Sharqa Hashmi, Muhammad Ahsan-ul-Haq, Javeria Zafar, M. A. Khaleel
A new one-parameter model for unit-interval datasets is introduced. The proposed distribution is termed “Unit Xgamma distribution.” Some mathematical properties of the new distribution are derived. We also characterize it using truncated moments and a hazard function. Maximum likelihood, least-squares, weighted least-squares, Anderson- Darling, Cramer-von Mises, and maximum product spacing are among the five estimation methods used to estimate the parameter. A Monte Carlo simulation was used to test the efficacy of these developed estimators. The flexibility of the proposed distribution was assessed using water capacity data. The proposed unit Xgamma distribution can be used for bounded datasets as an alternative to the well-known competitive distributions available in the literature.
{"title":"Unit Xgamma Distribution: Its Properties, Estimation and Application","authors":"Sharqa Hashmi, Muhammad Ahsan-ul-Haq, Javeria Zafar, M. A. Khaleel","doi":"10.53560/ppasa(59-1)636","DOIUrl":"https://doi.org/10.53560/ppasa(59-1)636","url":null,"abstract":"A new one-parameter model for unit-interval datasets is introduced. The proposed distribution is termed “Unit Xgamma distribution.” Some mathematical properties of the new distribution are derived. We also characterize it using truncated moments and a hazard function. Maximum likelihood, least-squares, weighted least-squares, Anderson- Darling, Cramer-von Mises, and maximum product spacing are among the five estimation methods used to estimate the parameter. A Monte Carlo simulation was used to test the efficacy of these developed estimators. The flexibility of the proposed distribution was assessed using water capacity data. The proposed unit Xgamma distribution can be used for bounded datasets as an alternative to the well-known competitive distributions available in the literature.","PeriodicalId":36961,"journal":{"name":"Proceedings of the Pakistan Academy of Sciences: Part A","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43300398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We have derived an analytical solution in low frequency using the idea of a fractional Laplacian equation. Fractional dimensional (FD) space has importance in describing the complex physics phenomena. Here, the Laplacian equation in spherical coordinated (r,θ,0) is expressed in fractional dimensional space using Gegenbauer polynomials. The analytical solution is obtained by the separation variable method. The general solution is a product of angular and radial solutions and is independent of ϕ due to azimuthal symmetry. The classical solution is retained by setting fractional parameter α=3. Further, numerical results are discussed for different values of α and compared with available literature.
{"title":"Mathematical Analysis on Conducting Sphere Embedded in Non Integer Dimensional Space","authors":"M. Shahzad, M. Akbar, Saeed Ahmed, I. Shahzad","doi":"10.53560/ppasa(59-1)756","DOIUrl":"https://doi.org/10.53560/ppasa(59-1)756","url":null,"abstract":"We have derived an analytical solution in low frequency using the idea of a fractional Laplacian equation. Fractional dimensional (FD) space has importance in describing the complex physics phenomena. Here, the Laplacian equation in spherical coordinated (r,θ,0) is expressed in fractional dimensional space using Gegenbauer polynomials. The analytical solution is obtained by the separation variable method. The general solution is a product of angular and radial solutions and is independent of ϕ due to azimuthal symmetry. The classical solution is retained by setting fractional parameter α=3. Further, numerical results are discussed for different values of α and compared with available literature.","PeriodicalId":36961,"journal":{"name":"Proceedings of the Pakistan Academy of Sciences: Part A","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45413737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The reactivity monitoring, prediction, and investigation is the most important parameter to ensure the safety and reliable operation of a nuclear power plant. This parameter is gained further importance in Pressurized Water Reactor (PWR) due to more sophisticated reactivity insertion mechanisms and innovative reactor core fuel loading scheme. Based on deterministic internal and external dynamics and neutronics analysis of Advanced PWR, all the reactivity feedback effects such as Doppler effect, moderator effect, control rod effect, liquid boron effect and reactor poisons effect are investigated, modeled and stochastically optimized using deep artificial intelligence. Advance Pressurized Water Reactor (APWR) of 600 MWe rating (AP-600) is used as a reference reactor model and based on the dynamics of AP-600, an Advanced Pressurized Water Reactor Dynamics and Intelligent Stochastic Optimization based Deterministic Neutronics Simulation (APD-ISO-DNS) Code is developed in the hybrid SIMULINK andLabVIEW environments. AP-600 reactor model is fine-tuned and adjusted for 300 MWe PWR (P-300) and 1070 MWe Advanced Chinese PWR (ACP-1000) using neutronics parameters and operational dynamic data of operating PWR nuclear power plants in Pakistan. Various load reduction transient experiments are conducted and dynamic transient simulations of P-300, AP-600 and ACP-1000 are evaluated in SIMULINK and in LabVIEW environments and found as per design basis.
{"title":"Advanced Multi-Modeling of PWR Dynamics and Deep Learning based Computational Tool in SIMULINK and LabVIEW","authors":"A. H. Malik, A. Memon, Feroza Arshad","doi":"10.53560/ppasa(59-1)748","DOIUrl":"https://doi.org/10.53560/ppasa(59-1)748","url":null,"abstract":"The reactivity monitoring, prediction, and investigation is the most important parameter to ensure the safety and reliable operation of a nuclear power plant. This parameter is gained further importance in Pressurized Water Reactor (PWR) due to more sophisticated reactivity insertion mechanisms and innovative reactor core fuel loading scheme. Based on deterministic internal and external dynamics and neutronics analysis of Advanced PWR, all the reactivity feedback effects such as Doppler effect, moderator effect, control rod effect, liquid boron effect and reactor poisons effect are investigated, modeled and stochastically optimized using deep artificial intelligence. Advance Pressurized Water Reactor (APWR) of 600 MWe rating (AP-600) is used as a reference reactor model and based on the dynamics of AP-600, an Advanced Pressurized Water Reactor Dynamics and Intelligent Stochastic Optimization based Deterministic Neutronics Simulation (APD-ISO-DNS) Code is developed in the hybrid SIMULINK andLabVIEW environments. AP-600 reactor model is fine-tuned and adjusted for 300 MWe PWR (P-300) and 1070 MWe Advanced Chinese PWR (ACP-1000) using neutronics parameters and operational dynamic data of operating PWR nuclear power plants in Pakistan. Various load reduction transient experiments are conducted and dynamic transient simulations of P-300, AP-600 and ACP-1000 are evaluated in SIMULINK and in LabVIEW environments and found as per design basis.","PeriodicalId":36961,"journal":{"name":"Proceedings of the Pakistan Academy of Sciences: Part A","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45283816","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the existing instrumentation and control system of an operating Pressurized Heavy Water Reactor (PHWR) based nuclear power plant, conventional controllers are used to control the reactor power. A new idea of Nonlinear Neural Model Predictive Controller (NNMPC) is introduced in this research work. The new 17th order nonlinear higher order model of Reactor Regulating System (RRS) is developed under different plant operating modes and various parametric conditions in Single Input Multi Output (SIMO) configuration with special emphasis on Helium Control Valve Dynamics (HCVD) and Coupled Nonlinear Iodine and Xenon Dynamics (CNIXD). The SIMO RRS model is developed based on first principle. The 17th order model is reduced to 9th order lower dynamic model using Balanced Truncation Method (BTM). The Reduced Order SIMO RRS (RO-SIMO-RRS) model is programmed, simulated and validated in SIMULINK environment. The plant Neural SIMO RRS (N-SIMO-RRS) model is developed using innovative data generated from RO-SIMO-RRS simulations. The plant neural N-SIMO-RRS model is optimized using Levenberg-Marquardt Algorithm (LMA). Using the identified N-SIMO-RRS model, the Nonlinear Neural Model Predictive Controller (NNMPC) is designed, trained, verified, validated, and finally optimized using the backtracking technique in the SIMULINK environment. The optimized results are obtained from designed closed loop RRS and found within the acceptable design limits. The performance of the proposed closed loop RRS is also tested in reference tracking mode with excellent fast tractability near the optimal target demanded power level.
{"title":"Higher Order Modeling of Reactor Regulating System and Nonlinear Neural Model Predictive Controller Design for a Nuclear Power Generating Station","authors":"A. H. Malik, A. Memon, Feroza Arshad","doi":"10.53560/ppasa(59-1)747","DOIUrl":"https://doi.org/10.53560/ppasa(59-1)747","url":null,"abstract":"In the existing instrumentation and control system of an operating Pressurized Heavy Water Reactor (PHWR) based nuclear power plant, conventional controllers are used to control the reactor power. A new idea of Nonlinear Neural Model Predictive Controller (NNMPC) is introduced in this research work. The new 17th order nonlinear higher order model of Reactor Regulating System (RRS) is developed under different plant operating modes and various parametric conditions in Single Input Multi Output (SIMO) configuration with special emphasis on Helium Control Valve Dynamics (HCVD) and Coupled Nonlinear Iodine and Xenon Dynamics (CNIXD). The SIMO RRS model is developed based on first principle. The 17th order model is reduced to 9th order lower dynamic model using Balanced Truncation Method (BTM). The Reduced Order SIMO RRS (RO-SIMO-RRS) model is programmed, simulated and validated in SIMULINK environment. The plant Neural SIMO RRS (N-SIMO-RRS) model is developed using innovative data generated from RO-SIMO-RRS simulations. The plant neural N-SIMO-RRS model is optimized using Levenberg-Marquardt Algorithm (LMA). Using the identified N-SIMO-RRS model, the Nonlinear Neural Model Predictive Controller (NNMPC) is designed, trained, verified, validated, and finally optimized using the backtracking technique in the SIMULINK environment. The optimized results are obtained from designed closed loop RRS and found within the acceptable design limits. The performance of the proposed closed loop RRS is also tested in reference tracking mode with excellent fast tractability near the optimal target demanded power level.","PeriodicalId":36961,"journal":{"name":"Proceedings of the Pakistan Academy of Sciences: Part A","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43344454","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The current study has been completed by collecting the 20 water samples from Allama Iqbal Town Lahore, including ten from WASA (Water And Sanitation Agency) filter plants in Iqbal Town other samples were collected from different depths from Allama Iqbal Town Lahore. After the collection of water samples, these were taken to the green lab for physiochemical analysis of samples. Water samples were subjected to Physicochemical analysis that includes temperature, pH, Total Dissolved Solids, Total Hardness, Chloride, Arsenic, Cadmium, Sodium, Nickle, Fluoride. APHA techniques were used to analysis of water samples. Comparison of samples results with values given by the World Health Organization, represented by graphs and location maps. The Filtration plant and tap water samples were odourless, tasteless, and colourless. The amount of Lead in all the parameters was below the detectable level. Correlation analysis was applied to all the parameters to check out the deep relationship among all the parameters.The correlation results showed that with the increase of pH value, all studied traits values were increased except turbidity Physiochemical parameters in all water samples of WASA (Water And Sanitation Agency) filtration plants were within the permissible limits. It revealed that water samples of filtration plants were fit for drinking purposes. Physiochemical parameters in all water samples collected from the different depths of Lahore were not within the permissible limits, and it revealed that the tap water had arsenic amount and water collected from shallow depth have not permissible limit of sulphate, Total Hardness and Total Dissolved Solids. This showed that Tap water samples were unfit for drinking.
{"title":"Assessment of drinking water quality of household bore well plants and WASA water supply system: A case study of Allama Iqbal Town Lahore","authors":"Mahmoona Ashraf, Ifthikhar Ahmed","doi":"10.53560/ppasa(58-4)626","DOIUrl":"https://doi.org/10.53560/ppasa(58-4)626","url":null,"abstract":"The current study has been completed by collecting the 20 water samples from Allama Iqbal Town Lahore, including ten from WASA (Water And Sanitation Agency) filter plants in Iqbal Town other samples were collected from different depths from Allama Iqbal Town Lahore. After the collection of water samples, these were taken to the green lab for physiochemical analysis of samples. Water samples were subjected to Physicochemical analysis that includes temperature, pH, Total Dissolved Solids, Total Hardness, Chloride, Arsenic, Cadmium, Sodium, Nickle, Fluoride. APHA techniques were used to analysis of water samples. Comparison of samples results with values given by the World Health Organization, represented by graphs and location maps. The Filtration plant and tap water samples were odourless, tasteless, and colourless. The amount of Lead in all the parameters was below the detectable level. Correlation analysis was applied to all the parameters to check out the deep relationship among all the parameters.The correlation results showed that with the increase of pH value, all studied traits values were increased except turbidity Physiochemical parameters in all water samples of WASA (Water And Sanitation Agency) filtration plants were within the permissible limits. It revealed that water samples of filtration plants were fit for drinking purposes. Physiochemical parameters in all water samples collected from the different depths of Lahore were not within the permissible limits, and it revealed that the tap water had arsenic amount and water collected from shallow depth have not permissible limit of sulphate, Total Hardness and Total Dissolved Solids. This showed that Tap water samples were unfit for drinking.","PeriodicalId":36961,"journal":{"name":"Proceedings of the Pakistan Academy of Sciences: Part A","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44717863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we present a single feed circularly polarized microstrip patch antenna operating at 2.4 GHz WLAN frequency. A typical microstrip patch antenna is fabricated on a metal coated dielectric substrate where the metallic antenna patch is defined on the top of the substrate, whereas the bottom of the substrate acts as a ground plate. These antennas are typically used for civil and military communication purposes. Before fabrication, the presented antenna was first designed, simulated and optimized in CST Microwave studio. The circular polarization was achieved by perturbation of the edges, making the design optimization a bit challenging. The simulated and measured return loss of the proposed antenna is -27 dB and -13.34dB, respectively. Whereas, the gain came out to be 6 dB. The obtained results show that the presented antenna has the quality of right hand circular polarized antenna.
{"title":"Design and Fabrication of a 2.4 GHz Right Hand Circular Polarized Micro-Strip Patch Antenna","authors":"M. Ahmad, F. A. Khalil","doi":"10.53560/ppasa(58-4)751","DOIUrl":"https://doi.org/10.53560/ppasa(58-4)751","url":null,"abstract":"In this paper, we present a single feed circularly polarized microstrip patch antenna operating at 2.4 GHz WLAN frequency. A typical microstrip patch antenna is fabricated on a metal coated dielectric substrate where the metallic antenna patch is defined on the top of the substrate, whereas the bottom of the substrate acts as a ground plate. These antennas are typically used for civil and military communication purposes. Before fabrication, the presented antenna was first designed, simulated and optimized in CST Microwave studio. The circular polarization was achieved by perturbation of the edges, making the design optimization a bit challenging. The simulated and measured return loss of the proposed antenna is -27 dB and -13.34dB, respectively. Whereas, the gain came out to be 6 dB. The obtained results show that the presented antenna has the quality of right hand circular polarized antenna. ","PeriodicalId":36961,"journal":{"name":"Proceedings of the Pakistan Academy of Sciences: Part A","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48624846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Muhammad Shakeel Rind Baloch, Z. Kalhoro, M. Khalil, Prof. Abdul Wasim Shaikh
The fundamental problem of linear algebra is to solve the system of linear equations (SOLE’s). To solve SOLE’s, is one of the most crucial topics in iterative methods. The SOLE’s occurs throughout the natural sciences, social sciences, engineering, medicine and business. For the most part, iterative methods are used for solving sparse SOLE’s. In this research, an improved iterative scheme namely, ‘’a new improved classical iterative algorithm (NICA)’’ has been developed. The proposed iterative method is valid when the co-efficient matrix of SOLE’s is strictly diagonally dominant (SDD), irreducibly diagonally dominant (IDD), M-matrix, Symmetric positive definite with some conditions and H-matrix. Such types of SOLE’s does arise usually from ordinary differential equations (ODE’s) and partial differential equations (PDE’s). The proposed method reduces the number of iterations, decreases spectral radius and increases the rate of convergence. Some numerical examples are utilized to demonstrate the effectiveness of NICA over Jacobi (J), Gauss Siedel (GS), Successive Over Relaxation (SOR), Refinement of Jacobi (RJ), Second Refinement of Jacobi (SRJ), Generalized Jacobi (GJ) and Refinement of Generalized Jacobi (RGJ) methods.
{"title":"A New Improved Classical Iterative Algorithm for Solving System of Linear Equations","authors":"Muhammad Shakeel Rind Baloch, Z. Kalhoro, M. Khalil, Prof. Abdul Wasim Shaikh","doi":"10.53560/ppasa(58-4)638","DOIUrl":"https://doi.org/10.53560/ppasa(58-4)638","url":null,"abstract":"The fundamental problem of linear algebra is to solve the system of linear equations (SOLE’s). To solve SOLE’s, is one of the most crucial topics in iterative methods. The SOLE’s occurs throughout the natural sciences, social sciences, engineering, medicine and business. For the most part, iterative methods are used for solving sparse SOLE’s. In this research, an improved iterative scheme namely, ‘’a new improved classical iterative algorithm (NICA)’’ has been developed. The proposed iterative method is valid when the co-efficient matrix of SOLE’s is strictly diagonally dominant (SDD), irreducibly diagonally dominant (IDD), M-matrix, Symmetric positive definite with some conditions and H-matrix. Such types of SOLE’s does arise usually from ordinary differential equations (ODE’s) and partial differential equations (PDE’s). The proposed method reduces the number of iterations, decreases spectral radius and increases the rate of convergence. Some numerical examples are utilized to demonstrate the effectiveness of NICA over Jacobi (J), Gauss Siedel (GS), Successive Over Relaxation (SOR), Refinement of Jacobi (RJ), Second Refinement of Jacobi (SRJ), Generalized Jacobi (GJ) and Refinement of Generalized Jacobi (RGJ) methods. ","PeriodicalId":36961,"journal":{"name":"Proceedings of the Pakistan Academy of Sciences: Part A","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42559243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work, we aim to identify the performance limiting factors and consequently improve the performance of PERC solar cells through extensive TCAD based device simulation and modelling. Initially, a simplified planar PERC solar cell structure is simulated in Silvaco (Athena/Atlas), where the device geometry is selected according to an experimentally fabricated cell with an efficiency of 17.86%. The J-V curves and solar cell parameters such as Jsc, FF, Voc and efficiency (η) of the simulated cell are then fitted to the experimental performance parameters by incorporating relevant models as suggested by the literature. These include: carriers’ generation-recombination, mobility, statistics and bandgap narrowing. A good agreement is obtained, where the average percentage difference between simulated and experimental performance parameters is 0.65%. The solar cell performance is then improved to 21.52% by optimising the anti-reflective coating stack composition and thickness, and adding surface texturing. This increase in efficiency is attributed to lower surface recombination and reduced reflection due to light trapping. In addition, a textured front surface enhances the path-length of light, causing it to undergo multiple internal reflections which further increases light trapping, thus increasing Jsc by 7.31 mA/cm2.
{"title":"Improved PERC Solar Cell Design by TCAD Simulation","authors":"A. Rehman, A. Siddiqui, M. Nadeem, M. Usman","doi":"10.53560/ppasa(58-4)637","DOIUrl":"https://doi.org/10.53560/ppasa(58-4)637","url":null,"abstract":"In this work, we aim to identify the performance limiting factors and consequently improve the performance of PERC solar cells through extensive TCAD based device simulation and modelling. Initially, a simplified planar PERC solar cell structure is simulated in Silvaco (Athena/Atlas), where the device geometry is selected according to an experimentally fabricated cell with an efficiency of 17.86%. The J-V curves and solar cell parameters such as Jsc, FF, Voc and efficiency (η) of the simulated cell are then fitted to the experimental performance parameters by incorporating relevant models as suggested by the literature. These include: carriers’ generation-recombination, mobility, statistics and bandgap narrowing. A good agreement is obtained, where the average percentage difference between simulated and experimental performance parameters is 0.65%. The solar cell performance is then improved to 21.52% by optimising the anti-reflective coating stack composition and thickness, and adding surface texturing. This increase in efficiency is attributed to lower surface recombination and reduced reflection due to light trapping. In addition, a textured front surface enhances the path-length of light, causing it to undergo multiple internal reflections which further increases light trapping, thus increasing Jsc by 7.31 mA/cm2. ","PeriodicalId":36961,"journal":{"name":"Proceedings of the Pakistan Academy of Sciences: Part A","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43254482","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
H. M. K. Rasheed, Hafsa Khan, R. Ahmed, Farrukh Jamal
In this article, some series are developed to generate circular nearly strongly balanced repeated measurements designs in periods of three different sizes when p3 (smallest period size) = 2 through method of cyclic shifts (Rule II). These designs with varied period sizes have diversified applications, e.g. medicine, pharmacology, animal sciences and psychology. These designs are mainly used to balance the first order residual effect. Our proposed designs possessat least 98% efficiency of separability, therefore these designs are highly efficient to estimate the residual effects and direct effects independently.
{"title":"Minimal Circular Nearly Strongly Balanced Repeated Measurements Designs in Unequal Period Sizes","authors":"H. M. K. Rasheed, Hafsa Khan, R. Ahmed, Farrukh Jamal","doi":"10.53560/ppasa(58-4)633","DOIUrl":"https://doi.org/10.53560/ppasa(58-4)633","url":null,"abstract":"In this article, some series are developed to generate circular nearly strongly balanced repeated measurements designs in periods of three different sizes when p3 (smallest period size) = 2 through method of cyclic shifts (Rule II). These designs with varied period sizes have diversified applications, e.g. medicine, pharmacology, animal sciences and psychology. These designs are mainly used to balance the first order residual effect. Our proposed designs possessat least 98% efficiency of separability, therefore these designs are highly efficient to estimate the residual effects and direct effects independently.","PeriodicalId":36961,"journal":{"name":"Proceedings of the Pakistan Academy of Sciences: Part A","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45928361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we have investigated electric potential and field analytically for homogeneous conducting sphere by solving the Laplacian equation in fractional dimensional space. The laplacian equation in fractional space describes complex phenomena of physics. The separation variable method is used to solve the Laplace differential equation. The mathematical formulae governing the interaction of a low-frequency source of electric current with a spherical anomaly are derived in fractional dimensional space. These formulae are used to determine the apparent resistivity and induced-polarization response. The potential due to the current point source in fractional space is derived using Gegenbauer polynomials. The electric field inrensity of the homogeneous conducting sphere is calculated using the electric potential due to a current point source outside the sphere. The results are compared analytically with classical results by setting the fractional parameter α=3.
{"title":"Response of Homogeneous Conducting Sphere in Non-Integer Dimensional Space","authors":"Saeed Ahmed, M. Akbar, M. Shahzad","doi":"10.53560/ppasa(58-4)755","DOIUrl":"https://doi.org/10.53560/ppasa(58-4)755","url":null,"abstract":"In this paper, we have investigated electric potential and field analytically for homogeneous conducting sphere by solving the Laplacian equation in fractional dimensional space. The laplacian equation in fractional space describes complex phenomena of physics. The separation variable method is used to solve the Laplace differential equation. The mathematical formulae governing the interaction of a low-frequency source of electric current with a spherical anomaly are derived in fractional dimensional space. These formulae are used to determine the apparent resistivity and induced-polarization response. The potential due to the current point source in fractional space is derived using Gegenbauer polynomials. The electric field inrensity of the homogeneous conducting sphere is calculated using the electric potential due to a current point source outside the sphere. The results are compared analytically with classical results by setting the fractional parameter α=3.","PeriodicalId":36961,"journal":{"name":"Proceedings of the Pakistan Academy of Sciences: Part A","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46031730","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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