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.

The bilinear transform is a special case of a conformal mapping ( namely, the Möbius transformation ), often used to convert a transfer function of a linear, time-invariant ( LTI ) filter in the continuous-time domain ( often called an analog filter ) to a transfer function of a linear, shift-invariant filter in the discrete-time domain ( often called a digital filter although there are analog filters constructed with switched capacitors that are discrete-time filters ).

In chemical thermodynamics the term used for the chemical potential energy is chemical potential, and for chemical transformation an equation most often used is the Gibbs-Duhem equation.

Originally during his appearances in Action Comics and later in his own magazine, the Man of Steel would strip to his costume and stand revealed as Superman, often with the transformation having already been completed.

In the Fleischer theatrical cartoons released by Paramount, the mild-mannered reporter often ducked into a telephone booth or stock room to make the transformation.

There, the transformation of graphs is often formalized and represented by graph rewrite systems.

In his preaching, he often emphasized the Quaker rejection of baptism by water ; this was a useful way of highlighting how the focus of Friends on inward transformation differed from what he saw as the superstition of outward ritual.

Although alteration or transformation of jazz by new influences has often been initially criticized as a “ debasement ,” Andrew Gilbert argues that jazz has the “ ability to absorb and transform influences ” from diverse musical styles.

In such analyses, the Laplace transform is often interpreted as a transformation from the time-domain, in which inputs and outputs are functions of time, to the frequency-domain, where the same inputs and outputs are functions of complex angular frequency, in radians per unit time.

Historians often argue this intellectual transformation was a bridge between the Middle Ages and the Modern era.

This awakening to moral and spiritual realities thus precedes a transformation of lifestyle and thought patterns often taking place over a long period of time and requiring a significant level of effort and commitment as described in the spiritual teachings of the world's great religions.

Historians and economists have often praised Jenkins for presiding over the transformation in Britain ’ s fiscal and current account positions towards the end of the 1960s.

Cook believes that both contemporary Jews and contemporary Christians need to reexamine the history of early Christianity, and the transformation of Christianity from a Jewish sect consisting of followers of a Jewish Jesus, to a separate religion often dependent on the tolerance of Rome while proselytizing among Gentiles loyal to the Roman empire, to understand how the story of Jesus came to be recast in an anti-Jewish form as the Gospels took their final form.

In other cases, the transformation was supposedly accomplished by Satanic allegiance for the most loathsome ends, often for the sake of sating a craving for human flesh.

This important transformation often colors discussion of sexual behavior in the later 20th century.

In molecular biology, the process of electroporation is often used for the transformation of bacteria, yeast, and plant protoplasts.

Morbidity is often a result of plexiform neuromas, optic gliomas, or acoustic neuromas, but mortality can also be associated with malignant transformation of the neuromas, such as neurofibrosarcomas ( often there is a malignant transformation in less than 3 % of the cases of NF1 ).

This is why often a diabatic transformation is applied, which retains part of the nuclear kinetic energy terms on the diagonal, removes the kinetic energy terms from the off-diagonal and creates coupling terms between the adiabatic PESs on the off-diagonal.

Ovid works his way through his subject matter, often in an apparently arbitrary fashion, by jumping from one transformation tale to another, sometimes retelling what had come to be seen as central events in the world of Greek mythology and sometimes straying in odd directions.

White blackface performers in the past used burnt cork and later greasepaint or shoe polish to blacken their skin and exaggerate their lips, often wearing woolly wigs, gloves, tailcoats, or ragged clothes to complete the transformation.

Assuming that translation is not used transformations can be combined by simply multiplying the associated transformation matrices.

A geometric interpretation can be given to the value of the determinant of a square matrix with real entries: the absolute value of the determinant gives the scale factor by which area or volume is multiplied under the associated linear transformation, while its sign indicates whether the transformation preserves orientation.

After becoming associated with repression of popular discontent in the years after 1815, the Tories underwent a fundamental transformation under the influence of Robert Peel, himself an industrialist rather than a landowner, who in his 1834 " Tamworth Manifesto " outlined a new " Conservative " philosophy of reforming ills while conserving the good.

Given a morphism f: B → A the associated natural transformation is denoted Hom ( f ,–).

Mapping each object A in C to its associated hom-functor h < sup > A </ sup > = Hom ( A ,–) and each morphism f: B → A to the corresponding natural transformation Hom ( f ,–) determines a contravariant functor h < sup >–</ sup > from C to Set < sup > C </ sup >, the functor category of all ( covariant ) functors from C to Set.

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.

It has been also been demonstrated that phosphorylation of a middle-T antigen on tyrosine is also associated with cell transformation, a change that is similar to cellular growth or reproduction.

The Council also supports an environmental science program that involves dozens of staff and associated scientists ; this includes a major program which seeks transformation of manufacturing industries to more sustainable production.

The left null space of A is the orthogonal complement to the column space of A, and is the cokernel of the associated linear transformation.

# transformation rules, algorithms, which may be carried out by associated human roles or machines, or a combination

Although technically not a doppelgänger, the imposture threatens Roth's self-identity and forces him to undergo a personal transformation, both themes associated with Doppelgangers in fiction.

All the characteristic temperatures associated to phases transformation, glass transitions and melting points, occurring during a sinterisation cycle of a particular ceramics formulation ( i. e., tails and frits ) can be easily obtained by observing the expansion-temperature curves during optical dilatometer thermal analysis.

Often, a single leader became associated with this revolutionary transformation, and came to be treated as a benevolent " guide " for the nation without whom the transformation to a better future couldn't occur.

Portrayed in more detail, it is associated with ( 1 ) a certain set of attitudes towards the world, the idea of the world as open to transformation, by human intervention ; ( 2 ) a complex of economic institutions, especially industrial production and a market economy ; ( 3 ) a certain range of political institutions, including the nation-state and mass democracy.

" character transformation "), from the Japanese 文字 ( moji ) " character " + 化け ( bake ) " transform ", is the presentation of incorrect, unreadable characters when software fails to render text correctly according to its associated character encoding.

The geological history of the Salar is associated with a sequential transformation between several vast lakes.

The Prandtl-Glauert transformation is found by linearizing the potential equations associated with compressible, inviscid flow.

The Prandtl-Glauert transformation is found by linearizing the potential equations associated with compressible, inviscid flow.

… At all events the incense-burner remained the centre of changes and transformations associated with worship, sacrifice, ascending perfume of sweet savour, fire, combustion, disintegration, transformation, vision, communication with spiritual beings, and assurances of immortality.

Jacques Vallee, Hynek's erstwhile associate, argued that a CE4 should be described as " cases when witnesses experienced a transformation of their sense of reality ," so as to also include non-abduction cases where absurd, hallucinatory or dreamlike events are associated with UFO encounters.