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.

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VIT University

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.

Department of Mathematics

School of Advanced Sciences

Vellore Campus

Journal of Analysis

Characterization of the condition spectrum of a compact operator

Let A be a complex unital Banach algebra, let be an element in it and let 0 < ϵ < 1.. In this article, we study the upper and lower hemicontinuity and joint continuity of the condition spectrum and its level set maps in appropriate settings. We emphasize that the empty interior of the -level set of a condition spectrum at a given plays a pivotal role in the continuity of the required maps at that point. Further, uniform continuity of the condition spectrum map is obtained in the domain of normal matrices. © 2019 Australian Mathematical Publishing Association Inc.

World University root node

Journal of the Australian Mathematical Society

CONTINUITY of A CONDITION SPECTRUM and ITS LEVEL SETS

Let A be a complex Banach algebra with unit e. Let p be a non trivial idempotent element in A and ε> 0. For a∈ A, it is proved that the interior of the level set of (p, e- p) - ε pseudo spectrum of a is empty in the unbounded component of (p, e- p) resolvent set of a. An example is constructed to show that the condition ‘unbounded component’ can not be dropped. Further, it is proved this ‘unbounded component’ can be dropped in the case when A is B(X) where X is a complex uniformly convex Banach space. That is, if T∈ B(X) then interior of the level set of (p, I- p) - ε pseudo spectrum is empty in (p, I- p) resolvent set of T. © 2017, Forum D'Analystes, Chennai.

Fulltext

Level sets of (p, e- p) outer generalized pseudo spectrum

VIT Unitversity

Journal of Electroanalytical Chemistry

In situ electrochemical synthesis of reduced graphene oxide-cobalt oxide nanocomposite modified electrode for selective sensing of depression biomarker in the presence of ascorbic acid and dopamine

For 0 < ε ≤ 1 and an element a of a complex unital Banach algebra A, we prove the following two topological properties about the level sets of the condition spectrum. (1) If ε = 1, then the 1-level set of the condition spectrum of a has an empty interior unless a is a scalar multiple of the unity. (2) If 0 < ε < 1, then the ε-level set of the condition spectrum of a has an empty interior in the unbounded component of the resolvent set of a. Further, we show that, if the Banach space X is complex uniformly convex or if X* is complex uniformly convex, then, for any operator T acting on X, the level set of the ε-condition spectrum of T has an empty interior. © 2017 by the Tusi Mathematical Research Group.

Annals of Functional Analysis

Level sets of the condition spectrum

The novel technique of developing Chebyshev Dumbbell DGS low pass filters (LPFs) is presented in this paper. The ground plane of a standard 50-ohm transmission line is perturbed by Dumbbell called defected ground structure (DGS) to generate ultra-rejection band at X-Band that is beneficial to higher order harmonic suppression. A comparison of Meander shaped, circular complementary split ring resonator (CSRR) and Dumbbell DGS has been evaluated. An improved Chebyshev Dumbbell DGS LPF with compensated microstrip line has better rejection bandwidth at the X-band frequency. © 2015 IEEE.

Electronics

School of Electronics Engineering

Chennai Campus

2015 International Conference on Communications and Signal Processing (ICCSP)

Wide bandstop filter using Chebyshev modulated Dumbbelled DGS

This paper presents design of antenna for worldwide interoperability for microwave access (2.3-2.4GHz and 2.5-2.69GHz) and Wireless Local area network (2.4-2.484GHz &amp; 5.15 GHz). The proposed design uses inset feed for achieving a good impedance matching with compactness. The fundamental frequency of the design is 2.6 GHz; Implementing defected ground structure provides additional frequency at 5.15 GHz and shifts the fundamental frequency to 2.5GHz. Different lengths of DGS and its effect on antenna performance and resonance frequency are analyzed. High Frequency Structure simulator is used to analyze the design. © 2015 IEEE.

2015 3rd International Conference on Signal Processing, Communication and Networking (ICSCN)

Dual band compact inset CPW feed antenna with DGS

In this paper L-strip Electromagnetically coupled rectangular patch antenna is proposed and simulated results were obtained by HFSS tool. The frequency range covered by this single antenna is 1800MHZ to 2370MHZ with -10db return loss with optimal height of the patch from the ground plane 16.8mm. The antenna parameters which influence the gain, bandwidth, return loss was analyzed and graphs are plotted. The design mainly focuses on 3G internet services. It covers the DCS, PCS and UMTS. In addition, significant matching and high gain of 10.8 dB at 2.4GHz is obtained. © 2015 IEEE.

2015 2nd International Conference on Signal Processing and Integrated Networks (SPIN)

Design and simulation of wideband patch antenna for wireless application

2015 Fifth International Conference on Advanced Computing & Communication Technologies

Compact S-Shaped EBG Structures for Reduction of Mutual Coupling

Log periodic antennas are widely used in ultra wideband applications. This paper compares the coplanar waveguide and microstrip feed of log periodic array antennas in terms of gain, bandwidth, design complexity and also the effect of the antenna on different substrates. The design criteria of both types of antennas are discussed in detail. The two different types of feeding techniques for the antenna are simulated using High Frequency Structure Simulator which uses efficient Finite Element Method for rigorous electromagnetic analysis. The results are compared and comparison table gives the clear idea of choosing the feed and also the substrate material. © 2015 IEEE.