The higher-dimensional chain rule can be proved using a technique similar to the second proof given above.

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.

* 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 ")

' In the second case, he cites an example that demonstrates ignorance of statistical principles in the lay press: ' Since no such proof is possible genetically modified food is harmless, the article in The New York Times was what is called a " bad rap " against the U. S. Department of Agriculture-a bad rap based on a junk-science belief that it's possible to prove a null hypothesis.

which is actually the theoretical proof of Kepler's second law ( A line joining a planet and the Sun sweeps out equal areas during equal intervals of time ).

The second part of the 1st Critique is Kant ’ s examination of the rationalist claims to absolute knowledge, taking on the most famous of these, the ontological proof of God ’ s existence, and showing that he can, through pure, non-experiential logic, both prove the affirmative and the negative of a proposition about a “ noumenal object ” ( i. e. an object like “ God ” which can never be an object of direct experience for a contingent being ).

In 1934, Pauli saw a failure of his car during a honeymoon tour with his second wife as proof of a real Pauli effect since it occurred without an obvious external cause.

Interestingly, the first proof begins with a basis for the column space, while the second builds from a basis for the row space.

The first proof is valid when the matrices are defined over any field of scalars, while the second proof works only on inner-product spaces.

Their conclusions about the empirical proof of DID were echoed by a second group, who still believed the diagnosis existed, but while the knowledge to date did not justify DID as a separate diagnosis, it also did not disprove its existence.

Newton's proof of Kepler's second law, as described in the book.

These two theorems are very different from each other ; the first one has a very simple proof and is very counterintuitive, while the proof of the second one is very technical but the result is not at all surprising.

A simplified proof of the second Nash embedding theorem was obtained by who reduced the set of nonlinear partial differential equations to an elliptic system, to which the contraction mapping theorem could be applied.

Many logicians believe that Gödel's incompleteness theorems struck a fatal blow to David Hilbert's second problem, which asked for a finitary consistency proof for mathematics.

Many anchors from the second and first millennium BC have been discovered in the town's bay, a proof of active shipping since ancient times.

A first glance at the second proof of Tychnoff may suggest that the proof uses no more than ( BPIT ), in contradiction to the above.

For the doctrine of proof, Galen quotes the second Analytic of Theophrastus, in conjunction with that of Aristotle, as the best treatises on that doctrine.

*-the second proof on 1826 in French

It is now common to interpret Hilbert's second question as asking in particular for a proof that Peano arithmetic is consistent.

Gödel's second incompleteness theorem shows that it is not possible for any proof that Peano Arithmetic is consistent to be carried out within Peano arithmetic itself.

One of the main goals of Hilbert's program was a finitistic proof of the consistency of the axioms of arithmetic: that is his second problem.

It becomes most evident in his description of Christ as the second Adam, who does indeed come to destroy sin, but whose work culminates in the achievement of immortality.

In the second example CH < sub > 3 </ sub > COOH undergoes the same transformation, in this case donating a proton to ammonia ( NH < sub > 3 </ sub >), but cannot be described using the Arrhenius definition of an acid because the reaction does not produce hydronium.

For a 256-bit block, the first row is unchanged and the shifting for the second, third and fourth row is 1 byte, 3 bytes and 4 bytes respectively — this change only applies for the Rijndael cipher when used with a 256-bit block, as AES does not use 256-bit blocks.

The second monochromator does not have an exit slit ; hence the spectral environment at both sides of the analytical line becomes visible at high resolution.

In air, compressibility effects are usually ignored when the Mach number in the flow does not exceed 0. 3 ( about 335 feet ( 102m ) per second or 228 miles ( 366 km ) per hour at 60 ° F ).

If a party has gained more direct mandates in a Land than it is entitled to according to the results of the second vote, it does not forfeit these mandates because all directly elected candidates are guaranteed a seat in the Bundestag.

This technique, famously practiced by Eddie Stanky of the Brooklyn Dodgers, is where the runner does not break immediately for second when the pitcher commits to the plate.

The dealer's hand receives its first card face up, and in " hole card " games receives its second card face down immediately ( the hole card ), which the dealer peeks at but does not reveal unless it makes the dealer's hand a blackjack.

The US version, however, has since 2001 taken on a significantly different format from the others in their second season, with a far stronger emphasis on strategy, competition and voting, where the public does not choose who to evict.

For the second exam, called the Principles and Practices, Part 2, or the Professional Engineering exam, candidates may select a particular engineering discipline's content to be tested on ; there is currently not an option for BME with this, meaning that any biomedical engineers seeking a license must prepare to take this examination in another category ( which does not affect the actual license, since most jurisdictions do not recognize discipline specialties anyway ).

If your side has two aces and a void, then you are not at risk of losing the first two tricks, so long as ( a ) your void is useful ( i. e., does not duplicate the function of an ace that your side holds ) and ( b ) you are not vulnerable to the loss of the first two tricks in the fourth suit ( because, for instance, one of the partnership hands holds a singleton in that suit or the protected king, giving your side second round control ).

Even adding a second execution unit ( see below ) does not improve performance much ; rather than one pathway being hung up, now two pathways are hung up and the number of unused transistors is increased.

At its second reading, if the Parliament approves the text or does not act, the text is adopted, otherwise the Parliament may propose further amendments to the Council's proposal.

The fact that a catalyst does not change the equilibrium is a consequence of the second law of thermodynamics.

In matters of marriage and divorce, the State of Israel relies on its Chief Rabbinate to determine who is Jewish ; the Chief Rabbinate, following Orthodox practice, does not recognize the validity of conversions performed by Conservative rabbis and will require a Jew who was converted by a Conservative rabbi to undergo a second, Orthodox conversion to be regarded as a Jew for marriage and other purposes.

Thus, interlaced video captures samples the scene motion twice as often as progressive video does, for the same number of frames per second.

While Duck Hunt does not have a traditional multiplayer mode, the manual states that a second player may plug in a standard NES controller in the other controller port and control the duck that appears.

This article uses the second definition and does not describe porpoises ( suborder Odontoceti, family Phocoenidae ).

" Beauchamp & Davidson also highlight Baruch Brody's " an act of euthanasia is one in which one person ... ( A ) kills another person ( B ) for the benefit of the second person, who actually does benefit from being killed ".

Although this is an independent definition that does not refer to the older basis of ephemeris time, it uses the same quantity as the value of the ephemeris second measured by the cesium clock in 1958.

" On second reading, the reader should realize that " breast " does not carry the general androgynous connotation of " chest " but instead the specific idea of a woman's breasts, which are so attractive that a man of any religion would kiss the Christian cross to be near.

As if to prove that lightning does occasionally strike twice, the second of the ' ones that got away ' came just a year later, the Dons finishing with a lamentable 7. 27 ( of which full forward Bill Brittingham contributed 2. 12 ) to tie with Melbourne ( who managed 10. 9 ) in the 1948 grand final.

If deactivation occurs during the first reading, the reader does not need to undergo deactivation in the second reading.

The first type allows the solid particles, i. e. the residue, to be collected intact ; the second type does not permit this.