Indian Mathematics Related to Architecture and Other Areas With Special Reference to Kerala

Department of Mathematics, Cochin University of Science and Technology

A compact dual-band modified T-shaped CPW-fed monopole antenna

A compact, dual band coplanar waveguide fed modified T-shaped uniplanar antenna is presented. The antenna has resonances at 1.77 and 5.54 GHz with a wide band from 1.47–1.97 GHz and from 5.13–6.48 GHz with an impedance bandwidth of 34% and 26%, respectively. Also the antenna has an average gain of 3 dBi in lower band and 3.5 dBi in higher band with an average efficiency of 90%.

Catalysis by Transition Metal Modified Ceria and Ceria-Zirconia Mixed Oxides Prepared via Sol-Gel Route

The aim of catalysis research is to apply the catalyst successfully in economically important reactions in an environmentally friendly way. The present work focuses on the modification of structural and surface properties of ceria and ceria-zirconia catalysts by the incorporation of transition metals. The applications of these catalysts in industrially important reactions like ethylbenzene oxidation, alkylation of aromatics are also investigated.Sol-gel method is effective for the preparation of transition metal modified ceria and ceria-zirconia mixed oxide since it produces catalyst with highly dispersed incorporated metal. Unlike that of impregnation method plugging of pores is not prominent for sol-gel derived catalyst materials. This prevents loss of surface area on metal modification as evident for BET surface area measurements.The powder X-ray diffraction analysis confirms the cubic structure of transition metal modified ceria and ceria-zirconia catalysts. The thermal stability is evident from TGA/DTA analysis. DR UV-vis spectra provide information on the coordination environment of the incorporated metal. EPR analysis ofCr, Mn and Cu modified ceria and a ceria-zirconia catalyst reveals the presence of different oxidation states of incorporated metal.Temperature programmed desorption of ammonia and thermogravimetric desorption of 2,6-dimethyl pyridine confirms the enhancement of acidity on metal incorporation. High a-methyl styrene selectivity in cumene cracking reaction implies the presence of comparatively more number of Lewis acid sites with some amount of Bronsted acid sites. The formation of cyclohexanone during cyclohexanol decomposition confirms the presence of basic sites on the catalyst surface.Mn and Cr modified catalysts show better activity towards ethylbenzene oxidation. A redox mechanism through oxometal pathway is suggested.All the catalysts were found to be active towards benzylation of toluene and a-xylene. The selectivity towards monoalkylated products remains almost 100%. The catalytic activity is correlated with the Lewis acidity of the prepared systems.The activity of the catalysts towards methylation of phenols depends on the strength acid sites as well as the redox properties of the catalysts. A strong dependence of methylation activity on the total acidity is illustrated.

Organic Reactions Catalysed by Modified Clays

Department of Applied Chemistry, Cochin University of Science and Technology

Modeling and Analysis of Some Heavy Tailed Time Series

The thesis has covered various aspects of modeling and analysis of finite mean time series with symmetric stable distributed innovations. Time series analysis based on Box and Jenkins methods are the most popular approaches where the models are linear and errors are Gaussian. We highlighted the limitations of classical time series analysis tools and explored some generalized tools and organized the approach parallel to the classical set up. In the present thesis we mainly studied the estimation and prediction of signal plus noise model. Here we assumed the signal and noise follow some models with symmetric stable innovations.We start the thesis with some motivating examples and application areas of alpha stable time series models. Classical time series analysis and corresponding theories based on finite variance models are extensively discussed in second chapter. We also surveyed the existing theories and methods correspond to infinite variance models in the same chapter. We present a linear filtering method for computing the filter weights assigned to the observation for estimating unobserved signal under general noisy environment in third chapter. Here we consider both the signal and the noise as stationary processes with infinite variance innovations. We derived semi infinite, double infinite and asymmetric signal extraction filters based on minimum dispersion criteria. Finite length filters based on Kalman-Levy filters are developed and identified the pattern of the filter weights. Simulation studies show that the proposed methods are competent enough in signal extraction for processes with infinite variance.Parameter estimation of autoregressive signals observed in a symmetric stable noise environment is discussed in fourth chapter. Here we used higher order Yule-Walker type estimation using auto-covariation function and exemplify the methods by simulation and application to Sea surface temperature data. We increased the number of Yule-Walker equations and proposed a ordinary least square estimate to the autoregressive parameters. Singularity problem of the auto-covariation matrix is addressed and derived a modified version of the Generalized Yule-Walker method using singular value decomposition.In fifth chapter of the thesis we introduced partial covariation function as a tool for stable time series analysis where covariance or partial covariance is ill defined. Asymptotic results of the partial auto-covariation is studied and its application in model identification of stable auto-regressive models are discussed. We generalize the Durbin-Levinson algorithm to include infinite variance models in terms of partial auto-covariation function and introduce a new information criteria for consistent order estimation of stable autoregressive model.In chapter six we explore the application of the techniques discussed in the previous chapter in signal processing. Frequency estimation of sinusoidal signal observed in symmetric stable noisy environment is discussed in this context. Here we introduced a parametric spectrum analysis and frequency estimate using power transfer function. Estimate of the power transfer function is obtained using the modified generalized Yule-Walker approach. Another important problem in statistical signal processing is to identify the number of sinusoidal components in an observed signal. We used a modified version of the proposed information criteria for this purpose.

Studies on Catalysis by Ordered Mesoporous SBA-15 Materials Modified with Transition Metals

To meet the challenges related to the chemical industry,development of efficient catalysts is necessary.The mesoporous materials like SBA-15 are considered as good catalyst candidates of 21st century.SBA-15 mesoporous materials are catalytically inactive,but allow the dispersion of catalytically active phases into the framework.So these materials can be considered as an interesting alternative for preparing catalytically active metal nanoparticles in-situ into it.In the present work various transition metals are incorporated to improve the catalytic activity of SBA-15 material.The fundamental aspects of the preparation,characterization and the activity studies are briefly viewed in this thesis. Systematic investigation of the physico-chemical properties and catalytic activity studies of the prepared materials were carried out and presented in this Study.

Studies on Photocatalysis by Nano Titania Modified with Non-Metals

The present work aims to prepare visible light responsive anion doped titania via sol-gel precipitation method.The prepared catalysts were characterized by various techniques.The photocatalytic abilities of the prepared catalysts were measured by the degradation of dyes,pesticides,hydrogen production through water splitting reaction and antibacterial study.We also compared the activities of prepared catalysts with pure titania prepared in the laboratory and one of the commercial anatase titania samples.

Development of Electrochemical Sensors for Various Pharmaceuticals

The development of electrochemical sensors is currently one of the active areas of research in analytical chemistry.Voltammetric sensors as an important class of electrochemical sensors are extensively used in pharmaceutical applications.In voltammetric analysis,many active compounds in dosage forms,in contrast to excipients,can be readily oxidised or reduced at the electrode surface by applying a potential.Chemically modified electrodes have great significance in the electrochemical determination of pharmaceuticals.The modification of electrode results in efficient determination of electroactive species at very lower potential without any major interferences.The present study involves the fabrication of 8 voltammetric sensors for the drugs Metronidazole Benzoate, Sulfamethoxazole, Acyclovir, Pam Chloride , Trimethoprim , Tamsulosin Hydrochloride and Ceftriaxone Sodium.Two sensors were developed for the drug tamsulosin hydrochloride while one sensor each was developed for the other drugs.

Polypropylene/metal oxide nanocomposites: fiber spinning and evaluation”

PP has been getting much attention over the years because it is a very durable polymer commonly used in aggressive environments including automotive battery casings, fuel containers etc. They are used to make bottles, fibers for clothing, components in cars etc. However, it has some shortcomings such as low dimensional and thermal stability. Materials such as metal oxides with sizes of the order 1–50 nm have received a great deal of attention because of their versatile applications in polymer/ inorganic nanocomposites, optoelectronic devices, biomedical materials, and other areas. They are stable under harsh process conditions and also regarded as safe materials to human beings and animals. In the present investigation, PP is modified by incorporating metal oxide nanoparticles such as ZnO and TiO2 by simple melt mixing method. Melt spinning method was used to prepare PP/metal oxide nanocomposite fibers. Various studies have been carried out on these composites and fibers. In the first part of the study, ZnO nanoparticles were prepared from ZnCl2 and NaOH in presence of chitosan, PVA, ethanol and starch. This is a simple and inexpensive method compared to other methods. Change in morphology and particle size of ZnO were studied. Least particle size was obtained in chitosan medium. The particles were characterized by using XRD, SEM, TEM, TGA and EDAX. Antibacterial properties of ZnO prepared in chitosan medium (NZO) and commercial zinc oxide (CZO) were evaluated using a gram positive and a gram negative bacteria

Studies on integrability of some perturbed nonlinear evolution equations

Usually typical dynamical systems are non integrable. But few systems of practical interest are integrable. The soliton concept is a sophisticated mathematical construct based on the integrability of a class ol' nonlinear differential equations. An important feature in the clevelopment. of the theory of solitons and of complete integrability has been the interplay between mathematics and physics. Every integrable system has a lo11g list of special properties that hold for integrable equations and only for them. Actually there is no specific definition for integrability that is suitable for all cases. .There exist several integrable partial clillerential equations( pdes) which can be derived using physically meaningful asymptotic teclmiques from a very large class of pdes. It has been established that many 110nlinear wa.ve equations have solutions of the soliton type and the theory of solitons has found applications in many areas of science. Among these, well-known equations are Korteweg de-Vries(KdV), modified KclV, Nonlinear Schr6dinger(NLS), sine Gordon(SG) etc..These are completely integrable systems. Since a small change in the governing nonlinear prle may cause the destruction of the integrability of the system, it is interesting to study the effect of small perturbations in these equations. This is the motivation of the present work.

Hydrogeological, Geophysical And Geochemical Studies In Parts Of Coastal And Midland Areas, Central Kerala - A Gis Approach

The present study deals with the different hydrogeological characteristics of the coastal region of central Kerala and a comparative analysis with corresponding hard rock terrain. The coastal regions lie in areas where the aquifer systems discharge groundwater ultimately into the sea. Groundwater development in such regions will require a precise understanding of the complex mechanism of the saline and fresh water relationship, so that the withdrawals are so regulated as to avoid situations leading to upcoming of the saline groundwater bodies as also to prevent migration of sea water ingress further inland. Coastal tracts of Kerala are formed by several drainage systems. Thick pile of semi-consolidated and consolidated sediments from Tertiary to Recent age underlies it. These sediments comprise phreatic and confined aquifer systems. The corresponding hard rock terrain is encountered with laterites and underlined by the Precambrian metamorphic rocks. Supply of water from hard rock terrain is rather limited. This may be due to the small pore size, low degree of interconnectivity and low extent of weathering of the country rocks. The groundwater storage is mostly controlled by the thickness and hydrological properties of the weathered zone and the aquifer geometry. The over exploitation of groundwater, beyond the ‘safe yield’ limit, cause undesirable effects like continuous reduction in groundwater levels, reduction in river flows, reduction in wetland surface, degradation of groundwater quality and many other environmental problems like drought, famine etc.

Studies on Catalysis by Nano Titania Modified with Metals and Nonmetals

Semiconductor photocatalysis has received much attention during last three decades as a promising solution for both energy generation and environmental problems. Heterogeneous photocatalytic oxidation allows the degradation of organic compounds into carbon dioxide and water in the presence of a semiconductor catalyst and UV light source. The •OH radicals formed during the photocatalytic processes are powerful oxidizing agents and can mineralise a number of organic contaminants. Titanium dioxide (TiO2), due to its chemical stability, non-toxicity and low cost represents one of the most efficient photocatalyst. However, only the ultraviolet fraction of the solar radiation is active in the photoexcitation processes using pure TiO2 and although, TiO2 can treat a wide range of organic pollutants the effectiveness of the process for pollution abatement is still low. A more effective and efficient catalyst therefore must be formulated. Doping of TiO2 was considered with the aim of improving photocatalytic properties. In this study TiO2 catalyst was prepared using the sol-gel method. Metal and nonmetal doped TiO2 catalysts were prepared. The photoactivity of the catalyst was evaluated by the photodegradation of different dyes and pesticides in aqueous solution. High photocatalytic degradation of all the pollutants was observed with doped TiO2. Structural and optical properties of the catalysts were characterized using XRD, BET surface area, UV-Vis. DRS, CHNS analysis, SEM, EDX, TEM, XPS, FTIR and TG. All the catalysts showed the anatase phase. The presence of dopants shifts the absorption of TiO2 into the visible region indicating the possibility of using visible light for photocatalytic processes.

Assessment of Water Quality along the Coastal Areas of Kerala: A Study of the Tsunami Impact on Groundwater

Everywhere, on the coastal belt it is proved without doubt that the pristine ground water quality was severely deteriorated after the 26 December 2004 Indian Ocean Tsunami. But how far is more relevant, as it is decided by the so-called pre-tsunamic situation of the region. In water quality studies it is this reference finger print which earmarks regional ground water chemistry based on which the monthly variability could rationally be interpreted. This Ph D thesis comprises the testing and evaluation of the facts: whether there is any significant difference in the water quality parameters under study between stations and between months in Tsunami Affected Dug Wells (TADW). Whether the selected water quality parameters vary significantly from BIS and WHO standards. Whether the water quality index (WQI) differ significantly between Tsunami Affected Dug Wells (TADW) and Bore Wells (BW). Whether there is any significant difference in the water quality parameters during December 2005 and December 2008. Is there any significant change in the Water Quality Parameters before 2001 and after tsunami (2005) in TADW.

Modified Block Adaptive Predictive Coder For Speech Processing

This thesis investigated the potential use of Linear Predictive Coding in speech communication applications. A Modified Block Adaptive Predictive Coder is developed, which reduces the computational burden and complexity without sacrificing the speech quality, as compared to the conventional adaptive predictive coding (APC) system. For this, changes in the evaluation methods have been evolved. This method is as different from the usual APC system in that the difference between the true and the predicted value is not transmitted. This allows the replacement of the high order predictor in the transmitter section of a predictive coding system, by a simple delay unit, which makes the transmitter quite simple. Also, the block length used in the processing of the speech signal is adjusted relative to the pitch period of the signal being processed rather than choosing a constant length as hitherto done by other researchers. The efficiency of the newly proposed coder has been supported with results of computer simulation using real speech data. Three methods for voiced/unvoiced/silent/transition classification have been presented. The first one is based on energy, zerocrossing rate and the periodicity of the waveform. The second method uses normalised correlation coefficient as the main parameter, while the third method utilizes a pitch-dependent correlation factor. The third algorithm which gives the minimum error probability has been chosen in a later chapter to design the modified coder The thesis also presents a comparazive study beh-cm the autocorrelation and the covariance methods used in the evaluaiicn of the predictor parameters. It has been proved that the azztocorrelation method is superior to the covariance method with respect to the filter stabf-it)‘ and also in an SNR sense, though the increase in gain is only small. The Modified Block Adaptive Coder applies a switching from pitch precitzion to spectrum prediction when the speech segment changes from a voiced or transition region to an unvoiced region. The experiments cont;-:ted in coding, transmission and simulation, used speech samples from .\£=_‘ajr2_1a:r1 and English phrases. Proposal for a speaker reecgnifion syste: and a phoneme identification system has also been outlized towards the end of the thesis.

“Catalysis by Nanocrystalline Ceria Modified with Transition Metals”

The objective of the present work is to improve the textural and structural properties of cerium oxide by the incorporation of transition metals as well as sulphate ions. We have incorporated tungsten, molybdenum and chromium oxide into pure as well as sulphated cerium oxide and the catalytic systems thus prepared were characterised using various techniques. lndustrially important reactions such as acetalization and deacetalization, oxidative dehydrogenation of ethylbenzene, MTBE synthesis and Beckmann rearrangement of cinnamaldoxime and salicylaldoxime have been selected for the measurement of the catalytic activity of the systems. The work is presented in eight chapters