Formally, that's applying subgame perfection to solve the game.

Formally, we have for the approximation to the full solution A, a series in the small parameter ( here called ), like the following:

“ Formally stated, interactivity is an expression of the extent that in a given series of communication exchanges, any third ( or later ) transmission ( or message ) is related to the degree to which previous exchanges referred to even earlier transmissions ” ( Sheizaf Rafaeli, “ Interactivity, From New Media to Communication ,” pages 110-34 in Advanced Communicational Science: Merging Mass and Interpersonal Processes, ed.

Formally speaking, a collation method typically defines a total order on a set of possible identifiers, called sort keys, which consequently produces a total preorder on the set of items of information ( items with the same identifier are not placed in any defined order ).

Formally, this definition includes as classical all objects with the current orbits that

Formally, an inner product space is a vector space V over the field together with an inner product, i. e., with a map

Formally, if M is a set, the identity function f on M is defined to be that function with domain and codomain M which satisfies

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, this sharing of dynamics is referred to as universality, and systems with precisely the same critical exponents are said to belong to the same universality class.

Formally, according to the Constitution, citizens of Turkmenistan have the right to set up political parties and other public associations, acting within the framework of the Constitution and laws, and public associations and groups of citizens have the right to nominate their candidates in accordance with the election law.

Formally, we start with a category C with finite products ( i. e. C has a terminal object 1 and any two objects of C have a product ).

Formally, a Markov chain is a random process with the Markov property.

Formally, an elliptic function is a function meromorphic on for which there exist two non-zero complex numbers and with ( in other words, not parallel ), such that and for all.

Formally, if is an open subset of the complex plane, a point of, and is a holomorphic function, then is called a removable singularity for if there exists a holomorphic function which coincides with on.

Formally, two variables are inversely proportional ( or varying inversely, or in inverse variation, or in inverse proportion or in reciprocal proportion ) if one of the variables is directly proportional with the multiplicative inverse ( reciprocal ) of the other, or equivalently if their product is a constant.

Formally it consists of a short lyric composed in a single metre with a single rhyme throughout.

Formally, powers with positive integer exponents may be defined by the initial condition

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, 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, the problem of supervised pattern recognition can be stated as follows: Given an unknown function ( the ground truth ) that maps input instances to output labels, along with training data assumed to represent accurate examples of the mapping, produce a function that approximates as closely as possible the correct mapping.

Formally the work is operatic, with the plot advanced entirely through dialogue sung with accompanying music.

Formally, the President is elected by the National People's Congress in accordance with Article 62 of the Constitution.

Formally the self-inductance of a wire loop would be given by the above equation with i

Formally, rotational symmetry is symmetry with respect to some or all rotations in m-dimensional Euclidean space.

Formally, f < sub > X, Y </ sub >( x, y ) is the probability density function of ( X, Y ) with respect to the product measure on the respective supports of X and Y.

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 market is complete with respect to a trading strategy,, if there exists a self-financing trading strategy, such that at any time, the returns of the two strategies, and are equal.

Formally, the right Kan extension of along consists of a functor and a natural transformation which is couniversal with respect to the specification, in the sense that for any functor and natural transformation, a unique natural transformation is defined and fits into a commutative diagram

Formally, for any dimension, the orientation of the image of an object under a direct isometry with respect to that object is the linear part of that isometry.

Formally, the problem can be stated as follows: given a desired property, expressed as a temporal logic formula p, and a structure M with initial state s, decide if.

a < sub > i </ sub >, a < sub > i + 1 </ sub >,..., which is a suffix of w. Formally, the satisfaction relation between a word and an LTL formula is defined as follows:

Formally a formula in the language of Peano arithmetic is a formula if it is of the form

Instead, we give a sketch of how one can derive Itō's lemma by expanding a Taylor series and applying the rules of stochastic calculus.

In 1887, he joined Frederick W. Taylor in applying scientific management principles to their work at Midvale Steel and Bethlehem Steel — working there with Taylor until 1893.

By the middle of April 1834 Taylor reported that two-thirds of his machinery was working and many of his former workers were applying for reinstatement.

Repeatedly differentiating the curve and applying the Frenet – Serret formulas gives the following Taylor approximation to the curve near s = 0:

This series of calculators was also noted for a large number of highly counter-intuitive mysterious undocumented features, somewhat similar to " synthetic programming " of the American HP-41, which were exploited by applying normal arithmetic operations to error messages, jumping to non-existent addresses and other techniques.

His unique teaching style allowed him to take incredibly complicated subjects and transform them into a series of lectures that even his rudimentary physics students were capable of comprehending and applying.

Typically, this is done by applying a series of " refactorings ", each of which is a ( usually ) tiny change in a computer program's source code that does not modify its conformance to functional requirements.

In 1967, applying a satirical angle to a fashion for the inclusion of " superman " inspired characters in UK television commercials, Milligan dressed up in a " Bat-Goons " outfit to head up a series of television commercials for British Petroleum.

Between 1875 and 1878 Gibbs wrote a series of papers applying his graphical techniques of thermodynamic analysis to multi-phase chemical systems.

He further developed the art of applying Aiki and is said to have remained powerful until very late in life, and-as a consequence of the success of Transparent Power-was featured in a series of articles in the Aiki News magazines prior to his death in 1998.

It has been proven possible to permanently correct cases of infantile idiopathic scoliosis by applying a series of plaster casts ( EDF: elongation, derotation, flexion ) on a specialized frame under corrective traction, which helps to " mould " the infant's soft bones and work with their growth spurts.

* ( W n ): National Assembly for Wales series: Statutory Instruments made by the National Assembly for Wales and applying to Wales only.

Beginning in 1997 Martin Lo, Shane D. Ross, and others wrote a series of papers identifying the mathematical basis and applying the technique to the Genesis solar wind sample return, along with Lunar and Jovian missions.

Definitive series have tended to be combinations of design types, each applying to a range of values.

This is accomplished by placing a D. C. blocking capacitor with a capacitance about 100 times greater than the maximum capacitance of the varicap diode in series with it and applying the D. C. from a high impedance source to the node between the varicap cathode and the blocking capacitor as shown in the upper left hand diagram, right.

For example, the circle method of Hardy and Littlewood was conceived as applying to power series near the unit circle in the complex plane ; it is now thought of in terms of finite exponential sums ( that is, on the unit circle, but with the power series truncated ).

NASA was not in the business of applying Rogallo's family of airfoils to personal aircraft such as kites, hang gliders, and powered light aircraft ; however what was already in the Paresev series of aircraft provided all the fundamental mechanics that could be simplified to lighter personal aircraft.

Many further results may be obtained, such as Fermi's golden rule, which relates the rate of transitions between quantum states to the density of states at particular energies, and the Dyson series, obtained by applying the iterative method to the time evolution operator, which is one of the starting points for the method of Feynman diagrams.

The reason is that we have obtained this series simply interchanging and and we can go from one to another applying this exchange.

In October 2001, the European Commission launched a series of surveys in the 13 countries that were applying for European Union membership under the heading Candidate Eurobarometer ( initially named Applicant Countries Eurobarometer or AC-EB ).

This and many of the following series may be obtained by applying Möbius inversion and Dirichlet convolution to known series.

A unity gain buffer amplifier may be constructed by applying a full series negative feedback ( Fig.

Parris resigned as an MP by applying for the Crown position of Steward of the Manor of Northstead and left Parliament specifically to take over from Brian Walden as host of ITV's influential Sunday lunchtime current-affairs series Weekend World in 1986.

* Since power series can be differentiated term-wise, applying the above argument in the reverse direction and the power series expression for