Iterative Type Research Articles

ON INEXACT NEWTON METHODS FOR SOLVING TWO NONLINEAR MATRIX EQUATIONS

In this paper we consider inexact Newton methods for finding the largest positive definite solutions of two nonlinear matrix equations X+ A∗X−1A = Q and X − A∗X−1A = Q, respectively. Using Newton’s method for considered equations requires solving a Stein’s equation at each iteration. For solving the Stein’s equation, we use Smith type iterations instead of exact methods. Nonlocal convergence of the process is shown. Numerical experiments are included to illustrate the theory.

Multiple meaning as a kind of iterative repetition in the Yakut language

The purpose of the article is to determine the semantic structure and features of the functioning of the means of expressing the proper multiple meaning as one of the subtypes of iterative repetition in the Yakut language. The object of the study is the semantics of an accurate or inaccurate quantitative account of situations. The subject of study is the so-called circumstances of multiplicity or counting complex. Based on the material of the Yakut language, the author, following I. B. Dolinina, adheres to the proposed terminology and suggests considering such cases of repeatability as an independent particular meaning of the iterative type of multiplicity. The main attention in identifying the semantic varieties of this meaning is paid to the use of such quantification features as certainty/uncertainty of the amount of repeatability and its limitation/unlimited. Depending on the correlation of these signs and the intensity of their manifestation, a list of representatives for each of them is determined. The main research method is functional–semantic, which uses the approach "from semantics to its formal expression" when describing linguistic material. Textual examples in the Yakut language are given using the method of morphemic glossing. The scientific novelty of the work lies in the systematization of the means of expression and the allocation of varieties of the actual multiple meaning, which had not previously become the subject of special research in Yakut linguistics. During the analysis of the functioning of adverbs with the semantics of multiplicity or counting, the methods of formation of representatives characteristic of each of the three subtypes of the actual multiple meaning (affixal, by reduplication and combination with the countable element "togul") were established. As an additional conclusion, we can cite the revealed dependence of the definition of the value in question on the temporal form of the predicate (statements with circumstances of multiplicity with a predicate in the form of the present-future and imperfect acquire habitual semantics). The theoretical significance of the results of this study is determined by the contribution to the study of the functional and semantic category of the aspectuality of the Yakut language, and may also be of interest for comparative and typological work in this field. Their practical significance is related to the possibility of their application in lexicographic and translation practice.

Convergence theorems of implicit type iterations in geodesic spaces with negative curvature

Convergence theorems of implicit type iterations in geodesic spaces with negative curvature

New N-acylated aminoalkanoic acids from tea roots derived biocontrol agent Clonostachys rosea 15020

Four new N-acylated aminoalkanoic acids, namely clonoroseins E−H (1−4), together with three previously identified analogs, clonoroseins A, B, and D (5−7), were identified from the endophytic fungus Clonostachys rosea strain 15020 (CR15020), using Feature-based Molecular Networking (FBMN). The elucidation of their chemical structures, including their absolute configurations, was achieved through spectroscopic analysis combined with quantum chemical calculations. Bioinformatics analyses suggested that an iterative type I HR-PKS (CrsE) generates the polyketide side chain of these clonoroseins. Furthermore, a downstream adenylate-forming enzyme of the PKS (CrsD) was suspected to function as an amide synthetase. CrsD potentially facilitates the transformation of the polyketide moiety into an acyl-AMP intermediate, followed by nucleophilic substitution with either β-alanine or γ-aminobutyric acid to produce amide derivatives. These findings significantly expand our understanding of PKS-related products originating from C. rosea and also underscore the powerful application of FBMN analytical methods in characterization of new compounds.

Parameterized complexity for iterated type partitions and modular-width

This paper deals with the complexity of some natural graph problems parameterized by some measures that are restrictions of clique-width, such as modular-width and neighborhood diversity. We introduce a novel parameter, called iterated type partition number, that can be computed in linear time and nicely places between modular-width and neighborhood diversity. We prove that the Equitable Coloring problem is W[1]-hard when parameterized by the iterated type partition number. This result extends to modular-width, answering an open question on the complexity of Equitable Coloring when parameterized by modular-width. On the contrary, we show that the Equitable Coloring problem is FPT when parameterized by neighborhood diversity.Furthermore, we present a scheme for devising FPT algorithms parameterized by iterated type partition number, which enables us to find optimal solutions for several graph problems. As an example, in this paper, we present algorithms parameterized by the iterated type partition number of the input graph for some generalized versions of the Maximum Clique, Minimum Graph Coloring, (Total) Minimum Dominating Set, Minimum Vertex Cover and Maximum Independent Set problems. Each algorithm outputs not only the optimal value but also the optimal solution. We stress that while the considered problems are already known to be FPT with respect to modular-width, the novel algorithms are both simpler and more efficient. We finally show that the proposed scheme can be used to devise polynomial kernels, with respect to iterated type partition number, for the decisional version of most of the problems mentioned above.

Strong convergence of Halpern's type iteration for α-nonexpansive semigroup in Banach spaces and CAT(0) spaces

Strong convergence of Halpern's type iteration for α-nonexpansive semigroup in Banach spaces and CAT(0) spaces

Convergence in Law of Iterates of Weakly Contractive in Mean Random-Valued Functions

We investigate the asymptotic behaviour of the sequence of forward type iterations of a given random-valued vector function on the state space being a separable and complete metric space. Assuming non-linear contraction in mean we prove that the considered sequence converges weakly to a random variable with a finite first moment and independent of the initial state. Moreover, we show that the speed of this convergence does not have to be geometric. We also present examples illustrating the result obtained.

Locally unitarily invariantizable NEPv and convergence analysis of SCF

We consider a class of eigenvector-dependent nonlinear eigenvalue problems (NEPv) without the unitary invariance property. Those NEPv commonly arise as the first-order optimality conditions of a particular type of optimization problems over the Stiefel manifold, and previously, special cases have been studied in the literature. Two necessary conditions, a definiteness condition and a rank-preserving condition, on an eigenbasis matrix of the NEPv that is a global optimizer of the associated optimization problem are revealed, where the definiteness condition has been known for the special cases previously investigated. We show that, locally close to the eigenbasis matrix satisfying both necessary conditions, the NEPv can be reformulated as a unitarily invariant NEPv, the so-called aligned NEPv, through a basis alignment operation — in other words, the NEPv is locally unitarily invariantizable. Numerically, the NEPv is naturally solved by a self-consistent field (SCF)-type iteration. By exploiting the differentiability of the coefficient matrix of the aligned NEPv, we establish a closed-form local convergence rate for the SCF-type iteration and analyze its level-shifted variant. Numerical experiments confirm our theoretical results.

Risk‐sensitive Markov decision processes with long‐run CVaR criterion

CVaR (Conditional value at risk) is a risk metric widely used in finance. However, dynamically optimizing CVaR is difficult, because it is not a standard Markov decision process (MDP) and the principle of dynamic programming fails. In this paper, we study the infinite‐horizon discrete‐time MDP with a long‐run CVaR criterion, from the view of sensitivity‐based optimization. By introducing a pseudo‐CVaR metric, we reformulate the problem as a bilevel MDP model and derive a CVaR difference formula that quantifies the difference of long‐run CVaR under any two policies. The optimality of deterministic policies is derived. We obtain a so‐called Bellman local optimality equation for CVaR, which is a necessary and sufficient condition for locally optimal policies and only necessary for globally optimal policies. A CVaR derivative formula is also derived for providing more sensitivity information. Then we develop a policy iteration type algorithm to efficiently optimize CVaR, which is shown to converge to a local optimum in mixed policy space. Furthermore, based on the sensitivity analysis of our bilevel MDP formulation and critical points, we develop a globally optimal algorithm. The piecewise linearity and segment convexity of the optimal pseudo‐CVaR function are also established. Our main results and algorithms are further extended to optimize the mean and CVaR simultaneously. Finally, we conduct numerical experiments relating to portfolio management to demonstrate the main results. Our work sheds light on dynamically optimizing CVaR from a sensitivity viewpoint.

How Does Iteration of Entrepreneurial Opportunities in User Enterprises Affect Entrepreneurial Performance? A Dual Case Study Based on Dual Strategic Orientations

The iteration of entrepreneurial opportunities is vital to the growth and maintenance of long-term competitive advantages of user enterprises. However, there needs to be more comprehensive theoretical discussion within the academic community on how entrepreneurial opportunity iteration contributes to the entrepreneurial performance of user enterprises. In this study, we investigate Smartmi Technology and Zepp Technology as the research subjects and employ the case study method encoded in the programmed rootedness theory to uncover the intrinsic mechanism by which the entrepreneurial opportunity iteration of user enterprises affects entrepreneurial performance and explicate the mechanistic model between different types of entrepreneurial opportunity iteration and the dual strategic orientations and entrepreneurial performance. Specifically, the entrepreneurial opportunity iterations of user enterprises are mainly categorized into efficiency-based and innovative entrepreneurial opportunity iterations. The dual strategic orientations of stakeholder long-termism and professionalism play a significant moderating role in promoting user and growth performance improvement.

New insights on a pair of quasi-contractive operators in Banach spaces: Results on Jungck type iteration algorithms and proposed open problems

In this paper, we explore relationships among the pairs of various well-known contractive type operators in Banach spaces. We also present a novel Jungck type iteration algorithm for a pair of quasi-contractive operators, which is thoroughly investigated in terms of strong convergence, stability, and data dependency. To demonstrate the efficacy of the proposed algorithm and reliability of each of the mentioned results, we furnish illustrative academic examples including both linear and nonlinear DEs. Furthermore, we present several open problems that warrant further study. Our results complement recent findings in the literature and contribute to further development in this area.

Two‐level multiscale enrichment finite volume method based on the Newton iteration for the stationary incompressible magnetohydrodynamics flow

In this paper, we propose a stabilized finite volume method based on the Newton's type iteration for the steady incompressible magnetohydrodynamics (MHD) problem. In order to reduce the computational complexity, the lowest order mixed finite element pair ( ‐ ‐ ) is adopted to approximate the velocity, pressure and magnetic fields, and the multiscale enrichment method is introduced to overcome the restriction of discrete inf‐sup (LBB) condition. We firstly solve the incompressible MHD equations by the Newton iterations on a coarse mesh with the mesh size , stability and convergence results of numerical solutions are provided. Secondly, the combination of the two‐level method with the Newton iteration is used to approximate the considered problem, a coupled nonlinear problem is solved on the coarse mesh , then the Stokes and Maxwell equations are considered on a fine mesh with the mesh size , the uniform stability and optimal error estimates of two‐level Newton iterative method are provided. Theoretical findings show that the two‐level method has the same order as the one‐level method in ‐norm as long as the mesh sizes satisfy . However, the two‐level method involves much less work than the one‐level method. Finally, some numerical examples are presented to demonstrate the effectiveness of the considered numerical schemes.

Methods Used in the Development of Common Data Models for Health Data: Scoping Review.

Common data models (CDMs) are essential tools for data harmonization, which can lead to significant improvements in the health domain. CDMs unite data from disparate sources and ease collaborations across institutions, resulting in the generation of large standardized data repositories across different entities. An overview of existing CDMs and methods used to develop these data sets may assist in the development process of future models for the health domain, such as for decision support systems. This scoping review investigates methods used in the development of CDMs for health data. We aim to provide a broad overview of approaches and guidelines that are used in the development of CDMs (ie, common data elements or common data sets) for different health domains on an international level. This scoping review followed the PRISMA-ScR (Preferred Reporting Items for Systematic Reviews and Meta-Analyses extension for Scoping Reviews) checklist. We conducted the literature search in prominent databases, namely, PubMed, Web of Science, Science Direct, and Scopus, starting from January 2000 until March 2022. We identified and screened 1309 articles. The included articles were evaluated based on the type of adopted method, which was used in the conception, users' needs collection, implementation, and evaluation phases of CDMs, and whether stakeholders (such as medical experts, patients' representatives, and IT staff) were involved during the process. Moreover, the models were grouped into iterative or linear types based on the imperativeness of the stages during development. We finally identified 59 articles that fit our eligibility criteria. Of these articles, 45 specifically focused on common medical conditions, 10 focused on rare medical conditions, and the remaining 4 focused on both conditions. The development process usually involved stakeholders but in different ways (eg, working group meetings, Delphi approaches, interviews, and questionnaires). Twenty-two models followed an iterative process. The included articles showed the diversity of methods used to develop a CDM in different domains of health. We highlight the need for more specialized CDM development methods in the health domain and propose a suggestive development process that might ease the development of CDMs in the health domain in the future.

A multi-objective mixed integer linear programming model for thesis defence scheduling

In this paper, we address the thesis defence scheduling problem, a critical academic scheduling management process, which has been overshadowed in the literature by its counterparts, course timetabling and exam scheduling. Specifically, we address the single defence assignment type of thesis defence scheduling problems, where each committee is assigned to a single defence, scheduled for a specific day, hour and room. We formulate a multi-objective mixed-integer linear programming model, which aims to be applicable to a broader set of cases than other single defence assignment models present in the literature, which have a focus on the characteristics of their universities. For such a purpose, we introduce a different decision variable, propose constraint formulations that are not regulation and policy specific, and cover and offer new takes on the more common objectives seen in the literature. We also include new objective functions based on our experience with the problem at our university and by applying knowledge from other academic scheduling problems. We also propose a two-stage solution approach. The first stage is employed to find the number of schedulable defences, enabling the optimisation of instances with unschedulable defences. The second stage is an implementation of the augmented ϵ-constraint method, which allows for the search of a set of different and non-dominated solutions while skipping redundant iterations. The methodology is tested for case-studies from our university, significantly outperforming the solutions found by human schedulers. A novel instance generator for thesis scheduling problems is presented. Its main benefit is the generation of the availability of committee members and rooms in availability and unavailability blocks, resembling their real-world counterparts. A set of 96 randomly generated instances of varying sizes is solved and analysed regarding their relative computational performance, the number of schedulable defences and the distribution of the considered types of iterations. The proposed method can find the optimal number of schedulable defences and present non-dominated solutions within the set time limits for every tested instance.

Localization for Almost-Periodic Operators with Power-law Long-range Hopping: A Nash-Moser Iteration Type Reducibility Approach

In this paper we develop a Nash-Moser iteration type reducibility approach to prove the (inverse) localization for some d-dimensional discrete almost-periodic operators with power-law long-range hopping. We also provide a quantitative lower bound on the regularity of the hopping. As an application, some results of Sarnak (Comm Math Phys 84(3):377–401, 1982), Pöschel (Comm Math Phys 88(4):447–463, 1983), Craig (Comm Math Phys 88(1):113–131, 1983) and Bellissard et al. (Comm Math Phys 88(4):465–477, 1983) are generalized to the power-law hopping case.

The Development of a Data-Based Leakage Pinpoint Detection Technique for Water Distribution Systems

Leakage is one of the abnormal conditions in water distribution systems (WDSs). Real-time monitoring can be used to prevent or recover quickly from leakage. However, this is not enough: for improved leakage detection, a status diagnosis of the WDS must be performed together with this real-time monitoring, and numerous studies have been conducted on this. Furthermore, the existing proposed methodology only provides optimal sensor location and fast recognition. This paper proposes a technique that can quantitatively evaluate the volume of leakage along with leakage detection using deep learning technology. The hydraulic data (e.g., pressure, velocity, and flow) from the calibrated hydraulic model were used as training data and deep learning techniques were applied to conduct a simultaneous detection of leakage volume and location. We examined various scenarios regarding leakage volume and location for the data configuration of a simulated leakage accident. Furthermore, for optimal leakage detection performance, the detection performance according to the size of the network, the meter types of meters, the number of meters, and the locations of the meters were analyzed. This study is expected to be helpful in various aspects such as recovery and restoration decision making after leakage, because it simultaneously identifies the amount and location of the leakage.

Application of Nanotechnology in a Novel Air Purifier for Remediation of Airborne Pathogen and to Prevent the Spread of COVID-19

The spread of COVID-19 occurs via airborne transmission. With a constant and variable spread of COVID-19, indoor air-quality has become a major concern all over the world. People who are infected with COVID can release particles and droplets of respiratory fluids that contain the SARS CoV-2 virus into the air when they exhale (e.g., quiet breathing, speaking, singing, exercise, coughing, sneezing). Once infectious droplets are exhaled, they move outward from the person (the source) into the surrounding environment; these droplets carry the virus and transmit infection. Indoors, the very fine droplets and particles will continue to spread through the air in the room or space and can accumulate. Harmful pathogenic organisms like fungi, bacteria and viruses, as the one responsible for causing contagious diseases like the ongoing pandemic of COVID-19 can also be successfully destroyed and neutralized. We have developed and studied the efficiency of the AFL Mini Sanifier II® in a simulated environment of a fiberglass chamber using various types of meters to assess the suspended particulate matter (PM) in the ambient air. We also report the development of a novel face mask that was assessed for safety measures and further improvement by the researchers in the West Texas A&M University. The mask is user friendly and portable, equipped with a small internal fan that supplies a continuous air to the user preventing the suffocating effect caused by the other masks. The novel mini air purifier is equipped with the advanced nanotechnology that cleans and sanitizes both the air and surfaces and subsequently has been shown to reduce common allergy, asthma and hay fever related symptoms. This mask and the mini air purifier function in an advanced way to combat all forms of airborne pathogens including the bacteria, viruses, mold spores and harmful Volatile Organic Compounds (VOC) present in the air.

A Seventh Order Family of Jarratt Type Iterative Method for Electrical Power Systems

A load flow study referred to as a power flow study is a numerical analysis of the electricity that flows through any electrical power system. For instance, if a transmission line needs to be taken out of service for maintenance, load flow studies allow us to assess whether the remaining line can carry the load without exceeding its rated capacity. So, we need to understand about the voltage level and voltage phase angle on each bus under steady-state conditions to keep the bus voltage within a specific range. In this paper, our goal is to present a higher order efficient iterative method to carry out a power flow study to determine the voltages (magnitude and angle) for a specific load, generation and network conditions. We introduce a new seventh-order three-step iterative scheme for obtaining approximate solution of nonlinear systems of equations. We attain the seventh-order convergence by using four function evaluations which makes it worthy of interest. Moreover, we show its applicability to the electrical power system for calculating voltages and phase angles. By calculating the bus angle and voltage level, we conclude that the performance of the power system is assessed in a more efficient manner using the new scheme. In addition, dynamical planes of the methods applied on nonlinear systems of equations show global convergence.

Hybrid framework for single-pointer meter identification.

Automated identification of single-pointer meter identification in substations is widely used in the construction of digital substations and it must accurately identify the value of the pointer meter. Current single-pointer meter identification methods are not universally applicable and can only identify one type of meter. In this study, we present a hybrid framework for single-pointer meter identification. First, the input image of the single-pointer meter is modeled to gain a priori knowledge, including the template image, dial position information, the pointer template image, and scale value positions. Based on a convolutional neural network to generate the input image and the template image feature points, image alignment is then applied through a feature point match to mitigate slight changes in the camera angle. Next, a pixel loss-free method of arbitrary point image rotation correction is presented for rotation template matching. Finally, by rotating the input gray mask image of the dial and matching it to the pointer template to get the optimal rotation angle, the meter value is calculated. The experimental findings demonstrate the method's effectiveness in identifying nine different types of single-pointer meters in substations with various ambient illuminations. This study provides a feasible reference for substations to identify the value of different types of single-pointer meters.

Real-Time Estimation of Support Provision Capability for Poor-Observable Distribution Networks

An indispensable step towards coordinating the actions of distribution and transmission system operators ( <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dso</small> s- <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tso</small> ) is to estimate the range of flexibility that can be offered to the <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tso</small> by <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dso</small> s. Within this context, a data-driven probabilistic approach is proposed to evaluate the capability of a distribution network in providing active and reactive power support in real-time. To this end, in an offline phase, a linear discriminant analysis model, together with a piecewise linear model of the distribution network are trained to delineate the boundary of a region representing the adherence to distribution network operational constraints. In the implementation phase, this region comprises the feasible set of a series of optimization problems, formulated to determine the support provision capability. These optimization problems are of iterative linear programming type, which allows for real-time applicability. The evaluated support capability can be deemed as the available reserve in real-time transmission operation, which enables providing a coordinated response towards unexpected events, and facilitates the participation of distributed resources in the balancing market by granting an up-to-date estimation of available supports. This approach is tested on the IEEE 123-node system and verified through comparison with an AC optimal power flow technique.