Formally, these reside in a complex separable Hilbert space-variously called the " state space " or the " associated Hilbert space " of the system-that is well defined up to a complex number of norm 1 ( the phase factor ).

Formally, most of these people were convicted by NKVD troikas (" triplets ")– special courts martial.

Formally it is precisely in allowing quantification over class variables α, β, etc., that we assume a range of values for these variables to refer to.

( Formally speaking, this then satisfies the premises of an axiom of well-founded induction, which asserts that these two conditions are sufficient for the proposition to hold for all x.

Formally most of these approaches are similar to an artificial neural network, as inputs to a node are summed up and the result serves as input to a sigmoid function, e. g., but proteins do often control gene expression in a synergistic, i. e. non-linear, way.

Formally, these prepositions are actually prepositional phrases.

Formally termed cladodes, these branchlets somewhat resemble pine needles, although sheoaks are actually flowering plants.

Formally, these failed when they were rejected by the Church of England's General Synod in 1972, however conversations and co-operation continued leading in 2003 to the signing of a covenant between the two churches.

Formally, each of the following definitions defines a concrete category, and every pair of these categories can be shown to be concretely isomorphic.

Formally, citizen science has been defined as " the systematic collection and analysis of data ; development of technology ; testing of natural phenomena ; and the dissemination of these activities by researchers on a primarily avocational basis ".

Formally these were examples of additional member systems.

Formally the Prince-Electors elected a King of the Romans, who was elected in Germany but became Holy Roman Emperor only when crowned by the Pope.

* Formally, when working over the reals, as here, this is accomplished by considering the limit as ε → 0 ; but the " infinitesimal " language generalizes directly to Lie groups over general rings.

Formally, such genes should increase in frequency when

In late 1900s the day that of the City was founded is Jakin School is a Private School is Formally Part of Jakin School Board was Grades One through Twelve there is no Football field on this school. In 1966 When Jakin School was Closed were Sent to Blakely-Union Elementary, Junior High, and High School ( which later Became Early County High, Middle, and Elementary School ). while Carver school was built for African-American students grades One through Twelve. although late 1960s when Carver school was closed along with Kestler School was based in Damascus were sent to Washington High & Elementary at Blakely. In addition to small farm agriculture, Jakin's early economic growth resulted from turpentine.

Formally, it is anything which when offered in payment extinguishes the debt.

Formally since 19 June 1971 when Lövenich ( now part of Cologne ) was an independent town.

Formally, knowing the step response of a dynamical system gives information on the stability of such a system, and on its ability to reach one stationary state when starting from another.

Formally, a composite number n = d · 2 < sup > s </ sup > + 1 with d being odd is called a strong pseudoprime to a relatively prime base a when one of the following conditions hold:

Formally, a graph is symmetric with respect to the origin if it is unchanged when reflected across both the x-axis and y-axis.

Formally, a natural number n is called superabundant precisely when, for any m < n,

Formally, arbitrage transactions have negative skew – prices can get a small amount closer ( but often no closer than 0 ), while they can get very far apart.

Formally, they were part of the non-resident sections, but in fact constituted a separate division, largely autonomous in their activities.

Formally, we are given a set of hypotheses and a set of manifestations ; they are related by the domain knowledge, represented by a function that takes as an argument a set of hypotheses and gives as a result the corresponding set of manifestations.

Formally, they are partial derivatives of the option price with respect to the independent variables ( technically, one Greek, gamma, is a partial derivative of another Greek, called delta ).

Formally, they are known as Ridunians, from the Latin Riduna.

Formally reported from November 1944 onwards, witnesses often assumed that the foo fighters were secret weapons employed by the enemy, but they remained unidentified post-war and were reported by both Allied and Axis forces.

By 1912, the Social Democrats, with an explicitly anti-antisemitic program, were the largest party in the German Reichstag, and the Progressives ran very strongly as well ... Formally, at least, the Jews had been fully emancipated with the establishment of the German Empire, although they were kept out of certain influential occupations, enjoyed extraordinary prosperity ... Germans intermarried with Jews: in the 1930s some 50, 000 Jews were living in mixed German-Jewish marriages, so at least 50, 000 Germans, and presumably parts of their families, had familial contact with the Jews.

Formally, they are appointed by the President for five-year terms coinciding with the term of the House of Representatives.

Formally, Liouville numbers and elementary numbers contain the algebraic numbers, and they include some but not all transcendental numbers.

Formally they adhered to the principles of the Shakers.

Formally system networks correspond to type lattices in formal lattice theory, although they are occasionally erroneously mistaken for flowcharts or directed decision trees.

Formally however they define it as any variable that does not directly affect the fundamentals of the economy.

Formally, they have always been considered Orthodox Christians, but most of them followed shamanism and animism as a part of their culture.

Formally, this meant that the whole peloton finished out of time limits, but the referees understandably used a rule saying that they could give clemency to any group of more than 20 % of the stage's starting riders, officially citing the weather conditions as their reason to do so.

Formally, oxidation state is the hypothetical charge that an atom would have if all bonds to atoms of different elements were 100 % ionic.

Formally neutral and reluctant to become involved with the great powers except as a last resort, Kuwait turned to the United States, the Soviet Union and Britain for naval protection of its tanker fleet after twenty-one ships were attacked in the gulf since late 1986.

Formally introduced in September 1979, Initial samples were released in February 1980, with production chips available over the counter in November.

Formally divided into lower and upper Ullern in 1740, both farms were bought by Herman Severin Løvenskiold, in 1878 and 1866 respectively.

* General Headquarters United Nations Command ( Korea ) ( UNC ) — Formally activated 10 July 1950, before then Allied forces were formally under American operational control.

Formally, official academic distinctions were made in the 1910s and 1890s, respectively.

Formally dedicated " as a memorial to the boys that were " on October 30, 1915, Alumni Field and its distinctive " maroon goal-posts on a field of green " were hailed in that evening's edition of the Boston Saturday Evening Transcript as " one of the sights in Boston.

Formally the Bataliony Chłopskie were dissolved in September 1945.

Formally, the 1772 Constitution was adopted by the Parliament ( Riksdag ) on 21 August 1772, but this took place as members of the Parliament and the Privy Council were under threat by the royal garrison on order by King Gustav III outside of Stockholm Palace, where the Parliament and Privy Council were assembled in different parts of the palace.

Many interior sets were built at the Castle Brae Business Centre ( Formally the Castlebrae High School ) in Edinburgh.

Formally known as the " Azov's Memory " its sailors were veterans of the 1906 revolutionary actions.