One of these, Itō's lemma, expresses the composite of an Itō process ( or more generally a semimartingale ) dX < sub > t </ sub > with a twice-differentiable function f. In Itō's lemma, the derivative of the composite function depends not only on dX < sub > t </ sub > and the derivative of f but also on the second derivative of f. The dependence on the second derivative is a consequence of the non-zero quadratic variation of the stochastic process, which broadly speaking means that the process can move up and down in a very rough way.

One can refine this statement ( via the splitting lemma or the below proof ) to be a statement about an isomorphism of spaces, not just dimensions.

One of Gelfand's original applications ( and one which historically motivated much of the study of Banach algebras ) was to give a much shorter and more conceptual proof of a celebrated lemma of Norbert Wiener ( see the citation below ), characterizing the elements of the group algebras L < sup > 1 </ sup >( R ) and whose translates span dense subspaces in the respective algebras.

One of the most important rules of the method forms the second lemma of the second book of the Principia.

She states in Volume One of her diaries that she drew inspiration from Marcel Proust, André Gide, Jean Cocteau, Paul Valéry, and Arthur Rimbaud.

One of the documents of that time states, " The Victory immediately gained the general sympathy of Russian society and it continued to grow.

One could note a certain irony: one of the first acts of many of the newly independent states was to adopt the law of the foreign sovereign from whom independence had just been gained.

One of the first studies of condensed states of matter was by English chemist Humphry Davy, when he observed that of the forty chemical elements known at the time, twenty-six had metallic properties such as lustre, ductility and high electrical and thermal conductivity.

One way to divide various consequentialisms is by the types of consequences that are taken to matter most, that is, which consequences count as good states of affairs.

One of these systems, which is operated by Cornell University and began operation in 2000, was controversial during the planning and building states for potential negative environmental impact.

But its long curing time of at least a month made it unpopular after World War One in the construction of highways and bridges and many states and construction firms turned to the use of Portland cement.

One particularly important physical result concerning conservation laws is Noether's Theorem, which states that there is a one-to-one correspondence between conservation laws and differentiable symmetries of physical systems.

One section states that if a man purchases a cow that is found to be pregnant, then he is the owner both of the cow and the calf that is born from it.

One critic states of psychologists that " Instead of replacing ' metaphysical ' terms such as ' desire ' and ' purpose ', they used it to legitimize them by giving them operational definitions ... the initial, quite radical operationalist ideas eventually came to serve as little more than a ' reassurance fetish ' ( Koch 1992 ) for mainstream methodological practice.

One example is the First Things First manifesto which was launched within the graphic design community and states " We propose a reversal of priorities in favor of more useful, lasting and democratic forms of communication – a mindshift away from product marketing and toward the exploration and production of a new kind of meaning.

One of the problems ( sometimes called his epitaph ) states:

One way to divide various consequentialisms is by the types of consequences that are taken to matter most, that is, which consequences count as good states of affairs.

One inscription found at Axum, states that he conquered the nation of the Bogos, and returned thanks to his father, the god Mars, for his victory.

One situation of affairs through objective acts of consciousness ( acts of constituting categorially ) can serve as the basis for constituting multiple states of affairs.

One approach is to harmonize the company law of the member states.

One supposes that the quantum spin-singlet states emitted by the source are actually approximate descriptions for " true " physical states possessing definite values for the z-spin and x-spin.

One theory states that stable wormholes are possible, but that any attempt to use a network of wormholes to violate causality would result in their decay.

One possible construction of the " internal evidence " states that the Beloved Disciple wrote an account of the life of Jesus.

One after another the German states switched to oppose Napoleon, but he rejected peace terms.

One, which remained unratified, provided for free trade among all of the states except Costa Rica.

One, as early as Thucydides, reported in Plutarch, the Suda and John Tzetzes, states that the Delphic oracle warned Hesiod that he would die in Nemea, and so he fled to Locris, where he was killed at the local temple to Nemean Zeus, and buried there.

One of the major states to emerge from the Mfecane was the Sotho Kingdom founded at Thaba Bosiu by Moshoeshoe I around 1821 to 1822.

One is tempted to say that, on the difference between the concepts of sovereignty in these two preambles, the worst war of the Nineteenth century was fought.

One prediction had been made about the difference in security or self-confidence between those subjects who shifted their Kohnstamm reactivity when informed and those who did not.

One experiment showed the greatest one-year difference occurring between the eleventh and twelfth years.

One striking difference when comparing the Bundestag with the British Parliament is the lack of time spent on serving constituents in Germany.

One significant difference of modern naval battles as opposed to earlier forms of combat is the use of marines, which introduced amphibious warfare.

One notable difference in the pilot, as in many pilots, is the casting.

One major difference between these two approaches is the agent's responsibility.

One difference between eukaryotic and prokaryotic genes is that eukaryotic genes can contain introns ( intervening DNA sequences ) which are not coding sequences, in contrast with exons, which are DNA coding sequences.

One of the main sources of confusion in popular classifications is the difference between a dialect and a language.

One major difference between DNA and RNA is the sugar, with the 2-deoxyribose in DNA being replaced by the alternative pentose sugar ribose in RNA.

One major difference lies in the nature of the problems that each subject tries to address.

One major difference between the Ramsay's family coat of arms and the university seal, is that while the Ramsay seal features a griffin and greyhound, the Dalhousie seal instead has two dragons supporting the eagle-adorned shield.

One henry is the inductance that will induce a potential difference of one volt if the current through it changes at a rate of one ampere per second.

One of the most remarkable features of American society is that the difference between the " uneducated " and the " educated " is so slight.

One important difference in modern field hockey is the absence of an offside rule.

One difference between false cognates and false friends is that while false cognates mean roughly the same thing in two languages, false friends bear two distinct ( sometimes even opposite ) meanings.

One difference between them is that the older black powder burns at nearly the same rate in the open as when contained, while in smokeless powders the burn rate accelerates more rapidly within a closed chamber, making for a sharper rise in pressure which could rupture older weapons designed for black powder.

One difference between the film and the novel is the staircase scene in which Rhett carries Scarlett up the stairs.

One major difference between Vista and earlier versions of Windows, Windows 95 and later, is that the original start button was replaced with just the Windows icon.

One key difference between the rugby and gridiron variants of the backward pass is that the gridiron lateral is based solely on the path of the ball, unlike in rugby, where it is based on the position of the player.

One way this difference of viewpoint plays out is in the philosophical debate as to whether mathematics is created ( as in art ) or discovered ( as in science ).

One notable difference, however, is that prokaryotic RNA polymerase associates with mRNA-processing enzymes during transcription so that processing can proceed quickly after the start of transcription.

One recent study notes that the difference between summer and winter flow volumes has increased significantly in the last 100 – 200 years.

One other difference in these controllers is that the earliest releases of the silver joystick were removable.