X-Nico

unusual facts about Infinite-dimensional



'Hours...'

For the album's initial release, a number of copies featured a lenticular version of the cover, lending a three-dimensional effect to the image.

Additive model

The AM uses a one dimensional smoother to build a restricted class of nonparametric regression models.

Barsoum elements

For these locations of the mid nodes, the Jacobian becomes singular at the corner node thus making displacement derivatives infinite and stresses and strains become infinite as well.

Catalan's constant

Simon Plouffe gives an infinite collection of identities between the trigamma function, π2 and Catalan's constant; these are expressible as paths on a graph.

Catholic Medical Center

The orthopedic surgeons now have access to the new O-ARM Imaging System, a high definition CT scan that provides real-time three dimensional images during spine surgery.

Channeling

Mediumistic channeling, the esoteric process of receiving messages or inspiration from extra-dimensional beings or spirits, whereby one is a medium or channel for such an entity.

Charles Hampden-Turner

1997, with Fons Trompenaars, Mastering the infinite game: how East Asian values are transforming business practices.

Composite fermion

Classical vortices are relevant to the Berezenskii–Kosterlitz–Thouless transition in two-dimensional XY model.

Dennis Sullivan

Sullivan is one of the founders of the surgery method of classifying high-dimensional manifolds, along with Browder, Sergei Novikov and C. T. C. Wall.

Dimensional Fund Advisors

Dimensional hosts a forum where Eugene Fama and Kenneth French express their opinions on topics related to finance and current events.

Electronic instrument cluster

For example, while an analog speedometer can theoretically display an infinite number of speeds, digital speedometers generally display speeds in whole numbers.

Endre Szemerédi

Ajtai and Szemerédi proved the corners theorem, an important step toward higher dimensional generalizations of the Szemerédi theorem.

Erik Winfree

In 1998, Winfree in collaboration with Nadrian Seeman published the creation of two-dimensional lattices of DNA tiles using the "double crossover" motif.

Fourier optics

A "wide" wave moving forward (like an expanding ocean wave coming toward the shore) can be regarded as an infinite number of "plane wave modes", all of which could (when they collide with something in the way) scatter independently of one other.

Galactic Pinball

A distinguishing features of the Colony board is where the user shoots down various meteors to save the Colony from attack in a three dimensional perspective.

Gaussian isoperimetric inequality

In mathematics, the Gaussian isoperimetric inequality, proved by Boris Tsirelson and Vladimir Sudakov and independently by Christer Borell, states that among all sets of given Gaussian measure in the n-dimensional Euclidean space, half-spaces have the minimal Gaussian boundary measure.

Gymnastic formation

The performance of the NGOs, such as the SGI, is widely variable, such as, bi-dimensional wave, sky rocket, windmill, walking wall, walking pyramid, catapult, instantaneous stand-up pyramid, instantaneous stand-up tower, three-layers' plane tower, four-layers' tower, and rarely five-layers' tower.

Heath–Jarrow–Morton framework

However, models developed according to the general HJM framework are often non-Markovian and can even have infinite dimensions.

Horst Knörrer

With Joel Feldman, Eugene Trubowitz: Riemann Surfaces of Infinite Genus, AMS (American Mathematical Society) 2003

Hypercomputation

In 1994, Hava Siegelmann proved that her new (1991) computational model, the Artificial Recurrent Neural Network (ARNN), could perform hypercomputation (using infinite precision real weights for the synapses).

Infinite-dimensional vector function

Moreover, for any set A, there exist infinite-dimensional vector spaces having the (Hamel) dimension of the cardinality of A (e.g., the space of functions A\rightarrow K with finitely-many nonzero elements, where K is the desired field of scalars).

Jonah David Mann

1989 he received together with Riccardo Giovanelli the Henry Draper Medal for the first three-dimensional view of some of the remarkable large-scale filamentary structures of our visible universe.

JPEG

Next, each 8×8 block of each component (Y, Cb, Cr) is converted to a frequency-domain representation, using a normalized, two-dimensional type-II discrete cosine transform (DCT), which was introduced by N. Ahmed, T. Natarajan and K. R. Rao in 1974; see Citation 1 in Discrete cosine transform.

Line drawing

Line art, a style of two-dimensional art featuring only two, unshaded, contrasting colors; or

Local class field theory

Higher dimensional class field theory was pioneered by A.N. Parshin in positive characteristic and K. Kato, I. Fesenko, Sh.

Melamine cyanurate

Melamine and cyanuric acid form a jigsaw puzzle-like two-dimensional hydrogen bonding network because of the complementarity of the two compounds, similar to DNA base pairing.

Michael W. Vannier

On July 19, 1983, M. Vannier (Mallinckrodt Institute of Radiology, St. Louis) and his co-workers J. Marsh (Cleft Palate and Craniofacial Deformities Institute, St. Louis Children's Hospital) and J. Warren (McDonnell Aircraft Company) published the first three-dimensional reconstruction of single CT slices of the human head.

Musée des Plans-Reliefs

The construction of models dates to 1668 when François-Michel le Tellier, Marquis de Louvois and minister of war to Louis XIV, began a collection of three-dimensional models of fortified cities for military purposes, known as 'plans-relief'.

Nick Wallace

His first published work was the short story Five Dimensional Thinking in the Big Finish Productions Bernice Summerfield short story collection, Life During Wartime (Big Finish Productions, 2003), edited by Paul Cornell.

Nintendo DS

Another modification device called Action Replay, manufactured by the company Datel, is a device which allows the user to input cheat codes that allows it to hack games, granting the player infinite "health", power-ups, access to any part of the game, etc.

Normal matrix

The concept of normal matrices can be extended to normal operators on infinite dimensional Hilbert spaces and to normal elements in C*-algebras.

Peter Lynds

Lynds in December 2006 put forward a new cosmology model in which time is cyclic and the universe repeats exactly an infinite number of times.

Philip Schram

He worked with Fleurette Morel, the daughter of race driver André Morel, on telling her father’s story through a multi-dimensional concept not seen previously in the market.

Pp-wave spacetime

A more general subclass consists of the axisymmetric pp-waves, which in general have a two dimensional Abelian Lie algebra of Killing vector fields.

Real field

Real numbers, the numbers that can be represented by infinite decimals

Robotics Toolbox for MATLAB

The Toolbox provides functions for manipulating and converting between datatypes such as: vectors;homogeneous transformations; roll-pitch-yaw and Euler angles and unit-quaternions which are necessary to represent 3-dimensional position and orientation.

Scalar-tensor theory

It uses a scalar field of infinite length scale (i.e. long-ranged), so, in the language of Yukawa's theory of nuclear physics, this scalar field is a massless field.

Self-adjoint operator

If V is finite dimensional with a given basis, this is equivalent to the condition that the matrix of A is Hermitian, i.e., equal to its conjugate transpose A*.

Self-assembled monolayer

Using this technique Chad Mirkin, Schatz and their co-workers were able to make complex two dimensional shapes, a representation of a shape created is shown to the right.

Stereo image

Stereogram, an image intended to give a 3-dimensional visual impression

Stereopticon

A stereopticon will not project or display stereoscopic/three-dimensional images.

Tomonaga

Luttinger liquid, also known as Tomonaga-Luttinger liquid, a theoretical model describing interacting fermions in a one-dimensional conductor

Transcendentals

Yet the proliferation of 20th Century post-modernist views dismissing the transcendentals as a serious area of philosophy did bring forth a number of influential philosophers such as G.K. Chesterton, Edith Stein, C.S. Lewis and Peter Kreeft, whose writings develop and re-propose truth, beauty and goodness as the universal aspirations of humanity, seeking an infinite good.

Two-dimensional nuclear magnetic resonance spectroscopy

The first two-dimensional experiment, COSY, was proposed by Jean Jeener, a professor at the Université Libre de Bruxelles, in 1971.

Unknown Component

Songs from the albums 'The Infinite Definitive' and 'Blood v. Electricity' have been featured on the nationally broadcast radio program Undercurrents and the song 'Set To Begin' off of the album 'From Anywhere But Here' was featured in the film The 4th Life which was distributed across the U.S. and Canada by Atopia, and was directed by Francois Miron.

Vitali covering lemma

The first result in this direction was given by David Preiss in 1979: there exists a Gaussian measure γ on an (infinite-dimensional) separable Hilbert space H so that the Vitali covering theorem fails for (H, Borel(H), γ).

Wang B-machine

Joachim Lambek (1961) received 15 June 1961 How to Program an Infinite Abacus, Mathematical Bulletin, vol.

Weakly compact

Weakly compact cardinal, an infinite cardinal number on which every binary relation has an equally large homogeneous subset

Limit point compact, a set in which every infinite subset of X has a limit point

Wind turbine aerodynamics

Buckingham π theorem can be applied to show that non-dimensional variable for power is given by the equation below.


see also

Initial value problem

More generally, the unknown function y can take values on infinite dimensional spaces, such as Banach spaces or spaces of distributions.

Kac–Moody algebra

In mathematics, a Kac–Moody algebra (named for Victor Kac and Robert Moody, who independently discovered them) is a Lie algebra, usually infinite-dimensional, that can be defined by generators and relations through a generalized Cartan matrix.

Kuiper's theorem

In mathematics, Kuiper's theorem (after Nicolaas Kuiper) is a result on the topology of operators on an infinite-dimensional, complex Hilbert space H.

Moore method

Professor David W. Cohen of Smith College implemented a modified Moore method for courses in Infinite-dimensional Linear Algebra and Real Analysis.

Robert Moody

He is the co-discover of Kac-Moody algebra, a Lie algebra, usually infinite-dimensional, that can be defined through a generalized root system.

Unit cube

Tychonoff cube, an infinite-dimensional analogue of the unit cube