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Seven Bridges of Königsberg

The Seven Bridges of Königsberg is a historically notable problem in mathematics. Its negative resolution by Leonhard Euler in 1736 laid the foundations of graph theory and prefigured the idea of topology.

The city of Königsberg in Prussia (now Kaliningrad, Russia) was set on both sides of the Pregel River, and included two large islands—Kneiphof and Lomse—which were connected to each other, and to the two mainland portions of the city, by seven bridges. The problem was to devise a walk through the city that would cross each of those bridges once and only once.

By way of specifying the logical task unambiguously, solutions involving either are explicitly unacceptable.
 * 1) reaching an island or mainland bank other than via one of the bridges, or
 * 2) accessing any bridge without crossing to its other end

Euler proved that the problem has no solution. The difficulty he faced was the development of a suitable technique of analysis, and of subsequent tests that established this assertion with mathematical rigor.

Euler's analysis
Euler first pointed out that the choice of route inside each land mass is irrelevant and that the only important feature of a route is the sequence of bridges crossed. This allowed him to reformulate the problem in abstract terms (laying the foundations of graph theory), eliminating all features except the list of land masses and the bridges connecting them. In modern terms, one replaces each land mass with an abstract "vertex" or node, and each bridge with an abstract connection, an "edge", which only serves to record which pair of vertices (land masses) is connected by that bridge. The resulting mathematical structure is a graph.

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Since only the connection information is relevant, the shape of pictorial representations of a graph may be distorted in any way, without changing the graph itself. Only the number of edges (possibly zero) between each pair of nodes is significant. It does not, for instance, matter whether the edges drawn are straight or curved, or whether one node is to the left or right of another.

Next, Euler observed that (except at the endpoints of the walk), whenever one enters a vertex by a bridge, one leaves the vertex by a bridge. In other words, during any walk in the graph, the number of times one enters a non-terminal vertex equals the number of times one leaves it. Now, if every bridge has been traversed exactly once, it follows that, for each land mass (except for the ones chosen for the start and finish), the number of bridges touching that land mass must be even (half of them, in the particular traversal, will be traversed "toward" the landmass; the other half, "away" from it). However, all four of the land masses in the original problem are touched by an odd number of bridges (one is touched by 5 bridges, and each of the other three is touched by 3). Since, at most, two land masses can serve as the endpoints of a walk, the proposition of a walk traversing each bridge once leads to a contradiction.

In modern language, Euler shows that the possibility of a walk through a graph, traversing each edge exactly once, depends on the degrees of the nodes. The degree of a node is the number of edges touching it. Euler's argument shows that a necessary condition for the walk of the desired form is that the graph be connected and have exactly zero or two nodes of odd degree. This condition turns out also to be sufficient—a result stated by Euler and later proved by Carl Hierholzer. Such a walk is now called an Eulerian path or Euler walk in his honor. Further, if there are nodes of odd degree, then any Eulerian path will start at one of them and end at the other. Since the graph corresponding to historical Königsberg has four nodes of odd degree, it cannot have an Eulerian path.

An alternative form of the problem asks for a path that traverses all bridges and also has the same starting and ending point. Such a walk is called an Eulerian circuit or an Euler tour. Such a circuit exists if, and only if, the graph is connected and all nodes have even degree. All Eulerian circuits are also Eulerian paths, but not all Eulerian paths are Eulerian circuits.

Euler's work was presented to the St. Petersburg Academy on 26 August 1735, and published as Solutio problematis ad geometriam situs pertinentis (The solution of a problem relating to the geometry of position) in the journal Commentarii academiae scientiarum Petropolitanae in 1741. It is available in English translation in The World of Mathematics by James R. Newman.

Significance in the history and philosophy of mathematics
In the history of mathematics, Euler's solution of the Königsberg bridge problem is considered to be the first theorem of graph theory and the first true proof in the theory of networks, a subject now generally regarded as a branch of combinatorics. Combinatorial problems of other types such as the enumeration of permutations and combinations had been considered since antiquity.

Euler's recognition that the key information was the number of bridges and the list of their endpoints (rather than their exact positions) presaged the development of topology. The difference between the actual layout and the graph schematic is a good example of the idea that topology is not concerned with the rigid shape of objects.

Hence, as Euler recognized, the "geometry of position" is not about "measurements and calculations" but about something more general. That called in question the traditional Aristotelian view that mathematics is the "science of quantity". Though that view fits arithmetic and Euclidean geometry, it did not fit topology and the more abstract structural features studied in modern mathematics.

Philosophers have noted that Euler's proof is not about an abstraction or a model of reality, but directly about the real arrangement of bridges. Hence the certainty of mathematical proof can apply directly to reality. The proof is also explanatory, giving insight into why the result must be true.

Present state of the bridges

Two of the seven original bridges did not survive the bombing of Königsberg in World War II. Two others were later demolished and replaced by a highway. The three other bridges remain, although only two of them are from Euler's time (one was rebuilt in 1935). These changes leave five bridges existing at the same sites that were involved in Euler's problem. In terms of graph theory, two of the nodes now have degree 2, and the other two have degree 3. Therefore, an Eulerian path is now possible, but it must begin on one island and end on the other.

The University of Canterbury in Christchurch has incorporated a model of the bridges into a grass area between the old Physical Sciences Library and the Erskine Building, housing the Departments of Mathematics, Statistics and Computer Science. The rivers are replaced with short bushes and the central island sports a stone tōrō. Rochester Institute of Technology has incorporated the puzzle into the pavement in front of the Gene Polisseni Center, an ice hockey arena that opened in 2014, and the Georgia Institute of Technology also installed a landscape art model of the seven bridges in 2018.

A popular variant of the puzzle is the Bristol Bridges Walk. Like historical Königsberg, Bristol occupies two river banks and two river islands. However, the configuration of the 45 major bridges in Bristol is such that an Eulerian circuit exists. This cycle has been popularized by a book and news coverage and has featured in different charity events.

title: Seven Bridges of Königsberg


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Reserve power

In a parliamentary or semi-presidential system of government, a reserve power, also known as discretionary power, is a power that may be exercised by the head of state (or their representative) without the approval of another branch or part of the government. Unlike in a presidential system of government, the head of state (or their representative) is generally constrained by the cabinet or the legislature in a parliamentary system, and most reserve powers are usable only in certain exceptional circumstances.

Constitutional monarchies
In monarchies with either an uncodified or partly unwritten constitution (such as the United Kingdom or Canada) or a wholly written constitution that consists of a text augmented by additional conventions, traditions, letters patent, etc., the monarch generally possesses reserve powers.

Typically these powers are: to grant pardon; to dismiss a prime minister; to refuse to dissolve parliament; and to refuse or delay royal assent to legislation (to withhold royal assent amounts to a veto of a bill, while to reserve royal assent, in effect, amounts to a decision to neither grant nor refuse assent, but to delay taking a decision for an undetermined period). There are usually strict constitutional conventions concerning when these powers may be used, and these conventions are enforced by public pressure. Using these powers in contravention of tradition would generally provoke a constitutional crisis.

Most constitutional monarchies employ a system that includes the principle of responsible government. In such an order, the reserve powers are thought to be the means by which the monarch and his or her viceregal representatives can legitimately exist as "constitutional guardians" or "umpires", tasked with guaranteeing that Cabinet and parliament adhere to the fundamental constitutional principles of the rule of law and responsible government itself. Some constitutional scholars, such as George Winterton, have stated that reserve powers are a good thing in that they allow for a head of state to handle an unforeseen crisis and that the use of convention to limit the use of reserve powers allows for more gradual and subtle constitutional evolution than is possible through formal amendment of a written constitution. Others, such as Herbert Evatt, believe or believed that reserve powers are vestigial and potentially open to abuse. Evatt felt that the reserve powers could be codified and still serve their intended function in a responsible government system, as they do in Ireland, Japan, and Sweden.

Belgium
In Belgium a constitutional provision explicitly states that no act of the monarch is valid without the signature of a member or members of the government, which thereby becomes solely responsible, hence excluding any reserve power for the crown. In legal terminology, a competence vested in 'the King' thus very often means the government, as opposed to formal laws which require a (sometimes qualified) parliamentary majority.

Constitutional precedence has even established the unwritten but binding rule that the Monarch must give assent to any parliamentary decision, regardless of any other considerations (which can only be advanced in private audience with government members, not imposed), as soon as the government presents it for royal signature and thus assumes full political responsibility.

In 1990, when a law liberalising Belgium's abortion laws was approved by parliament, King Baudouin refused to give his royal assent, only the second time in Belgium's history the monarch elected to do so. Instead, he requested that the cabinet declare him unable to reign for a day, which it did, thereby assuming the king's constitutional powers. All members of the government then signed the bill, passing it into law. The bicameral legislature approved a proposition that Baudouin was capable of reigning again the next day.

Commonwealth realms
Within the Dominions, until the 1920s, most reserve powers were exercised by a governor-general on the advice of either the local or the British government, though the latter took precedence. After the Balfour Declaration was produced by the 1926 Imperial Conference, formally establishing the autonomy and equal status of Commonwealth governments, governors-general ceased to be advised in any way by the British government. For example, the first Governor-General of the Irish Free State, Tim Healy, was instructed by the British Dominions Office in 1922 to withhold the royal assent on any bill passed by the two houses of the Oireachtas (the Irish parliament) that attempted to change or abolish the Oath of Allegiance. However, no such bill was introduced during Healy's period in office. By the time the oath was abolished by the Irish Parliament in 1933, the Irish governor-general was formally advised exclusively by the Irish government.

Australia
While the reserve power to dismiss a government has not been used in the United Kingdom since 1834, this power has been exercised more recently in Australia, on two occasions:
 * 1) On 13 May 1932, when the Governor of New South Wales Sir Philip Game dismissed the Government of New South Wales.
 * 2) On 11 November 1975, when the Governor-General of Australia Sir John Kerr dismissed the Commonwealth Government.

In both cases an election was held very soon afterwards and, again in both cases, the dismissed government was massively defeated by popular vote.

In Queensland in 1987, during a tense period of leadership succession, the Governor of Queensland, Sir Walter Campbell, exercised reserve power in declining to follow the advice of the Premier, Sir Joh Bjelke-Petersen. Campbell initially refused to redistribute ministerial portfolios on the sole advice of the premier, who lacked the confidence of his cabinet. Subsequently, during a period when Queensland had a "Premier who is not leader" and the governing party had a "Leader who is not Premier", there was speculation on the potential exercise of vice-regal reserve power by Campbell, in dismissing the premier in the absence of a parliamentary motion of no confidence. Ultimately, Campbell was praised for his handling of the undesirable situation.

These are among several exercises of the reserve powers in Australia in the 20th century at state and federal levels.

Canada
The reserve powers in Canada fall within the royal prerogative and belong specifically to the monarch, as the Constitution Act, 1867, vests all executive power in the country's sovereign. King George VI in 1947 issued Letters Patent permitting the governor general "to exercise all powers and authorities lawfully belonging to Us [the monarch] in respect of Canada."

The reserve power of dismissal has never been used in Canada, although other reserve powers have been employed to force the prime minister to resign on two occasions: The first took place in 1896, when the Prime Minister, Sir Charles Tupper, refused to step down after his party did not win a majority in the House of Commons during that year's election, leading Governor General the Earl of Aberdeen to no longer recognize Tupper as prime minister and disapprove of several appointments Tupper had recommended. On the second occasion, which took place in 1925 and came to be known as the King–Byng affair, Prime Minister William Lyon Mackenzie King, facing a non-confidence motion in the House of Commons, advised the Governor General, the Viscount Byng of Vimy, to dissolve the new parliament, but Byng refused.

At the provincial level, on 29 June 2017 Lieutenant Governor of British Columbia Judith Guichon used her reserve powers to deny the request of Premier Christy Clark to dissolve the legislature and call a new election only 51 days after the recent provincial election. Clark had advised Guichon to dissolve the legislature as, in her view, the appointment of a Speaker would have resulted in frequent tie votes and an untenable position. Guichon refused this advice and instead asked John Horgan to form a government, becoming the new premier.

No modern governor general has disallowed a bill, though provincial lieutenant governors have.

Peter Hogg, a constitutional scholar, has opined that "a system of responsible government cannot work without a formal head of state who is possessed of certain reserve powers." Further, Eugene Forsey stated "the reserve power is indeed, under our Constitution, an absolutely essential safeguard of democracy. It takes the place of the legal and judicial safeguards provided in the United States by written Constitutions, enforceable in the courts."

New Zealand
New Zealand's early governors, the predecessors of today's governors-general, exercised considerable power, with exclusive authority over some matters such as foreign and Māori affairs. They also had a real choice in selecting premiers – parliaments of the period being composed of independent members who formed loose and shifting factions – and were not always obliged to act on the advice of their ministers. As New Zealand's political system matured, the Colonial Office increasingly instructed the governors to follow the advice of local ministers, and the powers of the office have continually shrunk. Important remnants of these early powers remain. The governor-general has a number of reserve powers, which may be used on behalf of King Charles III. Sir Kenneth Keith describes the use of these powers as based on the principle that "The Queen reigns, but the government rules, so long as it has the support of the House of Representatives".

The most visible reserve powers are the power to appoint a prime minister and the related power to accept a prime minister's resignation. This power is exercised every time a general election results in a change of government, most recently in 2023. It may also be exercised if a prime minister loses the confidence of Parliament and resigns instead of advising a dissolution of Parliament; the last such occasion was in 1911. Finally, it may happen if a Prime Minister is maneuvered out of their position by their own party, retires or resigns for personal reasons, or dies in office. Though the power of appointment is listed among the reserve powers, in fact the governor-general abides by strict conventions, and has always appointed the leader of the dominant faction in the House of Representatives. The governor-general retains the theoretical power to appoint as prime minister a member of the House of Representatives who clearly does not have the support of a majority of MPs, but no governor-general has sought to use this power since New Zealand gained responsible government, though some cabinets in the 19th century proved extremely short-lived. In earlier times, if a prime minister died, became incapacitated, or resigned unexpectedly, a governor-general might be able to choose a temporary prime minister from among several senior ministers, while the governing party decided on a new leader who would then be duly appointed prime minister. Today, however, the practice of appointing – on prime-ministerial advice – a permanent deputy prime minister, who becomes acting prime minister when needed, has largely removed even this discretion from the governor-general.

The governor-general has a number of other legal powers. They may dismiss an incumbent prime minister and Cabinet, an individual minister, or any other official who holds office "during the King's pleasure" or "during the Governor-General's pleasure". Conventionally, the governor-general follows the advice of the prime minister or another appropriate minister in matters of appointment and dismissal. Likewise, by convention, the Government as a whole remains in office as long as it keeps the confidence of the House.

The governor-general can also dissolve Parliament and call elections without prime-ministerial advice. Dissolving Parliament and calling for elections is part of the governor-general's normal duties; every parliamentary dissolution and subsequent general election in New Zealand's history has been called by the governor or governor-general. However, all elections since responsible government was introduced, including snap elections, have been requested by the incumbent premier or prime minister, and are accordingly not examples of use of the reserve powers. A prime minister who has lost the confidence of the House will conventionally either advise a dissolution of Parliament and new elections, or tender their resignation. If a defeated prime minister refuses to do either of these two things, the governor-general could use the reserve powers to either dismiss the prime minister (see above), or dissolve Parliament without the prime minister's advice. Likewise, if the prime minister tenders their resignation, the governor-general could theoretically refuse to accept it, and dissolve Parliament against the Prime Minister's advice.

A governor-general can also refuse a prime minister's request to dissolve Parliament and hold elections. If a prime minister has been defeated by a vote of no confidence, a refusal by the governor-general to dissolve Parliament would, in effect, force the prime minister to resign and make way for a successor. See the Lascelles Principles for factors which might guide the governor-general in making a decision on whether or not to grant a dissolution in those circumstances. A governor-general could also legally refuse a request for a snap election from a prime minister in whom the House has confidence, but such a refusal would be extremely unlikely.

The power to withhold royal assent to Bills is controversial. Many constitutional commentators believe that the governor-general (or the sovereign) no longer has the power to refuse royal assent to any bill properly passed by the House of Representatives – former law professor and Prime Minister Sir Geoffrey Palmer and Professor Matthew Palmer argue any refusal of royal assent would lead to a constitutional crisis. Others, such as Professor Philip Joseph, believe the Governor-General does retain the power to refuse royal assent to Bills in exceptional circumstances - such as the abolition of democracy. A similar controversial power is the ability to refuse to make Orders and regulations advised by the Government or by individual Ministers.

There have been a handful of occasions when reserve powers were used, or at least considered.

In the 1890s, Premier John Ballance advised the Governor to make several new appointments to the (since abolished) Legislative Council. Two successive Governors, the Earl of Onslow and the Earl of Glasgow, refused to make the appointments, until the Colonial Office intervened in Ballance's favour. This incident markedly reduced the discretionary powers of the Governor. Though these remained the same in law for the time being, later Governors and governments considered that there would be far fewer scenarios in which their use would be appropriate.

Almost a century later, in 1984, there was a brief constitutional crisis. The outgoing Prime Minister, Sir Rob Muldoon, had just lost an election, but refused to advise the Governor-General, Sir David Beattie, to make urgent regulations desired not only by the incoming Prime Minister, David Lange, but also by many in Muldoon's own party and cabinet. At the time, the option of Beattie dismissing Muldoon and replacing him, without waiting for Muldoon's resignation, was reportedly discussed. Muldoon eventually relented under pressure from his own cabinet, making the use of Beattie's reserve powers unnecessary.

Saint Kitts and Nevis
A constitutional crisis occurred in Saint Kitts and Nevis in 1981, when the governor, Sir Probyn Inniss, used his reserve powers to refuse assent to a bill passed by the government of Sir Kennedy Simmonds, the country's premier. Inniss believed that the bill was unconstitutional, and would soon be struck down by the West Indies Associated States Supreme Court. The situation was resolved when Queen Elizabeth II, at the request of Simmonds, terminated Inniss's commission as governor.

Tuvalu
The Constitution of Tuvalu provides, in article 52, that the Governor-General exercises his powers "only in accordance with the advice of (a) the Cabinet; or (b) the Prime Minister [...] except where he is required to act (c) in accordance with the advice of any other person or authority [...] or (e) in his own deliberate judgment (in which case he shall exercise an independent discretion)".

In 2013, Governor-General Sir Iakoba Italeli was requested by the Opposition to act without (and indeed against) the Prime Minister's advice. On 28 June, Prime Minister Willy Telavi's government had lost a crucial by-election, which gave the Opposition a majority of one in Parliament. The Opposition immediately called for the government to reconvene Parliament, so that a motion of no confidence could be introduced, and a new government formed. Prime Minister Telavi responded that, under the Constitution, he was only required to convene Parliament once a year (for a vote on the budget), and was thus under no obligation to summon it until December. The Opposition turned to the Governor-General. On 3 July, Italeli exercised his reserve powers in ordering Parliament to convene, against the Prime Minister's wishes, on 30 July.

In the end, the Governor-General dismissed the Prime Minister from office.

United Kingdom
In the UK, the monarch has numerous theoretical personal prerogatives, but beyond the appointment of a prime minister, there are in practice few circumstances in modern British government where these prerogatives could be justifiably exercised; they have rarely been exercised in the last century. In October 2003 the Government made public the following prerogatives but it said at the time that a comprehensive catalogue of prerogative powers could not be supplied:
 * To refuse to dissolve Parliament when requested by the prime minister. This was last reputedly considered in 1910, but George V later changed his mind. Harold Wilson, leading a minority government in 1974, was told that Elizabeth II might refuse to dissolve Parliament if she could identify an alternative prime minister able to command a cross-party majority. See Lascelles Principles.
 * To appoint a prime minister of his [her] own choosing. This was last done in Britain in 1963 when Elizabeth II appointed Sir Alec Douglas-Home as prime minister, on the advice of outgoing Harold Macmillan.
 * To dismiss a prime minister and his or her government on the monarch's own authority. This was last done in Britain in 1834 by King William IV.
 * To summon and prorogue Parliament
 * To command the armed forces
 * To dismiss and appoint ministers
 * To commission officers in the armed forces
 * To appoint King's Counsel
 * To issue and withdraw passports
 * To create corporations via royal charter
 * To appoint bishops and archbishops of the Church of England
 * To grant honours
 * To grant the prerogative of mercy
 * To delay a bill's assent through the use of his or her reserve powers in near-revolutionary situations, thereby vetoing the bill
 * To refuse the royal assent of a parliamentary bill on the advice of ministers, last exercised by Queen Anne when she withheld royal assent from the Scottish Militia Bill 1708
 * To declare war and peace
 * To deploy the armed forces overseas
 * To ratify and make treaties
 * To refuse the "King's Consent", where direct monarchical assent is required for a bill affecting, directly or by implication, the prerogative, hereditary revenues—including ultimus haeres, treasure trove, and bona vacantia—or the personal property or interests of the Crown to be heard in Parliament. In 1999, Queen Elizabeth II, acting on the advice of the government, refused to signify her consent to the Military Action Against Iraq (Parliamentary Approval) Bill, which sought to transfer from the monarch to Parliament the power to authorise military strikes against Iraq.

These powers could be exercised in an emergency such as a constitutional crisis (such as surrounded the People's Budget of 1909) or in wartime. They would also be very relevant in the event of a hung parliament.

For example, in the hung parliament in 1974, the serving Prime Minister, Edward Heath, attempted to remain in power but was unable to form a working majority. The Queen then asked Harold Wilson, leader of the Labour Party, which had the largest number of seats in the Commons but not an overall majority, to attempt to form a government. Subsequently, Wilson asked that if the government were defeated on the floor of the House of Commons, the Queen would grant a dissolution, which she agreed to.

Japan
Unlike most other constitutional monarchs, the Emperor of Japan has no reserve powers. Following Japan's defeat in World War II, the Emperor's role is defined in Chapter I of the 1947 Constitution of Japan, as decided by the foreign powers that had defeated the country. It states that sovereignty rests with the Japanese citizenry, not the Emperor who is merely the symbol of the State and the unity of the people.

Malaysia
The Yang di-Pertuan Agong (the elected supreme federal ruler, commonly glossed as “King”) has no reserve powers. Article 40 of the Malaysian constitution specifies only three powers of the Agong: to reject a request to dissolve Parliament, to convene a meeting of the Conference of Rulers; and to appoint the Prime Minister, whom he has no power to dismiss.

Spain
The Spanish Constitution of 1978 does not specifically grant emergency powers to the government, though does state in Article 56 that the monarch "arbitrates and moderates the regular functioning of the institutions", and invests the monarch with the responsibility of overseeing that the forms of the constitution are observed. It is through this constitutional language that wider "reserve powers" are granted to the monarch. It is through this clause and his position as commander-in-chief of the Spanish Armed Forces that King Juan Carlos I undermined the attempted 23-F military coup in 1981.

Title II, Articles 56

''The King is Head of State, the symbol of its unity and permanence. He arbitrates and moderates the regular functioning of the institutions, assumes the highest representation of the Spanish State in international relations, especially with the nations of its historical community, and exercises the functions expressly conferred on him by the Constitution and the laws''.

The Spanish Constitution of 1978, Title II The Crown, Article 62, delineates the powers of the monarch, while Title IV Government and Administration, Article 99, defines the monarch's role in government. Title VI Judicial Power, Article 117, Articles 122 through 124, outlines the monarch's role in the country's independent judiciary. However, by constitutional convention established by Juan Carlos I, the monarch exercises prerogatives after having solicited government advice, while remaining politically non-partisan and independent. Receiving government advice does not necessarily bind the monarch into executing said advice, except where prescribed by the Constitution.

It is incumbent upon the King:
 * a. To Sanction and promulgate the laws
 * b. To summon and dissolve the Cortes Generales and to call for elections under the terms provided for in the Constitution.
 * c. To Call for a referendum in the cases provided for in the Constitution.
 * e. To appoint and dismiss members of the Government on the President of the Government's proposal.
 * f. To issue the decrees approved in the Council of Ministers, to confer civil and military honours and distinctions in conformity with the law.
 * g. To be informed of the affairs of State and, for this purpose, to preside over the meetings of the Council of Ministers whenever, he sees fit, at the President of the Government's request.
 * h. To exercise supreme command of the Armed Forces
 * i. To exercise the right of clemency in accordance with the law, which may not authorize general pardons.
 * j. To exercise the High Patronage of the Royal Academies.

Once a General Election has been announced by the monarch, political parties nominate their candidates to stand for the presidency of the government.

Following the General Election of the Cortes Generales (Cortes), and other circumstances provided for in the Constitution, the monarch meets with and interviews the political party leaders represented in the Congress of Deputies, and then consults with the Speaker of the Congress of Deputies (officially,  Presidente de Congreso de los Diputados de España, who, in this instance, represents the whole Cortes Generales) before nominating his candidate for the presidency, according to Section 99 of Title IV. Often minor parties form part of a larger major party, and through that membership it can be said that the monarch fulfills the constitutional mandate of consulting with party representatives with Congressional representation.

Title IV Government and Administration Section 99(1) & (2)
 * (1) After each renewal of the Congress and the other cases provided for under the Constitution, the King shall, after consultation with the representatives appointed by the political groups with parliamentary representation, and through the Speaker of the Congress, nominate for the Presidency of the Government.
 * (2) The candidate nominated in accordance with the provisions of the foregoing subsection shall submit to the Congress the political program of the Government he or she intends to form and shall seek the confidence of the House.

The Spanish Constitution of 1978 explicitly says that the monarch is not subject to any responsibility but for his acts to be valid must be endorsed by the Government and will not be valid without such an endorsement. The only exception is that the monarch is free to appoint and remove the members of private and military advisors (Casa Real).

Title IV of the Constitution invests the monarch with sanction (Royal Assent) and promulgation (publication) of laws, while Title III The Cortes Generals, Chapter 2 Drafting of Bills outlines the method by which bills are passed. According to Article 91, within fifteen days that a bill has been passed by the Cortes Generales, the monarch shall give assent and publish the new law. Article 92 invests the monarch with the right to call for a referendum on the advice of the president and the previous authorization of Congress.

No provision within the Constitution invests the monarch with the ability to veto legislation directly, however no provision forbids the denial of royal assent – effectively a veto. When the media asked King Juan Carlos if he would endorse the bill legalizing gay marriages, he answered "Soy el Rey de España y no el de Bélgica" ("I am the King of Spain, and not that of Belgium") – a reference to King Baudouin I of Belgium who had refused to sign the Belgian law legalising abortion. The King gave his royal assent to Law 13/2005 on 1 July 2005; the law was gazetted in the Boletín Oficial del Estado on 2 July, and came into effect on 3 July 2005.

Sweden
Much like the Emperor of Japan, the King of Sweden does not have any constitutional responsibility for the governance of the Realm, with strictly ceremonial and representative functions remaining. Under the 1974 Instrument of Government, the supreme executive authority is the Government (composed of the Prime Minister and other cabinet ministers), which is responsible to the Riksdag. The King, however, is not subordinate to the Government and thus could play an independent role as moral authority, but the prevailing convention, expressed in the preparatory works of the 1974 Instrument of Government, is that the King should stay away from anything which could reasonably be interpreted as partisan politics or criticism of the Government in office.

Republics
Reserve powers can also be written into a republican constitution that separates the offices of head of state and head of government. This was the case in Germany under the Weimar Republic and is still the case in the French Fifth Republic, the Italian republic, and the Republic of Ireland. Reserve powers may include, for instance, the right to issue emergency legislation or regulation bypassing the normal processes. In most states, the head of state's ability to exercise reserve powers is explicitly defined and regulated by the text of the constitution.

Bangladesh
The President of Bangladesh must consult with the Prime Minister for all decisions except the appointment of the Prime Minister and the Chief Justice. However, the President has the authority to dissolve the government or parliament, grant pardon to criminals, block bills/budgets by the legislature or declare an emergency.

During the regime of the caretaker government, the President's power expanded dramatically; effectively (s)he is no longer a ceremonial head of state.

France
Article 16 of the Constitution of France allows the President of the Republic to exercise exceptional powers in case of a national emergency. During this time, the President may not use his prerogative to dissolve the National Assembly and call early elections. He must still consult the Prime Minister, the leaders of both houses of Parliament and the Constitutional Council.

The inspiration for this disposition in the Constitution was the institutional chaos and lack of government authority which contributed to the French debacle in the Battle of France in 1940. On a larger scale, this is consistent with a tradition of the Roman Republic (which has always been an inspiration for the successive French Republics), to give six months of dictatorial power to a citizen in case of an imminent danger of invasion.

Article 16 rule has only been exercised once, in 1961, during a crisis related to the Algerian War in which Charles de Gaulle needed those emergency powers to foil a military plot to take over the government. In 1962, the Council of State ruled itself incompetent to judge measures of a legislative nature issued by the President under Article 16.

In his book, Le Coup d'État permanent (The Permanent Coup), François Mitterrand criticized Article 16 for allowing an ambitious politician the opportunity to become a dictator. However, he made no move to put away his reserve powers after he himself became president.

Germany
The German constitution limits the powers available to the President to prevent a situation in which the executive could effectively rule without legislative approval, which was the case in the Weimar Republic. In particular, the president cannot rule by decree. However, in case of a "legislative emergency" the German President can accept legislation without approval of the "Bundestag" (parliament). Article 81 of the German constitution states the possibility that the President can by this means keep a government capable of action even in case of loss of a constructive majority in the Bundestag.

Furthermore, the German President can dissolve the Bundestag (parliament) if the Chancellor loses a motion of confidence and asks the President to do so. The German President has exercised this right three times since the founding of the Federal Republic in 1949. President Gustav Heinemann dissolved the Bundestag at the request of Chancellor Willy Brandt in 1972, and in 1982 President Karl Carstens did so at the request of Chancellor Helmut Kohl. Both Brandt and Kohl were reelected with larger majorities. Most recently, on 1 July 2005, President Horst Köhler dissolved the Bundestag at the request of Chancellor Gerhard Schröder. Schröder unexpectedly lost the election that followed.

The President has the right to refuse his signature to laws passed by the parliament (veto) in certain circumstances. These may be formal errors in the law-making process or violations of the Basic Law inherent to the new law. This reserve power has been used 8 times as of May 2013.

The President nominates the first candidate for Chancellor put to vote in the Bundestag. The president can also dissolve the Bundestag if no candidate won the absolute majority of the members of parliament after three votes.

The President has the right to pardon criminals for federal crimes with the countersignature of a member of the cabinet. The refusal of a pardon does not need a countersignature.

Ireland
The President of Ireland does not possess executive powers: executive powers are held by the Government, which is headed by a Taoiseach (Prime Minister), who is chosen by and accountable to Dáil Éireann (House of Representatives).

The President's powers are principally defined by Article 13 of the Constitution of Ireland. For the most part, these ceremonial duties may be performed only on the authority, and with the binding advice, of the Government.

However, the President has certain reserve powers, also known as "discretionary powers" in Ireland, which can be exercised by the President at his or her discretion – without, or even contrary to, the Government's advice.

The two most politically important discretionary powers are:

 * 1) Refusing to dissolve the Dáil on the advice of a Taoiseach who has lost the confidence of the Dáil.
 * 2) Referring legislation to the Supreme Court.

The first of these means that a Taoiseach who has been defeated by a vote of no-confidence cannot automatically expect to appeal to the people by calling a general election. The question of whether or not the Taoiseach has lost the confidence of the Dáil could be a discretionary matter for the President to decide – in principle, the President could refuse to dissolve the Dáil on the advice of a Taoiseach who has not yet been defeated in a vote of no-confidence, but who appears likely to be defeated were such a vote to be held. This power has not so far been used, but it could be a crucial power in the event of the collapse of a governing coalition.

By the second of these powers, the President may refuse to assent to legislation passed by Parliament when he or she considers it to be unconstitutional. The President refers the matter to the Supreme Court, which makes the final decision. This power has been used several times by various Presidents.

In addition to these powers, the President has various other discretionary powers in the Constitution, which are of lesser political significance (in normal circumstances). The President may decide to call a referendum on legislation "of great national significance". This power, granted by Article 27 of the Constitution, has not so far been used. The President cannot initiate a referendum, but must wait for an application by a majority of the Seanad (Senate) and one-third of the Dáil. Generally, owing to the way in which the Seanad is elected, the Government's coalition controls a majority of the seats, and strong party discipline means that Senators rarely go against their own party, so getting Seanad support for a referendum is difficult. If the Seanad were to be reformed, this power could potentially become much more significant. Similarly, the President has a latent role in resolving disputes between the Dáil and the Seanad. The President may convene a special committee to resolve questions of privilege between the Dáil and the Seanad with regard to Money Bills, and with regard to speeding the passage of urgent bills through the Seanad. Again, owing to the method by which the Seanad is elected, disputes of this nature tend not to emerge in practice.

The exercise of these powers is entirely at the President's discretion, for which the President is neither legally nor politically responsible. However, prior to their exercise, the President is bound, in most cases, to consult the Council of State, an advisory body consisting of a mixture of senior ex-officio and nominated members.

Italy
The President of the Italian Republic's powers are defined by articles 87 through 90 of the Constitution of Italy. The President of the Republic:
 * can send official messages to the chambers of Parliament;
 * appoints the President of the Council of Ministers;
 * may appoint up to five senators for life;
 * appoints a third of the judges of the Constitutional Court;
 * can grant pardons and commutations of sentences;
 * can call for new elections for both or only one of the chambers, except during the last six months of his term.

The President of the Republic can refuse to sign laws he deems clearly against the Constitution, while less obvious cases are dealt with later on by the Constitutional Court. If the rejected law is passed again by a majority in the Parliament, however, the President must sign it.

Given his monocratic nature, this organ joins in itself prerogatives that in all other collegial organs are attributed collectively.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Reserve power


text:
Yokosuka MXY-7 Ohka

The Yokosuka MXY-7 Ohka (櫻花) was a purpose-built, rocket-powered human-guided kamikaze attack-aircraft deployed by Japan against Allied ships in the Pacific Ocean theater towards the end of World War II. Although extremely fast, the Ohka had a very short range, so it had to be carried into action as a parasite aircraft by a much larger bomber, which was itself vulnerable to carrier-borne fighters. In action during the Battle of Okinawa in 1945, Ohkas succeeded in sinking or damaging some escort-vessels and transport ships, but never sank any major warships. The Japanese developed improved versions in an attempt to overcome the aircraft's shortcomings, but they came too late for deployment.

Allied personnel referred to the aircraft as "Baka Bombs" (baka being a Japanese pejorative term meaning "fool" or "idiot").

Design and development
The MXY-7 Navy Suicide Attacker Ohka was a manned flying bomb that was usually carried underneath a Mitsubishi G4M2e Model 24J "Betty" bomber to within range of its target. On release, the pilot would first glide towards the target and when close enough he would fire the Ohka's three solid-fuel rockets, one at a time or in unison, and fly the missile towards the ship that he intended to destroy.

The design was conceived by Ensign Mitsuo Ohta of the 405th Kōkūtai, aided by students of the Aeronautical Research Institute at the University of Tokyo. Ohta submitted his plans to the Yokosuka research facility. While Ohta had started work on the design in 1943 the authorities would not take an interest until the following year. The Imperial Japanese Navy decided the idea had merit and Yokosuka engineers of the Yokosuka Naval Air Technical Arsenal (Dai-Ichi Kaigun Koku Gijitsusho, or in short Kugisho ) created formal blueprints for what was to be the MXY-7. The only variant which saw service was the Model 11, and it was powered by three Type 4 Mark 1 Model 20 rockets. 155 Ohka Model 11s were built at Yokosuka, and another 600 were built at the Kasumigaura Naval Air Arsenal.

The final approach was difficult for a defender to stop because the aircraft gained high speed (650 km/h in level flight and 930 km/h or even 1000 km/h in a dive. Later versions were designed to be launched from coastal air bases and caves, and even from submarines equipped with aircraft catapults, although none were actually used in this way. The Allen M. Sumner-class destroyer USS Mannert L. Abele (DD-733) was the first Allied ship to be sunk by Ohka aircraft, near Okinawa on 12 April 1945.  Over the course of the war, Ohkas sank or damaged three ships beyond repair, significantly damaged three more ships, with a total of seven U.S. ships damaged or sunk by Ohkas.

The Ohka pilots, members of the Jinrai Butai (Thunder Gods Corps), are honored in Japan at Ohka Park in Kashima City, the Ohka Monument in Kanoya City, the Kamakura Ohka Monument at Kenchō-ji Zen temple in Kamakura, Kanagawa, and the Yasukuni Shrine in Tokyo.

The only operational Ohka was the Model 11. Essentially a 1200 kg bomb with wooden wings, powered by three Type 4 Model 1 Mark 20 solid-fuel rocket motors, the Model 11 achieved great speed, but with limited range. This was problematic, as it required the slow, heavily laden mother aircraft to approach within 37 km of the target, making it very vulnerable to defending fighters. There was one experimental variant of the Model 11, the Model 21, which had thin steel wings manufactured by Nakajima. It had the engine of the Model 11 and the airframe of the Model 22.

The Ohka K-1 was an unpowered trainer version with water ballast instead of warhead and engines, that was used to provide pilots with handling experience. Unlike the combat aircraft, it was also fitted with flaps and a landing skid. The water ballast was dumped before landing but it remained a challenging aircraft to fly, with a landing speed of 130 mph. Forty-five were built by Dai-Ichi Kaigun Koku Gijitsusho.

The Model 22 was designed to overcome the short standoff distance problem by using a Campini-type motorjet engine, the Ishikawajima Tsu-11, giving a level speed of only 276 mph at 13,125 feet but extending the range to 81 miles. This engine was successfully tested, and 50 Model 22 Ohkas were built at Yokosuka to accept this engine. The Model 22 was to be launched by the more agile Yokosuka P1Y3 Ginga "Frances" bomber, necessitating a shorter wing span and much smaller 600 kg warhead. The first flight of a Model 22 Ohka took place in June 1945; none appear to have been used operationally, and only approximately 20 of the experimental Tsu-11 engines are known to have been produced.

The Model 33 was a larger version of the Model 22 powered by an Ishikawajima Ne-20 turbojet with an 800 kg warhead. The mothership was to be the Nakajima G8N Renzan. The Model 33 was cancelled due to the likelihood that the Renzan would not be available.

Other unbuilt planned variants were the Model 43A with folding wings, to be launched from submarines, and the Model 43B, a catapult/rocket-assisted version, also with folding wings so that it could be hidden in caves. A trainer version was also under development for this version, the two-seat Model 43 K-1 Kai Wakazakura (Young Cherry), fitted with a single rocket motor. In place of the warhead, a second seat was installed for the student pilot. Two of this version were built. Finally, the Model 53 would also use the Ne-20 turbojet, but was to be towed like a glider and released near its target.

Operational history
The Yokosuka MXY-7 Ohka was used mostly against U.S. ships invading Okinawa, and if launched from its mothership, could be effective because of its high speed in the dive. In the first two attempts to transport the Ohkas to Leyte Gulf using aircraft carriers, the carriers JAPANESE AIRCRAFT CARRIER Shinano and JAPANESE AIRCRAFT CARRIER Unryu were sunk by the U.S. submarines USS Archerfish (SS-311) and USS Redfish (SS-395).

Attacks intensified in April 1945. On 1 April 1945, six G4Ms attacked the U.S. fleet off Okinawa. At least one made a successful attack; its Ohka was thought to have hit one of the 406 mm (16 in) turrets on the battleship USS West Virginia (BB-48), causing moderate damage. Postwar analysis indicated that no hits were recorded and that a near-miss took place. The transports USS Alpine (APA-92), USS Achernar (AKA-53), and USS Tyrrell (AKA-80) were also hit by kamikaze aircraft, but it is unclear whether any of these were Ohkas from the other G4Ms. None of the G4Ms returned.

The U.S. military quickly realized the danger and concentrated on extending their "defensive rings" outward to intercept the G4M/Ohka combination aircraft before the suicide mission could be launched. On 12 April 1945, nine G4Ms attacked the U.S. fleet off Okinawa. The destroyer USS Mannert L. Abele (DD-733) was hit, broke in two, and sank. USS Jeffers (DD-621) destroyed an Ohka with AA fire 45 m (50 yd) from the ship, but the resulting explosion was still powerful enough to cause extensive damage, forcing Jeffers to withdraw. The destroyer USS Stanly (DD-478) was attacked by two Ohkas. One struck above the waterline just behind the ship's bow, its charge passing completely through the hull and splashing into the sea, where it detonated underwater, causing little damage to the ship. The other Ohka narrowly missed (its pilot probably killed by anti-aircraft fire) and crashed into the sea, knocking off the Stanly's ensign in the process. One Betty returned. On 14 April 1945, seven G4Ms attacked the U.S. fleet off Okinawa. None returned. None of the Ohkas appeared to have been launched. Two days later, six G4Ms attacked the U.S. fleet off Okinawa. Two returned, but no Ohkas had hit their targets. Later, on 28 April 1945, four G4Ms attacked the U.S. fleet off Okinawa at night. One returned. No hits were recorded.

May 1945 saw another series of attacks. On 4 May 1945, seven G4Ms attacked the U.S. fleet off Okinawa. One Ohka hit the bridge of a destroyer, USS Shea (DM-30), causing extensive damage and casualties. USS Gayety (AM-239) was also damaged by an Ohka's near miss. One G4M returned. On 11 May 1945, four G4Ms attacked the U.S. fleet off Okinawa. The destroyer USS Hugh W. Hadley (DD-774) was hit and suffered extensive damage and flooding. The vessel was judged beyond repair. On 25 May 1945, 11 G4Ms attacked the fleet off Okinawa. Bad weather forced most of the aircraft to turn back, and none of the others hit targets.

On 22 June 1945, six G4Ms attacked the fleet. Two returned, but no hits were recorded. Postwar analysis concluded that the Ohka's impact was negligible, since no U.S. Navy capital ships had been hit during the attacks because of the effective defensive tactics that were employed. In total, of the 300 Ohka available for the Okinawa campaign, 74 actually undertook operations, of which 56 were either destroyed with their parent aircraft or in making attacks. The Allied nickname for the aircraft was "Baka", a Japanese word meaning "foolish" or "idiotic".

Variants

 * MXY-7: Rocket powered suicide attacker, unpowered glider prototypes; ten built

 * Navy Suicide Attacker Ohka Model 11: Long designation of the operational attacker

 * Ohka Model 11: Suicide attacker powered by 3 × 2.616 kN Navy Type 4 Mark 1 Model 20 solid-fueled rocket motors, firing for 8–10 seconds; 755 built

 * Ohka Model 21: Suicide attacker, fitted with steel-built wings built by Nakajima; one built

 * Ohka Model 22: Suicide attacker, powered by an Ishikawajima Tsu-11 thermo-jet engine with reduced span wings and 600 kg warhead, to be carried by Yokosuka P1Y1 Ginga bombers. 50 built by the First Naval Air Technical Arsenal (第一海軍航空技術廠)
 * Ohka Model 33: Suicide attacker, powered by an Ishikawajima Ne-20 turbojet engine, with an 800 kg warhead, to be carried by the Nakajima G8N1 Renzan bomber

 * Ohka Model 43A Ko: Suicide attacker, powered by a Ne-20 turbojet engine, with folding wings, to be catapult launched from submarines

 * Ohka Model 43B Otsu: Suicide attacker similar to the Model 43A for catapult launching from caves

 * Ohka Model 53: Suicide attacker for aerotow launch, powered by a Ne-20 turbojet engine

 * Ohka K-1: Suicide attack training glider

 * Ohka Model 43 K-1 Kai Wakazakura (若桜): Two-seat suicide attack glider trainer with flaps and retractable skid undercarriage, fitted with a single Type 4 Mark 1 Model 20 rocket motor, for limited powered flight

 * "Suzuka-24" (Japanese designation unknown): Alleged interceptor version with warhead replaced by a fuel tank for a Ne-20 jet engine and two 20 mm autocannon (Unknown Ho-5 or Type 99 with 60 / 150 rounds per gun) mounted on top. Supposedly employed at least twice against B-29 formations in April 1945

India

 * Model 11 on static display at the Indian Air Force Museum in Palam, New Delhi.

Japan

 * On display
 * Model 11 on static display at Iruma Air Force Base in Iruma, Saitama.
 * On static display at the Kawaguchiko Motor Museum in Narusawa, Yamanashi.

United Kingdom

 * On display
 * Model 11 on static display at the Fleet Air Arm Museum in Yeovilton, Somerset.
 * Model 11 on static display at the Imperial War Museum in London.
 * Model 11 on static display at the Royal Air Force Museum Cosford in Cosford, Shropshire.
 * Model 11 on static display at the Science and Industry Museum in Manchester.

United States

 * On display
 * Model 11 on static display at the National Museum of the Marine Corps in Triangle, Virginia.
 * Model 11 on static display at the Planes of Fame Air Museum in Chino, California.
 * Model 11 on static display at the Yanks Air Museum in Chino, California.
 * Model 22 on static display at the Steven F. Udvar-Hazy Center of the National Air and Space Museum in Chantilly, Virginia, the only surviving Model 22.
 * Model 43B K-1 Kai Wakazakura on static display at the Pima Air & Space Museum in Tucson, Arizona. It is on loan from the National Air and Space Museum.
 * K-1 on static display at the National Museum of the United States Air Force in Dayton, Ohio.
 * K-1 on static display at the National Museum of the U.S. Navy in Washington, D.C.

Japan

 * Model 11 on static display at the Yūshūkan of the Yasukuni Shrine in Tokyo.
 * Model 11 on static display at Usashi Heiwa Museum in Usa, Oita.

United States

 * Model 11 on static display at the National Warplane Museum in Geneseo, New York.

title: Yokosuka MXY-7 Ohka


text:
UNIVAC 1102

The UNIVAC 1102 or ERA 1102 was designed by Engineering Research Associates for the United States Air Force's Arnold Engineering Development Center in Tullahoma, Tennessee in response to a request for proposal issued in 1950. The Air Force needed three computers to do data reduction for two wind tunnels and an engine test facility.

The 1102 was a variant of the UNIVAC 1101, using its 24-bit word and a smaller (only 8,192 words) drum memory. The machine had 2,700 vacuum tubes, weighed 14000 lb, and occupied 122 sqft of floor area.

The computers were connected to data channels coming from the wind tunnels and the engine facility. There were five typewriters for printed output, five paper tape punches, and four pen plotters to produce graphs.

The three computers and related peripherals were delivered between July 1954 and July 1956 at a total price of $1,400,000. Software for the computers was developed entirely at the Arnold Engineering Development center. All programming was done in machine code (assemblers and compilers were never developed).

title: UNIVAC 1102


text:
User:Miri~enwiki

ja:%E5%88%A9%E7%94%A8%E8%80%85:Miri

I am Japanese and a university student.

I started editing Wikipedia(en) on March 7, 2003.

title: User:Miri~enwiki