Probability Theory. Stochastic Processes And Their Applications Probabilistic Analysis Of Some Queueing And Inventory Models

In this thesis we attempt to make a probabilistic analysis of some physically realizable, though complex, storage and queueing models. It is essentially a mathematical study of the stochastic processes underlying these models. Our aim is to have an improved understanding of the behaviour of such models, that may widen their applicability. Different inventory systems with randon1 lead times, vacation to the server, bulk demands, varying ordering levels, etc. are considered. Also we study some finite and infinite capacity queueing systems with bulk service and vacation to the server and obtain the transient solution in certain cases. Each chapter in the thesis is provided with self introduction and some important references

Analysis of some Stochastic models in inventories and Queues

The thesis entitled Analysis of Some Stochastic Models in Inventories and Queues. This thesis is devoted to the study of some stochastic models in Inventories and Queues which are physically realizable, though complex. It contains a detailed analysis of the basic stochastic processes underlying these models. In this thesis, (s,S) inventory systems with nonidentically distributed interarrival demand times and random lead times, state dependent demands, varying ordering levels and perishable commodities with exponential life times have been studied. The queueing system of the type Ek/Ga,b/l with server vacations, service systems with single and batch services, queueing system with phase type arrival and service processes and finite capacity M/G/l queue when server going for vacation after serving a random number of customers are also analysed. The analogy between the queueing systems and inventory systems could be exploited in solving certain models. In vacation models, one important result is the stochastic decomposition property of the system size or waiting time. One can think of extending this to the transient case. In inventory theory, one can extend the present study to the case of multi-item, multi-echelon problems. The study of perishable inventory problem when the commodities have a general life time distribution would be a quite interesting problem. The analogy between the queueing systems and inventory systems could be exploited in solving certain models.

The effects of work control and job demands on employee adjustment and work performance

The present study examined the effects of work control and job demands on employee adjustment and work performance using a multidimensional measure of work control (assessing levels of task control, decision control and work scheduling control). It was proposed that the negative effects of job demands and employee adjustment would be moderated by high levels of task control. It was also proposed that there would be evidence of main effects of both job demands and work control (particularly task-related levels of control) on employee adjustment. To test these predictions, a study of 135 university employees holding administrative positions was undertaken. Methodological improvements over previous research included the use of both self-reported adjustment measures and supervisor ratings of work performance as outcome variables, and the assessment of the predictor and outcome measures at different points in time (self-reported adjustment was assessed at both Times 1 and 2). The results revealed some support for the proposal that the effects of job demands would be buffered by high levels of task control, but not more peripheral aspects of work control. There were also significant main effects of task control on job satisfaction.

Effects of Ethanol on the Surface and Bulk Properties of a Microwave-Processed PMMA Denture Base Resin

Purpose: This study evaluated the effect of different concentrations of ethanol on hardness, roughness, flexural strength, and color stability of a denture base material using a microwave-processed acrylic resin as a model system. Materials and Methods: Sixty circular (14 x 4 mm) and 60 rectangular microwave-polymerized acrylic resin specimens (65 x 10 x 3 mm(3)) were employed in this study. The sample was divided into six groups according to the ethanol concentrations used in the immersion solution, as follows: 0% (water), 4.5%, 10%, 19%, 42%, and 100%. The specimens remained immersed for 30 days at 37 degrees C. The hardness test was performed by a hardness tester equipped with a Vickers diamond penetrator, and a surface roughness tester was used to measure the surface roughness of the specimens. Flexural strength testing was carried out on a universal testing machine. Color alterations (Delta E) were measured by a portable spectrophotometer after 12 and 30 days. Variables were analyzed by ANOVA/Tukey`s test (alpha = 0.05). Results: For the range of ethanol-water solutions for immersion (water only, 4.5%, 10%, 19.5%, 42%, and 100%), the following results were obtained for hardness (13.9 +/- 2.0, 12.1 +/- 0.7, 12.9 +/- 0.9, 11.2 +/- 1.5, 5.7 +/- 0.3, 2.7 +/- 0.5 VHN), roughness (0.13 +/- 0.01, 0.15 +/- 0.07, 0.13 +/- 0.05, 0.13 +/- 0.02, 0.23 +/- 0.05, 0.41 +/- 0.19 mu m), flexural strength (90 +/- 12, 103 +/- 18, 107 +/- 16, 90 +/- 25, 86 +/- 22, 8 +/- 2 MPa), and color (0.8 +/- 0.6, 0.8 +/- 0.3, 0.7 +/- 0.4, 0.9 +/- 0.3, 1.3 +/- 0.3, 3.9 +/- 1.5 Delta E) after 30 days. Conclusions: The findings of this study showed that the ethanol concentrations of tested drinks affect the physical properties of the investigated acrylic resin. An obvious plasticizing effect was found, which could lead to a lower in vivo durability associated with alcohol consumption.

Interactions between physical and psychosocial demands of work associated to low back pain

OBJECTIVE: To examine the interaction between physical and psychosocial demands of work associated to low back pain. METHODS: Cross-sectional study carried out in a stratified proportional random sample of 577 plastic industry workers in the metropolitan area of the city of Salvador, Northeast Brazil in 2002. An anonymous standard questionnaire was administered in the workplace by trained interviewers. Physical demands at work were self-rated on a 6-point numeric scale, with anchors at each end of the scale. Factor analysis was carried out on 11 physical demand variables to identify underlying factors. Psychosocial work demands were measured by demand, control and social support questions. Multivariate analysis was performed using the likelihood ratio test. RESULTS: The factor analysis identified two physical work demand factors: material handling (factor 1) and repetitiveness (factor 2). The multiple logistic regression analysis showed that factor 1 was positively associated with low back pain (OR=2.35, 95% CI 1.50;3.66). No interaction was found between physical and psychosocial work demands but both were independently associated to low back pain. CONCLUSIONS: The study found independent effects of physical and psychosocial work demands on low back pain prevalence and emphasizes the importance of physical demands especially of material handling involving trunk bending forward and trunk rotation regardless of age, gender, and body fitness.

Method to estimate soil macroporosity and microporosity based on sand content and bulk density

Macroporosity is often used in the determination of soil compaction. Reduced macroporosity can lead to poor drainage, low root aeration and soil degradation. The aim of this study was to develop and test different models to estimate macro and microporosity efficiently, using multiple regression. Ten soils were selected within a large range of textures: sand (Sa) 0.07-0.84; silt 0.03-0.24; clay 0.13-0.78 kg kg-1 and subjected to three compaction levels (three bulk densities, BD). Two models with similar accuracy were selected, with a mean error of about 0.02 m³ m-3 (2 %). The model y = a + b.BD + c.Sa, named model 2, was selected for its simplicity to estimate Macro (Ma), Micro (Mi) or total porosity (TP): Ma = 0.693 - 0.465 BD + 0.212 Sa; Mi = 0.337 + 0.120 BD - 0.294 Sa; TP = 1.030 - 0.345 BD 0.082 Sa; porosity values were expressed in m³ m-3; BD in kg dm-3; and Sa in kg kg-1. The model was tested with 76 datum set of several other authors. An error of about 0.04 m³ m-3 (4 %) was observed. Simulations of variations in BD as a function of Sa are presented for Ma = 0 and Ma = 0.10 (10 %). The macroporosity equation was remodeled to obtain other compaction indexes: a) to simulate maximum bulk density (MBD) as a function of Sa (Equation 11), in agreement with literature data; b) to simulate relative bulk density (RBD) as a function of BD and Sa (Equation 13); c) another model to simulate RBD as a function of Ma and Sa (Equation 16), confirming the independence of this variable in relation to Sa for a fixed value of macroporosity and, also, proving the hypothesis of Hakansson & Lipiec that RBD = 0.87 corresponds approximately to 10 % macroporosity (Ma = 0.10 m³ m-3).

Long-tailed trapping times and Lévy flights in a self-organized critical granular system

We present a continuous time random walk model for the scale-invariant transport found in a self-organized critical rice pile [K. Christensen et al., Phys. Rev. Lett. 77, 107 (1996)]. From our analytical results it is shown that the dynamics of the experiment can be explained in terms of Lvy flights for the grains and a long-tailed distribution of trapping times. Scaling relations for the exponents of these distributions are obtained. The predicted microscopic behavior is confirmed by means of a cellular automaton model.

The influence of time on lead toxicity and bioaccumulation determined by the OECD earthworm toxicity test

Internationally agreed standard protocols for assessing chemical toxicity of contaminants in soil to worms assume that the test soil does not need to equilibrate with the chemical to be tested prior to the addition of the test organisms and that the chemical will exert any toxic effect upon the test organism within 28 days. Three experiments were carried out to investigate these assumptions. The first experiment was a standard toxicity test where lead nitrate was added to a soil in solution to give a range of concentrations. The mortality of the worms and the concentration of lead in the survivors were determined. The LC(50)s for 14 and 28 days were 5311 and 5395 mug(Pb) g(soil)(-1) respectively. The second experiment was a timed lead accumulation study with worms cultivated in soil containing either 3000 or 5000 mug(Pb) g(soil)(-1). The concentration of lead in the worms was determined at various sampling times. Uptake at so' Sol both concentrations was linear with time. Worms in the 5000 mug g(-1) soil accumulated lead at a faster rate (3.16 mug Pb g(tissue)(-1) day(-1)) tiss than those in the 3000 mug g(-1) soil (2.21 mug Pb-tissue g(-1) day(-1)). The third experiment was a timed experiment with worms cultivated in tiss soil containing 7000 mugPb g(soil)(-1). Soil and lead nitrate solution were mixed and stored at 20 degreesC. Worms were added at various times over a 35-day period. The time to death increased from 23 h, when worms were added directly after the lead was added to the soil, to 67 It when worms were added after the soil had equilibrated with the lead for 35 days. In artificially Pb-amended soils the worms accumulate Pb over the duration of their exposure to the Pb. Thus time limited toxicity tests may be terminated before worm body load has reached a toxic level. This could result in under-estimates of the toxicity of Pb to worms. As the equilibration time of artificially amended Pb-bearing soils increases the bioavailability of Pb decreases. Thus addition of worms shortly after addition of Pb to soils may result in the over-estimate of Pb toxicity to worms. The current OECD acute worm toxicity test fails to take these two phenomena into account thereby reducing the environmental relevance of the contaminant toxicities it is used to calculate. (C) 2002 Elsevier Science Ltd. All rights reserved.

Influence of different dentin etching times and concentrations and air-abrasion technique on dentin microtensile bond strength

Purpose: To determine the influence of different dentin treatments on the microtensile bond strengths of adhesive resins to dentin. Methods: Fifteen human molars were ground to 600-grit to obtain flat root-dentin surfaces. Five different dentin treatments were evaluated: Group 1 - 10% phosphoric acid for 30 seconds; Group 2 - 37% phosphoric acid for 15 seconds; Group 3 - air-abrasion for 10 seconds followed by 10% phosphoric acid for 30 seconds; Group 4 - air-abasion for 10 seconds followed by 37% phosphoric acid for 15 seconds. The dental adhesive (OptiBond Solo Plus) was applied according to manufacturer's instructions and followed by composite (Z100) application to provide sufficient bulk for microtensile bond testing. All samples were placed in distilled water for 24 hours at 37degreesC, thermocycled for 500 cycles in distilled water at 10degreesC and 50degreesC, and serially sliced perpendicular to the adhesive surface and subjected to tensile forces (0.5 mm/minute). Additional samples were prepared for SEM to observe the adhesive interface. Results: Group 2 exhibited significantly (P< 0.05) lower bond strength values than all other treatments. The bond strengths of the different conditions were (in MPa): Group 1: 43.0 +/- 16.1; Group 2: 29.2 +/- 8.3; Group 3: 48.1 +/- 14.2; Group 4: 41.0 +/- 9.3. The dentin treated with phosphoric acid 37% for 15 seconds showed the lowest values of microtensile bond strength. The results obtained with Groups 1, 3 and 4 were statistically similar.

Chemical composition of ferromanganese micronodules and bulk sediments from ODP Hole 199-1216A

Distribution, size, mineral, and chemical compositions of ferromanganese micronodules (FMMNs) and chemical composition of host sediments were examined in a series of red clay samples with ages from Eocene to the present at Ocean Drilling Program Leg 199, Site 1216, south of the Molokai Fracture Zone in the Central Pacific Basin. The number of FMMNs changed drastically throughout the 40-m-long red clay intervals. FMMNs are abundant in the upper 9 m of core, decrease between 9 and 25 meters below seafloor (mbsf) with depth, and are very rare from 30 to 40 mbsf. Chemical composition of FMMNs showed high Mn/Fe ratios and Ni and Cu contents and a distinct positive Ce anomaly because of the existence of buserite. This suggests that FMMNs in the red clay from 25 mbsf to the top of the cored interval were deposited continuously in an oxic diagenetic bottom environment. The red clay below 30 mbsf with higher Mn contents contains few FMMNs but abundant tiny Mn particles within brown silicates coated by Fe (oxy-hydro)oxides. This indicates that the mode of manganese deposition changed between 25 and 30 mbsf.

Physics, geochemistry and bulk sedimentology on cores from the Peru Basin

Empirical relationships between physical properties determined non-destructively by core logging devices and calibrated by carbonate and opal measurements determined on discrete samples allow extraction of carbonate and opal records from the non-destructive measurements in biogenic settings. Contents of detrital material can be calculated as a residual. For carbonate and opal the correlation coefficients (r) are 0.954 and ?0.916 for sediment density, ?0.816 and 0.845 for compressional-wave velocity, 0.908 and ?0.942 for acoustic impedance, and 0.886 and ?0.865 for sediment color (lightness). Carbonate contents increase in concert with increasing density and acoustic impedance, decreasing velocity and lighter sediment color. The opposite is true for opal. The advantages of deriving the sediment composition quantitatively from core logging are: (i) sampling resolution is increased significantly, (ii) non-destructive data can be gathered rapidly, and (iii) laboratory work on discrete samples can be reduced. Applied to paleoceanographic problems, this method offers the opportunity of precise stratigraphic correlations and of studying processes related to biogenic sedimentation in more detail. Density is most promising because it is most strongly affected by changes in composition.

Mineralogy and geochemistry of sulfide minerals and bulk rocks from ODP Hole 176-735B

Ocean Drilling Program (ODP) Leg 176 built upon the work of ODP Leg 118 wherein the 500-m section that was sampled represented the most complete recovery of an intact portion of lower oceanic crust ever described. During Leg 176, we deepened Hole 735B to >1500 m below seafloor in an environment where gabbroic rocks have been tectonically exposed at the Southwest Indian Ridge. This new expedition extended the remarkable recovery (>85%) that allowed unprecedented investigations into the nature of the lower oceanic crust as a result of Leg 118. Sulfide mineral and bulk rock compositions were determined from samples in the 1000-m section of oceanic gabbros recovered during Leg 176. The sulfide assemblage of pyrrhotite, chalcopyrite, pentlandite, and troilite is present throughout this section, as it is throughout the 500-m gabbroic section above that was sampled during Leg 118. Troilite is commonly present as lamellae, and the only interval where troilite was not observed is from the uppermost 150 m of the section sampled during Leg 118, which is intensely metamorphosed. The common presence of troilite indicates that much of the sulfide assemblage from Hole 735B precipitated from a magmatic system and subsequently underwent low-temperature reequilibration. Evaluation of geochemical trends in bulk rock and sulfides indicates that the combined effects of olivine accumulation in troctolites and high pentlandite to pyrrhotite ratios account for the sporadic bulk rock compositions high in Ni. Bulk rock and sulfide mineral geochemical indicators that are spatially coincident with structural and physical properties anomalies indicate a heretofore unrecognized lithologic unit boundary in this section. Platinum-group element (PGE) compositions were also determined for 36 samples from throughout the section that were recovered during Leg 176. Whereas most samples had low (<0.4 ppb) PGE concentrations, rare samples had elevated PGE values, but no unique common trend between these samples is evident.

Lead 210 and silicate profiles from sediments of the equatorial Pacific and South Atlantic

Particle mixing rates have been determined for 5 South Atlantic/Antarctic and 3 equatorial Pacific deep-sea cores using excess 210Pb and 32Si measurements. Radionuclide profiles from these siliceous, calcareous, and clay-rich sediments have been evaluated using a steady state vertical advection diffusion model. In Antarctic siliceous sediments210Pb mixing coefficients (0.04-0.16 cm**2/y) are in reasonable agreement with the 32Si mixing coefficient (0.2 or 0.4 cm**2/y, depending on 32Si half-life). In an equatorial Pacific sediment core, however, the 210Pb mixing coefficient (0.22 cm**2/y) is 3-7 times greater than the 32Si mixing coefficient (0.03 or 0.07 cm**2/y). The difference in 210Pb and 32Si mixing rates in the Pacific sediments results from: (1) non-steady state mixing and differences in characteristic time and depth scales of the two radionuclides, (2) preferential mixing of fine-grained clay particles containing most of the 210Pb activity relative to coarser particles (large radiolaria) containing the 32Si activity, or (3) the supply of 222Rn from the bottom of manganese nodules which increases the measured excess 210Pb activity (relative to 226Ra) at depth and artificially increases the 210Pb mixing coefficient. Based on 32Si data and pore water silica profiles, dissolution of biogenic silica in the sediment column appears to have a minor effect on the 32Si profile in the mixed layer. Deep-sea particle mixing rates reported in this study and the literature do not correlate with sediment type, sediment accumulation rate, or surface productivity. Based on differences in mixing rate among three Antarctic cores collected within 50 km of each other, local variability in the intensity of deep-sea mixing appears to be as important as regional differences in sediment properties.

Physical properties and bulk minerals from IODP Holes 308-U1322B, U1322D and U1324B

How the micro-scale fabric of clay-rich mudstone evolves during consolidation in early burial is critical to how they are interpreted in the deeper portions of sedimentary basins. Core samples from the Integrated Ocean Drilling Program Expedition 308, Ursa Basin, Gulf of Mexico, covering seafloor to 600 meters below sea floor (mbsf) are ideal for studying the micro-scale fabric of mudstones. Mudstones of consistent composition and grain size decrease in porosity from 80% at the seafloor to 37% at 600 mbsf. Argon-ion milling produces flat surfaces to image this pore evolution over a vertical effective stress range of 0.25 (71 mbsf) to 4.05 MPa (597 mbsf). With increasing burial, pores become elongated, mean pore size decreases, and there is preferential loss of the largest pores. There is a small increase in clay mineral preferred orientation as recorded by high resolution X-ray goniometry with burial.