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Page "Kummer theory" ¶ 23
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If and ground
If he spun out now, he would join his opponent on the ground.
If your pool is located on or near sloping ground, it may have natural drainage which is certainly more desirable than to be faced with the annual expense and labor of first pumping out the water and then scooping out all the debris.
If the platform is not too high off the ground, a transit can be mounted on a stand to raise it up to the platform.
If a circular building is aerodynamically smooth, and cooler than the ground, it can be passively cooled by the " dome effect.
If X and Y are Banach spaces over the same ground field K, the set of all continuous K-linear maps T: X → Y is denoted by B ( X, Y ).
If we take the simple molecular orbital description of the ground state and combine that function with the functions describing all possible excited states using unoccupied orbitals arising from the same set of atomic orbitals, we also reach the full configuration interaction wavefunction.
If the air mass is colder than the ground below it, it is labeled k. If the air mass is warmer than the ground below it, it is labeled w. While air mass identification was originally used in weather forecasting during the 1950s, climatologists began to establish synoptic climatologies based on this idea in 1973.
If however it has already saved its life by self-castration and is again pursued, then it stands up and reveals that it offers no ground for their eager pursuit, and releases the hunters from all further exertions, for they esteem its flesh less.
If not specified, there's no penalty for a disc landing any height above the ground.
If no player is able to legally catch the ball it is an incomplete pass and the ball becomes dead the moment it touches the ground.
If a match is drawn, there is a replay, usually at the ground of the team who were away for the first game.
If a fatwā does not break new ground, then it is simply called a ruling.
If a player contacts the ground inside the goal perimeter he must take the most direct path out of it.
If a ham has been cut into pieces and molded, it must be labelled " sectioned and formed ", or " chunked and formed " if coarsely ground.
If an isomorphism can be found from a relatively unknown part of mathematics into some well studied division of mathematics, where many theorems are already proved, and many methods are already available to find answers, then the function can be used to map whole problems out of unfamiliar territory over to " solid ground " where the problem is easier to understand and work with.
If the cannon fires its ball with a low initial velocity, the trajectory of the ball curves downward and hits the ground ( A ).
If the cannonball is fired with sufficient velocity, the ground curves away from the ball at least as much as the ball falls — so the ball never strikes the ground.
If the inverting input is held at ground ( 0 V ) directly or by a resistor, and the input voltage V < sub > in </ sub > applied to the non-inverting input is positive, the output will be maximum positive ; if V < sub > in </ sub > is negative, the output will be maximum negative.
If light ( photons ) of frequency ν < sub > 12 </ sub > pass through the group of atoms, there is a possibility of the light being absorbed by atoms which are in the ground state, which will cause them to be excited to the higher energy state.
If a collection of atoms are in the excited state, spontaneous decay events to the ground state will occur at a rate proportional to N < sub > 2 </ sub >, the number of atoms in the excited state.
If an atom is already in the excited state, it may be perturbed by the passage of a photon that has a frequency ν < sub > 21 </ sub > corresponding to the energy gap ΔE of the excited state to ground state transition.

If and field
If private brand competition hasn't been felt in your product field as yet, have you thought how you will cope with it if and when it does appear??
If Af is the change per unit volume in Gibbs function caused by the shear field at constant P and T, and **yr is the density of the fluid, then the total potential energy of the system above the reference height is Af.
If laying ties on a railroad track, which he once did for $1 an hour, paid more than playing right field for the Yankees, Maris would lay ties on a railroad track.
If working in a zinc mine, which he once did for 87-1/2 cents an hour, paid more than playing center field for the Yankees, Mantle would work in a zinc mine.
If K is a number field, its ring of integers is the subring of algebraic integers in K, and is frequently denoted as O < sub > K </ sub >.
If one quantizes a real scalar field, then one finds that there is only one kind of annihilation operator ; therefore, real scalar fields describe neutral bosons.
If under the existing system he could not assemble forces quickly enough to intercept mobile Viking raiders, the obvious answer was to have a standing field force.
If a is algebraic over K, then K, the set of all polynomials in a with coefficients in K, is not only a ring but a field: an algebraic extension of K which has finite degree over K. In the special case where K = Q is the field of rational numbers, Q is an example of an algebraic number field.
If a Game 5 is needed, the teams return to the higher seed's field.
If a Game 5 is needed, the teams return to the higher seed's field.
If X is a Banach space and K is the underlying field ( either the real or the complex numbers ), then K is itself a Banach space ( using the absolute value as norm ) and we can define the continuous dual space as X ′ = B ( X, K ), the space of continuous linear maps into K.
If a bubble touches identically-colored bubbles, forming a group of three or more, those bubbles — as well as any bubbles hanging from them — are removed from the field of play, and points are awarded.
If the ball has left the field along the sidelines, the referee must decide which team touched the ball last, and award a restart stroke to the opposing team, just like football's throw-in.
If the vector field represents the flow velocity of a moving fluid, then the curl is the circulation density of the fluid.
If φ is a scalar valued function and F is a vector field, then
If one set is used, pieces race across the field into empty, opposite corners.
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 scores a field goal, the scoring team must kickoff from their own 35-yard line.
If a kicked ball goes out of bounds, or the kicking team scores a single or field goal as a result of the kick, the other team likewise gets possession.
If they make what would normally be a field goal, they score one point ; what would normally be a touchdown scores two points ( a " two-point conversion ").
If not " true " crannogs, small occupied islets ( often at least partially artificial in nature ) may be referred to as island duns, although rather confusingly, 22 islet-based sites are classified as ' proper ' crannogs due to the different interpretations of the inspectors or excavators who drew up field reports Canmore search for crannog in the Western Isles Hebridean island dwellings or crannogs were commonly built on both natural and artificial islets, usually reached by means of a stone causeway.

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