If we try to study T using characteristic values, we are confronted with two problems.

If one characteristic distinguishes Boris Godunov, it is the consistency with which every person on the stage -- including the chorus -- comes alive in the music.

If a group has an involution with a 2-component that is a group of Lie type of odd characteristic, the goal is to show that it has a centralizer of involution in " standard form " meaning that a centralizer of involution has a component that is of Lie type in odd characteristic and also has a centralizer of 2-rank 1.

If the graph G is connected, then the rank of the free group is equal to 1 − χ ( G ): one minus the Euler characteristic of G.

If the cooling is sufficiently rapid ( relative to the characteristic crystallization time ) then crystallization is prevented and instead the disordered atomic configuration of the supercooled liquid is frozen into the solid state at T < sub > g </ sub >.

If the field of scalars of the vector space has characteristic p, and if p divides the order of the group, then this is called modular representation theory ; this special case has very different properties.

If the field had characteristic p > 0, then − 1 would be the sum of p − 1 ones, but − 1 is not positive ).

If f is the characteristic function of a set B, B is also said to be A-computable, and M is said to be a Turing reduction from B to A.

If the person is infected with scabies, the characteristic zigzag or S pattern of the burrow will appear across the skin ; however, interpreting this test may be difficult, as the burrows are scarce and may be obscured by scratch marks.

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 is the characteristic impedance of the line, then for a wave moving rightward, or for a wave moving leftward.

If the transmission line is uniform along its length, then its behaviour is largely described by a single parameter called the characteristic impedance, symbol Z < sub > 0 </ sub >.

If the current and voltage come from a single wave ( with no reflection ), then V ( x ) / I ( x ) = Z < sub > 0 </ sub >, where Z < sub > 0 </ sub > is the characteristic impedance of the line.

If two people were in a room and one of them wanted to refer to a characteristic of a chair in the room he would say " this chair has four legs " instead of " a chair has four legs.

If the characteristic of the ground field K is not 2, then one can rewrite this fundamental identity in the form

If one puts a detector screen on the other side, the pattern of detected particles shows interference fringes characteristic of waves ; however, the detector screen responds to particles.

If it is desired to sample more of the exponential electron portion of the characteristic, an asymmetric double probe may be used, with one electrode larger than the other.

If one bends and deforms the surface, its Euler characteristic, being a topological invariant, will not change, while the curvatures at some points will.

If ( d < sub > n </ sub >: A < sub > n </ sub > → A < sub > n-1 </ sub >) is a chain complex such that all but finitely many A < sub > n </ sub > are zero, and the others are finitely generated abelian groups ( or finite dimensional vector spaces ), then we can define the Euler characteristic

If A is abelian, then the torsion subgroup T is a fully characteristic subgroup of A and the factor group A / T is torsion-free.

The compactness theorem implies Robinson's principle: If a first-order sentence holds in every field of characteristic zero, then there exists a constant p such that the sentence holds for every field of characteristic larger than p. This can be seen as follows: suppose φ is a sentence that holds in every field of characteristic zero.

`` If William agrees, we should insist on a public debate '', he said at length.

If, in a certain part of the range, it starts life 1 foot longer than do any of the other ( relatively large ) giants, and reaches maturity at, let us guess, 18 inches longer than the others, a quadrupling of the maturity length would result in a maximum of ( nearly ) 40 feet.

If T is the total `` length '' of the process, its feed state may be denoted by a vector p(T) and the product state by p(Q).

* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =

If a description of s, d ( s ), is of minimal length ( i. e. it uses the fewest number of characters ), it is called a minimal description of s. Thus, the length of d ( s ) ( i. e. the number of characters in the description ) is the Kolmogorov complexity of s, written K ( s ).

If the square mile is divided into quarters, each quarter has a side length of mile ( 880 yards ) and is square mile in area, or 160 acres.

If the sets are short to medium length the caller will often try to run the dance until each couple has danced with every other couple both as a 1 and a 2 and returned to where they started.

If numerical iterative methods have to be employed, the aim is to iterate until full machine accuracy is obtained ( the best that is possible with a finite word length on the computer, and within the mathematical and / or physical approximations made ).

If the cannon is bronze, it will often have a vent piece made of copper screwed into the length of the vent.

If the weight of the roadway per unit length is w and the weight of the cable and the wire supporting the bridge is negligible in comparison, then the weight on the cable from c to r is wx where x is the horizontal distance between c to r. Proceeding as before gives the differential equation

If, for the same focal length setting, the subject distance is adjusted to provide the same field of view at the subject, at the same f-number and final-image size, the smaller format has greater DOF, as with the “ same picture ” comparison above.

If pictures are taken from the same distance using the same f-number, same focal length, and the final images are the same size, the smaller format has less DOF.

If pictures taken from the same subject distance using the same focal length, are given the same enlargement, both final images will have the same DOF.

If no bulk flow occurs in an element of length dx, the rates of diffusion of two gases A and B must be equal and opposite, that is.

If we draw an ellipse twice as long as it is wide, and draw the circle centered at the ellipse's center with diameter equal to the ellipse's longer axis, then on any line parallel to the shorter axis the length within the circle is twice the length within the ellipse.

If is time-dependent, the diffusion length becomes.

If the symbol width is n, the codes of width n + 1 fall naturally into two blocks: the lower block of 2 < sup > n </ sup > codes for coding single symbols, and the upper block of 2 < sup > n </ sup > codes that will be used by the decoder for sequences of length greater than one.

If the length of the intervals on the x-axis are all 1, then a histogram is identical to a relative frequency plot.

If the reloaded cartridges are going to be used in the same firearm in which they were previously fired, though, and if that firearm has a bolt action or other action with a strong camming action on closing, then full length resizing may not be needed.

# If A is a cartesian product of intervals I < sub > 1 </ sub > × I < sub > 2 </ sub > × ... × I < sub > n </ sub >, then A is Lebesgue measurable and Here, | I | denotes the length of the interval I.

If two quarks have unaligned spins, the spin vectors add up to make a vector of length S = 0 and only one spin projection ( S < sub > z </ sub > = 0 ), called the spin-0 singlet.

If the edge length of a regular octahedron is a, the radius of a circumscribed sphere ( one that touches the octahedron at all vertices ) is

: If a person traveling with a yardstick, measures the length of such yardstick, the physical quantity of length would be written as