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

The main aim of the study is a mathematical model of COVID-19 using the variable Atangana-Baleanu (AB) fractional derivatives with the Mittag-Leffler kernel in the Caputo sense. Only the AB kernel is a crossover for the waiting time distribution from stretched exponential to a power law. The Caputo-Fabrizio (CF) derivative is less noisy. In contrast, the fractional AB derivative provides an excellent description due to its Mittag-Leffler memory, distinguishing between dynamical systems at different scales without a steady state. With the help of the fixed point theory and Picard-Lindelöf method, we explore the existence and uniqueness of the solution for the proposed COVID-19 model. Moreover, we discuss the generalized Ulam-Hyers stability and the generalized Ulam-Hyers-Rassias stability.

In this paper, we define a new hypergraph (mathcal {H(V,E)}) on a loop L, where (mathcal {V}) is the set of points of the loop L and (mathcal {E}) is the set of hyperedges (e={x,y,z}) such that x, y and z associate in the order they are written. We call this hypergraph as the associating hypergraph on a loop L. We study certain properties of associating hypergraphs on the Moufang loop (M(D_n,2)), where (D_n) denotes the dihedral group of order 2n.

The perovskite, LaNiO₃, was synthesised in nanocrystalline form through reverse micellar route by varying the surfactants (CTAB, Triton X-100, Tergitol). These oxides were calcined at different temperatures from 750 to 800 °C. The structural and magnetic properties of LaNiO₃ was investigated by PXRD, FESEM-EDX, TEM. PXRD of all samples show pure phase of LaNiO₃ crystallizing in the rhombohedral system. The particle size of nanoparticles varies from 12 to 300 nm with the variation in the microemulsion system used for synthesis. The magnetic susceptibility data shows antiferromagnetic behaviour with the possibility of weak ferromagnetic contribution at low temperatures. The band gap obtained from UV–Visible spectroscopy vary in the range of 2.82–3.08 eV. The Mott–Schottky studies show that the all the samples of LaNiO₃ have a n-type behaviour.

Ancient Fingerprint impressions are found impinged on pottery and clay tablets as paleodermatoglyphics; painted or engraved on rocks as petroglyphs; and as accompaniment to cuneiform script on contracts. Whether these impressions served as marks of individualization, comparable to the present-day identification process, or were mere pieces of arts is debatable. However, these do assist us in understanding the social patterns of the communities whose members excogitated such marks in the first place. This communication highlights the potential of the rich corpus of ancient fingerprints in conceptualizing the individuals within the societies of bygone era.

As per conventional demand pattern, there is a daily rise in the need for power consumption. Therefore, producing large amounts of power is important, or losses should be kept to a minimum. Hence for enhancing efficiency in the design of power distribution networks, Distributed Generations (DGs) and Electric Vehicles (EVs) collaboration with hybrid monte carlo genetic algorithm (MC-GA) approach is increasingly essential. Consequently, to boost the efficiency of the electricity system qualities, few steps may be taken like minimising actual and reactive power losses, maximising loadability, DGs and EVs must be properly coordinated. The other electrical quality of power parameters, such as the system's stability, the line's capacity for short circuits, and the rise in the power system’s voltage profile, are also improved. New dimension of research in this field, is significant amount of attention paid to DG and EV integration into the electrical distribution networks. This review paper offers hybrid MC-GA optimization approach for building distribution networks with DGs, EVs, and DGs with EVs while using a realistic load model. With varied goal function views, like the reduction in the losses of actual and reactive power in power system networks, the various power system performances are taken into account during planning. This survey study provides an insight in the most recent models as well as techniques which are used over DGs and EVs in the process of assessment, planning and categorising scope of research in the present as well as future pertaining to this field. The writers are certain that figuring out their comparable references would be extremely helpful for researchers, practitioners, academics, industrial people, and scientific research people in this survey study.

Hybrid numbers are defined as a non-commutative number system generalizing the complex, dual, and hyperbolic numbers with the relation (ih=-hi=varepsilon +i). This paper aims to provide new polar representations for hybrid numbers. To achieve this we first introduce truncated hybrid numbers (or hybrid number triplets) obtained by truncating a vector component of a hybrid number. Therefore there are three types of truncated hybrid numbers. Then, we determine the conditions for the multiplication of two truncated hybrid numbers to be closed and commutative. Finally, we use what we call h-truncated hybrid numbers to provide a new polar representation for hybrid numbers. Many numerical examples are provided to support the theory of this paper.

This article presents a new solution for the convex hull problem. The convex hull is a widely known problem in computational geometry. As nature is a rich source of ideas in the field of algorithms, the solution has been inspired by nature. A tight elastic band is modeled using agents and also nails as points of the problem. The convex hull problem will be solvable by simulating an elastic band with nails in a given environment. The algorithm runs in O(S) in which S is the area between the elastic band and convex hull polygon. This feature enables the algorithm to be computationally grown linearly as the number of points increases in a situation where there is a compact set of points. The algorithm is output-sensitive and can be implemented in a 2D and also a 3D space.

A map is considered to be semi-equivelar if all of the face-cycles at its vertices are of the same type. In this article, we show that a surface with Euler characteristic of (-2) admits 39 distinct types of semi-equivelar maps. Moreover, we classify (up to isomorphism) a specific category of semi-equivelar maps on this surface. This approach can be extended to classify the other types of maps. For every orientable surface of genus (g> 2), there is a regular covering of an orientable surface with genus 2 by the cyclic group of covering transformations. This result was algebraically demonstrated by Harvey (Q J Math 17:86–97, 1966). In this article, we provide a combinatorial explanation of a similar result for a class of semi-equivelar maps using the concept of a connected sum. For semi-equivelar maps on surfaces with Euler characteristic (-2), we demonstrate the existence of m-th covering maps on higher genus surfaces. We also show that the symmetry groups of the m-th covering maps are either (mathbb {D}_m) (dihedral group of order 2m) or (mathbb {Z}_m) (cyclic group of order m).

The enhanced power graph ({mathcal {P}}_E(G)) of a group G is a simple undirected graph with the vertex set G and two vertices are adjacent if they belong to the same cyclic subgroup of G. In this paper, we have obtained the metric dimension and the resolving polynomial of the enhanced power graph of the non-abelian group of order p³, where p is an odd prime. We also study the coloring and detour distance properties of the graph ({mathcal {P}}_E(G)).

The COVID-19 pandemic has emerged as one of the most devastating infectious disease in the history of mankind. Though the collective efforts of various institutions across the globe have potentially managed to control the pandemic, the infection still continues to pose a public health risk. In this paper, we develop a modified SEIQHRD model to study the transmission dynamics of the COVID-19 across a region. The basic reproduction number, which measures the potential spread of the virus is computed. Disease free equilibrium point for the model is shown to be locally as well as globally asymptotically stable whenever (R_0 le 1). Further, existence of endemic equilibrium along with its local and global asymptotic stability is proved when (R_0>1). Sensitivity analysis is performed for the associated parameters in the model. Finally, numerical simulation is done for the formulated model that demonstrates and validates the theoretical results derived in the paper.