If the vertex is at Af, and if the interior of C is on the left as one moves in the direction of increasing t, then every such corner can be found from the curve obtained by rotating C clockwise through 90-degrees about the vertex.

Thus if E is sufficiently small, there can be only one intersection of C and Af near Q, for if there were more than one intersection for every E then the difference between C and Af near Q would not be a monotone function.

Thus, during any given year ( A ) if the revenues from the residential service are $7,000,000, ( B ) if the operating expenses imputed to this class of service come to $5,000,000, and ( C ) if the net investment in ( or value of ) the plant and equipment deemed devoted to this service amounts to $30,000,000, the cost analyst will report that residential service, in the aggregate, has yielded a return of $2,000,000 or 6-2/3 per cent.

The automorphism group of an object X in a category C is denoted Aut < sub > C </ sub >( X ), or simply Aut ( X ) if the category is clear from context.

Each ballot can therefore be viewed as a small " delta " which separates two groups of candidates, or a single-pair of ranks ( e. g. if a ballot indicates that A & C are approved and B & D are not, the ballot can be considered to convey the ranking >).

C. S. Lewis argued that, if evolutionary naturalism is accepted, human morality becomes worthless moral statements cannot be right or wrong.

He has said that if stranded on an island with only one programming language it would have to be C.

* Convex cone, a subset C of a vector space V is a convex cone if αx + βy belongs to C, for any positive scalars α, β, and any x, y in C

The two functors F and G are called naturally isomorphic if there exists a natural transformation from F to G such that η < sub > X </ sub > is an isomorphism for every object X in C.

* Two compact Hausdorff spaces X < sub > 1 </ sub > and X < sub > 2 </ sub > are homeomorphic if and only if their rings of continuous real-valued functions C ( X < sub > 1 </ sub >) and C ( X < sub > 2 </ sub >) are isomorphic.

If is an outward pointing in-plane normal, whereas is the unit vector perpendicular to the plane ( see caption at right ), then the orientation of C is chosen so that a tangent vector to C is positively oriented if and only if forms a positively oriented basis for R < sup > 3 </ sup > ( right-hand rule ).

If A is the major axis of an ellipsoid and B and C are the other two axes, the radius of curvature in the ab plane at the end of the axis Af, and the difference in pressure along the A and B axes is Af.

Consider a simple, closed, plane curve C which is a real-analytic image of the unit circle, and which is given by Af.

On C, from the point P at Af to the point Q at Af, we construct the chord, and upon the chord as a side erect a square in such a way that as S approaches zero the square is inside C.

As S approaches T the square will be outside C and therefore both Af and Af must cross C an odd number of times as S varies from zero to T.

Suppose Af crosses C when Af.

The set of intersections of Af, the rotated curve, with the original curve C consists of just the set of forward corner points on C corresponding to the vertex at Af, plus the vertex itself.

We note that two such curves C and Af, cannot coincide at more than a finite number of points ; ;

We will refer to the plane of C and Af as the C-plane and to the plane of the graph as the Aj.

The Secretary of the Treasury, upon the concurrence of the Secretary of State, is authorized and directed, out of the sum covered into the Yugoslav Claims Fund pursuant to subsection ( B ) of this section, after completing the payments of such funds pursuant to subsection ( C ) of this Section, to make payment of the balance of any sum remaining in such fund to the Government of the Federal People's Republic of Yugoslavia to the extent required under Article 1 ( C ) of the Yugoslav Claims Agreement of 1948.

It is agreed that any goods delivered or services rendered after the date of this agreement for projects within categories A, B, and C under paragraph 2 above which may later be approved by the United States will be eligible for financing from currency granted or loaned to the Government of India.

With regard to the rupees accruing to uses indicated under Article 2, of the Agreement, the understanding of the Government of the United States of America, with respect to both paragraphs 1 ( B ) and 1 ( C ) of Article 2, is as follows: ( 1 )

The `` C '' club is composed of the men of the College who have won an official letter in Carleton athletics.

Bar `` C '' is 2-3/4'' '' long.

Since the circulating thyroid hormones are the amino acids thyroxine and tri-iodothyronine ( cf. Section C ), it is clear that some mechanism must exist in the thyroid gland for their release from proteins before secretion.

With the vertex at Af in the C-plane we assume that Af is the parametric location on C of an ordinary intersection Q between C and Af.

But Af is just the curve Af translated without rotation through a small arc, for Af is always obtained by rotating C through exactly 90-degrees.

* The spectrum of any bounded linear operator on a Banach space is a nonempty compact subset of the complex numbers C. Conversely, any compact subset of C arises in this manner, as the spectrum of some bounded linear operator.

For instance, a diagonal operator on the Hilbert space may have any compact nonempty subset of C as spectrum.

As such, the curl operator maps C < sup > 1 </ sup > functions from R < sup > 3 </ sup > to R < sup > 3 </ sup > to C < sup > 0 </ sup > functions from R < sup > 3 </ sup > to R < sup > 3 </ sup >.

The algebra M < sub > n </ sub >( C ) of n-by-n matrices over C becomes a C *- algebra if we consider matrices as operators on the Euclidean space, C < sup > n </ sup >, and use the operator norm ||.|| on matrices.

A *( B *( C * D )) where A, B, C, D are partially transparent image layers and "*" denotes a compositing operator ( with the left layer on top of the right layer ).

To form F with an associative operator, we need only do two additional compositing operations to integrate the new layer C: F = S *( C * D ).

The word is equivalent to this function written in the C programming language using the ternary operator:

These lead naturally to the definition of C *- algebras and other operator algebras.

In computer science, it is the remainder operator that is usually indicated by either "%" ( e. g. in C, Java, Javascript, Perl and Python ) or " mod " ( e. g. in Pascal, BASIC, SQL, Haskell ), with exceptions ( e. g. Excel ).

In this case, the addition operator is overloaded to allow addition on a user-defined type " Time " ( in C ++):

This has the advantage of avoiding a classic C error of mistaking an assignment operator for an equality operator in conditions: is valid C code but causes a syntax error in Python.

Templates are of great utility to programmers in C ++, especially when combined with multiple inheritance and operator overloading.

At 2200 B. C., a marked increase in aridity and wind circulation, subsequent to a volcanic eruption, induced a considerable degradation of land-use conditions.

Instead, with the topology of compact convergence, C ( a, b ) can be given the structure of a Fréchet space: a locally convex topological vector space whose topology can be induced by a complete translation-invariant metric.

If V is a real vector space, then we replace V by its complexification V ⊗< sub > R </ sub > C and let g denote the induced bilinear form on V ⊗< sub > R </ sub > C. Let W be a maximal isotropic subspace, i. e. a maximal subspace of V such that g |< sub > W </ sub > = 0.

* A space X is completely regular if and only if it has the initial topology induced by C ( X ) or C *( X ).

Let ρ be the initial topology on X induced by C < sub > τ </ sub >( X ) or, equivalently, the topology generated by the basis of cozero sets in ( X, τ ).

In fact, the collection of all left cosets ( or right cosets ) of C in G is equal to the collection of all components of G. Therefore, the quotient topology induced by the quotient map from G to G / C is totally disconnected.

Chou, J. C. Lin and D. Christensen, 1975, Microwave induced acoustic effects in mammalian auditory systems and physical materials, Annals of New York Academy of Sciences, 247: 194 – 218

From the accidental discovery in 1907 that scurvy could be induced in guinea pigs, to their use to prove the chemical structure of the " ascorbutic factor " in 1932, the guinea pig model proved a crucial part of vitamin C research.

The " induced emf " around a stationary closed path C is:

Desferrioxamine is an iron-chelating compound, and excretion induced by desferrioxamine is enhanced by administration of Vitamin C. It cannot be used during pregnancy or breast-feeding due to risk of defects in the child.

Therefore induced conflicts started from 171 BC, when consul C. Cassius Longinus first attacked Iapydes.

September 6, 1828, James C. Haile made a contract with the proprietors, and built a sawmill and a small grist mill on the Oswegatchie ; he induced other settlers to come.

All maps in this long exact sequence are induced by the maps between the chain complexes, except for the maps H < sub > n </ sub >( C ) → H < sub > n-1 </ sub >( A ) The latter are called connecting homomorphisms and are provided by the snake lemma.

C < sub > Di </ sub > is known as the induced drag coefficient and it is produced by the body lift.

There is an induced homomorphism of fundamental groups p < sub >#</ sub >: π < sub > 1 </ sub >( C, c ) → π < sub > 1 </ sub >( X, x ) which is injective by the lifting property of coverings.

At the point of minimum drag, C < sub > D, o </ sub > ( drag coefficient of aircraft when lift equals zero ) is equal to C < sub > D, i </ sub > ( induced drag coefficient, or coefficient of drag created by lift ).

* full, i. e. for any two objects c < sub > 1 </ sub > and c < sub > 2 </ sub > of C, the map Hom < sub > C </ sub >( c < sub > 1 </ sub >, c < sub > 2 </ sub >) → Hom < sub > D </ sub >( Fc < sub > 1 </ sub >, Fc < sub > 2 </ sub >) induced by F is surjective ;

* faithful, i. e. for any two objects c < sub > 1 </ sub > and c < sub > 2 </ sub > of C, the map Hom < sub > C </ sub >( c < sub > 1 </ sub >, c < sub > 2 </ sub >) → Hom < sub > D </ sub >( Fc < sub > 1 </ sub >, Fc < sub > 2 </ sub >) induced by F is injective ; and