A Grassmann-Rayleigh quotient iteration for computing invariant subspaces

The classical Rayleigh quotient iteration (RQI) allows one to compute a one-dimensional invariant subspace of a symmetric matrix A. Here we propose a generalization of the RQI which computes a p-dimensional invariant subspace of A. Cubic convergence is preserved and the cost per iteration is low compared to other methods proposed in the literature.

A Grassman-Rayleigh quotient iteration for computing invariant subspaces

The classical Rayleigh Quotient Iteration (RQI) computes a 1-dimensional invariant subspace of a symmetric matrix A with cubic convergence. We propose a generalization of the RQI which computes a p-dimensional invariant subspace of A. The geometry of the algorithm on the Grassmann manifold Gr(p,n) is developed to show cubic convergence and to draw connections with recently proposed Newton algorithms on Riemannian manifolds.

Subtraction of scattering parameters for adiabatic intrinsic responses of semiconductor lasers

Thermal effects will make chip temperature change with bias current of semiconductor lasers, which results in inaccurate intrinsic response by the conventional subtraction method. In this article, an extended subtraction method of scattering parameters for characterizing adiabatic responses of laser diode is proposed. The pulsed injection operation is used to determine the chip temperature of packaged semiconductor laser, and an optimal injection condition is obtained by investigating the dependence of the lasing wavelength on the width and period of the injection pulse in a relatively wide temperature range. In this case, the scattering parameters of laser diode are measured on adiabatic condition and the adiabatic intrinsic responses of packaged laser diode are first extracted. It is found that the adiabatic intrinsic responses are evidently superior to those without thermal consideration. The analysis results indicate that inclusion of thermal. effects is necessary to acquire accurate intrinsic responses of semiconductor lasers. (C) 2008 Wiley Periodicals, Inc.

Evaluation of holonomic quantum computation: Adiabatic versus nonadiabatic

Based on the analytical solution to the time-dependent Schrodinger equations, we evaluate the holonomic quantum computation beyond the adiabatic limit. Besides providing rigorous confirmation of the geometrical prediction of holonomies, the present dynamical resolution offers also a practical means to study the nonadiabaticity induced effects for the universal qubit operations.

Subtraction of S-parameters for adiabatic small-signal modulation characteristics of laser diode - art. no. 60201V

An extended subtraction method of scattering parameters for characterizing laser diode is introduced in this paper. The intrinsic small-signal response can be directly extracted from the measured transmission coefficients of laser diode by the method. However the chip temperature may change with the injection bias current due to thermal effects, which causes inaccurate intrinsic response by our method. Therefore, how to determine the chip temperature and keep the laser chip adiabatic is very critical when extracting the intrinsic response. To tackle these problems, the dependence of the lasing wavelength of the laser diode on the chip temperature is investigated, and an applicable measurement setup which keeps the chip temperature stable is presented. The scattering parameters of laser diode are measured on diabatic and adiabatic conditions, and the extracted intrinsic responses for both conditions are compared. It is found that the adiabatic intrinsic responses are evidently superior to those without thermal consideration. The analysis indicates that inclusion of thermal effects is necessary to acquire accurate intrinsic response.

Optimized logarithmic phase masks used to generate defocus invariant modulation transfer function for wavefront coding system

In a previous Letter [Opt. Lett. 33, 1171 (2008)], we proposed an improved logarithmic phase mask by making modifications to the original one designed by Sherif. However, further studies in another paper [Appl. Opt. 49, 229 (2010)] show that even when the Sherif mask and the improved one are optimized, their corresponding defocused modulation transfer functions (MTFs) are still not stable with respect to focus errors. So, by further modifying their phase profiles, we design another two logarithmic phase masks that exhibit more stable defocused MTF. However, with the defocus-induced phase effect considered, we find that the performance of the two masks proposed in this Letter is better than the Sherif mask, but worse than our previously proposed phase mask, according to the Hilbert space angle. (C) 2010 Optical Society of America

Knotted wave dislocation with the hopf invariant

We study the wave dislocations with an induced gauge potential. The topological current characterized the wave dislocations is constructed with the dual of Abelian gauge field. And the topological charges and locations of the wave dislocations are determined by the phi-mapping topological current theory. Furthermore, it is shown that the knotted wave dislocations can be described with a Hopf invariant in the wave field. At last we discussed the evolution of the knotted wave dislocations.

BRST invariant theory of a generalized 1+1 Dimensional nonlinear sigma model with topological term

We give a generalized Lagrangian density of 1 + 1 Dimensional O( 3) nonlinear sigma model with subsidiary constraints, different Lagrange multiplier fields and topological term, find a lost intrinsic constraint condition, convert the subsidiary constraints into inner constraints in the nonlinear sigma model, give the example of not introducing the lost constraint. N = 0, by comparing the example with the case of introducing the lost constraint, we obtain that when not introducing the lost constraint, one has to obtain a lot of various non-intrinsic constraints. We further deduce the gauge generator, give general BRST transformation of the model under the general conditions. It is discovered that there exists a gauge parameter beta originating from the freedom degree of BRST transformation in a general O( 3) nonlinear sigma model, and we gain the general commutation relations of ghost field.

Thermodynamic study of ibuprofen by adiabatic calorimetry and thermal analysis

Molar heat capacities of ibuprofen were precisely measured with a small sample precision automated adiabatic calorimeter over the temperature range from 80 to 400 K. The polynomial functions of C-p,C-m (J K-1 mol(-1)) versus T were established on the heat capacity measurements by means of the least fitting square method. The functions are as follows: for solid ibuprofen, at the temperature range of 79.105 K less than or equal to T less than or equal to 333.297 K, C-p,C-m = 144.27 + 77.046X + 3.5171X(2) + 10.925X(3) + 11.224X(4), where X = (T - 206.201)/127.096; for liquid ibuprofen, at the temperature range of 353.406 K less than or equal to T less than or equal to 378.785 K, C-p,C-m = 325.79 + 8.9696X - 1.6073X(2) - 1.5145 X-3, where X = (T - 366.095)/12.690. A fusion transition at T = 348.02 K was found from the C-p-T curve. The molar enthalpy and entropy of the fusion transition were determined to be 26.65 kJ mol(-1) and 76.58 J mol(-1) K-1, respectively. The thermodynamic functions on the base of the reference temperature of 298.15 K, (H-T - H-298.15) and (S-T - S-298.15), were derived. Thermal characteristic of ibuprofen was studied by thermo-gravimetric analysis (TG-DTG) and differential scanning calorimeter (DSC). The temperature of fusion, the molar enthalpy and entropy of fusion obtained by DSC were well consistent with those obtained by adiabatic calorimeter. The evaporation process of ibuprofen was investigated further by TG and DTG, and the activation energy of the evaporation process was determined to be 80.3 +/- 1.4 kJ mol(-1). (C) 2003 Elsevier B.V. All rights reserved.

Local histogram based geometric invariant image watermarking

Compared with other existing methods, the feature point-based image watermarking schemes can resist to global geometric attacks and local geometric attacks, especially cropping and random bending attacks (RBAs), by binding watermark synchronization with salient image characteristics. However, the watermark detection rate remains low in the current feature point-based watermarking schemes. The main reason is that both of feature point extraction and watermark embedding are more or less related to the pixel position, which is seriously distorted by the interpolation error and the shift problem during geometric attacks. In view of these facts, this paper proposes a geometrically robust image watermarking scheme based on local histogram. Our scheme mainly consists of three components: (1) feature points extraction and local circular regions (LCRs) construction are conducted by using Harris-Laplace detector; (2) a mechanism of grapy theoretical clustering-based feature selection is used to choose a set of non-overlapped LCRs, then geometrically invariant LCRs are completely formed through dominant orientation normalization; and (3) the histogram and mean statistically independent of the pixel position are calculated over the selected LCRs and utilized to embed watermarks. Experimental results demonstrate that the proposed scheme can provide sufficient robustness against geometric attacks as well as common image processing operations. (C) 2010 Elsevier B.V. All rights reserved.