Let Q be a nonsingular quadric surface bearing reguli Af and Af, and let **zg be a Af curve of order K on Q.

The class of the congruence is Af, since an arbitrary plane meets **zg in K points.

Since the complex of singular lines is of order K and since there is no complex of invariant lines, it follows from the formula Af that the order of the involution is Af.

Since C is rational, this correspondence has K coincidences, each of which implies a line of the pencil which meets its image.

For if such were the case, either the plane of the two lines would meet **zg in more than K points or, alternatively, the order of the image regulus of the pencil determined by the two lines would be too high.

The K factor, a term used to denote the rate of heat transmission through a material ( B.t.u./sq. ft. of material/hr./*0F./in. of thickness ) ranges from 0.24 to 0.28 for flexible urethane foams and from 0.12 to 0.16 for rigid urethane foams, depending upon the formulation, density, cell size, and nature of blowing agents used.

Table 1,, p. 394, shows a comparison of K factor ratings of a number of commercial insulating materials in common use, including two different types of rigid urethane foam.

The man most firmly at grips with the problem is the University of Minnesota's Physiologist Ancel Keys, 57, inventor of the wartime K ( for Keys ) ration and author of last year's bestselling Eat Well And Stay Well.

* in J. Barnes, M. Schofield, and R. R. K. Sorabji, eds .( 1975 ).

* Pfeiff, K. A., 1943.

The equilibrium constant K is an expression of the equilibrium concentrations of the molecules or the ions in solution.

The acid dissociation constant K < sub > a </ sub > is generally used in the context of acid-base reactions.

The stronger of two acids will have a higher K < sub > a </ sub > than the weaker acid ; the ratio of hydrogen ions to acid will be higher for the stronger acid as the stronger acid has a greater tendency to lose its proton.

Charles K. Smith argues that Swift ’ s rhetorical style persuades the reader to detest the speaker and pity the Irish.

To do this, Moseley measured the wavelengths of the innermost photon transitions ( K and L lines ) produced by the elements from aluminum ( Z = 13 ) to gold ( Z = 79 ) used as a series of movable anodic targets inside an x-ray tube.

Maj. Gen. Polk ignored the problems of Fort Henry and Fort Donelson when he took command and, after Johnston took command, at first refused to comply with Johnston's order to send an engineer, Lt. Joseph K. Dixon, to inspect the forts.

Paul Thompson is the W. K.

K. Paul, Trench, Trübner & co., ltd., 1898.

K. Paul, Trench, Trübner & co., ltd., 1898.

More significant still is the change in the use of sacrificial language: for Paul the Eucharist is a receiving of gifts from God, the Christian sacrifice is the offering of our bodies ( Romans 12 ).< Barrett, C. K.

Paul K. Davis wrote that " Caesar's victory took him to the pinnacle of power, effectively ending the Republic.

Historian Paul K. Davis wrote, " Having defeated Eudes, he turned to the Rhine to strengthen his northeastern borders-but in 725 was diverted south with the activity of the Muslims in Acquitane.

* Baack, Jessica K. and Paul V. Switzer.

* Paul, B. K et al.

In literature and journalism, Dartmouth has produced nine Pulitzer Prize winners: Thomas M. Burton, Richard Eberhart, Robert Frost, Paul Gigot, Jake Hooker, Nigel Jaquiss, Martin J. Sherwin, David K. Shipler, and Joseph Rago.

Antonín Dvořák's String Quintet in G major, Op. 77 and Wolfgang Amadeus Mozart's Serenade in G major, K. 525 (" Eine kleine Nachtmusik ") are the most popular pieces in this repertoire, along with works by Darius Milhaud, Luigi Boccherini ( 3 quintets ), Harold Shapero, and Paul Hindemith.

Economists who studied with Hayek at the LSE in the 1930s and the 1940s include Arthur Lewis, Ronald Coase, John Kenneth Galbraith, Abba Lerner, Nicholas Kaldor, George Shackle, Thomas Balogh, Vera Smith, L. K. Jha, Arthur Seldon, Paul Rosenstein-Rodan, and Oskar Lange.

Paul K. Benedict had joined the Berkeley team in 1938, and in 1942 he published his own classification, where he overtly excluded Vietnamese ( placing it in Mon – Khmer ), Miao – Yao, and Tai – Kadai (' Kadai ', placing it in Austro-Tai ).

* Miller, Paul Allen, Platter, Charles, and Gold, Barbara K. Sex and gender in medieval and Renaissance texts: the Latin tradition.

* Summers, Montague, The Werewolf London: K. Paul, Trench, Trubner, 1933.

* Feyerabend, Paul K. 2005.

* Davis, Paul K. ( 2001 ).

As Paul K. Davis writes, " William's victory placed a foreign ruler on the throne of England, introducing European rather than Scandinavian society onto the isolated island " in " the last successful invasion of England.

* Ogden Tweto and Paul K. Sims, Precambrian Ancestry of the Colorado Mineral Belt.

Writing in 1999, Paul K. Davis estimates the Umayyad forces at 80, 000 and the Franks at about 30, 000, while noting that modern historians have estimated the strength of the Umayyad army at Tours at between 20 – 80, 000.

* Davis, Paul K. ( 1999 ) " 100 Decisive Battles From Ancient Times to the Present " ISBN 0-19-514366-3

* < span id =" CITEREFR_Hansma1996 "> Hansma, Paul K. 1996.

Paul K. Davis writes, " Constantine ’ s victory gave him total control of the Western Roman Empire paving the way for Christianity to become the dominant religion for the Roman Empire and ultimately for Europe.

* Paul K. Davis Besieged: 100 Great Sieges from Jericho to Sarajevo ( Oxford: Oxford University Press, 2001 )

For example, Paul K. Davis wrote, " Mongol victory broke the southern Sung dynasty, leading to the establishment of the Yüan dynasty.

Beard and typified by Howard K. Beale ) argued that the Republican Party in the 1860s was a tool of corrupt business interests, and that Johnson stood for the people.

Reuben Breed ( Episcopal ), Michael Lodsin ( Baptist ), Brigadier Thomas Johnson ( Salvation Army ), Ludmila K. Foxlee ( YWCA ), Athena Marmaroff ( Woman's Christian Temperance Union ), Alexander Harkavy ( HIAS ), and Cecilia Greenstone and Cecilia Razovsky ( National Council of Jewish Women ).

In his 2004 study of the Lavender Scare, the historian David K. Johnson attacked the speculations about Hoover's homosexuality as relying on " the kind of tactics Hoover and the security program he oversaw perfected – guilt by association, rumor, and unverified gossip ”.

* Handbook of Organizational Performance, Thomas C. Mawhinney, William K. Redmon & Carl Merle Johnson.

As of 2007, Tennessee had 32 dedicated historical markers linked to Nathan Bedford Forrest, more than are dedicated to the three former Presidents associated with the state: Andrew Jackson, James K. Polk, and Andrew Johnson ( none of whom were born in Tennessee ).< ref >

* Johnson, M. K. ( 2001 ).

* Alberts, B., Johnson, A., Lewis, J., Raff, M., Roberts, K., Walter, P., ( 2002 ), Molecular Biology of the Cell, Fourth Edition, ( 428-429 ) Garland Science, 0-8153-4072-9 ( Web Edition, Free access )

Among past guest speakers are Andrew Lloyd Webber, J. K. Rowling, Vivienne Westwood, Ian McKellen, Kevin Warwick, Boris Johnson, Rowan Atkinson, Ralph Fiennes, Terry Wogan, King Constantine II of Greece, Katie Price, Zoe Wanamaker, Boris Berezovsky and Kit Hesketh-Harvey.

Even former president Jackson conceded that Johnson was " dead weight ", and threw his support to James K. Polk.

As historian David K. Johnson explains:

The modern organization was founded by Englishman Samuel Shenton in 1956 and was later led by Charles K. Johnson, who based the organization in his home in Lancaster, California.

Shenton died in 1971 and Charles K. Johnson, inheriting part of Shenton's library from Shenton's wife, established and became the president of the International Flat Earth Research Society of America and Covenant People's Church in California.

The group rose to about 2, 000 members during its peak under Charles K. Johnson.

" The society was further affected by a fire at the house of Charles K. Johnson which destroyed all of the records and contacts of members of the Flat Earth Society.

Charles K. Johnson himself died on March 19, 2001.

Every adult citizen of this small settlement signed the small petition ; E. K Dyer and his wife, William Johnson, Joseph Otis and his wife, Hiram Walker and his wife, Joseph Pease and R. H. Valentine.

Historic Kirtland structures, many of which are related to early Mormon history, include the NK Whitney home ( original structure ), Newel K. Whitney Store ( original structure ), a sawmill ( replica ), an ashery, the Sidney Rigdon home ( original structure ), and the John Johnson Inn.

Among notable natives of the township was Johnson K. Duncan, one of a handful of Northern-born Confederate generals in the American Civil War.

Over the years the inn hosted U. S. Presidents Andrew Jackson, Andrew Johnson, and James K. Polk.

A few of them were: Jedediah Knight, Joseph Nielson, Pleasant Minchey, Frank Foote, Charley and Ammon Foote, George Merrick, Oscar Beebe, Orson Davis, Heber C. K. Petty, Sr., Joseph Evans, Rasmus Johnson, Carl Magnus Olsen, Peter Nielson, Peter Hansen, Heber Broderick, Peter Christensen, George A. Whitlock, Peter Victor Bunderson, Rasmus Albrechtson, Christian A. Larsen, Lafe Allred, Hyrum Strong, Peter Jensen, Isaac Kimball, William George Petty, Niels Jensen, Wiley Payne Allred, Andrew C. Anderson, Stephen Williams and David Pratt.

Another strikingly different element of the group's second album was the inclusion of the track, " C is the Heavenly Option ," featuring the guest vocals of K Records founder Calvin Johnson, who released Heavenly's records in the USA.

Calvin Johnson was one of the founders of seminal indie-rock label K Records.

* Swain, M. & Johnson, R. K. ( 1997 ).

In R. K. Johnson & M. Swain ( Eds.