* Young's inequality

and, by Young's inequality,

* Young's inequality

In mathematics, Young's inequality is either of two inequalities: one about the product of two numbers, and one about the convolution of two functions.

This form of Young's inequality is a special case of the inequality of weighted arithmetic and geometric means and can be used to prove Hölder's inequality.

Young's inequality follows by exponentiating.

An elementary case of Young's inequality is the inequality with exponent 2,

which also gives rise to the so-called Young's inequality with ε ( valid for every ε > 0 ), sometimes called the Peter – Paul inequality.

Young's inequality with exponent 2 is the special case p

Young's inequality with ε follows by applying Young's inequality with exponent 2 to

b < sup > q </ sup >/ q with q such that 1 / p + 1 / q = 1, and thus Young's inequality for conjugate Hölder exponents mentioned above is a special case.

In real analysis, the following result is also called Young's inequality:

An example application is that Young's inequality can be used to show that the heat semigroup is a contraction semigroup using the L < sup > 2 </ sup > norm.

# REDIRECT Young's inequality

These must have been for local calls strictly, as in May 1900 the `` only long distance telephone '' in town was transferred from C. B. Carleton's to Young's shoe store.

Flight day seven was to be Young's and Duke's third and final day on the lunar surface, for they would return to orbit to rejoin Ken Mattingly in the Command / Service Module following the day's moonwalk.

After the season, Young received an offer to play for the minor league Canton team, which started Young's professional career.

In 1921, Johnson broke Young's career record for strikeouts.

A second and more contemporary collaboration with Harris and Ronstadt, Trio II ( 1999 ), was released and its cover of Neil Young's " After the Gold Rush " won a Grammy Award for Best Country Collaboration with Vocals.

Young's investigations clearly demonstrated the desperate need for major financial reforms in Honduras, whose always precarious budgetary situation was considerably worsened by the renewal of revolutionary activities.

Young's recommendations for reducing the military budget, however, found little favor with the new López Gutiérrez administration, and the government's financial condition remained a major problem.

Ever since its rediscovery, the stone has been the focus of nationalist rivalries, including its transfer from French to British possession during the Napoleonic Wars, a long-running dispute over the relative value of Young's and Champollion's contributions to the decipherment, and since 2003, demands for the stone's return to Egypt.

Thomas Young's work is acknowledged in Champollion's 1822 Lettre à M. Dacier, but incompletely, according to British critics: for example, James Browne, a sub-editor on the Encyclopædia Britannica ( which had published Young's 1819 article ), contributed anonymously a series of review articles to the Edinburgh Review in 1823, praising Young's work highly and alleging that the " unscrupulous " Champollion plagiarised it.

The resulting Huygens – Fresnel principle was extremely successful at reproducing light's behavior and, subsequently supported by Thomas Young's discovery of double-slit interference, was the beginning of the end for the particle light camp.

This principle was first introduced in Young's study of light and, within some specific contexts ( for example, scattering of sound by sound ), is still a researched area in the study of sound.

Some of Young's conclusions appeared in the famous article " Egypt " he wrote for the 1818 edition of the Encyclopædia Britannica.

This sacred subject carved on early Christian tombs, where the sepulchral carvings have a deeply important formal symbolic purpose, a faithful wish for immortality, " with the victory of the cock and his supporting genius analogous to the hope of resurrection, the victory of the soul over death ", with further understanding as to that of the gallantry of cocks being taken in the context of a religious instilling vessel of " a girt one of the loins "( Young's Literal Translation ) that which is " stately in his stride " and " move with stately bearing " within the Book of Proverbs 30: 29-31.

By late 2002 however, the OA Board, faced with mounting deficits, announced that Young's future visions for the company were ' unsustainable ' and decided not to renew her contract after the end of 2003.

In State Board of Equalization v. Young's Market Co.,, the Supreme Court recognized that " Prior to the Twenty-first Amendment it would obviously have been unconstitutional " for a state to require a license and fee to import beer anywhere within its borders.

The Court criticized its earliest rulings on the issue, ( including State Board of Equalization v. Young's Market Co .) and promulgated its most limited interpretation to date: The aim of the Twenty-first Amendment was to allow States to maintain an effective and uniform system for controlling liquor by regulating its transportation, importation, and use.

* Connee Boswell recorded the song for Decca on July 8, 1941 with Victor Young's Orchestra.

Young's school was the nucleus of the later Wrangell Institute, a boarding school for Alaska Natives through the mid-20th century.

Upon Dr. Young's death, his children created the River Bay Company to manage the property for development.

The source for this first steam locomotive that came to Plymouth, comes from Celestia Young's diary entry of that date, in which she states: " A lovely showery day.

" Young's campaign staff credited Barack Obama's presidential campaign for increasing registration of black and young voters in Philadelphia, many of whom voted for Young.

A major influence on Reed's recording, and an important source for an understanding of Reed's seriousness with the album, was the mid-1960s drone music work of La Monte Young's Theater of Eternal Music ( whose members included John Cale, Tony Conrad, Angus Maclise and Marian Zazeela ).< ref > The album listed ( misspelling included ) " Drone cognizance and harmonic possibilities vis a vis Lamont 74465 99752 2 ( reissue ).

Gesner's method of purifying the distillation products appears to have been superior to Young's, resulting in a cleaner and better-smelling fuel.

TSR published quite a number of fantasy and science fiction novels unconnected with their gaming products, such as L. Dean James ' " Red Kings of Wynnamyr " novels, Sorcerer's Stone ( 1991 ) and Kingslayer ( 1992 ); Mary H. Herbert's five " Gabria " novels ( Valorian, Dark Horse, Lightning's Daughter, City of the Sorcerers and Winged Magic ); and humorous fantasy fiction, including Roy V. Young's " Count Yor " novels Captains Outrageous ( 1994 ) and Yor's Revenge ( 1995 ).

The magazine has since excised the article from subsequent editions of the Illustrated History book ; a transcription of it can be found at the link below ( despite his scathing view of Young's career, Marsh gave the album the highest possible rating ).

The double-slit experiment, sometimes called Young's experiment ( after Young's interference experiment ), is a demonstration that matter and energy can display characteristics of both waves and particles, and demonstrates the fundamentally probabilistic nature of quantum mechanical phenomena.

Furthermore, the idea can be traced back to a paper by Leonhard Euler published in 1727, some 80 years before Thomas Young's 1807 paper.

The relationship between forces / moments and strains / curvatures for an isotropic material can be described with the following material properties: Young's Modulus, the shear Modulus and the Poisson's ratio, in relatively simple mathematical relationships.

Young's modulus, E, can be calculated by dividing the tensile stress by the tensile strain in the elastic ( initial, linear ) portion of the stress-strain curve:

The Young's modulus of a material can be used to calculate the force it exerts under specific strain.

Young's modulus can vary somewhat due to differences in sample composition and test method.

In terms of Young's modulus and Poisson's ratio, Hooke's law for isotropic materials can then be expressed as

This relationship only applies in the elastic range and indicates that the slope of the stress vs. strain curve can be used to find Young's modulus.

In quantum mechanics, a single wave can interfere with itself, but this is due to its quantum behavior and is still an addition of two waves ( see Young's slits experiment ).

For instance, in Young's Double-slit experiment electrons can be used in the place of light waves.

For the special case of unconstrained uniaxial tension or compression, Young's modulus can be thought of as a measure of the stiffness of a material.

* In Batman: Arkham Asylum, Ra's al Ghul's body can be found zipped up in a body bag in the morgue part of Arkham Mansion near Dr. Penny Young's office, which serves as the answer to the riddle " It'll be a cold day in hell when this Ghul rises again .".

Don't Bet on Women ( 1931 ) was a non-musical drawing room comedy in which playboy Edmund Lowe bets his happily married friend Roland Young that he can seduce Young's wife ( MacDonald ).

Both of Elizabeth Young's volumes of literary criticism from this period deal extensively and exclusively with this range of authors and the contexts in which their works can be viewed.

From these measurements properties such as Young's modulus, Poisson's ratio, yield strength, and strain-hardening characteristics can be determined.

Mathematically, the modulus of resilience can be expressed by the product of the square of the yield stress divided by two times the Young's modulus.

where E is the Young's modulus, ν is Poisson's ratio, and K < sub > I </ sub > is the stress intensity factor in mode I. Irwin also showed that the strain energy release rate of a planar crack in a linear elastic body can be expressed in terms of the mode I, mode II ( sliding mode ), and mode III ( tearing mode ) stress intensity factors for the most general loading conditions.

Young's most famous advertisement slogan was " A hog can cross the country without changing trains-but you can't.

It can be used to measure Young's modulus, Shear modulus, Poisson's ratio and damping coefficient in a non destructive way.

Extensive notes on the remastering process can be found on Young's website.