Since the theorem was also discovered independently by E. T. Whittaker, by Vladimir Kotelnikov, and by others, it's also known as the Nyquist – Shannon – Kotelnikov, Whittaker – Shannon – Kotelnikov, Whittaker – Nyquist – Kotelnikov – Shannon, WKS, as well as the Cardinal Theorem of Interpolation Theory.

* 1984 Lennart Carleson for his papers: An interpolation problem for bounded analytic functions, American Journal of Mathematics, volume 80 ( 1958 ), pp. 921-930 ; Interpolation by bounded analytic functions and the Corona problem, Annals of Mathematics ( 2 ), volume 76 ( 1962 ), pp. 547-559 ; and On convergence and growth of partial sums of Fourier series, Acta Mathematica volume 116 ( 1966 ), pp. 135-157.

A fragment of the ' Stone Classics ' ( 熹平石經 ); these stone-carved Five Classics installed during Emperor Ling of Han | Emperor Ling's reign along the roadside of the Taixue | Imperial University ( right outside Luoyang ) were made at the instigation of Cai Yong ( 132 – 192 CE ), who feared the Classics housed in the imperial library were being Interpolation ( manuscripts ) | interpolated by University Academicians.

* 1942, Extrapolation, Interpolation and Smoothing of Stationary Time Series.

Interpolation search ( sometimes referred to as extrapolation search ) is an algorithm for searching for a given key value in an indexed array that has been ordered by the values of the key.

However, Dynamic Interpolation Search is possible in o ( log log n ) time using a novel data structure.

Interpolation of simple look-up tables of trigonometric functions is still used in computer graphics, where only modest accuracy may be required and speed is often paramount.

* August 25 – September 5 – Darmstädter Ferienkurse held in Darmstadt, with lectures by Włodzimierz Kotoński, György Ligeti, Andrzej Markowski, Yoritsune Matsudaira, Werner Meyer-Eppler, Luigi Nono, Henri Pousseur, Karlheinz Stockhausen, and Bo Wallner, and world premieres of Claude Baillif's Mouvements pour deux, Sylvano Bussotti's Piano Pieces for David Tudor, Cornelius Cardew's Two Books of Study for Pianists and Piano Piece 1959, Niccolo Castiglioni's Cangiati per pianoforte, Roman Haubenstock-Ramati's Interpolation: Mobile pour flûte, Mauricio Kagel's Transición II, Angelo Paccagnini's Canti brevi: secondo libro, and Stockhausen's Zyklus.

Interpolation with polynomials evaluated at equally spaced points in b yields the Newton – Cotes formulas, of which the rectangle rule and the trapezoidal rule are examples.

Interpolation may then put chroma values there which are incompatible with the luma value there, and further post-processing of that Y ' CbCr into R ' G ' B ' for that pixel is what ultimately produces false luminance upon display.

* Interpolation, while not usually advertised, is present in most recent CD players.

Interpolation is a way to correct errors that may be present on a compact disc, perhaps due to dust, scratches or dirt.

Interpolation effects, digital compositing, and computer generated " virtual " scenery were used to improve the fluidity of the apparent camera motion.

* Gridpoint Statistical Interpolation, a type of data assimilation.

" Yellow Peril " is also the nickname of a book named Extrapolation, Interpolation and Smoothing of Stationary Time Series with Engineering Applications MIT Press.

* Stein, M. L. ( 1999 ), Statistical Interpolation of Spatial Data: Some Theory for Kriging, Springer, New York.

Figure 1: Interpolation with cubic splines between eight points.

* April-Leslie Comrie publishes an article " On the Construction of Tables by Interpolation ", describing the use of punched card equipment for interpolating tables of data, and becomes the first to use such equipment for scientific calculations, using Fourier synthesis to compute the principal terms in the motion of the Moon for 1935 – 2000.

* Interpolation of charge and current source terms to the field mesh.

* Interpolation of the fields from the mesh to the particle locations.

* Paul Bourke, Interpolation methods, 1999.

In April 1928 his article On the Construction of Tables by Interpolation described the use of punched card equipment for interpolating tables of data, comparing this with the less efficient and more error-prone methods using mechanical devices such as the pinwheel calculators under the Brunsviga brand name.

Two of Kripke's earlier works, A Completeness Theorem in Modal Logic and Semantical Considerations on Modal Logic, the former written while he was still a teenager, were on the subject of modal logic.

" A Completeness Theorem in Modal Logic ", Journal of Symbolic Logic 24 ( 1 ): 1 – 14.

* Edgar F. Codd-Luminary in Computational Logic and Relational Theory ( Codds Theorem )

These include Studies in Logic, Grammar and Rhetoric, Intelligent Computer Mathematics, Interactive Theorem Proving, Journal of Automated Reasoning and the Journal of Formalized Reasoning.

* Stanford Encyclopedia of Philosophy: " Frege's Logic, Theorem, and Foundations for Arithmetic " -- by Edward Zalta.

1990b, Review of V. A. Uspensky, Gödel's Incompleteness Theorem, Journal of Symbolic Logic 55: 889-891.

These three ground-breaking articles were " A Functional Calculus of First Order Based on Strict Implication ", Journal of Symbolic Logic ( JSL, 1946 ), " The Deduction Theorem in a Functional Calculus of First Order Based on Strict Implication " ( JSL, 1946 ), " The Identity of Individuals in a Strict Functional Calculus of Second Order ", ( JSL, 1947 ).

* Rewrite-Based Equational Theorem Proving with Selection and Simplification, Leo Bachmair and Harald Ganzinger, Journal of Logic and Computation 3 ( 4 ), 1994.

An utter refutation of the ' Fundamental Theorem of the HapMap ' European Journal of Human Genetics 14, 426 – 437

* Kahneman, D., Knetsch, J. L., Thaler, R. H. " Experimental Tests of the Endowment Effect and the Coase Theorem " ( 1990 ) Journal of Political Economy, 98 ( 6 ), 1325-1348.

* Lovell, M., 2008, A Simple Proof of the FWL ( Frisch, Waugh, Lovell ) Theorem, Journal of Economic Education.

" An Extension of a Theorem of Gaifman-Hales-Solovay ," Fundamenta Mathematicae, Vol.

* Anshel, Iris Lee ; Anshel, Michael, " From the Post-Markov Theorem Through Decision Problems to Public-Key Cryptography ", The American Mathematical Monthly, Vol.

* Brown, R., Higgins, P. J. and Sivera, R .. 2011, EMS Tracts in Mathematics Vol. 15 ( 2011 ) Nonabelian Algebraic Topology: filtered spaces, crossed complexes, cubical homotopy groupoids ; ( The first of three Parts discusses the applications of the 1-and 2-dimensional versions of the Seifert-van Kampen Theorem.

* Murray Eisenberg, Robert Guy, A Proof of the Hairy Ball Theorem, The American Mathematical Monthly, Vol.

# Mark Fey, " May ’ s Theorem with an Infinite Population ", Social Choice and Welfare, 2004, Vol.

* L. Le Cam ( 1986 ) The Central Limit Theorem Around 1935, Statistical Science, Vol.

" The Goldstone Theorem in the Jahn-Teller Effect ", Proceedings of the Physical Society of London, Vol.

The reader will find it helpful to think of the special case when the primes are of degree 1, and even more particularly, to think of the proof of Theorem 10, a special case of this theorem.

Theorem 12.

Since Af are distinct prime polynomials, the polynomials Af are relatively prime ( Theorem 8, Chapter 4 ).

In the notation of the proof of Theorem 12, let us take a look at the special case in which the minimal polynomial for T is a product of first-degree polynomials, i.e., the case in which each Af is of the form Af.

By Theorem 10, D is a diagonalizable operator which we shall call the diagonalizable part of T.

Theorem 13.

If T is a linear operator on an arbitrary vector space and if there is a monic polynomial P such that Af, then parts ( A ) and ( B ) of Theorem 12 are valid for T with the proof which we gave.

If Af is the null space of Af, then Theorem 12 says that Af.

Theorem: K is not a computable function.

He is most famous for proving Fermat's Last Theorem.

Wiles discovered Fermat's Last Theorem on his way home from school when he was 10 years old.

* Lawrence C. Paulson of the University of Cambridge, work on higher-order logic system, co-developer of the Isabelle Theorem Prover

* Theorem If X is a normed space, then X ′ is a Banach space.

* Theorem Let X be a normed space.

* Theorem Every reflexive normed space is a Banach space.

many small primes p, and then reconstructing B < sub > n </ sub > via the Chinese Remainder Theorem.

George Boolos ( 1989 ) built on a formalized version of Berry's paradox to prove Gödel's Incompleteness Theorem in a new and much simpler way.

* Weisstein, Eric W. " Second Fundamental Theorem of Calculus.

: Theorem XXX: " The following classes of partial functions are coextensive, i. e. have the same members: ( a ) the partial recursive functions, ( b ) the computable functions.

: Turing's thesis: " Turing's thesis that every function which would naturally be regarded as computable is computable under his definition, i. e. by one of his machines, is equivalent to Church's thesis by Theorem XXX.