Applied Analysis

Hunter, John K.; Nachtergaele, Bruno

doi:10.1142/4319

Cited by 171 publications

(158 citation statements)

References 0 publications

Supporting

Mentioning

154

Contrasting

Unclassified

Order By: Relevance

“…(ii) If λ ∈ σ r (T ), thenλ is an eigenvalue of T * , i.e., Ker (T * −λI) = {0} [14]. Since, by assumption, Ang{T * x, x} ≤ γ for all x = 0, we can apply again the argument in (i) to T * ,λ and conclude that |ω| ≤ γ.…”

Section: A Generic Results On the Convergence Of The Magnus Series 31mentioning

confidence: 93%

See 1 more Smart Citation

Sufficient conditions for the convergence of the Magnus expansion

Casas¹

2007

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

Two different sufficient conditions are given for the convergence of the Magnus expansion arising in the study of the linear differential equationThe first one provides a bound on the convergence domain based on the norm of the operator A(t). The second condition links the convergence of the expansion with the structure of the spectrum of Y (t), thus yielding a more precise characterization. Several examples are proposed to illustrate the main issues involved and the information on the convergence domain provided by both conditions.

show abstract

Section: A Generic Results On the Convergence Of The Magnus Series 31mentioning

confidence: 93%

“…If, on the other hand, dim H = ∞ and λ ∈ σ(T ), λ = 0, then, as is well known, either (i) λ belongs to the approximate spectrum of T , σ ap (T ), or (ii) λ is in the residual spectrum, σ r (T ) [14].…”

Section: A Generic Results On the Convergence Of The Magnus Series 31mentioning

confidence: 99%

Sufficient conditions for the convergence of the Magnus expansion

Casas¹

2007

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…For azimuthal numbers other than zero, these waveguide modes involve coupled TE and TM potentials. As the hole region is radially finite, the waveguide modes are also a complete discrete basis [32]. The unknown coefficients are determined by enforcing boundary conditions on the upper and lower horizontal interfaces over a single unit cell.…”

Section: Scalar Decompositionmentioning

confidence: 99%

The Role of Hybrid Modes in Extraordinary Optical Transmission Through a Plasmonic Nanohole Array

Trampel¹

2017

PIER C

View full text Add to dashboard Cite

Abstract-A mode-matching solution to plane wave scattering by a plasmonic nanohole array consisting of a silver film perforated by an infinite square array of circular holes is presented. A complete orthonormal basis set consisting of waveguide modes satisfying an impedance boundary condition on the hole wall is derived. Impedance boundary conditions are satisfied on the upper and lower horizontal surfaces of the film and on the walls of the hole. Extraordinary optical transmission (EOT) is studied over optical wavelengths. Theory predicts a peak transmission value that is in better agreement with experiment than previous modal studies. The effect of film thickness on coupling between modes bound to the upper and lower surfaces is studied. The transmission profile for thinner films evinces two peaks at different wavelengths resulting from strong coupling between surface waves bound to the upper and lower surfaces. For thicker films, the surface waves decouple and a single peak is observed. The effect of hole radius on EOT is considered. It is demonstrated that transmission peaks occur for holes of a roughly constant electrical size. A relationship between the lattice constant and the transmission-to-area efficiency is quantified.

show abstract

“…The evolution of the sampling rate τ can be presented as a sequence (τ k ) based on the concept of sequences of real numbers discussed in [11], [12]. When convergence tests show that the sequence has converged, it implies that an optimal sampling period has been realized.…”

Section: Stopping Criterion For Sampling Rate Adaptationmentioning

confidence: 99%

“…The sampling rate is, therefore, decreased. A stopping criterion, based on convergence tests [11], [12] of subsequences of the sequence of the sampling period, is also proposed in order to ensure that the mechanism switches off when the sampling period has converged.…”

Section: Introductionmentioning

confidence: 99%

Distance Based Triggering and Dynamic Sampling Rate Estimation for Fuzzy Systems in Communication Networks

Nyirenda

Dong

Hirota

2011

INT J COMPUT COMMUN

View full text Add to dashboard Cite

To reduce computational cost in fuzzy systems in communication networks, distance based triggering and sampling rate adaptation probabilities are proposed based on the concept of probability via expectation. The triggering probability, which is calculated by using the square of distance between subsequent input vectors, governs the rate at which the fuzzy system is triggered. The dynamic sampling rate probability, which governs the adaptation of the sampling rate, is computed by using the exponentially weighted moving average (EWMA) of the triggering probability. A stopping criterion, based on convergence tests, is also proposed to ensure that the mechanism switches off when the sampling period has converged. The triggering mechanism reduces the number of computations in the Fuzzy Logic Congestion Detection (FLCD) in wireless Local Area Networks (WLANs) by more than 45%. Performance, in terms of packet loss rate, delay, jitter, and throughput, however, remains virtually the same. On the other hand, the dynamic sampling rate mechanism leads to more than 150% improvement in sampling rate and more than 70% reduction in fuzzy computations while performance in the other key metrics remains virtually the same. As part of future work, the proposed mechanism will be tested in fuzzy systems in wireless sensor/actuator networks.

show abstract

Applied Analysis

Cited by 171 publications

References 0 publications

Sufficient conditions for the convergence of the Magnus expansion

Sufficient conditions for the convergence of the Magnus expansion

The Role of Hybrid Modes in Extraordinary Optical Transmission Through a Plasmonic Nanohole Array

Distance Based Triggering and Dynamic Sampling Rate Estimation for Fuzzy Systems in Communication Networks

Contact Info

Product

Resources

About