In this paper we present an entropy characterization of general exponential model and use entropy of regular model to construct a testing of hypothesis for parameters of some common distributions such as normal, exponential, gamma and beta. Furthermore we use these concepts and methods to construct interval estimators for H(θ ) and for θ if H(θ ) is one to one, where H(θ ) is Shannon’s entropy of X with density function f (x) θ or probability mass function P (X = x) θ .

Promoting productivity in education not only contributes to socio-economic development but also through the training of efficient and creative human resources can lead to the development of the country. The main purpose of this study was to identify and rank the productivity indicators of The managers of Khorasan Razavi offices. research methodology: The present research interms of purpose is in research area and classification development and interms of how data collection is in exploratory mixed research group and was done in two qualitative and quantitative phases. The statistical population of the study in qualitative stage were professors and experts familiar with the topic of productivity 13 educational mangement professors were selected by theoretical sampling method. In the quantitative phases of research the statistical population were academic professors of educational mangement that 13 people were selected by census sampling method. In order to collect data the researcher was used from interview and researcher made questionnaire. Findings: The research questionnaire consisted of 20 items and 4 components. To answer the first question was used from interview and thematic analysis method and also has been identified 4 major indicators (individual ‘,managerial ‘,organisational‘,environmental )and 20 categories. From shannon entropy analysis was used to rank indicators. And the results showed that the managerial category with 0. 252 Significance factor had the most importance and environmental category with 0. 248 significance factor had the least importance among indicators. Conclusion: According to the findings of the study these four presented indicators are able to evaluate the productivity of the managers of education offices and they can consider these indicators.

Introduction Landslide is one of the most important and disastrous natural hazards which can bring many financial losses and heavy casualties worldwide every year. Entropy means a quantity of disorder between causes, results or decisions taken in different situations, it can be highly effective particularly in geomorphological studies such as landslide, where existing data are confused with uncertainties. Material and Methods Topographic maps 1: 25000 scaled, geological map of Makran and Marzanabad scale map 1: 100000 and ASAR images from ENVISAT since 2003 till 2009 in the region were used as the main data in this model. Active landslide also detected in the basin. Then, 17 zones were selected via field visiting and Google earth software images. Also location of landslides recorded using GPS. Analyzing the data and providing the required maps were done using Arc Gis10 and SAGA. A total number of 13 effective parameters were selected based on condition of studied areas for next step. Then slide layer, slide direction, elevation, geology, land use, distance to fault, distance from the river and distance from the road obtained by Arc Gis10 analysis, vegetation layer (NDVI) measured by ENVI4. 2 software and the layers of surface area ratio (ASR), topography index (TPI), Topographic Wetness Index (TWI) and slide length index (SLS ) were analyzed by SAGA software. After providing the information layers and importing the landslide locations, the properties of each slip extracted due to the mentioned layers and scoring was regarding to the role of each factor in the occurrence of slide. And the primary matrix was formed according to the entropy method. The decision matrix contains information which can be evaluated by entropy as a criterion. Then by calculating the entropy matrix and weight of 13 factors (WJ), the (HI) index will be obtained as landslide risk hazard Results and discussions At first due to the characteristics of the occurred landslide, each class was scored from the information layers which were obtained by examining the region after two field visits, study of aerial photographs and satellite imagery and identification of the affecting factors and their roles to create slip. Then the information layers used in the research were categorized and scored as a raster data and utilized as the main data in the formation of an entropy matrix for further analysis. To convert qualitative values into quantitative a bipolar scale is used. The bipolar interval scale is a general method for ranking quantitative and qualitative indexes. Measurement in this technique is based on a 10-point scale so that zero specifies the lowest possible value which is practically comprehensible and ten represents the maximum possible value of the intended index. The middle point is also the point of dividing the scale into favorable and unfavorable data. Conclusion Prioritizing the effective factors using the Shannon entropy index indicates that data layers such as slides direction, land use, elevation, slope, normalized vegetation index and the distance from the river had the greatest effect on the landslide occurrence in the area. And the topography, moisture index, geology, distance from fault and road, and the rest of the information layers had the least effect. Based on landslide hazard map of Taleghan watershed, very low to low risks regions are some areas in the northeast, central and southwest regions, while most of the studied areas have a moderate to very high risks. In general, site locations which could be at risk in the event of a landslide are limited to residential areas, roads, rivers, lakes and power lines. There are various land use in the region and Residential and demographic areas are at the top of the priority list. One the other hand there is Taleghan dam which can create a much greater potential risk if landslide happens at its location.

Objective: The purpose of this article is to investigate and explain the amount of attention paid to the selected economic components and its analysis in the content of selected official education books of the elementary school in Iran (including document content analysis). In the country of Iran, all textbooks in the formal education system are prepared and adjusted based on the document on the new development of the education system, which is an abstract of the national document and all the upper documents set in the strategic plan of education in the whole country. The main question of the research that pursues the goal is: Is there enough attention paid to selected economic areas and components in the contents of selected primary school textbooks (which are written based on the guidelines of the fundamental transformation document or upstream documents) in a way which can be a generator of wealth and create economic growth and prosperity in the country in the future by influencing the thinking and behavior of students? Sub questions. In the content of selected elementary school books (academic year 97-98), which of the educational fields (knowledge, attitude, skill) has been given more attention? In the contents of the selected elementary school books (academic year 97-98), which of the selected economic components has been given more attention? Method: The selection of these components is based on the theoretical foundations of classical economics in the description of "rational man" and the theory of Inkels in the description of "modern man" and includes the most important components of achieving development. The statistical population includes 10 volumes of books selected from the elementary school, whose reliability and face validity have been checked and confirmed by experts. Analytical research community: In this research, a total of 10 volumes of elementary school books were examined as follows:-All Persian primary school books in all grades.-All elementary school social studies books in all grades.-Sixth grade thinking and research. Based on the theoretical foundations related to the modern human being and with emphasis on the three areas of knowledge, attitude and skills, a set of economic components were extracted and then their formal and conceptual validity and their suitability with the subject of the article were calculated by several experts. In order to carry out content analysis, the initial 25 components were converted and divided into sub-components or selected objective and behavioral economic manifestations, and in this way, a content verification checklist was formed transparently and operationally. It should be noted that in the text of the books (statistical society), the following components have been investigated and counted, either openly, or the themes that have been mentioned. Some of these components are: giving importance to material life, importance to increasing productivity and efficiency and finding new ways of doing things, a sense of patriotism as a motivation to advance society, opposition to traditions that are against development, belief in human power. In overcoming nature and going through the steps of progress towards progress regularly and continuously, and. . . Results: The results of the research count showed that only about 3. 4 percent (7463 words out of 219069 words) of the total words counted in these books are dedicated to selected economic components. According to the obtained results and in response to the first sub-question of the research (in the contents of the selected primary school books, which of the educational fields has been given more attention? ), it can be said: The most attention has been given to the attitudinal area and the least amount of attention to the knowledge area. And in response to the second sub-question of the research (in the contents of the selected primary school books, which of the selected economic characteristics has been given more attention? ), it should be said: in all the selected primary school books, the patriotism component with 19 frequency has the highest rate and the resource value component with 1 frequency have the lowest number of counts (Table 2). Finally, according to the analysis of the results obtained from this research and in response to the main question, is the content of the selected primary school textbooks sufficiently focused on the selected economic areas and components, in such a way that it can influence thinking in the future? And the behavior of the students will generate wealth and create economic growth and prosperity in the country? Conclusion: The results of this study indicate little attention to the selected economic components in selected primary school textbooks.

Despite the government's policies and efforts to boost fertility rates in Iran, the total fertility rate has been declining over the past two decades. This research aims to identify the weight of determinants of fertility in Iran's provinces and provide relevant policy recommendations. The study utilizes the mathematical methods of Shannon entropy and K-means clustering. The findings reveal that per capita gross product holds the highest weight coefficient among fertility determinants across the provinces. Furthermore, the influence of economic, social, and demographic indicators on fertility varies among provinces. Provinces with higher coefficients in social and demographic indicators tend to exhibit higher fertility rates. Notably, provinces such as Sistan and Baluchistan, North Khorasan, and South Khorasan, despite low economic indicators, maintain fertility levels above replacement level. In conclusion, this research emphasizes the significance of understanding localized determinants of fertility and advocating for tailored policy interventions at the provincial level. Hence, a nuanced approach to regional politics becomes imperative. Furthermore, provinces like Alborz, Semnan, Gilan, Kermanshah, Ilam, and Isfahan, which score low on the overall index, should be prioritized for targeted population policies. Extended AbstractIntroductionThe population and fertility rates have long been a subject of concern for policymakers and researchers. Total fertility rate (TFR) has significantly declined over the past three decades in Iran. TFR dropped from 7 children per woman in the 1960s to 1.65 in 2023. This decline is attributed to various factors including increased female education, delayed marriages, greater independence for women, and the success of family planning programs. Despite government efforts to reverse this trend through pronatalist policies, such as financial incentives and family support programs, fertility continues to decline. This suggests that a more nuanced, regionally tailored approach is needed, as fertility determinants vary across Iran’s diverse ethnic and cultural regions. The study aims to explore these regional differences and examine whether uniform policies can effectively raise fertility levels across the country. Methods and DataThis research is quantitative and employs the Shannon entropy method. The data was sourced from the Statistical Center of Iran, specifically the 2016 Population and Housing Census. The statistical population includes all provinces of Iran (31 provinces), with each province serving as the unit of analysis. Initially, the key factors influencing low fertility were identified through brainstorming and a review of previous research. Using Shannon’s entropy method, the weight of each factor was calculated and interpreted for all 31 provinces.The weights assigned to each index were multiplied by the corresponding index values to calculate the score for each province in that specific function. Finally, the provinces were categorized based on their evaluation scores using k-means clustering. The clustering was then performed based on the provinces' scores in economic, social, and demographic functions. FindingsCompared with 2016, the TFR in 2021 is much lower, although the government has taken some serious measures toward increasing fertility over recent decades. TFR decreased from 1.65 in 2016 to 1.2 in 2021, and such a reduction also has taken place for all provinces except Khuzestan. In 2021, Sistan and Baluchistan, South Khorasan, and Khuzestan had fertility rates above the replacement level. The provinces of Golestan, North Khorasan, and Razavi Khorasan had fertility rates near replacement level (2 to 2.1 children), while the remaining 25 provinces had fertility rates below replacement.Table 1 presents the calculated weighting of fertility determinants using the entropy method. The results indicate that GDP per capita holds the highest rank and carries the most weight. Conversely, the ratio of women to men, with the lowest weight, is ranked last.         Table 1- Normalized weight for each index using the Shannon entropy method  The provinces of Tehran, Khuzestan, and Bushehr have the highest economic ranks, while Chaharmahal and Bakhtiari, Sistan and Baluchistan, and North Khorasan rank the lowest. Of Iran's 31 provinces, only 11 have an economic score above the national average. Regarding economic clustering, 23 provinces fall into the third cluster (indicating poor conditions), while only six are in the first cluster, representing the best conditions. These findings highlight significant economic disparities across the provinces.Regarding social function, the provinces of Sistan and Baluchistan, North Khorasan, and South Khorasan rank the highest, while Tehran, Semnan, and Alborz rank the lowest. Regarding social clustering, West Azarbaijan, Bushehr, and Qom are in the first cluster (better conditions), whereas Tehran, Semnan, and Alborz fall into the third cluster (weaker conditions). Regarding demographic function, Sistan and Baluchistan, Hormozgan, and North Khorasan hold the highest ranks, while provinces like Tehran and Isfahan rank among the lowest. In total function, Sistan and Baluchistan rank first, while Gilan, Semnan, and Alborz rank the lowest.Finally, it is important to note that, given the significant ethnic and religious diversity across Iran's provinces, it was expected that ethnic and religious minorities would cluster together based on economic, social, and demographic factors. However, the observed clustering appeared to be more geographically based. Conclusion and DiscussionPolicies aimed at increasing fertility should consider both the economic and social diversity among provinces, as uniform policies may not yield the desired results. Given the provincial differences in fertility rates, each province should adopt policies that align with its specific demographic realities. Therefore, the unique conditions of each province or region, based on various indicators, must be considered when formulating policies. The second point is that, based on the overall index's function, we can conclude that in provinces where a balance among the indicators is maintained (such as Khuzestan), there is hope that the fertility rate will remain above replacement level and not decline. Additionally, considering the strong correlation between social indicators and total fertility rates, it can be inferred that if national policy shifts towards a regional focus—emphasizing the most influential indicators in each province—the potential for increasing TFR is within reach.Based on these findings, it is recommended to implement a population policy targeting the central and northern provinces, with a focus on prioritizing and planning efforts to improve key social indicators. These include increasing the overall marriage rate, reducing divorce rates, lowering the average age of marriage for both men and women and providing support packages for families. These efforts should be coordinated across various departments. Second, the economic and demographic indicators in the eastern and western provinces of the country were less favorable. It is therefore necessary to closely monitor and address these indicators in these regions to stabilize and improve the total fertility rate. AcknowledgmentsThis article is based on the master's thesis of the third author in the field of demography, completed at the Faculty of Economic and Social Sciences, Bu-Ali Sina University. We would like to express our sincere gratitude to the esteemed referees of both the thesis and the article.

Selection of appropriate material is a crucial step in engineering design and manufacturing process.Without a systematic technique, many useful engineering materials may be ignored for selection. The category of multiple attribute decision-making (MADM) methods is an effective set of structured techniques. Having uncomplicated assumptions and mathematics, the MULTIMOORA method as an MADM approach can be effectively utilized for materials selection. In this paper, we developed an extension of MULTIMOORA method based on Shannon entropy concept to tackle materials selection process. The entropy concept was considered to assign relative importance to decision-making attributes. The proposed model consists of two scenarios named the weighted and entropyweighted MULTIMOORA methods. In the first scenario, subjective weight was considered in the formulation of the approach like most of conventional MADM methods. The general form of entropy weight that is a combination of subjective and objective weighting factors was employed for the second scenario. We examined two popular practical examples concerning materials selection to show the application of the suggested approach and to reveal the effect of entropy weights. Our results were compared with the earlier studies.

Instantaneous unit hydrograph (IUH) is a hydrograph that has used for calculation of direct runoff hydrograph in watersheds and recent addition to formal methods, Shannon entropy theory consider for calculation of direct runoff hydrograph. If the system disorderly is measured in terms of entropy then the probability distribution of the events, provides in terms of entropy. In this theory, defined travel time as a random variable, the maximizing the entropy on based this parameter and also specifies constraints, the least-biased probability density function, determining parameters of the IUH and finally obtaining applicable IUH equation. In this study, six events of Lighvan watershed has been studied that located in Northwest Iran. After calculating travel time and determining parameters on based entropy, derivation applicable IUH equation and calculated direct runoff hydrograph. For estimated and more evaluated IUH and direct runoff hydrograph has used Gamma distribution that result showed good accuracy of the entropy theory. The results indicate acceptable performance of the entropy model shows the average correlation coefficient (0.828), mean error of peak (17.35%), entropy index (2.47 knot) and nash-sutcliff value (NS=0.742) in verification events.

Introduction: English language teaching curriculum is very important in effective teaching and learning of students. In order to pay attention to the importance of teaching English as one of the most important communication tools, it is necessary to develop a curriculum that can accommodate all the necessary English language teaching needs. Therefore, the purpose of this study was to analyze the content of the first high school English language curriculum textbooks by Shannon Entropy method. Methods: The research method is content analysis by "Shannon entropy" method that presents data processing in the context of content analysis with a new, quantitative and qualitative look. Entropy in information theory is an indicator for measuring uncertainty, which is represented by a probability distribution. The content of the layout was responsive (first-language English textbooks) and seven major components and 45 sub-components of English language teaching. Results: Shannon entropy content analysis results showed that the study of English language books in the first course of high school, the component of English learning strategies with the 1391 cases was the most frequent, and the least amount related to the challenges of learning English with zero cases. Conclusion: In the content of official textbooks, some of the components of English language education are less or less attentive, while the design, implementation and administration of English language education programs in the field of education are of particular importance.