Add holes in top, forming `` S '' for salt and `` P '' for pepper.

If Af is the change per unit volume in Gibbs function caused by the shear field at constant P and T, and **yr is the density of the fluid, then the total potential energy of the system above the reference height is Af.

Since Af and P divides Af for Af, we have Af.

It is clear that each vector in the range of Af is in Af for if **ya is in the range of Af, then Af and so Af because Af is divisible by the minimal polynomial P.

Thus Af is divisible by the minimal polynomial P of T, i.e., Af divides Af.

In the primary decomposition theorem, it is not necessary that the vector space V be finite dimensional, nor is it necessary for parts ( A ) and ( B ) that P be the minimal polynomial for T.

If T is a linear operator on an arbitrary vector space and if there is a monic polynomial P such that Af, then parts ( A ) and ( B ) of Theorem 12 are valid for T with the proof which we gave.

If D denotes the differentiation operator and P is the polynomial Af then V is the null space of the operator p (, ), because Af simply says Af.

Ten students act as managers for a high-school football team, and of these managers a proportion P are licensed drivers.

The word `` binomial '' means `` of two names '' or `` of two terms '', and both usages apply in our work: the first to the names of the two outcomes of a binomial trial, and the second to the terms P and Af that represent the probabilities of `` success '' and `` failure ''.

The constancy of P and the independence are the conditions most likely to give trouble in practice.

Obviously, very slight changes in P do not change the probabilities much, and a slight lack of independence may not make an appreciable difference.

We shall find a formula for the probability of exactly X successes for given values of P and N.

Therefore each binomial trial can be thought of as producing a value of a random variable associated with that trial and taking the values 0 and 1, with probabilities Q and P respectively.

On C, from the point P at Af to the point Q at Af, we construct the chord, and upon the chord as a side erect a square in such a way that as S approaches zero the square is inside C.

As S increases we consider the two free corner points of the square, Af and Af, adjacent to P and Q respectively.

We again consider a fixed point P at Af and a variable point Q at Af on C.

We erect a square with PQ as a side and with free corners Af and Af adjacent to P and Q respectively.

Now with P fixed at Af, Af-values occur when the corner Af crosses C, and are among the values of S such that Af.

Moreover, if Af and Af are two planes intersecting in a line l, tangent to Q at a point P, the two free intersections of the image curves Af and Af must coincide at P', the image of P, and at this point Af and Af must have a common tangent l'.

To do this we must first show that every line which meets **zg in a point P meets its image at P.

But if this is the case, then an arbitrary pencil of lines having a point, P, of **zg as vertex is transformed into a ruled surface of order Af having Af generators concurrent at P.

* Pavlik, B. M., Muick, P., Johnson, S., & Popper, M. ( 1991 ).

Basic's list of authors includes Christopher Andrew, Anthony Appiah, Isaac Asimov, Robert Axelrod, Susan R. Barry, Daniel Bell, John Bradshaw, Allan Brandt, Richard Brookhiser, Zbigniew Brzezinski, William F. Buckley, Stephen Carter, Iris Chang, George Chauncey, Stephanie Coontz, Dinesh D ’ Souza, Devra Davis, Richard Dawkins, Hernando de Soto, Jared Diamond, Michael Eric Dyson, Thomas B. Edsall, Richard Evans, Graham Farmelo, Niall Ferguson, Richard Feynman, Richard Florida, Robin Lane Fox, Sigmund Freud, Howard Gardner, Henry Louis Gates, Jr., Clifford Geertz, George Gilder, Barry Glassner, Robert Harms, Judith L. Herman, Christopher Hitchens, Douglas Hofstadter, Samuel P. Huntington, Jacqueline Jones, June Jordan, Leszek Kołakowski, Lawrence Krauss, Irving Kristol, George Lakoff, Edward Larson, Christopher Lasch, Mary Lefkowitz, Lawrence Lessig, Claude Levi-Strauss, Bernard Lewis, Robert Jay Lifton, Jeff Madrick, Nelson Mandela, Benoit Mandelbrot, Ernst Mayr, Walter A. McDougall, John McWhorter, Dana Milbank, Alice Miller, Walter Mosley, Charles Murray, Richard John Neuhaus, Donald Norman, Robert Nozick, Joseph S. Nye, Jr., James T. Patterson, Orlando Patterson, Jean Piaget, Steven Pinker, Karl Popper, Samantha Power, Diane Ravitch, Eugene Rogan, Juliet Schor, Brent Scowcroft, Anne-Marie Slaughter, Lee Smolin, Timothy Snyder, Thomas Sowell, Ian Stewart, Cass Sunstein, Beverly Daniel Tatum, Lester Thurow, Sherry Turkle, Archbishop Desmond Tutu, Michael Walzer, Elizabeth Warren, George Weigel, Steven Weinberg, Cornel West, Frank Wilczek, A. N.

As Karl P. Wentersdorf points out, A Shrew and The Shrew have " similar plot lines and parallel though differently named characters.

* Wentersdorf, Karl P. " The Authenticity of The Taming of the Shrew ", Shakespeare Quarterly, 5: 1 ( Spring, 1954 ), 11 – 32

## Shuker, Karl P. N. ( 1997 ), From Flying Toads To Snakes With Wings, LLewellyn

The collection includes: over 3, 000 textile items from the 1920s through the 1990s, including film and stage costumes as well as over a thousand items from Dietrich's personal wardrobe ; 15, 000 photographs, by Cecil Beaton, Horst P. Horst, George Hurrell, Lord Snowdon and Edward Steichen ; 300, 000 pages of documents, including correspondence with Burt Bacharach, Yul Brynner, Maurice Chevalier, Noël Coward, Jean Gabin, Ernest Hemingway, Karl Lagerfeld, Nancy and Ronald Reagan, Erich Maria Remarque, Josef von Sternberg, Orson Welles, and Billy Wilder ; as well as other items like film posters and sound recordings.

* R. Staehelin, " Hagenbach, Karl Rudolf ," in P. Schaff, J. J. Herzog, A. Hauck, eds., The New Schaff-Herzog Encyclopedia of Religious Knowledge, vol.

* Karl Leydecker, Marriage and divorce in the plays of Hermann Sudermann, Frankfurt am Main: P. Lang, 1996

Among his pupils the most eminent were Peter von Bohlen, C. P. W. Gramberg, A. G. Hoffmann, Hermann Hupfeld, Emil Rödiger, J. F. Tuch, Johann Karl Wilhelm Vatke and Theodor Benfey.

Dunkerley went on to identify a wide range of philosophical influences upon the thinking of the intellectuals in the cabinet, ranging from post-structuralism to the works of Marxist thinkers Karl Marx, René Zavaleta Mercado and E. P.

* Strunk, P .; Abels, J. Das große Abenteuer 2. Teil, Verlag Karl Wenzel, Marburg, 1986

His students include Samuel Adler, Leroy Anderson, Arthur Berger, Leonard Bernstein, Gordon Binkerd, Elliott Carter, John Davison, Irving Fine, John Harbison, Karl Kohn, Ellis B. Kohs, Gail Kubik, Billy Jim Layton, Noël Lee, Robert Middleton, Robert Moevs, Conlon Nancarrow, William P. Perry, Daniel Pinkham, Frederic Rzewski, Allen Sapp, Harold Shapero, and Claudio Spies.

* Karl P. Schmidt Memorial Herpetological Library: Named for Karl Patterson Schmidt.

* Karl Kraus in Sebstzeugnissen und Bilddokumenten by P. Schick ( 1965 )

* Pedagogics as a System Johann Karl Friedrich Rosenkranz, 1848, Translated 1872 by Anna C. Brackett, R. P.

Alumni also include current United States Supreme Court Justices Clarence Thomas, Samuel Alito and Sonia Sotomayor, as well as a number of former Justices, including Abe Fortas, Potter Stewart and Byron White ; several heads of state around the world, including Karl Carstens, the fifth President of Germany, and Jose P. Laurel, the president of the Republic of the Philippines ; and the current deans of eight of the ten top-ranked law schools in the United States: Yale, Harvard, Columbia, Chicago, NYU, Michigan, Virginia, and Penn.

LaVey's primary dedication was to Bernardino Nogara ( misprinted as " Logara "), Karl Haushofer, Grigori Rasputin, Basil Zaharoff, Alessandro Cagliostro, Barnabas, Ragnar Redbeard, William Mortensen, Hans Brick, Max Reinhardt, Orrin Klapp, Fritz Lang, Friedrich Nietzsche, W. C. Fields, P. T. Barnum, Hans Poelzig, Reginald Marsh, Wilhelm Reich, and Mark Twain.

Many European and North American linguists ( e. g., Einar Haugen, Gianrenzo P. Clivio, Hans Göbl, Helmut Lüdtke, George Bossong, Klaus Bochmann, Karl Gebhardt, and Guiu Sobiela Caanitz ) acknowledge Piedmontese as an independent language, though in Italy it is often still considered a dialect.

In all, the astronauts who trained at the planetarium were Buzz Aldrin, Joseph P. Allen, William A. Anders, Neil A. Armstrong, Charles A. Bassett II, Alan L. Bean, Frank Borman, Vance D. Brand, John S. Bull, M. Scott Carpenter, Gerald P. Carr, Eugene A. Cernan, Roger B. Chaffee, Philip K. Chapman, Michael Collins, Charles Conrad Jr., L. Gordon Cooper, R. Walter Cunningham, Charles M. Duke Jr., Donn F. Eisele, Anthony W. England, Joe H. Engle, Ronald E. Evans, Theodore C. Freeman, Edward G. Givens Jr., John H. Glenn Jr., Richard F. Gordon Jr., Virgil I. Grissom, Fred W. Haise Jr., Karl G. Henize, James B. Irwin, Joseph P. Kerwin, William B. Lenoir, Don L. Lind, John A. Llewellyn, Jack R. Lousma, James A. Lovell Jr., Thomas K. Mattingly Jr., Bruce McCandless II, James A. McDivitt, F. Curtis Michel, Edgar D. Mitchell, Story Musgrave, Brian T. O ’ Leary, Robert A. Parker, William R. Pogue, Stuart A. Roosa, Walter M. Schirra Jr., Russell L. Schweickart, David R. Scott, Elliot See, Alan B. Shepard Jr., Donald K. Slayton, Thomas P. Stafford, John L. Swigert Jr., William E. Thornton, Paul J. Weitz, Edward H. White, Clifton C. Williams Jr., Alfred M. Worden, and John W. Young.

Founded by Murray N. Rothbard, Karl Hess, George Resch, and Leonard P. Liggio, it was edited and largely written by Murray Rothbard.

This view, first proposed by F. W. Ghillany, afterward independently by Cornelis Petrus Tiele, and more fully by Stade, has been more completely worked out by Karl Budde ; and is accepted by H. Guthe, Gerrit Wildeboer, H. P. Smith, and G. A. Barton.

On October 9, 1957, Urry, Karl Kordesch, and P. A.