A fourth view is the transformation of emotion, as in Housman's fine phrase on the arts: they `` transform and beautify our inner nature ''.

Clearly, the transformation is involutorial.

Moreover, from the definitive transformation of intercepts on the generators of Af, it is clear that the only points of Q at which a line can meet its image are the points of Aj.

Now consider the transformation of the lines of a bundle with vertex, P, on **zg which is effected by the involution as a whole.

the way in which the transformation of state depends on the operating variables for the main types of reactors is discussed in the next chapter.

He recognized that whatever transformation may be effected in the first stage of an R-stage process, the remaining stages must use an optimal Af-stage policy with respect to the state resulting from the first stage, if there is to be any chance of optimizing the complete process.

This transformation is uniquely determined by Af and we therefore speak of the process as deterministic.

The whole role, by the way, is a considerable transformation for anyone who has seen Seigner in his other parts.

According to Cauchy's functional equation theorem, the logarithm is the only continuous transformation that transforms real multiplication to addition.

To avoid attacks based on simple algebraic properties, the S-box is constructed by combining the inverse function with an invertible affine transformation.

Bruce Hindmarsh suggests that the secular popularity of " Amazing Grace " is due to the absence of any mention of God in the lyrics until the fourth verse ( by Excell's version, the fourth verse begins " When we've been there ten thousand years "), and that the song represents the ability of humanity to transform itself instead of a transformation taking place at the hands of God.

James Basker also acknowledged this force when he explained why he chose " Amazing Grace " to represent a collection of anti-slavery poetry: " there is a transformative power that is applicable ...: the transformation of sin and sorrow into grace, of suffering into beauty, of alienation into empathy and connection, of the unspeakable into imaginative literature.

A transformation of a thermodynamic system can be considered adiabatic when it is quick enough that no significant heat is transferred between the system and the outside.

At the opposite extreme, a transformation of a thermodynamic system can be considered isothermal if it is slow enough so that the system's temperature remains constant by heat exchange with the outside.

The shift in Aalto's design approach from classicism to modernism is epitomised by the Viipuri Library ( 1927 – 35 ), which went through a transformation from an originally classical competition entry proposal to the completed high-modernist building.

Some theories connect these flows directly, implying that there is significant upwelling of dense deep waters within the Southern Ocean, transformation of these waters into light surface waters, and a transformation of waters in the opposite direction to the north.

This is because such flows can produce a net southward flow in the troughs and a net northward flow over the ridges without requiring any transformation of density.

Skewing is an example of a transformation not usually considered.

This gradual transformation is an important consideration when studying the properties of elemental berkelium and its chemical compounds, since the formation of californium brings not only chemical contamination, but also self-radiation damage, and self-heating from the emitted alpha particles.

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.

The category of sets is closed monoidal, but so is the category of vector spaces, giving the notion of bilinear transformation above.

While most elements are generally viewed as stable, a small amount of natural transformation of one element to another also occurs in the present time, through decay of radioactive elements as well as other natural nuclear processes.

Digital filtering generally consists of some linear transformation of a number of surrounding samples around the current sample of the input or output signal.

This image transformation generally requires digital signal processing, so letterboxing was the only way in which films were presented in widescreen on home video prior to the DVD format ( with a few exceptions outside the mass market, such as Squeeze LD ).

Punctuated equilibrium is commonly contrasted against the theory of phyletic gradualism, which states that evolution generally occurs uniformly and by the steady and gradual transformation of whole lineages ( called anagenesis ).

NGOs are organizations that work in many different fields, but the term is generally associated with those seeking social transformation and improvements in quality of life.

From an evolutionary perspective, a convoluted structure such as the inverted retina can generally come about as a consequence of two alternative processes ; ( a ) an advantageous " good " compromise between competing functional limitations, or ( b ) as a historical maladaptive relic of the convoluted path of organ evolution and transformation.

Rasterization systems generally use a transformation stack to move the stream of input vertices into place.

His love themes are honeyed and chromatic and generally richly scored, and he is often fond of the warmth and serenity of diatonic harmony as balm after torrential chromatic textures, notably at the end of Don Quixote, where the solo cello has a surpassingly beautiful D major transformation of the main theme.

Spectral models generally use a gaussian grid, because of the mathematics of transformation between spectral and grid-point space.

Among these features are mapping between screen-and world-coordinates, generation of texture mipmaps, drawing of quadric surfaces, NURBS, tessellation of polygonal primitives, interpretation of OpenGL error codes, an extended range of transformation routines for setting up viewing volumes and simple positioning of the camera, generally in more human-friendly terms than the routines presented by OpenGL.

A length-preserving transformation which reverses orientation is an improper rotation, that is a reflection or more generally a rotoinversion.

In Greek mythology, Zeus frequently transformed himself and his love to escape Hera's wrath, or that of the women's fathers, but generally in a simplified form, with only one transformation.

Maxwell's equations can also be expressed in a generally covariant form, which is as invariant under general coordinate transformation as Einstein's field equation.

DES-exposed daughters are at an increased risk of abnormalities of the reproductive tract, including vaginal epithelial changes ( which as vaginal adenosis, means a type of tissue develops on the surface of the vagina that is not generally found there ), an increased cervical transformation zone, and uterine abnormalities, such as T-shaped uterus.

Although figurines showing such combinations of features are generally termed " transformation figures ", some researchers argue that they represent humans in animal masks or animal suits, while others state that they likely represent shamans.

or more generally an affine transformation and hence represented by a matrix.

Transfection differs from transformation since the DNA is not generally incorporated into the cell's genome, it is only transiently expressed.

Most still tend to have an evangelical, or even fundamentalist, statement of faith ; however, they are generally more concerned with being inclusive than exclusive, and often will attempt to accommodate individuals and churches with more liberal theological views if they share a compatible vision of the goals and means of transformation.

It is generally agreed that the transformation from dance to symphony in the Fourth is accomplished with less success than is the metamorphosis from The Flaming Angel to the Third Symphony, and whether in reworking the 1930 version Prokofiev wholly succeeded remains open to question.

Another aspect of the transformations that added to the show's camp factor involved Dr. Chase's clothing during a transformation: He was depicted generally wearing a three-piece suit and tie, and the viewer would see it rip off of him as he shape-shifted into an animal, though once the transformation was complete there would be no sign of his discarded clothing.

These n + 1-dimensional transformation matrices are called, depending on their application, affine transformation matrices, projective transformation matrices, or more generally non-linear transformation matrices.