It will be noted that point f has seven nearest neighbors, h and e have six, and p has only one, while the remaining points have intermediate numbers.

In any social system in which communications have an importance comparable with that of production and other human factors, a point like f in Figure 2 would ( other things being equal ) be the dwelling place for the community leader, while e and h would house the next most important citizens.

In some neighborhood in the f-plane of any ordinary point of the graph, the function f is a single-valued, continuous function.

The graph of f has at least one component whose support is the entire interval Aj.

A choice function is a function f, defined on a collection X of nonempty sets, such that for every set s in X, f ( s ) is an element of s. With this concept, the axiom can be stated:

: For any set X of nonempty sets, there exists a choice function f defined on X.

: For any set A there is a function f such that for any non-empty subset B of A, f ( B ) lies in B.

: There is a set A such that for all functions f ( on the set of non-empty subsets of A ), there is a B such that f ( B ) does not lie in B.

* There exists a model of ZF ¬ C in which there is a function f from the real numbers to the real numbers such that f is not continuous at a, but f is sequentially continuous at a, i. e., for any sequence

Exports: $ 1. 225 billion f. o. b. ( 2008 )

Imports: $ 3. 546 billion f. o. b. ( 2008 )

The simple names s orbital, p orbital, d orbital and f orbital refer to orbitals with angular momentum quantum number l = 0, 1, 2 and 3 respectively.

The repeating periodicity of the blocks of 2, 6, 10, and 14 elements within sections of the periodic table arises naturally from the total number of electrons which occupy a complete set of s, p, d and f atomic orbitals, respectively.

** Haliotis brazieri f. hargravesi ( Cox, 1869 ) – synonym: Haliotis ethologus, the Mimic abalone, Haliotis hargravesi, the Hargraves ’ s abalone

That is, it is the equivalence class of functions on M vanishing at x determined by g o f.

A frequent particular case occurs when f is a function from X to another set Y ; if x < sub > 1 </ sub > ~ x < sub > 2 </ sub > implies f ( x < sub > 1 </ sub >) = f ( x < sub > 2 </ sub >) then f is said to be a morphism for ~, a class invariant under ~, or simply invariant under ~.

Since the possible values of f are well-ordered, this property can be established by proving for any r ( not in I ) with minimal value of f ( r ) in its class.

:: To solve the uniform word problem for a class K of groups it is sufficient to find a recursive function f ( P, w ) that takes a finite presentation P for a group G and a word w in the generators of G such that whenever in G ∈ K:

Often f is a simple function that maps all values above a certain threshold to the first class and all other values to the second class.

A more complex f might give the probability that an item belongs to a certain class.

In Arthur – Merlin protocols, Babai defined a similar class AM which allowed f ( n ) rounds, but he put one extra condition on the machine: the verifier must show the prover all the random bits it uses in its computation.

It is a Shapley class f and Trumpler class I 2 p cluster, meaning that it appears to be a fairly rich cluster overall, though it has fewer than 50 stars.

We need to prove that some time class TIME ( g ( n )) is strictly larger than some time class TIME ( f ( n )).

Let us assume that H < sub > f </ sub > is in this time complexity class, and we will attempt to reach a contradiction.

If H < sub > f </ sub > is in this time complexity class, it means we can construct some machine K which, given some machine description and input x, decides whether the tuple (, x ) is in H < sub > f </ sub > within.

In other words, the complexity class NTIME ( f ( n )) is a strict subset of NTIME ( g ( n )).

* The notation || f ||< sub > p </ sup > with 1 ≤ p ≤ ∞ is a slight abuse, because in general it is only a norm of f if || f ||< sub > p </ sup > is finite and f is considered as equivalence class of μ-almost everywhere equal functions.

Both are Trumpler class I 3 r clusters, though NGC 869 is a Shapley class f and NGC 884 is a Shapley class e cluster.

There were no less than six or seven saloons in Ganado, not counting the lower class dives, all vying for the trade of celebrating miners and teamsters.

`` When I was in college '', I grinned, `` I remember a poem I had to read in my lit class.

Now, he was just in the late poems of Holderlin and therefore had most of the nineteenth century before him -- plus next semester's class preparation.

The big man with the whitened hair murmured something: his words sounded as if they were in the Manu tongue, which I recognized, having studied the dialect in my Anthropology 6, class at the University of Chicago.

He simply would not work his arithmetic problems when the teacher held his class.

Monogamy is the vice from which the abjectly fearful middle class continue to suffer, whereas the beatnik has the courage to break out of that prison of respectability.

And it is precisely in this poorer economic class that one finds, and has always found, the most racial friction.

By virtue of his self-reliance, his individualism and his freedom from external restraint, the private eye is a perfect embodiment of the middle class conception of liberty, which amounts to doing what you please and let the devil take the hindmost.

At the same time, because the personal code of the detective coincides with the legal dictates of his society, because he likes to catch criminals, he is in middle class eyes a virtuous man.

It was in order to avoid the stuffy routine of middle class life that Holmes became a detective in the first place.

The writer took a class of college students to the state hospital for the mentally ill in St. Joseph, Missouri.

Since a civilizational crisis involves also a crisis in private interests and in the ruling class, reaction is normally found among those who feel themselves to be among the ruling class.

It would be profitable, I believe, to read these realistic humorists alongside Faulkner's works, the thought being not that he necessarily read them and owed anything to them directly, but rather that they dealt a hundred years ago with a class of people and a type of life which have continued down to our time, to Faulkner's time.

With the rise to power of the middle class the centre of gravity in human affairs shifted from the public to the private.

The novel was not only the presenter of the new, secular, rationalistic, private world of the middle class.

This intervention could only be controlled by priests, and thus the invasions caused a rapid rise in the influence of the sacred class.

Adams contended that once such a special class had been created it became a vested interest and sought to maintain itself by assuming exclusive control over the relationships between God and man.

Yet, the idea imbedded in each was identical: to surround the unknown with mystery and to isolate that class which had been given special dominion over the secrets of God.

Writers of this class of science fiction have clearly in mind the assumptions that man can master the principles of this cause-and-effect universe and that such mastery will necessarily better the human lot.

The concept of labor as a special class is outmoded, and in the task confronting America as bastion of the free world, labor must learn to put the national interest first if it is itself to survive.

Economy class fares and charter flights have attracted almost all new passengers to the airlines.

The other children in the class use this same coloring book and do a fairly good job with things their proper color.

He recalls with a wry smile the wit who said, on returning from a homecoming reunion, that he would never go again because all his class had changed so much they didn't even recognize him.

Then epistolatory me was a foreign correspondent dispatching exciting cables and communiques, full of dash and wit and glamor, quoting from the books I read, imitating the grand styles of the authors recommended by a teacher in whose special, after-school class I was enrolled.