( The proof is actually completed in Volume II, 1st edition, page 86, accompanied by the comment, " The above proposition is occasionally useful.

He wanted useful links with Britain to remain, best understood by his comment: ' The channel sea forbids union ; the ocean forbids separation '.

Since the comment field was too small to write anything useful, he decided to trim it by two bytes and use those two bytes to store the track number.

Kenneth Newquist, of Nuketown, gave Libris Mortis a rating of 9 / 10, with the comment " Libris Mortis isn't an essential source book, but it is a useful one.

We may further grant to those of her ( Poetry's ) defenders who are lovers of poetry and yet not poets, the permission to speak in prose on her behalf: let them show not only that she is pleasant but also useful to States and to human life, and we will listen in a kindly spirit ; ;

Moreover, Col. Faget's information on Cuba was too outdated to be useful in `` screening '' Castro agents ; ;

Small Business Administration, What It Is, What It Does, SBA Services For Community Economic Development, and various other useful publications on currently important management, technical production, and marketing topics are available, on request, from Small Business Administration, Washington 25, D.C..

The president who appoints strong men who have an all-college or university point of view and a talent and respect for administration can count on useful assistance.

It should be possible, however, to put useful limits on the diameters of the radio sources by observing with large reflectors or with interferometers.

It is of course useful to have a sovereign cause on one's social criticism, for it makes diagnosis and prescription much easier than they might otherwise be.

A concurrent effort is needed to make oceanographic data useful on the spot.

The aim is to collect a very broad range of physical, chemical, morphological, and structural data for crystals on an encyclopedic scale and to seek all possible useful and revealing correlations of properties with internal structure.

You may think we didn't need Nancy and Jean, but you always get what you can when you can, and we had no guarantee that a fingerprint record on them couldn't be useful before we were through with this case.

But humans can do something equally useful, in the case of certain enumerably infinite sets: They can give explicit instructions for determining the nth member of the set, for arbitrary finite n. Such instructions are to be given quite explicitly, in a form in which they could be followed by a computing machine, or by a human who is capable of carrying out only very elementary operations on symbols.

His commentaries on Aristotle were considered so useful that he was styled, by way of pre-eminence, " the commentator " ( ὁ ἐξηγητής ).

By the 6th century Alexander's commentaries on Aristotle were considered so useful that he was referred to as " the commentator " ().

He went on to declare that public schools and colleges, fill the heads of students with inept useless knowledge, which excludes useful knowledge.

* 08081707788, it does have a long introductory message, but it is useful on COCOTs which have 17070 barred.

Speeding up the low portion of memory is particularly useful on 6502 derived machines because that processor has a faster addressing mode for the first 256 bytes and so it is common for software to put any variables involved in time critical sections of program into that region.

The axiom of regularity is arguably the least useful ingredient of Zermelo – Fraenkel set theory, since virtually all results in the branches of mathematics based on set theory hold even in the absence of regularity ( see chapter 3 of ).

This ability is very useful in a mobile conflict and particularly on the advance.

At these lower speeds, ATM provides a useful ability to carry multiple logical circuits on a single physical or virtual medium, although other techniques exist, such as Multi-link PPP and Ethernet VLANs, which are optional in VDSL implementations.

This is a useful technique for researchers in neuroscience because it allows them to quickly increase the intracellular cAMP levels in particular neurons, and to study the effect of that increase in neural activity on the behavior of the organism.

Pure solar heaters are especially useful for laundries, swimming pools and external baths, because these can be scheduled for use on sunny days.

Considered a " dogfight Sparrow ", the AIM-7E-2 was intended to be used at shorter ranges where the missile was still travelling at high speeds, and in the head-on aspect, making it much more useful in the visual limitations imposed on the engagements.

It is most useful for detailed research on specific topics.

In this case, is the smallest σ-algebra that contains the open intervals of R. While there are many Borel measures μ, the choice of Borel measure which assigns for every interval is sometimes called " the " Borel measure on R. In practice, even " the " Borel measure is not the most useful measure defined on the σ-algebra of Borel sets ; indeed, the Lebesgue measure is an extension of " the " Borel measure which possesses the crucial property that it is a complete measure ( unlike the Borel measure ).

Such graphs are useful in calculus to understand the nature and behavior of a function or relation.

In mechanics, the second law in conjunction with the fundamental thermodynamic relation places limits on a system's ability to do useful work.

When hypoglycemia occurs repeatedly, a record or " diary " of the spells over several months, noting the circumstances of each spell ( time of day, relation to last meal, nature of last meal, response to carbohydrate, and so forth ) may be useful in recognizing the nature and cause of the hypoglycemia.

The harmonic mean is an average which is useful for sets of numbers which are defined in relation to some unit, for example speed ( distance per unit of time ).

I have called this principle, by which each slight variation, if useful, is preserved, by the term of Natural Selection, in order to mark its relation to man's power of selection.

The second relation is especially useful at constant T and p, conditions which are easy to achieve experimentally, and which approximately characterize living creatures.

Semantics is useful for investigating a logic ( i. e. a derivation system ) only if the semantical entailment relation reflects its syntactical counterpart, the consequence relation ( derivability ).

When a single or a cluster of flower ( s ) is located at the axil of a bract, the location of the bract in relation to the stem holding the flower ( s ) is indicated by the use of different terms and may be a useful diagnostic indicator.

This relation is useful when time is not known explicitly.

The Food and Agriculture Organization of the United Nations ( FAO ) developed a supra-national classification, also called World Soil Classification, which offers useful generalizations about soils pedogenesis in relation to the interactions with the main soil-forming factors.

If a DAG G represents a partial order ≤, then the transitive reduction of G is a subgraph of G with an edge u → v for every pair in the covering relation of ≤; transitive reductions are useful in visualizing the partial orders they represent, because they have fewer edges than other graphs representing the same orders and therefore lead to simpler graph drawings.

* A patent may be granted in relation to an invention that is new, useful and not simply an obvious advancement over what existed when the application was filed.

Greville's marriage would be useful to Sir William, as it relieved him of having Greville as a poor relation.

This solution is useful for showing the relation between anti-particle and particle.

Quadratic irrationals have useful properties, especially in relation to continued fractions, where we have the result that all quadratic irrationals, and only quadratic irrationals, have periodic continued fraction forms.

Optical processing is especially useful in real time applications where rapid processing of massive amounts of 2D data is required, particularly in relation to pattern recognition.

For a swept-tuned architecture, this relation for sweep time is useful:

If VBW is less than RBW, this relation for sweep time is useful:

Detractors of this argument might point out that the same thing could be said about any concept-object relation, and that the brain-computer analogy can be a perfectly useful model if there is a strong isomorphism between the two.

The energy needed to produce energy is a measure of our difficulty in learning how to make remaining energy resources useful in relation to the effort expended.

of which a useful generalization is the distribution relation

" The use of generalization / specialization relationship between actors is useful in modeling overlapping behaviours between actors and does not violate this constraint since a generalization relation is not a type of association.

If nothing else, the relation between D-brane geometry and gauge theory offers a useful pedagogical tool for explaining gauge interactions, even if string theory fails to be the " theory of everything ".