The same thing goes for a complex-valued function.

The domain of a complex-valued function may be extended to include the point at infinity as well.

In this case, the vector can be written as a complex-valued function on the spectrum of (usually the real line).

The essential range can be defined for measurable real or complex-valued functions on a measure space.

This can be done for real or complex-valued functions in several steps as follows:

Its elements are square integrable complex-valued functions on the sphere.

This is done by encoding number-theoretic information in complex-valued functions.

Let be a real-valued or complex-valued function of variables.

As noted above, the theorem does not hold for differentiable complex-valued functions.

The derivative operator is defined also for complex-valued functions of a complex argument.

Consider a complex-valued function ƒ of a real variable.

The sign of ω is also preserved in the complex-valued function:

Let f be a Borel-measurable, complex-valued function defined on a measure space .

These negative frequency components can be discarded with no loss of information, provided one is willing to deal with a complex-valued function instead.

To understand this formula, we may express s(t) as the sum of two complex-valued functions:

For any complex-valued functions f, g on with finite support, one can take the convolution of them:

The wave function for N particles each with spin is the complex-valued function:

The real-valued sinusoidal function representing either voltage or current may be broken into two complex-valued functions.

Visualizing complex-valued functions in the plane.

To define the contour integral in this way one must first consider the integral, over a real variable, of a complex-valued function.

In mathematics, a character group is the group of representations of a group by complex-valued functions.

As a consequence of the principle of causality the complex-valued function has poles only in the lower half-plane.

More generally, consider linear differential operators acting on infinitely differentiable complex-valued functions of compact support.

Our "quantum" phase space, on the other hand, involves a complex-valued function on a 3N dimensional space.

Let G be a finite group and consider the space H of complex-valued functions on G.

He is best known for his works on complex functions and potential theory.

This approach will become especially helpful when you get to more complex functions later.

A few more complex functions are "reserved for future use in C99".

It is a complex function of density and cell size.

This allows faster and more complex functions using less power.

And yet, we still do not understand how the brain performs all of its complex functions.

In the area of children, youth, and family services, local foundations often take on these more complex functions.

On the other hand, conditions are identified under which the acquisition of complex functions is possible.

The value is a complex function of range, time, aspect, etc.

It is the body's chemical factory with over 100 complex functions.

More complex function blocks are to be built from these E elements.

We show that setting up on-line tech support is not a complex function.

It is seldom that anything so complex functions as well in the early stages.

The method can also be extended to complex functions and to systems of equations.

He has to his credit more than 100 research articles in complex function theory and Multimedia.

Can these be applied to complex functions as well?

An entire book may be imposed and many complex functions applied in an instant.

As such, the channel is essential for enzyme complex function.

It is needed to perform calculations that requires more complex functions.

The different studies suggest that there is a correlation between sleep and the complex functions of memory.

Design and build a logic circuit that will perform a complex function.

A redundant bit may be a complex function of many original information bits.

A great site if you are studying complex functions.

It may also make inferences involving more complex functions, such as position or find.

However, no such guarantee is given for more complex functions and they are typically only accurate to within the last bit at best.