International Journal Of Nonlinear Analysis And Applications
Volume:15 Issue: 3, Mar 2024

This paper proves an equality for the case of twice-differentiable convex functions involving conformable fractional integrals. Using the established equality, we give new Simpson-type inequalities for the case of twice-differentiable convex functions via conformable fractional integrals. We also consider some special cases which can be deduced from the main results.

Here, we propose a practical method for solving nonsmooth convex problems by using conjugate gradient-type methods. The conjugate gradient method is one of the most remarkable methods to solve smooth and large-scale optimization problems. As a result of this fact, We present a modified HS conjugate gradient method. In the case that we have a nonsmooth convex problem, by the Moreau-Yosida regularization, we convert the nonsmooth objective function to a smooth function and then we use our method, by making use of a nonmonotone line search, for solving a nonsmooth convex optimization problem. We prove that our algorithm converges to an optimal solution under standard condition. Our algorithm inherits the performance of HS conjugate gradient method.

In this article, we present new research on the impact of various optical filters on the functionality of an orthogonal Optical Frequency Division Duplexing (OFDM) system for the first time. This paper focused on long-haul optical systems using four Quadrature Amplitude Modulation (4-QAM) methods for OFDM systems. The analysis demonstrates the impact of choosing a Gaussian, Rectangular, or Trapezoidal optical Filter on the effectiveness of the optical system used for long-distance high data rate transmission. Compared with other systems for long-distance transmission using various filter types, 4-QAM OFDM showed a high Bit Error Rate (BER) performance. Significant findings like transmitting Power received Power, and Error Vector Magnitude (EVM) is compared with the system's propagation length.

Systemic risk is the risk imposed by a financial institution on the entire economy, the importance of which has become clear to many policymakers and economists since the financial crisis of 2008, and its measurement has been put on the agenda of many researchers. The present study deals with the influence of the risk of financial institutions on each other and the need to pay attention to the systemic risk of the banking sector, in which the risk based on three criteria ΔCoVaR, MES and SRISK for current banks in the capital market during the period of 2014-2018 has been investigated. After calculating these indicators, using correlation and regression analysis, the effect of some of the most important intrinsic variables of banks as well as macroeconomic variables was estimated on the mentioned indicators. Based on the obtained results, the value at risk (VAR) of each bank has a positive effect on the MES and ΔCoVaR criteria, and systemic risk is not limited to large banks, and small banks also play a role in the emergence and expansion of systemic risk. It was also found that the concentration of banks only On the ownership ratio and capital adequacy, cannot control systemic risk. And with the increase in the leverage ratio, the systemic risk increases. However, ΔCoVaR has a direct and positive relationship with the increase in the inflation rate, and MES decreases with the improvement of economic growth.

Nowadays, the lack of natural resources and reserves of raw materials, besides the increased production costs and the problems with burying and destroying industrial waste, have attracted attention to product recovery and waste recycling in the framework of a closed-loop and sustainable supply chain, also able to create a competitive advantage. On the other hand, researches indicate that taking resilience approaches into account in supply chain design may protect buyers against disruptions such as natural, human, or technological disasters. The present paper presents a multi-objective mathematical model of a single-period, multi-product, and multi-level closed-loop supply chain, considering the dimensions of resilience and sustainability under conditions of uncertainty. Hence, a deterministic mixed integer linear programming model is initially presented; subsequently, to eliminate the uncertainty of the demand parameters and costs, its stochastic counterpart was presented based on Pishvaee's robust possibilistic programming (RPP) model. In order to solve the model, the Augmented Epsilon Constraint method was employed in the GAMS software environment. Ultimately, the model was solved and evaluated by a numerical example.

The present study aimed to analyze the network governance theories with an emphasis on the requirements and challenges of the health system in Iran according to theoretical principles and studies, as well as formulating the network governance model of the health system of Iran after interviewing experts. The research was applied in terms of purpose, and qualitative in terms of method. Since the research was exploratory in terms of purpose, the use of grounded theory was the main strategy in applying the research. Taking notes was initially performed using the study of theoretical principles and research background, and then the final dimensions, components, and indices for the network governance model of Iran's health system were identified and determined by classification and tabulation, the semi-structured interviews with experts, obtaining the necessary agreement, and then analyzing the data using the MAXQDA software. According to the analysis of previous studies, interviews with 15 experts, analysis of data, removing duplicate codes and categories, and integrating similar codes and categories, 767 key points, 53 abstract concepts, 18 sub-categories, and finally, 6 main categories were extracted as mentioned below: External effective categories with 2 sub-categories; predictive factors with 4 subcategories; contextual factors with 3 subcategories; elements with 3 subcategories; functions with 3 subcategories, and the results of implementing the network governance model in the health system with 3 subcategories. According to the results, the health system is a multifaceted and complex phenomenon, and a set of strategies must be implemented for its improvement. The effective implementation of the presented strategies can have many consequences, the most important of which is the society and citizens' health promotion. The research results are presented in a model with the main predictive categories, internal effective categories, elements, contextual categories, functions, results, and consequences.

The central subject of this study is the economic analysis of Quality Assurance (QA) in the German healthcare system. With the help of the study, an estimate of the total costs in the German healthcare market shall be given. The focus of the analysis is on Companies, Political Bodies, Liberal Professions and Public Corporations which are part of the healthcare system including Certification Bodies, which lead to costs from using QA and interacting with the healthcare system. First, a systematic literature search was conducted to determine the costs. It was found that there are no articles or publications that address the topic of the total cost of QA. A continuation/update of existing studies was therefore not possible. To be able to estimate the total costs of QA in the German healthcare market, the QA costs were surveyed using a bottom-up analysis. After identifying organizations and collecting relevant data, the total costs of QA in the German healthcare market were estimated using a mathematical calculation. In general, ensuring quality is an original part of the actions of all professional groups and institutions working in the health care system. Due to this importance, it is remarkable that an economic analysis of the total costs has never taken place before. One reason for this may be the "complexity of the German health care system". Furthermore, the costs of QA are not listed separately, but as part of general administrative expenses. Controlling and transparent presentation of the costs is therefore not possible. The cost estimation and the database created for this study about the parties involved in QA in the German healthcare market can be a useful support for further studies in this field of research.

In this paper, we introduce a three-step iterative scheme, called the MF-iteration process to approximate a common fixed point for a hybrid pair $\{\tau, T\}$  of single-valued and multi-valued maps satisfying a generalized contractive condition defined on uniformly convex Banach spaces. We establish the strong convergence theorem for the proposed process under some basic boundary conditions. We give a numerical example to prove our results' convergence rate. Further, we compare the convergence speed of Sokhuma and Kaewkhao [29] and MF-iterations. we show numerically that the considered iterative scheme converges faster than Sokhuma and Kaewkhao [29] for single-valued and multi-valued non-expansive mappings. Our newly proven results generalize several relevant results in the literature.

The concept of justice is considered one of the most important words in the dictionary of human civilization, and on the other hand, according to Article 78 of the Sixth Development Plan, the government is obliged to achieve social justice and support vulnerable groups, and expand relief, support and insurance coverage, and prevent and reduce social harms. Design and implement the necessary programs to achieve the goals of the 6th Development Plan. The research method used is a mixed method, which is in the qualitative part of thematic analysis and in the quantitative part of Structural Equation Modeling. The statistical population of the qualitative section is targeted and using the snowball method, 11 experts are selected, and in the quantitative section, 200 members of the Ministry of Welfare were randomly selected. Using the theme analysis method and using semi-structured interviews, 20 organizer themes were counted, which were categorized in the theme network format. Using the structural equations model and confirmatory factor analysis, the effectiveness of all identified factors was confirmed. The findings of the research showed that according to the prioritization of the identified factors, the realization of the social justice model ranked first, accountability and responsibility ranked second, and meritocracy in distributive justice ranked third.

In this article, the relationship between risk premium spending and important financial and macroeconomic variables in Iran in the years 2013-2014 has been investigated. In this regard, standard OLS regression and the Hodrick-Prescott filter were used. The results of the research showed that there is a positive and significant relationship between the change and evolution of the money supply process and the variable of risk premium. This is while the variables of the gap between private consumption and its trend, exchange rate and stock index of the 50 largest companies in the stock market have a negative and significant effect on the amount of risk premium i.e. ERP in Iran.

Image segmentation can be used in object recognition systems. Today, it is considered in most branches of science and industry, and in many of these branches the identification of the main components of the image is very important. For example, automatic detection and tracking of moving targets in military applications and segregation of different products in industrial applications, identification of road signs, segmentation of colonies, land use and land cover classification. It is also widely used in medicine, such as diagnosing brain and tumors and self-driving. In this study, image sections are performed by a feature extraction process using a neural network. In the process of applying the neural network method, optimization was performed using the ant colony algorithm. The results show that the identification of image segments using the neural network has an accuracy of 87% alone, but increased to 90% after optimization using ant colony optimization.

The increased purchase of products and services from external suppliers has augmented the dependence of buying firms on the capabilities and performance of their suppliers. so, the implementation of supplier development activities is a need of manufacturing organizations to make long-term relationships with their key supplier to increase supplier capabilities.  This research model introduced six elements of supplier development programs such as information sharing within and between firms, communication methods, top management support, trust between trading partners and supplier quality support and also revealed three major factors of buying firm's performance such as inventory management, product quality improvement and financial performance. Product quality improvement, as a mediator endogenous variable in the purpose model, was also studied and tested. A cross-sectional method was used to gather data from 377 Iranian manufacturing SMEs. The measures and hypotheses were analysed with the help of Structural Equation Modelling (SEM). The research supported the idea that information sharing within firms, communication methods, top management support and trust between trading partners have a positive influence on information sharing between firms. Further, the research conducted the positive effects of information sharing between firms on inventory management and product quality on buying firms. Also, the research showed the positive effect of supplier quality support on product quality improvement and financial performance. In addition, the study conducted also revealed that product quality improvement played a partial mediation effect on supplier quality support and financial performance of manufacturing SMEs.

Employees' political awareness highlights their ability to adapt socially within the organizational structure and understand the governing principles behind how behavior impacts work. The ability of employees to understand the politics within an organization and how it affects their work is an important factor in organizational success in a competitive environment. This research aims to develop a model for political intelligence among employees of state-owned companies in Iran, in order to improve organizational competitiveness. The study uses a mixed-method approach, including thematic analysis in the qualitative method and statistical tests such as Pearson, Friedman, and T-Stevenett in the quantitative method. The results show that network capability and effective management are significant factors in developing employees' political intelligence and improving competitiveness. Thus, the political intelligence of employees can help in understanding the dynamics of competitive power. Increasing political intelligence leads to enhanced success, reduced anxiety, and improved foreign relations, while individuals with high political intelligence have the ability to improve group performance. The results of the analysis indicate that social awareness has the highest impact on political intelligence, accounting for 32% of the variability. On the other hand, the influence of power dynamics is relatively low, explaining only 11.6% of the variability in political intelligence across the organizations studied.

Trust has recently become the main tool in achieving collaboration in inter-organizational and inter-individual relations and it has raised the social capital volume. The present study aimed to design a transcendent trust model in Tehran Municipality and develop a descriptive paradigm that reveals the way of forming citizens' trust in Tehran Municipality. To achieve the research purpose, dimensions and effective factors of transcendent trust were first extracted in Tehran Municipality using desk studies and taking notes. Thereafter, the most important dimensions of transcendent trust and its determinants in Tehran Municipality were identified using the Delphi technique and the views of 29 experts in this field. Furthermore, the random sampling method (snowball) was applied and the sample size was determined based on the Morgan table and simple random sampling, and 385 clients of Tehran Municipality were selected and received a questionnaire containing dimensions and factors. The data were analyzed using structural equation modeling. The model of effective factors in improving transcendent trust was created with 12 latent variables in two aspects, namely dimensions of transcendent trust (instrumental trust and axiological trust) and their determinants (including e-service quality, public affairs administration communication, accountability, cultural adjustment, legitimacy, online social media, civic engagement, Iranian-Islamic lifestyle, transparency, and citizens' satisfaction). The results indicated that transcendent trust in the municipality was not merely dependent on the functions of municipalities, but other contextual and environmental factors can also play roles in this equation. Therefore, the general authority of Tehran Municipality to the aforementioned background and contextual factors based on the influence of strategic components of the environment where social institutions and other actors operate and interact will generate the best outcome for municipalities to design a relatively comprehensive model in this field.

In this paper, using variational methods and critical point theory we establish the existence of multiple solutions for a class of elliptic equations on Carnot groups depending on one real positive parameter and involving a subcritical nonlinearity. Some recent results are extended and improved.

The purpose of this study was to investigate the effect of employer premium rate on operating profit per share and change in net sales income of companies listed on the Tehran Stock Exchange. This study, in terms of the type of research; Correlation is cross-sectional and is considered as a practical goal. The statistical population of the study included 666 companies listed on the Tehran Stock Exchange from the beginning of 2013 to the end of 2019, of which 111 companies were selected as a sample by systematic elimination method. In descriptive statistics, population parameters including central indices and population dispersion were measured and data analysis was performed using regression method based on composite data and Hausman's tests, F (Limer), by Oveys software. The results showed that there is a significant relationship between the employer's share insurance rate, operating profit per share and the change in net sales income of companies listed on the Tehran Stock Exchange. Therefore, it is better for the Social Security Organization to consider the premium rate according to the inflationary conditions and labor income in order to support the industries in attracting labor and the high premium rate should not cause the managers of the companies to increase the total price. Goods and services are driven.

The purpose of this research was to identify the factors affecting the job regeneration of employees and provide a model to improve performance and productivity in the social security organization using the Grounded theory and structural equation model. The method used in this study was a hybrid method including a qualitative method based on the Grounded theory approach and a quantitative method based on the structural equation approach. In the present study, the data obtained from the text of the interviews were analyzed by MAXQDA software in order to increase the accuracy and speed of the research. In this research, 195 codes extracted from 15 detailed interviews with experts and specialists in the field of research have become 89 more abstract concepts and finally, 3 categories (Cognitive, Duty, Communicational) have been identified. The coefficients obtained from the structural equations show that the cognitive, task and communication variables have a positive and significant effect on improving performance and productivity in the social security organization.

This study aimed to evaluate the effect of companies’ debt structure and investment on the financial distress of companies listed on the Tehran Stock Exchange. This applied study was conducted on companies listed on the Tehran Stock Exchange in 2016-2021, 120 of which were selected by screening. The research hypotheses were tested, and the results were analyzed using panel data, Generalized least-squares (GLS) regression, and EViews software version 10. Based on the results, the capital structure had a positive and significant effect on the financial distress of listed companies. In addition, there was a significant negative relationship between investment and financial distress.

Daylight Glare Probability (DGP), founded on the latest glare metric, is the main challenge related to daylight glare inside buildings. Studies showed that the DGP depends on several factors, such as vertical illuminance values at the human eye factor, which is an essential parameter. In this study, we implement machine learning techniques to estimate and predict the DGP classifications, which are imperceptible, perceptible, disturbing, and intolerable based on the various influenced factors. A series of machine learning simulations have been conducted to investigate how those factors can be influenced by the degree of glare and classifications. In this research, different machine learning algorithms such as Artificial Neural Networks (multi-layer perceptron), K-Nearest Neighbors (KNN), Support Vector Machines (SVM), and Random Forest (RF) were employed to determine or predict the DGP classifications accurately. Results showed that the RF is the most effective method to classify the DGP and can predict with up to 99 % accuracy. Furthermore, the results displayed that vertical illuminance at eye level (lux), Ev, compared with other factors, has the largest influence on the DGP classifications. Consequently, machine learning is a powerful, promising, and viable option to implement in building constructions to optimize energy consumption, a global issue in the current century.

This study was performed with the aim of identifying indicators and factors affecting consumers' purchase intention of cosmeceutical masks made of Nano-gelatin textiles in Iran in three steps. In the first step, indicators affecting the purchase intention were identified based on a systematic review of theoretical literature and qualitative content analysis of the indicators and using NVIVO software. In this step, the opinions of 12 university experts were analyzed by the Delphi technique in EXCEL software, and 57 main indicators were confirmed. In the third step, in order to classify indicators and identify factors affecting the intention to buy cosmeceutical masks made of Nano-gelatin textiles, 10 final factors were extracted by performing exploratory and confirmatory factor analysis. These included the Firm's functional actions, Firm strategic measures, Cultural factors, Knowing the consumer, Consumers' behavior, Personal factors, Interpersonal factors, Consumers' attitude, competitors and consumers' beliefs. In general, competitive advantage for companies is achieved through value creation for customers by providing differentiated products with more benefits compared to competitors based on core competencies. In general, achieving a competitive advantage for companies is achieved through value creation for customers by providing differentiated products with more benefits than competitors based on core competencies. The main focus of marketing strategy is the appropriate allocation and coordination of marketing activities and resources to meet the company's operational goals in a specific product market. Strategic market planning is also a tool that helps companies to gain a competitive advantage and create synergies by making a suitable plan to combine marketing elements according to the needs and desires of potential customers in the target market.

The sustainable smart city is primarily a concept and there is still not a clear and consistent definition among practitioners and academia. In a simplistic explanation, a smart city is a place where traditional networks and services are made more flexible, efficient, and sustainable with the use of information, digital and telecommunication technologies, to improve its operations for the benefit of its inhabitants. Smart cities are greener, safer, faster and friendlier. The different components of a smart city include smart infrastructure, smart transportation, smart energy, smart healthcare, and smart technology. These components are what make cities smart and efficient. Information and communication technology are enabling keys for transforming traditional cities into smart cities. The two closely related emerging technology frameworks Internet of Things and Big Data make smart cities efficient and responsive. The technology has matured reasonably to allow smart cities to emerge. However, there is much need in terms of physical infrastructure, and renewable energy to make the majority of cities worldwide smart. Even today, there are not enough studies on how regulations collaborate to make cities smarter and more sustainable. This paper contributes to filling this gap by investigating the main guidelines of the new City Statute that have the greatest potential to contribute to having smarter and more sustainable smart cities connect people and places using innovative technologies such as Data Mining (DM), Machine Learning (ML), big data, and the Internet of Things (IoT). More recently, the challenges posed by the increasing urbanization experienced by most countries have increased societal demands for more efficient and sustainable urban services, in a digital revolution environment and more sustainability. The study aims to identify the main Data Mining techniques used in the context of smart cities and how the research field of Data Mining for smart cities. To prioritize the guidelines of the contemporary City, the methodology used the strategies of smart city and significant applications of nonlinear analysis to make integration with the main principles of sustainability to enhance the concept of the sustainable smart city so The systems are under increasing environmental, social and economic pressures for sustainable prosperity.

The role of the capital market in the economy of all countries is fundamental and decisive. It has a significant effect in aggregating and moving resources towards production and economic activities. According to the existence of such markets, the collection of small and large financial resources from the members of the society is facilitated. Therefore, this research is aimed at providing a model for measuring the impact of economic policy uncertainty on the tax capacity of e-commerce. In this research, 40 variables affecting economic policy uncertainty were included in the model. Finally, using the Bayesian averaging model approach, the most important variables affecting this index were determined. According to the results of the BMA model, the most important variables affecting the economic policy uncertainty index are the real interest rate, government debt to the central bank, liquidity (M2), inflation, current expenditures, land price index in urban areas, unofficial exchange rate, real exchange rate, Economic growth and oil revenues were determined. Based on the principal components approach, we calculated the economic policy uncertainty index using the most important variables affecting this variable. Then, by using the GARCH model, we extracted the uncertain part of the economic policy uncertainty index, and finally, by using the powerful non-linear TVPFAVAR model, we analyzed the shock caused by the economic policy uncertainty variable on the tax capacity in the field of e-commerce in the research period. We analyzed. The results indicated the fact that the shock caused by the variable fluctuation of economic policy uncertainty has increased the tax capacity in the field of e-commerce in recent years.

The current research was conducted with the aim of monitoring and measuring the health of the administrative system and fighting corruption in the headquarters of the Ministry of Economic Affairs and Finance. The statistical population of this research consists of two groups, the first group includes experts who are familiar with the theories of monitoring and measuring the health of the administrative system and fighting corruption, whose number is unknown and is scattered throughout the country, and their selection is selective and in This research has been used in the section of compiling and designing the model according to them, and the second group includes the employees of the headquarters of the Ministry of Economic Affairs and Finance (600 people), according to Cochran's formula, 234 of them were selected as a sample. The methodology of carrying out descriptive-survey research was used in the field of data collection from managers' competence and organization development questionnaires. The results indicate that there is a significant relationship between the health of the administrative system, internal organizational factors, external organizational factors, management factors, behavioral factors, individual factors, and the fight against corruption in the headquarters of the Ministry of Economic Affairs and Finance.

In this paper, we consider the q-analog of Kostant's Partition Function of Lie algebras  $\mathfrak{sl_\textrm{4}(\mathbb{C})} $ and $\mathfrak{sp_\textrm{6}(\mathbb{C})}$ and present a closed formula for the values of these functions.

Investment in the agricultural sector has a crucial role in the economic growth of the country. The variability of investment expenses on the one hand, and the extent and potential capacities of the agricultural sector on the other hand, increases the necessity of investigating the factors affecting the improvement of investment in this sector. Developing a dynamic model is an appropriate approach for analyzing complex feedback systems to improve investment in the agricultural sector of the country. In the present study, library research and interviews with experts were used to identify the factors affecting the improvement of investment in the agricultural sector in the country to develop a dynamic model. The participants of the present study include 20 experts in the natural resources management organization of the country and several university expert professors in the field of agriculture finance were interviewed. Based on the opinion of experts the key variables were identified and cause-and-effect and mathematical relationships between these variables were evaluated in the form of two diagrams of cause and effect and the flow state diagram in the dynamics system approach during the years 2011 to 2025 were simulated in the Vensim software. Then different scenarios were examined aimed to increase and improve the investment in the agricultural sector of the country. The findings show that by implementing policies to improve investment in the agricultural sector through increasing exports and implementing land protection laws and regulations, investment in the agricultural sector of the country can be improved.

Companies should evaluate the nature of the crisis after a detailed pathology of the factors causing the problem and look for appropriate solutions to get out of this crisis. This study was conducted on 144 companies from 2010-2021 to prioritize the factors affecting the exit from bankruptcy and financial revival of the companies using the analysis of multiplayer artificial neural networks. First, financial ratios obtained from the literature review and expert evaluation were independentist of each other through principal component analysis. Then, the main components affecting exit from bankruptcy under logistic regression models were identified, and finally, the final logistic model for exit from bankruptcy was presented. Based on the results, the essential financial variable in exiting bankruptcy is the change in capital increase policies from the place of stock issuance. The least critical variable is the change in dividend policies.

The present research aims to investigate the important and fundamental obstacles to the export of Khuzestan dates; Presented a mental model of date export obstacles in Khuzestan province. This research was a type of exploratory mixed research, with the qualitative part based on the theory derived from the data and the quantitative part based on the descriptive-survey method. The qualitative part of the tool was a semi-structured interview and the quantitative part was based on a questionnaire. The statistical population in the qualitative section included experts, specialists, and date exporters, and saturation was achieved after interviewing 20 people. In this research, the qualitative part was analyzed with Max Kyuda software and the quantitative part was analyzed based on Lisrel software. The results showed the causal factors: thinking; decision-making power; individual understanding; type of behavior; Creativity; Understanding export behavior and simplifying issues. Based on the impact on the central category of the mental model of obstacles to date export, based on the intervening factors, the level of complexity of the issues; Work experience; analyze ; Interaction; mental perceptions; regulations; Decision making; inductive thinking; Deductive thinking; Emotional Intelligence; emotional intelligence and business intelligence and the underlying factors of the organization's strategies; environmental uncertainty; Uncertainty of information; big data; ability to predict; systems performance; the power of market analysis; idea generation in relation to future research strategies; predicting issues; planning; organizational perspective; Communication skills; Information and Communications Technology; administrative bureaucracy; organizational rules; International rights; Organizational concentration or lack of concentration; organizational processes; organizational hierarchy; consequences of interactions between businesses; dynamic changes; greater competitiveness; adapting to environmental changes; logical interpretation of data; Crisis Management; It leads to the change of individual attitudes and beliefs and organizational flexibility.

The reliability of financial statements plays an important role in increasing the profit of a company; therefore, the purpose of this study was to investigate the effect of financing costs on the reliability of financial statements of companies active on the Tehran Stock Exchange. The statistical population of this descriptive-correlation study included all the companies accepted and active in the Tehran Stock Exchange from the years 2015 to 2019, and the data of the financial statements of 119 active companies during this time period were analyzed using regression models. The results showed that the cost of financing had an inverse and significant effect on the reliability of the companies financial statements. Therefore, taking advantage of the reliable structure of financial statements for financing can be one of the goals of companies in order to increase profits.

In this paper, we define R-norm entropy and conditional R-norm entropy of partitions of algebraic structures, and we establish some of their basic properties. We show that the Shannon entropy and the conditional Shannon entropy of partitions can be derived from the R-norm entropy and the conditional R-norm entropy of partitions, respectively, by letting R tend to 1. Finally, using the notion of entropy for partitions, we define the R-norm entropy of a dynamical system. We prove that the R-norm entropies of isomorphic dynamical systems are equal.

In this study, we compare the different conditions which are used to detect the unique solvability of the absolute value equation (AVE) $Ax- B \vert x \vert =b$. Also, analyzing which condition is more suitable to use according to our problem and later, we will see the advantage and disadvantages of different unique solvability conditions. Further, we take an example where existing conditions are invalid to judge the unique solvability of the AVE.