This work addresses the idea of the uniqueness and existence results for a class of boundary value problems (BVPs) for implicit Volterra-Fredholm integro-differential equations (V-FIDEs) with fractional η-Hilfer nonlinear equations and multi-point fractional boundary non-instantaneous conditions. The conclusions are confirmed by the fixed point of Krasnoselskii's theorem and the Banach contraction principle. Finally, a concrete example is given to illustrate our main conclusions.
{"title":"On a New Class of Impulsive η-Hilfer Fractional Volterra-Fredholm Integro-Differential Equations","authors":"F. M. Ismaael","doi":"10.47836/mjms.17.4.10","DOIUrl":"https://doi.org/10.47836/mjms.17.4.10","url":null,"abstract":"This work addresses the idea of the uniqueness and existence results for a class of boundary value problems (BVPs) for implicit Volterra-Fredholm integro-differential equations (V-FIDEs) with fractional η-Hilfer nonlinear equations and multi-point fractional boundary non-instantaneous conditions. The conclusions are confirmed by the fixed point of Krasnoselskii's theorem and the Banach contraction principle. Finally, a concrete example is given to illustrate our main conclusions.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":"2 2","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139002564","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 Goldreich-Goldwasser-Halevi (GGH) cryptosystem is declared broken due to the modified versions of the embedding attacks, known as Nguyen's σ, Nguyen's 2σ and Lee-Hahn's attacks. Despite using the same approach as the original embedding attack, these attacks deployed different strategies and resulted in different performances for breaking the GGH cryptosystem. In this paper, we described those strategies in detail. Moreover, we investigated the mathematical factors behind these attacks' ability and performance discrepancies. Mathematical proof examines and discusses the factors that triggered those variances. As a result, the expected lattice gap and implemented lattice dimensions are mathematically proven as the factors that significantly influenced these attacks' performance. By demonstrating how the attacks manipulated these factors, any lattice-based cryptosystem that relies on the hardness of the CVP could avoid repeating the same slipup as the GGH. Hence, precautionary action could be proactively taken to prevent it from being threatened by embedding-based attacks.
{"title":"The Efficiency of Embedding-Based Attacks on the GGH Lattice-Based Cryptosystem","authors":"A. Mandangan,, H. Kamarulhaili,, M. A. Asbullah,","doi":"10.47836/mjms.17.4.09","DOIUrl":"https://doi.org/10.47836/mjms.17.4.09","url":null,"abstract":"The Goldreich-Goldwasser-Halevi (GGH) cryptosystem is declared broken due to the modified versions of the embedding attacks, known as Nguyen's σ, Nguyen's 2σ and Lee-Hahn's attacks. Despite using the same approach as the original embedding attack, these attacks deployed different strategies and resulted in different performances for breaking the GGH cryptosystem. In this paper, we described those strategies in detail. Moreover, we investigated the mathematical factors behind these attacks' ability and performance discrepancies. Mathematical proof examines and discusses the factors that triggered those variances. As a result, the expected lattice gap and implemented lattice dimensions are mathematically proven as the factors that significantly influenced these attacks' performance. By demonstrating how the attacks manipulated these factors, any lattice-based cryptosystem that relies on the hardness of the CVP could avoid repeating the same slipup as the GGH. Hence, precautionary action could be proactively taken to prevent it from being threatened by embedding-based attacks.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":"23 8","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138971173","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}
R. Hidayat,, N. A. Kamarazan,, N. Nasir,, A. F. M. Ayub,
GeoGebra software has been identified as a potential aid in the teaching and learning process. This study aims to examine the impact of GeoGebra software on achievement and enjoyment in the context of the polygon topic. A non-equivalent group pretest-posttest design was utilized, and 60 students were randomly assigned to either the experimental or control group. The data collected was analyzed using descriptive and inferential statistical methods with the assistance of SPSS version 26. The findings revealed that the level of achievement and engagement among Form Two students in the study population was already high regarding the Polygon topic. However, the results demonstrated that students who received instruction utilizing GeoGebra software achieved even higher levels of achievement and engagement than those who experienced traditional teaching methods. As a result, integrating GeoGebra software into the classroom proved to be an effective tool for enhancing student achievement and engagement on the Polygon topic among Form Two students. Finally, we found a significant relationship between the experience of enjoyment and the academic performance of second-year students.
{"title":"The Effect of GeoGebra Software on Achievement and Engagement Among Secondary School Students","authors":"R. Hidayat,, N. A. Kamarazan,, N. Nasir,, A. F. M. Ayub,","doi":"10.47836/mjms.17.4.06","DOIUrl":"https://doi.org/10.47836/mjms.17.4.06","url":null,"abstract":"GeoGebra software has been identified as a potential aid in the teaching and learning process. This study aims to examine the impact of GeoGebra software on achievement and enjoyment in the context of the polygon topic. A non-equivalent group pretest-posttest design was utilized, and 60 students were randomly assigned to either the experimental or control group. The data collected was analyzed using descriptive and inferential statistical methods with the assistance of SPSS version 26. The findings revealed that the level of achievement and engagement among Form Two students in the study population was already high regarding the Polygon topic. However, the results demonstrated that students who received instruction utilizing GeoGebra software achieved even higher levels of achievement and engagement than those who experienced traditional teaching methods. As a result, integrating GeoGebra software into the classroom proved to be an effective tool for enhancing student achievement and engagement on the Polygon topic among Form Two students. Finally, we found a significant relationship between the experience of enjoyment and the academic performance of second-year students.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":"1993 10","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138973926","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}
This paper introduces an innovative concept known as n-polar Z-hesitant Anti-Fuzzy Soft Sets (MZHAFSs) within the framework of BCK/BCI-algebras. Soft set theory originates in the captivating field of fuzzy set theory. Our approach is a harmonious synthesis of n-polar anti-fuzzy set theory, soft set models, and Z-hesitant anti-fuzzy sets, skillfully applied within the framework of BCK/BCI-algebras. This effort leads to the introduction of a new variant of fuzzy sets termed MZHAFSs (n-polar Z-hesitant anti-fuzzy soft sets) in the context of BCK/BCI-algebras. Additionally, we elucidate the concept of n-polar Z-hesitant anti-fuzzy soft sets to provide a comprehensive understanding. Furthermore, we introduce and define various related concepts, including n-polar Z-hesitant anti-fuzzy soft subalgebras, n-polar Z-hesitant anti-fuzzy soft ideals, n-polar Z-hesitant anti-fuzzy soft closed ideals, and n-polar Z-hesitant anti-fuzzy soft commutative ideals, and establish meaningful connections between them. We also present and rigorously prove several theorems that are pertinent to these newly introduced notions.
本文在BCK/BCI代数框架内引入了一个创新概念，即n极Z-hesitant反模糊软集（MZHAFSs）。软集理论起源于引人入胜的模糊集理论领域。我们的方法是将 n 极反模糊集合理论、软集合模型和 Z-hesitant 反模糊集合和谐地综合在一起，并巧妙地应用于 BCK/BCI 算法框架中。这一努力导致在 BCK/BCI-algebras 的背景下引入了一种新的模糊集变体，称为 MZHAFSs（n-polar Z-hesitant anti-fuzzy soft sets）。此外，我们还阐明了 n 极 Z-hesitant 反模糊软集的概念，以提供一个全面的理解。此外，我们还介绍和定义了各种相关概念，包括 n 极 Z-hesitant反模糊软子代数、n 极 Z-hesitant反模糊软理想、n 极 Z-hesitant反模糊软封闭理想和 n 极 Z-hesitant反模糊软交换理想，并建立了它们之间的有意义的联系。我们还提出并严格证明了与这些新引入概念相关的几个定理。
{"title":"n-polar Z-hesitant Complementary Fuzzy Soft Set in BCK/BCI-Algebras","authors":"K. Alsager","doi":"10.47836/mjms.17.4.07","DOIUrl":"https://doi.org/10.47836/mjms.17.4.07","url":null,"abstract":"This paper introduces an innovative concept known as n-polar Z-hesitant Anti-Fuzzy Soft Sets (MZHAFSs) within the framework of BCK/BCI-algebras. Soft set theory originates in the captivating field of fuzzy set theory. Our approach is a harmonious synthesis of n-polar anti-fuzzy set theory, soft set models, and Z-hesitant anti-fuzzy sets, skillfully applied within the framework of BCK/BCI-algebras. This effort leads to the introduction of a new variant of fuzzy sets termed MZHAFSs (n-polar Z-hesitant anti-fuzzy soft sets) in the context of BCK/BCI-algebras. Additionally, we elucidate the concept of n-polar Z-hesitant anti-fuzzy soft sets to provide a comprehensive understanding. Furthermore, we introduce and define various related concepts, including n-polar Z-hesitant anti-fuzzy soft subalgebras, n-polar Z-hesitant anti-fuzzy soft ideals, n-polar Z-hesitant anti-fuzzy soft closed ideals, and n-polar Z-hesitant anti-fuzzy soft commutative ideals, and establish meaningful connections between them. We also present and rigorously prove several theorems that are pertinent to these newly introduced notions.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":"2016 13","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139001744","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}
Mathematical modeling in biology is quite interesting in the field of real-world problems. This research paper focused on the interaction between two prey and one predator species. Here, our interaction is based upon the competition between two prey and one predator including an additive Allee effect in the predator population along with a Holling type II functional response. Further, this intuition allowed us to prove the positive invariance and boundedness of the model. This analysis shows that there are six equilibrium points including the coexistence of all three populations. Stability analyses are also derived and proved both locally and globally. Also in this paper, we discussed the optimal control approach to reduce the population affected by an Allee effect by the predator population. Numerical simulations are carried out to support our theoretical results.
{"title":"Dynamical Analysis of Two-Preys and One Predator Interaction Model with An Allee Effect on Predator","authors":"G. S. Kumar, C. Gunasundari","doi":"10.47836/mjms.17.3.03","DOIUrl":"https://doi.org/10.47836/mjms.17.3.03","url":null,"abstract":"Mathematical modeling in biology is quite interesting in the field of real-world problems. This research paper focused on the interaction between two prey and one predator species. Here, our interaction is based upon the competition between two prey and one predator including an additive Allee effect in the predator population along with a Holling type II functional response. Further, this intuition allowed us to prove the positive invariance and boundedness of the model. This analysis shows that there are six equilibrium points including the coexistence of all three populations. Stability analyses are also derived and proved both locally and globally. Also in this paper, we discussed the optimal control approach to reduce the population affected by an Allee effect by the predator population. Numerical simulations are carried out to support our theoretical results.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135785703","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}
S. S. P. M. Isa, S. Parvin, N. M. Arifin, F. M. Ali, K. Ahmad
The two-dimensional mathematical model ofwater-based hybrid nanofluid, where the nanoparticles of the model are alumina (Al2O3) and copper (Cu) is analyzed in this article. It describes the heat and mass transfer which are induced by concentration and temperature differences, respectively. The current mathematical model extended the works by implementing both directions of moving sheet in the boundary conditions: stretching and shrinking, and use the exponential variations of the sheet velocity, temperature, and concentration of the hybrid nanofluid at the sheet. The final numerical solutions can be obtained by implementing Matlab bvp4c, which involves the step of choosing the most reliable solution in an actual fluid situation. This selection technique on numerical solutions is known as stability analysis and only needs to apply when more than one numerical solution appears in the Matlab bvp4c program. Finally, the controlling parameters such as nanoparticle solid volume fraction, suction, shrinking/stretching, Soret and Dufour cause an increment or decrement in the flow, heat and mass transfer in the hybrid nanofluid. For the stable solution, fluid velocity becomes slower whereas temperature and concentration of the fluid increase when the percentage of Cu, as well as Al2O3, rises into the water. Moreover, in case of local Nusselt number and local Sherwood number it is proved that Soret effect is the opposite phenomenon of Dufour effect.
{"title":"Soret-Dufour Effects on The Waterbased Hybrid Nanofluid Flow with Nanoparticles of Alumina and Copper","authors":"S. S. P. M. Isa, S. Parvin, N. M. Arifin, F. M. Ali, K. Ahmad","doi":"10.47836/mjms.17.3.04","DOIUrl":"https://doi.org/10.47836/mjms.17.3.04","url":null,"abstract":"The two-dimensional mathematical model ofwater-based hybrid nanofluid, where the nanoparticles of the model are alumina (Al2O3) and copper (Cu) is analyzed in this article. It describes the heat and mass transfer which are induced by concentration and temperature differences, respectively. The current mathematical model extended the works by implementing both directions of moving sheet in the boundary conditions: stretching and shrinking, and use the exponential variations of the sheet velocity, temperature, and concentration of the hybrid nanofluid at the sheet. The final numerical solutions can be obtained by implementing Matlab bvp4c, which involves the step of choosing the most reliable solution in an actual fluid situation. This selection technique on numerical solutions is known as stability analysis and only needs to apply when more than one numerical solution appears in the Matlab bvp4c program. Finally, the controlling parameters such as nanoparticle solid volume fraction, suction, shrinking/stretching, Soret and Dufour cause an increment or decrement in the flow, heat and mass transfer in the hybrid nanofluid. For the stable solution, fluid velocity becomes slower whereas temperature and concentration of the fluid increase when the percentage of Cu, as well as Al2O3, rises into the water. Moreover, in case of local Nusselt number and local Sherwood number it is proved that Soret effect is the opposite phenomenon of Dufour effect.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":"90 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135785705","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 diameter of an artery can narrow due to atherosclerosis or stenosis, making it challenging to resolve solute dispersion issues as blood flows via a stenosed artery. The stenosis occurrence restricted drug dispersion and blood flow. This research introduces the establishment of a mathematical model in examining the unsteady dispersion with respect to the solute in overlapping stenosis arteries depicting blood as a Herschel-Bulkley (H-B) fluid model. Note that fluid velocity was obtained by analytically solving the governing and constitutive equations. The transport equation has been solved by employing a generalised dispersion model (GDM), in which the dispersion process is described. Accordingly, yield stress, stenosis height, slug input of solute length, as well as a rise in the power-law index have improved the peak with regard to the mean concentration and solute concentration. The maximum mean concentration yielded the effective dose for therapeutic concentration. In conclusion, this study is relevant to disease arteries, coagulating hemodynamics and may help physiologists in furnishing a more refined understanding of diffusion processes in cardiovascular hydrodynamics. An interesting application related to the present study is the transportation of drugs in the arterial blood flow.
{"title":"Exact Analysis of Unsteady Solute Dispersion in Blood Flow: A Theoretical Study","authors":"S. N. A. M. Abidin, N. A. Jaafar, Z. Ismail","doi":"10.47836/mjms.17.3.07","DOIUrl":"https://doi.org/10.47836/mjms.17.3.07","url":null,"abstract":"The diameter of an artery can narrow due to atherosclerosis or stenosis, making it challenging to resolve solute dispersion issues as blood flows via a stenosed artery. The stenosis occurrence restricted drug dispersion and blood flow. This research introduces the establishment of a mathematical model in examining the unsteady dispersion with respect to the solute in overlapping stenosis arteries depicting blood as a Herschel-Bulkley (H-B) fluid model. Note that fluid velocity was obtained by analytically solving the governing and constitutive equations. The transport equation has been solved by employing a generalised dispersion model (GDM), in which the dispersion process is described. Accordingly, yield stress, stenosis height, slug input of solute length, as well as a rise in the power-law index have improved the peak with regard to the mean concentration and solute concentration. The maximum mean concentration yielded the effective dose for therapeutic concentration. In conclusion, this study is relevant to disease arteries, coagulating hemodynamics and may help physiologists in furnishing a more refined understanding of diffusion processes in cardiovascular hydrodynamics. An interesting application related to the present study is the transportation of drugs in the arterial blood flow.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135785702","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}
Convection heat transfer especially Rayleigh-Bénard convection plays a significant role either in nature or industry applications. Particularly, in industry, the instability of the Rayleigh-Bénard convection process is important to see whether the quality of final goods is excellent or not. Therefore, in this study linear stability theory has been performed to investigate the influence of cubic temperature gradient and cubic concentration gradient on the onset of convection in a double-diffusive micropolar fluid. By adopting the single-term Galerkin procedure, parameters N1,N3,N5 , and Rs have been analyzed to investigate their influence on the onset of convection. The results found that the coupling parameter N1 and micropolar heat conduction parameter N5 will put the system in stable conditions. Meanwhile, the couple stress parameter N3 and solutal Rayleigh number Rs will destabilize the system. The results also show that by increasing the value of the solutal Rayleigh number Rs , the value of the critical Rayleigh number Rac will decrease. By enclosing the micron-sized suspended particles, we can slow down the process of Rayleigh-Bénard convection in double-diffusive micropolar fluids. It is possible to control the process of the onset of Rayleigh-Bénard convection by selecting suitable non-uniform temperature and concentration gradient profiles.
{"title":"Behaviour of the Onset of Rayleigh-Bénard Convection in Double-Diffusive Micropolar Fluids Under the Influence of Cubic Temperature and Concentration Gradient","authors":"R. Idris, A. Alias, A. Miqdady","doi":"10.47836/mjms.17.3.12","DOIUrl":"https://doi.org/10.47836/mjms.17.3.12","url":null,"abstract":"Convection heat transfer especially Rayleigh-Bénard convection plays a significant role either in nature or industry applications. Particularly, in industry, the instability of the Rayleigh-Bénard convection process is important to see whether the quality of final goods is excellent or not. Therefore, in this study linear stability theory has been performed to investigate the influence of cubic temperature gradient and cubic concentration gradient on the onset of convection in a double-diffusive micropolar fluid. By adopting the single-term Galerkin procedure, parameters N1,N3,N5 , and Rs have been analyzed to investigate their influence on the onset of convection. The results found that the coupling parameter N1 and micropolar heat conduction parameter N5 will put the system in stable conditions. Meanwhile, the couple stress parameter N3 and solutal Rayleigh number Rs will destabilize the system. The results also show that by increasing the value of the solutal Rayleigh number Rs , the value of the critical Rayleigh number Rac will decrease. By enclosing the micron-sized suspended particles, we can slow down the process of Rayleigh-Bénard convection in double-diffusive micropolar fluids. It is possible to control the process of the onset of Rayleigh-Bénard convection by selecting suitable non-uniform temperature and concentration gradient profiles.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135785546","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}
Circular intuitionistic fuzzy sets (CIFS) are a recent extension of intuitionistic fuzzy sets (IFS) that can handle imprecise membership values effectively. However, its representation is limited to the space under the intuitionistic fuzzy interpretation triangle (IFIT). To address this, a new generalization of CIFS called circular q-rung orthopair fuzzy sets (Cq-ROFS) is proposed, extending the IFIT to cover a larger space of imprecision. Several relations and operations, including algebraic operations for Cq-ROFS are proposed. In addition, modal operators and their properties are then investigated.
{"title":"Circular q-Rung Orthopair Fuzzy Set and Its Algebraic Properties","authors":"B. Yusoff, A. Kilicman, D. Pratama, R. Hasni","doi":"10.47836/mjms.17.3.08","DOIUrl":"https://doi.org/10.47836/mjms.17.3.08","url":null,"abstract":"Circular intuitionistic fuzzy sets (CIFS) are a recent extension of intuitionistic fuzzy sets (IFS) that can handle imprecise membership values effectively. However, its representation is limited to the space under the intuitionistic fuzzy interpretation triangle (IFIT). To address this, a new generalization of CIFS called circular q-rung orthopair fuzzy sets (Cq-ROFS) is proposed, extending the IFIT to cover a larger space of imprecision. Several relations and operations, including algebraic operations for Cq-ROFS are proposed. In addition, modal operators and their properties are then investigated.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135785545","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, firstly, we obtain an inequality in Lγ analogue concerning the polar derivative for a polynomial p(ξ) = Xm ν=0 cνξν of degree m having no zero in |ξ| < r, r ≥ 1 proved by Govil et al. [15]. Secondly, we also prove Lγ version for the polar derivative of an ordinary inequality for a polynomial having all its zeros in |ξ| ≤ r, r ≤ 1 proved in that same paper. Our results generalize and improve some known inequalities.
{"title":"Lγ Inequalities for the Polar Derivative of Polynomials","authors":"M. S. Singh, N. Reingachan, M. T. Devi, B. Chanam","doi":"10.47836/mjms.17.3.06","DOIUrl":"https://doi.org/10.47836/mjms.17.3.06","url":null,"abstract":"In this paper, firstly, we obtain an inequality in Lγ analogue concerning the polar derivative for a polynomial p(ξ) = Xm ν=0 cνξν of degree m having no zero in |ξ| < r, r ≥ 1 proved by Govil et al. [15]. Secondly, we also prove Lγ version for the polar derivative of an ordinary inequality for a polynomial having all its zeros in |ξ| ≤ r, r ≤ 1 proved in that same paper. Our results generalize and improve some known inequalities.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135785700","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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