Total Progeny in a Subcritical Branching Process with two Types of Immigration

2000 Mathematics Subject Classification: 60J80, 60F05

Simulation and Robust Modifications of Estimates in Branching Processes

This study is focused on the comparison and modification of different estimates arising in the branching processes. Simulations of models with or without migration are put through. Due to the complexity of the computations the algorithms are designed with the language of technical computing MATLAB. Using the simulations, estimates of the o spring mean of the generated processes are calculated. It is well known in the literature that under certain conditions the asymptotic distribution of the estimates is proved to be normal. Using the asymptotic normality a modified method of maximum likelihood is proposed. The aim is to obtain trimmed maximum likelihood estimates based on several sample paths with the same number of generations. Thus in a natural way the observations, inconsistent with the aprior information about the asymptotic normality are excluded from the model. The computation of the standard error allows the comparison of different types of estimates.

A Computational Approach for the Statistical Estimation of Discrete Time Branching Processes with Immigration

2010 Mathematics Subject Classification: 60J80.

Lp Microlocal Supercritical Markov Branching Processes with Non-Homogeneous Poisson Immigration

2010 Mathematics Subject Classification: 60J80.

Time to Extinction in Branching Processes and its Application in Epidemiology

2010 Mathematics Subject Classification: Primary 60J80; Secondary 92D30.

Crump-Mode-Jagers Branching Process: Modelling and Application for Human Population

2010 Mathematics Subject Classification: 60J85, 92D25.

Limit Theorems for Non-Critical Branching Processes with Continuous State Space

2000 Mathematics Subject Classification: Primary 60J80, Secondary 60G99.

Molecular characterization of Cladium peat from the Florida Everglades: biomarker associations with humic fractions

The accumulation and preservation of peat soils in Everglades freshwater marshes and mangrove swamps is an essential process in the ecological functioning of these ecosystems. Human intervention and climate change have modified nutrient dynamics and hydroperiod in the Everglades and peat loss due to such anthropogenic activities is evident. However, not much is known on the molecular level regarding the biogeochemical characteristics, which allow peat to be preserved in the Everglades. Lipid biomarkers trapped within or bound to humic-type structures can provide important geochemical information regarding the origin and microbial transformation of OM in peat. Four lipid fractions obtained from a Cladium peat, namely the freely extractable fraction and those associated with humin, humic acid, and fulvic acid fractions, showed clear differences in their molecular distribution suggesting different OM sources and structural and diagenetic states of the source material. Both, higher plant derived and microbial lipids were found in association with these humic-type substances. Most biomarker distributions suggest an increment in the microbial/terrestrial lipid ratio from the free to humin to humic to fulvic fractions. Microbial reworking of lipids, and the incorporation of microbial biomarkers into the humic-type fractions was evident, as well as the preservation of diagenetic byproducts. The lipid distribution associated with the fulvic acids suggests a high degree of microbial reworking for this fraction. Evidence for this 3D structure was obtained through the presence of the relatively high abundance of α,ω-dicarboxylic acids and phenolic and benzenecarboxylic compounds. The increment in structural complexity of the phenolic and benzencarboxylic compounds in combination with the reduction in the carbon chain length of the dicarboxylic acids from the free to fulvic fraction suggests the latter to be structurally the most stable, compacted and diagenetically altered substrate. This analytical approach can now be applied to peat samples from other areas within the Everglades ecosystem, affected differently by human intervention with the aim to assess changes in organic matter preservation.

What Teaching Strategies Can I Employ to Improve Student Achievement in the Addition of Fractions with Different Denominators?

The purpose of this action research was to determine what instructional strategies could be used to improve student achievement in fraction addition. An eighth grade intensive math class practiced multiplication facts and hands-on applications of fractions concepts for 2 months. Pretests/posttests were used to measure improvement in computation and understanding.

A study of branching fluid networks for enhancing the performance of thermal -fluid devices

Compact thermal-fluid systems are found in many industries from aerospace to microelectronics where a combination of small size, light weight, and high surface area to volume ratio fluid networks are necessary. These devices are typically designed with fluid networks consisting of many small parallel channels that effectively pack a large amount of heat transfer surface area in a very small volume but do so at the cost of increased pumping power requirements. ^ To offset this cost the use of a branching fluid network for the distribution of coolant within a heat sink is investigated. The goal of the branch design technique is to minimize the entropy generation associated with the combination of viscous dissipation and convection heat transfer experienced by the coolant in the heat sink while maintaining compact high heat transfer surface area to volume ratios. ^ The derivation of Murray's Law, originally developed to predict the geometry of physiological transport systems, is extended to heat sink designs which minimze entropy generation. Two heat sink designs at different scales are built, and tested experimentally and analytically. The first uses this new derivation of Murray's Law. The second uses a combination of Murray's Law and Constructal Theory. The results of the experiments were used to verify the analytical and numerical models. These models were then used to compare the performance of the heat sink with other compact high performance heat sink designs. The results showed that the techniques used to design branching fluid networks significantly improves the performance of active heat sinks. The design experience gained was then used to develop a set of geometric relations which optimize the heat transfer to pumping power ratio of a single cooling channel element. Each element can be connected together using a set of derived geometric guidelines which govern branch diameters and angles. The methodology can be used to design branching fluid networks which can fit any geometry. ^

Analysis of Students’ Misconceptions and Error Patterns in Mathematics: The Case of Fractions

This study analyzed three fifth grade students’ misconceptions and error patterns when working with equivalence, addition and subtraction of fractions. The findings revealed that students used both conceptual and procedural knowledge to solve the problems. They used pictures, gave examples, and made connections to other mathematical concepts and to daily life topics. Error patterns found include using addition and subtraction of numerators and denominators, and finding the greatest common factor.

Optimization of three-dimensional branching networks of microchannels for thermal management of microelectronics

The aim of this work is to present a methodology to develop cost-effective thermal management solutions for microelectronic devices, capable of removing maximum amount of heat and delivering maximally uniform temperature distributions. The topological and geometrical characteristics of multiple-story three-dimensional branching networks of microchannels were developed using multi-objective optimization. A conjugate heat transfer analysis software package and an automatic 3D microchannel network generator were developed and coupled with a modified version of a particle-swarm optimization algorithm with a goal of creating a design tool for 3D networks of optimized coolant flow passages. Numerical algorithms in the conjugate heat transfer solution package include a quasi-ID thermo-fluid solver and a steady heat diffusion solver, which were validated against results from high-fidelity Navier-Stokes equations solver and analytical solutions for basic fluid dynamics test cases. Pareto-optimal solutions demonstrate that thermal loads of up to 500 W/cm2 can be managed with 3D microchannel networks, with pumping power requirements up to 50% lower with respect to currently used high-performance cooling technologies.

Geochemical data and radiocarbon ages of organic matter fractions and bacteriohopanepolyol data of sediment core GeoB6518-1 from the Congo River basin

The age of organic material discharged by rivers provides information about its sources and carbon cycling processes within watersheds. While elevated ages in fluvially-transported organic matter are usually explained by erosion of soils and sediments, it is commonly assumed that mainly young organic material is discharged from flat tropical watersheds due to their extensive plant cover and high carbon turnover. Here we present compound-specific radiocarbon data of terrigenous organic fractions from a sedimentary archive offshore the Congo River in conjunction with molecular markers for methane-producing land cover reflecting wetland extent in the watershed. We find that the Congo River has been discharging aged organic matter for several thousand years with increasing ages from the mid- to the Late Holocene. This suggests that aged organic matter in modern samples is concealed by radiocarbon from nuclear weapons testing. By comparison to indicators for past rainfall changes we detect a systematic control of organic matter sequestration and release by continental hydrology mediating temporary carbon storage in wetlands. As aridification also leads to exposure and rapid remineralization of large amounts of previously stored labile organic matter we infer that this process may cause a profound direct climate feedback currently underestimated in carbon cycle assessments.

(Table 5, page 626), Tin and main metal elements composition of ferromanganese concretions (acid-soluble fractions)

Concentrations of tin in sea water decreased from estuarine and shelf (0.02-0.04 µg/kg) to surface Atlantic waters (0.009 µg/kg). Mean contents (ppm) in other materials included: ultramafic rocks, 0.8; basalts, 1.7; silicic rocks, 2.5; red clays, 3.4; amphibolites, 1.2. Oceanic ferromanganese deposits contained from 0.2 to 5.8 ppm; tin and cobalt contents were correlated.