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Fair cake-cutting is a kind of fair division problem. The problem involves a heterogeneous resource, such as a cake with different toppings, that is assumed to be divisible – it is possible to cut arbitrarily small pieces of it without destroying their value. The resource has to be divided among several partners who have different preferences over different parts of the cake, i.e., some people prefer the chocolate toppings, some prefer the cherries, some just want as large a piece as possible. The division should be unanimously fair – each person should receive a piece believed to be a fair share.

The "cake" is only a metaphor; procedures for fair cake-cutting can be used to divide various kinds of resources, such as land estates, advertisement space or broadcast time.

The prototypical procedure for fair cake-cutting is divide and choose, which is mentioned in the book of Genesis. It solves the fair division problem for two people. The modern study of fair cake-cutting was initiated during World War II, when Hugo Steinhaus asked his students Stefan Banach and Bronisław Knaster to find a generalization of divide-and-choose to three or more people. They developed the last diminisher procedure. Today, fair cake-cutting is the subject of intense research in mathematics, computer science, economics and political science.

Jazelle DBX (direct bytecode execution) is an extension that allows some ARM processors to execute Java bytecode in hardware as a third execution state alongside the existing ARM and Thumb modes. Jazelle functionality was specified in the ARMv5TEJ architecture and the first processor with Jazelle technology was the ARM926EJ-S. Jazelle is denoted by a "J" appended to the CPU name, except for post-v5 cores where it is required (albeit only in trivial form) for architecture conformance.

Jazelle RCT (Runtime Compilation Target) is a different technology based on ThumbEE mode; it supports ahead-of-time (AOT) and just-in-time (JIT) compilation with Java and other execution environments.

The most prominent use of Jazelle DBX is by manufacturers of mobile phones to increase the execution speed of Java ME games and applications. A Jazelle-aware Java virtual machine (JVM) will attempt to run Java bytecode in hardware, while returning to the software for more complicated, or lesser-used bytecode operations. ARM claims that approximately 95% of bytecode in typical program usage ends up being directly processed in the hardware.

The published specifications are very incomplete, being only sufficient for writing operating system code that can support a JVM that uses Jazelle. The declared intent is that only the JVM software needs to (or is allowed to) depend on the hardware interface details. This tight binding facilitates the hardware and JVM evolving together without affecting other software. In effect, this gives ARM Holdings considerable control over which JVMs are able to exploit Jazelle. It also prevents open source JVMs from using Jazelle. These issues do not apply to the ARMv7 ThumbEE environment, the nominal successor to Jazelle DBX.

Non-explosive demolition agents are chemicals that are an alternative to explosives and gas pressure blasting products in demolition, mining, and quarrying. To use non-explosive demolition agents in demolition or quarrying, holes are drilled in the base rock as they would be for use with conventional explosives. A slurry mixture of the non-explosive demolition agent and water is poured into the drill holes. Over the next few hours the slurry expands, cracking the rock in a pattern somewhat like the cracking that would occur from conventional explosives.

Non-explosive demolition agents offer many advantages including that they are silent and do not produce vibration the way a conventional explosive would. In some applications conventional explosives are more economical than non-explosive demolition agents. In many countries these are available without restriction, unlike explosives which are highly regulated.

The active ingredient is typically calcium oxide, "burnt lime," and is typically mixed with Portland cement and modifiers.

These agents are much safer than explosives, but they have to be used as directed to avoid steam explosions during the first few hours after being placed.

Many patents describe non-explosive demolition agents containing CaO, SiO₂ and/or cement.

"Old Man Trump" is a song with lyrics written by American folk singer-songwriter Woody Guthrie in 1954. The song describes the racist housing practices and discriminatory rental policies of his landlord, Fred Trump (the father of the 45th president of the United States, Donald Trump). Although the lyrics were written in 1954, it was never recorded by Guthrie. In January 2016, Will Kaufman, a Guthrie scholar and professor of American literature and culture at the University of Central Lancashire, unearthed the handwritten lyrics while conducting research at the Woody Guthrie Archives in Tulsa, Oklahoma.

In Thailand, lèse-majesté is a crime according to Section 112 of the Thai Criminal Code. It is illegal to defame, insult, or threaten the monarch of Thailand (king, queen, heir-apparent, heir-presumptive, or regent). Modern Thai lèse-majesté law has been on the statute books since 1908. Thailand is the only constitutional monarchy to have strengthened its lèse-majesté law since World War II. With penalties ranging from three to fifteen years imprisonment for each count, it has been described as the "world's harshest lèse majesté law" and "possibly the strictest criminal-defamation law anywhere". Its enforcement has been described as being "in the interest of the palace".^: 134

The law has criminalised acts of insult since 1957. There is substantial room for interpretation, which causes controversy. Broad interpretation of the law reflects the inviolable status of the king, resembling feudal or absolute monarchs. Thailand's Supreme Court decided the law also applies to prior monarchs. Criticism of any privy council member has raised the question whether lèse-majesté applies by association. Even attempting to commit lèse-majesté, making sarcastic comments about the King's pet, and failure to rebuke an offense have been prosecuted as lèse-majesté.

Anyone can file a lèse-majesté complaint, and the police formally investigate all of them. Details of the charges are rarely made public. A Section 112 defendant meets with official obstruction throughout the case. There are months-long pretrial detentions, and courts routinely deny bail to those charged. The United Nations Working Group on Arbitrary Detention determined that the pretrial detention of an alleged lèse-majesté offender violated international human rights law. The courts seem not to recognise the principle of granting defendants the benefit of the doubt. Judges have said accusers did not have to prove the factuality of the alleged lèse-majesté material but only claim it is defamatory. Pleading guilty, then asking for a royal pardon, is seen as the quickest route to freedom for any accused.

Since the 1976 coup, coup makers have regularly cited a surge of alleged lèse-majesté charges as a reason for overthrowing elected governments. This was cited as one of the major reasons for the 2006 coup and that of 2014. In 2006 and 2007, there were notable changes in the trend. Those targeted by lèse-majesté complaints included more average citizens who were given longer jail sentences. Human rights groups condemned its use as a political weapon and a means to restrict freedom. The 2014 junta government granted authority to army courts to prosecute lèse-majesté, which has usually resulted in secret trials and harsh sentences. Prior to the law's revival in 2020, for three years the Thai government often invoked other laws, such as the Computer Crimes Act and sedition laws, to deal with perceived damages and insults to the monarchy. The longest recorded sentence was in 2021: 87 years imprisonment, reduced to 43 years because the defendant pleaded guilty. In 2023, the Supreme Court ordered a female politician from the Move Forward Party to be banned from politics for life due to her alleged lèse-majesté posts on social media.

Isaac Newton's rotating bucket argument (also known as Newton's bucket) was designed to demonstrate that true rotational motion cannot be defined as the relative rotation of the body with respect to the immediately surrounding bodies. It is one of five arguments from the "properties, causes, and effects" of "true motion and rest" that support his contention that, in general, true motion and rest cannot be defined as special instances of motion or rest relative to other bodies, but instead can be defined only by reference to absolute space. Alternatively, these experiments provide an operational definition of what is meant by "absolute rotation", and do not pretend to address the question of "rotation relative to what?" General relativity dispenses with absolute space and with physics whose cause is external to the system, with the concept of geodesics of spacetime.

Cancer Alley (French: Allée du Cancer) is the regional nickname given to an 85-mile (137 km) stretch of land along the Mississippi River between Baton Rouge and New Orleans, in the River Parishes of Louisiana, which contains over 200 petrochemical plants and refineries. This area accounts for 25% of the petrochemical production in the United States. Environmentalists consider the region a sacrifice zone where rates of cancer caused by air pollution exceed the federal government's own limits of acceptable risk. Others have referred to the same region as "Death Alley".

Community leaders such as Sharon Lavigne have led the charge in protesting the expansion of the petrochemical industry in Cancer Alley, as well as addressing the associated racial and economic disparities.

The mathematical manuscripts of Karl Marx are a manuscript collection of Karl Marx's mathematical notes where he attempted to derive the foundations of infinitesimal calculus from first principles.

The notes that Marx took have been collected into four independent treatises: On the Concept of the Derived Function, On the Differential, On the History of Differential Calculus, and Taylor's Theorem, MacLaurin's Theorem, and Lagrange's Theory of Derived Functions, along with several notes, additional drafts, and supplements to these four treatises. These treatises attempt to construct a rigorous foundation for calculus and use historical materialism to analyze the history of mathematics.

Marx's contributions to mathematics did not have any impact on the historical development of calculus, and he was unaware of many more recent developments in the field at the time, such as the work of Cauchy. However, his work in some ways anticipated, but did not influence, some later developments in 20th century mathematics. These manuscripts, which are from around 1873–1883, were not published in any language until 1968 when they were published in the Soviet Union alongside a Russian translation. Since their publication, Marx's independent contributions to mathematics have been analyzed in terms of both his own historical and economic theories, and in light of their potential applications of nonstandard analysis.

The number 6174 is known as Kaprekar's constant after the Indian mathematician D. R. Kaprekar. This number is renowned for the following rule:

1. Take any four-digit number, using at least two different digits (leading zeros are allowed).
2. Arrange the digits in descending and then in ascending order to get two four-digit numbers, adding leading zeros if necessary.
3. Subtract the smaller number from the bigger number.
4. Go back to step 2 and repeat.

The above process, known as Kaprekar's routine, will always reach its fixed point, 6174, in at most 7 iterations. Once 6174 is reached, the process will continue yielding 7641 – 1467 = 6174. For example, choose 1459:

The only four-digit numbers for which Kaprekar's routine does not reach 6174 are repdigits such as 1111, which give the result 0000 after a single iteration. All other four-digit numbers eventually reach 6174 if leading zeros are used to keep the number of digits at 4. For numbers with three identical numbers and a fourth number that is one number higher or lower (such as 2111), it is essential to treat 3-digit numbers with a leading zero; for example: 2111 – 1112 = 0999; 9990 – 999 = 8991; 9981 – 1899 = 8082; 8820 – 288 = 8532; 8532 – 2358 = 6174.

Y, or y, is the 25th and penultimate letter of the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. According to some authorities, it is the sixth (or seventh if including W) vowel letter of the English alphabet. In the English writing system, it mostly represents a vowel and seldom a consonant, and in other orthographies it may represent a vowel or a consonant. Its name in English is wye (pronounced ), plural wyes.