One rule of thumb: " If the largest standard deviation

If placing a tile causes three or four chains to merge, then the merger steps are handled between the largest and second-largest chain, then with the third-largest chain, and finally with the smallest chain.

If their estimates are correct, 6. 1 percent of North Korea's total population was in the military, numerically the world's fifth largest military force, in the late 1980s ( fourth largest as of 2006 ).

( If there are no unused cards, the largest hand is played without a trump suit.

If there is more than one denomination of chip in the pot, the largest value chip is done first, and then progressively smaller value chips.

If the distribution of each X < sub > i </ sub > is limited to the right ( or left ) then the asymptotic distribution of the range is equal to the asymptotic distribution of the largest ( smallest ) value.

If no party has an absolute majority, the leader of the largest party is given the first opportunity to form a coalition.

If counted as a single nation state, the Visegrad Group is the seventh largest economy in Europe and the 15th in the world.

If this building were standing today, it would rank second in volume and third in footprint on List of largest buildings ( 130, 000m < sup > 2 </ sup >, 8, 500, 000m < sup > 3 </ sup >).

If no candidate succeeds in passing this threshold, a second round of voting is held with the participation of the two candidates who received the largest and second largest number of votes respectively.

If ranked today, the United Arab Republic would be the 25th largest nation on the planet ( Egypt is 30th and Syria is 88th ).

If the container contains particles of different sizes, the downward-moving region at the sides is often narrower than the largest particles.

) If formulated in von Neumann – Bernays – Gödel set theory, the surreal numbers are the largest possible ordered field ; all other ordered fields, such as the rationals, the reals, the rational functions, the Levi-Civita field, the superreal numbers, and the hyperreal numbers, are subfields of the surreals ; it has also been shown that the maximal class hyperreal field is isomorphic to the maximal class surreal field.

If h = 1, then simply move the disk from peg A to peg C. If h > 1, then somewhere along the sequence of moves, the largest disk must be moved from peg A to another peg, preferably to peg C. The only situation that allows this move is when all smaller h-1 disks are on peg B.

If one counts in Gray code of a bit size equal to the number of disks in a particular Tower of Hanoi, begins at zero, and counts up, then the bit changed each move corresponds to the disk to move, where the least-significant-bit is the smallest disk and the most-significant-bit is the largest.

Morrison's father had what was at the time one of the largest record collections in Ulster ( acquired during his sojourn in Detroit, Michigan in the early 1950s ), and the young Morrison grew up listening to artists such as Jelly Roll Morton, Ray Charles, Lead Belly, and Solomon Burke ; of whom Morrison later said, " If it weren't for guys like Ray and Solomon, I wouldn't be where I am today.

If the idol holder had received the most number of votes, the player with the next largest number of votes was then immediately voted out.

* If a contestant plays the hidden immunity idol, any votes cast for that contestant will not count, and the person with the next largest number of votes will be eliminated.

If the city were to annex the entire area within its planning area, it would become the largest city by area in Arizona, surpassing Phoenix.

If incorporated, Tucker would be the second largest city in the county after Dunwoody ( excluding Atlanta which is mostly in Fulton County ).

If the positive growth trends of Pleasure Ridge Park keep pace with the negative growth trends in the Louisville suburb of Jeffersontown, Pleasure Ridge Park will overtake Jeffersontown as the largest Louisville suburb on the Kentucky side of the river in the next few years ( all of this pre-merger, of course ).

If Sunrise Manor were to be incorporated, it would be one of the largest cities in Nevada.

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 such an eigenvalue is not stable, the dynamics of this eigenvalue will be present in the closed-loop system which therefore will be unstable.

If λ < sub > 1 </ sub >, ..., λ < sub > ν </ sub > are the eigenvalues of J they will be resonant if one eigenvalue is an integer linear combination of two or more of the others.

If n is odd, there is at least one real eigenvalue, + 1 or − 1 ; for a 3 × 3 rotation, the eigenvector associated with + 1 is the rotation axis.

If the system is a flow and the trajectory does not converge to a single point, one exponent is always zero — the Lyapunov exponent corresponding to the eigenvalue of with an eigenvector in the direction of the flow.

If a vector v of size n happens to be an eigenvector of A with eigenvalue λ, in other words if, then

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

If the system is in state ψ, then immediately after measurement the system will occupy a state which is an eigenvector e of A and the observed value λ will be the corresponding eigenvalue of the equation A e

If T is a compact operator, then it can be shown that any nonzero λ in the spectrum is an eigenvalue.

If we specifically choose the Euclidean norm on both R < sup > n </ sup > and R < sup > m </ sup >, then we obtain the matrix norm which to a given matrix A assigns the square root of the largest eigenvalue of the matrix A < sup >*</ sup > A ( where A < sup >*</ sup > denotes the conjugate transpose of A ).

If an algebra A acts on a vector space V over F to any simultaneous eigenspace corresponds an algebra homomorphism from A to F assigning to each element of A its eigenvalue.

If an observable is measured and the result is a certain eigenvalue, the corresponding eigenvector is the state of the system immediately after the measurement.

If an eigenvalue algorithm does not produce eigenvectors, a common practice is to use an inverse iteration based algorithm with set to a close approximation to the eigenvalue.

If the dynamic is given by a differentiable map f then a point is hyperbolic if and only if the differential of ƒ < sup > n </ sup > ( where n is the period of the point ) has no eigenvalue on the ( complex ) unit circle when computed at the point.

If the dimension, n, is odd, there will be a " dangling " eigenvalue of 1 ; and for any dimension the rest of the polynomial factors into quadratic terms like the one here ( with the two special cases noted ).

# If λ ∈ σ ( T ) is not an eigenvalue and the range of T − λ, Ran ( T − λ ), is dense in X, λ is said to be in the continuous spectrum, σ < sub > c </ sub >( T ), of T.

If is an eigenvalue, we have:

If λ is an eigenvalue of a matrix A

If α < sub > 1 </ sub > = 0. 852 then the real part of one of the complex eigenvalue pair becomes positive and there is a strange attractor.

Its simplest combinatorial version is due to Zuk: let be a discrete group generated by a finite subset S, closed under taking inverses and not containing the identity, and define a finite graph with vertices S and an edge between g and h whenever g < sup >− 1 </ sup > h lies in S. If this graph is connected and the smallest non-zero eigenvalue of its Laplacian is greater than ½, then has property ( T ).

If at least one eigenvalue has negative real part and at least one has positive real part, the equilibrium is a saddle point.

If equality holds ( i. e. if μ = ρ ( A ) e < sup > iφ </ sup > is eigenvalue for B ), then B