Here dot means the r derivative of the functions.

( Here, the wedge product is used.

Here, a " specification " can be manifested as either a plan or a finished product, and " primitives " are the elements from which the design object is composed.

Here, each vertex ( pole ) is associated with a face plane ( polar plane or just polar ) so that the ray from the center to the vertex is perpendicular to the plane, and the product of the distances from the center to each is equal to the square of the radius.

Here n is the number of electrons / mole product, F is the Faraday constant ( coulombs / mole ), and ΔE is cell potential.

As explained above, Gaussian elimination writes a given m × n matrix A uniquely as a product of an invertible m × m matrix S and a row-echelon matrix T. Here, S is the product of the matrices corresponding to the row operations performed.

# 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 the last product means that a first electron, r < sub > 1 </ sub >, is in an atomic hydrogen-orbital centered at the second nucleus, whereas the second electron runs around the first nucleus.

Here 3 and 4 are the " factors " and 12 is the " product ".

Here a rank 1 tensor ( matrix product of a column vector and a row vector ) is the same thing as a rank 1 matrix of the given size.

Here, customers and suppliers must be integrated into the product development process in order to reduce time to market.

Here is the particle's velocity and × denotes the cross product.

Here, G × G is viewed as a topological space by using the product topology.

Here the random vector is the vector r of random returns on the individual assets, and the portfolio return p ( a random scalar ) is the inner product of the vector of random returns with a vector w of portfolio weights — the fractions of the portfolio placed in the respective assets.

Here, the product is the direct product, but the coproduct is the free product.

( Here stands for the scalar product ).

Here we introduce a nonnegative weight function in the definition of this inner product.

Here Mirbeau featured the character of Isidore Lechat, predecessor of the modern master of business intrigue, a product of the new world, a figure who makes money from everything and spreads his tentacles out over the world.

Here denotes the standard complex inner product on and.

Here, if one exponentiates 1, the product is 2. 71828 ; thus, the exponential function is the reciprocal of the natural logarithm.

Here, economies of scope make product diversification efficient if they are based on the common and recurrent use of proprietary know-how or on an indivisible physical asset.

( Here we think of V as a group under its operation of addition, and use the defining representation of GL ( V ) on V to define the semidirect product.

( Here, the product is taken over all primes p ; in the following, a sum or product taken over p always represents a sum or product taken over a specified set of primes, unless noted otherwise.

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.

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 0 denotes the trivial abelian group with a single element, the map from Z to Z is multiplication by 2, and the map from Z to the factor group Z / 2Z is given by reducing integers modulo 2.

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 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.