Despite the absence of conditional jumps, the Z3 was a Turing complete computer ( ignoring the fact that no physical computer can be truly Turing complete because of limited storage size ).

It follows immediately from the fact that satisfies the guiding equation that also the configuration satisfies a guiding equation identical to the one presented in the formulation of the theory, with the universal wave function replaced with the conditional wave function.

Also, the fact that is random with probability density given by the square modulus of implies that the conditional probability density of given is given by the square modulus of the ( normalized ) conditional wave function ( in the terminology of Dürr et al.

this fact is called the fundamental conditional probability formula ).

This is to be contrasted with an indicative conditional, which indicates what is ( in fact ) the case if its antecedent is ( in fact ) true — for example, " if you drink this, it will make you well ".

The Markov property states that the conditional probability distribution for the system at the next step ( and in fact at all future steps ) depends only on the current state of the system, and not additionally on the state of the system at previous steps.

This follows from the fact that a conditional with a contradictory antecedent that does not share any propositional or predicate letters with the consequent cannot be true ( or derivable ).

In fact, the CR may be any new response to the previously neutral CS that can be clearly linked to experience with the conditional relationship of CS and US.

In fact, Marx argues that the whole purpose of production in this situation becomes the growth of capital, i. e. that production of output becomes conditional on capital accumulation.

Thus, a mortgage was on its face an absolute conveyance of a fee simple estate, but was in fact conditional, and would be of no effect if certain conditions were met.

In fact, the concept of conditional probability itself is actually defined in terms of conditional expectation.

In fact, this is a sufficient condition to define both conditional expectation and conditional probability.

In the definition of conditional expectation that we provided above, the fact that Y is a real random variable is irrelevant: Let U be a measurable space, that is, a set equipped with a σ-algebra of subsets.

This is to be contrasted with an indicative conditional, which indicates what is ( in fact ) the case if its antecedent is ( in fact ) true ( which it may or may not be ).

Given a counterfactual conditional, e. g., ' If there had been a circle on the blackboard then there would have been a triangle ', and the subsequent information ' in fact there was no triangle ', participants make the modus tollens inference ' there was no circle ' more often than they do from an indicative conditional ( Byrne and Tasso, 1999 ).

All these effects are a consequence of the fact that light propagates as a wave.

Again, though, other physicists believe that tunneling experiments in which particles appear to spend anomalously short times inside the barrier are in fact fully compatible with relativity, although there is disagreement about whether the explanation involves reshaping of the wave packet or other effects.

The solution of the Schrödinger equation ( wave equations ) for the hydrogen atom uses the fact that the Coulomb potential produced by the nucleus is isotropic ( it is radially symmetric in space and only depends on the distance to the nucleus ).

The latter became as famous as the best-known fourierist communes ( Brook Farm in Massachusetts & the North American Phalanx in New Jersey ) — in fact, Modern Times became downright notorious ( for “ Free Love ”) & finally foundered under a wave of scandalous publicity.

The main reason for his rejection stemmed from the fact that both men could apparently only envision light to be a longitudinal wave, like sound and other mechanical waves in fluids.

In fact, in quantum mechanics, particles themselves are fields, as described theoretically by the wave function.

The typical convention of using the cosine phase instead of the sine phase when describing a wave is based on the fact that the cosine is the real part of the complex exponential in the wave

In fact, the modern explanation of the uncertainty principle, extending the Copenhagen interpretation first put forward by Bohr and Heisenberg, depends even more centrally on the wave nature of a particle: Just as it is nonsensical to discuss the precise location of a wave on a string, particles do not have perfectly precise positions ; likewise, just as it is nonsensical to discuss the wavelength of a " pulse " wave traveling down a string, particles do not have perfectly precise momenta ( which corresponds to the inverse of wavelength ).

He completed Maxwell's set of equations in his later 1865 paper A Dynamical Theory of the Electromagnetic Field and demonstrated the fact that light is an electromagnetic wave.

The imaginary component in that instance however has not been introduced for the purpose of mathematical expediency but is in fact an inherent part of the “ wave ”.

The key to TDR ’ s success is its ability to accurately determine the permittivity ( dielectric constant ) of a material from wave propagation, and the fact that there is a strong relationship between the permittivity of a material and its water content, as demonstrated in the pioneering works of Hoekstra and Delaney ( 1974 ) and Topp et al.

The lateral intensity distribution on the screen has in fact the shape of a squared zeroth Bessel function of the first kind when close to the optical axis and using a plane wave source ( point source at infinity ):

One disadvantage of AC, the fact that the arc must be re-ignited after every zero crossing, has been addressed with the invention of special power units that produce a square wave pattern instead of the normal sine wave, making rapid zero crossings possible and minimizing the effects of the problem.

" Carrier Sense " describes the fact that a transmitter uses feedback from a receiver that detects a carrier wave before trying to send.

In fact, as far as prediction goes, the quantum development is at least as predictable as the classical motion, but the key is that it describes wave functions that cannot be easily expressed in ordinary language.

" The fundamental idea of 1924 thesis was the following: The fact that, following Einstein's introduction of photons in light waves, one knew that light contains particles which are concentrations of energy incorporated into the wave, suggests that all particles, like the electron, must be transported by a wave into which it is incorporated ... My essential idea was to extend to all particles the coexistence of waves and particles discovered by Einstein in 1905 in the case of light and photons.

In fact, the wave aspect of matter was formalized by a wavefunction defined by the Schrödinger equation, which is a pure mathematical entity having a probabilistic interpretation, without the support of real physical elements.

The fact that there can not be any limit points of the set except in closed intervals follows from the argument used in Lemma 1, namely, that near any tangent point in the C-plane the curves C and Af are analytic, and therefore the difference between them must be a monotone function in some neighborhood on either side of the tangent point.

Closely related to this function is the fact that the religious system provides a body of ultimate ends for the society, which are compatible with the supreme eternal ends.

We are abstracting from the fact of strikes here, but it should be obvious that the extent to which the public-limit price is raised by a given increase in the basic wage rate is also a function of the show of resistance put up by the industry.

For a statement of costs per kilowatt-hour would ignore the fact that many of these costs are not a function of kilowatt-hour output ( or consumption ) of energy.

In 1870, Eduard Heine showed that a continuous function defined on a closed and bounded interval was in fact uniformly continuous.

Observe that the characteristic function is not differentiable at the origin: this corresponds to the fact that the Cauchy distribution does not have an expected value.

The fact that the Carnot function could be the temperature, measured from zero, was suggested by Joule in a letter to Kelvin, and this allowed Kelvin to establish his absolute temperature scale.

a fact that cannot be seen directly from the definition of elementary function but can be proven using the Risch algorithm.

There is in fact no complex number z for which, and hence the reciprocal gamma function is an entire function, with zeros at z = 0, − 1, − 2 ,.... We see that the gamma function has a local minimum at where it attains the value.

This is also because an important result in complex analysis is that every holomorphic function is complex analytic, a fact that does not follow directly from the definitions.

In fact, f coincides with its Taylor series at a in any disk centered at that point and lying within the domain of the function.

( The trigonometric functions are in fact closely related to and can be defined via the exponential function using Euler's formula ).

So the logarithm function is in fact a group isomorphism from the group ( R < sup >+</ sup >,< big >×</ big >) to the group ( R ,< big >+</ big >).

) In fact, if this method is used, Newton inversion of the natural logarithm may conversely be used to calculate the exponential function efficiently.

The utility of artificial neural network models lies in the fact that they can be used to infer a function from observations.

In short, it is essential that a language is shareable, but this does not imply that for a language to function that it is in fact already shared.

In fact, it is difficult to devise a computable function that is not primitive recursive, although some are known ( see the section on Limitations below ).

This may be represented more starkly by the fact that, as of the proposed missionary goals of 2009, missionaries as a function of total church membership represent less than % 0. 008.

So the syntactic category for an intransitive verb is a complex formula representing the fact that the verb acts as a function word requiring an NP as an input and produces a sentence level structure as an output.

The French prefix sur means over or above and relates to the fact that the image of the domain of a surjective function completely covers the function's codomain.

The success of such a model is largely due to the mathematical fact that any function ( such as the position of a planet ) can be decomposed into a set of circular functions ( the Fourier modes ).

Web banners function the same way as traditional advertisements are intended to function: notifying consumers of the product or service and presenting reasons why the consumer should choose the product in question, a fact first documented on HotWired in 1996 by researchers Rex Briggs and Nigel Hollis.