Simple Iteration Research Articles

Exploring Fast and Flexible Zero‐Shot Low‐Light Image/Video Enhancement

AbstractLow‐light image/video enhancement is a challenging task when images or video are captured under harsh lighting conditions. Existing methods mostly formulate this task as an image‐to‐image conversion task via supervised or unsupervised learning. However, such conversion methods require an extremely large amount of data for training, whether paired or unpaired. In addition, these methods are restricted to specific training data, making it difficult for the trained model to enhance other types of images or video. In this paper, we explore a novel, fast and flexible, zero‐shot, low‐light image or video enhancement framework. Without relying on prior training or relationships among neighboring frames, we are committed to estimating the illumination of the input image/frame by a well‐designed network. The proposed zero‐shot, low‐light image/video enhancement architecture includes illumination estimation and residual correction modules. The network architecture is very concise and does not require any paired or unpaired data during training, which allows low‐light enhancement to be performed with several simple iterations. Despite its simplicity, we show that the method is fast and generalizes well to diverse lighting conditions. Many experiments on various images and videos qualitatively and quantitatively demonstrate the advantages of our method over state‐of‐the‐art methods.

Two-sided Lieb–Thirring bounds

We prove upper and lower bounds for the number of eigenvalues of semi-bounded Schrödinger operators in all spatial dimensions. As a corollary, we obtain two-sided estimates for the sum of the negative eigenvalues of atomic Hamiltonians with Kato potentials. Instead of being in terms of the potential itself, as in the usual Lieb–Thirring result, the bounds are in terms of the landscape function, also known as the torsion function, which is a solution of (−Δ + V + M)uM = 1 in Rd; here M∈R is chosen so that the operator is positive. We further prove that the infimum of (uM−1−M) is a lower bound for the ground state energy E0 and derive a simple iteration scheme converging to E0.

An Aero Engine Disk Sizing and Weight Estimation Approach with Improved Temperature Profiles

Abstract During the predesign phase of an aero engine, interdisciplinary parametric studies are crucial for identifying an optimum engine. As innovative engine concepts emerge, it is essential to study trends aiming to minimize climate impact and one of its key contributors, fuel burn. The comparatively heavy disks, subjected to high thermal and mechanical loads, are central to this analysis due to their high impact on the overall module mass. This paper proposes an approach to achieve a first lightweight mechanical design of disks in the predesign phase. Based on a performance and aerodynamic baseline, the design space and physical boundary conditions are set. Firstly, an initial mass optimized disk is derived using simplified temperature profiles and stress calculations under the Mechanical Design Point conditions. Subsequently, all the module disks are considered and an estimation for each bore temperature is achieved through a novel loop over the entire module and all available operating points. By evaluating the temperature and stress profiles across various operating conditions, the lowcyclefatigue life of each disk can be studied. As part of a highly modular engine predesign framework, this method allows for zooming capabilities of single disk calculations by prescribing individual boundary conditions. The proposed approach already yields an initial assessment of the rotors within a short runtime, facilitating simple iterations with the succeeding design phases due to method and tool commonalities. While the primary focus of the current work is on compressor design, the principles presented are adaptable and expandable to turbine disk applications as well.

A new fast four-point rainflow cycle counting algorithm by employing a new loop iteration mode for fatigue life estimation

Purpose In order to improve the computation efficiency of the four-point rainflow algorithm, a new fast four-point rainflow cycle counting algorithm (FFRA) using a novel loop iteration mode is proposed.Design/methodology/approach In this new algorithm, the loop iteration mode is simplified by reducing the number of iterations, tests and deletions. The high efficiency of the new algorithm makes it a preferable candidate in fatigue life online estimation of structural health monitoring systems.Findings The extensive simulation results show that the extracted cycles by the new FFRA are the same as those by the four-point rainflow cycle counting algorithm (FRA) and the three-point rainflow cycle counting algorithm (TRA). Especially, the simulation results indicate that the computation efficiency of the FFRA has improved an average of 12.4 times compared to the FRA and an average of 8.9 times compared to the TRA. Moreover, the equivalence of cycle extraction results between the FFRA and the FRA is proved mathematically by utilizing some fundamental properties of the rainflow algorithm. Theoretical proof of the efficiency improvement of the FFRA in comparison to the FRA is also given.Originality/value This merit makes the FFRA preferable in online monitoring systems of structures where fatigue life estimation needs to be accomplished online based on massive measured data. It is noticeable that the high efficiency of the FFRA attributed to the simple loop iteration, which provides beneficial guidance to improve the efficiency of existing algorithms.

Решение оптимизационной задачи оценивания моделей полносвязной линейной регрессии

<p>This article is devoted to the problem of estimating fully connected linear regression models using the maximum likelihood method. Previously, a special numerical method was developed for this purpose, based on solving a nonlinear system using the method of simple iterations. At the same time, the issues of choosing initial approximations and fulfilling sufficient conditions for convergence were not studied. This article proposes a new method for solving the optimization problem of estimating fully connected regressions, similar to the method of estimating orthogonal regressions. It has been proven that, with equal error variances of interconnected variables, estimates of b-parameters of fully connected regression are equal to the components of the eigenvector corresponding to the smallest eigenvalue of the inverse covariance matrix. And if the ratios of the error variances of the variables are equal to the ratios of the variances of the variables, then the b-parameter estimates are equal to the components of the eigenvector corresponding to the smallest eigenvalue of the inverse correlation matrix, multiplied by the specific ratios of the standard deviations of the variables. A numerical experiment was carried out to confirm the correctness of the developed mathematical apparatus. The proposed method for solving the optimization problem of estimating fully connected regressions can be effectively used when solving problems of constructing multiple fully connected linear regressions.</p>

On the External Estimation of Reachable and Null-Controllable Limit Sets for Linear Discrete-Time Systems with a Summary Constraint on the Scalar Control

The problem of constructing reachable and null-controllable sets for stationary linear discrete-time systems with a summary constraint on the scalar control is considered. For the case of quadratic constraints and a diagonalizable matrix of the system, these sets are built explicitly in the form of ellipsoids. In the general case, the limit reachable and null-controllable sets are represented as fixed points of a contraction mapping in the metric space of compact sets. On the basis of the method of simple iteration, a convergent procedure for constructing their external estimates with an indication of the a priori approximation error is proposed. Examples are given.

A Block Hybrid Method with Equally Spaced Grid Points for Third-Order Initial Value Problems

In this paper, we extend the block hybrid method with equally spaced intra-step points to solve linear and nonlinear third-order initial value problems. The proposed block hybrid method uses a simple iteration scheme to linearize the equations. Numerical experimentation demonstrates that equally spaced grid points for the block hybrid method enhance its speed of convergence and accuracy compared to other conventional block hybrid methods in the literature. This improvement is attributed to the linearization process, which avoids the use of derivatives. Further, the block hybrid method is consistent, stable, and gives rapid convergence to the solutions. We show that the simple iteration method, when combined with the block hybrid method, exhibits impressive convergence characteristics while preserving computational efficiency. In this study, we also implement the proposed method to solve the nonlinear Jerk equation, producing comparable results with other methods used in the literature.

A fresh look at the nested soft-collinear subtraction scheme: NNLO QCD corrections to N-gluon final states in qq¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ q\\overline{q} $$\\end{document} annihilation

We describe how the nested soft-collinear subtraction scheme [1] can be used to compute the next-to-next-to-leading order (NNLO) QCD corrections to the production of an arbitrary number of gluonic jets in hadron collisions. We show that the infrared subtraction terms can be combined into recurring structures that in many cases are simple iterations of those terms known from next-to-leading order. The way that these recurring structures are identified and computed is fairly general, and can be applied to any partonic process. As an example, we explicitly demonstrate the cancellation of all singularities in the fully-differential cross section for the qq¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ q\\overline{q} $$\\end{document} → X + Ng process at NNLO in QCD. The finite remainder of the NNLO QCD contribution, which arises upon cancellation of all ϵ-poles, is expressed via relatively simple formulas, which can be implemented in a numerical code in a straightforward way. Our approach can be extended to describe arbitrary processes at NNLO in QCD; the largest remaining challenge at this point is the combinatorics of quark and gluon collinear limits.

Studi kasus: Analisis kriteria konvergensi iterasi sederhana berdasarkan tebakan awal

The simple iteration material in the numerical methods course is material related to functions and derivatives. Apart from this, simple iteration material requires one or two initial guesses that do not require bracketing the roots. This method will produce a root approximation as a solution, which will show convergent or divergent results. The convergence criteria are influenced by the derived results and the initial guesses provided. Because of this, this research aims to analyze the results of student answers to prove the convergence criteria of a given simple iterative problem. The method used in this research is a case study, analyzing the results of the answers of five randomly selected students studying numerical methods courses. Based on the results of the analysis of the convergence criteria based on initial guesses, it was concluded that only 5 students could prove the convergence criteria correctly. In general, students made mistakes in deriving algebraic functions, carried out division operations, and incorrectly determined the convergence criteria because they only proved the possibility of the function. given so that students only focus on convergence criteria without carrying out iterative analysis.

Programa de aplicação para resolver sistemas de equações não lineares

Introduction: Application programs in mathematics have had a significant impact on solving nonlinear systems of equations and are impacting various areas. In a nonlinear equation, it is not always easy to determine its root or convergence point; one must analyze and restrict the behavior of the functions that comprise it. Objective: To develop a mathematical program to solve nonlinear systems of equations, selecting the most efficient method and presenting results that include the analysis of convergence and stability of the implemented iterative methods. Method: To solve the system of type V(X)=0, methods such as Simple Iteration, Gradient, Newton, Modified Newton, and Quasi-Newton were used. Visual C++ 6.0 programming language along with Matlab 6.5 libraries were used for the development of the application program for mathematical notations. Results: An application program named SMENLI (Mathematical Software for solving Nonlinear Equations) was developed, which implemented various iterative methods to solve 20 systems of nonlinear equations. Of these, 15 converged and 5 diverged. Some did not converge due to the initial point provided to the program, which utilizes a lexical analyzer. Additionally, it is important to remember that not all systems of nonlinear equations have a solution. Conclusions: It was found that the Newton and Modified Newton methods are the most efficient in terms of convergence, standing out for their shorter time and fewer iterations compared to other implemented methods. However, in exceptional cases with certain systems of nonlinear equations, the Quasi-Newton method may prove superior to others.

AN EFFICIENT ALGORITHM FOR THE NUMERICAL SOLUTION OF A THREE-DIMENSIONAL THERMAL CONDUCTIVITY ISSUE

A mathematical model of slab heating based on a numerical solution of a three-dimensional thermal conductivity problem has been created and programmatically implemented in the work. To solve a system of difference equations, a layer-by-layer method is proposed that allows using the run-through method to solve a system of difference equations of a three-dimensional problem within a rapidly converging iterative procedure. Comparative calculations of slab heating are carried out using the proposed layer-by-layer method and the method of simple iteration with different degrees of grinding of the spatial grid. As a result, it was found that with the grinding of the mesh, the effectiveness of the layered method in relation to the simple iteration method increases.

Generation a solution to the equations of elasticity theory for a layered strip basing on the principle of compressed mappings

A systematic presentation of the modified classical semi-inverse SaintVenant method as an iterative one is given on the example of generating a solution to the differential equations of elasticity theory for a long layered strip. The firstorder differential equations of the plane problem are reduced to the dimensionless form and replaced by integral equations with respect to the transverse coordinate, just as it is done in the Picard method of simple iterations. In this case, a small parameter appears in the integral equations before the integral sign as a multiplying factor, which is used to ensure convergence of solutions in accordance with the Banach’s principle of compressed mappings. The equations and elasticity relations are converted to a form that enables to calculate the unknowns consecutively, so that the unknowns being calculated in one equation are the inputs for the next equation, and etc. Fulfillment of the boundary conditions at the long edges leads to ordinary differential equations for slowly and rapidly changing singular components of the solution with sixteen effective stiffness coefficients that are defined by integrals from the given ones as a stepped function of Young's moduli for each layer. Integrating of these ordinary differential equations makes it possible to obtain the formulas for all the required unknowns of the problem, including transverse stresses that are not defined in the classical theory of the beam and solutions of the edge effect type, and to fulfill all the boundary conditions for the elasticity theory problem. The solution of three boundary value problems of the strip elasticity theory is provided such as for a two-layer strip with layers of the same thickness and different thicknesses, and a strip with an arbitrary number of layers. Formulas for all unknowns of the problem are obtained.

Magnetic feature and regression analysis of Reiner-Philippoff boundary layer flow

The design and optimization of magnetic fluid-based processes, such as magnetohydrodynamic power generation and magnetic drug targeting, have become significant in recent times. To understand the magnetic and radiation features, as well as the sensitivity of engineering physical quantities to each dimensionless parameter in fluid flow, the Reiner-Philippoff (RP) fluid is best suited in this instance, as it exhibits shear-thickening, shear-thinning, and Newtonian behavior. The non-similar transformation is used to transform the partial differential equations that describe the flow into two-variable differential equations. The transformed dynamical equations are solved numerically using a spectral-based numerical technique; namely, the bivariate simple iteration method (BSIM). The effects of magnetic field strength and radiation parameter on the stretching and shrinking sheets are examined. The investigation reveals that both the magnetic field strength and radiation parameter have a significant impact on the flow behavior and rate of heat transfer. For the radiation parameter R∈[0,0.5], the skin friction coefficient and Nusselt number increase by 22.6% and 5.98%, respectively. Additionally, an 100% increment in Prandtl parameter reduces the Nusselt number by 287.36%. Regression analysis is performed to identify the most significant parameter affecting the engineering quantities. The results show that the Bingham constant, γ, is the only parameter that is not significant on the skin friction coefficient, while all the parameters have significant impact on the Nusselt number. The findings in this study have important implications in the biomedical industry, the design of machines, and the fourth industrial revolution.

Rethinking gender from the ethnographic museum. Introduction to the special issue

The present proposed volume takes as its fulcrum the concept of gender, and in its most simple iteration asks: What happens when, we – that is, the varied individuals and communities who take a vested interest in the collections housed by ethnographic museums – think more deliberately from the objects in our museums? How might we theorize gender in ways that allow us to think our relationships to each other in Povinelli's (2011) ‘otherwise’ ways? Ultimately this volume brings together cutting-edge thinking in gender studies, material culture, and museum practice, centering the lens on the ethnographic as a critical category of analysis that continues to regiment how we organize the very collections in our museums.

A velocity-coefficient independent pressure correction equation for accelerated convergence of linear systems in incompressible flows

A velocity-coefficient independent pressure correction equation is proposed based on a modified SIMPLE algorithm for the solution of incompressible Navier-Stokes equations. In the conventional approach of SIMPLE, the central velocity coefficient of linearized momentum equation updates with every non-linear iteration within a time step. Since the pressure correction equation is coupled to the velocity coefficient term the pressure matrix coefficients obtained from the discretized pressure Poisson’s equation also get updated. As a consequence, the preconditioning step used to accelerate the convergence of pressure linear system becomes computationally expensive as the preconditioner is computed at every SIMPLE iteration. In the proposed approach this difficulty is circumvented wherein the velocity coefficient term in the pressure correction equation is repositioned with the velocity term such that the pressure matrix coefficients no longer depend on the same. Hence the preconditioner is computed only once at the first non-linear iteration that is stored and re-used for the subsequent iterations thereby reducing the overall CPU time of simulation.

Integral Method for Determining the Stress State of an Anisotropic Reinforced Concrete Shell

The article deals with the issue of estimating the strength and stress-strain state of a reinforced concrete shell by the method of membrane theory and the theory of infinitesimal bending. A brief description of the methodology consists in the fact that the ground stress state of the shell is allocated to an independent problem, when, without introducing boundary effects, two of the four boundary conditions of the general moment theory are distinguished, which, together with the equations of the momentless theory, determine the ground stress state, and then boundary effects are superimposed. The equilibrium equations of the moment theory in forces and moments, geometric equations, components of tangential deformation and displacement, and the physical equations of state connecting them, expressing forces and moments through the components of deformation, are presented, since the characteristics of the stress-strain state of the shell depend not only on the variability of external influences and forces, but also on the length of the structure. The provisions laid down in the article shall be retained in the case of casings made of anisotropic material, provided that the presented elastic ratio is met. A system of equations of the generalized semi-membrane (semi-bending) state of an arbitrary shell of zero curvature, which determines the accuracy of this approach, is solved. The equations of the semi-torque theory for a circular cylindrical shell are presented, as well as describing the semi-membrane stress state of a long shell of zero curvature. The most important result of the study is the method of constructing integrals of the ground stress state of the shell based on the method of simple iterations, which expands the possibilities of the reliability theory, which makes it possible to build the foundations for the practical calculation of reinforced concrete shells according to the membrane theory and the theory of infinitesimal bending.

Complex Three-Dimensional Mathematical Model of the Ignition of a Coniferous Tree via a Cloud-to-Ground Lightning Discharge: Electrophysical, Thermophysical and Physico-Chemical Processes

Thunderstorms are the main natural source of forest fires. The ignition mechanism of trees begins with the impact of cloud-to-ground lightning discharge. A common drawback of all predicting systems is that they ignore the physical mechanism of forest fire as a result of thunderstorm activity. The purpose of this article is to develop a physically based mathematical model for the ignition of a coniferous tree via cloud-to-ground lightning discharge, taking into account thermophysical, electrophysical, and physicochemical processes. The novelty of the article is explained by the development of an improved mathematical model for the ignition of coniferous trees via cloud-to-ground lightning discharge, taking into account the processes of soot formation caused by the thermal decomposition phase of dry organic matter. Mathematically, the process of tree ignition is described by a system of non-stationary nonlinear differential equations of heat conduction and diffusion. In this research, a locally one-dimensional method is used to solve three-dimensional partial differential equations. The finite difference method is used to solve one-dimensional heat conduction and diffusion equations. Difference analogues of the equations are solved using the marching method. To resolve nonlinearity, a simple iteration method is used. Temperature distributions in a structurally inhomogeneous trunk of a coniferous tree, as well as distributions of volume fractions of phases and concentrations of gas mixture components, are obtained. The conditions for tree trunk ignition under conditions of thunderstorm activity are determined. As a result, a complex three-dimensional mathematical model is developed, which makes it possible to identify the conditions for the ignition of a coniferous tree trunk via cloud-to-ground lightning discharge.

A Readily Achieved Potentiostatic Method in Density Functional Theory Calculation for Improved Prediction of the Performance for Electrocatalytic Nitrogen Reduction Reaction.

Accurate prediction of the catalytic performance of nitrogen reduction reaction catalysts based on density functional theory (DFT) calculation is of great significance for developing catalytic materials for nitrogen fixation. However, the applied electrode potential induced the fixation of Fermi level and solvation effect are commonly ignored in the current computational hydrogen electrode method, which leads to the large deviation between the calculation predicted limit potential and the experimentally measured limit potential. In this work, the simple external iteration method is proposed to simulate the Fermi level of the catalysts that are fixed by the applied electrode potential, along with the hybrid solvent model to describe the strong interaction, such as hydrogen bond, between the solvent molecules and the intermediates. This method allowed the theoretical and experimental limit potentials to be in good agreement, indicating the significant effect of the electrode potential and solvation in the DFT calculation. These results will guide the calculation-based prediction of other reaction systems in the field of electrocatalysis.

An Adaptive Two-Grid Solver for DPG Formulation of Compressible Navier–Stokes Equations in 3D

Abstract We present an overlapping domain decomposition iterative solver for linear systems resulting from the discretization of compressible viscous flows with the Discontinuous Petrov–Galerkin (DPG) method in three dimensions. It is a two-grid solver utilizing the solution on the auxiliary coarse grid and the standard block-Jacobi iteration on patches of elements defined by supports of the coarse mesh base shape functions. The simple iteration defined in this way is used as a preconditioner for the conjugate gradient procedure. Theoretical analysis indicates that the condition number of the preconditioned system should be independent of the actual finite element mesh and the auxiliary coarse mesh, provided that they are quasiuniform. Numerical tests confirm this result. Moreover, they show that presence of strongly flattened or elongated elements does not slow the convergence. The finite element mesh is subject to adaptivity, i.e. dividing the elements with large errors until a required accuracy is reached. The auxiliary coarse mesh is adjusting to the nonuniform actual mesh.

Optimal polynomial smoothers for multigrid V‐cycles

AbstractThe idea of using polynomial methods to improve simple smoother iterations within a multigrid method for a symmetric positive definite system is revisited. A two‐level bound going back to Hackbusch is optimized by a very simple iteration, a close cousin of the Chebyshev semi‐iterative method, but based on the Chebyshev polynomials of the fourth instead of first kind. A full V‐cycle bound for general polynomial smoothers is derived using the V‐cycle theory of McCormick. The fourth‐kind Chebyshev iteration is quasi‐optimal for the V‐cycle bound. The optimal polynomials for the V‐cycle bound can be found numerically, achieving about an 18% lower error contraction factor bound than the fourth‐kind Chebyshev iteration, asymptotically as the number of smoothing steps . Implementation of the optimized iteration is discussed, and the performance of the polynomial smoothers is illustrated with numerical examples.