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The present paper addresses a novel two-echelon multi-product Location-Allocation-Routing problem (LARP). It also considers the integration of issues such as disruption, environmental pollution, and energy-efficient vehicles as currently critical issues in a Supply Chain Network (SCN) that includes production plants, central warehouses, and retailers. The aim of this study is to minimize the total cost, which involves costs related to the establishment, shipment processes, environmental pollution, travelling, vehicle usage, and fuel consumption, in a way to cover the total demand of retailers. The problem is NP-hard; thus, to solve it approximately, we developed Grey Wolf Optimization (GWO) and Particle Swarm Optimization (PSO) algorithms. The numerical analysis showed that the proposed algorithms yielded high-quality results in a short computational time where the average gaps of GWO and PSO against CPLEX are 0.78% and 0.9%, respectively. Then, a case study of a dairy factory in Iran is conducted to evaluate the applicability of the proposed methodology and find the optimal policy. Finally, a set of sensitivity analyses is carried out to suggest managerial insights and decision aids. [ABSTRACT FROM AUTHOR]

Conflict of interests is a situation when someone is in need of other people's trust on one the hand and has personal or general interests on the other hand, resulting in conflict with the given responsibility. In this research work, an attempt was made to find the relation between declarations of conflict of interests and reporting positive outcomes in the dental journals in Iran (2000–2016). In this analytical/cross-sectional study, first Health and Biomedical Information was searched and all the Persian and English dental journals published in Iran were collected. Then, all the papers published in the journals from December 2000 to December 2016 were collected and categorized in terms of the year of publication, author or authors' affiliations, Persian and English journal, type of the substance or the drug used (including the manufacturing company), declarations of conflict of interests and the positive or negative conclusion of the report. Data were analyzed with the Fisher's exact test and Chi squared test, using the program SPSS 18. In numerical analysis, the significance was set at P < 0.05. Seventeen dental journals in Persian and English were analyzed: 10 in English and 7 in Persian. Reviewing these studies showed that of 1021 articles in Persian, in 128 cases there was no mention of a declaration of conflict of interests and in 11 cases, the COI had been stated. In addition, from 1220 articles in English, in 825 cases there was no mention of declarations of conflict of interests and in 45 cases, the declarations of COI had been mentioned. There was no significant relation between the COI and 'no' COI and the reporting of positive outcomes in papers in Iranian dental journals in terms of the journal type, year of publication and the journals' guarantee form (P = 0.25, P = 0.41 and P = 0.09). A total of 83% of studies with declarations of COI had one positive outcome, with a significant relationship in this field; however, in 73% of studies with no COI, there was one positive outcome, too. In general, the society expects that doctors would not consider any incentives except the health of the patients in the efforts made by them. The severity of the consequences of COI is of higher value when the patients' health is endangered due to it. In addition, COI might change the attitude and approach of other doctors and peers. [ABSTRACT FROM AUTHOR]

These two-part paper series aim to optimize the rates of inspection-based maintenance or routine-test on power system equipment. Part I introduced a novel probabilistic model using Markov chains for the inspection-based maintenance and derived the relationships between the transition rates. Part II demonstrates how the proposed method can effectively address budget and data availability constraints. It also presents the derived relationships between the optimal preventive maintenance rate and risk indices. The results presented in this paper are based on an industrial project conducted to optimize the preventive maintenance period of high-voltage equipment in Iran. Additionally, this companion paper provides practical insights, including implementation remarks, and a comprehensive dataset for failure and defect analysis, which proves useful for future research and applications. • A case study on a real sub-transmission substation for the proposed model. • Derived relations between the optimal preventive maintenance rate and risk indices. • Analysis of the simultaneity in the inspection of series components. • How to overcome data and budget limitations by the proposed sensitivity analysis. • Practically, how to use the available data to optimize the inspection rate. [ABSTRACT FROM AUTHOR]

Due to its location in one of the most seismically active regions in the world, Iran has witnessed many devastating earthquakes through history. To finance a part of these losses and reconstruction expenses, earthquake insurance has been offered as a rider of fire policy by the Iranian insurers. This mechanism, if well operated, can substantially contribute to disaster risk management. On the other hand, if the pricing and management of catastrophe risk lack a sound, risk-based practice, it might add to the problems and act to the detriment of disaster risk management. In this paper, we first compare the current earthquake insurance pricing and risk management in the Iranian insurance industry with a state-of-the-art insurance regulation in the European Union (Solvency-II). Then, we examine the consequence of following each approach in terms of business profitability and viability by conducting a numerical analysis on a hypothetical portfolio of property risks in Iran. The results suggest that maintaining the current insurance pricing and risk management techniques in Iran will probably lead to a substantial accumulation of earthquake risk for domestic firms and eventually endanger the solvency of these companies in the event of large- scale earthquake losses in future. [ABSTRACT FROM AUTHOR]

In this paper, a recursive training procedure with forgetting factor is proposed for on-line calibration of temporal neural networks. The forgetting factor discounts old measurements through an on-line model calibration. The forgetting factor approach enables the recursive algorithm to reduce the effect of the older error data by multiplying the error data by a discounting factor. The proposed procedure is used to calibrate a temporal neural network for reservoir inflow modeling. The mean monthly inflow of the Karoon-III reservoir dam in the south-western part of Iran is used to test the performance of the proposed approach. An autoregressive moving average (ARMA) model is also applied to the same data. The temporal neural network, which is trained with the proposed approach, has shown a significant improvement in the forecast accuracy in comparison with the network trained by the conventional method. It is also demonstrated that the neural network trained with forgetting factor results in better forecasts compared to the statistical ARMA model, which has been calibrated through this approach. [ABSTRACT FROM AUTHOR]

This paper reports the morphological characters of 18 Iranian species of the genus Alchemilla using light and scanning electron microscopy. The pollen grains are monad, radially symmetrical, isopolar, or subisopolar; small to medium in size; triand tetracolporate; rectangular to cylindrical (from equatorial view) and triangular to circular (from polar view) in outline; and prolate-spheroidal to subprolate and prolate in shape. The exine ornamentation is psilate and microechinate. Based on the exine sculpturing and microechinate distribution pattern, three main types, four subtypes, and two categories of pollen grains were recognized. We used cluster analysis and principal component analysis to determine the potential contribution of pollen morphological characters to the species relationships. Our findings revealed the significance of palynological evidence in explaining the species relationship. The results of two multivariate analyses showed a close affinity among the seven studied species (A. amardica, A. sericata, A. fluminea, A. kurdica, A. hyrcana, A. sedelmeyeriana, and A. pesudocartalinica). [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the concept of vulnerability is used to measure the capacity to withstand earthquake disasters in different regions. The purpose of vulnerability analysis is to identify appropriate actions that can be taken to reduce the vulnerability before the potential for damage is realized. The objective of this paper is to determine the vulnerability of different parts of a city against earthquake by data envelopment analysis (DEA). A numerical example demonstrates the application of the DEA for the 20th district of Tehran. [Copyright &y& Elsevier]

Abstract: This paper presents an updated study and numerical modelling of the Tabas, eastern Iran earthquake (), which occurred on September 16, 1978, using new techniques recently proposed by various researchers. Firstly, the near-fault ground motions recorded at a station very close to the fault were examined based on the characteristics of the velocity pulses and the frequency content of the motions. Evidence of directivity effects in recorded, near-fault ground motion, has been investigated using various methods. In the second part of this paper, stochastic simulations of near-fault, strong ground motion, using finite-fault modelling, based on a dynamic corner frequency recently proposed by Motazedian and Atkinson [Motazedian, D. and Atkinson, G. “Stochastic finite-fault modelling based on a dynamic corner frequency”, Bull. Seismol. Soc. Amer., 95(2), pp. 995–1010 (2005)], have been presented. In order to model the impulsive behaviour of near-fault ground motion, the finite-fault model was combined with the mathematical expression of Mavroeidis and Papageorgiou [Mavroeidis, G.P. and Papageorgiou, A.S. “A mathematical representation of near-fault ground motions”, Bull. Seismol. Soc. Amer., 3, pp. 1099–1131 (2003)] for modelling pulse characteristics. A new set of modelling parameters has been recommended and good agreement has been found between the recorded and simulated response spectra. The velocity pulses observed in near-fault ground motion records could also be mimicked. [Copyright &y& Elsevier]

This paper reviews the dynamic stability of the right abutment of the Gotvand Dam, the highest earth fill dam located at the southwest of Iran, using the distinct element method. The right abutment comprises a soft clayey layer called the Lower Mudstone Siltstone interlayer (LMST) covered by disturbed conglomerate blocks. According to the results of the dynamic numerical analyses, no collapse will occur at the right abutment area. However, the residual shear displacement of disturbed blocks on the LMST layer will be 20–60 fcm for Maximum Credible Earthquake (MCE) loading. Such a displacement can cause cracking in the cut-off wall, and hence it was considered the main indicator of the right abutment instability. Investigating different solutions, such as buttressing and excavation, showed that these approaches are not effectively preventing abutment shear displacement. Therefore, the designing process was carried out by accepting the risk of cut-off wall cracking in seismic loading conditions. However, some pre-remedial solutions (as discussed thoroughly in the text) have been considered in the construction process to minimize the risk of water seepage from the cut-off wall. [ABSTRACT FROM AUTHOR]

This study provides a multi-disciplinary overview of the seismology and geodetic data with tectonics analysis in order to provide an evaluation of stress trajectories, and probabilistic fault rupture hazard assessment. Based on the different scenarios obtained from the comparison of several overviews and their interpretation, we investigated the kinematics and active tectonics of different structural zones. In this study, the magnitudes and directions of seismic and geodetic strain rates (SSR and GSR) were evaluated using reliable earthquake focal mechanisms and all available GPS data (1999–2015) in the structural subzones of northern Iran, where have experienced more than 14 strong instrumental earthquakes (Mw ≥ 6). In addition, a tectonic stress model was inferred from the Focal Mechanism Stress Inversion (FMSI). The new crustal stress map was proposed by the weighted average analysis of the SSR, GSR, and FMSI. N35.5° E and N104° E were estimated for the Alborz and Talesh mountains, respectively. The numerical analysis of stress regimes confirms the slip partitioning mechanism of oblique shortening on the sub-parallel thrusts and strike-slip faults in the area. Four main stress regime categories were defined, including thrust (49.37%), strike-slip (39.24%), thrust with a strike-slip component (2.53%), normal (1.27%), and unknown faulting (7.59%). Seismic and geodetic moment rates (SMR and GMR) and their comparison were also calculated in order to evaluate the function of these parameters in determining the seismicity arrangement. The ratio of the seismic/geodetic moment rates for the area is ~70.7%. This ratio for the Alborz, western Koppeh-Dagh, north part of Central Iran, South Caspian Basin, and Talesh is ~0.9, 0.3, 11.9, 0.3, and 57.3, respectively, which indicates the most elastic energy has been released in the Talesh and the north part of Central Iran. The comparison of geodetic moment rates in the subzones of the area indicates that geodetic deformation is high in the Central Alborz (networks 8, 9, 17) and western Koppeh-Dagh (networks 5, 13). [ABSTRACT FROM AUTHOR]

Highlights: [•] This paper addresses a new clustering-classification method for classifying the severity of road accidents in Iran. [•] k-Means and some classification methods are used for running numerical experiments. [•] Some activation functions have been used for training the neural networks. The results of them are compared together. [•] Also, the accuracy of classification is compared by using different approaches in k-mean. [•] Silhouette technique was used to confirm the validity of the clusters. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the hourly measured wind speed data for years 2007–2010 at 10 m, 30 m and 40 m height for Binalood region in Iran have been statically analyzed to determine the potential of wind power generation. The study showed that the long-term wind speeds were found to be relatively high. The numerical values of the dimensionless Weibull shape parameter (k) and Weibull scale parameters (c) were also determined. Based on these data, it was found that the numerical values of the shape and scale parameters for Binalood varied over a wide range. The yearly values of k at 40 m elevation range from 2.165 to 2.211 with a mean value of 2.186, while those of c are in the range of 7.683–8.016 with a mean value of 7.834. However, the yearly mean wind speed, mean power density and power density of Binalood at 40 m height are found as 5.923 m/s, 305.514 W/m2 and 2676.30 (kWh/m2/year) respectively. The results show that Binalood has available great wind energy potential for grid connection system. [Copyright &y& Elsevier]

Abstract: Employing the multifractal detrended fluctuation analysis (MF-DFA), the multifractal properties of trading behavior of individual and institutional traders in the Tehran Stock Exchange (TSE) are numerically investigated. Using daily trading volume time series of these two categories of traders, the scaling exponents, generalized Hurst exponents, generalized fractal dimensions and singularity spectrum are derived. Furthermore, two main sources of multifractality, i.e. temporal correlations and fat-tailed probability distributions are also examined. We also compare our results with data of S&P 500. Results of this paper suggest that for both classes of investors in TSE, multifractality is mainly due to long-range correlation while for S&P 500, the fat-tailed probability distribution is the main source of multifractality. [Copyright &y& Elsevier]

Abstract: As multivariate numerical classification become increasingly available to Earth Scientists, there is a corresponding need to introduce a scientific criterion or stopping rule to determine the optimum number of classifications. The increasing interest in comparative, experimental numerical zoning makes such a criterion highly desirable. In this research multivariate data comprising new and updated geological and geophysical characteristics of Iran have been used to construct Automatic Integrated Self-Organized Optimum Zoning (AISOOZ) maps. The Wilk''s Lambda Criterion and the relative discrepancy of Wilk''s Lambda have been applied for the first time as stopping rules to measure the relative usefulness of zoning maps. The application of these criteria has eventually led to an optimum map with 11 zones. Our AISOOZ map reveals some remarkable features that cannot be observed on conventional tectonic maps of Iran. For example: contrary to the conventional maps, the AISOOZ map reveals the much disputed extent and rigidity of the microplate in the central and eastern parts of Iran and makes a clear distinction between the Makran ranges and the eastern Iran mountains. The AISOOZ method is a new approach to zoning, organized in a hierarchy of increasing complexity, and developed from reductionist approach. Based on this logic, the AISOOZ method casts an interesting light on the connection between the zoning hierarchy and the geodynamic evolution of the study area. It also helps to estimate the likelihood of earthquake occurrence for each zone. The AISOOZ map not only can be re-assessed quite often, but also provides us with a means for on-line information availability. The information can be tailored to the user''s specific needs and down-loaded to the user''s computer. Furthermore, the general approach presented in this paper could readily be adapted to pattern recognition and zoning maps of any space, regardless of context or scale. [Copyright &y& Elsevier]

Abstract: The conventional deterministic approach based (DAB) methods are simple and widely used to determine an adequate chain pillar size in coal mines where geological settings, coal characterizations and mining methods have been explored. It is evident that such deterministic methods have some intrinsic limitations in handling uncertainties in material properties, non-regular geometries and different mining operations. In the deterministic stability analysis of a chain pillar, the safety factors as well as all input parameters are deterministic. Although, these parameters generally exhibit uncertainty and should lead to a probabilistic expression for the safety factor. The probabilistic analysis provides a confidence interval to express the reliability of chain pillars stability. In this paper, safety factor is defined as a probabilistic function and the failure probability of designed chain pillar of Tabas coal mine is then evaluated using the First Order Second Moment (FOSM) and the Advanced Second Moment (ASM) methods. The results of the probabilistic stability analysis show that the confidence interval for designed pillars with both mentioned methods applied are similar and their values vary from 84% to 88%. The results of such analyses can be used as a basis for decision-making about the size of chain pillars and reduce the risk of pillars stability as well as the uncertainties. However, a trade-off between cost is essential for making the final decision. [Copyright &y& Elsevier]

The study presented in this paper attempts to evaluate some interpolation techniques for mapping spatial distribution of soil pH. salinity and plant cover in Hormorgan province, Iran. The relationships among environmental factors and distribution of vegetation types were also investigated. Plot sampling was applied in the study area, Landform parameters of each plot were recorded and canopy cover percentages of each species were measured while stoniness and browsing damage were estimated. Results indicated that there was a significant difference in vegetation cover for high and low slope steepness. Also, vegetation cover was greater than other cases in the mountains with calcareous lithology. In general, there were no significant relationships among vegetation cover and soil properties such as pH, EC, and texture. Other soil properties, such as soil depth and gravel percentage were significantly affected by vegetation cover. Moreover, the geostatistical results showed that kriging and cokriging methods were better than inverse distance weighting (IDW) method for prediction of the spatial distribution of soil properties. Also, the results indicated that all the concerned soil and plane parameters were better determined by means of a cokriging method. Land elevation, which was highly correlated with studied parameters, was used as an auxiliary parameter. [ABSTRACT FROM AUTHOR]

Abstract: Longwall mining is a common mining method in Iran that is often affected by out-of-seam dilution (OSD). The field investigations performed in Tabas coal mine show that OSD often occurs due to roof falls in front of the face area before support setting and also removing some floor material. The increase in unsupported roof span above the shearer may cause difficulty in controlling the roof and consequently increases dilution of the run of mine (ROM) coal. The paper presents the results of a study on some dominant factors causing OSD in prop-free front of the face in longwall retreat mining method. A series of two-dimensional numerical models are developed and analyzed to examine the effects of mining depth, in-situ stress, unsupported roof geometry above the shearer as well as roof and floor strata quality and dip of coal seam on OSD. Two criteria were established, one considers the roof falls, defined as low stress level or plasticity zones under yield tension which roof material unravels and other is about removing floor, defined as depth of support and shearer sinking into the floor. The equivalent linear relaxation depth (ELRD) and depth of removing floor (DRF) concepts were used to quantify OSD. The methodology presented in this study is useful since it can be applied to develop mine-specific design tools for the prediction of OSD. [Copyright &y& Elsevier]

The application of numerical weather prediction (NWP) products is increasing dramatically. Existing reports indicate that ensemble predictions have better skill than deterministic forecasts. In this study, numerical ensemble precipitation forecasts in the TIGGE database were evaluated using deterministic, dichotomous (yes/no), and probabilistic techniques over Iran for the period 2008-16. Thirteen rain gauges spread over eight homogeneous precipitation regimes were selected for evaluation. The Inverse Distance Weighting and Kriging methods were adopted for interpolation of the prediction values, downscaled to the stations at lead times of one to three days. To enhance the forecast quality, NWP values were post-processed via Bayesian Model Averaging. The results showed that ECMWF had better scores than other products. However, products of all centers underestimated precipitation in high precipitation regions while overestimating precipitation in other regions. This points to a systematic bias in forecasts and demands application of bias correction techniques. Based on dichotomous evaluation, NCEP did better at most stations, although all centers overpredicted the number of precipitation events. Compared to those of ECMWF and NCEP, UKMO yielded higher scores in mountainous regions, but performed poorly at other selected stations. Furthermore, the evaluations showed that all centers had better skill in wet than in dry seasons. The quality of post-processed predictions was better than those of the raw predictions. In conclusion, the accuracy of the NWP predictions made by the selected centers could be classified as medium over Iran, while post-processing of predictions is recommended to improve the quality. [ABSTRACT FROM AUTHOR]

The expansion of the Neyriz marble mine into deeper levels caused an unexpected failure particularly in the toes of lower benches. This phenomenon can impact the overall stability of the quarry and results in undesirable environmental and technical consequences. To understand the failure mechanism, a comprehensive study including-laboratory testing, in situ field testing and theoretical analyses are carried out. The theory of the brittle failure which was mainly developed based on the experiences gained during excavation in granite rocks is adopted and augmented in this study to explain the governing mechanism of failure. Mechanical properties of the marble are determined using conventional rock mechanics tests, and the in situ stress field was evaluated using a modified under coring test. Analyzing the laboratory and field data with the available empirical criteria for brittle failure shows that the level of stress in the lower bench is high enough to initiate the brittle failure. Finally, constitutive models developed for this failure mode are adopted in conjunction with numerical modeling to investigate the observed failure in the quarry. Two modeling strategies, based on elastic and elastic-plastic analyses, are considered. Comparing the predicted failure surface with the observed failure profile, it can be concluded that the brittle failure criteria can very well capture the failure mechanism in this marble quarry. This shows that the criteria proposed to describe spalling failure around underground excavation in granite can be effectively employed for assessing the brittle failure in deep open cast and quarry mines in good quality rocks such as marble. [ABSTRACT FROM AUTHOR]

In order to prevent problems like casualties, delays in tunneling procedure, and increasing tunneling costs, predicting groundwater inflow into tunnels and designing an efficient drainage system are necessary. Several analytical solutions exist in the literature, but they cannot accurately estimate groundwater inflow due to simplifying assumptions. Numerical methods, however, are increasingly used to predict groundwater inflow with higher accuracy. This study is aimed at predicting the steady state groundwater ingress into Tabriz line 2 metro tunnel (TML2: a shallow urban tunnel) by considering model dimensions as critical factors in the numerical analysis process. A 2-D numerical finite element analysis of steady state groundwater inflow was performed along the tunnel based on geological and geotechnical investigations. Water inflow into TML2 was then estimated based on optimum model dimensions. The total amount of groundwater inflow into TML2 was estimated to be 7013.6 l/min. The maximum cumulative water inflow into the tunnel was also predicted to occur between 15.55 and 16.25 km in the tunnel with a 4754 l/min inflow rate, which demands an effective drainage program. Finally, for validation of the methodology groundwater inflow values obtained through 2D finite element analysis were compared to those calculated with a well-known inflow evaluation method (Raymer solution). [ABSTRACT FROM AUTHOR]

Energy, due to its increasing usage in various broad areas has been maintained as a vital factor in economic growth and development of societies. Meanwhile, natural gas is considered as one of the most important energy sources. Therefore, the efficiency and the productivity of the gas companies are crucial to be assessed. Numerous examples from industrial multistage processes including internal structures exist, such as petrochemical industry, perfume manufacturing, etc. Despite the fact that internal structures are not considered in conventional DEA, they are being taken into account in Network DEA. An evaluation of efficiency via Network DEA has been conducted in Iranian gas companies during 2002-2004 and the results are discussed in the following pages. After acquiring companies' efficiency scores, we ranked them through Cross Efficiency (CE) technique thoroughly. Ultimately, we indicated the effectiveness of each input /output selected factors in efficiency measurement. [ABSTRACT FROM AUTHOR]

This study investigated the export status of stone fruits in Iran during 1997 to 2010. Export trends and revealed comparative advantage of indices, namely, Revealed Comparative Advantage (RCA), Revealed Symmetric Comparative Advantage (RSCA), and Relative Export Advantage (RXA) as well as Trade Mapping (TM) were investigated for cherries, plums, peaches, and apricots. Target markets for these products were ranked using numerical taxonomies. The results showed that Iran had export's comparative advantage for stone fruits only in 2007 and 2010. But, this index had a positive growth for the stone fruits in those years, indicating an increasing trend in the export status of these products. Trade mapping analysis indicates that although the export market for these products has declined during the period studied, Iran has taken a greater share of the market and is among the winner groups. The principal export markets in decreasing order were found to be Germany, The UK, France, Italy, the Netherlands, Russia, Saudi Arabia, Bahrain, Switzerland, the UAE, and Afghanistan. [ABSTRACT FROM AUTHOR]

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This research focuses on the ASTER DEM generation for visual and mathematical analysis of topography, landscapes and landforms, as well as modeling of surface processes of Central Alborz, Iran. ASTER DEM 15 m generated using tie points over the Central Alborz and Damavand volcano with 5671 m height from ASTER (Advanced Space borne Thermal Emission and Reflection Radiometer) satellite data using PCI Geomatica 9. 1. Geomorphic parameters are useful to identify and describe geomorphologic forms and processes, which were extracted from ASTER DEM in GIS environment such as elevation, aspect, slope angle, vertical curvature, and tangential curvature. Although the elevation values are slightly low in altitudes above 5500 m asl., the ASTER DEM is useful in interpretation of the macro- and mesa-relief, and provides the opportunity for mapping especially at medium scales (1:100,000 and 1:50,000). ASTER DEM has potential to be a best tool to study 3D model for to geomorphologic mapping and processes of glacial and per glacial forms above 4300 m asl. [ABSTRACT FROM AUTHOR]

Few industries and undoubtedly no other resources have played such a significant role in modern world development as petroleum. Nowadays, access to geological formations bearing petroleum is slightly difficult due to most shallow reservoirs being close to the end of their economic life. Meanwhile, drilling operations have to get access to deeper reservoirs with more harsh conditions, leading to a considerable rise in instability potential. The consequences of failure are severe, and even simple bore hole instability may lead to the loss of millions of dollars in equipment and natural resources. The bore hole instabilities are not particular, and can happen in simple and very sophisticated drilling operations. In addition, these instabilities are not restricted to the drilling operation, and maybe happen even after many years that the completed well is subjected to the production. The authors intended to develop a new model for the collapse strength analysis of the casing design based on the geomechanical model and heaviest fluid used to drill the well and set the casing. This is based on the hypothesis that indeed the geomechanical in situ stresses and drilling fluid (used to drill the well and set the casing) in the annulus between the drilled well and casing exert radial stresses to the outside of the casing that may collapse the well. This survey leads to the easily computed equation to design the casing collapse strength based on the reality of the well and casing characteristics. This research is used and verified against a numerical model and field data in the South Pars gas field (Phases 6, 7, and 8 and well number SPDG-8) in the Persian Gulf and Cheshmeh Khosh oilfield in southwest of Iran. The results indicate that the proposed model is optimum and possesses satisfactory accuracy and precision. [ABSTRACT FROM AUTHOR]

Since Kermack and McKendrick have introduced their famous epidemiological SIR model in 1927, mathematical epidemiology has grown as an interdisciplinary research discipline including knowledge from biology, computer science, or mathematics. Due to current threatening epidemics such as COVID-19, this interest is continuously rising. As our main goal, we establish an implicit time-discrete SIR (susceptible people–infectious people–recovered people) model. For this purpose, we first introduce its continuous variant with time-varying transmission and recovery rates and, as our first contribution, discuss thoroughly its properties. With respect to these results, we develop different possible time-discrete SIR models, we derive our implicit time-discrete SIR model in contrast to many other works which mainly investigate explicit time-discrete schemes and, as our main contribution, show unique solvability and further desirable properties compared to its continuous version. We thoroughly show that many of the desired properties of the time-continuous case are still valid in the time-discrete implicit case. Especially, we prove an upper error bound for our time-discrete implicit numerical scheme. Finally, we apply our proposed time-discrete SIR model to currently available data regarding the spread of COVID-19 in Germany and Iran. [ABSTRACT FROM AUTHOR]