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The linear programming method is one of the important methods of operations research that has been used to address many practical issues and provided optimal solutions for many institutions and companies, which helped decision makers make ideal decisions through which companies and institutions achieved maximum profit, but these solutions remain ideal and appropriate in If the conditions surrounding the work environment are stable, because any change in the data provided will affect the optimal solution and to avoid losses and achieve maximum profit, we have, in previous research, reformulated the linear models using the concepts of neutrosophic science, the science that takes into account the instability of conditions and fluctuations in the work environment and leaves nothing to chance. While taking data, neutrosophic values carry some indeterminacy, giving a margin of freedom to decision makers. In another research, we reformulated one of the most important methods used to solve linear models, which is the simplex method, using the concepts of this science, and as a continuation of what we did in the previous two researches, we will reformulate in this research. The graphical method for solving linear models using the concepts of neutrosophics. We will also shed light on a case that is rarely mentioned in most operations research references, which is that when the difference between the number of unknowns and the number of constraints is equal to one, two, or three, we can also find the optimal solution graphically for some linear models. This is done by taking advantage of the conditions of non-negativity that linear models have, and we will explain this through an example in which the difference is equal to two. Also, through examples, we will explain the difference between using classical values and neutrosophic values and the extent of this’s impact on the optimal solution.

Abstract A Mueller matrix covers all the polarization information of the measured sample, however the combination of its 16 elements is sometimes not intuitive enough to describe and identify the key characteristics of polarization changes. Within the Poincaré sphere system, this study achieves a spatial representation of the Mueller matrix: the Global-Polarization Stokes Ellipsoid (GPSE). With the help of Monte Carlo simulations combined with anisotropic tissue models, three basic characteristic parameters of GPSE are proposed and explained, where the V parameter represents polarization maintenance ability, and the E and D † parameters represent the degree of anisotropy. Furthermore, based on GPSE system, a dynamic analysis of skeletal muscle dehydration process demonstrates the monitoring effect of GPSE from an application perspective, while confirming its robustness and accuracy.

One of the main reasons for the decline of urban historic areas in China is the co-existence of multiple property rights. It also deeply affects conservation and regeneration practice. This paper aims to propose a graphical method that illustrates the association between property rights, space, and resident behavior. Based on typological maps and justified graphs, a three-step method was proposed to visualize the relationships between these three elements. The final graph and quantitative data were used to observe the evolution of the courtyard building from a diachronic perspective, as well as to compare the residential behavior in different types from a synchronic perspective. The results show that following the subdivision of property rights, the building layout become more diverse due to various illegal additions, while the residential behavior within different building types tends to be consistent. Moreover, the study observed the traditional Chinese courtyard buildings’ adaptability. The findings contribute to understand the evolution of Chinese urban historic areas and internal motivation, and provide guidance for the conservation and regeneration practice.

This study investigated the role of mobile applications as aids in solving systems of linear equations with two variables through the graphical method. The use of mobile applications was examined in a group of primary and lower school students to evaluate their effectiveness in learning mathematics and improving their skills in solving systems of linear equations. The main goal of this scientific paper is to investigate and evaluate the role of mobile applications as aids in solving systems of linear equations, involving students in the research process. The research method included a mixed-methods design including quantitative analysis of mobile application results and qualitative analysis of students' experiences and opinions. Data collection was conducted through individual interviews and classroom observations. The results show that the use of these technological tools has a positive impact on the involvement of students, increasing the interest and efficiency of learning. The findings also highlight challenges and suggestions for improving the use of mobile applications in the mathematics teaching context. This study contributes to the understanding of the use of mobile technology for the development of mathematical skills at the lower secondary school level. [ABSTRACT FROM AUTHOR]

A Mueller matrix covers all the polarization information of the measured sample, however the combination of its 16 elements is sometimes not intuitive enough to describe and identify the key characteristics of polarization changes. Within the Poincaré sphere system, this study achieves a spatial representation of the Mueller matrix: the Global-Polarization Stokes Ellipsoid (GPSE). With the help of Monte Carlo simulations combined with anisotropic tissue models, three basic characteristic parameters of GPSE are proposed and explained, where the V parameter represents polarization maintenance ability, and the E and D † parameters represent the degree of anisotropy. Furthermore, based on GPSE system, a dynamic analysis of skeletal muscle dehydration process demonstrates the monitoring effect of GPSE from an application perspective, while confirming its robustness and accuracy., (© 2024. The Author(s).)

We describe a simple yet rigorous graphical method for eliminating bias in theory-based program evaluation. The method is an application to social and international development program evaluation of the graphical causal models used to test medical treatments. We implement a graphical causal model for the World Bank's well-known Bangladesh Integrated Nutrition Project. We show how to construct the graphical causal model to represent program theory in context in explicitly causal terms. We then show how to visually inspect the graphical causal model to distinguish causal from non-causal associations between variables in evaluation data. Finally, we show how to select a set of adjustment variables to neutralize non-causal associations, eliminating bias in all forms of causal inference—qualitative and quantitative, linear and non-linear. [ABSTRACT FROM AUTHOR]

This study presents a method for finite element (FE) simulation of a deep drawing process of a cold-rolled carbon steel (SPCC) sheet material based on the graphical method. First, uniaxial tensile specimens were prepared and experimental tests were conducted to determine the flow stress curves. The calculation of the fracture points at special strain modes (plane strain, uniaxial tensile strain, and biaxial tensile strain) was presented using the modified maximum force criterion (MMFC). After that, the graphical method was adopted for the estimation of the forming limit curve (FLC) based on several hardening laws. FE models for a deep drawing process of the SPCC sheet were then built using the calculated FLCs. Using FE simulations, the fracture heights of cylinder cups formed by the deep drawing process were finally determined and compared with those from experiments. The results showed a good agreement between simulated and measured fracture height with a maximum of 3.6 % deviation. Additionally, simulations and corresponding experiments were performed to investigate the effects of the blank holder force, punch corner radius, and drawing ratio on the fracture height of cylinder cups.

This study presents an improvement of the graphical method for plotting the shear and moment diagrams for the structural members under linearly varying loads (triangular and trapezoidal loads). Based on the parabolic nature of the shear function, when the loading varies linearly, and on the relations among load, shear, and moment, a mathematical equation is developed to locate the zero-shear point, while a geometric technique is presented to calculate the parabolic shear area. Five comprehensive examples of beams loaded with linearly varying loads are selected to illustrate the steps of the solution for the proposed techniques. The results demonstrated the applicability of the presented method, and gave exact diagrams compared with the basic graphical method. It is concluded that the proposed improved method is generally more convenient, less time-consuming, and has less computational efforts because it does not require sectioning, solving equilibrium equations, and quadratic formulas compared with the basic graphical method.

This paper focuses on robustly stabilizing stable and unstable fractional-order plants with one uncertain fractional-order term and interval uncertainties using fractional order $ PI^{\mu }D^{\lambda } $ PIμDλ controllers. Two necessary and sufficient conditions are provided to check the robust stability of the closed-loop control system. Moreover, the D-decomposition technique is utilized to determine the robust stability region of the system. Subsequently, evolutionary algorithms, such as the Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Differential Evolution (DE), can be utilized to discover a fractional-order controller within the region of robust stability. This work introduces three primary contributions, outlined as follows: (1) Utilizing a graphical approach, a set of stabilizing controller is obtained. (2) Rather than employing just a single stabilizing fractional-order controller, a collection of controllers is provided for the control system. (3) Employing evolutionary algorithms to find an optimal fractional-order controller. Finally, four numerical examples are presented to validate the results. [ABSTRACT FROM AUTHOR]

The linear programming method is one of the important methods of operations research that has been used to address many practical issues and provided optimal solutions for many institutions and companies, which helped decision makers make ideal decisions through which companies and institutions achieved maximum profit, but these solutions remain ideal and appropriate in If the conditions surrounding the work environment are stable, because any change in the data provided will affect the optimal solution and to avoid losses and achieve maximum profit, we have, in previous research, reformulated the linear models using the concepts of neutrosophic science, the science that takes into account the instability of conditions and fluctuations in the work environment and leaves nothing to chance. While taking data, neutrosophic values carry some indeterminacy, giving a margin of freedom to decision makers. In another research, we reformulated one of the most important methods used to solve linear models, which is the simplex method, using the concepts of this science, and as a continuation of what we did in the previous two researches, we will reformulate in this research. The graphical method for solving linear models using the concepts of neutrosophics. We will also shed light on a case that is rarely mentioned in most operations research references, which is that when the difference between the number of unknowns and the number of constraints is equal to one, two, or three, we can also find the optimal solution graphically for some linear models. This is done by taking advantage of the conditions of non-negativity that linear models have, and we will explain this through an example in which the difference is equal to two. Also, through examples, we will explain the difference between using classical values and neutrosophic values and the extent of this’s impact on the optimal solution. [ABSTRACT FROM AUTHOR]

Item response theory (IRT) is a statistical paradigm for developing educational tests and assessing students. IRT, however, currently lacks an established graphical method for examining model fit for the three-parameter logistic model, the most flexible and popular IRT model in educational testing. A method is presented here to do this. The graph, which is referred to herein as a "bin plot," is the IRT equivalent of a scatterplot for linear regression. Bin plots display a conventional IRT trace line (with ability on the horizontal axis and probability correct on the vertical axis). Students are binned according to how well they performed on the entire test, and the proportion of students in each bin who answered the focal question correctly is displayed on the graph as points above or below the trace line. With this arrangement, the difference between each point and the trace line is the residual for the bin. Confidence intervals can be added to the observed proportions in order to display uncertainty. Computer simulations were used to test four alternative ways for binning students. These simulations showed that binning students according to number of questions they answered correctly on the entire test works best. Simulations also showed confidence intervals for bin plots had coverage probabilities close to nominal values for common testing scenarios, but that there are scenarios in which confidence intervals had inflated error rates.

The main purpose of this paper is to propose a new graphical method for a planetary gear train (PGT) analysis. This is a fully graphical method that determines the rotational speeds of all transmission components, as well as the torque, power flow, power losses, and efficiency of any PGT. With this method, a sketcher workbench available in any modern computer-aided design (CAD) system can be used. This provides an interactive way to work. Both the construction of the geometric model and the interpretation of the results are intuitive, which facilitates error identification. Observing the impact of the selected input data or model parameters on the model behavior is extremely easy and can even be animated. It is believed that the presented method can streamline the PGT design process.