Kraft's inequality characterizes the sets of code word lengths that are possible in a prefix code.

Virtually, any uniquely decodable one-to-many code, not necessary a prefix one, must satisfy Kraft's inequality.

This is an infinite sum which has one summand for every p in the domain of F. The requirement that the domain be prefix-free, together with Kraft's inequality, ensures that this sum converges to a real number between 0 and 1.

In coding theory, Kraft's inequality, named after Leon Kraft, gives a sufficient condition for the existence of a prefix code and necessary condition for the existence of a uniquely decodable code for a given set of codeword lengths.

More specifically, Kraft's inequality limits the lengths of codewords in a prefix code: if one takes an exponential function of each length, the resulting values must look like a probability mass function.

Kraft's inequality can be thought of in terms of a constrained budget to be spent on codewords, with shorter codewords being more expensive.

* If Kraft's inequality holds with strict inequality, the code has some redundancy.

* If Kraft's inequality holds with strict equality, the code in question is a complete code.

* If Kraft's inequality does not hold, the code is not uniquely decodable.

However, Kraft's paper discusses only prefix codes, and attributes the analysis leading to the inequality to Raymond Redheffer.

Kraft's inequality states that

Hence the bit strings are prefix codes, and Kraft's inequality gives that.

Kraft's inequality therefore also holds for any prefix code.

* Kraft's inequality ( NIST )

The Kraft's new family home in Midway City, the only one on the block at that time, was a small, wood-frame Women's Army Corps dormitory on Beach Boulevard that Kraft's father Harold turned into a three-bedroom house.

Beach Boulevard was expanded from two-lanes to four-lanes in 1954, when Kraft was 9, and the Kraft home and chicken farm eventually was sandwiched between a blacksmith shop and the Red Garter cocktail lounge, whose patrons often left used condoms in Kraft's backyard that Kraft was tasked to shovel up every Sunday morning after church.

Graves died of AIDS before police could question him, so the question of Kraft's accomplice was never raised in court.

At that point Kraft's systems controller, Don Arabian, reported that telemetry was showing a " Segment 51 " indicator.

The Bunyip Parish of St. Thomas ' was originally part of the Gippsland Forest mission in 1879 and early services were held in Kraft's Hall.

In 2005, a minor international incident was caused when it was reported that Russian President Vladimir Putin had inadvertently taken one of Kraft's three Super Bowl rings.

It was made by Kraft's Post brand from 1993, when Philip Morris ( the owner of Kraft ) acquired all Nabisco cereal products, until 2008.

Joseph Dukette, who was also a gay bartender, was considered Kraft's first victim.

With CBS in the middle of a talent raid that had already lured Jack Benny and other NBC stars, Peary was offered a CBS deal of his own, after he chafed over NBC's and Kraft's reluctance to let him use his singing voice more often on Gildersleeve and to give him more part in the show's ownership than he already had.

Kraft's memoirs ( Aus meinem Leben ) were prepared in retirement near Dresden, and the first volume ( 1897 ) created such a sensation that eight years were allowed to elapse before the publication was continued.

He was in his agent Richard Kraft's film Finding Kraftland.

Kraft's published books include Confronting Powerless Christianity ( 2002 ), Culture, Communication and Christianity ( 2001 ), I Give You Authority ( 1997 ), Anthropology for Christian Witness ( 1996 ), Deep Wounds, Deep Healing ( 1994 ), Defeating Dark Angels ( 1992 ), Communication Theory for Christian Witness ( 1983, 1991 ), and Christianity in Culture ( 1979, revised 2005 ).

Starting with Swamp Thing Annual # 6, Collins moved on to write Swamp Thing # 110-138, dramatically overhauling the series by restoring the pre-Alan Moore tone and incorporating a new set of supporting cast members into the book .< ref >" Nancy Collins: Swamp Thing < nowiki >'</ nowiki > s New Scripter Speaks ," David Anthony Kraft's Comics Interview, # 102 ( 1991 ), pp. 4-13 .</ ref > Collins resurrected Anton Arcane along with the Sunderland Corporation as foils for Swamp Thing.

The media took up the search on Kraft's behalf with all eight children identified in eight days and resulted in many TV specials and interviews in the Australian National media.

* On September 24, 2012, UnitedHealth Group replaced Kraft Foods following Kraft's spinning off its North American grocery business.

There, Wirtanen makes an appearance to warn Campbell of Kraft's plot, and of Resi's complicity in it.

During the Second World War, rationing of meat and dairy products lead to Kraft's wide popularity.

April 2, 2007 marked Kraft's first day trading as an independent company on the New York Stock Exchange.

Kraft's parents moved to California from Wyoming prior to his birth.

Kraft's mother Opal served on the PTA at Kraft's school, Midway City Elementary, and baked cookies for Kraft's Cub Scout meetings.

Dukette is thought to be Kraft's first victim.

To date, 22 of Kraft's 67 estimated victims remain unrecovered and unidentified.

Certain details surrounding some of Kraft's murders have caused many to suspect that Kraft did not always act alone.

* Forensic evidence in two cases point to an accomplice — an extra set of footprints and semen that did not match Kraft's DNA.

* The snapshots Kraft had of the dead men were processed somewhere, but no photo developer reported Kraft's morbid images to the police.

) Jackson also told McDougal that the list included only Kraft's " more memorable " murders, saying the total body count stood closer to 100.

The maximum speedup in an improved sequential program, where some part was sped up times is limited by inequality

Corrado Gini ( May 23, 1884 – March 13, 1965 ) was an Italian statistician, demographer and sociologist who developed the Gini coefficient, a measure of the income inequality in a society.

For instance, in two studies by the American Mosaic Project, racial inequality in the United States was framed as either “ Black Disadvantage ” or “ White Privilege .” When the term “ black disadvantage ” was used to describe racial inequality, white participants felt less collectively responsible for the harm done to the out-group, which lessened collective guilt.

report that the inequality in education and income was predominantly due to genes, with shared environmental factors playing a subordinate role.

Rousseau posits that the original, deeply flawed Social Contract ( i. e., that of Hobbes ), which led to the modern state, was made at the suggestion of the rich and powerful, who tricked the general population into surrendering their liberties to them and instituted inequality as a fundamental feature of human society.

It was developed by Max O. Lorenz in 1905 for representing inequality of the wealth distribution.

Based on the extent to which the application of neoliberal policies has contributed to income disparities and inequality, both Klein and Noam Chomsky have suggested that the primary role of neoliberalism was as an ideological cover for capital accumulation by multinational corporations.

Another argument was that the natural inequality of people could be used to situate them in the most appropriate place in society.

This was 1935, but in 1964 it was shown by John Bell ( see Bell inequality ) that-although Einstein was correct in identifying seemingly paradoxical implications of quantum mechanical nonlocality-these implications could be experimentally tested.

The Gini coefficient was originally developed to measure income inequality and is equivalent to one of the L-moments.

This goal was not fully reached because the roots of gender inequality were not explicitly challenged.

A more formal inequality relating the standard deviation of position σ < sub > x </ sub > and the standard deviation of momentum σ < sub > p </ sub > was derived by Earle Hesse Kennard later that year ( and independently by Hermann Weyl in 1928 ),

According to the CIA the gini index which measures income inequality ( the higher the less equal the income distribution ) was clocked at 45. 0 in 2005, compared to 32. 0 in the European Union and 28. 3 in Germany.

This inequality of the two wings and the geographical distance between them was believed to be holding up the adoption of a new constitution.

The inequality for sums was published by, while the corresponding inequality for integrals was first stated by

The finite-dimensional case of this inequality for real vectors was proved by Cauchy in 1821, and in 1859 Cauchy's student Bunyakovsky noted that by taking limits one can obtain an integral form of Cauchy's inequality.