Some Generalizations of Fuzzy Metrizability

The main purpose of the study is to extent concept of the class of spaces called ‘generalized metric spaces’ to fuzzy context and investigates its properties. Any class of spaces defined by a property possessed by all metric spaces could technically be called as a class of ‘generalized metric spaces’. But the term is meant for classes, which are ‘close’ to metrizable spaces in some under certain kinds of mappings. The theory of generalized metric spaces is closely related to ‘metrization theory’. The class of spaces likes Morita’s M- spaces, Borges’s w-spaces, Arhangelskii’s p-spaces, Okuyama’s  spaces have major roles in the theory of generalized metric spaces. The thesis introduces fuzzy metrizable spaces, fuzzy submetrizable spaces and proves some characterizations of fuzzy submetrizable spaces, and also the fuzzy generalized metric spaces like fuzzy w-spaces, fuzzy Moore spaces, fuzzy M-spaces, fuzzy k-spaces, fuzzy -spaces study of their properties, prove some equivalent conditions for fuzzy p-spaces. The concept of a network is one of the most useful tools in the theory of generalized metric spaces. The -spaces is a class of generalized metric spaces having a network.

Studies on Some New Metal-Hydrazone Complexes and Their Zeolite Encapsulated Analogues

The thesis deals with the synthesis, characterization and catalytic activity studies of some new Fe (III), Co (II), Ni (II) and Cu (II) complexes of hydrazones and their zeolite encapsulated analogues. Hydrazones have diverse applications in biological, non-biological and biochemical front. During the present study three hydrazone types of ligands namely, acetylacetone- 2-hydroxyphenylhydrazone (APAcAc), acetoacetanilide- 2-hydroxyphenylhydrazone (APAcAcA) and acetoacetanilide-3,5-dihydro-2,4-dione pyrimidylhydrazone (AUAcAcA) were synthesized by diazotization of primary amine and coupling with compounds containing active methylene group. First part of the thesis deals with the synthesis of Fe, Co, Ni and Cu complexes using three hydrazone types of ligands are given. Details regarding the characterization of these complexes with a view to establishing the molecular structures are presented in this part. The other part contains the method of encapsulation of these complexes in zeolite cavities and their characterizations of the encapsulated metal species are described. A comparitive account of the catalytic activities of the pure and encapsulated complexes for cyclohexanol oxidation was also carried out.

Complexation and ion removal studies of a polystyrene anchored Schiff base

This paper reports the synthesis of a series of six new polystyrene anchored metal complexes of Co(II), Fe(III), Ni(II), Cu(II), Zn(II), and dioxouanium(VI) using the polystyrene anchored Schiff base of 2-nitrobenzaldehyde and the corresponding metal salts. The metal salts used were anhydrous FeCl3, CoCl2 Æ 6H2O, Ni(CH3COO)2 Æ 4H2O, Cu(CH3- COO)2 Æ H2O, Zn(CH3COO)2 Æ 2H2O, and UO2(CH3COO) Æ 2H2O. Physico chemical characterizations have been made from diffuse reflectance and vibrational spectra, elemental analysis, magnetic measurements, and TG studies. The elemental analysis suggest a 1:2 metal:ligand ratio when the complexation has carried out at 70 C for about 12 h reflux. The ligand is monodentate and coordinates through the azomethine nitrogen. The Fe(III), Co(II), Ni(II), and Cu(II) complexes are all paramagnetic whereas Zn(II) and U(VI) are diamagnetic. Zn(II) is assigned a tetrahedral structure, Cu(II) and Co(II) are assigned a square planar structure and Fe(III), Ni(II), and U(VI) are all assigned an octahedral structure. The polystyrene anchored ligand has been developed as an excellent reagent for the removal of Cu(II). Optimum conditions have been developed for the removal of metal ion from solutions by studying the effect of change of concentration of metal ion, ligand, effect of pH, time of reflux, and interference effect of other ions. It was found that within a span of 20 min it is possible to remove 90% of the metal ion from a 30 ppm metal ion solution in the pH range 4–5.5.

The Edge C4 Graph of a Graph

Abstract. The edge C4 graph E4(G) of a graph G has all the edges of Gas its vertices, two vertices in E4(G) are adjacent if their corresponding edges in G are either incident or are opposite edges of some C4. In this paper, characterizations for E4(G) being connected, complete, bipartite, tree etc are given. We have also proved that E4(G) has no forbidden subgraph characterization. Some dynamical behaviour such as convergence, mortality and touching number are also studied

Photoinduced oxidation of benzhydrol over lanthana modified sol-gel titania

Lanthana modified sol-gel titania is prepared through particulate sol-gel route and the physico-chemical characterizations of the prepared systems were done using X-Ray diffration, EDX, BET surface area-pore volume measurements and TG-DTG analysis. Benzophenone was observed to be the sole product in the TiO2 photocatalyzed oxidation of benzhydrol in oxygen purged acetonitrile. The influence of various parameters, like irradiation time, amount of catalyst, concentration of the catalyst and other factors on the photocatalytic oxidation has been investigated. The proposed mechanism envisages the involvement of a superoxide radical anion.

Investigations on the Radiation Characteristics of Planar Printed UWB Antennas With Modified Ground Planes

A major challenge in the transmission of narrow pulses is the radiation characteristics of the antenna. Designing the front ends for UWB systems pose challenges compared to their narrow and wide band counterparts because in addition to having electrically small size, high efficiency and band width, the antenna has to have excellent transient response. The present work deals with the design of four novel antenna designs- Square Monopole, Semi-Elliptic Slot, Step and Linear Tapered slot - and an assay on their suitability in UWB Systems. Multiple resonances in the geometry are matched to UWB by redesigning the ground-patch interfaces. Techniques to avoid narrow band interference is proposed in the antenna level and their effect on a nano second pulse have also been investigated. The thesis proposes design guidelines to design the antenna on laminates of any permittivity and the analyzes are complete with results in the frequency and time domains.

Investigations on some technologically important polymer nanocomposite films and semi crystalline Polypyrrole films

The present work deals with investigations on some technologically important polymer nanocomposite films and semi crystalline polypyrrole films.The work presented in the thesis deals with the realization of novel polymer nanocomposites with enhanced functionalities and prospects of applications in the fields related to nanophotonics. The development of inorganic/polymer nanocomposites is a rapidly expanding multidisciplinary research area with profound industrial applications. The incorporation of suitable inorganic nanoparticles can endow the resulting nanocomposites with excellent electrical, optical and mechanical properties. The first chapter gives a general introduction to nanotechnology, nanocomposites and conducting polymers. It also emphasizes the significance of ZnO among other semiconductor materials, which forms the inorganic filler in the polymer nanocomposites of the present study. This chapter also gives general ideas on the properties and applications of conducting polymers with special reference to polypyrrole. The objectives of the present investigations are also clearly addressed in this chapter. The second chapter deals with the theoretical aspects and details of all the experimental techniques used in the present work for the synthesis of polymer nanocomposites and polypyrrole samples and their various characterizations. Chapter 3 is based on the preparation and properties of ZnO/Polystyrene nanocomposite film samples. The optical properties of these nanocomoposite films are discussed in detail.Chapter 4 deals with the detailed investigations on the dependence of the optical properties of ZnO/PS nanocomposite films on the size of the nanostructured ZnO filler material. The excellent UV shielding properties of these nanocomposite films form the highlight of this chapter. Chapter 5 gives a detailed analysis of the nonlinear optical properties of ZnO/PS nanocomposite films using Z scan technique. The effect of ZnO particle size in the composite films on the nonlinear properties is discussed. The present study involves two phases of research activities. In the first phase, the linear and nonlinear optical properties of ZnO/polymer nanocomposites are investigated in detail. The second phase of work is centered on the synthesis and related studies on highly crystalline polypyrrole films. In the present study, nanosized ZnO is synthesized using wet chemical method at two different temperatures

Some concepts and models usefulninthe analysis of discrete life time data

This thesis entitled Reliability Modelling and Analysis in Discrete time Some Concepts and Models Useful in the Analysis of discrete life time data.The present study consists of five chapters. In Chapter II we take up the derivation of some general results useful in reliability modelling that involves two component mixtures. Expression for the failure rate, mean residual life and second moment of residual life of the mixture distributions in terms of the corresponding quantities in the component distributions are investigated. Some applications of these results are also pointed out. The role of the geometric,Waring and negative hypergeometric distributions as models of life lengths in the discrete time domain has been discussed already. While describing various reliability characteristics, it was found that they can be often considered as a class. The applicability of these models in single populations naturally extends to the case of populations composed of sub-populations making mixtures of these distributions worth investigating. Accordingly the general properties, various reliability characteristics and characterizations of these models are discussed in chapter III. Inference of parameters in mixture distribution is usually a difficult problem because the mass function of the mixture is a linear function of the component masses that makes manipulation of the likelihood equations, leastsquare function etc and the resulting computations.very difficult. We show that one of our characterizations help in inferring the parameters of the geometric mixture without involving computational hazards. As mentioned in the review of results in the previous sections, partial moments were not studied extensively in literature especially in the case of discrete distributions. Chapters IV and V deal with descending and ascending partial factorial moments. Apart from studying their properties, we prove characterizations of distributions by functional forms of partial moments and establish recurrence relations between successive moments for some well known families. It is further demonstrated that partial moments are equally efficient and convenient compared to many of the conventional tools to resolve practical problems in reliability modelling and analysis. The study concludes by indicating some new problems that surfaced during the course of the present investigation which could be the subject for a future work in this area.

Some characterization problems associated with the bivariate exponential and geometric distributions

It is highly desirable that any multivariate distribution possessescharacteristic properties that are generalisation in some sense of the corresponding results in the univariate case. Therefore it is of interest to examine whether a multivariate distribution can admit such characterizations. In the exponential context, the question to be answered is, in what meaning— ful way can one extend the unique properties in the univariate case in a bivariate set up? Since the lack of memory property is the best studied and most useful property of the exponential law, our first endeavour in the present thesis, is to suitably extend this property and its equivalent forms so as to characterize the Gumbel's bivariate exponential distribution. Though there are many forms of bivariate exponential distributions, a matching interest has not been shown in developing corresponding discrete versions in the form of bivariate geometric distributions. Accordingly, attempt is also made to introduce the geometric version of the Gumbel distribution and examine several of its characteristic properties. A major area where exponential models are successfully applied being reliability theory, we also look into the role of these bivariate laws in that context. The present thesis is organised into five Chapters

Characterization of CNTs and CNTs/MnO2 composite for supercapacitor application

Màster en Nanociència i Nanotecnologia

Almost Self-Centered Median And Chordal Graphs

Almost self-centered graphs were recently introduced as the graphs with exactly two non-central vertices. In this paper we characterize almost selfcentered graphs among median graphs and among chordal graphs. In the first case P4 and the graphs obtained from hypercubes by attaching to them a single leaf are the only such graphs. Among chordal graph the variety of almost self-centered graph is much richer, despite the fact that their diameter is at most 3. We also discuss almost self-centered graphs among partial cubes and among k-chordal graphs, classes of graphs that generalize median and chordal graphs, respectively. Characterizations of almost self-centered graphs among these two classes seem elusive

Identification of models using failure rate and mean residual life of doubly truncated random variables

In this paper, we study the relationship between the failure rate and the mean residual life of doubly truncated random variables. Accordingly, we develop characterizations for exponential, Pareto 11 and beta distributions. Further, we generalize the identities for fire Pearson and the exponential family of distributions given respectively in Nair and Sankaran (1991) and Consul (1995). Applications of these measures in file context of lengthbiased models are also explored

Quantile based entropy function

Quantile functions are efficient and equivalent alternatives to distribution functions in modeling and analysis of statistical data (see Gilchrist, 2000; Nair and Sankaran, 2009). Motivated by this, in the present paper, we introduce a quantile based Shannon entropy function. We also introduce residual entropy function in the quantile setup and study its properties. Unlike the residual entropy function due to Ebrahimi (1996), the residual quantile entropy function determines the quantile density function uniquely through a simple relationship. The measure is used to define two nonparametric classes of distributions

Quantile based entropy function in past lifetime

Di Crescenzo and Longobardi (2002) introduced a measure of uncertainty in past lifetime distributions and studied its relationship with residual entropy function. In the present paper, we introduce a quantile version of the entropy function in past lifetime and study its properties. Unlike the measure of uncertainty given in Di Crescenzo and Longobardi (2002) the proposed measure uniquely determines the underlying probability distribution. The measure is used to study two nonparametric classes of distributions. We prove characterizations theorems for some well known quantile lifetime distributions

Bivariate distributions with weighted marginals and reliablity modelling

In this paper, a family of bivariate distributions whose marginals are weighted distributions in the original variables is studied. The relationship between the failure rates of the derived and original models are obtained. These relationships are used to provide some characterizations of specific bivariate models