These numbers also arise in combinatorics, where gives the number of different combinations of b elements that can be chosen from an n-element set.

These meandering loops can be stretched easily in different directions, which gives knitting much more elasticity than woven fabrics ; depending on the yarn and knitting pattern, knitted garments can stretch as much as 500 %.

These two polymorphs differ by a " kinking " of bonds ; this change in structure gives β-quartz greater symmetry than α-quartz, and they are thus also called high quartz ( β ) and low quartz ( α ).

These and other sources such as A. T. Bryant gives us a more Zulu-centred picture.

These services, especially UDDI, have proved to be of far less interest, but an appreciation of them gives a more complete understanding of the expected role of SOAP compared to how web services have actually evolved.

These tails undulate periodically, which gives a Zora's head the unique semblance of a fish.

These political marriages were summed up in the following Latin elegiac couplet: Bella gerant aliī, tū fēlix Austria nūbe / Nam quae Mars aliīs, dat tibi regna Venus, " Let others wage war, but thou, O happy Austria, marry ; for those kingdoms which Mars gives to others, Venus gives to thee.

These orbitals are known as Landau levels, and at weak magnetic fields, their existence gives rise to many interesting " quantum oscillations " such as the Shubnikov – de Haas oscillations and the de Haas – van Alphen effect ( which is often used to map the Fermi surface of metals ).

These primary elements can only be named, they cannot be thought of as existing or not-he gives examples of words like ' itself, or that, each, alone or this ' ( 202a ).

These plugs will dissolve within a few days, so it gives the patient a chance to see if there is any improvement in comfort.

These legends belong to an age when higher ideas of law and of social duty were being established ; the implacable blood-feud of primitive society gives place to a fair trial, and in Athens, when the votes of the judges are evenly divided, mercy prevails.

These stories about the universe or universes that existed before the retcon are usually not canonical, unless the franchise-holder gives permission.

These messages nearly always include a rhyme which gives hints to the nature of the challenge and sometimes include props that may be useful for the upcoming challenge, allowing tribes and players to attempt to form a strategy prior to the challenge.

) However, this computer display gives 2160 as the year Archer's captaincy of Enterprise came to an end, which is contradicted by the 2161 date given in " These Are the Voyages ...".

These relations are a direct consequence of the basic properties of determinants: evaluation of the ( i, j ) entry of the matrix product on the left gives the expansion by column j of the determinant of the matrix obtained from M by replacing column i by a copy of column j, which is if and zero otherwise ; the matrix product on the right is similar, but for expansions by rows.

These trees are intended to be grown in small gardens, and their strong apical dominance combined with a dwarfing rootstock gives a compact narrow tree with very short fruiting side branches.

These three themes are repeated several times, which gives the section the character of a development.

These are insectivorous ground feeding birds, most of which have the red tail which gives the group its name ; " start " is the modern English reflex of Middle English stert, Old English steort, tail of an animal.

These programs are a landmark agreement which gives students a unique opportunity to earn two masters degrees in two years, one from each institution.

These birds are characterised by the mandibles crossing at their tips, which gives the group its English name.

" These policies generally include a tuition fee that is large enough that it gives parents “ a responsibility to cover some portion of their children ’ s higher education costs.

These structures, based on an external flow of molecules and energy, produce the components which, in turn, continue to maintain the organized bounded structure that gives rise to these components ( not unlike a wave propagating through a medium ).

These include one that tells her the direction of somebody channeling the One Power be it the male or female half, one that senses a man's ability to channel, one that stores a small amount of saidar, one that goes cool when a woman embraces saidar and one that gives her the ability to disrupt an illusion when in close proximity to it.

These signs are the inventories of unsold houses in some areas of the country and the moderate rise in vacancy rates for apartments ( 7.6% in September ).

These problems have been made even more difficult by the rise of conceptual art since the 1960s.

These developments gave rise to the Islamist and Islamic movement opposed to the increasing communist and Soviet influence over Afghanistan.

These elaborations and disputes gave rise to various schools in early Buddhism of Abhidhamma, and to the Mahayana traditions and schools of the prajnaparamita, Madhyamaka, buddha-nature and Yogacara.

These uniforms differentiated them from the Army and the Regular RIC, and gave rise to the force's nickname: Christopher O ' Sullivan wrote in the Limerick Echo on 25 March 1920 that, meeting a group of recruits on a train at Limerick Junction, the attire of one reminded him of the Scarteen Hunt, whose " Black and Tans " nickname derived from the coloration of its Kerry Beagles.

These early experimental designs later gave rise to the era of specialized supercomputers like those made by Cray Inc.

These changes also entailed the rise of labour movements.

These colorful, small-patterned printed fabrics gave rise to the use of the word calico to describe a cat coat color: " calico cat ".

These stresses may be sufficient to cause failure along existing fault planes, giving rise to intraplate earthquakes.

These rivers rise in the foothills of the Taurus Mountains along the Syro – Turkish border and add comparatively little water to the Euphrates.

These are defining characteristics of mercantilism in economics, which dominated most European thinking about political economy until the rise of classical economics.

* Linear algebraic groups ( or more generally affine group schemes ) — These are the analogues of Lie groups, but over more general fields than just R or C. Although linear algebraic groups have a classification that is very similar to that of Lie groups, and give rise to the same families of Lie algebras, their representations are rather different ( and much less well understood ).

These internal and external factors contributed to the rise of a Confederation national consciousness, in which the term fatherland ( patria ) began to take on meaning beyond an individual canton.

These ideas still retain some power, with faith healing and shrines still used in some places, although the rise of scientific medicine over the past millennium has altered or replaced mysticism in most cases.

These variants were consolidated during the Renaissance with the strength of Italian and the rise of humanism in the arts.

These obstacles weakened the movement and it was not until the rise of the Internet that it began to regain momentum.

These included rising populations, the growth of white settlement and slaving that dispossessed native peoples both at the Cape and in Portuguese Mozambique, and the rise of ambitious " new men.

These kilns were built up the side of a slope, such that a fire could be lit at the bottom and the heat would rise up into the kiln.

These tribes and kingdoms were soon overshadowed by the rise of the Gok-Turks in 555, the Uyghurs in 745 and the Yenisei Kirghizs in 840.

These " modernist " landmarks include the atonal ending of Arnold Schoenberg's Second String Quartet in 1908, the expressionist paintings of Wassily Kandinsky starting in 1903 and culminating with his first abstract painting and the founding of the Blue Rider group in Munich in 1911, and the rise of fauvism and the inventions of cubism from the studios of Henri Matisse, Pablo Picasso, Georges Braque and others in the years between 1900 and 1910.

These vents act as a compensator, thus counteracting the tendency of machine pistols to rise when fired in automatic mode.

These were steps that had different rise height or thread depth from the rest and would cause anyone running up the stairs to stumble or fall, so slowing down the attackers ' progress.

These pagan currents coincided with Romanticist interest in folklore and occultism, the widespread emergence of pagan themes in popular literature, and the rise of nationalism.

These ozone amounts fall over the course of the summer to their lowest amounts in October, and then rise again over the course of the winter.