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

If F is an antiderivative of f, and the function f is defined on some interval, then every other antiderivative G of f differs from F by a constant: there exists a number C such that G ( x ) = F ( x ) + C for all x.

However, their derivatives are known: f ′ is − 6. 5 ° C / km, and g ′ is 2. 5 km / h.

Let M be a smooth manifold and let x be a point in M. Let I < sub > x </ sub > be the ideal of all functions in C < sup >∞</ sup >( M ) vanishing at x, and let I < sub > x </ sub >< sup > 2 </ sup > be the set of functions of the form, where f < sub > i </ sub >, g < sub > i </ sub > ∈ I < sub > x </ sub >.

Let M be a smooth manifold and let f ∈ C < sup >∞</ sup >( M ) be a smooth function.

We can then define the differential map d: C < sup >∞</ sup >( M ) → T < sub > x </ sub >< sup >*</ sup > M at a point x as the map which sends f to df < sub > x </ sub >.

The distance from the center C to either focus is f

Every continuous map f: X → Y induces an algebra homomorphism C ( f ): C ( Y ) → C ( X ) by the rule C ( f )( φ ) = φ o f for every φ in C ( Y ).

In Analytical Geometry a section of a line can be given by the formula where ( c, d )&( e, f ) are the endpoints of the line & m: n is the ratio of division

If we define the function f ( n ) = A ( n, n ), which increases both m and n at the same time, we have a function of one variable that dwarfs every primitive recursive function, including very fast-growing functions such as the exponential function, the factorial function, multi-and superfactorial functions, and even functions defined using Knuth's up-arrow notation ( except when the indexed up-arrow is used ).

The oblique asymptote, for the function f ( x ), will be given by the equation y = mx + n.

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 k, m, and n are 1, so that and, then the Jacobian matrices of f and g are.

This implies that for each natural number n, the set of sequences f in Cantor space such that f ( n )

Some genetic studies seem to prove a Celtic descendence of most inhabitants in the region, but not Germanic in fact, that is reinforced by the Gaulish toponyms such as those ending with the suffix-ago < Celtic -* ako ( n ) ( f. e.

Model example: if U and V are two connected open subsets of R < sup > n </ sup > such that V is simply connected, a differentiable map f: U → V is a diffeomorphism if it is proper and if

for some natural number n. Moreover, since, the commutator subgroup is normal in G. For any homomorphism f: G → H,

If m and n are natural numbers and f ( x ) is a smooth ( meaning: sufficiently often differentiable ) function defined for all real numbers x in the interval, then the integral

− 1 / 30, … are the Bernoulli numbers, and R is an error term which is normally small for suitable values of p and depends on n, m, p and f. ( The formula is often written with the subscript taking only even values, since the odd Bernoulli numbers are zero except for B < sub > 1 </ sub >.

Specifically, by the Casorati – Weierstrass theorem, for any transcendental entire function f and any complex w there is a sequence with, is necessarily a polynomial, of degree at least n.

Define f ( n ) = | n |, the absolute value of n.

From the radian frequency, the natural frequency, f < sub > n </ sub >, can be found by simply dividing ω < sub > n </ sub > by 2π.

* Gaius Licinius P. f. ( C. n .) Varus, father of Publius and Gaius Licinius Crassus, consuls in 171 and 168 BC.

* Publius Licinius P. f. P. n. Crassus Dives, censor in 208 BC and consul in 205, during the Second Punic War.

* Gaius Licinius P. f. P. n. Crassus Dives, son of the consul of 205 BC.

* Publius Licinius C. f. P. n. Crassus, consul in 171 BC, defeated by Perseus of Macedon.

* Gaius Licinius C. f. P. n. Crassus, consul in 168 BC, assigned the province of Gallia Cisalpina, but brought his army to Macedonia instead.

* Gaius Licinius ( C. f. C. n .) Crassus, tribunus plebis in 145 BC, proposed a bill to fill vacant priesthoods by popular election ; it was defeated following a speech by the praetor, Gaius Laelius Sapiens.

* Gaius Licinius ( C. f. C. n .) Crassus, probably son of the tribune of 145 BC.

* Marcus Licinius P. f. P. n. Crassus Agelastus, grandfather of the triumvir, he was said to have obtained his surname because he never laughed.

* Licinia P. f. P. n., sister of Marcus Licinius Crassus Agelastus.

* Licinia P. f. P. n., daughter of Publius Licinius Crassus Mucianus, married Gaius Sulpicius Galba, son of the orator Servius Sulpicius Galba.

* Licinia P. f. P. n., daughter of Publius Licinius Crassus Mucianus, married Gaius Sempronius Gracchus, the tribune.

* Publius Licinius M. f. P. n. Crassus Dives, father of the triumvir ; he was consul in 97 BC, and triumphed over the Lusitani.

* Lucius Licinius L. f. Crassus, the greatest orator of his day, was consul in 95 BC, and censor in 92.

* Publius Licinius P. f. M. n. Crassus Dives, brother of the triumvir, he was slain by the horsemen of Gaius Flavius Fimbria, one of the partisans of Marius, in 87 BC.

* Licinius P. f. M. n. Crassus Dives, a brother of the triumvir who escaped the massacre of 87 BC.

* Marcus Licinius P. f. M. n. Crassus Dives, the triumvir, was consul in 70 and 55 BC, and censor in 65.

* Publius Licinius P. f. P. n. Crassus Dives, a nephew of the triumvir, squandered his fortune.

* Marcus Licinius M. f. P. n. Crassus Dives, elder son of the triumvir, he was Caesar's quaestor in Gaul, and praefectus of Gallia Cisalpina at the beginning of the Civil War in 49 BC.

* Publius Licinius M. f. P. n. Crassus Dives, younger son of the triumvir, he was Caesar's legate in Gaul from 58 to 55 BC.

* Marcus Licinius M. f. M. n. Crassus, consul in 30 BC.

* Marcus Licinius M. f. M. n. Crassus Dives, consul in 14 BC.

* Marcus Licinius M. f. Crassus, son Marcus Licinius Crassus Frugi, he was slain by the emperor Nero.