We can describe this symmetry as the symmetry under the exchange of labels attached to the particles ( i. e., to the single-particle Hilbert spaces ).

: We refer to the relations which supposedly describe a certain physical situation, as a model.

We can describe this probabilistic state by eight nonnegative numbers A, B, C, D, E, F, G, H ( where A

We will describe an algorithm which takes inputs a and i and determines whether program a halts when given input i.

We can describe trie lookup ( and membership ) easily.

We often wish to describe the behavior of a function f ( x ), as either the argument x or the function value f ( x ) gets " very big " in some sense.

We perhaps need to revive the phrase " social fascism " to describe the modern British development of the corporate state and its bureaucratic attack on personal liberty.

We consider two such regular expressions equal if they describe the same language.

We will also describe the reasons and circumstances which led him to become an undisputed leader who commanded for many years an incredible and real crusade against the " coronéis ",-( the landlords ), in the most desolated and mystic region of Brazil, the northeast.

: I compare human life to a large Mansion of Many Apartments, two of which I can only describe, the doors of the rest being as yet shut upon me-The first we step into we call the infant or thoughtless Chamber, in which we remain as long as we do not think-We remain there a long while, and notwithstanding the doors of the second Chamber remain wide open, showing a bright appearance, we care not to hasten to it ; but are at length imperceptibly impelled by awakening of the thinking principle-within us-we no sooner get into the second Chamber, which I shall call the Chamber of Maiden-Thought, than we become intoxicated with the light and the atmosphere, we see nothing but pleasant wonders, and think of delaying there for ever in delight: However among the effects this breathing is father of is that tremendous one of sharpening one's vision into the nature and heart of Man — of convincing one's nerves that the World is full of misery and Heartbreak, Pain, sickness and oppression — whereby This Chamber of Maiden Thought becomes gradually darken'd and at the same time on all sides of it many doors are set open-but all dark-all leading to dark passages — We see not the balance of good and evil.

We can describe the transitive closure of R in more concrete terms as follows, intuitively constructing it step by step.

" We canot describe the structure of natural language in some other kind of system, for any system in which we could identify the selements and meanings of a given language would have to have already the same essential structure of words and sentences as the language to be described.

We can further describe Turing machines that will eventually halt and give an answer for any input in a language, but which may run forever for input strings which are not in the language.

We fancifully began to use the word daemon to describe background processes which worked tirelessly to perform system chores.

Frank Capra's Academy Award-winning movie series Why We Fight, the installments The Battle of China and Prelude to War describe the Tanaka Memorial as the document that was the Japanese plan for war with the United States.

We can describe this pattern by stating how many throws later the ball is thrown again.

We would like to be able to describe all of the basic types of I / O operations, e. g. write text to standard output, read text from standard input, read and write files, send data over networks, etc.

We know how false this is ; for soldiers and politicians can only describe such sacrifices as necessary when they are justified by successes in other fields which outweight the sacrifice.

We take it as a good sign that neither we nor any of our fans can describe our sound.

We also need to create features that describe the examples and are informative enough to allow a learning algorithm to discriminate keyphrases from non-keyphrases.

We next describe a general framework for defining a large class of these algebras.

We now describe the most common ones.

We can now describe the occupation of particles on the lattice as a ` ket ' of the form.

We first need to describe the Weyl group action centered at.

We have staved off a war and, since our behavior has involved all these elements, we can only keep adding to our ritual without daring to abandon any part of it, since we have not the slightest notion which parts are effective.

We shall return to these statements and deal with them more fully as the evidence for them accumulates.

We feel the quality of these powers initially as in some degree wholesome or threatening.

We feel uncomfortable at being bossed by a corporation or a union or a television set, but until we have some knowledge about these phenomena and what they are doing to us, we can hardly learn to control them.

We are learning how to do these things in some of the vast organized structures of modern society ; ;

We have far less to fear in the migrant family than we have in the migrant developer under these conditions.

We feel that The Detroit News is to be complimented upon arranging for articles on these subjects and we hope that it will continue to provide material along wholesome lines.

We should avoid these congestion points or, putting it another way, keep cars starting and ending on the East side of the river -- on the East side.

We are not given to lamentations, neither personally nor in these Reports.

We believe that these improved facilities will contribute income and effect savings which will fully justify the investment.

We have developed an ingenious method of interlocking these so that you can make the major part of your house in your own workshop, panel by panel, according to plan.

We may then dismiss the time difference between these courses and the usual four year course of the interior design student as not having serious bearing on the subject.

We have these positions, which compare directly: Af

We are reporting these investigations here briefly because of their relevancy to problems of the study of apparently simple exchange reactions of chlorine and because the results furnish some information on the activation energy for abstraction of chlorine atoms from carbon tetrachloride.

We stressed the reciprocal relation of these systems with respect to the autonomic-somatic downward discharge as well as regarding the hypothalamic-cortical discharge.

We now generalize these ideas for general binomial experiments.

We define these values as Af, and define g{t} in the same way for each T.

We now shall show that any involution with these characteristics is necessarily of the type we have just described.

We shall consider these in the inverse order of their presentation.

We shall not be able entirely to pass over these connections to the East as we consider Ripe Geometric pottery, the epic and the myth, and the religious evolution of early Greece ; ;

`` We must solve the problems which have forced these people to depend upon ADC for subsistence '', Martin said.

We are evidently trying hard to think of new ways to deal with the problem of fear these days.

We have already seen that odd numbers were considered as being Yang, while the even numbers were Yin, so that the eight outer numbers of the Lo Shu represented these two principles in balanced equilibrium around the axial center.

: We bring these amaranths, these white lilies,