<i>Operational Calculus in Two Variables and Its Applications</i>

Ditkin, V. A.; Prudnikov, A. P.; Wishart, D. M. G.; Sneddon, I. N.; Ulam, Stanislaw M.; Stark, Marion E.; Gillis, J.

doi:10.1063/1.3050726

Cited by 51 publications

(41 citation statements)

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“…Roberts & Kaufman (1966, p. 223, no. 20), and the shift theorem (Gardner & Barnes, 1942) This integral can be compared with the result (Ditkin & Prudnikov, 1962) The result is identical to eqn. (11) in Jack & Redman (1971), and is the response at the end of a short cable of length L, or at the centre of a cable of length 2L, to a current impulse applied at X.…”

Section: Determination Of Tmsupporting

confidence: 54%

An electrical description of the motoneurone, and its application to the analysis of synaptic potentials

Jack¹,

Redman²

1971

The Journal of Physiology

140

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SUMMARY1. The Rall model of the motoneurone, which consists of a lumped resistance and capacitance, representing the soma, in parallel with a distributed resistance-capacitance network of finite length, representing the equivalent dendritic cable, has been used to investigate the effects of varying electrical and geometrical parameters on the time course of transients generated at the model soma.2. An analytical solution has been obtained for the voltage at the model soma, following a brief current injection at any point on the dendritic cable, in terms of the dendritic to soma conductance ratio, the electrotonic length of the cable, the membrane time constant, and the electrotonic distance between the point of current injection and the soma. This solution has been used to study the response at the soma to currents with a smooth time course, and to brief rectangular current pulses. Computations of these voltage transients are given to illustrate the effect of the above parameters on voltage time course.3. A method for determining the membrane time constant, the dendritic to soma conductance ratio, and the electrotonic length of the dendritic cable, is described. The method involves measurements from the decay time course of the transient at the soma following a brief current pulse being applied at the soma.4. A method is described whereby the time course of a synaptic potential, assumed to be generated by synaptic knobs located exclusively at the soma, may be used to determine the motoneurone parameters, and a parameter describing the time course of current injection.

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Section: Determination Of Tmsupporting

confidence: 54%

An electrical description of the motoneurone, and its application to the analysis of synaptic potentials

Jack¹,

Redman²

1971

The Journal of Physiology

140

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“…When the originals are replaced by the transforms. the differential equation (1.83) transforms to an algebraic equation which can be solved for a semi-infinite region [21] ( 1.47) The transforms of the initial and boundary conditions are not independent but related by the "compatibility condition ":…”

Section: Yj'mentioning

confidence: 99%

Switching in Semiconductor Diodes

Nosov

1969

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“…Definition 2.5 ( [11,17]). If f(x, y) and g(x, y) are integrable functions, then double convolution of f(x, y) and g(x, y) is given by…”

Section: Definition 24 ([29]mentioning

confidence: 99%

On double Natural transform and its applications

Kılıçman¹,

Omran²

2017

J. Nonlinear Sci. Appl.

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In this work, we generalize the concept of one dimensional Natural transform to two dimensional Natural transform namely, double Natural transform and some of its properties are given. We also set a relation between double Natural transform and double Laplace, double Sumudu transforms. Further the convolution theorem with a proof is investigated with some details. Double Natural transform is applied to get the solutions of some general linear telegraphs, wave and partial integro-differential equations.

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Operational Calculus in Two Variables and Its Applications

Cited by 51 publications

References 0 publications

An electrical description of the motoneurone, and its application to the analysis of synaptic potentials

An electrical description of the motoneurone, and its application to the analysis of synaptic potentials

Switching in Semiconductor Diodes

On double Natural transform and its applications

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