* Weisstein, Eric W. " Second Fundamental Theorem of Calculus.

Although sometimes mentioned in subsequent rulings, the clear and present danger test was never endorsed by the Supreme Court as a test to be used by lower courts when evaluating the constitutionality of legislation that regulated speech .< ref name = K60 > Killian, pp 1096, 1100 .</ br > Currie, David P., The Constitution in the Supreme Court: The Second Century, 1888-1986, Volume 2, University of Chicago Press, 1994, p 269, ISBN 9780226131122 .</ br > Konvitz, Milton Ridvad, Fundamental Liberties of a Free People: Religion, Speech, Press, Assembly, Transaction Publishers, 2003, p 304, ISBN 9780765809544. Eastland, p 47 .</ ref >

The Second Fundamental theorem says that for every k distinct values a < sub > j </ sub > on the Riemann sphere, we have

This theorem is called the Second Fundamental Theorem of Nevanlinna Theory, and it allows to give an upper bound for the characteristic function in terms of N ( r, a ).

For example, if f is a transcendental entire function, using the Second Fundamental theorem with k = 3 and a < sub > 3 </ sub > = ∞, we obtain that f takes every value infintiely often, with at most two exceptions,

The Second Fundamental Theorem can also be derived from the metric-topological theory of Ahlfors, which can be considered as an extension of the Riemann – Hurwitz formula to the coverings of infinite degree.

The proofs of Nevanlinna and Ahlfors indicate that the constant 2 in the Second Fundamental Theorem is related to the Euler characteristic of the Riemann sphere.

This is one of the main corollaries from the Second Fundamental Theorem.

Many other Picard-type theorems can be derived from the Second Fundamental Theorem.

As another corollary from the Second Fundamental Theorem, one can obtain that

# The Second Fundamental Theorem of Asset Pricing: An arbitrage-free market ( S, B ) consisting of a collection of stocks S and a risk-free bond B is complete if and only if there exists a unique risk-neutral measure that is equivalent to P and has numeraire B.

In his 1854 memoir " On a Modified Form of the Second Fundamental Theorem in the Mechanical Theory of Heat " Clausius states:

Pareto-optimal solutions are not unique, and according to the Second Fundamental Theorem of Welfare Economics, a social planner can achieve any Pareto-optimal outcome by an appropriate redistribution of wealth by means of competitive market.

The Second Main Theorem, more difficult than the first one tells that there are relatively few values which the function assumes less often than average.

*" The Surprise Examination Paradox and the Second Incompleteness Theorem " by Shira Kritchman and Ran Raz, at ams. org

In it he integrates Gödel's Incompleteness Theorem, Heisenberg's Uncertainty principle, and the Second Law of Thermodynamics to provide a context and rationale for the development of the OODA Loop.

The mathematical proof of the Fluctuation Theorem and in particular the Second Law Inequality shows that, given a non-equilibrium starting state, the probability of seeing its entropy increase is greater than the probability of seeing its entropy decrease-see The Fluctuation Theorem from Advances in Physics 51: 1529.

The modal-logical treatment of provability helped demonstrate the " intensionality " of Gödel's Second Incompleteness Theorem, meaning that the theorem's correctness depends on the precise formulation of the provability predicate.

The unclear status of the Second Theorem was noted for several decades by logicians such as Georg Kreisel and Leon Henkin, who asked whether the formal sentence expressing " This sentence is provable " ( as opposed to the Gödel sentence, " This sentence is not provable ") was provable and hence true.

This was derived from the Second Law ( any of the two, Clausius ' or Lord Kelvin's statement can be used since they are equivalent ) and using the Clausius ' Theorem ( see Kerson Huang ISBN-13: 978-0471815181 ).

These three ground-breaking articles were " A Functional Calculus of First Order Based on Strict Implication ", Journal of Symbolic Logic ( JSL, 1946 ), " The Deduction Theorem in a Functional Calculus of First Order Based on Strict Implication " ( JSL, 1946 ), " The Identity of Individuals in a Strict Functional Calculus of Second Order ", ( JSL, 1947 ).

As many other important theorems, the Second Main Theorem has several different proofs.

" How to Extend the Semantic Tableaux and Cut-Free Versions of the Second Incompleteness Theorem to Robinson's Arithmetic Q ".

A well documented classical application of the " Second Theorem " as illustrated in the diagram is the determination of chord BC subtending 12 degrees of arc.

Godel's Second Incompleteness Theorem for Q.

Second, the prefix " co " implies " first variable of the ".

As the name implies, the events of the essay are focused around magical artefacts: the Rings of Power, and also the history of the Second and Third Ages of Middle-earth.

Entropy can be thought of as a measure of microscopic disorder ; thus the Second Law implies that time is asymmetrical with respect to the amount of order in an isolated system: as a system advances through time, it will statistically become more disordered.

And this is, Zola implies, what is about to happen to the Second Empire.

Second with respect to lowest-low fertility countries in Europe, momentum implies that these countries may experience population decline even if they bring their fertility levels up to replacement.

In July 1862, the Second Confiscation Act was passed, which set up court procedures that could free the slaves of anyone convicted of aiding the rebellion.

Bradman's men were greeted by packed crowds across the country, and records for Test attendances in England were set in the Second and Fourth Tests at Lord's and Headingley respectively ; the crowd at Headingley remains a record, and it was there that Australia set a world record by chasing down 404 on the last day for a seven-wicket victory.

Charlton became one of the famed Busby Babes, the collection of precociously talented footballers who emerged through the system at Old Trafford in the 1940s, 1950s and 1960s as Matt Busby set about a long-term plan of rebuilding the club after the Second World War.

The Council of Chalcedon was convened by Emperor Marcian, with the reluctant approval of Pope Leo the Great, to set aside the 449 Second Council of Ephesus, better known as the " Robber Council ".

The problem set was launched as a talk " The Problems of Mathematics " presented during the course of the Second International Congress of Mathematicians held in Paris.

Lord Lytton, the viceroy, ordered a diplomatic mission to set out for Kabul in September 1878 but the mission was turned back as it approached the eastern entrance of the Khyber Pass, triggering the Second Anglo-Afghan War.

* TIB = The Interpreter ’ s Bible, The Holy Scriptures in the King James and Revised Standard versions with general articles and introduction, exegesis, exposition for each book of the Bible in twelve volumes, George Arthur Buttrick, Commentary Editor, Walter Russell Bowie, Associate Editor of Exposition, Paul Scherer, Associate Editor of Exposition, John Knox Associate Editor of New Testament Introduction and Exegesis, Samuel Terrien, Associate Editor of Old Testament Introduction and Exegesis, Nolan B. Harmon Editor, Abingdon Press, copyright 1955 by Pierce and Washabaugh, set up printed, and bound by the Parthenon Press, at Nashville, Tennessee, Volume XI, Philippians, Colossians and Exegesis by Francis W. Beare, Exposition by G. Preston MacLeod, Thessalonians, Pastoral Epistles First and Second Epistles to Timothy, and the Epistle to Titus, Philemon, Hebrews

During his reign, he also set about creating the Second Mexican Empire ( headed by his choice of Maximilian I of Mexico, a member of the House of Habsburg ), to regain France's hold in the Americas and to achieve greatness for the ' Latin ' race.

With Conté as president, the CMRN set about dismantling Touré's oppressive regime, abolishing the authoritarian constitution, dissolving the sole political party and its mass youth and women's organizations, and announcing the establishment of the Second Republic.

Durgapur along with Rourkela Steel Plant | Rourkela and Bhilai Steel Plant | Bhilai were the three integrated steel plants set up under India's Five-Year Plans of India # Second Five-Year Plan ( 1956 – 1961 ) | Second Five-Year Plan in the late 1950s.

In 1878, during the Second Anglo-Afghan War, the British again invaded and set up camps in Jalalabad but withdrew two years later.

Burgess, who had been given a post as Second Secretary at the British Embassy, took up residence in the Philby family home and rapidly set about causing offence to all and sundry.

The Second Thule Expedition ( 1916 – 1918 ) was larger with a team of seven men, which set out to map a little known area of Greenland's north coast.

However, the theory has been traced back to Treatise of Taxes, written in 1662 by Sir William Petty and to John Locke's notion, set out in the Second Treatise on Government ( 1689 ), that property derives from labor through the act of " mixing " one's labor with items in the common store of goods, though this has alternatively been seen as a labor theory of property.

This was followed by Cryptonomicon in 1999, a novel concerned with concepts ranging from computing and Alan Turing's research into codebreaking and cryptography during the Second World War at Bletchley Park, to a modern attempt to set up a data haven.

The Nuremberg Code is a set of research ethics principles for human experimentation set as a result of the Subsequent Nuremberg Trials at the end of the Second World War.

Turkey, as a neutral country during the Second World War, was a place where both the Axis and Allied powers sought to set up networks of spies.

Since Filmer's views essentially require that the Stuart family be uniquely descended from the patriarchs of the Bible, and since even in the late 17th century that was a difficult view to uphold, Locke attacked Filmer's views in his First Treatise on Government, freeing him to set out his own views in the Second Treatise on Civil Government.

Second, the New York Public Library released a two-volume set of " The Collected Works of Scott Joplin ," which renewed interest in Joplin among musicians and prompted new stagings of Joplin's opera Treemonisha.

* The Past Doctor Adventures novel The Murder Game, set after The Power of the Daleks, has the Second Doctor escaping from a locked room with a box-shaped sonic device, in which he muses on the advantages of building a smaller model.

The novel Dreams of Empire by Justin Richards, set after The Ice Warriors and before Fury from the Deep, features the Second Doctor utilising the device to break through a concrete wall.

One later volume, Catch the Saint, was an experiment in returning The Saint to his period, prior to the Second World War ( as opposed to recent Saint books set in the present day ).