Solution Method Research Articles

AuBr3 Induces CsPb(Br/I)3 QDs to Self-Assemble into Nanowires.

Perovskite quantum dots can form various forms such as nanowires, nanorods, and nanosheets through self-assembly. Nanoscale self-assembly can be used to fabricate materials with excellent device properties. This study introduces AuBr3 into CsPb(Br/I)3 quantum dots, causing them to assemble into nanowires. The nanowires form because part of Au3+ is surface-doped to replace Pb2+, and the [PbX6]4- octahedral structure is distorted. The symmetry of the structural surface is broken, and a dipole-moment-induced field is generated, thus promoting self-assembly. Moreover, the presence of Au nanoparticles (NPs) causes a localized surface plasmon resonance and generates strong van der Waals forces that promote self-assembly. Finally, to test other applications of perovskite nanowires, the solution method is used to prepare films by compounding the sample solution and polystyrene (PS) for backlighted displays.

Novel design and motion analysis of an omni-tread snake-like robot for narrow space inspection

Snake-like robots have a slender body and strong environmental adaptability. This paper aims to propose an omni-tread snake-like robot that can adapt to the needs of specific narrow space exploration missions and provide a basis for design work through necessary motion analysis. The robot adopts the form of three modules in series, and the modules are connected through differential driving joints, which increases the joint torque of the robot. The nested omni-tread structure improves the robot's motion efficiency and environmental adaptability. This paper conducts configuration and motion analysis of the robot. The simulation is performed using the optimization solution method to obtain the joint torque and walking torque of the robot, which guides the design of the robot. The experiment is also conducted with the developed prototype to verify the robot's performance. From the simulation results, the joint torque and walking torque are obtained, and the motors are selected. The motion performance and field applicability of the robot are verified through experiment tests. The experiment results further verify the robot design and analysis work. The structural design of robots and optimization solution method in this paper has certain reference values for other researchers.

Unveiling Afghanistan's wind and hydrogen potential: a comparative study.

Given the detrimental environmental impacts of fossil fuels, there is a gradual worldwide shift towards renewable energy sources. Wind power, renowned for its cost-effectiveness and simplicity, has been widely embraced. Despite Afghanistan facing significant challenges in its energy sector, its considerable wind energy potential offers a chance to mitigate some of these issues. This study employed a multi-criteria decision-making approach to evaluate potential wind-hydrogen project sites in Afghanistan, encompassing economic, technical, social, risk, and environmental considerations. Five criteria and sub-criteria for wind-hydrogen project implementation were analyzed using the Step-wise Weight Assessment Ratio Analysis (SWARA) method. The Weighted Aggregated Sum Product Assessment (WASPAS), Additive Ratio Assessment (ARAS), Evaluation based on Distance from Average Solution (EDAS), and Technique of Order Preference Similarity to the Ideal Solution (TOPSIS) methods were then applied to prioritize provinces for wind-hydrogen project implementation. The analysis found that the Duration of the Payback Period and Levelized Cost of Electricity (LCOE) with weight of 6.6% and 5.6% were critical sub-criteria. Farah, Herat, and Nimroz emerged as Afghanistan's most promising provinces for wind-hydrogen energy development. In Farah, utilizing 900-kW turbines, it is feasible to generate 2679.8 MWh of electricity and produce 43.4 tons of hydrogen annually, with a Levelized Cost of Electricity of 0.0690 $/kWh and Levelized Cost of Hydrogen of 1.747 $/kg.

Collaborative Fabrication of High-Quality Perovskite Films for Efficient Solar Modules through Solvent Engineering and Vacuum Flash System.

The vacuum flash solution method has gained widespread recognition in the preparation of perovskite thin films, laying the foundation for the industrialization of perovskite solar cells. However, the low volatility of dimethyl sulfoxide and its weak interaction with formamidine-based perovskites significantly hinder the preparation of cell modules and the further improvement of photovoltaic performance. In this study, we describe an efficient and reproducible method for preparing large-scale, highly uniform formamidinium lead triiodide (FAPbI3) perovskite films. This is achieved by accelerating the vacuum flash rate and leveraging the complex synergism. Specifically, we designed a dual pump system to accelerate the depressurization rate of the vacuum system and compared the quality of perovskite film formed at different depressurization rates. Further, to overcome the limitations posed by DMSO, we substituted N-methylpyrrolidone as the ligand solvent, creating a stable intermediate complex phase. After annealing, it can be transformed into a uniform and pinhole-free FAPbI3 film. Due to the superior quality of these films, the large area perovskite solar module achieved a power conversion efficiency of 22.7% with an active area of 21.4 cm2. Additionally, it obtained an official certified efficiency of 22.1% with an aperture area of 22 cm2, and it demonstrated long-term stability.

Target Damage Calculation Method of Nash Equilibrium Solution Based on Particle Swarm between Projectile and Target Confrontation Game

In order to scientifically evaluate the target damage effect of uncertain intersection between projectile and target confrontation game, this paper establishes a basic model of target damage in the intersection between projectile and target game, which is through the spatial relationship between the explosive position of the projectile and the target position and gives a calculation method of target damage evaluation. The study applies Nash equilibrium theory to analyze income-loss functions in an adversarial game model. According to the definition of the possibility degree of interval number in uncertain multi-attribute decision-making, we proposed a method of solving the Nash equilibrium value of the income matrix of both sides of the game, which is using the interval possibility degree. We used quantitative calculations to analyze game strategies and changes in target damage under different states, such as fragment numbers, velocities, and angles of hit in the confrontation game between projectile and target. Based on the Nash equilibrium value solution method of the particle swarm optimization algorithm, we quantitatively calculated the fitness change relationship between the projectile and the target under different strategy sets. Based on the actual projectile confrontation game test, we analyze the damage probability effects of two projectiles at different explosion positions and different rendezvous angle angles on the three cabins. The results show that in the same area, the intersection angle is smaller, the probability of target damage is greater, and the intersection distance is farther, the damage probability is smaller.

Enhanced resilience in urban stormwater management through model predictive control and optimal layout schemes under extreme rainfall events

Optimizing the layout of urban stormwater management systems is an effective method for mitigating the risk of urban flooding under extreme storms. However, traditional approaches that consider only economic costs or annual runoff control rates cannot dynamically respond to the uncertainties of extreme weather, making it difficult to completely avoid large accumulations of water and flooding in a short period. This study proposes an integrated method combining system layout optimization and Model Predictive Control(MPC)to enhance the system's resilience and effectiveness in flood control. An optimization framework was initially built to identify optimal system layouts, balancing annual average life cycle cost (AALCC) and resilience index. The MPC was then applied to the optimal layout selected using the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method, aiming to alleviate inundation cost-effectively. The adaptability of MPC to varying sets of control horizons and its efficacy in managing the hydrograph and flood dynamics of urban drainage system were examined. Conducted in Yubei, Chongqing, this study revealed patterns in optimal layout fronts among various extreme design rainfalls, showing that peak position rate and return period significantly influence system resilience. The contribution of MPC to the optimal system layout was particularly notable, resulting in improved instantaneous and overall flood mitigation. The application of MPC increased the resilience index by an average of 0.0485 and offered cost savings of 0.0514 million yuan in AALCC. Besides, our findings highlighted the importance of selecting an optimal set of control horizons for MPC, which could reduce maximum flood depth from 0.43m to 0.19m and decrease conduit peak flow by up to 14% at a flood-prone downstream location.

High-Temperature Resistance of Anchorage System for Carbon Fiber-Reinforced Polymer Composite Cable—A Review

Unidirectional carbon fiber-reinforced polymer (CFRP) may exhibit significant mechanical softening in the transverse direction at an elevated temperature. While significant transverse compressive stress exists on CFRP due to the clamping force from anchorage, a CFRP cable may exhibit anchorage failure when suffering an accidental fire disaster. The high-temperature resistance of a CFRP cable anchorage is critical, and clarifying the performance deterioration and failure mechanism of a CFRP cable anchorage system at elevated temperature is fundamental for clarifying its fire resistance. This paper reviews the current research status of the high-temperature resistance of CFRP cable anchorage systems from two aspects, including the high-temperature resistance of the comprising materials and the anchorage system. The reviews on the high-temperature properties of the comprising materials are summarized from two aspects. Firstly, the mechanical performance degradation of bonding epoxy resin at elevated temperatures and the effect of a filler on its mechanical–thermal properties are analyzed. Secondly, the mechanical performances of CFRP composites at elevated temperatures are summarized, with consideration of the stress state of the CFRP cable under the constraint of an anchorage device. The reviews on the high-temperature resistance of the anchorage system also include two aspects. Firstly, the temperature field solution method for the anchorage system is summarized and discussed. Secondly, the current research status of the anchorage performance at elevated temperatures is also summarized and discussed. Based on these reviews, the research shortage of the high-temperature resistance of CFRP cable anchorage systems is summarized, and further research is recommended.

A simplified SP3 NEM solver within a unified formulation for pin-by-pin core multi-group calculations

This study addresses the development and verification of a pin-by-pin core multigroup SP3 solver CTRP-Clouds that employs NEM (Nodal Expansion Method) and three simplified NEM methods within a unified formulation for simultaneously solving the coupling 0th and 2nd SP3 equations. In this work, the solver using this unified formulation does not only include the original NEM and its simplifications but also the EFEN (Exponential Function Expansion Nodal) method and FDM (Finite Difference Method) for the comprehensive evaluation. Also, the solver was accelerated using CMFD (Coarse Mesh Finite Difference) method and parallelized using OpenMP. The computational efficiency of different solution methods was investigated for the 2D KAIST benchmark problems and their modified one for considering 3D extension. The results showed the simplified NEM with flat leakage approximation gives acceptable accuracies of less than 1.2 % in RMS of pin-power discrepancies of all the cases with 1x1 mesh per pin-cell, with a reduction of 20 % computing time compared to the original NEM. Particularly, the calculation time of flat leakage NEM is comparable to EFEN while the pin-wise accuracy is better. Besides, the simplified NEM with 2nd-order flux expansion gives substantially improved accuracy in comparison with FDM within comparable computing time.

A local meshless method for the numerical solution of multi-term time-fractional generalized Oldroyd-B fluid model

This work presents an accurate and efficient method, for solving a two dimensional time-fractional Oldroyd-B fluid model. The proposed method couples the Laplace transform (LT) with a radial basis functions based local meshless method (LRBFM). The suggested numerical scheme first uses the LT which transform the given equation to an elliptic equation in LT space, and then it utilizes the LRBFM to solve transformed equation in LT space, and then the solution is converted back into the time domain via the improved Talbot's scheme. The local meshless methods are widely recognized for scattered data interpolation and for solving PDEs in complex shaped domains. The adaptability, simplicity, and ease of use are features that have led to the popularity of local meshless methods. The local meshless methods are easy and straightforward, they only requires to solve linear system of equations. The main objective of using the LT is to avoid the computation of costly convolution integral in time-fractional derivative and the effect of time stepping on accuracy and stability of numerical solution. The stability and the convergence of the proposed numerical scheme are discussed. Further, the Ulam-Hyers (UH) stability of the proposed model is discussed. The accuracy and efficiency of the suggested numerical approach have been demonstrated using numerical experiments on five different domains with regular nodes distribution.

Innovative Strategies for Bio-Waste Collection in Major Cities during the COVID-19 Pandemic: A Comprehensive Model for Sustainable Cities—The City of Athens Experience

This paper introduces an innovative model for the organization and management of municipal bio-waste collection networks in major cities, particularly relevant in the context of the COVID-19 pandemic. Embracing circular economy principles and sustainable city practices, the proposed model addresses the urgent need for sustainable urban bio-waste management systems. Delving into the dynamic urban landscape, with a focus on the city of Athens, the study highlights the necessity of a robust decision-making methodology, the implementation of resilient processes, and the evaluation of their efficacy, especially during challenging times. The model centers on the effective collection, transportation, and monitoring of bio-waste, with a strategic aim to moderate environmental impacts, limit greenhouse gas emissions, and advance sustainable development goals. Utilizing the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method, this paper thoroughly examines critical components of an innovative bio-waste collection network, including infrastructure, technology, and human resources. By merging best practices from global urban centers and accounting for the unique characteristics of Athens, the model envisions a transition toward a circular economy. Notably, the proposed municipal bio-waste collection network at the source anticipates substantial contributions to achieving Sustainable Development Goals in major cities. The study concludes by showcasing the successful application of these methodologies in the Municipality of Athens, providing tangible evidence of their positive impact.

Integrating topographic factors for effective urban sponge construction in mountainous regions: A case study

The construction of sponge cities in mountainous areas is crucial to achieving high-quality development in these regions. Owing to rugged terrain, significant changes in elevation, and uneven distribution of cities, the construction of sponge cities in mountainous areas faces challenges such as difficulties in clearing mountains and roads, high cost, and varying regional development requirements. However, there is currently limited research focusing on the impact of terrain on sponge city construction plans. In this study, we developed an optimal low impact development (LID) system layout method based on the annual runoff control rate. This study suggests implementing LID plans in stages to balance cost-effectiveness and enhance resilience. The optimized case1_100 scheme, which takes regional differences into account, can effectively achieve a runoff control coefficient of less than 0.25 in 98.86% of the area. Remarkably, this achievement comes at a significantly lower total cost of only 1.22 billion RMB compared to the unoptimized case2_100 scheme (which does not consider regional differences) with a cost of 3.03 billion RMB. Interestingly, the optimized case1_100 plan, selected using the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method, has an LID layout that is closely related to the surface terrain. Structural equation modeling analysis indicates that terrain affects land types, which in turn impacts the surface impermeability and runoff coefficients, ultimately influencing the corresponding LID deployment plan. The coefficients of relative elevation and slope on the final plan are determined as −0.13 and −0.77, respectively, with a high overall explanatory power of 0.84. This indicates that terrain characteristics have a significant impact on the spatial patterns and surface features of typical mountainous cities in China and the optimal LID strategy largely depends on the initial terrain conditions. This study provides valuable insights for optimizing LID construction in sponge cities, particularly in the context of new mountainous urban planning.

Innovative Strategies for Bio-Waste Collection in Major Cities during the COVID-19 Pandemic: A Comprehensive Model for Sustainable Cities—The City of Athens Experience

This paper introduces an innovative model for the organization and management of municipal bio-waste collection networks in major cities, particularly relevant in the context of the COVID-19 pandemic. Embracing circular economy principles and sustainable city practices, the proposed model addresses the urgent need for sustainable urban bio-waste management systems. Delving into the dynamic urban landscape, with a focus on the city of Athens, the study highlights the necessity of a robust decision-making methodology, the implementation of resilient processes, and the evaluation of their efficacy, especially during challenging times. The model centers on the effective collection, transportation, and monitoring of bio-waste, with a strategic aim to moderate environmental impacts, limit greenhouse gas emissions, and advance sustainable development goals. Utilizing the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method, this paper thoroughly examines critical components of an innovative bio-waste collection network, including infrastructure, technology, and human resources. By merging best practices from global urban centers and accounting for the unique characteristics of Athens, the model envisions a transition toward a circular economy. Notably, the proposed municipal bio-waste collection network at the source anticipates substantial contributions to achieving Sustainable Development Goals in major cities. The study concludes by showcasing the successful application of these methodologies in the Municipality of Athens, providing tangible evidence of their positive impact.

A novel optimization model for tackling capacity challenges in natural gas gathering systems

In the layout optimization of natural gas gathering pipeline network, a lot of work has been done, but few scholars focus on the capacity optimization of gas gathering station (short for station). The structural relationship parameters of dendritic pipeline network and the flow parameters of pipeline network are complicated, which makes it difficult to establish the model, and at the same time, the existence of nonlinear term causes the difficulty of solving the problem. In the current two stage star-dendritic natural gas gathering pipeline network, pipeline sizes and station capacity are not well taken into account for the optimization of pipeline network layout at the same time. In this paper, a consideration station capacity and pipeline sizes: Two-stage star-dendritic network layout optimization model (SCPSTSDLO-Model) is constructed by integrating the factors of site discrete characteristics, station capacity and pipeline sizes, and considering the hydraulic pressure drop conditions of the network, and a solution framework based on the nonlinear processing is proposed, which can obtain the optimization results of optimal affiliation, station type, station site and pipeline sizes at the same time. Five cases are used to verify the validity and accuracy of the model and algorithm, compare the sensitivity analysis and solution algorithm, compare the hydraulic pressure drop conditions, and analyze the application in different forms of pipeline networks. The results show that the SCPSTSDLO-Model and the solution method established in this paper can obtain the optimal solutions under different topologies according to the application requirements, taking into account the capacity of stations and pipeline sizes.

Donor-acceptor bulk-heterojunction sensitizer for efficient solid-state infrared-to-visible photon up-conversion.

Solid-state infrared-to-visible photon up-conversion is important for spectral-tailoring applications. However, existing up-conversion systems not only suffer from low efficiencies and a need for high excitation intensity, but also exhibit a limited selection of materials and complex fabrication processes. Herein, we propose a sensitizer with a bulk-heterojunction structure, comprising both an energy donor and an energy acceptor, for triplet-triplet annihilation up-conversion devices. The up-conversion occurs through charge separation at the donor-acceptor interface, followed by the formation of charge transfer state between the energy donor and annihilator following the spin statistics. The bulk-heterojunction sensitizer ensures efficient charge generation and low charge recombination. Hence, we achieve a highly efficient solid-state up-conversion device with 2.20% efficiency and low excitation intensity (10 mW cm-2) through a one-step solution method. We also demonstrate bright up-conversion devices on highly-flexible large-area substrates. This study introduces a simple and scalable platform strategy for fabricating efficient up-conversion devices.

Hazard Identification and Risk Assessment for Sustainable Shipyard Floating Dock Operations: An Integrated Spherical Fuzzy Analytical Hierarchy Process and Fuzzy CoCoSo Approach

Background: This study investigated the process of selecting sustainable safety protocols for floating dock operations in shipyards by identifying potential workplace risks in emergency situations. Thirteen occupational hazards for shipyard floating dock operations were identified through a literature review and expert discussions. Methods: We incorporated four risk elements (consequence: C, frequency: F, probability: P, and number of people at risk: NP) from the Fine–Kinney and Hazard Rating Number System (HRNS) approaches as the risk assessment criteria. We obtained the importance weights of the risk assessment criteria via the Spherical Fuzzy Analytical Hierarchy Process (SF-AHP) and extended the Combined Compromise Solution (CoCoSo) method within the fuzzy framework to prioritize occupational hazards. This study demonstrated the practicality and efficiency of the proposed emergency risk assessment model for shipyard floating dock operations through a case example of occupational risk assessment. Results: The analysis results show that H4 is the occupational hazard with the highest priority, with a score of 3.553. H4 represents the hazard associated with insufficient access to the entire pool area. The second and third most important hazards are the inability of cranes to move freely in and out of the berthing dock and the inability to dispatch emergency teams. These hazards, denoted H1 and H12, follow closely behind with scores of 3.391 and 3.344, respectively. H10 is deemed the least concerning hazard, with a score of 1.802. Conclusions: Professionals can handle complex and uncertain risk assessment data more flexibly using the proposed system, which excels in accurately organizing occupational hazards.

Evaluation of Age-Friendly Retrofits for Urban Communities in China Using a Social–Ecological–Technological Systems Framework

To address the problem of accurately evaluating age-friendly retrofit indicators in urban communities, this study constructs an evaluation model that takes into account user preferences and their interaction needs based on the social–ecological–technological systems (SETS) theory. The model aims to establish a set of precise community retrofit indicators, covering aspects such as public participation level, public ancillary facilities, green space layout, living environment building, health service support, and accessible design. By employing prioritization strategies, the model seeks to maximize resident satisfaction and promote harmonious coexistence between the community and the environment. Firstly, the retrofit evaluation indicators are formulated using the SETS theory. The entropy weight method (EWM) is then applied to determine the initial weights of these evaluation indicators, followed by the use of the Decision-Making Trial and Evaluation Laboratory (DEMATEL) method to analyze the interrelationships among the indicators. The Kano model is integrated to adjust the weights, reflecting their importance. The final weights of the indicators are determined through normalization. Based on this, the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method is employed to rank and analyze the importance of age-friendly retrofits in the community. Finally, six communities in Dalian, Liaoning Province, China, are selected as samples to evaluate and analyze the age-friendly retrofit indicators. Different methods are compared, and their advantages and disadvantages are ranked to validate the effectiveness and feasibility of the proposed approach. Based on the analysis results, specific design schemes for improving the identified shortcomings in age-friendly aspects of these communities are proposed, considering the needs of aging populations and taking into account community public facilities, accessible design renovations, and the enhancement of green space layouts. This study aims to explore the comprehensive benefits of an age-friendly retrofit in urban communities and provide reference for the deep integration of social, ecological, and technological benefits in urban renewal. The evaluation indicators, methods, and conclusions presented can serve as a decision-making basis for the renovation and renewal of aging urban communities, particularly in terms of age-friendly updates.

Hazard Identification and Risk Assessment for Sustainable Shipyard Floating Dock Operations: An Integrated Spherical Fuzzy Analytical Hierarchy Process and Fuzzy CoCoSo Approach

Background: This study investigated the process of selecting sustainable safety protocols for floating dock operations in shipyards by identifying potential workplace risks in emergency situations. Thirteen occupational hazards for shipyard floating dock operations were identified through a literature review and expert discussions. Methods: We incorporated four risk elements (consequence: C, frequency: F, probability: P, and number of people at risk: NP) from the Fine–Kinney and Hazard Rating Number System (HRNS) approaches as the risk assessment criteria. We obtained the importance weights of the risk assessment criteria via the Spherical Fuzzy Analytical Hierarchy Process (SF-AHP) and extended the Combined Compromise Solution (CoCoSo) method within the fuzzy framework to prioritize occupational hazards. This study demonstrated the practicality and efficiency of the proposed emergency risk assessment model for shipyard floating dock operations through a case example of occupational risk assessment. Results: The analysis results show that H4 is the occupational hazard with the highest priority, with a score of 3.553. H4 represents the hazard associated with insufficient access to the entire pool area. The second and third most important hazards are the inability of cranes to move freely in and out of the berthing dock and the inability to dispatch emergency teams. These hazards, denoted H1 and H12, follow closely behind with scores of 3.391 and 3.344, respectively. H10 is deemed the least concerning hazard, with a score of 1.802. Conclusions: Professionals can handle complex and uncertain risk assessment data more flexibly using the proposed system, which excels in accurately organizing occupational hazards.

Special Methods Controllability and Observability in Optimal Control Systems

This article explores a specific case study that examines controllability and observability in general and in specific so that it is easy for the reader to understand these two concepts, which are fundamental in optimal control theory. Algorithms have been written to determine the controllability and observability of optimal control systems using the MATLAB programming language, and new techniques have been developed to deal with them. In addition, a critical test was created in which the state variables of the system or, more precisely, their corresponding states were split together, illustrating this with more than one example. Divided into four groups in a linear manner, as the article explains. To understand the controllability and observability of some more complex systems, this article is a starting point for the future expansion of these two concepts through the development of new algorithms or other applied solution methods or the creation of new algorithms.

Developing a scalable analytical framework for predicting the contact behavior of elastic rings against rigid surfaces

An elastic ring interacting with rigid surfaces is a fundamental engineering challenge with vast practical implications in various disciplines. However, the exploration of closed-form solutions for this issue has been limited, and existing studies often present complex, numerically unstable solution methods influenced by specific boundary conditions. Furthermore, the lack of scalable design principles for the ring-in-contact scenario has hindered its broader application across different geometries and materials. This study introduces a streamlined analytical and numerical approach to predict the contact behavior of orthotropic rings against centrosymmetric rigid surfaces, encompassing both flat and curved surfaces. Our approach, which simplifies the closed-form solution for extensible Timoshenko curved beams coupled with a contact algorithm that prevents penetration, yields robust and accurate predictions of nonlinear contact behaviors in elastic rings, including deformation patterns, contact angles, stresses, and stiffness. Additionally, we present a design map that serves as a scalable guideline for engineering elastic rings in contact, facilitating the choice of geometry and materials, such as ring radius, thickness, and elastic moduli. This research enhances the theoretical underpinnings of elasticity concerning ring contact and expands the engineering viewpoint on designing elastic rings in various contact scenarios.

Special Methods Controllability and Observability in Optimal Control Systems

This article explores a specific case study that examines controllability and observability in general and in specific so that it is easy for the reader to understand these two concepts, which are fundamental in optimal control theory. Algorithms have been written to determine the controllability and observability of optimal control systems using the MATLAB programming language, and new techniques have been developed to deal with them. In addition, a critical test was created in which the state variables of the system or, more precisely, their corresponding states were split together, illustrating this with more than one example. Divided into four groups in a linear manner, as the article explains. To understand the controllability and observability of some more complex systems, this article is a starting point for the future expansion of these two concepts through the development of new algorithms or other applied solution methods or the creation of new algorithms.