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Published Journal Articles

2020

Risk perception and behavioral change during epidemics: Comparing models of individual and collective learning

2020-01
PloS one (Issue : 1) (Volume : 15)
Modern societies are exposed to a myriad of risks ranging from disease to natural hazards and technological disruptions. Exploring how the awareness of risk spreads and how it triggers a diffusion of coping strategies is prominent in the research agenda of various domains. It requires a deep understanding of how individuals perceive risks and communicate about the effectiveness of protective measures, highlighting learning and social interaction as the core mechanisms driving such processes. Methodological approaches that range from purely physics-based diffusion models to data-driven environmental methods rely on agent-based modeling to accommodate context-dependent learning and social interactions in a diffusion process. Mixing agent-based modeling with data-driven machine learning has become popularity. However, little attention has been paid to the role of intelligent learning in risk appraisal and protective decisions, whether used in an individual or a collective process. The differences between collective learning and individual learning have not been sufficiently explored in diffusion modeling in general and in agent-based models of socio-environmental systems in particular. To address this research gap, we explored the implications of intelligent learning on the gradient from individual to collective learning, using an agent-based model enhanced by machine learning. Our simulation experiments showed that individual intelligent judgement about risks and the selection of coping strategies by groups with majority votes were outperformed by leader-based groups and even individuals deciding alone. Social interactions appeared essential for both individual learning and group learning. The choice of how to represent social learning in an agent-based model could be driven by existing cultural and social norms prevalent in a modeled society.
2019

Bayesian networks for spatial learning: a workflow on using limited survey data for intelligentlearning in spatial agent-based models

2019-04
GeoInformatica (Issue : 02) (Volume : 32)
Machine learning (ML) algorithms steer agent decisions in agent-based models (ABMs), serving as a vehicle for implementing behaviour changes during simulation runs. However, when training an ML algorithm, obtaining large sets of micro-level human behaviour data is often problematic. Information on human behaviour is often collected via surveys of relatively small sample sizes. This paper presents a methodology for training a learning algorithm to guide agent behaviour in a spatial ABM using a limited survey data sample. We apply different implementation strategies using survey data and Bayesian networks (BNs). By being grounded in probabilistic directed graphical models, BNs stand out among other learning algorithms in that they can be based on expert knowledge and/or known datasets. This paper presents four alternative implementations of data-driven BNs to support agent decisions in a spatial ABM. We differentiate between training BNs prior to, or during the simulation runs, using only survey data or a combination of survey data and expert knowledge. The four different implementations are then illustratedusing aspatialABMofcholeradiffusion for Kumasi,Ghana. The results indicate that a balance between expert knowledge and survey data provides the best control over the learning process of the agents and produces the most realistic agent behaviour.
2018

Intelligent judgements over health risks in a spatial agent-based model

2018-03
International Journal of Health Geographics, https://doi.org/10.1186/s12942-018-0128-x (Issue : 1) (Volume : 17)
Background Millions of people worldwide are exposed to deadly infectious diseases on a regular basis. Breaking news of the Zika outbreak for instance, made it to the main media titles internationally. Perceiving disease risks motivate people to adapt their behavior toward a safer and more protective lifestyle. Computational science is instrumental in exploring patterns of disease spread emerging from many individual decisions and interactions among agents and their environment by means of agent-based models. Yet, current disease models rarely consider simulating dynamics in risk perception and its impact on the adaptive protective behavior. Social sciences offer insights into individual risk perception and corresponding protective actions, while machine learning provides algorithms and methods to capture these learning processes. This article presents an innovative approach to extend agent-based disease models by capturing behavioral aspects of decision-making in a risky context using machine learning techniques. We illustrate it with a case of cholera in Kumasi, Ghana, accounting for spatial and social risk factors that affect intelligent behavior and corresponding disease incidents. The results of computational experiments comparing intelligent with zero-intelligent representations of agents in a spatial disease agent-based model are discussed. Methods We present a spatial disease agent-based model (ABM) with agents’ behavior grounded in Protection Motivation Theory. Spatial and temporal patterns of disease diffusion among zero-intelligent agents are compared to those produced by a population of intelligent agents. Two Bayesian Networks (BNs) designed and coded using R and are further integrated with the NetLogo-based Cholera ABM. The first is a one-tier BN1 (only risk perception), the second is a two-tier BN2 (risk and coping behavior). Results We run three experiments (zero-intelligent agents, BN1 intelligence and BN2 intelligence) and report the results per experiment in terms of several macro metrics of interest: an epidemic curve, a risk perception curve, and a distribution of different types of coping strategies over time. Conclusions Our results emphasize the importance of integrating behavioral aspects of decision making under risk into spatial disease ABMs using machine learning algorithms. This is especially relevant when studying cumulative impacts of behavioral changes and possible intervention strategies.
2016

Landsat LDCM Imagery for Estimat- ing and Mapping Burned Forest Areas Caused By Jet Attacks in Duhok Gover- norate, Kurdistan Region - Iraq

2016-06
Journal of University of Duhok (Issue : 1) (Volume : 19)
Estimating fire damage in the forest areas is an important task and a main target for the forestry directorate. This paper presents an approach for estimating burned forest areas in Duhok Governorate that caused by Turkish jet attacks on July 2015. The presented approach is based on using Landsat Data Continuity Mission LDCM (Landsat-8) satellite images. The spectral bands of Landsat-8 imagery were analyzed and the most sensitive bands to the burned areas were identified. Moreover, spectral indices: Normalized difference vegetation index (NDVI) and Normalized Burned Ratio (NBR) were used to identify and determine the burned areas. As a result, a map of burned areas was created with 8981 hectares of the total areas. This approach can be applied for the whole Kurdistan region over multi-temporal interval to estimate burned areas that happened either by Turkish jet attack or by other sources.

Estimating of Diameter at Breast Height for Scattered Pinus brutia ten. Trees using Remote Sensing Techniques, in Zawita Sub-District, Duhok, Kurdistan Region - Iraq

2016-06
Journal of University of Duhok (Issue : 1) (Volume : 19)
Pinus brutiaTen. is the most important coniferous tree species grow naturally in some mountains of Iraqi Kurdistan Region. It is well adapted to both climatically and soil conditions. The diameter at breast height (DBH) is the significant character which has a major effect on both volume, and height of the tree, and indirectly with the site index. The purpose of this study was to utilize remote sensing techniques in estimating the DBH. This is performed by developing models between the collected DBH measurements from the field and the extracted tree crown area from high resolution satellite imagery (WorldView-2). Five models were developed and the selection of the best model was based on coefficient of determination (R 2 ), Root Mean Square Error (RMSE), Bias, and Accuracy criteria. Accordingly, the model DBH= 1.2768 TCA − 14.381 was the most appropriate model to estimate the DBH for Pinus brutia Ten. in this study.
2014

High Spatial Resolution WorldView-2 Imagery for Mapping and Classification of Tree Species in Zawita Sub-district, Duhok, Kurdistan Region-Iraq

2014-06
Journal of University of Duhok (Issue : 2) (Volume : 17)
Forest sustainability requires an effective programme such as monitoring, managing, analyzing and classifying tree species through collecting required information. For such a purpose, field-based assessment provides the needed information. However, this method is costly, time consuming, and therefore assessment frequency is low. This often allows undesirable forest information to develop that do not coincide with management objectives. Satellite remote sensing and its techniques provide an efficient methodology and potentially low-cost alternative to field-based assessment. However, these techniques require the development of methods; such as semi-automatic tree detection and classification. These methods help to easily and accurately extract the required information in a fastest period. In this study, we investigated the potential of the newly developed high resolution satellite sensor, 8-band WorldView-2 (WV-2) imagery for identifying and mapping tree species in the Zawita sub-district, Duhok, Kurdistan region-Iraq. We performed object-based classification method to identify and map of Sixteen tree species including: calabrain pine (Pinus brutia), Almand (prunus duclis), Azarole hawthorn (Crataegus azarolus), Judas tree (cercis siliquastrum L), oriental plane (platanus orientalis), white poplar, silver (populus alba), white willow (Salix alba), Valonia Oak (Quercus aegilops), Gall Oak (Quercus Infectoria), common walnut (juglans Nigra), chinaberry (Melia azedarach), Tera Binth (pistacia khinjuk Stocks), syrian ash (fraxinus syriaca), White Mulberry (Morus alba), common fig (ficus carica), oleaster (Elaeagnus angustifolia). The accuracy assessment is achieved based on the random selection of validation samples, which showed an overall classification accuracy of 77% with Kappa coefficient of 69%. Based on the results of this study we concluded that the WV-2 sensor; with high spatial resolution and additional bands (coastal, yellow, red-edge and NIR2), is attributed as a proper satellite imagery for forest trees classification.

Future Prospects for Macro Rainwater Harvesting (RWH) Technique in North East Iraq

2014-04
Journal of Water Resource and Protection (Issue : 5) (Volume : 6)
Countries in Middle East and North Africa (MENA region) are considered as arid and semi-arid areas that are suffering from water scarcity. They are expected to have more water shortages problem due to climatic change. Iraq is located in the Middle East covering an area of 433,970 square kilometers populated by 31 million inhabitants. One of the solutions suggested to overcome water scarcity is Rainwater Harvesting (RWH). In this study Macro rainwater harvesting technique had been tested for future rainfall data that were predicted by two emission scenarios of climatic change (A2 and B2) for the period 2020-2099 at Sulaimaniyah Governorate north east of Iraq. Future volumes of total runoff that might be harvested for different conditions of maximum, average, and minimum future rainfall seasons under both scenarios (A2 and B2) were calculated. The results indicate that the volumes of average harvested runoff will be reduced when average rainfall seasons are considered due to the effect of climatic change on future rainfall. The reduction reached 10.82 % and 43.0% when scenarios A2 and B2 are considered respectively.

Spatial estimation of rainfall distribution and its classification in Duhok Governorate using GIS

2014-02
Journal of Water Resource and Protection (Issue : 2) (Volume : 6)
Rainfall is a significant portion of hydrologic data. Rainfall records, however, are often incomplete due to several factors. In this study, the inverse distance weighting (IDW) method integrated with GIS is used to estimate the rainfall distribution in Duhok Governorate. A total of 25 rain fall stations and rainfall data between 2000 and 2010 were used, where 6 rainfall stations were used for cross-validation. In addition, the relationship between interpolation accuracy and two critical parameters of IDW (Power α value, and a radius of influence) was evaluated. Also, the rainfall distribution of Duhok Governorate was classified. As an output of this study and in most cases, the optimal parameters for IDW in interpolating rainfall data must have a radius of influence up to (15 - 60 km). However, the optimal α values varied between 1 and 5. Based on the results of this study, we concluded that the IDW is an appropriate method of spatial interpolation to predict the probable rainfall data in Duhok Governorate using α = 1 and search radius = 105 km for all the 25 rainfall stations.
2013

Estimation of annual harvested runoff at Sulaymaniyah Governorate, Kurdistan region of Iraq

2013-12
Natural Science (Issue : 12) (Volume : 5)
Kurdistan Region (KR) of Iraq has suffered from the drought period during the seasons 2007- 2008 and 2008-2009 that affected the human and economic activities of the region. Macro rainwater harvesting (Macro RWH) is one of the techniques that can ensure water availability for a region having limited water resources. This technique is based on Soil Conservation ServiceCurve Number (SCS-CN) method and the Watershed Modeling System (WMS) was used to estimate the runoff. Rainfall records of Sulaymaniyah area for the period 2002-2012 were studied and an average season was selected (2010-2011). The results of the application of the WMS model showed that about 10.76 million cubic meters could be harvested. The results also showed that the quantity of the harvested runoff was highly affected by rainfall depth, curve number values, antecedent moisture conditions (AMC) and the area of the basins.

Macro Rain Water Harvesting Network to Estimate Annual Runoff at Koysinjaq (Koya) District, Kurdistan Region of Iraq

2013-12
Engineering (Issue : 12) (Volume : 5)
Macro rainwater harvesting techniques (Macro RWH) are getting more popular to overcome the problem of water scarcity in arid and semi-arid areas. Iraq is experiencing serious water shortage problem now despite of the presence of Tigris and Euphrates Rivers. RWH can help to overcome this problem. In this research, RWH was applied in Koya City in its districts, North West Iraq. Twenty-two basins were identified as the catchment area for the application of RWH technique. Watershed modeling system (WMS), based on Soil Conservation Service-curve number (SCS-CN) method, was applied to calculate direct runoff from individual daily rain storm using average annual rainfall records of the area. Two consecutive adjustments for the curve number were considered. The first was for the antecedent moisture condition (AMC) and the second was for the slope. These adjustments increased the total resultant harvested runoff up to 79.402 × 106 m3. The average percentage of increase of harvested runoff volume reached 9.28%. This implies that water allocation is of the order of 2000 cubic meter per capita per year. This quantity of water will definitely help to develop the area.

Improvement of spatio-temporal growth estimates in heterogeneous forests using Gaussian Bayesian networks

2013-11
IEEE Transactions on Geoscience and Remote Sensing (Issue : 8) (Volume : 52)
Canopy leaf area index (LAI) is a quantitative measure of canopy foliar area. LAI values can be derived from Moderate Resolution Imaging Spectroradiometer (MODIS) images. In this paper, MODIS pixels from a heterogeneous forest located in The Netherlands were decomposed using the linear mixture model using class fractions derived from a high-resolution aerial image. Gaussian Bayesian networks (GBNs) were applied to improve the spatio-temporal estimation of LAI by combining the decomposed MODIS images with a spatial version of physiological principles predicting growth (3PG) model output at different moments in time. Results showed that the spatial-temporal output obtained with the GBN was 40% more accurate than the spatial 3PG, with a root-mean-square error below 0.25. We concluded that the GBNs improved the spatial estimation of LAI values of a heterogeneous forest by combining a spatial forest growth model with satellite imagery.

Satellite remote sensing and geographic information systems (GIS) to assess changes in the water level in the Duhok dam

2013-06
International Journal of Water Resources and Environmental Engineering (Issue : 6) (Volume : 5)
The use of satellite remote sensing (RS) has salient progress in water budget calculation and it performs in watershed management. An RS technique can properly enhance hydrogeologic surveys. Moreover, to have an intimate understanding of the changes in water level fluctuations, it is also important to relate them to the surrounding eomorphic, structural, climatic and geologic factors. This research serves twofold. The first one is to operationalize the use of RS and Geographic Information Systems (GIS) techniques to assess the change of water surface area in Duhok dam located in Duhok city, Kurdistan region-Iraq. The second is to present and interpret the available statistical data on water level fluctuations in Duhok dam. The change of water surface in the Duhok dam is examined over a 11 year period using satellite images taken between 2001 and 2012. Three Landsat Enhanced Thematic Mapper Plus (Landsat 7 ETM+) images acquired on 13 June, 2001, 11 June, 2006 and on 11 June, 2012, respectively, were used. The change is tracked from the images using Band 7 with the help of Normalized Difference Water Index (NDWI). The accuracy assessed by using the Normalized Difference Area index (NDAI), and the change in water surface area analysed by comparing it with the related meteorological data of the dam. Results show that the estimated water surface area by RS matches the one on the ground with small relative error (less than 2.15%). A decrease of slightly more than 23% was observed in the water surface area this 11 year period. In addition, over this time period, climate conditions (rainfall, temperature and evaporation) in the study area have been changed significantly. These changes could have affected the reservoir surface area, but so also could external human interference around the dam.

Rainwater Harvesting at Koysinjaq (Koya), Kurdistan Region, Iraq

2013-04
Journal of Earth Sciences and Geotechnical Engineering (Issue : 4) (Volume : 3)
Macro Rainwater Harvesting (RWH) has been tested at Koysinjaq (Koya) District, Kurdistan region of Iraq, due to its limited source of water.The studied area consists of four basins with total area of 228.96 km2. The estimating volumes of harvested runoff for the four selected basins together for the study period (2002-2011) were calculated using the Watershed Modeling System (WMS) which is based on Soil Conservation Service Curve Number (SCS-CN) method.In this research, a comparison between maximum and minimum rainfall seasons was conducted to give better understanding for the events that is governing the harvested runoff collection.The results show that, the total harvested runoff ranged from14.83 to 80.77(*106 m3) from the four selected basins together. This indicates that the technique of Macro RWH can be considered to provide a new source of water to contribute to reduce the problem of water scarcity.

Satellite Remote Sensing for Spatio-Temporal Estimation of Leaf Area Index in Heterogeneous Forests

2013-04
nternational Journal of Environmental Protection (Issue : 4) (Volume : 3)
Biophysical parameter values such as LAI have proved useful in a number of environmental applications. An approach is presented for producing the spatio-temporal estimation of leaf area index (LAI) of a heterogeneous forest using Moderate Resolution Imaging Spectroradiometer (MODIS) satellite images. This is performed by decomposing MODIS LAI for a heterogeneous forest using the Linear Mixture Model (LMM) and the information about the class fraction from an aerial image. Results showed that the decomposed MODIS LAI values were estimated well with maximum and minimum RMSE of 0.37, and 0.17, respectively. We concluded that our approach can be used to decompose MODIS LAI successfully for any heterogeneous forest.
2012

Monitoring and evaluating land cover change in the Duhok city, Kurdistan region-Iraq, by using remote sensing and GIS

2012-12
International Journal of Engineering Inventions (Issue : 11) (Volume : 1)
The rapid urban development in the Duhok city since the 1990s has dramatically enhanced the potential impact of human activities. To identify and monitor this urban development effectively, remote sensing provides a viable source of data from which updated land cover information can be extracted efficiently and cheaply. In this study, three satellite datasets, Landsat Thematic Mapper (Landsat TM), and two Landsat Enhanced Thematic Mapper Plus (Landsat 7 ETM+), acquired during 1989, 2001 and 2012, respectively, were used to detect and evaluate Duhok’s urban expansion. Two change detection techniques were tested to detect areas of change. The techniques considered were image differencing, and post-classification comparison. The land use/land cover (LULC) maps of the years 1989, 2001 and 2012 were produced and the changes were determined with significant accuracies. The simplicity of our methods and the minimal investment of time and money make incorporation of remotely sensed data into urban growth a potentially powerful tool for the urban planner/manager. Moreover, the understanding of the spatial and temporal dynamics of Duhok’s urban expansion is the cornerstone for formulating a view about the future urban uses and for making the best use of the limited resources that are available.

Application of the Expectation Maximization Algorithm to Estimate Missing Values in Gaussian Bayesian Network Modeling for Forest Growth

2012-05
IEEE Transactions on Geoscience and Remote Sensing (Issue : 5) (Volume : 50)
The leaf area index (LAI) is a biophysical variable related to atmosphere-biosphere exchange of CO2. One way to obtain LAI value is by the Moderate Resolution Imaging Spectroradiometer (MODIS) biophysical products. In this paper, we use this product to improve the physiological principles predicting growth model within a Gaussian Bayesian network (GBN) setup. The MODIS time series, however, contains gaps caused by persistent clouds, cloud contamination, and other technique problems. We used the Expectation Maximization (EM) algorithm to estimate these missing values. During a period of 26 successive months, the EM algorithm is applied to four different cases: successively and not successively missing values during two different winter seasons, successively and not successively missing values during one spring season, and not successively missing values during the full study. Results show that the maximum value of the averaged absolute error between the original values and those estimated equals 0.16. This low value indicates that the estimated values well represent the original values. Moreover, the root mean square error of the GBN output reduces from 1.57 to 1.49 when performing the EM algorithm to estimate the not successively missing values. We conclude that the EM algorithm within a GBN can adequately handle missing MODIS LAI values and improves the estimation of the LAI.

Improving forest growth estimates using a Bayesian network approach

2012-01
Photogrammetric Engineering and Remote Sensing (Issue : 1) (Volume : 78)
Estimating the contribution of forests to carbon sequestration is commonly done by applying forest growth models. Such models inherently use field observations, such as leaf area index ( LAI ), whereas relevant information is also available from remotely sensed images. The purpose of this study is to improve the LAI estimated from the Physiological Principles Predicting Growth ( 3 -PG ) model by combining its output with LAI derived from Advanced Spaceborne Thermal Emission and Reflection Radiometer ( ASTER ) satellite imagery. A Bayesian network ( BN ) approach is proposed to take care of the different structure of the inaccuracies in the two data sources. It addresses the bias in the 3 -PG model and the noise of the ASTER images. Moreover, the EM algorithm is introduced into BN to estimate missing the LAI ASTER data, since they are not available for long time series due to the atmospheric conditions. This paper shows that the outputs obtained with the BN were more accurate than the 3 -PG estimate, as the root mean square error reduces to 0.46, and the relative error to 5.86 percent. We conclude that the EM -algorithm within a BN can adequately handle missing LAI ASTER values, and BN s can improve the estimation of LAI values. Ultimately, this method may be used as a predicting model of LAI values, and handling the missing data of ASTER images time series.
2011

Application of the EM-algorithm for Bayesian Network Modelling to Improve Forest Growth Estimates

2011-10
Procedia Environmental Sciences (Issue : 1) (Volume : 7)
Leaf area index (LAI) is a biophysical variable that is related to atmosphere-biosphere exchange of CO 2 . One way to obtain LAI value is by the Moderate Resolution Imaging Spectroradiometer (MODIS) biophysical products (LAI MODIS). The LAI MODIS has been used to improve the physiological principles predicting growth (3-PG) model within a Bayesian Network (BN) set-up. The MODIS time series, however, contains gaps caused by persistent clouds, cloud contamination, and other retrieval problems. We therefore formulated the EM-algorithm to estimate the missing MODIS LAI values. The EM-algorithm is applied to three different cases: successive and not successive two winter seasons, and not successive missing MODIS LAI during the time study of 26 successive months at which the performance of the BN is assessed. Results show that the MODIS LAI is estimated such that the maximum value of the mean absolute error between the original MODIS LAI and the estimated MODIS LAI by EM-algorithm is 0.16. This is a low value, and shows the success of our approach. Moreover, the BN output improves when the EM-algorithm is carried out to estimate the inconsecutive missing MODIS LAI such that the root mean square error reduces from 1.57 to 1.49. We conclude that the EM-algorithm within a BN can handle the missing MODIS LAI values and that it improves estimation of the LAI.

Bayesian Network Modeling for Improving Forest Growth Estimates

2011-02
IEEE Transactions on Geoscience and Remote Sensing (Issue : 2) (Volume : 49)
Estimating the contribution of the forests to carbon sequestration is commonly done by applying forest growth models. Such models inherently use field observations such as leaf area index (LAI), whereas a relevant information is also available from remotely sensed images. This paper aims to improve the LAI estimated from the forest growth model [physiological principals predicting growth (3-PG)] by combining these values with the LAI derived from the Moderate Resolution Imaging Spectroradiometer (MODIS) satellite imagery. A Bayesian networks (BNs) approach addresses the bias in the 3-PG model and the noise of the MODIS images. A novel inference strategy within the BN has been developed in this paper to take care of the different structures of the inaccuracies in the two data sources. The BN is applied to the Speulderbos forest in The Netherlands, where the detailed data were available. This paper shows that the outputs obtained with the BN were more accurate than either the 3-PG or the MODIS estimate. It was also found that the BN is more sensitive to the variation of the LAI derived from MODIS than to the variation of the LAI 3-PG values. In this paper, we conclude that the BNs can improve the estimation of the LAI values by combining a forest growth model with satellite imagery.

Bayesian Network Modeling for Improving Forest Growth Estimates

2011-02
IEEE Transactions on Geoscience and Remote Sensing (Issue : 2) (Volume : 49)
Estimating the contribution of the forests to carbon sequestration is commonly done by applying forest growth models. Such models inherently use field observations such as leaf area index (LAI), whereas a relevant information is also available from remotely sensed images. This paper aims to improve the LAI estimated from the forest growth model [physiological principals predicting growth (3-PG)] by combining these values with the LAI derived from the Moderate Resolution Imaging Spectroradiometer (MODIS) satellite imagery. A Bayesian networks (BNs) approach addresses the bias in the 3-PG model and the noise of the MODIS images. A novel inference strategy within the BN has been developed in this paper to take care of the different structures of the inaccuracies in the two data sources. The BN is applied to the Speulderbos forest in The Netherlands, where the detailed data were available. This paper shows that the outputs obtained with the BN were more accurate than either the 3-PG or the MODIS estimate. It was also found that the BN is more sensitive to the variation of the LAI derived from MODIS than to the variation of the LAI 3-PG values. In this paper, we conclude that the BNs can improve the estimation of the LAI values by combining a forest growth model with satellite imagery.
2007

Solving System of a Linear Fractional Differential Equations by Using Laplace Transformation

2007-12
Al-Rafiden Journal of Computer and Mathematics (Issue : 2) (Volume : 21)
In this paper, we provide a solution to the system of non-integer differential equation of order 0 < q < 1, by the technique of Laplace transformation and with interest to property of Mittag-Leffler function, with the help of the programming technique of Maple.
2006

On Limit Cycles of a Certain Quintic System

2006-01
Journal of University of Duhok (Issue : 1) (Volume : 9)
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2005

On Lopsided Heptagonal System

2005-09
Journal of University of Duhok (Issue : 2) (Volume : 8)
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On limit cycles of a certain Lopsided octagonal System

2005-09
Journal of University of Duhok (Issue : 2) (Volume : 8)
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