And here again we hear the same refrain mentioned above: `` the paramount goal of the United States set long ago was to guard the rights of the individual, ensure his development, enlarge his opportunity ''.

Without the good magazines, without their book reviews, their hospitality to European writers, without above all their awareness of literary standards, we might very well have had a generation of Krim's heroes -- Wolfes, Farrells, Dreisers, and I might add, Sandburgs and Frosts and MacLeishes in verse -- and then where would we be??

In the above development we have applied the thermodynamics of equilibrium ( referred to by some as thermostatics ) to the steady state.

if we take Af above, that will be large enough.

With the above results we can make the following remarks about the graph of F.

Simultaneously we should be underlining the interrelationships of technical progress in various fields, showing how agricultural training can be introduced into education, how health affects labor productivity, how small business can benefit the rural farm community, and, above all, how progress in each field relates to national progress.

It is said that another heaven is to the southward and upward of this one, and it is called Andlang ' Endlong ' but the third heaven is yet above that, and it is called Vídbláin ' Wide-blue ' and in that heaven we think this abode is.

Referring to the above sketch of Spartan history, we find Agesilaus shining most in its first and last period, as commencing and surrendering a glorious career in Asia, and as, in extreme age, maintaining his prostrate country.

As already pointed out above, we have to distinguish between medium-resolution spectrometers that are used for LS AAS and high-resolution spectrometers that are designed for CS AAS.

Using the above theorem it is easy to see that the original Borsuk Ulam statement is correct since if we take a map f: S < sup > n </ sup > → ℝ < sup > n </ sup > that does not equalize on any antipodes then we can construct a map g: S < sup > n </ sup > → S < sup > n-1 </ sup > by the formula

If we look at this situation from far above, so that we cannot see the supporters, we see the large balloon as a small object animated by erratic movement.

If we wish to implement this filter as a digital filter, we can apply the bilinear transform by substituting for the formula above ; after some reworking, we get the following filter representation:

If in the above we relax Banach space to normed space the analogous structure is called a normed algebra.

If we attempt to use the above formula to compute the derivative of f at zero, then we must evaluate 1 / g ′( f ( 0 )).

So the above product is always equal to the difference quotient, and to show that the derivative of at a exists and to determine its value, we need only show that the limit as x goes to a of the above product exists and determine its value.

By doing this to the formula above, we find:

Since the entries of the Jacobian matrix are partial derivatives, we may simplify the above formula to get:

I therefore believe it is realistic to assume a modest drop in the total value of home entertainment electronics to about $1.8 million, slightly below 1960, but above 1959.

If we assume the controller C, the plant P, and the sensor F are linear and time-invariant ( i. e., elements of their transfer function C ( s ), P ( s ), and F ( s ) do not depend on time ), the systems above can be analysed using the Laplace transform on the variables.

For the sake of simplicity, we might assume that the weights are normalized so that they sum up to 1 ( which can be easily done by dividing each weight by their sum ), thus allowing some terms in the above formulae to be omitted:

We assume that A is an m-by-n matrix over either the real numbers or the complex numbers, and we define the linear map f by f ( x ) = Ax as above.

Many people assume that Chomsky means UG * when he writes UG ( and in some cases he might actually mean UG *, though not in the passage quoted above ).

Some researchers, such as Philip Lieberman, Dennis Klatt, Brant de Boer and Kenneth Stevens using computer-modeling techniques have suggested that the species-specific human tongue allows the vocal tract ( the airway above the larynx ) to assume the shapes necessary to produce speech sounds that enhance the robustness of human speech.

As one main object of " probate " is to " prove " title to the real estate interests in the property held by a deceased person at the time of death, and the earliest recorded use the word in this capacity is 1463, it is reasonable to assume this tradition dates back to the death of the first owner of the ' allodial land ' referred in the etymology section above to die.

In the example above we see only upper case Roman characters, so if we assume this is the input then there are 26 possible letters for each position in the string.

Therefore, New Keynesian models assume instead that firms use their market power to maintain their prices above marginal cost, so that even if they fail to set prices optimally they will remain profitable.

Hence, in the sentence above, the reader would be able to make use of plausibility information in order to assume that " the evidence " is being examined instead of doing the examining.

Hamilton's equations above work well for classical mechanics, but not for quantum mechanics, since the differential equations discussed assume that one can specify the exact position and momentum of the particle simultaneously at any point in time.

As above, we assume a symmetric window function, which is therefore of the form where w and z are length-N / 2 vectors and R denotes reversal as before.

Note that the general pseudo-code above does not assume that the valid solutions are always leaves of the potential search tree.

The above formulas assume a spherical earth ; the formulas for the spheroid are of course more complicated, but not hopelessly so.

The formulae above for the margin of error assume that there is an infinitely large population and thus do not depend on the size of the population of interest.

For general surfaces this is no longer true, so for the classification above one needs to assume that the surface is second countable ( or metrizable ).

Many linear, unbranched homopolymers — in solution, or above their melting temperatures — assume ( approximate ) random coils.

Using the same example as above, assume the first investment opportunity is a government bond that will pay interest of 5 % per year and the principal and interest payments are guaranteed by the government.

It rests on a continuous and plain basement of granite, and only above the flat roofing of the chapels does the structure assume a varied outline.

The current President of the Italian Republic Giorgio Napolitano, elected on May 10, 2006, is also a former DS member ( as usual, although not mandatory, he renounced his party affiliation before being sworn in, because the office he was going to assume is considered to be above party politics ).

It also gives us a rough estimate that may be good enough for some purposes: if we want to start a store in Chicago that sells piano tuning equipment, and we calculate that we need 10, 000 potential customers to stay in business, we can reasonably assume that the above estimate is far enough below 10, 000 that we should consider a different business plan ( and, with a little more work, we could compute a rough upper bound on the number of piano tuners by considering the most extreme reasonable values that could appear in each of our assumptions ).

To see that the parity's eigenvalues are phase factors, we assume an eigenstate of the parity operation ( this is realized because the intrinsic parity is a property of a particle species ) and use the fact that two parity transformations leave the particle in the same state, thus the new wave function can differ by only a phase factor, i. e.: thus, since these are the only eigenstates satisfying the above equation.

Beckington is buried at Wells Cathedral and has an unusual monument there, his effigy is depicted twice ; one above the other in a two tier arrangement, the bottom effigy depicting his decaying corpse whilst unwrapped from its shroud, and the effigy above depicting him wearing his attire that one can assume would have been worn in his duties as bishop.

In ancient Rome until the end of the second century AD, two species of goatfish ( Mullus barbatus and Mullus surmuletus ) were highly sought-after and expensive, however not as a delicacy, but for aesthetic pleasure, since the fish assume a variety of colors and shades also during death ( see also above ).