In Shannon's revolutionary and groundbreaking paper, the work for which had been substantially completed at Bell Labs by the end of 1944, Shannon for the first time introduced the qualitative and quantitative model of communication as a statistical process underlying information theory, opening with the assertion that

A relationship to music as actually practised was not part of this study, but the framework of classical harmonics would substantially influence the content and structure of music theory as practised both in European and Islamic cultures.

One modern academic theory of religion, social constructionism, says that religion is a modern concept that suggests all spiritual practice and worship follows a model similar to the Abrahamic religions as an orientation system that helps to interpret reality and define human beings, and thus religion, as a concept, has been applied inappropriately to non-Western cultures that are not based upon such systems, or in which these systems are a substantially simpler construct.

Nevertheless, Freud's theory of the unconscious was substantially transformed by some of his followers, among them Carl Jung and Jacques Lacan.

Such elements include the essential idea of narrative structure, with identifiable beginnings, middles and endings, or exposition-development-climax-resolution-denouement, normally constructed into coherent plot lines ; a strong focus on temporality, which includes retention of the past, attention to present action, and protention / future anticipation ; a substantial focus on characters and characterization which is " arguably the most important single component of the novel "; a given heterogloss of different voices dialogically at play – " the sound of the human voice, or many voices, speaking in a variety of accents, rhythms and registers "; possesses a narrator or narrator-like voice, which by definition " addresses " and " interacts with " reading audiences ( see Reader Response theory ); communicates with a Wayne Booth-esque rhetorical thrust, a dialectic process of interpretation, which is at times beneath the surface, conditioning a plotted narrative, and other at other times much more visible, " arguing " for and against various positions ; relies substantially on now-standard aesthetic figuration, particularly including the use of metaphor, metonymy, synecdoche and irony ( see Hayden White, Metahistory for expansion of this idea ); is often enmeshed in intertextuality, with copious connections, references, allusions, similarities, parallels, etc.

In particular, in the area of petroleum geology, it seems that many in the Western hemisphere are under the impression that the theory of abiotic formation of petroleum, right or wrong, was originated or developed substantially by him, as evidenced by the foreword above, since he often did not properly credit his sources in this area of research ( including this book ).

This feature could in theory lead to potential arbitrage profits if the market price of the ETF were to diverge substantially from its NAV.

The open-ended theory suggests that the levels Coral and beyond are not yet substantially formed and will solidify as a greater portion of society develops towards those memes.

Although Rawls never retreated from the core argument of A Theory of Justice, he modified his theory substantially in subsequent works such as Justice as Fairness: A Restatement ( 2001 ), in which he clarified and re-organised much of the argument of A Theory of Justice.

Such elements include the essential idea of narrative structure, with identifiable beginnings, middles and ends, or exposition-development-climax-denouement, with important inciting incidents, normally constructed into coherent plot lines ; a strong focus on temporality that includes retention of the past, attention to present action and protention / future anticipation ; a substantial focus on characters and characterization which is " arguably the most important single component of the novel " ( David Lodge The Art of Fiction 67 ); a given hetergloss of different voices dialogically at play, " the sound of the human voice, or many voices, speaking in a variety of accents, rhythms and registers " ( Lodge The Art of Fiction 97 ; see also the theory of Mikhail Bakhtin for expansion of this idea ); possesses a narrator or narrator-like voice, which by definition " addresses " and " interacts with " reading audiences ( see Reader Response theory ); communicates with a Wayne Booth-esque rhetorical thrust, a dialectic process of interpretation, which is at times beneath the surface, conditioning a plotted narrative, and other at other times much more visible, " arguing " for and against various positions ; relies substantially on now-standard aesthetic figuration, particularly including the use of metaphor, metonymy, synecdoche and irony ( see Hayden White, Metahistory for expansion of this idea ); is often enmeshed in intertextuality, with copious connections, references, allusions, similarities, parallels, etc.

The former, not to be confused with ' New Keynesian and the many offsprings and various syntheses of ' The General Theory ', take the fact that a commodity-commodity economy is substantially altered in content once it becomes a commodity-money-commodity economy, or once money becomes not only a facilitator of exchange as is its only function in marginalist theory but a store of value and means of payment as well.

A South Carolina appeals court upheld a $ 24, 000 jury verdict against Peck for slander ( the jury had stricken the outrageous conduct count, which is substantially the same as a claim for intentional infliction of emotional distress ), on the theory that when Peck cast an aspersion upon Wardlaw's chastity, his public remarks were slanderous per se.

In modern dramatic theory the term dramatic arc has substantially the same meaning, though with slightly different divisions.

This is correct and, in fact, when one realizes that any two-dimensional harmonic function is the real part of a complex analytic function, one sees that the subject of two-dimensional potential theory is substantially the same as that of complex analysis.

Although his arguments sometimes lacked mathematical rigor even by physicists ' standards and glossed over details such as the derivation of Ward-Takahashi identities of the quantum theory, his calculations worked, and Freeman Dyson soon demonstrated that his method was substantially equivalent to those of Julian Schwinger and Sin-Itiro Tomonaga, with whom Feynman shared the 1965 Nobel Prize in Physics.

The terror management theory can help to explain why a leader's popularity can grow substantially during times of crisis.

Marxism comprised a theory of history ( historical materialism ) as well as a political, economic and philosophical theory.

In this theory, he stated that the spinal cord is comprised by a chain of units that functions as an independent reflex arcs, and their activity integrates sensory and motor nerves at the segment of the spinal cord from which these nerves originate.

This can only be for one of two reasons: either the two are quite different and will require totally different theory ( and hence techniques ), or our existing theories are insufficiently general.

It was not always easy to develop theory and doctrine which would square the two conditions.

The discovery of this particle the next year removed the last two objections to his theory.

This is an example of renormalization in quantum field theory — the field theory being necessary because the number of particles changes from one to two and back again.

Others have discredited the theory about the Galilean Tekoa, citing that the difference in elevation between the two locations is not significant.

For some time Rome and Antioch have been in favor, and Blass combined both views in his theory of two editions.

Adherents of this theory argue that even when the two versions diverge, they both have similarities in vocabulary and writing style — suggesting that the two shared a common author.

In the language of valence bond theory, the carbon atoms in an alkyne bond are sp hybridized: they each have two unhybridized p orbitals and two sp hybrid orbitals.

This theory of Homer's influence on Beowulf remained very prevalent in the 1920s, but started to die out in the following decade when a handful of critics stated that the two works were merely “ comparative literature ” although Greek was known in contemporary England.

The choice between the two definitions usually matters only in very formal contexts, like category theory.

In basic electric circuit theory, when studying band-pass and band-reject filters, the bandwidth represents the distance between the two points in the frequency domain where the signal is of the maximum signal amplitude ( half power ).

Pascal was an important mathematician, helping create two major new areas of research: he wrote a significant treatise on the subject of projective geometry at the age of sixteen, and later corresponded with Pierre de Fermat on probability theory, strongly influencing the development of modern economics and social science.

The Big Bang theory depends on two major assumptions: the universality of physical laws and the cosmological principle.

A major modification to Noth's theory was made in 1973 by the American scholar Frank M. Cross, to the effect that two editions of the history could be distinguished, the first and more important from the court of king Josiah in the late 7th century, and the second Noth's 6th century Exilic history, and other scholars have detected many more authors / editors than either Noth or Cross allowed for.

There are two parts to Einstein's theory: the first part consists in the formulation of a diffusion equation for Brownian particles, in which the diffusion coefficient is related to the mean squared displacement of a Brownian particle, while the second part consists in relating the diffusion coefficient to measurable physical quantities.

In the past two decades computer analysis has contributed significantly to chess theory as understood by human players, particularly in the endgame.

It should be noted that while there are very strong connections between graph theory and combinatorics, these two are sometimes thought of as separate subjects.

Using terms from formal language theory, the precise mathematical definition of this concept is as follows: Let S and T be two finite sets, called the source and target alphabets, respectively.

Eventually in 1965, John Bardeen, Leon Cooper and John Schrieffer developed the so-called BCS theory of superconductivity, based on the discovery that arbitrarily small attraction between two electrons can give rise to a bound state called a Cooper pair.

In his two volume work The Open Society and Its Enemies, Karl Popper used the term " conspiracy theory " to criticize the ideologies driving fascism, nazism, and Stalinism.

The octet rule and VSEPR theory are two examples.

It is possible to prove many theorems using neither the axiom of choice nor its negation ; such statements will be true in any model of Zermelo – Fraenkel set theory ( ZF ), regardless of the truth or falsity of the axiom of choice in that particular model.

Based on this theory some statements, or hypotheses, will be proposed ( e. g., " Listening to vocal music has a negative effect on learning a word list .").

Many-worlds is often referred to as a theory, rather than just an interpretation, by those who propose that many-worlds can make testable predictions ( such as David Deutsch ) or is falsifiable ( such as Everett ) or by those who propose that all the other, non-MW interpretations, are inconsistent, illogical or unscientific in their handling of measurements ; Hugh Everett argued that his formulation was a metatheory, since it made statements about other interpretations of quantum theory ; that it was the " only completely coherent approach to explaining both the contents of quantum mechanics and the appearance of the world.

The Hausdorff maximal principle is one of many statements equivalent to the axiom of choice over Zermelo – Fraenkel set theory.

The long-term importance of the Resolutions lies not in their attack on the Alien and Sedition Acts, but rather in their strong statements of states ' rights theory, which led to the rather different concepts of nullification and interposition.

Then the theory at hand, which is assumed to prove certain facts about numbers, also proves facts about its own statements.

Questions about the provability of statements are represented as questions about the properties of numbers, which would be decidable by the theory if it were complete.

Thus in theory, if law enforcement officials decline to offer a Miranda warning to an individual in their custody, they may still interrogate that person and act upon the knowledge gained, but may not use that person's statements to incriminate him or her in a criminal trial.

The Talmud records a tradition that unattributed statements of the law represent the views of Rabbi Meir ( Sanhedrin 86a ), which supports the theory ( recorded by Rav Sherira Gaon in his famous Iggeret ) that he was the author of an earlier collection.

While the theory of combining multiple arts into one art is quite old, and has been revived periodically, the postmodern manifestation is often in combination with performance art, where the dramatic subtext is removed, and what is left is the specific statements of the artist in question or the conceptual statement of their action.

In its axiomatic form, mathematical statements about probability theory carry the same sort of epistemological confidence shared by other mathematical statements in the philosophy of mathematics.

In the above, P is the proposition we wish to disprove respectively prove ; and S is a set of statements, which are the premises — these could be, for example, the axioms of the theory we are working in, or earlier theorems we can build upon.

When a statistical procedure has been specified in the study protocol, then statistical theory provides well-defined probability statements for the method when applied to all populations that could have arisen from the randomization used to generate the data.

This type of theory posits a relationship between thoughts or statements on one hand, and things or objects on the other.

However, the truth of any one of these statements is always relative to the whole theory.

This is, in ordinary language, where statements such as " He is a terrible person " cannot be judged to be true or false without reference to some interpretation of who " He " is and for that matter what a " terrible person " is under the theory.

Gödel's incompleteness theorem shows that no consistent, recursively enumerable theory ( that is, one whose theorems form a recursively enumerable set ) in which the concept of natural numbers can be expressed, can include all true statements about them.

At least some of the elementary theorems of a philosophical theory are statements whose truth cannot necessarily be scientifically tested through empirical observation.

Logic, especially in the field of proof theory, considers theorems as statements ( called formulas or well formed formulas ) of a formal language.

The most famous result is Gödel's incompleteness theorem ; by representing theorems about basic number theory as expressions in a formal language, and then representing this language within number theory itself, Gödel constructed examples of statements that are neither provable nor disprovable from axiomatizations of number theory.