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.

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.

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.

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.

Since a ruled surface of order N with N concurrent generators is necessarily a cone, it follows finally that every line through a point, P, of **zg meets its image at P, as asserted.

Now consider the transformation of the lines of a bundle with vertex, P, on **zg which is effected by the involution as a whole.

Moreover, in this involution there is a cone of invariant lines of order Af, namely the cone of secants of **zg which pass through P.

Af is the friction force between chip and knife surfaces, and P is the normal force acting on the face of the knife.

which takes as input a key K of bit length k, called the key size, and a bit string P of length n, called the block size, and returns a string C of n bits.

A Bézier curve is defined by a set of control points P < sub > 0 </ sub > through P < sub > n </ sub >, where n is called its order ( n

The points P < sub > i </ sub > are called control points for the Bézier curve.

The polygon formed by connecting the Bézier points with lines, starting with P < sub > 0 </ sub > and finishing with P < sub > n </ sub >, is called the Bézier polygon ( or control polygon ).

The general class of questions for which some algorithm can provide an answer in polynomial time is called " class P " or just " P ".

According to it, Central Asia includes Mongolia, Tibet, northeast Iran ( Golestan, North Khorasan and Razavi provinces ), Afghanistan, Northern Areas, Khyber Pakhtunkhwa ( also called N. W. F. P.

Lépicié and P .- L. Sugurue ), which brought Chardin income in the form of " what would now be called royalties ".

" Either P or Q " is a disjunction ; P and Q are called the statement's disjuncts.

" Elaine Donnelly called such efforts " a big P. R.

Now we define a new property G: if x is an object in some possible world, then G ( x ) is true if and only if P ( x ) is true in that same world for all positive properties P. G is called the " God-like " property.

Contemporary French writer Michel Houellebecq wrote a literary biography of Lovecraft called H. P. Lovecraft: Against the World, Against Life.

For example, P. Schuyler Miller called Arthur C. Clarke's 1961 novel A Fall of Moondust hard SF, and the designation remains valid even though a crucial plot element, the existence of deep pockets of " moondust " in lunar craters, is now known to be incorrect.

Additionally, they were able to plasmolyze the bacteriophages so that they went into osmotic shock, which effectively created a solution containing most of the < sup > 32 </ sup > P and a heavier solution containing structures called “ ghosts ” which contained the < sup > 35 </ sup > S and the protein coat of the virus.

In Rap School, rapper / actor Ice-T teaches eight teens from York Preparatory School in New York called the " York Prep Crew " (" Y. P.

Let us define a linear operator P, called the exchange operator.

A membrane, or brane, is a multidimensional object, usually called a P-brane, with P referring to the number of dimensions in which it exists.

Devices that function only as transit routers are similarly called P ( Provider ) routers.

Despite his influence in the financial world ( at least one source called him the most powerful American financier since J. P. Morgan ), Milken was an intensely private man who shunned publicity.

: Example: Stream ciphers encrypt plaintext P to ciphertext C by deriving a key stream K from a given key and IV and computing C as C

Let further P < sub > Alice </ sub > denote the first plaintext block of Alice's message, let E denote encryption, and let P < sub > Eve </ sub > be Eve's guess for the first plaintext block.

Now, if Eve can determine the initialization vector IV < sub > 2 </ sub > of the next message she will be able to test her guess by forwarding a plaintext message to Alice starting with ( IV < sub > 2 </ sub > xor IV < sub > 1 </ sub > xor P < sub > Eve </ sub >)); if her guess was correct this plaintext block will get encrypted to C < sub > Alice </ sub > by Alice.

Assume the attacker knows a set of plaintext P and ciphertext C that satisfies the following:

that is a plaintext P is encrypted multiple times using a repetition of the same block cipher

The following steps describe how to handle the last two blocks of the plaintext, called P < sub > n − 1 </ sub > and P < sub > n </ sub >, where the length of P < sub > n − 1 </ sub > equals the block size of the cipher in bits, B, the length of the last block, P < sub > n </ sub >, is M bits, and K is the key that is in use.

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

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.

* 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 ).

In 1935, the new film studio Photo Chemical Laboratories, known as P. C. L.

The 25-year-old Kurosawa joined P. C. L.

Quantum states of a particle and an antiparticle can be interchanged by applying the charge conjugation ( C ), parity ( P ), and time reversal ( T ) operators.

* Hanson, R. P. C., The Search for the Christian Doctrine of God: The Arian Controversy, 318-381 ( T .& T.

Washington, D. C .: U. S. G. P. O., 1999.

* Blitz, a robot dog from the cartoon, C. O. P. S.

of the C. P. S. S., and the Soviet Government.

* Rosenfeld, C. P.

This is one of the reasons C. P. E.

Many consider this breakthrough to have been made by C. P. E.

Indeed, C. P. E.

* P. M. Chaikin and T. C. Lubensky ( 2000 ).

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

The 21 consonant letters in the English alphabet are B, C, D, F, G, H, J, K, L, M, N, P, Q, R, S, T, V, X, Z, and usually W and Y: The letter Y stands for the consonant in " yoke ", the vowel in " myth " and the vowel in " funny ", and " yummy " for both consonant and vowel, for examples ; W almost always represents a consonant except in rare words ( mostly loanwords from Welsh ) like " crwth " " cwm ".

* Brian D ' Arcy ( 1945 – ), C. P.

John C. Hammond and Henry P. Field, both Amherst graduates, introduced Coolidge to the law practice in the county seat of Hampshire County.

* Kent, J. P. C., Hirmer, M. & Hirmer, A. Roman Coins ( Thames and Hudson, 1978 )