Analysis of Some Stochastic Inventory Models with Pooling/ Retrial of Customers

In this thesis we have presented several inventory models of utility. Of these inventory with retrial of unsatisfied demands and inventory with postponed work are quite recently introduced concepts, the latt~~ being introduced for the first time. Inventory with service time is relatively new with a handful of research work reported. The di lficuity encoLlntered in inventory with service, unlike the queueing process, is that even the simplest case needs a 2-dimensional process for its description. Only in certain specific cases we can introduce generating function • to solve for the system state distribution. However numerical procedures can be developed for solving these problem.

Decreased GyBAA Receptor Function in the Brain Stem during Pancreatic Regeneration in Rats

Gamma amino outyric acid is a major inhibitory neurotrarsr titter in the central nervous system. In the preset study sv, Have investigate(' the alteration of GABA receptor, In t he hrain stem of rats during pancreatic regeneration. Three groups of rats were used for the study: sham operated, 72 It and 7 days partially pancreatectonnsea. GABA was (juan- (ified by [H]GABA receptor iispiacement method. GABA receptor kin: 10, pat at i et•ers were studied by using the binding of F'.](iAhA as ligand to the Triton X-100 treated me,i1,;-:mes a1,J displacement with unlabelled GABA. GhRA,v receptor activity was studied by using the [` -1 h3cuculline and displacement with unlabellecV euculline. ;.\13A content significantly decreased (1' < (1.(101 ) it, 0-e brain stern during the regeneration of pancreas. 'I hl, high affinity (IAI3A receptor binding sho?:ed it sigii'f cant decrease in 131„.,\ (P < 11.01) and K,I 1).05) n 72 h and 7 days after partial pancreatee 'timv. ";:flhicuculline hin(Iing showed it signih eat, 'le ( r(, :,e in /Jn1,s and K,I (P < 0.001) in 72 h pa^.rcreaw,, mised rats when compared with sham wt--tt' as P,n and K,I reversed to near sham after 7 da,s of pancreatectomv. The results sugge,) that GAB A throur,r; ('GABA receptors in brain Atcem has a regulatory uie during active regeneration of pancreas which will have inunense clinical significance in the treatment of cliahetcs.

Gaba Receptor Gene Expression during Rat Liver Cell Proliferation and Its Function in Hepatocyte Cultures

The present thesis is an attempt to understand the role of GABA, GABAA and GABAB receptors in the regulation of liver cell proliferation using in vivo and in vitro models. The work also focuses on the brain GABAergic changes associated with normal and neoplastic cell growth in liver and to delineate its regulatory function. The investigation of mechanisms involving mitogenic models without cell necrosis may contribute our knowledge about both on cell growth, carcinogenesis, liver pathology and treatment. Objectives of the present study are, to induce controlled liver cell proliferation by partial hepatectomy and lead nitrate administration and uncontrolled cell proliferation by N-nitrosodiethylamine treatment in male Wistar rats, the changes in the content of GABA, GABAA,GABAB in various rat brain regions. To study the GABAA and GABAB receptor changes in brain stem, hypothalamus, cerebellum and cerebral cortex during the active cortex during the period of active DNA synthesis in liver of different experimental groups. The changes in GABAA and GABAB receptor function of the brain stem, hypothalamus and cerebellum play an important role sympathetic regulation of cell proliferation and neoplastic growth in liver. The decrease in GABA content in brain stem, hypothalamus and cerebellum during regeneration and neoplasia in liver. The time course of brain GABAergic changes was closely correlated with that of heptic DNA synthesis. The functional significance of these changes was further explored by studying the changes in GABAA and GABAB receptors in brain.

Regression models for bivariate survival data

Multivariate lifetime data arise in various forms including recurrent event data when individuals are followed to observe the sequence of occurrences of a certain type of event; correlated lifetime when an individual is followed for the occurrence of two or more types of events, or when distinct individuals have dependent event times. In most studies there are covariates such as treatments, group indicators, individual characteristics, or environmental conditions, whose relationship to lifetime is of interest. This leads to a consideration of regression models.The well known Cox proportional hazards model and its variations, using the marginal hazard functions employed for the analysis of multivariate survival data in literature are not sufficient to explain the complete dependence structure of pair of lifetimes on the covariate vector. Motivated by this, in Chapter 2, we introduced a bivariate proportional hazards model using vector hazard function of Johnson and Kotz (1975), in which the covariates under study have different effect on two components of the vector hazard function. The proposed model is useful in real life situations to study the dependence structure of pair of lifetimes on the covariate vector . The well known partial likelihood approach is used for the estimation of parameter vectors. We then introduced a bivariate proportional hazards model for gap times of recurrent events in Chapter 3. The model incorporates both marginal and joint dependence of the distribution of gap times on the covariate vector . In many fields of application, mean residual life function is considered superior concept than the hazard function. Motivated by this, in Chapter 4, we considered a new semi-parametric model, bivariate proportional mean residual life time model, to assess the relationship between mean residual life and covariates for gap time of recurrent events. The counting process approach is used for the inference procedures of the gap time of recurrent events. In many survival studies, the distribution of lifetime may depend on the distribution of censoring time. In Chapter 5, we introduced a proportional hazards model for duration times and developed inference procedures under dependent (informative) censoring. In Chapter 6, we introduced a bivariate proportional hazards model for competing risks data under right censoring. The asymptotic properties of the estimators of the parameters of different models developed in previous chapters, were studied. The proposed models were applied to various real life situations.

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.

ARMA modeling of time series based on rational approximation of spectral density function

This study is concerned with Autoregressive Moving Average (ARMA) models of time series. ARMA models form a subclass of the class of general linear models which represents stationary time series, a phenomenon encountered most often in practice by engineers, scientists and economists. It is always desirable to employ models which use parameters parsimoniously. Parsimony will be achieved by ARMA models because it has only finite number of parameters. Even though the discussion is primarily concerned with stationary time series, later we will take up the case of homogeneous non stationary time series which can be transformed to stationary time series. Time series models, obtained with the help of the present and past data is used for forecasting future values. Physical science as well as social science take benefits of forecasting models. The role of forecasting cuts across all fields of management-—finance, marketing, production, business economics, as also in signal process, communication engineering, chemical processes, electronics etc. This high applicability of time series is the motivation to this study.

Adrenergic and serotonergic function in dna synthesis during rat liver regeneration and in hepatocyte cultures

The adult mammalian liver is predominantly in a quiescent state with respect to cell division. This quiescent state changes dramatically, however, if the liver is injured by toxic, infectious or mechanic agents (Ponder, 1996). Partial hepatectomy (PH) which consists of surgical removal of two-thirds of the liver, has been used to stimulate hepatocyte proliferation (Higgins & Anderson 1931). This experimental model of liver regeneration has been the target of many studies to probe the mechanisms responsible for liver cell growth control (Michalopoulos, 1990; Taub, 1996). After PH most of the remaining cells in the renmant liver respond with co-ordinated waves of DNA synthesis and divide in a process called compensatory hyperplasia. Hence, liver regeneration is a model of relatively synchronous cell cycle progression in vivo. In contrast to hepatomas, cell division is terminated under some intrinsic control when the original cellular mass has been regained. This has made liver regeneration a useful model to dissect the biochemical and molecular mechanisms of cell division regulation. The liver is thus, one of the few adult organs that demonstrates a physiological growth rewonse (Fausto & Mead, 1989; Fausto & Webber, 1994). The regulation of liver cell proliferation involves circulating or intrahepatic factors that are involved in either the priming of hepatocytes to enter the cell cycle (Go to G1) or progression through the cell cycle. In order to understand the basis of liver regeneration it is mandatory to define the mechanisms which (a) trigger division, (b) allow the liver to concurrently grow and maintain dilferentiated fimction and (c) terminate cell proliferation once the liver has reached the appropriate mass. Studies on these aspects of liver regeneration will provide basic insight of cell growth and dilferentiation, liver diseases like viral hepatitis, toxic damage and liver transplant where regeneration of the liver is essential. In the present study, Go/G1/S transition of hepatocytes re-entering the cell cycle after PH was studied with special emphasis on the involvement of neurotransmitters, their receptors and second messenger function in the control of cell division during liver regeneration

Characterizations of some continuous distributions using partial moments

Inthis paper,we define partial moments for a univariate continuous random variable. A recurrence relationship for the Pearson curve using the partial moments is established. The interrelationship between the partial moments and other reliability measures such as failure rate, mean residual life function are proved. We also prove some characterization theorems using the partial moments in the context of length biased models and equilibrium distributions

Quantile based reliability aspects of partial moments

Partial moments are extensively used in literature for modeling and analysis of lifetime data. In this paper, we study properties of partial moments using quantile functions. The quantile based measure determines the underlying distribution uniquely. We then characterize certain lifetime quantile function models. The proposed measure provides alternate definitions for ageing criteria. Finally, we explore the utility of the measure to compare the characteristics of two lifetime distributions

A Study of Single Stage Semi‐Dry Anaerobic Digestion of Organic Fraction of Municipal Solid Waste

Solid waste generation is a natural consequence of human activity and is increasing along with population growth, urbanization and industrialization. Improper disposal of the huge amount of solid waste seriously affects the environment and contributes to climate change by the release of greenhouse gases. Practicing anaerobic digestion (AD) for the organic fraction of municipal solid waste (OFMSW) can reduce emissions to environment and thereby alleviate the environmental problems together with production of biogas, an energy source, and digestate, a soil amendment. The amenability of substrate for biogasification varies from substrate to substrate and different environmental and operating conditions such as pH, temperature, type and quality of substrate, mixing, retention time etc. Therefore, the purpose of this research work is to develop feasible semi-dry anaerobic digestion process for the treatment of OFMSW from Kerala, India for potential energy recovery and sustainable waste management. This study was carried out in three phases in order to reach the research purpose. In the first phase, batch study of anaerobic digestion of OFMSW was carried out for 100 days at 32°C (mesophilic digestion) for varying substrate concentrations. The aim of this study was to obtain the optimal conditions for biogas production using response surface methodology (RSM). The parameters studied were initial pH, substrate concentration and total organic carbon (TOC). The experimental results showed that the linear model terms of initial pH and substrate concentration and the quadratic model terms of the substrate concentration and TOC had significant individual effect (p < 0.05) on biogas yield. However, there was no interactive effect between these variables (p > 0.05). The optimum conditions for maximizing the biogas yield were a substrate concentration of 99 g/l, an initial pH of 6.5 and TOC of 20.32 g/l. AD of OFMSW with optimized substrate concentration of 99 g/l [Total Solid (TS)-10.5%] is a semi-dry digestion system .Under the optimized condition, the maximum biogas yield was 53.4 L/kg VS (volatile solid).. In the second phase, semi-dry anaerobic digestion of organic solid wastes was conducted for 45 days in a lab-scale batch experiment for substrate concentration of 100 g/l (TS-11.2%) for investigating the start-up performances under thermophilic condition (50°C). The performance of the reactor was evaluated by measuring the daily biogas production and calculating the degradation of total solids and the total volatile solids. The biogas yield at the end of the digestion was 52.9 L/kg VS for the substrate concentration of 100 g/l. About 66.7% of volatile solid degradation was obtained during the digestion. A first order model based on the availability of substrate as the limiting factor was used to perform the kinetic studies of batch anaerobic digestion system. The value of reaction rate constant, k, obtained was 0.0249 day-1. A laboratory bench scale reactor with a capacity of 36.8 litres was designed and fabricated to carry out the continuous anaerobic digestion of OFMSW in the third phase. The purpose of this study was to evaluate the performance of the digester at total solid concentration of 12% (semi-dry) under mesophlic condition (32°C). The digester was operated with different organic loading rates (OLRs) and constant retention time. The performance of the reactor was evaluated using parameters such as pH, volatile fatty acid (VFA), alkalinity, chemical oxygen demand (COD), TOC and ammonia-N as well as biogas yield. During the reactor’s start-up period, the process is stable and there is no inhibition occurred and the average biogas production was 14.7 L/day. The reactor was fed in continuous mode with different OLRs (3.1,4.2 and 5.65 kg VS/m3/d) at constant retention time of 30 days. The highest volatile solid degradation of 65.9%, with specific biogas production of 368 L/kg VS fed was achieved with OLR of 3.1 kg VS/m3/d. Modelling and simulation of anaerobic digestion of OFMSW in continuous operation is done using adapted Anaerobic Digestion Model No 1 (ADM1).The proposed model, which has 34 dynamic state variables, considers both biochemical and physicochemical processes and contains several inhibition factors including three gas components. The number of processes considered is 28. The model is implemented in Matlab® version 7.11.0.584(R2010b). The model based on adapted ADM1 was tested to simulate the behaviour of a bioreactor for the mesophilic anaerobic digestion of OFMSW at OLR of 3.1 kg VS/m3/d. ADM1 showed acceptable simulating results.