Some problems of discrete function theory

An attempt is made by the researcher to establish a theory of discrete functions in the complex plane. Classical analysis q-basic theory, monodiffric theory, preholomorphic theory and q-analytic theory have been utilised to develop concepts like differentiation, integration and special functions.

(1−x)MgAl2O4-xTiO2 dielectrics for microwave and millimeter wave applications

The MgAl2O4 ceramics were prepared by the conventional solid-state ceramic route and the dielectric properties studied in the microwave frequency region (3–13 GHz). The phase purity and crystal structure were identified using the X-ray diffraction technique. The MgAl2O4 spinel ceramics show interesting microwave dielectric properties (εr = 8.75, Qux f = 68 900 GHz (loss tangent = 0.00017 at 12.3 GHz), τf =−75 ppm/◦C). The MgAl2O4 has high negative τf, which precludes its immediate use in practical applications. Hence the microwave dielectric properties of MgAl2O4 spinels were tailored by adding different mole fractions of TiO2. The εr and Q factor of the mixed phases were increased with the molar addition of TiO2 into the spinel to form mixtures based on (1−x)MgAl2O4-xTiO2 (x = 0.0−1.0). For x = 0.25 in (1−x)MgAl2O4-xTiO2, the microwave quality factor reaches a maximum value of Qux f = 105 400 GHz (loss tangent = 0.00007 at 7.5 GHz) where εr and τf are 11.035 and −12 ppm/◦C, respectively. The microwave dielectric properties of the newly developed 0.75MgAl2O4-0.25TiO2 dielectric is superior to several commercially available low loss dielectric substrates.

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.

Studies on the Nature and Chemistry of Sediments and Water of Periyar and Chalakudy Rivers, Kerala, India

The present study is an attempt to address issues related to sediment properties like texture, mineralogy and geochemistry as well as water quality of two important rivers of central Kerala-the Periyar and the Chalakudy rivers. The main objectives of the study are to investigate the textural and mineralogical characteristics as well as transportation and depositional mechanisms of the sediments of Periyar and Chalakudy rivers, to find out the geochemical variability of organic carbon, phosphorus and certain major (Na,K,Ca and Mg) and minor/trace(Mn,Pb,Ni,Cr, and Zn) elements in the bulk sediments and mud fraction of these rivers, to evaluate the status of heavy metal pollution registered in the sediments of these rivers, to assess the physico-chemical characteristics and water quality of Periyar and Chalakudy rivers and to estimate the dissolved nutrient flux through the Periyar and Chalakudy rivers into the receiving coastal waters. The granulometric characteristics as well as statistical parameters of the sediments of Periyar and Chalakudy rivers depend on the flow pattern controlled by the gradient of the terrain. Compared to Periyar, fluctuations in the dispersal of particles are more in Chalakudy river. In Periyar river, the P and Fe in bulk sediments show a positive correlation with C-org, while in Chalakudy river, both the elements are related to THM concentration. In general, C-org, Fe and P Shows an increasing trend downstream. In Periyar river, the P and Fe in bulk sediments show a positive correlation with C-org, while in Chalakudy river, both the elements are related to THM concentration. Among these two rivers, the pollution of water is several fold higher in Periyar river due to influx due to influx of considerable quantity of liquid and solid wastes of industrial/domestic/urban origin. Nutrient analysis reveals 2-3 times increase in N and P during monsoon season whereas SiO2-Si shows a decreasing trend.

The Effect of Glass Additives on the Microwave Dielectric Properties of Ba(Mg 1 /3Ta2/3)03 Ceramics

The effect of glass additives on the densification , phase evolution, microstructure and microwave dielectric properties of Ba(Mg1;3 Ta2i3)03 (BMT) was investigated . Different weight percentages of quenched glass such as B203 , Si02, B203-SiO2, ZnO-B203, 5ZnO-2B2O3, Al203-SiO2, Na20-2B203.10H20, BaO-B203-SiO2, MgO-B203-SiO2, PbO-B203-SiO2 , ZnO-B203-SiO2 and 2MgO-Al203-5SiO2 were added to calcined BMT precursor . The sintering temperature of the glass -added BMT samples were lowered down to 1300 °C compared to solid-state sintering where the temperature was 1650 °C. The formation of high temperature satellite phases such as Ba5Ta4O15 and Ba7Ta6O22 were found to be suppressed by the glass addition . Addition of glass systems such as B203, ZnO-B203, 5ZnO-2B203 and ZnO-B203-SiO2 improved the densification and microwave dielectric properties. Other glasses were found to react with BMT to form low-Q phases which prevented densification . The microwave dielectric properties of undoped BMT with a densification of 93 . 1 % of the theoretical density were Cr = 24 . 8, Tr = 8 ppm/°C and Q„ x f= 80,000 GHz. The BMT doped with 1.0 wt% of B203 has Q„ x f = 124,700GHz, Cr = 24.2, and T f = -1.3 ppm /°C. The unloaded Q factor of 0.2 wt% ZnO-B203-doped BMT was 136,500 GHz while that of 1.0 wt% of 5ZnO-2B203 added ceramic was Q„ x f= 141,800 GHz . The best microwave quality factor was observed for ZnO -B203-SiO2 (ZBS) glass-added ceramics which can act as a perfect liquid-phase medium for the sintering of BMT. The microwave dielectric properties of 0.2wt% ZBS-added BMT dielectric was Q„ x f= 152,800 GHz, F,= 25.5, and Tr = - 1.5 ppm/°C

Nutrient Mobility in Chalakudy River,Typified With Riparian Buffer Zone and Its Adjoining Estuary:Spatiotemporal Manifestation

This study was aimed at to characterize the spatio-temporal trends in the distributional characteristics of various species of nitrogen and phosphorus as well as to elucidate the factors and processes aflecting these nutrients in the dissolved, particulate and sedimentary phases of a river estuarine system. The main area of study is Chalakudy river in Kerala, which is a fresh water system originating from Anamalai hills and ending at Arabian Sea. Its basin is between I00 05 ’ to I00 35’ North latitude and 76” 15 ’ to 760 55’ East longitude. Being a riparian bufler zone, the dynamics of nutrient mobility tend to be more complex and variable in this river-estuarine system.The diflerent species of nitrogen estimated from the filtrate were nitrite-N, nitrateN, ammonia-N, urea-N, total nitrogen and residual nitrogen. The diflerent forms of phosphorus estimated from the filtrate were phosphate-P, total-P and residualP. Pre weighed sediments as well as particulate matter were analysed for quantijying nitrite-N, nitrate-N, ammonia-N and urea-N. Total nitrogen was estimated after digestion with potassium persulfate. Fractionation of phosphorus in sediment/particulate matter was performed by applying sequential extraction procedure. The dijferent forms of phosphorus thus estimated were loosely bound (exchangeable) P, Fe/Al bound P, polyphosphates, Ca bound P and refractory P. Sedimental total P was also measured directly by applying digestion method.The analyses carried out in this bimonthly annual survey have revealed specific information on the latent factors influencing the water quality pattern ofthe river. There was dependence among the chemical components of the river sediment and suspended matter, reflecting the water quality. A period of profound environmental change occurred and changes in various species had been noted in association with seasonal variations in the waterway, especially following enhanced river runoff during the monsoon. The results also successfully represented the distribution trend of nutrients during the rainy as well as dry season. Thus, the information gathered in this work will also be beneficial for those interested or involved in river management, conservation, regulation and policy making in regional and national levels.

Analysis discrete function theory

There is a recent trend to describe physical phenomena without the use of infinitesimals or infinites. This has been accomplished replacing differential calculus by the finite difference theory. Discrete function theory was first introduced in l94l. This theory is concerned with a study of functions defined on a discrete set of points in the complex plane. The theory was extensively developed for functions defined on a Gaussian lattice. In 1972 a very suitable lattice H: {Ci qmxO,I qnyo), X0) 0, X3) 0, O < q < l, m, n 5 Z} was found and discrete analytic function theory was developed. Very recently some work has been done in discrete monodiffric function theory for functions defined on H. The theory of pseudoanalytic functions is a generalisation of the theory of analytic functions. When the generator becomes the identity, ie., (l, i) the theory of pseudoanalytic functions reduces to the theory of analytic functions. Theugh the theory of pseudoanalytic functions plays an important role in analysis, no discrete theory is available in literature. This thesis is an attempt in that direction. A discrete pseudoanalytic theory is derived for functions defined on H.

" Studies on Laser induced Phatothermal Phenomena in Selected Organic Compounds and Fullerenes"

In the pre—laser era it was difficult to believe that the optical properties of a medium depend upon the intensity of the radiation incident on it. The basis for this conclusion is that the electric field strength associated with the conventional light sources used before the advent of lasers was much smaller than (103 V/cm) the field sttrengths of atomic or interatomic fields (2 107 —- 10” V/cm). The radiation with such low intensity is not able to affect atomic fields to the extent of changing optical parameters. The invention of laser in 1960 was a turning point. The high degree of coherence of the laser radiation provides high spatial concentration of optical power. With the availability of the femtosecond lasers it has become possible to get extremely high peak powers 2 1013 W/cmz). At such high fields, the relationship between electric ‘polarization P and the electric field strength E ceases to be linear and several nonlinear effects begin to occur. Nonlinear absorption, a branch of nonlinear optics, refers to the interaction between radiation and matter accompanied by absorption of more than one photon. Nonlinear absorption has acquired great importance after the invention of high power lasers. One of the objectives of the present work is to investigate the nonlinear absorption processes occurring in fullerene, selected organic solvents and laser dyes. Fullerenes and laser dyes were chosen because of their highly nonlinear behaviour. Fullerenes, the most beautiful among molecules, offer fascinating field of research owinglto their significant structural properties. As toluene, benzene and carbon disulphide are themost widely used solvents for fullerenes, it seems important to study the nonlinear properties of these liquids as well. Like fullerenes, laser dyes also possess highly delocalized 7r electrons which are responsible for their nonlinear absorption. Dye lasers were the fulfillment of an experimenter’s pipe dream - to have a laser that is easily tunable over a wide range of wavelengths. A better understandingof the photophysical properties of laser dyes can significantly enhance the development and technology of dye lasers. We studied the nonlinear absorption properties of two rhodamine dyes to have some insight into their nonlinear optical properties.

Fabrication of a quantum well heterostructure based on plasma polymerized aniline and its characterization using STM/STS

Two-dimensional electronic systems play a crucial role in modern electronics and offer a multitude of opportunities to study the fundamental phenomena at low dimensional physics. A quantum well heterostructure based on polyaniline (P) and iodine doped polyaniline (I) thin films were fabricated using radio frequency plasma polymerization on indium tin oxide coated glass plate. Scanning probe microscopy and scanning electron microscopy studies were employed to study the morphology and roughness of the polymer thin films. Local electronic density of states (LDOS) of the P–I–P heterostructures is probed using scanning tunnelling spectroscopy (STS). A step like LDOS is observed in the P–I–P heterostructure and is attributed to the quantum well confinement of electrons in the polymer heterostructure.

The Ratios of Carbon, Nitrogen, and Phosphorus in a Wetland Coastal Ecosystem of Southern India

The fertility of the coastal and estuarine waters is of great concern because of its influence on the productivity of these waters. Seasonal variations in the distribution of organic carbon, total nitrogen and total phosphorus in the sediments of Kuttanad Waters, a part of the tropical Cochin Estuary on the south west coast of India, are examined to identify the contribution of sediments to the fertility of the aquatic systems. The adjoining region has considerable agricultural activity. The fresh water zones had higher quantities of silt and clay whereas the estuarine zone was more sandy. Organic carbon, total phosphorus and total nitrogen were higher in the fresh water zones and lower in the estuarine zones. Total phosphorus and organic carbon showed the lowest values during monsoon periods. No significant trends were observed in the seasonal distributions of total nitrogen. Ratios of C/N, C/P and N/P, and the phosphorus and nitrogen content indicate significant modification in the character of the organic matter. Substantial amounts of the organic matter can contribute to reducing conditions and modify diagenetic processes