Iterative Expansion Research Articles

Reliable approach of iterative method for nonlinear fractional differential equations

In this paper, a new approach of the iterative method is developed to handle nonlinear differential equations of fractional order. For this reason, an efficient modification of iterative method, namely iterative-Laurent method, is introduced based on iterative method and Laurent series expansion. The proposed approach is capable of reducing the size of calculations and easily overcome the difficulty arising in calculating complicated integrals. Furthermore, the new approach is compared with the variational iteration method and Adomian decomposition method in various nonlinear fractional differential equations and the obtained results reveal that the proposed method is more accurate and efficient.

Approximation on attraction domain of Cohen–Grossberg neural networks

In this paper, approximations of attraction domains of the asymptotically stable equilibrium points of some typical Cohen–Grossberg neural networks are achieved. Most Cohen–Grossberg neural networks are highly nonlinear systems which makes it difficult to approximate their attraction domain. Under some weak assumptions, we are allowed to employ the optimal Lyapunov method to obtain a Lyapunov function for asymptotically stable equilibrium points of a given Cohen–Grossberg neural network. With the help of this Lyapunov function, we approximate the corresponding attraction domain by the iterative expansion approach. Numerical simulations also illustrate that the approximation obtained is really part of the attraction domain.

The variational iteration solution method for a classof nonlinear disturbed evolution equations

Using the generalized variational iteration method, a class of nonlinear disturbed evolution equations are studied. Firstly, a functional is introduced, then its variational is computed, and the iteration expansion is finally constructed. The approximate and exact analytic solutions to the problem are obtained.

Travelling wave solution of disturbed Vakhnenko equation for physical model

A kind of disturbed Vakhnemko equation is considered. The modified asymptotic method is given. Firstly, we obtain corresponding traveling wave solution of the typical Vakhnemko equation. Secondly, introducing a functional, constructing the iteration expansion of solution, the nonlinear equation is converted into a set of iteration sequence. And then, the corresponding approximations of solution are solved successively. Finally, the approximate expansion for arbitrary order accuracy of the travelling wave solution for the original disturbed Vakhnemko model is obtained and its accuracy is discussed.

ChemInform Abstract: First Total Synthesis and Structural Confirmation of Fluvirucinine A2 via an Iterative Ring Expansion Strategy.

AbstractThe total synthesis is achieved by the multiple application of a ring‐expansion reaction, mediated by LiN(Tms)2.

Identification of Eukaryotic and Prokaryotic Methylthiotransferase for Biosynthesis of 2-Methylthio-N6-threonylcarbamoyladenosine in tRNA

Bacterial and eukaryotic transfer RNAs have been shown to contain hypermodified adenosine, 2-methylthio-N(6)-threonylcarbamoyladenosine, at position 37 (A(37)) adjacent to the 3'-end of the anticodon, which is essential for efficient and highly accurate protein translation by the ribosome. Using a combination of bioinformatic sequence analysis and in vivo assay coupled to HPLC/MS technique, we have identified, from distinct sequence signatures, two methylthiotransferase (MTTase) subfamilies, designated as MtaB in bacterial cells and e-MtaB in eukaryotic and archaeal cells. Both subfamilies are responsible for the transformation of N(6)-threonylcarbamoyladenosine into 2-methylthio-N(6)-threonylcarbamoyladenosine. Recently, a variant within the human CDKAL1 gene belonging to the e-MtaB subfamily was shown to predispose for type 2 diabetes. CDKAL1 is thus the first eukaryotic MTTase identified so far. Using purified preparations of Bacillus subtilis MtaB (YqeV), a CDKAL1 bacterial homolog, we demonstrate that YqeV/CDKAL1 enzymes, as the previously studied MTTases MiaB and RimO, contain two [4Fe-4S] clusters. This work lays the foundation for elucidating the function of CDKAL1.

First Total Synthesis and Structural Confirmation of Fluvirucinine A2 via an Iterative Ring Expansion Strategy

The first asymmetric total synthesis of fluvirucinine A(2) has been accomplished. A key feature of the synthesis is an iterative lactam ring expansion to provide rapid access to the 14-membered lactam skeleton and three stereogenic centers. The excellent remote control of the three stereogenic centers relied on stereoselective amidoalkylation followed by an amide-enolate-induced aza-Claisen rearrangement. In addition, the structure of fluvirucinine A(2) has been completely elucidated by our total synthesis.

Existence and uniqueness of positive solutions for a third-order three-point problem on time scales

In this paper, a class of third-order three-point boundary value problem on time scales is considered. Using monotone iterative technique and cone expansion and compression fixed point theorem of norm type, we do not only obtain the existence and uniqueness of positive solutions of the problem, but also establish the iterative schemes for approximating the solutions.

An iterative asymptotic expansion method for elliptic eigenvalue problems with oscillating coefficients

In this work we propose a method for obtaining fine-scale eigensolution based on the coarse-scale eigenso- lution in elliptic eigenvalue problems with oscillating coef- ficient. This is achieved by introducing a 2-scale asymptotic expansion predictor in conjunction with an iterative correc- tor. The eigensolution predictor equation is formulated using the weak form of an auxiliary problem. It is shown that large errors exist in the higher eigenmodes when the 2-scale asymptotic expansion is used. The predictor solution is then corrected by the combined inverse iteration and Rayleigh quotient iteration. The numerical examples demonstrate the effectiveness of this approach.

Elastic scattering of positrons by helium, neon, argon and krypton atoms

An elaborate computer code is constructed for the investigation of the elastic scattering of positrons from noble gases using an iterative Green's function partial-wave expansion formalism. Model static and polarization potentials are derived for describing the interactions of positrons with closed shell atoms. Quite accurate variational pictures are employed for describing the atomic targets. The efficiency of the developed code is tested by investigating the collisions of positrons from the atoms of four ideal gases, namely, helium, neon, argon and krypton. In each case, sufficient integration range and number of iterations are used for calculating the elastic phase shifts of 8 partial waves as well as the total elastic cross sections for an extended range of incident energies. Comparison between our results and both experimental and theoretical values available in the literature indicates that our results are very close to the experimental ones. They are as accurate as the theoretical results obtained with more complicated approaches.

Rough surface scattering in a Born approximation from a two-way coupled-mode formalism

Scattering from a rough surface in an ocean waveguide is described in a new derivation from a two-way coupled-mode representation. The general formalism, which contains scattering effects to all orders, is truncated to the first-order terms of an iterative (Born) expansion. Both two- and three-dimensional ocean waveguide geometries are discussed. By reducing the mode functions in terms of plane wave reflection coefficients, the off-diagonal components of the scattering kernel that is derived are shown to be consistent with a standard solution, but the diagonal components are different from the standard solution.

Optimal colourization for greyscale images

This paper proposes a user friendly interactive colourization system that utilizes iterative region expansion and linear programming to carry out colourization. The region corresponding to each scribbled colour is iteratively expanded using a sequence of increasing threshold values. Usually a few pixels remain unassigned to any colour region after this stage, each of which is then simply assigned to the nearest region based on an intrinsic distance measure. The optimal colours for the brightest pixel and the darkest pixel in each region are determined by employing linear programming, and then the whole region is colourized using linear interpolation. The proposed system provides several colourization modes users can select from. The user simply needs to scribble on the given greyscale image and select the colouring mode they want. The experimental results show that the proposed system provides natural and satisfactory colouring results.

Z-Complementary Sets Based on Sequences with Periodic and Aperiodic Zero Correlation Zone

Methods of constructing Z-complementary sequence sets are described. Different from those constructions using complementary sequences as a kernel, the proposed constructions are based on sequences with periodic and aperiodic zero-correlation zone (PAZCZ). These PAZCZ sequences are unitary sequences, not complementary sequences. By means of interleaving iteration and orthogonal matrix expansion of PAZCZ sequences, desirable bivalued zero cross-correlation zone (ZCCZ) characteristics can be obtained. Compared with Z-complementary sequence sets with single value ZCCZ which is generally equal to the length of an element sequence, the proposed Z-complementary sequence sets with bivalued ZCCZ have larger set size and then can support more users.

Fully automated deconvolution method for on-line analysis of time-resolved fluorescence spectroscopy data based on an iterative Laguerre expansion technique

Time-resolved fluorescence spectroscopy (TRFS) is a powerful analytical tool for quantifying the biochemical composition of organic and inorganic materials. The potential of TRFS for tissue diagnosis has been recently demonstrated. To facilitate the translation of TRFS to the clinical arena, algorithms for online TRFS data analysis are essential. A fast model-free TRFS deconvolution algorithm based on the Laguerre expansion method has previously been introduced. One limitation of this method, however, is the need to heuristically select two parameters that are crucial for the accurate estimation of the fluorescence decay: the Laguerre parameter alpha and the expansion order. Here, a new implementation of the Laguerre deconvolution method is introduced, in which a nonlinear least-square optimization of the Laguerre parameter alpha is performed, and the optimal expansion order is selected based on a minimum description length criterion (MDL). In addition, estimation of the zero-time delay between the recorded instrument response and fluorescence decay is also performed based on normalized mean square error criterion (NMSE). The method is validated on experimental data from fluorescence lifetime standards, endogenous tissue fluorophores, and human tissue. The proposed automated Laguerre deconvolution method will facilitate online applications of TRFS, such as real-time clinical tissue diagnosis.

The Role of the Granuloma in Expansion and Dissemination of Early Tuberculous Infection

Granulomas, organized aggregates of immune cells, form in response to persistent stimuli and are hallmarks of tuberculosis. Tuberculous granulomas have long been considered host-protective structures formed to contain infection. However, work in zebrafish infected with Mycobacterium marinum suggests that granulomas contribute to early bacterial growth. Here we use quantitative intravital microscopy to reveal distinct steps of granuloma formation and assess their consequence for infection. Intracellular mycobacteria use the ESX-1/RD1 virulence locus to induce recruitment of new macrophages to, and their rapid movement within, nascent granulomas. This motility enables multiple arriving macrophages to efficiently find and phagocytose infected macrophages undergoing apoptosis, leading to rapid, iterative expansion of infected macrophages and thereby bacterial numbers. The primary granuloma then seeds secondary granulomas via egress of infected macrophages. Our direct observations provide insight into how pathogenic mycobacteria exploit the granuloma during the innate immune phase for local expansion and systemic dissemination.

A disk expansion segmentation method for ultrasonic breast lesions

Automatically extracting lesion boundaries in ultrasound images is difficult due to the variance in shape and interference from speckle noise. An effective scheme of removing speckle noise can facilitate the segmentation of ultrasonic breast lesions, which can be performed with an iterative disk expansion method. In this study, a disk expansion segmentation method is proposed to semi-automatically find lesion contours in ultrasonic breast image. To evaluate the performance of the proposed method, the simulations with seven types of cysts, three in vitro phantom images and 10 clinical breast images are introduced. The mean normalized true positive area overlap between simulated contours and contours obtained by the proposed method is over 85% in simulation results. A strong correlation exists between physicians’ manual delineations and detected contours in clinical breast images. In addition, the method is also verified to be able to simultaneously contour multiple lesions in a single image. In comparison with the conventional active contour model, our proposed method does not require any initial seed within a lesion and thus, it is more convenient and applicable.

ChemInform Abstract: Tandem Conjugate Additions and 3‐Aza‐Cope Rearrangements of Tertiary Allyl Amines and Cyclic α‐Vinylamines with Acetylenic Sulfones. Applications to Simple and Iterative Ring Expansions Leading to Medium and Large‐Ring Nitrogen Heterocycles.

AbstractChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 200 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.

Tandem Conjugate Additions and 3-Aza-Cope Rearrangements of Tertiary Allyl Amines and Cyclic α-Vinylamines with Acetylenic Sulfones. Applications to Simple and Iterative Ring Expansions Leading to Medium and Large-Ring Nitrogen Heterocycles

Tertiary acyclic allyl amines and tertiary cyclic alpha-vinyl amines undergo conjugate additions to acetylenic sulfones to produce zwitterion intermediates, followed by 3-aza-Cope rearrangements. In the case of cyclic alpha-vinyl amines, the process results in ring-expansion, providing a novel route to 9- to 17-membered cyclic amines. The Hammett plot for the reaction of 8b with 2a- 2f shows rho = +1.19, which is consistent with formation of the proposed zwitterion in the rate-determining step, where electron-withdrawing substituents on the arylsulfonyl moiety stabilize the negative charge and enhance the rate of the reaction. Alternative pathways were observed in methanol in the case of 11, where a methoxy substituent promotes a dissociative mechanism of the corresponding zwitterion via a stabilized allyl cation, whereas the zwitterion derived from amine 12 undergoes ring-opening by direct attack of methanol upon the strained aziridinium moiety instead of by rearrangement. An iterative process was developed, where the product of one ring-expansion is converted into a new cyclic alpha-vinyl amine, followed by a repetition of the conjugate addition and [3,3] rearrangement. This protocol was illustrated by its application to the synthesis of motuporamine A and B.

Mass-weighting methods for sensor placement using sensor set expansion techniques

Placement of sensors is one of the most important tasks performed during pretest planning. The purpose of this work was to develop and investigate the use of an iterative Guyan expansion for mass weighting of target modes for sensor placement analogous to the common iterative Guyan reduction technique. The goal was to determine the appropriate mass-weighting approach to use in conjunction with effective independence sensor set expansion. In either sensor set expansion, or reduction, mass weighting requires a reduction of the FEM mass matrix to the current sensor set size Test-Analysis-Model (TAM). A general theory is presented for target mode mass weighting that can accommodate any type of reduction technique. The theory predicts that sensor set expansion using static mass weighting will result in sensor configurations that produce poor static TAMs. In contrast, sensor set expansion using modal mass weighting exactly reproduces the correct mass distribution during the expansion process. The results of a numerical example corroborate the theory. The modal mass sensor set expansion process produced significantly more accurate static TAMs than the static mass expansion. The modal expansion process was not quite as accurate as the iterative static reduction approach, but modal expansion was over 1600 times faster.

Robust and efficient CAD topology generation using adaptive tolerances

AbstractA topology generation algorithm, commonly known as geometry repairing/healing, is presented to detect commonly found geometrical and topological issues like cracks, gaps, overlaps, intersections, T‐connections and no/invalid topology in the model, process them and build correct topological information. The present algorithm is based on the iterative vertex pair contraction and expansion operations called stitching and filling, respectively. The algorithm closes small gaps/overlaps via the stitching operation and fills larger gaps by adding faces through the filling operation to process the model accurately. Moreover, the topology generation algorithm can process manifold as well as non‐manifold models, which makes the procedure more general and flexible. Most of the existing techniques use a constant tolerance for topology generation and suffer from the reliability issues and cannot preserve small details of the same size of gaps/overlaps. This algorithm uses an automatic and adaptive tolerance that enhances reliability of the process and preserves small features in the model. In this way, the combination of generality, accuracy, reliability and efficiency of this algorithm seems to be a significant improvement over existing techniques. Copyright © 2007 John Wiley & Sons, Ltd.