Pub Date : 2023-11-23DOI: 10.1007/s40010-023-00855-7
S. Atchaya, J. Meena Devi
In this paper, we present the structural, optical, electrical and magnetic properties of the copper oxide nanoparticles prepared by co-precipitation method. The prepared copper oxide nanoparticles have been characterized by scanning electron microscopy, X-ray diffraction, X-ray electron spectroscopy and Fourier transform infrared spectroscopy. CuO nanoparticles exhibit spherical shape with the average particle size of around 42 nm. The X-ray diffraction pattern reaveals the crystalline monoclinic phase. The optical properties of the CuO nanoparticles studied by diffuse reflectance spectroscopy show the blue-shifted band gap of 1.45 eV. The electrical conductivity value of the sample has been measured using Keithley meter and it is 0.16 S/m. The magnetic properties measured using vibrating sample magnetometer at room temperature show a weak ferromagnetic behaviour with the dominant paramagnetic contribution of the CuO nanoparticles. The weak room temperature ferromagnetic behaviour may be associated with the oxygen vacancies and spin ordering induced by thermal energy and reduction in particle size.
{"title":"Experimental Investigation on Structural, Optical, Electrical and Magnetic Properties of Copper Oxide Nanoparticles","authors":"S. Atchaya, J. Meena Devi","doi":"10.1007/s40010-023-00855-7","DOIUrl":"10.1007/s40010-023-00855-7","url":null,"abstract":"<div><p>In this paper, we present the structural, optical, electrical and magnetic properties of the copper oxide nanoparticles prepared by co-precipitation method. The prepared copper oxide nanoparticles have been characterized by scanning electron microscopy, X-ray diffraction, X-ray electron spectroscopy and Fourier transform infrared spectroscopy. CuO nanoparticles exhibit spherical shape with the average particle size of around 42 nm. The X-ray diffraction pattern reaveals the crystalline monoclinic phase. The optical properties of the CuO nanoparticles studied by diffuse reflectance spectroscopy show the blue-shifted band gap of 1.45 eV. The electrical conductivity value of the sample has been measured using Keithley meter and it is 0.16 S/m. The magnetic properties measured using vibrating sample magnetometer at room temperature show a weak ferromagnetic behaviour with the dominant paramagnetic contribution of the CuO nanoparticles. The weak room temperature ferromagnetic behaviour may be associated with the oxygen vacancies and spin ordering induced by thermal energy and reduction in particle size.</p><h3>Graphic Abstract</h3><div><figure><div><div><picture><source><img></source></picture></div></div></figure></div></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"94 1","pages":"153 - 160"},"PeriodicalIF":0.8,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138514981","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}
Pub Date : 2023-11-17DOI: 10.1007/s40010-023-00856-6
Reza Akbari-Hasanjani, Mohammad Amin Mianroodi, Reza Sabbaghi-Nadooshan
The quantum-dot cellular automata (QCA) technology is one of the technologies for CMOS replacement which work based on columbic interacts. In this study, two two-bit comparator circuits are presented based on QCA and evaluated in terms of cell count, latency, and occupied area. Moreover, this study aims to reduce the occupied area, complexity, and energy dissipation of the comparator circuits, so the two comparator circuits have different power consumption levels. The proposed two-bit comparators are more compact and perform more consistently compared to previous designs. Design parameters of the two proposed circuits are optimized by reducing the cell count and occupied area compared to previous studies. The simulation results show that the proposed designs have a completely correct performance. In the first proposed two-bit comparator, 122 cells are used on an area of 0.14 µm2 with a latency of 2.25 clock cycles. The second proposed two-bit comparator uses 107 cells on an area of 0.17 µm2 with a latency of 1.75 clock cycles. Moreover, the values of energy dissipation of the proposed two-bit comparators at tunneling energies of 0.5, 1, and 1.5 Ek are calculated. In the first proposed two-bit comparator, the average energy dissipation for tunneling energies of 0.5, 1, and 1.5 Ek are calculated as 161.43, 222.83 and 296.52 meV, respectively. In the second proposed two-bit comparator, the average energy dissipation for tunneling energies of 0.5, 1, and 1.5 Ek are calculated as 139.36, 192.92, and 257.06 meV, respectively.
{"title":"Optimal Design of Two-Bit QCA Comparator Circuits","authors":"Reza Akbari-Hasanjani, Mohammad Amin Mianroodi, Reza Sabbaghi-Nadooshan","doi":"10.1007/s40010-023-00856-6","DOIUrl":"10.1007/s40010-023-00856-6","url":null,"abstract":"<div><p>The quantum-dot cellular automata (QCA) technology is one of the technologies for CMOS replacement which work based on columbic interacts. In this study, two two-bit comparator circuits are presented based on QCA and evaluated in terms of cell count, latency, and occupied area. Moreover, this study aims to reduce the occupied area, complexity, and energy dissipation of the comparator circuits, so the two comparator circuits have different power consumption levels. The proposed two-bit comparators are more compact and perform more consistently compared to previous designs. Design parameters of the two proposed circuits are optimized by reducing the cell count and occupied area compared to previous studies. The simulation results show that the proposed designs have a completely correct performance. In the first proposed two-bit comparator, 122 cells are used on an area of 0.14 µm<sup>2</sup> with a latency of 2.25 clock cycles. The second proposed two-bit comparator uses 107 cells on an area of 0.17 µm<sup>2</sup> with a latency of 1.75 clock cycles. Moreover, the values of energy dissipation of the proposed two-bit comparators at tunneling energies of 0.5, 1, and 1.5 E<sub>k</sub> are calculated. In the first proposed two-bit comparator, the average energy dissipation for tunneling energies of 0.5, 1, and 1.5 E<sub>k</sub> are calculated as 161.43, 222.83 and 296.52 meV, respectively. In the second proposed two-bit comparator, the average energy dissipation for tunneling energies of 0.5, 1, and 1.5 E<sub>k</sub> are calculated as 139.36, 192.92, and 257.06 meV, respectively.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"94 1","pages":"27 - 36"},"PeriodicalIF":0.8,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138514982","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}
Hollow porous polymeric fibers have been fabricated to facilitate the adsorption of analyses on chemically modified synthetic membrane for rapid decontamination of contaminates. The pocket water filtration cartridge which could fit into plastic water bottle of standard nozzle size has been developed using polymeric membrane and electro spun nanofibers-based changeable pre-filters. During and several days after flooding, there is serious shortage of water to drink, cook, washing or cleaning as water become contaminated. The unique feature of our air droppable water filtration cartridges enables mass scale supply of drinkable water during natural calamities. This complete indigenous polymer nanofibers-based product has already successfully completed field trials at two major Indian government organizations for sustained supply of drinkable water. The hydration packs for long-range reconnaissance patrol have also been designed and developed with this portable filtration cartridges to supply the potable water during uninterrupted surveillances. Our clean and safe water solution has many added advantages compared to commercially available products in terms of higher filtration rate, easier operation and custom specific design to address the polluted water treatment challenges at much reduced cost.
{"title":"Mitigation Strategies Using Nano-enabled Technologies for Sustainable Development Goals","authors":"Debmalya Roy, Subhash Mandal, Kingsuk Mukhopadhyay","doi":"10.1007/s40010-023-00854-8","DOIUrl":"10.1007/s40010-023-00854-8","url":null,"abstract":"<div><p>Hollow porous polymeric fibers have been fabricated to facilitate the adsorption of analyses on chemically modified synthetic membrane for rapid decontamination of contaminates. The pocket water filtration cartridge which could fit into plastic water bottle of standard nozzle size has been developed using polymeric membrane and electro spun nanofibers-based changeable pre-filters. During and several days after flooding, there is serious shortage of water to drink, cook, washing or cleaning as water become contaminated. The unique feature of our air droppable water filtration cartridges enables mass scale supply of drinkable water during natural calamities. This complete indigenous polymer nanofibers-based product has already successfully completed field trials at two major Indian government organizations for sustained supply of drinkable water. The hydration packs for long-range reconnaissance patrol have also been designed and developed with this portable filtration cartridges to supply the potable water during uninterrupted surveillances. Our clean and safe water solution has many added advantages compared to commercially available products in terms of higher filtration rate, easier operation and custom specific design to address the polluted water treatment challenges at much reduced cost.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"94 1","pages":"143 - 151"},"PeriodicalIF":0.8,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40010-023-00854-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135243592","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}
Pub Date : 2023-09-30DOI: 10.1007/s40010-023-00853-9
Prateek Agarwal, Tanuj Kumar Garg, Adesh Kumar
In contrast to scalar CPUs, end scaling refers to the use of heterogeneous multiprocessor systems-on-chip. Calculations made by an application consume less energy when it is run on the appropriate processor elements (PEs) that have been enhanced for difficult operations. However, as the PEs are increased, communication becomes more and more important. The on-chip interconnect technology of NoC uses scaled-down communication techniques from networks. A router is a physical or virtual device that acts as a shared form of gateway for material between two or more packet-switched processor networks. The router is used for NoC connection in SoC and concerned designs for router–router communication. This paper presents the hardware chip design of the 2D routers and employs router–router chip communication between two routers using independent chips and integrated NoC. The router hardware chip design is done in Xilinx Integrated System Environment (ISE) 14.7 software. Modelsim 10.0 is used for logic verification utilizing data packets sent from all input/output ports.
{"title":"Electronics Hardware Chip Design for Router–Router Communication","authors":"Prateek Agarwal, Tanuj Kumar Garg, Adesh Kumar","doi":"10.1007/s40010-023-00853-9","DOIUrl":"10.1007/s40010-023-00853-9","url":null,"abstract":"<div><p>In contrast to scalar CPUs, end scaling refers to the use of heterogeneous multiprocessor systems-on-chip. Calculations made by an application consume less energy when it is run on the appropriate processor elements (PEs) that have been enhanced for difficult operations. However, as the PEs are increased, communication becomes more and more important. The on-chip interconnect technology of NoC uses scaled-down communication techniques from networks. A router is a physical or virtual device that acts as a shared form of gateway for material between two or more packet-switched processor networks. The router is used for NoC connection in SoC and concerned designs for router–router communication. This paper presents the hardware chip design of the 2D routers and employs router–router chip communication between two routers using independent chips and integrated NoC. The router hardware chip design is done in Xilinx Integrated System Environment (ISE) 14.7 software. Modelsim 10.0 is used for logic verification utilizing data packets sent from all input/output ports.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"93 4","pages":"703 - 710"},"PeriodicalIF":0.9,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134878469","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}
Pub Date : 2023-09-29DOI: 10.1007/s40010-023-00849-5
Anirban Tarafdar, Pinki Majumder, Uttam Kumar Bera
In this paper, a type-3 fuzzy logic-based system has been created by accumulating the demand as the input variable to design the ideal inventory level that would minimize the overall inventory cost for the economic order quantity model. The new adaptation law based on the extended Kalman filter, and the unscented Kalman filter is carried out to tune the rule parameters and antecedent parameters of the suggested IT3-FLS. A real-life data set is collected to feed and test the IT3-FLS model. Some statistical measures like root-mean-square error, variance, correlation coefficient (R), and Theil’s coefficient are calculated to examine the prediction accuracy. The lowest RMSE observed is 0.02138, and the highest R is 0.99975 for IT3-FLS. Furthermore, the optimal total variable cost is calculated by collecting the estimated inventory. Additionally, to demonstrate the applicability of the suggested methodology, one real-life issue and its managerial resolution have been highlighted.
{"title":"An Advanced Learned Type-3 Fuzzy Logic-Based Hybrid System to Optimize Inventory Cost for a New Business Policy","authors":"Anirban Tarafdar, Pinki Majumder, Uttam Kumar Bera","doi":"10.1007/s40010-023-00849-5","DOIUrl":"10.1007/s40010-023-00849-5","url":null,"abstract":"<div><p>In this paper, a type-3 fuzzy logic-based system has been created by accumulating the demand as the input variable to design the ideal inventory level that would minimize the overall inventory cost for the economic order quantity model. The new adaptation law based on the extended Kalman filter, and the unscented Kalman filter is carried out to tune the rule parameters and antecedent parameters of the suggested IT3-FLS. A real-life data set is collected to feed and test the IT3-FLS model. Some statistical measures like root-mean-square error, variance, correlation coefficient (<i>R</i>), and Theil’s coefficient are calculated to examine the prediction accuracy. The lowest RMSE observed is 0.02138, and the highest <i>R</i> is 0.99975 for IT3-FLS. Furthermore, the optimal total variable cost is calculated by collecting the estimated inventory. Additionally, to demonstrate the applicability of the suggested methodology, one real-life issue and its managerial resolution have been highlighted.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"93 4","pages":"711 - 727"},"PeriodicalIF":0.9,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134797940","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}
Pub Date : 2023-09-27DOI: 10.1007/s40010-023-00850-y
Rajesh Kumar, Vipin Gupta, Vijayata Pathania, Rajneesh Kumar, M. S. Barak
This study discusses the behavior of plane waves in a double porous thermoelastic with nonlocal dual-phase-lag solid half-space ((M_{1} )) in contact with inviscid liquid half-space ((M_{2} )). The governing equations are expressed in two-dimensional form, and normal mode analysis is adopted to solve the problem for further investigation. It has been found that there exist four coupled longitudinal, one transverse wave in the medium (M_{1}), and one mechanical wave in the medium (M_{2}). These waves are under the influence of parameters of nonlocal dual-phase-lag and double porosity. Secular equations are determined by applying interfacial mechanical and thermal conditions. The compact form of wave characteristics like phase velocity, attenuation coefficient, penetrating depth, and specific loss is obtained. The component of displacement, temperature change, and volume fraction fields in the medium (M_{1}), along with normal velocity and acoustic pressure in the medium, (M_{2}) are obtained in closed form. Numerically simulated results are displayed in the form of graphs to depict the behavior of nonlocal and phase lag on basic characteristics of waves.
{"title":"Analysis of Waves at Boundary Surfaces at Distinct Media with Nonlocal Dual-Phase-Lag","authors":"Rajesh Kumar, Vipin Gupta, Vijayata Pathania, Rajneesh Kumar, M. S. Barak","doi":"10.1007/s40010-023-00850-y","DOIUrl":"10.1007/s40010-023-00850-y","url":null,"abstract":"<div><p>This study discusses the behavior of plane waves in a double porous thermoelastic with nonlocal dual-phase-lag solid half-space <span>((M_{1} ))</span> in contact with inviscid liquid half-space <span>((M_{2} ))</span>. The governing equations are expressed in two-dimensional form, and normal mode analysis is adopted to solve the problem for further investigation. It has been found that there exist four coupled longitudinal, one transverse wave in the medium <span>(M_{1})</span>, and one mechanical wave in the medium <span>(M_{2})</span>. These waves are under the influence of parameters of nonlocal dual-phase-lag and double porosity. Secular equations are determined by applying interfacial mechanical and thermal conditions. The compact form of wave characteristics like phase velocity, attenuation coefficient, penetrating depth, and specific loss is obtained. The component of displacement, temperature change, and volume fraction fields in the medium <span>(M_{1})</span>, along with normal velocity and acoustic pressure in the medium, <span>(M_{2})</span> are obtained in closed form. Numerically simulated results are displayed in the form of graphs to depict the behavior of nonlocal and phase lag on basic characteristics of waves.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"93 4","pages":"573 - 585"},"PeriodicalIF":0.9,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134797781","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}
Pub Date : 2023-09-26DOI: 10.1007/s40010-023-00852-w
Pratibha Verma, Surabhi Tiwari
This article studies some important results in a Banach space for non-discrete nonlinear integro-differential equations with variable order (0<sigma (theta )<1)
The contraction mapping principle and Krasnoselskii fixed-point theorem are employed to investigate the results, and Ulam–Hyers definitions are used for stability theory. Further, we have discussed the maximal and minimal solutions with the continuation theorem for (sigma (theta ) rightarrow 1).
{"title":"Existence, Uniqueness and Stability of Solutions of a Variable-Order Nonlinear Integro-differential Equation in a Banach Space","authors":"Pratibha Verma, Surabhi Tiwari","doi":"10.1007/s40010-023-00852-w","DOIUrl":"10.1007/s40010-023-00852-w","url":null,"abstract":"<div><p>This article studies some important results in a Banach space for non-discrete nonlinear integro-differential equations with variable order <span>(0<sigma (theta )<1)</span></p><div><div><span>$$begin{aligned}{} & {} D^{sigma (theta )}_{0,theta } vartheta (theta ) =eta (theta ,vartheta (theta ))+vartheta (theta ) int _{0}^{theta } kappa (theta ,a,vartheta (a)){textrm{d}}a,quad theta in aleph =[0,Theta ],quad Theta >0, {} & {} vartheta (0)=vartheta _0. end{aligned}$$</span></div></div><p>The contraction mapping principle and Krasnoselskii fixed-point theorem are employed to investigate the results, and Ulam–Hyers definitions are used for stability theory. Further, we have discussed the maximal and minimal solutions with the continuation theorem for <span>(sigma (theta ) rightarrow 1)</span>.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"93 4","pages":"587 - 600"},"PeriodicalIF":0.9,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134797777","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}
Pub Date : 2023-09-25DOI: 10.1007/s40010-023-00848-6
S. Prakash, M. Subbiah
The hydromagnetic stability of inviscid compressible flows with axial and azimuthal velocity components in an annular channel has been studied to axisymmetric disturbances. An estimate for the growth rate of arbitrary unstable disturbances is obtained. It is shown that the complex phase-velocity of any unstable magneto-subsonic axisymmetric mode must lie in a semiellipse-type region, which depends on the parameters of compressibility, stratification and the magnetic field. For a monotonic axial velocity profile, this semiellipse-type instability region reduces to the line (c_{i}=0) as the minimum Richardson number ({widetilde{J}}_{m}rightarrow frac{1}{4}-) in accord with the Richardson number criterion. Further, an semi-elliptical instability region depending on the minimum local Richardson number is also obtained for a class of magneto-supersonic axisymmetric disturbances.
{"title":"On the Hydromagnetic Stability Analysis of Inviscid Compressible Annular Flows","authors":"S. Prakash, M. Subbiah","doi":"10.1007/s40010-023-00848-6","DOIUrl":"10.1007/s40010-023-00848-6","url":null,"abstract":"<div><p>The hydromagnetic stability of inviscid compressible flows with axial and azimuthal velocity components in an annular channel has been studied to axisymmetric disturbances. An estimate for the growth rate of arbitrary unstable disturbances is obtained. It is shown that the complex phase-velocity of any unstable magneto-subsonic axisymmetric mode must lie in a semiellipse-type region, which depends on the parameters of compressibility, stratification and the magnetic field. For a monotonic axial velocity profile, this semiellipse-type instability region reduces to the line <span>(c_{i}=0)</span> as the minimum Richardson number <span>({widetilde{J}}_{m}rightarrow frac{1}{4}-)</span> in accord with the Richardson number criterion. Further, an semi-elliptical instability region depending on the minimum local Richardson number is also obtained for a class of magneto-supersonic axisymmetric disturbances.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"93 4","pages":"601 - 611"},"PeriodicalIF":0.9,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134797489","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}
Pub Date : 2023-09-20DOI: 10.1007/s40010-023-00851-x
Ajay K. Gupt, Akhilesh Prasad, U. K. Mandal
In this paper, the boundedness of the fractional maximal function and Riesz potential for the LS transform from (L^p(mathbb {R}_+;frac{exp ({-x cos (rho )})}{sqrt{x}}mathrm{{dx}})) to (L^p(mathbb {R}_+;x^{frac{p}{2}}mathrm{{dx}})) and from (L^1(mathbb {R}_+;frac{exp ({-x cos (rho )})}{sqrt{x}}mathrm{{dx}})) to the weak space (mathrm{{WL}}^1(mathbb {R}_+;x^{frac{1}{2}}mathrm{{dx}})) are studied. Relevance of the work In this work, we define the fractional integral and the fractional maximal operators using the translation operator associated with LS transform. The boundedness of these integral operators is investigated in the framework of Lebesgue spaces. These fractional integral operators are applied to the study of partial differential equations and Sobolev spaces.
本文研究了从(L^p(mathbb {R}_+;frac{exp ({-x cos (rho )})}{sqrt{x}}mathrm{{dx}}))到(L^p(mathbb {R}_+;x^{frac{p}{2}}mathrm{{dx}}))和从(L^1(mathbb {R}_+;frac{exp ({-x cos (rho )})}{sqrt{x}}mathrm{{dx}}))到弱空间(mathrm{{WL}}^1(mathbb {R}_+;x^{frac{1}{2}}mathrm{{dx}}))的LS变换的分数极大函数和Riesz势的有界性。在这项工作中,我们使用与LS变换相关的平移算子定义了分数阶积分算子和分数阶极大算子。在Lebesgue空间的框架下研究了这些积分算子的有界性。这些分数阶积分算子应用于偏微分方程和Sobolev空间的研究。
{"title":"The Fractional Maximal and Riesz Potential Operators Involving the Lebedev–Skalskaya Transform","authors":"Ajay K. Gupt, Akhilesh Prasad, U. K. Mandal","doi":"10.1007/s40010-023-00851-x","DOIUrl":"10.1007/s40010-023-00851-x","url":null,"abstract":"<div><p>In this paper, the boundedness of the fractional maximal function and Riesz potential for the LS transform from <span>(L^p(mathbb {R}_+;frac{exp ({-x cos (rho )})}{sqrt{x}}mathrm{{dx}}))</span> to <span>(L^p(mathbb {R}_+;x^{frac{p}{2}}mathrm{{dx}}))</span> and from <span>(L^1(mathbb {R}_+;frac{exp ({-x cos (rho )})}{sqrt{x}}mathrm{{dx}}))</span> to the weak space <span>(mathrm{{WL}}^1(mathbb {R}_+;x^{frac{1}{2}}mathrm{{dx}}))</span> are studied. <i>Relevance of the work</i> In this work, we define the fractional integral and the fractional maximal operators using the translation operator associated with LS transform. The boundedness of these integral operators is investigated in the framework of Lebesgue spaces. These fractional integral operators are applied to the study of partial differential equations and Sobolev spaces.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"93 4","pages":"613 - 620"},"PeriodicalIF":0.9,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134797014","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}
Pub Date : 2023-08-23DOI: 10.1007/s40010-023-00845-9
Neeraj Khare
{"title":"Special Isssue on Advances in Memory Materials","authors":"Neeraj Khare","doi":"10.1007/s40010-023-00845-9","DOIUrl":"10.1007/s40010-023-00845-9","url":null,"abstract":"","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"93 3","pages":"423 - 423"},"PeriodicalIF":0.9,"publicationDate":"2023-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4888660","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}