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Comecon

The Council for Mutual Economic Assistance (Сове́т Экономи́ческой Взаимопо́мощи, СЭВ; English abbreviation COMECON, CMEA , CEMA , or CAME ) was an economic organization from 1949 to 1991 under the leadership of the Soviet Union that comprised the countries of the Eastern Bloc along with a number of socialist states elsewhere in the world.

The descriptive term was often applied to all multilateral activities involving members of the organization, rather than being restricted to the direct functions of Comecon and its organs. This usage was sometimes extended as well to bilateral relations among members because in the system of communist international economic relations, multilateral accords – typically of a general nature –  tended to be implemented through a set of more detailed, bilateral agreements.

Comecon was the Eastern Bloc's response to the formation in Western Europe of the Marshall Plan and the OEEC, which later became the OECD.

Foundation
The Comecon was founded in 1949 by the Soviet Union, Bulgaria, Czechoslovakia, Hungary, Poland, and Romania. The primary factors in Comecon's formation appear to have been Joseph Stalin's desire to cooperate and strengthen the international relationships at an economic level with the smaller states of Central Europe, and which were now, increasingly, cut off from their traditional markets and suppliers in the rest of Europe. Czechoslovakia, Hungary, and Poland had remained interested in Marshall aid despite the requirements for a convertible currency and market economies. These requirements, which would inevitably have resulted in stronger economic ties to free European markets than to the Soviet Union, were not acceptable to Stalin, who in July 1947, ordered these communist governments to pull out of the Paris Conference on the European Recovery Programme. This has been described as "the moment of truth" in the post-World War II division of Europe. According to the Soviet view the "Anglo-American bloc" and "American monopolists ... whose interests had nothing in common with those of the European people" had spurned east–west collaboration within the framework agreed within the United Nations, that is, through the Economic Commission for Europe.

Some say that Stalin's precise motives in establishing Comecon were "inscrutable" They may well have been "more negative than positive", with Stalin "more anxious to keep other powers out of neighbouring buffer states… than to integrate them." Furthermore, GATT's notion of ostensibly nondiscriminatory treatment of trade partners was thought to be incompatible with notions of socialist solidarity. In any event, proposals for a customs union and economic integration of Central and Eastern Europe date back at least to the Revolutions of 1848 (although many earlier proposals had been intended to stave off the Russian and/or communist "menace") and the state-to-state trading inherent in centrally planned economies required some sort of coordination: otherwise, a monopolist seller would face a monopsonist buyer, with no structure to set prices.

Comecon was established at a Moscow economic conference January 5–8, 1949, at which the six founding member countries were represented; its foundation was publicly announced on January 25; Albania joined a month later and East Germany in 1950.

Recent research by the Romanian researcher Elena Dragomir suggests that Romania played a rather important role in the Comecon's creation in 1949. Dragomir argues that Romania was interested in the creation of a "system of cooperation" to improve its trade relations with the other people's democracies, especially with those able to export industrial equipment and machinery to Romania. According to Dragomir, in December 1948, the Romanian leader Gheorghe Gheorghiu-Dej sent a letter to Stalin, proposing the creation of the Comecon.

At first, planning seemed to be moving along rapidly. After pushing aside Nikolai Voznesensky's technocratic, price-based approach (see further discussion below), the direction appeared to be toward a coordination of national economic plans, but with no coercive authority from Comecon itself. All decisions would require unanimous ratification, and even then governments would separately translate these into policy. Then in summer 1950, probably unhappy with the favorable implications for the effective individual and collective sovereignty of the smaller states, Stalin "seems to have taken [Comecon's] personnel by surprise," bringing operations to a nearly complete halt, as the Soviet Union moved domestically toward autarky and internationally toward an "embassy system of meddling in other countries' affairs directly" rather than by "constitutional means". Comecon's scope was officially limited in November 1950 to "practical questions of facilitating trade."

One important legacy of this brief period of activity was the "Sofia Principle", adopted at the August 1949 Comecon council session in Bulgaria. This radically weakened intellectual property rights, making each country's technologies available to the others for a nominal charge that did little more than cover the cost of documentation. This, naturally, benefited the less industrialized Comecon countries, and especially the technologically lagging Soviet Union, at the expense of East Germany and Czechoslovakia and, to a lesser extent, Hungary and Poland. (This principle would weaken after 1968, as it became clear that it discouraged new research – and as the Soviet Union itself began to have more marketable technologies.)

In a recent paper by Faudot, Nenovsky and Marinova (2022) the functioning and the collapse of the Comecon has been studied. It focuses on the evolution of the monetary mechanisms and some technical problems of multilateral payments and the peculiarities of the transfer ruble. Comecon as an organization proved unable to develop multilateralism mainly because of issues related to domestic planning that encouraged autarky and, at best, bilateral exchanges.

Nikita Khrushchev era
After Stalin's death in 1953, Comecon again began to find its footing. In the early 1950s, all Comecon countries had adopted relatively autarkic policies; now they began again to discuss developing complementary specialties, and in 1956, ten permanent standing committees arose, intended to facilitate coordination in these matters. The Soviet Union began to trade oil for Comecon manufactured goods. There was much discussion of coordinating five-year plans.

However, once again, trouble arose. The Polish protests and Hungarian uprising led to major social and economic changes, including the 1957 abandonment of the 1956–60 Soviet five-year plan, as the Comecon governments struggled to reestablish their legitimacy and popular support. The next few years saw a series of small steps toward increased trade and economic integration, including the introduction of the "convertible rouble", revised efforts at national specialization, and a 1959 charter modeled after the 1957 Treaty of Rome.

Once again, efforts at transnational central planning failed. In December 1961, a council session approved the Basic Principles of the International Socialist Division of Labour, which talked of closer coordination of plans and of "concentrating production of similar products in one or several socialist countries." In November 1962, Soviet Premier Nikita Khrushchev followed this up with a call for "a common single planning organ." This was resisted by Czechoslovakia, Hungary, and Poland, but most emphatically by increasingly nationalistic Romania, which strongly rejected the notion that they should specialize in agriculture. In Central and Eastern Europe, only Bulgaria happily took on an assigned role (also agricultural, but in Bulgaria's case this had been the country's chosen direction even as an independent country in the 1930s). Essentially, by the time the Soviet Union was calling for tight economic integration, they no longer had the power to impose it. Despite some slow headway – integration increased in petroleum, electricity, and other technical/scientific sectors – and the 1963 founding of an International Bank for Economic Co-operation, Comecon countries all increased trade with the West relatively more than with one another.

Leonid Brezhnev era
From its founding until 1967, Comecon had operated only on the basis of unanimous agreements. It had become increasingly obvious that the result was usually failure. In 1967, Comecon adopted the "interested party principle", under which any country could opt out of any project they chose, still allowing the other member states to use Comecon mechanisms to coordinate their activities. In principle, a country could still veto, but the hope was that they would typically choose just to step aside rather than either veto or be a reluctant participant. This aimed, at least in part, at allowing Romania to chart its own economic course without leaving Comecon entirely or bringing it to an impasse (see de-satellization of Communist Romania).

Also until the late 1960s, the official term for Comecon activities was cooperation. The term integration was always avoided because of its connotations of monopolistic capitalist collusion. After the "special" council session of April 1969 and the development and adoption (in 1971) of the Comprehensive Program for the Further Extension and Improvement of Cooperation and the Further Development of Socialist Economic Integration by Comecon Member Countries, Comecon activities were officially termed integration (equalization of "differences in relative scarcities of goods and services between states through the deliberate elimination of barriers to trade and other forms of interaction"). Although such equalization had not been a pivotal point in the formation and implementation of Comecon's economic policies, improved economic integration had always been Comecon's goal.

While such integration was to remain a goal, and while Bulgaria became yet more tightly integrated with the Soviet Union, progress in this direction was otherwise continually frustrated by the national central planning prevalent in all Comecon countries, by the increasing diversity of its members (which by this time included Mongolia and would soon include Cuba) and by the "overwhelming asymmetry" and resulting distrust between the many small member states and the Soviet "superstate" which, in 1983, "accounted for 88 percent of Comecon's territory and 60 percent of its population."

In this period, there were some efforts to move away from central planning, by establishing intermediate industrial associations and combines in various countries (which were often empowered to negotiate their own international deals). However, these groupings typically proved "unwieldy, conservative, risk-averse, and bureaucratic," reproducing the problems they had been intended to solve.

One economic success of the 1970s was the development of Soviet oil fields. While doubtless "(Central and) East Europeans resented having to defray some of the costs of developing the economy of their hated overlord and oppressor," they benefited from low prices for fuel and other mineral products. As a result, Comecon economies generally showed strong growth in the mid-1970s. They were largely unaffected by the 1973 oil crisis. Another short-term economic gain in this period was that détente brought opportunities for investment and technology transfers from the West. This also led to an importation of Western cultural attitudes, especially in Central Europe. However, many undertakings based on Western technology were less than successful (for example, Poland's Ursus tractor factory did not do well with technology licensed from Massey Ferguson); other investment was wasted on luxuries for the party elite, and most Comecon countries ended up indebted to the West when capital flows died out as détente faded in the late 1970s, and from 1979 to 1983, all of Comecon experienced a recession from which (with the possible exceptions of East Germany and Bulgaria) they never recovered in the Communist era. Romania and Poland experienced major declines in the standard of living.

Perestroika
The 1985 Comprehensive Program for Scientific and Technical Progress and the rise to power of Soviet general secretary Mikhail Gorbachev increased Soviet influence in Comecon operations and led to attempts to give Comecon some degree of supranational authority. The Comprehensive Program for Scientific and Technical Progress was designed to improve economic cooperation through the development of a more efficient and interconnected scientific and technical base. This was the era of perestroika ("restructuring"), the last attempt to put the Comecon economies on a sound economic footing. Gorbachev and his economic mentor Abel Aganbegyan hoped to make "revolutionary changes" in the economy, foreseeing that "science will increasingly become a 'direct productive force', as Marx foresaw… By the year 2000… the renewal of plant and machinery… will be running at 6 percent or more per year."

The program was not a success. "The Gorbachev regime made too many commitments on too many fronts, thereby overstretching and overheating the Soviet economy. Bottlenecks and shortages were not relieved but exacerbated, while the (Central and) East European members of Comecon resented being asked to contribute scarce capital to projects that were chiefly of interest to the Soviet Union…" Furthermore, the liberalization that by June 25, 1988, allowed Comecon countries to negotiate trade treaties directly with the European Community (the renamed EEC), and the "Sinatra doctrine" under which the Soviet Union allowed that change would be the exclusive affair of each individual country marked the beginning of the end for Comecon. Although the Revolutions of 1989 did not formally end Comecon, and the Soviet government itself lasted until 1991, the March 1990 meeting in Prague was little more than a formality, discussing the coordination of non-existent five-year plans. From January 1, 1991, the countries shifted their dealings with one another to a hard currency market basis. The result was a radical decrease in trade with one another, as "(Central and) Eastern Europe… exchanged asymmetrical trade dependence on the Soviet Union for an equally asymmetrical commercial dependence on the European Community."

The final Comecon council session took place on June 28, 1991, in Budapest, and led to an agreement to dissolve in 90 days. The Soviet Union was dissolved on December 26, 1991.

Post-Cold War activity after Comecon
After the fall of the Soviet Union and communist rule in Eastern Europe, East Germany (now unified with West Germany) automatically joined the European Union (then the European Community) in 1990. The Baltic States (Estonia, Latvia and Lithuania), Czech Republic, Hungary, Poland, Slovakia, and Slovenia joined the EU in 2004, followed by Bulgaria and Romania in 2007 and Croatia in 2013. To date, Czech Republic, Estonia, Germany (former GDR), Hungary, Latvia, Lithuania, Poland, Slovakia, and Slovenia are now members of the Organisation for Economic Co-operation and Development. All four Central European states are now members of the Visegrád Group.

Russia, the successor to the Soviet Union along with Ukraine and Belarus founded the Commonwealth of Independent States which consists of most of the ex-Soviet republics. The country also leads the Shanghai Cooperation Organisation with Kazakhstan, Kyrgyzstan and Uzbekistan and the Eurasian Economic Union with Armenia, Belarus, Kazakhstan and Kyrgyzstan. Along with Ukraine, Georgia, Azerbaijan and Moldova are also part of the GUAM.

Vietnam and Laos joined the Association of Southeast Asian Nations (ASEAN) in 1995 and 1997 respectively.

Full members
Albania had stopped participating in Comecon activities in 1961 following the Soviet–Albanian split, but formally withdrew in 1987. East Germany reunified with the West and withdrew from Comecon on 2 October 1990.

Associate status

 * undefined (1964)

Observer status
• People's Republic of China (1949; stopped participating in Comecon activities in 1961 following the Sino-Soviet split)

• 🇰🇵 North Korea (1949)

•  North Vietnam (1949)

• 🇫🇮 Finland (1973)

•  undefined (1975)

• 🇲🇽 Mexico (1975)

•  undefined (1976)

• 🇳🇮 Nicaragua (1984)

•  undefined (1985)

•  undefined (1986)

• 🇪🇹 Ethiopia (1986)

•  Laos (1986)

•  South Yemen (1986)

In the late 1950s, a number of communist-ruled non-member countries – the People's Republic of China, North Korea, Mongolia, Vietnam, and Yugoslavia –  were invited to participate as observers in Comecon sessions. Although Mongolia and Vietnam later gained full membership, China stopped attending Comecon sessions after 1961. Yugoslavia negotiated a form of associate status in the organization, specified in its 1964 agreement with Comecon. Collectively, the members of the Comecon did not display the necessary prerequisites for economic integration: their level of industrialization was low and uneven, with a single dominant member (the Soviet Union) producing 70% of the community national product.

In the late 1980s, there were ten full members: the Soviet Union, six East European countries, and three extra-regional members. Geography, therefore, no longer united Comecon members. Wide variations in economic size and level of economic development also tended to generate divergent interests among the member countries. All these factors combined to give rise to significant differences in the member states' expectations about the benefits to be derived from membership in Comecon. Unity was provided instead by political and ideological factors. All Comecon members were "united by a commonality of fundamental class interests and the ideology of Marxism-Leninism" and had common approaches to economic ownership (state versus private) and management (plan versus market). In 1949 the ruling communist parties of the founding states were also linked internationally through the Cominform, from which Yugoslavia had been expelled the previous year. Although the Cominform was disbanded in 1956, interparty links continued to be strong among Comecon members, and all participated in periodic international conferences of communist parties. Comecon provided a mechanism through which its leading member, the Soviet Union, sought to foster economic links with and among its closest political and military allies. The East European members of Comecon were also militarily allied with the Soviet Union in the Warsaw Pact.

There were three kinds of relationships – besides the 10 full memberships – with the Comecon:
 * Yugoslavia was the only country considered to have associate member status. On the basis of the 1964 agreement, Yugoslavia participated in twenty-one of the thirty-two key Comecon institutions as if it were a full member.
 * Finland, Iraq, Mexico, and Nicaragua had a cooperant status with Comecon. Because the governments of these countries were not empowered to conclude agreements in the name of private companies, the governments did not take part in Comecon operations. They were represented in Comecon by commissions made up of members of the government and the business community. The commissions were empowered to sign various "framework" agreements with Comecon's Joint Commission on Cooperation.
 * After 1956, Comecon allowed certain countries with communist or pro-Soviet governments to attend sessions as observers. In November 1986, delegations from Afghanistan, Ethiopia, Laos, and South Yemen attended the 42nd Council Session as observers.

Exchange
Working with neither meaningful exchange rates nor a market economy, Comecon countries had to look to world markets as a reference point for prices, but unlike agents acting in a market, prices tended to be stable over a period of years, rather than constantly fluctuating, which assisted central planning. Also, there was a tendency to underprice raw materials relative to the manufactured goods produced in many of the Comecon countries.

International barter helped preserve the Comecon countries' scarce hard currency reserves. In strict economic terms, barter inevitably harmed countries whose goods would have brought higher prices in the free market or whose imports could have been obtained more cheaply and benefitted those for whom it was the other way around. Still, all of the Comecon countries gained some stability, and the governments gained some legitimacy, and in many ways this stability and protection from the world market was viewed, at least in the early years of Comecon, as an advantage of the system, as was the formation of stronger ties with other socialist countries.

Within Comecon, there were occasional struggles over how this system should work. Early on, Nikolai Voznesensky pushed for a more "law-governed" and technocratic price-based approach. However, with the August 1948 death of Andrei Zhdanov, Voznesensky lost his patron and was soon accused of treason as part of the Leningrad Affair; within two years he was dead in prison. Instead, what won out was a "physical planning" approach that strengthened the role of central governments over technocrats. At the same time, the effort to create a single regime of planning "common economic organization" with the ability to set plans throughout the Comecon region also came to nought. A protocol to create such a system was signed January 18, 1949, but never ratified. While historians are not unanimous on why this was stymied, it clearly threatened the sovereignty not only of the smaller states but even of the Soviet Union itself, since an international body would have had real power; Stalin clearly preferred informal means of intervention in the other Comecon states. This lack of either rationality or international central planning tended to promote autarky in each Comecon country because none fully trusted the others to deliver goods and services.

With few exceptions, foreign trade in the Comecon countries was a state monopoly, and the state agencies and captive trading companies were often corrupt. Even at best, this tended to put several removes between a producer and any foreign customer, limiting the ability to learn to adjust to foreign customers' needs. Furthermore, there was often strong political pressure to keep the best products for domestic use in each country. From the early 1950s to Comecon's demise in the early 1990s, intra-Comecon trade, except for Soviet petroleum, was in steady decline.

Oil transfers
Beginning no later than the early 1970s, Soviet petroleum and natural gas were routinely transferred within Comecon at below-market rates. Most Western commentators have viewed this as implicit, politically motivated subsidization of shaky economies to defuse discontent and reward compliance with Soviet wishes. Other commentators say that this may not have been deliberate policy, noting that whenever prices differ from world market prices, there will be winners and losers. They argue that this may have been simply an unforeseen consequence of two factors: the slow adjustment of Comecon prices during a time of rising oil and gas prices, and the fact that mineral resources were abundant in the Comecon sphere, relative to manufactured goods. A possible point of comparison is that there were also winners and losers under EEC agricultural policy in the same period. Russian and Kazakh oil kept the Comecon countries' oil prices low when the 1973 oil crisis quadrupled Western oil prices.

As one of the Comecon members deemed underdeveloped, Cuba obtained oil in direct exchange for sugar at a rate highly favorable to Cuba. Within the socialist economic paradigm, the subsidies in favor of Cuba and other underdeveloped Comecon members were viewed as rational and fair because they counteracted unequal exchange.

Ineffective production
The organization of Comecon was officially focused on common expansion of states, more effective production and building relationships between countries within. And as in every planned economy, operations did not reflect state of market, innovations, availability of items or the specific needs of a country. One example came from former Czechoslovakia. In the 1970s, the Communist party of Czechoslovakia finally realized that there was a need for underground trains. Czechoslovak designers projected a cheap but technologically innovative underground train. The train was a state-of-the-art project, capable of moving underground or on the surface using standard rails, had a high number of passenger seats, and was lightweight. According to the designers, the train was technologically more advanced than the trains used in New York's Subway, London's Tube or the Paris Metro. However, due to the plan of Comecon, older Soviet trains were used, which guaranteed profit for the Soviet Union and work for workers in Soviet factories. That economical change lead to the cancellation of the R1 trains by A. Honzík. The Comecon plan, though more profitable for the Soviets, if less resourceful for the Czechs and Slovaks, forced the Czechoslovak government to buy trains "Ečs (81-709)" and "81-71", both of which were designed in early 1950s and were heavy, unreliable and expensive. (Materials available only in Czech Republic and Slovakia, video included)

On the other hand, Czechoslovak trams (Tatra T3) and jet trainers (L-29) were the standard for all Comecon countries, including the USSR, and other countries could develop their own designs but only for their own needs, like Poland (respectively, Konstal trams and TS-11 jets). Poland was a manufacturer of light helicopters for Comecon countries (Mi-2 of the Soviet design). The USSR developed their own model Kamov Ka-26 and Romania produced French helicopters under license for their own market. In a formal or informal way, often the countries were discouraged from developing their own designs that competed with the main Comecon design.

Structure
Although not formally part of the organization's hierarchy, the Conference of First Secretaries of Communist and Workers' Parties and of the Heads of Government of the Comecon Member Countries was Comecon's most important organ. These party and government leaders gathered for conference meetings regularly to discuss topics of mutual interest. Because of the rank of conference participants, their decisions had considerable influence on the actions taken by Comecon and its organs.

The official hierarchy of Comecon consisted of the Session of the Council for Mutual Economic Assistance, the executive committee of the council, the Secretariat of the council, four council committees, twenty-four standing commissions, six interstate conferences, two scientific institutes, and several associated organizations.

The Session
The Session of the Council for Mutual Economic Assistance, officially the highest Comecon organ, examined fundamental problems of economic integration and directed the activities of the Secretariat and other subordinate organizations. Delegations from each Comecon member country attended these meetings. Prime ministers usually headed the delegations, which met during the second quarter of each year in a member country's capital (the location of the meeting was determined by a system of rotation based on Cyrillic script). All interested parties had to consider recommendations handed down by the Session. A treaty or other kind of legal agreement implemented adopted recommendations. Comecon itself might adopt decisions only on organizational and procedural matters pertaining to itself and its organs.

Each country appointed one permanent representative to maintain relations between members and Comecon between annual meetings. An extraordinary Session, such as the one in December 1985, might be held with the consent of at least one-third of the members. Such meetings usually took place in Moscow.

Executive committee
The highest executive organ in Comecon, the executive committee, was entrusted with elaborating policy recommendations and supervising their implementation between sessions. In addition, it supervised work on plan coordination and scientific-technical cooperation. Composed of one representative from each member country, usually a deputy prime minister, the executive committee met quarterly, usually in Moscow. In 1971 and 1974, the executive committee acquired economic departments that ranked above the standing commissions. These economic departments considerably strengthened the authority and importance of the executive committee.

Other entities
There were four council committees: Council Committee for Cooperation in Planning, Council Committee for Scientific and Technical Cooperation, Council Committee for Cooperation in Material and Technical Supply, and Council Committee for Cooperation in Machine Building. Their mission was "to ensure the comprehensive examination and a multilateral settlement of the major problems of cooperation among member countries in the economy, science, and technology." All committees were headquartered in Moscow and usually met there. These committees advised the standing commissions, the Secretariat, the interstate conferences, and the scientific institutes in their areas of specialization. Their jurisdiction was generally wider than that of the standing commissions because they had the right to make policy recommendations to other Comecon organizations.

The Council Committee for Cooperation in Planning was the most important of the four. It coordinated the national economic plans of Comecon members. As such, it ranked in importance only after the Session and the executive committee. Made up of the chairmen of Comecon members' national central planning offices, the Council Committee for Cooperation in Planning drew up draft agreements for joint projects, adopted a resolution approving these projects, and recommended approval to the concerned parties. If its decisions were not subject to approval by national governments and parties, this committee would be considered Comecon's supranational planning body.

The international Secretariat, Comecon's only permanent body, was Comecon's primary economic research and administrative organ. The secretary, who has been a Soviet official since Comecon creation, was the official Comecon representative to Comecon member states and to other states and international organizations. Subordinate to the secretary were his deputy and the various departments of the Secretariat, which generally corresponded to the standing commissions. The Secretariat's responsibilities included preparation and organization of Comecon sessions and other meetings conducted under the auspices of Comecon; compilation of digests on Comecon activities; conduct of economic and other research for Comecon members; and preparation of recommendations on various issues concerning Comecon operations.

In 1956, eight standing commissions were set up to help Comecon make recommendations pertaining to specific economic sectors. The commissions have been rearranged and renamed a number of times since the establishment of the first eight. In 1986 there were twenty-four standing commissions, each headquartered in the capital of a member country and headed by one of that country's leading authorities in the field addressed by the commission. The Secretariat supervised the actual operations of the commissions. The standing commissions had authority only to make recommendations, which had then to be approved by the executive committee, presented to the Session, and ratified by the interested member countries. Commissions usually met twice a year in Moscow.

The six interstate conferences (on water management, internal trade, legal matters, inventions and patents, pricing, and labor affairs) served as forums for discussing shared issues and experiences. They were purely consultative and generally acted in an advisory capacity to the executive committee or its specialized committees.

The scientific institutes on standardization and on economic problems of the world economic system concerned themselves with theoretical problems of international cooperation. Both were headquartered in Moscow and were staffed by experts from various member countries.

Affiliated agencies

Several affiliated agencies, having a variety of relationships with Comecon, existed outside the official Comecon hierarchy. They served to develop "direct links between appropriate bodies and organizations of Comecon member countries."

These affiliated agencies were divided into two categories: intergovernmental economic organizations (which worked on a higher level in the member countries and generally dealt with a wider range of managerial and coordinative activities) and international economic organizations (which worked closer to the operational level of research, production, or trade). A few examples of the former are the International Bank for Economic Cooperation (managed the transferable rouble system), the International Investment Bank (in charge of financing joint projects), and Intermetall (encouraged cooperation in ferrous metallurgy).

International economic organizations generally took the form of either joint enterprises, international economic associations or unions, or international economic partnerships. The latter included Interatominstrument (nuclear machinery producers), Intertekstilmash (textile machinery producers), and Haldex (a Hungarian-Polish joint enterprise for reprocessing coal slag).

Nature of operation
Comecon was an interstate organization through which members attempted to coordinate economic activities of mutual interest and to develop multilateral economic, scientific, and technical cooperation:
 * The Charter (1959) stated that "the sovereign equality of all members" was fundamental to the organization and procedures of Comecon.
 * The Comprehensive Program further emphasized that the processes of integration of members' economies were "completely voluntary and do not involve the creation of supranational bodies." Hence under the provisions of the Charter, each country had the right to equal representation and one vote in all organs of Comecon, regardless of the country's economic size or the size of its contribution to Comecon's budget.
 * From 1967, the "interestedness" provisions of the Charter reinforced the principle of "sovereign equality." Comecon's recommendations and decisions could be adopted only upon agreement among the interested members, and each had the right to declare its "interest" in any matter under consideration.
 * Furthermore, in the words of the Charter (as revised in 1967), "recommendations and decisions shall not apply to countries that have declared that they have no interest in a particular matter."
 * Although Comecon recognized the principle of unanimity, from 1967 disinterested parties did not have a veto but rather the right to abstain from participation. A declaration of disinterest could not block a project unless the disinterested party's participation was vital. Otherwise, the Charter implied that the interested parties could proceed without the abstaining member, affirming that a country that had declared a lack of interest "may subsequently adhere to the recommendations and decisions adopted by the remaining members of the Council." However, a member country could also declare an "interest" and exercise a veto.

Over the years of its functioning, Comecon acted more as an instrument of mutual economic assistance than a means of economic integration, with multilateralism as an unachievable goal. J.F. Brown, a British historian of Eastern Europe, cited Vladimir Sobell, a Czech-born economist, for the view that Comecon was an "international protection system" rather than an "international trade system", in contrast with the EEC, which was essentially the latter. Whereas the latter was interested in production efficiency and in allocation via market prices, the former was interested in bilateral aid to fulfill central planning goals. Writing in 1988, Brown stated that many people in both the West and the East had assumed that a trade and efficiency approach was what Comecon was meant to pursue, which might make it an international trade system more like the EEC, and that some economists in Hungary and Poland had advocated such an approach in the 1970s and 1980s, but that "it would need a transformation of every [Eastern Bloc] economy along Hungarian lines [i.e., only partly centrally planned] to enable a market-guided Comecon to work. And any change along those lines has been ideologically unacceptable up to now."

Comecon versus the European Economic Community

Although Comecon was loosely referred to as the "European Economic Community (EEC) of (Central and) Eastern Europe," important contrasts existed between the two organizations. Both organizations administered economic integration; however, their economic structure, size, balance, and influence differed:

In the 1980s, the EEC incorporated 270 million people in Europe into economic association through intergovernmental agreements aimed at maximizing profits and economic efficiency on a national and international scale. The EEC was a supranational body that could adopt decisions (such as removing tariffs) and enforce them. Activity by members was based on initiative and enterprise from below (on the individual or enterprise level) and was strongly influenced by market forces.

Comecon joined 450 million people in 10 countries and on 3 continents. The level of industrialization from country to country differed greatly: the organization linked two underdeveloped countries – Mongolia, and Vietnam – with some highly industrialized states. Likewise, a large national income difference existed between European and non-European members. The physical size, military power, and political and economic resource base of the Soviet Union made it the dominant member. In trade among Comecon members, the Soviet Union usually provided raw materials, and Central and East European countries provided finished equipment and machinery. The three underdeveloped Comecon members had a special relationship with the other seven. Comecon realized disproportionately more political than economic gains from its heavy contributions to these three countries' underdeveloped economies. Economic integration or "plan coordination" formed the basis of Comecon's activities. In this system, which mirrored the member countries' planned economies, the decisions handed down from above ignored the influences of market forces or private initiative. Comecon had no supranational authority to make decisions or to implement them. Its recommendations could only be adopted with the full concurrence of interested parties and (from 1967 ) did not affect those members who declared themselves disinterested parties.

As remarked above, most Comecon foreign trade was a state monopoly, placing several barriers between a producer and a foreign customer. Unlike the EEC, where treaties mostly limited government activity and allowed the market to integrate economies across national lines, Comecon needed to develop agreements that called for positive government action. Furthermore, while private trade slowly limited or erased national rivalries in the EEC, state-to-state trade in Comecon reinforced national rivalries and resentments.

Prices, exchange rates, coordination of national plans

 * See: Comprehensive Program for Socialist Economic Integration

International relations within the Comecon

 * See: International relations within the Comecon

Soviet domination of Comecon was a function of its economic, political, and military power. The Soviet Union possessed 90 percent of Comecon members' land and energy resources, 70 percent of their population, 65 percent of their national income, and industrial and military capacities second in the world only to those of the United States. The location of many Comecon committee headquarters in Moscow and the large number of Soviet nationals in positions of authority also testified to the power of the Soviet Union within the organization.

Soviet efforts to exercise political power over its Comecon partners, however, were met with determined opposition. The "sovereign equality" of members, as described in the Comecon Charter, assured members that if they did not wish to participate in a Comecon project, they might abstain. Central and East European members frequently invoked this principle in fear that economic interdependence would further reduce political sovereignty. Thus, neither Comecon nor the Soviet Union as a major force within Comecon had supranational authority. Although this fact ensured some degree of freedom from Soviet economic domination of the other members, it also deprived Comecon of necessary power to achieve maximum economic efficiency.

title: Comecon


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Talk:Mahjong solitaire

History of the solitaire game
Any thoughts as to whether this might be related to the history of the game? http://www.gamesmuseum.uwaterloo.ca/Archives/Culin/Dice1893/ryonghpai.htm Rjstoneus (talk) 00:07, 8 March 2010 (UTC)

Does anyone know the history of this game? Rmhermen 17:54 22 Jul 2003 (UTC)
 * added :) -- Ebricca 09:46, 1 Dec 2003 (UTC)

Hmm... when was Gunshy? After all, it's mostly the same game using icons instead of Mahjong tiles. --Spikey 05:14, 16 Feb 2004 (UTC)

"Microsoft Taipei"??? ARE YOU SURE?

Speculation on unreleased software
"A significantly upgraded version of this game, retitled Mahjong Titans, is set to be included in Microsoft's Windows Vista for a 2007 release."

Interesting but I removed it from the main page and put it here. Given the history many software companies have of vapourware and failure to release software as promised such speculation seem not only inappropriate for an encyclopedia but a whole lot like advertising or astroturfing. Horkana

Scoring
What governs the scoring of Mahjong Titans? I can't find rules for scoring posted anywhere. Shorter times don't seem to increase scores...? Clearing 4 of a kind doesn't seem to increase score...? Unsigned question by 207.55.0.250
 * I don't know for Mahjong Titans, however for Kmahjongg the scoring is as follows:
 * 20 points for every tile removed (so it is possible to score with a "stuck" game)
 * 1 point for every second of gametime left under 20 minutes.
 * 20 points off for every cheat used (hint etc)
 * 200 points off for a reshuffle
 * The maximum theoretically obtainable score is 2880(stones)+1200(time)=4080 points (if solved immediately). Interestingly, it pays off to get "stuck" as soon as possible: a direct "stuck" board will yield 1200 points, well enough to get you into the default high scores (the "default" high score is set at only 400, where I usually get between 2800 and 3800 points (Yes, I'm slow, I know). IIVQ 18:12, 24 June 2007 (UTC)

Fair use rationale for Image:Taipei.png
Image:Taipei.png is being used on this article. I notice the image page specifies that the image is being used under fair use but there is no explanation or rationale as to why its use in this Wikipedia article constitutes fair use. In addition to the boilerplate fair use template, you must also write out on the image description page a specific explanation or rationale for why using this image in each article is consistent with fair use.

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BetacommandBot (talk) 06:32, 24 January 2008 (UTC)

Removed AcChen paragraph
I removed the following paragraph because of multiple errors:

"A game called Ac Chen was released for the NeXTStep system, which was basically mahjong solitaire with pop culture symbols on the pieces instead of traditional Chinese pictures. It is now also available on the Nintendo DS, on the Clubhouse Games games compilation in the US and the 42 All-Time Classics in Europe."

AcChen is a port resp. remake of Sarakon by the original coder (Stefan Preuss). Sarakon is a variant of Shisen-Sho, not a Shanghai-type game. Like Shanghai, it has layers, but the rules for removing stones are the same as in Shisen-Sho. For this article it is not really relevant.—Graf Bobby (talk) 12:04, 14 June 2009 (UTC)

Long Lead
The lead is longer than the article itself. I'm thinking the organization could be instead be as follows:

Lead:

The lead would only contain its current first paragraph, minus the sentence about GNOME. The first two sentences of the second paragraph could be useful too.

Article: 71.61.181.39 (talk) 05:29, 12 February 2011 (UTC)
 * 1) History
 * 2) Variations (from lead paragraphs 3 and 4 and the sentence about GNOME from lead paragraph 1)
 * 3) Playing Strategies (from lead paragraphs 2 and 5)

 * Done. You could've done it yourself; cf. WP:BOLD -- TimNelson (talk) 13:22, 17 July 2011 (UTC)

Confusion about Name
The article says "As the game is based on mahjong tiles, some confusion arose with the 4-player mahjong game.", which seems to be rather an understatement. It would be intriguing to find out about exact numbers, but my suspicion is that hardly anyone in Europe has any idea that "Mahjong" is actually something else than the single-player game where you stack bricks that can be played on the computer in so many variants. 129.69.215.37 (talk) 12:31, 30 June 2014 (UTC)

Frozen page
I used coins to move past highlighted tiles. It said I moved to another Country, city, etc. It took the coins, but the page is frozen & I can’t get to the next playing game 2603:7080:7A03:7100:C425:7786:D4D2:7E2F (talk) 19:57, 2 August 2022 (UTC)

RfC
Please comment at Talk:Solitaire Onceinawhile (talk) 20:15, 29 August 2023 (UTC)

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

title: Talk:Mahjong solitaire


text:
User talk:Commonchaos

Hey there!

Replaceable fair use Image:Official_Photograph_of_Paul_Kagame.jpg
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title: User talk:Commonchaos


text:
Place Pigalle

The Place Pigalle is a public square located in the 9th arrondissement of Paris, between the Boulevard de Clichy and the Boulevard de Rochechouart, near Sacré-Cœur, at the foot of the Montmartre hill.

Location and access
The square is located between Boulevard de Clichy and Boulevard de Rochechouart, near the Sacré-Coeur, at the bottom of Montmartre hill. It is the best known place in the Pigalle district.

This site is served by lines 2 and 12 at Pigalle metro station.

Origin of the name
The place takes its name from the sculptor, Jean-Baptiste Pigalle (1714–1785), and it is the best-known district of the Quartier Pigalle, the Pigalle district.

History
In 1826, Mr. Brack was authorized to form on his land and on land that the city conceded to him by way of exchange, in accordance with the deliberation of the Conseil municipal of 1 June 1826, a street 12 meters wide, from Rue Laval (now Rue Victor-Massé) to the Porte Montmartre (Montmartre gate), and a semi-circular square in front of this gate. In 1864, this place, named Place de la Barrière-Montmartre, was renamed Place Pigalle.

On 18 March 1871, General Clément Thomas, having learned that General Claude Lecomte had been seized by the insurgents during the Paris Commune uprising, set out to find him. Dressed in disguise as a civilian, he arrived at around 5 pm. on Place Pigalle. When one of the rebels recognized him by his big white beard, he was taken to the Rue des Rosiers and executed.

By 1900 the square and the surrounding streets were a neighbourhood of painters' studios and literary cafés of which the most renowned was the Nouvelle Athènes (New Athens). The Place Pigalle inspired a celebrated song by Georges Ulmer: "Un p'tit jet d'eau, une station de métro, entourée de bistrots, Pigalle ... ."  ("A little spritz of water, a subway station, surrounded by bistros, Pigalle ... .") "Place Pigalle" is also the title of a song written by Alex Alstone and Maurice Chevalier. It was recorded by Chevalier with orchestra (Jacques Hélian, conductor) in Paris on 9 April 1946. Figure 8—Elliott Smith's fifth album and the last he released in his lifetime—was initially titled Place Pigalle. It's also the name of one of his unreleased songs, and he had "two or three more songs" about it. Hungarian pop star Eva Csepregi, of Neoton Familia, mentions the square and its notoriety as a red-light district in her 1987 solo single "Párizsi Lány" ("Paris Girl").

Remarkable buildings and memorable places

 * No 1: former location of the Café L'Abbaye de Thélème, which exhibited painters.
 * No 3, at the corner with Avenue Frochot: former location of the Café du Rat Mort, which was open at the end of the 19th century all night.
 * No 5: location of the workshop of Gabriel Dauchot (1927-2005), painter from the School of Paris.
 * No 9: former location of the Café de la Nouvelle Athènes. Photographer Paul Sescau (1858-1926) opened his second studio above in 1896 to be as close as possible to his artistic clientele. The Café de la Nouvelle Athènes became Le Sphynx in the 1920s and 1940s, a strip tease place, then the New Moon, which was a lesbian cabaret in the 60s and 70s then in the 1980s and 1990s welcomed rock groups. The entire original building burnt down in 2004 and was demolished. This place, which was the property for over thirty years of Hélène Martini, was the subject of a serious study in the work, published at the end of 2017 in Le Seuil, by David Dufresne, writer and former journalist, notably at Libération. The cabaret and the book are the subject of a cultural program (in free download) in October 2017 and on 1 January 2018 (France Culture).
 * No 11: the Folies Pigalle, a former Italian theater, then cabaret and finally cinema hall, which became a nightclub from 1991.

title: Place Pigalle


text:
Intersection number

In mathematics, and especially in algebraic geometry, the intersection number generalizes the intuitive notion of counting the number of times two curves intersect to higher dimensions, multiple (more than 2) curves, and accounting properly for tangency. One needs a definition of intersection number in order to state results like Bézout's theorem.

The intersection number is obvious in certain cases, such as the intersection of the x- and y-axes in a plane, which should be one. The complexity enters when calculating intersections at points of tangency, and intersections which are not just points, but have higher dimension. For example, if a plane is tangent to a surface along a line, the intersection number along the line should be at least two. These questions are discussed systematically in intersection theory.

Definition for Riemann surfaces
Let X be a Riemann surface. Then the intersection number of two closed curves on X has a simple definition in terms of an integral. For every closed curve c on X (i.e., smooth function $$c : S^1 \to X$$), we can associate a differential form $$\eta_c$$ of compact support, the Poincaré dual of c, with the property that integrals along c can be calculated by integrals over X:

 * $$\int_c \alpha = -\iint_X \alpha \wedge \eta_c = (\alpha, *\eta_c)$$, for every closed (1-)differential $$\alpha$$ on X,

where $$\wedge$$ is the wedge product of differentials, and $$*$$ is the Hodge star. Then the intersection number of two closed curves, a and b, on X is defined as

 * $$a \cdot b := \iint_X \eta_a \wedge \eta_b = (\eta_a, -*\eta_b) = -\int_b \eta_a$$.

The $$\eta_c$$ have an intuitive definition as follows. They are a sort of dirac delta along the curve c, accomplished by taking the differential of a unit step function that drops from 1 to 0 across c. More formally, we begin by defining for a simple closed curve c on X, a function fc by letting $$\Omega$$ be a small strip around c in the shape of an annulus. Name the left and right parts of $$\Omega \setminus c$$ as $$\Omega^{+}$$ and $$\Omega^{-}$$. Then take a smaller sub-strip around c, $$\Omega_0$$, with left and right parts $$\Omega_0^{-}$$ and $$\Omega_0^{+}$$. Then define fc by

 * $$f_c(x) = \begin{cases} 1, & x \in \Omega_0^{-} \\ 0, & x \in X \setminus \Omega^{-} \\ \mbox{smooth interpolation}, & x \in \Omega^{-} \setminus \Omega_0^{-} \end{cases}$$.

The definition is then expanded to arbitrary closed curves. Every closed curve c on X is homologous to $$\sum_{i=1}^N k_i c_i$$ for some simple closed curves ci, that is,

 * $$\int_c \omega = \int_{\sum_i k_i c_i} \omega = \sum_{i=1}^N k_i \int_{c_i} \omega$$, for every differential $$\omega$$.

Define the $$\eta_c$$ by

 * $$\eta_c = \sum_{i=1}^N k_i \eta_{c_i}$$.

Definition for algebraic varieties
The usual constructive definition in the case of algebraic varieties proceeds in steps. The definition given below is for the intersection number of divisors on a nonsingular variety X.

1. The only intersection number that can be calculated directly from the definition is the intersection of hypersurfaces (subvarieties of X of codimension one) that are in general position at x. Specifically, assume we have a nonsingular variety X, and n hypersurfaces Z1, ..., Zn which have local equations f1, ..., fn near x for polynomials fi(t1, ..., tn), such that the following hold:

 * $$n = \dim_k X$$.
 * $$f_i(x) = 0$$ for all i. (i.e., x is in the intersection of the hypersurfaces.)
 * $$\dim_x \cap_{i=1}^n Z_i = 0$$ (i.e., the divisors are in general position.)
 * The $$f_i$$ are nonsingular at x.

Then the intersection number at the point x (called the intersection multiplicity at x) is

 * $$(Z_1 \cdots Z_n)_x := \dim_k \mathcal{O}_{X, x} / (f_1, \dots, f_n)$$,

where $$\mathcal{O}_{X, x}$$ is the local ring of X at x, and the dimension is dimension as a k-vector space. It can be calculated as the localization $$k[U]_{\mathfrak{m}_x}$$, where $$\mathfrak{m}_x$$ is the maximal ideal of polynomials vanishing at x, and U is an open affine set containing x and containing none of the singularities of the fi.

2. The intersection number of hypersurfaces in general position is then defined as the sum of the intersection numbers at each point of intersection.

 * $$(Z_1 \cdots Z_n) = \sum_{x \in \cap_i Z_i} (Z_1 \cdots Z_n)_x$$

3. Extend the definition to effective divisors by linearity, i.e.,

 * $$(n Z_1 \cdots Z_n) = n(Z_1 \cdots Z_n)$$ and $$((Y_1 + Z_1) Z_2 \cdots Z_n) = (Y_1 Z_2 \cdots Z_n) + (Z_1 Z_2 \cdots Z_n)$$.

4. Extend the definition to arbitrary divisors in general position by noticing every divisor has a unique expression as D = P – N for some effective divisors P and N. So let Di = Pi – Ni, and use rules of the form

 * $$((P_1 - N_1) P_2 \cdots P_n) = (P_1 P_2 \cdots P_n) - (N_1 P_2 \cdots P_n)$$

to transform the intersection.

5. The intersection number of arbitrary divisors is then defined using a "Chow's moving lemma" that guarantees we can find linearly equivalent divisors that are in general position, which we can then intersect.

Note that the definition of the intersection number does not depend on the order in which the divisors appear in the computation of this number.

Serre's Tor formula
Let V and W be two subvarieties of a nonsingular projective variety X such that dim(V) + dim(W) = dim(X). Then we expect the intersection V ∩ W to be a finite set of points. If we try to count them, two kinds of problems may arise. First, even if the expected dimension of V ∩ W is zero, the actual intersection may be of a large dimension: for example the self-intersection number of a projective line in a projective plane. The second potential problem is that even if the intersection is zero-dimensional, it may be non-transverse, for example, if V is a plane curve and W is one of its tangent lines.

The first problem requires the machinery of intersection theory, discussed above in detail, which replaces V and W by more convenient subvarieties using the moving lemma. On the other hand, the second problem can be solved directly, without moving V or W. In 1965 Jean-Pierre Serre described how to find the multiplicity of each intersection point by methods of commutative algebra and homological algebra. This connection between a geometric notion of intersection and a homological notion of a derived tensor product has been influential and led in particular to several homological conjectures in commutative algebra.

Serre's Tor formula states: let X be a regular variety, V and W two subvarieties of complementary dimension such that V ∩ W is zero-dimensional. For any point x ∈ V ∩ W, let A be the local ring $$\mathcal{O}_{X, x}$$ of x. The structure sheaves of V and W at x correspond to ideals I, J ⊆ A. Then the multiplicity of V ∩ W at the point x is
 * $$e(X; V, W; x) = \sum_{i=0}^{\infty} (-1)^i \mathrm{length}_A(\operatorname{Tor}_i^A(A/I, A/J))$$

where length is the length of a module over a local ring, and Tor is the Tor functor. When V and W can be moved into a transverse position, this homological formula produces the expected answer. So, for instance, if V and W meet transversely at x, the multiplicity is 1. If V is a tangent line at a point x to a parabola W in a plane at a point x, then the multiplicity at x is 2.

If both V and W are locally cut out by regular sequences, for example if they are nonsingular, then in the formula above all higher Tor's vanish, hence the multiplicity is positive. The positivity in the arbitrary case is one of Serre's multiplicity conjectures.

Further definitions
The definition can be vastly generalized, for example to intersections along subvarieties instead of just at points, or to arbitrary complete varieties.

In algebraic topology, the intersection number appears as the Poincaré dual of the cup product. Specifically, if two manifolds, X and Y, intersect transversely in a manifold M, the homology class of the intersection is the Poincaré dual of the cup product $$D_M X \smile D_M Y$$ of the Poincaré duals of X and Y.

Snapper–Kleiman definition of intersection number
There is an approach to intersection number, introduced by Snapper in 1959-60 and developed later by Cartier and Kleiman, that defines an intersection number as an Euler characteristic.

Let X be a scheme over a scheme S, Pic(X) the Picard group of X and G the Grothendieck group of the category of coherent sheaves on X whose support is proper over an Artinian subscheme of S.

For each L in Pic(X), define the endomorphism c1(L) of G (called the first Chern class of L) by
 * $$c_1(L)F= F - L^{-1} \otimes F.$$

It is additive on G since tensoring with a line bundle is exact. One also has: The intersection number
 * $$c_1(L_1)c_1(L_2) = c_1(L_1) + c_1(L_2) - c_1(L_1 \otimes L_2)$$; in particular, $$c_1(L_1)$$ and $$c_1(L_2)$$ commute.
 * $$c_1(L)c_1(L^{-1}) = c_1(L) + c_1(L^{-1}).$$
 * $$\dim \operatorname{supp} c_1(L)F \le \dim \operatorname{supp} F - 1$$ (this is nontrivial and follows from a dévissage argument.)
 * $$L_1 \cdot {\dots} \cdot L_r$$

of line bundles Li's is then defined by:
 * $$L_1 \cdot {\dots} \cdot L_r \cdot F = \chi(c_1(L_1) \cdots c_1(L_r) F)$$

where χ denotes the Euler characteristic. Alternatively, one has by induction:
 * $$L_1 \cdot {\dots} \cdot L_r \cdot F = \sum_0^r (-1)^i \chi(\wedge^i (\oplus_0^r L_j^{-1}) \otimes F).$$

Each time F is fixed, $$L_1 \cdot {\dots} \cdot L_r \cdot F$$ is a symmetric functional in Li's.

If Li = OX(Di) for some Cartier divisors Di's, then we will write $$D_1 \cdot {\dots } \cdot D_r$$ for the intersection number.

Let $$f:X \to Y$$ be a morphism of S-schemes, $$L_i, 1 \le i \le m$$ line bundles on X and F in G with $$m \ge \dim \operatorname{supp}F$$. Then
 * $$f^*L_1 \cdots f^* L_m \cdot F = L_1 \cdots L_m \cdot f_* F$$.

Intersection multiplicities for plane curves
There is a unique function assigning to each triplet $$(P,Q,p)$$ consisting of a pair of projective curves, $$P$$ and $$Q$$, in $$K[x,y]$$ and a point $$p \in K^2$$, a number $$I_p(P,Q)$$ called the intersection multiplicity of $$P$$ and $$Q$$ at $$p$$ that satisfies the following properties:

 * 1) $$I_p(P,Q) = I_p(Q,P)$$
 * 2) $$I_p(P,Q) = \infty$$ if and only if $$P$$ and $$Q$$ have a common factor that is zero at $$p$$
 * 3) $$I_p(P,Q) = 0$$ if and only if one of $$P(p)$$ or $$Q(p)$$ is non-zero (i.e. the point $$p$$ is not in the intersection of the two curves)
 * 4) $$I_p(x,y) = 1$$ where $$p = (0,0)$$
 * 5) $$I_p(P,Q_1Q_2) = I_p(P,Q_1) + I_p(P,Q_2)$$
 * 6) $$I_p(P + QR,Q) = I_p(P,Q)$$ for any $$R \in K[x,y]$$

Although these properties completely characterize intersection multiplicity, in practice it is realised in several different ways.

One realization of intersection multiplicity is through the dimension of a certain quotient space of the power series ring $$Kx,y$$. By making a change of variables if necessary, we may assume that $$p = (0,0)$$. Let $$P(x,y)$$ and $$Q(x,y)$$ be the polynomials defining the algebraic curves we are interested in. If the original equations are given in homogeneous form, these can be obtained by setting $$z = 1$$. Let $$I = (P,Q)$$ denote the ideal of $$Kx,y$$ generated by $$P$$ and $$Q$$. The intersection multiplicity is the dimension of $$Kx,y/I$$ as a vector space over $$K$$.

Another realization of intersection multiplicity comes from the resultant of the two polynomials $$P$$ and $$Q$$. In coordinates where $$p = (0,0)$$, the curves have no other intersections with $$y = 0$$, and the degree of $$P$$ with respect to $$x$$ is equal to the total degree of $$P$$, $$I_p(P,Q)$$ can be defined as the highest power of $$y$$ that divides the resultant of $$P$$ and $$Q$$ (with $$P$$ and $$Q$$ seen as polynomials over $$K[x]$$).

Intersection multiplicity can also be realised as the number of distinct intersections that exist if the curves are perturbed slightly. More specifically, if $$P$$ and $$Q$$ define curves which intersect only once in the closure of an open set $$U$$, then for a dense set of $$(\epsilon,\delta) \in K^2$$, $$P - \epsilon$$ and $$Q - \delta$$ are smooth and intersect transversally (i.e. have different tangent lines) at exactly some number $$n$$ points in $$U$$. We say then that $$I_p(P,Q) = n$$.

Example
Consider the intersection of the x-axis with the parabola $$y = x^2 $$ at the origin.

Writing $$P = y, $$ $$Q = y - x^2,\ $$and $$p = (0,0)$$ we get

 * $$I_p(P,Q) = I_p(y,y - x^2) = I_p(y,x^2) = I_p(y,x) + I_p(y,x) = 1 + 1 = 2.\,$$

Thus, the intersection multiplicity is two; it is an ordinary tangency. Similarly one can compute that the curves $$y = x^m $$ and $$y = x^n $$ with integers $$m>n\geq 0 $$ intersect at the origin with multiplicity ''$$n. $$''

Self-intersections
Some of the most interesting intersection numbers to compute are self-intersection numbers. This means that a divisor is moved to another equivalent divisor in general position with respect to the first, and the two are intersected. In this way, self-intersection numbers can become well-defined, and even negative.

Applications
The intersection number is partly motivated by the desire to define intersection to satisfy Bézout's theorem.

The intersection number arises in the study of fixed points, which can be cleverly defined as intersections of function graphs with a diagonals. Calculating the intersection numbers at the fixed points counts the fixed points with multiplicity, and leads to the Lefschetz fixed-point theorem in quantitative form.

title: Intersection number


text:
1798 in music

Events

 * July 11 – United States Marine Band established by Act of Congress.
 * September 2 – Opening of the Teatro Comunale (Ferrara) in Italy with a performance of Portogallo's Gli Orazi e i Curiazi.
 * Opening of the Teatro della Concordia in Iesi, Ancona, "one of the few opera houses in Italy from the late 1700s that has never been destroyed by fire or bombs".
 * Completion of the first São João National Theatre in Porto, Portugal as an opera house.
 * Michael Haydn takes on Carl Maria von Weber as a pupil without charge.
 * First edition of Niemetschek's biography of Mozart published.

Classical music

 * Ludwig van Beethoven – Piano Sonata No. 8 in C minor, Op. 13 (Sonata Pathétique)
 * Joseph Eybler – Clarinet Concerto in B-flat major
 * Joseph Haydn
 * The Creation
 * Missa in Angustiis
 * Leopold Kozeluch – Sinfonia Concertante in E-flat major
 * Paul Wranitzky – Grande Sinfonie caracteristique in C minor, Op. 31

Published popular music

 * Edward Jones (Bardd y Brenin) – Popular Cheshire Melodies

Births

 * January 31 – Carl Gottlieb Reissiger, kapellmeister and composer (d. 1859)
 * March 9 – Mathilda Berwald, Hovsångare (d. 1877)
 * October 28 – Henri Bertini, pianist and composer (d. 1876)
 * date unknown
 * Andrea Maffei, librettist (d. 1885)
 * Louis-Désiré Véron, opera manager (d. 1867)
 * Lovisa Charlotta Borgman, violinist (d. 1884)

Deaths

 * January 4 – Giuseppe Giordani, opera composer (b. 1751)
 * January 20 – Christian Cannabich, composer (b. 1731)
 * January 28 – Christian Gottlob Neefe, composer and conductor (b. 1748)
 * July 15 – Gaetano Pugnani, violinist (b. 1731)
 * November 30 – Friedrich Fleischmann, composer (b. 1766)
 * December 16 – Gaetano Brunetti, composer (b. 1744)

title: 1798 in music


text:
1796 in music

Events

 * The father of Gioachino Rossini is imprisoned for collaborating with the French, and Rossini's mother takes him to Bologna.

Classical music

 * Ludwig van Beethoven
 * Three Piano Sonatas, Op. 2 in F minor, A and C
 * Notturno in D major, Op.42
 * Ah! Perfido, Op.65
 * Duet mit zwei obligaten Augengläsern, WoO 32
 * Sonatina for Mandolin and Harpsichord, WoO 43a
 * Adagio for Mandolin and Harpsichord, WoO 43b
 * Allegretto, WoO 53
 * Abschiedsgesang an Wiens Bürger, WoO 121
 * Francois-Adrien Boieldieu – Duo No.2 in B-flat major for Harp and Piano
 * Muzio Clementi
 * Concerto for piano in C major
 * Three Piano Sonatas, Op. 35
 * Johann Baptist Cramer – Piano Concerto No.2, Op. 16
 * Adalbert Gyrowetz – 3 String Quartets, Op. 13
 * Joseph Haydn
 * Trumpet Concerto in E Flat Major
 * Die Worte des Erlösers am Kreuze, Hob.XX:2
 * Mass in C major, Hob.XXII:9 Missa in tempore belli ("Mass in Time of War")
 * Mass in B-flat major, Hob.XXII:10
 * Guarda qui, che lo vedrai, Hob.XXVa:1
 * Saper vorrei se m'ami, Hob.XXVa:2
 * Hyacinthe Jadin – 3 Piano Sonatas, Op. 5
 * Rodolphe Kreutzer – Études ou caprices
 * Ignaz Pleyel – 6 Duos, B.574-579
 * Giovanni Punto – Horn Concerto No.6
 * Jakub Jan Ryba – Missa pastoralis bohemica
 * Carl Friedrich Zelter – 12 Lieder am Clavier zu singen, Z.120

Opera

 * Domenico Cimarosa
 * I nemici generosi
 * Gli Orazi e i Curiazi
 * Nicolas Dalayrac – Marianne
 * Johann Simon Mayr – La Lodoiska
 * Antonio Salieri – Il Moro
 * Gaspare Spontini – Li puntigli delle donne
 * Peter Winter – Das unterbrochene Opferfest

Popular music

 * "It Was A' For Our Rightful King", 1796 Jacobite song with lyrics by Robert Burns

Methods and theory writings

 * Charles Burney – Memoirs of the Life and Writings of the Abate Metastasio
 * Wenzel Hause – Méthode de contrebasse
 * António da Silva Leite – Estudo de guitarra
 * Bernard Viguerie – L'art de toucher le piano-forte

Births

 * January 23 – Jean Reboul, librettist and poet (died 1864)
 * February 17 – Giovanni Pacini, composer (died 1867)
 * June 14 – Mathilda d'Orozco, composer (died 1863)
 * June 25 – Ferdinando Giorgetti, Italian composer (died 1867)
 * July 22 – Carlo Pepoli, librettist and politician (died 1881)
 * July 23 – Franz Berwald, composer (died 1868)
 * July 24 – Jan Czeczot, librettist and poet (died 1847)
 * July 28 – Ignaz Bösendorfer, piano manufacturer (died 1859)
 * July 29 – Christian Winther, lyricist and poet (died 1876)
 * August 25 – James Lick, piano builder (died 1876)
 * August 27 – Elise Barensfeld, soprano (died after 1820)
 * September 3 – Henriette Widerberg, soprano (died 1872)
 * September 20 – Franz Wilhelm Ferling, composer and oboist (died 1874)
 * November 30 – Carl Loewe, German composer (died 1869)
 * December 9 – Emilie Zumsteeg, composer and musician (died 1857)
 * date unknown – Mirzə Şəfi Vazeh, lyricist and poet (died 1852)
 * date unknown – Mirzə Şəfi Vazeh, lyricist and poet (died 1852)

Deaths

 * January 1 – Alexandre-Théophile Vandermonde, chemist and musician, 60
 * February 16 (or April 16) – Caterina Gabrielli, operatic soprano, 65
 * February 17 – James Macpherson, librettist and writer (born 1736)
 * February 28 – Friedrich Wilhelm Rust, composer and violinist (born 1739)
 * March 19 – Stephen Storace, composer, 33
 * June 8 – Felice Giardini, violinist and composer, 80
 * July 17 – Thomas Sanders Dupuis, English composer (born 1733)
 * July 21 – Robert Burns, librettist and poet (born 1759)
 * August 12 – Mary Ann Wrighten Pownall, librettist and singer (born 1751)
 * October 17 – Franz Paul Rigler, composer and piano virtuoso (born c.1748)
 * October 31 – Thomas Haxby, musical instrument maker, 67
 * date unknown
 * Luffman Atterbury, carpenter, builder and musician
 * Samuel Green, organ builder (born 1740)
 * Nicola Sabatino, composer (born 1705)
 * Nicola Sabatino, composer (born 1705)

title: 1796 in music


text:
1795 in music

Events

 * Joseph Haydn returns to Vienna following second London visit.
 * Franz Krommer settles in Vienna.
 * Ludwig van Beethoven makes his public performance debut as a pianist

Opera

 * Louis Emmanuel Jadin Le Cabaleur
 * Vicente Martín y Soler – La Capricciosa Correta
 * Antonio Salieri – Palmira

Classical music

 * Johann Georg Albrechtsberger – 6 String Trios, Op. 9
 * Ludwig van Beethoven
 * 12 Minuets, WoO 7
 * German Dances, WoO 8
 * 6 Minuets, WoO 9
 * 6 Minuets, WoO 10
 * Variations on 'Là ci darem la mano', WoO 28
 * 9 Variations on 'Quant'e piu bello', WoO 69
 * 6 Variations on 'Nel cor piu non mi sento', WoO 70
 * Im Arm der Liebe ruht sich's wohl, WoO 159
 * Three Piano Trios, Op. 1
 * String Quintet in E-flat major, Op.4
 * Sextet in E-flat major, Op.81b
 * Rondo a capriccio, Op.129
 * Muzio Clementi – 2 Piano Sonatas and 2 Capriccios, Op. 34
 * Jean-Louis Duport – 6 Cello Sonatas, Op. 4
 * Adalbert Gyrowetz
 * Three Flute Quartets, Op. 11
 * 3 String Quartets, Op. 19
 * Thomas Haigh – 3 Keyboard Sonatas, Op. 10
 * Joseph Haydn
 * Symphonies 103 in E-flat "Drum Roll" and 104 in D "London"
 * Piano Trios Op. 82, Including XV:24, 25, 26
 * Piano Trio in E-flat minor, Hob.XV:31
 * 150 Scottish Songs, Hob.XXXIa:1–150 (Volume III, 101–150)
 * Heinrich Anton Hoffmann – 3 String Quartets, Op. 3
 * Johann Nepomuk Hummel – Piano Sonata No. 8
 * Hyacinthe Jadin
 * 3 String Quartets, Op. 1
 * 3 Piano Sonatas, Op. 4
 * Hans Georg Nägeli – Freut euch des Lebens (song)
 * Ignaz Pleyel – Keyboard Trio in D major, B.461
 * Joseph Reicha – Concerto Concertant, Op. 3
 * Daniel Gottlob Turk – 120 Handstücke für angehende Klavierspieler, Vol 2.
 * Giovanni Battista Viotti – Violin Concerto No.24 in B minor
 * Friedrich Witt – Horn concerto in E major
 * Francesco Molino - 3 Guitar Sonatas, Op.6

Methods and theory writings

 * Johann Ernst Altenburg – Versuch einer Anleitung zur heroisch-musikalischen Trompeter und Pauker-Kunst
 * Giuseppe Aprile – The Modern Italian Method of Singing
 * Giuseppe Maria Cambini – Méthode pour la flûte traversiere
 * Justin Heinrich Knecht – Vollständige Orgelschule
 * Heinrich Christoph Koch – Über den Charakter der Solo- und Ripienstimmen

Births

 * January 18 – Joseph Merk, cellist (died 1852)
 * March 14 – Robert Lucas Pearsall, composer (died 1856)
 * March 23 – Leopold Jansa, composer (died 1875)
 * April 4 – Joseph Böhm, violinist and music teacher (died 1876)
 * April 14 – Pedro Albéniz, pianist and composer (died 1855)
 * June 13 – Anton Felix Schindler, biographer of Beethoven (died 1864)
 * May 27 – Friedrich August Belcke, trombonist (died 1874)
 * August 16 – Heinrich Marschner, composer (died 1861)
 * August 17 – Pierre-Louis Parisis, dedicatee and bishop (died 1866)
 * September 16 – Saverio Mercadante, Italian composer (died 1870)
 * September 29 – Kondraty Ryleyev, lyricist and poet (died 1826)
 * October 17 – Johann Christoph Biernatzki, librettist and writer (died 1840)
 * October 31 – John Keats, lyricist and poet (died 1821)
 * November 17 – Antonio Bagioli, composer and music teacher (died 1871)
 * December 10 – Kaspar Kummer, composer and flautist (died 1870)
 * date unknown – Jeanne-Catherine Pauwels, Belgian pianist (died 1889)

Deaths

 * January 19 – Maria Teresa Agnesi, Italian composer (born 1720)
 * January 21 – Michel Corrette, organist and composer (b. 1707)
 * January 26 – Johann Christoph Friedrich Bach, composer (b. 1732)
 * February 11 – Carl Michael Bellman, composer (b. 1740)
 * March 5 – Josef Reicha, cellist, conductor and composer (b. 1752)
 * May 22 – Friedrich Wilhelm Marpurg, composer and music critic (b. 1718)
 * July – Ranieri de' Calzabigi, librettist (b. 1714)
 * August 19 – Friedrich Hartmann Graf, German composer (born 1727)
 * August 31 – François-André Danican Philidor, French composer and chess player (born 1726)
 * September 22 – Sayat-Nova, composer and musician (born 1712)
 * October 3 – John Christopher Smith, English composer (born 1712)
 * October 11 – Franz Christoph Neubauer, German composer (born 1750)
 * October 25 – Francesco Antonio Baldassare Uttini, Italian composer (born 1723)
 * November 6 – Georg Benda, composer (b. 1722)
 * November 19 – Thomas Linley the elder, conductor and composer (b. 1733)
 * December 6 – Sofia Liljegren, Finnish soprano (b. 1765)

title: 1795 in music


text:
1794 in music

Events

 * Joseph Haydn begins his second visit to London
 * Carl Ditters von Dittersdorf is expelled from the palace in Johannesberg after a dispute with his patron Philipp Gotthard von Schaffgotsch, ending nearly a quarter of a century in his service there.

Classical music

 * Ludwig van Beethoven – String Trio No. 1 in E-flat major
 * William Billings – The Continental Harmony
 * Benjamin Carr – The Federal Overture
 * Domenico Cimarosa – Il trionfo della fede, sacred oratorio premiered May 3 in Naples
 * Muzio Clementi
 * Violin Sonata in C major, Op.30
 * Flute Sonata in A major, Op.31
 * 3 Piano Sonatas, Op. 33
 * Piano Trio, WO 6
 * Jan Ladislav Dussek – 12 Leçons progressives
 * Anton Eberl – Piano Sonata in C minor, Op. 1
 * Joseph Eybler
 * Christmas Oratorio
 * 3 String Quartets, Op. 1
 * Lev Gurilyov – Piano Sonata No.1
 * Joseph Haydn
 * Symphony No. 100 in G major, "Military"
 * Symphony No. 101 in D major, "Clock"
 * Symphony No. 102 in B-flat major, Hob.I:102
 * Divertimento in C major, Hob.IV:1
 * Divertimento in G major, Hob.IV:4
 * Piano Trios, Op.36
 * Piano Trio in G major, Hob.XV:32
 * Piano Sonata No. 51 in D major, Hob XVI:51
 * Piano Sonata No. 52 in E-flat, Hob XVI:52
 * 6 Psalms, Hob.XXIII:suppl.
 * 6 English Canzonettas, Hob.XXVIa:25-30
 * Johann Nepomuk Hummel – 3 Fugues, Op. 7
 * Jean Xavier Lefèvre – Clarinet Concerto No.4 in G minor, IJL 1
 * Johann Simon Mayr – La Passione, oratorio in Italian
 * Etienne Nicolas Méhul – Chant du départ
 * F. D Mouchy – La Mort de Louis XVI, Op.3
 * William Parkinson – 3 Sonatas for the pianoforte or harpsichord, Op. 1
 * William Parsons – The Court Minuets for His Majesty's Birth Day, 1794
 * Ignaz Pleyel – 3 Keyboard Trios, B.446-448
 * Pierre Rode – Air varié, Op.10
 * Antonio Rosetti – Symphony in F major, M.A49/I:25 or 24
 * Friedrich Wilhelm Rust – Keyboard Sonata No. 12 in D major, CzaR 11
 * Christian Gotthilf Tag – 12 Kurze und leichte Orgelvorspiele, 1 Orgelsinfonie
 * Giovanni Battista Viotti – Violin Concerto No.27 in C major
 * Christoph Ernst Friedrich Weyse – Piano Sonatas No. 5-8

Opera

 * Luigi Cherubini – Eliza (premiered Dec. 13 in Paris)
 * Domenico Cimarosa
 * Le astuzie femminili (premiered Aug. 26 in Naples)
 * Penelope (premiered Dec. 26 in Naples)
 * Francois-Joseph Gossec – Le triomphe de la République, RH 618 (divertissement, premiered Jan. 27 in Paris)
 * Friedrich Heinrich Himmel – Il primo navigatore
 * Johann Simon Mayr – Saffo
 * Étienne Méhul – Horatius Coclès, Mélidore et Phrosine
 * Carl Ditters von Dittersdorf – Das Gespenst mit der Trommel

Methods and theory writings

 * Matthew Camidge – Instructions, 8 Sonatinas, and Useful Preludes
 * Francois Devienne – Nouvelle méthode théorique et pratique pour la flûte
 * Anton Joseph Hampel – Méthode pour Cor
 * Nicola Sala – Regole del contrappunto pratico

Births

 * January 6 – Kašpar Mašek, composer (d. 1873)
 * April 7 – Giovanni Battista Rubini, tenor
 * April 9
 * Aristide Farrenc, musician and music publisher (died 1865)
 * Theobald Boehm, composer and flautist (died 1881)
 * May 23 – Ignaz Moscheles, composer and piano virtuoso (d. 1870)
 * August 10 – Princess Amalie of Saxony, composer (d. 1870)
 * September 10 – François Benoist, organist and composer (d. 1878)
 * September 16 – Wenzel Gährich, composer (died 1864)
 * September 29 – William Michael Rooke, violinist and composer (d. 1849)
 * October 4 – Justina Casagli, operatic soprano
 * October 7 – Wilhelm Müller, lyricist (died 1827)
 * October 13 – Anselm Hüttenbrenner, composer (d. 1868)
 * October 18 – Ferdinand Schubert, Austrian composer (died 1859)
 * October 23 – Joseph Panny, composer and violinist (died 1838)
 * October 29 – William Bingham Tappan, hymnist (died 1849)
 * November 3 – William Cullen Bryant, patron of the arts and poet (died 1878)
 * December 6 – Luigi Lablache, operatic bass
 * date unknown
 * Mirza Shafi Vazeh, lyricist (died 1852)

Deaths

 * April 26 – Johan Foltmar, composer (b. 1714)
 * May 6 – Jean-Jacques Beauvarlet-Charpentier, composer and organist (born 1734)
 * July 13 – Josse-François-Joseph Benaut, composer and musician (born 1741)
 * July 17 – Jean-Frédéric Edelmann, composer (b. 1749) (executed)
 * July 22 – Jean-Benjamin de Laborde, composer (born 1734)
 * July 25 – André Chénier, lyricist (born 1762)
 * August 7 – Edmund Angerer, composer (born 1740)
 * August 11 – Jakob Friedrich Kleinknecht, German composer (born 1722)
 * August 25 – Leopold August Abel, composer (b. 1717)
 * November 9 – Gregory Skovoroda, poet and composer (b. 1722)
 * November 20 – Mattia Verazi, Italian librettist (born c. 1730)
 * November 22 – Alison Cockburn, lyricist (born 1712)

title: 1794 in music


text:
1793 in music

Events

 * September 25 – The Chevalier de Saint-Georges, the "black Mozart", loses his command and is imprisoned at Houdainville.
 * Niccolò Paganini debuts as a violin virtuoso at age 11 in his birthplace of Genoa.
 * Westminster Quarters first written, for the bells of a new clock at the Church of St Mary the Great, Cambridge, by Prof. Joseph Jowett, probably with Prof. John Randall or William Crotch.

Popular Music

 * Nehemiah Shumway – The American Harmony, including "Schenectady"
 * George Thomson – A Select Collection of Original Scottish Airs for the Voice

Classical music

 * Jean-Jacques Beauvarlet-Charpentier – Variations on La Marseillaise
 * Ludwig van Beethoven – Ein Selbstgespräch, WoO 114
 * Domenico Cimarosa – Concerto for 2 Flutes in G major, G.1077
 * Muzio Clementi
 * 3 Piano Trios, Op. 29
 * 3 Piano Trios, Op. 32
 * Jan Ladislav Dussek
 * 6 Piano Sonatinas, Op. 19
 * Piano Concerto No.5, Op. 22
 * The Sufferings of the Queen of France, Op. 23
 * Joseph Haydn
 * String Quartets, Opp. 71 & 74 "Apponyi"
 * Variations in F minor
 * 12 German Dances, Hob.IX:10
 * Piano Trio in G major, Hob.XV:32
 * Michael Haydn – Missa in honorem Sanctae Ursulae
 * Leopold Kozeluch – Three Piano Sonatas, Op. 38
 * Giovanni Battista Viotti – Violin Concerto No.26 in B-flat major
 * Paul Wranitzky
 * Concerto for Flute in D major, Op. 24
 * Six String Quartets, Op. 23

Opera

 * Felice Alessandri – Virginia
 * Samuel Arnold – The Mountaineers
 * Thomas Attwood – Ozmyn and Daraxa
 * François-Adrien Boïeldieu – La fille coupable
 * Domenico Cimarosa – I traci amanti
 * Francesco Gardi – Pirro
 * Johann Baptist Henneberg – Die Waldmänner
 * Étienne Méhul – Le jeune sage et le vieux fou
 * Johann Friedrich Reichardt – Erwin und Elmire
 * Josef Seger – 8 Toccatas and Fugues
 * Daniel Steibelt – Roméo et Juliette

Methods and theory writings

 * Pierre Baillot – Méthode de Violon
 * Joseph Frike – A Guide in Harmony
 * Othon-Joseph Vandenbroek – Traité général de tous les instruments à vent
 * Georg Joseph Vogler – Verbesserung der Forkel’schen Veränderungen über 'God save the King'

Births

 * January 18 – William Henry Havergal, hymn-writer and composer (d. 1870)
 * February 14 – William Crathern, composer of sacred music (d. c.1851)
 * February 27 – Elisabeth Frösslind, opera singer (d. 1861)
 * July 22 – Eugène Walckiers, composer (died 1866)
 * August 21 – Peter Casper Krossing, composer (d. 1838)
 * September 2 – Caroline Ridderstolpe, composer (d. 1878)
 * December 26 – François Hünten, composer (died 1878)
 * date unknown – William Bartholomew, arranger and composer (died 1867)

Deaths

 * January 24 (bur.) – Marged ferch Ifan, harpist and wrestler (b. 1696)
 * March 17 – Leopold Hofmann, composer (b. 1738)
 * May 3 – Martin Gerbert, music writer (b. 1720)
 * May 7 – Pietro Nardini, composer (b. 1722)
 * July 26 – Alessandro Besozzi, Italian composer (born 1702)
 * September 10 – Marc-Antoine Désaugiers, opera composer (b. 1742)
 * September 14 – Benjamin Cooke, organist and composer (b. 1734)
 * October 21 – Johann Hartmann, composer (b. 1726)
 * October 25 – Giovanni Battista Ferrandini, composer (b. 1710)
 * date unknown
 * Philip Phile, violinist and composer (b. c.1734)
 * Marie-Anne-Catherine Quinault, singer and composer (b. 1695)

title: 1793 in music


text:
Mammalian embryogenesis

Mammalian embryogenesis is the process of cell division and cellular differentiation during early prenatal development which leads to the development of a mammalian embryo.

Difference from embryogenesis of lower chordates
Due to the fact that placental mammals and marsupials nourish their developing embryos via the placenta, the ovum in these species does not contain significant amounts of yolk, and the yolk sac in the embryo is relatively small in size, in comparison with both the size of the embryo itself and the size of yolk sac in embryos of comparable developmental age from lower chordates. The fact that an embryo in both placental mammals and marsupials undergoes the process of implantation, and forms the chorion with its chorionic villi, and later the placenta and umbilical cord, is also a difference from lower chordates.

The difference between a mammalian embryo and an embryo of a lower chordate animal is evident starting from blastula stage. Due to that fact, the developing mammalian embryo at this stage is called a blastocyst, not a blastula, which is more generic term.

There are also several other differences from embryogenesis in lower chordates. One such difference is that in mammalian embryos development of the central nervous system and especially the brain tends to begin at earlier stages of embryonic development and to yield more structurally advanced brain at each stage, in comparison with lower chordates. The evolutionary reason for such a change likely was that the advanced and structurally complex brain, characteristic of mammals, requires more time to develop, but the maximum time spent in utero is limited by other factors, such as relative size of the final fetus to the mother (ability of the fetus to pass mother's genital tract to be born), limited resources for the mother to nourish herself and her fetus, etc. Thus, to develop such a complex and advanced brain in the end, the mammalian embryo needed to start this process earlier and to perform it faster.

Another difference is that during the development of embryonic genitourinary tract, in case of female embryo of placental and marsupial mammals, the uterus is formed, a structure that neither monotremata nor lower chordates have. In every case, including monotremata embryos, the milk glands also develop.

Difference from human embryogenesis
Most mammals develop similarly to humans; during the earliest stages of development, the embryo is largely indistinguishable from another mammal. However, there are phenomena found in human beings not found in all other mammals, as well as phenomena occurring in other mammals, but not in humans.

Humans
Mammals do not have the same human chorionic gonadotropin released from their embryo.

Non-human mammals
The anatomy of the area surrounding an embryo or fetus is different in litter-bearing animals compared to humans: each unborn animal is surrounded by placental tissue and is lodged along one of two long uterine horns rather than in the center of the pear-shaped uterus found in a human female.

title: Mammalian embryogenesis


text:
User:Quickwon

Hi Quickwon

Most of the things on my todo list have been filled in, though a few remain. Maybe I need to add a few new things!

Do you want to tackle formal specification? Some of these things get filled in by others - which is surely what Wikipedia is all about. You can do the same by filling in a list of things here which you might like to know about, or have others work on. I notice that Johan Halvorsen (1864-1935) which I flagged has now been filled in, though there is still a need for an article about Daum. Also, sometimes I put down titles which need working on. David Martland 10:10, 1 Dec 2003 (UTC)

title: User:Quickwon


text:
User talk:Mendalus~enwiki

[http://en.wikipedia.org/w/wiki.phtml?title=User_talk:Mendalus&action=edit&section=new Please click here to leave me a new message. Remember to sign your posts by adding four tildes ( ~ ) at the end. ]

User:Mendalus added to Wikipedians from Norway
Hi there; welcome! I took the liberty of adding you to the list of Norwegian contributors (Wikipedians/Norway). And thanks for the Arne Næss jr. stuff. I did some work on it too (and on related articles; I now actually feel quite sure I know much more about Diana Ross than I ever wanted or needed...). --Wernher 01:35, 14 Jan 2004 (UTC)

Thank you! I have found one of the great advantages with this encyclopedia to be that even though my skills in the English language has several flaws, as soon as I've written an article, someone else correct my English. :) Mendalus 08:50, 14 Jan 2004 (UTC)

More messages
Write messages to me here

ghostwritten by pharmaceutical companies
In Alternative medicine I feel like writing how 50% of the drug research studies are ghostwritten by pharmaceutical companies. And, how the Peer reviewed respectable journals, however, like NEJM, Lancet, JAMA, and BMJ have been unable to prevent biased papers ghostwritten by pharmaceutical companies from being published. I am also considering making major changes to Medicine to attactk it for the above, in the same manner that science geeks feel a perverse need to screw up Alternative medicine. Need, I remind you that 85% of current conventional medical practice has not been verified by science? -- Mr-Natural-Health 04:40, 15 Jan 2004 (UTC)

 * There is a very great divergence in the published research, and I doubt anyone is fooled by it. I'd assume it's more a case of people never reading it in the first place.
 * That said, vandalism is not acceptable on either of the two pages, and the purpose of WP is not to advocate either school of thought, but rather do document both in an encyclopædic manner, based on verifiable sources. There's plenty of pages I'd just love to tear to shreds for a variety of different reasons, but I'm a guest in this house, as are you, and I behave accordingly.
 * So, rather than screwing up the pages related to the western medical tradition (a subset of which I actually work on; without being automatically biased against alternative medicine), please consider contributing actively to the pages about alternative medicine, and do so in an exemplary manner, with good sources, well-written articles, and a healthy distance to a topic you obviously care about.
 * There's plenty to object to in both schools, in my experience. No need to make a crusade out of it, and definitely not worth spilling it over here; just because some people do so, doesn't mean you need to. Zuiram 19:12, 16 December 2006 (UTC)

Norwegian
Thanks a lot for the help with my Noewegian Wikipedia user page. Obviously, I don't actually speak any Norwegian (although I can kind of make out some of it when I read it). Thanks. -Branddobbe 09:07, Jul 23, 2004 (UTC)

statute of limitations
The article on Erich Priebke in the English Wikipedia is apparently a translation of the Norwegian article. Does it also (apparently) incorrectly claim that Argentina has a statute of limitations for murder? This is at least not true in most countries. --Espoo (talk) 08:19, 6 July 2011 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Mendalus. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Mendalus~enwiki that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name. If you think you might own all of the accounts with this name and this message is in error, please visit Special:MergeAccount to check and attach all of your accounts to prevent them from being renamed.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 01:27, 20 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 16:13, 22 April 2015 (UTC)

Speedy deletion nomination of Arne Næss, Jr.

A tag has been placed on Arne Næss, Jr. requesting that it be speedily deleted from Wikipedia. This has been done under section A7 of the criteria for speedy deletion, because the article appears to be about a person or group of people, but it does not indicate how or why the subject is important or significant: that is, why an article about that subject should be included in an encyclopedia. Under the criteria for speedy deletion, such articles may be deleted at any time. Please read more about what is generally accepted as notable.

If you think this page should not be deleted for this reason, you may contest the nomination by visiting the page and clicking the button labelled "Click here to contest this speedy deletion". This will give you the opportunity to explain why you believe the page should not be deleted. However, be aware that once a page is tagged for speedy deletion, it may be removed without delay. Please do not remove the speedy deletion tag from the page yourself, but do not hesitate to add information in line with Wikipedia's policies and guidelines. If the page is deleted, and you wish to retrieve the deleted material for future reference or improvement, then please contact the deleting administrator. 217IP (talk) 00:41, 27 June 2015 (UTC)

Nomination of Arne Næss, Jr. for deletion
A discussion is taking place as to whether the article Arne Næss, Jr. is suitable for inclusion in Wikipedia according to Wikipedia's policies and guidelines or whether it should be deleted.

The article will be discussed at Articles for deletion/Arne Næss, Jr. until a consensus is reached, and anyone is welcome to contribute to the discussion. The nomination will explain the policies and guidelines which are of concern. The discussion focuses on high-quality evidence and our policies and guidelines.

Users may edit the article during the discussion, including to improve the article to address concerns raised in the discussion. However, do not remove the article-for-deletion notice from the top of the article. 217IP (talk) 15:40, 27 June 2015 (UTC)

Nomination of TV3 (Viasat) for deletion
A discussion is taking place as to whether the article TV3 (Viasat) is suitable for inclusion in Wikipedia according to Wikipedia's policies and guidelines or whether it should be deleted.

The article will be discussed at Articles for deletion/TV3 (Viasat) until a consensus is reached, and anyone, including you, is welcome to contribute to the discussion. The nomination will explain the policies and guidelines which are of concern. The discussion focuses on high-quality evidence and our policies and guidelines.

Users may edit the article during the discussion, including to improve the article to address concerns raised in the discussion. However, do not remove the article-for-deletion notice from the top of the article until the discussion has finished. AlexandraAVX (talk) 11:10, 3 February 2024 (UTC)

title: User talk:Mendalus~enwiki


text:
User:Mendalus~enwiki

My name is Fredrik Garmannslund and I'm a student from Norway.

I live in Norway's second largest town, Bergen, where I study at the University of Bergen.

da:Bruger:Mendalus fr:Utilisateur:Mendalus no:Bruker:Mendalus nn:Brukar:Mendalus

title: User:Mendalus~enwiki