A Study of Elementary Operators

Department of Mathematics, Cochin University of Science and Technology

Investigations on the Radiation Characteristics of Broadband Strip Loaded Slotted Microstrip Antennas

With the recent progress and rapid increase in mobile terminals, the design of antennas for small mobile terminals is acquiring great importance. In view of this situation, several design concepts are already been addressed by the scientists and engineers. Compactness and efficiency are the major criteria for mobile terminal antennas. The challenging task of the microwave scientists and engineers is to device compact printed radiating systems having broadband behavior, together with good efficiency. Printed antenna technology has received popularity among antenna scientists after the introduction of microstrip antenna in 1970s. The successors in this kind such as printed monopoles and planar inverted F are also equally important. Scientists and Engineers are trying to explore this technology as a viable coast effective solution for forthcoming microwave revolution. The transmission line perspectives of antennas are very interesting. The concept behind any electromagnetic radiator is simple. Any electromagnetic system with a discontinuity is radiating electromagnetic energy. The size, shape and the orientation of the discontinuities controls the radiation characteristics of the system such as radiation pattern, gain, polarization etc. It can be either resonant or non resonant structure. Microstrip antennas are suitable for wireless applications due to their low cost, high gain and ease of fabrication. But the major disadvantage of micro strip antennas is their inherent narrow bandwidth. A lot of techniques are introduced by the researchers all over the world to enhance the bandwidth of micro strip patch antennas. The thesis addresses an attempt to enhance the bandwidth of micro strip patch antennas by incorporating impedance matching strip as a part of the micro strip patch antenna. The first part of the thesis deals with the broadband operation of the tilted square slot and polygonal slot loaded square micro strip patch antennas. The resonant mechanisms are clearly mentioned using the simulation and experimental studies. The bandwidth of the polygonal slotted broadband patch antenna is again enhanced by implementing an Lstrip feed mechanism. In the second major part of the thesis, a novel gain enhancement technique for single band and broadband square micro strip patch antennas is achieved by implementing offset stacked configurations.

Development and Investigations of Mobile Antennas for less Radiation Hazards

Antennas, the key element in wireless communication devices had undergone amazing developments especially in the direction of compactness and safety aspects. In the last two decades, the use of the cellular phones has become the most popular mode of communication across the globe. At the same time, the concerns about the radiation effects have increased in the general public. The main concern of this thesis is to develop a mobile antenna which gives reduced RF interference to the user. The reduction of the power absorbed by the user can tremendously avoid any possible health hazards. The radiation characteristic of a monopole antenna is modified with good radiation characteristics suitable for a mobile handset. The modification is implemented by using different resonating structures which provides reduced radiation along one direction. The direction of less radiation can be changed by modifying the planar antenna structure to a ground folded antenna. This modified structure with excellent radiation characteristic is suitable for modern wireless handheld devices with less user RF interference. Specific Absorption Rate (SAR) is an important parameter for mobile handset. The SAR is estimated for the newly developed antenna for different conditions and discussed in this thesis.

“Design and Development of Coplanar Strip Fed Planar Antennas”

With the recent progress and rapid increase in the field of communication, the designs of antennas for small mobile terminals with enhanced radiation characteristics are acquiring great importance. Compactness, efficiency, high data rate capacity etc. are the major criteria for the new generation antennas. The challenging task of the microwave scientists and engineers is to design a compact printed radiating structure having broadband behavior along with good efficiency and enhanced gain. Printed antenna technology has received popularity among antenna scientists after the introduction of planar transmission lines in mid-seventies. When we view the antenna through a transmission line concept, the mechanism behind any electromagnetic radiator is quite simple and interesting. Any electromagnetic system with a discontinuity is radiating electromagnetic energy. The size, shape and orientation of the discontinuities control the radiation characteristics of the system such as radiation pattern, gain, polarization etc. It can be either resonant or non-resonant. This thesis deals with antennas that are developed from a class of transmission lines known as coplanar strip-CPS, a planar analogy of parallel pair transmission line. The specialty of CPS is its symmetric structure compared to other transmission lines, which makes the antenna structures developed from CPS quite simple for design and fabrication. The structural modifications on either metallic strip of CPS results in different antennas. The first part of the thesis discusses a single band and dual band design derived from open ended slot lines which are very much suitable for 2.4 and 5.2 GHz WLAN applications. The second section of the study is vectored into the development of enhanced gain dipoles. A single band dipole and a wide band enhanced gain dipole suitable for 5.2/5.8 GHZ band and imaging applications are developed and discussed. Last part of the thesis discusses the development of directional UWBs. Three different types of ultra-compact UWBs are developed and almost all the frequency domain and time domain analysis of the structures are discussed.

Design Of Compact Microstrip Antennas Using A Modified Ground Plane

A method for simultaneously enhancing the bandwidth and reducing the size of microstrip antennas (MSAs) using a modified ground plane (GP) has been proposed with design formulas. A combshaped truncated GP is used for this purpose. This method provides an overall compactness up to 85% for proximity-coupled MSAs in the frequency range of 900 MHz–5.5 GHz with an improvement inbandwidth up to seven times when compared with the conventional ones

Informality in the City: a Theoretical Analysis

This thesis theoretically studies the relationship between the informal sector (both in the labor and the housing market) and the city structure.

Toeplitz operators with distributional symbols on Bergman spaces

We study the boundedness and compactness of Toeplitz operators Ta on Bergman spaces , 1 < p < ∞. The novelty is that we allow distributional symbols. It turns out that the belonging of the symbol to a weighted Sobolev space of negative order is sufficient for the boundedness of Ta. We show the natural relation of the hyperbolic geometry of the disc and the order of the distribution. A corresponding sufficient condition for the compactness is also derived.

New results and open problems on Toeplitz operators in Bergman spaces

We discuss some of the recent progress in the field of Toeplitz operators acting on Bergman spaces of the unit disk, formulate some new results, and describe a list of open problems -- concerning boundedness, compactness and Fredholm properties -- which was presented at the conference "Recent Advances in Function Related Operator Theory'' in Puerto Rico in March 2010.

Spectral theory of Toeplitz and Hankel operators on the Bergman space A1

The Fredholm properties of Toeplitz operators on the Bergman space A2 have been well-known for continuous symbols since the 1970s. We investigate the case p=1 with continuous symbols under a mild additional condition, namely that of the logarithmic vanishing mean oscillation in the Bergman metric. Most differences are related to boundedness properties of Toeplitz operators acting on Ap that arise when we no longer have 1compactness of Hankel operators on A1.

Hankel operators on Fock spaces

We study Hankel operators on the weighted Fock spaces Fp. The boundedness and compactness of these operators are characterized in terms of BMO and VMO, respectively. Along the way, we also study Berezin transform and harmonic conjugates on the plane. Our results are analogous to Zhu's characterization of bounded and compact Hankel operators on Bergman spaces of the unit disk.

O_3-N_2O correlations from the Atmospheric Chemistry Experiment: revisiting a diagnostic of transport and chemistry in the stratosphere

Our knowledge of stratospheric O3-N2O correlations is extended, and their potential for model-measurement comparison assessed, using data from the Atmospheric Chemistry Experiment (ACE) satellite and the Canadian Middle Atmosphere Model (CMAM). ACE provides the first comprehensive data set for the investigation of interhemispheric, interseasonal, and height-resolved differences of the O_3-N_2O correlation structure. By subsampling the CMAM data, the representativeness of the ACE data is evaluated. In the middle stratosphere, where the correlations are not compact and therefore mainly reflect the data sampling, joint probability density functions provide a detailed picture of key aspects of transport and mixing, but also trace polar ozone loss. CMAM captures these important features, but exhibits a displacement of the tropical pipe into the Southern Hemisphere (SH). Below about 21 km, the ACE data generally confirm the compactness of the correlations, although chemical ozone loss tends to destroy the compactness during late winter/spring, especially in the SH. This allows a quantitative comparison of the correlation slopes in the lower and lowermost stratosphere (LMS), which exhibit distinct seasonal cycles that reveal the different balances between diabatic descent and horizontal mixing in these two regions in the Northern Hemisphere (NH), reconciling differences found in aircraft measurements, and the strong role of chemical ozone loss in the SH. The seasonal cycles are qualitatively well reproduced by CMAM, although their amplitude is too weak in the NH LMS. The correlation slopes allow a "chemical" definition of the LMS, which is found to vary substantially in vertical extent with season.

Correlations of long-lived chemical species in a middle atmosphere general circulation model

Correlations between various chemical species simulated by the Canadian Middle Atmosphere Model, a general circulation model with fully interactive chemistry, are considered in order to investigate the general conditions under which compact correlations can be expected to form. At the same time, the analysis serves to validate the model. The results are compared to previous work on this subject, both from theoretical studies and from atmospheric measurements made from space and from aircraft. The results highlight the importance of having a data set with good spatial coverage when working with correlations and provide a background against which the compactness of correlations obtained from atmospheric measurements can be confirmed. It is shown that for long-lived species, distinct correlations are found in the model in the tropics, the extratropics, and the Antarctic winter vortex. Under these conditions, sparse sampling such as arises from occultation instruments is nevertheless suitable to define a chemical correlation within each region even from a single day of measurements, provided a sufficient range of mixing ratio values is sampled. In practice, this means a large vertical extent, though the requirements are less stringent at more poleward latitudes.

Nanostructures in the terahertz range

With advances in technology, terahertz imaging and spectroscopy are beginning to move out of the laboratory and find applications in areas as diverse as security screening, medicine, art conservation and field archaeology. Nevertheless, there is still a need to improve upon the performance of existing terahertz systems to achieve greater compactness and robustness, enhanced spatial resolution, more rapid data acquisition times and operation at greater standoff distances. This chapter will review recent technological developments in this direction that make use of nanostructures in the generation, detection and manipulation of terahertz radiation. The chapter will also explain how terahertz spectroscopy can be used as a tool to characterize the ultrafast carrier dynamics of nanomaterials.

Evidence for the conspecificity of Palisada papillosa with P. perforata (Ceramiales, Rhodophyta) from the western and eastern Atlantic Ocean on the basis of morphological and molecular analyses

Morphological and molecular studies were carried out on Palisada papillosa and P. perforata from the Canary Islands (type locality of P. perforata), Mexico and Brazil. The two species have been distinguished by features of their external morphology such as size and degree of compactness of the thalli, presence or absence of arcuate branches, branching pattern and basal system. A detailed morphological comparison between these taxa showed that none of the vegetative anatomical or reproductive characters was sufficient to separate these species. The presence or absence of cortical cells in a palisade-like arrangement, also previously used to. distinguish these species, is not applicable. The species present all characters typical of the genus, and both share production of the first pericentral cell underneath the basal cell of the trichoblast, production of two fertile pericentral cells (the second and the third additional, the first remaining sterile), spermatangial branches produced from one of two laterals on the suprabasal cell of trichoblasts, and the procarpbearing segment with four pericentral cells. Details of the procarp are described for the species for the first time. The phylogenetic position of these species was inferred by analysis of the chloroplast-encoded rbcL gene sequences from 39 taxa, using one other Rhodomelacean taxon and two Ceramiaceae as outgroups. Relationships within the clade formed by P. papillosa and P. perforata have not been resolved due to the low level of genetic variation in their rbcL sequences (0-0.4%). Considering this and the morphological similarities, we conclude that P. papillosa is a taxonomic synonym of P. perforata. The phylogenetic analyses also supported the nomenclatural transfer of two species of Chondrophycus to Palisada, namely, P. patentiramea (Montagne) Cassano, Senties, Gil-Rodriguez & M.T. Fujii comb. nov. and P. thuyoides (Kutzing) Cassano, Senties, Gil-Rodriguez & M.T. Fujii comb. nov.

Quality indices for (practical) clustering evaluation

Clustering quality or validation indices allow the evaluation of the quality of clustering in order to support the selection of a specific partition or clustering structure in its natural unsupervised environment, where the real solution is unknown or not available. In this paper, we investigate the use of quality indices mostly based on the concepts of clusters` compactness and separation, for the evaluation of clustering results (partitions in particular). This work intends to offer a general perspective regarding the appropriate use of quality indices for the purpose of clustering evaluation. After presenting some commonly used indices, as well as indices recently proposed in the literature, key issues regarding the practical use of quality indices are addressed. A general methodological approach is presented which considers the identification of appropriate indices thresholds. This general approach is compared with the simple use of quality indices for evaluating a clustering solution.