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

Set-theoretically, one may represent a binary function as a subset of the Cartesian product X × Y × Z, where ( x, y, z ) belongs to the subset if and only if f ( x, y ) = z.

In linear algebra, a bilinear transformation is a binary function where the sets X, Y, and Z are all vector spaces and the derived functions f < sup > x </ sup > and f < sub > y </ sub > are all linear transformations.

f and g are not known exactly: For example, the altitude where the car starts is not known and the temperature on the mountain is not known.

To compute the temperature change in such a model, it would be necessary to know g and not just g ′, because without knowing g it is not possible to know where to evaluate f ′.

In the special case where, so that f is a real-valued function, then this formula simplifies even further:

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 >.

where θ ∈ T < sub > f ( x )</ sub >< sup >*</ sup > N and X < sub > x </ sub > ∈ T < sub > x </ sub > M.

where f

For a function of one variable, f, the set of all points ( x, y ) where y

This functional relationship is often denoted y = f ( x ), where f denotes the function.

In the case of total life extinction, a similar factor may be applicable for f < sub > ℓ </ sub >, that is, how many times life may appear on a planet where it has appeared once.

( where again a and b are one-half of the ellipse's major and minor axes respectively, and f is the focal distance ) or, as expressed in terms using the flattening factor

where v is the speed of the wave ( c in a vacuum, or less in other media ), f is the frequency and λ is the wavelength.

where B < sub > r </ sub > is the disk of radius r and denotes the supremum norm of f ( z ) on B < sub > r </ sub >.

This is called gating error and causes an average error in the calculated frequency of Δf = 1 /( 2 T < sub > m </ sub >), or a fractional error of Δf / f = 1 /( 2 f T < sub > m </ sub >) where T < sub > m </ sub > is the timing interval and f is the measured frequency.

If the baseband data signal ( the message ) to be transmitted is and the sinusoidal carrier is, where f < sub > c </ sub > is the carrier's base frequency and A < sub > c </ sub > is the carrier's amplitude, the modulator combines the carrier with the baseband data signal to get the transmitted signal:

Given two groups G and H and a group homomorphism f: G → H, let K be a normal subgroup in G and φ the natural surjective homomorphism G → G / K ( where G / K is a quotient group ).

Given a trigonometric series f ( x ) with S as its set of zeros, Cantor had discovered a procedure that produced another trigonometric series that had S ' as its set of zeros, where S ' is the set of limit points of S. If p ( 1 ) is the set of limit points of S, then he could construct a trigonometric series whose zeros are p ( 1 ).

We write gf for, where f ' G ( x, y ), and g ' G ( y, z );

radius ) a and flattening f. The quantity f = ( a − b )/ a, where b is the semi-minor axis ( polar radius ), is a purely geometrical one.

He also offers a conversion table ( see Cohen, 1988, p. 283 ) for eta squared ( η < sup > 2 </ sup >) where 0. 0099 constitutes a small effect, 0. 0588 a medium effect and 0. 1379 a large effect.

Reactions of acids are often generalized in the form HA H < sup >+</ sup > + A < sup >−</ sup >, where HA represents the acid and A < sup >−</ sup > is the conjugate base.

The numerical value of K < sub > a </ sub > is equal to the concentration of the products divided by the concentration of the reactants, where the reactant is the acid ( HA ) and the products are the conjugate base and H < sup >+</ sup >.

Because the range of possible values for K < sub > a </ sub > spans many orders of magnitude, a more manageable constant, pK < sub > a </ sub > is more frequently used, where pK < sub > a </ sub >

These nodes are areas where the action potential is amplified using a high density of sodium ( Na < big >+</ big >) ions and is subsequently passed along the axon.

functions as real combinations of spherical harmonics Y < sub > lm </ sub >( θ, φ ) ( where l and m are quantum numbers ).

Within a shell where n is some integer n < sub > 0 </ sub >, ranges across all ( integer ) values satisfying the relation.

It lacks the NH < sub > 2 </ sub > group because of the cyclization of the side-chain and is known as an imino acid ; it falls under the category of special structured amino acids .</ ref > where R is an organic substituent known as a " side-chain "); often the term " amino acid " is used to refer specifically to these.

½ ( pKa < sub > 1 </ sub > + pKa < sub > R </ sub >), where pKa < sub > R </ sub > is the side-chain pKa.

## < tt > SubBytes </ tt >— a non-linear substitution step where each byte is replaced with another according to a lookup table.

## < tt > ShiftRows </ tt >— a transposition step where each row of the state is shifted cyclically a certain number of steps.

The < tt > MixColumns </ tt > function takes four bytes as input and outputs four bytes, where each input byte affects all four output bytes.

where n < sup > c </ sup > denotes the charge conjugate state, i. e., the antiparticle.

where we use the symbol k to denote the quantum numbers p and σ of the previous section and the sign of the energy, E ( k ), and a < sub > k </ sub > denotes the corresponding annihilation operators.

where E < sub > 0 </ sub > is an infinite negative constant.

The Battle of Qarqar is mentioned in extra-biblical records, and was perhaps at Apamea where Shalmaneser III of Assyria fought a great confederation of princes from Cilicia, Northern Syria, Israel, Ammon, and the tribes of the Syrian desert ( 853 BC ), including Ahab ( A-ha-ab-bu < sup > mat </ sup >) ( Adad -' idri ).

where < big ></ big > is the number of degrees of freedom divided by two, R is the universal gas constant and n is the number of moles in the system ( a constant ).

We could, alternatively, choose an encoding for Turing machines, where an encoding is a function which associates to each Turing Machine M a bitstring < M >.

where p is a program in L < sub > 2 </ sub >.

Aimoin ( c. 960-c. 1010 ), French chronicler, was born at Villefranche-de-Longchat about 960, and in early life entered the monastery of Fleury, where he became a monk and passed the greater part of his life.

For a vector with linear addressing, the element with index i is located at the address B + c · i, where B is a fixed base address and c a fixed constant, sometimes called the address increment or stride.

For a two-dimensional array, the element with indices i, j would have address B + c · i + d · j, where the coefficients c and d are the row and column address increments, respectively.

* SV — Save: number of games where the pitcher enters a game led by the pitcher's team, finishes the game without surrendering the lead, is not the winning pitcher, and either ( a ) the lead was three runs or fewer when the pitcher entered the game ; ( b ) the potential tying run was on base, at bat, or on deck ; or ( c ) the pitcher pitched three or more innings

A binary operation, ab, depends on the ordered pair ( a, b ) and so ( ab ) c ( where the parentheses here mean first operate on the ordered pair ( a, b ) and then operate on the result of that using the ordered pair (( ab ), c )) depends in general on the ordered pair (( a, b ), c ).

Detailed analysis shows that the complexity class is unchanged by allowing error as high as 1 / 2 − n < sup >− c </ sup > on the one hand, or requiring error as small as 2 < sup >− n < sup > c </ sup ></ sup > on the other hand, where c is any positive constant, and n is the length of input.

According to the theorem, it is possible to expand the power ( x + y )< sup > n </ sup > into a sum involving terms of the form ax < sup > b </ sup > y < sup > c </ sup >, where the exponents b and c are nonnegative integers with, and the coefficient a of each term is a specific positive integer depending on n and b. When an exponent is zero, the corresponding power is usually omitted from the term.

Inspired by a concert where he saw John Lee Hooker perform, he supplemented his work as a carpenter and mechanic with a developing career playing on street corners with friends, including Jerome Green ( c. 1934 – 1973 ), in a band called The Hipsters ( later The Langley Avenue Jive Cats ).

9 ( 1 )( c ) of the Radiocommunication Act creates a prohibition against all decoding of encrypted programming signals, followed by an exception where authorization is received from the person holding the lawful right in Canada to transmit and authorize decoding of the signal.

Columba is the patron saint of the city of Derry, Ireland where he founded a monastic settlement in c. AD 540.

The tension at c is tangent to the curve at c and is therefore horizontal, and it pulls the section to the left so it may be written (− T < sub > 0 </ sub >, 0 ) where T < sub > 0 </ sub > is the magnitude of the force.

Finally, weight of the chain is represented by ( 0, − λgs ) where λ is the mass per unit length, g is the acceleration of gravity and s is the length of chain between c and r.

where the limits of integration are c and r. Balancing forces as in the uniform chain produces

If the weight of the roadway per unit length is w and the weight of the cable and the wire supporting the bridge is negligible in comparison, then the weight on the cable from c to r is wx where x is the horizontal distance between c to r. Proceeding as before gives the differential equation