The mean temperature of the surface was then computed according to the following relation: Af where x is the fraction of the plug area covered by the hot spot.

This system can also be used for three-dimensional geometry, where every point in Euclidean space is represented by an ordered triple of coordinates ( x, y, z ).

*( V, x ) where x is a value of unspecified nature ; and

As in so many programming languages, the operation ( V, x ) is often written V ← x ( or some similar notation ), and ( V ) is implied whenever a variable V is used in a context where a value is required.

Thus, all the antiderivatives of x < sup > 2 </ sup > can be obtained by changing the value of C in F ( x ) = ( x < sup > 3 </ sup >/ 3 ) + C ; where C is an arbitrary constant known as the constant of integration.

For any system, the following restrictions on measurement results apply, where is the reduced Planck constant and is any direction vector such as x, y, or z:

The coordinates of the points on the curve are of the form ( x, 1 / x ) where x is a number other than 0.

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.

If the filter shows amplitude ripple within the passband, the x dB point refers to the point where the gain is x dB below the nominal passband gain rather than x dB below the maximum gain.

Every Hilbert space X is a Banach space because, by definition, a Hilbert space is complete with respect to the norm associated with its inner product, where a norm and an inner product are said to be associated if for all x ∈ X.

for all x and y in X, and where is the norm on X.

respectively, where e < sub > x </ sub >, e < sub > y </ sub >, e < sub > z </ sub > denotes the cartesian basis vectors ( all are orthogonal unit vectors ) and A < sub > x </ sub >, A < sub > y </ sub >, A < sub > z </ sub > are the corresponding coordinates, in the x, y, z directions.

where is the Gelfand representation of x defined as follows: is the continuous function from Δ ( A ) to C given by The spectrum of in the formula above, is the spectrum as element of the algebra C ( Δ ( A )) of complex continuous functions on the compact space Δ ( A ).

where X is the energy level corresponding to the principal quantum number n, type is a lower-case letter denoting the shape or subshell of the orbital and it corresponds to the angular quantum number l, and y is the number of electrons in that orbital.

Many of the sweets produced in this region, such as quince, sweet potato, molasses and dulce de cayote jams, have given rise to a very well known and easily made dessert referred to as vigilante, or to so-called queso y dulce ( where a piece of fresh cheese is served with one of the sweets mentioned above ).

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.

where i, j, and k are the unit vectors for the x -, y -, and z-axes, respectively.

If is a wrapped Cauchy distribution with the parameter representing the parameters of the corresponding " unwrapped " Cauchy distribution in the variable y where, then

( x ( s ), y ( s )) where s represents arc length and r is the position vector.

The equation of a circle is ( x − a )< sup > 2 </ sup > + ( y − b )< sup > 2 </ sup > = r < sup > 2 </ sup > where a and b are the coordinates of the center ( a, b ) and r is the radius.

To rotate a figure counterclockwise around the origin by some angle is equivalent to replacing every point with coordinates ( x, y ) by the point with coordinates ( x < nowiki >'</ nowiki >, y < nowiki >'</ nowiki >), where

In more generality, reflection across a line through the origin making an angle with the x-axis, is equivalent to replacing every point with coordinates ( x, y ) by the point with coordinates ( x < nowiki >'</ nowiki >, y < nowiki >'</ nowiki >), where

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

If S is an arbitrary set, then the set S < sup > N </ sup > of all sequences in S becomes a complete metric space if we define the distance between the sequences ( x < sub > n </ sub >) and ( y < sub > n </ sub >) to be, where N is the smallest index for which x < sub > N </ sub > is distinct from y < sub > N </ sub >, or 0 if there is no such index.

As Daniels used the word, an abugida contrasts with a syllabary, where letters with shared consonants or vowels show no particular resemblance to each another, and with an alphabet proper, where independent letters are used to denote both consonants and vowels.

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 denotes the vector cross product and square brackets denote evaluation in the rotating frame of reference.

where vertical bars |...| denote the vector magnitude, which in the case of r ( t ) is simply the radius R of the path.

where primes are introduced to denote derivatives with respect to s. The magnitude of this displacement is ds, showing that:

where the outermost brackets denote the floor function.

Falsifiability is an important concept within the creation – evolution controversy, where proponents of both sides claim that Popper developed falsifiability to denote ideas as unscientific or pseudoscientific and use it to make arguments against the views of the respective other side.

x, y, u and v denote here tuples of variables rather than single variables ; e. g. really stands for where are some distinct variables.

Some breeds denote the country, or state, where conception took place as the origin of the foal.

* is a finite subset of, the < em > transition relation </ em >, where denote the set of strings over and denotes the empty string.

where c is the speed of light, and Δr and Δt denote differences of the space and time coordinates, respectively, between the events.

What follows is a list of the twelve signs of the modern zodiac ( with the ecliptic longitudes of their first points ), where 0 ° Aries is understood as the vernal equinox, with their Latin, Greek, Sanskrit, and Babylonian names ( but note that the Sanskrit and the Babylonian name equivalents denote the constellations only, not the tropical zodiac signs ).

Pullman earlier proposed to name the series The Golden Compasses, also a reference to Paradise Lost, where they denote God's circle-drawing instrument used to establish and set the bounds of all creation:

where angular brackets denote averaging over many wave cycles.

The term is only relevant in the case of signaling systems that use discrete signals ( e. g. a combination of tones to denote one digit ), as opposed to signaling systems which are message-oriented ( such as SS7 and ISDN Q. 931 ) where each message is able to convey multiple items of information ( e. g. multiple digits of the called telephone number ).

where the angular brackets denote the ensemble average.

"( COOH )" can be COOH or H, or ( more rarely ) other substituent s. The arrows denote where the polymer continues.

where denotes a yet-to-be-determined real number that will specify a time-independent energy level or eigenvalue, and the solution will denote the wave function for the corresponding energy eigenstate.

Let θ denote the angle between and, where is the vector along the waveplate's fast axis.

It is never used to denote pounds weight ( lb is commonly used for this ) or pounds sterling ( where "£" is used ).

* Some international models of adding machines and printing calculators use the asterisk to denote the total, or the terminal sum or difference of an addition or subtraction sequence, respectively, sometimes on the keyboard where the total key is marked with an asterisk and sometimes a capital T, and on the printout.

where the circumflexes (" hats ") denote these observables are operators.

Let, where denote a point on Boy's surface.

where the brackets denote a commutator.