If there is one particular coordinate change that leads to a decrease in the total energy in both directions, the stationary point is a transition structure and the coordinate is the reaction coordinate.

If the eigenvalues are all positive, then the frequencies are all real and the stationary point is a local minimum.

If one eigenvalue is negative ( i. e., an imaginary frequency ), then the stationary point is a transition structure.

If more than one eigenvalue is negative, then the stationary point is a more complex one, and is usually of little interest.

If the spheres only appear to rotate ( that is, we are watching stationary spheres from a rotating frame ), the zero tension in the string is accounted for by observing that the centripetal force is supplied by the centrifugal and Coriolis forces in combination, so no tension is needed.

If the ranges of the morphisms of the inverse system of abelian groups ( A < sub > i </ sub >, f < sub > ij </ sub >) are stationary, that is, for every k there exists j ≥ k such that for all i ≥ j: one says that the system satisfies the Mittag-Leffler condition.

If the current is sufficiently small, the vortices are stationary, and the resistivity vanishes.

< p > If the stationary organism is a man and the traveling one is his twin, then the traveler returns home to find his twin brother much aged compared to himself.

If the room is not at negative pressure, the smoke will be blown outward or will stay stationary.

If f is a differentiable function on R ( or an open interval ) and x is a local maximum or a local minimum of f, then the derivative of f at x is zero ; points where are called critical points or stationary points ( and the value of f at x is called a critical value ).

The statcoulomb is defined as follows: If two stationary objects each carry a charge of 1 statC and are 1 cm apart, they will electrically repel each other with a force of 1 dyne.

If it is, then Ψ is a stationary state, and the proportionality constant, E, is the energy of the state Ψ.

If L ′ is of finite height, or at least verifies the ascending chain condition ( all ascending sequences are ultimately stationary ), then such an x ′ may be obtained as the stationary limit of the ascending sequence x ′< sub > n </ sub > defined by induction as follows: x ′< sub > 0 </ sub >=⊥ ( the least element of L ′) and x ′< sub > n + 1 </ sub >= f ′( x ′< sub > n </ sub >).

If the shear line becomes active with thunderstorms, it may support formation of a tropical storm or a regeneration of the feature back into a stationary front.

If there is a nonzero probability for any two paths to reach the same point at the same time, this stationary distribution does not depend on the initial conditions.

If the aether were stationary relative to the Sun, Michelson expected ( using his incorrect formula ) that the Earth's motion would produce a fringe shift 4 % the size of a single fringe of yellow light.

If the camera is fixed to the vehicle, the enforcement vehicle does not necessarily have to be stationary, and can be moved either with or against the flow of traffic.

Translating this analogy into space, then, a " stationary " observer sees a planet moving left at speed U and a spaceship moving right at speed v. If the spaceship has the proper trajectory, it will pass close to the planet, moving at speed U + v relative to the planet's surface because the planet is moving in the opposite direction at speed U. When the spaceship leaves orbit, it is still moving at U + v relative to the planet's surface but in the opposite direction ( to the left ).

If is a maximum of for the original constrained problem, then there exists such that is a stationary point for the Lagrange function ( stationary points are those points where the partial derivatives of are zero, i. e. ).

If the observational record is long enough and conditions are stationary ( i. e. there is no significant long-term trend ), a meaningful annual cycle will result that can be used to calculate an anomaly time series.

If this happens in the middle of a performance, the guitar is not going to be of much use to a guitarist who would like to sound " in-tune ", which is perhaps most users of the Floyd-Rose ( since the main advantage of the system is to achieve pitch-bends without losing intonation when the whammy bar returns to its stationary position ).

If the signal is not wide-sense stationary, or strictly stationary, then the autocorrelation function must be a function of two variables.

If it comes down too hard on the potential dangers of fallout, it will box the President on resuming atmospheric tests.

* Split ( only available as first decision of a hand ): If the first two cards have the same value, the player can split them into two hands, by moving a second bet equal to the first into an area outside the betting box of the original bet.

If instead the roll is 4, 5, 6, 8, 9, 10 then the come bet will be moved by the base dealer onto a box representing the number the shooter threw.

If instead the roll is 4, 5, 6, 8, 9, 10 then the don't come bet will be moved by the base dealer onto a box representing the number the shooter threw.

", " Well, the answer to that ", Benaud replied, " If there is, as there always can be, some emergency or a sensational happening on or off the field where it would be quite ridiculous not to go into the commentary box, of course I'll be in there doing my job and doing it as professionally as I can.

If the ball hits the net but lands in the service box, this is a let or net service, which is void, and the server retakes that serve.

If the ball hits the net on the first serve and bounces over into the correct diagonal box then it is called a " let " and the server gets two more additional serves to get it in.

If the server misses his or her first serve and gets a let on the second serve, then they get one more try to get the serve in the box.

If chiral pairs ( D and S ) are considered as identical, the remaining seven pieces can fill a 7 × 2 × 2 box.

" If we placed a living organism in a box ... one could arrange that the organism, after any arbitrary lengthy flight, could be returned to its original spot in a scarcely altered condition, while corresponding organisms which had remained in their original positions had already long since given way to new generations.

If a box containing hazardous material is moved around and shifted into different positions, it is still easy to recognize the symbol.

If an original manuscript, typewritten text, or recording is available, then the medium itself ( or its packaging — anything from a box to e-mail headers ) can help prove or disprove the authenticity of the document.

In 1963, the 10-minute halt was introduced, to occur after the completion of phases A, B, and C. It took place in a marked out area ( the 10-minute box ), where the horse was checked by two judges and one veterinary official who would make sure the horse was fit to continue onto phase D. If the horse was unfit, the panel would pull it from the competition.

Prior to the film's release, executive producer and Apple Computer founder Steve Jobs stated " If Toy Story is a modest hit — say $ 75 million at the box office — we'll and Disney both break even.

If we had a black box that solved FIND-SUBSET-SUM in unit time, then it would be easy to solve SUBSET-SUM.

If we had a black box that solved SUBSET-SUM in unit time, then we could use it to solve FIND-SUBSET-SUM.

If you ’ ve scrolled so a color legend is not in view, allowing your cursor to dwell over a cell will cause a pop-up text box to indicate that isotope ’ s half-life.

If a cell has a colored border, information on the isomer ’ s half-life is included in the pop-up text box when your cursor dwells over the cell.

If the Predictor predicts that both boxes will be taken, then box B will contain nothing.

If the Predictor predicts that only box B will be taken, then box B will contain $ 1, 000, 000.

If there are no true stumps available a bin, deckchair, boogie board or cool box may be used.

If the data are normally distributed, the locations of the seven marks on the box plot will be equally spaced.

If the user has magnified a document so that only part of it is visible on his computer screen, and then scrolls in it, it is useful to use a bounding box ( or in this case, a bounding rectangle scheme ) to quickly determine which scene graph elements are visible and thus actually need to be drawn.

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