Two-dimensional projective transformations are a type of automorphism of the projective plane onto itself. Planar transformations can be defined synthetically as follows: point X on a "subjective" plane must be transformed to a point T also on the subjective plane. The transformations uses these tools: a pair of "observation points" P and Q, and an "objective" plane. The subjective and objective planes and the two poin ...

See also:

Projective transformation, Projective transformation - Transformations on the projective line, Projective transformation - Analysis, Projective transformation - Inverse transformation, Projective transformation - Identity transformation, Projective transformation - Composition of transformations, Projective transformation - The cross-ratio defined by means of a projection, Projective transformation - Conservation of cross-ratio, Projective transformation - Transformations on the projective plane, Projective transformation - Analysis, Projective transformation - Trilinear transformations, Projective transformation - Composition of trilinear transformations, Projective transformation - Planar transformations of lines, Projective transformation - Planar transformations of conic sections, Projective transformation - Planar projectivities and cross-ratio, Projective transformation - Example, Projective transformation - Transformations in projective 3-space, Projective transformation - Analysis, Projective transformation - Quadrilinear transformations, Projective transformation - Properties of quadrilinear transformations, Projective transformation - Spatial transformations of planes, Projective transformation - Reference

Read more here: » Projective transformation: Encyclopedia II - Projective transformation - Transformations on the projective plane

A transformer usually has: two or more insulated windings, to carry current a core, in which the mutual magnetic field couples the windings. In transformers designed to operate at low frequencies, the windings are usually formed around an iron or steel core. This helps to confine the magnetic field within the transformer and increase its efficiency, although the presence of the core causes energy losses. Transformers made to operate at high frequencies may use other l ...

See also:

Transformer, Transformer - Introduction, Transformer - Basic principles, Transformer - Flux coupling, Transformer - Electrical laws, Transformer - Invention, Transformer - Practical considerations, Transformer - Classification, Transformer - Losses, Transformer - High frequency operation, Transformer - Construction, Transformer - Cores, Transformer - Windings, Transformer - Insulation, Transformer - Shielding, Transformer - Coolant, Transformer - Terminals, Transformer - Transformer designs, Transformer - Autotransformers, Transformer - Polyphase transformers, Transformer - Resonant transformers, Transformer - Instrument transformers, Transformer - Pulse transformers, Transformer - RF transformers, Transformer - Uses of transformers

Read more here: » Transformer: Encyclopedia II - Transformer - Construction

Covariant transformation - Derivative of a function transforms covariant. The explicit form of a covariant transformation is best introduced with the transformation properties of the derivative of a function. Consider a scalar function f (like the temperature in a space) defined on a set of points p, identifiable in a given coordinate system (such a collection is called a manifold). If we adopt a new coordinates system then for each i, the original coordinate x< ...

See also:

Covariant transformation, Covariant transformation - Examples of covariant transformation, Covariant transformation - Derivative of a function transforms covariant, Covariant transformation - Basis vectors transform covariant, Covariant transformation - Contravariant transformation, Covariant transformation - Differential form transforms contravariant, Covariant transformation - Dual properties, Covariant transformation - Co- and contravariant tensor components, Covariant transformation - Without coordinates, Covariant transformation - With coordinates

Read more here: » Covariant transformation: Encyclopedia II - Covariant transformation - Examples of covariant transformation

The transformer is one of the simplest of electrical devices. A good mechanical analogy is that of a gearbox. Its design and principles have changed little over the last one hundred years, yet the transformer still plays a substantial role in the continuing development of high-voltage power transmission. It permits the economical transmission of power over large distances, allowing generating stations to be located physically further from sites of electricity demand and nearer to their sources of fuel. The simplicity, reliability, and econom ...

See also:

Transformer, Transformer - Introduction, Transformer - Basic principles, Transformer - Flux coupling, Transformer - Electrical laws, Transformer - Invention, Transformer - Practical considerations, Transformer - Classification, Transformer - Losses, Transformer - High frequency operation, Transformer - Construction, Transformer - Cores, Transformer - Windings, Transformer - Insulation, Transformer - Shielding, Transformer - Coolant, Transformer - Terminals, Transformer - Transformer designs, Transformer - Autotransformers, Transformer - Polyphase transformers, Transformer - Resonant transformers, Transformer - Instrument transformers, Transformer - Pulse transformers, Transformer - RF transformers, Transformer - Uses of transformers

Read more here: » Transformer: Encyclopedia II - Transformer - Introduction

Fourier transform - Continuous Fourier transform. Most often, the unqualified term "Fourier transform" refers to the continuous Fourier transform, representing any square-integrable function f(t) as a sum of complex exponentials with angular frequencies ω and complex amplitudes F(ω): This is actually the inverse continuous Fourier transform, whereas the Fourier transform expresses F(ω) in terms of f(t); the original function and its t ...

See also:

Fourier transform, Fourier transform - Applications, Fourier transform - Variants of the Fourier transform, Fourier transform - Continuous Fourier transform, Fourier transform - Fourier series, Fourier transform - Discrete Fourier transform, Fourier transform - Other variants, Fourier transform - Family of Fourier transforms, Fourier transform - Interpretation in terms of time and frequency, Fourier transform - Applications in signal processing

Read more here: » Fourier transform: Encyclopedia II - Fourier transform - Variants of the Fourier transform

The inverse Z-Transform is where is a counterclockwise closed path encircling the origin and entirely in the region of convergence (ROC). The contour or path, , must encircle all of the poles of . A special case of this contour integral that is simply that where is the unit circle (and can be used when the ROC includes the unit circle) is the inverse Discrete ...

See also:

Z-transform, Z-transform - Definition, Z-transform - Bilateral Z-Transform, Z-transform - Unilateral Z-Transform, Z-transform - Inverse Z-Transform, Z-transform - Region of convergence, Z-transform - Example 1 No ROC, Z-transform - Example 2 causal ROC, Z-transform - Example 3 anticausal ROC, Z-transform - Examples conclusion, Z-transform - Properties, Z-transform - Table of common Z-transform pairs, Z-transform - Relationship to Laplace, Z-transform - Relationship to Fourier, Z-transform - Linear constant coefficient difference equation, Z-transform - Transfer function, Z-transform - Zeros and poles, Z-transform - Output response, Z-transform - Bibliography

Read more here: » Z-transform: Encyclopedia II - Z-transform - Inverse Z-Transform

Matrices allow arbitrary linear transformations to be represented in a consistent format, suitable for computation. This also allows transformations to be concatenated easily (by multiplying their matrices). Linear transformations are not the only ones that can be represented by matrices. Using homogeneous coordinates, both affine transformations and perspective projections on Rn can be represented as linear transformations on RPn+1 (that is, n+1-dimensional real projective space). For this reason, 4x4 transformation mat ...

See also:

Transformation matrix, Transformation matrix - Uses, Transformation matrix - Finding the matrix of a transformation, Transformation matrix - Examples in 2D graphics, Transformation matrix - Rotation, Transformation matrix - Scaling, Transformation matrix - Shearing, Transformation matrix - Reflection, Transformation matrix - Orthogonal projection, Transformation matrix - Composing and inverting transformations, Transformation matrix - Other kinds of transformations, Transformation matrix - Affine transformations, Transformation matrix - Perspective projection

Read more here: » Transformation matrix: Encyclopedia II - Transformation matrix - Uses

When one says "the Laplace transform" without qualification, the unilateral or one-sided transform is normally intended. The Laplace transform can be alternatively defined as the bilateral Laplace transform or two-sided Laplace transform by extending the limits of integration to be the entire real axis. If that is done the common unilateral transform simply becomes a special case of the bilateral transform where the definition of the function being transformed is multiplied by the Heaviside step function. The bilate ...

See also:

Laplace transform, Laplace transform - Formal definition, Laplace transform - Region of convergence, Laplace transform - Inverse Laplace transform, Laplace transform - Bilateral Laplace transform, Laplace transform - Laplace transform of a function's derivative, Laplace transform - Applications, Laplace transform - Example #1: Solving a differential equation, Laplace transform - Example #2: Deriving the complex impedance for a capacitor, Laplace transform - Example #3: Finding the transfer function from the impulse response, Laplace transform - Relationship to other transforms, Laplace transform - Fourier transform, Laplace transform - Mellin transform, Laplace transform - Z-transform, Laplace transform - Fundamental relationships, Laplace transform - Properties and theorems, Laplace transform - Table of selected Laplace transforms, Laplace transform - Examples: How to apply the properties and theorems, Laplace transform - Example #1: Method of partial fraction expansion, Laplace transform - Example #2: Mixing sines cosines and exponentials, Laplace transform - Example #3, Laplace transform - Example #4: Phase delay

Read more here: » Laplace transform: Encyclopedia II - Laplace transform - Bilateral Laplace transform

A repaint of the original Beast Machines toy of the same name, a character called Obsidian was released as a Decepticon in the RiD toyline. Due to the RiD universe not being directly connected to the Beast Machines universe, and the fact that this Obsidian did not appear in the TV show or in any other fiction, nor did he receive any sort of biography from Hasbro; it is unknown as to how similar he is to the original. ...

See also:

Obsidian Transformers, Obsidian Transformers - Transformers - Beast Machines, Obsidian Transformers - Transformers - Robots in Disguise, Obsidian Transformers - Transformers - Universe

Read more here: » Obsidian Transformers: Encyclopedia II - Obsidian Transformers - Transformers - Robots in Disguise

If η : F → G and ε : G → H are natural transformations between functors F,G:C → D, then we can compose them to get a natural transformation εη : F → H. This is done componentwise: (εη)X = εXηX. This "vertical composition" of natural transformation is associative and has an identity, and allows one to consider the collection of all functor ...

See also:

Natural transformation, Natural transformation - Definition, Natural transformation - Examples, Natural transformation - A worked example, Natural transformation - Further examples, Natural transformation - Operations with natural transformations, Natural transformation - Functor categories, Natural transformation - Yoneda lemma, Natural transformation - Historical notes

Read more here: » Natural transformation: Encyclopedia II - Natural transformation - Operations with natural transformations

Laplace transform - Fourier transform. The continuous Fourier transform is equivalent to evaluating the bilateral Laplace transform with complex argument s = iω: Note that this expression excludes the scaling fac ...

See also:

Laplace transform, Laplace transform - Formal definition, Laplace transform - Region of convergence, Laplace transform - Inverse Laplace transform, Laplace transform - Bilateral Laplace transform, Laplace transform - Laplace transform of a function's derivative, Laplace transform - Applications, Laplace transform - Example #1: Solving a differential equation, Laplace transform - Example #2: Deriving the complex impedance for a capacitor, Laplace transform - Example #3: Finding the transfer function from the impulse response, Laplace transform - Relationship to other transforms, Laplace transform - Fourier transform, Laplace transform - Mellin transform, Laplace transform - Z-transform, Laplace transform - Fundamental relationships, Laplace transform - Properties and theorems, Laplace transform - Table of selected Laplace transforms, Laplace transform - Examples: How to apply the properties and theorems, Laplace transform - Example #1: Method of partial fraction expansion, Laplace transform - Example #2: Mixing sines cosines and exponentials, Laplace transform - Example #3, Laplace transform - Example #4: Phase delay

Read more here: » Laplace transform: Encyclopedia II - Laplace transform - Relationship to other transforms

Obsidian is a legendary Cybertronian general who scored countless victories alongside his consort Strika. The two were captured by Megatron, who placed their sparks in Vehicon bodies. Obisidian became a helicopter, leading the aerial forces in place of the fallen Jetstorm. He quickly proved a dangerous foe to the Maximals, though during Megatron's absence and apparent death he joined them. When Megatron returned, Obisidian resumed command of the Vehicon air drones. He disappeared along with Strika during the final battle, and reportedly returned and refused reformatting as ...

See also:

Obsidian Transformers, Obsidian Transformers - Transformers - Beast Machines, Obsidian Transformers - Transformers - Robots in Disguise, Obsidian Transformers - Transformers - Universe

Read more here: » Obsidian Transformers: Encyclopedia II - Obsidian Transformers - Transformers - Beast Machines

Although the assorted Transformers series which followed the original often paid homage to many popular characters by naming new characters after them, or sculpting them to share their likeness, Shockwave was without an homage until the 2004 series, Transformers: Energon, where his likeness was paid homage to in the character of Shockblast. Hasbro had since lost the trademark to the name "Shockwave" to Lanard Toys, and compensated as best they could through use of this altered name, which was also used for the Alternator ...

See also:

Shockwave Transformers, Shockwave Transformers - Generation One, Shockwave Transformers - Animated Series, Shockwave Transformers - Marvel Comics, Shockwave Transformers - Dreamwave Comics, Shockwave Transformers - Alternators/Binaltech, Shockwave Transformers - Transformers: Energon Shockblast, Shockwave Transformers - Transformers: Cybertron

Read more here: » Shockwave Transformers: Encyclopedia II - Shockwave Transformers - Transformers: Energon Shockblast

The Z-transform, like many other integral transforms, can be defined as either a one-sided or two-sided transform. Z-transform - Bilateral Z-Transform. The bilateral or two-sided Z-transform of a discrete-time signal x[n] is the function X(z) defined as where n is an integer and z is, in general, a complex number: z = Aejφ where A is the magnitude of z, and φ is the angular ...

See also:

Z-transform, Z-transform - Definition, Z-transform - Bilateral Z-Transform, Z-transform - Unilateral Z-Transform, Z-transform - Inverse Z-Transform, Z-transform - Region of convergence, Z-transform - Example 1 No ROC, Z-transform - Example 2 causal ROC, Z-transform - Example 3 anticausal ROC, Z-transform - Examples conclusion, Z-transform - Properties, Z-transform - Table of common Z-transform pairs, Z-transform - Relationship to Laplace, Z-transform - Relationship to Fourier, Z-transform - Linear constant coefficient difference equation, Z-transform - Transfer function, Z-transform - Zeros and poles, Z-transform - Output response, Z-transform - Bibliography

Read more here: » Z-transform: Encyclopedia II - Z-transform - Definition

The inverse Laplace transform is the Bromwich integral, which is a complex integral given by: where is a real number so that the contour path of integration is in the region of convergence of normally requiring for every singularity of and . If all singularities are in the left half-plane, that is for every , then can be set to zero and the above inverse integral fo ...

See also:

Laplace transform, Laplace transform - Formal definition, Laplace transform - Region of convergence, Laplace transform - Inverse Laplace transform, Laplace transform - Bilateral Laplace transform, Laplace transform - Laplace transform of a function's derivative, Laplace transform - Applications, Laplace transform - Example #1: Solving a differential equation, Laplace transform - Example #2: Deriving the complex impedance for a capacitor, Laplace transform - Example #3: Finding the transfer function from the impulse response, Laplace transform - Relationship to other transforms, Laplace transform - Fourier transform, Laplace transform - Mellin transform, Laplace transform - Z-transform, Laplace transform - Fundamental relationships, Laplace transform - Properties and theorems, Laplace transform - Table of selected Laplace transforms, Laplace transform - Examples: How to apply the properties and theorems, Laplace transform - Example #1: Method of partial fraction expansion, Laplace transform - Example #2: Mixing sines cosines and exponentials, Laplace transform - Example #3, Laplace transform - Example #4: Phase delay

Read more here: » Laplace transform: Encyclopedia II - Laplace transform - Inverse Laplace transform

Notice: Some authors, e.g., Bracewell, use our as their definition of the forward transform. A consequence is that the right column of this table would be negated. Hilbert transform - The narrowband approximation. Many signals can be accurately modeled as the product of a relatively slowly varying function, , and a sinusoidal "carrier": where is much greater than the bandwidth of . Then: which means that the Hilbert transform significan ...

See also:

Hilbert transform, Hilbert transform - Hilbert transform examples, Hilbert transform - The narrowband approximation, Hilbert transform - Applications, Hilbert transform - Practical considerations, Hilbert transform - Discrete Hilbert transform

Read more here: » Hilbert transform: Encyclopedia II - Hilbert transform - Hilbert transform examples

The TF community does not seem to have a specific name for its members; often the generic "TF fan" is used, however this term is also applied to people who have a non-sexual interest in Transformation fiction. The internet community consists mainly of webpages featuring artwork or stories dealing with transformations, although there is no distinct barrier between fetish and non-fetish material. Most TF media share a few characteristics. They involve a human (of either gender, but most often a female) being transformed into another for ...

See also:

Transformation fetish, Transformation fetish - Overview, Transformation fetish - Categories of transformation fetishes, Transformation fetish - Animal transformations, Transformation fetish - Inanimate transformations, Transformation fetish - Age regression/Progression, Transformation fetish - Body modification, Transformation fetish - Transgender

Read more here: » Transformation fetish: Encyclopedia II - Transformation fetish - Overview

Transformers series - US. Transformers (1984 - 1987) (98 episodes) Beast Wars: Transformers (1996 - 1999) (52 episodes) Beast Machines: Transformers (1999) (26 episodes) Transformers: Robots in Disguise (2001) (39 episodes) Transformers: Armada (2002) (52 episodes) Transformers: Energon (2004) (52 episodes) Transformers: Cybertron (2005)See also:

Transformers series, Transformers series - Transformers TV series, Transformers series - US, Transformers series - Japan, Transformers series - Backstories, Transformers series - The Transformers G1 1984-1987 U.S. 98 episodes, Transformers series - Transformers: Headmasters 1987 Japan 35 episodes, Transformers series - Super God Masterforce 1988 Japan 43 episodes, Transformers series - Transformers: Victory 1989 Japan 44 episodes, Transformers series - Transformers: Zone 1990 Japan, Transformers series - Battlestars: Return of Convoy 1991 Japan, Transformers series - Operation Combination 1992 Japan, Transformers series - Transformers Generation 2 1992-95 U.S., Transformers series - Beast Wars: Transformers 1996-1999 Canada 52 episodes, Transformers series - Beast Wars Second: Super Lifeform Transformers 1998 Japan 43 episodes, Transformers series - Beast Wars Neo: Super Lifeform Transformers 1999 Japan 25 episodes, Transformers series - Beast Machines: Transformers 1999-2001 Canada 26 episodes, Transformers series - Transformers: Car Robots 2000 Japan 39 episodes, Transformers series - Transformers: Armada 2002-2003 U.S./Japan 52 episodes, Transformers series - Transformers: Energon 2004-2005 Japan/U.S. 52 episodes, Transformers series - Transformers: Cybertron 2005 Japan/U.S.

Read more here: » Transformers series: Encyclopedia II - Transformers series - Transformers TV series

Three-dimensional transformations can be defined synthetically as follows: point X on a "subjective" 3-space must be transformed to a point T also on the subjective space. The transformations uses these elements: a pair of "observation points" P and Q, and an "objective" 3-space. The subjective and objective spaces and the two points all lie in four-dimensional space, and the two 3-spaces can intersect at some plane. Draw line l1 through points X and P. This line intersects t ...

See also:

Projective transformation, Projective transformation - Transformations on the projective line, Projective transformation - Analysis, Projective transformation - Inverse transformation, Projective transformation - Identity transformation, Projective transformation - Composition of transformations, Projective transformation - The cross-ratio defined by means of a projection, Projective transformation - Conservation of cross-ratio, Projective transformation - Transformations on the projective plane, Projective transformation - Analysis, Projective transformation - Trilinear transformations, Projective transformation - Composition of trilinear transformations, Projective transformation - Planar transformations of lines, Projective transformation - Planar transformations of conic sections, Projective transformation - Planar projectivities and cross-ratio, Projective transformation - Example, Projective transformation - Transformations in projective 3-space, Projective transformation - Analysis, Projective transformation - Quadrilinear transformations, Projective transformation - Properties of quadrilinear transformations, Projective transformation - Spatial transformations of planes, Projective transformation - Reference

Read more here: » Projective transformation: Encyclopedia II - Projective transformation - Transformations in projective 3-space

There are two broad categories of chirplet transform: fixed adaptive These categories may be further subdivided by: choice of chirp choice of window In either the fixed or adaptive case, the chirplets may be: q-chirplets (quadratic chirplets) of the form exp(i 2π (a t2 + b t + c)) or, in general, some kind of quadratically varying exponent, linear swept wave packet, or the like. These are sometimes called linear FM chirplets (linear freque ...

See also:

Chirplet transform, Chirplet transform - Similarity to other transforms, Chirplet transform - What is a chirplet?, Chirplet transform - Applications, Chirplet transform - Taxonomy of chirplet transforms, Chirplet transform - Related work, Chirplet transform - Further ongoing work, Chirplet transform - External link

Read more here: » Chirplet transform: Encyclopedia II - Chirplet transform - Taxonomy of chirplet transforms

The following equation expresses an affine transformation in GF(2) (with "+" representing XOR): where [M] is the matrix and {v} is the vector For instance, the affine transformation of the element {a} = x7 + x6 + x3 + x = {11001010} in big-endian binary notation = {CA} in big-endian hexadecimal notation, is calculated as follows: ...

See also:

Affine transformation, Affine transformation - Affine transformation of the plane, Affine transformation - Example of an affine transformation

Read more here: » Affine transformation: Encyclopedia II - Affine transformation - Example of an affine transformation