A second fundamental principle is that involved particularly in the present proceeding -- the difference between nighttime and daytime propagation conditions with respect to the standard broadcast frequencies.

The second division, based on bore diameter in relation to length, determines whether the fundamental tone or the first overtone is the lowest partial practically available to the player:

Starting from the first and second laws of thermodynamics, four equations called the " fundamental equations of Gibbs " can be derived.

In his 1799 doctorate in absentia, A new proof of the theorem that every integral rational algebraic function of one variable can be resolved into real factors of the first or second degree, Gauss proved the fundamental theorem of algebra which states that every non-constant single-variable polynomial with complex coefficients has at least one complex root.

The second law is then a consequence of this definition and the fundamental postulate of statistical mechanics.

In mechanics, the second law in conjunction with the fundamental thermodynamic relation places limits on a system's ability to do useful work.

In number theory, the fundamental theorem of arithmetic, also called the unique factorization theorem or the unique-prime-factorization theorem, states that every integer greater than 1 is either prime itself or is the product of prime numbers, and that, although the order of the primes in the second case is arbitrary, the primes themselves are not.

Primary properties of visible light are intensity, propagation direction, frequency or wavelength spectrum, and polarisation, while its speed in a vacuum, 299, 792, 458 meters per second ( about 300, 000 kilometers per second ), is one of the fundamental constants of nature.

The poem is fundamental to the modern Western canon, and is the second oldest extant work of Western literature, the Iliad being the first.

With the advent of atomic clocks, it became feasible to define the second based on fundamental properties of nature.

Vocoders also often include a second system for generating unvoiced sounds, using a noise generator instead of the fundamental frequency.

* 1285 – The second Statute of Westminster is passed in England, reforming various laws ; it includes the famous clause de donis conditionalibus, considered one of the fundamental institutes of medieval law in England.

During its second reading, Powell warned of passing legislation " in haste and under the immediate pressure of indignation on matters which touch the fundamental liberties of the subject ; for both haste and anger are ill counsellors, especially when one is legislating for the rights of the subject ".

The SOIC ( Small Outline IC ), a surface-mount package which is currently very popular, particularly in consumer electronics and personal computers, is essentially a shrunk version of the standard IC PDIP, the fundamental difference which makes it an SMT device being a second bend in the leads to flatten them parallel to the bottom plane of the plastic housing.

F is the fundamental frequency ; the first overtone is the third harmonic, 3F, and the second overtone is the fifth harmonic, 5F for such a pipe, which is a good model for a panflute.

Fingering in the second register is generally the same as in the first / fundamental, though alternate fingerings are sometimes employed in the higher end of the registers to correct a flattening effect caused by higher aircolumn velocity.

Addison Wesley, Reading 5 / 9 / 2003 ISBN 0-321-15495-9 ( This book, now in second edition, eloquently covers the fundamental concepts of the discipline.

The deep arch causes these modes to align and create a consonant arrangement of intervals: a fundamental pitch, a pitch two octaves above that, and a third pitch an octave and a major third above the second.

For the F3 bar that usually forms the lowest note on a vibraphone, there would be F3 as the fundamental, F5 as the first overtone and A6 as the second overtone.

Fazlur Khan, another engineer at SOM, is considered " the greatest structural engineer of the second half of the 20th century "; he is best known for his design and construction of the Willis Tower ( formerly the Sears Tower ), and John Hancock Center and for his designs of structural systems that remain fundamental to all high-rise skyscrapers.

In the SI system, there are seven fundamental units: kilogram, meter, candela, second, ampere, kelvin, and mole.

The intrinsic and extrinsic curvature of a surface can be combined in the second fundamental form.

For unit tangent vectors X, the second fundamental form assumes the maximum value k < sub > 1 </ sub > and minimum value k < sub > 2 </ sub >, which occur in the principal directions u < sub > 1 </ sub > and u < sub > 2 </ sub >, respectively.

Thus, by the principal axis theorem, the second fundamental form is

They are a set of axioms strong enough to prove many important facts about number theory and they allowed Gödel to establish his famous second incompleteness theorem.

For a binomial involving subtraction, the theorem can be applied as long as the opposite of the second term is used.

* 1799: Doctoral dissertation on the Fundamental theorem of algebra, with the title: Demonstratio nova theorematis omnem functionem algebraicam rationalem integram unius variabilis in factores reales primi vel secundi gradus resolvi posse (" New proof of the theorem that every integral algebraic function of one variable can be resolved into real factors ( i. e., polynomials ) of the first or second degree ")

The first case was done by the Gorenstein – Walter theorem which showed that the only simple groups are isomorphic to L < sub > 2 </ sub >( q ) for q odd or A < sub > 7 </ sub >, the second and third cases were done by the Alperin – Brauer – Gorenstein theorem which implies that the only simple groups are isomorphic to L < sub > 3 </ sub >( q ) or U < sub > 3 </ sub >( q ) for q odd or M < sub > 11 </ sub >, and the last case was done by Lyons who showed that U < sub > 3 </ sub >( 4 ) is the only simple possibility.

Gödel's second incompleteness theorem, proved in 1931, showed that this was not possible – at least not within arithmetic itself.

The theorem is stating two things: first, that 1200 can be represented as a product of primes, and second, no matter how this is done, there will always be four 2s, one 3, two 5s, and no other primes in the product.

The first generalization of the theorem is found in Gauss's second monograph ( 1832 ) on biquadratic reciprocity.

As long as the second stagnation point is at its initial location on the upper surface of the wing, the circulation around the airfoil is zero and, in accordance with the Kutta – Joukowski theorem, there is no lift.

There is a classical analogue to the quantum no-cloning theorem, which we might state as follows: given only the result of one flip of a ( possibly biased ) coin, we cannot simulate a second, independent toss of the same coin.

Gödel's second incompleteness theorem ( 1931 ) shows that no formal system extending basic arithmetic can be used to prove its own consistency.

Then according to the second isomorphism theorem S ∩ T is normal in T and ST / S ≅ T /( S ∩ T ).

One might expect that by the Hahn-Banach theorem for bounded linear functionals, every bounded linear functional on C < sub > c </ sub >( X ) extends in exactly one way to a bounded linear functional on C < sub > 0 </ sub >( X ), the latter being the closure of C < sub > c </ sub >( X ) in the supremum norm, and that for this reason the first statement implies the second.

) In second order logic, however, the well-ordering theorem is strictly stronger than the axiom of choice: from the well-ordering theorem one may deduce the axiom of choice, but from the axiom of choice one cannot deduce the well-ordering theorem.

Using a uniqueness theorem and showing that a potential satisfies Laplace's equation ( second derivative of V should be zero i. e. in free space ) and the potential has the correct values at the boundaries, the potential is then uniquely defined.

In essence, the theorem shows that a bandlimited analog signal can be perfectly reconstructed from an infinite sequence of samples if the sampling rate exceeds 2B samples per second, where B is the highest frequency of the original signal.

The second follows simply from the space hierarchy theorem.

-- For a second month in a row, Multnomah County may be short of general assistance money in its budget to handle an unusually high summer month's need, the state public welfare commission was told Friday.

Michael Freeden in his study Ideologies and Political Theory ( 1996 ) states that all socialists share five themes: the first is that socialism posits that society is more than a mere collection of individuals ; second, that it considers human welfare a desirable objective ; third, that it considers humans by nature to be active and productive ; fourth, it holds the belief of human equality ; and fifth, that history is progressive and will create positive change on the condition that humans work to achieve such change.

Katsura was increasingly unpopular during his second term over public perception that he was using his office to further his personal fortune, and the interests of the military ( gunbatsu ) over the welfare of the people.

From 1750, welfare began to increase again, first thanks to agricultural innovations and in the second half of the 19th century thanks to the effects of the Industrial Revolution.

Under the second model, the state distributes welfare with as little bureaucratic interference as possible, to all people who fulfill easily established criteria ( e. g. having children, receiving medical treatment, etc .).

The central themes of the mythology of Chhinnamasta are her self-sacrifice – with a maternal aspect ( in the Pranotasani Tantra versions ) or for the welfare of the world ( in oral version 2 ) – her sexual dominance ( second Pranotasani Tantra version ) and her self-destructive fury ( in oral legend 1 ).

This can in part be explained by the party standing in many more municipalities, but it can also be seen as a reaction to the so-called ' right-wing winter ' in national politics, as the welfare reforms of the right-wing second Balkenende cabinet were called by its centre-left and left-wing opponents.

The second national policy combined a commitment to the GATT system, Keynesian macroeconomic policies, and the construction of a domestic social welfare net.

His views developed in the second half of the 20th Century, when democracies with capitalist economies established liberal welfare states that focused on the individual.

However, it was believed that because Clement Attlee's Labour government had a clear mandate to deliver the policies of nationalisation and welfare state measures, the House of Lords should not oppose such legislation at second reading.

After a period of time talking with professional wildlife managers and hunt supporters, he concluded that: " I find it repugnant that some people will kill another living creature for recreational purposes " but said that the dogs easily outpace the fox within a minute or two and kill it within a second or two and that how the fox is located is " totally irrelevant " to animal welfare considerations.

According to the newly amended Indian animal welfare act, 2011 cruelty to animals is an offence and is punishable with a fine which shall not be less than ten thousand Rupees, which may extend to twenty five thousand Rupees or with imprisonment up to two years or both in the case of a first offence. In the case of second or subsequent offence, with a fine which shall not be less than fifty thousand Rupees, but may extend to one lakh Rupees and with imprisonment with a term which shall not be less than one year but may extend to three years.

The earliest example of direct intervention by government in human welfare dates back to Umar ibn al-Khattāb's rule as the second caliph of Islam in the 6th century.

Les Boubou Macoutes was the popular nickname of special inspectors who visited the homes and investigated suspected " welfare cheats " in the Canadian province of Quebec during the second government of Premier Robert Bourassa, in the 1990s.

Octavia Hill ( 3 December 1838 – 13 August 1912 ) was an English social reformer, whose main concern was the welfare of the inhabitants of cities, especially London, in the second half of the nineteenth century.

The second approach “ is to specify the material conditions of a moral issue, for example, that moral rules and judgments ‘ must bear on the interest or welfare either of society as a whole or at least of persons other than the judge or agent ’ ”.

The first was that the governmental interest involved was different because the government functions primarily as “ an insurer for private investors .” The significance of this distinction is that the government ’ s “ freedom to pursue social goals is limited by the need to avoid excessive losses .” The second basis of distinction was based on the interest of the tenants: the tenants were not “ entitled ” to low rents in the same sense that recipients of welfare in Goldberg and that a rental increase is not as serious an injury.

In welfare economics, the theory of the second best concerns what happens when one or more optimality conditions cannot be satisfied.

A second response to the " rediscovery " of hunger in the mid sixties had been extensive lobbying of politicians to improve welfare.

The right to respect for family life is qualified by the broad principle that the welfare of the child is paramount and parental rights must take second place.

The main thesis deals with the changes brought on by the realisation of modernity's ideals, such as universal suffrage and education, the welfare state, civil and political rights, changes that marked the shift to the second modernity.

The second objective was to allow national governments the freedom to provide generous welfare programmes and to intervene in their economies to maintain full employment.

Hochschild illustrates the ways in which an unequal division of the second shift undermines family welfare by reducing marital equality and spousal satisfaction.

His first cabinet began building the modern Finnish welfare state, and the second government laid the foundation for Finland's EEC agreement.