Multiplicity results for second-order two-point boundary value problems with nonlinearities across several eigenvalues

We consider the boundary value problems for nonlinear second-order differential equations of the form u '' + a(t)f (u) = 0, 0 < t < 1, u(0) = u (1) = 0. We give conditions on the ratio f (s)/s at infinity and zero that guarantee the existence of solutions with prescribed nodal properties. Then we establish existence and multiplicity results for nodal solutions to the problem. The proofs of our main results are based upon bifurcation techniques. (c) 2004 Elsevier Ltd. All rights reserved.

Multiplicity results for second-order two-point boundary value problems with superlinear or sublinear nonlinearities

We consider boundary value problems for nonlinear second order differential equations of the form u + a(t) f(u) = 0, t epsilon (0, 1), u(0) = u(1) = 0, where a epsilon C([0, 1], (0, infinity)) and f : R --> R is continuous and satisfies f (s)s > 0 for s not equal 0. We establish existence and multiplicity results for nodal solutions to the problems if either f(0) = 0, f(infinity) = infinity or f(0) = infinity, f(0) = 0, where f (s)/s approaches f(0) and f(infinity) as s approaches 0 and infinity, respectively. We use bifurcation techniques to prove our main results. (C) 2004 Elsevier Inc. All rights reserved.

Time trials on second-order and variable-learning-rate algorithms

The performance of seven minimization algorithms are compared on five neural network problems. These include a variable-step-size algorithm, conjugate gradient, and several methods with explicit analytic or numerical approximations to the Hessian.

Discrimination between strain and temperature effects using first and second-order diffraction from a long period grating

We study the effects of temperature and strain on the spectra of the first and second-order diffraction attenuation bands of a single long-period grating (LPG) in step-index fibre. The primary and second-order attenuation bands had comparable strength with the second-order bands appearing in the visible and near-infra red parts of the spectrum. Using first and second-order diffraction to the eighth cladding mode a sensitivity matrix was obtained with limiting accuracy given by cross-sensitivity of ~1.19% of the measurement. The sensing scheme presented as a limiting temperature and strain resolution of ±0.7 °C and ~±25 µ.

What is second-order vision for? Discriminating illumination versus material changes

The human visual system is sensitive to second-order modulations of the local contrast (CM) or amplitude (AM) of a carrier signal. Second-order cues are detected independently of first-order luminance signals; however, it is not clear why vision should benet from second-order sensitivity. Analysis of the first-and second-order contents of natural images suggests that these cues tend to occur together, but their phase relationship varies. We have shown that in-phase combinations of LM and AM are perceived as a shaded corrugated surface whereas the anti-phase combination can be seen as corrugated when presented alone or as a flat material change when presented in a plaid containing the in-phase cue. We now extend these findings using new stimulus types and a novel haptic matching task. We also introduce a computational model based on initially separate first-and second-order channels that are combined within orientation and subsequently across orientation to produce a shading signal. Contrast gain control allows the LM + AM cue to suppress responses to the LM-AM when presented in a plaid. Thus, the model sees LM -AM as flat in these circumstances. We conclude that second-order vision plays a key role in disambiguating the origin of luminance changes within an image. © ARVO.

Simultaneous measurement of strain and temperature using the first- and second-order diffraction wavelengths of Bragg gratings

A method of discriminating between temperature and strain effects in fibre sensing using a conventionally written, in-fibre Bragg grating is presented. The technique uses wavelength information from the first and second diffraction orders of the grating element to determine the wavelength dependent strain and temperature coefficients, from which independent temperature and strain measurements can be made. The authors present results that validate this matrix inversion technique and quantify the strain and temperature errors which can arise for a given uncertainty in the measurement of the reflected wavelength.

Quasi-lossless transmission using second-order Raman amplification and fibre Bragg gratings

A novel distributed amplification scheme for quasi-lossless transmission is presented. The system is studied numerically and shown to be able to strongly reduce signal power variations in comparison with currently employed schemes of similar complexity. As an example, variations of less than 3.1 dB for 100 km distance between pumps and below 0.42 dB for 60 km are obtained when using standard single-mode fibre as the transmission medium with an input signal average power of 0 dBm, and a total pump power of about 1.7 W. © 2004 Optical Society of America.

Simultaneous measurement of strain and temperature using the first- and second-order diffraction wavelengths of Bragg gratings

A method of discriminating between temperature and strain effects in fibre sensing using a conventionally written, in-fibre Bragg grating is presented. The technique uses wavelength information from the first and second diffraction orders of the grating element to determine the wavelength dependent strain and temperature coefficients, from which independent temperature and strain measurements can be made. The authors present results that validate this matrix inversion technique and quantify the strain and temperature errors which can arise for a given uncertainty in the measurement of the reflected wavelength.

Discrimination between strain and temperature effects using first and second-order diffraction from a long-period grating

We study the effects of temperature and strain on the spectra of the first and second-order diffraction attenuation bands of a single long-period grating (LPG) in step-index fibre. The primary and second-order attenuation bands had comparable strength with the second-order bands appearing in the visible and near-infra red parts of the spectrum. Using first and second-order diffraction to the eighth cladding mode a sensitivity matrix was obtained with limiting accuracy given by cross-sensitivity of ∼ 1.19% of the measurement. The sensing scheme presented as a limiting temperature and strain resolution of ± 0.7 °C and ∼ ± 25 με. © 2002 Elsevier Science B.V. All rights reserved.

An iterative procedure for solving a Cauchy problem for second order elliptic equations

An iterative method for reconstruction of solutions to second order elliptic equations by Cauchy data given on a part of the boundary, is presented. At each iteration step, a series of mixed well-posed boundary value problems are solved for the elliptic operator and its adjoint. The convergence proof of this method in a weighted L2 space is included. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Second order distributed Raman amplification for quasi-lossless transmission

A novel distributed Raman amplification scheme for quasi-lossless transmission is presented. The scheme is able to keep signal power variations below 3 dB in a 100 km periodic cell and 0.36 dB in 60 km.

Long-haul transmission performance evaluation of ultra-long Raman fibre laser based amplification influenced by second order co-pumping

A transmission performance investigation using ultra-long Raman fibre laser based amplification with different co-pump power is presented. We attribute Q2 factor degradation to RIN of co-pump and induced fibre laser as well as increased SBS.