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.

Effect of chlorine concentration on the spectral characteristics of electroluminescence in ZnS: Cu: Cl phosphor

ZnS: Cu: Cl phosphor prepared under a vacuum firing process is found to give blue electroluminescence with emission peak at 460 nm which remams unaltered with the frequency of the excitation voltage. Addition of excess chlorine in the phosphor gives blue, green and red emission at 460, 520 and 640 run. The intensity of the blue band decreases and It fmally disappears as chlorine concentration is increased. A scheme involving three energy levels attributed to Cu2+, Cu+ and Cl- centres in Zns explains the experimental results completely.

Modification of spectral characteristics and optogalvanic response in neon hollow cathode under laser excitation

The changes in emission characteristics of a neon hollow cathode discharge by resonant laser excitation of 1s 5→2p 2 and 1s 5→2p 4 transition have been studied by simultaneously monitoring the optogalvanic effect and the laser induced fluorescence. It has been observed that resonant excitation causes substantial variation in the relative intensities of lines in the emission spectrum of neon discharge.

Studies in Fuzzy Commutative Algebra

The main objective of this thesis was to extend some basic concepts and results in module theory in algebra to the fuzzy setting.The concepts like simple module, semisimple module and exact sequences of R-modules form an important area of study in crisp module theory. In this thesis generalising these concepts to the fuzzy setting we have introduced concepts of ‘simple and semisimple L-modules’ and proved some results which include results analogous to those in crisp case. Also we have defined and studied the concept of ‘exact sequences of L-modules’.Further extending the concepts in crisp theory, we have introduced the fuzzy analogues ‘projective and injective L-modules’. We have proved many results in this context. Further we have defined and explored notion of ‘essential L-submodules of an L-module’. Still there are results in crisp theory related to the topics covered in this thesis which are to be investigated in the fuzzy setting. There are a lot of ideas still left in algebra, related to the theory of modules, such as the ‘injective hull of a module’, ‘tensor product of modules’ etc. for which the fuzzy analogues are not defined and explored.

Spectral Analysis of Bounded Self-adjoint operators - A Linear Algebraic Approach

This thesis Entitled Spectral theory of bounded self-adjoint operators -A linear algebraic approach.The main results of the thesis can be classified as three different approaches to the spectral approximation problems. The truncation method and its perturbed versions are part of the classical linear algebraic approach to the subject. The usage of block Toeplitz-Laurent operators and the matrix valued symbols is considered as a particular example where the linear algebraic techniques are effective in simplifying problems in inverse spectral theory. The abstract approach to the spectral approximation problems via pre-conditioners and Korovkin-type theorems is an attempt to make the computations involved, well conditioned. However, in all these approaches, linear algebra comes as the central object. The objective of this study is to discuss the linear algebraic techniques in the spectral theory of bounded self-adjoint operators on a separable Hilbert space. The usage of truncation method in approximating the bounds of essential spectrum and the discrete spectral values outside these bounds is well known. The spectral gap prediction and related results was proved in the second chapter. The discrete versions of Borg-type theorems, proved in the third chapter, partly overlap with some known results in operator theory. The pure linear algebraic approach is the main novelty of the results proved here.

A study on fuzzy semi inner product spaces

Mathematical models are often used to describe physical realities. However, the physical realities are imprecise while the mathematical concepts are required to be precise and perfect. Even mathematicians like H. Poincare worried about this. He observed that mathematical models are over idealizations, for instance, he said that only in Mathematics, equality is a transitive relation. A first attempt to save this situation was perhaps given by K. Menger in 1951 by introducing the concept of statistical metric space in which the distance between points is a probability distribution on the set of nonnegative real numbers rather than a mere nonnegative real number. Other attempts were made by M.J. Frank, U. Hbhle, B. Schweizer, A. Sklar and others. An aspect in common to all these approaches is that they model impreciseness in a probabilistic manner. They are not able to deal with situations in which impreciseness is not apparently of a probabilistic nature. This thesis is confined to introducing and developing a theory of fuzzy semi inner product spaces.

A study on fuzzy semi inner product spaces

Mathematical models are often used to describe physical realities. However, the physical realities are imprecise while the mathematical concepts are required to be precise and perfect. The 1st chapter give a brief summary of the arithmetic of fuzzy real numbers and the fuzzy normed algebra M(I). Also we explain a few preliminary definitions and results required in the later chapters. Fuzzy real numbers are introduced by Hutton,B [HU] and Rodabaugh, S.E[ROD]. Our definition slightly differs from this with an additional minor restriction. The definition of Clementina Felbin [CL1] is entirely different. The notations of [HU]and [M;Y] are retained inspite of the slight difference in the concept.the 3rd chapter In this chapter using the completion M'(I) of M(I) we give a fuzzy extension of real Hahn-Banch theorem. Some consequences of this extension are obtained. The idea of real fuzzy linear functional on fuzzy normed linear space is introduced. Some of its properties are studied. In the complex case we get only a slightly weaker analogue for the Hahn-Banch theorem, than the one [B;N] in the crisp case