H28O), one of the primary chemical compounds involved in the process by which light is converted to nerve impulses in the retina of the eye. Vitamin A is also required for a number of other biochemical reactions in the body, including growth and development of tissue and maintenance of the immune system.
Vitamin A is synthesized in animal bodies through a variety of pathways. One important source of vitamin A is a group of related compounds called the carotenes, substances responsible for the yellowish or orangish appearance of fruits and vegetables such as carrots, sweet potatoes, squash, cantaloupe, apricots, pumpkin, and mangos. Some leafy green vegetables, such as collard greens, spinach, and kale, are also good sources of the carotenes. The most important of the carotenes is β-carotene (beta-carotene), C40H56. The oxidation of carotenes in animal bodies converts them to retinol.
The chemical structure of retinol was determined in 1931 by Swiss chemist Paul Karrer (1889–1971), and the compound was first prepared synthetically shortly thereafter by Austrian-German chemist Richard Kuhn (1900–1967). The first successful process for producing retinol commercially was developed in the mid-1940s by German chemist Otto Isler (1920–1992), then employed at the pharmaceutical company Roche, located in Sissein, Germany. Isler's process involved a complex series of reactions that begins with the combination of a fourteen carbon hydrocarbon and a six carbon hydrocarbon to create the fundamental backbone from which the retinol molecule is constructed. Regular production of vitamin A began in 1948 with a projected output of 10 kilograms per month, which before long was raised to 50 kilograms per month. The Roche plant at Sissein continues to produce retinol today.
Vitamin A is probably best known for its role in maintaining normal vision. Deficiencies of the compound are likely to manifest themselves earliest in a variety of eye problems, most commonly night blindness. Night blindness is a condition in which one loses the ability to distinguish objects in reduced light. If left untreated, vitamin A deficiencies may lead to decreased ability to see in normal light and, eventually, to complete blindness.
Animals that live in very cold climates have high concentrations of retinol in their livers. A polar bear liver contains enough retinol to kill a human who eats it. Vitamin A deficiency is the leading cause of childhood blindness in the world today.
But vitamin A has been shown to have a number of other functions in the body. It is essential for the maintenance of growth, bone formation, reproduction, proper immune system function, and healing of wounds. A number of additional claims have been made for the compound, although evidence is not as strong as it is for the above functions. For example, it may be effective in preventing or treating a variety of conditions such as measles, intestinal parasites, osteoporosis, inflammatory bowel disease, bone marrow disorders, certain types of cancer, tuberculosis, peritonitis, osteoarthritis, food poisoning, Alzheimer's disease, miscarriage, and HIV/AIDS. In each of these cases, evidence is not yet strong enough to show a clear-cut connection between retinol and disease, but research is being conducted to determine how strong the association may be.
Retinol is available commercially in a variety of formulations, including tablets, capsules, and creams. Such products usually contain a modified form of retinol that is more easily absorbed by the body. For example, a product known as tretinoin is a synthetic form of retinol known as all-trans retinoic acid. The term all trans means that all of the double bonds in retinoic acid are located on the same side of the molecule. Products containing tretinoin are used to treat acne, pimples, wrinkles, blackheads, freckles, sun-spots, and even pre-cancerous lesions. They work by increasing the rate with which the skin sheds old cells and replaces them with new cells.
Vitamin A supplements in pill or capsule form are available in two formulations, those that contain retinol and those that contain beta carotene. It is not possible to take too much of the latter type of vitamin A. The body will not convert excess amounts of carotene into retinol but will, instead, excrete the excess in the urine or stool. An excess of retinol-based vitamin A, by contrast, may result in certain medical problems. Since the vitamin is fat soluble, in may be stored in body fat and reach relatively high concentrations if too much is ingested. An excess of retinol in the body may be associated with liver damage, osteoporosis, rash, fatigue, bone and joint pain, nausea, insomnia, and personality changes.
Powers, Jennifer I. "Acne Medication." In Chemistry: Foundations and Applications. Volume 1. Edited by J. J. Lagowski. New York: Macmillan Reference USA, 2004, 12-15.
"Vitamin A." Bristol University School of Chemistry. http://www.chm.bris.ac.uk/webprojects2002/schnepp/vitamina.html (accessed on November 3, 2005).
"Vitamin A (Retinol)." Hypertexts for Biomedical Sciences. http://arbl.cvmbs.colostate.edu/hbooks/pathphys/misc_topics/vitamina.html (accessed on November 3, 2005).
"Vitamin A (Retinol)." University of Maryland Medical Center. http://www.umm.edu/altmed/ConsSupplements/VitaminARetinolcs.html (accessed on November 3, 2005).
"Retinol." Chemical Compounds. . Encyclopedia.com. 18 Apr. 2019 <https://www.encyclopedia.com>.


Bulgaria had a lot of work to do in providing disabled access to public buildings, the country's anti-discrimination commission said on October 2 in its intermediate report on the progress of the ongoing Accessible Bulgaria programme.
As part of the programme, the commission has checked a total of 538 public buildings for disabled access and found that only 60 buildings, or one in nine, had taken adequate measures to facilitate access for disabled people.
Those buildings would be included in a special register for future disabled access certification, while the other 478 were in various stages of infringement proceedings, the commission said in a statement.
Should building owners fail to implement the commission's recommendations, they could be subject to fines of up to 20 000 leva, or 10 225 euro.
The anti-discrimination commission launched the Accessible Bulgaria programme on December 3 2017, which is also marked as teh International Day of Persons with Disabilities. The programme does not have an end date and the commission said on October 2 that it aims to provide quarterly updates about its progress.
Although the commission did not provide a detailed break-down of the 60 buildings that it found to meet disabled access criteria, it did have data for the inspected buildings that failed to do so.
Of those, nearly a third (149 buildings) were government and municipal buildings. Among privately-owned buildings, bank branches (165 buildings) and mobile carrier stores (89 buildings) were the most frequent offenders.
Currently, the checks under the Accessible Bulgaria programme are focusing on state institutions, banks and insurance companies, mobile carrier stores and post offices, pharmacies and other larger stores.
Once those are checked, the commission plans to focus on other public buildings, such as theatres, cinemas and restaurants, the report said.
Geographically, the largest number of infringement proceedings were in Sofia (both the capital city and the district around it) – 66 in total, including 45 bank branches. The district of Lovech was next, with 30 ongoing infringements, and Varna was third with 26 cases.
But disabled access was a nation-wide problem, the commission's report said, with infringements recorded in all 28 districts of the country.


text:
Q: Permutation equation. How to solve an equation when having a big exponent $\sigma =\bigg(\begin{matrix} 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 \\ 3 & 4 & 5 & 7 & 9 & 2 & 8 & 6 & 1 & 11 & 10 \end{matrix}\bigg) \in S_{11}$
Find $ \tau \in S_{11} $ for which: $\tau^{2011}=\sigma$
I do really have no idea on how to do that. Can you please help me?

A: As we already have seen in other answers, $\sigma$ has order $20$. Now $1 = 11 \cdot 2011 - 1106 \cdot 20  $ and so we have
$$ \sigma = \sigma^{11 \cdot 2011 - 1106 \cdot 20} = (\sigma^{11})^{2011} \cdot (\sigma^{20})^{-1106} = (\sigma^{11})^{2011}$$
Thus $\tau = \sigma^{11}$ does the job.


We had a hard freeze a couple of weeks ago and thus ends the 2018 gardening season!
Later this winter I will turn all the garden beds and mix in composted manure, to make things ready for 2019!
This entry was posted in Uncategorized on November 26, 2018 by Brett Elliott.


What Should You Consider When Hiring A Tree Service Company?
It may not seem like it at first but, trees are a great part of your home and how it melds on the exterior of your home could greatly affect your home's value and of course, its appearance. With its great effect on the appearance and value of your home, it is evident that you don't just pick any tree services in the market. You certainly wouldn't want to end up in a situation where you'll hire a company who do not place great importance on results and would rather hire workers who are not skilled just to save money. It isn't weird that with such workers that are not skilled for the job, you'll end up with results that would only utterly disappoint you. Get to know more about how you could find the right tree services by reading on the information below.
To put you at much ease when hiring a company, it is imperative that you make sure that they are equipped with credentials that are befitting of their company. Credentials would obviously pertain to the business license of the company and this would make it more apparent to you that they are operating legally. It would also bode you a better result if the company comes with workers who are equipped with certifications as this would mean that they are all qualified to do the services and aren't just any random people hired by the company.
Accidents and other forms of damages could happen at some point in time even with the most skilled workers. You should look at the company's insurances and if they have properly setup some countermeasures for accidents or damages, so you would have absolutely nothing to be worried about even in the face of the worst situation.
Getting the point-of-view or perspective of the company's past clients would give you more idea as to what you're going to experience with the tree services company so get references from them which you could talk to. By contacting references of the company, this would give you the best perspective possible about the quality of work which the tree services company provide along with their attitude and behavior when it comes to serving their clients.
You should never jump into a conclusion without a clear perspective on the price that you're going to pay for the services they'll provide. The best way for you to have the most accurate price is to invite the company to take a look at your home and provide you with their estimate on how their service is going to cost you – it would surely be better if they provide free estimation services as this further makes it apparent that they are more reputable and dedicated to their array of consumers. It would surely be more beneficial if you'll take the effort to talk to few companies and compare their services and prices from each other so you'll be more confident about the decision you'll make.


Samantha closed her eyes and tiled her head so that Joel could kiss her cheek. Joel smiled then floated off the ground to add eighteen inches to his height. He put a hand through Samantha's long blond hair and behind her neck and pulled her face towards his and into a passionate kiss on the mouth. Her eyes pooped open in surprise. She squirmed a bit then gave in for five or six seconds, then she pushed against Joel's chest so hard that he was thrown fifteen yards. He would have gone further but he struck the base of a large tree. The tree's trunk cracked and the tree topped towards Samantha. She blew a puff of air towards the tree and it shifted course and fell nearby. Samantha ended up getting dusted with snow. Joel just laid at the base of the tree with a silly smile on his face.
Joel said, "Step back until you feel better." Joel gazed into the ground and said, "Oh. This one is pitiful! If you weren't so sensitive, I probably wouldn't have noticed … HEY! There's a bigger one. That's the one that probably made you feel sick. They are definitely getting bigger!" Joel plunged his hand into the ground and pulled out a rock the size of his fist. Then he dug deeper and pulled out one the size of a football.
Joel said, "I guess I was just born lucky. Speaking of hurling, check out my aim on this one!" Joel threw the rocks into the air. They saw the rocks fly to a pile that Joel was making two miles away from the mansion.
Joel shouted, "GREAT! These weird plants are probably mutated by it. This is the crater. There it is! YES! You'd better back off. There are a lot of little ones down there too!" Joel ran down into the depression. In a second he had cleared the dirt from around the largest of the rocks. It was the size of a mini van.
Samantha gasped in horror. She screamed, "BE CAREFUL JOEL! You might not be TOTALLY immune. That thing could KILL you!
Joel hesitantly stepped closer and Samantha grabbed him with her free hand. She lifted him by his coat and began kissing him. Joel was in Heaven for a couple minutes then Samantha put him on the ground and leaned over him. She started touching him in strange ways and he began loosing control of his body heat.
Joel started to get up but Samantha pushed him back to the ground and started to unfasten Joel's pants. Joel raised his feet to Samantha's abdomen and pushed her away. She landed deep in the crater and started screaming. Almost instantly, Joel was by her side. He pried open her hand and took the red stones away from her. He flung them to his pile. He picked up a small piece of the other kind of stone and put it in his pocket. He lifted Samantha gently, carried her out of the crater and laid her on her back on the ground.
Samantha continued to cry as she said, "Mom said that I couldn't have red stones … but these were for her … not for me … they would have looked pretty with her red hair. My MOM! You're not going to tell my Mom or Dad … or anyone else … what I did … ARE YOU?! IF YOU DO I'LL NEVER EVER TALK TO YOU AGAIN!" Samantha wailed and cried loudly.
Samantha said, "Eight or nine more … and I'll go home! The kissing I did doesn't count, only the one you did. Hey. I'm feeling a little weak. Do you have some kryptonite in your pocket or do you have some strange power over me?" Joel decided that Samantha was acting normal enough that he no longer needed to protect himself from her. He reached into his pocket and fished out the small fragment of kryptonite. Without taking his eyes off Samantha's face, he flung the kryptonite so that it would land with the now enormous pile of green kryptonite that he was gathering. He smiled at Samantha and she smiled back. He lowered his face and began a long and gentle kiss. When he lifted his head, she said, "Do that eight more times and I'll stop helping you!" Joel took at deep breathe and prayed that he would be able to stop before Samantha's honor would force her to leave him alone to face the task he had set for himself.
Before anything else could be said, the kryptonite Christmas tree took off into the air.
Clara stood there with her mouth hanging open.
On his 28th birthday, Joel decided to do something he had long promised himself that he would do. He traveled back in time to thank the man that had saved his Mother so many years before. He saw his Mother run from Smallville High School. He couldn't believe that his Mother didn't look any younger than the woman he had said goodbye to just an hour earlier. He could see how upset she was. He wanted to go to her and tell her that everything would be all right -- just as she had told him the same thing on so many occasions when he was sure that nothing would ever be all right ever again. But he knew that he mustn't change anything. The events must remain as they had been or his very existence could be at risk. He followed her to LaSalle State park and vibrated to make himself intangible to even her keen senses whenever she looked his direction. Then it happened, just as she told him it had. She tumbled into the crater. She tried to get up but couldn't. She tried to crawl away, but she couldn't. Her cries for help were heartbreaking, but he kept focused on why he was there. He watched as his Mother passed out. He heard her talking to her dead parents while she was unconscious. He looked around and waited for whoever was going to come and rescue her. Where could he be? He kept watch on his Mother. She was turning a darker shade of green. He could hardly stand it. Then he saw two people standing near her. It was a man and a woman in strange clothes. They just stood there doing nothing. He couldn't control himself for another second. He shouted, "What are you doing? For God's sake help her." The two people turned, looked up at him they smiled up at him. In the woman and man he recognized his Mother. He couldn't believe it. They motioned to him as they vanished from sight. He looked back at his Mother. She was smiling now, but there was no sign of life in her. Joel ran down into the crater. He lifted her. Her body was so cold. He carried her out of the crater and sat her at the base of a tree. He removed his cape and wrapped it about her. He quickly gathered some wood and lit a fire with his heat vision. He said, "Mom, I can't leave you here alone." He stood over her and watched her sleep. When she started to wake, he quickly walked off then floated into the air and continued to watch her. She got up and looked around. She called out asking who was there. Joel resisted his temptation to answer her. When she looked his direction, he would vibrate so that she wouldn't notice him. She put out the fire and marveled at the cape that he had mistakenly left with her. She took the cape and was soon gone. William stayed a while to wait for the man that was supposed to have rescued his Mother. After a while he was getting impatient and was ready to give up. Then it hit him and he laughed. He said, "Well, thank me for saving Mom. Thank me very much." He laughed again and his laughed echoed long after he was far away in time.


Zimbabwe's largest draw is undoubtedly the majestic Victoria Falls, one of the seven pure wonders of the world. 3.) Individuals travel to seek for work as a result of they want to experience the best way to work from one other place. 6-9 months at dwelling adopted by 2-three months of traveling. More folks with extra money equal an increased spending power and the travel trade is getting a huge piece of that pie.
The nation's largest national park, each in dimension and variety of wild game and hen life; also one of many few remaining elephant sanctuaries in Africa, with herds of up to 100 strong seen; the only area in the nation the place gemsbok and brown hyena occur in reasonable numbers and where the population of wild canine is considered the most important surviving in Africa at the moment.
Travel could be enjoyable, and it may be dangerous on the identical time. So now that we have looked at a couple of issues that make actual travel so nice and how you can really throw your self into a culture let us take a look at how vacationing is totally different from traveling. After a few months of travelling you'll hit a peak.
During his time in workplace, 'Hare Worldwide Airport (which became the world's busiest) began operations, the Sears Tower (one of many world's tallest buildings) was erected and McCormick Place Convention Middle (the biggest in North America) opened.
Famend since antiquity for its fine Parian marble, Paros is taken into account to be some of the beautiful islands of the Aegean Sea in Greece and is one of the hottest destinations for tourists. Although "going home" presented its personal issues as I did not have a house to return to. I left with the intention of travelling indefinitely, yet even once I had been again within the States I moved usually, leaving one location for one more every couple months, sometimes throughout the same city, sometimes throughout the country.
For the sake of love, folks will travel for hours to spend as much time as they will with the love of their life. If airplane is your preferred mode of traveling then you can very nicely select to land on Toronto Pearson Worldwide Airport.
Travel destinations are many and easy methods to attain them is a matter of concern nowadays! So other than distinctive individuals and unique meals there are a couple of other issues which can be nice about travel versus trip. Frankly, it's comprehensible why most people would be hesitant to travel now. Positioned in northern Thailand, Pai is accessible by bus from Chiang Mai (4 hours), the second hottest worldwide gateway to the country, and Mae Hong Son (4 hours), a significant hill-tribe trekking center.


Everything i am... cause you believed in me.
Almost twenty years ago my wife Jenine and her best friend Chaya Bender started The Special Children's Center from a one-room apartment. Back then they were just teenagers with a dream to change the world, one child at a time. They felt a tremendous need for special children to have a place to flourish, to receive the care and attention they need, and to wrap it up in happiness. With the help of so many believers, that endeavor grew into a multi faceted Center for more than three hundred special children across three locations. While there is no end to the demand, there is also no end to their determination. While traveling and performing all over the world for the last fifteen years I've seen with my own eyes the gift that music can give and the depths it can reach. The power is within every one of us; you can be anything, no matter what challenges you face. That is the magic of love, and the magic of this song. It is for you, the children and staff of the Center, and for you, all children around the world -- each of you is precious, you can be anything. This song is for you.