However, aside from formulating the Hardy – Weinberg principle in population genetics, his famous work on integer partitions with his collaborator Ramanujan, known as the Hardy – Ramanujan asymptotic formula, has been widely applied in physics to find quantum partition functions of atomic nuclei ( first used by Niels Bohr ) and to derive thermodynamic functions of non-interacting Bose-Einstein systems.

However, by formulating the problem as the solution of a Toeplitz matrix and using Levinson recursion, we can relatively quickly estimate a filter with the smallest mean squared error possible.

However, the Socialist Party has experienced considerable difficulty in formulating an alternative to right-wing policy.

However, Russell himself thought highly of the vast majority of Meinong's work and, until formulating his theory of descriptions, held similar views about non-existent objects.

However the key assumption he made in formulating the collision term was " molecular chaos ", an assumption which breaks time-reversal symmetry as is necessary for anything which could imply the second law.

However, the general negotiations between the main parties dragged on, because France kept formulating new demands.

However, what role if any he played in formulating the country's new constitution has not been established.

However, there is a large-scale housing project currently under construction, and Haringey Council is formulating plans to redevelop the area.

However, Article 138 of the Basic Law requires the HKSAR to improve medical and health services by formulating policies to develop Western and Chinese medicine.

However, Canada has disagreed with American policies regarding the Vietnam War, the status of Cuba, the Iraq War, Missile Defense, and the War on Terrorism.

However, in the 1980s, under the leadership of Margaret Thatcher, and the influence of Keith Joseph, there was a dramatic shift in the ideological direction of British conservatism, with a movement towards free-market economic policies.

However, in an effort to reassert its dominant role, IBM patented the bus, and placed stringent licensing and royalty policies on its use.

However, new trade policies have made agricultural production much more responsive to market demands, putting global food reserves at their lowest since 1983.

However, Germany is giving increasing attention to coordinating its policies with the European Union through the Common Foreign and Security Policy.

However, reaching those goals required policies that moved away from balancing the budget, lowering inflation, and reducing the deficit and external debt to attract investment and stimulate economic growth.

However, wage and price controls have sometimes been part of the mix of policies used to halt hyperinflation.

However, he changed his press policies after the 1929 stock market crash, screening reporters and greatly reducing his availability.

However, Hoover did pursue many policies in an attempt to pull the country out of depression.

However, their numbers grew as the Vichy regime resorted to more strident policies in order to fulfill the enormous demands of the Nazis and the eventual decline of Nazi Germany became more obvious.

However, central policies are voted upon by the server admin community which is archived for referencing.

However, Sardar Patel died in 1950, leaving Nehru as the sole remaining iconic national leader, and soon the situation became such that Nehru was able to implement many of his basic policies without hindrance.

However the people of Basutoland opposed this and when the South African Nationalist party put its apartheid policies into place the possibility of annexation was halted.

However, as a result of conservative fiscal policies and a sound financial system, in 2010 the country credit rating improved slightly to BB + and was kept at that level in 2011.

" However, it could be done if " you could re-establish a world in which government's budget accounted for 10 percent of the national income, in which laissez-faire reigned, in which governments did not interfere with economic activities and in which full employment policies had been relegated to the dustbin ..."

However, her marriage to Philip was unpopular among her subjects, and her religious policies resulted in deep-seated resentment.

However, this did not mean that their economic interests lay with the ' laissez-faire ' policies of those representing them politically.

However, this approach did not work well because the members could not agree on a leader or on policies, and often worked at odds with each other.

However, the progressive " co-ed " policies initiated at Genesee would soon find controversy at the new university in Syracuse.

However, senior politicians of all main parties have voiced concerns in regard to the West Lothian Question, which is raised where certain policies for England are set by MPs from all four constituent nations whereas similar policies for Scotland or Wales might be decided in the devolved assemblies by legislators from those countries alone.

However, it would be impossible to attain this full-employment target using only demand-side Keynesian stimulus without getting below the NAIRU and suffering from accelerating inflation ( absent incomes policies ).

However, this move increased Uzbek nationalism, which had long resented Soviet policies such as the imposition of cotton monoculture and the suppression of Islamic traditions.

However, Alexander's policies later encountered opposition from other European powers stemming from developments in Italy and Germany, where Fascists and Nazis rose to power, and the Soviet Union, where Joseph Stalin became absolute ruler.

However, by comparing the TV snatches, two different radio station re-runs, and the censored Los Angeles Times version, I found that the radio stations had edited out questions ( ABC removed the one regarding Laos ) or even a paragraph out of the middle of the President's answer.

However, there is disagreement among expert bodies regarding the long-term use of benzodiazepines for panic disorder.

However, researchers hold contrary opinions regarding the effects of long-term administration.

However, since the contras failed to win widespread popular support or military victories within Nicaragua, since opinion polls indicated that a majority of the U. S. public was not supportive of the contras, since the Reagan administration lost much of its support regarding its contra policy within Congress after disclosure of CIA mining of Nicaraguan ports, and since a report of the Bureau of Intelligence and Research commissioned by the State Department found Reagan's allegations about Soviet influence in Nicaragua " exaggerated ", Congress cut off all funds for the contras in 1985 by the third Boland Amendment.

However, the peace was not stable and further conflicts arose regarding demarcation of the Samogitian borders.

However, public opposition to increases in defence spending — during a period when economic constraints require reduced spending for social welfare — has created differences among the political parties regarding a broadly acceptable level of new defence expenditure.

However, since the economic crisis, there has been extensive talk and debate regarding the reintroduction of third-level fees.

However, abiotic mechanisms for stromatolitic growth are also known, leading to a decades-long and sometimes-contentious scientific debate regarding biogenesis of certain formations, especially those from the lower to middle Archean eon.

However Mussolini later became unimpressed by Lenin, regarding Lenin as merely a new version of Tsar Nicholas.

However, there is some degree of debate regarding Clement's exact meaning of " spiritual gospel "; care must be taken not to ascribe to his phrase modern prejudices or expectations.

However another study, had observed that pusher syndrome is also present in patients with left hemisphere lesions, leading to aphasia, providing a stark contrast to what was previously believed regarding hemispatial neglect, which mostly occurs with a right hemisphere lesion.

However a later reference to Albanians from the same Attaliates, regarding the participation of Albanians in a rebellion around 1078, is undisputed.

However no specific conclusions can be made regarding whether material that is sulfur-free enters the bacterial cell after phage adsorption.

However, they did not make any conclusions regarding the specific function of DNA as hereditary material, and only said that it must have some undefined role.

However, it has been suggested that the recent change in the European Union's position regarding the many organizations " that have been too easily included in the UN terror list " might have influenced the UN's position.

However the Type 1 service provides no guarantees regarding the order of the received frames compared to the order in which they have been sent ; the sender does not even get an acknowledgment that the frames have been received.

However, information about a tender offer ( usually regarding a merger or acquisition ) is held to a higher standard.

However, the variety of single parent families regarding gender of the main parent has rarely been taken into reason when understanding the relation between family and child's negative outcomes.

However, he states that scholars are divided on the tone of the original reference and while some scholars believe that it had a negative tone which was softened by Christian interpolators, others believe that it had a neutral tone, in keeping with the style and approach of Josephus regarding the issue.

However, due to AT & T policy regarding source-code distribution, this improved curses library did not have much acceptance in the BSD community.

However, in light of continuing uncertainty about Wittgenstein's intentions regarding this material, the fourth edition ( 2009 ) re-titles " Part I " as " Philosophical Investigations " proper, and " Part II " as " Philosophy of Psychology-A Fragment.

" ( However, the novel prompted a heated debate in the scientific community regarding the plausibility of developing ethnic bioweapons ).

However, the change had not yet been officially ratified by Britain when Rhodesia declared itself independent, and as a result, the British Government continued to refer to the breakaway colony as " Southern Rhodesia " throughout its existence, a stance it maintained regarding the June – December 1979 successor state of Zimbabwe Rhodesia.