139 Sentences With "corollaries" | Random Sentence Generator

The ensuing corollaries are predictability, dependability, responsibility, discipline and orderliness.

There are other Chinese corollaries to ShareChat's business that may be informative.

The album's cumulative effect is to take a sobering look at the corollaries of romance.

What's fascinating are the corollaries in other areas of tech, like with Uber, for instance.

There are corollaries there in terms of the logical frameworks that are appealing to people.

Most vegetable substitutes for animal proteins lacked the flavor, texture and nutritional heft of their animal corollaries.

The big news of this release is probably that more standalone iPhone apps are getting watchOS corollaries.

No, I mean, as with a lot of these things, without real world corollaries, they wouldn't exist.

He's the showrunner for both, corollaries to his role as the chief creative officer of Archie Comics.

You write that some "dumbed-down corollaries" of postmodernism have seeped into the thinking of the populist right.

All of these trends have corollaries in their American peers, and hold enormous implications for consumer brands around the globe.

And one of the corollaries to the debt issue is -- is that they begin to worry about money leaving the country.

The Dakotas and Montana are known as ranching states, but their Steak House corollaries, named with rapier-like irony, are vegetarian.

Insomniacs suffer mood and memory impairments, among other undesirable corollaries, researchers from the University of Pittsburgh School of Medicine have verified.

Further, with "women" and "family" as go-to cultural corollaries, studies show, terrifyingly, that these biases are being adopted by artificial intelligence, too.

Friston himself tended to take a more measured tone as our talks went on, suggesting only that active inference and its corollaries were quite promising.

On of the corollaries is that sometimes you get it wrong and your child is not ready — or is much farther along than you thought.

"We have experienced the consequences of Ivoirite: interminable political crises with their corollaries of thousands of deaths," Joel N'Guessan, an RDR vice president, said in a statement.

The installation is chaotic, but manages to draw corollaries between selections from the CU Museum of Natural History, the university's greenhouse, and the art museum's permanent collection.

But developments in the Papadopoulos and Manafort cases Monday—unique among perhaps all previous cases in the Justice Department—provide some corollaries for us to consider going forward.

In the disembodied world of social media, food is appreciated as an almost exclusively visual medium, enshrined in hyper-processed, highly mannered photos without true corollaries in the physical world.

In recent years, psychologists and society at large have begun wrestling with the problems of screen addiction and its corollaries in online pornography addiction, gambling addiction and gaming addiction more broadly.

Like Wilson's work, these terms are operating here on multiple levels, referring simultaneously to the literal color (or absence of color) of many of the pieces on display and their racial corollaries.

It took a while for Washington to sober up from its missionary zeal, and to realize the importance of China's bold and seemingly unstoppable economic development — with all of its political and security corollaries.

The absurd corollaries to ignoring IMF rules are the accusations of trade protectionism that come whenever Washington denounces the inappropriate, beggar-thy-neighbor, economic and trade policies of surplus countries that refuse to balance their trade accounts.

He felt and showed the necessity to imbue his painting with modern and contemporary critique involving corollaries that befits serious and open engagement with processes and materials while examining the world, and contributing a different proposition and realization to it.

However, I do believe that women are held to different implicit cultural biases and vernacular corollaries and my point was meant to express how important it is to be aware of these complacent tags we put on women and mothers.

Once we regard living things as agents performing a computation—collecting and storing information about an unpredictable environment—capacities and considerations such as replication, adaptation, agency, purpose and meaning can be understood as arising not from evolutionary improvisation, but as inevitable corollaries of physical laws.

Through a series of experiments intended to peel back the psychological layers around this phenomenon, Thibodeau found evidence to support a new theory that "moist" is hated not for its phonetic properties, but for its semantic corollaries that make us think of bodily fluids, or effluvia.

Her male contemporaries, most notably Frank Stella and Carl Andre (whose influences can be felt in Hammond's work), rejected the expressive drives that had characterized Abstract Expressionism's "action painting" the decade prior, electing instead an industrial vocabulary of materials and processes that erased sentient corollaries of gesture and touch.

Tyson Ventures has invested in New Wave Foods, a startup making a plant-based shrimp substitute What has set Impossible Foods and Beyond Meat apart from other competitors — at least in the eyes of the investors — is the research and development teams that are working on flavor profiles and products that simply are more direct corollaries to the products they're looking to supplant.

The Not Company co-founders Karim Pichara, Matias Muchnick and Pablo Zamora The Not Company co-founders Karim Pichara, Matias Muchnick and Pablo Zamora At the heart of The Not Company's work, like its incredibly well-funded, once-troubled US-based competitor Just (which was formerly known as Hampton Creek) is a machine learning technology that maps the similarities between the genetic properties of plants and their corollaries in animals.

Further research is necessary to discover the genetic corollaries to delayed gratification.

One of the corollaries of his formal egressions was an unhappiness with the exact identity of every text he published.

However, lemmas are sometimes embedded in the proof of a theorem, either with nested proofs, or with their proofs presented after the proof of the theorem. Corollaries to a theorem are either presented between the theorem and the proof, or directly after the proof. Sometimes, corollaries have proofs of their own that explain why they follow from the theorem.

Both lines are only briefly combined corollaries to the main lines to major towns however were from 1923 until 1996 in the same ownership.

Energy metabolism. Tissue determinants and cellular corollaries. 61–79 Raven Press New York. making a 160 fold difference between the energy consumption of inactive and active muscles.

Atiyah and Hirzebruch then specialised and refined in the case X = a point, where the condition becomes the existence of a spin structure on Y. Corollaries are on Pontryagin classes and the J-homomorphism.

For instance, by Simplicius in his Corollaries on Place. The most significant early critique was made in terms of geometry by the 11th- century Arab polymath al-Hasan Ibn al-Haytham (Alhazen) in his Discourse on Place.

They are the building blocks of geometric concepts, since they specify the properties that the primitives have. # The laws of logic. # The theoremsIn this context no distinction is made between different categories of theorems. Propositions, lemmas, corollaries, etc.

With the evolution of the digital age, application of freedom of speech and its corollaries (freedom of information, access to information) becomes more controversial as new means of communication and restrictions arise including government control or commercial methods putting personal information to danger.

Theorems and Theories , Sam Nelson.Mark C. Chu- Carroll, March 13, 2007:Theorems, Lemmas, and Corollaries. Good Math, Bad Math blog. A physical theory similarly differs from a mathematical theory, in the sense that the word "theory" has a different meaning in mathematical terms.

Several corollaries are immediate from the theorem. For instance, a densely defined closed operator T as above has R(T)=Y if and only if the transpose T' has a continuous inverse. Similarly, R(T') = X' if and only if T has a continuous inverse.

Seek information on the acquisition-learning hypothesis to learn more about the differentiations between learning and acquisition It must be stressed, however, that just any input is not sufficient; the input received must be comprehensible. According to Krashen, there are three corollaries to his theory.

There are now several different manuscripts (see below) with details of the proof. The Poincaré conjecture and the spherical space form conjecture are corollaries of the geometrization conjecture, although there are shorter proofs of the former that do not lead to the geometrization conjecture.

The development of the field of Tauberian theorems received a fresh turn with Norbert Wiener's very general results, namely Wiener's Tauberian theorem and its large collection of corollaries. The central theorem can now be proved by Banach algebra methods, and contains much, though not all, of the previous theory.

1838) and Döllinger (1799-1890) he carried on their methods and helped to establish what was the special character of the German school, exact investigation of the historical development of theology, rather than philosophical speculation about the corollaries of dogma. He died on 19 June 1883 at Würzburg.

This has strikingly simple immediate corollaries, such as the fact that any closed smooth 3-manifold which admits a Riemannian metric of positive curvature also admits a Riemannian metric of constant positive sectional curvature. Such results are notable in highly restricting the topology of such manifolds; the space forms of positive curvature are largely understood. There are other corollaries, such as the fact that the topological space of Riemannian metrics of positive Ricci curvature on a closed smooth 3-manifold is path-connected. These "convergence theorems" of Hamilton have been extended by later authors, in the 2000s, to give a proof of the differentiable sphere theorem, which had been a major conjecture in Riemannian geometry since the 1960s.

Most important, the Bohemian Diet would have authority over all other local issues. The “Nationality Laws” came as corollaries to the “Fundamental Articles.” They created administrative areas which would be nationally homogenous. Furthermore, the Czech and German languages would become the official languages for all functions pertaining to all of Bohemia.

Mathematical statements have their own moderately complex taxonomy, being divided into axioms, conjectures, propositions, theorems, lemmas and corollaries. And there are stock phrases in mathematics, used with specific meanings, such as "", "" and "without loss of generality". Such phrases are known as mathematical jargon. The vocabulary of mathematics also has visual elements.

In mathematics, Thales used geometry to calculate the heights of pyramids and the distance of ships from the shore. He is the first known individual to use deductive reasoning applied to geometry, by deriving four corollaries to Thales' theorem. He is the first known individual to whom a mathematical discovery has been attributed.

Watching his son practice skateboarding, Miles drew corollaries between skateboarding and the Apache warrior tradition, as both involved increase concentration, stamina, and the ability to withstand pain. After finding no skate decks available relevant to Apache culture, Miles painted a skateboard deck himself. He gave it to his son, and this spawned Apache Skateboards.Koht, Peter.

This meant that he thought that all human actions were self- directed through the four causes - material, formal, efficient, and final causes - and not through mechanistic or deterministic causes.Logical learning theory: Propositions, corollaries, and research evidence. Rychlak, Joseph F. Journal of Personality and Social Psychology, Vol 40(4), Apr 1981, 731-749. doi: 10.1037/0022-3514.40.

These laws can be applied in time and frequency domains and form the basis for network analysis. Both of Kirchhoff's laws can be understood as corollaries of Maxwell's equations in the low-frequency limit. They are accurate for DC circuits, and for AC circuits at frequencies where the wavelengths of electromagnetic radiation are very large compared to the circuits.

Specifically, applying the structure theorem for finitely generated modules over a principal ideal domain to this algebra yields as corollaries the various canonical forms of matrices, such as Jordan canonical form. In some approaches to noncommutative geometry, the free noncommutative algebra (polynomials in non- commuting variables) plays a similar role, but the analysis is much more difficult.

The Book of Daniel (1971) is a semi-historical novel by E. L. Doctorow, loosely based on the lives, trial and execution of Julius and Ethel Rosenberg. Doctorow tells the story of Paul and Rochelle Isaacson (corollaries to the Rosenbergs) through the persons of their older son, Daniel, and his sister, Susan, who are college students deeply involved in 1960s politics.

The second principle is known as Resource Investment. This principle of COR states that people will tend to invest resources in order to protect against resource loss, to recover from losses, and to gain resources. Within the context of coping, people will invest resources to prevent future resource losses. From these two principles, COR has suggested a number of corollaries that can be applied to resource changes.

Autònoma de Barcelona, 2006. p.48 and on In mathematics, a definition is used to give a precise meaning to a new term, by describing a condition which unambiguously qualifies what a mathematical term is and is not. Definitions and axioms form the basis on which all of modern mathematics is to be constructed.Richard J. Rossi (2011) Theorems, Corollaries, Lemmas, and Methods of Proof.

Therefore, the only type of organized human behavior consistent with the operation of reason is that of voluntary cooperation. Persuasion is the method of reason. By its nature, the overtly irrational cannot rely on the use of persuasion and must ultimately resort to force to prevail. Thus, Rand argued that reason and freedom are correlates, just as she argued that mysticism and force are corollaries.

The proof now proceeds using spectral decomposition. The trick here is to split the Perron root from the other eigenvalues. The spectral projection associated with the Perron root is called the Perron projection and it enjoys the following property: The Perron projection of an irreducible non-negative square matrix is a positive matrix. Perron's findings and also (1)–(5) of the theorem are corollaries of this result.

They cited her as an anti-Guardist influence on the dictator's wife, Maria Antonescu. Jean Ancel, "Anatomia unei repetate falsificări" , in Revista 22, Nr. 864, October 2006 Manuilă did however support the passage of Jewish segregation laws, adopting the corollaries of economic antisemitism, according to which Jewish wealth and influence needed to be kept in check.Achim (2005), pp. 142, 146–147; Bucur, pp. 203, 252; Deletant, p.

Routledge, 1995. p. 47. Walter Laqueur argues that: :The corollaries of the cult of war and physical danger were the cult of brutality, strength, and sexuality....[fascism is] a true counter-civilization: rejecting the sophisticated rationalist humanism of Old Europe, fascism sets up as its ideal the primitive instincts and primal emotions of the barbarian. Italian Fascism pursued what it called "moral hygiene" of youth, particularly regarding sexuality.Maria Sop Quine.

A path of four upward-sloping edges in a set of 17 points. By the Erdős–Szekeres theorem, every set of 17 points has a path of this length that slopes either upward or downward. The 16-point subset with the central point removed has no such path. In mathematics, the Erdős–Szekeres theorem is a finitary result that makes precise one of the corollaries of Ramsey's theorem.

His method improves Remak's use of idempotents to create the appropriate central automorphisms. Both Remak and Schmidt published subsequent proofs and corollaries to their theorems. Wolfgang Krull (Über verallgemeinerte endliche Abelsche Gruppen, M. Z. 23 (1925) 161–196), returned to G.A. Miller's original problem of direct products of abelian groups by extending to abelian operator groups with ascending and descending chain conditions. This is most often stated in the language of modules.

Among the 88 possible unique elementary cellular automata, Rule 110 is the only one for which Turing completeness has been proven, although proofs for several similar rules should follow as simple corollaries (e.g. Rule 124, which is the horizontal reflection of Rule 110). Rule 110 is arguably the simplest known Turing complete system. Rule 110, like the Game of Life, exhibits what Wolfram calls "Class 4 behavior", which is neither completely stable nor completely chaotic.

In the English tradition this appeal to a moral sense was innovative. Primarily emotional and non-reflective, it becomes rationalised by education and use. Corollaries are that morality stands apart from theology, and the moral qualities of actions are determined apart from the will of God; and that the moralist is not concerned to solve the problems of free will and determinism. Shaftesbury in this way opposed also what is to be found in Locke.

Cantwell, p. 73 The 459th Group headquarters moved without personnel or equipment to Davis-Monthan and the group and squadron became corollaries of Strategic Air Command (SAC)'s 43d Bombardment Group, a B-29 unit. Along with all other reserve corollary units, the group was mobilized for the Korean War.Cantwell, p. 87 Once the squadron was mobilized in May 1951 SAC reassigned its personnel to other units and the unit inactivated the following month.

Tomb of Allan Kardec, founder of spiritism. The inscription says in French "To be born, die, again be reborn, and so progress unceasingly, such is the law". Spiritism, a Christian philosophy codified in the 19th century by the French educator Allan Kardec, teaches reincarnation or rebirth into human life after death. According to this doctrine, free will and cause and effect are the corollaries of reincarnation, and reincarnation provides a mechanism for man's spiritual evolution in successive lives.

Customer and a prostitute illustrated on an ancient Greek wine cup In ancient Greece, both women and men engaged in prostitution. The Greek word for prostitute is porne (Gr: πόρνη), derived from the verb pernemi (to sell). The English word pornography, and its corollaries in other languages, are directly derivative of the Greek word pornē (Gr: πόρνη).List of Greek words starting with πορν- (porn-), on Perseus Female prostitutes could be independent and sometimes influential women.

Both Beer's Law and Planck's Law can be derived from Schwarzschild's equation. In a sense, they are corollaries of Schwarzschild's equation. When the spectral intensity of radiation is not changing as it passes through a medium, dIλ = 0\. In that situation, Schwarzschild's equation simplifies to Planck's law: : 0 = n\sigma_\lambda[B _\lambda(T) - I_\lambda] \, ds : I_\lambda = B_\lambda(T) When Iλ > Bλ(T), dI is negative and when Iλ < Bλ(T), dI is positive.

Before the Disquisitiones was published, number theory consisted of a collection of isolated theorems and conjectures. Gauss brought the work of his predecessors together with his own original work into a systematic framework, filled in gaps, corrected unsound proofs, and extended the subject in numerous ways. The logical structure of the Disquisitiones (theorem statement followed by proof, followed by corollaries) set a standard for later texts. While recognising the primary importance of logical proof, Gauss also illustrates many theorems with numerical examples.

Perhaps among his most recognized results in 3-manifolds concern the classification of incompressible surfaces in certain 3-manifolds and their boundary slopes. William Floyd and Hatcher classified all the incompressible surfaces in punctured-torus bundles over the circle. William Thurston and Hatcher classified the incompressible surfaces in 2-bridge knot complements. As corollaries, this gave more examples of non-Haken, non-Seifert fibered, irreducible 3-manifolds and extended the techniques and line of investigation started in Thurston's Princeton lecture notes.

Bilski points out, and the PTO recently emphasized in a memorandum to its Examining Staff, Guidance for Examining Process Claims in view of In re Bilski ("Guidance Memo"). that there are two "corollaries" to the machine-or-transformation test. First, a mere field-of-use limitation is generally insufficient to make an otherwise ineligible method claim patent-eligible.The Supreme Court so held in Flook, where the claim's limitation to use in a hydrocracking process was ineffective to confer patent-eligibility.

Important corollaries exist between the disegno interno, which substituted for the disegno esterno (external design) in Mannerist painting. This notion of projecting a deeply subjective view as superseding nature or established principles (perspective, for example), in essence, the emphasis away from the object to its subject, now emphasizing execution, displays of virtuosity, or unique techniques. This inner vision is at the heart of commedia performance. For example, in the moment of improvisation the actor expresses his virtuosity without heed to formal boundaries, decorum, unity, or text.

It was written between 1661 and 1675Genevieve Lloyd, Routledge philosophy guidebook to Spinoza and The ethics, Routledge, 2002, p. 24. and was first published posthumously in 1677. The book is perhaps the most ambitious attempt to apply the method of Euclid in philosophy. Spinoza puts forward a small number of definitions and axioms from which he attempts to derive hundreds of propositions and corollaries, such as "When the Mind imagines its own lack of power, it is saddened by it",Part 3, proposition 55.

Thales used geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. As a result, he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. Pythagoras established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number".

One of the earliest known mathematicians was Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number".

The thesis of Robert Remak (1911) derived the same uniqueness result as Wedderburn but also proved (in modern terminology) that the group of central automorphisms acts transitively on the set of direct decompositions of maximum length of a finite group. From that stronger theorem Remak also proved various corollaries including that groups with a trivial center and perfect groups have a unique Remak decomposition. Otto Schmidt (Sur les produits directs, S. M. F. Bull. 41 (1913), 161–164), simplified the main theorems of Remak to the 3 page predecessor to today's textbook proofs.

Many profound insights into vortex dynamics were generated during the pursuit of this theory. Other interesting corollaries were the first counting of simple knots by P. G. Tait, today considered a pioneering effort in graph theory, topology and knot theory. Ultimately, Kelvin's vortex atom was seen to be wrong-headed but the many results in vortex dynamics that it precipitated have stood the test of time. Kelvin himself originated the notion of circulation and proved that in an inviscid fluid circulation around a material contour would be conserved.

South of Egypt the ancient Nubians established a system of geometry including early versions of sun clocks. In the 7th century BC, the Greek mathematician Thales of Miletus used geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' theorem. Pythagoras established the Pythagorean School, which is credited with the first proof of the Pythagorean theorem,Eves, Howard, An Introduction to the History of Mathematics, Saunders, 1990, .

It is said Thales, most widely regarded as the first philosopher in the Greek tradition,Aristotle, Metaphysics Alpha, 983b18. measured the height of the pyramids by their shadows at the moment when his own shadow was equal to his height. Thales was said to have had a sacrifice in celebration of discovering Thales' theorem just as Pythagoras had the Pythagorean theorem.Prof.T.Patronis & D.Patsopoulos Thales is the first known individual to use deductive reasoning applied to geometry, by deriving four corollaries to his theorem, and the first known individual to whom a mathematical discovery has been attributed.

In Roman Catholic theology, a theological censure is a doctrinal judgment by which the Church stigmatizes certain teachings as detrimental to faith or morals.John Hardon, Modern Catholic DictionaryJoseph Sollier, "Theological Censures" in Catholic Encyclopedia 1908 Theological censures have been described as the "negative corollaries" of theological notes. That they are directed at teachings distinguishes them from canonical censures, which are spiritual punishments imposed on people. The history of theological censures begins in the 13th century; William of Ockham appears to have been the first to attempt to formally categorise them.

The felt necessities of the time, the prevalent moral and political theories, intuitions of public policy, avowed or unconscious, and even the prejudices which judges share with their fellow-men, have had a good deal more to do than syllogism in determining the rules by which men should be governed. The law embodies the story of a nation's development through many centuries, and it cannot be dealt with as if it contained only the axioms and corollaries of a book of mathematics., Holmes, The Common Law,1881. In Lochner v.

However, in spite of their theoretical advantages, these proposals have not been very successful outside of academic circles, because of regional variations in pronunciation and incompatibility with existing literature. More recently, on December 14, 2017, the Modern International Manual of Venetian Spelling has been approved by the new Commission for Spelling of 2010. It has been translated in three languages (Italian, Venetian and English) and it exemplifies and explains every single letter and every sound of the Venetian language. The graphic accentuation and punctuation systems are added as corollaries.

XXXIX, no. 1 (1994), pp. 45-46. The phenomenon of multiple independent discoveries and inventions can be viewed as a consequence of Bolesław Prus' three laws of gradualness, dependence, and combination (see "Discoveries and inventions", above). The first two laws may, in turn, be seen as corollaries to the third law, since the laws of gradualness and dependence imply the impossibility of certain scientific or technological advances pending the availability of certain theories, facts, or technologies that must be combined to produce a given scientific or technological advance.

The first treatise, consisting of 17 chapters, contains Garzoni's theory of magnetism. The second treatise contains the description of a number of experiments, presented as 90 conclusions or doubts, and 39 corollaries. In the first treatise Garzoni explains the two principal magnetic effects displayed by the loadstone: its tendency to the poles and its interaction with other loadstones, or with iron. Firstly, the author ascertains that the motion towards the poles is a natural one, ascribes it to an internal mover ant its appropriate instrument, which he names the qualità delle due facce (quality of two faces).

The social construction of gender is a theory in feminism and sociology about the manifestation of cultural origins, mechanisms, and corollaries of gender perception and expression in the context of interpersonal and group social interaction. Specifically, the social construction of gender stipulates that gender roles are an achieved "status" in a social environment, which implicitly and explicitly categorize people and therefore motivate social behaviors. : See also: :: An intimately related, though notably distinct matter in feminist theory is the relationship between the ascribed status of biological sex- male and female; and their achieved status counterparts in gender- masculine and feminine.

Social constructionism is a theory of knowledge which describes the relationship between the objectivity of reality and the capacity of human senses and cognition. Specifically it asserts that reality exists as the summation of social perceptions and expression; and that the reality which is perceived is the only reality worth consideration. This is accompanied by the corollaries that any perceived reality is valid, that reality is subject to manipulation via control over social perceptions and expressions. The social constructionist movement emerged in relation to both criticism and rejection of Objectivism developed by Russian-American writer Ayn Rand.

In order to register a civic association, three citizens are required to provide their names and addresses and the name, goal organizational structure, executive bodies, and budgetary rules of the group. A concordat with the Holy See provides the legal framework for relations between the government and the domestic Catholic Church and the Holy See. Two corollaries cover the operation of Catholic religious schools, the teaching of Catholic religious education as a subject, and Catholic priests serving as military chaplains. An agreement between the government and 11 of the 17 other registered religious groups provides similar status to those groups.

Castronova, Edward, et al. "A Test of the Law of Demand in a Virtual World: Exploring the Petri Dish." Discoveries in Gaming and Computer- Mediated Simulations: New Interdisciplinary Applications (2011): 301. In fact, there are often very direct corollaries between physical world economic decisions and virtual world economic decisions, such as the decision by prisoners of war in World War II to adopt cigarettes as currency and the adoption of Stones of Jordan as currency in Diablo II. The value of objects in a virtual economy is usually linked to their usefulness and the difficulty of obtaining them.

"My Little Grass Shack in Kealakekua, Hawaii" was originally written as a parody of the chorus of "Back in Hackensack, New Jersey", composed in 1924 by Dan A. Russo and Art L. Biner. The opening lines of the chorus are, "I wanna go back to a black little shack, back in Hackensack, New Jersey, I wanna see all the gals and pals that I used to know". The chord structure is nearly identical, the melody slightly altered. Other verses in "Hackensack", with completely different chord structures and melodies, have no corollaries in "My Little Grass Shack".

The second and third corollaries are explored most in the introductory and concluding episodes, and they represent the downside of an interconnected history. If history progresses because of the synergistic interaction of past events and innovations, then as history does progress, the number of these events and innovations increases. This increase in possible connections causes the process of innovation to not only continue, but to accelerate. Burke poses the question of what happens when this rate of innovation, or more importantly change itself, becomes too much for the average person to handle, and what this means for individual power, liberty, and privacy.

There will also be primitive terms which are not defined, as they cannot be defined without circularity. For example, one can define a line as a set of points, but to then define a point as the intersection of two lines would be circular. Because of these interesting characteristics of formal systems, Bertrand Russell humorously referred to mathematics as "the field where we don't know what we are talking about, nor whether or not what we say is true". All theorems and corollaries are proven by exploring the implications of the axiomata and other theorems that have previously been developed.

In this way, Stevens's poems adopt attitudes that are corollaries to those earlier spiritual longings that persist in the unconscious currents of the imagination. "The poem refreshes life so that we share, / For a moment, the first idea ... It satisfies / Belief in an immaculate beginning / And sends us, winged by an unconscious will, / To an immaculate end."Stevens, Collected Poetry and Prose, supra, p. 330-31. The "first idea" is that essential reality that stands before all others, that essential truth; but since all knowledge is contingent on its time and place, that supreme fiction will surely be transitory.

Then, the probability is the sum of the probabilities of all possible favoured events. # For independent events, the probability of the occurrence of all is the probability of each multiplied together. # For events not independent, the probability of event B following event A (or event A causing B) is the probability of A multiplied by the probability that, given A, B will occur. # The probability that A will occur, given that B has occurred, is the probability of A and B occurring divided by the probability of B. # Three corollaries are given for the sixth principle, which amount to Bayesian probability.

Led by a faculty of professional designers who are committed to teaching, students are introduced to contexts of culture and meaning as they develop the formal, conceptual, and technical skills necessary to confidently enter a professional setting. The School of Art & Art History programs comprise artists, scholars, museum workers, educators, and researchers, all within the nation’s most diverse public research university. Affirming that humanity survives and advances through radical imagination and the arts, they educate students to rigorously engage in art’s vibrant corollaries: dialogue, critique, experimentation, and social justice. The School of Theatre & Music programs provide innovative, rigorous, and comprehensive academic and performance programs as part of an urban context.

This is the uncanny genre valley that publicists-cum-neologicians live in and for." Chillwave—termed sarcastically in a 2009 blog post—was one of the first music genres to formulate online. The term did not gain mainstream currency until early 2010, when it was the subject of articles by the Wall Street Journal and the New York Times. Writing in 2019, journalist Emilie Friedlander, called chillwave "the internet electronic micro-genre that launched a hundred internet electronic micro-genres (think: vaporwave, witch house, seapunk, shitgaze, distroid, hard vapor), not to mention its corollaries in this decade’s internet rap, which largely shared its collagist, hyper-referential approach to sound.

One property he discovered was that the denominators of the fractions of Bernoulli numbers are always divisible by six. He also devised a method of calculating based on previous Bernoulli numbers. One of these methods follows: It will be observed that if n is even but not equal to zero, # is a fraction and the numerator of in its lowest terms is a prime number, # the denominator of contains each of the factors 2 and 3 once and only once, # is an integer and consequently is an odd integer. In his 17-page paper "Some Properties of Bernoulli's Numbers" (1911), Ramanujan gave three proofs, two corollaries and three conjectures.

In addition to the main result, Ioannidis lists six corollaries for factors that can influence the reliability of published research: # The smaller the studies conducted in a scientific field, the less likely the research findings are to be true. # The smaller the effect sizes in a scientific field, the less likely the research findings are to be true. # The greater the number and the lesser the selection of tested relationships in a scientific field, the less likely the research findings are to be true. # The greater the flexibility in designs, definitions, outcomes, and analytical modes in a scientific field, the less likely the research findings are to be true.

These cells target and kill other cells lacking such MHC markers, a concept known as "missing self". One distinct possibility is that sperm and eggs are recognized via oligosaccharides expressed on their surfaces. For example, human gametes are coated with carbohydrate sequences that have been implicated in the suppression of NK cell mediated responses. One of the major corollaries of the eu-FEDS hypothesis is that persistent pathogens and aggressive tumor cells are able to either mimic or acquire the same carbohydrate functional groups used to suppress any immune response that could interfere with the reproductive imperative, thus enabling them to similarly resist the human immune response.

The matrix Mk/rk will be conjugate (1, (r2/r)k, ... , (rn/r)k), which tends to (1,0,0,...,0), for k → ∞, so the limit exists. The same method works for general M (without assuming that M is diagonalizable). The projection and commutativity properties are elementary corollaries of the definition: MMk/rk = Mk/rk M ; P2 = lim M2k/r2k = P. The third fact is also elementary: M(Pu) = M lim Mk/rk u = lim rMk+1/rk+1u, so taking the limit yields M(Pu) = r(Pu), so image of P lies in the r-eigenspace for M, which is one-dimensional by the assumptions.

The transcendence of and are direct corollaries of this theorem. Suppose is a non-zero algebraic number; then is a linearly independent set over the rationals, and therefore by the first formulation of the theorem is an algebraically independent set; or in other words is transcendental. In particular, is transcendental. (A more elementary proof that is transcendental is outlined in the article on transcendental numbers.) Alternatively, by the second formulation of the theorem, if is a non-zero algebraic number, then is a set of distinct algebraic numbers, and so the set is linearly independent over the algebraic numbers and in particular cannot be algebraic and so it is transcendental.

Cantwell, p. 73 The group's 756th Squadron moved on paper to Smoky Hill Air Force Base, Kansas, where it was reassigned and became a corollary of Strategic Air Command's 301st Bombardment Wing. Meanwhile group headquarters moved without personnel or equipment to Davis–Monthan Air Force Base, where the 57th Fighter Squadron was inactivated and the group and its 759th Squadron became corollaries of Strategic Air Command (SAC)'s 43d Bombardment Group. Along with all other reserve corollary units, the group was mobilized for the Korean War.Cantwell, p. 87 Once the group was mobilized in May 1951 SAC reassigned its personnel to other units and the unit inactivated the following month.

Intermediate value theorem: Let f be a continuous function defined on and let s be a number with f(a) < s < f(b). Then there exists some x between a and b such that f(x) = s. In mathematical analysis, the intermediate value theorem states that if f is a continuous function whose domain contains the interval [a, b], then it takes on any given value between f(a) and f(b) at some point within the interval. This has two important corollaries: # If a continuous function has values of opposite sign inside an interval, then it has a root in that interval (Bolzano's theorem).

Newton enunciated a principle of relativity himself in one of his corollaries to the laws of motion:See the Principia on line at Andrew Motte Translation This principle differs from the special principle in two ways: first, it is restricted to mechanics, and second, it makes no mention of simplicity. It shares with the special principle the invariance of the form of the description among mutually translating reference frames.However, in the Newtonian system the Galilean transformation connects these frames and in the special theory of relativity the Lorentz transformation connects them. The two transformations agree for speeds of translation much less than the speed of light.

Dembski formulates and proposes a law of conservation of information as follows: > This strong proscriptive claim, that natural causes can only transmit CSI > but never originate it, I call the Law of Conservation of Information. > Immediate corollaries of the proposed law are the following: # The specified > complexity in a closed system of natural causes remains constant or > decreases. # The specified complexity cannot be generated spontaneously, > originate endogenously or organize itself (as these terms are used in > origins-of-life research). # The specified complexity in a closed system of > natural causes either has been in the system eternally or was at some point > added exogenously (implying that the system, though now closed, was not > always closed).

Brigadier Mobolaji Johnson, military governor of Lagos State demolished Ajele Cemetery in December 1971 in order to situate the Lagos State Secretariat. The demolition met with a lot of criticism and many historians and commentators noted the loss of valuable history. Prof J.D.Y. Peel noted that the demolition had deprived "Lagosians not only of a precious green space in the heart of the city but of the memorials of their forebears". Nobel Laureate Wole Soyinka called the demolition "the violation of that ancestral place" noting that "the order came from the military governor: 'Dig up those dead and forgotten ancestors and plant a modern council building - with all its lucrative corollaries on that somnolent spot".

He argued that the NF's vote share was best explained by the "working-class authoritarianism" phenomenon examined in the United States by S. M. Lipset. Christopher Husbands instead believed that "local working-class cultures" were "the crucial factor for understanding some pro-NF susceptibility". He cited earlier studies indicating that "territorial sensitivity" was an element of English working-class culture, with this "localism" manifesting as corollaries of "parochialism and a sensitivity to supposed threat". He argued that this led many working-class English people to create personal identities based on their neighbourhood rather than their profession, leaving many more susceptible to far-right appeals based on location rather than leftist ones based on workplace solidarity.

Dale Sandler, chief epidemiologist for the National Institutes of Health, said she is working to design a study that draws the strongest possible corollaries, even if absolute causation is not possible to determine: "I want to be able to say that workers who did this particular job are more likely to suffer this particular consequence." In 2013 it was reported that the agency had completed telephone interviews with more than 32,000 workers, and home visits with 9,967 of those. Preliminary results of testing show that workers are carrying biomarkers of chemicals contained in the oil in their bodies. The data collected by the GuLF study has been used by other researchers to study specific groups or symptoms.

Johnson's administration was responsible for the demolition and disinterment of people buried at Ajele Cemetery such as Samuel Ajayi Crowther, James Pinson Labulo Davies, Madam Tinubu, Thomas Babington Macaulay, and many others. The demolition met with a lot of criticism: Prof J.D.Y. Peele noted that the demolition had deprived "Lagosians not only of a precious green space in the heart of the city but of the memorials of their forebears". Nobel Laureate Wole Soyinka called the demolition "the violation of that ancestral place" noting that "the order came from the military governor [Mobolaji Johnson]: 'Dig up those dead and forgotten ancestors and plant a modern council building – with all its lucrative corollaries on that somnolent spot".

The ASPIRE Sports Hall is multi-purpose sports hall with a wide range of corollaries. The sports hall features a gymnasium with an audience seating capacity of 200 persons, judo and karate area with a viewer’s seating capacity of 150 persons, a fencing hall with a spectators seating capacity of 150 persons, a table tennis hall with squash court with an audience seating capacity of 500 persons, Olympic swimming and diving pools, a football court with a seating capacity of 200 persons and a host of other amenities. The total seating capacity of the sports hall is 3000. The support services include restaurants, changing rooms, cafeterias, shops museum, and technical support areas etc.

It was also revealed in May of 2020 that there was a finished and yet unreleased Conan Neutron and the Secret Friends record about depression and mental health, as well as Neutron's participation in the band Household Gods with David Pajo of Slint, Vern Rumsey of Unwound and Lauren K. Newman. Neutron was a guest on a two part edition of the podcast The Operative, where he discussed corollaries with the band and both Nick Cave as well as the work of the Birthday Party (Band), Grinderman, and Nick Cave and the Bad Seeds. He was also a guest on the podcast Tomorrow We Die, which had a focus on tour stories as well as the band’s origins.

Goetz's academic work focused primarily on the Christian doctrine of the atonement. Beginning in 1975 and continuing over more than two decades, he published articles and delivered lectures questioning key elements of traditional atonement theories while developing his own counterproposal. Goetz believed that the three historic theories of the atonement — the Ransom (Christus Victor), Substitutionary, and Moral Influence theories — are no longer sustainable, in part because they were formulated against the background of an obsolete, pre- Darwinian anthropology. Each of these theories, as well as their modern corollaries, assumes in some sense that primordial human sin disrupted and disfigured an originally peaceful and perfectly ordered creation, and that human sin is therefore responsible for introducing suffering, death, and evil into God's world.

The position of Gauleiter in Schleswig-Holstein was held by Hinrich Lohse from its establishment on 26 February 1925 throughout the history of the Gau, with the exception of a six-month period in 1932 when the office was held by Joachim Meyer-Quade. From 1941 onward Lohse was simultaneously in charge of the Reichskommissariat Ostland where he was responsible for the implementation of Nazi Germanization policies built on the foundations of the Generalplan Ost: the killing of almost all Jews, Romani people and Communists and the oppression of the local population were its necessary corollaries. He was sentenced to ten years in prison in 1948 but released in 1951, an extradition request by the Soviet Union having been refused, and died in 1964.

Book 1 contains some proofs with little connection to real-world dynamics. But there are also sections with far-reaching application to the solar system and universe: Propositions 57–69 deal with the "motion of bodies drawn to one another by centripetal forces". This section is of primary interest for its application to the Solar System, and includes Proposition 66 along with its 22 corollaries: here Newton took the first steps in the definition and study of the problem of the movements of three massive bodies subject to their mutually perturbing gravitational attractions, a problem which later gained name and fame (among other reasons, for its great difficulty) as the three-body problem. Propositions 70–84 deal with the attractive forces of spherical bodies.

The interplay of the results of these isolated events is what drives history and innovation, and is also the main focus of the series and its sequels. Burke also explores three corollaries to his initial thesis. The first is that, if history is driven by individuals who act only on what they know at the time, and not because of any idea as to where their actions will eventually lead, then predicting the future course of technological progress is merely conjecture. Therefore, if we are astonished by the connections Burke is able to weave among past events, then we will be equally surprised to what the events of today eventually will lead, especially events we weren't even aware of at the time.

Conflict of interests have been described as the most pervasive issue facing modern lawyers. Legal conflicts rules are at their core corollaries to a lawyer's two basic fiduciary duties: (1) the duty of loyalty and (2) the duty to preserve client confidences.Gregory C. Sisk et al, Legal Ethics, Professional Responsibility, and the Legal Profession §4-7.1 (2018). The lawyer's duty of loyalty is fundamental to the attorney-client relationship and has developed from the biblical maxim that no person can serve more than one master. Just as fundamental is the lawyer's duty to maintain client confidences, which protects clients’ legitimate expectations that they can make full disclosure of all facts to their attorneys without fear of exposure.A Concise Restatement of the Law Governing Lawyers §60 (Am.

The developmental niche is seen as the composite of three interacting subsystems: # Physical and social settings – who is there, what affordances are provided by the physical space # Customs and practices of child rearing – inherited and adapted ways of nurturing, entertaining, educating, and protecting the child # The psychology of the caretakers, particularly parental ethnotheories of child development and parenting, which play a directive role in actual practices. The three subsystems of the developmental niche - settings, customs, and caretaker psychology - share the common function of mediating the child's developmental experience within the larger culture. Of particular significance for integrating research on these components are three corollaries: # The three components of the developmental niche operate together with powerful though incomplete coordination as a system.

Suppose the decision-maker answers: "I prefer _21 to _12" (i.e. good experience and poor references is preferred to poor experience and good references). This preference can be represented by '_21 ≻_12', which corresponds, in terms of total score equations, to b2 + c1 > b1 + c2 [where ‘≻’ and ‘~’ (used later) denote strict preference and indifference respectively, corresponding to the usual relations ‘>’ and ‘=’ for the total score equations]. Central to the PAPRIKA method is the identification of all undominated pairs implicitly ranked as corollaries of the explicitly ranked pairs. Thus, given a2 > a1 (i.e. good education ≻ poor education), it is clear that (i) b2 + c1 > b1 + c2 (as above) implies pair (iv) (see Figure 2) is ranked as a2 + b2 + c1 > a1 + b1 + c2.

In algebraic geometry, the existence of canonical metrics as proposed by Calabi allows one to give equally canonical representatives of characteristic classes by differential forms. Due to Yau's initial efforts at disproving the Calabi conjecture by showing that it would lead to contradictions in such contexts, he was able to draw striking corollaries to his primary theorem. In particular, the Calabi conjecture implies the Miyaoka–Yau inequality on Chern numbers of surfaces, as well as homotopical characterizations of the complex structures of the complex projective plane and of quotients of the two-dimensional complex unit ball. In string theory, it was discovered in 1985 by Philip Candelas, Gary Horowitz, Andrew Strominger, and Edward Witten that Calabi-Yau manifolds, due to their special holonomy, are the appropriate configuration spaces for superstrings.

300x300px Quasispecies theory was developed in the 1970s by Manfred Eigen and Peter Schuster to explain self-organization and adaptability of primitive replicons (a term used to refer to any replicating entity), as an ingredient of hypercyclic organizations that link genotypic and phenotypic information, as an essential step in the origin of life. The theory portrayed early replicon populations as organized mutant spectra dominated by a master sequence, the one endowed with the highest fitness (replicative capacity) in the distribution. It introduced the notion of a mutant ensemble as a unit of selection, thus emphasizing the relevance of intra-population interactions to understand the response to selective constraints. One of its corollaries is the error threshold relationship, which marks the maximum mutation rate at which the master (or dominant) sequence can stabilize the mutant ensemble.

Epistemologically, therefore, what Howell will admit as truth is a broad spectrum of styles, and their heterogeneous nature, rather than undermining his viewpoint, confirms it in that the various styles that he uses do indeed clash with one another, demonstrating themselves as corollaries of the elemental conflicts in the extra-textual world, and upon which, as a neo-Stoic, he believed that world was based. This shall be discussed further below. On a first reading, these clashing registers of discourse are particularly noticeable; set uncomfortably with the parergon of the allegory, the text's main framework, sit a variety of discourses: an exposition of the various lands of Europe strides the topoi and genres of travel narrative in the first section, whilst later, diplomatic history and the romance ideal chafe against one another when Prince Charles' visit to Spain is dealt with.

In the opening paragraphs of the book, he famously summarized his own view of the history of the common law: > The life of the law has not been logic; it has been experience. The felt > necessities of the time, the prevalent moral and political theories, > intuitions of public policy, avowed or unconscious, and even the prejudices > which judges share with their fellow-men, have had a good deal more to do > than syllogism in determining the rules by which men should be governed. The > law embodies the story of a nation's development through many centuries, and > it cannot be dealt with as if it contained only the axioms and corollaries > of a book of mathematics. In the book, Holmes set forth his view that the only source of law, properly speaking, was a judicial decision enforced by the state.

The felt > necessities of the time, the prevalent moral and political theories, > intuitions of public policy, avowed or unconscious, even the prejudices > which judges share with their fellow men, have had a good deal more to do > than the syllogism in determining the rules by which men should be governed. > The law embodies the story of a nation's development through many centuries, > and it cannot be dealt with as if it contained only the axioms and > corollaries of a book of mathematics. In the early 20th century, Louis Brandeis, later appointed to the United States Supreme Court, became noted for his use of policy-driving facts and economics in his briefs, and extensive appendices presenting facts that lead a judge to the advocate's conclusion. By this time, briefs relied more on facts than on Latin maxims.

When asked about common themes in The Kite Runner and A Thousand Splendid Suns, Khaled Hosseini replied: > "Both novels are multigenerational, and so the relationship between parent > and child, with all of its manifest complexities and contradictions, is a > prominent theme. I did not intend this, but I am keenly interested, it > appears, in the way parents and children love, disappoint, and in the end > honor each other. In one way, the two novels are corollaries: The Kite > Runner was a father-son story, and A Thousand Splendid Suns can be seen as a > mother-daughter story." He ultimately considers both novels to be "love stories" in that it is love that "draws characters out of their isolation, that gives them the strength to transcend their own limitations, to expose their vulnerabilities, and to perform devastating acts of self-sacrifice".

A characteristic instance of his vacillation is afforded by his most important religious work, the Rosh Amanah (The Pinnacle of Faith) (Amsterdam, 1505), whose title derives from Song of Songs 4:8. This work, devoted to the championship of the Maimonidean 13 articles of belief against the attacks of Hasdai Crescas and Joseph Albo, ends with the statement that Maimonides compiled these articles merely in accordance with the fashion of other nations, which set up axioms or fundamental principles for their science. However, he holds that Judaism has nothing in common with human science; that the teachings of the Torah are revelations from God, and therefore are all of equal value; that among them are neither principles nor corollaries from principles. Abarbanel agrees with and supports some of Maimonides' ideas; however he assails Maimonides' conception that the prophetic visions were the creations of imagination.

This corollary is the core of the Fifth Theorem as chronicled by Copernicus following Ptolemy in Almagest. Let \theta_3=90^\circ. Then \theta_1+(\theta_2+\theta_4)=90^\circ . Hence : \sin\theta_1\sin\theta_3+\sin\theta_2\sin\theta_4=\sin(\theta_3+\theta_2)\sin(\theta_3+\theta_4) : \cos(\theta_2+\theta_4)+\sin\theta_2\sin\theta_4=\cos\theta_2\cos\theta_4 : \cos(\theta_2+\theta_4)=\cos\theta_2\cos\theta_4-\sin\theta_2\sin\theta_4 Formula for compound angle cosine (+) Despite lacking the dexterity of our modern trigonometric notation, it should be clear from the above corollaries that in Ptolemy's theorem (or more simply the Second Theorem) the ancient world had at its disposal an extremely flexible and powerful trigonometric tool which enabled the cognoscenti of those times to draw up accurate tables of chords (corresponding to tables of sines) and to use these in their attempts to understand and map the cosmos as they saw it.

Calculus on Manifolds is a brief monograph on the theory of vector-valued functions of several real variables (f : Rn→Rm) and differentiable manifolds in Euclidean space. In addition to extending the concepts of differentiation (including the inverse and implicit function theorems) and Riemann integration (including Fubini's theorem) to functions of several variables, the book treats the classical theorems of vector calculus, including those of Cauchy–Green, Ostrogradsky–Gauss (divergence theorem), and Kelvin–Stokes, in the language of differential forms on differentiable manifolds embedded in Euclidean space, and as corollaries of the generalized Stokes' theorem on manifolds-with-boundary. The book culminates with the statement and proof of this vast and abstract modern generalization of several classical results: The cover of Calculus on Manifolds features snippets of a July 2, 1850 letter from Lord Kelvin to Sir George Stokes containing the first disclosure of the classical Stokes' theorem (i.e., the Kelvin–Stokes theorem).

In the Dialogues of Plato, though Socrates sometimes seems to support a mystical side, discussing reincarnation and the mystery religions, this is generally attributed to Plato. Regardless, this view of Socrates cannot be dismissed out of hand, as we cannot be sure of the differences between the views of Plato and Socrates; in addition, there seem to be some corollaries in the works of Xenophon. In the culmination of the philosophic path as discussed in Plato's Symposium, one comes to the Sea of Beauty or to the sight of "the beautiful itself" (211C); only then can one become wise. (In the Symposium, Socrates credits his speech on the philosophic path to his teacher, the priestess Diotima, who is not even sure if Socrates is capable of reaching the highest mysteries.) In the Meno, he refers to the Eleusinian Mysteries, telling Meno he would understand Socrates's answers better if only he could stay for the initiations next week.

The Court accepted the case to decide the question: > Whether the government edicts doctrine extends to—and thus renders > uncopyrightable—works that lack the force of law, such as the annotations in > the Official Code of Georgia Annotated. Oral arguments were held on December 2, 2019, at which many of the justices focused on the role of the legislature in approving the annotated statutes for publication, questioning whether this made the annotations equivalent to legislation, which can not be copyrighted. On April 27, 2020, the Court ruled in a 5-to-4 decision, that Georgia does not have copyright over its annotated legal code. Chief Justice John Roberts authored the majority opinion, joined by Associate Justices Sonia Sotomayor, Elena Kagan, Neil Gorsuch, and Brett Kavanaugh: he noted that, binding law or not, official works of the Georgia legislature could not be copyrighted, as they could deprive citizens of knowledge of those laws and their corollaries.

Lewis Thomas put fastidiousness and the challenge of culturing isolates into logical context in his 1974 book Lives of a Cell: "It has been estimated that we probably have real knowledge of only a small proportion of the microbes of the earth, because most of them cannot be cultivated alone. They live together in dense, interdependent communities, feeding and supporting the environment for each other, regulating the balance of populations between different species by a complex system of chemical signals. With our present technology, we can no more isolate one from the rest, and rear it alone, than we can keep a single bee from drying up like a desquamated cell when removed from his hive." One of the logical corollaries of this passage is that the inseparability of many species from their native ecological contexts is quite natural and reflects only the ubiquity of interdependencies in ecological systems—not any weakness, frailty, stubbornness, or rarity of any species.

The effect of using a Schmitt trigger (B) instead of a comparator (A) Many common digital electronic circuits employ positive feedback. While normal simple boolean logic gates usually rely simply on gain to push digital signal voltages away from intermediate values to the values that are meant to represent boolean '0' and '1', but many more complex gates use feedback. When an input voltage is expected to vary in an analogue way, but sharp thresholds are required for later digital processing, the Schmitt trigger circuit uses positive feedback to ensure that if the input voltage creeps gently above the threshold, the output is forced smartly and rapidly from one logic state to the other. One of the corollaries of the Schmitt trigger's use of positive feedback is that, should the input voltage move gently down again past the same threshold, the positive feedback will hold the output in the same state with no change.

Shoenfield's absoluteness theorem shows that \Pi^1_2 and \Sigma^1_2 sentences in the analytical hierarchy are absolute between a model V of ZF and the constructible universe L of the model, when interpreted as statements about the natural numbers in each model. The theorem can be relativized to allow the sentence to use sets of natural numbers from V as parameters, in which case L must be replaced by the smallest submodel containing those parameters and all the ordinals. The theorem has corollaries that \Sigma^1_3 sentences are upward absolute (if such a sentence holds in L then it holds in V) and \Pi^1_3 sentences are downward absolute (if they hold in V then they hold in L). Because any two transitive models of set theory with the same ordinals have the same constructible universe, Shoenfield's theorem shows that two such models must agree about the truth of all \Pi^1_2 sentences. One consequence of Shoenfield's theorem relates to the axiom of choice.

In the years 1993-2016 she devoted herself to 60 field research projects in Latin America on the aforementioned issues. The projects were conducted within 11 grants financed by: the State Committee for Scientific Research, the Ministry of Science and Higher Education, the National Science Centre, and the EC (in eight of them she was the leader). Between 2010 and 2014 she was also the Polish coordinator of the prestigious MISEAL project (Medidadas para la Inclusión Social y Equidad en Instituciones de Educación Superior en América Latina) of the EU programme ALFA III, which joins together scientific units from twelve Lain American and four European countries (Germany, Spain, Great Britain and Poland). Corollaries to the field research projects were: participation in over 100 international congresses and conferences (including the recurring: the International Congress of Americanists, the International Union of Anthropological and Ethnological Sciences, Consejo Europeo de Investigaciones sobre América Latina [CEISAL - eng.

Of course, most real-world value models have more criteria and categories than the simple example above, which means they have many more undominated pairs. For example, the value model referred to earlier with eight criteria and four categories within each criterion (and 48 = 65,536 possible alternatives) has 2,047,516,416 undominated pairs in total (analogous to the nine identified in Figure 2), of which, excluding replicas, 402,100,560 are unique (analogous to the six in the example above). (As mentioned earlier, for a model of this size the decision-maker is required to explicitly rank approximately 95 pairs defined on two criteria at-a-time, which most decision-makers are likely to be comfortable with.) For such real-world value models, the simple pairwise- comparisons approach to identifying undominated pairs used in the previous sub-section (represented in Figure 2) is highly impractical. Likewise, identifying all pairs implicitly ranked as corollaries of the explicitly ranked pairs becomes increasingly intractable as the numbers of criteria and categories increase.

3, No. 3, pp. 4–9. Accordingly, in this article Section II attempts to unify these four versions by making one the foundation, while the others work as its corollaries. Then, after creating a better account of the 'Principle of Charity' Johnson spends Section III of the article addresses some of the issues involved in the application of the 'Principle of Charity' and finally Section IV addresses a proposed restriction for the use of the 'Principle of Charity'.1981 "Charity Begins at Home: Some Reflections on the Principle of Charity," Informal Logic Newsletter, Vol. 3, No. 3, pp. 4–9. In his article "The Principle of Vulnerability" in Informal Logic seeks to offer defence to the principle that all arguments should be considered susceptible to criticisms. As such Johnson argues that the arguer of an argument should not seek to "immunize" their argument from criticism. The article also takes considerations both in support of, and opposed to the principle into account.

The gravitational problem of three bodies in its traditional sense dates in substance from 1687, when Isaac Newton published his Principia (Philosophiæ Naturalis Principia Mathematica). In Proposition 66 of Book 1 of the Principia, and its 22 Corollaries, Newton took the first steps in the definition and study of the problem of the movements of three massive bodies subject to their mutually perturbing gravitational attractions. In Propositions 25 to 35 of Book 3, Newton also took the first steps in applying his results of Proposition 66 to the lunar theory, the motion of the Moon under the gravitational influence of the Earth and the Sun. The physical problem was addressed by Amerigo Vespucci and subsequently by Galileo Galilei; in 1499, Vespucci used knowledge of the position of the Moon to determine his position in Brazil. It became of technical importance in the 1720s, as an accurate solution would be applicable to navigation, specifically for the determination of longitude at sea, solved in practice by John Harrison's invention of the marine chronometer.

By thus manipulating the conventions and structures of figurative painting, he creates corollaries for literary, philosophical, and historical concepts in visual allegories about the nature and implications of perception, meaning, and interpretation in art. His work is in major collections including Modern Art Museum, Fort Worth; Walker Art Center, Minneapolis; Broad Art Foundation, Los Angeles; and Smithsonian American Art Museum, Washington D.C. Solo exhibitions include Kunsthalle Museum, Basel (1990); "Mark Tansey: Art and Source", Seattle Art Museum, Washington (1990, traveled to Montreal Museum of Fine Arts, Canada, St. Louis Art Museum, Missouri, Walker Art Center, Minneapolis, Minnesota, List Visual Art Center, MIT, Cambridge, Massachusetts, and Modern Art Museum of Fort Worth, Texas through 1991); Fisher Landau Center for Art, Long Island City, New York (2005) and Museum Kurhaus Kleve, Germany (2005, traveled to Württembergischer Kunstverein, Stuttgart, Germany). In the 1970s, influenced by the work of René Magritte's eight methods, he began to search for ways of displaying oppositions and contradictions as the motivation for a painting. From this he decided that illustration and representation were fundamentally necessary to heal the rift between art and practice, between symbol and meaning.