Including replication in a DOE allows separation of experimental error into its components: lack of fit and random ( pure ) error.

Mordell's theorem had an ad hoc proof ; Weil began the separation of the infinite descent argument into two types of structural approach, by means of height functions for sizing rational points, and by means of Galois cohomology, which was not to be clearly named as that for two more decades.

The separation sciences follow a similar time line of development and also become increasingly transformed into high performance instruments.

They were first divided into separate books by the early Christian scholar Origen, in the 3rd century AD, and the separation became entrenched in the 5th century AD when it was followed by Jerome in his Latin translation of the Bible.

It was not until the Middle Ages that the separation was introduced into Jewish Bibles.

The first step in the evolution of the Breviary was the separation of the Psalter into a choir-book.

Printed calico was imported into the United States from Lancashire in the 1780s, and here a linguistic separation occurred, while Europe maintained the word calico for the fabric, in the States it was used to refer to the printed design.

The column improves separation by providing a larger surface area for the vapor and condensate to come into contact.

The denaturation of nucleic acids such as DNA due to high temperatures is the separation of a double strand into two single strands, which occurs when the hydrogen bonds between the strands are broken.

It is probable that these viruses evolved before the separation of eukaryoyes into the extant crown groups.

The earliest doctoral degrees ( theology, law, and medicine ) reflected the historical separation of all university study into these three fields.

The Spanish founded modern day Quito and Guayaquil as part of the political-administration era which lasted until the war of Independence, the rise of Gran Colombia and Simón Bolívar to the final separation of his vision into what is known today as the Republic of Ecuador.

Excessive volatility often results in the development of pressure within rounds of ammunition and separation of mixtures into their constituents.

The division of power into separate branches of government is central to the idea of the separation of powers.

In mathematics, the four color theorem, or the four color map theorem states that, given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color.

The intuitive statement of the four color theorem, i. e. ' that given any separation of a plane into contiguous regions, called a map, the regions can be colored using at most four colors so that no two adjacent regions have the same color ', needs to be interpreted appropriately to be correct.

This division of coding theory into compression and transmission is justified by the information transmission theorems, or source – channel separation theorems that justify the use of bits as the universal currency for information in many contexts.

The separation of the term Jurassic into three sections goes back to Leopold von Buch (* 1774, † 1853 ).

GAME, a major computer game and hardware retailer also operate a cashback card scheme, which was merged with Electronics Boutique's programme following the separation of their northern European stores into the hands of GAME.

Meiosis generates genetic diversity in two ways: ( 1 ) independent alignment and subsequent separation of homologous chromosome pairs during the first meiotic division allows a random and independent selection of each chromosome segregates into each gamete ; and ( 2 ) physical exchange of homologous chromosomal regions by homologous recombination during prophase I results in new combinations of DNA within chromosomes.

Land reclamation in the 17th century made Macau into a peninsula, and a barrier gate was built to mark the separation between the peninsula and the mainland.

Some modern scholars have suggested that Manichaean ways of thinking influenced the development of some of Augustine's ideas, such as the nature of good and evil, the idea of hell, the separation of groups into elect, hearers, and sinners, and the hostility to the flesh and sexual activity.

These changes can result in tissue elongation, thinning, folding or separation of one tissue into distinct layers.

* 1791 – A Constitutional Act is introduced by the British House of Commons in London which envisages the separation of Canada into Lower Canada ( Quebec ) and Upper Canada ( Ontario ).

It is enough to deform the nucleus into a double-lobed " drop ," to the point that nuclear fragments exceed the distances at which the nuclear force can hold two groups of charged nucleons together, and when this happens, the two fragments complete their separation and then are driven further apart by their mutually repulsive charges, in a process which becomes irreversible with greater and greater distance.

Selective permeability is essential for effective separation of a cell or organelle from its surroundings.

It lays out ten ideals: Free inquiry as opposed to censorship and imposition of belief ; separation of church and state ; the ideal of freedom from religious control and from jingoistic government control ; ethics based on critical intelligence rather than that deduced from religious belief ; moral education ; religious skepticism ; reason ; a belief in science and technology as the best way of understanding the world ; evolution ; and education as the essential method of building humane, free, and democratic societies.

Barrowe, on the other hand, regarded the whole established church order as polluted by the relics of Roman Catholicism, and insisted on separation as essential to pure worship and discipline.

Although the producers believed the plot development was essential, the fan response to Rhoda and Joe's separation was overwhelmingly negative and hostile.

As Rubel Shelly put it, " he motive behind all restoration movements is to tear down the walls of separation by a return to the practice of the original, essential and universal features of the Christian religion.

Subsequent to this act, Oneness believers hold that separation from the world in both practical and moral areas is essential to spiritual life.

Electroosmotic flow is an essential component in chemical separation techniques, notably capillary electrophoresis.

Schmitt also posits an essential division between the liberal doctrine of separation of powers and what he holds to be the nature of democracy itself, the identity of the rulers and the ruled.

As trains needed to be moving at some speed to pick-up enough water, a suitable separation between trough locations and commercial stopping points is essential.

Radar speed guns do not work reliably in traffic, and significant vehicle separation is essential for proper operation when used for speed monitoring.

The essential feature of this classification is that the first split in the family resulted in the separation of all dialects of Japanese from all varieties of Ryukyuan.

The essential part of this process was that the church was becoming more and more gentile, and less and less Jewish, but the separation manifested itself in different ways in each local community where Jews and Christians dwelt together.

These four proteins are essential in yeast, and a mutation in any of them will produce premature sister chromatid separation.

He regarded the whole established church order as polluted by the relics of Roman Catholicism, and insisted on separation as essential to pure worship and discipline.

Its use is founded on Title 10, United States Code, Section 12305 ( a ) which states in part: "... the President may suspend any provision of law relating to promotion, retirement, or separation applicable to any member of the armed forces who the President determines is essential to the national security of the United States " and Paragraph 10 ( c ) of DD Form 4 / 1 ( The Armed Forces Enlistment Contract ) which states: " In the event of war, my enlistment in the Armed Forces continues until six ( 6 ) months after the war ends, unless the enlistment is ended sooner by the President of the United States.

Although these rules are specific to the separation of Galerina from certain Psilocybe, since mixed patches of Psilocybe and Galerina can occur, it is essential to be sure of the identity of each sporocarp collected.

The render safe procedure ( RSP ) is the portion of the explosive ordnance disposal procedures involving the application of special explosive ordnance disposal procedures, methods and tools to provide the interruption of functions or separation of essential components of unexploded ordnance ( including improvised explosive devices ) to prevent an unacceptable detonation.

Tracking is regarded as an essential life saving skill for all freefall skydivers engaging in relative work with others, allowing the jumpers to gain horizontal separation after building a formation and before opening their parachutes.

Without this foresight, the development of the B-17 ’ s and B-24 ’ s, essential to eventual separation of the Air Force from the Army, would not have taken place.

Protective separation is essential as the transmitter unit would seriously damage the very sensitive low ( µV ) micro-voltage, front-end receiver amplifier unit at the antenna.

Its essential features, which officially remained secret for nearly three decades, are: 1 ) separation of stages into a triggering " primary " explosive and a much more powerful " secondary " explosive, 2 ) compression of the secondary by X-rays coming from nuclear fission in the primary, a process called the " radiation implosion " of the secondary, and 3 ) heating of the secondary, after cold compression, by a second fission explosion inside the secondary.

This is their essential function when incorporated into a membrane electrode assembly ( MEA ) of a proton exchange membrane fuel cell or of a proton exchange membrane electrolyser: separation of reactants and transport of protons.

This concept of separation is essential to Borgmann's notion of availability and to Heidegger's concept of technology.

Madison viewed the separation of power as essential because without it only one power would rule the country, which could easily lead to abusive ruling.