A line search trust-region algorithm with nonmonotone adaptive radius for a system of nonlinear equations

In this paper, a trust-region procedure is proposed for the solution of nonlinear equations. The proposed approach takes advantages of an effective adaptive trust-region radius and a nonmonotone strategy by combining both of them appropriately. It is believed that selecting an appropriate adaptive radius based on a suitable nonmonotone strategy can improve the efficiency and robustness of the trust-region frameworks as well as decrease the computational cost of the algorithm by decreasing the required number subproblems that must be solved. The global convergence and the local Q-quadratic convergence rate of the proposed approach are proved. Preliminary numerical results of the proposed algorithm are also reported which indicate the promising behavior of the new procedure for solving the nonlinear system.     

Prime and primary submodules of certain modules

In this paper we characterize all prime and primary submodules of the free R-module R ⁿ for a principal ideal domain R and find the minimal primary decomposition of any submodule of R ⁿ . In the case n = 2, we also determine the height of prime submodules.     

Characterizations of continuous distributions through inequalities involving the expected values of selected functions

Nanda (2010) and Bhattacharjee et al. (2013) characterized a few distributions with help of the failure rate, mean residual, log-odds rate and aging intensity functions. In this paper, we generalize their results and characterize some distributions through functions used by them and Glaser’s function. Kundu and Ghosh (2016) obtained similar results using reversed hazard rate, expected inactivity time and reversed aging intensity functions. We also, via w(·)-function defined by Cacoullos and Papathanasiou (1989), characterize exponential and logistic distributions, as well as Type 3 extreme value distribution and obtain bounds for the expected values of selected functions in reliability theory. Moreover, a bound for the varentropy of random variable X is provided.     

Using the atomic force microscope as a nanomechanical partner to support evanescent field imaging

Quantum Dot (QD)/microsphere structures supporting Whispering Gallery Modes (WGMs) are attached to Atomic Force Microscope (AFM) cantilevers for characterization of the evanescent field around the QD/microsphere and utilization of the evanescent field for sensing at the apical surface of live cells. Following laser excitation, QD emission couples to WGMs that circumnavigate the microsphere via total internal reflection at the internal surfaces of the microsphere. The resulting evanescent field is characterized utilizing the high spatial control of an AFM in approaching a dye monolayer on a test surface. The measured evanescent field extends approximately 50 nm from the microsphere surface, matching theoretical predictions. This system was then used to sense the accumulation of integrin and formation of focal adhesions at the apical surface of cells.     

Effect of aluminum content on the mechanochemical synthesis of in-situ TiN in the Al–Ti–AlN system and subsequent shock consolidation

To determine the effect of aluminum content on the formation of in-situ TiN in the Al–Ti–AlN system, a mixture of aluminum, titanium and aluminum nitride powders was subjected to high energy milling. Al content of the mixture was changed according to the following stoichiometric reaction: Ti+AlN+XAl→TiN+(1+X)Al. The value of X was varied from 5.35 to 19.65 based on the stoichiometric calculation of the molar mass of each component expected to result in aluminum matrix composite with TiN weights of 30%, 20% and 10%, respectively, in addition to reaction corresponding to X=0(Ti+AlN→TiN+Al). Thermodynamic factors determine that the amount of Al in the mixture plays a key role in the formation of in-situ TiN. XRD and EPMA results showed that at lower Al content (X=0, 5.35), reaction proceed through a gradual mode. By increasing Al content (X=19.65), no mechanochemical reaction occurred between Ti and AlN. Continuation of the milling process allowed acquisition of in-situ TiN in the designed compositions of AlN–TiN, Al–Ti–AlN–30%TiN, and to some extent, of Al–Ti–AlN–20%TiN. A nanocrystalline solid solution evolved by mechanical alloying (MA) was sustained for prolonged milling time. The mean TiN crystallite size obtained was 10 nm for the AlN–TiN composition. The end product milled powder after 40 h of milling time, equating to the Al–Ti–AlN–30%TiN composition was consolidated into bulk compact using the underwater shock compaction method. The milled specimens were characterized by XRD, scanning electron microscopy (SEM), electron probe microanalysis (EPMA) and microhardness testing. The sample had a uniform and fine-grained composite structure with 99% theoretical density and average microhardness of 434 HV0.1. The results confirmed the possibility of fabricating reliable bulk nanostructured materials by imposing shock compaction on submicron sized powders.     

Noninvasive estimation of tissue temperature via high-resolution spectral analysis techniques

We address the noninvasive temperature estimation from pulse-echo radio frequency signals from standard diagnostic ultrasound imaging equipment. In particular, we investigate the use of a high-resolution spectral estimation method for tracking frequency shifts at two or more harmonic frequencies associated with temperature change. The new approach, employing generalized second-order statistics, is shown to produce superior frequency shift estimates when compared to conventional high-resolution spectral estimation methods Seip and Ebbini (1995). Furthermore, temperature estimates from the new algorithm are compared with results from the more commonly used echo shift method described in Simon et al. (1998).     

Quantifying 3-D vascular structures in MRA images using hybrid PDE and geometric deformable models

The aim of this paper is to present a hybrid approach to accurate quantification of vascular structures from magnetic resonance angiography (MRA) images using level set methods and deformable geometric models constructed with 3-D Delaunay triangulation. Multiple scale filtering based on the analysis of local intensity structure using the Hessian matrix is used to effectively enhance vessel structures with various diameters. The level set method is then applied to automatically segment vessels enhanced by the filtering with a speed function derived from enhanced MRA images. Since the goal of this paper is to obtain highly accurate vessel borders, suitable for use in fluid flow simulations, in a subsequent step, the vessel surface determined by the level set method is triangulated using 3-D Delaunay triangulation and the resulting surface is used as a parametric deformable model. Energy minimization is then performed within a variational setting with a first-order internal energy; the external energy is derived from 3-D image gradients. Using the proposed method, vessels are accurately segmented from MRA data.     

Tag surface reconstruction and tracking of myocardial beads from SPAMM-MRI with parametric B-spline surfaces

Magnetic resonance imaging (MRI) is unique in its ability to noninvasively and selectively alter tissue magnetization, and create tag planes intersecting image slices. The resulting grid of signal voids allows for tracking deformations of tissues in otherwise homogeneous-signal myocardial regions. In this paper, we propose a specific spatial modulation of magnetization (SPAMM) imaging protocol together with efficient techniques for measurement of three-dimensional (3-D) motion of material points of the human heart (referred to as myocardial beads) from images collected with the SPAMM method. The techniques make use of tagged images in orthogonal views by explicitly reconstructing 3-D B-spline surface representation of tag planes (tag planes in two orthogonal orientations intersecting the short-axis (SA) image slices and tag planes in an orientation orthogonal to the short-axis tag planes intersecting long-axis (LA) image slices). The developed methods allow for viewing deformations of 3-D tag surfaces, spatial correspondence of long-axis and short-axis image slice and tag positions, as well as nonrigid movement of myocardial beads as a function of time.     

An Iterative LMI-Based Reduced-Order Observer Design for Fractional-Order Chaos Synchronization

In this paper, attempts are made to design a reduced-order observer for a nonlinear Lipschitz class of fractional-order systems. It is assumed that nonlinear terms not only depend on measurable states but depend on unknown states and inputs as well. The sufficient conditions for stability of the observer based on the Lyapunov technique are derived and converted into linear matrix inequalities (LMIs). To overcome the main drawback of previous research studies which assumed that the sum of terms in infinite series coming from fractional derivative of a Lyapunov function is bounded and its upper bound is predefined, we used an iterative LMI-based algorithm to find out this bound. A four-wing chaotic system is implemented in both PSpice and MATLAB software as a case study. Simulation results are reported to show the effectiveness of the proposed iterative LMI-based reduced-order observer in tracking the unmeasurable state variables of the chaotic fractional system in different initial conditions.     

A robust spread spectrum based image watermarking in ridgelet domain

A new robust method of spread spectrum based image watermarking is proposed in this article. Spread spectrum technique and scrambling are used for increasing robustness and invisibility of the algorithm. Our suggested method is carried out using ridgelet transform as an efficient transform for representing images with line singularities. In embedding part, the host image is partitioned into non-overlapping blocks and ridgelet transform is applied to each single block. In this way, a curved edge is divided into some straight edges so that ridgelet transform shows optimal performance even for complicated images with curve edges. To embed the watermark bits, the best directions of ridgelet coefficients are selected with respect to their variance intensity. In extraction part, a computationally efficient detection method is used for detecting watermark logo blindly from distorted watermarked image. To achieve more robust algorithm firstly, we find the best place to insert the watermark bits and secondly, we encode the scrambled watermark bits by pseudo random sequences with an authentication key. Robustness of our proposed method is tested against different kinds of attacks. According to the experimental results, proposed method shows much improved performance in comparison to other published works.