Compact sets in Banach spaces may also carry natural measures: the Hilbert cube, for instance, carries the product Lebesgue measure.
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 with finitely-many nonzero elements, where K is the desired field of scalars).
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AARON cannot learn new styles or imagery on its own, each new capability must be hand-coded by Harold Cohen, but it is capable of producing a practically infinite supply of distinct images in its own style.
On the other hand, the sinusoid is certainly not an algebraic curve, having an infinite number of monotone arcs.
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.
Cahen's constant, an infinite series of unit fractions, with alternating signs, derived from Sylvester's sequence
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.
1997, with Fons Trompenaars, Mastering the infinite game: how East Asian values are transforming business practices.
The tetralogy mentioned above has been published in English translation by Keith Waldrop as : Reversal (1973); The Notion of Obstacle (1985), and Objects Contain the Infinite (1995).
Limit comparison test, a method of testing for the convergence of an infinite series.
Death Is Infinite is the second EP by the American metalcore band Himsa and is the first recording with lead singer John Pettibone.
Other times major action takes place in dreams, allowing the filmmaker to explore infinite possibilities, as Michel Gondry demonstrates in The Science of Sleep.
For example, while an analog speedometer can theoretically display an infinite number of speeds, digital speedometers generally display speeds in whole numbers.
with Joel Feldman, Horst Knörrer: Riemann Surfaces of Infinite Genus, AMS (American Mathematical Society) 2003
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.
However, models developed according to the general HJM framework are often non-Markovian and can even have infinite dimensions.
With Joel Feldman, Eugene Trubowitz: Riemann Surfaces of Infinite Genus, AMS (American Mathematical Society) 2003
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).
Personalistic idealists Borden Parker Bowne and Edgar S. Brightman and realistic personal theist Saint Thomas Aquinas address a core issue, namely that of dependence upon an infinite personal God.
Infinite Comics is an imprint of comic books published by Marvel Comics, featuring original, made-for-digital stories about the company's superhero characters, including Spider-Man, Wolverine, the Guardians of the Galaxy, the Silver Surfer, the X-Men and the Avengers.
Infinite Love Songs is the debut album by German musician Maximilian Hecker.
Noam Elkies was first to find an infinite series of solutions to Euler's equation with exactly one variable equal to zero, thus disproving Euler's sum of powers conjecture for the fourth power.
His play, Speak, Oppenheimer, written for Montreal's Infinite Theatre, involves three physicists, including J. Robert Oppenheimer.
He saw belief in God as superstition, in the manner of the atheists of the Enlightenment, but he also accounted for this belief in a manner that resembles Ludwig Feuerbach's theory of religious alienation: because human beings are powerless, they project omnipotence onto an imaginary God; because they are poor and suffering, they project infinite luxury and happiness onto an imaginary heaven.
In the main Garbhagriha, the idols of the Tirthankaras are flanked by mirrors on both sides, thus their images are seen infinite times.
Perttu Kivilaakso (Apocalyptica) plays cello on the tracks 'The Evil That Men Do' and 'Infinite Dreams'.
It can be written as an infinite series involving the one dimensional probability densities and Hermite polynomials of x and y (see the link to Slepian).
Wayne Proudfoot traces the roots of the notion of "religious experience" further back to the German theologian Friedrich Schleiermacher (1768–1834), who argued that religion is based on a feeling of the infinite.
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.
The concept of normal matrices can be extended to normal operators on infinite dimensional Hilbert spaces and to normal elements in C*-algebras.
Parallels of Infinite Torture is the fourth studio album by American death metal band Disgorge.
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.
Nick & Norah's Infinite Playlist was made into a movie directed by Peter Sollett and starred Michael Cera and Kat Dennings as Nick and Norah.
Real numbers, the numbers that can be represented by infinite decimals
He is the co-discover of Kac-Moody algebra, a Lie algebra, usually infinite-dimensional, that can be defined through a generalized root system.
In August 2005 a notable new garden was constructed, the Garden of Infinite Compassion, designed by landscape designer Martin Mosko, Zen Buddhist monk and abbot of the Hakubai Temple in Boulder, Colorado.
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.
The song features references to John Candy, JonBenét Ramsey, where one of the verses said "Got JonBenet Ramsey in my '98 Camry", Richard Pryor, and Steve Stout, while Eminem's line referring to the band as "five more zany-actin' maniacs in action" harks back to his original underground album Infinite.
Swell has a number of projects including Slammin' The Infinite (w/Sabir Mateen, Matthew Heyner, Klaus Kugel), Fire Into Music (w/William Parker, Jemeel Moondoc, Hamid Drake), Unified Theory Of Sound (w/Cooper-Moore, Matt Lavelle) and his large ensemble Nation Of We (aka NOW Ensemble).
The soundtrack to 3rd Strike features three songs and announcer tracks by Canadian rapper Infinite.
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.
MOSCED, a model for estimating limiting activity coefficients at infinite dilution
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.
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The music video "When The Illusion Is What It Seems" from the album 'The Infinite Definitive' received a Silver award at the 2012 ADDY Awards.
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).
Joachim Lambek (1961) received 15 June 1961 How to Program an Infinite Abacus, Mathematical Bulletin, vol.
Weakly compact cardinal, an infinite cardinal number on which every binary relation has an equally large homogeneous subset
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Limit point compact, a set in which every infinite subset of X has a limit point
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Sequentially compact space, a set in which every infinite sequence has a convergent subsequence
Peter Lynds has put forward a cosmology model in which time is cyclic and the universe repeats exactly an infinite number of times.