Mathematically, the diffraction pattern is characterized by the wavelength of light illuminating the circular aperture, and the aperture's size.

Mathematically, we shall not distinguish the experiment of three dice tossed once from that of one die tossed three times.

Mathematically, the total electromagnetic energy density ( radiation energy density ) in thermodynamic equilibrium from Planck's law is

Mathematically, quasicrystals have been shown to be derivable from a general method, which treats them as projections of a higher-dimensional lattice.

Mathematically, this follows from:

Mathematically, the factor of two relating physical angles to their counterparts in Stokes space derives from the use of second-order moments and correlations, and incorporates the loss of information due to absolute phase invariance.

Mathematically, the return from a short position is equivalent to that of owning ( being " long ") a negative amount of the instrument.

Mathematically gifted, he was very young when he joined Enrico Fermi's team in Rome as one of the " Via Panisperna boys ", who took their name from the street address of their laboratory.

Mathematically, the climatological annual cycle is commonly estimated from observational data or model output by taking the average of all Januaries, all Februaries, and so forth.

Mathematically talented, Lamarr also co-invented — with composer George Antheil — an early technique for spread spectrum communications and frequency hopping, necessary for wireless communication from the pre-computer age to the present day.

Mathematically the switching mixer is not much different from a multiplying mixer, just because instead of the LO sine wave term we would use the signum function.

Mathematically, the difference between artificial perspective projection ( perspective projection onto a flat surface ) and natural perspective projection ( perspective projection onto a spherical surface ) is a distortion resulting from the small-angle approximation which results from projecting onto a flat surface.

Mathematically, apart from discretization ( whole euros both for income and for tax ), the tax is a continuous, convex, piecewise linear function of income.

Mathematically, the axiom states that the probability of selecting item i from a pool of j items is given by:

Mathematically, texture filtering is a type of anti-aliasing, but it filters out high frequencies from the texture fill whereas other AA techniques generally focus on visual edges.

Mathematically a stock can be seen as an accumulation or integration of flows over time-with outflows subtracting from the stock.

Mathematically, the problem of recovering conductivity from surface measurements of current and potential is a non-linear inverse problem and is severely ill-posed.

Mathematically, the cyclomatic complexity of a structured program is defined with reference to the control flow graph of the program, a directed graph containing the basic blocks of the program, with an edge between two basic blocks if control may pass from the first to the second.

Mathematically, two Luenberger observers can be used, if is properly selected, using, for example, positive systems properties: one for the upper bound ( that ensures that converges to zero from above when, in the absence of noise and uncertainty ), and a lower bound ( that ensures that converges to zero from below ).

Mathematically, nominal numbering is a one-to-one function from a set of objects being named to the set of numerals: it is a function because each object is assigned a numeral, and it is one-to-one because different objects are assigned different numerals.

Mathematically, barrel and pincushion distortion are quadratic, meaning they increase as the square of distance from the center.

Mathematically, the URR is closely related to Kt / V, and the two quantities can be derived from another with more or less precision, depending on the amount of additional information available about a given dialysis session.

§ — Mathematically eliminated from the chase.

Mathematically, the motion of a continuum using the Eulerian description is expressed by the mapping function

Mathematically, this means that for a causal linear system to be stable all of the poles of its transfer function must have negative-real values, i. e. the real part of all the poles are less than zero.

Mathematically, the catenary curve is the graph of the hyperbolic cosine function.

Mathematically, a sequence of coin flips ( fair or not ) is an example of a Bernoulli process, and its entropy is given by the binary entropy function.

Mathematically, a neuron's network function is defined as a composition of other functions, which can further be defined as a composition of other functions.

Mathematically, the E field can be thought of as a function that associates a vector with every point in space.

Mathematically a bijective function is used on the characters ' positions to encrypt and an inverse function to decrypt.

Mathematically, the LM curve is defined by the equation, where the supply of money is represented as the real amount M / P ( as opposed to the nominal amount M ), with P representing the price level, and L being the real demand for money, which is some function of the interest rate i and the level Y of real income.

Mathematically, a scalar field on a region U is a real or complex-valued function or distribution on U. The region U may be a set in some Euclidean space, Minkowski space, or more generally a subset of a manifold, and it is typical in mathematics to impose further conditions on the field, such that it be continuous or often continuously differentiable to some order.

Mathematically, the modulated Dirac comb is equivalent to the product of the comb function with s ( t ).

Mathematically, the ( real valued ) amplitude of one wave component is represented by a scalar wave function u that depends on both space and time:

Mathematically, the gradient of a two-variable function ( here the image intensity function ) is at each image point, a 2D vector with the components given by the derivatives in the horizontal and vertical directions.

Mathematically, the function is expressed as the derivative of the consumption function with respect to disposable income.

Mathematically speaking, both in a standard and a TD approach, we would try to optimize some cost function, related to the error in our predictions of the expectation of some random variable, E. However, while in the standard approach we in some sense assume E = z ( the actual observed value ), in the TD approach we use a model.

Mathematically, this is governed by the kernel function ( symbol ).

Mathematically, the process of constructing a flownet consists of contouring the two harmonic or analytic functions of potential and stream function.

Mathematically, applying a Gaussian blur to an image is the same as convolving the image with a Gaussian function ; this is also known as a two-dimensional Weierstrass transform.

Mathematically, torque is defined as the cross product of force and the lever-arm distance, which tends to produce rotation.

Mathematically, the Levenshtein distance between two strings is given by where

Mathematically, the Chebyshev distance is a metric induced by the supremum norm or uniform norm.