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More formally, the Liskov substitution principle ( LSP ) is a particular definition of a subtyping relation, called ( strong ) behavioral subtyping, that was initially introduced by Barbara Liskov in a 1987 conference keynote address entitled Data abstraction and hierarchy.
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More and formally
More formally, it is the theoretical temperature at which entropy reaches its minimum value.
More formally, the complexity of a string is the length of the shortest possible description of the string in some fixed universal description language ( the sensitivity of complexity relative to the choice of description language is discussed below ).
More formally, a block cipher is specified by an encryption function
More formally a k-combination of a set S is a subset of k distinct elements of S. If the set has n elements the number of k-combinations is equal to the binomial coefficient
More formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets ( sets that have the same cardinality as subsets of the natural numbers, including rational numbers but not real numbers ).
More formally design has been defined as follows.
More formally, it is " the study of mathematical models of conflict and cooperation between intelligent rational decision-makers.
More formally, such coordinates can be obtained from three-dimensional coordinates using the artifice of a map projection.
More formally, a " representation " means a homomorphism from the group to the automorphism group of an object.
More formally, case has been defined as " a system of marking dependent nouns for the type of relationship they bear to their heads.
More formally, if a, b, c, and d are all integers, then the fraction < sup > a </ sup >⁄< sub > b </ sub > is irreducible if and only if there is no other equal fraction < sup > c </ sup >⁄< sub > d </ sub > such that | c | < | a | or | d | < | b |, where | a | means the absolute value of a.
More formally, the Klein bottle is the quotient space described as the square × with sides identified by the relations for and for:
More formally, a lexicon is a language's inventory of lexemes.
More formally, the environment is modeled as a Markov decision process ( MDP ) with states and actions with the following probability distributions: the instantaneous cost distribution, the observation distribution and the transition, while a policy is defined as conditional distribution over actions given the observations.
( More work is required to derive this result formally.
More formally, statistical theory defines a statistic as a function of a sample where the function itself is independent of the sample's distribution ; that is, the function can be stated before realization of the data.
More formally, # P is the class of function problems of the form " compute ƒ ( x )," where ƒ is the number of accepting paths of a nondeterministic Turing machine running in polynomial time.
More formally, the output must satisfy two conditions:
More formally, we can state the Transfinite Recursion Theorem as follows.
More formally, ubiquitous computing is defined as " machines that fit the human environment instead of forcing humans to enter theirs.
More formally, complex systems often exhibit hysteresis.
More formally, two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry, i. e., a combination of translations, rotations and reflections.
More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints.
More formally, ( X, Σ, μ ) is complete if and only if
More formally, we can think of a truth condition as what makes for the truth of a sentence in an inductive definition of truth ( for details, see the semantic theory of truth ).
More and substitution
More rigorously, metonymy and synecdoche may be considered as sub-species of metaphor, intending metaphor as a type of conceptual substitution ( as Quintilian does in Institutio oratoria Book VIII ).
More common methods of password cracking, such as dictionary attacks, pattern checking, word list substitution, etc., attempt to reduce the number of trials required and will usually be attempted before brute force.
More complicated algorithms include the Luhn algorithm ( 1954 ), which captures 98 % of single digit transposition errors ( it does not detect 90 ↔ 09 ), while more sophisticated is the Verhoeff algorithm ( 1969 ), which catches all single digit substitution and transposition errors, and many ( but not all ) more complex errors.
More complex algorithms can be formed by mixing substitution and transposition in a product cipher ; modern block ciphers such as DES iterate through several stages of substitution and transposition.
More specifically, if Christ did not make a one-to-one substitution, but a general substitution, the issue does not arise.
More and principle
More recently, the principle has been generalized to the relativistic concept that humans are not privileged observers of the universe.
More recently the likelihood principle as a general principle of inference has been championed by A. W. F. Edwards.
More generally, non-standard analysis is any form of mathematics that relies on non-standard models and the transfer principle.
More than any other linguist, Benjamin Lee Whorf has become associated with what he himself called " the principle of linguistic relativity ".
More advanced designs use baffles and expansion chambers to slow down the escaping gases ; this is the basic principle behind a linear compensator.
More recently, low-cost current sensors based on the principle of a Rogowski coil have been developed.
More modern voice-mail systems work on the same principle, but some of the components may be shared with other systems, such as email systems.
More specifically, subsection ( a ) sets the basic principle that the YCJA attempts to address underlying behaviour, such as pre-existing conditions or circumstances that would lead to an offending behaviour.
More symbolically, an accounting model expresses some principle of conservation in the form
More recent developments of the basic oscillating cam principle have been used in the Nissan VVEL and the Toyota Valvematic.
More specifically, one can agree in part or agree in principle.
Both Henry More and Ralph Cudworth ( the Younger, 1617 – 1688 ), through their reconciliation of Platonic idealism with Christian doctrines of deific generation, came to see the divine lifeforce as the informing principle in the world.
More specifically, due to the Heisenberg uncertainty principle, an electron in a crystal cannot have both an exactly-defined k and an exact position in the crystal.
More formally it is a principle that is used to control certain forcing arguments.
More recently, the principle has been used in a modified form ( see Uti possidetis juris ) to establish the frontiers of newly independent states following decolonization, by ensuring that the frontiers followed the original boundaries of the old colonial territories from which they emerged.
More modern electronic ignition systems operate on exactly the same principle, but some rely on charging the capacitor to around 400 volts rather than charging the inductance of the coil.
More generally and accurately, the pseudocounts should be set in proportion to the prior estimate of their probabilities ; equal only if there is no prior reason to prefer one over another — see the principle of indifference.
More generally, there doesn't exist any " one organizational principle " which is always the best for every situation, and at all times.
More moderate fiscal conservatives argue that " free market economics " is the most efficient way to promote economic growth: they support it not based on some moral principle, but pragmatically, because they hold that it just " works.
More precisely, provided that no phenomenon violates the principle of relativity of motion, there is no means to measure the velocity of an inertial observer with regard to a possible medium of propagation of quantum waves.
3.597 seconds.