A choice function is a function f, defined on a collection X of nonempty sets, such that for every set s in X, f ( s ) is an element of s. With this concept, the axiom can be stated:

With Robert Morison ’ s 1672 Plantarum umbelilliferarum distribution nova it became the first group of plants for which a systematic study was published.

With curtailment of the MCC funding, the European Union may replace the US as Armenia ’ s chief source of foreign aid for the first time since independence.

With the signing of the Treaty of Alfred and Guthrum, an event most commonly held to have taken place around 880 when Guthrum ’ s people began settling East Anglia, Guthrum was neutralised as a threat.

With the critical and commercial success in the United States of such memoirs as Angela ’ s Ashes and The Color of Water, however, more and more people have been encouraged to try their hand at this genre.

With the ruse thus revealed, the main characters run for their lives, resulting in a madcap chase across the stage with both Miles and Senex pursuing all three " Philia " s ( Domina, Hysterium, and the actual Philia — all wearing identical white robes and veils ).

With a chain drive transmission, a chainring attached to a crank drives the chain, which in turn rotates the rear wheel via the rear sprocket ( s ) ( cassette or freewheel ).

" With Marlborough ’ s departure north, the French now transferred troops from the Moselle valley to reinforce Villeroi in Flanders, while Villars marched off to the Rhine.

With these reverses, the Dutch now refused to contemplate Marlborough ’ s ambitious march to Italy or, indeed, any plan that denuded their borders of the Duke and their army.

With a short lift in the mist, Cadogan soon discovered the smartly ordered lines of Villeroi ’ s advance guard some four miles ( 6 km ) off ; a galloper hastened back to warn Marlborough.

With assistance from Libya, Goukouni regained control of the capital and other urban centers by year ’ s end.

With a scanning speed of 1. 2 m / s, the playing time is 74 minutes, or 650 MB of data on a CD-ROM.

With Constantine ’ s death in 337, Constans and his two brothers, Constantine II and Constantius II divided the Roman world between themselves, after first deposing of virtually all of the relatives of their father who could possibly have a claim on the throne.

With rates above 75-120 frames / s no improvement in realism or smoothness is perceivable due to the way the eye and brain process images.

With an estimated 35, 000 dolmen, Korea alone accounts for nearly 40 % of the world ’ s total.

With good range ( up to 200 m indoors and 6 km using directional antennae outdoors ), dedicated spectrum, high interference immunity, open interoperability and data speeds of around 500 kbit / s, DECT appeared at one time to be a superior alternative to Wi-Fi.

With the advent of digital intermediate (" DI "), the physical negative does not necessarily need to be physically cut and hot spliced together ; rather the negative is optically scanned into computer ( s ) and a cut list is conformed by a DI editor.

With Stilicho ’ s fall, Olympius moved against all of his former father-in-law ’ s allies, killing and torturing key individuals and ordering the confiscation of the property of anyone who had borne any office while Stilicho was in command.

With the advent of second wave feminism, women ’ s roles were questioned in this " subversive, mind expanding genre.

With the reunification of Germany in 1990 the Marine took over the former East German Volksmarine (“ People ’ s Navy ”).

For positive values of a and b, the binomial theorem with n = 2 is the geometrically evident fact that a square of side can be cut into a square of side a, a square of side b, and two rectangles with sides a and b. With n = 3, the theorem states that a cube of side can be cut into a cube of side a, a cube of side b, three a × a × b rectangular boxes, and three a × b × b rectangular boxes.

With this stratagem, it is not necessary to check the value of i against the list length n: even if x was not in A to begin with, the loop will terminate when i =

With =

With the PV = nrt equation, you will want to use the second of the R values, because the first value is for finding energy ( hence the unit of Joules ) in another equation.

< http :// www. oxfordreference. com. ezproxy. library. yorku. ca / views / ENTRY. html? entry = t133. e215 & srn = 1 & ssid = 954689030 </ ref > With this in mind, the play incorporates these aspects to depict how Dionysus is present in ancient Greek life.

With the increased development of the area, many distinguished families moved away: in 1842 there were few of the wealthy Jews who had once settled in Hackney .< ref name = brithist >< cite > ' Hackney: Judaism ', A History of the County of Middlesex: Volume 10: Hackney ( 1995 ), pp. 145-48.

* alt = With the completion of the Mike O ' Callaghan – Pat Tillman Memorial Bridge, the proposed Interstate 11 would run through Kingman, replacing U. S. 93.

With a = b an elliptic paraboloid is a paraboloid of revolution: a surface obtained by revolving a parabola around its axis.

With 128 bits from MD5 plus 32 bits from the rolling checksum, and assuming maximum entropy in these bits, the probability of a hash collision with this combined checksum is 2 < sup >−( 128 + 32 )</ sup > = 2 < sup >− 160 </ sup >.

With =

With an ( average or constant ) branching factor of b, and a search depth of d plies, the maximum number of leaf node positions evaluated ( when the move ordering is pessimal ) is O ( b * b *...* b ) = O ( b < sup > d </ sup >) – the same as a simple minimax search.

As derived above, the ordinary generating function for the sequence of squares is With r = 1, α = 0, β = 3, A ( x ) = 0, and B ( x ) = x ( x + 1 ), we can verify that the squares grow as expected, like the squares:

With r = 1 / 4, α = 1, β = − 1 / 2, A ( x ) = 1 / 2, and B ( x ) = − 1 / 2, we can conclude that, for the Catalan numbers,

With each vertex we associate certain numerical values, namely the set of positive differences in the parameter T between the vertex and its corresponding forward corner points.

With " Tertiary " being discouraged as a formal time or rock unit by the International Commission on Stratigraphy, the K – T extinction event is now called the Cretaceous – Paleogene ( or K – Pg ) extinction event by many researchers.

* With T < sub > d </ sub > symmetry, it is a cantellated tetrahedron.

* von Bismark, Friedrich Wilhelm, Graf, Beamish, North Ludlow, ( translator ), On the Uses and Application of Cavalry in War from the Text of Bismark: With Practical Examples Selected from Antient and Modern History, T. & W. Boone, London, 1855

With the reduced state variables, i. e. V < sub > r </ sub >= V < sub > m </ sub >/ V < sub > c </ sub >, P < sub > r </ sub >= P / P < sub > c </ sub > and T < sub > r </ sub >= T / T < sub > c </ sub >, the reduced form of the Van der Waals equation can be formulated:

With this expression one can, in principle, determine the enthalpy if C < sub > p </ sub > and V are known as functions of p and T.

With his reputation as " Mr. T ", Tureaud attracted strange offers and was frequently approached with odd commissions, which included: assassination, tracking runaway teenagers, locating missing persons, and large firms asking him to collect past-due payments by force.

With the addition of an additional radio frequency pulse and additional manipulation of the magnetic gradients, a T < sub > 2 </ sub >- weighted sequence can be converted to a FLAIR sequence, in which free water is now dark, but edematous tissues remain bright.

With purely a health emphasis, T ' ai chi classes have become popular in hospitals, clinics, community and senior centers in the last twenty years or so, as baby boomers age and the art's reputation as a low stress training for seniors became better known.

With the rise of the realistic novel, the short story evolved in a parallel tradition, with some of its first distinctive examples in the tales of E. T. A. Hoffmann.

* Bolman, L. G., and Deal, T. E. Leading With Soul.

With the creation of the Federal Communications Commission in 1934, the government regulated the rates charged by AT & T.

With q as the electronic charge, is the wavelength of interest, h is Planck's constant, c is the speed of light, k is Boltzmann's constant, T is the temperature of the detector, is the zero-bias dynamic resistance area product ( often measured experimentally, but also expressible in noise level assumptions ), is the quantum efficiency of the device, and is the total flux of the source ( often a blackbody ) in photons / sec / cm².

With the advent of computers, many more values of n have been checked ; T. Oliveira e Silva is running a distributed computer search that has verified the conjecture for n ≤ 4 × 10 < sup > 18 </ sup > ( and double-checked up to 2 × 10 < sup > 17 </ sup >).

With guitarist Miko Weaver and long-time keyboardist Doctor Fink gone, Prince added bass player Sonny T., Tommy Barbarella on keyboards, and a brass section known as the Hornheads to go along with Levi Seacer ( taking over on guitar ), Rosie Gaines, Michael Bland, and the Game Boyz.

With Stankevich he also read Goethe, Schiller, and E. T. A.

With T. 38, two successive lost packets are needed to actually lose any data.

" With Becket in Murder in the Cathedral ", T. S. Eliot-The Man and His Work, Tate, Allen ( ed ), Delta, New York, 1966

With additional features added by AT & T, Telidon became the basis for the NAPLPS standard.

** With a Song in My Heart-Thomas T. Moulton

With the assistance and support of the Honorable Judge Robert E. Lewis ( 1927-1993 ), the city of Gadsden, and the Gadsden City Board of Education, the C. I. T. Y.

With AT & T, Huntsville and Madison are local calls ( Madison County only ), but Athens is long distance.