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.

I had turned at the corner of the field and I had to look back to raise the plow and then to drop it again into the earth, and I was thinking of the boy and the water anyway, and when I looked again down the furrow, the snake was there.

The Assyrians and Hittites were then left in the field to battle over control over eastern and southern Anatolia and colonial territories in Syria.

Also, no finite field F is algebraically closed, because if a < sub > 1 </ sub >, a < sub > 2 </ sub >, …, a < sub > n </ sub > are the elements of F, then the polynomial ( x − a < sub > 1 </ sub >)( x − a < sub > 2 </ sub >) ··· ( x − a < sub > n </ sub >) + 1

If one quantizes a real scalar field, then one finds that there is only one kind of annihilation operator ; therefore, real scalar fields describe neutral bosons.

After the packet is identified as an AEP packet, the packet is then copied and a field in the packet is altered to create an AEP reply packet, and is then returned to the source node.

If a is algebraic over K, then K, the set of all polynomials in a with coefficients in K, is not only a ring but a field: an algebraic extension of K which has finite degree over K. In the special case where K = Q is the field of rational numbers, Q is an example of an algebraic number field.

because if M is any algebraically closed field containing K, then the elements of M which are algebraic over K form an algebraic closure of K.

Since then, there have been many refinements to increase the field of view, mass and position resolution, and data acquisition rate of the instrument.

The central dogma of molecular biology where genetic material is transcribed into RNA and then translated into protein, despite being an oversimplified picture of molecular biology, still provides a good starting point for understanding the field.

If X is a Banach space and K is the underlying field ( either the real or the complex numbers ), then K is itself a Banach space ( using the absolute value as norm ) and we can define the continuous dual space as X ′ = B ( X, K ), the space of continuous linear maps into K.

In Gregory ’ s day, history was not recognized as an independent field of study ; it was a branch of grammar or rhetoric, and historia ( defined as ‘ story ’) summed up the approach of the learned when they wrote what was, at that time, considered ‘ history .’ Gregory ’ s Dialogues Book Two, then, an authentic medieval hagiography cast as a conversation between the Pope and his deacon Peter, is designed to teach spiritual lessons.

Only then was it sent out to the Secret Intelligence Service ( MI6 ), the intelligence chiefs in the relevant ministries, and later on to high-level commanders in the field.

The Orioles of the IL won nine league championships, first in 1908, followed by a lengthy run from 1919 to 1925, and then dramatically in 1944, after they had lost their home field Oriole Park in a disastrous mid-season fire.

“ They may produce global epidemics and impair the health of future generations .” He then stated that, in recognition of these dangers, the United States had decided to destroy its entire stockpile of biological agents and confine its future biological research program to defensive measures, such as vaccines and field detectors.

: Squash would then be planted in the spaces between the patches of corn in the field.

The field may also be referred to as computational biology, and can be defined as, " conceptualizing biology in terms of molecules and then applying informatics techniques to understand and organize the information associated with these molecules, on a large scale.

Sandberg, then not known for his power, slugged a home run to left field against the Cardinals ' ace closer.

Sandberg then shocked the national audience by hitting a second home run, even farther into the left field bleachers, to tie the game again.

African slaves were then imported to work the plantations as field labor.

If the vector field represents the flow velocity of a moving fluid, then the curl is the circulation density of the fluid.

Both the extent to which this is true and the limits of the field of perceptual skill involved should be acknowledged.

`` It would be a disgrace, and, as I have already said to the people of Tennessee, if Hearst is nominated, we may as well pen a dispatch, and send it back from the field of battle: ' All is lost, including our honor ' ''.

Some historians have found his point of view not to their taste, others have complained that he makes the Tory tradition appear `` contemptible rather than intelligible '', while a sympathetic critic has remarked that the `` intricate interplay of social dynamics and political activity of which, at times, politicians are the ignorant marionettes is not a field for the exercise of his talents ''.

One's daily work becomes sacred, since it is performed in the field of influence of the moral law, dealing as it does with people as well as with matter and energy.

To obey the moral law is just ordinary common sense, applied to a neglected field.

Such is the field for exercising our reverence.

In the field of political values, it is certainly true that students are not radical, not rebels against their parents or their peers.

Although because of the important achievements of nineteenth century scholars in the field of textual criticism the advance is not so striking as it was in the case of archaeology and place-names, the editorial principles laid down by Stevenson in his great edition of Asser and in his Crawford Charters were a distinct improvement upon those of his predecessors and remain unimproved upon today.

For it is their catastrophic concept of the Anglo-Saxon invasions rather than Kemble's gradualist approach which dominates the field.

The national average is more than $4 and that figure is considered by experts in the mental health field to be too low.

This is one of the most constructive suggestions made in this critical field in years, and I certainly hope it sparks some action.

A small business is defined as one which is independently owned and operated and which is not dominant in its field.

The Office of Foreign and Domestic Commerce is also active in the field of international trade, assisting Rhode Island firms in developing and enlarging markets abroad.

We do not favor one field over another: we think that all inquiry, all scholarly and artistic creation, is good -- provided only that it contributes to a sense and understanding of the true ends of life, as all first-rate scholarship and artistic creation does.

Recently added is the Brown & Sharpe turret drilling machine which introduces the company to an entirely new field of tool development.

Under the auspices of the Women's Recreation Association, interclass competition is organized in badminton, basketball, field hockey, golf, tennis, and swimming.

Mossberg's latest contribution to the field is the Model 500 ( from $73.50 ) ; ;

It is usually helpful to make a sketch map in the field, showing the size and location of the features of interest and to take photographs at the site.

Your competition is now proportionately greater -- you are competing not only against manufacturers in the same field but also against a vast array of manufacturers of other appealing consumer products.

New to the field is a duplex type butyrate laminate in which the two sheets of the laminate are of different color.