The classical definition of angular momentum as can be carried over to quantum mechanics, by reinterpreting r as the quantum position operator and p as the quantum momentum operator.

The term " concept " is traced back to 1554 – 60 ( Latin conceptum-" something conceived "), but what is today termed " the classical theory of concepts " is the theory of Aristotle on the definition of terms.

There is no official definition of ' cubewano ' or ' classical KBO '.

According to this definition, an object qualifies as a classical KBO if:

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

Unlike other schemes, this definition includes the objects with major semi-axis less than 39. 4 AU ( 2: 3 resonance ) – named Inner classical belt, or more than 48. 7 ( 1: 2 resonance ) – named Outer classical belt while reserving the term Main classical belt for the orbits between these two resonances.

In classical thought, a definition was taken to be a statement of the essence of a thing.

A nominal definition is the definition explaining what a word means, i. e. which says what the ' nominal essence ' is, and is definition in the classical sense as given above.

" Yet the definition according to the esthesic level does not allow that the sounds of classical music are complex, are noises, rather they are regular, periodic, even, musical sounds.

Usually, they have involved substantive attempts to provide a definition of knowledge different from the classical one, either by recasting knowledge as justified true belief with some additional fourth condition, or as something else altogether.

This definition holds for most " classical " hormones, but there are also paracrine mechanisms ( chemical communication between cells within a tissue or organ ), autocrine signals ( a chemical that acts on the same cell ), and intracrine signals ( a chemical that acts within the same cell ).

Historically, the classical thermodynamics definition developed first, and it has more recently been extended in the area of non-equilibrium thermodynamics.

The frequentist interpretation is a philosophical approach to the definition and use of probabilities ; it is one of several, and, historically, the earliest to challenge the classical interpretation.

Hayek identified himself as a classical liberal but noted that in the United States it had become almost impossible to use " liberal " in its original definition, and the term " libertarian " has been used instead.

The classical definition of a sheaf begins with a topological space X.

Although this is not the technical definition of the Hamiltonian in classical mechanics, it is the form it most commonly takes.

According to the what economist Nicholas Barr describes as the " classical definition of income :" the 1938 Haig-Simons definition, " income may be defined as the ... sum of ( 1 ) the market value of rights exercised in consumption and ( 2 ) the change in the value of the store of property rights ..." Since the consumption potential of non-monetary goods, such as leisure, cannot be measured, monetary income may be thought of as a proxy for full income.

In Ricardo and other classical economists, this definition serves as a measure of " real cost ", " absolute value ", or a " measure of value " invariable under changes in distribution and technology.

The liberal arts education ( Latin: artes liberales ) is a type of education with those subjects or skills that in classical antiquity were considered essential for a free person, in other words, a citizen, to know in order to take an active part in civic life and public debate and most importantly, military service ( slaves and resident aliens were by definition excluded from the duties and responsibilities of citizenship ).

This definition corresponds to the classical definition using Cauchy sequences, except with a constructive twist: for a classical Cauchy sequence, it is required that, for any given distance, there exists ( in a classical sense ) a member in the sequence after which all members are closer together than that distance.

* Bertrand's paradox: a paradox in classical probability, solved by E. T.

In the classical interpretation, probability was defined in terms of the principle of indifference, based on the natural symmetry of a problem, so, e. g. the probabilities of dice games arise from the natural symmetric 6-sidedness of the cube.

This is related to the emergence of classical probability rules in quantum decoherence.

The proof of this statement uses the linearity of classical probability, and has exactly the same structure as the proof of the quantum no-cloning theorem.

The first attempt at mathematical rigour in the field of probability, championed by Pierre-Simon Laplace, is now known as the classical definition.

An important guide for making these choices is the correspondence principle, which states that the predictions of quantum mechanics reduce to those of classical mechanics when a system moves to higher energies or — equivalently — larger quantum numbers, i. e. whereas a single particle exhibits a degree of randomness, in systems incorporating millions of particles averaging takes over and, at the high energy limit, the statistical probability of random behaviour approaches zero.

Quantum interference involves adding together probability amplitudes, whereas classical " waves " infer that there is an adding together of intensities.

Since the probability amplitudes of the states are represented with complex numbers, the phase between any two states is a meaningful parameter, which is a key difference between quantum computing and probabilistic classical computing.

Thus, measuring a quantum state described by complex coefficients ( a, b ,..., h ) gives the classical probability distribution and we say that the quantum state " collapses " to a classical state as a result of making the measurement.

In the case of a classical computer, we sample from the probability distribution on the three-bit register to obtain one definite three-bit string, say 000.

In classical information theory, the Shannon entropy, is associated to a probability distribution ,, in the following way:

It is a classical result that the Shannon entropy achieves its maximum at, and only at, the uniform probability distribution

The variance of a probability distribution is analogous to the moment of inertia in classical mechanics of a corresponding mass distribution along a line, with respect to rotation about its center of mass.

The times of the paths near the classical reflection site of the mirror will be nearly the same, so as a result the probability amplitudes will point in nearly the same direction — thus, they will have a sizable sum.

He believed quantum theory offers a complete description of nature, albeit one that is simply ill suited for everyday experiences – which are better described by classical mechanics and probability.

Vector quantization is a classical quantization technique from signal processing which allows the modeling of probability density functions by the distribution of prototype vectors.

So if the wave function itself is reality ( rather than probability of classical coordinates ), quantum mechanics can be said to be deterministic.

) More generally, fuzzy logic is one of many different proposed extensions to classical logic, known as probabilistic logics, intended to deal with issues of uncertainty in classical logic, the inapplicability of probability theory in many domains, and the paradoxes of Dempster-Shafer theory.

As the energy increases, the probability density becomes concentrated at the classical " turning points ", where the state's energy coincides with the potential energy.

The theory is based on a consistency criterion that allows the history of a system to be described so that the probabilities for each history obey the additive rules of classical probability.

The density matrix is the quantum-mechanical analogue to a phase-space probability measure ( probability distribution of position and momentum ) in classical statistical mechanics.