On Distance Energy of Graphs

The D-eigenvalues of a graph G are the eigenvalues of its distance matrix D, and the D-energy ED(G) is the sum of the absolute values of its D-eigenvalues. Two graphs are said to be D-equienergetic if they have the same D-energy. In this note we obtain bounds for the distance spectral radius and D-energy of graphs of diameter 2. Pairs of equiregular D-equienergetic graphs of diameter 2, on p = 3t + 1 vertices are also constructed.

ON DISTANCE ENERGY OF GRAPHS

The D-eigenvalues of a graph G are the eigenvalues of its distance matrix D, and the D-energy ED(G) is the sum of the absolute values of its D-eigenvalues. Two graphs are said to be D-equienergetic if they have the same D-energy. In this note we obtain bounds for the distance spectral radius and D-energy of graphs of diameter 2. Pairs of equiregular D-equienergetic graphs of diameter 2, on p = 3t + 1 vertices are also constructed.

Thermal lens spectrum of organic dyes using optical parametric oscillator

The wavelength dependence of thermal lens signal from organic dyes are studied using dual beam thermal lens technique. It is found that the profile of thermal lens spectrum widely differ from the conventional absorption spectrum in the case of rhodamine B unlike in the case of crystal violet. This is explained on the basis of varying contribution of nonradiative relaxations from the excited vibronic levels.

Study on the determination of molecular distance in organic dye mixtures using dual beam thermal lens technique

A sensitive method based on the principle of photothermal phenomena to study the energy transfer processes in organic dye mixtures is presented. A dual beam thermal lens method can be very effectively used as an alternate technique to determine the molecular distance between donor and acceptor in fluorescein–rhodamine B mixture using optical parametric oscillator.

High resolution optogalvanic spectrum of N2-rotational structure of (11, 7) band in the first positive system

High resolution optogalvanic spectrum of the (11, 7) band in the first positive system of nitrogen molecule has been recorded from 17179 to 17376 cm- 1. Assignment of 432 rotational lines belonging to the 27 branches of this band has been carried out.

Spatial analysis of C2 band emission from laser produced plasma

Time and space resolved spectroscopic studies of the molecular band emission from C2 are performed in the plasma produced by irradiating a graphite target with 1:06 m radiation from a Q-switched Nd:YAG laser. High-resolution spectra are recorded from points located at distances up to 15 mm from the target in the presence of ambient helium gas pressure. Depending on the laser irradiance, time of observation and position of the sampled volume of the plasma the features of the emission spectrum are found to change drastically. The vibrational temperature and population distribution in the different vibrational levels of C2 molecules have been evaluated as a function of distance for different time delays and laser irradiance. It is also found that the vibrational temperature of C2 molecules decreases with increasing helium pressure.

Time resolved study of CN band emission from plasma generated by laser irradiation of graphite

Time and space resolved studies of emission from CN molecules have been carried out in the plasma produced from graphite target by 1.06 urn pulses from a Q-switched Nd:YAG laser. Depending on the laser pulse energy, time of observation and position of the sampled volume of the plasma, the features of the emission spectrum are found to change drastically. The vibrational temperature and population distribution in the different vibrational levels have been studied as functions of distance, time, laser energy and ambient gas pressure. Evidence for nonlinear effects of the plasma medium such as self focusing which exhibits threshold-like behaviour are also obtained. Temperature and electron density of the plasma have been evaluated using the relative line intensities of successive ionization stages of carbon atom. These electron density measurements are verified by using Stark broadening method.

Thermal lens spectrum of organic dyes using optical parametric oscillator

The wavelength dependence of thermal lens signal from organic dyes are studied using dual beam thermal lens technique. It is found that the profile of thermal lens spectrum widely differ from the conventional absorption spectrum in the case of rhodamine B unlike in the case of crystal violet. This is explained on the basis of varying contribution of nonradiative relaxations from the excited vibronic levels.

Side illumination fluorescence emission characteristics from a dye doped polymer optical fiber under two-photon excitation.

Two-photon excited (TPE) side illumination fluorescence studies in a Rh6G-RhB dye mixture doped polymer optical fiber (POF) and the effect of energy transfer on the attenuation coefficient is reported. The dye doped POF is pumped sideways using 800 nm, 70 fs laser pulses from a Ti:sapphire laser, and the TPE fluorescence emission is collected from the end of the fiber for different propagation distances. The fluorescence intensity of RhB doped POF is enhanced in the presence of Rh6G as a result of energy transfer from Rh6G to RhB. Because of the reabsorption and reemission process in dye molecules, an effective energy transfer is observed from the shorter wavelength part of the fluorescence spectrum to the longer wavelength part as the propagation distance is increased in dye doped POF. An energy transfer coefficient is found to be higher at shorter propagation distances compared to longer distances. A TPE fluorescence signal is used to characterize the optical attenuation coefficient in dye doped POF. The attenuation coefficient decreases at longer propagation distances due to the reabsorption and reemission process taking place within the dye doped fiber as the propagation distance is increased.

Photoacoustic spectrum of samarium phthalocyanine powder

Photoacoustic spectrum of samarium phthalocyanine powder is recorded and compared with previously reported UV–vis absorption spectra of the same dissolved in different liquid and solid host media. The Davidov splitting of Q band is observed in the PA spectrum but the two bands are overlapped considerably and the shorter wavelength band is more intense and dominating one in the powder spectrum.

Recurrence Quantification Analysis of System Signals for Detecting Tool and Chatter in Turning

In this thesis, the applications of the recurrence quantification analysis in metal cutting operation in a lathe, with specific objective to detect tool wear and chatter, are presented.This study is based on the discovery that process dynamics in a lathe is low dimensional chaotic. It implies that the machine dynamics is controllable using principles of chaos theory. This understanding is to revolutionize the feature extraction methodologies used in condition monitoring systems as conventional linear methods or models are incapable of capturing the critical and strange behaviors associated with the metal cutting process.As sensor based approaches provide an automated and cost effective way to monitor and control, an efficient feature extraction methodology based on nonlinear time series analysis is much more demanding. The task here is more complex when the information has to be deduced solely from sensor signals since traditional methods do not address the issue of how to treat noise present in real-world processes and its non-stationarity. In an effort to get over these two issues to the maximum possible, this thesis adopts the recurrence quantification analysis methodology in the study since this feature extraction technique is found to be robust against noise and stationarity in the signals.The work consists of two different sets of experiments in a lathe; set-I and set-2. The experiment, set-I, study the influence of tool wear on the RQA variables whereas the set-2 is carried out to identify the sensitive RQA variables to machine tool chatter followed by its validation in actual cutting. To obtain the bounds of the spectrum of the significant RQA variable values, in set-i, a fresh tool and a worn tool are used for cutting. The first part of the set-2 experiments uses a stepped shaft in order to create chatter at a known location. And the second part uses a conical section having a uniform taper along the axis for creating chatter to onset at some distance from the smaller end by gradually increasing the depth of cut while keeping the spindle speed and feed rate constant.The study concludes by revealing the dependence of certain RQA variables; percent determinism, percent recurrence and entropy, to tool wear and chatter unambiguously. The performances of the results establish this methodology to be viable for detection of tool wear and chatter in metal cutting operation in a lathe. The key reason is that the dynamics of the system under study have been nonlinear and the recurrence quantification analysis can characterize them adequately.This work establishes that principles and practice of machining can be considerably benefited and advanced from using nonlinear dynamics and chaos theory.

Studies on the Spectrum and the Energy of Graphs

Department of Mathematics, Cochin University of Science and Technology

Isolation and characterization of broad spectrum bacteriophages lytic to Vibrio harveyi from shrimp farms of Kerala, India

Of 33 phages isolated from various shrimp farms in Kerala, India, six were segregated to have broad spectrum lytic efficiency towards 87 isolates of Vibrio harveyi with cross-infecting potential to a few other important aquaculture pathogens. They were further tested on beneficial aquaculture micro-organisms such as probiotics and nitrifying bacterial consortia and proved to be noninfective. Morphological characterization by transmission electron microscopy (TEM) and molecular characterization by RAPD and SDS-PAGE proved them distinct and positioned under Caudovirales belonging to Myoviridae and Siphoviridae

Strongly distance-balanced graphs and graph products

A graph G is strongly distance-balanced if for every edge uv of G and every i 0 the number of vertices x with d.x; u/ D d.x; v/ 1 D i equals the number of vertices y with d.y; v/ D d.y; u/ 1 D i. It is proved that the strong product of graphs is strongly distance-balanced if and only if both factors are strongly distance-balanced. It is also proved that connected components of the direct product of two bipartite graphs are strongly distancebalanced if and only if both factors are strongly distance-balanced. Additionally, a new characterization of distance-balanced graphs and an algorithm of time complexity O.mn/ for their recognition, wheremis the number of edges and n the number of vertices of the graph in question, are given

Equal opportunity networks, distance-balanced graphs, and Wiener game

Given a graph G and a set X ⊆ V(G), the relative Wiener index of X in G is defined as WX (G) = {u,v}∈X 2  dG(u, v) . The graphs G (of even order) in which for every partition V(G) = V1 +V2 of the vertex set V(G) such that |V1| = |V2| we haveWV1 (G) = WV2 (G) are called equal opportunity graphs. In this note we prove that a graph G of even order is an equal opportunity graph if and only if it is a distance-balanced graph. The latter graphs are known by several characteristic properties, for instance, they are precisely the graphs G in which all vertices u ∈ V(G) have the same total distance DG(u) = v∈V(G) dG(u, v). Some related problems are posed along the way, and the so-called Wiener game is introduced.