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.

By Theorem 10, D is a diagonalizable operator which we shall call the diagonalizable part of T.

The diagonalizable operator D and the nilpotent operator N are uniquely determined by ( A ) and ( B ) and each of them is a polynomial in T.

We have just observed that we can write Af where D is diagonalizable and N is nilpotent, and where D and N not only commute but are polynomials in T.

Then every linear operator T in V can be written as the sum of a diagonalizable operator D and a nilpotent operator N which commute.

These operators D and N are unique and each is a polynomial in T.

The Iliad with an English Translation by A. T. Murray, Ph. D. in two volumes.

Res Gestae ( Rerum gestarum Libri XXXI ) was originally in thirty-one books, but the first thirteen are lost ( modern historian T. D.

* Orsi, A. H., T. Whitworth and W. D.

In the 20th century excavations were carried out at Carchemish, Turkey, between 1911 and 1914 and in 1920 by D. G. Hogarth and Leonard Woolley, the latter assisted by T. E. Lawrence.

* Powell J., Blakeley D. W., Powell, T. Biographical Dictionary of Literary Influences: The Nineteenth Century, 1800 – 1914.

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 ".

As a special case, the three naturally occurring isotopes of the element hydrogen are often specified as H for < sup > 1 </ sup > H ( protium ), D for < sup > 2 </ sup > H ( deuterium ), and T for < sup > 3 </ sup > H ( tritium ).

The Odyssey with an English Translation by A. T. Murray, PH. D. in two volumes, Cambridge, MA., Harvard University Press ; London, William Heinemann, Ltd. 1919.

* T. Liu, D. Raabe and S. Zaefferer " A 3D tomographic EBSD analysis of a CVD diamond thin film " Sci.

* Vessey, D. W. T. C.

Johannesburg: Witwatersrand University Press, 1961 ( with D. T. Cole ).

Saint Catherine of Siena, T. O. S. D, ( 25 March 1347 in Siena – 29 April 1380 in Rome ) was a tertiary of the Dominican Order, and a Scholastic philosopher and theologian.

* Otis, Alison T., William D. Honey, Thomas C. Hogg, and Kimberly K. Lakin The Forest Service and The Civilian Conservation Corps: 1933-42 ( United States Forest Service FS-395, August 1986 ) online

* Bell, C. D., E. J. Edwards, S. T. Kim, & M. J. Donoghue.

In this case, we might compute T = A *( B * D ) only once and simply blend T * C to produce F, a single operation.

), Doctor of Physical Therapy ( D. P. T.

Some important contributors to the field of experimental designs are C. S. Peirce, R. A. Fisher, F. Yates, C. R. Rao, R. C. Bose, J. N. Srivastava, Shrikhande S. S., D. Raghavarao, W. G. Cochran, O. Kempthorne, W. T. Federer, V. V. Fedorov, A. S. Hedayat, J.

Though a layman, he received the degree of S. T. D.