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Active Circuits With Diodes: Topological Conditions Sufficient to Determine the State of a Diode
Full text linkLet N be a circuit composed of a finite number of positive and negative linear resistors, ideal diodes, nullators, norators and independent current and voltage sources. In this article, we consider the problem to determine, without any numerical computation, the state of a diode of N. We propose a set of topological conditions such that, when verified by a diode of N, the state of the diode is determined and the same in all the solutions of N. Our results may simplify, sometimes dramatically, the usual trial-and-error procedure to find the solutions of N
Inextensible elastic points admitting an affine response function for the determinate Cauchy stress
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Linear networks depending polynomially on parameters: dynamic behaviour for large values subject to tolerance errors
No full textA note on smooth matrices of constant rank
Full text linkWe show that, given a time–varying matrix A(t) of constant rank, there exists a matrix H(t) such that the rows of H(t)A(t) are an orthonormal basis of the space spanned by the rows of A(t). We present some consequences of this result and, in particular, we prove a version for matrices of Doležal's Theorem. These results are not new, and references are given. All the proofs of the results stated in these references, with the exception of those based on the use of differential equations — which holds only for —, find suitable matrices defined on overlapping subsets of the domain and then patch them together without losing regularity and the other required properties. In our approach the patching needs to be done only for matrices consisting of one row and all the remaining results are obtained by usual algebraic tools
Conditions for the existence and uniqueness of DC solutions of networks containing OpAmps with ideal model
No full textLinear networks and systems polynomially depending on parameters: Behaviour of the solutions for large and small values
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