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Algebraically and .
Algebraically, these units can be thought of as the squares of the corresponding length units.
; Algebraically closed field: A field F is algebraically closed if every polynomial in F has a root in F ; equivalently: every polynomial in F is a product of linear factors.
; Algebraically independent elements: Elements of an extension field of F are algebraically independent over F if they don't satisfy any non-zero polynomial equation with coefficients in F.
Algebraically, a map is anticonformal if at every point the Jacobian is a scalar times an orthogonal matrix with negative determinant: in two dimensions the Jacobian must be a scalar times a reflection at every point.
Algebraically compact modules share many other properties with injective objects because of the following: there exists an embedding of R-Mod into a Grothendieck category G under which the algebraically compact R-modules precisely correspond to the injective objects in G.
Algebraically, a lattice is a set with two associative, commutative idempotent binary operations linked by corresponding absorption laws.
Algebraically it is generated by applying the rules of vectors and coordinate geometry to a space with four dimensions.

means and standard
That means that, if we are to achieve a new standard of leadership, we must think in terms of the total context of our situation.
Selection by lottery was the standard means as it was regarded as the more democratic: elections would favour those who were rich, noble, eloquent and well-known, while allotment spread the work of administration throughout the whole citizen body, engaging them in the crucial democratic experience of, to use Aristotle's words, " ruling and being ruled in turn " ( Politics 1317b28 – 30 ).
* Red Book ( CD standard ), the original means of playing back audio on the medium
According to the 802. 16-2004 standard, broadband means " having instantaneous bandwidths greater than 1 MHz and supporting data rates greater than about 1. 5 Mbit / s.
Money was primarily a standardized medium of exchange, and final means of payment, that serves to measure the value of all goods and commodities in a standard of value.
:::" One inning more to play " in standard baseball jargon means that the home team has one set of at-bats remaining: the poem is set just before the start of Mudville's final turn ( of a regulation game ), in the bottom of the ninth inning ( Mudville was the home team and the home team bats last in an inning ).
In terms of varnasrama principles, the highest standard of brahmacarya means the vow not to marry but to observe strict celibacy throughout life.
This means that the spoken language in this part of Sweden is descended from a regional variant of Danish, while the written language used is standard Swedish, which evolved in Uppsala and Stockholm.
The DECT standard fully specifies a means for a portable unit, such as a cordless telephone, to access a fixed telecoms network via radio.
If the electrode has a positive potential with respect to the SHE, then that means it is a strongly reducing electrode which forces the SHE to be the anode ( an example is Cu in aqueous CuSO < sub > 4 </ sub > with a standard electrode potential of 0. 337 V ).
This means it can handle four times as much traffic as standard GPRS.
Acclimatization, the means by which the body adapts to higher altitudes, only partially restores pO < sub > 2 </ sub > to standard levels.
This means that a driver can be ordered " by an authorised person ... upon production of evidence of his authorisation, require him to stop the running of the engine of that vehicle " and a " person who fails to comply ... shall be guilty of an offence and be liable on summary conviction to a fine not exceeding level 3 on the standard scale ".
In practical terms, the equivalence of inertial reference frames means that scientists within a box moving uniformly cannot determine their absolute velocity by any experiment ( otherwise the differences would set up an absolute standard reference frame ).
While one standard deviation is 15 points, and two SDs are 30 points, and so on, this does not imply that mental ability is linearly related to IQ, such that IQ 50 means half the cognitive ability of IQ 100.
International English is the concept of the English language as a global means of communication in numerous dialects, and also the movement towards an international standard for the language.
While this effort has by no means converted all, or even most, Muslims to the Wahhabist interpretation of Islam, it has done much to overwhelm more moderate local interpretations, and has set the Saudi-interpretation of Islam as the " gold standard " of religion in Muslims ' minds.
In practical terms that means for an older standard definition TV set the ideal viewing distance was about 8 times the height ( not diagonal ) of the screen away.
Since 2001, trim levels are also indicated by including a number after the main index: '- 00 ' means base trim level, '- 01 ' means standard trim and '- 02 ' designates deluxe version ; for example, VAZ-21121-02 means Lada 112 hatchback with an 1. 6L SOHC engine and deluxe trim.
Some computer sound cards include a standard MIDI connector, whereas others connect by any of various means that include the D-subminiature DA-15 game port, USB, FireWire, Ethernet or a proprietary connection.
It is also common practice for major mining companies to do the rehabilitation of the dumps to an international acceptable standard, which in some cases means that higher standards than the local regulatory standard are applied.
Any agency wanting to read PGP messages would probably use easier means than standard cryptanalysis, e. g. rubber-hose cryptanalysis or black-bag cryptanalysis i. e. installing some form of trojan horse or keystroke logging software / hardware on the target computer to capture encrypted keyrings and their passwords.

means and generates
Whereas the vocoder analyzes speech, transforms it into electronically transmitted information, and recreates it, The Voder ( from Voice Operating Demonstrator ) generates synthesized speech by means of a console with fifteen touch-sensitive keys and a pedal, basically consisting of the " second half " of the vocoder, but with manual filter controls, needing a highly trained operator.
Following the formula above, this means the J-2 powered version generates a Δv of ( 414 s * 9. 81 ) ln ( 119, 900 / 13, 311 ), or 8, 900 m / s.
A learning procedure then generates a model that attempts to meet two sometimes conflicting objectives: Perform as well as possible on the training data, and generalize as well as possible to new data ( usually, this means being as simple as possible, for some technical definition of " simple ", in accordance with Occam's Razor ).
In modern terms, this means that the time of descent is π √, where r is the radius of the circle which generates the cycloid and g is the gravity of Earth.
The relative simplicity of the hardware means that Crusoe consumes less power ( and therefore generates less heat ) than other x86-compatible microprocessors running at the same frequency.
If the tested number n is composite, the strong liars a coprime to n are contained in a proper subgroup of the group, which means that if we test all a from a set which generates, one of them must be a witness for the compositeness of n. Assuming the truth of the generalized Riemann hypothesis ( GRH ), it is known that the group is generated by its elements smaller than O (( log n )< sup > 2 </ sup >), which was already noted by Miller.
The holodeck also generates impressive recreations of humanoid and other forms of life by means of precisely-shaped force fields covered by holographic imagery, with the effect that they seem solid to the touch.
That means, practically, that a timeless and intrinsic value generates reasons for anyone.
Since the right ventricle generates far lower pressures than the left ventricle ( approximately 20 mmHg versus around 120 mmHg, respectively, in the healthy individual ) but nonetheless generates cardiac output exactly equal to the left ventricle, this means that a small increase in pulmonary vascular resistance causes a large increase in amount of work the right ventricle must perform.
Meanwhile a son, Yaldabaoth, born to her from her contact with the waters, having in him a certain breath of the incorruptible light left him from his mother, by means of which he works, generates from the waters a son without any mother.
With some operating systems, the Alt key generates characters by means of their individual codes.
If ord < sub > n </ sub > a is actually equal to φ ( n ) and therefore as large as possible, then a is called a primitive root modulo n. This means that the group U ( n ) is cyclic and the residue class of a generates it.
Parallel parsing means that the reader generates multiple interpretations of the sentence and stores them until disambiguating information is given, at which point only the correct interpretation is maintained.
# The subcollection B generates the topology T. This means that T is the smallest topology containing B: any topology U on X containing B must also contain T.
Real process generates the production output from input, and it can be described by means of the production function.
To say that a grammar generates a sentence means that the grammar " assigns a structural description " to the sentence.
This means that, with enough replicates, the algorithm generates a sample from the desired distribution.
This means that even if an attacker has access to an oracle which possesses the secret key and generates MACs for messages of the attacker's choosing, the attacker cannot guess the MAC for other messages ( which were not used to query the oracle ) without performing infeasible amounts of computation.
The system generates a graphic image of the ball path and playing area, which means that information can be provided to judges, television viewers or coaching staff in near real time.
Weak keys usually represent a very small fraction of the overall keyspace, which usually means that, if one generates a random key to encrypt a message, weak keys are very unlikely to give rise to a security problem.
At the same time, privatization generates a means for profit for the capitalist class ; after a transaction they can then sell or rent to the public what used to be commonly owned.
This means that if a data point has either a categorical or multinomial distribution, and the prior distribution of the data point's parameter ( the vector of probabilities that generates the data point ) is distributed as a Dirichlet, then the posterior distribution of the parameter is also a Dirichlet.
Bhavanah, according to Sankara's interpretation, means " One who generates the fruits of Karmas of all Jivas ( souls ) for them to enjoy.
Offline generation of executable tests means that a model-based testing tool generates test cases as computer-readable assets that can be later run automatically ; for example, a collection of Python classes that embodies the generated testing logic.

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