Help


[permalink] [id link]
+
Page "Religion and mythology" ¶ 29
from Wikipedia
Edit
Promote Demote Fragment Fix

Some Related Sentences

. and T
Directly across from the Gardens I found a bus stop sign for T 4 and rode it down to the Bosphorus, with the sports center on my left just before I reached the water and the entrance to Dolmabahce Palace immediately after that.
He also bought a huge square of pegboard for hanging up his tools, and lumber for his workbench, sandpaper and glue and assorted nails, levels and T squares and plumb lines and several gadgets that he had no idea how to use or what they were for.
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.
The lines are asymmetric and over the range of field Af gauss and temperature Af the asymmetry increases with increasing Af and decreasing T.
We are trying to study a linear operator T on the finite-dimensional space V, by decomposing T into a direct sum of operators which are in some sense elementary.
We can do this through the characteristic values and vectors of T in certain special cases, i.e., when the minimal polynomial for T factors over the scalar field F into a product of distinct monic polynomials of degree 1.
If we try to study T using characteristic values, we are confronted with two problems.
Second, even if the characteristic polynomial factors completely over F into a product of polynomials of degree 1, there may not be enough characteristic vectors for T to span the space V.
This is clearly a deficiency in T.
The second situation is illustrated by the operator T on Af ( F any field ) represented in the standard basis by Af.
The characteristic polynomial for A is Af and this is plainly also the minimal polynomial for A ( or for T ).
Thus T is not diagonalizable.
If ( remember this is an assumption ) the minimal polynomial for T decomposes Af where Af are distinct elements of F, then we shall show that the space V is the direct sum of the null spaces of Af.
Let T be a linear operator on the finite-dimensional vector space V over the field F.
Let p be the minimal polynomial for T, Af, where the Af, are distinct irreducible monic polynomials over F and the Af are positive integers.
( C ) if Af is the operator induced on Af by T, then the minimal polynomial for Af is Af.
It is certainly clear that the subspaces Af are invariant under T.
If Af is the operator induced on Af by T, then evidently Af, because by definition Af is 0 on the subspace Af.
Thus Af is divisible by the minimal polynomial P of T, i.e., Af divides Af.
If Af are the projections associated with the primary decomposition of T, then each Af is a polynomial in T, and accordingly if a linear operator U commutes with T then U commutes with each of the Af, i.e., each subspace Af is invariant under U.
In the notation of the proof of Theorem 12, let us take a look at the special case in which the minimal polynomial for T is a product of first-degree polynomials, i.e., the case in which each Af is of the form Af.

. and Robinson
and Robinson Roy, who had gone down this line ten minutes before to set a new depth record for the free dive, was already back on the surface.
The German courteously indicated that Robinson should mount first.
Robinson clambered heavily into the boat, sat down, and stripped off his triple-tank assembly.
`` That's right '', Robinson said.
`` Nobody's giving anything up '', Robinson said.
Now it did not occur to him even to wonder whether it was wise for Robinson to dive again: Rob was his boy, the kid he had rescued from the streets, the object of his pride.
Now, in that same cabin, Robinson fell to his knees beside a bunk.
`` You know I know it '', Robinson answered warily.
It so happened that sports writer Arthur Robinson got out of the hospital that morning after promising his doctor that he be back in an hour or two to continue his convalescence.
Arthur Robinson traveled with the baseball clubs as staff correspondent for the American.
Robinson asked Herford to escort him to the club's lavatory before they sat down for a highball and a game of cards.
Finally he learned through the grapevine that the culprit might be one James W. Robinson in Pope County.
Without further inquiry, Pike jumped to the conclusion that Robinson was guilty, and, following the honorable route that would eventually lead to the dueling ground, sent a message to Robinson through his friends, demanding that he either confirm or deny his complicity.
Robinson did neither.
To Pike, silence was tantamount to an admission of guilt, and he determined to get Robinson onto the dueling ground at all costs.
On April 11th he wrote an open letter in The Advocate, making it known `` to the world that Jas. W. Robinson is by his own admission a base liar and a slanderer ''.
If Robinson was a liar and a slanderer, he was also a very canny gentleman, for nothing that Pike could do would pry so much as a single word out of him.
Preoccupied with his own defense and his attempts to get Robinson to fight, Pike lessened his attacks on Woodruff, and finally stopped them altogether.
And Pike never did find out if Robinson was really responsible for the `` Vale '' letter.
Brooks Robinson is great, and it is conceivable that he'll do even better in 1961 than he did in 1960.
At least five years ago, Tom Robinson of Marlin made up an over/under double rifle for me in this caliber, using the now defunct Model 90 action in 20-gauge size.
Three were doubles, Brooks Robinson getting a pair and Marv Breeding one.
In the ninth, Robinson led off with his second double of the night, a blast off the fence 375 feet deep into left.
The Orioles got a run in the first inning when Breeding, along with Robinson, the two Birds who got a pair of hits, doubled to right center, moved to third on Russ Snyder's single to right and crossed on Kunkel's wild pitch into the dirt in front of the plate.

0.062 seconds.