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Page "Exact sequence" ¶ 23
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Here and 0
: Here N ( 0 ) is the electronic density of states at the Fermi energy.
Here the expression has the value 1 if m = 0 and 0 otherwise ( Iverson bracket ).
Here k is first-order rate constant having dimension 1 / time, ( t ) is concentration at a time t and < sub > 0 </ sub > is the initial concentration.
Here, i is the complex number whose square is the real number − 1 and is identified with the point with coordinates ( 0, 1 ), so it is not the unit vector in the direction of the x-axis ( this confusion is just an unfortunate historical accident ).
Here is estimated to be-1. 77 and is estimated to be 0. 83.
Here, the internal state ( q < sub > 1 </ sub >) is shown inside the head, and the illustration describes the tape as being infinite and pre-filled with " 0 ", the symbol serving as blank.
Here, the impulses are delayed for about 0. 1s before spreading to the walls of the ventricle.
Here 0 is the initial object of C. Cogroup objects occur naturally in algebraic topology.
Here for real a, b and c, if Δ > 0, the polynomial has two real roots, if Δ = 0, the polynomial has one real root, and if Δ < 0, the polynomial has no real roots.
Here, < math > 0 <
Here A < sub >–</ sub > and A < sub >+</ sub > are the absorbances of LCP or RCP, respectively ; ω is the modulator frequency – usually a high acoustic frequency such as 50 kHz ; t is time ; and δ < sub > 0 </ sub > is the time-dependent wavelength shift.
Here only the digit 9 is replaced by the digit 0, such that identities like 1. 000 ... = 0. 999 ... can spoil the result.
Here the homogeneous elements are either of degree 0 ( even ) or 1 ( odd ).
Here G is final average grain size, G < sub > 0 </ sub > is the initial average grain size, t is time, m is a factor between 2 and 4, and K is a factor given by:
Here Q is the molar activation energy, R is the ideal gas constant, T is absolute temperature, and K < sub > 0 </ sub > is a material dependent factor.
Here are some examples of TIFF extensions defined in TIFF 6. 0 specification:
Here it can be seen that it would not be relevant for merger law in the U. S. ( being under 0. 18 ) or in the EU ( because there is not a change over 0. 025 ).
* Here is an example of a set of second category in R with Lebesgue measure 0.
Here | z | is the absolute value or modulus of the complex number z ; θ, the argument of z, is usually taken on the interval 0 ≤ θ < 2π ; and the last equality ( to | z | e < sup > iθ </ sup >) is taken from Euler's formula.

Here and denotes
Here, < sub > n </ sub > denotes the sample mean of the first n samples ( x < sub > 1 </ sub >, ..., x < sub > n </ sub >), s < sup > 2 </ sup >< sub > n </ sub > their sample variance, and σ < sup > 2 </ sup >< sub > n </ sub > their population variance.
Here the term yoga denotes a kind of " meta-theory " that can be used heuristically ; Michel Raynaud writes the other terms " Ariadne's thread " and " philosophy " as effective equivalents.
Here K denotes the field of real numbers or complex numbers, I is a closed and bounded interval b and p, q are real numbers with 1 < p, q < ∞ so that
Here highbit ( S ) denotes the most significant bit of S ; the '< tt >*</ tt >' operator denotes unsigned integer multiplication with lost overflow ; '< tt >^</ tt >' is the bitwise exclusive or operation applied to words ; and P is a suitable fixed word.
# 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.
Here is the particle's velocity and × denotes the cross product.
Let ρ, θ, and φ be spherical coordinates for the source point P. Here θ denotes the angle with the vertical axis, which is contrary to the usual American mathematical notation, but agrees with standard European and physical practice.
Here denotes the maximum-likelihood estimate, and is the sample mean of the observations.
Here, denotes the natural logarithm.
Here C < sub > b </ sub >( X ) denotes the C *- algebra of all continuous bounded functions on X with sup-norm.
Here denotes vertical composition of natural transformations, and denotes horizontal composition.
Here the t denotes the matrix transpose.
( Here V0, V1, and V2 denote verbs and Ny denotes a noun.
Here y *( w ) denotes the value of the linear functional y * ( which is an element of the dual space of W ) when evaluated at the element w ∈ W. This scalar in turn is multiplied by x to give as the final result an element of the space V.
Here, || ||< sub > 2 </ sup > is the matrix 2-norm, c < sub > n </ sub > is a small constant depending on n, and ε denotes the unit round-off.
Here, denotes the radical of J and I ( U ) is the ideal of all polynomials which vanish on the set U.
Here, " prequel " denotes status as a " franchise-renewing original " that depicts events earlier in the ( internally inconsistent ) narrative cycle than those of a previous installment.
Here N < sub > m </ sub > denotes the number of turns in loop m, Φ < sub > m </ sub > the magnetic flux through this loop, and L < sub > m, n </ sub > are some constants.
( Here K ( a ) denotes the smallest subfield of L containing K and a )
Here denotes the standard complex inner product on and.
Here it also denotes a hand gesture, now linked to three other hand mudrās — the action ( karma ), pledge ( samaya ), and dharma mudrās — but also involves " mantra recitations and visualizations that symbolize and help to effect one ’ s complete identification with a deity ’ s divine form or awakening mind ( bodhicitta ).
Here, denotes the resolution limit in arcseconds and is in millimeters.

0.424 seconds.