A Note on Energy of Some Graphs

Eigenvalue of a graph is the eigenvalue of its adjacency matrix. The energy of a graph is the sum of the absolute values of its eigenvalues. In this note we obtain analytic expressions for the energy of two classes of regular graphs.

SOME NEW INTEGRAL GRAPHS

The eigenvalue of a graph is the eigenvalue of its adjacency matrix . A graph G is integral if all of its cigenvalues are integers. In this paper some new classes of integral graphs are constructed.

On infinite graphs and related matrices

This thesis Entitled On Infinite graphs and related matrices.ln the last two decades (iraph theory has captured wide attraction as a Mathematical model for any system involving a binary relation. The theory is intimately related to many other branches of Mathematics including Matrix Theory Group theory. Probability. Topology and Combinatorics . and has applications in many other disciplines..Any sort of study on infinite graphs naturally involves an attempt to extend the well known results on the much familiar finite graphs. A graph is completely determined by either its adjacencies or its incidences. A matrix can convey this information completely. This makes a proper labelling of the vertices. edges and any other elements considered, an inevitable process. Many types of labelling of finite graphs as Cordial labelling, Egyptian labelling, Arithmetic labeling and Magical labelling are available in the literature. The number of matrices associated with a finite graph are too many For a study ofthis type to be exhaustive. A large number of theorems have been established by various authors for finite matrices. The extension of these results to infinite matrices associated with infinite graphs is neither obvious nor always possible due to convergence problems. In this thesis our attempt is to obtain theorems of a similar nature on infinite graphs and infinite matrices. We consider the three most commonly used matrices or operators, namely, the adjacency matrix

Photosensitivity of Laser Dye Mixtures in Polymer Matrix – A Photoacoustic Study

Laser induced photoacoustic (PA) technique is used in the study of photostability of polymethyl methacrylate (PMMA) films doped with Rhodamine 6G -Rhodamine B dye system. Energy transfer from a donor molecule to an acceptor molecule in a dye mixture affects the output of the dye system. Details of investigations on the role of laser power, modulation frequency and the irradiation wavelength on the photosensitivity of the dye mixture doped PMMA films are presented.

Complex methylene-blue-sensitized polyvinyl chloride: a polymer matrix for hologram recording

A new polymer matrix sensitized with methylene blue for use as an optical recording material is described here. The characterization is done to determine the optimal recording conditions. These films need no chemical development and are found to be stable for several months. The matrix has excellent shelf life and needs an exposure only as short as 20 s. Direct imaging was done on this material.

Preparation and Characterisation of Spinel Ferrites - Their Incorporation in Rubber Matrix and Evaluation of Properties

The objectives of the proposed work are preparation of ceramic nickel zinc ferrite belonging to the series Ni1-XZnXFe2O4 with x varying from 0 to 1in steps of 0.2, structrural, magnetic and electrical characterization of Ni1-XZnXFe2O4, preparation and evaluation of Cure characteristics of Rubber Ferrite Composites (RFCs), magnetic characterization of RFCs using vibrating sample magnetometer (VSM), electrical characterization of RFCs and estimation of magnetostriction constant form HL parameters. The study deals with the structural and magnetic properties of ceramic fillers, variation of coercivity with composition and the variation of magnetization for different filler loadings are compared and correlated. The dielectric properties of ceramic Ni1-XZnXFe2O4 and rubber ferrite composites containing Ni1-XZnXFe2O4 were evaluated and the ac electrical conductivity (ac) of ceramic as well as composite samples can be calculated by using a simple relationship of the form ac = 2f tan 0r, with the data available from dielectric measurements. The results suggest that the ac electrical conductivity is directly proportional to the frequency

Laser-induced thermal characterization of nano Ag metal dispersed ceramic alumina matrix

In this paper, we report the measurements of thermal diffusivity of nano Ag metal dispersed ceramic alumina matrix sintered at different temperatures using laser induced non-destructive photoacoustic technique. Measurements of thermal diffusivity also have been carried out on specimens with various concentration of nano metal. Analysis of the data is done on the basis of one-dimensional model of Rosencwaig and Gersho. The present measurements on the thermal diffusivity of nano metal dispersed ceramic alumina shows that porosity has a great influence on the heat transport and the thermal diffusivity value. The present analysis also shows that the inclusion of nano metal into ceramic matrix increases its interconnectivity and hence the thermal diffusivity value. The present study on the samples sintered at different temperature shows that the porosity of the ceramics varies considerably with the change in sintering temperature. The results are interpreted in terms of phonon assisted heat transfer mechanism and the exclusion of pores with the increase in sintering temperature.

Laser-induced thermal characterization of nano Ag metal dispersed ceramic alumina matrix

In this paper, we report the measurements of thermal diffusivity of nano Ag metal dispersed ceramic alumina matrix sintered at different temperatures using laser induced non-destructive photoacoustic technique. Measurements of thermal diffusivity also have been carried out on specimens with various concentration of nano metal. Analysis of the data is done on the basis of one-dimensional model of Rosencwaig and Gersho. The present measurements on the thermal diffusivity of nano metal dispersed ceramic alumina shows that porosity has a great influence on the heat transport and the thermal diffusivity value. The present analysis also shows that the inclusion of nano metal into ceramic matrix increases its interconnectivity and hence the thermal diffusivity value. The present study on the samples sintered at different temperature shows that the porosity of the ceramics varies considerably with the change in sintering temperature. The results are interpreted in terms of phonon assisted heat transfer mechanism and the exclusion of pores with the increase in sintering temperature

Laser-induced thermal characterization of nano Ag metal dispersed ceramic alumina matrix

In this paper, we report the measurements of thermal diffusivity of nano Ag metal dispersed ceramic alumina matrix sintered at different temperatures using laser induced non-destructive photoacoustic technique. Measurements of thermal diffusivity also have been carried out on specimens with various concentration of nano metal. Analysis of the data is done on the basis of one-dimensional model of Rosencwaig and Gersho. The present measurements on the thermal diffusivity of nano metal dispersed ceramic alumina shows that porosity has a great influence on the heat transport and the thermal diffusivity value. The present analysis also shows that the inclusion of nano metal into ceramic matrix increases its interconnectivity and hence the thermal diffusivity value. The present study on the samples sintered at different temperature shows that the porosity of the ceramics varies considerably with the change in sintering temperature. The results are interpreted in terms of phonon assisted heat transfer mechanism and the exclusion of pores with the increase in sintering temperature

Emission spectral studies of phthalocyanines in borate glass matrix

Cochin University of Science & Technology

Spectral studies of naphthalocyanine (Nc) and rare earth phthalocyanine (RePc) molecules in an inorganic glassy borate matrix

Optical absorption and emission spectral studies of free and metal naphthalocyanine doped borate glass matrix are reported for the first time. Absorption spectra recorded in the UV- VIS-NIR region show the characteristic absorption bands, namely, the B-band and Q-band of the naphthalocyanine (Nc) molecule. Some of the important spectral parameters, namely, the optical absorption coefficient (α), molar extinction coefficient (ε) and absorption cross section (σa) of the principal absorption transitions are determined. Optical band gap (Eg) of the materials evaluated from the functional dependence of absorption coefficient on photon energy lies in the range 1.6 eV≤Eg≤2.1 eV. All fluorescence spectra except that of EuNc consist of an intense band in the 765 nm region corresponding to the excitation of Q-band. In EuNc the maximum fluorescence intensity band is observed at 824 nm. The intensity of the principal fluorescence band is maximum in ZnNc, whereas it is minimum in H2Nc. Radiative parameters of the principal fluorescence transitions corresponding to the Q-band excitation are also reported for the naphthalocyanine and phthalocyanine based matrices.

Optical properties of phthalocyanine molecules in cyano acrylate polymer matrix

Optical absorption and emission spectral studies of various phthalocyanine molecules, viz., LaPc, NdPc, SmPc, EuPc, CuPc and ZnPc in a polymer matrix of cyano acrylate are reported for the first time. All the absorption spectra show an intense B band (Soret) in the UV region followed by a weaker Q band in the visible region. The positions of the Q and B bands are found to have dependence on the metallic substitution. Values of the important spectral parameters, viz., molar extinction coefficient (ϵ), oscillator strength (f), radiative transition rate and decay time of the excited singlet state are also presented and compared with other solid matrices. The recorded fluorescence spectrum shows two broad emission bands in the case of NdPc, whereas for ZnPc only a very weak band is observed. The absence of emission bands for the other metallated phthalocyanines is attributed to increased spin orbit interaction and intersystem crossing.

Optical properties of porphyrins in borate glassy matrix

Optical properties of free and substituted porphyrins (PP) doped borate glass matrix are reported for the first time. Absorption spectral measurements of H2TPP, CdTPP, MgTPP and ZnTPP doped borate glass matrix have been made in the 200–1100 nm region and the spectra obtained are analyzed to obtain the optical bandgap (Eg) and other important spectral parameters viz. oscillator strength (f), molar extinction coefficient (ε), electric dipole strength (q2), absorption cross-section (σa) and molecular concentration (N). Intense fluorescence was observed in the region 668–685 nm for CdTPP, ZnTPP and MgTPP doped matrices, whereas no such fluorescence was observed in H2TPP doped matrix. Fluorescence intensity was observed to be almost similar in all the metallated porphyrine matrices. Fluorescence bandwidth (Δλ), decay time (τ), stimulated emission cross-section (σ) and optical gain (G) of the principal fluorescence transitions corresponding to the Q-band excitation were also evaluated and discussed.

Optical-limiting response of rare-earth metallo-phthalocyanine-doped copolymer matrix

The nanosecond optical-limiting characteristics (at 532 nm) of some rare-earth metallo-phthalocyanines (Sm(Pc)2, Eu(Pc)2, and LaPc) doped in a copolymer matrix of poly(methyl methacrylate) and methyl-2-cyanoacrylate have been studied for the first time to our knowledge. The optical-limiting response is attributed to reverse saturable absorption due to excited-state absorption. The performance of LaPc in a copolymer host is studied at different linear transmissions. The laser damage thresholds of all the samples are also reported.

Influence of additives on the charactaristics of stone matrix asphalt

The increase in traffic growth and maintenance expenditures demands the urgent need for building better, long-lasting, and more efficient roads preventing or minimizing bituminous pavement distresses. Many of the principal distresses in pavements initiate or increase in severity due to the presence of water. In Kerala highways, where traditional dense graded mixtures are used for the surface courses, major distress is due to moisture induced damages. The Stone Matrix Asphalt (SMA) mixtures provide a durable surface course. Proven field performance of test track at Delhi recommends Stone Matrix Asphalt as a right choice to sustain severe climatic and heavy traffic conditions. But the concept of SMA in India is not so popularized and its application is very limited mainly due to the lack of proper specifications. This research is an attempt to study the influence of additives on the characteristics of SMA mixtures and to propose an ideal surface course for the pavements. The additives used for this investigation are coir, sisal, banana fibres (natural fibres), waste plastics (waste material) and polypropylene (polymer). A preliminary investigation is conducted to characterize the materials used in this study. Marshall test is conducted for optimizing the SMA mixtures (Control mixture-without additives and Stabilized mixtures with additives). Indirect tensile strength tests, compression strength tests, triaxial strength tests and drain down sensitivity tests are conducted to study the engineering properties of stabilized mixtures. The comparison of the performance of all stabilized mixtures with the control mixture and among themselves are carried out. A statistical analysis (SPSS package Ver.16) is performed to establish the findings of this study