If the resulting linear differential equations have constant coefficients one can take their Laplace transform to obtain a transfer function.

This rate can be quantified through the calculation and application of mass transfer coefficients for an overall process.

These mass transfer coefficients are typically published in terms of dimensionless numbers, often including Péclet numbers, Reynolds numbers, Sherwood numbers and Schmidt numbers, among others

A lumped LTI system is specified by a finite number of parameters, be it the zeros and poles of its transfer function, or the coefficients of its differential equation, whereas specification of a distributed LTI system requires a complete function

* Bode plot applet-Accepts transfer function coefficients as input, and calculates magnitude and phase response

The population count is of great importance to Brazil's cities, because the annual grant of funds from the Municipalities Participation Fund is determined mainly by the estimates of population variation provided by IBGE, which directly influence the calculation of the coefficients used to transfer the fund to the municipalities.

* The Takahashi correlation is an expression used in mass transfer equations for chemical engineering that corrects for high pressure in calculating diffusion coefficients between two molecules

The partition coefficients can be transformed to free energy of transfer which includes enthalpic and entropic components, ΔG = ΔH-TΔS.

* Heat transfer coefficients ( h, U )

The concentrations of individual compounds can be derived largely using the count rates of the precursor and product ions, and the reaction rate coefficients, k. Exothermic proton transfer reactions with H < sub > 3 </ sub > O < sup >+</ sup > are assumed to proceed at the collisional rate ( see Collision Theory ), the coefficient for which, k < sub > c </ sub >, is calculable using the method described by Su and Chesnavich, providing the polarizability and dipole moment are known for the reactant molecule.

In design, operative temperature can be defined as the average of the mean radiant and ambient air temperatures, weighted by their respective heat transfer coefficients.

This function lets you collect aerodynamic coefficients from static and dynamic analyses and transfer them into MATLAB as a cell array of structures, with each structure containing information about a Digital DATCOM output file.

High heat transfer coefficients are required in order to achieve equally balanced heat transfer resistances.

The combination of these effects allows very high heat transfer coefficients.

This orthogonality relation can then be used to extract the coefficients in the Fourier – Bessel series, where a function is expanded in the basis of the functions J < sub > α </ sub >( x u < sub > α, m </ sub >) for fixed α and varying m.

In his 1799 doctorate in absentia, A new proof of the theorem that every integral rational algebraic function of one variable can be resolved into real factors of the first or second degree, Gauss proved the fundamental theorem of algebra which states that every non-constant single-variable polynomial with complex coefficients has at least one complex root.

This function can be found experimentally from the coefficients and through the mathematically deducible relation

The graphs on the right side depict the ( finite ) coefficients that modulate the infinite amplitudes of a comb function whose teeth are spaced at the reciprocal of the time-domain periodicity.

For instance, if all of the coefficients were equal to unity, a so-called boxcar function, then it would implement a low-pass filter with a low frequency gain of N + 1 and a frequency response given by the sinc function.

The graphs on the right side depict the ( finite ) coefficients that modulate the infinite amplitudes of a comb function whose teeth are spaced at intervals of 1 / P.

The Fourier transform of a periodic function, s < sub > P </ sub >( t ), with period P, becomes a Dirac comb function, modulated by a sequence of complex coefficients:

Thus, any periodic summation in the frequency domain can be represented by a Fourier series, whose coefficients are samples of a related continuous time function:

The DTFT of a periodic sequence, s < sub > N </ sub >, with period N, becomes another Dirac comb function, modulated by the coefficients of a Fourier series.

To facilitate computations by hand, large books were produced with formulas and tables of data such as interpolation points and function coefficients.

As a consequence of the Weierstrass approximation theorem, one can show that the space C is separable: the polynomial functions are dense, and each polynomial function can be uniformly approximated by one with rational coefficients ; there are only countably many polynomials with rational coefficients.

which is a periodic function and its equivalent representation as a Fourier series, whose coefficients are x.

hence the above Newton interpolation formula ( by matching coefficients in the expansion of an arbitrary function f ( x ) in such symbols ), and so on.

Attenuation coefficients are used to quantify different media according to how strongly the transmitted ultrasound amplitude decreases as a function of frequency.

The " weights ", or coefficients, of the terms in the Fourier expansion of a function can be thought of as components of a vector in an infinite dimensional space known as a Hilbert space.

In the case of a periodic function, such as a continuous, but not necessarily sinusoidal, musical tone, the Fourier transform can be simplified to the calculation of a discrete set of complex amplitudes, called Fourier series coefficients.

As T increases the Fourier coefficients more closely represent the Fourier transform of the function.

The Cauchy – Kowalevski theorem states that the Cauchy problem for any partial differential equation whose coefficients are analytic in the unknown function and its derivatives, has a locally unique analytic solution.

In algebra, the discriminant of a polynomial is a function of its coefficients which gives information about the nature of its roots.

For higher degrees, the discriminant is always a polynomial function of the coefficients.

The differential equation provides a linear difference equation relating these coefficients.

Borcherds then used this, and methods from string theory, to prove the monstrous moonshine conjecture by Conway and Norton, relating the monster group to the coefficients of the q-expansion of the j-invariant.

The values at 1 of the Lusztig – Vogan polynomials give the coefficients of the matrices relating the standard representations ( whose characters are easy to describe ) with the irreducible representations.

The Recursive least squares ( RLS ) adaptive filter is an algorithm which recursively finds the filter coefficients that minimize a weighted linear least squares cost function relating to the input signals.

A digital filter system usually consists of an analog-to-digital converter to sample the input signal, followed by a microprocessor and some peripheral components such as memory to store data and filter coefficients etc.

If we now restrict our attention to that portion of the cos ( ωt ) coefficient which varies linearly with V, and then ask ourselves, at what input voltage level, V, will the coefficients of the first and third order terms have equal magnitudes ( i. e., where the magnitudes intersect ), we find that this happens when

The original concept of Reed – Solomon coding describes encoding of k message symbols by viewing them as coefficients of a polynomial p ( x ) of maximum degree k − 1 over a finite field of order N, and evaluating the polynomial at n > k distinct input points.

In multirate filters, the number of coefficients by taking advantage of its bandwidth limits, where the input signal is downsampled ( e. g. to its critical frequency ), and upsampled after filtering.

Suppose that hunting requires also some arrows, with input coefficients equal to, meaning that to catch for instance one beaver you need to use arrows, besides hours of labour.

A path of reflected sound waves in a multilayered structure can be defined by an input acoustic impedance ( ultrasound sound wave ) and the Reflection and transmission coefficients of the relative structures

Thus, the output of the second filter vanishes when the coefficients of the first one are input into it.

Now the reflection coefficients are very large and more power is reaching the load than was injected in the input port.

When the Fourier coefficients for a square wave were input to the machine, the graph would oscillate at the discontinuities.

The value of a convolution at a point is a linear combination of the input signal, with coefficients ( weights ) the values of the kernel.

If a kernel is non-negative, such as for a Gaussian kernel, then the value of the filtered signal will be a convex combination of the input values ( the coefficients ( the kernel ) integrate to 1, and are non-negative ), and will thus fall between the minimum and maximum of the input signal – it will not undershoot or overshoot.

The optimum matched filter for separating any waveform from white noise is obtained by sampling that shape and using those samples in reverse order as the coefficients of the filter — giving the filter an impulse response that is the time-reverse of the expected input signal.

* The fact that all the model's relationships and coefficients are stochastic, so that the error term becomes very large quickly, and the available snapshot of the input parameters is already out of date.

Let us use the notations, for the input and the output vectors of the stoichiometric coefficients of the rth elementary reaction.

if and only if is the vector of the input stoichiometric coefficients for the rth elementary reaction ; if and only if is the vector of the output stoichiometric coefficients for the rth elementary reaction.

This function may be considered as the sum of the reaction rates for deformed input stoichiometric coefficients.

The SWT is an inherently redundant scheme as the output of each level of SWT contains the same number of samples as the input – so for a decomposition of N levels there is a redundancy of N in the wavelet coefficients.