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.

Therefore, given any positive integer n, it produces a string with Kolmogorov complexity at least as great as n. The program itself has a fixed length U. The input to the program GenerateComplexString is an integer n. Here, the size of n is measured by the number of bits required to represent n, which is log < sub > 2 </ sub >( n ).

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 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 < sub > 2 </ sub > is reduced to I < sup >–</ sup > and S < sub > 2 </ sub > O < sub > 3 </ sub >< sup > 2 –</ sup > ( thiosulfate anion ) is oxidized to S < sub > 4 </ sub > O < sub > 6 </ sub >< sup > 2 –</ sup >.

The simplest, and original, implementation of the protocol uses the multiplicative group of integers modulo p, where p is prime and g is primitive root mod p. Here is an example of the protocol, with non-secret values in < span style =" color: blue "> blue </ span >, and secret values in < span style =" color: red "> boldface red </ span >:

Here is the center of the ellipse, and is the angle between the < math > X </ Math >- axis and the major axis of the ellipse.

Here C < sub > p </ sub > is the heat capacity at constant pressure and α is the coefficient of ( cubic ) thermal expansion

Here ( Z / 2Z ) is the polynomial ring of Z / 2Z and ( Z / 2Z )/( T < sup > 2 </ sup >+ T + 1 ) are the equivalence classes of these polynomials modulo T < sup > 2 </ sup >+ T + 1.

Here the kets and columns are identified with the vectors of V and the bras and rows with the dual vectors or linear functionals of the dual space V < sup >*</ sup >, with conjugacy associated with duality.

Here, R < sub > ij </ sub > is the Ricci tensor.

# 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.

The pre-release single, " Om du var här " ( If You Were Here ), became a hit as would the second single, " Saker man ser " ( Things You See ).

Here,, and will be used to denote the initial velocity, the velocity along the direction of < var > x </ var > and the velocity along the direction of < var > y </ var >, respectively.

In 3 dimensions, a differential 0-form is simply a function f ( x, y, z ); a differential 1-form is the following expression: a differential 2-form is the formal sum: and a differential 3-form is defined by a single term: ( Here the a-coefficients are real functions ; the " wedge products ", e. g. can be interpreted as some kind of oriented area elements,, etc.

Here, x is the angle that a line connecting the origin with a point on the unit circle makes with the positive real axis, measured counter clockwise and in radians.

Here Person ( x ) is interpreted to mean x is a person, Time ( y ) to mean that y is a moment of time, and Canfool ( x, y ) to mean that ( person ) x can be fooled at ( time ) y.

Here ( x, y | x ', y ') means that instead of ψ we are writing a different formula, in which x and y are replaced with x ' and y '.

Here, we have < tt >( λx. xx )( λx. xx ) → ( xx ):= λx. xx = ( x := λx. xx )( x := λx. xx ) = ( λx. xx )( λx. xx )</ tt >.

Here the summation is over all prime powers up to x.

Here m is the particle's mass and V ( x ) is the applied potential.

Here x is the node on which the splay operation is performed and root is the root node of the tree.

The Wildhearts song ' 29 x The Pain ', which namedrops the bands major influences, opens with the lyrics ' Here, sitting in my room, with the Replacements and Hüsker Dü '.

Here u ( x ) measures the distance from the equilibrium of the mass situated at x.

Here N < sub > x </ sub > is the number of x atoms per volume, λ the electron escape depth, θ the analyzer angle, T the transmission of the analyzer, I ( t ) the electron excitation flux at depth t, dΩ the solid angle, and δt is the thickness of the layer being probed.

Here e ( x → a ) is the evaluation which gives x the

Here u ( x, t ) is the temperature of the rod at position x and time t and α is a constant that depends on how fast heat diffuses through the rod.

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 is an example of cracking of butane CH < sub > 3 </ sub >- CH < sub > 2 </ sub >- CH < sub > 2 </ sub >- CH < sub > 3 </ sub >

Here the majority of the Hanse members decided in a Hanseatic diet on 1 May 1388 for an embargo against the Flemish cities, while Prussia could not prevail with its plea for further negotiations .< ref name =" Dollinger 1998 107 "> Philippe Dollinger, Die Hanse Hanse ( XII < sup > e </ sup >- XVII < sup > e </ sup > siècles ); German, see references for bibliographical details, p. 107.

( Here the velocity and position axes have been reversed from the standard convention in order to align the two diagrams )

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

Here is the tensor derivative of the velocity vector, equal in Cartesian coordinates to the component by component gradient.

Here u might describe the displacement of a stretched string from equilibrium, or the difference in air pressure in a tube, or the magnitude of an electromagnetic field in a tube, and c is a number that corresponds to the velocity of the wave.

Here is a variable which parametrizes the curve Streamlines are calculated instantaneously, meaning that at one instance of time they are calculated throughout the fluid from the instantaneous flow velocity field.

Here, is density, u, v, and are the components of wind velocity, and is the 2-dimensional ( i. e. horizontal-component-only ) del.

Here, the horizontal axis gives the position and vertical axis the velocity.

( Here the velocity and position axes have been reversed from the standard convention in order to align the two diagrams )

Here the velocity dispersion is much smaller.

where v < sub > x </ sub >, v < sub > y </ sub > and v < sub > z </ sub > are the Cartesian components of the velocity v. Here, H is short for Hamiltonian, and used henceforth as a symbol for energy because the Hamiltonian formalism plays a central role in the most general form of the equipartition theorem.

Here, the wave is said to be ducted or trapped, and a vertically standing wave may form, where the vertical component of group velocity approaches zero.

Here v < sub > F </ sub > ~ 10 < sup > 6 </ sup > is the Fermi velocity in graphene which replaces the velocity of light in the Dirac theory ; is the vector of the Pauli matrices, is the two-component wave function of the electrons, and E is their energy.

Here is the vacuum velocity of light, and is the d ' Alembertian operator.

Here, the speed of light is constant in all directions in the stationary aether, and completely independent of the velocity of the source ;

Here, air resistance is assumed to be in the direction opposite of the projectile's velocity.

Here is the velocity of the fluid, is the gradient of the pressure, and is the dynamic viscosity.

Here, since the curl gives a scalar field in 2-dimensions ( vortex ) corresponding to the vector-valued velocity solving in the incompressible Navier – Stokes equations, we can integrate its square over a surface S to retrieve a continuous linear operator on the space of possible velocity fields, known as a current.

Here we have chosen a simplified version of the enstrophy derived from the incompressibility condition, which is equivalent to vanishing divergence of the velocity field,