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Flagship

A flagship is a vessel used by the commanding officer of a group of naval ships, characteristically a flag officer entitled by custom to fly a distinguishing flag. Used more loosely, it is the lead ship in a fleet of vessels, typically the first, largest, fastest, most heavily armed, or best known.

Over the years, the term "flagship" has become a metaphor used in industries such as broadcasting, automobiles, education, technology, airlines, and retail to refer to their highest profile or most expensive products and locations.

Naval use
In common naval use, the term flagship is fundamentally a temporary designation; the flagship is wherever the admiral's flag is being flown. However, admirals have always needed additional facilities, including a meeting room large enough to hold all the captains of the fleet and a place for the admiral's staff to make plans and draw up orders. Historically, only larger ships could accommodate such requirements.

The term was also used by commercial fleets, when the distinction between a nation's navy and merchant fleet was not clear. An example was Sea Venture, flagship of the fleet of the Virginia Company, which was captained by Royal Navy Vice-Admiral Christopher Newport yet bore the Merchant Navy admiral of the company's fleet, Sir George Somers, during the ill-fated Third Supply of 1609.

In the age of sailing ships, the flagship was typically a first rate; the aft of one of the three decks would become the admiral's quarters and staff offices. This can be seen on HMS Victory, the flagship of Admiral Horatio Nelson at the Battle of Trafalgar in 1805, still serving the Royal Navy as the ceremonial flagship of the First Sea Lord from Portsmouth, England. Non-first rates could serve as flagships, however: USS Constitution, a frigate (a fourth rate), served as flagship for parts of the United States Navy during the early 19th century.

In the 20th century, ships became large enough that the larger types, cruisers and up, could accommodate a commander and staff. Some larger ships may have a separate flag bridge for use by the admiral and his staff while the captain commands from the main navigation bridge. Because its primary function is to coordinate a fleet, a flagship is not necessarily more heavily armed or armored than other ships. During World War II, admirals often preferred a faster ship over the largest one.

Modern flagships are designed primarily for command and control rather than for fighting, and are also known as command ships.

Flagship as metaphor
As with many other naval terms, flagship has crossed over into general usage, where it means the most important or leading member of a group, as in the flagship station of a broadcast network. The word can be used as a noun or an adjective describing the most prominent or highly touted product, brand, location, or service offered by a company. Derivations include the "flagship brand" or "flagship product" of a manufacturing company, "flagship store" of a retail chain, or "flagship service" of a hospitality or transportation concern.

The term "flagship" may have specific applications:
 * Auto companies may have a flagship in the form of their leading or highest-priced car.
 * Electronics companies may have a series of products considered to be their flagship, usually consisting of one or two products that are updated periodically. For example, the Samsung Galaxy S series consists of several flagship smartphones that are released on a yearly basis.
 * In rail transport, a "flagship service" is either the fastest or most luxurious. Often it is also a named train or service.

Colleges and universities in the United States
Most states in the United States provide public university education through one or more university systems, with each system having multiple campuses located throughout the state. The phrase flagship institution or flagship university may be applied to an individual school or campus within each state system. The College Board, for example, defines flagship universities as the first to be established as well as the most research-intensive public universities. These schools are often land-grant research universities. According to Robert M. Berdahl, then-chancellor of the University of California, Berkeley, the phrase "flagship" came into existence in the 1950s when the Morrill Act schools were joined by newer institutions built in a wave of post-war expansion of state university systems.

Berdahl notes further that because flagships are generally the oldest schools within a system, they are often the largest and best financed and are perceived as elite relative to non-flagship state schools. He comments that "Those of us in 'systems' of higher education are frequently actively discouraged from using the term 'flagship' to refer to our campuses because it is seen as hurtful to the self-esteem of colleagues at other institutions in our systems. The use of the term is seen by some as elitist and boastful. It is viewed by many, in the context of the politics of higher education, as 'politically incorrect.' ... Only in the safe company of alumni is one permitted to use the term."

Nevertheless, the term "flagship university" is still used in official contexts by various state university system boards of governors, state legislatures, and scholars. Additionally, state universities often self-designate themselves as flagships. Higher education agencies, research journals, and other organizations also use the term, though their lists of flagship universities can differ greatly. One list of 50 flagship universities (one per state) is employed by the Higher Education Coordinating Board, the College Board, the Princeton Review and many other state and federal educational and governmental authorities for a variety of purposes including tuition and rate comparisons, research studies  and public policy analyses.

Despite its ubiquity, this list of 50 flagships is not the only state-by-state examination of flagships. In a 2010 article, Standard & Poor's created its own list of flagship universities, noting that each state had typically one or two institutions with flagship characteristics. The Education Sector, an education policy organization, used a different list of 51 flagship universities in an August 2011 study of college debt. Several states had multiple universities categorized as flagships due to "less of a clear distinction between a single flagship and other public universities" in those states. Additionally, several states were not included in the study due to insufficient comparative data. There are many instances in which more than one school in a state has claimed to be, or has been described as, a "flagship".

In February 2012, Idaho's State Board of Education made a controversial decision to strike the word "flagship" from the University of Idaho's mission statement. The Board's President Richard Westerberg explained that this revision was made as part of the board's many changes made to multiple Idaho universities' mission statements in an effort to ensure all statements were consistent and collegial in nature rather than comparative or competitive.

Retailing
Flagship stores are core stores for brand name retailers, larger than their standard outlets and stocking greater inventory, often found in prominent shopping districts such as Fifth Avenue in New York, Oxford Street in London, İstiklal Avenue in İstanbul or Tokyo's Ginza.

Broadcasting
A flagship station is the principal station of a radio or television broadcast network. It can be the station that produces the largest amount of material for the network, or the station in the parent company's home city, or both. The term dates back to the mid twentieth century years of broadcasting when headquarters stations produced programs for their networks.

For example, the flagship stations of the ABC, NBC and CBS television and radio networks are their owned and operated outlets in New York City. Likewise, public television's WNET served as primary member station for National Educational Television (NET), a forerunner to the US Public Broadcasting Service (PBS).

In sports broadcasting, the "flagship" is a team's primary station in their home market, which produces game broadcasts and feeds them to affiliates. For example, WGN was the flagship station of the Chicago Cubs baseball team, which has an extensive Cubs radio network spanning several states.

Automobiles
The term flagship is also used to describe an automaker's top (i.e. largest/most expensive/most prestigious) vehicle. Modern examples include the Mercedes-Benz S-Class, Toyota Century, Hongqi L5, and Land Rover's Range Rover.

Airlines
American Airlines obtained copyright to the term "Flagship" on May 3, 1937, per the Catalog of Copyright Entries. As of December 20, 2019 as stated in a legal document, this includes "the marks "Flagship," "Flagship Lounge" and "Flagship Suite" (the "Flagship Marks")—to describe premium air travel services for first and business class passengers since the 1930s and 1940s." Delta Air Lines also uses/used the word "Flagship" to describe its top lines, as pointed out by AA and being argued legally in December 2019 and into 2020.

Conservation
Within conservation biology, the term flagship species refers to a species or taxon that is a symbol or rallying point to catalyze conservation actions.

title: Flagship


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Talk:Politics of South Korea

Untitled
State-run KBS said Roh's Millennium Democratic Party's had scored 49.1 percent of the vote, while Lee of the Grand National Party had 46.8 percent. The broadcaster said its poll had a 2.2 percent margin of error.

Talk more about the voting system, please.
Does South Korea use a mixed member proportional system? How exactly is "half" of the representation obtained proportionally? Are party lists used? If a party has 20% of the vote but wins none of the non-proportional seats, will they end up with 20% of the legislature, or only 20% of the half that's elected proportionally? Scott Ritchie 07:21, 24 May 2005 (UTC)

Group of 77?
Is Korea in the G-77 developing nations? I think it's in the G-20 industrial nations. (LeeJun7 00:09, 1 August 2007 (UTC))

Important notice
The government section of the "Outline of South Korea" needs to be checked, corrected, and completed -- especially the subsections for the government branches.

When the country outlines were created, temporary data (that matched most of the countries but not all) was used to speed up the process. Those countries for which the temporary data does not match must be replaced with the correct information.

Please check that this country's outline is not in error.

If you have any questions or comments, please contact The Transhumanist.

Thank you.

File nominated for deletion on commons
The file c:File:Emblem of Korean Courts.svg used in this article has been nominated for deletion on Commons Reason: I think time has come to finish the long-forgotten (or ignored) question: Is free? I doubt its freeness, based on the fact that we do not have definite answer for Template talk:KOGL. To save your click...   We, as of 2018, do not have a final answer for this. And this means, we have to delete these images, including some VIs and FPs. Deletion request: link Message automatically deposited by a robot - -Harideepan (talk) 06:15, 23 March 2018 (UTC).

File nominated for deletion on commons
The file c:File:Emblem of the Government of the Republic of Korea.svg used in this article has been nominated for deletion on Commons Reason: I think time has come to finish the long-forgotten (or ignored) question: Is free? I doubt its freeness, based on the fact that we do not have definite answer for Template talk:KOGL. To save your click...   We, as of 2018, do not have a final answer for this. And this means, we have to delete these images, including some VIs and FPs. Deletion request: link Message automatically deposited by a robot - -Harideepan (talk) 07:50, 23 March 2018 (UTC).

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Talk:Politics of South Korea


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Talk:Internment Camp

This is a dumb redirect. Needs a proper entry. Redirecting it to Internment Racklever 16:51, 11 December 2005 (UTC)

title: Talk:Internment Camp


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Gualdo Tadino

Gualdo Tadino (Latin: Tadinum) is an ancient town of Italy, in the province of Perugia in northeastern Umbria, on the lower flanks of Monte Penna, a mountain of the Apennines. It is 47 km NE of Perugia.

History
Gualdo has a long history and was originally an Umbrian village known as Tarsina. Conquered by the Romans in 266 BC and re-christened Tadinum, it was a station on the Via Flaminia. In 217 BC, it was destroyed by Hannibal's troops. A similar defeat was inflicted on it in 47 BC by Julius Caesar and in 410 AD by Alaric's Visigoths.

In 552, the Byzantine general Narses briefly restored Italy to the empire by defeating the Ostrogoth king Baduila in what is now known as the Battle of Taginae, the exact site of which is not known, but thought by most scholars to be a few kilometers from the town, in the plain to the west at a place called Taino. This suspicion may have received confirmation in 2004.

The ancient city survived that war, only to be destroyed in a later war at the instigation of the Holy Roman Emperor Otto III in 966. It was later rebuilt, only to be destroyed a second time by fire in 1237. Finally, the Emperor Frederick II ordered the city rebuilt for a third time in 1239, and it is this incarnation which survives today.

Gualdo Tadino sister cities are: West Pittston, PA (USA) and Audun-le-Tiche, France

Religious architecture or sites

 * Gualdo Tadino Cathedral: Church of St Benedict with an external fountain attributed to Antonio da Sangallo the Elder (16th century).
 * San Francesco: 13th-century church housing frescoes by Matteo da Gualdo.
 * Santa Chiara: 13th century church
 * San Donato: 13th-century church
 * ''Santa Maria dei Raccomandati: 13th century oratory with traces of ancient frescoes
 * San Facondino, Gualdo Tadino: 11th-century pilgrimage church

Secular architecture or sites

 * Rocca Flea, a 12th-century castle which is now the main monument of the town.
 * Palazzo del Podestà.
 * Torre Civica (Town Tower).
 * Civic Gallery, with works by Matteo da Gualdo and others.

Economy
The city was famous in the Middle Ages for the manufacture of ceramic ware; in the late 20th century, the ceramic industry was revived, and Gualdo is now an important center for the manufacture of industrial ceramics and bathroom fittings.

Transportation
Gualdo Tadino has a railway station on the line from Ancona to Rome. The journey time to Ancona is typically one hour and 45 minutes, and to Rome two hours.

Frazioni
Boschetto, Busche, Caprara, Cerqueto, Corcia, Crocicchio, Gaifana, Grello, Palazzo Mancinelli, Petroia, Piagge, Pieve di Compresseto, Poggio Sant'Ercolano, Rasina, Rigali, Roveto, San Lorenzo, San Pellegrino, Vaccara

title: Gualdo Tadino


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Irreducible polynomial

In mathematics, an irreducible polynomial is, roughly speaking, a polynomial that cannot be factored into the product of two non-constant polynomials. The property of irreducibility depends on the nature of the coefficients that are accepted for the possible factors, that is, the ring to which the coefficients of the polynomial and its possible factors are supposed to belong. For example, the polynomial $x^{2} − 2$ is a polynomial with integer coefficients, but, as every integer is also a real number, it is also a polynomial with real coefficients. It is irreducible if it is considered as a polynomial with integer coefficients, but it factors as $$\left(x - \sqrt{2}\right)\left(x + \sqrt{2}\right)$$ if it is considered as a polynomial with real coefficients. One says that the polynomial $x^{2} − 2$ is irreducible over the integers but not over the reals.

Polynomial irreducibility can be considered for polynomials with coefficients in an integral domain, and there are two common definitions. Most often, a polynomial over an integral domain $R$ is said to be irreducible if it is not the product of two polynomials that have their coefficients in $R$, and that are not unit in $R$. Equivalently, for this definition, an irreducible polynomial is an irreducible element in the rings of polynomials over $R$. If $R$ is a field, the two definitions of irreducibility are equivalent. For the second definition, a polynomial is irreducible if it cannot be factored into polynomials with coefficients in the same domain that both have a positive degree. Equivalently, a polynomial is irreducible if it is irreducible over the field of fractions of the integral domain. For example, the polynomial $$2(x^2-2)\in \Z[x]$$ is irreducible for the second definition, and not for the first one. On the other hand, $$x^2-2$$ is irreducible in $$\Z[x]$$ for the two definitions, while it is reducible in $$\R[x].$$

A polynomial that is irreducible over any field containing the coefficients is absolutely irreducible. By the fundamental theorem of algebra, a univariate polynomial is absolutely irreducible if and only if its degree is one. On the other hand, with several indeterminates, there are absolutely irreducible polynomials of any degree, such as $$x^2 + y^n - 1,$$ for any positive integer $n$.

A polynomial that is not irreducible is sometimes said to be a reducible polynomial.

Irreducible polynomials appear naturally in the study of polynomial factorization and algebraic field extensions.

It is helpful to compare irreducible polynomials to prime numbers: prime numbers (together with the corresponding negative numbers of equal magnitude) are the irreducible integers. They exhibit many of the general properties of the concept of "irreducibility" that equally apply to irreducible polynomials, such as the essentially unique factorization into prime or irreducible factors. When the coefficient ring is a field or other unique factorization domain, an irreducible polynomial is also called a prime polynomial, because it generates a prime ideal.

Definition
If F is a field, a non-constant polynomial is irreducible over F if its coefficients belong to F and it cannot be factored into the product of two non-constant polynomials with coefficients in F.

A polynomial with integer coefficients, or, more generally, with coefficients in a unique factorization domain R, is sometimes said to be irreducible (or irreducible over R) if it is an irreducible element of the polynomial ring, that is, it is not invertible, not zero, and cannot be factored into the product of two non-invertible polynomials with coefficients in R. This definition generalizes the definition given for the case of coefficients in a field, because, over a field, the non-constant polynomials are exactly the polynomials that are non-invertible and non-zero.

Another definition is frequently used, saying that a polynomial is irreducible over R if it is irreducible over the field of fractions of R (the field of rational numbers, if R is the integers). This second definition is not used in this article. The equivalence of the two definitions depends on R.

Simple examples
The following six polynomials demonstrate some elementary properties of reducible and irreducible polynomials:

 * $$\begin{align}

p_1(x) &= x^2 + 4x + 4\, = {(x + 2)^2}\\ p_2(x) &= x^2 - 4\, = {(x - 2)(x + 2)}\\ p_3(x) &= 9x^2 - 3\, = 3\left(3x^2 - 1\right)\, = 3\left(x\sqrt{3} - 1\right)\left(x\sqrt{3} + 1\right)\\ p_4(x) &= x^2 - \frac{4}{9}\, = \left(x - \frac{2}{3}\right)\left(x + \frac{2}{3}\right)\\ p_5(x) &= x^2 - 2\, = \left(x - \sqrt{2}\right)\left(x + \sqrt{2}\right)\\ p_6(x) &= x^2 + 1\, = {(x - i)(x + i)} \end{align}$$

Over the integers, the first three polynomials are reducible (the third one is reducible because the factor 3 is not invertible in the integers); the last two are irreducible. (The fourth, of course, is not a polynomial over the integers.)

Over the rational numbers, the first two and the fourth polynomials are reducible, but the other three polynomials are irreducible (as a polynomial over the rationals, 3 is a unit, and, therefore, does not count as a factor).

Over the real numbers, the first five polynomials are reducible, but $$p_6(x)$$ is irreducible.

Over the complex numbers, all six polynomials are reducible.

Over the complex numbers
Over the complex field, and, more generally, over an algebraically closed field, a univariate polynomial is irreducible if and only if its degree is one. This fact is known as the fundamental theorem of algebra in the case of the complex numbers and, in general, as the condition of being algebraically closed.

It follows that every nonconstant univariate polynomial can be factored as

 * $$a\left(x - z_1\right) \cdots \left(x - z_n\right)$$

where $$n$$ is the degree, $$a$$ is the leading coefficient and $$z_1, \dots, z_n$$ are the zeros of the polynomial (not necessarily distinct, and not necessarily having explicit algebraic expressions).

There are irreducible multivariate polynomials of every degree over the complex numbers. For example, the polynomial
 * $$x^n + y^n - 1,$$

which defines a Fermat curve, is irreducible for every positive n.

Over the reals
Over the field of reals, the degree of an irreducible univariate polynomial is either one or two. More precisely, the irreducible polynomials are the polynomials of degree one and the quadratic polynomials $$ax^2 + bx + c$$ that have a negative discriminant $$b^2 - 4ac.$$ It follows that every non-constant univariate polynomial can be factored as a product of polynomials of degree at most two. For example, $$x^4 + 1$$ factors over the real numbers as $$\left(x^2 + \sqrt{2}x + 1\right)\left(x^2 - \sqrt{2}x + 1\right),$$ and it cannot be factored further, as both factors have a negative discriminant: $$\left(\pm\sqrt{2}\right)^2 - 4 = -2 < 0.$$

Unique factorization property
Every polynomial over a field $F$ may be factored into a product of a non-zero constant and a finite number of irreducible (over $F$) polynomials. This decomposition is unique up to the order of the factors and the multiplication of the factors by non-zero constants whose product is 1.

Over a unique factorization domain the same theorem is true, but is more accurately formulated by using the notion of primitive polynomial. A primitive polynomial is a polynomial over a unique factorization domain, such that 1 is a greatest common divisor of its coefficients.

Let $F$ be a unique factorization domain. A non-constant irreducible polynomial over $F$ is primitive. A primitive polynomial over $F$ is irreducible over $F$ if and only if it is irreducible over the field of fractions of $F$. Every polynomial over $F$ may be decomposed into the product of a non-zero constant and a finite number of non-constant irreducible primitive polynomials. The non-zero constant may itself be decomposed into the product of a unit of $F$ and a finite number of irreducible elements of $F$. Both factorizations are unique up to the order of the factors and the multiplication of the factors by a unit of $F$.

This is this theorem which motivates that the definition of irreducible polynomial over a unique factorization domain often supposes that the polynomial is non-constant.

All algorithms which are presently implemented for factoring polynomials over the integers and over the rational numbers use this result (see Factorization of polynomials).

Over the integers and finite fields
The irreducibility of a polynomial over the integers $$\mathbb{Z}$$ is related to that over the field $$\mathbb{F}_p$$ of $$p$$ elements (for a prime $$p$$). In particular, if a univariate polynomial $f$ over $$\mathbb Z$$ is irreducible over $$\mathbb{F}_p$$ for some prime $$p$$ that does not divide the leading coefficient of $f$ (the coefficient of the highest power of the variable), then $f$ is irreducible over $$\mathbb{Z}$$ (that is, it is not the product of two non-constant polynomials with integer coefficients). Eisenstein's criterion is a variant of this property where irreducibility over $$p^2$$ is also involved.

The converse, however, is not true: there are polynomials of arbitrarily large degree that are irreducible over the integers and reducible over every finite field. A simple example of such a polynomial is $$x^4 + 1.$$

The relationship between irreducibility over the integers and irreducibility modulo p is deeper than the previous result: to date, all implemented algorithms for factorization and irreducibility over the integers and over the rational numbers use the factorization over finite fields as a subroutine.

The number of degree $n$ irreducible monic polynomials over a field $$\mathbb{F}_q$$ for $q$ a prime power is given by Moreau's necklace-counting function:
 * $$M(q, n) = \frac{1}{n}\sum_{d\mid n} \mu(d)q^\frac{n}{d},$$

where $μ$ is the Möbius function. For $q = 2$, such polynomials are commonly used to generate pseudorandom binary sequences.

In some sense, almost all polynomials with coefficients zero or one are irreducible over the integers. More precisely, if a version of the Riemann hypothesis for Dedekind zeta functions is assumed, the probability of being irreducible over the integers for a polynomial with random coefficients in ${0, 1}$ tends to one when the degree increases.

Algorithms
The unique factorization property of polynomials does not mean that the factorization of a given polynomial may always be computed. Even the irreducibility of a polynomial may not always be proved by a computation: there are fields over which no algorithm can exist for deciding the irreducibility of arbitrary polynomials.

Algorithms for factoring polynomials and deciding irreducibility are known and implemented in computer algebra systems for polynomials over the integers, the rational numbers, finite fields and finitely generated field extension of these fields. All these algorithms use the algorithms for factorization of polynomials over finite fields.

Field extension
The notions of irreducible polynomial and of algebraic field extension are strongly related, in the following way.

Let x be an element of an extension L of a field K. This element is said to be algebraic if it is a root of a nonzero polynomial with coefficients in K. Among the polynomials of which x is a root, there is exactly one which is monic and of minimal degree, called the minimal polynomial of x. The minimal polynomial of an algebraic element x of L is irreducible, and is the unique monic irreducible polynomial of which x is a root. The minimal polynomial of x divides every polynomial which has x as a root (this is Abel's irreducibility theorem).

Conversely, if $$P(X) \in K[X]$$ is a univariate polynomial over a field K, let $$L = K[X]/P(X)$$ be the quotient ring of the polynomial ring $$K[X]$$ by the ideal generated by $P$. Then $L$ is a field if and only if $P$ is irreducible over $K$. In this case, if $x$ is the image of $X$ in $L$, the minimal polynomial of $x$ is the quotient of $P$ by its leading coefficient.

An example of the above is the standard definition of the complex numbers as $$\mathbb{C} = \mathbb{R}[X]\;/\left(X^2 + 1\right).$$

If a polynomial $P$ has an irreducible factor $Q$ over $K$, which has a degree greater than one, one may apply to $Q$ the preceding construction of an algebraic extension, to get an extension in which $P$ has at least one more root than in $K$. Iterating this construction, one gets eventually a field over which $P$ factors into linear factors. This field, unique up to a field isomorphism, is called the splitting field of $P$.

Over an integral domain
If R is an integral domain, an element f of R that is neither zero nor a unit is called irreducible if there are no non-units g and h with f = gh. One can show that every prime element is irreducible; the converse is not true in general but holds in unique factorization domains. The polynomial ring F[x] over a field F (or any unique-factorization domain) is again a unique factorization domain. Inductively, this means that the polynomial ring in n indeterminates (over a ring R) is a unique factorization domain if the same is true for R.

title: Irreducible polynomial


text:
Talk:Vanadium

Proposed merge of Native vanadium into Vanadium
Extremely narrowly scope article about a rare form of a metal, better covered as a redirect and section Sadads (talk) 01:15, 10 August 2023 (UTC)
 * Support: non-notable as a standalone article.  141 Pr  {contribs} 12:23, 12 September 2023 (UTC)
 * ✅ Klbrain (talk) 12:04, 20 September 2023 (UTC)

Suspicious reference

 * "It is oxidized in air at about 933 K (660 °C, 1220 °F), although an oxide passivation layer forms even at room temperature.[21]"

I can't find anything verify about this inside reference [21]. When I go deeper via that query string at the link of [21], I found this that have everything very similar to Wikipedia. I suspect citogenesis happened here. Nucleus hydro elemon (talk) 07:33, 9 July 2024 (UTC)

title: Talk:Vanadium


text:
Decomposition

Decomposition or rot is the process by which dead organic substances are broken down into simpler organic or inorganic matter such as carbon dioxide, water, simple sugars and mineral salts. The process is a part of the nutrient cycle and is essential for recycling the finite matter that occupies physical space in the biosphere. Bodies of living organisms begin to decompose shortly after death. Animals, such as earthworms, also help decompose the organic materials. Organisms that do this are known as decomposers or detritivores. Although no two organisms decompose in the same way, they all undergo the same sequential stages of decomposition. The science which studies decomposition is generally referred to as taphonomy from the Greek word taphos, meaning tomb. Decomposition can also be a gradual process for organisms that have extended periods of dormancy.

One can differentiate abiotic decomposition from biotic decomposition (biodegradation). The former means "the degradation of a substance by chemical or physical processes", e.g., hydrolysis; the latter means "the metabolic breakdown of materials into simpler components by living organisms", typically by microorganisms.

Animal decomposition

Decomposition begins at the moment of death, caused by two factors: autolysis, the breaking down of tissues by the body's own internal chemicals and enzymes, and putrefaction, the breakdown of tissues by bacteria. These processes release compounds such as cadaverine and putrescine, that are the chief source of the unmistakably putrid odor of decaying animal tissue.

Prime decomposers are bacteria or fungi, though larger scavengers also play an important role in decomposition if the body is accessible to insects, mites and other animals. Additionally, soil animals are considered key regulators of decomposition at local scales but their role at larger scales is unresolved. The most important arthropods that are involved in the process include carrion beetles, mites, the flesh-flies (Sarcophagidae) and blow-flies (Calliphoridae), such as the green bottle flies seen in the summer. In North America, the most important non-insect animals that are typically involved in the process include mammal and bird scavengers, such as coyotes, dogs, wolves, foxes, rats, crows and vultures. Some of these scavengers also remove and scatter bones, which they ingest at a later time. Aquatic and marine environments have break-down agents that include bacteria, fish, crustaceans, fly larvae and other carrion scavengers.

Stages of decomposition
Five general stages are typically used to describe the process of decomposition in vertebrate animals: fresh, bloat, active decay, advanced decay, and dry/remains. The general stages of decomposition are coupled with two stages of chemical decomposition: autolysis and putrefaction. These two stages contribute to the chemical process of decomposition, which breaks down the main components of the body. With death the microbiome of the living organism collapses and is followed by the necrobiome that undergoes predictable changes over time.

Fresh
Among those animals that have a heart, the fresh stage begins immediately after the heart stops beating. From the moment of death, the body begins cooling or warming to match the temperature of the ambient environment, during a stage called algor mortis. Shortly after death, within three to six hours, the muscular tissues become rigid and incapable of relaxing, during a stage called rigor mortis. Since blood is no longer being pumped through the body, gravity causes it to drain to the dependent portions of the body, creating an overall bluish-purple discoloration termed livor mortis or, more commonly, lividity. Depending on the position of the body, these parts would vary. For instance, if the person was flat on their back when they died, the blood would collect in the parts that are touching the ground. If the person was hanging, it would collect in their fingertips, toes and earlobes.

Once the heart stops, the blood can no longer supply oxygen or remove carbon dioxide from the tissues. The resulting decrease in pH and other chemical changes cause cells to lose their structural integrity, bringing about the release of cellular enzymes capable of initiating the breakdown of surrounding cells and tissues. This process is known as autolysis.

Visible changes caused by decomposition are limited during the fresh stage, although autolysis may cause blisters to appear at the surface of the skin.

The small amount of oxygen remaining in the body is quickly depleted by cellular metabolism and aerobic microbes naturally present in respiratory and gastrointestinal tracts, creating an ideal environment for the proliferation of anaerobic organisms. These multiply, consuming the body's carbohydrates, lipids and proteins, to produce a variety of substances including propionic acid, lactic acid, methane, hydrogen sulfide and ammonia. The process of microbial proliferation within a body is referred to as putrefaction and leads to the second stage of decomposition known as bloat.

Blowflies and flesh flies are the first carrion insects to arrive and they seek a suitable oviposition site.

Bloat
The bloat stage provides the first clear visual sign that microbial proliferation is underway. In this stage, anaerobic metabolism takes place, leading to the accumulation of gases, such as hydrogen sulfide, carbon dioxide, methane and nitrogen. The accumulation of gases within the bodily cavity causes the distention of the abdomen and gives a cadaver its overall bloated appearance. The gases produced also cause natural liquids and liquefying tissues to become frothy. As the pressure of the gases within the body increases, fluids are forced to escape from natural orifices, such as the nose, mouth and anus, and enter the surrounding environment. The buildup of pressure combined with the loss of integrity of the skin may also cause the body to rupture.

Intestinal anaerobic bacteria transform haemoglobin into sulfhemoglobin and other colored pigments. The associated gases which accumulate within the body at this time aid in the transport of sulfhemoglobin throughout the body via the circulatory and lymphatic systems, giving the body an overall marbled appearance.

If insects have access, maggots hatch and begin to feed on the body's tissues. Maggot activity, typically confined to natural orifices, and masses under the skin, causes the skin to slip, and hair to detach from the skin. Maggot feeding, and the accumulation of gases within the body, eventually leads to post-mortem skin ruptures which will then further allow purging of gases and fluids into the surrounding environment. Ruptures in the skin allow oxygen to re-enter the body and provide more surface area for the development of fly larvae and the activity of aerobic microorganisms. The purging of gases and fluids results in the strong distinctive odors associated with decay.

Active decay
Active decay is characterized by the period of greatest mass loss. This loss occurs as a result of both the voracious feeding of maggots and the purging of decomposition fluids into the surrounding environment. The purged fluids accumulate around the body and create a cadaver decomposition island (CDI). Liquefaction of tissues and disintegration become apparent during this time and strong odors persist. The end of active decay is signaled by the migration of maggots away from the body to pupate.

Advanced decay
Decomposition is largely inhibited during advanced decay due to the loss of readily available cadaveric material. Insect activity is also reduced during this stage. When the carcass is located on soil, the area surrounding it will show evidence of vegetation death. The CDI surrounding the carcass will display an increase in soil carbon and nutrients such as phosphorus, potassium, calcium and magnesium; changes in pH; and a significant increase in soil nitrogen.

Dry/remains
As the ecosystem recovers from the disturbance, the CDI moves into the dry/remains stage, which is characterized by a decrease in the intensity of the disturbance and an increase in the amount of plant growth around the affected area. This is a sign that the nutrients and other ecological resources present in the surrounding soil have not yet returned to their normal levels.

During this stage, it is important to monitor the ecosystem for any signs of continued disturbance or ecological stress. The resurgence of plant growth is a positive sign, but it may take several years for the ecosystem to fully recover and return to its pre-disturbance state. All that remains of the cadaver at this stage is dry skin, cartilage, and bones, which will become dry and bleached if exposed to the elements. If all soft tissue is removed from the cadaver, it is referred to as completely skeletonized, but if only portions of the bones are exposed, it is referred to as partially skeletonized.

Exposure to the elements
A dead body that has been exposed to the open elements, such as water and air, will decompose more quickly and attract much more insect activity than a body that is buried or confined in special protective gear or artifacts. This is due, in part, to the limited number of insects that can penetrate soil and the lower temperatures under the soil.

The rate and manner of decomposition in an animal body are strongly affected by several factors. In roughly descending degrees of importance, they are:
 * Temperature;
 * The availability of oxygen;
 * Prior embalming;
 * Cause of death;
 * Burial, depth of burial, and soil type;
 * Access by scavengers;
 * Trauma, including wounds and crushing blows;
 * Humidity, or wetness;
 * Rainfall;
 * Body size and weight;
 * Composition;
 * Clothing;
 * The surface on which the body rests;
 * Foods/objects inside the specimen's digestive tract (bacon compared to lettuce).

The speed at which decomposition occurs varies greatly. Factors such as temperature, humidity, and the season of death all determine how fast a fresh body will skeletonize or mummify. A basic guide for the effect of environment on decomposition is given as Casper's Law (or Ratio): if all other factors are equal, then, when there is free access of air a body decomposes twice as fast as if immersed in water and eight times faster than if buried in the earth. Ultimately, the rate of bacterial decomposition acting on the tissue will depend upon the temperature of the surroundings. Colder temperatures decrease the rate of decomposition while warmer temperatures increase it. A dry body will not decompose efficiently. Moisture helps the growth of microorganisms that decompose the organic matter, but too much moisture could lead to anaerobic conditions slowing down the decomposition process.

The most important variable is the body's accessibility to insects, particularly flies. On the surface in tropical areas, invertebrates alone can easily reduce a fully fleshed corpse to clean bones in under two weeks. The skeleton itself is not permanent; acids in soils can reduce it to unrecognizable components. This is one reason given for the lack of human remains found in the wreckage of the Titanic, even in parts of the ship considered inaccessible to scavengers. Freshly skeletonized bone is often called green bone and has a characteristic greasy feel. Under certain conditions (underwater, but also cool, damp soil), bodies may undergo saponification and develop a waxy substance called adipocere, caused by the action of soil chemicals on the body's proteins and fats. The formation of adipocere slows decomposition by inhibiting the bacteria that cause putrefaction.

In extremely dry or cold conditions, the normal process of decomposition is halted – by either lack of moisture or temperature controls on bacterial and enzymatic action – causing the body to be preserved as a mummy. Frozen mummies commonly restart the decomposition process when thawed (see Ötzi the Iceman), whilst heat-desiccated mummies remain so unless exposed to moisture.

The bodies of newborns who never ingested food are an important exception to the normal process of decomposition. They lack the internal microbial flora that produces much of decomposition and quite commonly mummify if kept in even moderately dry conditions.

Anaerobic vs aerobic
Aerobic decomposition takes place in the presence of oxygen. This is most common to occur in nature. Living organisms that use oxygen to survive feed on the body. Anaerobic decomposition takes place in the absence of oxygen. This could be a place where the body is buried in organic material and oxygen cannot reach it. This process of putrefaction has a bad odor accompanied by it due to the hydrogen sulfide and organic matter containing sulfur.

Artificial preservation
Embalming is the practice of delaying the decomposition of human and animal remains. Embalming slows decomposition somewhat but does not forestall it indefinitely. Embalmers typically pay great attention to parts of the body seen by mourners, such as the face and hands. The chemicals used in embalming repel most insects and slow down bacterial putrefaction by either killing existing bacteria in or on the body themselves or by fixing cellular proteins, which means that they cannot act as a nutrient source for subsequent bacterial infections. In sufficiently dry environments, an embalmed body may end up mummified and it is not uncommon for bodies to remain preserved to a viewable extent after decades. Notable viewable embalmed bodies include those of:
 * Eva Perón of Argentina, whose body was injected with paraffin, was kept perfectly preserved for many years, and still is as far as is known (her body is no longer on public display).
 * Vladimir Lenin of the Soviet Union, whose body was kept submerged in a special tank of fluid for decades and is on public display in Lenin's Mausoleum.
 * Other Communist leaders with pronounced cults of personality such as Mao Zedong, Kim Il Sung, Ho Chi Minh, Kim Jong Il and most recently Hugo Chávez have also had their cadavers preserved in the fashion of Lenin's preservation and are now displayed in their respective mausoleums.
 * Pope John XXIII, whose preserved body can be viewed in St. Peter's Basilica.
 * Padre Pio, whose body was injected with formalin before burial in a dry vault from which he was later removed and placed on public display at the San Giovanni Rotondo.

Environmental preservation
A body buried in a sufficiently dry environment may be well preserved for decades. This was observed in the case for murdered civil rights activist Medgar Evers, who was found to be almost perfectly preserved over 30 years after his death, permitting an accurate autopsy when the case of his murder was re-opened in the 1990s.

Bodies submerged in a peat bog may become naturally embalmed, arresting decomposition and resulting in a preserved specimen known as a bog body. The generally cool and anoxic conditions in these environments limits the rate of microbial activity, thus limiting the potential for decomposition. The time for an embalmed body to be reduced to a skeleton varies greatly. Even when a body is decomposed, embalming treatment can still be achieved (the arterial system decays more slowly) but would not restore a natural appearance without extensive reconstruction and cosmetic work, and is largely used to control the foul odors due to decomposition.

An animal can be preserved almost perfectly, for millions of years in a resin such as amber.

There are some examples where bodies have been inexplicably preserved (with no human intervention) for decades or centuries and appear almost the same as when they died. In some religious groups, this is known as incorruptibility. It is not known whether or for how long a body can stay free of decay without artificial preservation.

Importance to forensic sciences
Various sciences study the decomposition of bodies under the general rubric of forensic science because the usual motive for such studies is to determine the time and cause of death for legal purposes:
 * Forensic taphonomy specifically studies the processes of decomposition to apply the biological and chemical principles to forensic cases to determine post-mortem interval (PMI), post-burial interval as well as to locate clandestine graves.
 * Forensic pathology studies the clues to the cause of death found in the corpse as a medical phenomenon.
 * Forensic entomology studies the insects and other vermin found in corpses; the sequence in which they appear, the kinds of insects, and where they are found in their life cycle are clues that can shed light on the time of death, the length of a corpse's exposure, and whether the corpse was moved.
 * Forensic anthropology is the medico-legal branch of physical anthropology that studies skeletons and human remains, usually to seek clues as to the identity, age, sex, height and ethnicity of their former owner.

The University of Tennessee Anthropological Research Facility (better known as the Body Farm) in Knoxville, Tennessee, has several bodies laid out in various situations in a fenced-in plot near the medical center. Scientists at the Body Farm study how the human body decays in various circumstances to gain a better understanding of decomposition.

Plant decomposition
Decomposition of plant matter occurs in many stages. It begins with leaching by water; the most easily lost and soluble carbon compounds are liberated in this process. Another early process is physical breakup or fragmentation of the plant material into smaller pieces, providing greater surface area for colonization and attack by decomposers. In fallen dead parts of plants (plant litter), this process is largely carried out by saprophagous (detritivorous) soil invertebrate fauna, whereas in standing parts of plants, primarily parasitic life-forms such as parasitic plants (e.g. mistletoes), insects (e.g. aphids) and fungi (e.g. polypores) play a major role in breaking down matter, both directly and indirectly via a multitrophic cascading effect

Following this, the plant detritus (consisting of cellulose, hemicellulose, microbial metabolites, and lignin) undergoes chemical alteration by microbes. Different types of compounds decompose at different rates. This is dependent on their chemical structure. For instance, lignin is a component of wood, which is relatively resistant to decomposition and can in fact only be decomposed by certain fungi, such as the white-rot fungi.

Wood decomposition is a complex process involving fungi which transport nutrients to the nutritionally scarce wood from outside environment. Because of this nutritional enrichment, the fauna of saproxylic insects may develop and, in turn, affect dead wood, contributing to decomposition and nutrient cycling in the forest floor. Lignin is one such remaining product of decomposing plants with a very complex chemical structure, causing the rate of microbial breakdown to slow. Warmth increases the speed of plant decay by roughly the same amount, regardless of the composition of the plant.

In most grassland ecosystems, natural damage from fire, detritivores that feed on decaying matter, termites, grazing mammals, and the physical movement of animals through the grass are the primary agents of breakdown and nutrient cycling, while bacteria and fungi play the main roles in further decomposition.

The chemical aspects of plant decomposition always involve the release of carbon dioxide. In fact, decomposition contributes over 90 percent of carbon dioxide released each year.

Food decomposition
The decomposition of food, either plant or animal, called spoilage in this context, is an important field of study within food science. Food decomposition can be slowed down by conservation. The spoilage of meat occurs, if the meat is untreated, in a matter of hours or days and results in the meat becoming unappetizing, poisonous or infectious. Spoilage is caused by the practically unavoidable infection and subsequent decomposition of meat by bacteria and fungi, which are borne by the animal itself, by the people handling the meat, and by their implements. Meat can be kept edible for a much longer time – though not indefinitely – if proper hygiene is observed during production and processing, and if appropriate food safety, food preservation and food storage procedures are applied.

Spoilage of food is attributed to contamination from microorganisms such as bacteria, molds and yeasts, along with natural decay of the food. These decomposition bacteria reproduce at rapid rates under conditions of moisture and preferred temperatures. When the proper conditions are lacking the bacteria may form spores which lurk until suitable conditions arise to continue reproduction. Decomposition rates and speed may differ or vary due to abiotic factors such as moisture level, temperature, and soil type. They also vary depending on the initial amount of breakdown caused by the prior consumers in the food chain. This means the form that organic matter is in, original plant or animal, partially eaten, or as faecal matter when the detritivore encounters it. The more broken down the matter, the faster the final decomposition.

Rate of decomposition
The rate of decomposition is governed by three sets of factors: the physical environment (temperature, moisture and soil properties), the quantity and quality of the dead material available to decomposers, and the nature of the microbial community itself.

Decomposition rates are low under very wet or very dry conditions. Decomposition rates are highest in damp, moist conditions with adequate levels of oxygen. Wet soils tend to become deficient in oxygen (this is especially true in wetlands), which slows microbial growth. In dry soils, decomposition slows as well, but bacteria continue to grow (albeit at a slower rate) even after soils become too dry to support plant growth. When the rains return and soils become wet, the osmotic gradient between the bacterial cells and the soil water causes the cells to gain water quickly. Under these conditions, many bacterial cells burst, releasing a pulse of nutrients. Decomposition rates also tend to be slower in acidic soils. Soils which are rich in clay minerals tend to have lower decomposition rates, and thus, higher levels of organic matter. The smaller particles of clay result in a larger surface area that can hold water. The higher the water content of a soil, the lower the oxygen content and consequently, the lower the rate of decomposition. Clay minerals also bind particles of organic material to their surface, making them less accessible to microbes. Soil disturbance like tilling increases decomposition by increasing the amount of oxygen in the soil and by exposing new organic matter to soil microbes.

The quality and quantity of the material available to decomposers is another major factor that influences the rate of decomposition. Substances like sugars and amino acids decompose readily and are considered labile. Cellulose and hemicellulose, which are broken down more slowly, are "moderately labile". Compounds which are more resistant to decay, like lignin or cutin, are considered recalcitrant. Litter with a higher proportion of labile compounds decomposes much more rapidly than does litter with a higher proportion of recalcitrant material. Consequently, dead animals decompose more rapidly than dead leaves, which themselves decompose more rapidly than fallen branches. As organic material in the soil ages, its quality decreases. The more labile compounds decompose quickly, leaving an increasing proportion of recalcitrant material called humus. Microbial cell walls also contain recalcitrant materials like chitin, and these also accumulate as the microbes die, further reducing the quality of older soil organic matter.

title: Decomposition