If the less developed countries are to be persuaded to adopt a long-term approach, the United States, as the principal supplier of external aid, must be prepared to give long-term commitments.

If you have neither a legal residence nor a principal place of business in any Internal Revenue district, your return should be filed with the District Director of Internal Revenue, Baltimore 2, Md..

If your principal place of abode for the tax year is outside the United States ( including Alaska and Hawaii ), Puerto Rico, or the Virgin Islands and you have no legal residence or principal place of business in any Internal Revenue district in the United States, you should file your return with the Office of International Operations, Internal Revenue Service, Washington 25, D.C..

If it is owned, taxes must be paid, and if the place is not free of mortgage, there will be interest and payments on the principal to take care of.

The key result is the structure theorem: If R is a principal ideal domain, and M is a finitely

If M is a free module over a principal ideal domain R, then every submodule of M is again free.

If the project gets the green-light to go into principal photography, he might hire a line producer to watch over the production day to day.

The Gaussian integers form a principal ideal domain with units 1, − 1, i, and − i. If x is a Gaussian integer, the four numbers x, ix, − x, and − ix are called the associates of x.

* If a village is the principal settlement of a civil parish, then any administrative body that administers it at parish level should be called a parish council or parish meeting, and not a town council or city council.

If we have just two variables and they have the same sample variance and are positively correlated, then the PCA will entail a rotation by 45 ° and the " loadings " for the two variables with respect to the principal component will be equal.

If mean subtraction is not performed, the first principal component might instead correspond more or less to the mean of the data.

Although the invitation was not signed by Churchill ( he was not, as yet, of sufficient political rank to be a signatory ), he declared his intention through William's principal English contact in The Hague – " If you think there is anything else that I ought to do, you have but to command me.

If the attorney-in-fact is being paid to act for the principal, the contract is usually separate from the power of attorney itself, so if that contract is in writing, it is a separate document, kept private between them, whereas the power of attorney is intended to be shown to various other people.

If we are given the components of the strain tensor in an arbitrary orthonormal coordinate system, we can find the principal strains using an eigenvalue decomposition determined by solving the system of equations

Steve Bell is probably best known for the daily strip called If ..., which has appeared in The Guardian newspaper since 1981, and since the mid-1990s he has also been that newspaper's principal editorial cartoonist.

* Spec k, the spectrum of the polynomial ring over a field k, which is also denoted, the affine line: the polynomial ring is known to be a principal ideal domain and the irreducible polynomials are the prime elements of k. If k is algebraically closed, for example the field of complex numbers, a non-constant polynomial is irreducible if and only if it is linear, of the form t − a, for some element a of k. So, the spectrum consists of one closed point for every element a of k and a generic point, corresponding to the zero ideal.

If one bends a slice horizontally along a radius, non-zero principal curvatures are created along the bend, dictating that the other principal curvature at these points must be zero.

* If both principal curvatures are the same sign: κ < sub > 1 </ sub > κ < sub > 2 </ sub >> 0, then the Gaussian curvature is positive and the surface is said to have an elliptic point.

* If the principal curvatures have different signs: κ < sub > 1 </ sub > κ < sub > 2 </ sub >< 0, then the Gaussian curvature is negative and the surface is said to have a hyperbolic point.

* If one of the principal curvature is zero: κ < sub > 1 </ sub > κ < sub > 2 </ sub >= 0, the Gaussian curvature is zero and the surface is said to have a parabolic point.

If we have a principal bundle over the manifold M with G as the structure group, and we pick X to be a covariant vector field as section of the tangent space of the principal bundle ( i. e. it has horizontal and vertical components ), then the covariant Lie derivative is just the Lie derivative with respect to X over the principal bundle.

If the city council fails to consider appointment of a full-time CD director, Mr. Hawksley said, then he plans to call a meeting early in September so that a civil defense organization will be developed locally.

If it fails to pass, he can throw up his hands and say the Legislature would not support him in his efforts to prevent integration.

If a single test fails, then the theory is falsified.

If this limit fails to exist then there is no oblique asymptote in that direction, even should the limit defining m exist.

If the bankrupt fails to lodge the document within a certain period of time, he or she can be prosecuted and fined.

If the bankrupt fails to pay the contributions due, the trustee can issue a notice to garnishee the bankrupt's wages.

If a team fails to gain ten yards in two downs they usually punt the ball on third down or try to kick a field goal ( see below ), depending on their position on the field.

* If the offence fails to make ten yards in three plays, the defence takes over on downs.

* If the offence fumbles ( a ball carrier drops the football, or has it dislodged by an opponent, or if the intended player fails to catch a lateral pass or a snap from centre, or a kick attempt is blocked by an opponent ), the ball may be recovered ( and advanced ) by either team.

He is still seeking greater autonomy from China, although Dolma Gyari, deputy speaker of the parliament-in-exile has stated " If the middle path fails in the short term, we will be forced to opt for complete independence or selfdetermination as per the UN charter ".

If the Dance Gauge is fully depleted during gameplay, the player fails the song, usually resulting in a game over.

< tr >< td > If variolation after infection with cowpox fails to produce a smallpox infection, immunity to smallpox has been achieved.

If power fails, all essential equipment will run off huge batteries for up to 20 minutes, during which time four one-megawatt diesel generators will take over.

If the implementation of the change should fail or, the post implementation testing fails or, other " drop dead " criteria have been met, the back out plan should be implemented.

If this continues far enough, the working end passes into the knot and the knot unravels and fails.

If a team does not attempt to score a field goal ( or the ball fails to make contact with the rim ) within 24 seconds of obtaining the ball, play is stopped and the ball given to its opponent.

If the egg fails to release from the follicle in the ovary an ovarian cyst may form.

If a player fails to make the contract and takes overtrick ( s ), he / she scores the number of tricks taken.

If he fails on the turn, he then has a 9 / 46 chance to fill on the river.

If any goal fails in the course of executing the program, all variable bindings that were made since the most recent choice-point was created are undone, and execution continues with the next alternative of that choice-point.

If this fails then watermark fluid may be used, which " wets " the stamp to reveal the mark.

If the vaulter fails to begin an attempt within this time, the vaulter is charged with a time foul and the attempt is a miss.

If one peer on the network fails to function properly, the whole network is not compromised or damaged.

If the child drops the gun and it breaks someone's foot, the HWR test fails, as a broken foot was not the type of harm anticipated.

If the visitor fails to do so, usually a quarantine fine of 220 Australian dollars are to be paid as quarantine infringement notice, and if not, the visitor may face criminal convictions of fining 100, 000 Australian dollars and 10 years imprisonment.