Water availability in the ecosystem is one of the most crucial environmental factors that determines global terrestrial biome distribution. However, aridity/humidity conditions in the geologic past are difficult to quantify, mainly owing to the lack of a proper parameter. By using modern global climatic data, we here examine five selected previously proposed aridity indices (AIs), in which the climatic variables involved, including both precipitation and temperature, are simple and likely available in studies of paleoclimatology and paleoecology, although with different degrees of uncertainty. They were first evaluated along the modern climatic zones of eastern China, with the main metric of Thornthwaite humidity index (HI) and with the supplementary reference of soil moisture index (SMI) and near-ground atmospheric relative humidity (RH). Then AIs and the mean annual precipitation (MAP) were further statistically compared with HI, SMI, and RH, respectively, based on 1189 monitored data sets from meteorological stations over the world. The results show that the Köppen aridity index (AIKöppen), expressed as mean annual precipitation divided by mean annual temperature plus a constant of 33, is the most accurate and precise index among all selected indices, supported by the highest correlation coefficient respectively to HI, SMI, and RH, three widely-employed major indicators sensitive to hydrological dynamics in climatology and meteorology. Specifically, AIKöppen does well mirror corresponding HI along four representative transects from North America, South America, Africa, and Australia, which cover the typical arid and humid climates and span the main terrestrial biome types. Moreover, our results also distinctly reveal that, as also shown by many studies on modern climate, precipitation alone is inadequate to measure the hydrological condition, because both temperature and evapotranspiration are two other critical factors that strongly influence water balance in the ecosystem, meanwhile evapotranspiration is mainly affected by temperature. Based on the validated AIKöppen, we briefly discuss the aridity/humidity condition in China during the middle Miocene. The results demonstrate that moisture did decrease westward, but it is also clear that western China in the middle Miocene appears not to have been as dry as previously thought, indicated by the AIKöppen values representing a sub-humid to humid climate.

Water availability in the ecosystem is one of the most crucial environmental factors that determines global terrestrial biome distribution. However, aridity/humidity conditions in the geologic past are difficult to quantify, mainly owing to the lack of a proper parameter. By using modern global climatic data, we here examine five selected previously proposed aridity indices (AIs), in which the climatic variables involved, including both precipitation and temperature, are simple and likely available in studies of paleoclimatology and paleoecology, although with different degrees of uncertainty. They were first evaluated along the modern climatic zones of eastern China, with the main metric of Thornthwaite humidity index (HI) and with the supplementary reference of soil moisture index (SMI) and near-ground atmospheric relative humidity (RH). Then AIs and the mean annual precipitation (MAP) were further statistically compared with HI, SMI, and RH, respectively, based on 1189 monitored data sets from meteorological stations over the world. The results show that the Köppen aridity index (AIKöppen), expressed as mean annual precipitation divided by mean annual temperature plus a constant of 33, is the most accurate and precise index among all selected indices, supported by the highest correlation coefficient respectively to HI, SMI, and RH, three widely-employed major indicators sensitive to hydrological dynamics in climatology and meteorology. Specifically, AIKöppen does well mirror corresponding HI along four representative transects from North America, South America, Africa, and Australia, which cover the typical arid and humid climates and span the main terrestrial biome types. Moreover, our results also distinctly reveal that, as also shown by many studies on modern climate, precipitation alone is inadequate to measure the hydrological condition, because both temperature and evapotranspiration are two other critical factors that strongly influence water balance in the ecosystem, meanwhile evapotranspiration is mainly affected by temperature. Based on the validated AIKöppen, we briefly discuss the aridity/humidity condition in China during the middle Miocene. The results demonstrate that moisture did decrease westward, but it is also clear that western China in the middle Miocene appears not to have been as dry as previously thought, indicated by the AIKöppen values representing a sub-humid to humid climate.

In this article, we consider the portfolio selection problem as a Bayesian decision problem. We compare the traditional mean–variance and mean–variance–skewness efficient portfolios. We develop bi-level programming problem to investigate the market’s preference for risk by using observed (market) weights. Numerical experiments are conducted on a portfolio formed by the 30 stocks in the Dow Jones Industrial Average. Numerical results show that the market’s preferences are better explained when skewness is included.

In this dissertation, the critical scaling behavior of magnetic Ising models with long range interactions is studied. These long range interactions, when imposed in addition to interactions on a regular lattice, lead to small-world graphs. By using large-scale Monte Carlo simulations, together with finite-size scaling, the critical behavior of a number of different models is obtained. The Ising models studied in this dissertation include the z-model introduced by Scalettar, standard small-world bonds superimposed on a square lattice, and physical small-world bonds superimposed on a square lattice. From the scaling results of the Binder 4th order cumulant, the order parameter, and the susceptibility, the long-range interaction is found to drive the systems behavior from Ising-like to mean field, and drive the critical point to a higher temperature. It is concluded that with a large amount of strong long-range connections (compared to the interactions on regular lattices), so the long-range connection density is non-vanishing, systems have mean field behavior. With a weak interaction that vanishes for an infinite system size or for vanishing density of long-range connections the systems have Ising-like critical behavior. The crossover from Ising-like to meanield behavior due to weak long-range interactions for systems with a large amount of long-range connections is also discussed. These results provide further evidence to support the existence of physical (quasi-) small-world nanomaterials.

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This thesis is concerned with the numerical solutions of initial value problems with ordinary differential equations and covers single step integration methods. focus is to study the numerical the various aspects of Specifically, its main methods of non-linear integration formula with a variety of means based on the Contraharmonic mean (C.M) (Evans and Yaakub [1995]), the Centroidal mean (C.M) (Yaakub and Evans [1995]) and the Root-Mean-Square (RMS) (Yaakub and Evans [1993]) for solving initial value problems. the applications of the second It includes a study of order C.M method for parallel implementation of extrapolation methods for ordinary differential equations with the ExDaTa schedule by Bahoshy [1992]. Another important topic presented in this thesis is that a fifth order five-stage explicit Runge Kutta method or weighted Runge Kutta formula [Evans and Yaakub [1996]) exists which is contrary to Butcher [1987] and the theorem in Lambert ([1991] ,pp 181). The thesis is organized as follows. An introduction to initial value problems in ordinary differential equations and parallel computers and software in Chapter 1, the basic preliminaries and fundamental concepts in mathematics, an algebraic manipulation package, e.g., Mathematica and basic parallel processing techniques are discussed in Chapter 2. Following in Chapter 3 is a survey of single step methods to solve ordinary differential equations. In this chapter, several single step methods including the Taylor series method, Runge Kutta method and a linear multistep method for non-stiff and stiff problems are also considered. Chapter 4 gives a new Runge Kutta formula for solving initial value problems using the Contraharmonic mean (C.M), the Centroidal mean (C.M) and the Root-MeanSquare (RMS). An error and stability analysis for these variety of means and numerical examples are also presented. Chapter 5 discusses the parallel implementation on the Sequent 8000 parallel computer of the Runge-Kutta contraharmonic mean (C.M) method with extrapolation procedures using explicit assignment scheduling Kutta RK(4, 4) method (EXDATA) strategies. A is introduced and the data task new Rungetheory and analysis of its properties are investigated and compared with the more popular RKF(4,5) method, are given in Chapter 6. Chapter 7 presents a new integration method with error control for the solution of a special class of second order ODEs. In Chapter 8, a new weighted Runge-Kutta fifth order method with 5 stages is introduced. By comparison with the currently recommended RK4 ( 5) Merson and RK5(6) Nystrom methods, the new method gives improved results. Chapter 9 proposes a new fifth order Runge-Kutta type method for solving oscillatory problems by the use of trigonometric polynomial interpolation which extends the earlier work of Gautschi [1961]. An analysis of the convergence and stability of the new method is given with comparison with the standard Runge-Kutta methods. Finally, Chapter 10 summarises and presents conclusions on the topics discussed throughout the thesis.

Thermal comfort in an indoor environment is largely dependent on the four environmental and two personal parameters which is most commonly measured by the Predicted Mean Vote (PMV) model developed by Fanger. It has been studied that variations in these parameters beyond a range could lead to discomfort complaints. However, little research has been done on the effect of mean radiant temperature variations and its influence on predicted mean vote and thermal comfort specially in an actual building environment. This study aims to investigate the relationship between mean radiant temperature and predicted mean vote in indoor environment. Using the methods of on-site measurement of indoor environmental parameters and subjective votes on thermal sensation in an educational building; it was found that rise in mean radiant temperature lead to rise in PMV value and discomfort vote amongst occupants seated near glazed façade. A very strong positive correlation was found between mean radiant temperature and PMV near the window side of the room under warm and sunny weather conditions. Analysis of indoor environmental data from the several measurement sessions concluded that rise in mean radiant temperature and PMV was not noticed until there was a direct solar transmission through the window. It is advisable to use solar shading on windows, but special consideration should be given to the trade-offs between energy consumption (heating or cooling) and lighting energy consumption. No conclusions could be made in terms of ankle draft discomfort due to experimental limitations and more research would be required to investigate this phenomenon. / Termisk komfort inomhusmiljö är till stor del beroende av de fyra miljö och två personlig parametrar som oftast mäts av Predicted Mean Vote (PMV) modell som utvecklats av Fanger. Det har studerats att variationer i dessa parametrar utanför en limit kan leda till missnöjeklagomål. Däremot har lite forskning gjorts på effekten av mean radiant tempratur och dess inverkan på predicted mean vote och termisk komfort speciellt i en verklig byggnadsmiljö. Syftet med denna studie är att undersöka sambandet mellan mean radiant tempratur och predicted mean vote i inomhusmiljö. Användning mätmetoderna av inomhusmiljöparametrar och subjektiva röster av termisk komfort uppfattning i en byggnad för utbildning; det konstaterades att stiga i medel leda mean radiant tempratur att stiga i predicted mean vote värde och missnöje rösta bland byggnad brukarna sitter nära glasfasaden. En väldigt positiv korrelation mellan men radiant tempratur och predicted mean vote nära en fönstersida under varma och soliga väder var noterat. Genom att analysera data av inomhusmiljön från de multipla mätningssessionerna konkluderat att ökningen i mean radiant tempratur och predicted mean vote inte märktes tills det fanns en direkt soltransmission genom fönstret. Det är rekommenderar att använda solskydd på fönster, men med tanke på kompromisser mellan energiförbrukning (värme eller kyla) och ljussättning konsumtion.   Inga slutsatser kan göras om luftdrag på fotled grund av experimentella begränsningar och mer forskning skulle krävas för att undersöka detta fenomen.

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Master of Science / Department of Kinesiology / Thomas J. Barstow / Purpose: Oxygen uptake (VO2) has been shown to be controlled by a nonlinear system, yet the VO2 response to ramp style exercise appears linear. We tested the hypothesis that an integrative model incorporating nonlinear parameter values could accurately estimate actual VO2 responses to ramp style exercise. Methods: Six healthy, men completed three bouts of varying ramp rate exercise (slow ramp (SR): 15 W/min, regular ramp (RR) 30 W/min, fast ramp (FR) 60W/min) and four bouts of extended-step incremental exercise, where each step lasted 5-15 min or until volitional fatigue on a cycle ergometer on separate days. The step-responses were then fit with a simple monoexponential starting at time zero (MONO) or allowing a time delay and using only the first 5 min of data (5TD). The resulting VO2 parameters from the step protocol were incorporated into an integrative model for the estimation of the VO2 response to each of the rates of ramp incremental exercise. The parameters from the actual and model ramp protocols were compared with 2 way repeated-measures ANOVAs. Results: Both Gain (G) and Mean Response Time (MRT) (or time constant) values increased significantly across work rate transitions (mean±SD; Gain:10.0±0.9, 11.6±1.1, 13.1±1.3, 17.6±3.3 ml O2/min/W; MRT:39.4±7.7, 54.0±5.4, 79.6±15.0, 180.1±56.2 s). Up to maximalVO2 the models over-estimated the actual VO2 response for FR (Gain: ACT 8.7±1.0, MONO 9.9±0.4, 5TD 10.3±0.3 ml O2/min/W). Up to 80% maximal VO2 the models accurately predicted the actual VO2 response across all ramp rates (Gain: ACT 10.7±1.1, 10.2±0.5, 9.2±1.0; MONO 11.0±0.8, 10.3±0.6, 9.2±0.5; 5TD 10.4±0.4, 10.2±0.3, 9.8±0.2 ml O2/min/W, values are listed SR,RR,FR). Conclusions: When variable parameter values (G and either MRT or time constant and time delay) were utilized by an integrative model, accurate estimations of the VO2 response to ramp incremental exercise were possible regardless of ramp rate (up to 80% maximal VO2). The increases in both G and MRT (or time constant) appear to balance each other to produce the quasi-linear VO2 responses.