Incorporating intermediate outputs into SFA using an equation system approach with application to transport

In this paper, we investigate how the sparsity of non-separable quadratic programming (QP) problems behaves in interior point methods. The target of our investigation is to compare the separable equivalent of QPs with the normal equation (NOR) and augmented system (AUG) approach on the non-separable form. We show that one can easily attribute the sparsity issues of non-separable QP problems to that of linear programming for which well-developed techniques are available. We describe how the structural properties of non-separable QP problems can be represented by a single matrix whose sparsity pattern can serve to determine a fill-reducing row permutation. We show that the heuristics developed for linear programming can be used for determining which of the AUG and NOR approaches is more advantageous. Numerical results are given on publicly available non-separable convex QP problems.

In the development of phytoremediation this method can be simulated quite concisely and precisely. Simulations are carried out to predict plant behavior towards several different treatments, for example plant species, also types and concentrations of contaminants. In this study a dynamic model of phytoremediation has been made using sunflower plants and 134Cs and 60Co radionuclides. This study was developed by mimicking the interaction of soil and plants to be simulated into Phytoremediation Dynamic Model (PDM). Diverse mathematical algorithms implemented to characterize phytoremediation, systems such as differential equation, statistical correlation, and dynamic system approach. The error value obtained is different for each contaminant for each variation in concentration, which ranges from 0,0006-0,6349 for 134Cs contaminants and 0,0089-0,4157 for 60Co contaminants. The error value is quite small, and the overall simulation data has approached the experimental data. Factors that influence the results of calculated data include saturation point values, as well as the absorption rate of each part of the plant obtained from calculations and estimates. This model has proven to be able to mimic plant responses to contaminants

The nonlinear equation system approach to solving dynamic user optimal simultaneous route and departure time choice problems

In dynamic stochastic user equilibrium simultaneous route and departure time choice (DSUE-SRDTC) problems, route travel costs can be non-monotone even if route travel times are monotone with respect to route flows. As a result, the mapping function of the variational inequality (VI) problems for the DSUE-SRDTC problems can be non-monotone, and many existing solution algorithms developed for the DSUE-SRDTC problems do not guarantee convergence under this non-monotone condition. This paper formulates the DSUE-SRDTC problem with fixed demand as a system of nonlinear equations. The mapping function of the proposed system of nonlinear equations is defined by a dynamic route choice problem, which can also be formulated as a VI problem with a strictly monotone mapping function under some assumptions. This property enables that the solution algorithm for the DSUE-SRDTC problem can avoid the requirement of the monotonicity of the route travel cost functions for the convergence of the solution procedure. A backtracking inexact Broyden–Fletcher–Goldfarb–Shanno (BFGS) method is adopted to solve the system of nonlinear equations, and iterative methods are developed to generate an initial solution for the BFGS method and solve the dynamic route choice problem. Finally, numerical examples are set up to show that the proposed method outperforms many existing algorithms for solving the DSUE-SRDTC problem in terms of guaranteeing solution convergence.

This study tests the hypothesis that institutional changes in the EC (introduction of CAP, enlargements by Denmark, Ireland, UK and Greece) caused structural changes in its import demand for soybeans. It used a simultaneous equation system approach to estimate EC's soybean import demand. A switching regression was used to identify structural changes from 1964 to 1983. It was found that structural changes occurred in 1977/1978 period. No structural shifts were found to have been caused by institutional changes.

Investigation Interaction between Exchange Rate and Stock Market in Iran: A Simultaneous Equation System Approach

Simulation of coupled chemical reactions and fluid flow in porous sedimentary basins over long time periods is a numerical challenge. Most models representing such a physical problem are solved as PDEs where efficient timestepping with controlled error is difficult. We use the differential algebraic equation system approach where robust adaptive timestepping algorithms are available in the solvers, e.g., RADAU5 and DASSL. Mathematical and numerical models for coupled chemical reactions and fluid flow are derived. The models have several interesting properties, e.g., strong nonlinearities and stiffness, which are discussed. We test the performance of our code.

Although the relationship between renewable energy and economic performance has attracted the interest of researchers in recent years, most of the analysis has focused on economic growth, which does not reflect the quality of standards of living. We employ a different approach measuring the impact of renewable energy consumption on the Human Development Index, which also considers qualitative characteristics. Using a simultaneous equation system approach that describes the interrelations between economic variables, renewable energy and pollution emissions with feedback effects, we provide robust evidence for a set of 28 OECD countries over the period 2004-2015, that renewable energy, human and physical capital are important factors for explaining the degree of sustainable development. Renewable energy consumption is mostly determined by higher levels of human capital, R&D, and the countries’ development stage. Furthermore, the development level, total energy consumption, and the education level are important for explaining environmental pollution.

To enhance the bridge between macroscopic and symbolic representations in chemistry, we crafted a laboratory module focusing on a three-equation system for chemical composition analysis. Students assess the composition of copper, tin, and aluminum alloys by measuring two properties: density and heat capacity. These non-destructive procedures fit within standard laboratory session durations. After gathering data, students tackle three linear equations linking element mass ratio to alloy composition, density, and heat capacity. By pooling data from various samples, the class achieves a comprehensive understanding. This method aligns with objectives for laboratory education, emphasizing scientific reasoning, practical skills, and subject mastery. Students’ results deviated by +/-10% from actual alloy compositions. The discussion of student-gathered data and results supports the feasibility of the laboratory experience for its implementation in introductory chemistry laboratories.

The primary excited state processes of phytochrome, the plant chromoprotein responsible for most photomorphogenetic responses, are investigated by picosecond intensity‐dependent transmission measurements. At sufficient high excitation intensity (starting at photon flux densities of about 1′1025 cm−2 s−l) a moderate bleaching of the absorption is observed. For the quantitative analysis of the experimental data a rate equation system approach for the energy levels responsible for the ultrafast transformation Pr→ lumi‐R and the photon transport through the sample was utilized. The following was found for the excited state parameters of the phytochrome Pr: (1) an excited state absorption of the same order of magnitude as the ground state absorption (cross section: S̀exc= 4′10−16 cm−2 at 650 nm), (2) a fast relaxation of the higher excited singlet state on the femtosecond time scale.

This paper examines the performance of three different approaches in estimating the firm parameters of structure models by simulation, including the simultaneous equation system approach, maximum likelihood estimation approach and the iteration approach. The simulation results show that iteration approach has smaller estimation errors than the other two approaches and thus performs the best.

This work uses a simultaneous equation system approach to analyze the relationship between the management and business quality of companies and their market price quality. Using panel data we found that both the management and the business quality of companies positively influence the market price quality of the studied American companies. Additionally, variables like the actual position of the company price quality compared to the industry average, being on the top or the bottom, or the beta value of a company, also influence the market price quality of the respective company. It is shown that the system equation approach is the most appropriate to explain the linkages between price, business, and management quality providing consistent estimates. Also, using ratings to express the three core variables in the system is the most adequate way to define the quality characteristics in terms of price, management, and business performance of the companies considered in this study.

Changing household characteristics and the away-from-home food market: a censored equation system approach

<div class="section abstract"><div class="htmlview paragraph">The aim of this paper is the study of the Centrifugal Pendulum Vibration Absorber (CPVA) dynamic behavior, with the background of improved vibration isolation and damping quality through a wide range of operating speeds.</div><div class="htmlview paragraph">The CPVAs are passive devices, which are used in rotating machinery to reduce the torsional vibration without decreasing performance. After a first use of these damping systems in the field of aeronautics, nowadays CPVAs are employed also in railway and automotive applications.</div><div class="htmlview paragraph">In principle, the CPVA is a mass, mounted on a rotor, which moves along a defined path relative to the rotor itself, driven by centrifugal effects and by the rotor's torsional vibrations.</div><div class="htmlview paragraph">The advantage that such absorbers provide is the capability to counteract torsional vibrations arising with frequencies proportional to the mean operating speed. This is in particular the case with Internal Combustion Engines (ICE) where the induced vibrations are caused by the combustions process.</div><div class="htmlview paragraph">The above-mentioned feature is obtained thanks to the tuning of the absorber on the specific ICE vibration order, obtained by means of its geometric characteristics.</div><div class="htmlview paragraph">The main goal of this work is to model and simulate different types of CPVAs, where simple vibration models can be implemented for first investigations. Special attention has been given to CPVAs modelled with circular, cycloidal and epicycloidal paths, using a general-path equation system approach. The CPVA unit performance has been analyzed by means of an n<sup>th</sup> order sine-signal torque.</div><div class="htmlview paragraph">In this simulation environment, the paper aims to highlight the capabilities of absorbing vibrations of CVPAs, emphasizing the configurations with cycloidal and epicycloidal paths where the vibrations of the designated order can be reduced to a level very close to zero, for a major part of the ICE speed range.</div><div class="htmlview paragraph">Furthermore the present work provides a simulation approach as basis for CPVA parameters optimization.</div></div>

Fundamental solutions to Helmholtz's equation for inhomogeneous media by a first-order differential equation system