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.

Animism encompasses the beliefs that there is no separation between the spiritual and physical ( or material ) world, and souls or spirits exist, not only in humans, but also in all other animals, plants, rocks, geographic features such as mountains or rivers, or other entities of the natural environment.

Lightning is also caused by a violent separation, this time of clouds by winds to create a bright, fire-like flash.

In the 1960s, the ACLU continued its decades-long effort to enforce separation of church and state, and it also defended several anti-war activists during the Vietnam War who burnt draft cards or wore armbands.

Some also claim it to be the oldest subway tunnel in the world, as it was built by the cut and cover method under a city street, specifically for the purposes of improved public safety, attaining grade separation and enhanced railway operations.

Physical stresses may also cause the separation of surfaces.

Chemistry is also concerned with the interactions between atoms ( or groups of atoms ) and various forms of energy ( e. g. photochemical reactions, changes in phases of matter, separation of mixtures, properties of polymers, etc.

Gas chromatography ( GC ), also sometimes known as Gas-Liquid chromatography, ( GLC ), is a separation technique in which the mobile phase is a gas.

It is very close to magnitude 6. 1 12 Cam, also 650 light-years from Earth, but the two stars are not a true double star because of their separation.

This separation, by successive distillations, is also referred to as rectification.

Such industrial fractionating towers are also used in air separation, producing liquid oxygen, liquid nitrogen, and high purity argon.

The acute accent and diaeresis are also occasionally used, to denote stress and vowel separation respectively.

Modern languages also generally support modular programming, the separation between the interface of a library module and its implementation.

The green vortex generator s prompt the transition to turbulent flow and prevent back-flow also called flow separation from the high pressure region in the back.

" Financial economics ", at least formally, also considers investment under " certainty " ( Fisher separation theorem, " theory of investment value ", Modigliani-Miller theorem ) and hence also contributes to corporate finance theory.

Gel electrophoresis can also be used for separation of nanoparticles.

Gels suppress the thermal convection caused by application of the electric field, and can also act as a sieving medium, retarding the passage of molecules ; gels can also simply serve to maintain the finished separation, so that a post electrophoresis stain can be applied.

Other methods may also be used to visualize the separation of the mixture's components on the gel.

However, the SGML concept of generalized markup is based on elements ( nested annotated ranges with attributes ) rather than merely print effects, with also the separation of structure and processing ; HTML has been progressively moved in this direction with CSS.

This condition is the third separation axiom ( after T < sub > 0 </ sub > and T < sub > 1 </ sub >), which is why Hausdorff spaces are also called T < sub > 2 </ sub > spaces.

Hydro-metallurgical, and magnetic separation methods were also tried, but the main breakthrough came in 1902 when Delprat and Potter independently devised processes that would eventually be patented as the Delprat-Potter method.

In more technologically advanced areas, modern hashish is now made with more advanced technologies by compressing and / or refining or purifying a great quantity of trichomes harvested from Cannabis sativa plants using such processes as ice-water separation, also known as " bubble melt ", producing " bubble hash " or " water hash ".

These laws are also known as niddah, literally " separation ", or family purity.