International Journal Of Nonlinear Analysis And Applications
Volume:15 Issue: 2, Feb 2024

In this article, we examine a nonsmooth vector optimization problem with locally Lipschitz approximately convex mappings in terms of the convexificator and provide some ideas for approximate effective solutions. Additionally, we define the relationship between the convexificator-based solutions of Stampacchia type vector variational inequalities ($VVI$) and the approximate efficient approximation convex function of nonsmooth vector optimization problems using the locally Lipschitz function. Furthermore, we provide a numerical example to demonstrate the veracity of our findings.

‎This ‎paper ‎adopts‎ the extended rational sinh-cosh as well as sine-cosine procedures to find precise solutions to the Hirota equation and Hirota-Maccari equation‎. ‎It is illustrated that seeking the precise solutions for these equations plays a foremost and effectual role in solving the numerous kinds of PDEs applied in optics, fluid mechanics, plasma physics and solid physics.‎‎ ‎Furthermore‎, ‎we are able to obtain some consequences of dark and cusp wave solutions‎. ‎Besides‎, ‎two-dimensional and three-dimensional surfaces have been drawn in order to acknowledge the concept of the acquired equations‎.

The PID controller's well-established advantages have led to its widespread application in practically all industrial operations. The effectiveness of the controller has a major impact on the overall performance of the system, making tuning an essential part of the system's operation, which made this a hot topic for academics to dig into for some time. This paper provides an overview of both contemporary and old PID tuning methods. Techniques can be categorized into two major groups, namely: Traditional and optimization tuning methods are two examples of tuning techniques. A comparison between some of the different methods has as well as being made available. The primary objective of this paper is to give thorough for PID professional controllers.

Diabetes is a dangerous disease in which the body is incapable of controlling blood sugar due to inadequate insulin hormone levels. This chronic disease increases blood sugar in patients. Therefore, if it is not controlled, it will cause many complications. A considerable number of people in the world suffer from this disease owing to its damage and lack of its initial diagnosis. The patient visits the doctor frequently to diagnose his/her illness and conducts various tests that are boring and costly. Increasing machine learning approaches through heuristics, and novel methods can somewhat decrease the problems. The current study aims to propose a model that can predict diabetes in patients with high accuracy. The paper introduces a new method based on the assortment of metaheuristic algorithms of a particle swarm and fuzzy inference system. The proposed method utilizes fuzzy systems to binary the particle swarm algorithm. The achieved model is applied to the diabetes dataset and then evaluated using a neural network classifier. The results indicate an increase in classification accuracy to 95.47% compared to other existing methods.

A smart gateway, which plays an important role in a smart home, generally connects the internal and external networks of the home, and also jointly manages the smart Internet of Things (IoT) devices equipped with the smart home. Protocols collect generated data from nearby devices and even perform some local data processing tasks. In this paper, we first review the entire research field of smart homes, focusing on a framework based on edge computing and multiple intelligent agents. Then, we divide the evolution of smart gates into three generations based on the timeline and various criteria including quality of experience (QoE), AI support, software-defined networking, etc. Next, we will discuss the key technologies and components of smart gateways such as operating systems, wireless communication protocols, and security. Finally, we examine the challenges and trends of smart gates. This article examines the importance of building a secure smart home system.

In this paper, we state the problem of the network flow interdiction in a set of initial and destination nodes so that each initial is capable of only delivering products to certain pre-determined destinations. The network user’s purpose is to deliver the highest value of flow from the sources to the sinks and the network interdictor’s purpose is to reduce the highest value of flow being used. In this paper, the networks flow interdiction in multi-source and multi-sink conditions are addressed in a way that the parameters of arc capacity are trapezoidal fuzzy sets.

The paper aims at developing a model for improving service productivity in public organizations based on the service complexity approach. This is an applied, descriptive qualitative and, quantitative paper. The population in the qualitative section (grounded theory) includes 16 experts in the field of productivity in the university and managers of government organizations in Tehran province who were selected by theoretical sampling method as a method of targeted sampling. The statistical population in the structural equations section includes three categories: 1) Managers and experts of government service organizations; 2) Experts and deputies of government service organizations and, 3) Consultants and experts of government service organizations. In this section, we used multi-stage relative stratified sampling, which according to Cochran's formula, a total of 384 samples acceptable. Thus, the questionnaires were randomly distributed in each of the five regions of the country and, the data from 390 questionnaires were completed through the data analysis algorithm in PLS software. Having analyzed the interviews based on the grounded theory method and in NVivo Plus 2020 software and by open coding, we obtained 143 items as basic concepts from the text of the interviews, which were classified into 31 sub-indices and 11 main indices and five dimensions. Then, we validated and approved the results of the qualitative section through the data analysis algorithm in the PLS software. Given the research findings, we presented and fitted the model of improving service productivity in public organizations based on service complexity in a paradigm model.

Weather prediction is vital in daily life routines, for risk mitigation and resource management such as floodrisk forecasting. Quantitative prediction of weather changes depends on different parameters such as rainfall time,temporal, barometric pressure, humidity, precipitation, solar radiation and wind. Therefore, a highly accurate systemor a model to forecast the highly nonlinear changing happening in the climate is required. The focus of this researchis direct prediction of forecasting from weather-changing parameters, the forecasts are performed using collected datavalues recorded in a big dataset (the dataset collects the weather parameter data of the Canary Islands (Las Palmas,Tenerife a Palma, Fuerteventura, La Gomera, Lanzarote and Hierro). The forecasting system is performed by proposinga deep learning approach (CNN). The research goal is predication the weather condition. The acquired classificationaccuracy for the climate condition using CNN (ShuffleNet) structure is 98%, and the recall and Precision results are 97.5and 96.9 respectively

The present study examined the behavior of solutions for a viscoelastic double-Kirchhoff-type wave equation with nonlocal degenerate damping term and variable exponent nonlinearities. Under appropriate conditions for the data and exponents, we prove the global existence, asymptotic stability, and blow up of solutions with arbitrary initial energy.

The optimization of reliability is crucial across various engineering domains. The redundancy allocation problem (RAP) is among the key challenges within reliability. This study introduces an RAP incorporating repairable components and a k-out-of-n sub-systems structure. The objective function aims to maximize system reliability while adhering to cost and weight constraints. The goal is to determine the optimal number of components for each subsystem, including the appropriate allocation of repairmen to each subsystem. Given that this model is classified as an Np-Hard problem, we employed a genetic algorithm (GA) to solve the proposed model. Additionally, response surface methodology (RSM) was utilized to fine-tune the algorithm parameters. To calculate the reliability of each subsystem, as well as the overall system reliability, a Monte Carlo simulation was employed. Lastly, a numerical example was solved to assess the algorithm's performance.

This study considers two agents, risk-neutral and risk-averse ones, and studies their investment behavior. There are two investment options-safe investments such as a bank account and a risky investment in a company. The company runs a risky project. In the case of success, its return is more than the bank’s, and that is less in the case of failure. When the project fails, the company divides the left amount among the investors based on the proportional bankruptcy rule. We model the problem as a strategic game and explore its Nash equilibrium.

This study aimed to provide an effective model for developing production strategies and techniques on a global scale in the West African market. The criteria weights were determined using Shannon’s entropy after collecting the opinions of West African market experts through questionnaires. The main and sub-components and production indicators were identified on a global scale and prepared and compiled in the form of a scoring checklist using the ISM model and examining the theoretical foundations of the research. Then, the indicators and components of the study were confirmed through the Delphi method. The causes of influence on production strategies and techniques on a global scale were designed based on structural-interpretive modeling. Further, the technique of analyzing the mutual effects of Mic Mac was used to investigate the impact of factors on each other in global scale production in the West African market. The research population was experts and specialists active in production on a global scale in the West African market. According to Saaty, 10 experts were selected as the statistical population of this research. The ISM results showed that all 28 leading indicators were finally approved by experts and were ranked from 1 to 28. The index of non-creation of waste from the sub-component of cost reduction was ranked first with an agreement coefficient of 0.798. In addition, reducing set-up time from the sub-component of cost reduction with an agreement coefficient of 0.782 was ranked second, and lean production from the sub-component of lean production with an agreement coefficient of 0.611 was ranked 28th. The second-round results of the Delphi indicated that all the sub-indicator were confirmed based on a mean >5, a low standard deviation, and an agreement coefficient >0.5. The approved model was designed based on two Delphi steps based on experts’ opinions, and the Mic Ma method showed that out of the 28 main factors, 12 were influential factors, nine were influential factors, and seven were independent factors. Finally, 10 of the main factors were determined as the key factors influencing production on a global scale in the West African market: 1) Cellular production, 2) Production without waste, 3) Activities with an environmental attitude, 4) Flexible system, 5) Field of operation, 6) No waste, 7) Operation improvement, 8) Communication with customers, 9) Clarity of business, 10) Participation and Companies relationship with suppliers.

The export of petrochemical products in Iran has a magnificent position due to making added value for the country. Exporting these products, which is considered the largest volume of non-oil exports of the country, has a great impact on the country's GDP. In addition, “Price” as the only element of the marketing mix that generates revenue, has great importance for petrochemical companies. In addition, pricing has been used as a major tool to increase company profitability & also been known as a key element in marketing strategy. Pricing strategy can be observed in a set of internal and external political and economic influences which affects the pricing decisions of a company. As well as the other companies petrochemical companies must be able to arrange for pricing commensurate with the value of their product. These factors depend on the strategies of the petrochemical companies by-product pricing and also how they envision themselves in the future. In this research, descriptive and inferential methods have been used; In the descriptive method, to determine the desired components, the exploratory factor analysis technique and through SPSS software and in the inferential method, the effect of the discovered components of the pricing strategy in increasing exports, using the SEM technique, the desired structural model through software AMOS is provided. Factor analysis of the research shows that 4 hypotheses including "Restriction of entry into the export market”, “Penetration strategy”, “Market development strategy” and “opportunity creating” have been recognized as effective in the export of petrochemical products in Iran.

The purpose of this research was to identify the factors affecting financial technology in small and medium businesses 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. Based on the qualitative tactics of content analysis and the foundation's data strategy, 98 initial codes were obtained. Three concepts of economic and employment factors, innovation in the economy and change in customers' behavior were obtained as causal conditions affecting the central phenomenon (formation of the financial technology market). The coefficients obtained from the structural equations show that the variables of economic and employment factors, innovation in the economy and the change in customer behavior have a positive and significant effect on the formation of the financial technology market.

The purpose of this research is to present mine managers with solutions for the sustainable development of mines with an emphasis on mine tourism. In the first step, identifying ways for mine sustainable development with the use of tourism potentials by studying articles on a national and global scale taken from the SID citation center, Emerald, and Science through content analysis using Nvivo software, was in order. In the second step, 12 main factors were identified and confirmed with the help of the Delphi method and 12 university and industry experts, using EXCEL software. Then, by using tourism potentials with the ISM method and the participation of experts from the previous section, the development model of mines in Iran was achieved and an interpretive structural model was extracted. Finally, in the third step, in order to check the application of the proposed model, structural equation modelling analysis was done using PLS3 software with the participation of 170 managers and supervisors of Iranian mines. The final results acknowledged 12 ways as the final methods of mine sustainable development considering tourism potentials. In the eyes of the expert, mines' innovative reconstruction based on a tourism standpoint, tourism infrastructure improvement, increase in the region's social capital, business and employment growth based on tourism as a necessity were deemed the most effective ways of sustainable development for mines using tourism potentials. Evaluation of the proposed model in the field showed that among 32 theories, only the relationship between innovative mining tourism strategies and business prosperity and job creation based on tourism, the development of mine workers human resources and the development of the region's social capital and the relationship between the development of mine workers human resources and the prosperity of business and employment based on tourism was not approved.

Classifying objects based on the simultaneous impact of various parameters has always been challenging due to heterogeneity, impact conflict, and sometimes parameter uncertainty. The purpose of this study is to provide a method for classifying such data. In the proposed method, fuzzy hypergraphs were used to define the granular structures in order to apply the simultaneous effect of heterogeneous and weighted parameters in the classification. This method has been implemented and validated on Fisher's intuitive research in relation to the classification of iris flowers. Evaluation and comparison of the proposed method with Fisher’s experimental results showed higher efficiency and accuracy in flower classification. The proposed method has been used to assess the seismic risk of 50,000 buildings based on 10 heterogeneous parameters. Seismic risk classification showed that more than 88% of buildings were classified, and 12% of buildings that could not be classified due to excessive scatter of parameter values were classified using a very small confidence radius. The results indicate the ability of the proposed method to classify objects with the least similarity and number of effective parameters in classification.

The development of computer technologies and automated learning techniques can make decision-making easier and more efficient. In the field of machine learning, where computers always make decisions or propose suggestions for proper decision-making, there exist many decision-making techniques such as decision trees, neural networks, etc. Flexibility and comprehensibility are one of the advantages of the decision tree model. The decision tree can provide the possible options, goals, financial profit, and information needed for an investment for the managers better than any other tool. The decision tree is one of the most applicable data mining algorithms. On the other hand, crowdfunding in knowledge-based companies is a new financial phenomenon in online financing of innovative projects and knowledge-based businesses that reduces financing costs and problems in addition to changing the nature of the investment. There are four types of crowdfunding in knowledge-based companies namely donation-based, equity-based, lending-based, and reward-based. Reward-based crowdfunding can be considered the most publicly familiar crowdfunding model, where backers will actively participate in the product development process along with investment. Low-cost crowdfunding websites act in the projects as an online mediatory between the initiators and the sponsors. Therefore, the factors affecting the success of crowdfunding were evaluated in this research regarding the initiators' performance and the sponsors' feedback, and the significant attributes were presented in the form of a decision tree structure using the data mining technique. The results reveal that the best performance of initiators is related to the field of direct investment attraction with 92% accuracy of the decision tree with the most important attributes of "number of updates during the investment period" and "number of dynamic technical and tactical analyses".

Financing decisions and capital structure are very important for companies and are influenced by several factors. This study aims to examine the relationship between managers' financing attitudes (internal or external) and their financing policies. In this examination, the survey population consists of companies listed on Tehran Stock Exchange whose CEO or financial manager (at least one) was unchanged between 2019 and 2021. Redman et al.'s (2002) questionnaire was applied to determine the attitude toward financing. Financing policies used by the managers were collected by referring to the audited financial statements of the companies. Totally, 51 usable answers were received from the respondents. The research hypotheses were dragging using a multivariate regression equation model in the form of panel data. The results show a significant relationship between the financing methods through retained earnings and debt with the attitudes toward financing from the place of retained earnings and debt. In contrast, the financing tendency through debt has no significant relationship with the policy of financing the stock issue through the issuance of shares.

In this paper,  a new version of a higher-order strongly convex function is introduced which is named    $(\omega-\sigma)$-higher-order strongly convex function. Sufficient conditions for the existence of minimum for  $(\omega-\sigma)$-higher order strongly convex function is provided. The vector version of $(\omega-\sigma)$-higher order strongly convex function is given and by using  KKM theory an existence results for a solution of it is proved. Moreover, the compactness of the solution set of the vector version of $(\omega-\sigma)$-higher order strongly convex function is investigated. The results of this article improve and extend the corresponding results presented in this area.

This study evaluated the effect of changing the program-based budgeting system to a performance-based budgeting system in advancing organizational goals, realizing the accountability system, and economic viability. The data of this comparative and analytical study were collected through library studies and questionnaire distribution. Therefore, a general opinion was obtained by asking the opinions of 15 experts and applying the Delphi method. Friedman’s test was used in SPSS software to determine the rank of each of the indicators related to each component to determine the ranking of the indicators approved by the experts. The results showed that operational objectives, as well as the indicators of the compilation of audit standards supported by the country’s health system, performance audit by the country’s health system, and approved standards in the health system, are critical factors for the transparency of performance-based budgeting.

In this paper, by providing an example, we show that the condition which produced by Radenovi\'{c} and Kadelburg in [Generalized weak contractions in partially ordered metric spaces, Comput. Math. Appl. 60 (2010) pp. 1776-1783] is not sufficient for the uniqueness of the fixed point. Furthermore, a new sufficient condition is introduced for the uniqueness of the fixed point. Some suitable examples are furnished to demonstrate the validity of the hypotheses of our results.

Today, banks are on the path of digital transformation to create a good experience for customers. In the meantime, Fintech companies have good knowledge of creating technological financial services, and banks need this distinctive fintech competency to succeed in digital banking. Based on this, banks form a strategic alliance with Fintech. One of the issues that play an important role in the formation and success of the strategic alliance between the bank and Fintech is the motivation of both parties to form the alliance. Accordingly, the present study was conducted with the aim of identifying the stimulants of banks in forming a strategic alliance with Fintech. The method used in this study is team analysis and the statistical population of this study includes 11 experts of the Refahe-Kargaran Bank who have been purposefully selected and interviewed semi-structured. In this study, the stimulants of banks in forming a strategic alliance with Fintech were identified in the form of 5 main themes and 9 sub-themes. These five themes are outsourcing technology services, leading digital innovation, organizational process agility, gaining competitive advantage and customers. Based on the research findings, banks have different incentives to form a strategic alliance with Fintechs, and examining and paying attention to these incentives has a great impact on the success and effectiveness of alliances.

Paying attention to sanitary landfill methods and calculating their potential risks are the most logical tools to avoid waste risks. The reduction of environmental consequences caused by unprincipled landfilling, reduction of economic costs of the municipal waste management (WM) system, etc. is among the most important advantages of environmental risk assessment for sanitary landfill which is possible by detecting and evaluating the risks of sanitary landfilling. Therefore, the present research assessed the environmental risk of the sanitary landfilling of Tehran city as a case study. The research was applied-developmental in terms of purpose and detected and classified risks using interviews with experts, qualitative analysis, and previous studies. Finally, the priorities of the main risk clusters in sanitary landfilling were calculated using the analytic network process (ANP). In sanitary landfilling, chemical risks with a weight of 0.289 were ranked first, social risks with a weight of 0.259 were ranked second, and physical risks with a weight of 0.182 were ranked third. In the present study, it was sought to provide preventive and corrective measures by prioritizing the risks to minimize the risks that might occur in the Aradkuh Kahrizak landfilling site in Tehran and spread to other regions due to sanitary landfilling, thereby making it easier for managers to make decisions on waste management in the region and Tehran.

The purpose of this study is to provide a structural model of audit quality based on the impact of auditing professional ethics and the moderating role of organizational culture. To achieve the research goal, 384 questionnaires were distributed and collected among auditors working in auditing firms and the auditing organization. The data collected by the questionnaires were analyzed by SPSS24 and Smart PLS3 software using structural equation modeling. The results of the research hypotheses in this study at a 99% confidence level showed that the professional ethics of auditing has a positive and significant effect on audit quality. Organizational audit culture has a positive and significant effect on audit quality. Finally, the results showed that organizational culture has a positive and significant effect on the relationship between auditors' professional ethics and corporate auditing quality.

In this paper, the existence of the solutions of a class of weakly singular integral equations in Banach algebra is investigated. ‎The basic tool used in investigations is the technique of the measure of non-compactness and Petryshyn’s fixed point theorem. Also, for the applicability of the obtained results, some examples are given.

The current research has been carried out with the aim of presenting the pattern of combined shopping behavior of customers in large chain stores. This research is applied in terms of purpose, and in terms of survey-exploratory approach. The statistical population of this research was a group of marketing experts in the retail industry and were interviewed in depth. This selection and conducting of interviews continued until theoretical saturation was reached and then it was stopped. In this research, the snowball sampling method was used and in this process, 9 experts were interviewed in depth. In this research, since the foundational data theory method was used, the main tool for data collection was in-depth and unstructured interviews with human resources experts. Finally, after three open, central and selective codings, the conceptual model of the research was designed based on the paradigm model.

In different societies, supporting vulnerable groups and improving income distribution has always been one of the concerns of the government, economists and sociologists. Income distribution is not only one of the economic issues, but also it is one of the important social and political indicators. One of the financial privatization methods in the world is the privatization of coupon payments (justice shares), whose goals are to prevent the income gap between different strata of society and help to distribute ownership and as a result, income more equitably in the country. The purpose of the research is to determine the factors affecting the optimal management of justice shares in order to increase social well-being. The current study is a fundamental (exploratory) research and a mixed method (qualitative-quantitative) has been used to investigate the research objectives. The statistical population of this research in the qualitative section includes university professors in the field of public administration, managers of privatization organizations and the Ministry of Economic Affairs and Finance, and managers of justice share provincial investment companies. The statistical population of this research is in the quantitative section, including high and middle managers, deputies and senior experts of the Privatization Organization, the Stock Exchange and Securities Organization, the Ministry of Economic Affairs and Finance, and justice share provincial investment companies. The data required for the research has been collected through a questionnaire. In order to analyze the data collected in the qualitative section, the grounded theory method is used. In the quantitative section, the DEMATEL method is used. The results showed that the causal, intervening, axial, contextual, individual and environmental factors had effects on the optimal management of justice shares in order to increase social welfare.

Corrosion that occurs in concentrated sulfuric acid production plants causes damage to equipment, pipes, tanks, and pumps, which affects the cost of maintenance time, which causes production stoppage and danger to workers due to the high acid concentration. The researchers used several types of alloys that help sustain production with different protection methods. Some of them are expensive, and some are highly corrosive, such as iron alloys, nickel alloys, polymers, and others in factory equipment. The current work is devoted to obtaining an alloy with mechanical and corrosive properties comparable to what is used in the concentrated sulfuric acid production plant in Iraq and the world to be used in the most important components of pipes and tanks to preserve the concentrated acid in the factory. Various alloys of a group of elements with an iron base were used and produced by the powders metallurgy method to achieve this purpose. Mechanical, corrosion tests and inspection (hardness, microstructure, dry slip corrosion, wear/abrasion, slight immersion, and Tafel testing were performed, XRD, EDX, SEM)The alloys used in this research are:$$\mathrm{A} 1(1 \% \mathrm{Cr}+1 \% \mathrm{Ni}+1 \% \mathrm{Mo}+0.5 \% \mathrm{Cu}+0.5 \% \mathrm{Si}+0.1 \% \mathrm{~W}+0.1 \% \mathrm{Ti}+1 \% \mathrm{Mn}) $$$$\mathrm{A} 2(1 \% \mathrm{Cr}+1 \% \mathrm{Ni}+1.5 \% \mathrm{Mo}+1.5 \% \mathrm{Cu}+1 \% \mathrm{Si}+0.2 \% \mathrm{~W}+0.2 \% \mathrm{Ti}+1 \% \mathrm{Mn}) $$$$ \mathrm{A} 3(2 \% \mathrm{Cr}+2 \% \mathrm{Ni}+2 \% \mathrm{Mo}+2.5 \% \mathrm{Cu}+0.5 \% \mathrm{Si}+0.2 \% \mathrm{~W}+0.2 \% \mathrm{Ti}+2 \% \mathrm{Mn}) $$$$ \mathrm{A} 4(2 \% \mathrm{Cr}+2 \% \mathrm{Ni}+1 \% \mathrm{Mo}+3.5 \% \mathrm{Cu}+1 \% \mathrm{Si}+0.2 \% \mathrm{~W}+0.3 \% \mathrm{Ti}+2 \% \mathrm{Mn})$$$$ \mathrm{A} 5(3 \% \mathrm{Cr}+3.5 \% \mathrm{Ni}+1.5 \% \mathrm{Mo}+4 \% \mathrm{Cu}+0.5 \% \mathrm{Si}+0.5 \% \mathrm{~W}+0.5 \% \mathrm{Ti}+3 \% \mathrm{Mn}) $$$$ \mathrm{A} 6(3 \% \mathrm{Cr}+3 \% \mathrm{Ni}+2 \% \mathrm{Mo}+3 \% \mathrm{Cu}+0.5 \% \mathrm{Si}+1 \% \mathrm{~W}+1 \% \mathrm{Ti}+3 \% \mathrm{Mn}) $$$$ \mathrm{A} 7(4 \% \mathrm{Cr}+4 \% \mathrm{Ni}+1 \% \mathrm{Mo}+4 \% \mathrm{Cu}+1 \% \mathrm{Si}+2 \% \mathrm{~W}+1.5 \% \mathrm{Ti}+2 \% \mathrm{Mn}) $$$$ \mathrm{A} 8(5 \% \mathrm{Cr}+5 \% \mathrm{Ni}+1.5 \% \mathrm{Mo}+3 \% \mathrm{Cu}+1 \% \mathrm{Si}+1.5 \% \mathrm{~W}+2 \% \mathrm{Ti}+3 \% \mathrm{Mn}) $$$$ \mathrm{A} 9(5 \% \mathrm{Cr}+5 \% \mathrm{Ni}+2 \% \mathrm{Mo}+4 \% \mathrm{Cu}+0.5 \% \mathrm{Si}+2 \% \mathrm{~W}+3 \% \mathrm{Ti}+3 \% \mathrm{Mn}) $$$$ \mathrm{A} 10(5 \% \mathrm{Cr}+5 \% \mathrm{Ni}+1.5 \% \mathrm{Mo}+3 \% \mathrm{Cu}+1 \% \mathrm{Si}+3 \% \mathrm{~W}+2 \% \mathrm{Ti}+2 \% \mathrm{Mn})$$Compared to the reference samples, an increase in corrosion resistance, hardness, and wear was observed in A9 and A10 alloy. The corrosion rate (corrosion/corrosion) of the alloy improved by a factor of (40 to 99) % compared to the reference samples (carbon steel, stainless steel 304, alloy 310). / 310S / 310H), and A9, A10 compared to (ZERON, 100 alloys Sandvik SX, ZECOR, SARAMET 23 and 35, improving (13%) A9 and (0.8%) A10. In simple immersion, the primary carbon steel alloys suffered from corrosion compared to improving the alloy (A1 to A10); the improvement percentage was more than (99) \%. Alloys (ZERON, ZECOR, Stainless Steel 304l), the improvement percentage in alloys only (A9, A10) from (24 to 55) %. The polarization test (Tafel) in concentrated acid on the alloy (A9 to A10) showed that the corrosion resistance of concentrated sulfuric acid was much better than that of carbon steel with a very high percentage. The improvement was about (99) % compared to carbon steel. Alloy A9 was the best in improving the resistance of carbon steel. Corrosion in all equipment and parts of the concentrated sulfuric acid plant (98%).

In evaluating the DMUs, two factors, namely the efficiency and the production size, are considered. When the production size of a unit is not optimal, its RTS determines that changing the resources in which direction, would enhance its productivity. In most past research, RTS is considered to be increasing or decreasing, and frontier analysis is used to determine it. In this paper, a method based on MPSS is developed that in addition to determining the RTS for each unit in a directional manner, the shortest changes in resources for achieving the suitable production size are also obtained. In this approach, the computational complexity and ambiguity in the unit’s RTS are absent.

In this work, we investigate the existence of weak solutions for the following semi-linear elliptic system\begin{equation*}\left\{\begin{array}{c}-\Delta u+p(x)u=\alpha u+\phi \left( x,v\right) \ \ \ \ \text{in }\Omega ,\\-\Delta v+q(x)v=\beta v+\psi \left( x,u\right)  \ \ \ \  \text{in }\Omega ,%\end{array}\right.\end{equation*}with Dirichlet boundary condition, where $\Omega $ is a bounded open set of $\mathbb{R}^{N}$ $\left( N\geq 2\right) ,$ $\alpha ,\beta $ two real parameters, $\left( p(x),q(x)\right) \in \left( L^{\infty }\left( \Omega \right) \right) ^{2}$ and $p(x),q(x)\geq 0.$ using the Leray-Schauder's topological degree and under some suitable conditions for the non linearities $\phi $ and $\psi$, we show the existence of nontrivial solutions.