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If M has boundary, then we insist that v be pointing in the outward normal direction along the boundary.
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If and M
* If S and T are in M then so are S ∪ T and S ∩ T, and also a ( S ∪ T )
* If S and T are in M with S ⊆ T then T − S is in M and a ( T − S ) =
* If a set S is in M and S is congruent to T then T is also in M and a ( S )
* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =
* If M is some set and S denotes the set of all functions from M to M, then the operation of functional composition on S is associative:
If M is a Turing Machine which, on input w, outputs string x, then the concatenated string < M > w is a description of x.
Let ( m, n ) be a pair of amicable numbers with m < n, and write m = gM and n = gN where g is the greatest common divisor of m and n. If M and N are both coprime to g and square free then the pair ( m, n ) is said to be regular, otherwise it is called irregular or exotic.
If ( m, n ) is regular and M and N have i and j prime factors respectively, then ( m, n ) is said to be of type ( i, j ).
If X is a set and M is a complete metric space, then the set B ( X, M ) of all bounded functions ƒ from X to M is a complete metric space.
If X is a topological space and M is a complete metric space, then the set C < sub > b </ sub >( X, M ) consisting of all continuous bounded functions ƒ from X to M is a closed subspace of B ( X, M ) and hence also complete.
If used, the word „ gothic “ was used to describe ( mostly early ) works of F. M. Dostoevsky.
If ψ is satisfiable in a structure M, then certainly so is φ and if ψ is refutable, then is provable, and then so is ¬ φ, thus φ is refutable.
If is satisfiable in a structure M, then, considering, we see that is satisfiable as well.
If the password is correct, then M releases the transferred sum to B ( 3b ), usually minus a small commission.
If M is an R module and is its ring of endomorphisms, then if and only if there is a unique idempotent e in E such that and.
If and has
`` If Blue Throat has his way he'll keep us all cooped up in here for days '', he said.
If Wilhelm Reich is the Moses who has led them out of the Egypt of sexual slavery, Dylan Thomas is the poet who offers them the Dionysian dialectic of justification for their indulgence in liquor, marijuana, sex, and jazz.
If the man on the sidewalk is surprised at this question, it has served as an exclamation.
If any one of them has any power to veto the Secretary General's decisions the nature of the organization will have changed.
If this new Bible does not increase in significance by repeated readings throughout the years, it will not survive the ages as has the King James Version.
If the case is thus determined by us to be domestic, the court has no jurisdiction.
If this capacity had not failed them, they would see that their enemy has made a disastrous miscalculation.
If the new Soviet series has followed the general pattern of previous Russian tests, the shots were roughly half fission and half fusion, meaning a fission yield of 30 to 40 megatons thus far.
If the superintendents do not receive more cooperation from Handlers, it has been suggested that licensed Judges also be qualified to judge this Class.
If your state has no provisions for the numbering of pleasure boats, you must apply for a number from the U.S. Coast Guard for any kind of boat with mechanical propulsion rated at more than 10 horsepower before it can be used on Federal waterways.
If design head has a deep cavity, clay lid will be quite thick at this point ; ;
If you run into excess plug fouling on one truck, check to be sure that the rig has a thermostat.
If we manage to keep track of a Bombus queen after she has left her feeding place, we may discover the snug little hideout which she has fixed up for herself when she woke up from her winter sleep.
If cell Af has not previously been assigned as the information cell of a form in the text-form list, it is now assigned as the information cell of Af.
If of the founders of glottochronology Swadesh has escaped our steady plodding, and Lees has repudiated his own share in the founding, that is no reason why we should swerve.
If the transferor has substantial assets other than the claim, it seems reasonable to assume no corporation would be willing to acquire all of its properties in the dim hope of collecting a claim for refund of taxes.
If the patient can perceive figure kinesthetically when he cannot perceive it visually, then, it would seem, the sense of touch has immediate contact with the spatial aspects of things in independence of visual representations, at least in regard to two dimensions, and, as we shall see, even this much spatial awareness on the part of unaided touch is denied by the authors.
If the distant patron of the suburban branch has been frightened away from downtown by traffic problems, however, the city store can only pressure the politicians to do something about the highways or await the completion of the federal highway program.
If a statement has been assigned an address in the index word area
If she has not had such experiences, the female's normal adolescent degree of indecision will be compounded.
If the change, at first sight, seems minor, we may recall that it took the Italian painters about two hundred years to make an analogous change, and the Italian painters, by universal consent, were the most brilliant group of geniuses any art has seen.
If Barnett doesn't call a special session in 1961, it will be the first year in the last decade that the Legislature has not met in regular or special session.
If the church has followed the plan of cultivation of prospects and carried through a program of membership preparation as outlined earlier in this book, the process of assimilation and growth will be well under way.
If and boundary
If antimatter-dominated regions of space existed, the gamma rays produced in annihilation reactions along the boundary between matter and antimatter regions would be detectable.
If their existence past the K – T boundary can be confirmed, these hadrosaurids would be considered a Dead Clade Walking.
If < math > c ^ 2 < 4km </ math > there are two complex conjugate roots a ± ib, and the solution ( with the above boundary conditions ) will look like this:
If we allow also the system boundary to move ( e. g. due to moving pistons ) we get a rather general form of the first law for open systems.
If some dances, such as polka, cross ethnic boundaries and even cross the boundary between " folk " and " ballroom dance ", ethnic differences are often considerable enough to mention, e. g., Czech polka vs. German polka.
If the beam of light is not orthogonal ( or rather normal ) to the boundary, the change in wavelength results in a change in the direction of the beam.
If one assumed that magnetopause was just a boundary between a magnetic field in a vacuum and a plasma with a weak magnetic field embedded in it, then the magnetopause would be defined by electrons and ions penetrating one gyroradius into the magnetic field domain.
If the IMF has a southward component, this not only pushes the magnetopause boundary closer to Earth ( at times to about half its usual distance ), but it also produces an injection of plasma from the tail, much more vigorous than the one associated with substorms.
If the polygon can be drawn on an equally spaced grid such that all its vertices are grid points, Pick's theorem gives a simple formula for the polygon's area based on the numbers of interior and boundary grid points.
If Period B can be presumed to descend from Period A there must be a boundary between A and B, the A-B boundary.
If there is no distinct boundary, then the population of A suddenly stopped using the customs characteristic of A and suddenly started using those of B, an unlikely scenario in the process of evolution.
If the symbol "#" stands for a word boundary ( initial or final ), the notation "/ __ #"
If the refractive index is lower on the other side of the boundary and the incident angle is greater than the critical angle, no light can pass through and all of the light is reflected.
* If θ > θ < sub > c </ sub >, the entire ray reflects from the boundary.
If the incident ray is precisely at the critical angle, the refracted ray is tangent to the boundary at the point of incidence.
If the boundary is a sphere in three space dimensions, the angular components of the eigenfunctions are spherical harmonics, and the radial components are Bessel functions of half-integer order.
If the surface is not closed, it has an oriented curve as boundary.
If the area affected by the boundary includes multiple jurisdictions a special urban planning agency may be created by the state or regional government to manage the boundary.
If Canada holds that the principle of natural prolongation applies to the Juan de Fuca Canyon on its Pacific Ocean coast, the assertion could undermine Canada's argument in the Gulf of Maine boundary dispute.
If a membrane is stretched over a curve C that forms the boundary of a domain D in the plane, its vibrations are governed by the wave equation
* If is an entire function-in particular, when is a polynomial, then is the boundary of the set of points which converge to infinity under iteration.
* If is a polynomial, then is the boundary of the filled Julia set ; that is, those points whose orbits under iterations of remain bounded.
If the ice contains enough ammonia or other antifreeze, Oberon may possess a liquid ocean layer at the core – mantle boundary.
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