Church subsequently modified his methods to include use of Herbrand – Gödel recursion and then proved ( 1936 ) that the Entscheidungsproblem is unsolvable: There is no generalized " effective calculation " ( method, algorithm ) that can determine whether or not a formula in either the recursive-or λ-calculus is " valid " ( more precisely: no method to show that a well formed formula has a " normal form ").

This generalized Euclidean algorithm can be put to many of the same uses as Euclid's original algorithm in the ring of integers: in any Euclidean domain, one can apply the Euclidean algorithm to compute the greatest common divisor of any two elements.

The original algorithm was described only for natural numbers and geometric lengths ( real numbers ), but the algorithm was generalized in the 19th century to other types of numbers, such as Gaussian integers and polynomials in one variable.

The Euclidean algorithm has been generalized further to other mathematical structures, such as knots and multivariate polynomials.

generalized the algorithm to digital waveguide synthesis, which could also be used to model acoustic waves in tubes and on drum membranes.

This generalized version of the game is NP-complete ; it is unlikely that any algorithm more efficient than a brute-force search exists that can find solutions for arbitrary generalized FreeCell configurations.

replaced this with a more efficient idea that later generalized as the " subgroup algorithm " ( in which form it works just as well for permutations and rotations ).

The Rete algorithm provides a generalized logical description of an implementation of functionality responsible for matching data tuples (" facts ") against productions (" rules ") in a pattern-matching production system ( a category of rule engine ).

Its original version, due to Gary L. Miller, is deterministic, but the determinism relies on the unproven generalized Riemann hypothesis ; Michael O. Rabin modified it to obtain an unconditional probabilistic algorithm.

One drawback is that, like Freenet, DHTs only directly support exact-match search, rather than keyword search, although Freenet's routing algorithm can be generalized to any key type where a closeness operation can be defined.

Bruun's algorithm is a fast Fourier transform ( FFT ) algorithm based on an unusual recursive polynomial-factorization approach, proposed for powers of two by G. Bruun in 1978 and generalized to arbitrary even composite sizes by H. Murakami in 1996.

The Bruun factorization, and thus the Bruun FFT algorithm, was generalized to handle arbitrary even composite lengths, i. e. dividing the polynomial degree by an arbitrary radix ( factor ), as follows.

Lloyd's Method I algorithm, originally described in 1957, can be generalized in a straighforward way for application to vector data.

The generalized Euclidean algorithm identifies the greatest common right or left divisor of two Hurwitz quaternions, where the " size " of the remainder is measured by the norm.

While Peterson's original formulation worked with only two processes, the algorithm can be generalized for more than two.

A generalized Feistel algorithm can be used to create strong permutations on small domains of size not a power of two ( see Format-Preserving Encryption ).

This is further generalized by DNA sequence alignment algorithms such as the Smith – Waterman algorithm, which make an operation's cost depend on where it is applied.

* 1996-Bruun's algorithm generalized to arbitrary even composite sizes by H. Murakami

In 1992, Deutsch and Jozsa produced a deterministic algorithm which was generalized to a function which takes bits for its input.

However, this theory needs to be generalized in ( 2 + 1 ) or ( 3 + 1 ) dimensions although, in principle, the field equations are amenable to such generalization as shown with the inclusion of a one-graviton process and yielding the correct Newtonian limit in d dimensions if a dilaton is included.

Contrary to a popular legend, de Broglie actually gave the correct rebuttal that the particular technique could not be generalized for Pauli's purpose, although the audience might have been lost in the technical details and de Broglie's mild mannerism left the impression that Pauli's objection was valid.

Color balance changes the overall mixture of colors in an image and is used for color correction ; generalized versions of color balance are used to get colors other than neutrals to also appear correct or pleasing.

Although the Af calculation is obvious by analogy with that for gravitational field and osmotic pressure, it is interesting to confirm it by a method which can be generalized to include related effects.

The meaning was eventually further generalized in its modern English usage to apply to any outrageous act or exhibition of pride or disregard for basic moral laws.

The Western suffix-e is from the Classical singular and the Eastern suffix-its is from the Classical plural ; both have been generalized for singular and plural in the dialects that use them.

Cognitive behavioral therapy ( CBT ) has been found to be effective treatment for panic disorder, social anxiety disorder, generalized anxiety disorder, and obsessive-compulsive disorder.

Since the early 1990s it was generalized in systemics for the investigation of functional human-like intelligence models, such as personoids, and, in parallel, developed as the SOAR environment.

This generated a flurry of interest in the topic, during which Maxwell's classmate Edward John Routh generalized Maxwell's results for the general class of linear systems.

Since the 1990s the term has been used ( interchangeably with " the Copernicus method ") for J. Richard Gott's Bayesian-inference-based prediction of duration of ongoing events, a generalized version of the Doomsday argument.

Not surprisingly, it is impractical for generalized correctness, which probably cannot even be defined, much less proven.

If this were generalized to the US population as a whole, it would make deism the fastest-growing religious classification in the US for that period, with the reported total of 49, 000 self-identified adherents representing about 0. 02 % of the US population at the time.

Most libraries create a separate fiction section to allow shelving in a more generalized fashion than Dewey provides for, or to avoid the space that would be taken up in the 800s, or simply to allow readers to find preferred authors by alphabetical order of surname.

It can also be generalized to explain variables across the economy, for example, total output ( estimated as real GDP ) and the general price level, as studied in macroeconomics.

η is the symbol for the linear predictor of a generalized linear model, and can also be used to denote the median of a population.

This result can sometimes substitute for the still-unproved generalized Riemann hypothesis.

Some genes that code for protein sub units of voltage-gated and ligand-gated ion channels have been associated with forms of generalized epilepsy and infantile seizure syndromes.

Interestingly, these patients are often first diagnosed when they have their first generalized tonic-clonic seizure later in life, when they experience sleep deprivation ( e. g., freshman year in college after staying up late to study for exams ).

For waves traveling through three dimensions, such as light waves, sound waves, and matter waves, the formulas for phase and group velocity are generalized in a straightforward way:

In particular, for, the generalized mean inequality implies the Pythagorean means inequality as well as the inequality of arithmetic and geometric means.

Some subject areas in the classification were regarded as inappropriately arranged and there was considerable pressure for more detail and for adaptation of the classification to make it more relevant for the evaluation of medical care, by classifying conditions to the chapters concerned with the part of the body affected rather than to those dealing with the underlying generalized disease.

A distinction, albeit not universally accepted, of sampling bias is that it undermines the external validity of a test ( the ability of its results to be generalized to the rest of the population ), while selection bias mainly addresses internal validity for differences or similarities found in the sample at hand.

Mies ' architecture was guided by principles at a high level of abstraction, and his own generalized descriptions of those principles intentionally leave much room for interpretation.

In 1991, when liquid crystal displays were already well established, Pierre-Gilles de Gennes received the Nobel Prize in physics " for discovering that methods developed for studying order phenomena in simple systems can be generalized to more complex forms of matter, in particular to liquid crystals and polymers ".