Except for the Dym equation and the Ginzburg – Landau equation, the above equations are linear in the sense that they can be written in the form Au = f for a given linear operator A and a given function f. Other important non-linear equations include the Navier – Stokes equations describing the flow of fluids, and Einstein's field equations of general relativity.

In Einstein's general relativity, coordinates like x, y, z, and t are not only " relative " in the global sense of translations like, rotations, etc., but become completely arbitrary, so that for example one can define an entirely new timelike coordinate according to some arbitrary rule such as, where has units of time, and yet Einstein's equations will have the same form.

If quantum mechanics can be made complete in Einstein's sense, it cannot be done locally ; this fact was demonstrated by John Stewart Bell with the formulation of Bell's inequality in 1964 ; however, should we live in a superdeterminist universe, that demonstration would not be valid, as admitted by Bell himself.

What is the history of criticism but the history of men attempting to make sense of the manifold elements in art that will not allow themselves to be reduced to a single philosophy or a single aesthetic theory??

Thus, in no ordinary sense of ' simplicity ' is the Ptolemaic theory simpler than the Copernican.

but on the theory before us such a belief would not make sense.

Perhaps one way to sharpen our sense of the modernity of Utopian communism is to contrast it with the principal earlier types of communistic theory.

These are equivalent in the sense that, in the presence of other basic axioms of set theory, they imply the axiom of choice and are implied by it.

In category theory, an automorphism is an endomorphism ( i. e. a morphism from an object to itself ) which is also an isomorphism ( in the categorical sense of the word ).

Occasionally, " almost all " is used in the sense of " almost everywhere " in measure theory, or in the closely related sense of " almost surely " in probability theory.

Against this, the Averroists, led by Agostino Nifo, introduced the modifying theory that universal reason in a sense individualizes itself in each soul and then absorbs the active reason into itself again.

According to the theory, the human experience of moral obligations was the result of evolutionary pressures, which attached a sense of morality to human psychology because it was useful for moral development ; this entail that moral values do not exist independently of the human mind.

This allows for the formation of sets based on properties, in a limited sense, while ( hopefully ) preserving the consistency of the theory.

In the sense of this article, a naive theory is a non-formalized theory, that is, a theory that uses a natural language to describe sets.

However, the term naive set theory is also used in some literature to refer to the set theories studied by Frege and Cantor, rather than to the informal counterparts of modern axiomatic set theory ; care is required to tell which sense is intended.

Category theory is also, in some sense, a continuation of the work of Emmy Noether ( one of Mac Lane's teachers ) in formalizing abstract processes ; Noether realized that in order to understand a type of mathematical structure, one needs to understand the processes preserving that structure.

From this perspective, much literary critical theory, since it is focused on interpretation and explanation rather than on social transformation, would be regarded as positivistic or traditional rather than critical theory in the Kantian or Marxian sense.

This sense of moderation and fairness is superbly exemplified in an exchange of letters between John Jay and a Tory refugee, Peter Van Schaack.

The process stipulates that the choreographer sense the quality of the initial movement he has discovered and that he feel the rightness of the quality that is to follow it.

It is not a mess you can make sense of ''.

In addition, they have been converted to Zen Buddhism, with its glorification of all that is `` natural '' and mysteriously alive, the sense that everything in the world is flowing.

Piepsam is not, certainly, religious in any conventional sense.

Mimesis here is not to be confused with literalism or realism in the conventional sense.

Neither is primary experience understood according to the attitude of modern empiricism in which nothing is thought to be received other than signals of sensory qualities producing their responses in the appropriate sense organs.

These desires presuppose a sense of causally efficacious powers in which one is involved, some working for one's good, others threatening ill.

he is questioning, also, every epistemology which stems from Hume's presupposition that experience is merely sense data in abstraction from causal efficacy, and that causal efficacy is something intellectually imputed to the world, not directly perceived.

As long as perception is seen as composed only of isolated sense data, most of the quality and interconnectedness of existence loses its objectivity, becomes an invention of consciousness, and the result is a philosophical scepticism.

The corporation in America is in reality our form of socialism, vying in a sense with the other socialistic form that has emerged within governmental bureaucracy.

The only way to describe Paula Sandburg is to say she is beautiful in a Grecian sense.

If in any one calculation Ptolemy had had to invoke 83 epicycles all at once, while Copernicus never required more than one third this number, then ( in the sense obvious to Margenau ) Ptolemaic astronomy would be simpler than Copernican.

The possible wagers are usually fewer than the wagers that are possible in sic bo and, in that sense, chuck-a-luck can be considered to be a simpler game.

In this sense, the higher-level multiverses are simpler.

On the other hand it is often claimed that, despite the apparently ever-increasing complexity of the mathematics of each new theory, in a deep sense associated with their underlying gauge symmetry and the number of fundamental physical constants, the theories are becoming simpler.

In religion, emergence grounds expressions of religious naturalism in which a sense of the sacred is perceived in the workings of entirely naturalistic processes by which more complex forms arise or evolve from simpler forms.

Put in simpler words, the particles postulated by the de Broglie – Bohm theory are anything but " hidden " variables: they are what the objects we see in everyday experience are made of ; it is the wavefunction itself which is " hidden " in the sense of being invisible and not-directly-observable.

Using Galois theory, certain problems in field theory can be reduced to group theory, which is in some sense simpler and better understood.

In a simpler sense, multistatic radars are systems which have two or more receiving sites with a common spatial coverage area, and data from these coverage areas are combined and processed at a central location.

:... projective geometry is simpler than algebra in a certain sense, because we use only five geometric axioms to derive the nine field axioms.

However, in one sense they are simpler: the use of a separate rectifier is unnecessary because they can provide either AC or DC.

Yet, there are some situations in which one wants to speak about elements that are in a sense much simpler ( or much more incomplete ) than a given state of information.

Besides appearing naturally in many parts of mathematics, bimodules play a clarifying role, in the sense that many of the relationships between left and right modules become simpler when they are expressed in terms of bimodules.

A drum is inferior to a belt in the sense that although it is simpler than a belt, it must be buffered gradually in parts rolling on the drum.

This simpler way is demonstrated to us in daily life, not the life we see on the news with its unending stories of human grief and horror, but what we feel when we experience a sense of life ’ s deep harmony, beauty, and power, of how we feel when we see people helping each other, when we feel creative, when we know we ’ re making a difference, when life feels purposeful.