Early life.

Fico was born on 15 September 1964, in the town of Topoľčany in the southwestern Nitra Region. His father, Ľudovit Fico, was a forklift operator, and his mother, Emilie Ficová, worked in a shoe store. He has two siblings; his brother Ladislav is a construction entrepreneur, and his sister Lucia Chabadová, who is fourteen years younger, is a prosecutor. Fico grew up and lived with his family in the village of Hrušovany, until the age of six, when they moved to the nearby town of Topoľčany.

Education.

Fico has described his childhood ambitions as wanting to become either a politician, a sports reporter, or an archeologist. After completing elementary school, he enrolled in the local Gymnasium of Topoľčany, graduating in the summer of 1982. Later the same year he enrolled in the Law Faculty of the Comenius University in Bratislava, in what was then Czechoslovakia. His teachers were impressed with him, and one of his teachers from university, the future prime minister Jozef Moravčík, described him as "ambitious, very confident and very involved in discussions." He graduated as "juris doctor" in 1986 specializing in criminal law.  After graduating from university, Fico completed his mandatory military service as an assistant military investigator, stationed in the (now-Czech) town of Janovice between 1986 and 1987. He later worked for the Institute of State and Law of the Slovak Academy of Sciences, as well as with the Justice Ministry until 1992. During this period he wrote and completed his PhD degree, with a thesis on "The death penalty in Czechoslovakia." In 2002 he completed his postgraduate study, earning him the title of associate professor.

Early political career.

Fico joined the Communist Party of Czechoslovakia in 1987, having applied in 1984. After the Velvet Revolution of 1989, and the collapse of the communist regime in Czechoslovakia, Fico joined the Party of the Democratic Left (SDĽ), a successor of the Communist Party of Slovakia. He was first elected as a Member of Parliament in 1992. From 1994 to 2000 Fico represented Slovakia as its legal counsel at the European Court of Human Rights but lost all 14 cases which he handled. In 1998 he was elected deputy chairman of the party. Later the same year, Fico ran for the post of general prosecutor, but his party endorsed another candidate instead, arguing Fico was too young.  In the 1998 elections that saw the fall of the government of Vladimír Mečiar, Fico received the biggest number of preferential votes among his party colleagues. A year later, when support for the SDĽ dropped below the threshold required to get into parliament, he left the party, saying he was disappointed with the way the government worked. Fico acted as an independent MP until the 2002 elections.  As early as in the autumn of 1998, a four-person group consisting of Fico, his associate Frantisek Határ, political strategist Fedor Flašík, and media executive Monika Flašíková-Beňová had begun to discuss and lay plans for launching a new political party on the left. These plans were driven by the falling popularity of the existing parties, and the rising popularity of Fico.  Almost immediately after leaving SDĽ, the group founded Direction – Social Democracy (SMER), which Fico first labelled a party of the third way, with himself as leader. Fico established himself as an opposition politician criticizing the unpopular reforms of the right-wing government of Mikuláš Dzurinda. In order to keep SMER from repeating the fate of his previous party, Fico introduced a strict set of regulations for his new party, called the "clean hands" policy. The rules stipulated that no one with ties from the previous communist regime or people who had background with other political parties was allowed to hold party office. This created a new generation of politicians uninvolved in previous corruption scandals; among them was Monika Flašíková-Beňová, Robert Kaliňák and Pavol Paška. Another rule was that all party chapters on the regional and local levels were to be 100% financially self-sufficient, and all financial donations were to be made public to the media.  Between 2002 and 2006 Smer was the main opposition party in the Slovak parliament. In 2004, it merged with nearly all the leftist parties active on the Slovak political scene, including its parent party SDĽ, becoming the dominant single political party in Slovakia.

First term of Prime Minister: 2006–2010.

In the elections in 2006 SMER won with 29.1% of the votes and formed a coalition government with Vladimír Mečiar's People's Party – Movement for a Democratic Slovakia (HZDS) and Ján Slota's Slovak National Party (SNS).  SNS is a right-wing populist party which has been known for making anti-Roma and anti-Hungarian comments, including a drunken public speech of Ján Slota, in which he threatened to "get in tanks and level Budapest to the ground."  One reaction to the coalition came from the EU-wide Party of European Socialists (PES), who suspended SMER's application to join the PES. In late February 2008, however, the Assembly of PES conditionally reinstated the application after both SMER and SNS signed a letter committing themselves to respect minority rights.  Fico has never publicly condemned SNS's remarks and speeches, and government-level relations between Slovakia and Hungary deteriorated in his first term in office. Several meetings between the two countries' prime ministers were abruptly cancelled, and those few that did take place resulted in little improvement of relations.

In opposition: 2010–12.

Before the 2010 elections, Fico's party was in a relatively strong position according to several polls. However, just before the election a political scandal broke out, described as one of the gravest in the country's 17-year history. A voice recording surfaced in which a voice strongly resembling that of Fico claims that he raised several million euros in undeclared funds for the 2002 election as well as calling for a "parallel financial structure" to be created for the financing of Smer's election campaign. Slovak media sources such as "SME" carried the news about the recording in great detail; however, Fico dismissed it as a forgery.  Fico also attacked the media sources that published information about the recording, saying "Should I go over there and give you a smack because you are scoundrels? What you are doing is unheard of. You are masturbating on the prime minister every day." Fico has since been questioned on the matter, "SME" announced. Former Minister of Justice Daniel Lipšic told the press he has "handed the recording to the general attorney office." In the election, Fico's SMER remained the biggest party in Parliament, with 62 seats. However, his coalition partners were decimated, with the HZDS being completely shut out. Unable to find a partner willing to give him the 14 seats he needed to stay in office, Fico resigned. He said he "respects the election result" and expressed his desire to lead a resolute opposition after his narrow loss.

Second term of Prime Minister: 2012–2016.

2012 parliamentary election.

Following the fall of the centre-right coalition government that replaced his, Fico's Smer-SD returned to power being the first party since the breakup of Czechoslovakia to win an absolute majority of seats. Fico initially sought to form a national unity government with SDKU or KDH, but when this failed he formed the first one-party government in Slovakia since 1993.

2014 presidential election.

On 18 December 2013, Fico officially announced his candidacy for the upcoming presidential election in 2014. "I understand my candidacy as a service to Slovakia," Fico said on December 18. He argued that he did not see his candidacy as an adventure, an escape or an attempt to culminate his political career. His campaign ran under the motto "Ready for Slovakia." On 9 January 2014, the Slovak Parliament, under Speaker Pavol Paška, officially approved the candidatures of Fico and 14 other candidates.  However, Fico was defeated by the independent candidate Andrej Kiska, whose support from the right wing of Slovak politics led him to victory by a wide margin (approximately 59%–41%) in the second round of voting on 29 March 2014.

2016 parliamentary election.

Fico's party won the 2016 parliamentary elections, amassing a plurality of seats, but failed to win a majority. On 7 March 2016, President of Slovakia Andrej Kiska invited each elected party, with the exception of Kotleba – People's Party Our Slovakia, for post-election talks. Fico was given the first opportunity by the President to form a stable coalition. On 17 March, incumbent Fico informed president Andrej Kiska that he would form a four-party government coalition, including Smer–SD, the Slovak National Party, Most–Híd and Network, which together held 85 of the 150 seats.

Resignation.

On 14 March 2018, Fico publicly stated that he was ready to tender his resignation as prime minister in order to avoid an early election as well as to "solve the political crisis" involving the murder of investigative journalist Ján Kuciak, who was writing stories on tax frauds and alleged cronies of the ruling party. Kuciak also examined the work of the Italian mafia 'Ndrangheta in Slovakia. According to the police, Mária Trošková, who is an assistant to Robert Fico, could have ties to 'Ndrangheta. Fico's announcement came after a meeting with President Kiska. In that meeting, Fico laid out a number of specific conditions that needed to be met by the president in order for him to resign. Those conditions were amongst others; that the result of the 2016 Slovak parliamentary election be respected, that the current ruling government coalition must continue, and lastly, that Smer-SD as the largest party currently in parliament name the next prime minister. Fico stated that he already had a candidate in mind; Slovak media widely reported that the next prime minister would be Deputy Prime Minister Peter Pellegrini. On 15 March, President Kiska formally accepted the resignations of prime minister Fico and his cabinet, and thereby tasked Pellegrini with forming a new government.

Domestic policy.

A large part of Fico's election victory in 2006 was attributed to his loud criticism of the previous right-wing government's economic, tax, social, pension and legislative reforms. The reforms were generally perceived as very positive and successful by such international bodies as the International Monetary Fund, the World Bank or the OECD. However, the reforms negatively affected large segments of the population, particularly low wage earners, the unemployed, and welfare and other social assistance recipients. While in opposition, and more vocally during the election campaign, Fico vowed to reverse and cancel the majority of these reforms. However, upon taking office Fico adopted a more cautious approach, as he wanted to ensure Slovakia could fulfill the Maastricht criteria required for Euro currency adoption. This was successful, and Slovakia adopted the Euro on 1 January 2009.

Labour policies.

Among the reforms Fico introduced, several established standards as to how many times employees could be kept on as temporary workers instead of being given permanent contracts. Under legislation of the Mikuláš Dzurinda government, an employer could keep new staff as temps and create a two-tier workforce, which many did. Slovakia's labor policies are now generally in tune with most other EU states.  At the start of his second term as Prime Minister in 2012, Fico introduced a new "Labour Code," which granted entitlement to a lay-off notice period as well as severance pay, reduced overtime, making layoffs more expensive for employers, shorter temporary work contracts and more power for trade unions. In addition, it curbed the ‘chaining’ of fixed-term employment contracts, whereby currently it is possible to extend a fixed-term employment contract three times over three years. The Code was revised in 2014 when it introduced severe restrictions of the work on agreement performed outside regular employment. Under the latest revision, employers will be able to conclude agreements with employees for 12 months only.  In 2010, Fico faced large-scale protests and a blockade of major cities by truckers upset about what they considered to be badly implemented tolls on the highways. Truckers demanded that fuel prices be lowered to compensate for the tolls. Fico initially refused to speak with representatives of the truckers, saying he would not "be blackmailed", but a few days later capitulated. The cuts given to truckers will amount to about €100,000,000.

Finance.

One of few modifications Fico's government did implement was a slight modification to the unusual flat tax system introduced by the previous government, in a way that slightly decreased or eradicated a tax-free part of income for higher income earners. A lower value added tax was imposed on medications and books, though in spite of his election promises Fico failed to extend this onto a wider group of products such as groceries. Among the measures were controversial legislative changes which effectively banned private health insurance companies from generating profit. As a result, Slovakia is being sued by several foreign shareholders of local health insurers through international arbitrations. In 2007, Fico unsuccessfully tried to regulate retail food prices, an unprecedented effort in a generally free market European Union.  In August 2008, Fico threatened the foreign shareholders of a local gas distributor SPP, the French Gaz de France and the German E.ON, with nationalization and seizure of their ownership shares in a dispute over retail gas prices.

Foreign policy.

European Union.

In foreign relations with Europe, Fico's government faced controversies due to its affiliation with the internationally isolated parties of Vladimír Mečiar and Ján Slota. Under his leadership however, Slovakia entered the Eurozone in 2009, and Fico himself in a speech to the Oxford Union praised Slovakia's entry into the European Union as a "success story." Fico opposed the unilateral declaration of independence by Kosovo, which he called a "major mistake," as a result of which Slovakia has not recognised Kosovo as a sovereign state.  Responding to the 2013 Euromaidan protests in Ukraine, Fico declared that the "EU is no religious obligation" as well as that the EU was "so in love with itself" that it is convinced there is no better alternative to it in the world. He subsequently condemned the use of violence, but acknowledged that the protests were an internal affair in Ukraine.  Fico rejected European Commission's plan to distribute refugees and economic migrants from the Middle East and Africa among EU member states, saying: "As long as I am prime minister, mandatory quotas will not be implemented on Slovak territory." He has subsequently sought to associate refugees and Muslims with terrorism, claiming that "thousands of terrorists and Islamic State fighters are entering Europe with migrants" and stating that "We monitor every single Muslim in Slovakia." In May 2016, he stated that Slovakia will not accept "one single Muslim" migrant into the country, weeks before the country was scheduled to take over the presidency of EU. He further stated "When I say something now, maybe it will seem strange, but I’m sorry, Islam has no place in Slovakia. I think it is the duty of politicians to talk about these things very clearly and openly. I do not wish there were tens of thousands of Muslims."  Commenting on Brexit in November 2016, he stated that it wasn't clear what the United Kingdom wanted, adding that it "must suffer" more than the 27 countries who will remain in the bloc. He also stated that the UK will not be allowed to make EU workers "second-class citizens" while still receiving the benefits of the single market. In light of election of Donald Trump, he commented that it might spur Europe to bolster its military.  In August 2017, Fico said: "The fundamentals of my policy are being close to the (EU) core, close to France, to Germany. I am very much interested in regional cooperation within the Visegrad Four but Slovakia's vital interest is the EU."

Russia.

Compensating for his lack of close political allies within the EU (the former head of the Czech Social Democratic Party, Jiří Paroubek, being a notable exception), Fico sought to strengthen relations with several non-EU countries such as Serbia and Russia. This broke with a pro-NATO, Western-focused trend established after the 1998 Slovak election.  After coming to power in 2006, Fico declared that Slovakia's relations with Russia would improve after eight years of "neglect." Fico referred to "Slavonic solidarity," which was a central theme of the Slovak National Awakening in the 1850s. On April 4, 2008, during a visit by Russian Prime Minister Viktor Zubkov, Fico said: "In Slovakia, there have been efforts to deliberately ignore Slavonic solidarity." Slovakia modernised Russian MiG fighters in Russia and did not buy new jets from the West. Additionally, Fico accused Georgia of provoking Russia when attacking South Ossetia in the 2008 Russia–Georgia war. Under his premiership, the Slovak foreign ministry rejected the Crimean referendum which incorporated Crimea into Russia. Fico himself, however, remained silent on the issue. Regarding the EU sanctions against Russia in 2014, Fico denounced them as "senseless," and a "threat to the Slovak economy."

Hungary.

Tension between Slovakia and Hungary, unstable from the past, was inflamed in 2006 following the parliamentary election and Fico's decision to include nationalist Ján Slota and his Slovak National Party into his governing coalition. Slota was known for his fierce anti-Hungarian rhetoric, including that "Hungarians are a tumor on the Slovak nation that needs to be immediately removed." In the wake of the election several incidents occurred which further inflamed nationalist sentiment on both sides, including the alleged beating of a Hungarian woman in South Slovakia. Fico reacted by condemning the extremism, but rebuked the Hungarian government by declaring "The Slovak government doesn’t need to be called on to strike against extremism." The row heated up again in September 2007, when Fico's government introduced a law making the Beneš decrees inviolable. This was in response to demands from ethnic Hungarian politicians that compensations should be made to persons affected by the decrees.  In May 2008, Fico labelled Hungary a potential threat during a speech commemorating the 161st anniversary of the day that Slovaks demanded national equality with other nations within the Austro-Hungarian Monarchy. Fico used the anniversary to openly criticise the political situation in Hungary and warn about the influence it might have on Slovakia. Especially he warned against the Hungarian right-wing politician Viktor Orbán, and his party Fidesz, which he called an "extreme nationalist party." Since then, however, relations between the two countries have slightly improved.

United States.

Fico was a vocal opponent of the one-time planned construction of new U.S. anti-ballistic missile and radar systems in military bases in neighbouring Czech Republic and Poland and one of his first steps upon taking office was a military pullout from Iraq. In November 2013, Fico visited the U.S. President Barack Obama in Washington D.C., where they spoke about the US-Slovak partnership, which is "based on shared democratic values and principles," after which he affirmed the strategic partnership between the two countries.

Relationship with the media.

During his press conferences he often verbally attacks, lectures and taunts the present journalists, often accusing them of bias and attacks on his government. On several occasions he has openly and on record used profanities against specific journalists ("idiots," "pricks"). After characterising journalists as "hyenas," the broadsheet "Pravda" adopted a hyena from Bratislava Zoo. In 2009, Fico repeatedly described the Slovak press as a "new opposition force" that was biased and was harming national and state interests. Fico also accused the press of failing to "stand behind the common people."  Fico has upheld a long-running boycott of one of the major Slovak daily newspapers, "SME". According to Fico, the boycott will last until it apologises for what he calls lies they published about him in the past, going as far as boycotting the main presidential debate prior to the 2014 presidential election, as it was co-hosted by "SME". As of March 2018 the boycott is still in place.  Fico, on at least one occasion, issued an apology to a foreign politician whose visit to Slovakia was largely ignored by the media. When Russian Prime Minister Viktor Zubkov visited in April 2008, most media did not consider the visit of the virtually unknown Zubkov substantially newsworthy. To make matters worse, during the press conference the journalists were not allowed to ask any questions. Subsequently, Fico sent Zubkov a letter of apology in which he apologized for the Slovak media's lack of interest in his visit.  In July 2012 Fico declared "Eternal Peace" between him and the Slovak press. He also stated his desire to change his attitude towards the media, saying "I think it is enough" and that he does not plan any further lawsuits against media outlets except in extraordinary situations. Fico further said: "You have to spend an incredible amount of energy on it [lawsuits], it means several years of conflict, one conflict takes usually five or six years [to resolve]," adding that lawsuits involve "legal fees, paying a lawyer, everything around that." In November 2016, he termed journalists questioning him about allegations of public procurement rules during Slovakia's EU presidency, as "dirty, anti-Slovak prostitutes." He also accused the accusations of being a targeted attack to smear the country's presidency of EU. After Fico stepped down from his post as prime minister early 2018, following the protests across the country, he renewed his hatred of the media, stating that he was planning on pursuing legal action against a number of notable journalists who slighted him during his time in power.

Personal life.

Fico is married to Svetlana Ficová (née Svobodová), a lawyer and associate professor from Žilina. They were classmates while both were studying law at the Comenius University in Bratislava, and they married in 1988. They have one son together, Michal, who studied at the University of Economics in Bratislava. In addition to his native Slovak, Fico speaks fluent Czech, English and Russian.

Religion.

Fico has rarely discussed in public his religious life. In his application to join the Communist Party in 1984, Fico stated that he was "strictly atheistic," as was required in order to be accepted. According to the testimonial from college added to the application, he held a "scientific Marxist-Leninist worldview" and "no problems with regards to religion."  In a promotional video during presidential election campaign in 2014, Fico said he grew up in a Roman Catholic family and that he considers himself a Catholic. He discussed his baptism, holy communion, confirmation and how the Catholic faith had impacted his childhood. He stated: "Perhaps if I am to do my profile in relation to the Catholic Church, I would end up better off than any MP of the KDH." He also described growing up with his grandfather, a man who "very strictly respected the rules of standard Christian life," stating that it profoundly impacted him. However, historian and former researcher of the National Memory Institute Patrik Dubovský consider it being an attempt to manipulate public opinion, because "confirmation was in direct conflict with Communist Party membership, which political programme was based on atheism." As Dubovský stated, religiously active people were severely persecuted, especially after the Charta 77 incident.  During televised debate Fico refused to answer a television presenter's question about whether he is a Christian (Catholic) or an Atheist, and said that he considered it a private matter. Regarding his baptism, holy communion and confirmation, Fico said that he was baptised as an infant and the holy communion with confirmation followed afterwards, as it was with every child who grew up in his home village, according to him.

Alleged extramarital affairs.

In August 2010, Fico was photographed around midnight in a gay bar in downtown Bratislava together with a woman, who was later revealed to be 25-year-old Jana Halászová, a secretary at the Smer-SD party headquarters. It was later revealed that Halászová had been given extensive privileges, including her own parking space in the Parliament car park, without being a member. Halászová had also bought a luxurious car worth around €30,000 and bought a new flat without a mortgage in August 2012 in a neighbourhood where a one-room flat costs approximately €100,000, despite being a secretary without education. In addition, both her sister and step-mother had recently been given jobs within various ministries.  In August 2013, Fico was photographed while embracing and kissing his now-secretary Halászová, after taking her for a private dinner at a chateau in Čereňany, 160 kilometres from Bratislava. The photos created another round of speculation about the true nature of their relationship as well as whether or not he had used public funds to pay for the dinner. A month later, the tabloid "7 Plus" reported that Fico and Halászová had been photographed together in a luxury restaurant while vacationing together in the Croatian town of Opatija. In response to this latest story, Fico filed a defamation lawsuit against "7 Plus" magazine.  In March 2018, after murder of Jan Kuciak, Slovak investigative journalist Eugen Korda in interview for public Česká televize TV alleged that Mária Trošková, Fico's assistant, is also his lover. Trošková escorted Fico on multiple high-level diplomatic meetings, including a summit with Angela Merkel, despite unofficial protests from German and Slovak diplomatic corps.  Subsequently, direct connection between and convicted 'Ndrangheta member was revealed by the press. While her romantic connection to Fico was not confirmed, her former relationship with Vadala was. Despite the evidence Fico was publicly supporting Trošková and the secretary of the Security Council Viliam Jasaň. After the public outrage, Trošková abandoned her position as State Counsellor and Fico's assistant and disappeared from the public eye.

Robert Fico (; born 15 September 1964) is a Slovak politician who served as Prime Minister of Slovakia from 2012 until his resignation in 2018. Fico also previously served as a Prime Minister from 4 July 2006 to 8 July 2010. He has been the leader of the Direction – Social Democracy (SMER-SD) party since 1999. First elected to Parliament in 1992 (whilst within Czechoslovakia), he was later appointed to the Council of Europe. Following his party's victory in the 2006 parliamentary election, he formed the first Fico Cabinet.

Robert Fico (* 15. září 1964 Topoľčany) je slovenský politik, v letech 2006–2010 a 2012–2018 předseda vlády Slovenské republiky. Je zakladatelem strany SMER – sociálna demokracia a jejím prvním předsedou.


Definition.

Let "G" be any group. Denote its group operation by multiplication and its identity element by 1. Let "b" be any element of "G". For any positive integer "k", the expression "b" denotes the product of "b" with itself "k" times: Similarly, let "b" denote the product of "b" with itself "k" times. For "k" = 0 and "b" ≠ 0, the "k"th power is the identity:.  Let "a" also be an element of "G". An integer "k" that solves the equation is termed a discrete logarithm (or simply logarithm, in this context) of "a" to the base "b". One writes "k" = log "a".

Examples.

Powers of 10.

The powers of 10 form an infinite subset "G" = {..., 0.001, 0.01, 0.1, 1, 10, 100, 1000,...} of the rational numbers. This set "G" is a cyclic group under multiplication, and 10 is a generator. For any element "a" of the group, one can compute log "a". For example, log 10000 = 4, and log 0.001 = −3. These are instances of the discrete logarithm problem.  Other base-10 logarithms in the real numbers are not instances of the discrete logarithm problem, because they involve non-integer exponents. For example, the equation log 53 = 1.724276... means that 10 = 53. While integer exponents can be defined in any group using products and inverses, arbitrary real exponents in the real numbers require other concepts such as the exponential function.

Powers of a fixed real number.

A similar example holds for any non-zero real number "b". The powers form a multiplicative subgroup "G" = {..., "b", "b", "b", 1, "b", "b", "b",...} of the non-zero real numbers. For any element "a" of "G", one can compute log "a".

Modular arithmetic.

One of the simplest settings for discrete logarithms is the group (Z). This is the group of multiplication modulo the prime "p". Its elements are congruence classes modulo "p", and the group product of two elements may be obtained by ordinary integer multiplication of the elements followed by reduction modulo "p".  The "k"th power of one of the numbers in this group may be computed by finding its "k"th power as an integer and then finding the remainder after division by "p". When the numbers involved are large, it is more efficient to reduce modulo "p" multiple times during the computation. Regardless of the specific algorithm used, this operation is called modular exponentiation. For example, consider (Z). To compute 3 in this group, compute 3 = 81, and then divide 81 by 17, obtaining a remainder of 13. Thus 3 = 13 in the group (Z).  The discrete logarithm is just the inverse operation. For example, consider the equation 3 ≡ 13 (mod 17) for "k". From the example above, one solution is "k" = 4, but it is not the only solution. Since 3 ≡ 1 (mod 17)—as follows from Fermat's little theorem—it also follows that if "n" is an integer then 3 ≡ 3 × (3) ≡ 13 × 1 ≡ 13 (mod 17). Hence the equation has infinitely many solutions of the form 4 + 16"n". Moreover, because 16 is the smallest positive integer "m" satisfying 3 ≡ 1 (mod 17), these are the only solutions. Equivalently, the set of all possible solutions can be expressed by the constraint that "k" ≡ 4 (mod 16).

Powers of the identity.

In the special case where "b" is the identity element 1 of the group "G", the discrete logarithm log "a" is undefined for "a" other than 1, and every integer "k" is a discrete logarithm for "a" = 1.

Properties.

Powers obey the usual algebraic identity "b" = "b" "b". In other words, the function defined by "f"("k") = "b" is a group homomorphism from the integers Z under addition onto the subgroup "H" of "G" generated by "b". For all "a" in "H", log "a" exists. Conversely, log "a" does not exist for "a" that are not in "H".  If "H" is infinite, then log "a" is also unique, and the discrete logarithm amounts to a group isomorphism  On the other hand, if "H" is finite of size "n", then log "a" is unique only up to congruence modulo "n", and the discrete logarithm amounts to a group isomorphism where Z denotes the additive group of integers modulo "n".  The familiar base change formula for ordinary logarithms remains valid: If "c" is another generator of "H", then

Algorithms.

The discrete logarithm problem is considered to be computationally intractable. That is, no efficient classical algorithm is known for computing discrete logarithms in general.  A general algorithm for computing log "a" in finite groups "G" is to raise "b" to larger and larger powers "k" until the desired "a" is found. This algorithm is sometimes called "trial multiplication". It requires running time linear in the size of the group "G" and thus exponential in the number of digits in the size of the group. Therefore, it is an exponential-time algorithm, practical only for small groups "G".  More sophisticated algorithms exist, usually inspired by similar algorithms for integer factorization. These algorithms run faster than the naïve algorithm, some of them proportional to the square root of the size of the group, and thus exponential in half the number of digits in the size of the group. However none of them run in polynomial time (in the number of digits in the size of the group).  There is an efficient quantum algorithm due to Peter Shor.  Efficient classical algorithms also exist in certain special cases. For example, in the group of the integers modulo "p" under addition, the power "b" becomes a product "bk", and equality means congruence modulo "p" in the integers. The extended Euclidean algorithm finds "k" quickly.  With Diffie–Hellman a cyclic group modulus a prime p is used, allowing an efficient computation of the discrete logarithm with Pohlig–Hellman if the order of the group (being p-1) is sufficiently smooth, e.g. has no large prime factors.

Comparison with integer factorization.

While computing discrete logarithms and factoring integers are distinct problems, they share some properties:

Cryptography.

There exist groups for which computing discrete logarithms is apparently difficult. In some cases (e.g. large prime order subgroups of groups (Z)) there is not only no efficient algorithm known for the worst case, but the average-case complexity can be shown to be about as hard as the worst case using random self-reducibility.  At the same time, the inverse problem of discrete exponentiation is not difficult (it can be computed efficiently using exponentiation by squaring, for example). This asymmetry is analogous to the one between integer factorization and integer multiplication. Both asymmetries (and other possibly one-way functions) have been exploited in the construction of cryptographic systems.  Popular choices for the group "G" in discrete logarithm cryptography (DLC) are the cyclic groups (Z) (e.g. ElGamal encryption, Diffie–Hellman key exchange, and the Digital Signature Algorithm) and cyclic subgroups of elliptic curves over finite fields ("see" Elliptic curve cryptography).  While there is no publicly known algorithm for solving the discrete logarithm problem in general, the first three steps of the number field sieve algorithm only depend on the group "G", not on the specific elements of "G" whose finite log is desired. By precomputing these three steps for a specific group, one need only carry out the last step, which is much less computationally expensive than the first three, to obtain a specific logarithm in that group.  It turns out that much Internet traffic uses one of a handful of groups that are of order 1024 bits or less, e.g. cyclic groups with order of the Oakley primes specified in RFC 2409. The Logjam attack used this vulnerability to compromise a variety of Internet services that allowed the use of groups whose order was a 512-bit prime number, so called export grade.  The authors of the Logjam attack estimate that the much more difficult precomputation needed to solve the discrete log problem for a 1024-bit prime would be within the budget of a large national intelligence agency such as the U.S. National Security Agency (NSA). The Logjam authors speculate that precomputation against widely reused 1024 DH primes is behind claims in leaked NSA documents that NSA is able to break much of current cryptography.

In the mathematics of the real numbers, the logarithm log "a" is a number "x" such that, for given numbers "a" and "b". Analogously, in any group "G", powers "b" can be defined for all integers "k", and the discrete logarithm log "a" is an integer "k" such that. In number theory, the more commonly used term is index: we can write "x" = ind "a" (mod "m") (read the index of "a" to the base "r" modulo "m") for "r" ≡ "a" (mod "m") if "r" is a primitive root of "m" and gcd("a","m") = 1.

Nechť formula_1 jsou přirozená čísla, pro něž platí formula_2. Potom každé číslo formula_3 odpovídající uvedené rovnici nazveme diskrétní logaritmus o základu formula_4 z formula_5 vzhledem k modulu formula_6. Tato definice nedefinuje číslo formula_3 jednoznačně, proto se někdy upravuje tak, že ze všech možných diskrétních logaritmů ve smyslu předchozí definice se vybere ten nejmenší.


History.

Origin to Middle Ages.

In the early Middle Ages, Ostend was a small village built on the east-end () of an island (originally called Testerep) between the North Sea and a beach lake. Although small, the village rose to the status of "town" around 1265, when the inhabitants were allowed to hold a market and to build a market hall.  The major source of income for the inhabitants was fishing. The North Sea coastline has always been rather unstable due to the power of the water. In 1395 the inhabitants decided to build a new Ostend behind large dikes and further away from the always-threatening sea.

15th to 18th century.

The strategic position on the North Sea coast had major advantages for Ostend as a harbour but also proved to be a source of trouble. The town was frequently taken, ravaged, ransacked and destroyed by conquering armies. The Dutch rebels, the Gueuzen, took control of the town. The Siege of Ostend, 1601 to 1604, of which it was said that "the Spanish assailed the unassailable and the Dutch defended the indefensible", cost a combined total of more than 80,000 dead or wounded, making it the single bloodiest battle of the Eighty Years' War. This shocking event set in motion negotiations that led to a truce several years later. When the truce broke down, it became a Dunkirker base.  After this era, Ostend was turned into a harbour of some importance. In 1722, the Dutch again closed off the entrance to the world's biggest harbour of Antwerp, the Westerschelde. Therefore, Ostend rose in importance because the town provided an alternative exit to the sea. The Belgium Austriacum had become part of the Austrian Empire. The Austrian Emperor Charles VI granted the town the trade monopoly with Africa and the Far-East. The Oostendse Compagnie (Ostend trade company) was allowed to found colonies overseas. However, in 1727 the Oostendse Compagnie was forced to stop its activities because of Dutch and British pressure. The Netherlands and Britain would not allow competitors on the international trade level. Both nations regarded international trade as "their" privilege.

19th century.

On 19 September 1826 the local artillery magazine exploded. At least 20 people were killed and a further 200 injured. The affluent quarter of d'Hargras was levelled and scarcely a building in the city escaped damage. Disease followed the devastation leading to further deaths.  The harbour of Ostend continued to expand because the harbour dock, as well as the traffic connections with the hinterland, were improved. In 1838, a railway connection with Brussels was constructed. Ostend became a transit harbour to England in 1846 when the first ferry sailed to Dover. An October 1854 meeting of American envoys led to the Ostend Manifesto. Important for the image of the town was the attention it started to receive from the Belgian kings Leopold I and Leopold II. Both monarchs liked to spend their holidays in Ostend. Important monuments and villas were built to please the Royal Family, including the Hippodrome Wellington horse racing track and the Royal Galleries. The rest of aristocratic Belgium followed and soon Ostend became known as "the queen of the Belgian sea-side resorts".  In 1866, Ostend was the venue for a crucial meeting of exile Spanish Liberals and Republicans which laid the framework for a major uprising in their country, culminating in Spain's Glorious Revolution two years later.

20th century.

Ostend (in common with nearly the entirety of the country) was occupied by German forces and used as an access point to the sea for submarines and other light naval forces for much of the duration of World War I. As a consequence the port was subjected to two naval assaults by the Royal Navy.  The town hosted all of the sailing events for the 1920 Summer Olympics for Antwerp. Only the finals of the 12 foot dinghy were sailed in Amsterdam. Ostend also hosted the polo events.  World War II involved a second occupation of the town by Germany within a period of little more than twenty years; an occupation which it shared this time with most of northern Europe. Both conflicts brought significant destruction to Ostend. In addition, other opulent buildings which had survived the wars were later replaced with structures in the modernist architecture style.

21st century.

Ostend's Winter in the Park festival draws more than 600,000 people to the seaside city. During December, Ostend's Christmas market, one of the largest in Europe, features vendors and food sellers along with ice skating, music and other events. A light-show tunnel on one of the major shopping streets attracts and amuses visitors from all over Belgium, Europe and beyond.  Ostend is becoming a year-round destination known for its beach, wide-variety of restaurants, activities for all ages and warm-welcoming people.

Sights.

Ostend is known for its sea-side esplanade, including the Royal Galleries of Ostend, pier, and fine-sand beaches. Ostend is visited by many day-trippers heading to the beaches, especially during July and August. Tourists from inland Belgium and foreigners mostly arrive by train (day trips) and head for the closest beach area, the "Klein Strand", located next to the pier. The locals and other residents in Belgium usually occupy the larger beach (het Groot Strand).  Near the beach is a well-preserved section of the fortified Atlantic Wall, open to the public as the Atlantic Wall Open Air Museum located in Raversijde. One can walk through the streets around "Het Vissersplein". At certain times, there are markets in the neighbourhood streets and in the summer the "Vissersplein" has music festivals. The "Vissersplein" ("Bonenstraat"/"Kadzandstraat") is a car free zone with many brasseries where patrons can sit outside and have a drink. Towards the port side there are many little fish outlets, and beyond that the ferries can be observed docking.  Notable sites include:

Museums.

The James Ensor museum can be visited in the house where the artist lived from 1917 until 1949.  The Mu.Zee (merged from the and the ) is the museum of modern art (from the 1830s to the present) and displays works of noted local painters such as James Ensor, Leon Spilliaert, Constant Permeke and the revolutionary post-war Belgian COBRA movement amongst others.

Climate.

Ostend has a maritime temperate climate, influenced by winds from the North Sea, making summers cooler than inland Europe. 24-hour average temperatures below the freezing point is a rare occurrence. According to the Köppen Climate Classification system, Ostend has a marine west coast climate, abbreviated "Cfb" on climate maps.

Transport.

Ostend–Bruges International Airport located 5 km from Ostend is primarily a freight airport but offers passenger flights to leisure destinations in Southern Europe and Turkey. TUI fly Belgium has its headquarters in Ostend. TAAG Angola Airlines's Ostend offices are on the grounds of Ostend Airport.  The Ostend railway station is a major hub on the National Railway Company of Belgium network with frequent InterCity trains serving Brugge railway station, Gent-Sint-Pieters, Brussels South and Liège-Guillemins on Belgian railway line 50A.  Ostend formerly had busy ferry routes to Dover and Ramsgate, but the last of these services ended with the failure of TransEuropa Ferries in 2013.

Notable residents.

References to these notable citizens of Ostend can be found on the oostende.be website.

In popular culture.

Ostend has been used as a film location by numerous directors. The movies "Place Vendôme" with Catherine Deneuve; "Daughters of Darkness" with Delphine Seyrig as Countess Bathory; "Armaguedon" with Alain Delon; "Camping Cosmos" with Lolo Ferrari; and "Ex Drummer" based on the novel by Herman Brusselmans were partially shot in Ostend.  The comic "", about a dreadful invasion of rats, is set in Ostend.

Ostend (, ; ; ; ) is a coastal city and municipality, located in the province of West Flanders in the Flemish Region of Belgium. It comprises the boroughs of Mariakerke, Raversijde, Stene and Zandvoorde, and the city of Ostend proper – the largest on the Belgian coast.

Ostende (nizozemsky "Oostende") je lázeňské a přístavní město v belgické provincii Západní Flandry ve Vlámském regionu. Je největším městem belgického pobřeží a leží přibližně v jeho středu 35 km od hranic s Nizozemskem a 30 km od hranic s Francií. Ostende má 70 618 obyvatel (údaj z 1. ledna 2015) a rozkládá se na ploše 37,72 km2.


History.

Early history.

Korea (Joseon) was not introduced to the sport of association football until the late 19th century; it is often said that soccer in Korea dates to 1882, when British sailors from played a game while their vessel was visiting the Incheon Port. Korea became a Japanese colony in 1905 and was annexed into it outright in 1910.  In 1921, the first All Joseon Football Tournament was held, and in 1928, the Joseon Football Association was organized, which created a foundation to disseminate and develop football in Korea. Korean teams participated in competitions with Japanese teams from around 1926; Joseon Football Club became a "de facto" national team for Koreans, and won the 1935 Emperor's Cup. Koreans also played on the Japanese national team, most notably Kim Yong-sik who played for Japan at the 1936 Summer Olympics.  The Joseon FA was reorganized in 1945 as Japanese occupation ended with the close of World War II. Following the establishment of the South Korean state in the late 1940s, a new Korea Football Association (KFA) was founded in 1948 and joined FIFA, the international football governing body. The same year, the South Korean national team made its international debut and won 5–3 against Mexico at the 1948 Summer Olympics in London.

The first World Cup team (1954).

In 1954, South Korea first entered the FIFA World Cup qualification, and qualified to participate at the 1954 FIFA World Cup by defeating Japan 7–3 on aggregate with Choi Chung-min's three goals. South Korea became the second Asian team ever to compete at the FIFA World Cup after the Dutch East Indies (Indonesia). South Korea played games against Hungary and Turkey, losing 9–0 and 7–0 respectively. The game scheduled against West Germany was never played because neither were seeded in their group, as per that tournament's rules. It would take thirty-two years before South Korea was able to participate at the World Cup finals again. South Korea succeeded in rally by winning the 1956 AFC Asian Cup.  In 1960, South Korea won the second AFC Asian Cup by defeating South Vietnam, Israel and Republic of China. However, South Korean players received fake medals, which are not made of gold, and returned them to the KFA. The KFA promised them to give real medal, but it wasn't achieved for over 50 years. South Korea didn't won the Asian Cup after the 1960 AFC Asian Cup and the incident was called the "Curse of the fake medal" in South Korea. On 4 January 2019, the KFA had an event to give gold medals to members and bereaved families.

Foundation of Yangzee (1967).

In 1965, the South Korean government had lack confidence about a football match against North Korea and withdrew the 1966 FIFA World Cup qualification to avoid them. Kim Yong-sik, the KFA vice-president at that time, had evaluated North Korea as a world class team, and actually they advanced to the quarter-finals at the 1966 FIFA World Cup. In 1967, the South Korean Central Intelligence Agency founded Yangzee FC and collected footballers, famous in South Korea including Lee Hoe-taik, Kim Ho and Kim Jung-nam, to train them intensively. The club also participated in the 1967 Merdeka Tournament and the 1969 Asian Club Championship. At the 1968 Summer Olympics qualification, South Korea was eliminated by goal difference although their points were tied with Japan, the group winners. South Korea also failed to qualify for the 1970 FIFA World Cup, but achieved a good result by winning the 1970 Asian Games.

Golden generation (1986).

In 1986, South Korea won the East Asian tournament of the 1986 FIFA World Cup qualification with two wins against Japan in the final round, and was able to qualify for the World Cup for the first time since 1954. The South Korean squad, joined Cha Bum-kun, one of the greatest forward of German Bundesliga at that time, in the existing team which included Park Chang-sun, Huh Jung-moo, Cho Kwang-rae, Choi Soon-ho, Kim Joo-sung, etc, was evaluated as the golden generation in their country before the 1986 FIFA World Cup. South Korea lost 3–1 to the eventual champion Argentina but Park Chang-sun scored the first South Korean goal of the World Cup in the first group match. They drew 1–1 with Bulgaria and faced the defending champion Italy in the crucial last match. They conceded Alessandro Altobelli's opening goal, but Choi Soon-ho scored the equalizer in the outside of the penalty area. However, Altobelli's second goal was followed by Cho Kwang-rae's fatal own goal, and South Korea lost 3–2 in the match although Huh Jung-moo pulled one back. Afterwards, South Korean newscasts and journalists criticized the referee David Socha, claiming that his judgements about situations of the game were poor. South Korea redeemed failure of World Cup with a gold at the 1986 Asian Games.

Tragedy of Marseille (1998).

In 1997, Cha Bum-kun became the head coach going into the 1998 FIFA World Cup qualification. South Korea consecutively won early four qualifiers against Kazakhstan, Uzbekistan, Japan and United Arab Emirates, and quickly solidified their position as first place of the group. At the 1998 FIFA World Cup, they lost their first match against Mexico 3–1. Ha Seok-ju turned a free kick into the opening goal, but three minutes after scoring, he was sent off after receiving a red card. They then faced the Netherlands, managed by Guus Hiddink, and lost 5–0 in Marseille. Cha Bum-kun was sacked after the loss to the Netherlands although the tournament was ongoing. However, the South Korean goalkeeper Kim Byung-ji struggled in the Netherlands' 17 shots on target, and became the only player who received acclaim, although conceded five goals. The team then managed a 1–1 draw against Belgium.

Hiddink's magic (2002).

On 18 December 2000, the KFA named Dutch coach Guus Hiddink as the manager of the team for the 2002 FIFA World Cup, co-hosted in South Korea. The KFA promised him to ensure long-term training camps and authority about management of coaching staff. At the 2001 FIFA Confederations Cup, they lost 5–0 against France, the eventual champions, and failed to advance to the semi-finals although defeating Australia and Mexico. South Korean journalists criticized Hiddnk and gave him a nickname "Oh-dae-ppang", meaning five to nothing, when South Korea lost 5–0 again at the friendly match against Czech Republic after the Confederations Cup. At the 2002 CONCACAF Gold Cup, South Korea finished in fourth place with two draws and three losses without a win. However, their results improved at three friendly matches prior to the World Cup against Scotland, England and France. South Korea co-hosted the 2002 FIFA World Cup tournament with Japan. They had never won a game in the World Cup previously but the South Korean team achieved their first ever victory in a World Cup with a 2–0 victory against Poland when the tournament began. Their next game was against the United States and earned a 1–1 draw, with striker Ahn Jung-hwan scoring a late game equalizer. Their last game was against the favored Portuguese side. Portugal earned two red cards in the match, reducing them to nine men and Park Ji-sung scored the winning goal in a 1–0 victory, allowing the South Korean team to qualify for the second round for the first time in their history. The team's success led to widespread euphoria from the South Korean public, with many people joining the Red Devils, which gained widespread attention with their passionate support of the team.  South Korea's second round opponents were Italy, who they defeated 2–1. The South Korean team was awarded an early penalty but Ahn Jung-hwan's effort was saved by Italian keeper Gianluigi Buffon. Christian Vieri then scored to put Italy ahead but Seol Ki-hyeon scored an equalizer in the 88th minute, allowing the game to go through to extra time. Francesco Totti was controversially sent off for an alleged dive and Ahn redeemed his missed penalty by scoring the winner with a headed golden goal, allowing them to advance to the quarter-final. South Korea faced Spain in the quarter-finals. Spain managed to score twice in this match, but both goals were cancelled by the referees. The game then went to the penalty shoot-out where South Korea won 5–3, thus becoming the first Asian team to reach the final four. The South Korean team's run was halted by a 1–0 loss to Germany in the semi-finals. They lost to Turkey 3–2 in the third-place match and finished the tournament in fourth place.  Team captain Hong Myung-bo received the Bronze Ball as the World Cup's third best player, the first Asian footballer to be awarded this. In addition Hong was selected for the team of tournament alongside teammate Yoo Sang-chul, the first and only time Asian footballers have been named. This level of success was unprecedented for a country that had never before won a game in the World Cup. They had gone further than any Asian team and upset several established European teams in the process, leading to an increase in the popularity of football in the country. Hiddink became a national hero in South Korea, becoming the first person to be granted honorary citizenship as well as being given a private villa.

Captain Park era (2008).

In 2008, South Korea chose Huh Jung-moo as their manager again and Park Ji-sung as the next captain. Under Huh Jung-moo's management, the South Korean team managed to win the 2008 EAFF Championship, go undefeated for 27 consecutive games in 2009. At the fourth round of the 2010 FIFA World Cup qualification, they recorded four wins and four draws without a loss against North Korea, Saudi Arabia, Iran and United Arab Emirates.  At the 2010 FIFA World Cup, they won their first game against Greece 2–0, with goals from Lee Jung-soo and Park Ji-sung. They then faced Argentina and suffered a large loss 4–1, including an own goal by forward Park Chu-young. They then obtained a 2–2 draw in a match against Nigeria, with Lee Jung-Soo scoring in the tournament once more and Park Chu-young redeeming his own goal from the previous game by scoring from a free kick. This allowed them to make it to the second round for the first time on foreign soil. In the knockout stage they met Uruguay, who took an early lead with a goal from Luis Suárez. South Korea equalized in the second half after Lee Chung-yong scored his second goal of the tournament but South Korea conceded another goal by Suárez in the 80th minute. Despite maintaining the majority of the possession in the second half, South Korea was unable to equalize again and were eliminated from the tournament.

Miracle of Kazan (2018).

For the combined qualification matches for the 2018 FIFA World Cup and the 2019 AFC Asian Cup, South Korea won all seven matches without conceding a goal in the second round but following a series of poor results in the third round of qualifiers, including losses to China and Qatar, the former manager Uli Stielike was sacked and was replaced by under-23 coach Shin Tae-yong for the remainder of the qualifying round. Under Shin Tae-yong, the team managed to qualify as the second-placed team in their group following two goalless draws against Iran and Uzbekistan, sending South Korea to the World Cup for the ninth consecutive time. At the 2018 World Cup, they lost their first game against Sweden 1–0 after conceding a penalty kick. They then faced Mexico and lost 2–1 after conceding another penalty kick. However, despite their two consecutive losses, South Korea was not eliminated just yet. To have any chance of advancing, South Korea would have to win their final group stage match against the defending champions Germany by at least two goals and Mexico would have to defeat Sweden in its last group stage game. South Korea for its part did what it had to do to stay in contention and won 2–0 against Germany with goals from Kim Young-gwon and Son Heung-min, causing them to be eliminated in the first round for the first time in 80 years. Germany had 28 shots with 6 on target, but the South Korea's defense, led by keeper Jo Hyeon-woo, did not concede once. However, Mexico lost to Sweden that same day and thus South Korea ultimately finished third in the group. As a result, South Korea saved Mexico from being eliminated and Mexican fans heavily praised the Koreans and celebrated their victory in front of the South Korean embassy. The match is also called the "Miracle of Kazan" in South Korea although they dropped out of the tournament.

Team image.

Kits and crest.

Red is the traditional shirt color of the South Korean national team, who are consequently nicknamed the "Reds", while the fans are called the "Red Devils". The away shirt has varied between white and blue. In 1994, the home shirt shifted from red to white, but in October 1995, red returned as home color, paired with black shorts.  South Korea used to wear the South Korean flag as their shirt badge until 2001, when their tiger crest was unveiled. On 5 February 2020, the KFA announced a new, more simplistic logo. The emblem retained the tiger, albeit in a more minimalist design, enclosed in a rectangular frame. Red, blue and white, South Korea's traditional colors, have been maintained in the new logo.

Supporters.

The official supporter group of the national team, the Red Devils, were founded in 1995. Known for their passionate support, they are commonly referred to as the 12th man. Their most common chant is "Dae~han Minguk" (Korean: "대~한민국"; meaning: Republic of Korea), followed by five claps. The FIFA Fan Fest was introduced at the 2002 FIFA World Cup in South Korea.

Rivalries.

The traditional rival of South Korea is Japan. The football rivalry is long-seated and is often seen as an extension of an overall rivalry that runs deep between the two nations. Controversies occasionally flare up in matches between the two nations. South Korea leads the all-time series with 42 wins, 23 draws and 14 losses.  A rivalry has also developed with Iran. They have played against each other officially since 1958, totalling 31 matches as of June 2019, including nine World Cup qualifiers. These two teams were among the strongest Asian national football teams during the 1960s and 1970s. Although the teams only had one chance to play against each other in the final match of the AFC Asian Cup, in 1972, they have faced each other five consecutive times in the quarter-finals between 1996 and 2011, with each team recording two wins, two losses, and a draw. Iran leads the all-time series with 13 wins, 9 draws and 9 losses.  South Korea has had great success against China, with China failing to defeat them in 28 competitive matches before finally winning a game in 2010. They also possesses a strong rivalry with North Korea, though matches are infrequent due to diplomatic and security reasons.

Competitive record.

Champions Runners-up Third place

Head-to-head records.

As of 18 December 2019, after the match against Japan.

Results and fixtures.

Recent results and fixtures.

The following matches were played or are scheduled to be played by the national team in the past or in the upcoming twelve months.

Players.

Current squad.

The following players were called-up for the 2019 EAFF E-1 Football Championship, held in December 2019. "Caps and goals updated as of 18 December 2019, after the match against Japan."

Recent call-ups.

The following players have also been called up to the South Korea squad within the last twelve months.

Player records.

Statistics below are from matches which the KFA consider as official.

Notable players.

The following players were inducted into the Korean Football Hall of Fame or were considered as one of the Korean Football All-time Best XI. <br>Players in bold are regarded as one of the greatest South Korean footballers of all time.  Goalkeepers  Midfielders Defenders  Forwards

The Korea Republic national football team () represents Korea Republic in men's international football and is governed by the Korea Football Association. Since the 1950s, Korea Republic has emerged as a major football power in Asia and is historically the most successful Asian football team, having participated in nine consecutive and ten overall FIFA World Cup tournaments, the most for any Asian country. Despite initially going through five World Cup tournaments without winning a match, Korea Republic became the only Asian team to reach the semi-final stages when they co-hosted the 2002 tournament with Japan. Korea Republic also recorded five titles and seven-time runners-up in the AFC Asian Cup and the senior Asian Games. The team is commonly nicknamed the "Reds" by both fans and the media due to the color of their primary kit. The national team's supporting group is officially referred to as the Red Devils.

Jihokorejská fotbalová reprezentace reprezentuje Korejskou republiku na mezinárodních fotbalových akcích, jako je mistrovství světa nebo Mistrovství Asie ve fotbale. Korea patří mezi nejúspěšnější asijské fotbalové týmy. Zúčastnila se devíti závěrečných turnajů mistrovství světa a roce 2002 dosáhla semifinále, což je nejlepší výsledek asijského mužstva.


Etymology and usage.

Literally, the feminine noun "niddah" means "moved" (i.e. "separated"), and generally refers to separation due to ritual impurity. Medieval Biblical commentator Abraham ibn Ezra writes that the word "niddah" is related to the term "menadechem" (), meaning "those that cast you out".

Hebrew Bible.

The noun "niddah" occurs 25 times in the Masoretic Text of the Hebrew Bible. The majority of these uses refer to forms of uncleanliness in Leviticus. For example, in Leviticus, if a man take his brother's wife, then that is "uncleanness", "niddah." The five uses in Numbers all concern the red heifer ceremony () and use the phrase "mei niddah", "waters of separation". 2 Chronicles 29:5 includes a single exhortation of Hezekiah to the Levites, to carry the "niddah", possibly idols of his father Ahaz, out of the temple in Jerusalem. Usage in Ezekiel follows that of Leviticus. Finally, the Book of Zechariah concludes with an eschatological reference to washing Jerusalem:

Application of the Torah.

The Leviticus description of "niddah" is essentially composed of two parts: the ritual purity ("tumah and taharah") aspect "and" the prohibition of sexual intercourse aspect.

Ritual purity aspect.

The Biblical regulations of Leviticus specify that a menstruating woman must "separate" for seven days (). Any object she sits on or lies upon during this period is becomes a "carrier of tumah" ("midras uncleanness"). One who comes into contact with her "midras," or her, during this period becomes ritually impure () In addition, a man who has sexual relations with her is rendered ritually impure for seven days—as opposed to one day of impurity for coming into contact with her or her "midras" ().  While the purity laws still exist in theory, in modern times there is generally no practical consequence to becoming impure (as, e.g., the Temple in Jerusalem cannot be visited), so the laws have no practical expression.  Some later rabbinic authorities encouraged (but did not require) avoiding the "midras" of the "niddah", as a remembrance for diasporic Jews so as to not forget the purity laws. This encouragement was only for the Biblically prescribed seven-day period, not the five-day extension due to Rabbi Zeira's stringency. The Lubavitcher rabbi Menachem Mendel Schneerson discouraged abstaining from the "midras" of a "niddah" in modern times.

Sexual relations.

Leviticus further prohibits sexual intercourse with a woman who is in her "niddah" state. "And to a woman in her (state of) "niddah" impurity you should not come close (with intent to) reveal her nudity" ().  The Torah concludes by imposing the punishment of "kareth" on both individuals (man and woman) if the prohibition is violated () This "issur" (prohibition) component of physical relations with the "niddah" is considered in full effect and mandatory for all children of Israel.

Practical laws.

Start of menstruation.

According to rabbinical law, a woman becomes a "niddah" when she is aware that blood has come from her womb, whether it is due to menstruation, childbirth, sexually transmitted disease, or other reasons. If menstruation began before she sees evidence of it, the rabbinic regulations regard her as not being "niddah" until she notices. Until this point, the regulations do not come into force.  It is not necessary for the woman to witness the flow of blood itself; it is sufficient for her to notice a stain that has indications of having originated in her womb; bloodstains alone are inadequate without such evidence, for example, if she finds a stain just after cutting her finger, she does not become a "niddah", as the blood is not obviously uterine. If she notices a bloodstain of uncertain origin, for example on her underclothing, there are a series of complicated criteria used by rabbinical law to determine whether she is "niddah" or not; the woman herself is not expected to know these criteria, and must seek the assistance of a rabbi.

Duration of niddah status.

The Biblical definition of "niddah" is any blood emission occurring within seven days from the beginning of the menstrual period. After this seven-day period, the woman may immerse in the mikveh immediately (if she has stopped menstruating). Any blood found after these seven days is considered abnormal ("zavah") blood and is subject to more stringent requirements, depending on the duration of said abnormal blood flow.  In the days of the Amoraim, because of possible confusion in determining when menstruation began and ended and hence whether blood was normal menstrual ("niddah") or abnormal ("zavah") blood, it became the accepted practice and practical halacha, that all women treat any emission as a continued abnormal flow ("zavah gedolah"—זבה גדולה), which requires counting seven abnormal-discharge-free days from the end of menstruation. This lengthening of the "niddah" period is known as Rabbi Zeira's stringency. All Orthodox and some Conservative authorities rule that these "seven clean days" must be observed.  Since according to the rules of "zavah", the seven days must be counted from the point that the abnormal discharge ceases, it has historically been considered important in Judaism to determine when this occurs. Because the leaking of semen nullifies the counting of a "clean" day, the sages enacted that the counting of seven days not begin until a minimum of 72 hours since the beginning of menstruation has passed.  Orthodox Ashkenazi Jewish custom has lengthened this to effectively five days, which has been instituted in all cases regardless of whether the woman had engaged in sexual intercourse recently or not. Thus the "niddah" state lasts at least twelve days in the Ashkenazic tradition—the five days' minimum menstrual flow, plus the subsequent seven days. The count of days begins when the woman first sees her menstrual blood, and ends twelve days later, or seven days after the flow ceases, whichever is later.  Non-Ashkenazic Jews follow a variety of customs. Although the count could start in the middle of the day, it is always considered to end on the evening of the final day. Most Sephardic Jews use a slightly more lenient calculation resulting in a minimum of eleven days.

Practices during "niddah".

In the Orthodox Jewish community, women may test whether menstruation has ceased; this ritual is known as the "hefsek taharah". The woman takes a bath or shower near sunset, wraps a special cloth around her finger, and swipes the vaginal circumference. If the cloth shows only discharges that are white, yellow, or clear, then menstruation is considered to have ceased. If discharge is red or pink, it indicates that menstruation continues. If it is any other color, like brown, it is subject to further inquiry, often involving consultation with a rabbi. The ritual requires that the cloth used to perform this test is first checked carefully to ensure that it is clean of any marks, colored threads, or specks; the cloth itself can be any clean white cloth, although there are small cloths designed for this ritual, known as "bedikah cloths" (meaning "checking").  In the Orthodox Jewish community, further rituals are practiced toward assurance regarding the cessation of the menstrual flow. After the "hefsek taharah", some women insert a cloth (or, in modern times, a tampon), consequently known as a "moch dachuk", for between 18 minutes and an hour, to ensure that there is absolutely no blood; this must be done carefully, as it could otherwise irritate the mucous membrane, causing bleeding unrelated to menstruation. If there is any fear of irritation causing bleeding, a rabbi may waive this practice. The "bedikah" is repeated each morning and evening of the seven days subsequent to the end of menstruation. Another tradition is the wearing of white underwear and use of white bedding during this period; conversely, the rest of the time, when not counting the "seven clean days", some women who suffer from spotting deliberately use coloured underwear and coloured toilet paper, since it is only when blood is seen on white material that it has any legal status in Jewish law. When not during their seven "clean" days, all women are advised to wear colored undergarments, for this reason. It is furthermore strongly recommended that women make an effort to refrain from looking at the toilet paper after wiping to avoid possible resultant questions.

Physical contact during niddah.

As with most forbidden relationships in Judaism, all physical contact in an affectionate or lustful manner is rabbinically forbidden when a woman is in her "niddah" status. Such contact is forbidden whether or not the man and woman are husband and wife.  In the case of husband and wife, however, the sages added on extra restrictions, including touch that is not in an affectionate or lustful manner, passing of objects even without touching, and sleeping in the same bed; these restrictions are to avoid the risk of leading to sexual contact. These laws are termed "harkhakot", meaning "spacers", and result in a need for relationships to be able to develop in non-physical ways, such as emotional and spiritual connections.  Some Conservative poseks are considerably more lenient in reference to the "harkhakot" than Medieval or contemporary Orthodox authorities. In a responsum written in the Committee on Jewish Law and Standards of the Rabbinical Assembly, Rabbi Miriam Berkowitz ruled that the ""harkhakot" are to be observed as much as possible, but left up to the discretion of each couple". In another responsum for the committee, Susan Grossman stated that touching that would be appropriate between siblings is permissible.  The classical regulations also forbid sexual relations on the day that a woman expects to start menstruating; there are three days that fall under this regulation, known as the "veset", namely the same day of the month as her previous menstruation began; the day exactly 30 days after the previous menstruation started; and the day that is the usual interval from the end of her previous menstruation. If the woman is not actually menstruating during a "veset" day, then there are certain circumstances wherein sexual activity is permitted according to most authorities, for example, if a woman's husband is about to travel, and will return only after menstruation has begun.

Niddah and fertility.

Because the night that the woman ritually traditionally immerses is about 12 days after menstruation began, it often coincides with a woman's ovulation, and thus improves the chances of successful conception if sexual relations occur on that night. However, for certain women, this period extends far past the date of ovulation, and in combination with the ban on sexual relations during the "niddah" state, effectively results in the woman being unable to conceive, a situation sometimes called "halachic infertility". In the case of this effective infertility, rabbis try on a case-by-case basis to relax halakhic strictures in order to facilitate conception. There have been some calls within Orthodox Judaism for the custom to be modified so that the time between the end of menstruation and the end of "niddah" is shorter for these women.

Checking by bedikah.

The "bedikah" cloth or "checking cloth", called an "eid" ["witness"] in Hebrew, is a clean piece of white cloth used in the process of purifying a "niddah". It is used by observant Jewish women to determine whether they have finished menstruation. The cloth is inserted into the vagina, and if no blood is found, the woman may start counting the seven blood-free days. On each of these days, she performs this examination in the morning and in the later afternoon before sunset. If no blood is found, she may go to the "mikveh" on the eighth evening after nightfall, and then engage in intercourse with her husband. Such cloths are about two by four inches, and are available at local Judaica stores, the local mikveh, stores in Orthodox neighborhoods in Israel, or may be cut from clean all-white soft cotton or linen fabric.  This practice is also occasionally used by Jewish men to check if he has gotten blood on himself from his wife after intercourse to determine whether she menstruated during intercourse.

Immersion in water.

There are differing customs about how many immersions are performed at each visit to a mikveh. It is the custom of many in the Orthodox community to immerse at least twice. Accordingly, they would immerse, recite the blessing, then immerse again. The other opinion states that like other commandments, here too the blessing should be recited before performing the commandment.  Immediate preparation for a mikveh includes a bath or shower wherein every part of the body (including the ears and underneath the nails) is thoroughly washed; plus other routine hygiene practices which include trimming fingernails and toenails, brushing and flossing the teeth, and combing the hair. At the mikvah itself, a female attendant is present to make certain that the woman immerses herself fully, including her hairs. Though that is the attendant's foremost duty, she may also help by checking a woman's back or answer questions regarding proper ritual protocol.

Newlyweds.

According to all Orthodox authorities, the first time a virgin has intercourse, she also becomes "niddah" as a result of her "dam betulim" (Hebrew: "hymenal blood flow"). This is observed even if no blood was discovered. However, a bride counts only four days before performing a "hefsek taharah" (Hebrew: lit. pause of purity), instead of the usual five. Some Conservative authorities rule that a woman is not a niddah in such a case unless uterine bleeding is observed.

Privacy of the niddah process.

Out of "tzniut" (Hebrew for "modesty"), many Orthodox Jews and some Conservative Jews follow a custom of keeping their times of "niddah" secret from the general public.

Conservative Judaism.

Conservative Judaism authorities teach that the laws of family purity are normative and still in force, including the requirement to refrain from sexual relations during "niddah", yet there is a difference of opinions over how much other strictures need to be observed, such as whether there should be complete prohibition on any touching during "niddah" and whether women are required to count seven "clean" days before immersing in the "mikveh".  In December 2006, the Rabbinical Assembly's Committee on Jewish Law and Standards passed three responsa discussing the extent of Biblical requirements and continuing applicability rabbinic prohibitions concerning niddah for Conservative Jews. Each responsum advocated different standards of observance; two responsa were passed as majority opinions, one by Rabbi Susan Grossman and one by Rabbi Avram Reisner, the third responsum, by Rabbi Miriam Berkowitz was passed as a minority opinion.  According to two majority opinions, by Rabbi Grossman and Rabbi Reisner, the "seven clean days" need not be observed today and women may immerse and resume sexual relations after seven days from the beginning of menstruation, or after its cessation, if it lasts longer than seven days. Rabbi Grossman, a majority opinion, and Rabbi Berkowitz, the minority opinion, ruled that women may rely on their own discretion about when menstruation has ended, and need not routinely engage in "bedikah" as described above.  Despite the official stance, the practices related to family purity have often not been widely followed by Conservative Jews. However, in an issue of the "United Synagogue Review" that focused on issues of "mikvah" and "niddah" (published in conjunction with the passing of the responsa mentioned above, in Fall/Winter 2006), Rabbi Myron S. Geller, a member of the Committee on Jewish Law and Standards, wrote about an upswing in the observance of the laws of family purity within the Conservative Jewish community:  Conservative Judaism has largely ignored this practice in the past, but recently has begun to reevaluate its silence in this area and to consider the spiritual implications of mikvah immersion for human sexuality and for women.

Reform Judaism.

Reform Judaism and other liberal denominations have largely rejected many of the rituals and prohibitions associated with menstruation, particularly the use of a "mikveh".

Niddah (or nidah; ), in traditional Judaism, describes a woman during menstruation, or a woman who has menstruated and not yet completed the associated requirement of immersion in a "mikveh" (ritual bath).

Nida ( nebo ) je v judaismu menstruující žena a doslova tento termín znamená oddělení. Obecně pak znamená oddělení od rituální nečistoty. Podle židovského náboženského práva je během období menstruace mezi manželi zapovězen mj. pohlavní styk a fyzický kontakt vůbec, stejně jako jiné formy sbližování. Po skončení menstruace následuje sedmidenní období, po němž se žena ponoří do rituální koupele ("mikve") a až poté je rituálně čistá. Nida je hlavní kategorií židovského zákona zabývající se sexuálními záležitostmi – eufemisticky nazývaného „čistota rodiny“ ("taharat mišpacha" – nehodilo by se, aby se zákon nazýval „nečistota rodiny“).


Description.

The titan beetle is one of the largest beetles, with the largest reliable measured specimen being in length, comparable to such beetles as "Xixuthrus heros" () and the Hercules beetle, "Dynastes hercules", in which giant males occasionally can grow up to, but the Hercules beetle males have an enormous horn on the pronotum or thorax making up around half of its total length. As such, the body of the Titan beetle is considerably larger than that of the Hercules beetles. The short, curved and sharp mandibles are known to snap pencils in half and cut into human flesh. Adult titan beetles do not feed, searching instead for mates via pheromones while in flight.  The larvae have never been found, but are thought to feed inside wood and may take several years to reach full size before they pupate. These beetles are also thought to feed on decaying wood below the ground. Boreholes thought to be created by titan beetle larvae seem to fit a grub over two inches wide and perhaps as much as one foot long. A famous "life-sized" photograph of a putative larva of this beetle appeared in "National Geographic" magazine, filling an entire page, but it turned out to be of a different species of beetle, possibly "Macrodontia cervicornis".  The adults defend themselves by hissing in warning and biting, and have sharp spines, as well as strong jaws.

Distribution.

It is known from the rain forests of Venezuela, Colombia, Ecuador, Peru, the Guianas, and north-central Brazil.

The titan beetle ("Titanus giganteus") is a neotropical longhorn beetle, the sole species in the genus Titanus, and one of the largest known beetles.

Titán obrovský ("Titanus giganteus", alternativní české názvy jsou titan obrovský a tesařík největší) je brouk, často udávaný jako jediný zástupce rodu "Titanus". Titán obrovský je největší známý brouk a zástupce recentního hmyzu vůbec. Jeho největší doložitelný exemplář má délku těla 16,7 cm (21-22 cm se započtením tykadel) a hmotnost 65 g. Obývá deštné pralesy Jižní Ameriky.


Background.

The lake is mostly within the borders of the Canton of Zug, with about at its southern end in the canton Schwyz, while the Canton of Lucerne claims about to the north of Immensee. Toward the south-west extremity of the lake the Rigi descends rather steeply to the water's edge, while part of its east shore forms a narrow level band at the foot of the 1,583 m (5,194 ft) Rossberg, and the Zugerberg. The culminating point of the lake's drainage basin is the summit of the Rigi at 1,798 m.  At its northern end, the shores are nearly level, while on the west shore the wooded promontory of Buonas (with its castles, old and new) projects picturesquely into the waters. The principal place on the lake is the town of Zug. Three railways follow the shore of the lake, one from Zurich via Zug and Arth-Goldau to the St Gotthard, one from Lucerne via Arth-Goldau to the St Gotthard, and the third from Zurich via Zug to Lucerne.  Many fish (including pike and carp of considerable weights) are taken in the lake, which is especially famous for an endemic kind of trout ("Salmo salvelinus", locally called "Rolheli").

History.

The first steamer was placed on the lake in 1852.  In the early 20th century, a railway (formerly part of the St. Gotthard main route) ran along its eastern shore past Walchwil to Arth at its south end, which was connected initially by a steam tramway with the Arth-Goldau station of the St Gotthard line. This line runs from Arth along the western shore to Immensee, where it bears south-west to Lucerne, while from Immensee another railway leads (at first some way from the shore) to Cham, west of Zug.

Public Transportation.

Public transportation on Lake Zug is done by the Zugersee Schifffahrt / Schifffahrtsgesellschaft für den Zugersee AG (SGZ).

Lake Zug () is a lake in Central Switzerland, situated between Lake Lucerne and Lake Zurich. It stretches for 14 km between Arth and the Cham-Zug bay. The Lorze as the main feeder river empties its waters into the lake at its northern extremity, but 1 km (0.6 mi) further west issues from the lake to pursue its course towards the Reuss. Due to this poor feeding, Environmental protection is very important as the lake would suffer long term damage if polluted as the second of the rivers, "Rigiaa", feeds only a marginal amount into the lake at its southern end. Already a great part of the fauna in the deep parts of the lake has been lost.

Zugské jezero () je jezero na severním úpatí Alp ve středním Švýcarsko. Nachází se ve staré ledovcové kotlině. Leží na území kantonů Zug, Schwyz a Lucern. Má rozlohu 38,3 km2. Je 13,7 km dlouhé a maximálně 4,6 km široké. Dosahuje maximální hloubky 198 m. Velikost povodí včetně plochy jezera je 246 km2. Leží v nadmořské výšce 413 m.