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

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.

Internet of things (IoT) plays a vital part in improving the value of life and achieving sustainability. Innovations can use technology to manage the increasingly waste problems in newly created smart cities. The goal of this study is to develop a hybrid MCDM framework, which analyses various deferred criteria, for the adoption of smart city waste management techniques in economies like India. This article presents a new hybrid MCDM method on the PF-MEREC and Stepwise Weight Assessment Ratio Analysis (SWARA) approaches. To do this, the objective and subjective weights are assessed by MEREC, SWARA model and the Additive Ratio Assessment approach is employed to rank the options on the Pythagorean fuzzy set. Thereafter, the presented approach is applied to identify the best IoT technique for SCWM. Next, a comparative discussion and analysis are submitted to display the reasonableness and sustainability of the evolved method to rank SCWM alternatives.

We propose a Beta-type integral generalization of the Bernstein operators associated with Bézier bases (tilde{p}_{m,l}(lambda ;x)) and a shape parameter (lambda). First, we study a Korovkin-type result for the proposed operators and then establish their rate of convergence with the help of the modulus of continuity and Peetre’s K-functional. We present a quantitative Voronovskaja type and a Grüss-Voronovskaja type results to study their rate of convergence. We estimate the error for absolutely continuous functions having derivatives of bounded variation. Finally, we provide some graphical examples to illustrate our theoretical results. Relevance of the work:- The generalized operator (1.5) is a powerful tool that can be used to approximate continuous functions, integrable functions, Lipschitz-type functions, and functions with derivatives of bounded variation on the bounded interval [0, 1]. This operator can also be used to solve differential equations and integral equations.

In this paper, we have analyzed the stability of multiple solutions for the forced convective flow of Ti-alloy-MWCNT and water-based hybrid nanofluid with inclined MHD and Joule effects over an exponentially shrinking sheet. To provide the mathematical modeling of hybrid nanofluid, the Choi and Eastman model has been adopted. The flow governing equations arising from this analysis are converted into a system of ODEs using suitable similarity variables and then solved numerically using the shooting method. The graphical representations of the results are illustrated to elaborate interesting features in the presence of physically effective parameters like inclined magnetic field, Joule parameter, volume fraction, and suction parameters. As a result, we noticed the existence of dual solutions within the limited range of inclined magnetic, shrinking, and suction parameters. Hence, the stability of these solutions is checked by using temporal stability analysis. Further, we noticed that first solution is stable, whereas second solution is unstable through the smallest eigenvalue approach. Also, the streamlines are displayed to visualize the flow patterns. Moreover, the flow separation point and the flow reversal are identified. Finally, the delay of boundary layer separation is pointed out.

The class of n-f-semiclean rings lies between the classes of n-f-clean rings and ((n+1))-f-clean rings. We give a characterization of n-f-semiclean rings in terms of its Pierce stalks. We prove that if e is an idempotent such that eRe and ((1-e)R(1-e)) are n-f-semiclean, then R is n-f-semiclean. Further, we find that matrix rings of an n-f-semiclean ring are n-f-semiclean. We give some characterizations of n-f-semiclean rings in terms of their extension rings.

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.