Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

&nbsp;

&nbsp;

VIT University

Department of Mathematics

The object of the present paper is to study contact CR-submanifolds of (LCS)n-manifolds. We obtain the integrability conditions of the distributions of contact CR-submanifolds of (LCS)n-manifolds. Finally, we give an interesting example of a contact CR-submanifold of (LCS)7-manifold. © 2021 by TJM.

World University root node

School of Advanced Sciences

Vellore Campus

Thai Journal of Mathematics

On contact CR-submanifolds of (LCS)n-manifolds

In this paper, we prove some fixed points, coupled coincidence point and coupled common fixed point results for mappings satisfying an almost generalized contraction conditions in partially ordered b-metric spaces. These results generalize, extend and unify many comparable results in the existing literature. Few examples are given to support our results. © World Scientific Publishing Company

Asian-European Journal of Mathematics

Coupled fixed points theorems for generalized weak contractions in ordered b-metric spaces

We establish coincidence point theorem for g-non-decreasing mappings under generalized (ψ, θ, φ)-contraction on partially ordered metric spaces. With the help of the obtain result, we indicate the formation of a coupled coincidence point theorem of generalized compatible pair of mappings F,G: X2 → X. We apply our result to obtain the solution of integral equation and also give an example to show the degree of validity of our hypothesis. Our results modify, improve, sharpen, enrich and generalize various known results. © 2021 by TJM.

Coincidence point results for generalized (ψ, θ, Φ) - contraction on partially ordered metric spaces

An analytical model has been considered to study the scattering phenomenon of the quasi-plane wave in functionally graded piezoelectric material (FGPM) layer sandwiched between two similar piezoelectric (PE) media. In more contrast, the effect of material gradient factor on amplitude ratios of various reflected and transmitted waves has been investigated. The composite structure consists of an FGPM layer bonded between two similar transversely isotropic PE half-spaces. It has been shown that incident quasi-longitudinal wave (qP-mode) at lower interface generates reflected and transmitted waves namely qP and quasi-shear vertical waves (qSV-mode). These transmitted waves further give rise to reflected and transmitted waves at the upper interface. At the interfaces of the FGPM layer, the stresses, displacements and electric potential functions are continuous. Due to the scattering of waves, 12 independent amplitude ratios of displacement components are obtained. Amplitude ratios of various reflected and transmitted waves (for the electrically short case) have been obtained by solving a set of linear algebraic equations (using Crammer’s rule). The impact of gradient factor has been examined on amplitude ratios against the angle of incidence and presented graphically. The plot of the slowness section is also demonstrated through graph. In addition, deduced results are compared with the earlier studies and found to be in agreement with the findings. © 2019 Taylor & Francis Group, LLC.

Mechanics Based Design of Structures and Machines

Analysis of wave scattering in 3-layer piezo composite structure [Pb[ZrxTi1-x]O3-ALN-Pb[ZrxTi1-x]O3]

Herein we report an exclusively ligand-centered redox controlled approach for the dehydrogenation of a variety of N-heterocycles using a Zn(II)-stabilized azo-anion radical complex as the catalyst. A simple, easy-to-prepare and bench-stable Zn(II)-complex (1b) featuring the tridentate arylazo pincer, 2-((4-chlorophenyl)diazenyl)-1,10-phenanthroline, in the presence of zinc-dust, undergoes reduction to form the azo-anion radical species [1b]- which efficiently dehydrogenates various saturated N-heterocycles such as 1,2,3,4-tetrahydro-2-methylquinoline, 1,2,3,4-tetrahydro-isoquinoline, indoline, 2-phenyl-2,3-dihydro-1H-benzoimidazole, 2,3-dihydro-2-phenylquinazolin-4(1H)-one and 1,2,3,4-tetrahydro-2-phenylquinazolines, among others, under air. The catalyst has further been found to be compatible with the cascade synthesis of these N-heterocycles via dehydrogenative coupling of alcohols with other suitable coupling partners under air. Mechanistic investigation reveals that the dehydrogenation reactions proceed via a one-electron hydrogen atom transfer (HAT) pathway where the zinc-stabilized azo-anion radical ligand abstracts the hydrogen atom from the organic substrate(s) and the whole catalytic cycle proceeds via the exclusive involvement of the ligand-centered redox events where the zinc acts only as the template.

ACS Catalysis

Zinc Stabilized Azo-anion Radical in Dehydrogenative Synthesis of N-Heterocycles. An Exclusively Ligand Centered Redox Controlled Approach

Purpose: The authors consider parallel four-state tandem open queueing network. The queue capacity is infinite. Passenger arrival rate is Poisson distribution and service rate is exponential distribution. The queue is constructed in the form of tandem queue, and each and every queue of tandem queue is single server (M/M/1) queue. In tandem queue, passengers will leave the system once they receive service from both the states. The purpose of this paper is to provide performance analysis for four-state tandem open queue network, and a governing equation is formulated with the help of transition diagram. Using Burke theorem, the authors formulated equation for average number of passenger in the system, average waiting time of passenger in the system, average number of passenger in the queue and average waiting time of passenger in the queue. Design/methodology/approach: This paper used Burke’s theorem. Findings: In this paper, performance analysis is done for parallel four-state tandem open queueing network and performance measure solved using Burkes theorem formula. K. Sreekanth et al. has done performance analysis for single tandem queue with three states. In this paper, the authors have done performance analysis for two tandem queues parallel with four states. This four-state tandem open queueing network is suitable for real world applications. This paper can extend for more number of service states and multi-server states according to the application, and in such case, the authors have to prove and explain with numerical examples. This analysis is more useful for the applications such as airports, railway stations, bus-stands and banks. Originality/value: In this paper, parallel four-state tandem open queueing network and performance measure has been solved using Burke’s theorem formula. © 2020, Emerald Publishing Limited.

International Journal of Pervasive Computing and Communications

Performance measures of parallel tandem open queueing network

In this paper, we introduce a modified implicit relation and obtain some new fixed point results for σ-implicit type contractive conditions in relational metric-like spaces. We present some nontrivial examples to illustrative facts and compare our results with the related work. We also discuss sufficient conditions for the existence of a unique positive definite solution of the non-linear matrix equation U = D +∑m i=1 A∗iG(U)Ai, where D is an n × n Hermitian positive definite matrix, A1, A2, …, Am are n × n matrices, and G is a non-linear self-mapping of the set of all Hermitian matrices which is continuous in the trace norm. Finally, we discuss a couple of examples, convergence and error analysis, average CPU time analysis and visualization of solution in surface plot. © 2021 the Author(s), licensee AIMS Press.

Fulltext

AIMS Mathematics

Unified relational-theoretic approach in metric-like spaces with an application

Let X be a complex Banach space. We say that X belongs to the class W if for each compact operator T defined on X such that ‖ I+ T‖ > 1 , I+ T attains norm. In this note, we characterize the ϵ- condition spectrum of any compact linear operator defined on X where X is Banach space which belongs to class W. © 2021, Forum D'Analystes, Chennai.

Journal of Analysis

Characterization of the condition spectrum of a compact operator

In this paper, we report on the comprehensive study on Molybdenum disulfide (MoS2) nanolayer coated etched Fiber Bragg Grating (eFBG) strain sensor. MoS2 nanolayer is coated using Physical Vapor Deposition (PVD) of Molybdenum (Mo) on eFBGs followed by sulfurization of the same in an inert atmosphere at 450° C. Such coating technique provides a direct control over the coating thickness of MoS2, thereby enabling a study based on the effect of nanolayer coating thickness on the intrinsic strain sensitivity as well as the power of the back reflected Bragg wavelength of eFBG in the 0.78eV spectral region. High uniformity of MoS2 nanolayer coating ensures consistent, repeatable and highly linear FBG strain sensors with a correlation coefficient of 0.988 in the range of 0 to $2500~\mu \varepsilon $. A maximum intrinsic strain sensitivity of 6.65 pm/ $\mu \varepsilon $ with a resolution of $\sim 150~\text{n}\varepsilon $ have been achieved with optimized MoS2 coated eFBG sensors. This kind of consistent, highly sensitive and linear strain sensors when incorporated with proper packaging schemes can be particularly useful for applications demanding high sensitivity of FBG sensors such detection of seismic vibrations, underwater acoustic signals, low amplitude accelerations, etc. © 2001-2012 IEEE.

IEEE Sensors Journal

A Study on MoS Nanolayer Coated Etched Fiber Bragg Grating Strain Sensor

In this paper, we propose a new conjecture that the complete graph K4m+1 can be decomposed into copies of two arbitrary trees, each of size m, m≥ 1. To support this conjecture we prove that the complete graph K4cm+1 can be decomposed into copies of an arbitrary tree with m edges and copies of the graph H, where H is either a path with m edges or a star with m edges and where c is any positive integer. Further, we discuss related open problems. © 2021, The Author(s), under exclusive licence to Springer Japan KK, part of Springer Nature.