Stochastic processes and their applications time dependent solutions for some queueing and inventory models

The objective of this thesis is to study the time dependent behaviour of some complex queueing and inventory models. It contains a detailed analysis of the basic stochastic processes underlying these models. In the theory of queues, analysis of time dependent behaviour is an area.very little developed compared to steady state theory. Tine dependence seems certainly worth studying from an application point of view but unfortunately, the analytic difficulties are considerable. Glosod form solutions are complicated even for such simple models as M/M /1. Outside M/>M/1, time dependent solutions have been found only in special cases and involve most often double transforms which provide very little insight into the behaviour of the queueing systems themselves. In inventory theory also There is not much results available giving the time dependent solution of the system size probabilities. Our emphasis is on explicit results free from all types of transforms and the method used may be of special interest to a wide variety of problems having regenerative structure.

Significance of Time Scales in Nonlinear Dynamical Analysis of Electroencephalogram Signals

We propose to show in this paper, that the time series obtained from biological systems such as human brain are invariably nonstationary because of different time scales involved in the dynamical process. This makes the invariant parameters time dependent. We made a global analysis of the EEG data obtained from the eight locations on the skull space and studied simultaneously the dynamical characteristics from various parts of the brain. We have proved that the dynamical parameters are sensitive to the time scales and hence in the study of brain one must identify all relevant time scales involved in the process to get an insight in the working of brain.

Activation of Progesterone Receptor by ATP

Progesterone-receptor complex from freshly prepared hen oviduct cytosol acquired the ability to bind to isolated nuclei, DNA-cellulose and ATP-Sepharose when incubated with 5-10 mM ATP at 4°C. The extent of this ATP-dependent activation was higher when compared with heat-activation achieved by warming the progesterone- receptor complex at 23 °C. The transformation of progesterone-receptor complex which occurred in a time-dependent manner was only partially dependent on hormone presence. The ATP effect was selective in causing this transformation whereas ADP, AMP and cAMP failed to show any such effect. The non-hydrolizable analogs of ATP, adenosine 5'-[a,/3-methylene]triphosphate and adenosine 5-[/l,y-imido]triphosphate were also found to be ineffective. Presence of 10 mM sodium molybdate blocked both the ATP and the heat-activation of progesterone-receptor complex. Mn" or Mg` had no detectable effect on the receptor activation but the presence of Ca" increased the extent of ATP-activation slightly. EDTA presence (> 5 mM) decreased the extent of receptor activation by about 40 % and was, therefore, not included in the buffers used for activation studies. Divalent cations were also ineffective when tested in the presence of 1- 5 mM EDTA. The properties of progesterone-receptor complex remained intact under the above conditions when analyzed for steroid-binding specificity and Scatchard analysis. However, the ATP-activated progesterone-receptor complex lost the ability to aggregate when tested on low-salt sucrose gradients. ATP was equally effective in activating the rat-uterine estradiol-receptor complex at 4 "C and influenced the transformation of 4-S receptor form into a 5-S form when analyzed on sucrose gradients containing 0.3 M KCI. The presence of ATP also increased the rate of activation of progesterone-receptor complex at 23 °C. These findings suggest a role for ATP in receptor function and offer a convenient method of studying the process of receptor activation at low temperature and mild assay conditions.

Structure Absorption Spectra Correlation in a Series of 2,6-Dimethyl-4-arylpyrylium Salts

A combined experimental and theoretical study of the absorption spectra of a group of closely related pyrylium perchlorates 1-11 are presented. Minor changes in the position of the substituents lead to drastic changes in the absorption spectra in this series of compounds. We have attempted to explain the observed changes using the x,y-band notation developed by Balaban and co-workers. Absorption spectra of all compounds are compared with results from time-dependent density functional theory (TDDFT) and Zerner’s intermediate neglect of differential overlap (ZINDO/S) level calculations. Results of the calculations are in good agreement with experimental observations and an interesting correlation between Balaban’s notations and the MO transitions are obtained for simple derivatives. It is suggested that for more complex systems such as R- and â-naphthyl substituted systems, the empirical method is not appropriate.

Cellular and humoral factors involved in defense mechanisms of Fenneropenaeus indicus (H. Milne Edwards, 1837)

The present investigation revealed three types of circulating haemocytes in the haemolymph of F. indicus: hyalinocytes, small-granule haemocytes, and large-granule haemocytes. Intermediate stages indicate the maturing process of a single cell. The presence of enzymes such as peroxidase, phenoloxidase and acid phosphatase in the haemocytes, and the substantial production of oxygen radicals during phagocytosis show that the haemocytes are capable of mounting a fme cellular defense mechanism. The enzyme activities of the serum and the presence of agglutinins in the serum, which may act as opsonins, agglutinate foreign particles and augment phagocytosis, confirm the presence of a superior humoral immune system in F. indicus.Bacterial infection caused considerable variations in the cellular and humoral factors, such as the number of circulating cells and haemagglutinating activity, especially in the initial hours of infection. The total haemocyte count, haemagglutination titer and phenoloxidase enzyme showed significant reductions on bacterial presence and could be used as indicators of bacterial infection.The number of circulating cells showed drastic fluctuation on exposure to pollutants. Nuvan at low concentrations was able to produce changes in the haemolymph factors and in the tissue organization, which implies that the animal is under stress and is easily prone to infections. Exposure to nuvan resulted in significant variation in all of the cellular and humoral factors, especially, the total haemocyte count, percentage of small granule haemocytes, phagocytic activity and the haemagglutinating activity, which might be good indicators of pesticide pollution. Heavy metal exposure caused significant increase in total haemocyte count and reduction in phenoloxidase enzyme activity Even changes in the physio-chemical parameters, such as salinity caused fluctuations in the defense factors, indicating stress in this euryhaline species. The dietary incorporation of a commercial immunostimulant containing P-l,3 glucan resulted in stimulation of some of the humoral defense factors of F indicus, but was time dependent. The modulations, on exposure to various external factors, in the cellular and humoral factors, especially, total haemocyte count, phagocytic activity, haemagglutinating activity and the phenoloxidase and acid phosphatase enzymes suggest that these parameters could be used as indicators of the health status of F indicus, which assist in better monitoring and effective health management of this important cultured species.

Numerical Investigations on Soil Structure Interaction of Multistorey Frames

Frames are the most widely used structural system for multistorey buildings. A building frame is a three dimensional discrete structure consisting of a number of high rise bays in two directions at right angles to each other in the vertical plane. Multistorey frames are a three dimensional lattice structure which are statically indeterminate. Frames sustain gravity loads and resist lateral forces acting on it. India lies at the north westem end of the Indo-Australian tectonic plate and is identified as an active tectonic area. Under horizontal shaking of the ground, horizontal inertial forces are generated at the floor levels of a multistorey frame. These lateral inertia forces are transferred by the floor slab to the beams, subsequently to the columns and finally to the soil through the foundation system. There are many parameters that affect the response of a structure to ground excitations such as, shape, size and geometry of the structure, type of foundation, soil characteristics etc. The Soil Structure Interaction (SS1) effects refer to the influence of the supporting soil medium on the behavior of the structure when it is subjected to different types of loads. Interaction between the structure and its supporting foundation and soil, which is a complete system, has been modeled with finite elements. Numerical investigations have been carried out on a four bay, twelve storeyed regular multistorey frame considering depth of fixity at ground level, at characteristic depth of pile and at full depth. Soil structure interaction effects have been studied by considering two models for soil viz., discrete and continuum. Linear static analysis has been conducted to study the interaction effects under static load. Free vibration analysis and further shock spectrum analysis has been conducted to study the interaction effects under time dependent loads. The study has been extended to four types of soil viz., laterite, sand, alluvium and layered.The structural responses evaluated in the finite element analysis are bending moment, shear force and axial force for columns, and bending moment and shear force for beams. These responses increase with increase in the founding depth; however these responses show minimal increase beyond the characteristic length of pile. When the soil structure interaction effects are incorporated in the analysis, the aforesaid responses of the frame increases upto the characteristic depth and decreases when the frame has been analysed for the full depth. It has been observed that shock spectrum analysis gives wide variation of responses in the frame compared to linear elastic analysis. Both increase and decrease in responses have been observed in the interior storeys. The good congruence shown by the two finite element models viz., discrete and continuum in linear static analysis has been absent in shock spectrum analysis.

Analysis of Stochastic Volatility Sequences Generated by Product Autoregressive Models

The classical methods of analysing time series by Box-Jenkins approach assume that the observed series uctuates around changing levels with constant variance. That is, the time series is assumed to be of homoscedastic nature. However, the nancial time series exhibits the presence of heteroscedasticity in the sense that, it possesses non-constant conditional variance given the past observations. So, the analysis of nancial time series, requires the modelling of such variances, which may depend on some time dependent factors or its own past values. This lead to introduction of several classes of models to study the behaviour of nancial time series. See Taylor (1986), Tsay (2005), Rachev et al. (2007). The class of models, used to describe the evolution of conditional variances is referred to as stochastic volatility modelsThe stochastic models available to analyse the conditional variances, are based on either normal or log-normal distributions. One of the objectives of the present study is to explore the possibility of employing some non-Gaussian distributions to model the volatility sequences and then study the behaviour of the resulting return series. This lead us to work on the related problem of statistical inference, which is the main contribution of the thesis