Because not all people who have accidents can find solvent defendants from which to recover damages in the courts, P. S. Atiyah has called the situation a " damages lottery.

* The Atiyah algebroid of a principal G-bundle P over a manifold M is a Lie algebroid with short exact sequence:

: The space of sections of the Atiyah algebroid is the Lie algebra of G-invariant vector fields on P.

Some of the mathematicians who were involved in the selection and presentation of the seven problems were Atiyah, Bombieri, Connes, Deligne, Fefferman, Milnor, Mumford, Wiles, and Witten.

* M. F. Atiyah, R. Bott, L. Garding, " Lacunas for hyperbolic differential operators with constant coefficients I ", Acta Math., 124 ( 1970 ), 109 – 189.

Atiyah, R. Bott, and L. Garding, " Lacunas for hyperbolic differential operators with constant coefficients II ", Acta Math., 131 ( 1973 ), 145 – 206.

Sir Michael Atiyah said of Witten, " Although he is definitely a physicist, his command of mathematics is rivaled by few mathematicians ... Time and again he has surprised the mathematical community by a brilliant application of physical insight leading to new and deep mathematical theorems ... he has made a profound impact on contemporary mathematics.

* M. F. Atiyah ; I. G. Macdonald: Introduction to Commutative Algebra.

An extremely far-reaching generalization of all the above-mentioned theorems is the Atiyah – Singer index theorem.

Rabbi Mordecai Atiyah was a leading advocate of this idea.

Other famous scholars who have worked at the institute include Alan Turing, Paul Dirac, Edward Witten, J. Robert Oppenheimer, Freeman Dyson, Julian Bigelow, Erwin Panofsky, Homer A. Thompson, George Kennan, Hermann Weyl, Stephen Smale, Atle Selberg, Noam Chomsky, Clifford Geertz, Paul Erdős, Michael Atiyah, Erich Auerbach, Nima Arkani-Hamed, Michael Walzer, Andrew Wiles, Stephen Wolfram, and Eric Maskin.

Michael Atiyah, in particular, has commented that whenever he examined a mathematical topic, he found that Weyl had preceded him ( The Mathematical Intelligencer ( 1984 ), vol. 6 no. 1 ).

* Michael F. Atiyah, K-Theory, ( Notes taken by D. W. Anderson, Fall 1964 ), published in 1967, W. A.

In 1997 he was appointed to the Savilian Chair of Geometry at Oxford University, a position previously held by his doctoral supervisor ( and later research collaborator ) Sir Michael Atiyah.

* conjectures about the Atiyah – Singer index theorem ;

* Atiyah, M. F., and I. G. MacDonald, Introduction to Commutative Algebra, Perseus Books, 1969, ISBN 0-201-00361-9

* Atiyah, M. F. and Macdonald, I. G., Introduction to Commutative Algebra, Perseus Books, 1969, ISBN 0-201-00361-9

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.

The photocathode sensitivities S, phosphor efficiencies P, and anode potentials V of the individual stages shall be distinguished by means of subscripts 1, and 2, in the text, where required.

The luminous gain of a single stage with Af ( flux gain ) is, to a first approximation, given by the product of the photocathode sensitivity S ( amp / lumen ), the anode potential V ( volts ), and the phosphor conversion efficiency P ( lumen/watt ).

Thus, if what is at issue is whether `` All S is P '', it is indifferent whether `` Some S is not P '' or `` No S is P '', since in either case the judgment in question is false.

* " Animal " ( Fuck Like a Beast )" by W. A. S. P.

* W. S. Judd, C. S. Campbell, E. A. Kellogg, P. F. Stevens, M. J. Donoghue, 2002.

* W. S. Judd, C. S. Campbell, E. A. Kellogg, P. F. Stevens, M. J. Donoghue ( 2002 ).

Carnegie sold it in 1901 for $ 480 million to J. P. Morgan, who created U. S. Steel.

* A. S. P.

Additional peripheral cartridge-holders by companies such as P. R. E. S.

Because the WD1770 is capable of single density mode and uses the same IBM360 derived floppy disc format as the Intel 8271 found in the BBC Micro, it was also possible to run a DFS filing system with an alternate ROM, such as the P. R. E. S AP4 interface.

Alternative WD1770 / DFS Interfaces such as the P. R. E. S AP4 left & PAGE at E00h.