arXiv subjects
Publications and source records attributed to Jyoti Rani.
In this paper, the $q$-numerical radius of operators in semi-Hilbertian spaces is studied. New characterizations are established, and sharp upper and lower bounds for the $q$-numerical radius are derived. Moreover, several inequalities involving operator monotone functions and matrix means for the $q$-numerical radius of sectorial matrices are obtained.
We study spectral constants for convex domains $\Omega$ containing the spectrum of an operator. We extend the Crouzeix--Palencia framework by obtaining bounds depending on a parameter $\gamma$ and relating these bounds to geometric properties of $\Omega$ and the numerical range $W(A)$. We generalise the proof that the numerical range is a $1+\sqrt{2}$-spectral set to scaled $q$-numerical ranges. We also propose a generalisation of Crouzeix's Conjecture in the context of $q$-numerical ranges.
In this article, we conduct a comprehensive study on the continuity, compactness, and spectral properties of Rhaly operators and generalized Ces\`aro operators, acting on weighted null sequence spaces. We determine the point spectrum, continuous spectrum, and residual spectrum for compact Rhaly operators and compact generalized Ces\`aro operators. Additionally, we explore Goldberg's classifications of Rhaly operators over weighted null sequence spaces.
This study utilizes Orlicz functions to provide refined lower and upper bounds on the q-numerical radius of an operator acting on a Hilbert space. Additionally, the concept of q-sectorial matrices is introduced and further bounds for the q-numerical radius are established. Our results unify several existing bounds for the q-numerical radius. Suitable examples are provided to supplement the estimations.
This study investigates the $A$-$q$-numerical range of an operator within the framework of semi-Hilbertian spaces. Several fundamental properties of the $A$-$q$-numerical range are established, including spectral inclusion results and a disk union formula. Bounds for the $A$-$q$-numerical radius are derived, extending and generalizing previously known results. Finally, the notion of $A$-nilpotent operator is introduced, and it is shown that the $A$-$q$-numerical range of an $A$-nilpotent operator with index $2$ is a disk (open or closed) in the complex plane.
This article focuses on several significant bounds of $q$-numerical radius $w_q(A)$ for sectorial matrix $A$ which refine and generalize previously established bounds. One of the significant bounds we have derived is as follows: \[\frac{|q|^2\cos^2\alpha}{2} \|A^*A+AA^*\| \le w_q^2(A)\le \frac{\left(\sqrt{(1-|q|^2)\left(1+2sin^2(\alpha)\right)}+ |q|\right)^2}{2} \|A^*A+AA^*\|,\] where $ A $ is a sectorial matrix. Also, upper bounds for commutator and anti-commutator matrices and relations between $w_q(A^t)$ and $w_q^t(A)$ for non-integral power $t\in [0,1]$ are also obtained. Moreover, a few significant estimations of $q$-numerical radius of off-diagonal $2\times2$ operator matrices are developed.
In this paper, a new class of band matrices is considered where the entries of each non-zero band form a sequence with two limit points. The compact perturbation technique is used to study the spectrum over the $\ell_{p}, (1<p<\infty)$ sequence space. Several spectral subdivisions such as fine spectrum, discrete spectrum, essential spectrum, etc. are obtained. In addition, a few sufficient conditions on the absence of point spectrum over the essential spectrum are also discussed.
This paper introduces and investigates the concept of the $q$-numerical range for tuples of bounded linear operators in Hilbert spaces. We establish various inequalities concerning the $q$-numerical radius associated with these operator tuples. Furthermore, we extend our study to define the $q$-numerical range in semi-Hilbert spaces and provide a proof of its convexity. Additionally, we explore several related results in this context.
Fault detection and isolation in complex systems are critical to ensure reliable and efficient operation. However, traditional fault detection methods often struggle with issues such as nonlinearity and multivariate characteristics of the time series variables. This article proposes a generative adversarial wavelet neural operator (GAWNO) as a novel unsupervised deep learning approach for fault detection and isolation of multivariate time series processes.The GAWNO combines the strengths of wavelet neural operators and generative adversarial networks (GANs) to effectively capture both the temporal distributions and the spatial dependencies among different variables of an underlying system. The approach of fault detection and isolation using GAWNO consists of two main stages. In the first stage, the GAWNO is trained on a dataset of normal operating conditions to learn the underlying data distribution. In the second stage, a reconstruction error-based threshold approach using the trained GAWNO is employed to detect and isolate faults based on the discrepancy values. We validate the proposed approach using the Tennessee Eastman Process (TEP) dataset and Avedore wastewater treatment plant (WWTP) and N2O emissions named as WWTPN2O datasets. Overall, we showcase that the idea of harnessing the power of wavelet analysis, neural operators, and generative models in a single framework to detect and isolate faults has shown promising results compared to various well-established baselines in the literature.
In this article, a comprehensive study is made on the continuity, compactness, and spectrum of the lower triangular terraced matrix, introduced by H. C. Rhaly, Jr. [Houston J. Math. 15(1): 137-146, 1989], acting on the weighted null sequence spaces with bounded, strictly positive weights. Several spectral subdivisions such as point spectrum, residual spectrum, and continuous spectrum are also discussed. In addition, a new class of operator ideal $χ_{c_0(r)}^{(s)}$ associated to the Rhaly operator on weighted $c_0$ space is defined using the concept of $s$-number and it is proved that under certain condition, $χ_{c_0(r)}^{(s)}$ forms a quasi-Banach closed operator ideal.
This paper demonstrates that some non-classical models of human decision-making can be run successfully as circuits on quantum computers. Since the 1960s, many observed cognitive behaviors have been shown to violate rules based on classical probability and set theory. For example, the order in which questions are posed in a survey affects whether participants answer 'yes' or 'no', so the population that answers 'yes' to both questions cannot be modeled as the intersection of two fixed sets. It can, however, be modeled as a sequence of projections carried out in different orders. This and other examples have been described successfully using quantum probability, which relies on comparing angles between subspaces rather than volumes between subsets. Now in the early 2020s, quantum computers have reached the point where some of these quantum cognitive models can be implemented and investigated on quantum hardware, by representing the mental states in qubit registers, and the cognitive operations and decisions using different gates and measurements. This paper develops such quantum circuit representations for quantum cognitive models, focusing particularly on modeling order effects and decision-making under uncertainty. The claim is not that the human brain uses qubits and quantum circuits explicitly (just like the use of Boolean set theory does not require the brain to be using classical bits), but that the mathematics shared between quantum cognition and quantum computing motivates the exploration of quantum computers for cognition modeling. Key quantum properties include superposition, entanglement, and collapse, as these mathematical elements provide a common language between cognitive models, quantum hardware, and circuit implementations.
Future spintronics requires the realization of thin film of half-metallic ferromagnets having high Curie temperature and 100\% spin polarization at the Fermi level for potential spintronics applications. In this paper, we report the epitaxial thin films growth of half-metallic CoFeMnGe Heusler alloy on MgO (001) substrate using pulsed laser deposition system, along with the study of structural, magnetic and transport properties. The magnetic property measurements of the thin film suggest a soft ferromagnetic state at room temperature with an in-plane magnetic anisotropy and a Curie temperature well above the room temperature. Anisotropic magnetoresistance (AMR) ratio and temperature dependent electrical resistivity measurements of the thin film indicate the compound to be half-metallic in nature and therefore suitable for the fabrications of spintronics devices.
Spin-gapless semiconductors with their unique band structures have recently attracted much attention due to their interesting transport properties that can be utilized in spintronics applications. We have successfully deposited the thin films of quaternary spin-gapless semiconductor CoFeMnSi Heusler alloy on MgO (001) substrates using a pulsed laser deposition system. These films show epitaxial growth along (001) direction and display uniform and smooth crystalline surface. The magnetic properties reveal that the film is ferromagnetically soft along the in-plane direction and its Curie temperature is well above 400 K. The electrical conductivity of the film is low and exhibits a nearly temperature independent semiconducting behaviour. The estimated temperature coefficient of resistivity for the film is -7x10^-10 Ohm.m/K, which is comparable to the values reported for spin-gapless semiconductors.