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Mathematically a stock can be seen as an accumulation or integration of flows over time-with outflows subtracting from the stock.
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Mathematically and can
Mathematically, this can be represented for n species as:
Mathematically the 0-1-knapsack problem can be formulated as:
Mathematically the bounded knapsack problem can be formulated as:
Mathematically, the potential of the ion cores can be treated by various models, the simplest being the nearly free electron model.
Mathematically this invariance can be ensured in one of two ways: by treating the four-vectors as Euclidean vectors and multiplying time by the square root of ; or by keeping time a real quantity and embedding the vectors in a Minkowski space.
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 modulated wave can be written in the form:
Mathematically ( using the Laplace transform ) the impedance of this network can be written as:
Mathematically, the E field can be thought of as a function that associates a vector with every point in space.
Mathematically, convection can be described by the convection – diffusion equation or the generic scalar transport equation.
Mathematically, the pressure of a mixture of gases can be defined as the summation
Mathematically corrected punch motions can be programmed to simulate any type and model of production tablet press.
Mathematically, this can be expressed by means of the signal to noise ratio ( SNR or S / N ).
Mathematically speaking, there are seventeen basic patterns, described as wallpaper groups, that can be used to tile an infinite plane.
Mathematically, evanescent waves can be characterized by a wave vector where one or more of the vector's components has an imaginary value.
Mathematically, the maximum lift-to-drag ratio can be estimated as:
Mathematically, this can be written as:
Mathematically the problem can be stated like this:
Mathematically, the criterion for whether spontaneous fission can occur in a time short enough to be observed by present methods, is approximately:
Mathematically, we can represent this constraint in terms of a surface integral:
Mathematically, a vector x in an n-dimensional Euclidean space can be defined as an ordered list of n real numbers ( the Cartesian coordinates of P ): x = x < sub > 2 </ sub >, ..., x < sub > n </ sub >.
Mathematically, we can describe the reciprocal lattice as the set of all vectors K that satisfy the above identity for all lattice point position vectors R. This reciprocal lattice is itself a Bravais lattice, and the reciprocal of the reciprocal lattice is the original lattice, which reveals the Pontryagin duality of their respective vector spaces.
Mathematically, the modulus of resilience can be expressed by the product of the square of the yield stress divided by two times the Young's modulus.
Mathematically, spin networks are related to group representation theory and can be used to construct knot invariants such as the Jones polynomial.
Mathematically, a basic parametric mixture model can be described as follows:
Mathematically and be
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, a baseband modulated signal may be approximated by a sinusoidal continuous wave signal with a frequency f < sub > m </ sub >.
Mathematically, quasicrystals have been shown to be derivable from a general method, which treats them as projections of a higher-dimensional lattice.
Mathematically, the equation may be rearranged to compute torque for a given power output.
Mathematically speaking, however, there seems to be no reason for us to reject the negative-energy solutions.
Mathematically, it refers to a property of solutions to the Schrödinger equation ; since the Schrödinger equation is linear, any linear combination of solutions to a particular equation will also be a solution of it.
Mathematically, assuming the terminator lies on a great circle, such a crescent will actually be the figure bounded by a half-ellipse and a half-circle, with the major axis of the ellipse coinciding with a diameter of the semicircle.
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, it may be represented as follows:
Mathematically, the Lorentz group may be described as the generalized orthogonal group O ( 1, 3 ), the matrix Lie group which preserves the quadratic form
Mathematically and seen
Mathematically, the angle of repose may be seen as a bifurcation.
Mathematically and over
Mathematically, this says that the state vector is confined to one of the two eigenspaces of P, and is not allowed to range over the entire Hilbert space.
Mathematically, this condition is also approached exponentially ; in theory it takes infinite time, but in practice it is over, for all intents and purposes, in a much shorter period.
Mathematically, a Yang – Mills instanton is a self-dual or anti-self-dual connection in a principal bundle over a four-dimensional Riemannian manifold that plays the role of physical space-time in non-abelian gauge theory.
Mathematically, Florida's 25 electoral votes became the key to an election win, despite the fact that both New Mexico and Oregon were declared in favor of Gore over the next few days.
Mathematically and from
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, the light received from stars as a function of star distance in a hypothetical fractal cosmos is:
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, 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.
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