While Diophantus is concerned largely with rational solutions, he assumes some results on integer numbers ; in particular, he seems to assume that every integer is the sum of four squares, though he never states as much explicitly.

Furthermore, one assumes that the set of solutions form an orthonormal set:

The reason we don't find these solutions in the above perturbation method is because these solutions diverge when while the ansatz assumes regular behavior in this limit.

As an example, consider the advection equation ( this example assumes familiarity with PDE notation, and solutions to basic ODEs ).

While not outrightly disawowing the movement's struggle for land reform as such, it has been noted that Brazilian media assumes a moralizing instance towards the MST: " to deplore the invasion of productive land, the MST's irrationality and lack of responsibility, the ill-using of distributed land parcels and to argue for the existence of alternate peaceful solutions ".

A tiny minority of physicists ( actually, a minority of one ) appear to believe that general relativity is unacceptable because it does not allow sufficiently general asymptotically flat solutions ( evidently this argument implicitly assumes that we have decisively rejected at least some Machian principles!

* Housing First-a service paradigm that assumes that individuals who are homeless are " ready " to be housed immediately and with appropriate supports can retain their housing.

The first book assumes that gamemasters will set their campaigns after the Patternfall war ; that is, after the end of the fifth book in the series, The Courts of Chaos, but uses material from the following books to describe those parts of Zelazny's cosmology that were featured there in more detail.

Freenet assumes that the Darknet ( a subset of the global social network ) is a small-world network, and nodes constantly attempt to swap locations ( using the Metropolis – Hastings algorithm ) in order to minimize their distance to their neighbors.

A deeper objection is that the very form of the Drake equation assumes that civilizations arise and then die out within their original solar systems.

Karl Popper used the term historicism in his influential books The Poverty of Historicism and The Open Society and Its Enemies, to mean: " an approach to the social sciences which assumes that historical prediction is their primary aim, and which assumes that this aim is attainable by discovering the ' rhythms ' or the ' patterns ', the ' laws ' or the ' trends ' that underlie the evolution of history ".

Though Jean encourages Cyclops to return to Madelyne, he finds their house abandoned and assumes that Madelyne has left him and taken their infant son ; Cyclops returns to X-Factor and he and Jean continue their relationship.

That the several states composing the United States of America are not united on the principle of unlimited submission to their general government ; but that, by compact, under the style and title of a Constitution for the United States, and of amendments thereto, they constituted a general government for special purposes, delegated to that government certain definite powers, reserving, each state to itself, the residuary mass of right to their own self-government ; and that whensoever the general government assumes undelegated powers, its acts are unauthoritative, void, and of no force ; that to this compact each state acceded as a state, and is an integral party, its co-States forming, as to itself, the other party ; that this government, created by this compact, was not made the exclusive or final judge of the extent of the powers delegated to itself, since that would have made its discretion, and not the Constitution, the measure of its powers ; but that, as in all other cases of compact among powers having no common judge, each party has an equal right to judge for itself, as well of infractions as of the mode and measure of redress.

* The second theory assumes that the document was created in order to protect the interests of Mieszko's second wife Oda and their sons ( who were named in the document ) after Mieszko's death.

The pope then assumes a place of honor as the rest of the cardinals wait in turn to offer their first " obedience " ( adoratio ) and to receive his blessing.

This article assumes that a scaling can have a scale factor of 1, so that all congruent shapes are also similar, but some school text books specifically exclude congruent triangles from their definition of similar triangles by insisting that the sizes must be different to qualify as similar.

) LTC also assumes that no suit can have more than 3 losing tricks and so suits longer than three cards are judged according to their three highest cards.

Cat form is the opposite, but also builds on physical damage abilities, with gameplay mechanics similar to that of rogues, including stealth and alternatives for most of their offensive moves ; Cats excel in damage dealing so in cat form the druid assumes the melee damage dealer role.

The Miranda warning assumes people don't understand what their rights are so it requires police officers to read a statement to people being arrested which informs them that they have certain rights, such as the right to remain silent and the right to have an attorney.

:: Example: The government's suggested approach assumes the validity of their conclusion even before the process of deduction has begun.

Male Kryptonians are shown wearing unique symbols on the chests of their robes, similar to a family crest ; Jor-El and Kal-El after him wear the familiar S-shield, which Lois Lane later assumes to be the letter S from the familiar Latin alphabet, and thus dubs him Superman.

Adopted by many as a textbook at a time when Romans were expanding their agricultural activities into larger scale and more specialized business ventures geared towards profitability, De Agri Cultura assumes a farm run and staffed by slaves.

It assumes a desire to ‘ develop ’ along the traditional ' Western ' model of economic development which a few countries, such as Cuba and Bhutan, have chosen not to allow their citizens to follow.

He assumes a Christ-figure pose which the people know well from their Christian associations ;

After their President Romana is assassinated, she assumes her identity, regaining her office, albeit in a different universe.

From their members, the Council selects the Mayor and the Mayor Pro Tem ( who assumes the duties of the Mayor when the Mayor is unavailable ).

Cooked beef irradiated in the absence of oxygen assumes an unnatural pink color.

After the glaze has reached its a certain temperature, the metal in the glaze assumes its color.

Molten sulfur assumes a dark red color above 200 ° C.

A highly heritable trait ( such as eye color ) assumes environmental inputs which ( though they are invariant in most populations ) are required for development: for instance temperatures and atmospheres supporting life, etc .).

Another common problem is, when using spatial anti-aliasing, the software assumes the background color is white.

This improved security assumes the user knows the meaning of the colors, and would choose to navigate away from the site if the color code was not commensurate with the purpose of the web site.

* Rainbow Raider – Dr. Quin is a supervillain who gains a different power for every color of the rainbow that he assumes.

* 29 July 1921 < span style =" color: red "> Adolf Hitler assumes leadership of the NSDAP.

These ratings are designed to provide color for prospective clients or investors regarding the relative risk that one assumes when engaging in business with the bank.

Solemn participation in various celebrations of Jesus Christ's Passion assumes particular color and vivacity in the procession of the Resurrected Christ held in Tarquinia in the late afternoon of Easter.

This causes difficulty for players with modern hardware, as the program automatically assumes that only systems running Win95 with 16-bit color are capable of supporting the game.

However, if one assumes a linear log absorption spectrum ( the Linner hypothesis from the realm of caramel color ), and knows the Linner Hue Index,, the absorptions are related by:

The tephra typically glows red when leaving the vent, but its surface cools and assumes a dark to black color and may significantly solidify before impact.

The party agreeing to buy the underlying asset in the future assumes a long position, and the party agreeing to sell the asset in the future assumes a short position.

Beauty becomes seriously ill after little Joe assumes Beauty does not need a blanket after a long, exhausting gallop.

This example assumes you are in Oak Brook, IL ( area code 630 ) and you have MCI as your long distance carrier.

Upon not seeing any trace of his money or the homeless man at the next station, Manni assumes the money is long gone.

Due to living so long, he assumes to have lost track of how old he is.

His neck is two feet eleven inches long, and twenty-three inches in circumference, his bill is about seventeen inches long, black in colour, measuring round the root about eleven inches ; for the first twelve inches the bill is straight, but after that assumes the shape of an eagle's and of proportionate strength.

SMBus protocol just assumes that if something takes too long, then it means that there is a problem on the bus and that all devices must reset in order to clear this mode.

Despite continuing to prove his usefulness, there is an ageist undertone that Mission Control assumes that he is no longer a valuable asset because of his age and long service.

LeChuck assumes the guise of " Charles L. Charles " and defeats Elaine in the election: the townspeople, feeling neglected by Elaine's long absence, do not believe her efforts to convince them of Charles ' true nature.

The pinch hitter may remain in the game following a pinch-hit at-bat and need not ( but may ) assume the same position as the player for whom he pinch-hits as long as some other player assumes that position.

After a long journey in disguise, he finally concludes that he is indeed a Khitan and he assumes his ancestral name " Xiao Feng ".

His grandfather had a paternal relationship with the Armenian villages that dot the land around Musa Dagh, a role that Gabriel Bagradian assumes not to be a real leader but more to help his French wife acclimate to what could be a long exile in the Turkish Levant.

Instead, uses a long list of skills and assumes that every character is " average " in all skills except those that the character is explicitly defined as being good at.

The Needle Palm assumes a shrublike clumping form with several stems growing from a single base, the stems growing very slowly and tightly together, eventually forming a dense base tall, with numerous sharp needle-like spines produced between the leaves ; these are long and protect the stem growing point from browsing animals.