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

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.

Abstract

The coupling of aldehyde, amine, and alkyne (known as A³-coupling) is a versatile strategy for the synthesis of propargylamines which are important precursors for the biologically active molecules. Recently, phenylglyoxylic acid as a surrogate of aldehyde has gained importance in the above reaction via decarboxylative coupling. Transition metal catalysts of Cu and Au have been reported for this reaction. However, metal waste and their disposal is the major challenge faced by chemical industries. In this work, we have explored chitosan-supported zinc catalysts for the decarboxylative coupling of phenylglyoxylic acid with amine and alkyne. We found that this reaction gives the best yield under solvent-less condition. For comparison purpose, the catalytic activity of synthesized catalysts in various molecular solvents has also been explored.

Graphical Abstract

The aim of this article is to define the Caputo derivative of bicomplex order for the functions of a bicomplex variable, which we refer to as the Bicomplex Caputo Derivative (BCD) throughout the paper. We achieve BCD via the development of the Caputo derivative of bicomplex order for the bicomplex-valued functions of real variable and discuss some of its significant properties. We also compare BCD with the bicomplex Riemann–Liouville derivative and integral. We demonstrate the advantages of the properties of BCD by finding the derivatives of some elementary bicomplex functions. The useful applications of BCD are found in constructing bicomplex fractional Maxwell’s equations in the vacuum and source-free domains. The solutions of bicomplex fractional Maxwell’s equations are obtained by considering a bicomplex vector field, and it is proved that in this way the number of equations is reduced by half.