He also lacked a symbol for a general number n. Where we would write, Diophantus has to resort to constructions like: ... a sixfold number increased by twelve, which is divided by the difference by which the square of the number exceeds three.

Where there is a difference in motion, then there is energy to be extracted at the interface.

Where reactive loads are present, such as with capacitors or inductors, energy storage in the loads results in a time difference between the current and voltage waveforms.

Whether it fits significantly better and should thus be preferred is determined by deriving the probability or p-value of the difference D. Where the null hypothesis represents a special case of the alternative hypothesis, the probability distribution of the test statistic is approximately a chi-squared distribution with degrees of freedom equal to df2 − df1.

Where the supply curve is more elastic than the demand curve, producers bear more of the tax and receive more of the subsidy than consumers as the difference between the price producers receive and the initial market price is greater than the difference borne by consumers.

Where the demand curve is more inelastic than the supply curve, the consumers bear more of the tax and receive more of the subsidy as the difference between the price consumers pay and the initial market price is greater than the difference borne by producers.

Where ΔT < sub > sa </ sub > is the superadiabatic temperature difference between the reference mantle temperature and the Core – mantle boundary and c is the specific heat capacity, which is a function of both pressure and temperature.

Where settlement is financial, the difference between the strike price and the spot price will determine the value, or " moneyness ", of the contract.

Where the fare paid to get the transfer is less than that required on the second bus, the difference must be paid on boarding.

Where gap is the absolute difference between the outlier in question and the closest number to it.

Where both R3 and R4 came with the same very basic level of trim the more powerful R4 cost less than 4 % above the price of the R3 which seems for most customers to have been too small a difference to justify the purchase of an R3.

Where you hit the china makes a huge difference to its sound.

Where Euler's Method uses the forward difference approximation to the first derivative in differential equations of order one, Verlet Integration can be seen as using the central difference approximation to the second derivative:

Where a large height difference has to be overcome, locks are built close together in a flight such as at Caen Hill Locks.

** Narrow therapeutic index: Where the difference between the effective dose and the toxic dose is small.

In his lecture course Society Must Be Defended, Foucault's tentative sojourner into biopolitical state racism, and its ' brilliant ' accomplished rationale of myth-making and narrative in which Foucault states the fundamental difference between biopolitics and discipline is :" Where discipline is the technology deployed to make individuals behave, to be efficient and productive workers, biopolitics is deployed to manage population ; for example, to ensure a healthy workforce ".

Where there is an American-British difference, the North of Britain generally agrees with America on this phoneme pair.

In a review published in his Consumer Guide column, Robert Christgau wrote, " Where Self Portrait was at least weird, splitting the difference between horrible and hilarious, is now forever professional — not a single remake honors or desecrates the original.

Where the acceptable boundaries lie in this area is very much a matter of opinion, and a matter of great controversy.

# We can distinguish between fields where the opinions and attitudes involved are static, and fields where those opinions and attitudes are subject to changes … Where opinions are relatively definite and static – for example, “ customs ” – one has to express or act according to this opinion in public or run the risk of becoming isolated.

Where one can be protected from a tyrant, it is much harder to be protected " against the tyranny of the prevailing opinion and feeling.

Shawe says: The Moravian ideal has been to gather together kindred hearts .... Where there are ' Christian hearts in love united ', there fellowship is possible in spite of differences of intellect and intelligence, of thought, opinion, taste and outlook.

( 1 ) Where, in the opinion of the Officer Administering the Government, it is necessary to regulate and control the use of the Flag of Rhodesia in order that it is not used for purposes which, in his opinion, are improper he may make such regulations restricting, regulating or controlling the application to any goods or the importation into Rhodesia of any goods to which there has been applied a reproduction of the Flag of Rhodesia or of a flag which resembles or is intended to resemble the Flag of Rhodesia as he may consider to be necessary or expedient for the purpose.

Where the defendant has represented him or herself as having more than average skills and abilities, this test expects standards which must be in accordance with a responsible body of opinion, even if others differ in opinion.

Where they differ in opinion on any of these issues, one and the same plant may be placed in taxa with different names.

Where a wrongful death statute exists, the compensation or other remedy available is limited to the remedy specified in the statute ( typically, an upper limit on the amount of damages ).

Where a double bond exists, there is the possibility of either a cis or a trans geometric isomerism, which significantly affects the molecule's molecular configuration.

Where it exists, it now often takes the form of constitutional monarchy, in which the monarch retains a unique legal and ceremonial role, but exercises limited or no political power pursuant to a constitution or tradition which allocates governing authority elsewhere.

Another is the use of French reflexive constructions in sentences such as the reply to a question like Where are you going ?, reply: Me I'm goin ' downtown ( this reflexive form of grammar also exists in Irish Gaelic and Jerriais ).

Where belief in malicious magic practices exists, such practitioners are typically forbidden by law as well as hated and feared by the general populace, while beneficial magic is tolerated or even accepted wholesale by the people – even if the orthodox establishment opposes it.

Where slavery exists or has existed, there is clearly a value put on living bodies separate from their instructional or social selves.

Where Universal suffrage exists, the right to vote is not restricted by gender, race, social status, or wealth.

Where Compulsory suffrage exists, those who are eligible to vote are required by law to do so.

Where full communion exists, there is but one Church.

Where the results of the test match the expectations of the scientific hypothesis, integrity exists between the cause and effect of the hypothesis by way of its methods and measures.

# Where the relative frequency of tornadoes is mentioned, it is the relative frequency in the United States, for which the best data exists.

Where the degree of hyperopia is large, the child may not be able to produce clear vision no matter how much extra-accommodation is exerted and thus no incentive exists for the over-accommodation and convergence that can give rise to the onset of esotropia.

Where more than one species of crane exists in a locality, each species will adopt separate niches in order to minimise competition and niche overlap.

Where universal suffrage exists, the right to vote is not restricted by race, sex, belief, sexual orientation, gender identity, wealth, social status or disability.

Where a monopoly exists, the price of a product is likely to be higher than in a competitive market and the quantity sold less, generating monopoly profits for the seller.

Where only one railway company exists, there is no need for a " joint station ".

Where a Homeowner's association exists, restrictive covenants may usually be modified or repealed by the association through procedures set forth in its bylaws.

Spengler writes that, " Comradeship breeds races … Where a race-ideal exists, as it does, supremely, in the Early period of a culture … the yearning of a ruling class towards this ideal, its will to be just so and not otherwise, operates ( quite independently of the choosing of wives ) towards actualizing this idea and eventually achieves it.

* Where a conflict exists, i. e. Kerry is KY, so Kilkenny is KK ; and County Waterford is WD, so Wexford is WX.

Where sufficient current information already exists the analysis may be tasked directly without reference to further collection.

Where a thin crust of non-liquefied soil exists between building foundation and liquefied soil, a ' punching shear ' type foundation failure may occur.

Where a revolt takes the form of armed rebellion, it may not be viewed as an insurgency if a state of belligerency exists between one or more sovereign states and rebel forces.

Where a different record exists for the top flight ( Football League First Division 1888-1992, Premier League 1992 -), this is also given.

# Where ground-level thick fog exists in a snow-covered environment, especially on open areas devoid of features.