Proceedings of the National Academy of Sciences, India Section A: Physical Sciences最新文献

The aim of this work is to create the SEIQR model for COVID-19 in Saudi Arabia. The inclusion of a quarantine compartment in the model’s architecture is crucial in halting the transmission of disease to the vulnerable class. Simulation had been run in two phases: Phase 1, which ran from January 4, 2020 to June 13, 2020, and phase 2, which ran from June 14, 2020 to March 6, 2021. The SEIQR model analysis yields local stability at the fundamental reproduction number and the disease-free equilibrium point when the next generation matrix approach is used. The reproduction number was determined to be 6.81 when (gamma) was (2.0 times 10^{-9}), 7.49 when (gamma) was (2.2 times 10^{-9}) and 8.17 when (gamma) was (2.4 times 10^{-9}). The outcomes of the simulation unambiguously show that phase 2 is the point at which the optimal condition is reached. The most important thing for any disease is to have control methods. Sensitivity analysis has been done as part of control strategies, and after that, a fuzzy reproduction number control approach has been put into practice.

This paper introduces a new quantity in Finsler geometry, called the generalized Berwald projective Weyl ((GBwidetilde{W})) metric. The C-projective invariance of these metrics is demonstrated, and it is shown that they constitute a proper subset of the class of generalized Douglas (GDW) metrics. The paper also proves that all GDW metrics with vanishing Landsberg curvature are of R-quadratic type. The class of GDW metrics contains all Finsler metrics of scalar curvature, which provides an extension of the well-known Numata’s theorem.

In recent years, a vital challenge faced by experts in data science is analyzing the gigantic volume of data coming at high speed. This data avalanche is not only difficult to collect but also demands high time and memory while getting processed. Clustering is a well-known solution to this problem as it not only helps in shrinking the database but also helps in gaining valuable insights from a completely unlabelled dataset. Complete Linkage Clustering is a well-known Hierarchical Clustering algorithm suitable for generating small and highly cohesive clusters but suffers from the disadvantage of high convergence time. The traditional methods require the complete dataset in advance to take a clustering decision which makes it unsuitable for clustering both large and dynamic datasets where new data points are added frequently. This is because, for every addition of data, the entire dataset will be processed again for taking a clustering decision. Our paper presents a fast Complete Linkage Clustering algorithm that uses triangle inequality to avoid a lot of redundant distance calculations making the algorithm faster and suitable for clustering both large and dynamic databases. Experiments have been conducted with various real-world datasets and Adjusted Rand Index has been used for comparing the result with the original Complete Linkage algorithm. The experimental result confirms the effectiveness of our algorithm for both static and dynamic databases.

In this paper we present the notion of bounded, convergent in Pringsheim sense, null in Pringsheim sense, regular, regular null and absolutely p-sumable double sequences of bi-complex numbers. We have also introduced the concept of repeated limit of the double sequences of bi-complex numbers. We have established that every P-convergent double sequence of bi-complex numbers is not always bounded but regular convergent double sequences of bi-complex numbers is bounded. It is shown that the introduced classes of double sequences of bi-complex numbers are linear spaces. With the help of the Euclidean norm defined on bi-complex numbers, it is shown that among these classes, the bounded classes are Banach spaces. We have established some of their algebraic and topological properties like solidity, monotonic, symmetric and convergence free. Suitable examples have been discussed to support the introduction of the classes of sequences and the properties, those fail to hold.

The outcrops of greenstone belt and granite complex along Ramagiri-Penakacherla tract are analyzed for tectonics and associated deformation history related to crustal evolution. Field data connote more than five deformation events. Initial ductile deformation regime (D₁-D₄) passes through brittle-ductile (D₅) to shallow brittle regime (D₆). Multiple deformation events (D₁-D₅) resulted in shear zones with variable trends and sense. Three major generations of folding (F₂–F₄) imprinted over and obscure F₁ folding in ductile regime. Younger granite intruded after F₃ hence exhibit only F₄ folds. Brittle regime (D₆) is manifested by faults with dominant E-W trend affected all earlier deformation features. They show mainly normal and few strike slip motion with episodic reactivation with dominantly N-S stretching (i.e., σ₃). Contact relationships between granite and country rocks give insight on depth and associated pressure-temperature condition. From deeper catazone through intermediate mesozone to shallow epizone granite the progressive increase in temperature contrast influence contact relationships with country rocks from concordant through gradational to sharp discordant. Structural attributes of the northern and southern end of the study area exhibit remarkable changes in granite character, which give information on changes in crustal depth. Supportive petro-mineralogical and geochemical evidences also imply for exhumed northerly tilted crust. Bhima and Kaladgi basins are developed due to this crustal block tilting and basin fill sediments were supplied from erosion of uplifted southern parts. During erosion, the exhumation leads to retrograde metamorphism which is better manifested in metabasic rocks. From the surface distance between epizone/mesozone and mesozone/catazone boundaries and average crustal depth difference between these two boundaries, a northerly tilt angle of 1.9⁰ is estimated. The obduction at the southern end of Dharwar Craton and late stage N-S stretching is responsible for such tilting.

The transition temperature T_c of the superconductor signals the onset of superconductivity. We were curious to see the variation of T_c with the formula mass (F_M) of well-studied high-T_c oxide superconductors to observe whether there exists any correlation between T_c and F_M of these oxide superconductors. Interestingly, it is observed that the ratios of T_c /F_m of 8 different high-T_c superconductors which exhibit transition temperature ≥ 90 K, converge to show a ratio of 0.136 with a 14% deviation. Other superconductors and bismuth-based which have T_c less than 90 K differ significantly. Extrapolating the transition temperature to 25 °C, a formula mass F_M of high-T_c oxide superconductor turns to be 2239 with only 14% deviation in different materials which have T_c ≥ 90 K. This means if oxide superconductors of formula mass 2239 are synthesized, then that materials could exhibit room-temperature superconductivity. The experimental work on YBCO superconductors is underway and results will be communicated essentially an extension of the present work.

The main aim of this treatise is to establish the conception of sequence of multiset and countability on multiset topological spaces. Unlike any topological space, there are two subspaces in this context which are also countable M-topological space. Also, we obtained the relationship of the variants of countable M-topological spaces in the light of sequences in this environment.

Numerous studies have been published on conventional electrochemical machining with different tools and workpiece materials, machining parameters, and machining profile accuracy. Also, some studies have been reported on modified electrochemical machining to address the tool replica issues in conventional electrochemical machining with a novel 3D-printed thermoplastic-based inter-electrode slit between the tool and the W/P. But hitherto, little has been reported on the aspect ratio, and machining profile accuracy (overcut) in modified electrochemical machining. This study outlines the machining profile accuracy of modified electrochemical machining with the use of a novel square profile/cross-section inter-electrode slit along with feed rate, slit thickness, tool, workpiece material, and voltage based on Taguchi L₁₈ orthogonal array. The machining profile accuracy of the cavity was ascertained in the form of the cavity dimensions along the X and Y axis, machined area, machining depth (Z), diagonal length (DL) of profile section, aspect ratio (DL/Z), and overcut. The study suggests that as per the multi-factor optimization approach for machining profile accuracy, the optimized settings of modified electrochemical machining are electrolyte concentration 100 g/l, voltage 21 V, workpiece/tool as Cu, feed rate 108 µm/min, inter-electrode slit thickness 4.5 mm with composite desirability 0.944. Further, at optimized settings of the modified electrochemical machining process in the present case study, porosity 23.95%, DL 10.955 mm, cavity length along the X-axis 4.817 mm, Y-axis 3.613 mm, and Z-axis 1.179 mm, aspect ratio of 9.29 and over cut 18.59 mm² was achieved.

The concept of fog computing refers to a paradigm of distributed computing that extends cloud computing to the most remote parts of the network. Simulators are useful for analyzing resource management techniques including load balancing, fault tolerance, and energy efficiency in fog computing settings. This could result in the creation of more effective resource management algorithms. Fog simulators offer a realistic environment for testing fog computing applications and systems, incorporating authentic network conditions, device capabilities, and application requirements. This aids in recognizing and resolving such problems before implementing fog computing systems in practical situations. Fog computing links the breach between the cloud and other networking edges, qualifying the decentralized operation of computing equipment. Traditional cloud computing has several problems, including latency, size, space, and network failure. Fog computing can quickly and easily fix these issues. Moreover, it creates a complicated set of issues for both the scientific community and business. Both have several unresolved issues to deal with, including standardizing architecture and dealing with issues like resource management, service management, quality of service (QoS), participation, and communication. The objective of the article is to present a study on simulators for fog computing and cloud information.

Taking into consideration that the superposition of two summability methods is superior to the individual one, in this paper we present the calculations of the degree of approximation of functions and their conjugates belonging to the weighted Lipschitz class by a trigonometric polynomial generated by the application of product means (mathcal {C}^{1}.mathcal {T}) on their trigonometric Fourier series and conjugate series, respectively. Here we also reduce some conditions imposed on the increasing function (Psi (t)). Further, with the help of an example, we demonstrate the application of the results in the circumstances when the Fourier series of the function has the Gibbs phenomenon. We also provide a few corollaries that follow directly from our results.