977 resultados para exponential sums


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The Baltic Sea was studied with respect to selected organic contaminants and their ecotoxicology. The research consisted of analyses of total hydrocarbons, polycyclic aromatic hydrocarbons, bile metabolites, hepatic ethoxyresorufin-O-deethylase (EROD) activity, polychlorinated biphenyls (PCBs) and organochlorine pesticides (OCPs). The contaminants were measured from various matrices, such as seawater, sediment and biota. The methods of analysis were evaluated and refined to comparability of the results. Polyaromatic hydrocarbons, originating from petroleum, are known to be among the most harmful substances to the marine environment. In Baltic subsurface water, seasonal dependence of the total hydrocarbon concentrations (THCs) was seen. Although concentrations of parent polycyclic aromatic hydrocarbons (PAHs) in sediment surface varied between 64 and 5161 ug kg-1 (dw), concentrations above 860 ug kg-1 (dw) were found in all the studied sub-basins of the Baltic Sea. Concentrations commonly considered to substantially increase the risk of liver disease and reproductive impairment in fish, as well as potential effects on growth (above 1000 ug kg-1 dw), were found in all the studied sub-basins of the Baltic Sea except Kattegat. Thus, considerable pollution in sediments was indicated. In bivalves, the sums of 12 PAHs varied on a wet weight basis between 44 and 298 ug kg-1 (ww). The predominant PAHs were high molecular weight and the PAH profiles of M. balthica differed from those found in sediment from the same area. The PAHs were both pyrolytic and petrogenic in origin, and a contribution from diesel engines was found, which indicates pollution of the Baltic Sea, most likely caused by the steadily increasing shipping in the area. The HPLC methods developed for hepatic EROD activity and bile metabolite measurements proved to be fast and suitable for the study of biological effects. A mixed function oxygenase enzyme system in Baltic Sea perch collected from the Gulf of Finland was induced slightly: EROD activity in perch varied from 0.30 14 pmol min-1 mg-1 protein. This range can be considered to be comparable to background values. Recent PAH exposure was also indicated by enhanced levels (213 and 1149 ug kg-1) of the bile metabolite 1-hydroxypyrene. No correlation was indicated between hepatic EROD activity and concentration of 1-hydroxypyrene in bile. PCBs and OCPs were observed in Baltic Sea sediment, bivalves and herring. Sums of seven CBs in surface sediment (0 5 cm) ranged from 0.04 to 6.2 ug kg-1 (dw) and sums of three DDTs from 0.13 to 5.0 ug kg-1 (dw). The highest levels of contaminants were found in the most eastern area of the Gulf of Finland where the highest total carbon and nitrogen content was found and where the lowest percentage proportion of p,p -DDT was found. The highest concentrations of CBs and the lowest concentration of DDTs were found in M. balthica from the Gulf of Finland. The highest levels of DDTs were found in M. balthica from the Hanö Bight, which is the outer part of the Bornholm Basin close to the Swedish mainland. In bivalves, the sums of seven CBs were 72 108 ug kg-1 (lw) and the sums of three DDTs were 66 139 ug kg-1 (lw). Results from temporal trend monitoring showed, that during the period 1985 2002, the concentrations of seven CBs in two-year-old female Baltic herring were clearly decreased, from 9 16 to 2 6 ug kg-1 (ww) in the northern Baltic Sea. At the same time, concentrations of three DDTs declined from 8 15 to 1 5 ug kg-1 (ww). The total concentration of the fat-soluble CBs and DDTs in Baltic herring muscle was shown to be age-dependent; the average concentrations in ten-year-old Baltic herring were three to five-fold higher than in two-year-old herring. In Baltic herring and bivalves, as well as in surface sediments, CB 138 and CB153 were predominant among CBs, whereas among DDTs p,p'-DDD predominated in sediment and p,p'-DDE in bivalves and Baltic herring muscle. Baltic Sea sediments are potential sources of contaminants that may become available for bioaccumulation. Based on ecotoxicological assessment criteria, cause for concern regarding CBs in sediments was indicated for the Gulf of Finland and the northern Baltic Proper, and for the northern Baltic Sea regarding CBs in Baltic herring more than two years old. Statistical classification of selected organic contaminants indicated high-level contamination for p,p'-DDT, p,p'-DDD, p,p'-DDE, total DDTs, HCB, CB118 and CB153 in muscle of Baltic herring in age groups two to ten years; in contrast, concentrations of a-HCH and g-HCH were found to be moderate. The concentrations of DDTs and CBs in bivalves is sufficient to cause biological effects, and demonstrates that long-term biological effects are still possible in the case of DDTs in the Hanö Bight.

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Molecular dynamics simulations of the orientational dynamics of water molecules confined inside narrow carbon nanorings reveal that reorientational relaxation is mediated by large amplitude angular jumps. The distribution of waiting time between jumps peaks at about 60 fs, and has a slowly decaying exponential tail with a timescale of about 440 fs. These time scales are much faster than the mean waiting time between jumps of the water molecules in bulk.

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Microwave treated water soluble and amide functionalized single walled carbon nanotubes have been investigated using femtosecond degenerate pump-probe and nonlinear transmission experiments. The time resolved differential transmission using 75 femtosecond pulse with the central wavelength of 790 nm shows a bi-exponential ultrafast photo-bleaching with time constants of 160 fs (130 fs) and 920 fs (300 fs) for water soluble (amide functionalized) nanotubes. Open and closed aperture z-scans show saturation absorption and positive (negative) nonlinear refraction for water soluble (amide functionalized) nanotubes. Two photon absorption coefficient, beta(0) similar to 250 cm/GW (650 cm/GW) and nonlinear index, gamma similar to 15 cm(2)/pW (-30 cm(2)/pW) are obtained from the theoretical fit in the saturation limit to the data for two types of nanotubes.

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The world is facing an energy crisis due to exponential population growth and limited availability of fossil fuels. Over the last 20 years, carbon, one of the most abundant materials found on earth, and its allotrope forms such as fullerenes, carbon nanotubes and graphene have been proposed as sources of energy generation and storage because of their extraordinary properties and ease of production. Various approaches for the synthesis and incorporation of carbon nanomaterials in organic photovoltaics and supercapacitors have been reviewed and discussed in this work, highlighting their benefits as compared to other materials commonly used in these devices. The use of fullerenes, carbon nanotubes and graphene in organic photovoltaics and supercapacitors is described in detail, explaining how their remarkable properties can enhance the efficiency of solar cells and energy storage in supercapacitors. Fullerenes, carbon nanotubes and graphene have all been included in solar cells with interesting results, although a number of problems are still to be overcome in order to achieve high efficiency and stability. However, the flexibility and the low cost of these materials provide the opportunity for many applications such as wearable and disposable electronics or mobile charging. The application of carbon nanotubes and graphene to supercapacitors is also discussed and reviewed in this work. Carbon nanotubes, in combination with graphene, can create a more porous film with extraordinary capacitive performance, paving the way to many practical applications from mobile phones to electric cars. In conclusion, we show that carbon nanomaterials, developed by inexpensive synthesis and process methods such as printing and roll-to-roll techniques, are ideal for the development of flexible devices for energy generation and storage – the key to the portable electronics of the future.

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Geometric constraints present in A2BO4 compounds with the tetragonal-T structure of K2NiF4 impose a strong pressure on the B---OII---B bonds and a stretching of the A---OI---A bonds in the basal planes if the tolerance factor is t congruent with RAO/√2 RBO < 1, where RAO and RBO are the sums of the A---O and B---O ionic radii. The tetragonal-T phase of La2NiO4 becomes monoclinic for Pr2NiO4, orthorhombic for La2CuO4, and tetragonal-T′ for Pr2CuO4. The atomic displacements in these distorted phases are discussed and rationalized in terms of the chemistry of the various compounds. The strong pressure on the B---OII---B bonds produces itinerant σ*x2−y2 bands and a relative stabilization of localized dz2 orbitals. Magnetic susceptibility and transport data reveal an intersection of the Fermi energy with the d2z2 levels for half the copper ions in La2CuO4; this intersection is responsible for an intrinsic localized moment associated with a configuration fluctuation; below 200 K the localized moment smoothly vanishes with decreasing temperature as the d2z2 level becomes filled. In La2NiO4, the localized moments for half-filled dz2 orbitals induce strong correlations among the σ*x2−y2 electrons above Td reverse similar, equals 200 K; at lower temperatures the σ*x2−y2 electrons appear to contribute nothing to the magnetic susceptibility, which obeys a Curie-Weiss law giving a μeff corresponding to S = 1/2, but shows no magnetic order to lowest temperatures. These surprising results are verified by comparison with the mixed systems La2Ni1−xCuxO4 and La2−2xSr2xNi1−xTixO4. The onset of a charge-density wave below 200 K is proposed for both La2CuO4 and La2NiO4, but the atomic displacements would be short-range cooperative in mixed systems. The semiconductor-metallic transitions observed in several systems are found in many cases to obey the relation Ea reverse similar, equals kTmin, where varrho = varrho0exp(−Ea/kT) and Tmin is the temperature of minimum resistivity varrho. This relation is interpreted in terms of a diffusive charge-carrier mobility with Ea reverse similar, equals ΔHm reverse similar, equals kT at T = Tmin.

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Pressurised hot water extraction (PHWE) exploits the unique temperature-dependent solvent properties of water minimising the use of harmful organic solvents. Water is environmentally friendly, cheap and easily available extraction medium. The effects of temperature, pressure and extraction time in PHWE have often been studied, but here the emphasis was on other parameters important for the extraction, most notably the dimensions of the extraction vessel and the stability and solubility of the analytes to be extracted. Non-linear data analysis and self-organising maps were employed in the data analysis to obtain correlations between the parameters studied, recoveries and relative errors. First, pressurised hot water extraction (PHWE) was combined on-line with liquid chromatography-gas chromatography (LC-GC), and the system was applied to the extraction and analysis of polycyclic aromatic hydrocarbons (PAHs) in sediment. The method is of superior sensitivity compared with the traditional methods, and only a small 10 mg sample was required for analysis. The commercial extraction vessels were replaced by laboratory-made stainless steel vessels because of some problems that arose. The performance of the laboratory-made vessels was comparable to that of the commercial ones. In an investigation of the effect of thermal desorption in PHWE, it was found that at lower temperatures (200ºC and 250ºC) the effect of thermal desorption is smaller than the effect of the solvating property of hot water. At 300ºC, however, thermal desorption is the main mechanism. The effect of the geometry of the extraction vessel on recoveries was studied with five specially constructed extraction vessels. In addition to the extraction vessel geometry, the sediment packing style and the direction of water flow through the vessel were investigated. The geometry of the vessel was found to have only minor effect on the recoveries, and the same was true of the sediment packing style and the direction of water flow through the vessel. These are good results because these parameters do not have to be carefully optimised before the start of extractions. Liquid-liquid extraction (LLE) and solid-phase extraction (SPE) were compared as trapping techniques for PHWE. LLE was more robust than SPE and it provided better recoveries and repeatabilities than did SPE. Problems related to blocking of the Tenax trap and unrepeatable trapping of the analytes were encountered in SPE. Thus, although LLE is more labour intensive, it can be recommended over SPE. The stabilities of the PAHs in aqueous solutions were measured using a batch-type reaction vessel. Degradation was observed at 300ºC even with the shortest heating time. Ketones and quinones and other oxidation products were observed. Although the conditions of the stability studies differed considerably from the extraction conditions in PHWE, the results indicate that the risk of analyte degradation must be taken into account in PHWE. The aqueous solubilities of acenaphthene, anthracene and pyrene were measured, first below and then above the melting point of the analytes. Measurements below the melting point were made to check that the equipment was working, and the results were compared with those obtained earlier. Good agreement was found between the measured and literature values. A new saturation cell was constructed for the solubility measurements above the melting point of the analytes because the flow-through saturation cell could not be used above the melting point. An exponential relationship was found between the solubilities measured for pyrene and anthracene and temperature.

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The object of this dissertation is to study globally defined bounded p-harmonic functions on Cartan-Hadamard manifolds and Gromov hyperbolic metric measure spaces. Such functions are constructed by solving the so called Dirichlet problem at infinity. This problem is to find a p-harmonic function on the space that extends continuously to the boundary at inifinity and obtains given boundary values there. The dissertation consists of an overview and three published research articles. In the first article the Dirichlet problem at infinity is considered for more general A-harmonic functions on Cartan-Hadamard manifolds. In the special case of two dimensions the Dirichlet problem at infinity is solved by only assuming that the sectional curvature has a certain upper bound. A sharpness result is proved for this upper bound. In the second article the Dirichlet problem at infinity is solved for p-harmonic functions on Cartan-Hadamard manifolds under the assumption that the sectional curvature is bounded outside a compact set from above and from below by functions that depend on the distance to a fixed point. The curvature bounds allow examples of quadratic decay and examples of exponential growth. In the final article a generalization of the Dirichlet problem at infinity for p-harmonic functions is considered on Gromov hyperbolic metric measure spaces. Existence and uniqueness results are proved and Cartan-Hadamard manifolds are considered as an application.

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This thesis consists of three articles on Orlicz-Sobolev capacities. Capacity is a set function which gives information of the size of sets. Capacity is useful concept in the study of partial differential equations, and generalizations of exponential-type inequalities and Lebesgue point theory, and other topics related to weakly differentiable functions such as functions belonging to some Sobolev space or Orlicz-Sobolev space. In this thesis it is assumed that the defining function of the Orlicz-Sobolev space, the Young function, satisfies certain growth conditions. In the first article, the null sets of two different versions of Orlicz-Sobolev capacity are studied. Sufficient conditions are given so that these two versions of capacity have the same null sets. The importance of having information about null sets lies in the fact that the sets of capacity zero play similar role in the Orlicz-Sobolev space setting as the sets of measure zero do in the Lebesgue space and Orlicz space setting. The second article continues the work of the first article. In this article, it is shown that if a Young function satisfies certain conditions, then two versions of Orlicz-Sobolev capacity have the same null sets for its complementary Young function. In the third article the metric properties of Orlicz-Sobolev capacities are studied. It is usually difficult or impossible to calculate a capacity of a set. In applications it is often useful to have estimates for the Orlicz-Sobolev capacities of balls. Such estimates are obtained in this paper, when the Young function satisfies some growth conditions.

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Pratylenchus thornei is a major pathogen of wheat in Australia. Two glasshouse experiments with four wheat cultivars that had different final populations (Pf) of P. thornei in the field were used to optimise conditions for assessing resistance. With different initial populations (Pi) ranging up to 5250 P. thornei/kg soil, Pf of P. thornei increased to 16 weeks after sowing, and then decreased at 20 weeks in some cultivar x Pi combinations. The population dynamics of P. thornei up to 16 weeks were best described by a modified exponential equation P f (t) = aP i e kt where P f (t) is the final population density at time t, P i is the initial population density, a is the proportion of P i that initiates population development, and k is the intrinsic rate of increase of the population. The cultivar GS50a had very low k values at Pi of 5250 and 1050 indicating its resistance, Suneca and Potam had high k values indicating susceptibility, whereas intolerant Gatcher had a low value at the higher Pi and a high value at the lower Pi. Nitrate fertiliser increased plant growth and Pf values of susceptible cultivars, but in unplanted soil it decreased Pf. Nematicide (aldicarb 5 mg/kg soil) killed P. thornei more effectively in planted than in unplanted soil and increased plant growth particularly in the presence of N fertiliser. In both experiments, the wheat cultivars Suneca and Potam were more susceptible than the cultivar GS50a reflecting field results. The method chosen to discriminate wheat cultivars was to assess Pf after growth for 16 weeks in soil with Pi ~1050–5250 P. thornei/kg soil and fertilised with 200 mg NO3–N/kg soil.

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This PhD Thesis is about certain infinite-dimensional Grassmannian manifolds that arise naturally in geometry, representation theory and mathematical physics. From the physics point of view one encounters these infinite-dimensional manifolds when trying to understand the second quantization of fermions. The many particle Hilbert space of the second quantized fermions is called the fermionic Fock space. A typical element of the fermionic Fock space can be thought to be a linear combination of the configurations m particles and n anti-particles . Geometrically the fermionic Fock space can be constructed as holomorphic sections of a certain (dual)determinant line bundle lying over the so called restricted Grassmannian manifold, which is a typical example of an infinite-dimensional Grassmannian manifold one encounters in QFT. The construction should be compared with its well-known finite-dimensional analogue, where one realizes an exterior power of a finite-dimensional vector space as the space of holomorphic sections of a determinant line bundle lying over a finite-dimensional Grassmannian manifold. The connection with infinite-dimensional representation theory stems from the fact that the restricted Grassmannian manifold is an infinite-dimensional homogeneous (Kähler) manifold, i.e. it is of the form G/H where G is a certain infinite-dimensional Lie group and H its subgroup. A central extension of G acts on the total space of the dual determinant line bundle and also on the space its holomorphic sections; thus G admits a (projective) representation on the fermionic Fock space. This construction also induces the so called basic representation for loop groups (of compact groups), which in turn are vitally important in string theory / conformal field theory. The Thesis consists of three chapters: the first chapter is an introduction to the backround material and the other two chapters are individually written research articles. The first article deals in a new way with the well-known question in Yang-Mills theory, when can one lift the action of the gauge transformation group on the space of connection one forms to the total space of the Fock bundle in a compatible way with the second quantized Dirac operator. In general there is an obstruction to this (called the Mickelsson-Faddeev anomaly) and various geometric interpretations for this anomaly, using such things as group extensions and bundle gerbes, have been given earlier. In this work we give a new geometric interpretation for the Faddeev-Mickelsson anomaly in terms of differentiable gerbes (certain sheaves of categories) and central extensions of Lie groupoids. The second research article deals with the question how to define a Dirac-like operator on the restricted Grassmannian manifold, which is an infinite-dimensional space and hence not in the landscape of standard Dirac operator theory. The construction relies heavily on infinite-dimensional representation theory and one of the most technically demanding challenges is to be able to introduce proper normal orderings for certain infinite sums of operators in such a way that all divergences will disappear and the infinite sum will make sense as a well-defined operator acting on a suitable Hilbert space of spinors. This research article was motivated by a more extensive ongoing project to construct twisted K-theory classes in Yang-Mills theory via a Dirac-like operator on the restricted Grassmannian manifold.

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Increasing organic carbon inputs to agricultural soils through the use of pastures or crop residues has been suggested as a means of restoring soil organic carbon lost via anthropogenic activities, such as land use change. However, the decomposition and retention of different plant residues in soil, and how these processes are affected by soil properties and nitrogen fertiliser application, is not fully understood. We evaluated the rate and extent of decomposition of 13C-pulse labelled plant material in response to nitrogen addition in four pasture soils of varying physico-chemical characteristics. Microbial respiration of buffel grass (Cenchrus ciliaris L.), wheat (Triticum aestivum L.) and lucerne (Medicago sativa L.) residues was monitored over 365-days. A double exponential model fitted to the data suggested that microbial respiration occurred as an early rapid and a late slow stage. A weighted three-compartment mixing model estimated the decomposition of both soluble and insoluble plant 13C (mg C kg−1 soil). Total plant material decomposition followed the alkyl C: O-alkyl C ratio of plant material, as determined by solid-state 13C nuclear magnetic resonance spectroscopy. Urea-N addition increased the decomposition of insoluble plant 13C in some soils (≤0.1% total nitrogen) but not others (0.3% total nitrogen). Principal components regression analysis indicated that 26% of the variability of plant material decomposition was explained by soil physico-chemical characteristics (P = 0.001), which was primarily described by the C:N ratio. We conclude that plant species with increasing alkyl C: O-alkyl C ratio are better retained as soil organic matter, and that the C:N stoichiometry of soils determines whether N addition leads to increases in soil organic carbon stocks.

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Many problems in analysis have been solved using the theory of Hodge structures. P. Deligne started to treat these structures in a categorical way. Following him, we introduce the categories of mixed real and complex Hodge structures. Category of mixed Hodge structures over the field of real or complex numbers is a rigid abelian tensor category, and in fact, a neutral Tannakian category. Therefore it is equivalent to the category of representations of an affine group scheme. The direct sums of pure Hodge structures of different weights over real or complex numbers can be realized as a representation of the torus group, whose complex points is the Cartesian product of two punctured complex planes. Mixed Hodge structures turn out to consist of information of a direct sum of pure Hodge structures of different weights and a nilpotent automorphism. Therefore mixed Hodge structures correspond to the representations of certain semidirect product of a nilpotent group and the torus group acting on it.

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The Minimum Description Length (MDL) principle is a general, well-founded theoretical formalization of statistical modeling. The most important notion of MDL is the stochastic complexity, which can be interpreted as the shortest description length of a given sample of data relative to a model class. The exact definition of the stochastic complexity has gone through several evolutionary steps. The latest instantation is based on the so-called Normalized Maximum Likelihood (NML) distribution which has been shown to possess several important theoretical properties. However, the applications of this modern version of the MDL have been quite rare because of computational complexity problems, i.e., for discrete data, the definition of NML involves an exponential sum, and in the case of continuous data, a multi-dimensional integral usually infeasible to evaluate or even approximate accurately. In this doctoral dissertation, we present mathematical techniques for computing NML efficiently for some model families involving discrete data. We also show how these techniques can be used to apply MDL in two practical applications: histogram density estimation and clustering of multi-dimensional data.

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Sulfuryl fluoride (SF) has been developed as a fumigant for control of insect pests in stored grain. However, there is very limited information on the sorption behaviour of this fumigant, which can be critical to its bioactivity, application and potential for residues. We undertook a comprehensive laboratory study of the sorption and desorption of SF by wheat (bread and durum), flour and semolina at 15, 25 and 35 °C, moisture contents 12% and 15%, and concentration × time combinations at CT = 1500 mgh/L (4.167 mg/L × 360 h, 8.928 mg/L × 168 h and 31.25 mg/L × 48 h). At each dosage, sorption rate increased as commodity temperature and moisture content increased. The highest rates of sorption occurred at 35 °C and 15% m.c., and lowest rates at 15 °C and 12% m.c., and the rate was independent of initial concentration. Sorption followed first order reaction kinetics described by the exponential decay equation, Ct = C0·e−k*t, where k is the sorption rate constant. The most important factors determining the rate of sorption were commodity particle size (exposed surfaces) and temperature. Little sorption of fumigant occurred within the first 24 h whereas longer fumigation times resulted in significant sorption. Unbound SF was rapidly lost from the commodity upon aeration with no further desorption detected under any of the test conditions.

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Modern Christian theology has been at pain with the schism between the Bible and theology, and between biblical studies and systematic theology. Brevard Springs Childs is one of biblical scholars who attempt to dismiss this “iron curtain” separating the two disciplines. The present thesis aims at analyzing Childs’ concept of theological exegesis in the canonical context. In the present study I employ the method of systematic analysis. The thesis consists of seven chapters. Introduction is the first chapter. The second chapter attempts to find out the most important elements which exercise influence on Childs’ methodology of biblical theology by sketching his academic development during his career. The third chapter attempts to deal with the crucial question why and how the concept of the canon is so important for Childs’ methodology of biblical theology. In chapter four I analyze why and how Childs is dissatisfied with historical-critical scholarship and I point out the differences and similarities between his canonical approach and historical criticism. The fifth chapter attempts at discussing Childs’ central concepts of theological exegesis by investigating whether a Christocentric approach is an appropriate way of creating a unified biblical theology. In the sixth chapter I present a critical evaluation and methodological reflection of Childs’ theological exegesis in the canonical context. The final chapter sums up the key points of Childs’ methodology of biblical theology. The basic results of this thesis are as follows: First, the fundamental elements of Childs’ theological thinking are rooted in Reformed theological tradition and in modern theological neo-orthodoxy and in its most prominent theologian, Karl Barth. The American Biblical Theological Movement and the controversy between Protestant liberalism and conservatism in the modern American context cultivate his theological sensitivity and position. Second, Childs attempts to dismiss negative influences of the historical-critical method by establishing canon-based theological exegesis leading into confessional biblical theology. Childs employs terminology such as canonical intentionality, the wholeness of the canon, the canon as the most appropriate context for doing a biblical theology, and the continuity of the two Testaments, in order to put into effect his canonical program. Childs demonstrates forcefully the inadequacies of the historical-critical method in creating biblical theology in biblical hermeneutics, doctrinal theology, and pastoral practice. His canonical approach endeavors to establish and create post-critical Christian biblical theology, and works within the traditional framework of faith seeking understanding. Third, Childs’ biblical theology has a double task: descriptive and constructive, the former connects biblical theology with exegesis, the later with dogmatic theology. He attempts to use a comprehensive model, which combines a thematic investigation of the essential theological contents of the Bible with a systematic analysis of the contents of the Christian faith. Childs also attempts to unite Old Testament theology and New Testament theology into one unified biblical theology. Fourth, some problematic points of Childs’ thinking need to be mentioned. For instance, his emphasis on the final form of the text of the biblical canon is highly controversial, yet Childs firmly believes in it, he even regards it as the corner stone of his biblical theology. The relationship between the canon and the doctrine of biblical inspiration is weak. He does not clearly define whether Scripture is God’s word or whether it only “witnesses” to it. Childs’ concepts of “the word of God” and “divine revelation” remain unclear, and their ontological status is ambiguous. Childs’ theological exegesis in the canonical context is a new attempt in the modern history of Christian theology. It expresses his sincere effort to create a path for doing biblical theology. Certainly, it was just a modest beginning of a long process.