Iterative Type Research Articles

A pointwise inequality for the fourth-order Lane–Emden equation

We prove that the following pointwise inequality holds −∆u ≥ √ 2 (p + 1)− cn |x| a 2 u p+1 2 + 2 n− 4 |∇u|2 u in R where cn := 8 n(n−4) , for positive bounded solutions of the fourth order Henon equation that is ∆u = |x|u in R for some a ≥ 0 and p > 1. Motivated by the Moser’s proof of the Harnack’s inequality as well as Moser iteration type arguments in the regularity theory, we develop an iteration argument to prove the above pointwise inequality. As far as we know this is the first time that such an argument is applied towards constructing pointwise inequalities for partial differential equations. An interesting point is that the coefficient 2 n−4 also appears in the fourth order Q-curvature and the Paneitz operator. This in particular implies that the scalar curvature of the conformal metric with conformal factor u 4 n−4 is positive.

English

In this paper, we compare the spatially adaptive iterative filtering (SAIF) approach with Weighted Encoding with Sparse Nonlocal Regularization (WESNR) to maintain the denoising strength locally for any spatial domain method. These approaches has ability of filtering local image content iteratively using the given base filter, and the type of iteration and the iteration number are automatically optimized with respect to estimated risk (i.e., mean squared error). Experimental result shows that approx. 7% enhancement in the SNR of SAIF method as compared to the WESNR method.

Extending explicit and linearly implicit ODE solvers for index-1 DAEs

Nonlinear differential-algebraic equations (DAE) are typically solved using implicit stiff solvers based on backward difference formula or RADAU formula, requiring a Newton–Raphson approach for the nonlinear equations or using Rosenbrock methods specifically designed for DAEs. Consistent initial conditions are essential for determining numeric solutions for systems of DAEs. Very few systems of DAEs can be solved using explicit ODE solvers. This paper applies a single-step approach to system initialization and simulation allowing for systems of DAEs to be solved using explicit (and linearly implicit) ODE solvers without a priori knowledge of the exact initial conditions for the algebraic variables. Along with using a combined process for initialization and simulation, many physical systems represented through large systems of DAEs can be solved in a more robust and efficient manner without the need for nonlinear solvers. The proposed approach extends the usability of explicit and linearly implicit ODE solvers and removes the requirement of Newton–Raphson type iteration.

Identification of linear continuous-time systems under irregular and random output sampling

This paper considers the problem of identifiability and parameter estimation of single-input–single-output, linear, time-invariant, stable, continuous-time systems under irregular and random sampling schemes. Conditions for system identifiability are established under inputs of exponential polynomial types and a tight bound on sampling density. Identification algorithms of Gauss–Newton iterative types are developed to generate convergent estimates. When the sampled output is corrupted by observation noises, input design, sampling times, and convergent algorithms are intertwined. Persistent excitation (PE) conditions for strongly convergent algorithms are derived. Unlike the traditional identification, the PE conditions under irregular and random sampling involve both sampling times and input values. Under the given PE conditions, iterative and recursive algorithms are developed to estimate the original continuous-time system parameters. The corresponding convergence results are obtained. Several simulation examples are provided to verify the theoretical results.

Halpern type iteration with multiple anchor points in a Hadamard space

In this paper, we consider an approximation sequence of a common fixed point generated by Halpern type iteration with a finite family of nonexpansive mappings in a Hadamard space. We propose another style of Halpern type iteration with multiple anchor points and prove that it converges strongly to a common fixed point.

Effects of Pipe Wall Offsets on Differential Pressure Meter Accuracy

Accurate flow measurement is essential for the management of any type of fluid system. This research investigated the effect on accuracy that five types of 12‐in. differential‐pressure flow meters have as a result of being installed in pipelines of differing inside diameter. The types of meters chosen for this research were the classical Venturi meter, Halmi Venturi Tube, wedge meter, V‐cone meter, and the X‐meter. Each meter was tested for accuracy with10 pipe wall offsets varying from a 0.125‐in. sudden contraction to a 0.937‐in. sudden expansion of the pipe radius. The meters' reading during each test series was compared with the meters' reading with no pipe wall offset at the same Reynolds number. This research demonstrated that for accurate flow measurement, most flow meters require that the inside diameter of the piping be the same as the inside diameter of the meter.

Convergence of Ishikawa type iteration process for three quasi-nonexpansive mappings in a convex metric space

Abstract The paper establishes some convergence theorems for Ishikawa type iteration processes associated with two and three quasi-nonexpansive mappings in a convex metric space.

Genome Mining of Streptomyces sp. Tü 6176: Characterization of the Nataxazole Biosynthesis Pathway.

Streptomyces sp. Tü 6176 produces the cytotoxic benzoxazole nataxazole. Bioinformatic analysis of the genome of this organism predicts the presence of 38 putative secondary-metabolite biosynthesis gene clusters, including those involved in the biosynthesis of AJI9561 and its derivative nataxazole, the antibiotic hygromycin B, and ionophores enterobactin and coelibactin. The nataxazole biosynthesis gene cluster was identified and characterized: it lacks the O-methyltransferase gene required to convert AJI9561 into nataxazole. This O-methyltransferase activity might act as a resistance mechanism, as AJI9561 shows antibiotic activity whereas nataxazole is inactive. Moreover, heterologous expression of the nataxazole biosynthesis gene cluster in S. lividans JT46 resulted in the production of AJI9561. Nataxazole biosynthesis requires the shikimate pathway to generate 3-hydroxyanthranilate and an iterative type I PKS to generate 6-methylsalicylate. Production of nataxazole was improved up to fourfold by disrupting one regulatory gene in the cluster. An additional benzoxazole, 5-hydroxynataxazole is produced by Streptomyces sp. Tü 6176. 5-Hydroxynataxazole derives from nataxazole by the activity of an as yet unidentified oxygenase; this implies cross-talk between the nataxazole biosynthesis pathway and an unknown pathway.

Multilevel Jacobi and Gauss–Seidel type iteration methods for solving ill-posed integral equations

Abstract In this paper, multilevel Jacobi and Gauss–Seidel type iteration methods with compression technique are developed for solving ill-posed integral equations by making use of the multiscale structure of the matrix representation of the integral operator. The methods are based on the combination of Tikhonov regularization and multiscale Galerkin methods, and lead to fast solutions of discrete regularization methods for the equations. Choice for an a posteriori regularization parameter is proposed. An optimal convergence order for the method with the choices of parameters is established. Numerical experiments are given to illustrate the efficiency of the method.

Radial Resolution Evaluation for Oblique-View Electron Cyclotron Emission for ITER

The differences in the electron cyclotron emission spectrum from a tokamak plasma between a direct line of sight (LOS) (normal to the toroidal magnetic field) and a slightly oblique LOS have been modeled. A typical ITER tokamak scenario has been chosen in this study. The usefulness of such an additional detector for obtaining a better radial resolution is examined. The intensities of the radiation, as observable from the low-field side, covering the first harmonic ordinary mode spectral frequencies ∼120 to 230 GHz have been compared. We find that at certain frequencies the radiation observed along the oblique view seems to come from a narrower region. This affords the possibility of realizing better radial spatial resolution, compared to that possible by a direct view alone, for localizing any fluctuations, identifying abrupt changes in the temperature profile, etc. The physical reasons for the code-predicted differences between the direct and oblique spectra are elucidated. The translation of the radial resolution calculations into realistic phenomena is studied for two situations: neoclassical tearing modes and a damped sinusoidal perturbation. For both cases, the oblique view yields a better reproduction of the situation.

Effects of the radial electric field on the confinement of fast ions in ITER

The effects of a radial electric field (EF) on the losses of alpha particles and neutral beam injection (NBI) fast ions in typical ITER operation scenarios for both error fields due to test blanket modules (TBMs) and toroidal field (TF) ripple were evaluated using an iterative method to execute an orbit-following Monte-Carlo code and a one-dimensional transport code. The EF effect on the loss of fast ions strongly depends on the operation scenario as well as on the error field. The electric field is very significant in the loss of fast ions in a 9 MA ITER operation scenario with a higher safety factor and in the error field associated with TBMs. The EF effect in the error field of TF ripple is very small in any operation scenario. The electric field is much more significant for the loss of NBI fast ions than for that of alpha particles. The radial electric field changes the toroidal precession of fast ions and consequently alters their condition of resonance with the error field, which may account for the EF effect on the loss of fast ions in ITER with TBMs.

Stability and convergence of two-level iterative methods for the stationary incompressible magnetohydrodynamics with different Reynolds numbers

In the paper we develop some two-level finite element iterative methods and use these methods to solve the stationary incompressible magnetohydrodynamics (MHD) with different Reynolds numbers under some different uniqueness conditions. Firstly, we use the Stokes type iterative method, Newton type iterative method and Oseen type iterative method of m times on a coarse mesh with mesh size H and then solve a linear problem with the Stokes type, Newton type and Oseen type correction of one time on a fine grid with mesh sizes h≪H. Furthermore, we analyze the uniform stability and convergence of these methods with respect to Reynolds numbers, mesh sizes h and H and iterative times m. Finally, the stationary incompressible MHD equations with large Reynolds number are researched by the one-level finite element method based on the Oseen type iteration on a fine mesh under a weak uniqueness condition.

Global convergence of Karnik–Mendel algorithms

Karnik–Mendel (KM) algorithms are the most commonly used iterative type reduction methods in interval type-2 fuzzy sets and systems, as well as new techniques for computing the fuzzy weighted average (FWA). Various extensions and improvements have been proposed. However, no proof has been provided for the convergence of these extensions. It is necessary to provide the proof because many of the iterative algorithms may have divergence cases. In the present study, we provide a theoretical proof that KM algorithms exhibit global convergence. Different initialization methods and iteration formats can always obtain the same unique optimal solution. Thus, there are no concerns about the possibility of divergence in extensions of KM algorithms. Our proof provides theoretical support for the applications of KM algorithms, especially the type reduction designs used in type-2 fuzzy systems and FWA computations because of the important roles of KM algorithms in these methods.

2D-to-3D Visual Human Motion Converting System for Home Optical Motion Capture Tool and 3-D Smart TV

Although 2-D visual human motion analyzers that work with a sequence of images have been widely studied, some consumer electronics equipment, such as home optical motion capture tools and smart TVs, require 3-D motion data. For this purpose, this paper proposes a 2D-to-3D visual human motion converter that reconstructs 3-D visual motion from the 2-D visual human motion in a sequence of images. Because home optical motion capture tools and smart TVs have a single channel, this paper designs a proposed 2D-to-3D converter that has a single channel. A common difficulty for the single channel is that most contemporary 3-D reconstruction processes based on 2-D motion are nonlinear iterative types. For more convenient use in real-time applications, this paper proposes an analytical solution type of 3-D reconstruction process instead of the nonlinear iterative types. To derive an analytical solution, this paper proposes an idea that formulates a human body joint as a 2-D universal joint model instead of the more common 3-D spherical joint models. To overcome the major limitation of analytical solution-type processes, i.e., the low accuracy, this paper formulates the estimation process as an optimization problem. The process thus designed is then applied to each joint in the human body, one after another. Performance evaluation shows that the proposed 2D-to-3D visual human motion converter has nearly the same high accuracy as a contemporary nonlinear iterative-type approach.1.

Numerical study of the two-species Vlasov–Ampère system: Energy-conserving schemes and the current-driven ion-acoustic instability

In this paper, we propose energy-conserving Eulerian solvers for the two-species Vlasov–Ampère (VA) system and apply the methods to simulate current-driven ion-acoustic instability. The two-species VA systems are of practical importance in applications, and they conserve many physical quantities including the particle number of each species and the total energy that is comprised of kinetic energy for both species and the electric energy.The main goal of this paper is to generalize our previous work for the single-species VA system [9] and Vlasov–Maxwell (VM) system [8] to the two-species case. The methodologies proposed involve careful design of temporal discretization and the use of the discontinuous Galerkin (DG) spatial discretizations. We show that the energy-conserving time discretizations for single-species equations [9,8] can also work for the two-species case if extended properly. Compared to other high order schemes, we emphasize that our schemes can preserve the total particle number and total energy on the fully discrete level regardless of mesh size, making them very attractive for long time simulations. We benchmark our algorithms on a test example to check the one-species limit, and the current-driven ion-acoustic instability. To simulate the current-driven ion-acoustic instability, a slight modification for the implicit method is necessary to fully decouple the split equations. This is achieved by a Gauss–Seidel type iteration technique. Numerical results verified the conservation and performance of our methods. Finally, we remark that the schemes in this paper can be readily extended to applications when the models take more general form, such as the multi-species VM equations.

Parameterized Markov decision process and its application to service rate control

In this paper, we discuss the optimization of Markov decision processes (MDPs) with parameterized policy, where the state space is partitioned and a parameter is assigned to each partition. The goal is to find the optimal parameters which maximize the long-run average performance. The traditional policy iteration is usually inapplicable to parameterized policy because the parameter tuning at different states are correlated. With some appropriate assumptions and special conditions, we develop a modified policy iteration type algorithm to find the optimal parameters. Compared with the traditional gradient-based approaches for MDP with parameterized policy, this policy iteration type approach is much more efficient. Finally, as an example, we apply this approach to a service rate control problem in closed Jackson networks. As compared with the gradient-based approach which is trapped into local optimum, our approach is demonstrated to efficiently find the optimal service rates in global scope.

A BIEM approach to a time-harmonic analysis of saturated soil–structure interaction with elastic-type contact conditions

This study presents a solution for the dynamic response of a porous saturated medium to a harmonic motion of a rigid inclusion where an elastic type intermediate layer is located at the interface. The problem has been solved using the Neumann series which terms are obtained by means of recurrence relationships of simple iteration type. To perform regularization we consider every singular integral as an integral in sense of finite part by Hadamard. A modified Shanks transform was used to accelerate the series convergence. The method allows avoid the solution of large system of the linear algebraic equations with densely filled matrix. However, for problems with complicate boundary, which includes segments with large curvature, the requested number of series members sharply increases. The approach is valid for problems which potential satisfied to the Hölder-Lipschitz condition of the first order.Using the proposed approach the problem of a linear harmonic motion of the circular inclusion was investigated and the effect of the frequency on the contact stresses has been studied. It was found that for this specific example, when the vibration frequency increases the maxima of both contact normal stress and porous pressure decrease, while the maximum of the contact shear stress remains almost unchanged.

Demiclosed principle and convergence theorems for total asymptoticallynonexpansive nonself mappings in hyperbolic spaces

AbstractIn this paper, we prove the demiclosed principle for total asymptoticallynonexpansive nonself mappings in hyperbolic spaces. Then we obtain convergencetheorems of the mixed Agarwal-O’Regan-Sahu type iteration for totalasymptotically nonexpansive nonself mappings. Our results extend some results inthe literature.MSC:47H09, 49M05.

A Hybrid Proximal Extragradient Self-Concordant Primal Barrier Method for Monotone Variational Inequalities

This paper presents a hybrid proximal extragradient (HPE) self-concordant primal barrier method for solving a monotone variational inequality over a closed convex set endowed with a self-concordant barrier and with an underlying map that has Lipschitz continuous derivative. In contrast to the iteration of a previous method developed by the first and third authors that has to compute an approximate solution of a linearized variational inequality, the one of the present method solves a simpler Newton system of linear equations. The method performs two types of iterations, namely, those that follow ever changing interior paths and those that correspond to large-step HPE iterations. Due to its first-order nature, the present method is shown to have a better iteration-complexity than its zeroth order counterparts such as Korpelevich's algorithm and Tseng's modified forward-backward splitting method, although its work per iteration is larger than the one for the latter methods.

Chemical chain termination resolves the timing of ketoreduction in a partially reducing iterative type I polyketide synthase.

Synthetic chain terminators were used to capture the biosynthetic intermediates from a partially reducing iterative type I polyketide synthase, which is integrated into a multimodular biosynthesis enzyme. The off-loaded metabolites clarified the timing of ketoreduction and aromatization in the assembly of the antibiotic micacocidin.