Interlacing Properties of Eigenvalues of Laplacian and Net-Laplacian Matrix of Signed Graphs

This paper explores interlacing inequalities in the Laplacian spectrum of signed cycles and investigates interlacing relationship between the spectrum of the net-Laplacian of a signed graph and its subgraph formed by removing a vertex together with its incident edges. Additionally, an inequality is derived between the net-Laplacian spectrum of a complete co-regular signed graph $\Gamma$ and the Laplacian spectrum of the graph obtained by removing any vertex $v$ from $\Gamma$. Also for a signed graph $\Gamma$, the net-Laplacian matrix is normalized and an inequality is derived between the spectrum of the normalized net-Laplacian of a signed graph and its subgraph, formed by contraction of edge and vertex

On Spectrum of Neighbourhood Corona Product of Signed Graphs

Given two signed graphs $\Gamma_1$ with nodes $\{u_1,u_2,\cdots,u_n\}$ and $\Gamma_2$, the neighbourhood corona, $\Gamma_1*\Gamma_2$ is the signed graph obtained by taking one copy of $\Gamma_1$ and $n_1$ copies of $\Gamma_2$, and joining every neighbour of the $i^{th}$ node with each nodes of the $i^{th}$ copy of $\Gamma_2$ by a new signed edge. In this paper we will determine the condition for $\Gamma_1*\Gamma_2$ to be balanced. We also determine the adjacency spectrum of $\Gamma_1*\Gamma_2$ for arbitrary $\Gamma_1$ and $\Gamma_2$, and Laplacian and signless Laplacian spectrum of $\Gamma_1*\Gamma_2$ for regular $\Gamma_1$ and arbitrary $\Gamma_2$, in terms of the corresponding spectrum of $\Gamma_1$ and $\Gamma_2$

Unique solvability of fractional functional differential equation on the basis of Vallée-Poussin theorem

summary:We propose explicit tests of unique solvability of two-point and focal boundary value problems for fractional functional differential equations with Riemann-Liouville derivative

OPEN LIQUID ELECTRON MICROSCOPY: IMAGING CRYSTALLINE POLYMERS AND POLYMER-GRAFTED ANISOTROPIC NANOPARTICLES

Gels and emulsions, a category of dispersed or swollen soft matter, exhibit diverse characteristics and applications. Understanding their behavior requires nanoscale visualization, making liquid-phase electron microscopy a promising approach. This thesis investigates solvated soft matter using open liquid SEM and TEM techniques, avoiding confinement by employing liquids of negligible or low volatility alongside specialized electron microscopes. We developed open liquid TEM and SEM-based high-resolution imaging methodologies for polymer gels and nanoparticle interfacial assemblies, contributing to an enhanced understanding of nanoscale features and rearrangements. A Variable Pressure Scanning Electron Microscope (VPSEM) enabled imaging of nanoparticle (NP) adsorption and dynamics on the surface of commonly used liquids such as glycerol. At low electron doses, NP motion at the liquid surface was negligibly affected by the electron beam. However, high electron doses and the use of hydrophobic liquid led to significant beam-induced artifacts. We were able to image the packing of nanorods (NRs) and nano-ellipsoids (NEs) in dense monolayers at an individual particle level on the surface of a variety of liquids with unprecedented resolution. In-situ imaging of the interfacial assembly of NRs and NEs revealed a slow reorientation behavior that depended on the NP shape, aspect ratio, polymeric ligands, and solvent. The packing of dense monolayers of rod-like NPs was influenced by the strength of interparticle interactions, which in turn depended on interparticle separation, polymeric ligands, and solvents. At high areal densities, strongly interacting NEs exhibited a morphology similar to ellipsoidal microparticles, while NEs with negligible interactions displayed local liquid crystalline order. The interfacial adsorption and packing of both NRs and NEs were significantly influenced by the grafted polymeric ligands. A TEM-based technique was used to image solvated crystalline polymers, specifically capturing PEG crystallization within thin ionic liquid films for the first time. This approach revealed novel PEG nano-crystallite morphologies that correlated with film thickness and substrate characteristics. Applying the same methodology, we characterized the gel network of PEG-IL gels, uncovering a heterogeneous network structure. Our observations revealed an interconnected gel network formed by fibrillar crystallites of PEG, spanning dimensions from a few nanometers to several hundred nanometers

Display device color management and visual surveillance of vehicles

Digital imaging has seen an enormous growth in the last decade. Today users have numerous choices in creating, accessing, and viewing digital image/video content. Color management is important to ensure consistent visual experience across imaging systems. This is typically achieved using color profiles. In this thesis we identify the limitations of profile-based color management systems and propose an alternative system based on display device models and look-up tables (LUT). We identify techniques to design LUTs which are optimal in terms of color reproduction accuracy under resource constraints. We show that a LUT-based color management system is more accurate and memory-efficient than a comparable ICC profile-based system. Visual surveillance is often used for security and law enforcement applications. In most cases the video data is either passively recorded for forensic applications or is remotely monitored by human operators. We propose the use of image and video analysis techniques to assist the operators. This would reduce human errors due to fatigue, boredom, and excess information. We describe a video surveillance system to observe vehicular traffic from a standoff range and detect anomalous behavior by analyzing the motion trajectories. We also extract physical information (such as make, tire size, and body type) which can help determine the “normal” behavior. The operator can also use this information to uniquely identify/describe individual vehicles. We describe low complexity techniques to perform the above analyses and show their effectiveness on real traffic videos

Periodic solution of a bioeconomic fishery model by coincidence degree theory

In this article we use coincidence degree theory to study the existence of a positive periodic solutions to the following bioeconomic model in fishery dynamics \begin{equation*}\label{eq1.3} \begin{cases} \frac{dn}{dt} = n \left(r(t) \left(1-\frac{n}{K}\right)-\frac{q(t)E}{n+D}\right),\\ \frac{dE}{dt} = E\left(\frac{A(t)q(t)}{\alpha(t)} \frac{n}{n+D}-\frac{q^2(t)}{\alpha(t)} \frac{n^2E}{(n+D)^2}-c(t)\right), \end{cases} \end{equation*} where the functions $r,q,A,c$ and $\alpha$ are continuous positive $T$-periodic functions. This is the model of a coastal fishery represented as a single site with $n(t)$ is the fish stock biomass, and $E(t)$ is the fishing effort. Examples are given to strengthen our results

A novel clustering strategy for efficient routing in adhoc networks

Routing in wireless mobile ad hoc networks should be time efficient and resource saving. One approach to reduce traffic during the routing process is to divide the network into clusters. Until now, there have been several approaches to cluster-based routing. We propose a voting based clustering strategy to form a network with spatial and temporal stability. The selection of cluster head and cluster size is done in a very efficient manner. We present algorithms for creation of clusters and their maintenance in the presence of various network events. Our strategy outperforms existing and conventional clustering approaches in terms of number of hops required, at a little overhead cost during topology updates. The strategy performs very well when the density of nodes is high.© IEE

Design and development of reverse osmosis (RO) plant status monitoring system for early fault prediction and predictive maintenance

Abstract Automation and reliability are the crucial elements of any advance reverse osmosis plant to meet the environmental and economic demands. Early fault indication, diagnosis and regular maintenance are the key challenges with most of the reverse osmosis plants in the Indian scenario. The present work introduces a modern reverse osmosis (RO) plant status monitoring unit to monitor different plant parameters in real time and early prediction for faults and maintenance. Developed RO plant status monitoring unit consists of a touch screen-based embedded monitoring unit, water quality sensors (pH, TDS), sampling chamber for controlled water flow, flow sensors, pressure and level sensors. The present system has been developed in a modular fashion so that it could be integrated with any capacity of RO plant units. Developed embedded system monitors various parameters of the plant such as input power, efficiency of the plant, level of input and output water tank and also guides operator with instructions for plant operation. Other than this, a dedicated smartphone app interface has been developed for the operator to acquire data from status monitoring unit, storage on smartphone, and transfer it to the cloud. The developed smartphone-based app also provides facility to integrate plant data with Google map with location information for easy understanding and quick action. The system has also a backup facility to transfer data to the server using 2G GSM module during the unavailability of the operator. A dedicated centralized Web server has been developed for real-time visualization of all installed RO plant status monitoring units. Different machine learning techniques have been implemented on acquired sensors data to predict early warnings related to power failure, membrane fouling and scaling, input water shortage, pipe, tank leakage, water quality sensors damage, non-operation or wrong operation of the plant along with different maintenance actions such as membrane water and chemical wash. Developed RO status monitoring unit has been tested with various RO plants having capacity from 500 LPH to 2000 LPH and deployed at various nearby villages of Rajasthan