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

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.

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.

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.

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.