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An Efficient Data-Driven Model for Millimeter-Wave 5G Channel Modeling Using Machine Learning and High-Performance Computing
IF 0.8 4区 综合性期刊 Q3 MULTIDISCIPLINARY SCIENCES Pub Date : 2025-03-06 DOI: 10.1007/s40010-025-00911-4
Animesh Tripathi, Shiv Prakash, Pradeep Kumar Tiwari, Narendra Kumar Shukla

The fifth generation (5G) technology is efficiently designed to perform many things for the betterment of lives, such as Artificial Intelligence, Cyber-Physical Systems, the Internet of Things, etc. To facilitate this huge amount of data very high bandwidth is needed, hence 5G extensively uses the millimeter wave (mm-Wave) to enhance bandwidth. The technology of mm-Wave communication operates at very high frequencies, typically between 30 and 300 GHz. Some of the challenges will be key to realizing the full potential of mm-Wave communication technology for high-speed wireless communication in the future. The difficulties caused by mm-Wave are directivity, propagation loss, and sensitivity to blockage. To overcome these difficulties, we surveyed existing solutions and standards and identified research gaps. As a high data rate, mm-Wave may be considered in future generation communication and propagation channel requirements for mm-Wave investigated precisely for the prior knowledge of the quality of service (QoS) parameters. Therefore, channel modeling is the key need for the estimation of QoS parameters namely delay, angle of arrival, path loss, angle of departure, etc. In this paper, an efficient data-driven model for mm-Wave 5G Channel modeling using machine learning and high-performance computing is proposed which outperformed the other state-of-the-art in terms of various performance matrices.

{"title":"An Efficient Data-Driven Model for Millimeter-Wave 5G Channel Modeling Using Machine Learning and High-Performance Computing","authors":"Animesh Tripathi,&nbsp;Shiv Prakash,&nbsp;Pradeep Kumar Tiwari,&nbsp;Narendra Kumar Shukla","doi":"10.1007/s40010-025-00911-4","DOIUrl":"10.1007/s40010-025-00911-4","url":null,"abstract":"<div><p>The fifth generation (5G) technology is efficiently designed to perform many things for the betterment of lives, such as Artificial Intelligence, Cyber-Physical Systems, the Internet of Things, etc. To facilitate this huge amount of data very high bandwidth is needed, hence 5G extensively uses the millimeter wave (mm-Wave) to enhance bandwidth. The technology of mm-Wave communication operates at very high frequencies, typically between 30 and 300 GHz. Some of the challenges will be key to realizing the full potential of mm-Wave communication technology for high-speed wireless communication in the future. The difficulties caused by mm-Wave are directivity, propagation loss, and sensitivity to blockage. To overcome these difficulties, we surveyed existing solutions and standards and identified research gaps. As a high data rate, mm-Wave may be considered in future generation communication and propagation channel requirements for mm-Wave investigated precisely for the prior knowledge of the quality of service (QoS) parameters. Therefore, channel modeling is the key need for the estimation of QoS parameters namely delay, angle of arrival, path loss, angle of departure, etc. In this paper, an efficient data-driven model for mm-Wave 5G Channel modeling using machine learning and high-performance computing is proposed which outperformed the other state-of-the-art in terms of various performance matrices.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"95 1","pages":"41 - 54"},"PeriodicalIF":0.8,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809226","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Computation of Beyer’s Nonlinearity Acoustic Parameter of Binary Ionic Liquids (RTIL’s) Mixtures
IF 0.8 4区 综合性期刊 Q3 MULTIDISCIPLINARY SCIENCES Pub Date : 2025-02-26 DOI: 10.1007/s40010-025-00913-2
Ramakant, Brijlesh Kumar Tiwari, Arvind Kumar Pandey, Subhash Chandra Shrivastava, J. D. Pandey

This study focuses on the computation of the nonlinearity acoustic parameter for binary ionic liquid mixtures, which is an important area of research in nonlinear acoustics. For the first time nonlinear acoustic parameter (B/A) of six binary ionic liquid mixture have been computed using four different methods namely Hartmann, Ballou, Johnson and thermoacoustic method of Sharma. The binary mixtures of six RTIL’s are DEAA + water, DEAS + water, TEAA + water, TEAS + water, TMAA + water and TMAS + water at 298.15 K. The experimental input data of density (ρ) and sound speed (u) have been taken from a very accurate and precise work of Venbatesu et al. (J Phys Chem 13:118, 2014. 5971). A comparative study of (B/A) values obtained from different methods has been presented.

{"title":"Computation of Beyer’s Nonlinearity Acoustic Parameter of Binary Ionic Liquids (RTIL’s) Mixtures","authors":"Ramakant,&nbsp;Brijlesh Kumar Tiwari,&nbsp;Arvind Kumar Pandey,&nbsp;Subhash Chandra Shrivastava,&nbsp;J. D. Pandey","doi":"10.1007/s40010-025-00913-2","DOIUrl":"10.1007/s40010-025-00913-2","url":null,"abstract":"<div><p>This study focuses on the computation of the nonlinearity acoustic parameter for binary ionic liquid mixtures, which is an important area of research in nonlinear acoustics. For the first time nonlinear acoustic parameter (B/A) of six binary ionic liquid mixture have been computed using four different methods namely Hartmann, Ballou, Johnson and thermoacoustic method of Sharma. The binary mixtures of six RTIL’s are DEAA + water, DEAS + water, TEAA + water, TEAS + water, TMAA + water and TMAS + water at 298.15 K. The experimental input data of density (ρ) and sound speed (u) have been taken from a very accurate and precise work of Venbatesu et al. (J Phys Chem 13:118, 2014. 5971). A comparative study of (B/A) values obtained from different methods has been presented.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"95 1","pages":"1 - 13"},"PeriodicalIF":0.8,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Group Invariance Method for Spherical Shock Wave in a Non-Ideal Gas under the Influence of Gravitational and Azimuthal Magnetic Fields
IF 0.8 4区 综合性期刊 Q3 MULTIDISCIPLINARY SCIENCES Pub Date : 2025-02-24 DOI: 10.1007/s40010-025-00908-z
G. Nath, Abhay Maurya

In the present work, we have applied the group invariance method to discuss the propagation of spherical shock wave using the concept of Roche model in a non-ideal gas under the influence of gravitational and magnetic fields for the adiabatic and isothermal flows. We have obtained the similarity solution with power law shock paths in both the ideal gas and non-ideal gas cases by the different choice of the arbitrary constant values appearing in the expression for infinitesimals. Numerical solutions are obtained for both the isothermal and adiabatic flows. The effect of the gravitational parameter, shock Cowling number, non-idealness parameter and adiabatic index on the shock strength, the density ratio across the shock front, and on the flow variables are studied. It is found that an increase in the gravitational parameter or non-idealness parameter or shock Cowling number or adiabatic index increases the density ratio across the shock front and decreases the shock strength.

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引用次数: 0
Influence of Hardener Type on the Particleboard Properties at Industrial Scale
IF 0.8 4区 综合性期刊 Q3 MULTIDISCIPLINARY SCIENCES Pub Date : 2025-02-18 DOI: 10.1007/s40010-025-00910-5
O. Çamlıbel, M. Aydın, E. Koç

Influence of the two different hardeners (ammonium chloride NH4Cl and ammonium sulphate (NH4)2SO4) on the physical (density, thickness, moisture content, thickness swelling and water absorption) and mechanical (modulus of rupture, modulus of elasticity, surface soundness and internal bonding strength) properties and formaldehyde emission of the particleboard was figured out. Boards were industrially produced (at continuous press line) using urea formaldehyde resin, liquid paraffin, and a 50:40:10 mixture of Scots pine, oak and poplar chips, respectively. Except for elasticity, boards produced using ammonium chloride had better mechanical properties, but their thickness swelling and water absorption capabilities were lower (approx. 55.5% and 45.9%, respectively) than those produced with ammonium sulphate. Utilization of ammonium chloride provided 30.3% higher surface soundness. There were less than 1% differences in the thickness and density. Around 36.4% less formaldehyde emission was determined for ammonium chloride-modified boards. According to the results, only means of IB did not present statistically significant differences.

{"title":"Influence of Hardener Type on the Particleboard Properties at Industrial Scale","authors":"O. Çamlıbel,&nbsp;M. Aydın,&nbsp;E. Koç","doi":"10.1007/s40010-025-00910-5","DOIUrl":"10.1007/s40010-025-00910-5","url":null,"abstract":"<div><p>Influence of the two different hardeners (ammonium chloride NH<sub>4</sub>Cl and ammonium sulphate (NH<sub>4</sub>)<sub>2</sub>SO<sub>4</sub>) on the physical (density, thickness, moisture content, thickness swelling and water absorption) and mechanical (modulus of rupture, modulus of elasticity, surface soundness and internal bonding strength) properties and formaldehyde emission of the particleboard was figured out. Boards were industrially produced (at continuous press line) using urea formaldehyde resin, liquid paraffin, and a 50:40:10 mixture of Scots pine, oak and poplar chips, respectively. Except for elasticity, boards produced using ammonium chloride had better mechanical properties, but their thickness swelling and water absorption capabilities were lower (approx. 55.5% and 45.9%, respectively) than those produced with ammonium sulphate. Utilization of ammonium chloride provided 30.3% higher surface soundness. There were less than 1% differences in the thickness and density. Around 36.4% less formaldehyde emission was determined for ammonium chloride-modified boards. According to the results, only means of IB did not present statistically significant differences.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"95 1","pages":"33 - 40"},"PeriodicalIF":0.8,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809277","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Convergence of Strong Cylindrical and Spherical Shock Waves in Solid Materials
IF 0.8 4区 综合性期刊 Q3 MULTIDISCIPLINARY SCIENCES Pub Date : 2025-02-01 DOI: 10.1007/s40010-025-00909-y
R. K. Anand

In this article, we present a description of the behaviour of shock-compressed solid materials following Geometrical Shock Dynamics (GSD) theory. GSD has been successfully applied to various gas dynamics problems, and here we have employed it to investigate the propagation of cylindrically and spherically symmetric converging shock waves in solid materials. The analytical solution of shock dynamics equations has been obtained in the strong-shock limit, assuming the solid materials to be homogeneous and isotropic and obeying the Mie-Grüneisen equation of state. The non-dimensional expressions are obtained for the velocity of shock, the pressure, the mass density, the particle velocity, the temperature, the speed of sound, the adiabatic bulk modulus, and the change-in-entropy behind the strong converging shock front. The influences as a result of changes in (i) the propagation distance r from the axis or centre ((r=0)) of convergence, (ii) the Grüneisen parameter, and (iii) the material parameter are explored on the shock velocity and the domain behind the converging shock-front. The results show that as the shock focuses at the axis or origin, the shock velocity, the pressure, the temperature, and the change-in-entropy increase in the shock-compressed titanium Ti6Al4V, stainless steel 304, aluminum 6061-T6, etc.

{"title":"On the Convergence of Strong Cylindrical and Spherical Shock Waves in Solid Materials","authors":"R. K. Anand","doi":"10.1007/s40010-025-00909-y","DOIUrl":"10.1007/s40010-025-00909-y","url":null,"abstract":"<div><p>In this article, we present a description of the behaviour of shock-compressed solid materials following Geometrical Shock Dynamics (GSD) theory. GSD has been successfully applied to various gas dynamics problems, and here we have employed it to investigate the propagation of cylindrically and spherically symmetric converging shock waves in solid materials. The analytical solution of shock dynamics equations has been obtained in the strong-shock limit, assuming the solid materials to be homogeneous and isotropic and obeying the Mie-Grüneisen equation of state. The non-dimensional expressions are obtained for the velocity of shock, the pressure, the mass density, the particle velocity, the temperature, the speed of sound, the adiabatic bulk modulus, and the change-in-entropy behind the strong converging shock front. The influences as a result of changes in (i) the propagation distance <i>r</i> from the axis or centre <span>((r=0))</span> of convergence, (ii) the Grüneisen parameter, and (iii) the material parameter are explored on the shock velocity and the domain behind the converging shock-front. The results show that as the shock focuses at the axis or origin, the shock velocity, the pressure, the temperature, and the change-in-entropy increase in the shock-compressed titanium Ti6Al4V, stainless steel 304, aluminum 6061-T6, etc.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"95 1","pages":"103 - 112"},"PeriodicalIF":0.8,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809100","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Ranking of Generalized Trapezoidal Fuzzy Numbers by Point of Intersection and its Application in Multi Criteria Decision Making Problems 按交点排列广义梯形模糊数及其在多标准决策问题中的应用
IF 0.8 4区 综合性期刊 Q3 MULTIDISCIPLINARY SCIENCES Pub Date : 2025-01-30 DOI: 10.1007/s40010-025-00907-0
P. G. Patil, S. Shivashankar, Vyshakha Elluru

The ranking of fuzzy numbers is essential in real time applications. The new ranking approach for fuzzy numbers that combines the idea of the point of intersection and average of numbers is proposed in the current work for both triangular and trapezoidal numbers. The proposed method involves simple calculations, also ranks the non-normal fuzzy numbers and the crisp numbers. The applicability of the proposed method is demonstrated by solving few numerical cases and illustrate the benefits. Some comparison study has been conducted with few other existing ranking methods.

{"title":"Ranking of Generalized Trapezoidal Fuzzy Numbers by Point of Intersection and its Application in Multi Criteria Decision Making Problems","authors":"P. G. Patil,&nbsp;S. Shivashankar,&nbsp;Vyshakha Elluru","doi":"10.1007/s40010-025-00907-0","DOIUrl":"10.1007/s40010-025-00907-0","url":null,"abstract":"<div><p>The ranking of fuzzy numbers is essential in real time applications. The new ranking approach for fuzzy numbers that combines the idea of the point of intersection and average of numbers is proposed in the current work for both triangular and trapezoidal numbers. The proposed method involves simple calculations, also ranks the non-normal fuzzy numbers and the crisp numbers. The applicability of the proposed method is demonstrated by solving few numerical cases and illustrate the benefits. Some comparison study has been conducted with few other existing ranking methods.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"95 1","pages":"71 - 83"},"PeriodicalIF":0.8,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Multi-Zone Fence Perimeter Surveillance: A New Edge-FOG Architecture for Efficient Detection and Classification of Intrusion
IF 0.8 4区 综合性期刊 Q3 MULTIDISCIPLINARY SCIENCES Pub Date : 2024-12-29 DOI: 10.1007/s40010-024-00904-9
Srinivasan Aruchamy, Anisom Chakraborty, Siva Ram Krishna Vadali, Manisha Das

In this paper, we propose a geophone based fence surveillance system with a FOG architecture for detection of intrusion and classification in spatially separated zones. In the proposed decentralized architecture − for edge layer we propose an efficient spectral-energy-comparison detector; and at FOG layer, we propose a highly accurate supervised machine learning algorithm in the form of linear support vector machine for classification of mode of intrusion; lastly, the FOG layer updates the intrusion status of respective zones to the cloud layer. Extensive analysis of field experimental data acquired with an ad hoc geographically distributed fence setup indicates that the proposed detector renders (99%) accuracy with very low false alarm rate and also outperforms known detectors. We perform feature engineering and demonstrate that the proposed classifier achieves (97.9%) accuracy for both man-made intrusions and natural events even with reduced feature set. We also show that the proposed classifier outperforms known fence perimeter surveillance schemes. Lastly, we validate the performance of proposed system through real life experiments and analysis therein.

{"title":"Multi-Zone Fence Perimeter Surveillance: A New Edge-FOG Architecture for Efficient Detection and Classification of Intrusion","authors":"Srinivasan Aruchamy,&nbsp;Anisom Chakraborty,&nbsp;Siva Ram Krishna Vadali,&nbsp;Manisha Das","doi":"10.1007/s40010-024-00904-9","DOIUrl":"10.1007/s40010-024-00904-9","url":null,"abstract":"<div><p>In this paper, we propose a geophone based fence surveillance system with a FOG architecture for detection of intrusion and classification in spatially separated zones. In the proposed decentralized architecture − for edge layer we propose an efficient spectral-energy-comparison detector; and at FOG layer, we propose a highly accurate supervised machine learning algorithm in the form of linear support vector machine for classification of mode of intrusion; lastly, the FOG layer updates the intrusion status of respective zones to the cloud layer. Extensive analysis of field experimental data acquired with an ad hoc geographically distributed fence setup indicates that the proposed detector renders <span>(99%)</span> accuracy with very low false alarm rate and also outperforms known detectors. We perform feature engineering and demonstrate that the proposed classifier achieves <span>(97.9%)</span> accuracy for both man-made intrusions and natural events even with reduced feature set. We also show that the proposed classifier outperforms known fence perimeter surveillance schemes. Lastly, we validate the performance of proposed system through real life experiments and analysis therein.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"95 1","pages":"17 - 32"},"PeriodicalIF":0.8,"publicationDate":"2024-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809209","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Correction: Bias Correction and Trend Analysis of Temperature and Rainfall in Eastern India 更正:印度东部气温和降雨量的偏差修正与趋势分析
IF 0.8 4区 综合性期刊 Q3 MULTIDISCIPLINARY SCIENCES Pub Date : 2024-12-13 DOI: 10.1007/s40010-024-00906-7
Rajiv Kumar Srivastava, Biplab Sadhukhan, Arun Chakraborty, Rabindra Kumar Panda
{"title":"Correction: Bias Correction and Trend Analysis of Temperature and Rainfall in Eastern India","authors":"Rajiv Kumar Srivastava,&nbsp;Biplab Sadhukhan,&nbsp;Arun Chakraborty,&nbsp;Rabindra Kumar Panda","doi":"10.1007/s40010-024-00906-7","DOIUrl":"10.1007/s40010-024-00906-7","url":null,"abstract":"","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"95 1","pages":"15 - 15"},"PeriodicalIF":0.8,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40010-024-00906-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A New Mean-Variance-Skewness Model for Portfolio Optimization Using Three-Part Zigzag Uncertain Variable
IF 0.8 4区 综合性期刊 Q3 MULTIDISCIPLINARY SCIENCES Pub Date : 2024-12-13 DOI: 10.1007/s40010-024-00905-8
Sanjoy Chhatri, Debasish Bhattacharya

A multi-objective portfolio selection problem involving newly introduced stocks has been studied here, and an innovative solution procedure for the same with a numerical illustration is also provided. The returns of these stocks are represented by a new uncertainty distribution, called the three-part zigzag uncertainty distribution, introduced in this paper. This newly defined uncertainty distribution function is regular and closer to an S-shaped curve than linear and zigzag uncertainty distribution functions. The properties of the three-part zigzag uncertainty distribution are studied, and the expression for the general order central moment of the distribution has been obtained. Using the expected value and the second, third order central moments, two maximizing objectives and one minimizing objective for the said optimization purpose are formed. Finally, using the “fmincon” function in Matlab 2018a, the constructed problem is solved. The solution obtained has been interpreted. The fact that it yields an efficient or Pareto optimal solution has also been proven.

Significance Statement A three-objective portfolio selection problem in an uncertain situation has been constructed using a newly defined uncertainty distribution. An innovative solution procedure that elicits efficient solutions is suggested to solve the problem. The work done can be applied to solve real-life portfolio selection problems with better accuracy.

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引用次数: 0
Diameter Estimation of ((m,rho ))-Quasi Einstein Manifolds 准爱因斯坦流形的直径估计
IF 0.8 4区 综合性期刊 Q3 MULTIDISCIPLINARY SCIENCES Pub Date : 2024-11-10 DOI: 10.1007/s40010-024-00899-3
Absos Ali Shaikh, Prosenjit Mandal, Chandan Kumar Mondal

This paper aims to study the ((m,rho ))-quasi Einstein manifold. This article shows that a complete and connected Riemannian manifold under certain conditions becomes compact. Also, we have determined an upper bound of the diameter for such a manifold. It is also exhibited that the potential function agrees with the Hodge-de Rham potential up to a real constant in an ((m,rho ))-quasi Einstein manifold. Later, some triviality and integral conditions are established for a non-compact complete ((m,rho ))-quasi Einstein manifold having finite volume. Finally, it is proved that with some certain constraints, a complete Riemannian manifold admits finite fundamental group. Furthermore, some conditions for compactness criteria have also been deduced.

本文旨在研究准爱因斯坦流形。本文表明,在某些条件下,一个完整且连通的黎曼流形会变得紧凑。同时,我们还确定了这样一个流形的直径上限。本文还证明了在((m,rho ))准爱因斯坦流形中,势函数与霍奇-德-拉姆势一致,直到一个实常数。随后,建立了具有有限体积的非紧凑完整的((m,rho ))准爱因斯坦流形的一些三性和积分性条件。最后,证明了在某些约束条件下,完全黎曼流形具有有限基群。此外,还推导出了紧凑性标准的一些条件。
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Proceedings of the National Academy of Sciences, India Section A: Physical Sciences
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