مجله پژوهش های نوین در ریاضی
پیاپی 40 (بهمن و اسفند 1401)

One of the best-known inequalities which are used in many inequities is Jensen’s inequality. It is a base of some inequality such as the arithmetic mean, harmonic mean inequality also in inequality with respect to entropies including Shannon’s inequality and information theory. One of the best fundamental inequality in mathematics is Jensen’s inequality. In fact, Jensen's inequality is a base of some inequality such as the arithmetic mean, harmonic mean inequality also in inequality with respect to entropies including Shannon’s inequality, Ky Fan’s inequality and etc. Recently, the generalizations and refinement for the Jensen inequality have been considered by many authors, it has been generalized to applications of information theory and etc. The purpose of this research article is to give a new interesting refinement of Jensen’s inequality form particular finite sequences. Also, we give some applications with respect to this inequality in information theory and other aspect of sciences.

Fractional calculus is a branch of classical mathematics, which deals with the generalization of fractional order derivative and integral operator. Recently, a great deal of research has been carried out on the fractional calculus to study the phenomena associated with fractal structures and processes. Fractals have a fractional dimension and occur naturally in non-linear and imbalanced phenomena in various forms and contexts. In recent years, various types of derivatives and fractional and fractal calculus have been proposed by many scientists and have been extensively utilized. Measurements are localized in physical processes, and local fractional calculus is a useful tool for solving some type of physical and engineering problems. Gangal studied the local fractional calculus and got the relation between it and the fractals. Using the local fractional calculus and fractal properties, he defined the fractal-alpha calculus on a subset of the real line, which is a simple calculs, useful, structural and algorithmic. In this study, we first describe the fractal-F alpha calculus. Next, we propose The generalized variational iteration method based on the fractal calculus. To show the efficiency of fractal calculus and the new method, we solve several fractal partial differential equations with this method and show that this method is better, easier and more suitable than the two other methods mention the above.

Rapid development toward globalization, a competitive market, significant technological advances, and high customer expectations have encouraged companies to reduce costs and increase their competitive advantage. One of the things that can help companies achieve a competitive advantage is supply chain management. Information acts as an intermediary between all activities and operations within the supply chain. The innovation of this research can be shown in two aspects of application and modeling. In terms of application, with a review of the literature and investigating the application of multi-stage and network data development analysis in the supply chain, it was revealed that so far, the efficiency of financial and physical flows in the literature has been evaluated more and the indicators are mostly related to two financial and physical flows in the supply chain, therefore there is more research opportunity to evaluate the efficiency of information flow within the supply chain. Measuring the efficiency of information flow should be an integral part of supply chain management. Therefore, this research aimed to present a model to evaluate the efficiency of information flow in the supply chain. In terms of mathematical modeling, research innovation is considering the model of the network and reversible relationship in the supply chain. With a review of the literature, the indicators are investigated to evaluate the efficiency of information flow in the supply chain, and the validity of indicators is examined by the fuzzy Delphi method. Then the decision making unit and inputs and outputs of the model are introduced. In this research, the fuzzy network data envelopment analysis is used. In order to implement the models, we used the GAMS software.

The purpose of this study is to identify and evaluate strategic and future-making drivers in the field of science and technology of the country's tax system. This research has been done using futures research method with group decision making approach (Delphi ازی fuzzy triangular technique) and interaction analysis based on environmental scanning and interviews with tax experts. The research method used is descriptive-analytical in nature and based on a mixed method from a methodological point of view. The research method used is descriptive-analytical in nature and based on a mixed method from a methodological point of view. After identifying the first 24 drivers in the question, interview and fuzzy Delphi questionnaire stages, in order to finalize and evaluate the effective and future-making drives, all identified drives are analyzed based on the triangular fuzzy mean and Mick Mac software is used for integrated analysis of interactions between propellants. Based on the research findings, 5 drivers: 1- Intelligence of tax system based on data-driven 2- Standardization of tax processes based on information technology 3- Development of software and intelligent auditing systems 4- Training of personnel according to the uses New software of the day 5- The need to use systems and mechanisms of income and sales in order to be transparent in economic exchanges, were approved as strategic and futuristic drivers. In the continuation of this research, by matching the voting model, the conformity of the research results with the triangular fuzzy Delphi method was confirmed.

An efficient banking system is the most effective means for economic development, and the most important task of banks is to allocate resources in the form of banking facilities, and the design and establishment of the credit rating model has an effective role in increasing the efficiency of banks in equipping resources. In the current research, the design and explanation of the credit rating model was done using the data envelopment analysis model. Statistical sample related to the information of legal clients admitted to the stock exchange and receiving facilities from Tejarat Bank during the years 2018 to 2019; expressed In this context, 30 explanatory variables including financial and non-financial variables were examined. Among the available variables, finally, using the factor analysis technique and Delphi method, the variables affecting credit risk were selected and entered into the data coverage analysis model, and the efficiency scores of law firms were obtained using them. The results of the comparison of two data coverage analysis models indicate that the validity of the financial model is 0.072 more than the combined model. In the financial approach, 7 companies were efficient and in the combined approach, 12 companies were recognized as efficient.

Calculating and deriving the properties of the Fibonacci length of finite groups have been done since 1990, where the Fibonacci length of the finite group is defined to be the least integer such that for the Fibonacci sequence of the elements of the group , all of the equalities hold. In this paper we calculate Fibonacci length of 2- sylow subgroups of , by giving suitable generating sets for it.