R. Zine, Hamed Ould Sidi, Y. Louartassi, M. Ould Sidi
In this work, we consider the regional averaged controllability (RAC) problem governed by a class of semilinear hyperbolic systems. We start by giving the definitions of the exact and approximate RAC systems. After that, we state the problem of RAC for semilinear systems. We propose two methods of solution: using a condition of the analytical operator to the nonlinear part of the system to characterize the optimal control via the fixed point theorem and the Hilbert Uniqueness Method (HUM) with an asymptotic condition on the nonlinear part to find the optimal control of the considered problem. Finally, we present a numerical example to show the effectiveness of the main results.
{"title":"Averaged Control Problems Governed by a Semilinear Distributed Systems","authors":"R. Zine, Hamed Ould Sidi, Y. Louartassi, M. Ould Sidi","doi":"10.1155/2023/6687006","DOIUrl":"https://doi.org/10.1155/2023/6687006","url":null,"abstract":"In this work, we consider the regional averaged controllability (RAC) problem governed by a class of semilinear hyperbolic systems. We start by giving the definitions of the exact and approximate RAC systems. After that, we state the problem of RAC for semilinear systems. We propose two methods of solution: using a condition of the analytical operator to the nonlinear part of the system to characterize the optimal control via the fixed point theorem and the Hilbert Uniqueness Method (HUM) with an asymptotic condition on the nonlinear part to find the optimal control of the considered problem. Finally, we present a numerical example to show the effectiveness of the main results.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"7 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85436411","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}
Ahsan Ali Naseer, M. Safdar, S. Taj, M. U. Ali, A. Zafar, Kwanghyok Kim, Jong Hyuk Byun
This study determines Lie point symmetries for differential equations that mathematically express a time-dependent thin film fluid flow with internal heating and thermal radiation to construct invariants. These invariants are used in the derivation of similarity transformations for reducing the flow equations into systems of equations that possess only one independent variable. The homotopy analysis method is employed to analytically solve the reduced system of equations. The new similarity transformations and the corresponding analytical solutions comprehensively consider flow dynamics and heat transfer under multiple physical conditions. These solutions are presented graphically to demonstrate the effects of variations in the radiative heat flux with internal heating on the flow dynamics and heat transfer properties. Moreover, the variations in fluid dynamics are described graphically using the obtained analytical homotopy solution under different values of the unsteadiness parameter and Prandtl number.
{"title":"Analytical Solutions for Unsteady Thin Film Flow with Internal Heating and Radiation","authors":"Ahsan Ali Naseer, M. Safdar, S. Taj, M. U. Ali, A. Zafar, Kwanghyok Kim, Jong Hyuk Byun","doi":"10.1155/2023/5612023","DOIUrl":"https://doi.org/10.1155/2023/5612023","url":null,"abstract":"This study determines Lie point symmetries for differential equations that mathematically express a time-dependent thin film fluid flow with internal heating and thermal radiation to construct invariants. These invariants are used in the derivation of similarity transformations for reducing the flow equations into systems of equations that possess only one independent variable. The homotopy analysis method is employed to analytically solve the reduced system of equations. The new similarity transformations and the corresponding analytical solutions comprehensively consider flow dynamics and heat transfer under multiple physical conditions. These solutions are presented graphically to demonstrate the effects of variations in the radiative heat flux with internal heating on the flow dynamics and heat transfer properties. Moreover, the variations in fluid dynamics are described graphically using the obtained analytical homotopy solution under different values of the unsteadiness parameter and Prandtl number.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"13 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89986406","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}
M. Dokuyucu, Burak Armağan, Ülkü Eliuz, A. Akdemir, Mehmet Emir Köksal
The main motivation point of the article and the main factor that provides originality are an analysis of the modeling of feelings in the perspective of the analysis of Olvido’s poetry with the help of two fractional operators that offer the most effective solutions to real-world problems. In the study, first of all, the effect and contribution of fractional analysis to be applied and theoretical sciences were examined. A mathematical model of the feelings described in Olvido’s poem has been created to establish an important connection between fractional operators, which are an effective tool in the explanation of many physical and applied phenomena, and literary works that try to describe human life and feelings. The solutions of this model are investigated with the help of Caputo and Atangana–Baleanu fractional derivative operators. The findings were supported by various graphics in the light of special values of the parameters of the operators. The study focuses on generalizing the effects of literature research on human life to a general framework, not only providing the realization of the outputs that the literature field brings to human life and literature with the help of a mathematical model. The study has a rare content in the literature in terms of bringing together poetry and mathematics, which deal with human life with different methodologies.
{"title":"Mathematical Modeling of Feelings in Viewpoint of Analysis of Olvido Poetry with Fractional Operators","authors":"M. Dokuyucu, Burak Armağan, Ülkü Eliuz, A. Akdemir, Mehmet Emir Köksal","doi":"10.1155/2023/5862652","DOIUrl":"https://doi.org/10.1155/2023/5862652","url":null,"abstract":"The main motivation point of the article and the main factor that provides originality are an analysis of the modeling of feelings in the perspective of the analysis of Olvido’s poetry with the help of two fractional operators that offer the most effective solutions to real-world problems. In the study, first of all, the effect and contribution of fractional analysis to be applied and theoretical sciences were examined. A mathematical model of the feelings described in Olvido’s poem has been created to establish an important connection between fractional operators, which are an effective tool in the explanation of many physical and applied phenomena, and literary works that try to describe human life and feelings. The solutions of this model are investigated with the help of Caputo and Atangana–Baleanu fractional derivative operators. The findings were supported by various graphics in the light of special values of the parameters of the operators. The study focuses on generalizing the effects of literature research on human life to a general framework, not only providing the realization of the outputs that the literature field brings to human life and literature with the help of a mathematical model. The study has a rare content in the literature in terms of bringing together poetry and mathematics, which deal with human life with different methodologies.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"41 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80563657","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}
Oussama Melkemi, Mohammed S Abdo, M. A. Aiyashi, M. D. Albalwi
Several cells and microorganisms, such as bacteria and somatic, have many essential features, one of which can be modeled by the chemotaxis system, which we consider to be our main interest in this article. More precisely, we studied the hyperbolic system derived from the chemotaxis model with fractional dissipation, which is a generalization for the hyperbolic system with classical dissipation. The results of this article are divided into two parts. In the first part, we used energy methods to obtain the existence of small solutions in the Besov spaces. The second one deals with the optimal decay of perturbed solutions using a refined time-weighted energy combined with the Littlewood-Paley decomposition technique. To the authors’ best knowledge, this type of system (with fractional dissipation) has not been studied in the literature.
{"title":"On the Global Well-Posedness for a Hyperbolic Model Arising from Chemotaxis Model with Fractional Laplacian Operator","authors":"Oussama Melkemi, Mohammed S Abdo, M. A. Aiyashi, M. D. Albalwi","doi":"10.1155/2023/1140032","DOIUrl":"https://doi.org/10.1155/2023/1140032","url":null,"abstract":"Several cells and microorganisms, such as bacteria and somatic, have many essential features, one of which can be modeled by the chemotaxis system, which we consider to be our main interest in this article. More precisely, we studied the hyperbolic system derived from the chemotaxis model with fractional dissipation, which is a generalization for the hyperbolic system with classical dissipation. The results of this article are divided into two parts. In the first part, we used energy methods to obtain the existence of small solutions in the Besov spaces. The second one deals with the optimal decay of perturbed solutions using a refined time-weighted energy combined with the Littlewood-Paley decomposition technique. To the authors’ best knowledge, this type of system (with fractional dissipation) has not been studied in the literature.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"18 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77471522","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}
Shams A. Ahmed, Mohamed Elbadri, Abdelgabar Adam Hassan, Walid Hdidi
In this paper, the coupled system of Whitham–Broer–Kaup equations of the Caputo fractional derivative (CFD) is studied using the Sumudu decomposition method (SDM). Using different dispersion relations, these equations are needed to describe the properties of waves in shallow water. The current investigation for the future scheme includes convergence and error analysis. We use two examples to demonstrate the leverage and effectiveness of the proposed scheme, and the error analysis is discussed to ensure its accuracy. The numerical simulation is carried out to ensure the accuracy of the future technique. The obtained numerical and graphical results are presented, and the proposed scheme is computationally very accurate and simple to study and solve fractionally coupled nonlinear complex phenomena encountered in science and technology.
{"title":"Numerical Solutions of Time-Fractional Whitham–Broer–Kaup Equations via Sumudu Decomposition Method","authors":"Shams A. Ahmed, Mohamed Elbadri, Abdelgabar Adam Hassan, Walid Hdidi","doi":"10.1155/2023/4664866","DOIUrl":"https://doi.org/10.1155/2023/4664866","url":null,"abstract":"In this paper, the coupled system of Whitham–Broer–Kaup equations of the Caputo fractional derivative (CFD) is studied using the Sumudu decomposition method (SDM). Using different dispersion relations, these equations are needed to describe the properties of waves in shallow water. The current investigation for the future scheme includes convergence and error analysis. We use two examples to demonstrate the leverage and effectiveness of the proposed scheme, and the error analysis is discussed to ensure its accuracy. The numerical simulation is carried out to ensure the accuracy of the future technique. The obtained numerical and graphical results are presented, and the proposed scheme is computationally very accurate and simple to study and solve fractionally coupled nonlinear complex phenomena encountered in science and technology.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"74 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85928317","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}
Dolat Khan, M. Almusawa, Waleed Hamali, M. A. Akbar
The water–ethylene glycol (50 : 50) nanofluid has applications in the manufacture of polyester as a raw agent, air conditioning systems, antifreeze formulation, dehydrating agents in the gas industry, a precursor in the plastic industry, and convective heat transfer. These developments in nanotechnology and nanoscience have caught the interest of several researchers. Because it keeps machines and engines cool by reducing friction between their different parts, grease is a vital part of many machinery and engines. Also, due to the extensive use of fractional derivatives, this work seeks to evaluate the combined impacts of free convection flow and heat transfer, magnetic field, and Brinkman-type water–ethylene glycol (50 : 50) dusty nanofluid among microchannel. The flow that the buoyant force provides helps to carry heat naturally via convection. While the left plate moves at a consistent velocity and the right plate stays stationary, the fluid is also evenly dispersed with all dust particles that have a spherical form. Partial differential equations (PDE) are used to present the mathematical modeling. The resultant PDEs are generalized by utilizing the Caputo–Fabrizio fractional derivative. The problem’s closed-form solution is produced by combining a Laplace transformation with a finite sine Fourier transformation. It has also been studied that temperature, Brinkman nanofluid, and dust particle velocity relate to a variety of other factors, such as the magnetic parameter, Grashof number, dusty fluid parameter, and volume friction parameter. The graphical outcomes for the dusty fluid, Brinkman nanofluid, and temperature profiles are plotted using Mathcad-15. The Brinkman nanofluid and dusty fluid behave similarly for a variety of embedded factors. It is found that compared to the traditional one, the fractional dusty nanofluid model displays more realistic characteristics. The addition of nanoparticles in water–ethylene glycol (50 : 50) dusty nanofluid enhances the rate of heat transfer up to 41.04478% by increasing their volume fractional.
{"title":"Analysis of a Two-Phase MHD Free Convection Generalized Water–Ethylene Glycol (50 : 50) Dusty Brinkman-Type Nanofluid Pass through Microchannel","authors":"Dolat Khan, M. Almusawa, Waleed Hamali, M. A. Akbar","doi":"10.1155/2023/3099858","DOIUrl":"https://doi.org/10.1155/2023/3099858","url":null,"abstract":"The water–ethylene glycol (50 : 50) nanofluid has applications in the manufacture of polyester as a raw agent, air conditioning systems, antifreeze formulation, dehydrating agents in the gas industry, a precursor in the plastic industry, and convective heat transfer. These developments in nanotechnology and nanoscience have caught the interest of several researchers. Because it keeps machines and engines cool by reducing friction between their different parts, grease is a vital part of many machinery and engines. Also, due to the extensive use of fractional derivatives, this work seeks to evaluate the combined impacts of free convection flow and heat transfer, magnetic field, and Brinkman-type water–ethylene glycol (50 : 50) dusty nanofluid among microchannel. The flow that the buoyant force provides helps to carry heat naturally via convection. While the left plate moves at a consistent velocity and the right plate stays stationary, the fluid is also evenly dispersed with all dust particles that have a spherical form. Partial differential equations (PDE) are used to present the mathematical modeling. The resultant PDEs are generalized by utilizing the Caputo–Fabrizio fractional derivative. The problem’s closed-form solution is produced by combining a Laplace transformation with a finite sine Fourier transformation. It has also been studied that temperature, Brinkman nanofluid, and dust particle velocity relate to a variety of other factors, such as the magnetic parameter, Grashof number, dusty fluid parameter, and volume friction parameter. The graphical outcomes for the dusty fluid, Brinkman nanofluid, and temperature profiles are plotted using Mathcad-15. The Brinkman nanofluid and dusty fluid behave similarly for a variety of embedded factors. It is found that compared to the traditional one, the fractional dusty nanofluid model displays more realistic characteristics. The addition of nanoparticles in water–ethylene glycol (50 : 50) dusty nanofluid enhances the rate of heat transfer up to 41.04478% by increasing their volume fractional.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"230 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80239084","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}
E. Badr, Mohamed EL-Hakeem, E. El-Sharawy, Thowiba E. Ahmed
Efficient time complexities for partial ordered sets or posets are well-researched field. Hopcroft and Karp introduced an algorithm that solves the minimal chain decomposition in O (n2.5) time. Felsner et al. proposed an algorithm that reduces the time complexity to O (kn2) such that n is the number of elements of the poset and k is its width. The main goal of this paper is proposing an efficient algorithm to compute the width of a given partially ordered set P according to Dilworth’s theorem. It is an efficient and simple algorithm. The time complexity of this algorithm is O (kn), such that n is the number of elements of the partially ordered set P and k is the width of P. The computational results show that the proposed algorithm outperforms other related algorithms.
{"title":"An Efficient Algorithm for Decomposition of Partially Ordered Sets","authors":"E. Badr, Mohamed EL-Hakeem, E. El-Sharawy, Thowiba E. Ahmed","doi":"10.1155/2023/9920700","DOIUrl":"https://doi.org/10.1155/2023/9920700","url":null,"abstract":"Efficient time complexities for partial ordered sets or posets are well-researched field. Hopcroft and Karp introduced an algorithm that solves the minimal chain decomposition in O (n2.5) time. Felsner et al. proposed an algorithm that reduces the time complexity to O (kn2) such that n is the number of elements of the poset and k is its width. The main goal of this paper is proposing an efficient algorithm to compute the width of a given partially ordered set P according to Dilworth’s theorem. It is an efficient and simple algorithm. The time complexity of this algorithm is O (kn), such that n is the number of elements of the partially ordered set P and k is the width of P. The computational results show that the proposed algorithm outperforms other related algorithms.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"35 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86993605","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}
Based on a completely distributive lattice M , we propose a new fuzzification approach to a module, which leads to the concept of an M -hazy module. Different from the traditional fuzzification approach that defines a fuzzy algebra as a fuzzy subset of a classical algebra, we introduce an M -hazy module by fuzzifications of algebraic operations. Then, we investigate the fundamental properties of M -hazy modules and M -hazy submodules. In particular, we present the M -hazy module homomorphism theorem.
{"title":"M-Hazy Module and Its Homomorphism Theorem","authors":"Donghua Huo, Hongyu Liu","doi":"10.1155/2023/3581113","DOIUrl":"https://doi.org/10.1155/2023/3581113","url":null,"abstract":"Based on a completely distributive lattice \u0000 \u0000 M\u0000 \u0000 , we propose a new fuzzification approach to a module, which leads to the concept of an \u0000 \u0000 M\u0000 \u0000 -hazy module. Different from the traditional fuzzification approach that defines a fuzzy algebra as a fuzzy subset of a classical algebra, we introduce an \u0000 \u0000 M\u0000 \u0000 -hazy module by fuzzifications of algebraic operations. Then, we investigate the fundamental properties of \u0000 \u0000 M\u0000 \u0000 -hazy modules and \u0000 \u0000 M\u0000 \u0000 -hazy submodules. In particular, we present the \u0000 \u0000 M\u0000 \u0000 -hazy module homomorphism theorem.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"6 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89810404","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}
B. Hasan, Md. Shaiful Islam, P. Kundu, Uzzwal Kumar Mallick
Algal blooms have a wide variety of detrimental effects on both the aquatic environment and human activities unfortunately, including a decrease in dissolved oxygen levels in water. In this study, a nonlinear mathematical model has been developed to study the effects of algal bloom on the depletion of dissolved oxygen in eutrophic water sources considering nutrient concentrations, density of algal population, detritus, and concentration of dissolved oxygen as variables. The model’s existence and uniqueness, stability at the equilibrium points, and characteristics with respect to state variables have been performed as some parts of analytical solution, whereas the numerical solution has been performed using the Runge–Kutta 4 t h order technique. The findings of this research reveal that an increase in the quantity of nutrients causes an algal bloom, which in turn lowers the equilibrium level of dissolved oxygen. However, higher levels of detritus ( > 4.7 mg/litre) are hazardous to the generation of dissolved oxygen in water systems. Maximum detritus of 1.0 mg/liter is required for fast algal and dissolved oxygen growth in water bodies; beyond that, algal and dissolved oxygen growth rates are lower. Therefore, increasing public awareness is an essential step in controlling this growing issue; failing to do so will result in problems for our water supply, which will in turn pose a danger to our ecosystem.
{"title":"Modeling the Effects of Algal Bloom on Dissolved Oxygen in Eutrophic Water Bodies","authors":"B. Hasan, Md. Shaiful Islam, P. Kundu, Uzzwal Kumar Mallick","doi":"10.1155/2023/2335570","DOIUrl":"https://doi.org/10.1155/2023/2335570","url":null,"abstract":"Algal blooms have a wide variety of detrimental effects on both the aquatic environment and human activities unfortunately, including a decrease in dissolved oxygen levels in water. In this study, a nonlinear mathematical model has been developed to study the effects of algal bloom on the depletion of dissolved oxygen in eutrophic water sources considering nutrient concentrations, density of algal population, detritus, and concentration of dissolved oxygen as variables. The model’s existence and uniqueness, stability at the equilibrium points, and characteristics with respect to state variables have been performed as some parts of analytical solution, whereas the numerical solution has been performed using the Runge–Kutta \u0000 \u0000 \u0000 \u0000 4\u0000 \u0000 \u0000 t\u0000 h\u0000 \u0000 \u0000 \u0000 order technique. The findings of this research reveal that an increase in the quantity of nutrients causes an algal bloom, which in turn lowers the equilibrium level of dissolved oxygen. However, higher levels of detritus (\u0000 \u0000 >\u0000 \u0000 4.7 mg/litre) are hazardous to the generation of dissolved oxygen in water systems. Maximum detritus of 1.0 mg/liter is required for fast algal and dissolved oxygen growth in water bodies; beyond that, algal and dissolved oxygen growth rates are lower. Therefore, increasing public awareness is an essential step in controlling this growing issue; failing to do so will result in problems for our water supply, which will in turn pose a danger to our ecosystem.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"68 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77150397","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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